LMFDB - Embedded newform 32.7.h.a.3.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [32,7,Mod(3,32)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("32.3"); S:= CuspForms(chi, 7); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(32, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([4, 3])) N = Newforms(chi, 7, names="a")

Level:	$ N $	$=$	$ 32 = 2^{5} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	32.h (of order $8$, degree $4$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$7.36173067584$
Analytic rank:	$0$
Dimension:	$92$
Relative dimension:	$23$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			3.2
Character	$\chi$	$=$	32.3
Dual form			32.7.h.a.11.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-7.86726 + 1.45129i) q^{2} +(-13.7231 + 33.1306i) q^{3} +(59.7875 - 22.8354i) q^{4} +(61.4842 + 148.436i) q^{5} +(59.8812 - 280.563i) q^{6} +(332.829 + 332.829i) q^{7} +(-437.223 + 266.421i) q^{8} +(-393.829 - 393.829i) q^{9} +(-699.136 - 1078.55i) q^{10} +(-637.963 - 1540.18i) q^{11} +(-63.9218 + 2294.17i) q^{12} +(-1428.92 + 3449.73i) q^{13} +(-3101.48 - 2135.42i) q^{14} -5761.52 q^{15} +(3053.09 - 2730.54i) q^{16} -1575.55i q^{17} +(3669.92 + 2526.79i) q^{18} +(-986.102 - 408.457i) q^{19} +(7065.58 + 7470.59i) q^{20} +(-15594.2 + 6459.35i) q^{21} +(7254.27 + 11191.1i) q^{22} +(15539.5 - 15539.5i) q^{23} +(-2826.62 - 18141.6i) q^{24} +(-7204.36 + 7204.36i) q^{25} +(6235.15 - 29213.7i) q^{26} +(-5699.84 + 2360.95i) q^{27} +(27499.3 + 12298.7i) q^{28} +(-8155.67 - 3378.19i) q^{29} +(45327.4 - 8361.65i) q^{30} +3618.95i q^{31} +(-20056.6 + 25912.8i) q^{32} +59781.8 q^{33} +(2286.58 + 12395.2i) q^{34} +(-28940.0 + 69867.4i) q^{35} +(-32539.3 - 14552.8i) q^{36} +(23269.9 + 56178.6i) q^{37} +(8350.71 + 1782.31i) q^{38} +(-94682.2 - 94682.2i) q^{39} +(-66428.7 - 48518.9i) q^{40} +(8441.89 + 8441.89i) q^{41} +(113310. - 73449.2i) q^{42} +(-20269.4 - 48934.7i) q^{43} +(-73312.8 - 77515.3i) q^{44} +(34244.1 - 82672.6i) q^{45} +(-99700.6 + 144805. i) q^{46} -89733.3 q^{47} +(48566.5 + 138622. i) q^{48} +103901. i q^{49} +(46222.9 - 67134.2i) q^{50} +(52198.8 + 21621.4i) q^{51} +(-6655.88 + 238881. i) q^{52} +(-56431.4 + 23374.6i) q^{53} +(41415.7 - 26846.3i) q^{54} +(189393. - 189393. i) q^{55} +(-234193. - 56847.7i) q^{56} +(27064.8 - 27064.8i) q^{57} +(69065.5 + 14740.8i) q^{58} +(140648. - 58258.3i) q^{59} +(-344467. + 131567. i) q^{60} +(329067. + 136304. i) q^{61} +(-5252.16 - 28471.2i) q^{62} -262155. i q^{63} +(120184. - 232971. i) q^{64} -599920. q^{65} +(-470319. + 86761.0i) q^{66} +(13446.0 - 32461.4i) q^{67} +(-35978.3 - 94198.0i) q^{68} +(301581. + 728081. i) q^{69} +(126281. - 591665. i) q^{70} +(289001. + 289001. i) q^{71} +(277115. + 67266.6i) q^{72} +(362307. + 362307. i) q^{73} +(-264602. - 408200. i) q^{74} +(-139818. - 337551. i) q^{75} +(-68283.8 - 1902.58i) q^{76} +(300283. - 724948. i) q^{77} +(882301. + 607477. i) q^{78} -131823. q^{79} +(593027. + 285303. i) q^{80} -627261. i q^{81} +(-78666.2 - 54162.9i) q^{82} +(-34007.1 - 14086.2i) q^{83} +(-784839. + 742289. i) q^{84} +(233868. - 96871.2i) q^{85} +(230483. + 355565. i) q^{86} +(223842. - 223842. i) q^{87} +(689268. + 503435. i) q^{88} +(-438387. + 438387. i) q^{89} +(-149425. + 700105. i) q^{90} +(-1.62376e6 + 672582. i) q^{91} +(574215. - 1.28391e6i) q^{92} +(-119898. - 49663.3i) q^{93} +(705955. - 130229. i) q^{94} -171487. i q^{95} +(-583266. - 1.02009e6i) q^{96} -965834. q^{97} +(-150790. - 817414. i) q^{98} +(-355319. + 857816. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 92 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9} + 2996 q^{10} - 4 q^{11} - 3892 q^{12} - 4 q^{13} - 8532 q^{14} - 8 q^{15} + 14096 q^{16} + 24296 q^{18} - 4 q^{19} - 14004 q^{20}+ \cdots + 5967768 q^{99}+O(q^{100}) $ 92 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9 + 2996 * q^10 - 4 * q^11 - 3892 * q^12 - 4 * q^13 - 8532 * q^14 - 8 * q^15 + 14096 * q^16 + 24296 * q^18 - 4 * q^19 - 14004 * q^20 - 4 * q^21 - 19552 * q^22 + 13116 * q^23 - 43568 * q^24 - 4 * q^25 + 5296 * q^26 - 68644 * q^27 + 85496 * q^28 - 4 * q^29 + 102980 * q^30 - 58904 * q^32 - 8 * q^33 - 139248 * q^34 + 162332 * q^35 - 328464 * q^36 - 4 * q^37 + 457684 * q^38 - 254404 * q^39 + 430952 * q^40 - 4 * q^41 - 256504 * q^42 + 145436 * q^43 - 808764 * q^44 - 2920 * q^45 - 197284 * q^46 - 8 * q^47 + 349488 * q^48 + 1254548 * q^50 - 157792 * q^51 - 71644 * q^52 + 443676 * q^53 - 455840 * q^54 - 232708 * q^55 - 619736 * q^56 - 4 * q^57 - 290272 * q^58 + 886140 * q^59 + 803000 * q^60 - 652996 * q^61 + 1415352 * q^62 - 1533928 * q^64 - 8 * q^65 - 308980 * q^66 - 1509604 * q^67 + 447632 * q^68 + 1083452 * q^69 - 676264 * q^70 - 267012 * q^71 - 1219564 * q^72 - 4 * q^73 - 661588 * q^74 + 2083672 * q^75 + 873980 * q^76 - 932964 * q^77 + 1480180 * q^78 - 1721864 * q^79 - 2377928 * q^80 - 1407364 * q^82 + 3074396 * q^83 + 2103584 * q^84 + 62496 * q^85 + 2146368 * q^86 - 2029892 * q^87 + 2855072 * q^88 - 4 * q^89 + 2497832 * q^90 - 3700804 * q^91 - 540888 * q^92 + 2912 * q^93 - 2438936 * q^94 + 3127168 * q^96 - 8 * q^97 + 2073880 * q^98 + 5967768 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/32\mathbb{Z}\right)^\times$.

