LMFDB - Embedded newform 546.4.s.b.43.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [546,4,Mod(43,546)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("546.43"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(546, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 1])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	546.s (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [20,0,30] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$32.2150428631$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 1316 x^{18} + 722042 x^{16} + 215100738 x^{14} + 38026916607 x^{12} + 4099786385782 x^{10} + \cdots + 10\!\cdots\!16 $ x^20 + 1316x^18 + 722042x^16 + 215100738x^14 + 38026916607x^12 + 4099786385782x^10 + 266708763555943x^8 + 9961497267724398x^6 + 191076845971065417x^4 + 1436901531373651968*x^2 + 103932021168930816
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			43.6
Root			$-17.3330i$ of defining polynomial
Character	$\chi$	$=$	546.43
Dual form			546.4.s.b.127.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.73205 + 1.00000i) q^{2} +(1.50000 - 2.59808i) q^{3} +(2.00000 + 3.46410i) q^{4} -17.0651i q^{5} +(5.19615 - 3.00000i) q^{6} +(6.06218 - 3.50000i) q^{7} +8.00000i q^{8} +(-4.50000 - 7.79423i) q^{9} +(17.0651 - 29.5576i) q^{10} +(48.9885 + 28.2835i) q^{11} +12.0000 q^{12} +(-27.5365 - 37.9307i) q^{13} +14.0000 q^{14} +(-44.3364 - 25.5976i) q^{15} +(-8.00000 + 13.8564i) q^{16} +(1.32779 + 2.29981i) q^{17} -18.0000i q^{18} +(56.4245 - 32.5767i) q^{19} +(59.1152 - 34.1302i) q^{20} -21.0000i q^{21} +(56.5670 + 97.9769i) q^{22} +(47.8724 - 82.9174i) q^{23} +(20.7846 + 12.0000i) q^{24} -166.217 q^{25} +(-9.76388 - 93.2345i) q^{26} -27.0000 q^{27} +(24.2487 + 14.0000i) q^{28} +(-11.2536 + 19.4918i) q^{29} +(-51.1953 - 88.6728i) q^{30} +17.2489i q^{31} +(-27.7128 + 16.0000i) q^{32} +(146.965 - 84.8505i) q^{33} +5.31117i q^{34} +(-59.7278 - 103.452i) q^{35} +(18.0000 - 31.1769i) q^{36} +(21.2442 + 12.2653i) q^{37} +130.307 q^{38} +(-139.852 + 14.6458i) q^{39} +136.521 q^{40} +(-270.300 - 156.058i) q^{41} +(21.0000 - 36.3731i) q^{42} +(-238.892 - 413.773i) q^{43} +226.268i q^{44} +(-133.009 + 76.7929i) q^{45} +(165.835 - 95.7448i) q^{46} -30.0698i q^{47} +(24.0000 + 41.5692i) q^{48} +(24.5000 - 42.4352i) q^{49} +(-287.896 - 166.217i) q^{50} +7.96676 q^{51} +(76.3229 - 171.251i) q^{52} -652.971 q^{53} +(-46.7654 - 27.0000i) q^{54} +(482.660 - 835.992i) q^{55} +(28.0000 + 48.4974i) q^{56} -195.460i q^{57} +(-38.9836 + 22.5072i) q^{58} +(624.634 - 360.633i) q^{59} -204.781i q^{60} +(-111.575 - 193.254i) q^{61} +(-17.2489 + 29.8760i) q^{62} +(-54.5596 - 31.5000i) q^{63} -64.0000 q^{64} +(-647.291 + 469.913i) q^{65} +339.402 q^{66} +(202.511 + 116.920i) q^{67} +(-5.31117 + 9.19922i) q^{68} +(-143.617 - 248.752i) q^{69} -238.911i q^{70} +(-791.870 + 457.187i) q^{71} +(62.3538 - 36.0000i) q^{72} +467.327i q^{73} +(24.5307 + 42.4884i) q^{74} +(-249.326 + 431.845i) q^{75} +(225.698 + 130.307i) q^{76} +395.969 q^{77} +(-256.876 - 114.484i) q^{78} +1306.50 q^{79} +(236.461 + 136.521i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(-312.115 - 540.599i) q^{82} +194.316i q^{83} +(72.7461 - 42.0000i) q^{84} +(39.2464 - 22.6589i) q^{85} -955.569i q^{86} +(33.7608 + 58.4754i) q^{87} +(-226.268 + 391.908i) q^{88} +(868.774 + 501.587i) q^{89} -307.172 q^{90} +(-299.689 - 133.565i) q^{91} +382.979 q^{92} +(44.8140 + 25.8734i) q^{93} +(30.0698 - 52.0824i) q^{94} +(-555.924 - 962.888i) q^{95} +96.0000i q^{96} +(915.000 - 528.275i) q^{97} +(84.8705 - 49.0000i) q^{98} -509.103i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 30 q^{3} + 40 q^{4} - 90 q^{9} - 48 q^{10} - 138 q^{11} + 240 q^{12} + 28 q^{13} + 280 q^{14} - 90 q^{15} - 160 q^{16} - 106 q^{17} + 60 q^{19} + 120 q^{20} - 64 q^{22} - 94 q^{23} - 304 q^{25} + 44 q^{26}+ \cdots + 5412 q^{97}+O(q^{100}) $ 20 * q + 30 * q^3 + 40 * q^4 - 90 * q^9 - 48 * q^10 - 138 * q^11 + 240 * q^12 + 28 * q^13 + 280 * q^14 - 90 * q^15 - 160 * q^16 - 106 * q^17 + 60 * q^19 + 120 * q^20 - 64 * q^22 - 94 * q^23 - 304 * q^25 + 44 * q^26 - 540 * q^27 - 166 * q^29 + 144 * q^30 - 414 * q^33 + 168 * q^35 + 360 * q^36 - 144 * q^37 + 48 * q^38 - 228 * q^39 - 384 * q^40 + 78 * q^41 + 420 * q^42 - 548 * q^43 - 270 * q^45 - 240 * q^46 + 480 * q^48 + 490 * q^49 - 144 * q^50 - 636 * q^51 + 416 * q^52 - 664 * q^53 + 2240 * q^55 + 560 * q^56 - 1032 * q^58 - 3204 * q^59 + 210 * q^61 - 436 * q^62 - 1280 * q^64 - 1502 * q^65 - 384 * q^66 + 1770 * q^67 + 424 * q^68 + 282 * q^69 - 1512 * q^71 + 548 * q^74 - 456 * q^75 + 240 * q^76 - 448 * q^77 - 492 * q^78 + 2096 * q^79 + 480 * q^80 - 810 * q^81 - 476 * q^82 - 6774 * q^85 + 498 * q^87 + 256 * q^88 + 1518 * q^89 + 864 * q^90 - 574 * q^91 - 752 * q^92 + 108 * q^93 + 448 * q^94 + 1502 * q^95 + 5412 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	1.73205	+	1.00000i	0.612372	+	0.353553i
$2$	1.73205	+	1.00000i	0.612372	+	0.353553i
$3$	1.50000	−	2.59808i	0.288675	−	0.500000i
$3$	1.50000	−	2.59808i	0.288675	−	0.500000i
$4$	2.00000	+	3.46410i	0.250000	+	0.433013i
$5$		−	17.0651i		−	1.52635i	−0.646193	−	0.763174i	$-0.723640\pi$
$5$		−	17.0651i		−	1.52635i	0.646193	−	0.763174i	$-0.276360\pi$
$6$	5.19615	−	3.00000i	0.353553	−	0.204124i
$7$	6.06218	−	3.50000i	0.327327	−	0.188982i
$7$	6.06218	−	3.50000i	0.327327	−	0.188982i
$8$			8.00000i			0.353553i
$9$	−4.50000	−	7.79423i	−0.166667	−	0.288675i
$10$	17.0651	−	29.5576i	0.539645	−	0.934693i
$11$	48.9885	+	28.2835i	1.34278	+	0.775254i	0.987215	−	0.159397i	$-0.0509550\pi$
$11$	48.9885	+	28.2835i	1.34278	+	0.775254i	0.355565	+	0.934651i	$0.384288\pi$
$12$	12.0000			0.288675
$13$	−27.5365	−	37.9307i	−0.587481	−	0.809238i
$13$	−27.5365	−	37.9307i	−0.587481	−	0.809238i
$14$	14.0000			0.267261
$15$	−44.3364	−	25.5976i	−0.763174	−	0.440619i
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	1.32779	+	2.29981i	0.0189434	+	0.0328109i	0.875342	−	0.483505i	$-0.160636\pi$
$17$	1.32779	+	2.29981i	0.0189434	+	0.0328109i	−0.856398	+	0.516316i	$0.827303\pi$
$18$		−	18.0000i		−	0.235702i
$19$	56.4245	−	32.5767i	0.681298	−	0.393347i	−0.119046	−	0.992889i	$-0.537984\pi$
$19$	56.4245	−	32.5767i	0.681298	−	0.393347i	0.800344	+	0.599541i	$0.204650\pi$
$20$	59.1152	−	34.1302i	0.660928	−	0.381587i
$21$		−	21.0000i		−	0.218218i
$22$	56.5670	+	97.9769i	0.548188	+	0.949489i
$23$	47.8724	−	82.9174i	0.434004	−	0.751716i	−0.563210	−	0.826314i	$-0.690434\pi$
$23$	47.8724	−	82.9174i	0.434004	−	0.751716i	0.997214	+	0.0745974i	$0.0237672\pi$
$24$	20.7846	+	12.0000i	0.176777	+	0.102062i
$25$	−166.217			−1.32974
$26$	−9.76388	−	93.2345i	−0.0736482	−	0.703261i
$27$	−27.0000			−0.192450
$28$	24.2487	+	14.0000i	0.163663	+	0.0944911i
$29$	−11.2536	+	19.4918i	−0.0720600	+	0.124812i	−0.899804	−	0.436294i	$-0.856291\pi$
$29$	−11.2536	+	19.4918i	−0.0720600	+	0.124812i	0.827744	+	0.561106i	$0.189624\pi$
$30$	−51.1953	−	88.6728i	−0.311564	−	0.539645i
$31$			17.2489i			0.0999353i	0.998751	+	0.0499677i	$0.0159118\pi$
$31$			17.2489i			0.0999353i	−0.998751	+	0.0499677i	$0.984088\pi$
$32$	−27.7128	+	16.0000i	−0.153093	+	0.0883883i
$33$	146.965	−	84.8505i	0.775254	−	0.447593i
$34$			5.31117i			0.0267900i
$35$	−59.7278	−	103.452i	−0.288453	−	0.499615i
$36$	18.0000	−	31.1769i	0.0833333	−	0.144338i
$37$	21.2442	+	12.2653i	0.0943926	+	0.0544976i	0.546453	−	0.837490i	$-0.315978\pi$
$37$	21.2442	+	12.2653i	0.0943926	+	0.0544976i	−0.452061	+	0.891987i	$0.649311\pi$
$38$	130.307			0.556277
$39$	−139.852	+	14.6458i	−0.574210	+	0.0601335i
$40$	136.521			0.539645
$41$	−270.300	−	156.058i	−1.02960	−	0.594441i	−0.112732	−	0.993625i	$-0.535960\pi$
$41$	−270.300	−	156.058i	−1.02960	−	0.594441i	−0.916871	+	0.399184i	$0.869293\pi$
$42$	21.0000	−	36.3731i	0.0771517	−	0.133631i
$43$	−238.892	−	413.773i	−0.847226	−	1.46744i	−0.883674	−	0.468103i	$-0.844938\pi$
$43$	−238.892	−	413.773i	−0.847226	−	1.46744i	0.0364481	−	0.999336i	$-0.488396\pi$
$44$			226.268i			0.775254i
$45$	−133.009	+	76.7929i	−0.440619	+	0.254391i
$46$	165.835	−	95.7448i	0.531544	−	0.306887i
$47$		−	30.0698i		−	0.0933218i	−0.998911	−	0.0466609i	$-0.985142\pi$
$47$		−	30.0698i		−	0.0933218i	0.998911	−	0.0466609i	$-0.0148580\pi$
$48$	24.0000	+	41.5692i	0.0721688	+	0.125000i
$49$	24.5000	−	42.4352i	0.0714286	−	0.123718i
$50$	−287.896	−	166.217i	−0.814294	−	0.470133i
$51$	7.96676			0.0218739
$52$	76.3229	−	171.251i	0.203540	−	0.456696i
$53$	−652.971			−1.69231			−0.846156	−	0.532936i	$-0.821089\pi$
$53$	−652.971			−1.69231			−0.846156	+	0.532936i	$0.821089\pi$
$54$	−46.7654	−	27.0000i	−0.117851	−	0.0680414i
$55$	482.660	−	835.992i	1.18331	−	2.04955i
$56$	28.0000	+	48.4974i	0.0668153	+	0.115728i
$57$		−	195.460i		−	0.454199i
$58$	−38.9836	+	22.5072i	−0.0882551	+	0.0509541i
