LMFDB - Embedded newform 43.7.h.a.3.17

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			3.17
Character	$\chi$	$=$	43.3
Dual form			43.7.h.a.29.17

$q$-expansion

$f(q)$	$=$	$q+(4.47573 - 9.29395i) q^{2} +(30.6638 + 2.29794i) q^{3} +(-26.4420 - 33.1572i) q^{4} +(-67.0797 + 217.467i) q^{5} +(158.600 - 274.703i) q^{6} +(521.839 - 301.284i) q^{7} +(217.132 - 49.5589i) q^{8} +(214.131 + 32.2751i) q^{9} +O(q^{10})$	\(q+(4.47573 - 9.29395i) q^{2} +(30.6638 + 2.29794i) q^{3} +(-26.4420 - 33.1572i) q^{4} +(-67.0797 + 217.467i) q^{5} +(158.600 - 274.703i) q^{6} +(521.839 - 301.284i) q^{7} +(217.132 - 49.5589i) q^{8} +(214.131 + 32.2751i) q^{9} +(1720.90 + 1596.76i) q^{10} +(1090.36 - 1367.27i) q^{11} +(-734.619 - 1077.49i) q^{12} +(-2017.10 + 1871.60i) q^{13} +(-464.506 - 6198.41i) q^{14} +(-2556.64 + 6514.23i) q^{15} +(1115.19 - 4885.99i) q^{16} +(-1266.53 + 390.672i) q^{17} +(1258.36 - 1845.67i) q^{18} +(897.955 + 5957.54i) q^{19} +(8984.32 - 3526.08i) q^{20} +(16693.9 - 8039.36i) q^{21} +(-7827.16 - 16253.3i) q^{22} +(-478.704 - 1219.72i) q^{23} +(6771.96 - 1020.71i) q^{24} +(-29882.3 - 20373.4i) q^{25} +(8366.53 + 27123.6i) q^{26} +(-15362.7 - 3506.43i) q^{27} +(-23788.2 - 9336.17i) q^{28} +(8931.60 - 669.331i) q^{29} +(49100.0 + 52917.2i) q^{30} +(-6189.16 + 4219.70i) q^{31} +(-29274.7 - 23345.8i) q^{32} +(36576.5 - 39420.0i) q^{33} +(-2037.75 + 13519.6i) q^{34} +(30514.5 + 133693. i) q^{35} +(-4591.90 - 7953.41i) q^{36} +(-7270.58 - 4197.67i) q^{37} +(59388.1 + 18318.8i) q^{38} +(-66152.9 + 52755.2i) q^{39} +(-3787.70 + 50543.4i) q^{40} +(-33757.3 - 16256.7i) q^{41} -191134. i q^{42} +(-42463.6 + 67217.6i) q^{43} -74166.0 q^{44} +(-21382.6 + 44401.5i) q^{45} +(-13478.5 - 1010.08i) q^{46} +(-74746.9 - 93729.6i) q^{47} +(45423.8 - 147260. i) q^{48} +(122719. - 212556. i) q^{49} +(-323094. + 186538. i) q^{50} +(-39734.3 + 9069.10i) q^{51} +(115393. + 17392.7i) q^{52} +(14520.8 + 13473.4i) q^{53} +(-101348. + 127086. i) q^{54} +(224195. + 328833. i) q^{55} +(98376.4 - 91279.9i) q^{56} +(13844.7 + 184744. i) q^{57} +(33754.7 - 86005.5i) q^{58} +(44337.5 - 194255. i) q^{59} +(283596. - 87477.8i) q^{60} +(-144301. + 211650. i) q^{61} +(11516.6 + 76408.0i) q^{62} +(121466. - 47671.9i) q^{63} +(-59019.6 + 28422.3i) q^{64} +(-271704. - 564200. i) q^{65} +(-202662. - 516373. i) q^{66} +(-309393. + 46633.5i) q^{67} +(46443.1 + 31664.4i) q^{68} +(-11876.1 - 38501.2i) q^{69} +(1.37911e6 + 314772. i) q^{70} +(387116. + 151932. i) q^{71} +(48094.2 - 3604.16i) q^{72} +(255790. + 275676. i) q^{73} +(-71554.1 + 48784.7i) q^{74} +(-869487. - 693393. i) q^{75} +(173792. - 187303. i) q^{76} +(157056. - 1.04200e6i) q^{77} +(194221. + 850939. i) q^{78} +(-113798. - 197103. i) q^{79} +(987734. + 570269. i) q^{80} +(-613871. - 189354. i) q^{81} +(-302177. + 240978. i) q^{82} +(-26640.0 + 355486. i) q^{83} +(-707982. - 340946. i) q^{84} -301634. i q^{85} +(434661. + 695502. i) q^{86} +275415. q^{87} +(168991. - 350914. i) q^{88} +(-1.30720e6 - 97961.3i) q^{89} +(316962. + 397458. i) q^{90} +(-488720. + 1.58439e6i) q^{91} +(-27784.5 + 48124.2i) q^{92} +(-199480. + 115170. i) q^{93} +(-1.20567e6 + 275185. i) q^{94} +(-1.35580e6 - 204355. i) q^{95} +(-844028. - 783144. i) q^{96} +(156144. - 195799. i) q^{97} +(-1.42623e6 - 2.09189e6i) q^{98} +(277609. - 257583. 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 $

$2$	4.47573	−	9.29395i	0.559466	−	1.16174i	−0.408985	−	0.912541i	$-0.634117\pi$
$2$	4.47573	−	9.29395i	0.559466	−	1.16174i	0.968451	−	0.249203i	$-0.0801685\pi$
$3$	30.6638	+	2.29794i	1.13570	+	0.0851087i	0.629279	−	0.777180i	$-0.283350\pi$
$3$	30.6638	+	2.29794i	1.13570	+	0.0851087i	0.506418	+	0.862288i	$0.330969\pi$
$4$	−26.4420	−	33.1572i	−0.413156	−	0.518081i
$5$	−67.0797	+	217.467i	−0.536638	+	1.73974i	0.127217	+	0.991875i	$0.459396\pi$
$5$	−67.0797	+	217.467i	−0.536638	+	1.73974i	−0.663855	+	0.747862i	$0.731081\pi$
$6$	158.600	−	274.703i	0.734258	−	1.27177i
$7$	521.839	−	301.284i	1.52140	−	0.878378i	0.521715	−	0.853120i	$-0.325293\pi$
$7$	521.839	−	301.284i	1.52140	−	0.878378i	0.999681	−	0.0252582i	$-0.00804078\pi$
$8$	217.132	−	49.5589i	0.424085	−	0.0967946i
$9$	214.131	+	32.2751i	0.293733	+	0.0442731i
$10$	1720.90	+	1596.76i	1.72090	+	1.59676i
$11$	1090.36	−	1367.27i	0.819203	−	1.02725i	−0.179848	−	0.983694i	$-0.557561\pi$
$11$	1090.36	−	1367.27i	0.819203	−	1.02725i	0.999051	−	0.0435536i	$-0.0138679\pi$
$12$	−734.619	−	1077.49i	−0.425127	−	0.623546i
$13$	−2017.10	+	1871.60i	−0.918117	+	0.851888i	−0.989348	−	0.145572i	$-0.953498\pi$
$13$	−2017.10	+	1871.60i	−0.918117	+	0.851888i	0.0712307	+	0.997460i	$0.477307\pi$
$14$	−464.506	−	6198.41i	−0.169281	−	2.25889i
$15$	−2556.64	+	6514.23i	−0.757524	+	1.93014i
$16$	1115.19	−	4885.99i	0.272264	−	1.19287i
$17$	−1266.53	+	390.672i	−0.257791	+	0.0795181i	−0.420957	−	0.907081i	$-0.638306\pi$
$17$	−1266.53	+	390.672i	−0.257791	+	0.0795181i	0.163166	+	0.986599i	$0.447829\pi$
$18$	1258.36	−	1845.67i	0.215768	−	0.316473i
$19$	897.955	+	5957.54i	0.130916	+	0.868573i	0.953817	+	0.300388i	$0.0971162\pi$
$19$	897.955	+	5957.54i	0.130916	+	0.868573i	−0.822901	+	0.568185i	$0.807646\pi$
$20$	8984.32	−	3526.08i	1.12304	−	0.440761i
$21$	16693.9	−	8039.36i	1.80260	−	0.868087i
$22$	−7827.16	−	16253.3i	−0.735082	−	1.52641i
$23$	−478.704	−	1219.72i	−0.0393445	−	0.100248i	0.909851	−	0.414935i	$-0.136196\pi$
$23$	−478.704	−	1219.72i	−0.0393445	−	0.100248i	−0.949196	+	0.314687i	$0.898100\pi$
$24$	6771.96	−	1020.71i	0.489870	−	0.0738360i
$25$	−29882.3	−	20373.4i	−1.91246	−	1.30390i
$26$	8366.53	+	27123.6i	0.476020	+	1.54322i
$27$	−15362.7	−	3506.43i	−0.780504	−	0.178145i
$28$	−23788.2	−	9336.17i	−1.08364	−	0.425299i
$29$	8931.60	−	669.331i	0.366214	−	0.0274440i	0.109648	−	0.993971i	$-0.465028\pi$
$29$	8931.60	−	669.331i	0.366214	−	0.0274440i	0.256567	+	0.966527i	$0.417409\pi$
$30$	49100.0	+	52917.2i	1.81852	+	1.95990i
$31$	−6189.16	+	4219.70i	−0.207753	+	0.141643i	−0.662727	−	0.748861i	$-0.730601\pi$
$31$	−6189.16	+	4219.70i	−0.207753	+	0.141643i	0.454974	+	0.890505i	$0.349649\pi$
$32$	−29274.7	−	23345.8i	−0.893394	−	0.712458i
$33$	36576.5	−	39420.0i	1.01779	−	1.09692i
$34$	−2037.75	+	13519.6i	−0.0518459	+	0.343975i
$35$	30514.5	+	133693.i	0.711708	+	3.11820i
$36$	−4591.90	−	7953.41i	−0.0984204	−	0.170469i
$37$	−7270.58	−	4197.67i	−0.143537	−	0.0828711i	0.426512	−	0.904482i	$-0.359742\pi$
$37$	−7270.58	−	4197.67i	−0.143537	−	0.0828711i	−0.570049	+	0.821611i	$0.693076\pi$
$38$	59388.1	+	18318.8i	1.08230	+	0.333846i
$39$	−66152.9	+	52755.2i	−1.11521	+	0.889347i
$40$	−3787.70	+	50543.4i	−0.0591828	+	0.789740i
$41$	−33757.3	−	16256.7i	−0.489798	−	0.235874i	0.172649	−	0.984983i	$-0.444767\pi$
$41$	−33757.3	−	16256.7i	−0.489798	−	0.235874i	−0.662446	+	0.749109i	$0.730482\pi$
$42$		−	191134.i		−	2.57983i
$43$	−42463.6	+	67217.6i	−0.534087	+	0.845430i
$43$	−42463.6	+	67217.6i	−0.534087	+	0.845430i
$44$	−74166.0			−0.870656
$45$	−21382.6	+	44401.5i	−0.234652	+	0.487259i
$46$	−13478.5	−	1010.08i	−0.138474	−	0.0103772i
$47$	−74746.9	−	93729.6i	−0.719945	−	0.902783i	0.278389	−	0.960468i	$-0.410199\pi$
$47$	−74746.9	−	93729.6i	−0.719945	−	0.902783i	−0.998335	+	0.0576852i	$0.981628\pi$
$48$	45423.8	−	147260.i	0.410733	−	1.33156i
$49$	122719.	−	212556.i	1.04310	−	1.80670i
$50$	−323094.	+	186538.i	−2.58475	+	1.49231i
$51$	−39734.3	+	9069.10i	−0.299540	+	0.0683681i
$52$	115393.	+	17392.7i	0.820673	+	0.123696i
$53$	14520.8	+	13473.4i	0.0975357	+	0.0904999i	0.727434	−	0.686178i	$-0.240713\pi$