$n$	$5$	$31$
$\chi(n)$	$e\left(\frac{3}{8}\right)$	$-1$

Coefficient data

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

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

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

$2$	−7.86726	+	1.45129i	−0.983407	+	0.181412i
$2$	−7.86726	+	1.45129i	−0.983407	+	0.181412i
$3$	−13.7231	+	33.1306i	−0.508264	+	1.22706i	0.436618	+	0.899647i	$0.356176\pi$
$3$	−13.7231	+	33.1306i	−0.508264	+	1.22706i	−0.944882	+	0.327411i	$0.893824\pi$
$4$	59.7875	−	22.8354i	0.934180	−	0.356803i
$5$	61.4842	+	148.436i	0.491873	+	1.18749i	0.953766	+	0.300551i	$0.0971706\pi$
$5$	61.4842	+	148.436i	0.491873	+	1.18749i	−0.461893	+	0.886936i	$0.652829\pi$
$6$	59.8812	−	280.563i	0.277228	−	1.29890i
$7$	332.829	+	332.829i	0.970346	+	0.970346i	0.999573	−	0.0292271i	$-0.00930459\pi$
$7$	332.829	+	332.829i	0.970346	+	0.970346i	−0.0292271	+	0.999573i	$0.509305\pi$
$8$	−437.223	+	266.421i	−0.853951	+	0.520354i
$9$	−393.829	−	393.829i	−0.540232	−	0.540232i
$10$	−699.136	−	1078.55i	−0.699136	−	1.07855i
$11$	−637.963	−	1540.18i	−0.479311	−	1.15716i	−0.959933	−	0.280231i	$-0.909589\pi$
$11$	−637.963	−	1540.18i	−0.479311	−	1.15716i	0.480621	−	0.876928i	$-0.340411\pi$
$12$	−63.9218	+	2294.17i	−0.0369918	+	1.32764i
$13$	−1428.92	+	3449.73i	−0.650398	+	1.57020i	0.161803	+	0.986823i	$0.448269\pi$
$13$	−1428.92	+	3449.73i	−0.650398	+	1.57020i	−0.812201	+	0.583377i	$0.801731\pi$
$14$	−3101.48	−	2135.42i	−1.13028	−	0.778213i
$15$	−5761.52			−1.70712
$16$	3053.09	−	2730.54i	0.745383	−	0.666636i
$17$		−	1575.55i		−	0.320690i	−0.987061	−	0.160345i	$-0.948739\pi$
$17$		−	1575.55i		−	0.320690i	0.987061	−	0.160345i	$-0.0512606\pi$
$18$	3669.92	+	2526.79i	0.629272	+	0.433264i
$19$	−986.102	−	408.457i	−0.143768	−	0.0595505i	0.309640	−	0.950854i	$-0.399792\pi$
$19$	−986.102	−	408.457i	−0.143768	−	0.0595505i	−0.453407	+	0.891304i	$0.649792\pi$
$20$	7065.58	+	7470.59i	0.883197	+	0.933824i
$21$	−15594.2	+	6459.35i	−1.68386	+	0.697479i
$22$	7254.27	+	11191.1i	0.681280	+	1.05101i
$23$	15539.5	−	15539.5i	1.27718	−	1.27718i	0.334941	−	0.942239i	$-0.391284\pi$
$23$	15539.5	−	15539.5i	1.27718	−	1.27718i	0.942239	−	0.334941i	$-0.108716\pi$
$24$	−2826.62	−	18141.6i	−0.204472	−	1.31232i
$25$	−7204.36	+	7204.36i	−0.461079	+	0.461079i
$26$	6235.15	−	29213.7i	0.354754	−	1.66214i
$27$	−5699.84	+	2360.95i	−0.289582	+	0.119949i
$28$	27499.3	+	12298.7i	1.25270	+	0.560255i
$29$	−8155.67	−	3378.19i	−0.334399	−	0.138513i	0.209165	−	0.977880i	$-0.432926\pi$
