LMFDB - Embedded newform 43.7.h.a.3.5

Newspace parameters

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	43.h (of order $42$, degree $12$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$9.89232559565$
Analytic rank:	$0$
Dimension:	$252$
Relative dimension:	$21$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			3.5
Character	$\chi$	$=$	43.3
Dual form			43.7.h.a.29.5

$q$-expansion

$f(q)$	$=$	$q+(-4.53656 + 9.42027i) q^{2} +(21.7428 + 1.62939i) q^{3} +(-28.2577 - 35.4340i) q^{4} +(33.0785 - 107.238i) q^{5} +(-113.987 + 197.431i) q^{6} +(-303.689 + 175.335i) q^{7} +(-190.398 + 43.4570i) q^{8} +(-250.765 - 37.7967i) q^{9} +O(q^{10})$	\(q+(-4.53656 + 9.42027i) q^{2} +(21.7428 + 1.62939i) q^{3} +(-28.2577 - 35.4340i) q^{4} +(33.0785 - 107.238i) q^{5} +(-113.987 + 197.431i) q^{6} +(-303.689 + 175.335i) q^{7} +(-190.398 + 43.4570i) q^{8} +(-250.765 - 37.7967i) q^{9} +(860.145 + 798.098i) q^{10} +(-1232.71 + 1545.78i) q^{11} +(-556.664 - 816.476i) q^{12} +(-1047.73 + 972.152i) q^{13} +(-273.998 - 3656.25i) q^{14} +(893.950 - 2277.75i) q^{15} +(1099.82 - 4818.61i) q^{16} +(-1809.82 + 558.254i) q^{17} +(1493.66 - 2190.80i) q^{18} +(-151.468 - 1004.92i) q^{19} +(-4734.58 + 1858.19i) q^{20} +(-6888.72 + 3317.43i) q^{21} +(-8969.33 - 18625.0i) q^{22} +(-59.8530 - 152.503i) q^{23} +(-4210.58 + 634.642i) q^{24} +(2504.23 + 1707.36i) q^{25} +(-4404.83 - 14280.1i) q^{26} +(-20887.1 - 4767.35i) q^{27} +(14794.4 + 5806.35i) q^{28} +(36846.2 - 2761.24i) q^{29} +(17401.5 + 18754.4i) q^{30} +(-25703.4 + 17524.3i) q^{31} +(30631.2 + 24427.6i) q^{32} +(-29321.3 + 31600.8i) q^{33} +(2951.44 - 19581.5i) q^{34} +(8756.95 + 38366.7i) q^{35} +(5746.74 + 9953.65i) q^{36} +(76977.3 + 44442.8i) q^{37} +(10153.8 + 3132.03i) q^{38} +(-24364.6 + 19430.1i) q^{39} +(-1637.83 + 21855.3i) q^{40} +(9640.56 + 4642.65i) q^{41} -79943.3i q^{42} +(-61790.1 - 50033.4i) q^{43} +89606.6 q^{44} +(-12348.1 + 25641.2i) q^{45} +(1708.14 + 128.008i) q^{46} +(-48380.9 - 60667.7i) q^{47} +(31764.5 - 102978. i) q^{48} +(2660.09 - 4607.40i) q^{49} +(-27444.4 + 15845.0i) q^{50} +(-40260.0 + 9189.09i) q^{51} +(64053.6 + 9654.53i) q^{52} +(-73846.7 - 68519.7i) q^{53} +(139665. - 175135. i) q^{54} +(124989. + 183325. i) q^{55} +(50202.1 - 46580.7i) q^{56} +(-1655.91 - 22096.6i) q^{57} +(-141143. + 359627. i) q^{58} +(38877.1 - 170332. i) q^{59} +(-105971. + 32687.6i) q^{60} +(-208106. + 305235. i) q^{61} +(-48478.3 - 321632. i) q^{62} +(82781.5 - 32489.4i) q^{63} +(-84078.8 + 40490.2i) q^{64} +(69594.0 + 144513. i) q^{65} +(-164670. - 419574. i) q^{66} +(813.274 - 122.581i) q^{67} +(70922.4 + 48354.0i) q^{68} +(-1052.88 - 3413.36i) q^{69} +(-401151. - 91560.1i) q^{70} +(-67890.5 - 26645.0i) q^{71} +(49387.5 - 3701.08i) q^{72} +(333971. + 359935. i) q^{73} +(-767875. + 523529. i) q^{74} +(51667.0 + 41203.1i) q^{75} +(-31328.4 + 33764.0i) q^{76} +(103333. - 685572. i) q^{77} +(-72505.3 - 317667. i) q^{78} +(193884. + 335817. i) q^{79} +(-480357. - 277334. i) q^{80} +(-269717. - 83196.7i) q^{81} +(-87470.0 + 69755.0i) q^{82} +(-1636.13 + 21832.6i) q^{83} +(312209. + 150352. i) q^{84} +212547. i q^{85} +(751643. - 355100. i) q^{86} +805637. q^{87} +(167531. - 347882. i) q^{88} +(856953. + 64219.7i) q^{89} +(-185529. - 232646. i) q^{90} +(147732. - 478935. i) q^{91} +(-3712.48 + 6430.21i) q^{92} +(-587416. + 339145. i) q^{93} +(790989. - 180538. i) q^{94} +(-112776. - 16998.3i) q^{95} +(626206. + 581034. i) q^{96} +(-433782. + 543946. i) q^{97} +(31335.3 + 45960.5i) q^{98} +(367547. - 341033. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 252q - 14q^{2} - 11q^{3} + 1180q^{4} - 11q^{5} - 118q^{6} + 126q^{7} - 2254q^{8} - 8178q^{9} + O(q^{10}) $	\( 252q - 14q^{2} - 11q^{3} + 1180q^{4} - 11q^{5} - 118q^{6} + 126q^{7} - 2254q^{8} - 8178q^{9} + 967q^{10} + 4090q^{11} - 484q^{12} + 1527q^{13} + 7812q^{14} - 8923q^{15} - 13760q^{16} - 3655q^{17} + 5596q^{18} + 38605q^{19} + 26085q^{20} + 24873q^{21} - 25214q^{22} + 27991q^{23} - 20480q^{24} - 24146q^{25} - 34923q^{26} - 14q^{27} - 77634q^{28} - 112735q^{29} + 375072q^{30} + 290647q^{31} - 344064q^{32} - 152174q^{33} - 198311q^{34} - 182471q^{35} - 930891q^{36} + 282762q^{37} + 487342q^{38} + 857290q^{39} + 745459q^{40} + 27674q^{41} + 148802q^{43} - 1255832q^{44} - 191310q^{45} - 1344785q^{46} + 69166q^{47} - 871241q^{48} + 1786604q^{49} + 837705q^{50} - 182756q^{51} + 2906416q^{52} + 7779q^{53} + 487154q^{54} - 529592q^{55} - 2464007q^{56} - 767855q^{57} - 1523780q^{58} + 1531338q^{59} - 1858647q^{60} + 646957q^{61} - 448559q^{62} - 2007847q^{63} + 3937366q^{64} - 1473542q^{65} + 1513319q^{66} - 575523q^{67} + 2717157q^{68} + 967041q^{69} + 4624473q^{70} - 2149319q^{71} - 9986371q^{72} - 514565q^{73} - 882972q^{74} - 6655138q^{75} + 1152658q^{76} - 341803q^{77} + 6322388q^{78} - 2476742q^{79} + 10750038q^{80} + 4308941q^{81} + 5079172q^{82} + 2318609q^{83} + 5578407q^{84} + 585292q^{86} - 1990710q^{87} - 2864890q^{88} - 4561993q^{89} - 17681545q^{90} - 4648506q^{91} - 1991714q^{92} - 8868294q^{93} - 10200218q^{94} + 10091737q^{95} + 6250318q^{96} - 1676750q^{97} + 7512700q^{98} + 18452884q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{42}\right)$

Coefficient data

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

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

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

$2$	−4.53656	+	9.42027i	−0.567070	+	1.17753i	0.398446	+	0.917192i	$0.369549\pi$
$2$	−4.53656	+	9.42027i	−0.567070	+	1.17753i	−0.965517	+	0.260342i	$0.916165\pi$
$3$	21.7428	+	1.62939i	0.805288	+	0.0603480i	0.471011	−	0.882127i	$-0.343889\pi$
$3$	21.7428	+	1.62939i	0.805288	+	0.0603480i	0.334276	+	0.942475i	$0.391508\pi$
$4$	−28.2577	−	35.4340i	−0.441526	−	0.553656i
$5$	33.0785	−	107.238i	0.264628	−	0.857902i	−0.721572	−	0.692340i	$-0.756580\pi$
$5$	33.0785	−	107.238i	0.264628	−	0.857902i	0.986199	−	0.165562i	$-0.0529438\pi$
$6$	−113.987	+	197.431i	−0.527716	+	0.914031i
$7$	−303.689	+	175.335i	−0.885390	+	0.511180i	−0.872432	−	0.488736i	$-0.837458\pi$
$7$	−303.689	+	175.335i	−0.885390	+	0.511180i	−0.0129582	+	0.999916i	$0.504125\pi$
$8$	−190.398	+	43.4570i	−0.371870	+	0.0848769i
$9$	−250.765	−	37.7967i	−0.343985	−	0.0518473i
$10$	860.145	+	798.098i	0.860145	+	0.798098i
$11$	−1232.71	+	1545.78i	−0.926157	+	1.16136i	0.0604378	+	0.998172i	$0.480750\pi$
$11$	−1232.71	+	1545.78i	−0.926157	+	1.16136i	−0.986594	+	0.163192i	$0.947821\pi$
$12$	−556.664	−	816.476i	−0.322143	−	0.472498i
$13$	−1047.73	+	972.152i	−0.476891	+	0.442490i	−0.881630	−	0.471942i	$-0.843553\pi$
$13$	−1047.73	+	972.152i	−0.476891	+	0.442490i	0.404738	+	0.914433i	$0.367363\pi$
$14$	−273.998	−	3656.25i	−0.0998534	−	1.33245i
$15$	893.950	−	2277.75i	0.264874	−	0.674888i
$16$	1099.82	−	4818.61i	0.268510	−	1.17642i
$17$	−1809.82	+	558.254i	−0.368373	+	0.113628i	−0.473414	−	0.880840i	$-0.656979\pi$
$17$	−1809.82	+	558.254i	−0.368373	+	0.113628i	0.105041	+	0.994468i	$0.466502\pi$
$18$	1493.66	−	2190.80i	0.256115	−	0.375652i
$19$	−151.468	−	1004.92i	−0.0220831	−	0.146512i	0.975072	−	0.221889i	$-0.0712221\pi$
$19$	−151.468	−	1004.92i	−0.0220831	−	0.146512i	−0.997155	+	0.0753768i	$0.975984\pi$
$20$	−4734.58	+	1858.19i	−0.591823	+	0.232273i
$21$	−6888.72	+	3317.43i	−0.743842	+	0.358216i
$22$	−8969.33	−	18625.0i	−0.842349	−	1.74915i
$23$	−59.8530	−	152.503i	−0.00491929	−	0.0125341i	0.928393	−	0.371600i	$-0.121191\pi$
$23$	−59.8530	−	152.503i	−0.00491929	−	0.0125341i	−0.933312	+	0.359066i	$0.883095\pi$
$24$	−4210.58	+	634.642i	−0.304585	+	0.0459087i
$25$	2504.23	+	1707.36i	0.160271	+	0.109271i
$26$	−4404.83	−	14280.1i	−0.250616	−	0.812478i
$27$	−20887.1	−	4767.35i	−1.06118	−	0.242207i
$28$	14794.4	+	5806.35i	0.673941	+	0.264502i
$29$	36846.2	−	2761.24i	1.51077	−	0.113217i	0.706599	−	0.707614i	$-0.250229\pi$
$29$	36846.2	−	2761.24i	1.51077	−	0.113217i	0.804171	+	0.594398i	$0.202609\pi$
$30$	17401.5	+	18754.4i	0.644501	+	0.694607i
$31$	−25703.4	+	17524.3i	−0.862790	+	0.588240i	−0.911835	−	0.410556i	$-0.865334\pi$