$53$	14520.8	+	13473.4i	0.0975357	+	0.0904999i	−0.629898	+	0.776678i	$0.716903\pi$
$54$	−101348.	+	127086.i	−0.643624	+	0.807079i
$55$	224195.	+	328833.i	1.34753	+	1.97646i
$56$	98376.4	−	91279.9i	0.560179	−	0.519770i
$57$	13844.7	+	184744.i	0.0747581	+	0.997578i
$58$	33754.7	−	86005.5i	0.173002	−	0.440801i
$59$	44337.5	−	194255.i	0.215882	−	0.945839i	−0.744603	−	0.667507i	$-0.767361\pi$
$59$	44337.5	−	194255.i	0.215882	−	0.945839i	0.960485	−	0.278332i	$-0.0897815\pi$
$60$	283596.	−	87477.8i	1.31295	−	0.404990i
$61$	−144301.	+	211650.i	−0.635738	+	0.932457i	0.364261	+	0.931297i	$0.381322\pi$
$61$	−144301.	+	211650.i	−0.635738	+	0.932457i	−0.999999	+	0.00115996i	$0.999631\pi$
$62$	11516.6	+	76408.0i	0.0483227	+	0.320600i
$63$	121466.	−	47671.9i	0.485772	−	0.190652i
$64$	−59019.6	+	28422.3i	−0.225142	+	0.108423i
$65$	−271704.	−	564200.i	−0.989365	−	2.05444i
$66$	−202662.	−	516373.i	−0.704920	−	1.79611i
$67$	−309393.	+	46633.5i	−1.02869	+	0.155051i	−0.641639	−	0.767007i	$-0.721745\pi$
$67$	−309393.	+	46633.5i	−1.02869	+	0.155051i	−0.387054	+	0.922057i	$0.626507\pi$
$68$	46443.1	+	31664.4i	0.147705	+	0.100703i
$69$	−11876.1	−	38501.2i	−0.0361514	−	0.117200i
$70$	1.37911e6	+	314772.i	4.02072	+	0.917704i
$71$	387116.	+	151932.i	1.08160	+	0.424496i	0.838163	−	0.545421i	$-0.183630\pi$
$71$	387116.	+	151932.i	1.08160	+	0.424496i	0.243436	+	0.969917i	$0.421725\pi$
$72$	48094.2	−	3604.16i	0.128853	−	0.00965621i
$73$	255790.	+	275676.i	0.657529	+	0.708648i	0.970496	−	0.241116i	$-0.0775135\pi$
$73$	255790.	+	275676.i	0.657529	+	0.708648i	−0.312967	+	0.949764i	$0.601323\pi$
$74$	−71554.1	+	48784.7i	−0.176579	+	0.120390i
$75$	−869487.	−	693393.i	−2.06101	−	1.64360i
$76$	173792.	−	187303.i	0.395902	−	0.426681i
$77$	157056.	−	1.04200e6i	0.344020	−	2.28242i
$78$	194221.	+	850939.i	0.409273	+	1.79314i
$79$	−113798.	−	197103.i	−0.230809	−	0.399773i	0.727238	−	0.686386i	$-0.240804\pi$
$79$	−113798.	−	197103.i	−0.230809	−	0.399773i	−0.958046	+	0.286613i	$0.907471\pi$
$80$	987734.	+	570269.i	1.92917	+	1.11381i
$81$	−613871.	−	189354.i	−1.15511	−	0.356303i
$82$	−302177.	+	240978.i	−0.548050	+	0.437056i
$83$	−26640.0	+	355486.i	−0.0465907	+	0.621710i	0.924220	+	0.381861i	$0.124717\pi$
$83$	−26640.0	+	355486.i	−0.0465907	+	0.621710i	−0.970810	+	0.239849i	$0.922902\pi$
$84$	−707982.	−	340946.i	−1.19450	−	0.575239i
$85$		−	301634.i		−	0.491161i
$86$	434661.	+	695502.i	0.683369	+	1.09346i
$87$	275415.			0.418244
$88$	168991.	−	350914.i	0.247980	−	0.514935i
$89$	−1.30720e6	−	97961.3i	−1.85427	−	0.138958i	−0.899617	−	0.436679i	$-0.856155\pi$
$89$	−1.30720e6	−	97961.3i	−1.85427	−	0.138958i	−0.954653	+	0.297721i	$0.903774\pi$
$90$	316962.	+	397458.i	0.434791	+	0.545210i
$91$	−488720.	+	1.58439e6i	−0.648539	+	2.10251i
$92$	−27784.5	+	48124.2i	−0.0356812	+	0.0618017i
$93$	−199480.	+	115170.i	−0.247999	+	0.143182i
$94$	−1.20567e6	+	275185.i	−1.45159	+	0.331315i
$95$	−1.35580e6	−	204355.i	−1.58134	−	0.238349i
$96$	−844028.	−	783144.i	−0.953989	−	0.885172i
$97$	156144.	−	195799.i	0.171084	−	0.214533i	−0.688896	−	0.724860i	$-0.741904\pi$
$97$	156144.	−	195799.i	0.171084	−	0.214533i	0.859980	+	0.510327i	$0.170476\pi$
$98$	−1.42623e6	−	2.09189e6i	−1.51534	−	2.22260i
$99$	277609.	−	257583.i	0.286106	−	0.265468i
$100$	114622.	+	1.52952e6i	0.114622	+	1.52952i
$101$	238399.	−	607431.i	0.231388	−	0.589567i	−0.767272	−	0.641322i	$-0.778386\pi$
$101$	238399.	−	607431.i	0.231388	−	0.589567i	0.998660	+	0.0517551i	$0.0164815\pi$
$102$	−93552.4	+	409880.i	−0.0881565	+	0.386239i
$103$	1.70415e6	−	525661.i	1.55954	−	0.481054i	0.609395	−	0.792867i	$-0.291412\pi$
$103$	1.70415e6	−	525661.i	1.55954	−	0.481054i	0.950144	+	0.311813i	$0.100936\pi$
$104$	−345222.	+	506348.i	−0.306901	+	0.450142i
$105$	628474.	+	4.16965e6i	0.542899	+	3.60190i
$106$	190212.	−	74652.7i	0.159706	−	0.0626799i
$107$	1.23933e6	−	596830.i	1.01166	−	0.487191i	0.146782	−	0.989169i	$-0.453108\pi$
$107$	1.23933e6	−	596830.i	1.01166	−	0.487191i	0.864881	+	0.501978i	$0.167394\pi$
$108$	289956.	+	602099.i	0.230176	+	0.477966i
$109$	310048.	+	789988.i	0.239414	+	0.610016i	0.999193	−	0.0401649i	$-0.0127883\pi$
$109$	310048.	+	789988.i	0.239414	+	0.610016i	−0.759779	+	0.650181i	$0.774693\pi$
$110$	4.05959e6	−	611885.i	3.05003	−	0.459718i
$111$	−213298.	−	145424.i	−0.155961	−	0.106333i
$112$	−890117.	−	2.88569e6i	−0.633567	−	2.05398i
$113$	−1.06344e6	−	242722.i	−0.737015	−	0.168219i	−0.162495	−	0.986709i	$-0.551954\pi$
$113$	−1.06344e6	−	242722.i	−0.737015	−	0.168219i	−0.574520	+	0.818491i	$0.694811\pi$
$114$	1.77897e6	+	698194.i	1.20075	+	0.471261i
$115$	297360.	−	22284.0i	0.195519	−	0.0146521i
$116$	−258362.	−	278448.i	−0.165522	−	0.178390i
$117$	−492331.	+	335666.i	−0.307397	+	0.209580i
$118$	−1.60696e6	−	1.28151e6i	−0.978044	−	0.779964i
$119$	−543220.	+	585452.i	−0.322356	+	0.347417i
$120$	−232291.	+	1.54115e6i	−0.134427	+	0.891868i
$121$	−286327.	−	1.25448e6i	−0.161624	−	0.708121i
$122$	1.32121e6	+	2.28841e6i	0.727602	+	1.26024i
$123$	−997772.	−	576064.i	−0.536187	−	0.309567i
$124$	303567.	+	93638.0i	0.159217	+	0.0491119i
$125$	3.65492e6	−	2.91470e6i	1.87132	−	1.49233i
$126$	100589.	−	1.34226e6i	0.0502850	−	0.671006i
$127$	113755.	+	54781.8i	0.0555343	+	0.0267439i	0.461445	−	0.887169i	$-0.347331\pi$
$127$	113755.	+	54781.8i	0.0555343	+	0.0267439i	−0.405910	+	0.913913i	$0.633046\pi$
$128$		−	1.72067e6i		−	0.820478i
$129$	−1.45656e6	+	1.96357e6i	−0.678514	+	0.914697i
$130$	−6.45972e6			−2.94025
$131$	940408.	−	1.95278e6i	0.418314	−	0.868638i	−0.580217	−	0.814462i	$-0.697032\pi$
$131$	940408.	−	1.95278e6i	0.418314	−	0.868638i	0.998531	−	0.0541764i	$-0.0172533\pi$
$132$	−2.27421e6	−	170429.i	−0.988802	−	0.0741004i
$133$	2.26350e6	+	2.83834e6i	0.962111	+	1.20645i
$134$	−951350.	+	3.08420e6i	−0.395390	+	1.28182i
$135$	1.79305e6	−	3.10566e6i	0.728773	−	1.26227i
$136$	−255642.	+	147595.i	−0.101628	+	0.0586752i
$137$	−2.25444e6	+	514561.i	−0.876752	+	0.200113i	−0.637133	−	0.770754i	$-0.719880\pi$
$137$	−2.25444e6	+	514561.i	−0.876752	+	0.200113i	−0.239619	+	0.970867i	$0.577023\pi$
$138$	−410982.	−	61945.6i	−0.156382	−	0.0235708i
$139$	2.99621e6	+	2.78008e6i	1.11565	+	1.03517i	0.999118	+	0.0419864i	$0.0133686\pi$
$139$	2.99621e6	+	2.78008e6i	1.11565	+	1.03517i	0.116533	+	0.993187i	$0.462822\pi$
$140$	3.62601e6	−	4.54688e6i	1.32143	−	1.65702i
$141$	−2.07664e6	−	3.04587e6i	−0.740805	−	1.08656i
$142$	3.14467e6	−	2.91783e6i	1.09827	−	1.01905i
$143$	359608.	+	4.79863e6i	0.122976	+	1.64100i
$144$	396494.	−	1.01025e6i	0.132785	−	0.338331i
$145$	−453572.	+	1.98723e6i	−0.148779	+	0.651844i
$146$	3.70697e6	−	1.14345e6i	1.19113	−	0.367416i
$147$	4.25148e6	−	6.23578e6i	1.33841	−	1.96308i
$148$	53065.5	+	352067.i	0.0163692	+	0.108602i
$149$	−444919.	+	174618.i	−0.134500	+	0.0527874i	−0.431636	−	0.902048i	$-0.642064\pi$
$149$	−444919.	+	174618.i	−0.134500	+	0.0527874i	0.297136	+	0.954835i	$0.403968\pi$
$150$	−1.03360e7	+	4.97753e6i	−3.06250	+	1.47482i
$151$	27523.8	+	57153.7i	0.00799424	+	0.0166002i	0.904928	−	0.425565i	$-0.139925\pi$
$151$	27523.8	+	57153.7i	0.00799424	+	0.0166002i	−0.896934	+	0.442165i	$0.854210\pi$
$152$	490223.	+	1.24907e6i	0.139593	+	0.355677i
$153$	−283812.	+	42777.8i	−0.0792423	+	0.0119439i
$154$	−8.98136e6	−	6.12338e6i	−2.45912	−	1.67660i
$155$	−502478.	−	1.62899e6i	−0.134934	−	0.437446i
$156$	3.49843e6	+	798493.i	0.921508	+	0.210328i
$157$	928059.	+	364236.i	0.239815	+	0.0941205i	0.482205	−	0.876058i	$-0.339836\pi$
$157$	928059.	+	364236.i	0.239815	+	0.0941205i	−0.242390	+	0.970179i	$0.577931\pi$