$29$	−8155.67	−	3378.19i	−0.334399	−	0.138513i	−0.543564	+	0.839368i	$0.682926\pi$
$30$	45327.4	−	8361.65i	1.67879	−	0.309691i
$31$			3618.95i			0.121478i	0.998154	+	0.0607390i	$0.0193457\pi$
$31$			3618.95i			0.121478i	−0.998154	+	0.0607390i	$0.980654\pi$
$32$	−20056.6	+	25912.8i	−0.612079	+	0.790796i
$33$	59781.8			1.66352
$34$	2286.58	+	12395.2i	0.0581768	+	0.315368i
$35$	−28940.0	+	69867.4i	−0.674986	+	1.62956i
$36$	−32539.3	−	14552.8i	−0.697430	−	0.311917i
$37$	23269.9	+	56178.6i	0.459399	+	1.10909i	0.968641	+	0.248464i	$0.0799256\pi$
$37$	23269.9	+	56178.6i	0.459399	+	1.10909i	−0.509243	+	0.860623i	$0.670074\pi$
$38$	8350.71	+	1782.31i	0.152185	+	0.0324813i
$39$	−94682.2	−	94682.2i	−1.59615	−	1.59615i
$40$	−66428.7	−	48518.9i	−1.03795	−	0.758107i
$41$	8441.89	+	8441.89i	0.122486	+	0.122486i	0.765693	−	0.643206i	$-0.222396\pi$
$41$	8441.89	+	8441.89i	0.122486	+	0.122486i	−0.643206	+	0.765693i	$0.722396\pi$
$42$	113310.	−	73449.2i	1.52939	−	0.991378i
$43$	−20269.4	−	48934.7i	−0.254939	−	0.615477i	0.743651	−	0.668568i	$-0.233093\pi$
$43$	−20269.4	−	48934.7i	−0.254939	−	0.615477i	−0.998590	+	0.0530914i	$0.983093\pi$
$44$	−73312.8	−	77515.3i	−0.860641	−	0.909975i
$45$	34244.1	−	82672.6i	0.375793	−	0.907244i
$46$	−99700.6	+	144805.i	−1.02429	+	1.48768i
$47$	−89733.3			−0.864291			−0.432145	−	0.901804i	$-0.642243\pi$
$47$	−89733.3			−0.864291			−0.432145	+	0.901804i	$0.642243\pi$
$48$	48566.5	+	138622.i	0.439150	+	1.25346i
$49$			103901.i			0.883142i
$50$	46222.9	−	67134.2i	0.369784	−	0.537074i
$51$	52198.8	+	21621.4i	0.393505	+	0.162995i
$52$	−6655.88	+	238881.i	−0.0473364	+	1.69891i
$53$	−56431.4	+	23374.6i	−0.379047	+	0.157006i	−0.564068	−	0.825728i	$-0.690765\pi$
$53$	−56431.4	+	23374.6i	−0.379047	+	0.157006i	0.185021	+	0.982734i	$0.440765\pi$
$54$	41415.7	−	26846.3i	0.263017	−	0.170492i
$55$	189393.	−	189393.i	1.13835	−	1.13835i
$56$	−234193.	−	56847.7i	−1.33355	−	0.323704i
$57$	27064.8	−	27064.8i	0.146144	−	0.146144i
$58$	69065.5	+	14740.8i	0.353979	+	0.0755505i
$59$	140648.	−	58258.3i	0.684821	−	0.283662i	−0.0130195	−	0.999915i	$-0.504144\pi$
$59$	140648.	−	58258.3i	0.684821	−	0.283662i	0.697841	+	0.716253i	$0.254144\pi$
$60$	−344467.	+	131567.i	−1.59475	+	0.609105i
$61$	329067.	+	136304.i	1.44975	+	0.600508i	0.962141	−	0.272552i	$-0.0878677\pi$
$61$	329067.	+	136304.i	1.44975	+	0.600508i	0.487613	+	0.873060i	$0.337868\pi$
$62$	−5252.16	−	28471.2i	−0.0220375	−	0.119462i
$63$		−	262155.i		−	1.04842i
$64$	120184.	−	232971.i	0.458464	−	0.888713i