$31$	−25703.4	+	17524.3i	−0.862790	+	0.588240i	0.0490455	+	0.998797i	$0.484382\pi$
$32$	30631.2	+	24427.6i	0.934791	+	0.745471i
$33$	−29321.3	+	31600.8i	−0.815908	+	0.879340i
$34$	2951.44	−	19581.5i	0.0750925	−	0.498206i
$35$	8756.95	+	38366.7i	0.204244	+	0.894850i
$36$	5746.74	+	9953.65i	0.123173	+	0.213341i
$37$	76977.3	+	44442.8i	1.51970	+	0.877398i	0.999731	+	0.0232120i	$0.00738926\pi$
$37$	76977.3	+	44442.8i	1.51970	+	0.877398i	0.519967	+	0.854186i	$0.325944\pi$
$38$	10153.8	+	3132.03i	0.185045	+	0.0570789i
$39$	−24364.6	+	19430.1i	−0.410738	+	0.327553i
$40$	−1637.83	+	21855.3i	−0.0255911	+	0.341489i
$41$	9640.56	+	4642.65i	0.139878	+	0.0673619i	0.502514	−	0.864569i	$-0.332409\pi$
$41$	9640.56	+	4642.65i	0.139878	+	0.0673619i	−0.362635	+	0.931931i	$0.618123\pi$
$42$		−	79943.3i		−	1.07903i
$43$	−61790.1	−	50033.4i	−0.777166	−	0.629296i
$43$	−61790.1	−	50033.4i	−0.777166	−	0.629296i
$44$	89606.6			1.05192
$45$	−12348.1	+	25641.2i	−0.135508	+	0.281385i
$46$	1708.14	+	128.008i	0.0175489	+	0.00131511i
$47$	−48380.9	−	60667.7i	−0.465994	−	0.584338i	0.492191	−	0.870487i	$-0.336196\pi$
$47$	−48380.9	−	60667.7i	−0.465994	−	0.584338i	−0.958185	+	0.286149i	$0.907625\pi$
$48$	31764.5	−	102978.i	0.287222	−	0.931151i
$49$	2660.09	−	4607.40i	0.0226104	−	0.0391623i
$50$	−27444.4	+	15845.0i	−0.219555	+	0.126760i
$51$	−40260.0	+	9189.09i	−0.303503	+	0.0692727i
$52$	64053.6	+	9654.53i	0.455548	+	0.0686627i
$53$	−73846.7	−	68519.7i	−0.496025	−	0.460244i	0.392049	−	0.919944i	$-0.371766\pi$
$53$	−73846.7	−	68519.7i	−0.496025	−	0.460244i	−0.888074	+	0.459700i	$0.847957\pi$
$54$	139665.	−	175135.i	0.886968	−	1.11222i
$55$	124989.	+	183325.i	0.751249	+	1.10188i
$56$	50202.1	−	46580.7i	0.285863	−	0.265242i
$57$	−1655.91	−	22096.6i	−0.00894156	−	0.119317i
$58$	−141143.	+	359627.i	−0.723396	+	1.84318i
$59$	38877.1	−	170332.i	0.189294	−	0.829353i	−0.787695	−	0.616065i	$-0.788726\pi$
$59$	38877.1	−	170332.i	0.189294	−	0.829353i	0.976989	−	0.213288i	$-0.0684171\pi$
$60$	−105971.	+	32687.6i	−0.490605	+	0.151332i
$61$	−208106.	+	305235.i	−0.916841	+	1.34476i	0.0217626	+	0.999763i	$0.493072\pi$
$61$	−208106.	+	305235.i	−0.916841	+	1.34476i	−0.938604	+	0.344996i	$0.887880\pi$
$62$	−48478.3	−	321632.i	−0.203410	−	1.34954i
$63$	82781.5	−	32489.4i	0.331064	−	0.129933i
$64$	−84078.8	+	40490.2i	−0.320735	+	0.154458i
$65$	69594.0	+	144513.i	0.253415	+	0.526221i
$66$	−164670.	−	419574.i	−0.572775	−	1.45941i
$67$	813.274	−	122.581i	0.00270404	−	0.000407568i	−0.147690	−	0.989034i	$-0.547184\pi$
$67$	813.274	−	122.581i	0.00270404	−	0.000407568i	0.150394	+	0.988626i	$0.451946\pi$
$68$	70922.4	+	48354.0i	0.225557	+	0.153782i
$69$	−1052.88	−	3413.36i	−0.00320503	−	0.0103905i
$70$	−401151.	−	91560.1i	−1.16954	−	0.266939i
$71$	−67890.5	−	26645.0i	−0.189685	−	0.0744460i	0.268597	−	0.963253i	$-0.413440\pi$
$71$	−67890.5	−	26645.0i	−0.189685	−	0.0744460i	−0.458282	+	0.888807i	$0.651535\pi$
$72$	49387.5	−	3701.08i	0.132318	−	0.00991588i
$73$	333971.	+	359935.i	0.858500	+	0.925243i	0.997886	−	0.0649950i	$-0.0207032\pi$
$73$	333971.	+	359935.i	0.858500	+	0.925243i	−0.139385	+	0.990238i	$0.544513\pi$
$74$	−767875.	+	523529.i	−1.89494	+	1.29195i
$75$	51667.0	+	41203.1i	0.122470	+	0.0976666i
$76$	−31328.4	+	33764.0i	−0.0713669	+	0.0769153i
$77$	103333.	−	685572.i	0.226344	−	1.50169i
$78$	−72505.3	−	317667.i	−0.152787	−	0.669403i
$79$	193884.	+	335817.i	0.393243	+	0.681116i	0.992875	−	0.119159i	$-0.0380199\pi$
$79$	193884.	+	335817.i	0.393243	+	0.681116i	−0.599633	+	0.800275i	$0.704687\pi$
$80$	−480357.	−	277334.i	−0.938197	−	0.541668i
$81$	−269717.	−	83196.7i	−0.507520	−	0.156549i
$82$	−87470.0	+	69755.0i	−0.158642	+	0.126513i
$83$	−1636.13	+	21832.6i	−0.00286143	+	0.0381831i	−0.998452	−	0.0556248i	$-0.982285\pi$
$83$	−1636.13	+	21832.6i	−0.00286143	+	0.0381831i	0.995590	+	0.0938079i	$0.0299040\pi$
$84$	312209.	+	150352.i	0.526754	+	0.253671i
$85$			212547.i			0.346097i
$86$	751643.	−	355100.i	1.18172	−	0.558284i
$87$	805637.			1.22344
$88$	167531.	−	347882.i	0.245837	−	0.510486i
$89$	856953.	+	64219.7i	1.21559	+	0.0910958i	0.667040	−	0.745022i	$-0.267561\pi$
$89$	856953.	+	64219.7i	1.21559	+	0.0910958i	0.548550	+	0.836118i	$0.315180\pi$
$90$	−185529.	−	232646.i	−0.254498	−	0.319130i
$91$	147732.	−	478935.i	0.196042	−	0.635554i
$92$	−3712.48	+	6430.21i	−0.00476761	+	0.00825774i
$93$	−587416.	+	339145.i	−0.730293	+	0.421635i
$94$	790989.	−	180538.i	0.952328	−	0.217363i
$95$	−112776.	−	16998.3i	−0.131537	−	0.0198259i
$96$	626206.	+	581034.i	0.707788	+	0.656731i
$97$	−433782.	+	543946.i	−0.475288	+	0.595992i	−0.960457	−	0.278428i	$-0.910187\pi$
$97$	−433782.	+	543946.i	−0.475288	+	0.595992i	0.485169	+	0.874420i	$0.338758\pi$
$98$	31335.3	+	45960.5i	0.0332932	+	0.0488322i
$99$	367547.	−	341033.i	0.378797	−	0.351472i
$100$	−10265.3	−	136981.i	−0.0102653	−	0.136981i
$101$	−92838.7	+	236549.i	−0.0901083	+	0.229592i	−0.968822	−	0.247756i	$-0.920307\pi$
$101$	−92838.7	+	236549.i	−0.0901083	+	0.229592i	0.878714	+	0.477348i	$0.158402\pi$
$102$	96078.4	−	420947.i	0.0905368	−	0.396668i
$103$	−1.75240e6	+	540542.i	−1.60369	+	0.494673i	−0.962174	−	0.272437i	$-0.912171\pi$
$103$	−1.75240e6	+	540542.i	−1.60369	+	0.494673i	−0.641516	+	0.767109i	$0.721694\pi$
$104$	157238.	−	230626.i	0.139784	−	0.205026i
$105$	127886.	+	848467.i	0.110473	+	0.732937i
$106$	980484.	−	384812.i	0.823233	−	0.323095i
$107$	380377.	−	183180.i	0.310501	−	0.149529i	−0.272143	−	0.962257i	$-0.587732\pi$
$107$	380377.	−	183180.i	0.310501	−	0.149529i	0.582644	+	0.812727i	$0.302018\pi$
$108$	421295.	+	874829.i	0.334438	+	0.694467i
$109$	645939.	+	1.64583e6i	0.498783	+	1.27088i	0.929644	+	0.368460i	$0.120115\pi$
$109$	645939.	+	1.64583e6i	0.498783	+	1.27088i	−0.430860	+	0.902419i	$0.641790\pi$
$110$	−2.29399e6	+	345764.i	−1.72351	+	0.259778i
$111$	1.60128e6	+	1.09174e6i	1.17084	+	0.798268i
$112$	510868.	+	1.65619e6i	0.363626	+	1.17885i
$113$	−2.16285e6	−	493657.i	−1.49897	−	0.342129i	−0.607172	−	0.794570i	$-0.707696\pi$
$113$	−2.16285e6	−	493657.i	−1.49897	−	0.342129i	−0.891794	+	0.452441i	$0.850553\pi$
$114$	215668.	+	84643.6i	0.145570	+	0.0571320i
$115$	−18333.9	+	1373.94i	−0.0120548	+	0.000903385i
$116$	−1.13903e6	−	1.22758e6i	−0.729728	−	0.786459i
$117$	299478.	−	204181.i	0.186985	−	0.127484i
$118$	1.42820e6	+	1.13895e6i	0.869247	+	0.693202i
$119$	451739.	−	486859.i	0.268069	−	0.288910i
$120$	−71221.8	+	472526.i	−0.0412163	+	0.273452i
$121$	−475626.	−	2.08385e6i	−0.268479	−	1.17628i
$122$	−1.93131e6	−	3.34513e6i	−1.06359	−	1.84218i
$123$	202048.	+	116652.i	0.108577	+	0.0626871i
$124$	1.34727e6	+	415578.i	0.706627	+	0.217966i
$125$	1.63686e6	−	1.30536e6i	0.838075	−	0.668342i
$126$	−69485.1	+	927214.i	−0.0347360	+	0.463520i
$127$	−2.54433e6	−	1.22529e6i	−1.24212	−	0.598172i	−0.306730	−	0.951796i	$-0.599235\pi$
$127$	−2.54433e6	−	1.22529e6i	−1.24212	−	0.598172i	−0.935388	+	0.353624i	$0.884949\pi$
$128$			1.53171e6i			0.730378i
$129$	−1.26196e6	−	1.18855e6i	−0.587865	−	0.553664i
$130$	−1.67707e6			−0.763347
$131$	294836.	−	612232.i	0.131149	−	0.272334i	−0.825045	−	0.565067i	$-0.808850\pi$
$131$	294836.	−	612232.i	0.131149	−	0.272334i	0.956194	+	0.292733i	$0.0945646\pi$
$132$	1.94830e6	+	146005.i	0.847097	+	0.0634811i
$133$	222197.	+	278627.i	0.0944461	+	0.118432i
$134$	−2534.72	+	8217.35i	−0.00105345	+	0.00341521i
$135$	−1.20215e6	+	2.08219e6i	−0.488606	+	0.846291i
$136$	320324.	−	184939.i	0.127342	−	0.0735212i
$137$	−1.24277e6	+	283655.i	−0.483315	+	0.110313i	−0.457234	−	0.889346i	$-0.651160\pi$
$137$	−1.24277e6	+	283655.i	−0.483315	+	0.110313i	−0.0260806	+	0.999660i	$0.508303\pi$
$138$	36931.2	+	5566.48i	0.0140526	+	0.00211809i
$139$	150367.	+	139521.i	0.0559898	+	0.0519510i	0.707671	−	0.706542i	$-0.249746\pi$
$139$	150367.	+	139521.i	0.0559898	+	0.0519510i	−0.651682	+	0.758493i	$0.725936\pi$
$140$	1.11203e6	−	1.39445e6i	0.405260	−	0.508180i
$141$	−953082.	−	1.39792e6i	−0.339995	−	0.498682i
$142$	558993.	−	518669.i	0.195227	−	0.181145i