$158$	−2.34120e6	+	175448.i	−0.593563	+	0.0444814i
$159$	414303.	+	446513.i	0.103069	+	0.111082i
$160$	7.04069e6	−	4.80026e6i	1.71892	−	1.17194i
$161$	−617287.	−	492270.i	−0.147914	−	0.117958i
$162$	−4.50737e6	+	4.85779e6i	−1.06018	+	1.14260i
$163$	−480840.	+	3.19017e6i	−0.111029	+	0.736632i	0.862162	+	0.506633i	$0.169110\pi$
$163$	−480840.	+	3.19017e6i	−0.111029	+	0.736632i	−0.973191	+	0.229998i	$0.926128\pi$
$164$	353585.	+	1.54916e6i	0.0801608	+	0.351208i
$165$	6.11902e6	+	1.05985e7i	1.36217	+	2.35934i
$166$	3.18463e6	+	1.83865e6i	0.696202	+	0.401952i
$167$	5.57731e6	+	1.72037e6i	1.19750	+	0.369380i	0.828468	−	0.560037i	$-0.189213\pi$
$167$	5.57731e6	+	1.72037e6i	1.19750	+	0.369380i	0.369032	+	0.929417i	$0.379689\pi$
$168$	3.22635e6	−	2.57293e6i	0.680430	−	0.542625i
$169$	205117.	−	2.73710e6i	0.0424954	−	0.567062i
$170$	−2.80337e6	−	1.35003e6i	−0.570603	−	0.274788i
$171$			1.30468e6i			0.260925i
$172$	3.35157e6	−	369392.i	0.658662	−	0.0725942i
$173$	6.26902e6			1.21077			0.605385	−	0.795933i	$-0.293019\pi$
$173$	6.26902e6			1.21077			0.605385	+	0.795933i	$0.293019\pi$
$174$	1.23268e6	−	2.55969e6i	0.233993	−	0.485892i
$175$	−2.17319e7	−	1.62858e6i	−4.05493	−	0.303875i
$176$	−5.46449e6	−	6.85225e6i	−1.00233	−	1.25688i
$177$	1.80594e6	−	5.85473e6i	0.325675	−	1.05581i
$178$	−6.76114e6	+	1.17106e7i	−1.19884	+	2.07644i
$179$	3.89740e6	−	2.25016e6i	0.679541	−	0.392333i	−0.120141	−	0.992757i	$-0.538335\pi$
$179$	3.89740e6	−	2.25016e6i	0.679541	−	0.392333i	0.799682	+	0.600424i	$0.205001\pi$
$180$	2.03763e6	−	465075.i	0.349388	−	0.0797454i
$181$	3.33385e6	+	502496.i	0.562225	+	0.0847417i	0.424005	−	0.905660i	$-0.360624\pi$
$181$	3.33385e6	+	502496.i	0.562225	+	0.0847417i	0.138220	+	0.990402i	$0.455862\pi$
$182$	1.25379e7	+	1.16335e7i	2.07974	+	1.92972i
$183$	−4.91116e6	+	6.15840e6i	−0.801366	+	1.00488i
$184$	−164390.	−	241115.i	−0.0263889	−	0.0387054i
$185$	1.40056e6	−	1.29953e6i	0.221201	−	0.205245i
$186$	177564.	+	2.36942e6i	0.0275941	+	0.368217i
$187$	−846817.	+	2.15766e6i	−0.129499	+	0.329957i
$188$	−1.13136e6	+	4.95679e6i	−0.170265	+	0.745980i
$189$	−9.07326e6	+	2.79873e6i	−1.34393	+	0.414549i
$190$	−7.96747e6	+	1.16861e7i	−1.16161	+	1.70377i
$191$	144464.	+	958458.i	0.0207329	+	0.137554i	0.996803	−	0.0799043i	$-0.0254615\pi$
$191$	144464.	+	958458.i	0.0207329	+	0.137554i	−0.976070	+	0.217458i	$0.930223\pi$
$192$	−1.87508e6	+	735914.i	−0.264921	+	0.103974i
$193$	9.32325e6	−	4.48984e6i	1.29687	−	0.624538i	0.347198	−	0.937792i	$-0.387133\pi$
$193$	9.32325e6	−	4.48984e6i	1.29687	−	0.624538i	0.949670	+	0.313253i	$0.101419\pi$
$194$	−1.12088e6	−	2.32754e6i	−0.153516	−	0.318780i
$195$	−7.03500e6	−	1.79249e7i	−0.948768	−	2.41742i
$196$	−1.02927e7	+	1.55137e6i	−1.36698	+	0.206039i
$197$	−3.60865e6	−	2.46034e6i	−0.472005	−	0.321807i	0.303849	−	0.952720i	$-0.401728\pi$
$197$	−3.60865e6	−	2.46034e6i	−0.472005	−	0.321807i	−0.775854	+	0.630913i	$0.782681\pi$
$198$	−1.15146e6	−	3.73295e6i	−0.148339	−	0.480902i
$199$	−4.27001e6	−	974603.i	−0.541839	−	0.123671i	−0.0571626	−	0.998365i	$-0.518205\pi$
$199$	−4.27001e6	−	974603.i	−0.541839	−	0.123671i	−0.484676	+	0.874694i	$0.661062\pi$
$200$	−7.49806e6	−	2.94277e6i	−0.937258	−	0.367847i
$201$	−9.59433e6	+	718995.i	−1.18148	+	0.0885397i
$202$	−4.57842e6	−	4.93437e6i	−0.555472	−	0.598656i
$203$	4.45919e6	−	3.04023e6i	0.533050	−	0.363428i
$204$	1.35136e6	+	1.07767e6i	0.159177	+	0.126940i
$205$	5.79972e6	−	6.25062e6i	0.673203	−	0.725540i
$206$	2.74185e6	−	1.81910e7i	0.313648	−	2.08092i
$207$	−63139.0	−	276630.i	−0.00711847	−	0.0311880i
$208$	6.89514e6	+	1.19427e7i	0.766220	+	1.32713i
$209$	9.12465e6	+	5.26812e6i	0.999487	+	0.577054i
$210$	4.15654e7	+	1.28212e7i	4.48822	+	1.38443i
$211$	−7.64673e6	+	6.09806e6i	−0.814007	+	0.649149i	−0.939348	−	0.342965i	$-0.888569\pi$
$211$	−7.64673e6	+	6.09806e6i	−0.814007	+	0.649149i	0.125341	+	0.992114i	$0.459997\pi$
$212$	62779.3	−	837732.i	0.00658884	−	0.0879220i
$213$	1.15213e7	+	5.54838e6i	1.19224	+	0.574153i
$214$		−	1.41895e7i		−	1.44786i
$215$	−1.17692e7	−	1.37434e7i	−1.18421	−	1.38286i
$216$	−3.50949e6			−0.348243
$217$	−1.95842e6	+	4.06669e6i	−0.191658	+	0.397981i
$218$	8.72980e6	+	654208.i	0.842626	+	0.0631461i
$219$	7.21001e6	+	9.04107e6i	0.686442	+	0.860771i
$220$	4.97503e6	−	1.61287e7i	0.467227	−	1.51471i
$221$	1.82354e6	−	3.15846e6i	0.168942	−	0.292616i
$222$	−2.30622e6	+	1.33150e6i	−0.210786	+	0.121698i
$223$	−1.16601e7	+	2.66135e6i	−1.05145	+	0.239987i	−0.713121	−	0.701041i	$-0.752719\pi$
$223$	−1.16601e7	+	2.66135e6i	−1.05145	+	0.239987i	−0.338330	+	0.941027i	$0.609862\pi$
$224$	−2.23104e7	−	3.36275e6i	−1.98501	−	0.299193i
$225$	−5.74117e6	−	5.32703e6i	−0.504026	−	0.467668i
$226$	−7.01550e6	+	8.79716e6i	−0.607762	+	0.762109i
$227$	3.77797e6	+	5.54126e6i	0.322984	+	0.473730i	0.953051	−	0.302811i	$-0.0979250\pi$
$227$	3.77797e6	+	5.54126e6i	0.322984	+	0.473730i	−0.630067	+	0.776541i	$0.716973\pi$
$228$	5.75953e6	−	5.34406e6i	0.485939	−	0.450886i
$229$	1.26261e6	+	1.68484e7i	0.105139	+	1.40298i	0.761319	+	0.648378i	$0.224552\pi$
$229$	1.26261e6	+	1.68484e7i	0.105139	+	1.40298i	−0.656180	+	0.754604i	$0.727829\pi$
$230$	1.12380e6	−	2.86338e6i	0.0923642	−	0.235340i
$231$	7.21039e6	−	3.15908e7i	0.584956	−	2.56286i
$232$	1.90616e6	−	587972.i	0.152650	−	0.0470861i
$233$	3.84438e6	−	5.63868e6i	0.303920	−	0.445768i	−0.643649	−	0.765321i	$-0.722580\pi$
$233$	3.84438e6	−	5.63868e6i	0.303920	−	0.445768i	0.947569	+	0.319553i	$0.103533\pi$
$234$	916118.	+	6.07805e6i	0.0714996	+	0.474369i
$235$	2.53971e7	−	9.96763e6i	1.95695	−	0.768048i
$236$	−7.61334e6	+	3.66639e6i	−0.579214	+	0.278935i
$237$	−3.03654e6	−	6.30544e6i	−0.228105	−	0.473664i
$238$	3.00986e6	+	7.66899e6i	0.223262	+	0.568862i
$239$	−3.66802e6	+	552866.i	−0.268682	+	0.0404973i	−0.282001	−	0.959414i	$-0.590998\pi$
$239$	−3.66802e6	+	552866.i	−0.268682	+	0.0404973i	0.0133194	+	0.999911i	$0.495760\pi$
$240$	2.89773e7	+	1.97564e7i	2.09616	+	1.42914i
$241$	4.80813e6	+	1.55876e7i	0.343498	+	1.11359i	0.948342	+	0.317250i	$0.102759\pi$
$241$	4.80813e6	+	1.55876e7i	0.343498	+	1.11359i	−0.604843	+	0.796344i	$0.706764\pi$
$242$	−1.29406e7	−	2.95361e6i	−0.913078	−	0.208404i
$243$	−7.69521e6	−	3.02015e6i	−0.536292	−	0.210479i
$244$	1.08333e7	−	811844.i	0.745747	−	0.0558860i
$245$	3.79920e7	+	4.09456e7i	2.58341	+	2.78425i
$246$	−9.81966e6	+	6.69493e6i	−0.659616	+	0.449719i
$247$	−1.29614e7	−	1.03364e7i	−0.860124	−	0.685926i
$248$	−1.13474e6	+	1.22296e6i	−0.0743945	+	0.0801782i
$249$	−1.63377e6	+	1.08393e7i	−0.105826	+	0.702109i
$250$	−1.07306e7	−	4.70140e7i	−0.686761	−	3.00890i
$251$	−7.24158e6	−	1.25428e7i	−0.457944	−	0.793182i	0.540908	−	0.841082i	$-0.318081\pi$
$251$	−7.24158e6	−	1.25428e7i	−0.457944	−	0.793182i	−0.998852	+	0.0478994i	$0.984747\pi$
$252$	−4.79247e6	−	2.76693e6i	−0.299473	−	0.172901i
$253$	−2.18964e6	−	675414.i	−0.135211	−	0.0417070i
$254$	1.01828e6	−	812049.i	0.0621391	−	0.0495543i
$255$	693136.	−	9.24926e6i	0.0418021	−	0.557810i
$256$	−1.97690e7	−	9.52027e6i	−1.17833	−	0.567452i
$257$			1.57904e7i			0.930237i	0.885248	+	0.465119i	$0.153988\pi$
$257$			1.57904e7i			0.930237i	−0.885248	+	0.465119i	$0.846012\pi$
$258$	1.17301e7	+	2.23256e7i	0.683037	+	1.30000i
$259$	−5.05876e6			−0.291169
$260$	−1.15229e7	+	2.39275e7i	−0.655603	+	1.36137i
$261$	1.93414e6	+	144944.i	0.108784	+	0.00815225i
$262$	−1.39400e7	−	1.74802e7i	−0.775102	−	0.971947i
$263$	−2.29568e6	+	7.44242e6i	−0.126196	+	0.409116i	−0.996519	−	0.0833642i	$-0.973434\pi$
$263$	−2.29568e6	+	7.44242e6i	−0.126196	+	0.409116i	0.870323	+	0.492480i	$0.163910\pi$