$59$	624.634	−	360.633i	1.37831	−	0.795769i	0.386356	−	0.922350i	$-0.373733\pi$
$59$	624.634	−	360.633i	1.37831	−	0.795769i	0.991956	+	0.126580i	$0.0404001\pi$
$60$		−	204.781i		−	0.440619i
$61$	−111.575	−	193.254i	−0.234193	−	0.405633i	0.724845	−	0.688912i	$-0.241911\pi$
$61$	−111.575	−	193.254i	−0.234193	−	0.405633i	−0.959038	+	0.283278i	$0.908578\pi$
$62$	−17.2489	+	29.8760i	−0.0353325	+	0.0611976i
$63$	−54.5596	−	31.5000i	−0.109109	−	0.0629941i
$64$	−64.0000			−0.125000
$65$	−647.291	+	469.913i	−1.23518	+	0.896700i
$66$	339.402			0.632992
$67$	202.511	+	116.920i	0.369263	+	0.213194i	0.673136	−	0.739518i	$-0.264947\pi$
$67$	202.511	+	116.920i	0.369263	+	0.213194i	−0.303874	+	0.952712i	$0.598280\pi$
$68$	−5.31117	+	9.19922i	−0.00947168	+	0.0164054i
$69$	−143.617	−	248.752i	−0.250572	−	0.434004i
$70$		−	238.911i		−	0.407934i
$71$	−791.870	+	457.187i	−1.32363	+	0.764198i	−0.984306	−	0.176471i	$-0.943532\pi$
$71$	−791.870	+	457.187i	−1.32363	+	0.764198i	−0.339324	+	0.940670i	$0.610198\pi$
$72$	62.3538	−	36.0000i	0.102062	−	0.0589256i
$73$			467.327i			0.749266i	0.927173	+	0.374633i	$0.122231\pi$
$73$			467.327i			0.749266i	−0.927173	+	0.374633i	$0.877769\pi$
$74$	24.5307	+	42.4884i	0.0385356	+	0.0667456i
$75$	−249.326	+	431.845i	−0.383862	+	0.664868i
$76$	225.698	+	130.307i	0.340649	+	0.196674i
$77$	395.969			0.586037
$78$	−256.876	−	114.484i	−0.372891	−	0.166190i
$79$	1306.50			1.86067			0.930333	−	0.366715i	$-0.119518\pi$
$79$	1306.50			1.86067			0.930333	+	0.366715i	$0.119518\pi$
$80$	236.461	+	136.521i	0.330464	+	0.190793i
$81$	−40.5000	+	70.1481i	−0.0555556	+	0.0962250i
$82$	−312.115	−	540.599i	−0.420334	−	0.728039i
$83$			194.316i			0.256975i	0.991711	+	0.128488i	$0.0410122\pi$
$83$			194.316i			0.256975i	−0.991711	+	0.128488i	$0.958988\pi$
$84$	72.7461	−	42.0000i	0.0944911	−	0.0545545i
$85$	39.2464	−	22.6589i	0.0500808	−	0.0289142i
$86$		−	955.569i		−	1.19816i
$87$	33.7608	+	58.4754i	0.0416039	+	0.0720600i
$88$	−226.268	+	391.908i	−0.274094	+	0.474744i
$89$	868.774	+	501.587i	1.03472	+	0.597394i	0.918333	−	0.395810i	$-0.129536\pi$
$89$	868.774	+	501.587i	1.03472	+	0.597394i	0.116385	+	0.993204i	$0.462869\pi$
$90$	−307.172			−0.359764
$91$	−299.689	−	133.565i	−0.345230	−	0.153862i
$92$	382.979			0.434004
$93$	44.8140	+	25.8734i	0.0499677	+	0.0288488i
$94$	30.0698	−	52.0824i	0.0329942	−	0.0571477i
$95$	−555.924	−	962.888i	−0.600385	−	1.03990i
$96$			96.0000i			0.102062i
$97$	915.000	−	528.275i	0.957775	−	0.552972i	0.0622873	−	0.998058i	$-0.480160\pi$
$97$	915.000	−	528.275i	0.957775	−	0.552972i	0.895487	+	0.445087i	$0.146827\pi$
$98$	84.8705	−	49.0000i	0.0874818	−	0.0505076i
$99$		−	509.103i		−	0.516836i
$100$	−332.434	−	575.793i	−0.332434	−	0.575793i
$101$	58.8615	−	101.951i	0.0579895	−	0.100441i	−0.835573	−	0.549379i	$-0.814864\pi$
$101$	58.8615	−	101.951i	0.0579895	−	0.100441i	0.893563	+	0.448938i	$0.148198\pi$
$102$	13.7988	+	7.96676i	0.0133950	+	0.00773360i
$103$	456.089			0.436308			0.218154	−	0.975914i	$-0.429996\pi$
$103$	456.089			0.436308			0.218154	+	0.975914i	$0.429996\pi$
$104$	303.446	−	220.292i	0.286109	−	0.207706i
$105$	−358.367			−0.333076
$106$	−1130.98	−	652.971i	−1.03632	−	0.598322i
$107$	589.512	−	1021.06i	0.532619	−	0.922523i	−0.466656	−	0.884439i	$-0.654541\pi$
$107$	589.512	−	1021.06i	0.532619	−	0.922523i	0.999275	−	0.0380840i	$-0.0121255\pi$
$108$	−54.0000	−	93.5307i	−0.0481125	−	0.0833333i
$109$			800.588i			0.703509i	0.936092	+	0.351754i	$0.114415\pi$
$109$			800.588i			0.703509i	−0.936092	+	0.351754i	$0.885585\pi$
$110$	1671.98	−	965.321i	1.44925	−	0.836725i
$111$	63.7326	−	36.7960i	0.0544976	−	0.0314642i
$112$			112.000i			0.0944911i
$113$	371.594	+	643.619i	0.309350	+	0.535811i	0.978220	−	0.207569i	$-0.0665551\pi$
$113$	371.594	+	643.619i	0.309350	+	0.535811i	−0.668870	+	0.743379i	$0.733222\pi$
$114$	195.460	−	338.547i	0.160583	−	0.278139i
$115$	−1414.99	−	816.946i	−1.14738	−	0.662440i
$116$	−90.0288			−0.0720600
$117$	−171.727	+	385.314i	−0.135693	+	0.304464i
$118$	1442.53			1.12539
$119$	16.0986	+	9.29455i	0.0124013	+	0.00715992i
$120$	204.781	−	354.691i	0.155782	−	0.269823i
$121$	934.413	+	1618.45i	0.702038	+	1.21597i
$122$		−	446.301i		−	0.331198i
$123$	−810.899	+	468.173i	−0.594441	+	0.343201i
$124$	−59.7520	+	34.4978i	−0.0432733	+	0.0249838i
$125$			703.373i			0.503293i
$126$	−63.0000	−	109.119i	−0.0445435	−	0.0771517i
$127$	−1378.93	+	2388.38i	−0.963467	+	1.66877i	−0.249788	+	0.968301i	$0.580361\pi$
$127$	−1378.93	+	2388.38i	−0.963467	+	1.66877i	−0.713679	+	0.700473i	$0.752972\pi$
$128$	−110.851	−	64.0000i	−0.0765466	−	0.0441942i
$129$	−1433.35			−0.978292
$130$	−1591.05	+	166.621i	−1.07342	+	0.112413i
$131$	1622.48			1.08211			0.541057	−	0.840986i	$-0.318024\pi$
$131$	1622.48			1.08211			0.541057	+	0.840986i	$0.318024\pi$
$132$	587.862	+	339.402i	0.387627	+	0.223797i
$133$	228.037	−	394.971i	0.148671	−	0.257506i
$134$	233.839	+	405.021i	0.150751	+	0.261108i
$135$			460.757i			0.293746i
$136$	−18.3984	+	10.6223i	−0.0116004	+	0.00669749i
$137$	−218.277	+	126.022i	−0.136122	+	0.0785899i	−0.566514	−	0.824052i	$-0.691708\pi$
$137$	−218.277	+	126.022i	−0.136122	+	0.0785899i	0.430393	+	0.902642i	$0.358375\pi$
$138$		−	574.469i		−	0.354362i
$139$	733.500	+	1270.46i	0.447587	+	0.775244i	0.998228	−	0.0594982i	$-0.0189501\pi$
$139$	733.500	+	1270.46i	0.447587	+	0.775244i	−0.550641	+	0.834742i	$0.685617\pi$
$140$	238.911	−	413.806i	0.144226	−	0.249807i
$141$	−78.1235	−	45.1046i	−0.0466609	−	0.0269397i
$142$	−1828.75			−1.08074
$143$	−276.157	−	2637.00i	−0.161492	−	1.54208i
$144$	144.000			0.0833333
$145$	332.629	+	192.044i	0.190506	+	0.109989i
$146$	−467.327	+	809.434i	−0.264906	+	0.458830i
$147$	−73.5000	−	127.306i	−0.0412393	−	0.0714286i
$148$			98.1228i			0.0544976i
$149$	−437.643	+	252.673i	−0.240625	+	0.138925i	−0.615464	−	0.788165i	$-0.711031\pi$
$149$	−437.643	+	252.673i	−0.240625	+	0.138925i	0.374839	+	0.927090i	$0.377698\pi$
$150$	−863.689	+	498.651i	−0.470133	+	0.271431i
$151$			467.529i			0.251967i	0.992032	+	0.125983i	$0.0402086\pi$
$151$			467.529i			0.251967i	−0.992032	+	0.125983i	$0.959791\pi$
$152$	260.613	+	451.396i	0.139069	+	0.240875i
$153$	11.9501	−	20.6982i	0.00631445	−	0.0109370i
$154$	685.839	+	395.969i	0.358873	+	0.207195i
$155$	294.354			0.152536
$156$	−330.438	−	455.169i	−0.169591	−	0.233607i
$157$	−1034.51			−0.525879			−0.262939	−	0.964812i	$-0.584692\pi$
$157$	−1034.51			−0.525879			−0.262939	+	0.964812i	$0.584692\pi$
$158$	2262.92	+	1306.50i	1.13942	+	0.657845i
$159$	−979.457	+	1696.47i	−0.488528	+	0.846156i
$160$	273.041	+	472.921i	0.134911	+	0.233673i
$161$		−	670.213i		−	0.328076i
$162$	−140.296	+	81.0000i	−0.0680414	+	0.0392837i
$163$	1197.04	−	691.113i	0.575212	−	0.332099i	−0.184016	−	0.982923i	$-0.558910\pi$
$163$	1197.04	−	691.113i	0.575212	−	0.332099i	0.759228	+	0.650824i	$0.225577\pi$
$164$		−	1248.46i		−	0.594441i
$165$	−1447.98	−	2507.98i	−0.683183	−	1.18331i
$166$	−194.316	+	336.565i	−0.0908544	+	0.157364i
$167$	1632.76	+	942.675i	0.756568	+	0.436805i	0.828062	−	0.560636i	$-0.189443\pi$
$167$	1632.76	+	942.675i	0.756568	+	0.436805i	−0.0714940	+	0.997441i	$0.522777\pi$
$168$	168.000			0.0771517
$169$	−680.482	+	2088.96i	−0.309732	+	0.950824i
$170$	90.6356			0.0408908
$171$	−507.820	−	293.190i	−0.227099	−	0.131116i
$172$	955.569	−	1655.09i	0.423613	−	0.733719i
$173$	−2034.32	−	3523.55i	−0.894026	−	1.54850i	−0.835005	−	0.550242i	$-0.814535\pi$
$173$	−2034.32	−	3523.55i	−0.894026	−	1.54850i	−0.0590209	−	0.998257i	$-0.518798\pi$
$174$			135.043i			0.0588367i
$175$	−1007.64	+	581.760i	−0.435259	+	0.251297i
$176$	−783.815	+	452.536i	−0.335695	+	0.193814i
$177$		−	2163.80i		−	0.918875i
$178$	1003.17	+	1737.55i	0.422422	+	0.731656i
$179$	−776.011	+	1344.09i	−0.324032	+	0.561240i	−0.981316	−	0.192403i	$-0.938372\pi$
$179$	−776.011	+	1344.09i	−0.324032	+	0.561240i	0.657284	+	0.753643i	$0.271705\pi$
$180$	−532.037	−	307.172i	−0.220309	−	0.127196i
$181$	2150.83			0.883258			0.441629	−	0.897198i	$-0.354401\pi$
$181$	2150.83			0.883258			0.441629	+	0.897198i	$0.354401\pi$
$182$	−385.511	−	531.030i	−0.157011	−	0.216278i
$183$	−669.451			−0.270422
$184$	663.339	+	382.979i	0.265772	+	0.153443i
$185$	209.309	−	362.534i	0.0831822	−	0.144076i
$186$	51.7467	+	89.6279i	0.0203992	+	0.0353325i
$187$			150.219i			0.0587437i
$188$	104.165	−	60.1395i	0.0404095	−	0.0233305i
$189$	−163.679	+	94.5000i	−0.0629941	+	0.0363696i
$190$		−	2223.69i		−	0.849073i
$191$	−1581.21	−	2738.73i	−0.599016	−	1.03753i	−0.992967	−	0.118395i	$-0.962225\pi$
$191$	−1581.21	−	2738.73i	−0.599016	−	1.03753i	0.393950	−	0.919132i	$-0.371108\pi$
$192$	−96.0000	+	166.277i	−0.0360844	+	0.0625000i
$193$	4212.40	+	2432.03i	1.57106	+	0.907054i	0.996039	+	0.0889189i	$0.0283412\pi$