$143$	−211175.	−	2.81794e6i	−0.0722163	−	0.963660i
$144$	−457923.	+	1.16677e6i	−0.153357	+	0.390748i
$145$	922706.	−	4.04264e6i	0.302663	−	1.32605i
$146$	−4.90577e6	+	1.51323e6i	−1.57633	+	0.486235i
$147$	65344.9	−	95843.4i	0.0205712	−	0.0301724i
$148$	−600410.	−	3.98346e6i	−0.185209	−	1.22878i
$149$	230513.	−	90469.8i	0.0696846	−	0.0273492i	−0.330243	−	0.943896i	$-0.607131\pi$
$149$	230513.	−	90469.8i	0.0696846	−	0.0273492i	0.399927	+	0.916547i	$0.369035\pi$
$150$	−622535.	+	299797.i	−0.184455	+	0.0888287i
$151$	−433607.	−	900395.i	−0.125941	−	0.261518i	0.828459	−	0.560049i	$-0.189218\pi$
$151$	−433607.	−	900395.i	−0.125941	−	0.261518i	−0.954400	+	0.298531i	$0.903503\pi$
$152$	72510.1	+	184753.i	0.0206475	+	0.0526090i
$153$	474938.	−	71585.4i	0.132606	−	0.0199871i
$154$	5.98949e6	+	4.08357e6i	1.63994	+	1.11809i
$155$	1.02903e6	+	3.33605e6i	0.276334	+	0.895853i
$156$	1.37697e6	+	314285.i	0.362703	+	0.0827846i
$157$	−4.21495e6	−	1.65425e6i	−1.08916	−	0.427466i	−0.248284	−	0.968687i	$-0.579867\pi$
$157$	−4.21495e6	−	1.65425e6i	−1.08916	−	0.427466i	−0.840880	+	0.541222i	$0.817962\pi$
$158$	−4.04305e6	+	302985.i	−1.02503	+	0.0768156i
$159$	−1.49399e6	−	1.61013e6i	−0.371668	−	0.400563i
$160$	3.63279e6	−	2.47680e6i	0.886913	−	0.604687i
$161$	44915.7	+	35819.1i	0.0107627	+	0.00858296i
$162$	2.00732e6	−	2.16338e6i	0.472142	−	0.508848i
$163$	−629781.	+	4.17832e6i	−0.145421	+	0.964804i	0.790467	+	0.612505i	$0.209838\pi$
$163$	−629781.	+	4.17832e6i	−0.145421	+	0.964804i	−0.935888	+	0.352299i	$0.885400\pi$
$164$	−107912.	−	472794.i	−0.0244646	−	0.107187i
$165$	2.41890e6	+	4.18966e6i	0.538476	+	0.932667i
$166$	−198246.	−	114458.i	−0.0433392	−	0.0250219i
$167$	3.49752e6	+	1.07884e6i	0.750950	+	0.231637i	0.646522	−	0.762895i	$-0.276223\pi$
$167$	3.49752e6	+	1.07884e6i	0.750950	+	0.231637i	0.104428	+	0.994532i	$0.466699\pi$
$168$	1.16743e6	−	930994.i	0.246208	−	0.196345i
$169$	−208048.	+	2.77621e6i	−0.0431026	+	0.575164i
$170$	−2.00225e6	−	964231.i	−0.407541	−	0.196261i
$171$			257725.i			0.0515428i
$172$	−26839.3	+	3.60330e6i	−0.00527456	+	0.708133i
$173$	−322464.			−0.0622793			−0.0311396	−	0.999515i	$-0.509914\pi$
$173$	−322464.			−0.0622793			−0.0311396	+	0.999515i	$0.509914\pi$
$174$	−3.65482e6	+	7.58931e6i	−0.693774	+	1.44064i
$175$	−1.05987e6	−	79426.1i	−0.197760	−	0.0148200i
$176$	6.09273e6	+	7.64004e6i	1.11757	+	1.40139i
$177$	1.12283e6	−	3.64013e6i	0.202486	−	0.656444i
$178$	−4.49259e6	+	7.78139e6i	−0.796593	+	1.37974i
$179$	−3.90800e6	+	2.25629e6i	−0.681390	+	0.393401i	−0.800378	−	0.599495i	$-0.795368\pi$
$179$	−3.90800e6	+	2.25629e6i	−0.681390	+	0.393401i	0.118989	+	0.992896i	$0.462035\pi$
$180$	1.25750e6	−	287016.i	0.215621	−	0.0492140i
$181$	8.27162e6	+	1.24675e6i	1.39494	+	0.210253i	0.803120	−	0.595818i	$-0.203172\pi$
$181$	8.27162e6	+	1.24675e6i	1.39494	+	0.210253i	0.591819	+	0.806071i	$0.298410\pi$
$182$	3.84150e6	+	3.56439e6i	0.637216	+	0.591250i
$183$	−5.02214e6	+	6.29756e6i	−0.819475	+	1.02759i
$184$	18023.2	+	26435.1i	0.00289320	+	0.00424354i
$185$	7.31224e6	−	6.78477e6i	1.15488	−	1.07157i
$186$	−529986.	−	7.07217e6i	−0.0823617	−	1.09904i
$187$	1.36805e6	−	3.48574e6i	0.209208	−	0.533052i
$188$	−782568.	+	3.42866e6i	−0.117774	+	0.516001i
$189$	7.17907e6	−	2.21445e6i	1.06337	−	0.328005i
$190$	671744.	−	985268.i	0.0979362	−	0.143646i
$191$	−1.78277e6	−	1.18279e7i	−0.255856	−	1.69749i	−0.635291	−	0.772273i	$-0.719120\pi$
$191$	−1.78277e6	−	1.18279e7i	−0.255856	−	1.69749i	0.379435	−	0.925218i	$-0.376118\pi$
$192$	−1.89408e6	+	743371.i	−0.267605	+	0.105027i
$193$	1.20225e7	−	5.78974e6i	1.67233	−	0.805354i	0.674593	−	0.738190i	$-0.264319\pi$
$193$	1.20225e7	−	5.78974e6i	1.67233	−	0.805354i	0.997742	−	0.0671642i	$-0.0213951\pi$
$194$	−3.15623e6	−	6.55399e6i	−0.432279	−	0.897637i
$195$	1.27770e6	+	3.25552e6i	0.172315	+	0.439052i
$196$	−238427.	+	35937.0i	−0.0316655	+	0.00477281i
$197$	−2.99777e6	−	2.04385e6i	−0.392103	−	0.267331i	0.351181	−	0.936308i	$-0.385780\pi$
$197$	−2.99777e6	−	2.04385e6i	−0.392103	−	0.267331i	−0.743284	+	0.668977i	$0.766733\pi$
$198$	1.54523e6	+	5.00951e6i	0.199066	+	0.645356i
$199$	−9.41584e6	−	2.14911e6i	−1.19481	−	0.272708i	−0.421557	−	0.906802i	$-0.638516\pi$
$199$	−9.41584e6	−	2.14911e6i	−1.19481	−	0.272708i	−0.773256	+	0.634094i	$0.781373\pi$
$200$	−550997.	−	216250.i	−0.0688746	−	0.0270313i
$201$	17882.6	−	1340.11i	0.00220212	−	0.000165026i
$202$	−1.80719e6	−	1.94768e6i	−0.219255	−	0.236300i
$203$	−1.07056e7	+	7.29897e6i	−1.27975	+	0.872517i
$204$	1.46326e6	+	1.16691e6i	0.172358	+	0.137451i
$205$	816762.	−	880260.i	0.0948056	−	0.102176i
$206$	2.85780e6	−	1.89602e7i	0.326911	−	2.16891i
$207$	9244.91	+	40504.6i	0.00104230	+	0.00456660i
$208$	3.53211e6	+	6.11779e6i	0.392504	+	0.679837i
$209$	1.74010e6	+	1.00465e6i	0.190606	+	0.110046i
$210$	−8.57294e6	−	2.64440e6i	−0.925704	−	0.285542i
$211$	1.19182e7	−	9.50446e6i	1.26871	−	1.01177i	0.269910	−	0.962885i	$-0.413006\pi$
$211$	1.19182e7	−	9.50446e6i	1.26871	−	1.01177i	0.998805	−	0.0488810i	$-0.0155655\pi$
$212$	−341192.	+	4.55289e6i	−0.0358089	+	0.477837i
$213$	−1.43271e6	−	689957.i	−0.148259	−	0.0713976i
$214$			4.41426e6i			0.450419i
$215$	−7.40939e6	+	4.97120e6i	−0.745534	+	0.500203i
$216$	4.18403e6			0.415178
$217$	4.73321e6	−	9.82862e6i	0.463209	−	0.961863i
$218$	−1.84344e7	−	1.38147e6i	−1.77935	−	0.133344i
$219$	6.67498e6	+	8.37016e6i	0.635503	+	0.796896i
$220$	2.96405e6	−	9.60921e6i	0.278367	−	0.902443i
$221$	1.35349e6	−	2.34432e6i	0.125395	−	0.217190i
$222$	−1.75488e7	+	1.01318e7i	−1.60394	+	0.926034i
$223$	−1.46320e7	+	3.33966e6i	−1.31944	+	0.301153i	−0.823555	−	0.567237i	$-0.808013\pi$
$223$	−1.46320e7	+	3.33966e6i	−1.31944	+	0.301153i	−0.495883	+	0.868390i	$0.665155\pi$
$224$	−1.35854e7	−	2.04767e6i	−1.20873	−	0.182186i
$225$	−563441.	−	522797.i	−0.0494654	−	0.0458972i
$226$	1.44623e7	−	1.81352e7i	1.25289	−	1.57107i
$227$	6.80114e6	+	9.97545e6i	0.581439	+	0.852815i	0.998425	−	0.0560981i	$-0.0178660\pi$
$227$	6.80114e6	+	9.97545e6i	0.581439	+	0.852815i	−0.416986	+	0.908913i	$0.636914\pi$
$228$	−736180.	+	683075.i	−0.0621126	+	0.0576320i
$229$	162340.	+	2.16627e6i	0.0135182	+	0.180387i	0.999876	+	0.0157699i	$0.00501992\pi$
$229$	162340.	+	2.16627e6i	0.0135182	+	0.180387i	−0.986357	+	0.164617i	$0.947361\pi$
$230$	70230.0	−	178943.i	0.00577217	−	0.0147073i
$231$	3.36382e6	−	1.47379e7i	0.272896	−	1.19564i
$232$	−6.89542e6	+	2.12696e6i	−0.552201	+	0.170331i
$233$	−9.47634e6	+	1.38992e7i	−0.749157	+	1.09881i	0.242530	+	0.970144i	$0.422023\pi$
$233$	−9.47634e6	+	1.38992e7i	−0.749157	+	1.09881i	−0.991688	+	0.128668i	$0.958930\pi$
$234$	564836.	+	3.74744e6i	0.0440833	+	0.292474i
$235$	−8.10623e6	+	3.18146e6i	−0.624619	+	0.245145i
$236$	−7.13411e6	+	3.43560e6i	−0.542755	+	0.261377i
$237$	3.66839e6	+	7.61750e6i	0.275569	+	0.572226i
$238$	2.53700e6	+	6.46417e6i	0.188187	+	0.479493i
$239$	−7.03189e6	+	1.05989e6i	−0.515085	+	0.0776365i	−0.401441	−	0.915885i	$-0.631490\pi$
$239$	−7.03189e6	+	1.05989e6i	−0.515085	+	0.0776365i	−0.113644	+	0.993522i	$0.536252\pi$
$240$	−9.99239e6	−	6.81270e6i	−0.722829	−	0.492817i
$241$	1.21961e6	+	3.95388e6i	0.0871304	+	0.282470i	0.988643	−	0.150283i	$-0.0480185\pi$
$241$	1.21961e6	+	3.95388e6i	0.0871304	+	0.282470i	−0.901513	+	0.432753i	$0.857542\pi$
$242$	2.17882e7	+	4.97301e6i	1.53736	+	0.350892i
$243$	8.80984e6	+	3.45761e6i	0.613973	+	0.240966i
$244$	1.66963e7	−	1.25121e6i	1.14934	−	0.0861314i
$245$	−406096.	−	437667.i	−0.0276141	−	0.0297609i
$246$	−2.01550e6	+	1.37414e6i	−0.135387	+	0.0923053i
$247$	1.13564e6	+	905640.i	0.0753613	+	0.0600987i
$248$	4.13231e6	−	4.45357e6i	0.270918	−	0.291980i
$249$	−71147.9	+	472035.i	−0.00460854	+	0.0305757i
$250$	4.87106e6	+	2.13415e7i	0.311748	+	1.36586i
$251$	4.30569e6	+	7.45768e6i	0.272284	+	0.471610i	0.969446	−	0.245304i	$-0.0788877\pi$
$251$	4.30569e6	+	7.45768e6i	0.272284	+	0.471610i	−0.697162	+	0.716913i	$0.745554\pi$
$252$	−3.49044e6	−	2.01521e6i	−0.218112	−	0.125927i
$253$	309517.	+	95473.3i	0.0191127	+	0.00589549i