$264$	5.98829e6	−	1.03720e7i	0.325455	−	0.563705i
$265$	−3.90407e6	+	2.25401e6i	−0.209787	+	0.121121i
$266$	3.65102e7	−	8.33321e6i	1.93985	−	0.442759i
$267$	−3.98587e7	−	6.00774e6i	−2.09406	−	0.315629i
$268$	9.72719e6	+	9.02552e6i	0.505339	+	0.468886i
$269$	1.44847e7	−	1.81632e7i	0.744136	−	0.933117i	−0.255294	−	0.966863i	$-0.582172\pi$
$269$	1.44847e7	−	1.81632e7i	0.744136	−	0.933117i	0.999430	+	0.0337460i	$0.0107437\pi$
$270$	−2.08386e7	−	3.05647e7i	−1.05871	−	1.55285i
$271$	1.98752e7	−	1.84415e7i	0.998626	−	0.926590i	0.00132418	−	0.999999i	$-0.499579\pi$
$271$	1.98752e7	−	1.84415e7i	0.998626	−	0.926590i	0.997302	+	0.0734096i	$0.0233880\pi$
$272$	496394.	+	6.62392e6i	0.0246672	+	0.329161i
$273$	−1.86269e7	+	4.74605e7i	−0.915486	+	2.33262i
$274$	−5.30796e6	+	2.32557e7i	−0.258033	+	1.13052i
$275$	−6.04382e7	+	1.86427e7i	−2.90612	+	0.896420i
$276$	−962566.	+	1.41183e6i	−0.0457829	+	0.0671512i
$277$	−4.84554e6	−	3.21480e7i	−0.227983	−	1.51257i	−0.751032	−	0.660266i	$-0.770443\pi$
$277$	−4.84554e6	−	3.21480e7i	−0.227983	−	1.51257i	0.523049	−	0.852303i	$-0.324795\pi$
$278$	3.92482e7	−	1.54038e7i	1.82678	−	0.716956i
$279$	−1.46148e6	+	703814.i	−0.0672948	+	0.0324075i
$280$	1.32513e7	+	2.75167e7i	0.603650	+	1.25349i
$281$	−2.29574e6	−	5.84945e6i	−0.103467	−	0.263631i	0.869760	−	0.493475i	$-0.164274\pi$
$281$	−2.29574e6	−	5.84945e6i	−0.103467	−	0.263631i	−0.973227	+	0.229844i	$0.926178\pi$
$282$	−3.76027e7	+	5.66769e6i	−1.67676	+	0.252731i
$283$	3.69089e7	+	2.51641e7i	1.62844	+	1.11025i	0.909954	+	0.414710i	$0.136117\pi$
$283$	3.69089e7	+	2.51641e7i	1.62844	+	1.11025i	0.718486	+	0.695541i	$0.244835\pi$
$284$	−5.19848e6	−	1.68531e7i	−0.226945	−	0.735739i
$285$	−4.11045e7	−	9.38184e6i	−1.77564	−	0.405278i
$286$	4.62078e7	+	1.81352e7i	1.97523	+	0.775219i
$287$	−2.25138e7	+	1.68717e6i	−0.952362	+	0.0713697i
$288$	−5.51515e6	−	5.94392e6i	−0.230877	−	0.248826i
$289$	−1.84919e7	+	1.26076e7i	−0.766106	+	0.522322i
$290$	1.64391e7	+	1.31098e7i	0.674038	+	0.537528i
$291$	5.23791e6	−	5.64512e6i	0.212559	−	0.229084i
$292$	2.37705e6	−	1.57707e7i	0.0954750	−	0.633435i
$293$	−2.43363e6	−	1.06624e7i	−0.0967500	−	0.423890i	0.903236	−	0.429144i	$-0.141185\pi$
$293$	−2.43363e6	−	1.06624e7i	−0.0967500	−	0.423890i	−0.999986	+	0.00525422i	$0.998328\pi$
$294$	−3.89265e7	−	6.74227e7i	−1.53180	−	2.65316i
$295$	3.92700e7	+	2.26726e7i	1.52966	+	0.883150i
$296$	−1.78670e6	−	551125.i	−0.0688933	−	0.0212508i
$297$	−2.15450e7	+	1.71816e7i	−0.822390	+	0.655834i
$298$	−368448.	+	4.91660e6i	−0.0139228	+	0.185787i
$299$	3.24842e6	+	1.56435e6i	0.121523	+	0.0585223i
$300$			4.71644e7i			1.74683i
$301$	−1.90759e6	+	4.78703e7i	−0.0699498	+	1.75536i
$302$	654373.			0.0237577
$303$	8.70607e6	−	1.80783e7i	0.312964	−	0.649876i
$304$	3.01099e7	+	2.25642e6i	1.07174	+	0.0803156i
$305$	−3.63473e7	−	4.55780e7i	−1.28107	−	1.60641i
$306$	−872692.	+	2.82920e6i	−0.0304577	+	0.0987414i
$307$	−8.82738e6	+	1.52895e7i	−0.305082	+	0.528418i	−0.977280	−	0.211954i	$-0.932017\pi$
$307$	−8.82738e6	+	1.52895e7i	−0.305082	+	0.528418i	0.672198	+	0.740372i	$0.265351\pi$
$308$	−3.87027e7	+	2.23450e7i	−1.32461	+	0.764765i
$309$	5.34637e7	−	1.22027e7i	1.81210	−	0.413601i
$310$	−1.73887e7	−	2.62093e6i	−0.583691	−	0.0879773i
$311$	2.95292e7	+	2.73991e7i	0.981680	+	0.910866i	0.996029	−	0.0890313i	$-0.0283771\pi$
$311$	2.95292e7	+	2.73991e7i	0.981680	+	0.910866i	−0.0143490	+	0.999897i	$0.504568\pi$
$312$	−1.17494e7	+	1.47333e7i	−0.386858	+	0.485105i
$313$	−942861.	−	1.38292e6i	−0.0307478	−	0.0450988i	0.810557	−	0.585660i	$-0.199164\pi$
$313$	−942861.	−	1.38292e6i	−0.0307478	−	0.0450988i	−0.841305	+	0.540561i	$0.818212\pi$
$314$	7.53893e6	−	6.99511e6i	0.243512	−	0.225946i
$315$	2.21916e6	+	2.96127e7i	0.0709998	+	0.947427i
$316$	−3.52636e6	+	8.98502e6i	−0.111755	+	0.284746i
$317$	3.43027e6	−	1.50290e7i	0.107684	−	0.471794i	−0.892116	−	0.451806i	$-0.850780\pi$
$317$	3.43027e6	−	1.50290e7i	0.107684	−	0.471794i	0.999800	−	0.0199881i	$-0.00636282\pi$
$318$	6.00417e6	−	1.85204e6i	0.186712	−	0.0575930i
$319$	8.82349e6	−	1.29417e7i	0.271812	−	0.398675i
$320$	−2.22190e6	−	1.47414e7i	−0.0678072	−	0.449871i
$321$	3.93741e7	−	1.54532e7i	1.19041	−	0.467200i
$322$	−7.33795e6	+	3.53377e6i	−0.219789	+	0.105845i
$323$	−3.46473e6	−	7.19459e6i	−0.102816	−	0.213500i
$324$	9.95352e6	+	2.53612e7i	0.292645	+	0.745648i
$325$	9.84064e7	−	1.48324e7i	2.86664	−	0.432077i
$326$	2.74971e7	+	1.87472e7i	0.793660	+	0.541108i
$327$	7.69190e6	+	2.49365e7i	0.219984	+	0.713169i
$328$	−8.13544e6	−	1.85686e6i	−0.230547	−	0.0526209i
$329$	−6.72450e7	−	2.63917e7i	−1.88831	−	0.741106i
$330$	1.25889e8	−	9.43405e6i	3.50304	−	0.262516i
$331$	−1.99578e7	−	2.15094e7i	−0.550337	−	0.593123i	0.395217	−	0.918588i	$-0.370670\pi$
$331$	−1.99578e7	−	2.15094e7i	−0.550337	−	0.593123i	−0.945554	+	0.325465i	$0.894479\pi$
$332$	1.24913e7	−	8.51644e6i	0.341345	−	0.232725i
$333$	−1.42138e6	−	1.13351e6i	−0.0384926	−	0.0306968i
$334$	4.09516e7	−	4.41353e7i	1.09909	−	1.18453i
$335$	1.06127e7	−	7.04109e7i	0.282288	−	1.87286i
$336$	−2.06632e7	−	9.05316e7i	−0.544729	−	2.38662i
$337$	1.53290e6	+	2.65506e6i	0.0400519	+	0.0693720i	0.885356	−	0.464913i	$-0.153914\pi$
$337$	1.53290e6	+	2.65506e6i	0.0400519	+	0.0693720i	−0.845305	+	0.534285i	$0.820581\pi$
$338$	−2.45204e7	−	1.41569e7i	−0.635006	−	0.366621i
$339$	−3.20513e7	−	9.88650e6i	−0.822708	−	0.253772i
$340$	−1.00013e7	+	7.97581e6i	−0.254461	+	0.202926i
$341$	−978953.	+	1.30632e7i	−0.0246887	+	0.329448i
$342$	1.21256e7	+	5.83939e6i	0.303127	+	0.145978i
$343$		−	7.70018e7i		−	1.90818i
$344$	−5.88896e6	+	1.66995e7i	−0.144665	+	0.410231i
$345$	9.16939e6			0.223297
$346$	2.80584e7	−	5.82639e7i	0.677384	−	1.40660i
$347$	−9.83421e6	−	736972.i	−0.235370	−	0.0176385i	−0.0434771	−	0.999054i	$-0.513844\pi$
$347$	−9.83421e6	−	736972.i	−0.235370	−	0.0176385i	−0.191893	+	0.981416i	$0.561463\pi$
$348$	−7.28251e6	−	9.13198e6i	−0.172800	−	0.216684i
$349$	−7.44554e6	+	2.41378e7i	−0.175154	+	0.567835i	0.824843	+	0.565362i	$0.191263\pi$
$349$	−7.44554e6	+	2.41378e7i	−0.175154	+	0.567835i	−0.999997	+	0.00247325i	$0.999213\pi$
$350$	−1.12402e8	+	1.94686e8i	−2.62162	+	4.54078i
$351$	3.75507e7	−	2.16799e7i	0.868353	−	0.501344i
$352$	−6.38400e7	+	1.45711e7i	−1.46374	+	0.334090i
$353$	−4.63816e7	−	6.99090e6i	−1.05444	−	0.158931i	−0.401129	−	0.916022i	$-0.631382\pi$
$353$	−4.63816e7	−	6.99090e6i	−1.05444	−	0.158931i	−0.653310	+	0.757091i	$0.726620\pi$
$354$	−4.63306e7	−	4.29885e7i	−1.04438	−	0.969043i
$355$	−5.90078e7	+	7.39935e7i	−1.31894	+	1.65390i
$356$	3.13169e7	+	4.59335e7i	0.694111	+	1.01807i
$357$	−1.80025e7	+	1.67039e7i	−0.395666	+	0.367125i
$358$	−3.46920e6	−	4.62933e7i	−0.0756103	−	1.00895i
$359$	892776.	−	2.27476e6i	0.0192956	−	0.0491645i	−0.920901	−	0.389796i	$-0.872546\pi$
$359$	892776.	−	2.27476e6i	0.0192956	−	0.0491645i	0.940197	+	0.340631i	$0.110641\pi$
$360$	−2.44236e6	+	1.07007e7i	−0.0523482	+	0.229352i
$361$	1.02698e7	−	3.16780e6i	0.218293	−	0.0673343i
$362$	1.95916e7	−	2.87356e7i	0.412994	−	0.605751i
$363$	−5.89716e6	−	3.91251e7i	−0.123289	−	0.817966i
$364$	6.54567e7	−	2.56899e7i	1.35722	−	0.532670i
$365$	−7.71088e7	+	3.71336e7i	−1.58572	+	0.763640i
$366$	3.52548e7	+	7.32074e7i	0.719077	+	1.49318i
$367$	−2.20286e7	−	5.61280e7i	−0.445645	−	1.13549i	−0.960518	−	0.278219i	$-0.910256\pi$
$367$	−2.20286e7	−	5.61280e7i	−0.445645	−	1.13549i	0.514872	−	0.857267i	$-0.327839\pi$
$368$	−6.49337e6	+	978719.i	−0.130295	+	0.0196388i
$369$	−6.70382e6	−	4.57058e6i	−0.133427	−	0.0909688i