$65$	−599920.			−2.18451
$66$	−470319.	+	86761.0i	−1.63592	+	0.301782i
$67$	13446.0	−	32461.4i	0.0447062	−	0.107930i	−0.899949	−	0.435995i	$-0.856396\pi$
$67$	13446.0	−	32461.4i	0.0447062	−	0.107930i	0.944655	+	0.328065i	$0.106396\pi$
$68$	−35978.3	−	94198.0i	−0.114423	−	0.299582i
$69$	301581.	+	728081.i	0.918029	+	2.21632i
$70$	126281.	−	591665.i	0.368165	−	1.72497i
$71$	289001.	+	289001.i	0.807466	+	0.807466i	0.984250	−	0.176783i	$-0.0565692\pi$
$71$	289001.	+	289001.i	0.807466	+	0.807466i	−0.176783	+	0.984250i	$0.556569\pi$
$72$	277115.	+	67266.6i	0.742443	+	0.180220i
$73$	362307.	+	362307.i	0.931339	+	0.931339i	0.997790	−	0.0664509i	$-0.0211676\pi$
$73$	362307.	+	362307.i	0.931339	+	0.931339i	−0.0664509	+	0.997790i	$0.521168\pi$
$74$	−264602.	−	408200.i	−0.652977	−	1.00734i
$75$	−139818.	−	337551.i	−0.331421	−	0.800121i
$76$	−68283.8	−	1902.58i	−0.155553	−	0.00433412i
$77$	300283.	−	724948.i	0.657747	−	1.58794i
$78$	882301.	+	607477.i	1.85923	+	1.28011i
$79$	−131823.			−0.267368			−0.133684	−	0.991024i	$-0.542681\pi$
$79$	−131823.			−0.267368			−0.133684	+	0.991024i	$0.542681\pi$
$80$	593027.	+	285303.i	1.15826	+	0.557232i
$81$		−	627261.i		−	1.18030i
$82$	−78666.2	−	54162.9i	−0.142675	−	0.0982336i
$83$	−34007.1	−	14086.2i	−0.0594752	−	0.0246354i	0.352748	−	0.935719i	$-0.385247\pi$
$83$	−34007.1	−	14086.2i	−0.0594752	−	0.0246354i	−0.412223	+	0.911083i	$0.635247\pi$
$84$	−784839.	+	742289.i	−1.32417	+	1.25238i
$85$	233868.	−	96871.2i	0.380815	−	0.157739i
$86$	230483.	+	355565.i	0.362363	+	0.559016i
$87$	223842.	−	223842.i	0.339926	−	0.339926i
$88$	689268.	+	503435.i	1.01144	+	0.738746i
$89$	−438387.	+	438387.i	−0.621853	+	0.621853i	−0.946005	−	0.324152i	$-0.894921\pi$
$89$	−438387.	+	438387.i	−0.621853	+	0.621853i	0.324152	+	0.946005i	$0.394921\pi$
$90$	−149425.	+	700105.i	−0.204973	+	0.960363i
$91$	−1.62376e6	+	672582.i	−2.15475	+	0.892526i
$92$	574215.	−	1.28391e6i	0.737414	−	1.64882i
$93$	−119898.	−	49663.3i	−0.149060	−	0.0617429i
$94$	705955.	−	130229.i	0.849950	−	0.156792i
$95$		−	171487.i		−	0.200013i
$96$	−583266.	−	1.02009e6i	−0.659255	−	1.15299i
$97$	−965834.			−1.05825			−0.529124	−	0.848545i	$-0.677479\pi$
$97$	−965834.			−1.05825			−0.529124	+	0.848545i	$0.677479\pi$
$98$	−150790.	−	817414.i	−0.160212	−	0.868488i
$99$	−355319.	+	857816.i	−0.366195	+	0.884074i
$100$	−266216.	+	595245.i	−0.266216	+	0.595245i
$101$	−198836.	−	480033.i	−0.192988	−	0.465915i	0.797533	−	0.603276i	$-0.206138\pi$