$193$	4212.40	+	2432.03i	1.57106	+	0.907054i	0.575025	+	0.818135i	$0.304992\pi$
$194$	2113.10			0.782020
$195$	249.932	+	2386.58i	0.0917847	+	0.876444i
$196$	196.000			0.0714286
$197$	−2293.51	−	1324.16i	−0.829471	−	0.478895i	0.0242008	−	0.999707i	$-0.492296\pi$
$197$	−2293.51	−	1324.16i	−0.829471	−	0.478895i	−0.853671	+	0.520812i	$0.825629\pi$
$198$	509.103	−	881.792i	0.182729	−	0.316496i
$199$	1903.56	+	3297.07i	0.678090	+	1.17449i	0.975555	+	0.219754i	$0.0705256\pi$
$199$	1903.56	+	3297.07i	0.678090	+	1.17449i	−0.297465	+	0.954733i	$0.596141\pi$
$200$		−	1329.74i		−	0.470133i
$201$	607.532	−	350.759i	0.213194	−	0.123088i
$202$	203.902	−	117.723i	0.0710223	−	0.0410048i
$203$			157.550i			0.0544722i
$204$	15.9335	+	27.5977i	0.00546848	+	0.00947168i
$205$	−2663.14	+	4612.69i	−0.907324	+	1.57153i
$206$	789.969	+	456.089i	0.267183	+	0.154258i
$207$	−861.703			−0.289336
$208$	745.876	−	78.1110i	0.248640	−	0.0260386i
$209$	3685.53			1.21978
$210$	−620.709	−	358.367i	−0.203967	−	0.117760i
$211$	856.669	−	1483.79i	0.279505	−	0.484116i	−0.691757	−	0.722130i	$-0.743163\pi$
$211$	856.669	−	1483.79i	0.279505	−	0.484116i	0.971262	+	0.238014i	$0.0764964\pi$
$212$	−1305.94	−	2261.96i	−0.423078	−	0.732792i
$213$			2743.12i			0.882420i
$214$	2042.13	−	1179.02i	0.652322	−	0.376619i
$215$	−7061.08	+	4076.72i	−2.23982	+	1.29316i
$216$		−	216.000i		−	0.0680414i
$217$	60.3712	+	104.566i	0.0188860	+	0.0327115i
$218$	−800.588	+	1386.66i	−0.248728	+	0.430809i
$219$	1214.15	+	700.990i	0.374633	+	0.216295i
$220$	3861.28			1.18331
$221$	50.6705	−	113.693i	0.0154229	−	0.0346054i
$222$	147.184			0.0444971
$223$	−5009.76	−	2892.38i	−1.50439	−	0.868558i	−0.999987	−	0.00508738i	$-0.998381\pi$
$223$	−5009.76	−	2892.38i	−1.50439	−	0.868558i	−0.504399	−	0.863471i	$-0.668286\pi$
$224$	−112.000	+	193.990i	−0.0334077	+	0.0578638i
$225$	747.977	+	1295.53i	0.221623	+	0.383862i
$226$			1486.37i			0.437487i
$227$	2304.57	−	1330.55i	0.673833	−	0.389037i	−0.123695	−	0.992320i	$-0.539474\pi$
$227$	2304.57	−	1330.55i	0.673833	−	0.389037i	0.797527	+	0.603283i	$0.206141\pi$
$228$	677.093	−	390.920i	0.196674	−	0.113550i
$229$			4819.93i			1.39087i	0.718587	+	0.695437i	$0.244789\pi$
$229$			4819.93i			1.39087i	−0.718587	+	0.695437i	$0.755211\pi$
$230$	−1633.89	−	2829.99i	−0.468416	−	0.811320i
$231$	593.954	−	1028.76i	0.169174	−	0.293019i
$232$	−155.934	−	90.0288i	−0.0441276	−	0.0254771i
$233$	3477.87			0.977866			0.488933	−	0.872321i	$-0.337386\pi$
$233$	3477.87			0.977866			0.488933	+	0.872321i	$0.337386\pi$
$234$	−682.753	+	495.657i	−0.190739	+	0.138471i
$235$	−513.143			−0.142442
$236$	2498.54	+	1442.53i	0.689156	+	0.397885i
$237$	1959.75	−	3394.38i	0.537128	−	0.930333i
$238$	18.5891	+	32.1973i	0.00506283	+	0.00876907i
$239$			7050.13i			1.90810i	0.299653	+	0.954048i	$0.403129\pi$
$239$			7050.13i			1.90810i	−0.299653	+	0.954048i	$0.596871\pi$
$240$	709.382	−	409.562i	0.190793	−	0.110155i
$241$	934.136	−	539.324i	0.249681	−	0.144153i	−0.369937	−	0.929057i	$-0.620621\pi$
$241$	934.136	−	539.324i	0.249681	−	0.144153i	0.619618	+	0.784904i	$0.287288\pi$
$242$			3737.65i			0.992832i
$243$	121.500	+	210.444i	0.0320750	+	0.0555556i
$244$	446.301	−	773.016i	0.117096	−	0.202817i
$245$	−724.161	−	418.095i	−0.188837	−	0.109025i
$246$	−1872.69			−0.485359
$247$	−2789.39	−	1243.17i	−0.718561	−	0.320248i
$248$	−137.991			−0.0353325
$249$	504.847	+	291.474i	0.128488	+	0.0741823i
$250$	−703.373	+	1218.28i	−0.177941	+	0.308203i
$251$	2609.72	+	4520.16i	0.656270	+	1.13669i	0.981574	+	0.191083i	$0.0612001\pi$
$251$	2609.72	+	4520.16i	0.656270	+	1.13669i	−0.325304	+	0.945610i	$0.605467\pi$
$252$		−	252.000i		−	0.0629941i
$253$	4690.39	−	2708.00i	1.16554	−	0.672926i
$254$	−4776.76	+	2757.86i	−1.18000	+	0.681274i
$255$		−	135.953i		−	0.0333872i
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	−955.389	+	1654.78i	−0.231889	+	0.401644i	−0.958364	−	0.285549i	$-0.907824\pi$
$257$	−955.389	+	1654.78i	−0.231889	+	0.401644i	0.726475	+	0.687193i	$0.241157\pi$
$258$	−2482.64	−	1433.35i	−0.599079	−	0.345879i
$259$	171.715			0.0411963
$260$	−2922.41	−	1302.46i	−0.697077	−	0.310673i
$261$	202.565			0.0480400
$262$	2810.22	+	1622.48i	0.662656	+	0.382585i
$263$	−3185.08	+	5516.72i	−0.746770	+	1.29344i	0.202593	+	0.979263i	$0.435063\pi$
$263$	−3185.08	+	5516.72i	−0.746770	+	1.29344i	−0.949363	+	0.314180i	$0.898270\pi$
$264$	678.804	+	1175.72i	0.158248	+	0.274094i
$265$			11143.0i			2.58306i
$266$	789.942	−	456.073i	0.182084	−	0.105127i
$267$	2606.32	−	1504.76i	0.597394	−	0.344906i
$268$			935.356i			0.213194i
$269$	−2755.89	−	4773.34i	−0.624645	−	1.08192i	−0.988609	−	0.150504i	$-0.951911\pi$
$269$	−2755.89	−	4773.34i	−0.624645	−	1.08192i	0.363965	−	0.931413i	$-0.381423\pi$
$270$	−460.757	+	798.055i	−0.103855	+	0.179882i
$271$	−359.074	−	207.312i	−0.0804878	−	0.0464697i	0.459216	−	0.888325i	$-0.348130\pi$
$271$	−359.074	−	207.312i	−0.0804878	−	0.0464697i	−0.539704	+	0.841855i	$0.681464\pi$
$272$	−42.4894			−0.00947168
$273$	−796.546	+	578.267i	−0.176590	+	0.128199i
$274$	−504.089			−0.111143
$275$	−8142.72	−	4701.20i	−1.78554	−	1.03088i
$276$	574.469	−	995.009i	0.125286	−	0.217002i
$277$	−1394.90	−	2416.05i	−0.302569	−	0.524065i	0.674148	−	0.738596i	$-0.264511\pi$
$277$	−1394.90	−	2416.05i	−0.302569	−	0.524065i	−0.976717	+	0.214531i	$0.931178\pi$
$278$			2934.00i			0.632984i
$279$	134.442	−	77.6201i	0.0288488	−	0.0166559i
$280$	827.613	−	477.822i	0.176640	−	0.101983i
$281$			70.8519i			0.0150415i	0.999972	+	0.00752077i	$0.00239396\pi$
$281$			70.8519i			0.0150415i	−0.999972	+	0.00752077i	$0.997606\pi$
$282$	−90.2093	−	156.247i	−0.0190492	−	0.0329942i
$283$	−130.142	+	225.412i	−0.0273361	+	0.0473476i	−0.879370	−	0.476139i	$-0.842036\pi$
$283$	−130.142	+	225.412i	−0.0273361	+	0.0473476i	0.852034	+	0.523487i	$0.175369\pi$
$284$	−3167.48	−	1828.75i	−0.661815	−	0.382099i
$285$	−3335.54			−0.693265
$286$	2158.68	−	4843.57i	0.446313	−	1.00142i
$287$	−2184.81			−0.449355
$288$	249.415	+	144.000i	0.0510310	+	0.0294628i
$289$	2452.97	−	4248.68i	0.499282	−	0.864782i
$290$	384.087	+	665.258i	0.0777737	+	0.134708i
$291$		−	3169.65i		−	0.638517i
$292$	−1618.87	+	934.653i	−0.324442	+	0.187317i
$293$	−4472.07	+	2581.95i	−0.891677	+	0.514810i	−0.874491	−	0.485043i	$-0.838804\pi$
$293$	−4472.07	+	2581.95i	−0.891677	+	0.514810i	−0.0171861	+	0.999852i	$0.505471\pi$
$294$		−	294.000i		−	0.0583212i
$295$	−6154.23	−	10659.4i	−1.21462	−	2.10378i
$296$	−98.1228	+	169.954i	−0.0192678	+	0.0333728i
$297$	−1322.69	−	763.655i	−0.258418	−	0.149198i
$298$	−1010.69			−0.196469
$299$	−4463.36	+	467.420i	−0.863286	+	0.0904067i
$300$	−1994.61			−0.383862
$301$	−2896.41	−	1672.25i	−0.554640	−	0.320221i
$302$	−467.529	+	809.783i	−0.0890836	+	0.154297i
$303$	−176.584	−	305.853i	−0.0334802	−	0.0579895i
$304$			1042.45i			0.196674i
$305$	−3297.90	+	1904.04i	−0.619138	+	0.357459i
$306$	41.3965	−	23.9003i	0.00773360	−	0.00446499i
$307$			9653.05i			1.79456i	0.441466	+	0.897278i	$0.354458\pi$
$307$			9653.05i			1.79456i	−0.441466	+	0.897278i	$0.645542\pi$
$308$	791.938	+	1371.68i	0.146509	+	0.253762i
$309$	684.133	−	1184.95i	0.125951	−	0.218154i
$310$	509.836	+	294.354i	0.0934089	+	0.0539296i
$311$	9091.61			1.65768			0.828839	−	0.559487i	$-0.189002\pi$
$311$	9091.61			1.65768			0.828839	+	0.559487i	$0.189002\pi$
$312$	−117.167	−	1118.81i	−0.0212604	−	0.203014i
$313$	−233.839			−0.0422280			−0.0211140	−	0.999777i	$-0.506721\pi$
$313$	−233.839			−0.0422280			−0.0211140	+	0.999777i	$0.506721\pi$
$314$	−1791.83	−	1034.51i	−0.322034	−	0.185926i
$315$	−537.550	+	931.064i	−0.0961509	+	0.166538i
$316$	2613.00	+	4525.85i	0.465167	+	0.805692i
$317$		−	6141.64i		−	1.08817i	−0.839031	−	0.544083i	$-0.816878\pi$
$317$		−	6141.64i		−	1.08817i	0.839031	−	0.544083i	$-0.183122\pi$
$318$	−3392.94	+	1958.91i	−0.598322	+	0.345442i
$319$	−1102.59	+	636.582i	−0.193521	+	0.111730i
$320$			1092.17i			0.190793i
$321$	−1768.53	−	3063.19i	−0.307508	−	0.532619i
$322$	670.213	−	1160.84i	0.115992	−	0.200905i
$323$	149.840	+	86.5102i	0.0258121	+	0.0149026i
$324$	−324.000			−0.0555556
$325$	4577.04	+	6304.74i	0.781195	+	1.07607i
$326$	2764.45			0.469659
$327$	2079.99	+	1200.88i	0.351754	+	0.203085i
$328$	1248.46	−	2162.40i	0.210167	−	0.364019i
$329$	−105.244	−	182.288i	−0.0176362	−	0.0305467i
$330$		−	5791.92i		−	0.966167i
$331$	376.473	−	217.357i	0.0625162	−	0.0360937i	−0.468416	−	0.883508i	$-0.655175\pi$
$331$	376.473	−	217.357i	0.0625162	−	0.0360937i	0.530932	+	0.847414i	$0.321842\pi$
$332$	−673.130	+	388.632i	−0.111273	+	0.0642438i
$333$		−	220.776i		−	0.0363317i
$334$	1885.35	+	3265.52i	0.308868	+	0.534975i
$335$	1995.24	−	3455.86i	0.325408	−	0.563623i
$336$	290.985	+	168.000i	0.0472456	+	0.0272772i
$337$	9984.16			1.61386			0.806932	−	0.590645i	$-0.201127\pi$