$370$	−5.80925e6	−	1.88331e7i	−0.114687	−	0.371807i
$371$	1.16368e7	+	2.65603e6i	0.227884	+	0.0520130i
$372$	9.09335e6	+	3.56888e6i	0.176642	+	0.0693270i
$373$	433697.	−	32501.1i	0.00835719	−	0.000626285i	−0.0705508	−	0.997508i	$-0.522476\pi$
$373$	433697.	−	32501.1i	0.00835719	−	0.000626285i	0.0789080	+	0.996882i	$0.474857\pi$
$374$	1.62630e7	+	1.75274e7i	0.310875	+	0.335044i
$375$	1.18771e8	−	8.09770e7i	2.25226	−	1.53556i
$376$	−2.08750e7	−	1.66473e7i	−0.392703	−	0.313170i
$377$	−1.67632e7	+	1.80665e7i	−0.312848	+	0.337170i
$378$	−1.45982e7	+	9.68527e7i	−0.270286	+	1.79323i
$379$	1.17935e7	+	5.16707e7i	0.216633	+	0.949132i	0.959945	+	0.280187i	$0.0903965\pi$
$379$	1.17935e7	+	5.16707e7i	0.216633	+	0.949132i	−0.743312	+	0.668945i	$0.766746\pi$
$380$	2.90743e7	+	5.03582e7i	0.529857	+	0.917739i
$381$	3.36229e6	+	1.94122e6i	0.0607940	+	0.0350994i
$382$	9.55444e6	+	2.94716e6i	0.171402	+	0.0528705i
$383$	9.95560e6	−	7.93932e6i	0.177203	−	0.141315i	−0.530872	−	0.847452i	$-0.678135\pi$
$383$	9.95560e6	−	7.93932e6i	0.177203	−	0.141315i	0.708075	+	0.706138i	$0.249564\pi$
$384$	3.95398e6	−	5.27622e7i	0.0698298	−	0.931815i
$385$	2.16065e8	+	1.04052e8i	3.78620	+	1.82334i
$386$		−	1.06745e8i		−	1.85604i
$387$	−1.12622e7	+	1.30229e7i	−0.194309	+	0.224685i
$388$	−1.06209e7			−0.181830
$389$	−4.68968e7	+	9.73822e7i	−0.796699	+	1.65436i	−0.0412552	+	0.999149i	$0.513136\pi$
$389$	−4.68968e7	+	9.73822e7i	−0.796699	+	1.65436i	−0.755444	+	0.655214i	$0.772579\pi$
$390$	−1.98080e8	−	1.48440e7i	−3.33923	−	0.250240i
$391$	1.08280e6	+	1.35779e6i	0.0181142	+	0.0227145i
$392$	1.61122e7	−	5.22344e7i	0.267483	−	0.867159i
$393$	3.33239e7	−	5.77186e7i	0.549007	−	0.950907i
$394$	−3.90176e7	+	2.25268e7i	−0.637928	+	0.368308i
$395$	5.04970e7	−	1.15256e7i	0.819360	−	0.187013i
$396$	−1.58813e7	−	2.39371e6i	−0.255740	−	0.0385467i
$397$	−3.55657e7	−	3.30002e7i	−0.568408	−	0.527405i	0.342770	−	0.939420i	$-0.388635\pi$
$397$	−3.55657e7	−	3.30002e7i	−0.568408	−	0.527405i	−0.911178	+	0.412014i	$0.864825\pi$
$398$	−2.81693e7	+	3.53232e7i	−0.446815	+	0.560288i
$399$	6.28852e7	+	9.22356e7i	0.989987	+	1.45204i
$400$	−1.32869e8	+	1.23284e8i	−2.07607	+	1.92631i
$401$	−2503.52	−	33407.1i	−3.88256e−5	−	0.000518091i	0.997184	−	0.0749891i	$-0.0238922\pi$
$401$	−2503.52	−	33407.1i	−3.88256e−5	−	0.000518091i	−0.997223	+	0.0744710i	$0.976273\pi$
$402$	−3.62593e7	+	9.23872e7i	−0.558138	+	1.42211i
$403$	4.58659e6	−	2.00952e7i	0.0700770	−	0.307027i
$404$	−2.64445e7	+	8.15704e6i	−0.401043	+	0.123705i
$405$	8.23566e7	−	1.20795e8i	1.23975	−	1.81838i
$406$	−8.29757e6	−	5.50508e7i	−0.123986	−	0.822593i
$407$	−1.36669e7	+	5.36385e6i	−0.202715	+	0.0795598i
$408$	−8.17812e6	+	3.93838e6i	−0.120413	+	0.0579878i
$409$	2.19610e6	+	4.56025e6i	0.0320983	+	0.0666529i	0.916401	−	0.400260i	$-0.131080\pi$
$409$	2.19610e6	+	4.56025e6i	0.0320983	+	0.0666529i	−0.884303	+	0.466913i	$0.845366\pi$
$410$	−3.21349e7	−	8.18784e7i	−0.466257	−	1.18800i
$411$	−7.03122e7	+	1.05979e7i	−1.01276	+	0.152648i
$412$	−6.24905e7	−	4.26053e7i	−0.893558	−	0.609217i
$413$	−3.53890e7	−	1.14728e8i	−0.502363	−	1.62862i
$414$	−2.85358e6	−	651310.i	−0.0402151	−	0.00917882i
$415$	−7.55194e7	−	2.96392e7i	−1.05661	−	0.414689i
$416$	1.02744e8	−	7.69961e6i	1.42718	−	0.106952i
$417$	8.54869e7	+	9.21330e7i	1.17894	+	1.27059i
$418$	8.98011e7	−	6.12253e7i	1.22957	−	0.838305i
$419$	9.70867e7	+	7.74241e7i	1.31983	+	1.05253i	0.994258	+	0.107011i	$0.0341279\pi$
$419$	9.70867e7	+	7.74241e7i	1.31983	+	1.05253i	0.325571	+	0.945518i	$0.394443\pi$
$420$	1.21636e8	−	1.31092e8i	1.64177	−	1.76941i
$421$	−6.17478e6	+	4.09670e7i	−0.0827514	+	0.549019i	0.908588	+	0.417694i	$0.137161\pi$
$421$	−6.17478e6	+	4.09670e7i	−0.0827514	+	0.549019i	−0.991339	+	0.131326i	$0.958077\pi$
$422$	2.24504e7	+	9.83615e7i	0.298735	+	1.30884i
$423$	−1.29805e7	−	2.24829e7i	−0.171503	−	0.297051i
$424$	3.82065e6	+	2.20586e6i	0.0501234	+	0.0289387i
$425$	4.58060e7	+	1.41293e7i	0.596700	+	0.184058i
$426$	1.03133e8	−	8.22456e7i	1.33404	−	1.06386i
$427$	−1.15349e7	+	1.53923e8i	−0.148160	+	1.97705i
$428$	−5.25596e7	−	2.53114e7i	−0.670379	−	0.322838i
$429$			1.47971e8i			1.87415i
$430$	−1.80406e8	+	4.78704e7i	−2.26906	+	0.602090i
$431$	7.64765e7			0.955204			0.477602	−	0.878576i	$-0.341506\pi$
$431$	7.64765e7			0.955204			0.477602	+	0.878576i	$0.341506\pi$
$432$	−3.42647e7	+	7.11514e7i	−0.425007	+	0.882535i
$433$	−1.32467e8	−	9.92699e6i	−1.63171	−	0.122280i	−0.772883	−	0.634549i	$-0.781186\pi$
$433$	−1.32467e8	−	9.92699e6i	−1.63171	−	0.122280i	−0.858825	+	0.512269i	$0.828805\pi$
$434$	2.90303e7	+	3.64029e7i	0.355126	+	0.445314i
$435$	−1.84748e7	+	5.98937e7i	−0.224445	+	0.727634i
$436$	1.79955e7	−	3.11692e7i	0.217123	−	0.376067i
$437$	6.83667e6	−	3.94715e6i	0.0819219	−	0.0472976i
$438$	1.16297e8	−	2.65441e7i	1.38404	−	0.315897i
$439$	−1.47159e8	−	2.21806e7i	−1.73937	−	0.262168i	−0.798760	−	0.601649i	$-0.794510\pi$
$439$	−1.47159e8	−	2.21806e7i	−1.73937	−	0.262168i	−0.940613	+	0.339481i	$0.889749\pi$
$440$	6.49763e7	+	6.02892e7i	0.762776	+	0.707753i
$441$	3.31383e7	−	4.15541e7i	0.386380	−	0.484505i
$442$	−2.11929e7	−	3.10843e7i	−0.245428	−	0.359976i
$443$	−6.53508e7	+	6.06367e7i	−0.751692	+	0.697468i	−0.959815	−	0.280634i	$-0.909455\pi$
$443$	−6.53508e7	+	6.06367e7i	−0.751692	+	0.697468i	0.208123	+	0.978103i	$0.433265\pi$
$444$	818164.	+	1.09176e7i	0.00934742	+	0.124733i
$445$	1.08990e8	−	2.77702e8i	1.23682	−	3.15137i
$446$	−2.74532e7	+	1.20280e8i	−0.309448	+	1.35578i
$447$	−1.40442e7	+	4.33206e6i	−0.157244	+	0.0485033i
$448$	−2.22355e7	+	3.26135e7i	−0.247294	+	0.362713i
$449$	−1.46441e7	−	9.71574e7i	−0.161780	−	1.07334i	−0.911415	−	0.411488i	$-0.865009\pi$
$449$	−1.46441e7	−	9.71574e7i	−0.161780	−	1.07334i	0.749636	−	0.661851i	$-0.230229\pi$
$450$	−7.52051e7	+	2.95158e7i	−0.825296	+	0.323905i
$451$	−5.90348e7	+	2.84297e7i	−0.643545	+	0.309915i
$452$	2.00714e7	+	4.16786e7i	0.217351	+	0.451334i
$453$	712648.	+	1.81580e6i	0.00766621	+	0.0195332i
$454$	6.84093e7	−	1.03110e7i	0.731051	−	0.110188i
$455$	−3.11770e8	−	2.12561e8i	−3.30979	−	2.25658i
$456$	1.21618e7	+	3.94277e7i	0.128264	+	0.415822i
$457$	7.57139e6	+	1.72812e6i	0.0793281	+	0.0181061i	0.262001	−	0.965068i	$-0.415618\pi$
$457$	7.57139e6	+	1.72812e6i	0.0793281	+	0.0181061i	−0.182673	+	0.983174i	$0.558475\pi$
$458$	1.62239e8	+	6.36742e7i	1.68873	+	0.662777i
$459$	2.08271e7	−	1.56078e6i	0.215373	−	0.0161400i
$460$	−8.60166e6	−	9.27038e6i	−0.0883708	−	0.0952410i
$461$	−2.67171e7	+	1.82154e7i	−0.272701	+	0.185924i	−0.691947	−	0.721948i	$-0.743247\pi$
$461$	−2.67171e7	+	1.82154e7i	−0.272701	+	0.185924i	0.419246	+	0.907873i	$0.362294\pi$
$462$	−2.61331e8	−	2.08405e8i	−2.65012	−	2.11340i
$463$	3.62915e6	−	3.91130e6i	0.0365647	−	0.0394074i	−0.714505	−	0.699631i	$-0.753348\pi$
$463$	3.62915e6	−	3.91130e6i	0.0365647	−	0.0394074i	0.751069	+	0.660223i	$0.229538\pi$
$464$	6.69013e6	−	4.43861e7i	0.0669700	−	0.444317i
$465$	−1.16646e7	−	5.11059e7i	−0.116014	−	0.508290i
$466$	−3.51991e7	−	6.09667e7i	−0.347836	−	0.602469i
$467$	1.62689e8	+	9.39283e7i	1.59737	+	0.922244i	0.991991	+	0.126308i	$0.0403128\pi$
$467$	1.62689e8	+	9.39283e7i	1.59737	+	0.922244i	0.605382	+	0.795935i	$0.293021\pi$
$468$	2.41479e7	+	7.44865e6i	0.235582	+	0.0726675i
$469$	−1.47403e8	+	1.17550e8i	−1.42886	+	1.13947i
$470$	2.10320e7	−	2.80652e8i	0.202575	−	2.70318i
$471$	2.76208e7	+	1.33015e7i	0.264347	+	0.127303i
$472$		−	4.43763e7i		−	0.422012i
$473$	4.56038e7	+	1.31350e8i	0.430941	+	1.24122i
$474$	−7.21932e7			−0.677893
$475$	9.45424e7	−	1.96319e8i	0.882157	−	1.83182i