$101$	−198836.	−	480033.i	−0.192988	−	0.465915i	−0.990521	+	0.137361i	$0.956138\pi$
$102$	−442040.	−	94345.7i	−0.416544	−	0.0889041i
$103$	411631.	+	411631.i	0.376701	+	0.376701i	0.869911	−	0.493210i	$-0.164176\pi$
$103$	411631.	+	411631.i	0.376701	+	0.376701i	−0.493210	+	0.869911i	$0.664176\pi$
$104$	−294323.	−	1.88900e6i	−0.261652	−	1.67931i
$105$	−1.91760e6	−	1.91760e6i	−1.65649	−	1.65649i
$106$	410037.	−	265793.i	0.344275	−	0.223165i
$107$	649623.	+	1.56833e6i	0.530286	+	1.28022i	0.931334	+	0.364166i	$0.118646\pi$
$107$	649623.	+	1.56833e6i	0.530286	+	1.28022i	−0.401048	+	0.916057i	$0.631354\pi$
$108$	−286866.	+	271313.i	−0.227723	+	0.215377i
$109$	−333992.	+	806328.i	−0.257903	+	0.622633i	−0.998799	−	0.0489864i	$-0.984401\pi$
$109$	−333992.	+	806328.i	−0.257903	+	0.622633i	0.740896	+	0.671619i	$0.234401\pi$
$110$	−1.21514e6	+	1.76487e6i	−0.912953	+	1.32597i
$111$	−2.18056e6			−1.59441
$112$	1.92496e6	+	107353.i	1.37015	+	0.0764115i
$113$			194897.i			0.135073i	0.997717	+	0.0675366i	$0.0215139\pi$
$113$			194897.i			0.135073i	−0.997717	+	0.0675366i	$0.978486\pi$
$114$	−173647.	+	252205.i	−0.117207	+	0.170231i
$115$	3.26204e6	+	1.35118e6i	2.14485	+	0.888424i
$116$	−564749.	−	15735.5i	−0.361811	−	0.0100810i
$117$	1.92136e6	−	795852.i	1.19964	−	0.496906i
$118$	−1.02196e6	+	662454.i	−0.621998	+	0.403190i
$119$	524387.	−	524387.i	0.311180	−	0.311180i
$120$	2.51907e6	−	1.53499e6i	1.45779	−	0.888305i
$121$	−712472.	+	712472.i	−0.402172	+	0.402172i
$122$	−2.78667e6	−	594765.i	−1.53464	−	0.327541i
$123$	−395534.	+	163835.i	−0.212553	+	0.0880425i
$124$	82640.2	+	216368.i	0.0433437	+	0.113482i
$125$	806970.	+	334258.i	0.413169	+	0.171140i
$126$	380464.	+	2.06244e6i	0.190196	+	1.03103i
$127$		−	3.11356e6i		−	1.52001i	−0.649918	−	0.760004i	$-0.725197\pi$
$127$		−	3.11356e6i		−	1.52001i	0.649918	−	0.760004i	$-0.274803\pi$
$128$	−607406.	+	2.00726e6i	−0.289634	+	0.957138i
$129$	1.89939e6			0.884802
$130$	4.71972e6	−	870660.i	2.14826	−	0.396295i
$131$	184299.	−	444936.i	0.0819801	−	0.197917i	−0.877574	−	0.479441i	$-0.840840\pi$
$131$	184299.	−	444936.i	0.0819801	−	0.197917i	0.959554	+	0.281523i	$0.0908396\pi$
$132$	3.57421e6	−	1.36514e6i	1.55402	−	0.593548i
$133$	−192257.	−	464149.i	−0.0817197	−	0.197289i
$134$	−58671.8	+	274896.i	−0.0243846	+	0.114250i
$135$	−700899.	−	700899.i	−0.284875	−	0.284875i
$136$	419759.	+	688865.i	0.166872	+	0.273853i
$137$	−628038.	−	628038.i	−0.244244	−	0.244244i	0.574359	−	0.818603i	$-0.305251\pi$
$137$	−628038.	−	628038.i	−0.244244	−	0.244244i	−0.818603	+	0.574359i	$0.805251\pi$