$337$	9984.16			1.61386			0.806932	+	0.590645i	$0.201127\pi$
$338$	−3267.59	+	2937.70i	−0.525839	+	0.472751i
$339$	2229.56			0.357207
$340$	156.985	+	90.6356i	0.0250404	+	0.0144571i
$341$	−487.860	+	844.997i	−0.0774753	+	0.134191i
$342$	−586.380	−	1015.64i	−0.0927129	−	0.160583i
$343$		−	343.000i		−	0.0539949i
$344$	3310.19	−	1911.14i	0.518818	−	0.299540i
$345$	−4244.98	+	2450.84i	−0.662440	+	0.382460i
$346$		−	8137.28i		−	1.26434i
$347$	1099.45	+	1904.30i	0.170090	+	0.294605i	0.938451	−	0.345412i	$-0.112261\pi$
$347$	1099.45	+	1904.30i	0.170090	+	0.294605i	−0.768361	+	0.640017i	$0.778927\pi$
$348$	−135.043	+	233.902i	−0.0208019	+	0.0360300i
$349$	5381.65	+	3107.10i	0.825424	+	0.476559i	0.852283	−	0.523080i	$-0.175217\pi$
$349$	5381.65	+	3107.10i	0.825424	+	0.476559i	−0.0268592	+	0.999639i	$0.508551\pi$
$350$	−2327.04			−0.355387
$351$	743.486	+	1024.13i	0.113061	+	0.155738i
$352$	−1810.14			−0.274094
$353$	−7086.04	−	4091.12i	−1.06842	−	0.616852i	−0.140669	−	0.990057i	$-0.544925\pi$
$353$	−7086.04	−	4091.12i	−1.06842	−	0.616852i	−0.927749	+	0.373205i	$0.878259\pi$
$354$	2163.80	−	3747.81i	0.324871	−	0.562694i
$355$	7801.93	+	13513.3i	1.16643	+	2.02032i
$356$			4012.69i			0.597394i
$357$	48.2959	−	27.8837i	0.00715992	−	0.00413378i
$358$	−2688.18	+	1552.02i	−0.396857	+	0.229125i
$359$		−	6229.62i		−	0.915840i	−0.888993	−	0.457920i	$-0.848595\pi$
$359$		−	6229.62i		−	0.915840i	0.888993	−	0.457920i	$-0.151405\pi$
$360$	−614.343	−	1064.07i	−0.0899409	−	0.155782i
$361$	−1307.02	+	2263.83i	−0.190556	+	0.330052i
$362$	3725.34	+	2150.83i	0.540883	+	0.312279i
$363$	5606.48			0.810644
$364$	−136.694	−	1305.28i	−0.0196833	−	0.187954i
$365$	7974.97			1.14364
$366$	−1159.52	−	669.451i	−0.165599	−	0.0956087i
$367$	−1739.63	+	3013.13i	−0.247433	+	0.428566i	−0.962813	−	0.270169i	$-0.912920\pi$
$367$	−1739.63	+	3013.13i	−0.247433	+	0.428566i	0.715380	+	0.698736i	$0.246254\pi$
$368$	765.958	+	1326.68i	0.108501	+	0.187929i
$369$			2809.04i			0.396294i
$370$	725.068	−	418.618i	0.101877	−	0.0588187i
$371$	−3958.43	+	2285.40i	−0.553939	+	0.319817i
$372$			206.987i			0.0288488i
$373$	2689.36	+	4658.11i	0.373324	+	0.646617i	0.990075	−	0.140542i	$-0.0448846\pi$
$373$	2689.36	+	4658.11i	0.373324	+	0.646617i	−0.616750	+	0.787159i	$0.711551\pi$
$374$	−150.219	+	260.186i	−0.0207690	+	0.0359730i
$375$	1827.42	+	1055.06i	0.251647	+	0.145288i
$376$	240.558			0.0329942
$377$	1049.22	−	109.879i	0.143336	−	0.0150107i
$378$	−378.000			−0.0514344
$379$	7874.54	+	4546.37i	1.06725	+	0.616177i	0.927429	−	0.373999i	$-0.122014\pi$
$379$	7874.54	+	4546.37i	1.06725	+	0.616177i	0.139822	+	0.990177i	$0.455347\pi$
$380$	2223.69	−	3851.55i	0.300192	−	0.519949i
$381$	4136.79	+	7165.13i	0.556258	+	0.963467i
$382$		−	6324.83i		−	0.847137i
$383$	−7519.44	+	4341.35i	−1.00320	+	0.579198i	−0.909194	−	0.416374i	$-0.863301\pi$
$383$	−7519.44	+	4341.35i	−1.00320	+	0.579198i	−0.0940065	+	0.995572i	$0.529967\pi$
$384$	−332.554	+	192.000i	−0.0441942	+	0.0255155i
$385$		−	6757.25i		−	0.894496i
$386$	4864.06	+	8424.81i	0.641384	+	1.11091i
$387$	−2150.03	+	3723.96i	−0.282409	+	0.489146i
$388$	3660.00	+	2113.10i	0.478887	+	0.276486i
$389$	−5934.67			−0.773521			−0.386761	−	0.922180i	$-0.626406\pi$
$389$	−5934.67			−0.773521			−0.386761	+	0.922180i	$0.626406\pi$
$390$	−1953.69	+	4383.61i	−0.253663	+	0.569161i
$391$	254.259			0.0328860
$392$	339.482	+	196.000i	0.0437409	+	0.0252538i
$393$	2433.72	−	4215.33i	0.312379	−	0.541057i
$394$	−2648.32	−	4587.02i	−0.338630	−	0.586524i
$395$		−	22295.5i		−	2.84002i
$396$	1763.58	−	1018.21i	0.223797	−	0.129209i
$397$	9783.08	−	5648.26i	1.23677	−	0.714051i	0.268339	−	0.963324i	$-0.413525\pi$
$397$	9783.08	−	5648.26i	1.23677	−	0.714051i	0.968433	+	0.249274i	$0.0801919\pi$
$398$			7614.25i			0.958965i
$399$	−684.110	−	1184.91i	−0.0858355	−	0.148671i
$400$	1329.74	−	2303.17i	0.166217	−	0.287896i
$401$	−7197.79	−	4155.65i	−0.896361	−	0.517514i	−0.0203429	−	0.999793i	$-0.506476\pi$
$401$	−7197.79	−	4155.65i	−0.896361	−	0.517514i	−0.876018	+	0.482279i	$0.839809\pi$
$402$	1403.03			0.174072
$403$	654.264	−	474.975i	0.0808715	−	0.0587101i
$404$	470.892			0.0579895
$405$	1197.08	+	691.136i	0.146873	+	0.0847971i
$406$	−157.550	+	272.885i	−0.0192588	+	0.0333573i
$407$	693.814	+	1201.72i	0.0844990	+	0.146356i
$408$			63.7341i			0.00773360i
$409$	−459.897	+	265.522i	−0.0556001	+	0.0321007i	−0.527542	−	0.849529i	$-0.676886\pi$
$409$	−459.897	+	265.522i	−0.0556001	+	0.0321007i	0.471942	+	0.881629i	$0.343553\pi$
$410$	−9225.37	+	5326.27i	−1.11124	+	0.641575i
$411$			756.134i			0.0907478i
$412$	912.178	+	1579.94i	0.109077	+	0.188927i
$413$	2524.43	−	4372.44i	0.300773	−	0.520953i
$414$	−1492.51	−	861.703i	−0.177181	−	0.102296i
$415$	3316.02			0.392233
$416$	1370.01	+	610.584i	0.161466	+	0.0719623i
$417$	4401.00			0.516829
$418$	6383.53	+	3685.53i	0.746958	+	0.431256i
$419$	−1539.33	+	2666.20i	−0.179478	+	0.310865i	−0.941702	−	0.336449i	$-0.890774\pi$
$419$	−1539.33	+	2666.20i	−0.179478	+	0.310865i	0.762224	+	0.647313i	$0.224107\pi$
$420$	−716.734	−	1241.42i	−0.0832691	−	0.144226i
$421$			5766.92i			0.667607i	0.942643	+	0.333804i	$0.108332\pi$
$421$			5766.92i			0.667607i	−0.942643	+	0.333804i	$0.891668\pi$
$422$	2967.59	−	1713.34i	0.342322	−	0.197640i
$423$	−234.371	+	135.314i	−0.0269397	+	0.0155536i
$424$		−	5223.77i		−	0.598322i
$425$	−220.702	−	382.267i	−0.0251897	−	0.0436298i
$426$	−2743.12	+	4751.22i	−0.311983	+	0.540370i
$427$	−1352.78	−	781.027i	−0.153315	−	0.0885165i
$428$	4716.09			0.532619
$429$	−7265.36	−	3238.02i	−0.817657	−	0.364413i
$430$	−16306.9			−1.82881
$431$	451.699	+	260.789i	0.0504817	+	0.0291456i	0.525028	−	0.851085i	$-0.324055\pi$
$431$	451.699	+	260.789i	0.0504817	+	0.0291456i	−0.474547	+	0.880230i	$0.657388\pi$
$432$	216.000	−	374.123i	0.0240563	−	0.0416667i
$433$	−284.804	−	493.296i	−0.0316093	−	0.0547489i	0.849788	−	0.527125i	$-0.176730\pi$
$433$	−284.804	−	493.296i	−0.0316093	−	0.0547489i	−0.881397	+	0.472376i	$0.843397\pi$
$434$			241.485i			0.0267088i
$435$	997.888	−	576.131i	0.109989	−	0.0635020i
$436$	−2773.32	+	1601.18i	−0.304628	+	0.175877i
$437$		−	6238.09i		−	0.682857i
$438$	1401.98	+	2428.30i	0.152943	+	0.264906i
$439$	1382.70	−	2394.91i	0.150325	−	0.260371i	−0.781022	−	0.624504i	$-0.785301\pi$
$439$	1382.70	−	2394.91i	0.150325	−	0.260371i	0.931347	+	0.364133i	$0.118635\pi$
$440$	6687.94	+	3861.28i	0.724625	+	0.418362i
$441$	−441.000			−0.0476190
$442$	201.457	−	146.251i	0.0216795	−	0.0157386i
$443$	16607.6			1.78115			0.890575	−	0.454836i	$-0.150302\pi$
$443$	16607.6			1.78115			0.890575	+	0.454836i	$0.150302\pi$
$444$	254.930	+	147.184i	0.0272488	+	0.0157321i
$445$	8559.62	−	14825.7i	0.911831	−	1.57934i
$446$	−5784.77	−	10019.5i	−0.614163	−	1.06376i
$447$			1516.04i			0.160417i
$448$	−387.979	+	224.000i	−0.0409159	+	0.0236228i
$449$	8326.03	−	4807.03i	0.875121	−	0.505252i	0.00607465	−	0.999982i	$-0.498066\pi$
$449$	8326.03	−	4807.03i	0.875121	−	0.505252i	0.869047	+	0.494730i	$0.164733\pi$
$450$			2991.91i			0.313422i
$451$	−8827.71	−	15290.0i	−0.921686	−	1.59641i
$452$	−1486.37	+	2574.48i	−0.154675	+	0.267905i
$453$	1214.68	+	701.293i	0.125983	+	0.0727365i
$454$	5322.19			0.550182
$455$	−2279.30	+	5114.21i	−0.234847	+	0.526941i
$456$	1563.68			0.160583
$457$	1278.06	+	737.886i	0.130820	+	0.0755292i	0.563982	−	0.825787i	$-0.309269\pi$
$457$	1278.06	+	737.886i	0.130820	+	0.0755292i	−0.433162	+	0.901316i	$0.642602\pi$
$458$	−4819.93	+	8348.37i	−0.491748	+	0.851733i
$459$	−35.8504	−	62.0947i	−0.00364565	−	0.00631445i
$460$		−	6535.57i		−	0.662440i
$461$	10540.8	−	6085.71i	1.06493	−	0.614837i	0.138138	−	0.990413i	$-0.455888\pi$
$461$	10540.8	−	6085.71i	1.06493	−	0.614837i	0.926792	+	0.375576i	$0.122555\pi$
$462$	2057.52	−	1187.91i	0.207195	−	0.119624i
$463$			4804.09i			0.482214i	0.970499	+	0.241107i	$0.0775104\pi$
$463$			4804.09i			0.482214i	−0.970499	+	0.241107i	$0.922490\pi$
$464$	−180.058	−	311.869i	−0.0180150	−	0.0312029i
$465$	441.531	−	764.754i	0.0440334	−	0.0762680i
$466$	6023.85	+	3477.87i	0.598818	+	0.345728i
$467$	−8327.55			−0.825168			−0.412584	−	0.910920i	$-0.635374\pi$
$467$	−8327.55			−0.825168			−0.412584	+	0.910920i	$0.635374\pi$
$468$	−1678.22	+	175.750i	−0.165760	+	0.0173591i
$469$	1636.87			0.161159
$470$	−888.790	−	513.143i	−0.0872273	−	0.0503607i
$471$	−1551.77	+	2687.74i	−0.151808	+	0.262939i
$472$	2885.06	+	4997.07i	0.281347	+	0.487307i
$473$		−	27026.8i		−	2.62726i
$474$	6788.77	−	3919.50i	0.657845	−	0.379807i
$475$	−9378.71	+	5414.80i	−0.905947	+	0.523049i
$476$			74.3564i			0.00715992i
$477$	2938.37	+	5089.41i	0.282052	+	0.488528i
$478$	−7050.13	+	12211.2i	−0.674614	+	1.16847i
$479$	−5474.45	−	3160.68i	−0.522201	−	0.301493i	0.215634	−	0.976474i	$-0.430818\pi$