$476$	3.37758e7	+	2.53114e6i	0.313173	+	0.0234691i
$477$	2.67451e6	+	3.35373e6i	0.0246427	+	0.0309010i
$478$	−1.12788e7	+	3.65649e7i	−0.103271	+	0.334796i
$479$	4.98382e7	−	8.63224e7i	0.453478	−	0.785447i	−0.545121	−	0.838357i	$-0.683516\pi$
$479$	4.98382e7	−	8.63224e7i	0.453478	−	0.785447i	0.998599	+	0.0529103i	$0.0168497\pi$
$480$	2.26925e8	−	1.31015e8i	2.05191	−	1.18467i
$481$	2.25219e7	−	5.14047e6i	0.202381	−	0.0461920i
$482$	1.66390e8	+	2.50792e7i	1.48589	+	0.223961i
$483$	−1.77972e7	−	1.65134e7i	−0.157946	−	0.146553i
$484$	−3.40240e7	+	4.26647e7i	−0.300088	+	0.376299i
$485$	3.21056e7	+	4.70903e7i	0.281421	+	0.412768i
$486$	−6.25108e7	+	5.80015e7i	−0.544560	+	0.505278i
$487$	1.34128e7	+	1.78982e8i	0.116127	+	1.54961i	0.685832	+	0.727760i	$0.259438\pi$
$487$	1.34128e7	+	1.78982e8i	0.116127	+	1.54961i	−0.569705	+	0.821849i	$0.692943\pi$
$488$	−2.08431e7	+	5.31073e7i	−0.179350	+	0.456977i
$489$	−2.20752e7	+	9.67177e7i	−0.188789	+	0.827141i
$490$	5.50588e8	−	1.69834e8i	4.67992	−	1.44356i
$491$	2.04162e7	−	2.99451e7i	0.172477	−	0.252977i	−0.730261	−	0.683168i	$-0.760602\pi$
$491$	2.04162e7	−	2.99451e7i	0.172477	−	0.252977i	0.902738	+	0.430191i	$0.141554\pi$
$492$	7.28240e6	+	4.83156e7i	0.0611476	+	0.405688i
$493$	−1.10506e7	+	4.33705e6i	−0.0922245	+	0.0361955i
$494$	−1.54077e8	+	7.41998e7i	−1.27808	+	0.615491i
$495$	3.73940e7	+	7.76494e7i	0.308309	+	0.640210i
$496$	1.37153e7	+	3.49459e7i	0.112398	+	0.286386i
$497$	2.47787e8	−	3.73479e7i	2.01841	−	0.304226i
$498$	9.34279e7	+	6.36981e7i	0.756464	+	0.515749i
$499$	−3.27604e7	−	1.06207e8i	−0.263662	−	0.854771i	−0.986501	−	0.163754i	$-0.947640\pi$
$499$	−3.27604e7	−	1.06207e8i	−0.263662	−	0.854771i	0.722839	−	0.691016i	$-0.242837\pi$
$500$	−1.93286e8	−	4.41164e7i	−1.54629	−	0.352931i
$501$	1.67068e8	+	6.55695e7i	1.32856	+	0.521421i
$502$	−1.48983e8	+	1.11648e7i	−1.17768	+	0.0882548i
$503$	−7.59366e7	−	8.18402e7i	−0.596688	−	0.643077i	0.360426	−	0.932788i	$-0.382631\pi$
$503$	−7.59366e7	−	8.18402e7i	−0.596688	−	0.643077i	−0.957114	+	0.289711i	$0.906441\pi$
$504$	2.40115e7	−	1.63708e7i	0.187555	−	0.127873i
$505$	1.16105e8	+	9.25903e7i	0.901520	+	0.718938i
$506$	−1.60775e7	+	1.73274e7i	−0.124099	+	0.133746i
$507$	1.25794e7	−	8.34586e7i	0.0965239	−	0.640394i
$508$	−1.19151e6	−	5.22035e6i	−0.00908881	−	0.0398207i
$509$	−1.29802e8	−	2.24824e8i	−0.984304	−	1.70486i	−0.644991	−	0.764190i	$-0.723139\pi$
$509$	−1.29802e8	−	2.24824e8i	−0.984304	−	1.70486i	−0.339313	−	0.940674i	$-0.610195\pi$
$510$	−8.28599e7	−	4.78392e7i	−0.624646	−	0.360639i
$511$	2.16538e8	+	6.67931e7i	1.62282	+	0.500575i
$512$	−9.08644e7	+	7.24620e7i	−0.676993	+	0.539884i
$513$	7.09471e6	−	9.46723e7i	0.0525512	−	0.701247i
$514$	1.46755e8	+	7.06736e7i	1.08070	+	0.520436i
$515$			4.05858e8i			2.97134i
$516$	1.03621e8	−	3.62527e6i	0.754219	−	0.0263871i
$517$	−2.09654e8			−1.51716
$518$	−2.26416e7	+	4.70158e7i	−0.162899	+	0.338263i
$519$	1.92232e8	+	1.44058e7i	1.37507	+	0.103047i
$520$	−8.69567e7	−	1.09040e8i	−0.618433	−	0.775491i
$521$	−5.39255e7	+	1.74822e8i	−0.381312	+	1.23618i	0.538097	+	0.842883i	$0.319143\pi$
$521$	−5.39255e7	+	1.74822e8i	−0.381312	+	1.23618i	−0.919409	+	0.393302i	$0.871333\pi$
$522$	1.00038e7	−	1.73270e7i	0.0703319	−	0.121818i
$523$	−2.42292e8	+	1.39887e8i	−1.69369	+	0.977853i	−0.742200	+	0.670179i	$0.766217\pi$
$523$	−2.42292e8	+	1.39887e8i	−1.69369	+	0.977853i	−0.951492	+	0.307675i	$0.900449\pi$
$524$	−8.96149e7	+	2.04540e7i	−0.622854	+	0.142162i
$525$	−6.62640e8	−	9.98769e7i	−4.57931	−	0.690220i
$526$	5.88946e7	+	5.46462e7i	0.404686	+	0.375494i
$527$	6.19023e6	−	7.76230e6i	0.0422936	−	0.0530345i
$528$	−1.51816e8	−	2.22673e8i	−1.03137	−	1.51275i
$529$	1.07259e8	−	9.95222e7i	0.724550	−	0.672284i
$530$	3.47514e6	+	4.63725e7i	0.0233424	+	0.311482i
$531$	1.57637e7	−	4.01652e7i	0.105287	−	0.268266i
$532$	3.42599e7	−	1.50103e8i	0.227537	−	0.996903i
$533$	9.85180e7	−	3.03888e7i	0.650630	−	0.200693i
$534$	−2.34232e8	+	3.43556e8i	−1.53824	+	2.25618i
$535$	4.66570e7	+	3.09549e8i	0.304688	+	2.02147i
$536$	−6.48678e7	+	2.54588e7i	−0.421245	+	0.165327i
$537$	1.24680e8	−	6.00426e7i	0.805143	−	0.387736i
$538$	−1.03979e8	−	2.15914e8i	−0.667724	−	1.38654i
$539$	−1.56813e8	−	3.99552e8i	−1.00142	−	2.55157i
$540$	−1.50387e8	+	2.26672e7i	−0.955056	+	0.143952i
$541$	1.62729e8	+	1.10947e8i	1.02772	+	0.700685i	0.954981	−	0.296667i	$-0.0958750\pi$
$541$	1.62729e8	+	1.10947e8i	1.02772	+	0.700685i	0.0727347	+	0.997351i	$0.476827\pi$
$542$	−8.24381e7	−	2.67258e8i	−0.517762	−	1.67854i
$543$	1.01074e8	+	2.30694e7i	0.631304	+	0.144091i
$544$	4.61979e7	+	1.81313e7i	0.286962	+	0.112624i
$545$	−1.92594e8	+	1.44330e7i	−1.18975	+	0.0891591i
$546$	3.57726e8	+	3.85537e8i	2.19772	+	2.36858i
$547$	3.62627e7	−	2.47235e7i	0.221564	−	0.151059i	−0.447452	−	0.894308i	$-0.647668\pi$
$547$	3.62627e7	−	2.47235e7i	0.221564	−	0.151059i	0.669015	+	0.743249i	$0.266716\pi$
$548$	7.66733e7	+	6.11449e7i	0.465910	+	0.371551i
$549$	−3.77303e7	+	4.06636e7i	−0.228020	+	0.245747i
$550$	−9.72407e7	+	6.45150e8i	−0.584467	+	3.87768i
$551$	1.20077e7	+	5.26093e7i	0.0717805	+	0.314491i
$552$	−4.48674e6	−	7.77127e6i	−0.0266756	−	0.0462035i
$553$	−1.18768e8	−	6.85708e7i	−0.702303	−	0.405475i
$554$	−3.20470e8	−	9.88518e7i	−1.88477	−	0.581373i
$555$	4.59328e7	−	3.66302e7i	0.268686	−	0.214270i
$556$	1.29538e7	−	1.72857e8i	0.0753657	−	1.00569i
$557$	−1.89759e8	−	9.13833e7i	−1.09809	−	0.528812i	−0.205032	−	0.978755i	$-0.565730\pi$
$557$	−1.89759e8	−	9.13833e7i	−1.09809	−	0.528812i	−0.893057	+	0.449943i	$0.851444\pi$
$558$			1.67330e7i			0.0963102i
$559$	−4.01508e7	−	2.15060e8i	−0.229858	−	1.23119i
$560$	6.87251e8			3.91337
$561$	−3.09248e7	+	6.42160e7i	−0.175153	+	0.363710i
$562$	−6.46396e7	−	4.84407e6i	−0.364158	−	0.0272899i
$563$	−1.76797e8	−	2.21696e8i	−0.990715	−	1.24232i	−0.970144	−	0.242529i	$-0.922023\pi$
$563$	−1.76797e8	−	2.21696e8i	−0.990715	−	1.24232i	−0.0205713	−	0.999788i	$-0.506549\pi$
$564$	−4.60821e7	+	1.49394e8i	−0.256859	+	0.832716i
$565$	1.24119e8	−	2.14981e8i	0.688166	−	1.19194i
$566$	3.99068e8	−	2.30402e8i	2.20088	−	1.27068i
$567$	−3.77391e8	+	8.61371e7i	−2.07034	+	0.472543i
$568$	9.15847e7	+	1.38042e7i	0.499779	+	0.0753295i
$569$	−7.29034e7	−	6.76445e7i	−0.395741	−	0.367194i	0.457055	−	0.889439i	$-0.348904\pi$
$569$	−7.29034e7	−	6.76445e7i	−0.395741	−	0.367194i	−0.852796	+	0.522245i	$0.825095\pi$
$570$	−2.71167e8	+	3.40033e8i	−1.46424	+	1.83610i
$571$	−1.23062e7	−	1.80499e7i	−0.0661024	−	0.0969544i	0.791764	−	0.610827i	$-0.209163\pi$
$571$	−1.23062e7	−	1.80499e7i	−0.0661024	−	0.0969544i	−0.857867	+	0.513872i	$0.828210\pi$
$572$	1.49600e8	−	1.38809e8i	0.799364	−	0.741702i
$573$	2.22735e6	+	2.97220e7i	0.0118393	+	0.157984i
$574$	−8.50850e7	+	2.16793e8i	−0.449901	+	1.14633i
$575$	−1.05450e7	+	4.62007e7i	−0.0554682	+	0.243022i
$576$	−1.35553e7	+	4.18125e6i	−0.0709318	+	0.0218795i
$577$	−1.36657e8	+	2.00439e8i	−0.711384	+	1.04341i	0.285007	+	0.958525i	$0.408004\pi$
$577$	−1.36657e8	+	2.00439e8i	−0.711384	+	1.04341i	−0.996391	+	0.0848827i	$0.972948\pi$
$578$	3.44094e7	+	2.28291e8i	0.178194	+	1.18224i
$579$	2.96204e8	−	1.16251e8i	1.52600	−	0.598912i
$580$	7.78842e7	−	3.75070e7i	0.399177	−	0.192233i
$581$	9.32003e7	+	1.93532e8i	0.475214	+	0.986791i
$582$	−2.90220e7	−	7.39469e7i	−0.147217	−	0.375103i
$583$	3.42546e7	−	5.16305e6i	0.172867	−	0.0260556i
$584$	6.92023e7	+	4.71813e7i	0.347442	+	0.236882i
$585$	−3.99708e7	−	1.29582e8i	−0.199653	−	0.647258i
$586$	−1.09988e8	−	2.51041e7i	−0.546579	−	0.124753i