$138$	−3.42927e6	−	5.29032e6i	−1.30486	−	2.01300i
$139$	1.93707e6	+	4.67651e6i	0.721276	+	1.74132i	0.669683	+	0.742647i	$0.266430\pi$
$139$	1.93707e6	+	4.67651e6i	0.721276	+	1.74132i	0.0515936	+	0.998668i	$0.483570\pi$
$140$	−134802.	+	4.83805e6i	−0.0491259	+	1.76314i
$141$	1.23142e6	−	2.97291e6i	0.439288	−	1.06053i
$142$	−2.69307e6	−	1.85422e6i	−0.940552	−	0.647584i
$143$	6.22480e6			2.12871
$144$	−2.27776e6	−	127028.i	−0.762818	−	0.0425415i
$145$		−	1.41830e6i		−	0.465226i
$146$	−3.37617e6	−	2.32455e6i	−1.08484	−	0.746930i
$147$	−3.44229e6	−	1.42584e6i	−1.08367	−	0.448869i
$148$	2.67411e6	+	2.82740e6i	0.824886	+	0.872171i
$149$	−5.83599e6	+	2.41734e6i	−1.76423	+	0.730768i	−0.768357	+	0.640022i	$0.778925\pi$
$149$	−5.83599e6	+	2.41734e6i	−1.76423	+	0.730768i	−0.995874	+	0.0907463i	$0.971075\pi$
$150$	1.58987e6	+	2.45268e6i	0.471073	+	0.726721i
$151$	701720.	−	701720.i	0.203813	−	0.203813i	−0.597818	−	0.801632i	$-0.703966\pi$
$151$	701720.	−	701720.i	0.203813	−	0.203813i	0.801632	+	0.597818i	$0.203966\pi$
$152$	539968.	−	84131.8i	0.153758	−	0.0239568i
$153$	−620496.	+	620496.i	−0.173247	+	0.173247i
$154$	−1.31029e6	+	6.13915e6i	−0.358762	+	1.68092i
$155$	−537182.	+	222508.i	−0.144254	+	0.0597518i
$156$	−7.82291e6	−	3.49870e6i	−2.06061	−	0.921581i
$157$	−2.30146e6	−	953297.i	−0.594709	−	0.246337i	0.0649658	−	0.997887i	$-0.479306\pi$
$157$	−2.30146e6	−	953297.i	−0.594709	−	0.246337i	−0.659675	+	0.751551i	$0.729306\pi$
$158$	1.03709e6	−	191314.i	0.262932	−	0.0485038i
$159$		−	2.19038e6i		−	0.544913i
$160$	−5.07956e6	−	1.38389e6i	−1.24013	−	0.337865i
$161$	1.03439e7			2.47861
$162$	910340.	+	4.93482e6i	0.214121	+	1.16072i
$163$	746210.	−	1.80151e6i	0.172305	−	0.415981i	−0.814010	−	0.580850i	$-0.802720\pi$
$163$	746210.	−	1.80151e6i	0.172305	−	0.415981i	0.986315	+	0.164869i	$0.0527202\pi$
$164$	697493.	+	311946.i	0.158128	+	0.0707208i
$165$	3.67564e6	+	8.87377e6i	0.818240	+	1.97541i
$166$	287986.	+	61465.6i	0.0629575	+	0.0134372i
$167$	2.96464e6	+	2.96464e6i	0.636535	+	0.636535i	0.949699	−	0.313164i	$-0.101389\pi$
$167$	2.96464e6	+	2.96464e6i	0.636535	+	0.636535i	−0.313164	+	0.949699i	$0.601389\pi$
$168$	5.09725e6	−	6.97881e6i	1.07500	−	1.47182i
$169$	−6.44574e6	−	6.44574e6i	−1.33540	−	1.33540i
$170$	−1.69931e6	+	1.10152e6i	−0.345880	+	0.224205i
$171$	227493.	+	549218.i	0.0454968	+	0.109839i
$172$	−2.32930e6	−	2.46282e6i	−0.457763	−	0.484003i
$173$	1.22629e6	−	2.96052e6i	0.236839	−	0.571781i	−0.760113	−	0.649791i	$-0.774857\pi$