$479$	−5474.45	−	3160.68i	−0.522201	−	0.301493i	−0.737835	+	0.674982i	$0.764152\pi$
$480$	1638.25			0.155782
$481$	−119.757	−	1143.55i	−0.0113523	−	0.108402i
$482$	2157.30			0.203863
$483$	−1741.27	−	1005.32i	−0.164038	−	0.0947074i
$484$	−3737.65	+	6473.80i	−0.351019	+	0.607983i
$485$	−9015.06	−	15614.5i	−0.844027	−	1.46190i
$486$			486.000i			0.0453609i
$487$	14389.5	−	8307.78i	1.33891	−	0.773022i	0.352267	−	0.935900i	$-0.385411\pi$
$487$	14389.5	−	8307.78i	1.33891	−	0.773022i	0.986646	+	0.162878i	$0.0520777\pi$
$488$	1546.03	−	892.602i	0.143413	−	0.0827996i
$489$		−	4146.68i		−	0.383475i
$490$	−836.189	−	1448.32i	−0.0770922	−	0.133528i
$491$	5462.73	−	9461.73i	0.502097	−	0.869657i	−0.497900	−	0.867234i	$-0.665895\pi$
$491$	5462.73	−	9461.73i	0.502097	−	0.869657i	0.999997	−	0.00242291i	$-0.000771237\pi$
$492$	−3243.60	−	1872.69i	−0.297221	−	0.171600i
$493$	−59.7698			−0.00546023
$494$	−3588.19	−	4942.63i	−0.326802	−	0.450161i
$495$	−8687.89			−0.788872
$496$	−239.008	−	137.991i	−0.0216366	−	0.0124919i
$497$	−3200.31	+	5543.09i	−0.288840	+	0.500285i
$498$	582.947	+	1009.69i	0.0524548	+	0.0908544i
$499$		−	12688.1i		−	1.13827i	−0.822245	−	0.569134i	$-0.807279\pi$
$499$		−	12688.1i		−	1.13827i	0.822245	−	0.569134i	$-0.192721\pi$
$500$	−2436.56	+	1406.75i	−0.217932	+	0.125823i
$501$	4898.29	−	2828.03i	0.436805	−	0.252189i
$502$			10438.9i			0.928106i
$503$	−6276.83	−	10871.8i	−0.556402	−	0.963716i	−0.997793	−	0.0664014i	$-0.978848\pi$
$503$	−6276.83	−	10871.8i	−0.556402	−	0.963716i	0.441391	−	0.897315i	$-0.354485\pi$
$504$	252.000	−	436.477i	0.0222718	−	0.0385758i
$505$	−1739.80	−	1004.48i	−0.153307	−	0.0885121i
$506$	10832.0			0.951662
$507$	4406.55	+	4901.38i	0.386000	+	0.429345i
$508$	−11031.4			−0.963467
$509$	6154.96	+	3553.57i	0.535980	+	0.309448i	0.743448	−	0.668793i	$-0.233189\pi$
$509$	6154.96	+	3553.57i	0.535980	+	0.309448i	−0.207468	+	0.978242i	$0.566522\pi$
$510$	135.953	−	235.478i	0.0118042	−	0.0204454i
$511$	1635.64	+	2833.02i	0.141598	+	0.245255i
$512$		−	512.000i		−	0.0441942i
$513$	−1523.46	+	879.570i	−0.131116	+	0.0756998i
$514$	−3309.57	+	1910.78i	−0.284005	+	0.163970i
$515$		−	7783.19i		−	0.665958i
$516$	−2866.71	−	4965.28i	−0.244573	−	0.423613i
$517$	850.478	−	1473.07i	0.0723481	−	0.125311i
$518$	297.419	+	171.715i	0.0252275	+	0.0145651i
$519$	−12205.9			−1.03233
$520$	−3759.30	−	5178.33i	−0.317031	−	0.436702i
$521$	−2610.89			−0.219549			−0.109775	−	0.993957i	$-0.535013\pi$
$521$	−2610.89			−0.219549			−0.109775	+	0.993957i	$0.535013\pi$
$522$	350.852	+	202.565i	0.0294184	+	0.0169847i
$523$	−2090.57	+	3620.98i	−0.174788	+	0.302742i	−0.940088	−	0.340932i	$-0.889257\pi$
$523$	−2090.57	+	3620.98i	−0.174788	+	0.302742i	0.765300	+	0.643674i	$0.222591\pi$
$524$	3244.96	+	5620.44i	0.270528	+	0.468569i
$525$			3490.56i			0.290172i
$526$	−11033.4	+	6370.16i	−0.914603	+	0.528046i
$527$	−39.6691	+	22.9030i	−0.00327896	+	0.00189311i
$528$			2715.22i			0.223797i
$529$	1499.97	+	2598.02i	0.123282	+	0.213530i
$530$	−11143.0	+	19300.3i	−0.913248	+	1.58179i
$531$	−5621.71	−	3245.69i	−0.459438	−	0.265256i
$532$	1824.29			0.148671
$533$	1523.73	+	14549.9i	0.123827	+	1.18242i
$534$	6019.04			0.487770
$535$	−17424.5	−	10060.1i	−1.40809	−	0.812962i
$536$	−935.356	+	1620.08i	−0.0753754	+	0.130554i
$537$	2328.03	+	4032.27i	0.187080	+	0.324032i
$538$		−	11023.5i		−	0.883381i
$539$	2400.43	−	1385.89i	0.191826	−	0.110751i
$540$	−1596.11	+	921.515i	−0.127196	+	0.0734364i
$541$		−	14710.3i		−	1.16903i	−0.811383	−	0.584516i	$-0.801285\pi$
$541$		−	14710.3i		−	1.16903i	0.811383	−	0.584516i	$-0.198715\pi$
$542$	−414.623	−	718.148i	−0.0328590	−	0.0569135i
$543$	3226.24	−	5588.01i	0.254975	−	0.441629i
$544$	−73.5938	−	42.4894i	−0.00580020	−	0.00334874i
$545$	13662.1			1.07380
$546$	−1957.92	+	205.041i	−0.153464	+	0.0160714i
$547$	−21123.2			−1.65112			−0.825560	−	0.564315i	$-0.809140\pi$
$547$	−21123.2			−1.65112			−0.825560	+	0.564315i	$0.809140\pi$
$548$	−873.108	−	504.089i	−0.0680608	−	0.0392949i
$549$	−1004.18	+	1739.29i	−0.0780642	+	0.135211i
$550$	−9402.40	−	16285.4i	−0.728945	−	1.26257i
$551$			1466.42i			0.113378i
$552$	1990.02	−	1148.94i	0.153443	−	0.0885906i
$553$	7920.23	−	4572.75i	0.609046	−	0.351633i
$554$		−	5579.62i		−	0.427898i
$555$	−627.927	−	1087.60i	−0.0480253	−	0.0831822i
$556$	−2934.00	+	5081.83i	−0.223794	+	0.387622i
$557$	15892.7	+	9175.68i	1.20897	+	0.698000i	0.962535	−	0.271159i	$-0.0874068\pi$
$557$	15892.7	+	9175.68i	1.20897	+	0.698000i	0.246437	+	0.969159i	$0.420740\pi$
$558$	310.480			0.0235550
$559$	−9116.48	+	20455.2i	−0.689778	+	1.54770i
$560$	1911.29			0.144226
$561$	390.279	+	225.328i	0.0293718	+	0.0169578i
$562$	−70.8519	+	122.719i	−0.00531799	+	0.00921102i
$563$	−6689.70	−	11586.9i	−0.500777	−	0.867371i	−1.00000		0.000897177i	$-0.999714\pi$
$563$	−6689.70	−	11586.9i	−0.500777	−	0.867371i	0.499223	−	0.866474i	$-0.333619\pi$
$564$		−	360.837i		−	0.0269397i
$565$	10983.4	−	6341.28i	0.817833	−	0.472176i
$566$	−450.824	+	260.283i	−0.0334798	+	0.0193296i
$567$			567.000i			0.0419961i
$568$	−3657.49	−	6334.96i	−0.270185	−	0.467974i
$569$	−2046.65	+	3544.89i	−0.150791	+	0.261177i	−0.931518	−	0.363694i	$-0.881515\pi$
$569$	−2046.65	+	3544.89i	−0.150791	+	0.261177i	0.780728	+	0.624871i	$0.214849\pi$
$570$	−5777.33	−	3335.54i	−0.424536	−	0.245106i
$571$	−2658.94			−0.194874			−0.0974369	−	0.995242i	$-0.531064\pi$
$571$	−2658.94			−0.194874			−0.0974369	+	0.995242i	$0.531064\pi$
$572$	8582.51	−	6230.63i	0.627365	−	0.455447i
$573$	−9487.24			−0.691684
$574$	−3784.19	−	2184.81i	−0.275173	−	0.158871i
$575$	−7957.21	+	13782.3i	−0.577111	+	0.999585i
$576$	288.000	+	498.831i	0.0208333	+	0.0360844i
$577$		−	6956.99i		−	0.501947i	−0.967994	−	0.250974i	$-0.919249\pi$
$577$		−	6956.99i		−	0.501947i	0.967994	−	0.250974i	$-0.0807507\pi$
$578$	8497.35	−	4905.95i	0.611493	−	0.353046i
$579$	12637.2	−	7296.10i	0.907054	−	0.523688i
$580$			1536.35i			0.109989i
$581$	680.105	+	1177.98i	0.0485637	+	0.0841148i
$582$	3169.65	−	5490.00i	0.225750	−	0.391010i
$583$	−31988.1	−	18468.3i	−2.27240	−	1.31197i
$584$	−3738.61			−0.264906
$585$	6575.42	+	2930.53i	0.464718	+	0.207115i
$586$	−10327.8			−0.728051
$587$	−9485.98	−	5476.73i	−0.666999	−	0.385092i	0.127940	−	0.991782i	$-0.459164\pi$
$587$	−9485.98	−	5476.73i	−0.666999	−	0.385092i	−0.794939	+	0.606690i	$0.792497\pi$
$588$	294.000	−	509.223i	0.0206197	−	0.0357143i
$589$	561.912	+	973.260i	0.0393093	+	0.0680857i
$590$		−	24616.9i		−	1.71773i
$591$	−6880.53	+	3972.47i	−0.478895	+	0.276490i
$592$	−339.907	+	196.246i	−0.0235981	+	0.0136244i
$593$		−	20599.7i		−	1.42652i	−0.700897	−	0.713262i	$-0.747217\pi$
$593$		−	20599.7i		−	1.42652i	0.700897	−	0.713262i	$-0.252783\pi$
$594$	−1527.31	−	2645.38i	−0.105499	−	0.182729i
$595$	158.612	−	274.725i	0.0109285	−	0.0189288i
$596$	−1750.57	−	1010.69i	−0.120312	−	0.0694625i
$597$	11421.4			0.782991
$598$	−8198.18	−	3653.76i	−0.560616	−	0.249855i
$599$	−19284.7			−1.31545			−0.657723	−	0.753260i	$-0.728480\pi$
$599$	−19284.7			−1.31545			−0.657723	+	0.753260i	$0.728480\pi$
$600$	−3454.76	−	1994.61i	−0.235066	−	0.135716i
$601$	−6273.82	+	10866.6i	−0.425814	+	0.737532i	−0.996496	−	0.0836393i	$-0.973346\pi$
$601$	−6273.82	+	10866.6i	−0.425814	+	0.737532i	0.570682	+	0.821171i	$0.306679\pi$
$602$	−3344.49	−	5792.83i	−0.226431	−	0.392189i
$603$		−	2104.55i		−	0.142129i
$604$	−1619.57	+	935.057i	−0.109105	+	0.0629916i
$605$	27619.0	−	15945.8i	1.85599	−	1.07155i
$606$		−	706.338i		−	0.0473482i
$607$	8088.73	+	14010.1i	0.540876	+	0.936824i	0.998854	+	0.0478607i	$0.0152403\pi$
$607$	8088.73	+	14010.1i	0.540876	+	0.936824i	−0.457978	+	0.888963i	$0.651426\pi$
$608$	−1042.45	+	1805.58i	−0.0695347	+	0.120438i
$609$	409.328	+	236.325i	0.0272361	+	0.0157248i
$610$	−7616.16			−0.505524
$611$	−1140.57	+	828.016i	−0.0755196	+	0.0548248i
$612$	95.6011			0.00631445
$613$	6752.52	+	3898.57i	0.444913	+	0.256871i	0.705679	−	0.708531i	$-0.250642\pi$
$613$	6752.52	+	3898.57i	0.444913	+	0.256871i	−0.260766	+	0.965402i	$0.583975\pi$
$614$	−9653.05	+	16719.6i	−0.634471	+	1.09894i
$615$	7989.41	+	13838.1i	0.523844	+	0.907324i
$616$			3167.75i			0.207195i
$617$	−9305.75	+	5372.68i	−0.607189	+	0.350561i	−0.771864	−	0.635787i	$-0.780676\pi$
$617$	−9305.75	+	5372.68i	−0.607189	+	0.350561i	0.164676	+	0.986348i	$0.447342\pi$
$618$	2369.91	−	1368.27i	0.154258	−	0.0890611i
$619$		−	20051.9i		−	1.30203i	−0.759066	−	0.651013i	$-0.774344\pi$
$619$		−	20051.9i		−	1.30203i	0.759066	−	0.651013i	$-0.225656\pi$
$620$	588.708	+	1019.67i	0.0381340	+	0.0660500i
$621$	−1292.55	+	2238.77i	−0.0835240	+	0.144668i
$622$	15747.1	+	9091.61i	1.01512	+	0.586078i
$623$	7022.22			0.451588
$624$	915.875	−	2055.01i	0.0587570	−	0.131837i
$625$	−8774.01			−0.561537