$587$	1.26996e8	+	4.98423e7i	0.627879	+	0.246424i	0.657877	−	0.753126i	$-0.271455\pi$
$587$	1.26996e8	+	4.98423e7i	0.627879	+	0.246424i	−0.0299979	+	0.999550i	$0.509550\pi$
$588$	−3.19178e8	+	2.39191e7i	−1.57001	+	0.117656i
$589$	−3.06966e7	−	3.30831e7i	−0.150226	−	0.161905i
$590$	3.86480e8	−	2.63497e8i	1.88179	−	1.28298i
$591$	−1.05001e8	−	8.37358e7i	−0.508666	−	0.405647i
$592$	−2.86179e7	+	3.08427e7i	−0.137934	+	0.148658i
$593$	3.51582e7	−	2.33260e8i	0.168602	−	1.11860i	−0.731155	−	0.682211i	$-0.761018\pi$
$593$	3.51582e7	−	2.33260e8i	0.168602	−	1.11860i	0.899757	−	0.436391i	$-0.143744\pi$
$594$	6.32551e7	+	2.77139e8i	0.301812	+	1.32232i
$595$	−9.08775e7	−	1.57404e8i	−0.431425	−	0.747251i
$596$	1.75544e7	+	1.01350e7i	0.0829176	+	0.0478725i
$597$	−1.28695e8	−	3.96972e7i	−0.604839	−	0.186568i
$598$	2.90781e7	−	2.31890e7i	0.135976	−	0.108437i
$599$	1.03874e7	−	1.38610e8i	0.0483310	−	0.644933i	−0.919461	−	0.393181i	$-0.871374\pi$
$599$	1.03874e7	−	1.38610e8i	0.0483310	−	0.644933i	0.967792	−	0.251751i	$-0.0810065\pi$
$600$	−2.23157e8	−	1.07467e8i	−1.03313	−	0.497531i
$601$		−	7.49553e7i		−	0.345286i	−0.984984	−	0.172643i	$-0.944769\pi$
$601$		−	7.49553e7i		−	0.345286i	0.984984	−	0.172643i	$-0.0552307\pi$
$602$	4.36367e8	+	2.31984e8i	2.00015	+	1.06333i
$603$	−6.77558e7			−0.309026
$604$	1.16727e6	−	2.42387e6i	0.00529739	−	0.0110001i
$605$	2.92015e8	+	2.18835e7i	1.31868	+	0.0988212i
$606$	−1.29053e8	−	1.61827e8i	−0.579897	−	0.727167i
$607$	−9.22709e6	+	2.99135e7i	−0.0412571	+	0.133752i	−0.973858	−	0.227156i	$-0.927057\pi$
$607$	−9.22709e6	+	2.99135e7i	−0.0412571	+	0.133752i	0.932601	+	0.360909i	$0.117533\pi$
$608$	1.12796e8	−	1.95369e8i	0.501862	−	0.869251i
$609$	1.43722e8	−	8.29780e7i	0.636315	−	0.367376i
$610$	−5.86280e8	+	1.33815e8i	−2.58295	+	0.589541i
$611$	3.26196e8	+	4.91662e7i	1.43006	+	0.215548i
$612$	8.92295e6	+	8.27929e6i	0.0389273	+	0.0361193i
$613$	1.24489e8	−	1.56104e8i	0.540442	−	0.677693i	−0.434367	−	0.900736i	$-0.643028\pi$
$613$	1.24489e8	−	1.56104e8i	0.540442	−	0.677693i	0.974808	+	0.223044i	$0.0715992\pi$
$614$	1.02591e8	+	1.50473e8i	0.443203	+	0.650059i
$615$	1.92205e8	−	1.78340e8i	0.826304	−	0.766698i
$616$	−1.75385e7	−	2.34035e8i	−0.0750325	−	1.00124i
$617$	−5.05131e7	+	1.28705e8i	−0.215055	+	0.547950i	−0.997170	−	0.0751838i	$-0.976046\pi$
$617$	−5.05131e7	+	1.28705e8i	−0.215055	+	0.547950i	0.782115	+	0.623134i	$0.214141\pi$
$618$	1.25877e8	−	5.51505e8i	0.533313	−	2.33660i
$619$	−6.31149e7	+	1.94684e7i	−0.266109	+	0.0820838i	−0.424938	−	0.905222i	$-0.639704\pi$
$619$	−6.31149e7	+	1.94684e7i	−0.266109	+	0.0820838i	0.158829	+	0.987306i	$0.449228\pi$
$620$	−4.07264e7	+	5.97346e7i	−0.170884	+	0.250640i
$621$	3.07731e6	+	2.04166e7i	0.0128498	+	0.0852530i
$622$	3.86810e8	−	1.51812e8i	1.60741	−	0.630862i
$623$	−7.11663e8	+	3.42719e8i	−2.94314	+	1.41734i
$624$	1.83988e8	+	3.82054e8i	0.757243	+	1.57243i
$625$	1.82225e8	+	4.64301e8i	0.746393	+	1.90178i
$626$	−1.70728e7	+	2.57331e6i	−0.0695956	+	0.0104898i
$627$	2.67691e8	+	1.82508e8i	1.08600	+	0.740424i
$628$	−1.24627e7	−	4.04029e7i	−0.0503190	−	0.163130i
$629$	1.08483e7	+	2.47605e6i	0.0435923	+	0.00994966i
$630$	2.85151e8	+	1.11913e8i	1.14039	+	0.447570i
$631$	3.57234e7	−	2.67710e6i	0.142189	−	0.0106556i	−0.00344562	−	0.999994i	$-0.501097\pi$
$631$	3.57234e7	−	2.67710e6i	0.142189	−	0.0106556i	0.145634	+	0.989338i	$0.453478\pi$
$632$	−3.44773e7	−	3.71577e7i	−0.136578	−	0.147196i
$633$	−2.48491e8	+	1.69418e8i	−0.979713	+	0.667957i
$634$	−1.24326e8	−	9.91465e7i	−0.487858	−	0.389054i
$635$	−1.95439e7	+	2.10633e7i	−0.0763291	+	0.0822632i
$636$	3.85011e6	−	2.55438e7i	0.0149659	−	0.0992920i
$637$	1.50282e8	+	6.58428e8i	0.581418	+	2.54736i
$638$	−8.07878e7	−	1.39929e8i	−0.311088	−	0.538821i
$639$	7.79901e7	+	4.50276e7i	0.298907	+	0.172574i
$640$	3.74189e8	+	1.15422e8i	1.42742	+	0.440300i
$641$	−1.56362e8	+	1.24694e8i	−0.593686	+	0.473449i	−0.873645	−	0.486563i	$-0.838250\pi$
$641$	−1.56362e8	+	1.24694e8i	−0.593686	+	0.473449i	0.279960	+	0.960012i	$0.409679\pi$
$642$	3.26066e7	−	4.35105e8i	0.123225	−	1.64433i
$643$	3.46249e8	+	1.66745e8i	1.30243	+	0.627219i	0.951057	−	0.309015i	$-0.0999992\pi$
$643$	3.46249e8	+	1.66745e8i	1.30243	+	0.627219i	0.351377	+	0.936234i	$0.385713\pi$
$644$			3.34841e7i			0.125366i
$645$	−3.29306e8	−	4.48469e8i	−1.22721	−	1.67130i
$646$	−8.23734e7			−0.305555
$647$	2.05202e8	−	4.26106e8i	0.757650	−	1.57328i	−0.0604312	−	0.998172i	$-0.519248\pi$
$647$	2.05202e8	−	4.26106e8i	0.757650	−	1.57328i	0.818081	−	0.575103i	$-0.195038\pi$
$648$	−1.42675e8	−	1.06920e7i	−0.524352	−	0.0392948i
$649$	−2.17255e8	−	2.72429e8i	−0.794760	−	0.996598i
$650$	3.02589e8	−	9.80970e8i	1.10183	−	3.57203i
$651$	−6.93975e7	+	1.20200e8i	−0.251537	+	0.435674i
$652$	1.18491e8	−	6.84110e7i	0.427507	−	0.246822i
$653$	3.46982e7	−	7.91964e6i	0.124614	−	0.0284424i	−0.159759	−	0.987156i	$-0.551072\pi$
$653$	3.46982e7	−	7.91964e6i	0.124614	−	0.0284424i	0.284373	+	0.958714i	$0.408215\pi$
$654$	2.66186e8	+	4.01210e7i	0.951593	+	0.143430i
$655$	3.61583e8	+	3.35500e8i	1.28672	+	1.19390i
$656$	−1.17076e8	+	1.46809e8i	−0.414721	+	0.520044i
$657$	4.58752e7	+	6.72865e7i	0.161764	+	0.237264i
$658$	−5.46254e8	+	5.06850e8i	−1.91742	+	1.77910i
$659$	−2.52702e7	−	3.37207e8i	−0.0882983	−	1.17826i	−0.848725	−	0.528835i	$-0.822629\pi$
$659$	−2.52702e7	−	3.37207e8i	−0.0882983	−	1.17826i	0.760426	−	0.649424i	$-0.224990\pi$
$660$	1.89616e8	−	4.83134e8i	0.659543	−	1.68049i
$661$	1.16767e8	−	5.11589e8i	0.404310	−	1.77140i	−0.205301	−	0.978699i	$-0.565817\pi$
$661$	1.16767e8	−	5.11589e8i	0.404310	−	1.77140i	0.609611	−	0.792700i	$-0.291326\pi$
$662$	−2.89233e8	+	8.92166e7i	−0.996952	+	0.307519i
$663$	6.31745e7	−	9.26600e7i	0.216771	−	0.317945i
$664$	1.18331e7	+	7.85074e7i	0.0404198	+	0.268168i
$665$	−7.69080e8	+	3.01842e8i	−2.61521	+	1.02639i
$666$	−1.68965e7	+	8.13692e6i	−0.0571971	+	0.0275447i
$667$	−5.09198e6	−	1.05736e7i	−0.0171597	−	0.0356325i
$668$	−9.04324e7	−	2.30418e8i	−0.303386	−	0.773014i
$669$	−3.63660e8	+	5.48129e7i	−1.21456	+	0.183065i
$670$	−6.06896e8	−	4.13774e8i	−2.01785	−	1.37575i
$671$	1.32043e8	+	4.28072e8i	0.437066	+	1.41693i
$672$	−6.76395e8	−	1.54383e8i	−2.22891	−	0.508734i
$673$	−2.74718e7	−	1.07819e7i	−0.0901242	−	0.0353711i	0.319851	−	0.947468i	$-0.396367\pi$
$673$	−2.74718e7	−	1.07819e7i	−0.0901242	−	0.0353711i	−0.409975	+	0.912097i	$0.634463\pi$
$674$	3.15368e7	−	2.36336e6i	0.103000	−	0.00771880i
$675$	3.87633e8	+	4.17769e8i	1.26040	+	1.35839i
$676$	−9.61783e7	+	6.55732e7i	−0.311341	+	0.212269i
$677$	2.44249e8	+	1.94782e8i	0.787168	+	0.627745i	0.932308	−	0.361666i	$-0.117792\pi$
$677$	2.44249e8	+	1.94782e8i	0.787168	+	0.627745i	−0.145140	+	0.989411i	$0.546363\pi$
$678$	−2.35337e8	+	2.53633e8i	−0.755095	+	0.813799i
$679$	2.24911e7	−	1.49219e8i	0.0718459	−	0.476666i
$680$	−1.49487e7	−	6.54943e7i	−0.0475418	−	0.208294i
$681$	1.03113e8	+	1.78598e8i	0.326493	+	0.565502i
$682$	1.17027e8	+	6.75658e7i	0.368922	+	0.212997i
$683$	5.40225e8	+	1.66637e8i	1.69556	+	0.523010i	0.983777	−	0.179393i	$-0.0574134\pi$
$683$	5.40225e8	+	1.66637e8i	1.69556	+	0.523010i	0.711779	+	0.702403i	$0.247890\pi$
$684$	4.32595e7	−	3.44983e7i	0.135180	−	0.107803i
$685$	3.93271e7	−	5.24783e8i	0.122354	−	1.63271i
$686$	−7.15651e8	−	3.44639e8i	−2.21681	−	1.06756i
$687$			5.19537e8i			1.60231i
$688$	2.81069e8	+	2.82437e8i	0.863073	+	0.867275i
$689$	−5.45067e7			−0.166645
$690$	4.10397e7	−	8.52199e7i	0.124927	−	0.259414i
$691$	4.84417e7	+	3.63020e6i	0.146820	+	0.0110026i	0.147937	−	0.988997i	$-0.452737\pi$