$254$	2.30850e7	−	1.84097e7i	1.40874	−	1.12343i
$255$	−346323.	+	4.62135e6i	−0.0208862	+	0.278708i
$256$	−1.98102e7	−	9.54009e6i	−1.18078	−	0.568634i
$257$		−	2.98412e7i		−	1.75799i	−0.476827	−	0.878997i	$-0.658213\pi$
$257$		−	2.98412e7i		−	1.75799i	0.476827	−	0.878997i	$-0.341787\pi$
$258$	1.69214e7	−	6.49613e6i	0.985319	−	0.378264i
$259$	−3.11695e7			−1.79403
$260$	3.15413e6	−	6.54961e6i	0.179456	−	0.372645i
$261$	−9.34409e6	−	700243.i	−0.525552	−	0.0393847i
$262$	4.42985e6	+	5.55486e6i	0.246312	+	0.308865i
$263$	−7.18735e6	+	2.33008e7i	−0.395095	+	1.28087i	0.511653	+	0.859192i	$0.329033\pi$
$263$	−7.18735e6	+	2.33008e7i	−0.395095	+	1.28087i	−0.906748	+	0.421674i	$0.861443\pi$
$264$	4.20942e6	−	7.29094e6i	0.228776	−	0.396252i
$265$	−9.79063e6	+	5.65262e6i	−0.526106	+	0.303747i
$266$	−3.63275e6	+	829152.i	−0.193015	+	0.0440544i
$267$	1.85279e7	+	2.79263e6i	0.973401	+	0.146717i
$268$	−27324.8	−	25353.7i	−0.00141955	−	0.00131715i
$269$	2.13753e7	−	2.68038e7i	1.09813	−	1.37702i	0.178638	−	0.983915i	$-0.442831\pi$
$269$	2.13753e7	−	2.68038e7i	1.09813	−	1.37702i	0.919495	−	0.393101i	$-0.128598\pi$
$270$	−1.41612e7	−	2.07706e7i	−0.719461	−	1.05526i
$271$	−1.27709e7	+	1.18496e7i	−0.641672	+	0.595385i	−0.932403	−	0.361420i	$-0.882292\pi$
$271$	−1.27709e7	+	1.18496e7i	−0.641672	+	0.595385i	0.290731	+	0.956805i	$0.406101\pi$
$272$	699545.	+	9.33478e6i	0.0347623	+	0.463871i
$273$	3.99247e6	−	1.01727e7i	0.196225	−	0.499973i
$274$	2.96581e6	−	1.29941e7i	0.144176	−	0.631674i
$275$	−5.72620e6	+	1.76630e6i	−0.275339	+	0.0849310i
$276$	−91196.9	+	133761.i	−0.00433764	+	0.00636214i
$277$	5.56340e6	+	3.69107e7i	0.261758	+	1.73665i	0.603949	+	0.797023i	$0.293593\pi$
$277$	5.56340e6	+	3.69107e7i	0.261758	+	1.73665i	−0.342190	+	0.939631i	$0.611169\pi$
$278$	−1.99647e6	+	783557.i	−0.0929242	+	0.0364700i
$279$	7.10786e6	−	3.42296e6i	0.327285	−	0.157612i
$280$	−3.33460e6	−	6.92437e6i	−0.151904	−	0.315432i
$281$	−7.81358e6	−	1.99087e7i	−0.352153	−	0.897271i	−0.991706	−	0.128524i	$-0.958976\pi$
$281$	−7.81358e6	−	1.99087e7i	−0.352153	−	0.897271i	0.639554	−	0.768747i	$-0.279119\pi$
$282$	1.74924e7	−	2.63656e6i	0.780016	−	0.117568i
$283$	2.68438e7	+	1.83018e7i	1.18436	+	0.807485i	0.985019	−	0.172444i	$-0.0551664\pi$
$283$	2.68438e7	+	1.83018e7i	1.18436	+	0.807485i	0.199344	+	0.979930i	$0.436119\pi$
$284$	974286.	+	3.15856e6i	0.0425335	+	0.137890i
$285$	−2.42437e6	−	553346.i	−0.104728	−	0.0239036i
$286$	2.75038e7	+	1.07944e7i	1.17569	+	0.461425i
$287$	−3.74175e6	+	280405.i	−0.158281	+	0.0118615i
$288$	−6.75795e6	−	7.28334e6i	−0.282903	−	0.304897i
$289$	−1.69796e7	+	1.15765e7i	−0.703452	+	0.479605i
$290$	3.38968e7	+	2.70318e7i	1.38984	+	1.10836i
$291$	−1.03179e7	+	1.11201e7i	−0.418710	+	0.451262i
$292$	3.31670e6	−	2.20049e7i	0.133216	−	0.883833i
$293$	7.06676e6	+	3.09615e7i	0.280943	+	1.23089i	0.896588	+	0.442867i	$0.146038\pi$
$293$	7.06676e6	+	3.09615e7i	0.280943	+	1.23089i	−0.615645	+	0.788024i	$0.711104\pi$
$294$	606429.	+	1.05037e6i	0.0238637	+	0.0413332i
$295$	−1.69800e7	−	9.80340e6i	−0.661411	−	0.381866i
$296$	−1.65876e7	−	5.11661e6i	−0.639601	−	0.197291i
$297$	3.31171e7	−	2.64100e7i	1.26411	−	1.00809i
$298$	−193488.	+	2.58192e6i	−0.00731148	+	0.0975649i
$299$	210966.	+	101596.i	0.00789220	+	0.00380068i
$300$		−	2.99507e6i		−	0.110929i
$301$	2.75376e7	+	4.36063e6i	1.00978	+	0.159901i
$302$	1.04490e7			0.379364
$303$	−2.40400e6	+	4.99196e6i	−0.0864185	+	0.179450i
$304$	−5.00893e6	−	375367.i	−0.178289	−	0.0133609i
$305$	2.58489e7	+	3.24135e7i	0.911050	+	1.14242i
$306$	−1.48023e6	+	4.79880e6i	−0.0516613	+	0.167482i
$307$	−3.28165e6	+	5.68398e6i	−0.113417	+	0.196443i	−0.917146	−	0.398552i	$-0.869513\pi$
$307$	−3.28165e6	+	5.68398e6i	−0.113417	+	0.196443i	0.803729	+	0.594995i	$0.202846\pi$
$308$	−2.72125e7	+	1.57112e7i	−0.931358	+	0.537720i
$309$	−3.89827e7	+	8.89754e6i	−1.32128	+	0.301574i
$310$	−3.60947e7	−	5.44040e6i	−1.21160	−	0.182619i
$311$	7.25929e6	+	6.73563e6i	0.241331	+	0.223922i	0.791560	−	0.611091i	$-0.209269\pi$
$311$	7.25929e6	+	6.73563e6i	0.241331	+	0.223922i	−0.550229	+	0.835014i	$0.685460\pi$
$312$	3.79458e6	−	4.75825e6i	0.124940	−	0.156669i
$313$	−1.34177e7	−	1.96801e7i	−0.437567	−	0.641792i	0.542594	−	0.839995i	$-0.317442\pi$
$313$	−1.34177e7	−	1.96801e7i	−0.437567	−	0.641792i	−0.980161	+	0.198202i	$0.936490\pi$
$314$	3.47048e7	−	3.22014e7i	1.12099	−	1.04012i
$315$	−745799.	−	9.95200e6i	−0.0238611	−	0.318404i
$316$	6.42063e6	−	1.63595e7i	0.203477	−	0.518452i
$317$	521286.	−	2.28390e6i	0.0163643	−	0.0716968i	−0.966086	−	0.258219i	$-0.916864\pi$
$317$	521286.	−	2.28390e6i	0.0163643	−	0.0716968i	0.982451	+	0.186522i	$0.0597216\pi$
$318$	2.19454e7	−	6.76927e6i	0.682438	−	0.210504i
$319$	−4.11526e7	+	6.03597e7i	−1.26772	+	1.85941i
$320$	1.56088e6	+	1.03558e7i	0.0476343	+	0.316033i
$321$	8.56891e6	−	3.36305e6i	0.259066	−	0.101676i
$322$	−541188.	+	260623.i	−0.0162099	+	0.00780629i
$323$	835133.	+	1.73417e6i	0.0247827	+	0.0514617i
$324$	4.67359e6	+	1.19081e7i	0.137409	+	0.350112i
$325$	−4.28357e6	+	645645.i	−0.124783	+	0.0188080i
$326$	−3.65039e7	−	2.48879e7i	−1.05362	−	0.718349i
$327$	1.13628e7	+	3.68373e7i	0.324969	+	1.05352i
$328$	−2.03729e6	−	464999.i	−0.0577341	−	0.0131774i
$329$	2.53299e7	+	9.94125e6i	0.711288	+	0.279160i
$330$	−5.04412e7	+	3.78004e6i	−1.40360	+	0.105185i
$331$	−4.06885e7	−	4.38517e7i	−1.12199	−	1.20921i	−0.975500	−	0.220000i	$-0.929394\pi$
$331$	−4.06885e7	−	4.38517e7i	−1.12199	−	1.20921i	−0.146485	−	0.989213i	$-0.546796\pi$
$332$	819849.	−	558964.i	0.0224037	−	0.0152746i
$333$	−1.76234e7	−	1.40542e7i	−0.477262	−	0.380604i
$334$	−2.60297e7	+	2.80533e7i	−0.698602	+	0.752914i
$335$	13756.5	−	91268.5i	0.000365910	−	0.00242765i
$336$	8.40909e6	+	3.68426e7i	0.221682	+	0.971254i
$337$	3.19979e6	+	5.54220e6i	0.0836050	+	0.144808i	0.904796	−	0.425845i	$-0.140023\pi$
$337$	3.19979e6	+	5.54220e6i	0.0836050	+	0.144808i	−0.821191	+	0.570654i	$0.806690\pi$
$338$	−2.52088e7	−	1.45543e7i	−0.652833	−	0.376913i
$339$	−4.62221e7	−	1.42576e7i	−1.18645	−	0.365972i
$340$	7.53138e6	−	6.00608e6i	0.191619	−	0.152811i
$341$	4.59635e6	−	6.13340e7i	0.115918	−	1.54682i
$342$	−2.42784e6	−	1.16918e6i	−0.0606933	−	0.0292284i
$343$		−	3.93903e7i		−	0.976128i
$344$	1.39390e7	+	6.84103e6i	0.342417	+	0.168053i
$345$	−400868.			−0.00976213
$346$	1.46288e6	−	3.03770e6i	0.0353167	−	0.0733359i
$347$	2.21978e7	+	1.66350e6i	0.531278	+	0.0398138i	0.337669	−	0.941265i	$-0.390362\pi$
$347$	2.21978e7	+	1.66350e6i	0.531278	+	0.0398138i	0.193609	+	0.981079i	$0.437981\pi$
$348$	−2.27654e7	−	2.85469e7i	−0.540179	−	0.677363i
$349$	2.01367e7	−	6.52817e7i	0.473710	−	1.53573i	−0.331918	−	0.943308i	$-0.607696\pi$
$349$	2.01367e7	−	6.52817e7i	0.473710	−	1.53573i	0.805628	−	0.592422i	$-0.201828\pi$
$350$	5.55637e6	−	9.62391e6i	0.129595	−	0.224464i
$351$	2.65187e7	−	1.53106e7i	0.613240	−	0.354054i
$352$	−7.55191e7	+	1.72368e7i	−1.73153	+	0.395210i
$353$	4.29160e7	+	6.46855e6i	0.975653	+	0.147056i	0.617469	−	0.786595i	$-0.288158\pi$
$353$	4.29160e7	+	6.46855e6i	0.975653	+	0.147056i	0.358184	+	0.933651i	$0.383396\pi$
$354$	2.91972e7	+	2.70911e7i	0.658161	+	0.610684i
$355$	−5.10307e6	+	6.39904e6i	−0.114063	+	0.143031i
$356$	−2.19399e7	−	3.21800e7i	−0.486279	−	0.713240i
$357$	1.06153e7	−	9.84960e6i	0.233308	−	0.216478i
$358$	−3.52592e6	−	4.70502e7i	−0.0768465	−	1.02544i
$359$	3.08141e7	−	7.85131e7i	0.665988	−	1.69691i	−0.0499552	−	0.998751i	$-0.515908\pi$
$359$	3.08141e7	−	7.85131e7i	0.665988	−	1.69691i	0.715943	−	0.698158i	$-0.245997\pi$
$360$	1.23677e6	−	5.41863e6i	0.0265082	−	0.116140i
$361$	4.39688e7	−	1.35626e7i	0.934595	−	0.288284i
$362$	−4.92694e7	+	7.22649e7i	−1.03861	+	1.52336i
$363$	−6.94600e6	−	4.60837e7i	−0.145216	−	0.963447i
$364$	−2.11451e7	+	8.29886e6i	−0.438436	+	0.172074i
$365$	4.96459e7	−	2.39082e7i	1.02095	−	0.491664i
$366$	−3.65415e7	−	7.58792e7i	−0.745320	−	1.54767i
$367$	2.79046e7	+	7.10998e7i	0.564518	+	1.43837i	0.873275	+	0.487228i	$0.161992\pi$
$367$	2.79046e7	+	7.10998e7i	0.564518	+	1.43837i	−0.308756	+	0.951141i	$0.599913\pi$