$626$	−405.021	−	233.839i	−0.0258593	−	0.0149299i
$627$	5528.29	−	9575.29i	0.352119	−	0.609889i
$628$	−2069.02	−	3583.65i	−0.131470	−	0.227712i
$629$			65.1434i			0.00412947i
$630$	−1862.13	+	1075.10i	−0.117760	+	0.0679889i
$631$	12974.3	−	7490.70i	0.818538	−	0.472583i	−0.0313737	−	0.999508i	$-0.509988\pi$
$631$	12974.3	−	7490.70i	0.818538	−	0.472583i	0.849912	+	0.526924i	$0.176655\pi$
$632$			10452.0i			0.657845i
$633$	−2570.01	−	4451.38i	−0.161372	−	0.279505i
$634$	6141.64	−	10637.6i	0.384725	−	0.666363i
$635$	40757.9	+	23531.6i	2.54713	+	1.47059i
$636$	−7835.66			−0.488528
$637$	−2284.24	+	239.215i	−0.142080	+	0.0148792i
$638$	−2546.33			−0.158010
$639$	7126.83	+	4114.68i	0.441210	+	0.254733i
$640$	−1092.17	+	1891.69i	−0.0674557	+	0.116837i
$641$	2995.34	+	5188.09i	0.184569	+	0.319683i	0.943431	−	0.331568i	$-0.107578\pi$
$641$	2995.34	+	5188.09i	0.184569	+	0.319683i	−0.758862	+	0.651251i	$0.774244\pi$
$642$		−	7074.14i		−	0.434882i
$643$	2101.45	−	1213.27i	0.128885	−	0.0744117i	−0.434171	−	0.900830i	$-0.642959\pi$
$643$	2101.45	−	1213.27i	0.128885	−	0.0744117i	0.563056	+	0.826419i	$0.309625\pi$
$644$	2321.69	−	1340.43i	0.142061	−	0.0820190i
$645$			24460.3i			1.49321i
$646$	173.020	+	299.680i	0.0105378	+	0.0182519i
$647$	−4929.02	+	8537.32i	−0.299505	+	0.518758i	−0.976023	−	0.217668i	$-0.930155\pi$
$647$	−4929.02	+	8537.32i	−0.299505	+	0.518758i	0.676518	+	0.736427i	$0.263488\pi$
$648$	−561.184	−	324.000i	−0.0340207	−	0.0196419i
$649$	40799.8			2.46769
$650$	1622.92	+	15497.2i	0.0979328	+	0.935152i
$651$	362.227			0.0218077
$652$	4788.17	+	2764.45i	0.287606	+	0.166049i
$653$	−11039.6	+	19121.2i	−0.661582	+	1.14589i	0.318618	+	0.947883i	$0.396781\pi$
$653$	−11039.6	+	19121.2i	−0.661582	+	1.14589i	−0.980200	+	0.198011i	$0.936552\pi$
$654$	2401.76	+	4159.98i	0.143603	+	0.248728i
$655$		−	27687.8i		−	1.65168i
$656$	4324.79	−	2496.92i	0.257401	−	0.148610i
$657$	3642.45	−	2102.97i	0.216295	−	0.124878i
$658$		−	420.977i		−	0.0249413i
$659$	11603.2	+	20097.3i	0.685880	+	1.18798i	0.973159	+	0.230132i	$0.0739159\pi$
$659$	11603.2	+	20097.3i	0.685880	+	1.18798i	−0.287279	+	0.957847i	$0.592751\pi$
$660$	5791.92	−	10031.9i	0.341591	−	0.591654i
$661$	1828.77	+	1055.84i	0.107611	+	0.0621294i	0.552840	−	0.833288i	$-0.313544\pi$
$661$	1828.77	+	1055.84i	0.107611	+	0.0621294i	−0.445228	+	0.895417i	$0.646878\pi$
$662$	869.428			0.0510442
$663$	−219.377	−	302.185i	−0.0128505	−	0.0177012i
$664$	−1554.53			−0.0908544
$665$	−6740.22	−	3891.47i	−0.393044	−	0.226924i
$666$	220.776	−	382.396i	0.0128452	−	0.0222485i
$667$	1077.47	+	1866.24i	0.0625486	+	0.108337i
$668$			7541.40i			0.436805i
$669$	−15029.3	+	8677.15i	−0.868558	+	0.501462i
$670$	6911.72	−	3990.48i	0.398542	−	0.230098i
$671$		−	12623.0i		−	0.726235i
$672$	336.000	+	581.969i	0.0192879	+	0.0334077i
$673$	−11704.8	+	20273.4i	−0.670413	+	1.16119i	0.307374	+	0.951589i	$0.400550\pi$
$673$	−11704.8	+	20273.4i	−0.670413	+	1.16119i	−0.977787	+	0.209601i	$0.932784\pi$
$674$	17293.1	+	9984.16i	0.988285	+	0.570587i
$675$	4487.86			0.255908
$676$	−8597.33	+	1820.66i	−0.489152	+	0.103588i
$677$	−4416.31			−0.250713			−0.125356	−	0.992112i	$-0.540007\pi$
$677$	−4416.31			−0.250713			−0.125356	+	0.992112i	$0.540007\pi$
$678$	3861.71	+	2229.56i	0.218744	+	0.126292i
$679$	3697.93	−	6405.00i	0.209004	−	0.362005i
$680$	181.271	+	313.971i	0.0102227	+	0.0177062i
$681$		−	7983.28i		−	0.449222i
$682$	−1689.99	+	975.719i	−0.0948875	+	0.0547833i
$683$	−22253.8	+	12848.2i	−1.24673	+	0.719800i	−0.970456	−	0.241280i	$-0.922433\pi$
$683$	−22253.8	+	12848.2i	−1.24673	+	0.719800i	−0.276274	+	0.961079i	$0.589100\pi$
$684$		−	2345.52i		−	0.131116i
$685$	2150.58	+	3724.92i	0.119955	+	0.207769i
$686$	343.000	−	594.093i	0.0190901	−	0.0330650i
$687$	12522.6	+	7229.90i	0.695437	+	0.401511i
$688$	7644.55			0.423613
$689$	17980.5	+	24767.7i	0.994201	+	1.36948i
$690$	−9803.36			−0.540880
$691$	20846.6	+	12035.8i	1.14767	+	0.662609i	0.948319	−	0.317319i	$-0.102783\pi$
$691$	20846.6	+	12035.8i	1.14767	+	0.662609i	0.199353	+	0.979928i	$0.436116\pi$
$692$	8137.28	−	14094.2i	0.447013	−	0.774249i
$693$	−1781.86	−	3086.27i	−0.0976729	−	0.169174i
$694$			4397.79i			0.240544i
$695$	21680.5	−	12517.2i	1.18329	−	0.683174i
$696$	−467.803	+	270.086i	−0.0254771	+	0.0147092i
$697$		−	828.849i		−	0.0450429i
$698$	6214.19	+	10763.3i	0.336978	+	0.583663i
$699$	5216.80	−	9035.77i	0.282286	−	0.488933i
$700$	−4030.55	−	2327.04i	−0.217629	−	0.125648i
$701$	26316.1			1.41789			0.708947	−	0.705262i	$-0.249171\pi$
$701$	26316.1			1.41789			0.708947	+	0.705262i	$0.249171\pi$
$702$	263.625	+	2517.33i	0.0141736	+	0.135343i
$703$	1598.26			0.0857459
$704$	−3135.26	−	1810.14i	−0.167847	−	0.0969068i
$705$	−769.714	+	1333.18i	−0.0411193	+	0.0712208i
$706$	−8182.25	−	14172.1i	−0.436180	−	0.755486i
$707$		−	824.061i		−	0.0438359i
$708$	7495.61	−	4327.59i	0.397885	−	0.229719i
$709$	21947.0	−	12671.1i	1.16254	−	0.671190i	0.210626	−	0.977567i	$-0.432450\pi$
$709$	21947.0	−	12671.1i	1.16254	−	0.671190i	0.951910	+	0.306376i	$0.0991166\pi$
$710$			31207.7i			1.64958i
$711$	−5879.25	−	10183.2i	−0.310111	−	0.537128i
$712$	−4012.69	+	6950.19i	−0.211211	+	0.365828i
$713$	1430.23	+	825.746i	0.0751230	+	0.0433723i
$714$	111.535			0.00584605
$715$	−45000.6	+	4712.64i	−2.35374	+	0.246493i
$716$	−6208.09			−0.324032
$717$	18316.8	+	10575.2i	0.954048	+	0.550820i
$718$	6229.62	−	10790.0i	0.323798	−	0.560835i
$719$	7242.37	+	12544.2i	0.375653	+	0.650651i	0.990425	−	0.138055i	$-0.0440850\pi$
$719$	7242.37	+	12544.2i	0.375653	+	0.650651i	−0.614771	+	0.788705i	$0.710752\pi$
$720$		−	2457.37i		−	0.127196i
$721$	2764.89	−	1596.31i	0.142815	−	0.0824545i
$722$	−4527.65	+	2614.04i	−0.233382	+	0.134743i
$723$		−	3235.94i		−	0.166454i
$724$	4301.66	+	7450.69i	0.220815	+	0.382462i
$725$	1870.54	−	3239.87i	0.0958208	−	0.165967i
$726$	9710.71	+	5606.48i	0.496416	+	0.286606i
$727$	−11989.6			−0.611648			−0.305824	−	0.952088i	$-0.598932\pi$
$727$	−11989.6			−0.611648			−0.305824	+	0.952088i	$0.598932\pi$
$728$	1068.52	−	2397.51i	0.0543984	−	0.122057i
$729$	729.000			0.0370370
$730$	13813.1	+	7974.97i	0.700334	+	0.404338i
$731$	634.399	−	1098.81i	0.0320986	−	0.0555964i
$732$	−1338.90	−	2319.05i	−0.0676056	−	0.117096i
$733$			17760.8i			0.894965i	0.894293	+	0.447483i	$0.147679\pi$
$733$			17760.8i			0.894965i	−0.894293	+	0.447483i	$0.852321\pi$
$734$	−6026.25	+	3479.26i	−0.303042	+	0.174962i
$735$	−2172.48	+	1254.28i	−0.109025	+	0.0629455i
$736$			3063.83i			0.153443i
$737$	6613.79	+	11455.4i	0.330559	+	0.572545i
$738$	−2809.04	+	4865.39i	−0.140111	+	0.242680i
$739$	−18516.7	−	10690.6i	−0.921713	−	0.532151i	−0.0375321	−	0.999295i	$-0.511950\pi$
$739$	−18516.7	−	10690.6i	−0.921713	−	0.532151i	−0.884181	+	0.467144i	$0.845283\pi$
$740$	1674.47			0.0831822
$741$	−7413.94	+	5382.29i	−0.367555	+	0.266833i
$742$	−9141.60			−0.452289
$743$	−30636.0	−	17687.7i	−1.51269	−	0.873350i	−0.999890	−	0.0148406i	$-0.995276\pi$
$743$	−30636.0	−	17687.7i	−1.51269	−	0.873350i	−0.512797	−	0.858510i	$-0.671391\pi$
$744$	−206.987	+	358.512i	−0.0101996	+	0.0176662i
$745$	4311.89	+	7468.42i	0.212048	+	0.367277i
$746$			10757.5i			0.527960i
$747$	1514.54	−	874.421i	0.0741823	−	0.0428292i
$748$	−520.372	+	300.437i	−0.0254368	+	0.0146859i
$749$		−	8253.16i		−	0.402622i
$750$	2110.12	+	3654.84i	0.102734	+	0.177941i
$751$	−5919.84	+	10253.5i	−0.287640	+	0.498208i	−0.973246	−	0.229765i	$-0.926204\pi$
$751$	−5919.84	+	10253.5i	−0.287640	+	0.498208i	0.685606	+	0.727973i	$0.259537\pi$
$752$	416.659	+	240.558i	0.0202048	+	0.0116652i
$753$	15658.3			0.757795
$754$	1927.19	+	858.907i	0.0930822	+	0.0414848i
$755$	7978.42			0.384588
$756$	−654.715	−	378.000i	−0.0314970	−	0.0181848i
$757$	−14044.3	+	24325.5i	−0.674306	+	1.16793i	0.302365	+	0.953192i	$0.402224\pi$
$757$	−14044.3	+	24325.5i	−0.674306	+	1.16793i	−0.976671	+	0.214740i	$0.931110\pi$
$758$	9092.74	+	15749.1i	0.435703	+	0.754660i
$759$		−	16248.0i		−	0.777028i
$760$	7703.10	−	4447.39i	0.367659	−	0.212268i
$761$	−22489.9	+	12984.6i	−1.07130	+	0.618515i	−0.928536	−	0.371242i	$-0.878932\pi$
$761$	−22489.9	+	12984.6i	−1.07130	+	0.618515i	−0.142763	+	0.989757i	$0.545599\pi$
$762$			16547.2i			0.786667i
$763$	2802.06	+	4853.31i	0.132951	+	0.230277i
$764$	6324.83	−	10954.9i	0.299508	−	0.518763i
$765$	−353.217	−	203.930i	−0.0166936	−	0.00963805i
$766$	−17365.4			−0.819109
$767$	−30879.3	−	13762.3i	−1.45370	−	0.647884i
$768$	−768.000			−0.0360844
$769$	−24729.4	−	14277.6i	−1.15964	−	0.669521i	−0.208426	−	0.978038i	$-0.566834\pi$
$769$	−24729.4	−	14277.6i	−1.15964	−	0.669521i	−0.951219	+	0.308517i	$0.900167\pi$
$770$	6757.25	−	11703.9i	0.316252	−	0.547765i
$771$	2866.17	+	4964.35i	0.133881	+	0.231889i
$772$			19456.3i			0.907054i