$691$	4.84417e7	+	3.63020e6i	0.146820	+	0.0110026i	−0.00111739	+	0.999999i	$0.500356\pi$
$692$	−1.65765e8	−	2.07863e8i	−0.500236	−	0.627277i
$693$	6.72613e7	−	2.18056e8i	0.202100	−	0.655191i
$694$	−5.08647e7	+	8.81002e7i	−0.152173	+	0.263571i
$695$	−8.05561e8	+	4.65091e8i	−2.39963	+	1.38543i
$696$	5.98013e7	−	1.36492e7i	0.177371	−	0.0404838i
$697$	4.91057e7	+	7.40149e6i	0.145022	+	0.0218585i
$698$	1.91012e8	+	1.77233e8i	0.561686	+	0.521168i
$699$	1.30841e8	−	1.64069e8i	0.383100	−	0.480392i
$700$	5.20635e8	+	7.63631e8i	1.51789	+	2.22633i
$701$	1.38013e8	−	1.28057e8i	0.400651	−	0.371749i	−0.453957	−	0.891024i	$-0.649988\pi$
$701$	1.38013e8	−	1.28057e8i	0.400651	−	0.371749i	0.854608	+	0.519274i	$0.173798\pi$
$702$	−3.34251e7	−	4.46027e8i	−0.0966188	−	1.28929i
$703$	1.84791e7	−	4.70841e7i	0.0531883	−	0.135522i
$704$	−2.54916e7	+	1.11686e8i	−0.0730599	+	0.320097i
$705$	8.01677e8	−	2.47285e8i	2.28787	−	0.705716i
$706$	−2.72564e8	+	3.99779e8i	−0.774560	+	1.13607i
$707$	−5.86032e7	−	3.88807e8i	−0.165830	−	1.10021i
$708$	−2.41879e8	+	9.49306e7i	−0.681551	+	0.267489i
$709$	3.58029e8	−	1.72418e8i	1.00457	−	0.483774i	0.142081	−	0.989855i	$-0.454621\pi$
$709$	3.58029e8	−	1.72418e8i	1.00457	−	0.483774i	0.862486	+	0.506081i	$0.168906\pi$
$710$	4.23588e8	+	8.79591e8i	1.18350	+	2.45757i
$711$	−1.80061e7	−	4.58788e7i	−0.0500970	−	0.127645i
$712$	−2.88690e8	+	4.35130e7i	−0.799819	+	0.120553i
$713$	8.10962e6	+	5.52904e6i	0.0223734	+	0.0152539i
$714$	7.46708e7	+	2.42077e8i	0.205143	+	0.665057i
$715$	−1.06767e9	−	2.43688e8i	−2.92091	−	0.666678i
$716$	−1.77664e8	−	6.97279e7i	−0.484016	−	0.189962i
$717$	−1.13746e8	+	8.52409e6i	−0.308588	+	0.0231255i
$718$	−1.71456e7	−	1.84786e7i	−0.0463213	−	0.0499225i
$719$	1.53952e8	−	1.04962e8i	0.414188	−	0.282389i	−0.338244	−	0.941058i	$-0.609833\pi$
$719$	1.53952e8	−	1.04962e8i	0.414188	−	0.282389i	0.752432	+	0.658670i	$0.228881\pi$
$720$	1.93099e8	+	1.53992e8i	0.517349	+	0.412572i
$721$	7.30918e8	−	7.87743e8i	1.95013	−	2.10174i
$722$	1.65233e7	−	1.09625e8i	0.0439021	−	0.291271i
$723$	1.11616e8	+	4.89023e8i	0.295333	+	1.29394i
$724$	−7.14921e7	−	1.23828e8i	−0.188383	−	0.326289i
$725$	−2.80533e8	−	1.61966e8i	−0.736156	−	0.425020i
$726$	−3.90021e8	−	1.20305e8i	−1.01924	−	0.314395i
$727$	−7.77502e7	+	6.20037e7i	−0.202348	+	0.161367i	−0.719421	−	0.694574i	$-0.755593\pi$
$727$	−7.77502e7	+	6.20037e7i	−0.202348	+	0.161367i	0.517073	+	0.855941i	$0.327021\pi$
$728$	−2.75959e7	+	3.68242e8i	−0.0715238	+	0.954419i
$729$	1.92916e8	+	9.29034e7i	0.497950	+	0.239800i
$730$			8.82845e8i			2.26943i
$731$	2.75213e7	−	1.01722e8i	0.0704559	−	0.260414i
$732$	3.34056e8			0.851699
$733$	−1.00653e8	+	2.09008e8i	−0.255572	+	0.530702i	−0.988794	−	0.149288i	$-0.952302\pi$
$733$	−1.00653e8	+	2.09008e8i	−0.255572	+	0.530702i	0.733221	+	0.679990i	$0.238016\pi$
$734$	−6.20245e8	−	4.64810e7i	−1.56847	−	0.117540i
$735$	1.07089e9	+	1.34285e9i	2.69701	+	3.38194i
$736$	−1.44614e7	+	4.68827e7i	−0.0362724	+	0.117592i
$737$	−2.73589e8	+	4.73870e8i	−0.683433	+	1.18374i
$738$	−7.24832e7	+	4.18482e7i	−0.180330	+	0.104114i
$739$	−1.92920e8	+	4.40326e7i	−0.478017	+	0.109104i	−0.454739	−	0.890625i	$-0.650267\pi$
$739$	−1.92920e8	+	4.40326e7i	−0.478017	+	0.109104i	−0.0232779	+	0.999729i	$0.507410\pi$
$740$	−8.01225e7	−	1.20765e7i	−0.197724	−	0.0298021i
$741$	−3.73694e8	−	3.46737e8i	−0.918461	−	0.852208i
$742$	7.67683e7	−	9.62645e7i	0.187919	−	0.235643i
$743$	3.07659e7	+	4.51252e7i	0.0750071	+	0.110015i	0.861909	−	0.507063i	$-0.169269\pi$
$743$	3.07659e7	+	4.51252e7i	0.0750071	+	0.110015i	−0.786902	+	0.617078i	$0.788316\pi$
$744$	−3.76057e7	+	3.48930e7i	−0.0913134	+	0.0847265i
$745$	−8.12860e6	−	1.08469e8i	−0.0196583	−	0.262322i
$746$	1.63905e6	−	4.17623e6i	0.00394798	−	0.0100593i
$747$	−1.71778e7	+	7.52608e7i	−0.0412103	+	0.180554i
$748$	9.39333e7	−	2.89746e7i	0.224448	−	0.0692329i
$749$	4.66915e8	−	6.84839e8i	1.11120	−	1.62983i
$750$	−2.21007e8	−	1.46629e9i	−0.523869	−	3.47564i
$751$	−2.27052e8	+	8.91114e7i	−0.536050	+	0.210384i	−0.617895	−	0.786261i	$-0.712014\pi$
$751$	−2.27052e8	+	8.91114e7i	−0.536050	+	0.210384i	0.0818443	+	0.996645i	$0.473919\pi$
$752$	−5.41319e8	+	2.60686e8i	−1.27292	+	0.613004i

Introduction	Features
Universe	News

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

\(f(q)\)	\(=\)	\(q+(4.47573 - 9.29395i) q^{2} +(30.6638 + 2.29794i) q^{3} +(-26.4420 - 33.1572i) q^{4} +(-67.0797 + 217.467i) q^{5} +(158.600 - 274.703i) q^{6} +(521.839 - 301.284i) q^{7} +(217.132 - 49.5589i) q^{8} +(214.131 + 32.2751i) q^{9} +O(q^{10})\)	\(q+(4.47573 - 9.29395i) q^{2} +(30.6638 + 2.29794i) q^{3} +(-26.4420 - 33.1572i) q^{4} +(-67.0797 + 217.467i) q^{5} +(158.600 - 274.703i) q^{6} +(521.839 - 301.284i) q^{7} +(217.132 - 49.5589i) q^{8} +(214.131 + 32.2751i) q^{9} +(1720.90 + 1596.76i) q^{10} +(1090.36 - 1367.27i) q^{11} +(-734.619 - 1077.49i) q^{12} +(-2017.10 + 1871.60i) q^{13} +(-464.506 - 6198.41i) q^{14} +(-2556.64 + 6514.23i) q^{15} +(1115.19 - 4885.99i) q^{16} +(-1266.53 + 390.672i) q^{17} +(1258.36 - 1845.67i) q^{18} +(897.955 + 5957.54i) q^{19} +(8984.32 - 3526.08i) q^{20} +(16693.9 - 8039.36i) q^{21} +(-7827.16 - 16253.3i) q^{22} +(-478.704 - 1219.72i) q^{23} +(6771.96 - 1020.71i) q^{24} +(-29882.3 - 20373.4i) q^{25} +(8366.53 + 27123.6i) q^{26} +(-15362.7 - 3506.43i) q^{27} +(-23788.2 - 9336.17i) q^{28} +(8931.60 - 669.331i) q^{29} +(49100.0 + 52917.2i) q^{30} +(-6189.16 + 4219.70i) q^{31} +(-29274.7 - 23345.8i) q^{32} +(36576.5 - 39420.0i) q^{33} +(-2037.75 + 13519.6i) q^{34} +(30514.5 + 133693. i) q^{35} +(-4591.90 - 7953.41i) q^{36} +(-7270.58 - 4197.67i) q^{37} +(59388.1 + 18318.8i) q^{38} +(-66152.9 + 52755.2i) q^{39} +(-3787.70 + 50543.4i) q^{40} +(-33757.3 - 16256.7i) q^{41} -191134. i q^{42} +(-42463.6 + 67217.6i) q^{43} -74166.0 q^{44} +(-21382.6 + 44401.5i) q^{45} +(-13478.5 - 1010.08i) q^{46} +(-74746.9 - 93729.6i) q^{47} +(45423.8 - 147260. i) q^{48} +(122719. - 212556. i) q^{49} +(-323094. + 186538. i) q^{50} +(-39734.3 + 9069.10i) q^{51} +(115393. + 17392.7i) q^{52} +(14520.8 + 13473.4i) q^{53} +(-101348. + 127086. i) q^{54} +(224195. + 328833. i) q^{55} +(98376.4 - 91279.9i) q^{56} +(13844.7 + 184744. i) q^{57} +(33754.7 - 86005.5i) q^{58} +(44337.5 - 194255. i) q^{59} +(283596. - 87477.8i) q^{60} +(-144301. + 211650. i) q^{61} +(11516.6 + 76408.0i) q^{62} +(121466. - 47671.9i) q^{63} +(-59019.6 + 28422.3i) q^{64} +(-271704. - 564200. i) q^{65} +(-202662. - 516373. i) q^{66} +(-309393. + 46633.5i) q^{67} +(46443.1 + 31664.4i) q^{68} +(-11876.1 - 38501.2i) q^{69} +(1.37911e6 + 314772. i) q^{70} +(387116. + 151932. i) q^{71} +(48094.2 - 3604.16i) q^{72} +(255790. + 275676. i) q^{73} +(-71554.1 + 48784.7i) q^{74} +(-869487. - 693393. i) q^{75} +(173792. - 187303. i) q^{76} +(157056. - 1.04200e6i) q^{77} +(194221. + 850939. i) q^{78} +(-113798. - 197103. i) q^{79} +(987734. + 570269. i) q^{80} +(-613871. - 189354. i) q^{81} +(-302177. + 240978. i) q^{82} +(-26640.0 + 355486. i) q^{83} +(-707982. - 340946. i) q^{84} -301634. i q^{85} +(434661. + 695502. i) q^{86} +275415. q^{87} +(168991. - 350914. i) q^{88} +(-1.30720e6 - 97961.3i) q^{89} +(316962. + 397458. i) q^{90} +(-488720. + 1.58439e6i) q^{91} +(-27784.5 + 48124.2i) q^{92} +(-199480. + 115170. i) q^{93} +(-1.20567e6 + 275185. i) q^{94} +(-1.35580e6 - 204355. i) q^{95} +(-844028. - 783144. i) q^{96} +(156144. - 195799. i) q^{97} +(-1.42623e6 - 2.09189e6i) q^{98} +(277609. - 257583. 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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