$368$	−800679.	+	120683.i	−0.0160663	+	0.00242160i
$369$	−2.24204e6	−	1.52859e6i	−0.0446235	−	0.0304238i
$370$	3.07419e7	+	9.96627e7i	0.606911	+	1.96756i
$371$	3.44403e7	+	7.86077e6i	0.674443	+	0.153937i
$372$	2.86163e7	+	1.12311e7i	0.555884	+	0.218168i
$373$	−3.84720e7	+	2.88308e6i	−0.741342	+	0.0555559i	−0.440047	−	0.897975i	$-0.645038\pi$
$373$	−3.84720e7	+	2.88308e6i	−0.741342	+	0.0555559i	−0.301296	+	0.953531i	$0.597419\pi$
$374$	2.66303e7	+	2.87007e7i	0.509051	+	0.548627i
$375$	3.77169e7	−	2.57150e7i	0.715224	−	0.487632i
$376$	1.18480e7	+	9.44849e6i	0.222886	+	0.177746i
$377$	−3.59205e7	+	3.87131e7i	−0.670376	+	0.722493i
$378$	−1.17076e7	+	7.76748e7i	−0.216766	+	1.43815i
$379$	−3.37174e6	−	1.47725e7i	−0.0619350	−	0.271355i	0.934473	−	0.356033i	$-0.115871\pi$
$379$	−3.37174e6	−	1.47725e7i	−0.0619350	−	0.271355i	−0.996408	+	0.0846781i	$0.973014\pi$
$380$	2.58448e6	+	4.47644e6i	0.0471001	+	0.0815797i
$381$	−5.33244e7	−	3.07868e7i	−0.964164	−	0.556660i
$382$	1.19510e8	+	3.68638e7i	2.14394	+	0.661318i
$383$	−588600.	+	469393.i	−0.0104767	+	0.00835488i	−0.628714	−	0.777636i	$-0.716418\pi$
$383$	−588600.	+	469393.i	−0.0104767	+	0.00835488i	0.618237	+	0.785991i	$0.287847\pi$
$384$	−2.49577e6	+	3.33037e7i	−0.0440768	+	0.588165i
$385$	−7.01011e7	−	3.37589e7i	−1.22841	−	0.591570i
$386$			1.39521e8i			2.42592i
$387$	1.36037e7	+	1.48821e7i	0.234706	+	0.256762i
$388$	3.15319e7			0.539827
$389$	−3.50005e7	+	7.26793e7i	−0.594601	+	1.23470i	0.358918	+	0.933369i	$0.383146\pi$
$389$	−3.50005e7	+	7.26793e7i	−0.594601	+	1.23470i	−0.953519	+	0.301333i	$0.902569\pi$
$390$	−3.64642e7	−	2.73261e6i	−0.614714	−	0.0460664i
$391$	193458.	+	242589.i	0.00323636	+	0.00405827i
$392$	−306250.	+	992838.i	−0.00508414	+	0.0164824i
$393$	7.40811e6	−	1.28312e7i	0.122048	−	0.211393i
$394$	3.28532e7	−	1.89678e7i	0.537141	−	0.310119i
$395$	4.24256e7	−	9.68337e6i	0.688394	−	0.157121i
$396$	−2.24702e7	−	3.38684e6i	−0.361844	−	0.0545392i
$397$	−2.62126e7	−	2.43218e7i	−0.418928	−	0.388708i	0.442350	−	0.896842i	$-0.354145\pi$
$397$	−2.62126e7	−	2.43218e7i	−0.418928	−	0.388708i	−0.861278	+	0.508134i	$0.830335\pi$
$398$	6.29607e7	−	7.89502e7i	0.998666	−	1.25229i
$399$	4.37719e6	+	6.42016e6i	0.0689092	+	0.101071i
$400$	1.09813e7	−	1.01892e7i	0.171583	−	0.159206i
$401$	−1.05720e6	−	1.41073e7i	−0.0163954	−	0.218782i	−0.999383	−	0.0351117i	$-0.988821\pi$
$401$	−1.05720e6	−	1.41073e7i	−0.0163954	−	0.218782i	0.982988	−	0.183670i	$-0.0587977\pi$
$402$	−68501.1	+	174538.i	−0.00105443	+	0.00268665i
$403$	9.89396e6	−	4.33483e7i	0.151166	−	0.662303i
$404$	1.10053e7	−	3.39468e6i	0.166900	−	0.0514819i
$405$	−1.78437e7	+	2.61718e7i	−0.268608	+	0.393975i
$406$	−2.01915e7	−	1.33962e8i	−0.301711	−	2.00172i
$407$	−1.63590e8	+	6.42042e7i	−2.42646	+	0.952314i
$408$	7.26608e6	−	3.49916e6i	0.106984	−	0.0515209i
$409$	2.77270e7	+	5.75758e7i	0.405260	+	0.841531i	0.999311	+	0.0371039i	$0.0118132\pi$
$409$	2.77270e7	+	5.75758e7i	0.405260	+	0.841531i	−0.594052	+	0.804427i	$0.702472\pi$
$410$	4.58699e6	+	1.16875e7i	0.0665544	+	0.169578i
$411$	−2.74835e7	+	4.14247e6i	−0.395864	+	0.0596670i
$412$	6.86722e7	+	4.68199e7i	0.981950	+	0.669482i
$413$	1.80585e7	+	5.85443e7i	0.256349	+	0.831064i
$414$	−423504.	−	96662.1i	−0.00596838	−	0.00136224i
$415$	2.28716e6	+	897643.i	0.0320001	+	0.0125591i
$416$	−5.58406e7	+	4.18467e6i	−0.775658	+	0.0581275i
$417$	3.04207e6	+	3.27857e6i	0.0419528	+	0.0452143i
$418$	−1.73582e7	+	1.18346e7i	−0.237670	+	0.162041i
$419$	9.61841e7	+	7.67043e7i	1.30756	+	1.04274i	0.995702	+	0.0926148i	$0.0295225\pi$
$419$	9.61841e7	+	7.67043e7i	1.30756	+	1.04274i	0.311857	+	0.950129i	$0.399049\pi$
$420$	2.64508e7	−	2.85072e7i	0.357019	−	0.384775i
$421$	−5.71046e6	+	3.78864e7i	−0.0765288	+	0.507735i	0.917423	+	0.397914i	$0.130266\pi$
$421$	−5.71046e6	+	3.78864e7i	−0.0765288	+	0.507735i	−0.993951	+	0.109821i	$0.964972\pi$
$422$	3.54668e7	+	1.55390e8i	0.471938	+	2.06770i
$423$	9.83918e6	+	1.70420e7i	0.129998	+	0.225164i
$424$	1.70379e7	+	9.83683e6i	0.223521	+	0.129050i
$425$	−5.48534e6	−	1.69200e6i	−0.0714557	−	0.0220412i
$426$	1.29992e7	−	1.03665e7i	0.168146	−	0.134092i
$427$	9.68104e6	−	1.29185e8i	0.124348	−	1.65931i
$428$	−1.72394e7	−	8.30204e6i	−0.219882	−	0.105890i
$429$		−	6.16139e7i		−	0.780381i
$430$	−1.32169e7	−	9.23506e7i	−0.166236	−	1.16154i
$431$	7.44662e6			0.0930095			0.0465048	−	0.998918i	$-0.485192\pi$
$431$	7.44662e6			0.0930095			0.0465048	+	0.998918i	$0.485192\pi$
$432$	−4.59440e7	+	9.54038e7i	−0.569873	+	1.18335i
$433$	1.06370e8	+	7.97135e6i	1.31026	+	0.0981902i	0.711469	−	0.702717i	$-0.248030\pi$
$433$	1.06370e8	+	7.97135e6i	1.31026	+	0.0981902i	0.598788	+	0.800907i	$0.295649\pi$
$434$	7.11157e7	+	8.91762e7i	0.869954	+	1.09089i
$435$	2.66492e7	−	8.63947e7i	0.323755	−	1.04959i
$436$	4.00654e7	−	6.93954e7i	0.483404	−	0.837281i
$437$	−144188.	+	83247.0i	−0.00172777	+	0.000997527i
$438$	−1.09131e8	+	2.49083e7i	−1.29875	+	0.296430i
$439$	2.17349e7	+	3.27601e6i	0.256900	+	0.0387214i	0.276229	−	0.961092i	$-0.410915\pi$
$439$	2.17349e7	+	3.27601e6i	0.256900	+	0.0387214i	−0.0193296	+	0.999813i	$0.506153\pi$
$440$	−3.17644e7	−	2.94730e7i	−0.372891	−	0.345993i
$441$	−841201.	+	1.05483e6i	−0.00980808	+	0.0122989i
$442$	1.59439e7	+	2.33854e7i	0.184641	+	0.270818i
$443$	−9.86375e7	+	9.15222e7i	−1.13457	+	1.05273i	−0.136498	+	0.990640i	$0.543585\pi$
$443$	−9.86375e7	+	9.15222e7i	−1.13457	+	1.05273i	−0.998071	+	0.0620859i	$0.980225\pi$
$444$	−6.56395e6	−	8.75898e7i	−0.0749922	−	1.00070i
$445$	3.52335e7	−	8.97734e7i	0.399830	−	1.01875i
$446$	3.49185e7	−	1.52988e8i	0.393596	−	1.72446i
$447$	5.15941e6	−	1.59147e6i	0.0577666	−	0.0178187i
$448$	1.84344e7	−	2.70384e7i	0.205020	−	0.300709i
$449$	−1.03959e6	−	6.89720e6i	−0.0114847	−	0.0761962i	0.982354	−	0.187030i	$-0.0598861\pi$
$449$	−1.03959e6	−	6.89720e6i	−0.0114847	−	0.0761962i	−0.993839	+	0.110833i	$0.964648\pi$
$450$	7.48098e6	−	2.93607e6i	0.0820958	−	0.0322202i
$451$	−1.90606e7	+	9.17908e6i	−0.207781	+	0.100062i
$452$	4.36250e7	+	9.05882e7i	0.472411	+	0.980971i
$453$	−7.96072e6	−	2.02836e7i	−0.0856363	−	0.218198i
$454$	−1.24825e8	+	1.88144e7i	−1.33393	+	0.201058i
$455$	−4.64732e7	−	3.16849e7i	−0.493365	−	0.336370i
$456$	1.27554e6	+	4.13518e6i	0.0134523	+	0.0436114i
$457$	−1.51838e8	−	3.46561e7i	−1.59086	−	0.363104i	−0.666768	−	0.745265i	$-0.732323\pi$
$457$	−1.51838e8	−	3.46561e7i	−1.59086	−	0.363104i	−0.924096	+	0.382161i	$0.875180\pi$
$458$	−2.11433e7	−	8.29813e6i	−0.220078	−	0.0863742i
$459$	4.04633e7	−	3.03230e6i	0.418430	−	0.0313570i
$460$	566757.	+	610819.i	0.00582269	+	0.00627537i
$461$	1.41045e6	−	961626.i	0.0143964	−	0.00981530i	−0.556100	−	0.831115i	$-0.687703\pi$
$461$	1.41045e6	−	961626.i	0.0143964	−	0.00981530i	0.570497	+	0.821300i	$0.306751\pi$
$462$	1.23574e8	+	9.85473e7i	1.25315	+	0.999353i
$463$	3.19593e7	−	3.44440e7i	0.321999	−	0.347033i	−0.551220	−	0.834360i	$-0.685838\pi$
$463$	3.19593e7	−	3.44440e7i	0.321999	−	0.347033i	0.873219	+	0.487327i	$0.162028\pi$
$464$	2.72187e7	−	1.80584e8i	0.272467	−	1.80770i
$465$	1.69383e7	+	7.42116e7i	0.168466	+	0.738096i
$466$	−8.79445e7	−	1.52324e8i	−0.869063	−	1.50526i
$467$	−7.47754e7	−	4.31716e7i	−0.734190	−	0.423885i	0.0857634	−	0.996316i	$-0.472667\pi$
$467$	−7.47754e7	−	4.31716e7i	−0.734190	−	0.423885i	−0.819953	+	0.572431i	$0.806000\pi$
$468$	−1.56975e7	−	4.84203e6i	−0.153141	−	0.0472379i
$469$	−225489.	+	179822.i	−0.00218579	+	0.00174311i
$470$	6.80420e6	−	9.07957e7i	0.0655365	−	0.874524i
$471$	−8.89492e7	−	4.28357e7i	−0.851294	−	0.409962i
$472$			3.41202e7i			0.324478i
$473$	1.53510e8	−	3.38367e7i	1.45062	−	0.319746i
$474$	−8.84008e7			−0.830082
$475$	1.33646e6	−	2.77518e6i	0.0124702	−	0.0258946i
$476$	−3.00165e7	−	2.24942e6i	−0.278316	−	0.0208569i
$477$	1.59283e7	+	1.99735e7i	0.146762	+	0.184034i
$478$	2.19162e7	−	7.10505e7i	0.200670	−	0.650555i
$479$	−9.32162e7	+	1.61455e8i	−0.848173	+	1.46908i	0.0346630	+	0.999399i	$0.488964\pi$
$479$	−9.32162e7	+	1.61455e8i	−0.848173	+	1.46908i	−0.882836	+	0.469681i	$0.844369\pi$