$773$	−13614.6	+	7860.37i	−0.633482	+	0.365741i	−0.782099	−	0.623154i	$-0.785851\pi$
$773$	−13614.6	+	7860.37i	−0.633482	+	0.365741i	0.148617	+	0.988895i	$0.452518\pi$
$774$	−7447.92	+	4300.06i	−0.345879	+	0.199693i
$775$		−	2867.06i		−	0.132888i
$776$	4226.20	+	7320.00i	0.195505	+	0.338625i
$777$	257.572	−	446.128i	0.0118923	−	0.0205981i
$778$	−10279.2	−	5934.67i	−0.473683	−	0.273481i
$779$	−20335.3			−0.935288
$780$	−7767.50	+	5638.95i	−0.356565	+	0.258855i
$781$	−51723.4			−2.36979
$782$	440.389	+	254.259i	0.0201384	+	0.0116269i
$783$	303.847	−	526.279i	0.0138680	−	0.0240200i
$784$	392.000	+	678.964i	0.0178571	+	0.0309295i
$785$			17654.0i			0.802674i
$786$	8430.66	−	4867.44i	0.382585	−	0.220885i
$787$	−5677.06	+	3277.65i	−0.257135	+	0.148457i	−0.623027	−	0.782200i	$-0.714097\pi$
$787$	−5677.06	+	3277.65i	−0.257135	+	0.148457i	0.365892	+	0.930657i	$0.380764\pi$
$788$		−	10593.3i		−	0.478895i
$789$	9555.24	+	16550.2i	0.431148	+	0.746770i
$790$	22295.5	−	38617.0i	1.00410	−	1.73915i
$791$	4505.33	+	2601.16i	0.202517	+	0.116923i
$792$	4072.82			0.182729
$793$	−4257.88	+	9553.67i	−0.190670	+	0.427819i
$794$	22593.0			1.00982
$795$	28950.4	+	16714.5i	1.29153	+	0.745664i
$796$	−7614.25	+	13188.3i	−0.339045	+	0.587244i
$797$	13776.3	+	23861.2i	0.612271	+	1.06049i	0.990857	+	0.134919i	$0.0430773\pi$
$797$	13776.3	+	23861.2i	0.612271	+	1.06049i	−0.378585	+	0.925566i	$0.623589\pi$
$798$		−	2736.44i		−	0.121390i
$799$	69.1546	−	39.9264i	0.00306197	−	0.00176783i
$800$	4606.34	−	2659.47i	0.203574	−	0.117533i
$801$		−	9028.56i		−	0.398263i
$802$	−8311.29	−	14395.6i	−0.365938	−	0.633823i
$803$	−13217.6	+	22893.6i	−0.580872	+	1.00610i
$804$	2430.13	+	1403.03i	0.106597	+	0.0615438i
$805$	−11437.2			−0.500758
$806$	1608.19	−	168.416i	0.0702806	−	0.00736006i
$807$	−16535.3			−0.721277
$808$	815.609	+	470.892i	0.0355112	+	0.0205024i
$809$	−2114.31	+	3662.09i	−0.0918853	+	0.159150i	−0.908304	−	0.418310i	$-0.862623\pi$
$809$	−2114.31	+	3662.09i	−0.0918853	+	0.159150i	0.816419	+	0.577460i	$0.195956\pi$
$810$	1382.27	+	2394.17i	0.0599606	+	0.103855i
$811$		−	41450.5i		−	1.79473i	−0.441294	−	0.897363i	$-0.645480\pi$
$811$		−	41450.5i		−	1.79473i	0.441294	−	0.897363i	$-0.354520\pi$
$812$	−545.770	+	315.101i	−0.0235872	+	0.0136181i
$813$	−1077.22	+	621.935i	−0.0464697	+	0.0268293i
$814$			2775.26i			0.119500i
$815$	−11793.9	−	20427.6i	−0.506898	−	0.877974i
$816$	−63.7341	+	110.391i	−0.00273424	+	0.00473584i
$817$	−26958.7	−	15564.6i	−1.15443	−	0.666508i
$818$	−1062.09			−0.0453973
$819$	307.562	+	2936.89i	0.0131222	+	0.125303i
$820$	−21305.1			−0.907324
$821$	−10374.9	−	5989.96i	−0.441032	−	0.254630i	0.263003	−	0.964795i	$-0.415287\pi$
$821$	−10374.9	−	5989.96i	−0.441032	−	0.254630i	−0.704035	+	0.710165i	$0.748620\pi$
$822$	−756.134	+	1309.66i	−0.0320842	+	0.0555714i
$823$	9553.93	+	16547.9i	0.404653	+	0.700879i	0.994281	−	0.106796i	$-0.0340591\pi$
$823$	9553.93	+	16547.9i	0.404653	+	0.700879i	−0.589628	+	0.807675i	$0.700726\pi$
$824$			3648.71i			0.154258i
$825$	−24428.2	+	14103.6i	−1.03088	+	0.595181i
$826$	8744.88	−	5048.86i	0.368370	−	0.212678i
$827$		−	12728.5i		−	0.535204i	−0.963530	−	0.267602i	$-0.913769\pi$
$827$		−	12728.5i		−	0.535204i	0.963530	−	0.267602i	$-0.0862311\pi$
$828$	−1723.41	−	2985.03i	−0.0723339	−	0.125286i
$829$	7222.21	−	12509.2i	0.302579	−	0.524082i	−0.674141	−	0.738603i	$-0.735486\pi$
$829$	7222.21	−	12509.2i	0.302579	−	0.524082i	0.976719	+	0.214521i	$0.0688192\pi$
$830$	5743.51	+	3316.02i	0.240193	+	0.138675i
$831$	−8369.43			−0.349377
$832$	1762.34	+	2427.57i	0.0734351	+	0.101155i
$833$	130.124			0.00541239
$834$	7622.75	+	4401.00i	0.316492	+	0.182727i
$835$	16086.8	−	27863.2i	0.666716	−	1.15479i
$836$	7371.06	+	12767.1i	0.304944	+	0.528179i
$837$		−	465.720i		−	0.0192326i
$838$	−5332.40	+	3078.66i	−0.219814	+	0.126910i
$839$	−32176.4	+	18577.1i	−1.32402	+	0.764423i	−0.984367	−	0.176128i	$-0.943643\pi$
$839$	−32176.4	+	18577.1i	−1.32402	+	0.764423i	−0.339653	+	0.940551i	$0.610310\pi$
$840$		−	2866.93i		−	0.117760i
$841$	11941.2	+	20682.8i	0.489615	+	0.848038i
$842$	−5766.92	+	9988.60i	−0.236035	+	0.408824i
$843$	184.079	+	106.278i	0.00752077	+	0.00434212i
$844$	6853.35			0.279505
$845$	35648.3	+	11612.5i	1.45129	+	0.472759i
$846$	−541.256			−0.0219962
$847$	11329.2	+	6540.89i	0.459592	+	0.265346i
$848$	5223.77	−	9047.84i	0.211539	−	0.366396i
$849$	390.425	+	676.236i	0.0157825	+	0.0273361i
$850$		−	882.808i		−	0.0356236i
$851$	2034.02	−	1174.34i	0.0819334	−	0.0473043i
$852$	−9502.44	+	5486.24i	−0.382099	+	0.220605i
$853$			14834.8i			0.595466i	0.954649	+	0.297733i	$0.0962305\pi$
$853$			14834.8i			0.595466i	−0.954649	+	0.297733i	$0.903769\pi$
$854$	−1562.05	−	2705.56i	−0.0625906	−	0.108410i
$855$	−5003.31	+	8665.99i	−0.200128	+	0.346632i
$856$	8168.51	+	4716.09i	0.326161	+	0.188309i
$857$	27509.7			1.09652			0.548258	−	0.836310i	$-0.315291\pi$
$857$	27509.7			1.09652			0.548258	+	0.836310i	$0.315291\pi$
$858$	−9345.94	−	12873.8i	−0.371871	−	0.512242i
$859$	18628.2			0.739912			0.369956	−	0.929049i	$-0.379373\pi$
$859$	18628.2			0.739912			0.369956	+	0.929049i	$0.379373\pi$
$860$	−28244.3	−	16306.9i	−1.11991	−	0.646581i
$861$	−3277.21	+	5676.29i	−0.129718	+	0.224678i
$862$	521.578	+	903.399i	0.0206091	+	0.0356959i
$863$			28590.6i			1.12774i	0.825865	+	0.563868i	$0.190687\pi$
$863$			28590.6i			1.12774i	−0.825865	+	0.563868i	$0.809313\pi$
$864$	748.246	−	432.000i	0.0294628	−	0.0170103i
$865$	−60129.6	+	34715.9i	−2.36355	+	1.36459i
$866$		−	1139.22i		−	0.0447023i
$867$	−7358.92	−	12746.0i	−0.288261	−	0.499282i
$868$	−241.485	+	418.264i	−0.00944300	+	0.0163558i
$869$	64003.4	+	36952.4i	2.49847	+	1.44249i
$870$	2304.52			0.0898053
$871$	−1141.59	−	10900.9i	−0.0444101	−	0.424069i
$872$	−6404.71			−0.248728
$873$	−8235.00	−	4754.48i	−0.319258	−	0.184324i
$874$	6238.09	−	10804.7i	0.241426	−	0.418163i
$875$	2461.81	+	4263.98i	0.0951135	+	0.164741i
$876$			5607.92i			0.216295i
$877$	11957.0	−	6903.37i	0.460386	−	0.265804i	−0.251820	−	0.967774i	$-0.581029\pi$
$877$	11957.0	−	6903.37i	0.460386	−	0.265804i	0.712207	+	0.701970i	$0.247696\pi$
$878$	4789.83	−	2765.41i	0.184110	−	0.106296i
$879$			15491.7i			0.594451i
$880$	7722.57	+	13375.9i	0.295827	+	0.512387i
$881$	−7533.99	+	13049.3i	−0.288112	+	0.499024i	−0.973359	−	0.229286i	$-0.926361\pi$
$881$	−7533.99	+	13049.3i	−0.288112	+	0.499024i	0.685247	+	0.728311i	$0.259694\pi$
$882$	−763.834	−	441.000i	−0.0291606	−	0.0168359i
$883$	−30918.6			−1.17836			−0.589181	−	0.808001i	$-0.700549\pi$
$883$	−30918.6			−1.17836			−0.589181	+	0.808001i	$0.700549\pi$
$884$	495.184	−	51.8576i	0.0188403	−	0.00197303i
$885$	−36925.4			−1.40252
$886$	28765.2	+	16607.6i	1.09073	+	0.629732i
$887$	10929.8	−	18931.0i	0.413740	−	0.716618i	−0.581556	−	0.813507i	$-0.697556\pi$
$887$	10929.8	−	18931.0i	0.413740	−	0.716618i	0.995295	+	0.0968886i	$0.0308890\pi$
$888$	294.368	+	509.861i	0.0111243	+	0.0192678i
$889$			19305.0i			0.728313i
$890$	29651.4	−	17119.2i	1.11676	−	0.644762i
$891$	−3968.07	+	2290.96i	−0.149198	+	0.0861394i
$892$		−	23139.1i		−	0.868558i
$893$	−979.573	−	1696.67i	−0.0367079	−	0.0635799i
$894$	−1516.04	+	2625.86i	−0.0567159	+	0.0982347i
$895$	22937.0	+	13242.7i	0.856648	+	0.494586i
$896$	−896.000			−0.0334077
$897$	−5480.64	+	12297.3i	−0.204006	+	0.457741i
$898$	19228.1			0.714534
$899$	−336.212	−	194.112i	−0.0124731	−	0.00720134i
$900$	−2991.91	+	5182.14i	−0.110811	+	0.191931i
$901$	−867.011	−	1501.71i	−0.0320581	−	0.0555262i
$902$		−	35310.8i		−	1.30346i
$903$	−8689.24	+	5016.74i	−0.320221	+	0.184880i
$904$	−5148.95	+	2972.75i	−0.189438	+	0.109372i
$905$		−	36704.1i		−	1.34816i
$906$	1402.59	+	2429.35i	0.0514325	+	0.0890836i
$907$	−10879.3	+	18843.5i	−0.398281	+	0.689842i	−0.993514	−	0.113711i	$-0.963726\pi$
$907$	−10879.3	+	18843.5i	−0.398281	+	0.689842i	0.595233	+	0.803553i	$0.297060\pi$
$908$	9218.30	+	5322.19i	0.336916	+	0.194519i
$909$	−1059.51			−0.0386597
$910$	−9062.08	+	6578.78i	−0.330115	+	0.239653i
$911$	−27743.6			−1.00899			−0.504493	−	0.863416i	$-0.668320\pi$
$911$	−27743.6			−1.00899			−0.504493	+	0.863416i	$0.668320\pi$
$912$	2708.37	+	1563.68i	0.0983369	+	0.0567748i
$913$	−5495.93	+	9519.23i	−0.199221	+	0.345061i
$914$	1475.77	+	2556.11i	0.0534072	+	0.0925040i
$915$			11424.2i			0.412758i
$916$	−16696.7	+	9639.87i	−0.602266	+	0.347719i
$917$	9835.77	−	5678.68i	0.354205	−	0.204500i
$918$		−	143.402i		−	0.00515573i
$919$	11214.2	+	19423.5i	0.402525	+	0.697194i	0.994030	−	0.109107i	$-0.0347992\pi$
$919$	11214.2	+	19423.5i	0.402525	+	0.697194i	−0.591505	+	0.806302i	$0.701466\pi$
$920$	6535.57	−	11319.9i	0.234208	−	0.405660i
$921$	25079.4	+	14479.6i	0.897278	+	0.518044i
$922$	24342.9			0.869511
$923$	39146.8	+	17446.9i	1.39603	+	0.622180i
$924$	4751.63			0.169174