$480$	8.30227e7	−	4.79332e7i	0.750711	−	0.433423i
$481$	−1.23857e8	+	2.82695e7i	−1.11297	+	0.254028i
$482$	−4.27794e7	−	6.44796e6i	−0.382027	−	0.0575812i
$483$	918229.	+	851992.i	0.00814910	+	0.00756126i
$484$	−6.03992e7	+	7.57382e7i	−0.532715	+	0.668004i
$485$	4.39827e7	+	6.45107e7i	0.385528	+	0.565466i
$486$	−7.25379e7	+	6.73053e7i	−0.631911	+	0.586328i
$487$	−5.52080e6	−	7.36699e7i	−0.0477986	−	0.637828i	−0.968732	−	0.248108i	$-0.920191\pi$
$487$	−5.52080e6	−	7.36699e7i	−0.0477986	−	0.637828i	0.920934	−	0.389719i	$-0.127428\pi$
$488$	2.63582e7	−	6.71596e7i	0.226807	−	0.577895i
$489$	−2.05013e7	+	8.98221e7i	−0.175329	+	0.768169i
$490$	5.96522e6	−	1.84003e6i	0.0507036	−	0.0156400i
$491$	−1.39862e7	+	2.05139e7i	−0.118156	+	0.173302i	−0.880760	−	0.473562i	$-0.842968\pi$
$491$	−1.39862e7	+	2.05139e7i	−0.118156	+	0.173302i	0.762605	+	0.646865i	$0.223920\pi$
$492$	−1.57594e6	−	1.04557e7i	−0.0132326	−	0.0877924i
$493$	−6.51433e7	+	2.55669e7i	−0.543662	+	0.213372i
$494$	−1.36833e7	+	6.58951e6i	−0.113503	+	0.0546603i
$495$	−2.44138e7	−	5.06957e7i	−0.201289	−	0.417980i
$496$	5.61736e7	+	1.43128e8i	0.460349	+	1.17295i
$497$	2.52894e7	−	3.81176e6i	0.206001	−	0.0310496i
$498$	−4.12393e6	−	2.81165e6i	−0.0333905	−	0.0227653i
$499$	5.41302e7	+	1.75486e8i	0.435650	+	1.41234i	0.861596	+	0.507594i	$0.169465\pi$
$499$	5.41302e7	+	1.75486e8i	0.435650	+	1.41234i	−0.425946	+	0.904748i	$0.640059\pi$
$500$	−9.25080e7	−	2.11143e7i	−0.740064	−	0.168915i
$501$	7.42879e7	+	2.91559e7i	0.590752	+	0.231853i
$502$	−8.97864e7	+	6.72856e6i	−0.709740	+	0.0531877i
$503$	1.55408e7	+	1.67490e7i	0.122115	+	0.131609i	0.791150	−	0.611622i	$-0.209483\pi$
$503$	1.55408e7	+	1.67490e7i	0.122115	+	0.131609i	−0.669035	+	0.743231i	$0.733292\pi$
$504$	−1.43495e7	+	9.78333e6i	−0.112084	+	0.0764179i
$505$	2.22960e7	+	1.77805e7i	0.173122	+	0.138060i
$506$	−2.30352e6	+	2.48261e6i	−0.0177804	+	0.0191627i
$507$	−9.04708e6	+	6.00234e7i	−0.0694200	+	0.460571i
$508$	2.84801e7	+	1.24780e8i	0.217246	+	0.951815i
$509$	−7.52842e7	−	1.30396e8i	−0.570888	−	0.988806i	−0.996475	−	0.0838891i	$-0.973266\pi$
$509$	−7.52842e7	−	1.30396e8i	−0.570888	−	0.988806i	0.425587	−	0.904917i	$-0.360067\pi$
$510$	−4.19633e7	−	2.42275e7i	−0.316343	−	0.182641i
$511$	−1.64532e8	−	5.07516e7i	−1.23307	−	0.380353i
$512$	1.03098e8	−	8.22176e7i	0.768137	−	0.612569i
$513$	−1.62710e6	+	2.17121e7i	−0.0120521	+	0.160824i
$514$	2.81112e8	+	1.35377e8i	2.07010	+	0.996906i
$515$			2.05803e8i			1.50671i
$516$	−6.45476e6	+	7.83020e7i	−0.0469819	+	0.569933i
$517$	1.53418e8			1.11021
$518$	1.41402e8	−	2.93625e8i	1.01734	−	2.11253i
$519$	−7.01127e6	−	525422.i	−0.0501527	−	0.00375843i
$520$	−1.95306e7	−	2.44907e7i	−0.138901	−	0.174177i
$521$	−9.61668e6	+	3.11765e7i	−0.0680005	+	0.220452i	−0.983194	−	0.182562i	$-0.941561\pi$
$521$	−9.61668e6	+	3.11765e7i	−0.0680005	+	0.220452i	0.915194	+	0.403014i	$0.132037\pi$
$522$	4.89865e7	−	8.48471e7i	0.344401	−	0.596521i
$523$	8.38679e7	−	4.84212e7i	0.586261	−	0.338478i	−0.177357	−	0.984147i	$-0.556755\pi$
$523$	8.38679e7	−	4.84212e7i	0.586261	−	0.338478i	0.763618	+	0.645669i	$0.223421\pi$
$524$	−3.00252e7	+	6.85306e6i	−0.208685	+	0.0476311i
$525$	−2.29150e7	−	3.45389e6i	−0.158359	−	0.0238688i
$526$	−1.86894e8	−	1.73412e8i	−1.28422	−	1.19158i
$527$	3.67354e7	−	4.60647e7i	0.250988	−	0.314729i
$528$	1.20024e8	+	1.76043e8i	0.815393	+	1.19596i
$529$	1.08498e8	−	1.00672e8i	0.732919	−	0.680049i
$530$	−8.83342e6	−	1.17874e8i	−0.0593337	−	0.791753i
$531$	−1.61870e7	+	4.12438e7i	−0.108114	+	0.275470i
$532$	3.59408e6	−	1.57467e7i	0.0238700	−	0.104581i
$533$	−1.46141e7	+	4.50784e6i	−0.0965138	+	0.0297706i
$534$	−1.10360e8	+	1.61869e8i	−0.724751	+	1.06301i
$535$	−7.06151e6	−	4.68500e7i	−0.0461144	−	0.305949i
$536$	−149518.	+	58681.6i	−0.000970957	+	0.000381073i
$537$	−8.86471e7	+	4.26902e7i	−0.572456	+	0.275680i
$538$	1.55528e8	+	3.22958e8i	0.998763	+	2.07395i
$539$	3.84288e6	+	9.79151e6i	0.0245409	+	0.0625293i
$540$	1.07750e8	−	1.62408e7i	0.684286	−	0.103140i
$541$	1.21852e8	+	8.30772e7i	0.769557	+	0.524675i	0.883285	−	0.468837i	$-0.155327\pi$
$541$	1.21852e8	+	8.30772e7i	0.769557	+	0.524675i	−0.113728	+	0.993512i	$0.536279\pi$
$542$	−5.36909e7	−	1.74062e8i	−0.337212	−	1.09321i
$543$	1.77817e8	+	4.05855e7i	1.11064	+	0.253496i
$544$	−6.90737e7	−	2.71094e7i	−0.429058	−	0.168393i
$545$	1.97861e8	−	1.48276e7i	1.22228	−	0.0915973i
$546$	7.77170e7	+	8.37591e7i	0.477462	+	0.514581i
$547$	−1.55596e8	+	1.06084e8i	−0.950687	+	0.648168i	−0.936103	−	0.351726i	$-0.885595\pi$
$547$	−1.55596e8	+	1.06084e8i	−0.950687	+	0.648168i	−0.0145844	+	0.999894i	$0.504643\pi$
$548$	4.51689e7	+	3.60210e7i	0.274472	+	0.218884i
$549$	6.37224e7	−	6.86764e7i	0.385102	−	0.415041i
$550$	9.33825e6	−	6.19552e7i	0.0561277	−	0.372383i
$551$	−8.35585e6	−	3.66094e7i	−0.0499501	−	0.218846i
$552$	348800.	+	604140.i	0.00207377	+	0.00359187i
$553$	−1.17761e8	−	6.79892e7i	−0.696346	−	0.402036i
$554$	−3.72948e8	−	1.15039e8i	−2.19340	−	0.676575i
$555$	1.70043e8	−	1.35605e8i	0.994674	−	0.793226i
$556$	694739.	−	9.27064e6i	0.00404201	−	0.0539368i
$557$	−1.89191e8	−	9.11095e7i	−1.09480	−	0.527227i	−0.202780	−	0.979224i	$-0.564997\pi$
$557$	−1.89191e8	−	9.11095e7i	−1.09480	−	0.527227i	−0.892019	+	0.451997i	$0.850712\pi$
$558$			8.24864e7i			0.474766i
$559$	1.13379e8	−	7.64784e6i	0.649081	−	0.0437828i
$560$	1.94505e8			1.10756
$561$	3.54248e7	−	7.35604e7i	0.200641	−	0.416635i
$562$	2.22992e8	+	1.67109e7i	1.25626	+	0.0941438i
$563$	−1.03454e8	−	1.29728e8i	−0.579727	−	0.726955i	0.402339	−	0.915491i	$-0.368197\pi$
$563$	−1.03454e8	−	1.29728e8i	−0.579727	−	0.726955i	−0.982066	+	0.188536i	$0.939626\pi$
$564$	−2.26018e7	+	7.32733e7i	−0.125981	+	0.408422i
$565$	−1.24483e8	+	2.15610e8i	−0.690182	+	1.19543i
$566$	−2.94186e8	+	1.69849e8i	−1.62246	+	0.936726i
$567$	9.64973e7	−	2.20249e7i	0.529378	−	0.120827i
$568$	1.40841e7	+	2.12283e6i	0.0768570	+	0.0115843i
$569$	1.07165e8	+	9.94344e7i	0.581722	+	0.539759i	0.915201	−	0.402998i	$-0.132032\pi$
$569$	1.07165e8	+	9.94344e7i	0.581722	+	0.539759i	−0.333479	+	0.942758i	$0.608222\pi$
$570$	1.62110e7	−	2.03279e7i	0.0875355	−	0.109766i
$571$	6.35207e7	+	9.31677e7i	0.341198	+	0.500446i	0.958037	−	0.286643i	$-0.0925395\pi$
$571$	6.35207e7	+	9.31677e7i	0.341198	+	0.500446i	−0.616839	+	0.787089i	$0.711587\pi$
$572$	−9.38836e7	+	8.71112e7i	−0.501651	+	0.465464i
$573$	−1.94900e7	−	2.60076e8i	−0.103597	−	1.38241i
$574$	1.43332e7	−	3.65203e7i	0.0757891	−	0.193107i
$575$	110491.	−	484093.i	0.000581198	−	0.00254639i
$576$	2.26144e7	−	6.97562e6i	0.118336	−	0.0365019i
$577$	−6.77877e7	+	9.94263e7i	−0.352877	+	0.517576i	−0.961104	−	0.276188i	$-0.910929\pi$
$577$	−6.77877e7	+	9.94263e7i	−0.352877	+	0.517576i	0.608227	+	0.793763i	$0.291881\pi$
$578$	−3.20247e7	−	2.12470e8i	−0.165845	−	1.10031i
$579$	2.70836e8	−	1.06295e8i	1.39531	−	0.547620i
$580$	−1.69320e8	+	8.15404e7i	−0.867811	+	0.417916i
$581$	−3.33114e6	−	6.91719e6i	−0.0169850	−	0.0352696i
$582$	−5.79462e7	−	1.47645e8i	−0.293938	−	0.748943i
$583$	1.96948e8	−	2.96851e7i	0.993907	−	0.149807i
$584$	−7.92290e7	−	5.40174e7i	−0.397782	−	0.271203i
$585$	−1.19896e7	−	3.88693e7i	−0.0598876	−	0.194151i
$586$	−3.23724e8	−	7.38880e7i	−1.60873	−	0.367182i
$587$	3.12199e8	+	1.22529e8i	1.54354	+	0.605794i	0.976042	−	0.217583i	$-0.0698172\pi$
$587$	3.12199e8	+	1.22529e8i	1.54354	+	0.605794i	0.567496	+	0.823376i	$0.307912\pi$
$588$	−5.24261e6	+	392879.i	−0.0257879	+	0.00193253i
$589$	2.15038e7	+	2.31756e7i	0.105237	+	0.113419i
$590$	1.69381e8	−	1.15482e8i	0.824726	−	0.562288i
$591$	−6.18496e7	−	4.93234e7i	−0.299623	−	0.238941i
$592$	2.98814e8	−	3.22044e8i	1.44024	−	1.55221i
$593$	−4.18635e7	+	2.77746e8i	−0.200757	+	1.33194i	0.630561	+	0.776140i	$0.282825\pi$
$593$	−4.18635e7	+	2.77746e8i	−0.200757	+	1.33194i	−0.831318	+	0.555797i	$0.812413\pi$
$594$	9.85516e7	+	4.31783e8i	0.470224	+	2.06018i
$595$	−3.72668e7	−	6.45481e7i	−0.176918	−	0.306431i
$596$	−9.71947e6	−	5.61154e6i	−0.0459096	−	0.0265059i
$597$	−2.01225e8	−	6.20696e7i	−0.945711	−	0.291713i
$598$	−1.91412e6	+	1.52646e6i	−0.00895086	+	0.00713808i
$599$	1.38186e7	−	1.84396e8i	0.0642960	−	0.857970i	−0.868067	−	0.496447i	$-0.834638\pi$
$599$	1.38186e7	−	1.84396e8i	0.0642960	−	0.857970i	0.932363	−	0.361523i	$-0.117743\pi$
$600$	−1.16278e7	−	5.59967e6i	−0.0538326	−	0.0259244i
$601$			2.07091e7i			0.0953978i	0.998862	+	0.0476989i	$0.0151888\pi$
$601$			2.07091e7i			0.0953978i	−0.998862	+	0.0476989i	$0.984811\pi$
$602$	−1.66004e8	+	2.39629e8i	−0.760903	+	1.09837i
$603$	−208574.			−0.000951278
$604$	−1.96519e7	+	4.08075e7i	−0.0891852	+	0.185195i
$605$	−2.39201e8	−	1.79256e7i	−1.08018	−	0.0809484i
$606$	−3.61197e7	−	4.52927e7i	−0.162303	−	0.203521i
$607$	−5.60321e7	+	1.81652e8i	−0.250536	+	0.812219i	0.739714	+	0.672921i	$0.234961\pi$
$607$	−5.60321e7	+	1.81652e8i	−0.250536	+	0.812219i	−0.990251	+	0.139298i	$0.955516\pi$
$608$	1.99082e7	−	3.44821e7i	0.0885773	−	0.153420i
$609$	−2.44663e8	+	1.41256e8i	−1.08322	+	0.625397i
$610$	−4.22608e8	+	9.64576e7i	−1.86187	+	0.424959i
$611$	1.09668e8	+	1.65298e7i	0.480792	+	0.0724678i
$612$	−1.59572e7	−	1.48061e7i	−0.0696150	−	0.0645933i
$613$	−1.80232e8	+	2.26003e8i	−0.782438	+	0.981146i	0.217549	+	0.976049i	$0.430194\pi$
$613$	−1.80232e8	+	2.26003e8i	−0.782438	+	0.981146i	−0.999987	+	0.00509683i	$0.998378\pi$
$614$	−3.86572e7	−	5.66997e7i	−0.167003	−	0.244949i
$615$	1.91930e7	−	1.78085e7i	0.0825119	−	0.0765599i
$616$	1.01185e7	+	1.35022e8i	0.0432886	+	0.577646i
$617$	−8.97018e7	+	2.28556e8i	−0.381896	+	0.973056i	0.602662	+	0.797997i	$0.294107\pi$
$617$	−8.97018e7	+	2.28556e8i	−0.381896	+	0.973056i	−0.984558	+	0.175059i	$0.943988\pi$
$618$	9.30301e7	−	4.07591e8i	0.394147	−	1.72687i
$619$	4.37112e8	−	1.34831e8i	1.84298	−	0.568484i	0.843470	−	0.537176i	$-0.180509\pi$
$619$	4.37112e8	−	1.34831e8i	1.84298	−	0.568484i	0.999510	−	0.0313077i	$-0.00996719\pi$
$620$	8.91314e7	−	1.30732e8i	0.373986	−	0.548537i
$621$	523122.	+	3.47069e6i	0.00218438	+	0.0144924i
$622$	−9.63837e7	+	3.78278e7i	−0.400527	+	0.157195i
$623$	−2.71507e8	+	1.30751e8i	−1.12284	+	0.540730i
$624$	6.68295e7	+	1.38773e8i	0.275052	+	0.571151i
$625$	−6.85368e7	−	1.74629e8i	−0.280727	−	0.715280i
$626$	2.46262e8	−	3.71180e7i	1.00386	−	0.151308i
$627$	3.61977e7	+	2.46792e7i	0.146852	+	0.100122i
$628$	6.04881e7	+	1.96098e8i	0.244226	+	0.791760i
$629$	−1.64125e8	−	3.74605e7i	−0.659512	−	0.150529i
$630$	9.71339e7	+	3.81222e7i	0.388462	+	0.152460i
$631$	7.00316e7	−	5.24814e6i	0.278744	−	0.0208890i	0.0653755	−	0.997861i	$-0.479175\pi$
$631$	7.00316e7	−	5.24814e6i	0.278744	−	0.0208890i	0.213369	+	0.976972i	$0.431556\pi$
$632$	−5.15086e7	−	5.55131e7i	−0.204046	−	0.219910i
$633$	2.74622e8	−	1.87234e8i	1.08274	−	0.738199i
$634$	1.91501e7	+	1.52717e7i	0.0751457	+	0.0599267i
$635$	−2.15560e8	+	2.32318e8i	−0.841872	+	0.907322i
$636$	−1.48369e7	+	9.84365e7i	−0.0576730	+	0.382635i
$637$	1.69204e6	+	7.41332e6i	0.00654626	+	0.0286810i
$638$	−3.81913e8	−	6.61493e8i	−1.47063	−	2.54720i
$639$	1.60174e7	+	9.24767e6i	0.0613890	+	0.0354430i
$640$	1.64258e8	+	5.06668e7i	0.626593	+	0.193278i
$641$	−1.15274e8	+	9.19283e7i	−0.437682	+	0.349040i	−0.817408	−	0.576059i	$-0.804590\pi$
$641$	−1.15274e8	+	9.19283e7i	−0.437682	+	0.349040i	0.379726	+	0.925099i	$0.376018\pi$
$642$	−7.19257e6	+	9.59781e7i	−0.0271818	+	0.362716i
$643$	−1.70875e8	−	8.22889e7i	−0.642754	−	0.309534i	0.0839654	−	0.996469i	$-0.473241\pi$
$643$	−1.70875e8	−	8.22889e7i	−0.642754	−	0.309534i	−0.726719	+	0.686935i	$0.758956\pi$
$644$		−	2.60371e6i		−	0.00974843i
$645$	−1.69201e8	+	9.60149e7i	−0.630555	+	0.357816i
$646$	−2.01250e7			−0.0746514
$647$	−1.17036e8	+	2.43027e8i	−0.432121	+	0.897309i	0.565255	+	0.824916i	$0.308778\pi$
$647$	−1.17036e8	+	2.43027e8i	−0.432121	+	0.897309i	−0.997376	+	0.0723930i	$0.976936\pi$
$648$	5.49689e7	+	4.11935e6i	0.202019	+	0.0151392i
$649$	2.15370e8	+	2.70066e8i	0.787864	+	0.987950i
$650$	1.33505e7	−	4.32814e7i	0.0486137	−	0.157602i
$651$	1.18928e8	−	2.05989e8i	0.431063	−	0.746623i
$652$	1.65851e8	−	9.57540e7i	0.598377	−	0.345473i
$653$	5.07833e7	−	1.15910e7i	0.182382	−	0.0416275i	−0.130354	−	0.991467i	$-0.541612\pi$
$653$	5.07833e7	−	1.15910e7i	0.182382	−	0.0416275i	0.312736	+	0.949840i	$0.398754\pi$
$654$	−3.98565e8	−	6.00740e7i	−1.42484	−	0.214760i
$655$	−5.59017e7	−	5.18692e7i	−0.198930	−	0.184580i
$656$	3.29740e7	−	4.13480e7i	0.116805	−	0.146468i
$657$	−7.01438e7	−	1.02882e8i	−0.247339	−	0.362780i
$658$	−2.08560e8	+	1.93515e8i	−0.732071	+	0.679262i
$659$	−2.12481e7	−	2.83536e8i	−0.0742443	−	0.990721i	−0.902589	−	0.430503i	$-0.858336\pi$
$659$	−2.12481e7	−	2.83536e8i	−0.0742443	−	0.990721i	0.828345	−	0.560218i	$-0.189283\pi$
$660$	8.01038e7	−	2.04101e8i	0.278626	−	0.709927i
$661$	4.30271e7	−	1.88514e8i	0.148983	−	0.652739i	−0.844185	−	0.536051i	$-0.819915\pi$
$661$	4.30271e7	−	1.88514e8i	0.148983	−	0.652739i	0.993169	−	0.116687i	$-0.0372275\pi$
$662$	5.97680e8	−	1.84360e8i	2.06013	−	0.635467i
$663$	3.32485e7	−	4.87665e7i	0.114086	−	0.167333i
$664$	−637265.	−	4.22797e6i	−0.00217678	−	0.0144420i
$665$	3.72292e7	−	1.46114e7i	0.126596	−	0.0496852i
$666$	2.12344e8	−	1.02259e8i	0.718815	−	0.346163i
$667$	−2.62645e6	−	5.45388e6i	−0.00885098	−	0.0183793i
$668$	−6.06041e7	−	1.54417e8i	−0.203317	−	0.518042i
$669$	−3.23582e8	+	4.87721e7i	−1.08070	+	0.162889i
$670$	797366.	+	543635.i	0.00265114	+	0.00180752i
$671$	−2.15290e8	−	6.97952e8i	−0.712616	−	2.31024i
$672$	−2.92047e8	−	6.66578e7i	−0.962377	−	0.219656i
$673$	2.35830e8	+	9.25564e7i	0.773666	+	0.303642i	0.719135	−	0.694871i	$-0.244538\pi$
$673$	2.35830e8	+	9.25564e7i	0.773666	+	0.303642i	0.0545312	+	0.998512i	$0.482634\pi$
$674$	−6.67251e7	+	5.00035e6i	−0.217926	+	0.0163313i
$675$	−4.41667e7	−	4.76004e7i	−0.143610	−	0.154774i
$676$	1.04251e8	−	7.10772e7i	0.337474	−	0.230086i
$677$	−3.13808e8	−	2.50254e8i	−1.01134	−	0.806519i	−0.0301488	−	0.999545i	$-0.509598\pi$
$677$	−3.13808e8	−	2.50254e8i	−1.01134	−	0.806519i	−0.981193	+	0.193027i	$0.938170\pi$
$678$	3.44000e8	−	3.70744e8i	1.10375	−	1.18956i
$679$	3.63622e7	−	2.41247e8i	0.116156	−	0.770643i
$680$	−9.23664e6	−	4.04684e7i	−0.0293756	−	0.128703i
$681$	1.31622e8	+	2.27976e8i	0.416760	+	0.721850i
$682$	5.56931e8	+	3.21544e8i	1.75569	+	1.01365i
$683$	3.16733e8	+	9.76991e7i	0.994102	+	0.306640i	0.748792	−	0.662805i	$-0.230634\pi$
$683$	3.16733e8	+	9.76991e7i	0.994102	+	0.306640i	0.245310	+	0.969445i	$0.421110\pi$
$684$	9.13222e6	−	7.28270e6i	0.0285370	−	0.0227575i
$685$	−1.06905e7	+	1.42655e8i	−0.0332603	+	0.443828i
$686$	3.71067e8	+	1.78697e8i	1.14942	+	0.553533i
$687$			4.73652e7i			0.146080i
$688$	−3.09049e8	+	2.42715e8i	−0.948992	+	0.745300i
$689$	1.43983e8			0.440203
$690$	1.81856e6	−	3.77629e6i	0.00553581	−	0.0114952i
$691$	−2.19869e8	−	1.64769e7i	−0.666391	−	0.0499391i	−0.262760	−	0.964861i	$-0.584633\pi$
$691$	−2.19869e8	−	1.64769e7i	−0.666391	−	0.0499391i	−0.403631	+	0.914922i	$0.632252\pi$
$692$	9.11209e6	+	1.14262e7i	0.0274979	+	0.0344813i
$693$	−5.18248e7	+	1.68012e8i	−0.155718	+	0.504824i
$694$	−1.16372e8	+	2.01563e8i	−0.348154	+	0.603020i
$695$	1.99358e7	−	1.15099e7i	0.0593853	−	0.0342861i
$696$	−1.53391e8	+	3.50105e7i	−0.454960	+	0.103842i
$697$	−2.00394e7	−	3.02046e6i	−0.0591816	−	0.00892019i
$698$	5.23619e8	+	4.85847e8i	1.53975	+	1.42868i
$699$	−2.28689e8	+	2.86767e8i	−0.669598	+	0.839649i
$700$	2.71350e7	+	3.97997e7i	0.0791108	+	0.116034i
$701$	−3.17584e8	+	2.94675e8i	−0.921944	+	0.855439i	−0.989830	−	0.142254i	$-0.954565\pi$
$701$	−3.17584e8	+	2.94675e8i	−0.921944	+	0.855439i	0.0678864	+	0.997693i	$0.478374\pi$
$702$	2.39260e7	+	3.19270e8i	0.0691606	+	0.922884i
$703$	3.30021e7	−	8.40880e7i	0.0949896	−	0.242029i
$704$	4.10564e7	−	1.79880e8i	0.117669	−	0.515542i
$705$	−1.81436e8	+	5.59655e7i	−0.517792	+	0.159718i
$706$	−2.55627e8	+	3.74936e8i	−0.726427	+	1.06547i
$707$	−1.32812e7	−	8.81151e7i	−0.0375820	−	0.249340i
$708$	−1.60713e8	+	6.30753e7i	−0.452847	+	0.177729i
$709$	1.10673e8	−	5.32972e7i	0.310529	−	0.149543i	−0.272128	−	0.962261i	$-0.587727\pi$