$925$	−3531.15	−	2038.71i	−0.125517	−	0.0724674i
$926$	−4804.09	+	8320.92i	−0.170488	+	0.295294i
$927$	−2052.40	−	3554.86i	−0.0727181	−	0.125951i
$928$		−	720.230i		−	0.0254771i
$929$	−36589.4	+	21124.9i	−1.29221	+	0.746056i	−0.979045	−	0.203643i	$-0.934722\pi$
$929$	−36589.4	+	21124.9i	−1.29221	+	0.746056i	−0.313162	+	0.949700i	$0.601388\pi$
$930$	1529.51	−	883.062i	0.0539296	−	0.0311363i
$931$		−	3192.51i		−	0.112385i
$932$	6955.74	+	12047.7i	0.244466	+	0.423428i
$933$	13637.4	−	23620.7i	0.478530	−	0.828839i
$934$	−14423.7	−	8327.55i	−0.505310	−	0.291741i
$935$	2563.49			0.0896633
$936$	−3082.51	−	1373.81i	−0.107644	−	0.0479749i
$937$	−1489.49			−0.0519312			−0.0259656	−	0.999663i	$-0.508266\pi$
$937$	−1489.49			−0.0519312			−0.0259656	+	0.999663i	$0.508266\pi$
$938$	2835.15	+	1636.87i	0.0986896	+	0.0569785i
$939$	−350.759	+	607.532i	−0.0121902	+	0.0211140i
$940$	−1026.29	−	1777.58i	−0.0356104	−	0.0616790i
$941$		−	11460.3i		−	0.397020i	−0.980099	−	0.198510i	$-0.936390\pi$
$941$		−	11460.3i		−	0.397020i	0.980099	−	0.198510i	$-0.0636103\pi$
$942$	−5375.48	+	3103.53i	−0.185926	+	0.107345i
$943$	−25879.8	+	14941.7i	−0.893703	+	0.515979i
$944$			11540.2i			0.397885i
$945$	1612.65	+	2793.19i	0.0555127	+	0.0961509i
$946$	27026.8	−	46811.8i	0.928877	−	1.60886i
$947$	−16373.8	−	9453.42i	−0.561856	−	0.324387i	0.192034	−	0.981388i	$-0.438491\pi$
$947$	−16373.8	−	9453.42i	−0.561856	−	0.324387i	−0.753890	+	0.657001i	$0.771825\pi$
$948$	15678.0			0.537128
$949$	17726.0	−	12868.5i	0.606335	−	0.440180i
$950$	−21659.2			−0.739702
$951$	−15956.4	−	9212.46i	−0.544083	−	0.314127i
$952$	−74.3564	+	128.789i	−0.00253141	+	0.00438454i
$953$	803.671	+	1392.00i	0.0273174	+	0.0473151i	0.879361	−	0.476156i	$-0.157970\pi$
$953$	803.671	+	1392.00i	0.0273174	+	0.0473151i	−0.852044	+	0.523471i	$0.824637\pi$
$954$			11753.5i			0.398882i
$955$	−46736.7	+	26983.4i	−1.58363	+	0.914307i
$956$	−24422.4	+	14100.3i	−0.826230	+	0.477024i
$957$			3819.49i			0.129014i
$958$	−6321.35	−	10948.9i	−0.213188	−	0.369252i
$959$	−882.156	+	1527.94i	−0.0297042	+	0.0514492i
$960$	2837.53	+	1638.25i	0.0953967	+	0.0550773i
$961$	29493.5			0.990013
$962$	936.127	−	2100.45i	0.0313742	−	0.0703963i
$963$	−10611.2			−0.355079
$964$	3736.55	+	2157.30i	0.124840	+	0.0720766i
$965$	41502.8	−	71885.0i	1.38448	−	2.39799i
$966$	−2010.64	−	3482.53i	−0.0669682	−	0.115992i
$967$		−	56856.8i		−	1.89079i	−0.325932	−	0.945393i	$-0.605678\pi$
$967$		−	56856.8i		−	1.89079i	0.325932	−	0.945393i	$-0.394322\pi$
$968$	−12947.6	+	7475.30i	−0.429909	+	0.248208i
$969$	449.520	−	259.531i	0.0149026	−	0.00860405i
$970$		−	36060.3i		−	1.19363i
$971$	6420.40	+	11120.5i	0.212194	+	0.367531i	0.952401	−	0.304848i	$-0.0986057\pi$
$971$	6420.40	+	11120.5i	0.212194	+	0.367531i	−0.740207	+	0.672379i	$0.765272\pi$
$972$	−486.000	+	841.777i	−0.0160375	+	0.0277778i
$973$	8893.21	+	5134.50i	0.293015	+	0.169172i
$974$	33231.1			1.09322
$975$	23245.7	−	2434.39i	0.763548	−	0.0799618i
$976$	3570.41			0.117096
$977$	−4765.78	−	2751.52i	−0.156060	−	0.0901014i	0.419936	−	0.907554i	$-0.362052\pi$
$977$	−4765.78	−	2751.52i	−0.156060	−	0.0901014i	−0.575996	+	0.817452i	$0.695386\pi$
$978$	4146.68	−	7182.25i	0.135579	−	0.234829i
$979$	28373.3	+	49143.9i	0.926265	+	1.60434i
$980$		−	3344.76i		−	0.109025i
$981$	6239.97	−	3602.65i	0.203085	−	0.117251i
$982$	18923.5	−	10925.5i	0.614941	−	0.355036i
$983$		−	44114.6i		−	1.43137i	−0.698423	−	0.715685i	$-0.746115\pi$
$983$		−	44114.6i		−	1.43137i	0.698423	−	0.715685i	$-0.253885\pi$
$984$	−3745.38	−	6487.19i	−0.121340	−	0.210167i
$985$	−22596.9	+	39138.9i	−0.730960	+	1.26606i
$986$	−103.524	−	59.7698i	−0.00334370	−	0.00193048i
$987$	−631.465			−0.0203645
$988$	−1272.30	−	12149.1i	−0.0409688	−	0.391208i
$989$	−45745.4			−1.47080
$990$	−15047.9	−	8687.89i	−0.483083	−	0.278908i
$991$	5675.34	−	9829.98i	0.181920	−	0.315095i	−0.760614	−	0.649204i	$-0.775102\pi$
$991$	5675.34	−	9829.98i	0.181920	−	0.315095i	0.942534	+	0.334109i	$0.108435\pi$
$992$	−275.983	−	478.016i	−0.00883312	−	0.0152994i
$993$		−	1304.14i		−	0.0416774i
$994$	−11086.2	+	6400.61i	−0.353755	+	0.204241i
$995$	56264.7	−	32484.5i	1.79268	−	1.03500i
$996$			2331.79i			0.0741823i
$997$	−12303.6	−	21310.5i	−0.390833	−	0.676942i	0.601727	−	0.798702i	$-0.294480\pi$
$997$	−12303.6	−	21310.5i	−0.390833	−	0.676942i	−0.992560	+	0.121760i	$0.961146\pi$
$998$	12688.1	−	21976.4i	0.402439	−	0.697044i
$999$	−573.593	−	331.164i	−0.0181659	−	0.0104881i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.4.s.b.43.6	✓	20
13.10	even	6	inner	546.4.s.b.127.10	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.4.s.b.43.6	✓	20	1.1	even	1	trivial
546.4.s.b.127.10	yes	20	13.10	even	6	inner

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	546.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.73205 + 1.00000i) q^{2} +(1.50000 - 2.59808i) q^{3} +(2.00000 + 3.46410i) q^{4} -17.0651i q^{5} +(5.19615 - 3.00000i) q^{6} +(6.06218 - 3.50000i) q^{7} +8.00000i q^{8} +(-4.50000 - 7.79423i) q^{9} +(17.0651 - 29.5576i) q^{10} +(48.9885 + 28.2835i) q^{11} +12.0000 q^{12} +(-27.5365 - 37.9307i) q^{13} +14.0000 q^{14} +(-44.3364 - 25.5976i) q^{15} +(-8.00000 + 13.8564i) q^{16} +(1.32779 + 2.29981i) q^{17} -18.0000i q^{18} +(56.4245 - 32.5767i) q^{19} +(59.1152 - 34.1302i) q^{20} -21.0000i q^{21} +(56.5670 + 97.9769i) q^{22} +(47.8724 - 82.9174i) q^{23} +(20.7846 + 12.0000i) q^{24} -166.217 q^{25} +(-9.76388 - 93.2345i) q^{26} -27.0000 q^{27} +(24.2487 + 14.0000i) q^{28} +(-11.2536 + 19.4918i) q^{29} +(-51.1953 - 88.6728i) q^{30} +17.2489i q^{31} +(-27.7128 + 16.0000i) q^{32} +(146.965 - 84.8505i) q^{33} +5.31117i q^{34} +(-59.7278 - 103.452i) q^{35} +(18.0000 - 31.1769i) q^{36} +(21.2442 + 12.2653i) q^{37} +130.307 q^{38} +(-139.852 + 14.6458i) q^{39} +136.521 q^{40} +(-270.300 - 156.058i) q^{41} +(21.0000 - 36.3731i) q^{42} +(-238.892 - 413.773i) q^{43} +226.268i q^{44} +(-133.009 + 76.7929i) q^{45} +(165.835 - 95.7448i) q^{46} -30.0698i q^{47} +(24.0000 + 41.5692i) q^{48} +(24.5000 - 42.4352i) q^{49} +(-287.896 - 166.217i) q^{50} +7.96676 q^{51} +(76.3229 - 171.251i) q^{52} -652.971 q^{53} +(-46.7654 - 27.0000i) q^{54} +(482.660 - 835.992i) q^{55} +(28.0000 + 48.4974i) q^{56} -195.460i q^{57} +(-38.9836 + 22.5072i) q^{58} +(624.634 - 360.633i) q^{59} -204.781i q^{60} +(-111.575 - 193.254i) q^{61} +(-17.2489 + 29.8760i) q^{62} +(-54.5596 - 31.5000i) q^{63} -64.0000 q^{64} +(-647.291 + 469.913i) q^{65} +339.402 q^{66} +(202.511 + 116.920i) q^{67} +(-5.31117 + 9.19922i) q^{68} +(-143.617 - 248.752i) q^{69} -238.911i q^{70} +(-791.870 + 457.187i) q^{71} +(62.3538 - 36.0000i) q^{72} +467.327i q^{73} +(24.5307 + 42.4884i) q^{74} +(-249.326 + 431.845i) q^{75} +(225.698 + 130.307i) q^{76} +395.969 q^{77} +(-256.876 - 114.484i) q^{78} +1306.50 q^{79} +(236.461 + 136.521i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(-312.115 - 540.599i) q^{82} +194.316i q^{83} +(72.7461 - 42.0000i) q^{84} +(39.2464 - 22.6589i) q^{85} -955.569i q^{86} +(33.7608 + 58.4754i) q^{87} +(-226.268 + 391.908i) q^{88} +(868.774 + 501.587i) q^{89} -307.172 q^{90} +(-299.689 - 133.565i) q^{91} +382.979 q^{92} +(44.8140 + 25.8734i) q^{93} +(30.0698 - 52.0824i) q^{94} +(-555.924 - 962.888i) q^{95} +96.0000i q^{96} +(915.000 - 528.275i) q^{97} +(84.8705 - 49.0000i) q^{98} -509.103i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 30 q^{3} + 40 q^{4} - 90 q^{9} - 48 q^{10} - 138 q^{11} + 240 q^{12} + 28 q^{13} + 280 q^{14} - 90 q^{15} - 160 q^{16} - 106 q^{17} + 60 q^{19} + 120 q^{20} - 64 q^{22} - 94 q^{23} - 304 q^{25} + 44 q^{26}+ \cdots + 5412 q^{97}+O(q^{100}) \) 20 * q + 30 * q^3 + 40 * q^4 - 90 * q^9 - 48 * q^10 - 138 * q^11 + 240 * q^12 + 28 * q^13 + 280 * q^14 - 90 * q^15 - 160 * q^16 - 106 * q^17 + 60 * q^19 + 120 * q^20 - 64 * q^22 - 94 * q^23 - 304 * q^25 + 44 * q^26 - 540 * q^27 - 166 * q^29 + 144 * q^30 - 414 * q^33 + 168 * q^35 + 360 * q^36 - 144 * q^37 + 48 * q^38 - 228 * q^39 - 384 * q^40 + 78 * q^41 + 420 * q^42 - 548 * q^43 - 270 * q^45 - 240 * q^46 + 480 * q^48 + 490 * q^49 - 144 * q^50 - 636 * q^51 + 416 * q^52 - 664 * q^53 + 2240 * q^55 + 560 * q^56 - 1032 * q^58 - 3204 * q^59 + 210 * q^61 - 436 * q^62 - 1280 * q^64 - 1502 * q^65 - 384 * q^66 + 1770 * q^67 + 424 * q^68 + 282 * q^69 - 1512 * q^71 + 548 * q^74 - 456 * q^75 + 240 * q^76 - 448 * q^77 - 492 * q^78 + 2096 * q^79 + 480 * q^80 - 810 * q^81 - 476 * q^82 - 6774 * q^85 + 498 * q^87 + 256 * q^88 + 1518 * q^89 + 864 * q^90 - 574 * q^91 - 752 * q^92 + 108 * q^93 + 448 * q^94 + 1502 * q^95 + 5412 * q^97

Introduction

L-functions

Modular forms

Varieties

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Database

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