$709$	1.10673e8	−	5.32972e7i	0.310529	−	0.149543i	0.582657	+	0.812718i	$0.302013\pi$
$710$	−3.71303e7	−	7.71019e7i	−0.103742	−	0.215422i
$711$	−3.59265e7	−	9.15392e7i	−0.0999554	−	0.254682i
$712$	−1.65952e8	+	2.50133e7i	−0.459773	+	0.0692997i
$713$	4.21092e6	+	2.87096e6i	0.0116174	+	0.00792060i
$714$	4.46287e7	+	1.44683e8i	0.122608	+	0.397486i
$715$	−3.09175e8	−	7.05671e7i	−0.845836	−	0.193057i
$716$	1.90380e8	+	7.47187e7i	0.518660	+	0.203559i
$717$	−1.54620e8	+	1.15872e7i	−0.419476	+	0.0314354i
$718$	5.99824e8	+	6.46457e8i	1.62051	+	1.74649i
$719$	4.74513e8	−	3.23517e8i	1.27662	−	0.870384i	0.280626	−	0.959817i	$-0.409458\pi$
$719$	4.74513e8	−	3.23517e8i	1.27662	−	0.870384i	0.995993	+	0.0894334i	$0.0285056\pi$
$720$	1.09974e8	+	8.77015e7i	0.294641	+	0.234968i
$721$	4.37407e8	−	4.71413e8i	1.16702	−	1.25775i
$722$	−7.17041e7	+	4.75726e8i	−0.190516	+	1.26399i
$723$	2.00753e7	+	8.79554e7i	0.0531185	+	0.232728i
$724$	−1.89560e8	−	3.28327e8i	−0.499494	−	0.865149i
$725$	9.69859e7	+	5.59948e7i	0.254504	+	0.146938i
$726$	4.65632e8	+	1.43628e8i	1.21684	+	0.375345i
$727$	2.47000e8	−	1.96976e8i	0.642828	−	0.512638i	−0.246952	−	0.969028i	$-0.579429\pi$
$727$	2.47000e8	−	1.96976e8i	0.642828	−	0.512638i	0.889780	+	0.456390i	$0.150858\pi$
$728$	−7.31471e6	+	9.76080e7i	−0.0189585	+	0.252983i
$729$	3.71305e8	+	1.78811e8i	0.958402	+	0.461542i
$730$			5.76139e8i			1.48101i
$731$	1.39760e8	+	5.60567e7i	0.357792	+	0.143508i
$732$	3.65062e8			0.930750
$733$	1.20404e8	−	2.50021e8i	0.305723	−	0.634841i	−0.690340	−	0.723485i	$-0.742539\pi$
$733$	1.20404e8	−	2.50021e8i	0.305723	−	0.634841i	0.996063	+	0.0886442i	$0.0282534\pi$
$734$	−7.96370e8	−	5.96797e7i	−2.01385	−	0.150917i
$735$	−8.11652e6	−	1.01778e7i	−0.0204413	−	0.0256325i
$736$	1.89191e6	−	6.13342e6i	0.00474533	−	0.0153840i
$737$	−813051.	+	1.40825e6i	−0.00203103	+	0.00351784i
$738$	2.45709e7	−	1.41860e7i	0.0611297	−	0.0352932i
$739$	1.84134e8	−	4.20273e7i	0.456247	−	0.104135i	0.0117798	−	0.999931i	$-0.496250\pi$
$739$	1.84134e8	−	4.20273e7i	0.456247	−	0.104135i	0.444467	+	0.895795i	$0.353393\pi$
$740$	−4.47038e8	−	6.73802e7i	−1.10319	−	0.166279i
$741$	2.32162e7	+	2.15415e7i	0.0570607	+	0.0529446i
$742$	−2.30291e8	+	2.88776e8i	−0.563723	+	0.706886i
$743$	2.54977e8	+	3.73983e8i	0.621634	+	0.911769i	0.999903	−	0.0139264i	$-0.00443306\pi$
$743$	2.54977e8	+	3.73983e8i	0.621634	+	0.911769i	−0.378269	+	0.925696i	$0.623481\pi$
$744$	9.71044e7	−	9.00997e7i	0.235787	−	0.218778i
$745$	−2.07675e6	−	2.77123e7i	−0.00502245	−	0.0670199i
$746$	1.47371e8	−	3.75496e8i	0.354974	−	0.904459i
$747$	1.23548e6	−	5.41301e6i	0.00296398	−	0.0129860i
$748$	−1.62172e8	+	5.00233e7i	−0.387498	+	0.119527i
$749$	−8.33984e7	+	1.22323e8i	−0.198478	+	0.291114i
$750$	7.11366e7	+	4.71961e8i	0.168620	+	1.11872i
$751$	2.13090e8	−	8.36317e7i	0.503088	−	0.197447i	−0.100206	−	0.994967i	$-0.531950\pi$
$751$	2.13090e8	−	8.36317e7i	0.503088	−	0.197447i	0.603293	+	0.797519i	$0.293855\pi$
$752$	−3.45544e8	+	1.66405e8i	−0.812550	+	0.391303i

Introduction	Features
Universe	News

Level:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	43.h (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.53656 + 9.42027i) q^{2} +(21.7428 + 1.62939i) q^{3} +(-28.2577 - 35.4340i) q^{4} +(33.0785 - 107.238i) q^{5} +(-113.987 + 197.431i) q^{6} +(-303.689 + 175.335i) q^{7} +(-190.398 + 43.4570i) q^{8} +(-250.765 - 37.7967i) q^{9} +O(q^{10})\)	\(q+(-4.53656 + 9.42027i) q^{2} +(21.7428 + 1.62939i) q^{3} +(-28.2577 - 35.4340i) q^{4} +(33.0785 - 107.238i) q^{5} +(-113.987 + 197.431i) q^{6} +(-303.689 + 175.335i) q^{7} +(-190.398 + 43.4570i) q^{8} +(-250.765 - 37.7967i) q^{9} +(860.145 + 798.098i) q^{10} +(-1232.71 + 1545.78i) q^{11} +(-556.664 - 816.476i) q^{12} +(-1047.73 + 972.152i) q^{13} +(-273.998 - 3656.25i) q^{14} +(893.950 - 2277.75i) q^{15} +(1099.82 - 4818.61i) q^{16} +(-1809.82 + 558.254i) q^{17} +(1493.66 - 2190.80i) q^{18} +(-151.468 - 1004.92i) q^{19} +(-4734.58 + 1858.19i) q^{20} +(-6888.72 + 3317.43i) q^{21} +(-8969.33 - 18625.0i) q^{22} +(-59.8530 - 152.503i) q^{23} +(-4210.58 + 634.642i) q^{24} +(2504.23 + 1707.36i) q^{25} +(-4404.83 - 14280.1i) q^{26} +(-20887.1 - 4767.35i) q^{27} +(14794.4 + 5806.35i) q^{28} +(36846.2 - 2761.24i) q^{29} +(17401.5 + 18754.4i) q^{30} +(-25703.4 + 17524.3i) q^{31} +(30631.2 + 24427.6i) q^{32} +(-29321.3 + 31600.8i) q^{33} +(2951.44 - 19581.5i) q^{34} +(8756.95 + 38366.7i) q^{35} +(5746.74 + 9953.65i) q^{36} +(76977.3 + 44442.8i) q^{37} +(10153.8 + 3132.03i) q^{38} +(-24364.6 + 19430.1i) q^{39} +(-1637.83 + 21855.3i) q^{40} +(9640.56 + 4642.65i) q^{41} -79943.3i q^{42} +(-61790.1 - 50033.4i) q^{43} +89606.6 q^{44} +(-12348.1 + 25641.2i) q^{45} +(1708.14 + 128.008i) q^{46} +(-48380.9 - 60667.7i) q^{47} +(31764.5 - 102978. i) q^{48} +(2660.09 - 4607.40i) q^{49} +(-27444.4 + 15845.0i) q^{50} +(-40260.0 + 9189.09i) q^{51} +(64053.6 + 9654.53i) q^{52} +(-73846.7 - 68519.7i) q^{53} +(139665. - 175135. i) q^{54} +(124989. + 183325. i) q^{55} +(50202.1 - 46580.7i) q^{56} +(-1655.91 - 22096.6i) q^{57} +(-141143. + 359627. i) q^{58} +(38877.1 - 170332. i) q^{59} +(-105971. + 32687.6i) q^{60} +(-208106. + 305235. i) q^{61} +(-48478.3 - 321632. i) q^{62} +(82781.5 - 32489.4i) q^{63} +(-84078.8 + 40490.2i) q^{64} +(69594.0 + 144513. i) q^{65} +(-164670. - 419574. i) q^{66} +(813.274 - 122.581i) q^{67} +(70922.4 + 48354.0i) q^{68} +(-1052.88 - 3413.36i) q^{69} +(-401151. - 91560.1i) q^{70} +(-67890.5 - 26645.0i) q^{71} +(49387.5 - 3701.08i) q^{72} +(333971. + 359935. i) q^{73} +(-767875. + 523529. i) q^{74} +(51667.0 + 41203.1i) q^{75} +(-31328.4 + 33764.0i) q^{76} +(103333. - 685572. i) q^{77} +(-72505.3 - 317667. i) q^{78} +(193884. + 335817. i) q^{79} +(-480357. - 277334. i) q^{80} +(-269717. - 83196.7i) q^{81} +(-87470.0 + 69755.0i) q^{82} +(-1636.13 + 21832.6i) q^{83} +(312209. + 150352. i) q^{84} +212547. i q^{85} +(751643. - 355100. i) q^{86} +805637. q^{87} +(167531. - 347882. i) q^{88} +(856953. + 64219.7i) q^{89} +(-185529. - 232646. i) q^{90} +(147732. - 478935. i) q^{91} +(-3712.48 + 6430.21i) q^{92} +(-587416. + 339145. i) q^{93} +(790989. - 180538. i) q^{94} +(-112776. - 16998.3i) q^{95} +(626206. + 581034. i) q^{96} +(-433782. + 543946. i) q^{97} +(31335.3 + 45960.5i) q^{98} +(367547. - 341033. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 252q - 14q^{2} - 11q^{3} + 1180q^{4} - 11q^{5} - 118q^{6} + 126q^{7} - 2254q^{8} - 8178q^{9} + O(q^{10}) \)	\( 252q - 14q^{2} - 11q^{3} + 1180q^{4} - 11q^{5} - 118q^{6} + 126q^{7} - 2254q^{8} - 8178q^{9} + 967q^{10} + 4090q^{11} - 484q^{12} + 1527q^{13} + 7812q^{14} - 8923q^{15} - 13760q^{16} - 3655q^{17} + 5596q^{18} + 38605q^{19} + 26085q^{20} + 24873q^{21} - 25214q^{22} + 27991q^{23} - 20480q^{24} - 24146q^{25} - 34923q^{26} - 14q^{27} - 77634q^{28} - 112735q^{29} + 375072q^{30} + 290647q^{31} - 344064q^{32} - 152174q^{33} - 198311q^{34} - 182471q^{35} - 930891q^{36} + 282762q^{37} + 487342q^{38} + 857290q^{39} + 745459q^{40} + 27674q^{41} + 148802q^{43} - 1255832q^{44} - 191310q^{45} - 1344785q^{46} + 69166q^{47} - 871241q^{48} + 1786604q^{49} + 837705q^{50} - 182756q^{51} + 2906416q^{52} + 7779q^{53} + 487154q^{54} - 529592q^{55} - 2464007q^{56} - 767855q^{57} - 1523780q^{58} + 1531338q^{59} - 1858647q^{60} + 646957q^{61} - 448559q^{62} - 2007847q^{63} + 3937366q^{64} - 1473542q^{65} + 1513319q^{66} - 575523q^{67} + 2717157q^{68} + 967041q^{69} + 4624473q^{70} - 2149319q^{71} - 9986371q^{72} - 514565q^{73} - 882972q^{74} - 6655138q^{75} + 1152658q^{76} - 341803q^{77} + 6322388q^{78} - 2476742q^{79} + 10750038q^{80} + 4308941q^{81} + 5079172q^{82} + 2318609q^{83} + 5578407q^{84} + 585292q^{86} - 1990710q^{87} - 2864890q^{88} - 4561993q^{89} - 17681545q^{90} - 4648506q^{91} - 1991714q^{92} - 8868294q^{93} - 10200218q^{94} + 10091737q^{95} + 6250318q^{96} - 1676750q^{97} + 7512700q^{98} + 18452884q^{99} + O(q^{100}) \)

\(n\)	\(3\)
\(\chi(n)\)	\(e\left(\frac{1}{42}\right)\)

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