$173$	1.22629e6	−	2.96052e6i	0.236839	−	0.571781i	0.996953	+	0.0780098i	$0.0248566\pi$
$174$	−1.43617e6	+	2.08589e6i	−0.272619	+	0.395953i
$175$	−4.79564e6			−0.894813
$176$	−6.15328e6	−	2.96032e6i	−1.12867	−	0.543001i
$177$			5.45923e6i			0.984490i
$178$	2.81268e6	−	4.08513e6i	0.498723	−	0.724346i
$179$	−6.77602e6	−	2.80672e6i	−1.18145	−	0.489373i	−0.296489	−	0.955036i	$-0.595816\pi$
$179$	−6.77602e6	−	2.80672e6i	−1.18145	−	0.489373i	−0.884962	+	0.465664i	$0.845816\pi$
$180$	159508.	−	5.72477e6i	0.0273504	−	0.981613i
$181$	1.01847e7	−	4.21864e6i	1.71756	−	0.711438i	0.717677	−	0.696376i	$-0.245206\pi$
$181$	1.01847e7	−	4.21864e6i	1.71756	−	0.711438i	0.999887	−	0.0150617i	$-0.00479446\pi$
$182$	1.17984e7	−	7.64792e6i	1.95708	−	1.26861i
$183$	−9.03165e6	+	9.03165e6i	−1.47372	+	1.47372i
$184$	−2.65416e6	+	1.09342e7i	−0.426063	+	1.75523i
$185$	−6.90818e6	+	6.90818e6i	−1.09106	+	1.09106i
$186$	1.01534e6	+	216707.i	0.157788	+	0.0336771i
$187$	−2.42663e6	+	1.00514e6i	−0.371089	+	0.153710i
$188$	−5.36493e6	+	2.04909e6i	−0.807403	+	0.308382i
$189$	−2.68286e6	−	1.11128e6i	−0.397386	−	0.164603i
$190$	248877.	+	1.34913e6i	0.0362848	+	0.196695i
$191$			1.67702e6i			0.240679i	0.992733	+	0.120339i	$0.0383983\pi$
$191$			1.67702e6i			0.240679i	−0.992733	+	0.120339i	$0.961602\pi$
$192$	6.06916e6	+	7.17884e6i	0.857482	+	1.01426i
$193$	1.10026e6			0.153046			0.0765231	−	0.997068i	$-0.475618\pi$
$193$	1.10026e6			0.153046			0.0765231	+	0.997068i	$0.475618\pi$
$194$	7.59846e6	−	1.40171e6i	1.04069	−	0.191978i
$195$	8.23278e6	−	1.98757e7i	1.11031	−	2.68051i
$196$	2.37261e6	+	6.21196e6i	0.315108	+	0.825013i
$197$	508458.	+	1.22753e6i	0.0665054	+	0.160558i	0.953638	−	0.300957i	$-0.0973060\pi$
$197$	508458.	+	1.22753e6i	0.0665054	+	0.160558i	−0.887132	+	0.461515i	$0.847306\pi$
$198$	1.55044e6	−	7.26433e6i	0.199738	−	0.935836i
$199$	438222.	+	438222.i	0.0556077	+	0.0556077i	0.734364	−	0.678756i	$-0.237481\pi$
$199$	438222.	+	438222.i	0.0556077	+	0.0556077i	−0.678756	+	0.734364i	$0.737481\pi$
$200$	1.23052e6	−	5.06931e6i	0.153815	−	0.633663i
$201$	890944.	+	890944.i	0.109714	+	0.109714i
$202$	2.26096e6	+	3.48797e6i	0.274308	+	0.423174i
$203$	−1.59008e6	−	3.83880e6i	−0.190078	−	0.458888i
$204$	3.61457e6	+	100712.i	0.425761	+	0.0118629i
$205$	−734037.	+	1.77212e6i	−0.0852033	+	0.205699i
$206$	−3.83581e6	−	2.64101e6i	−0.438788	−	0.302112i
$207$	−1.22398e7			−1.37995
$208$	5.05700e6	+	1.44341e7i	0.561957	+	1.60398i
$209$			1.77935e6i			0.194905i
$210$	1.78692e7	+	1.23032e7i	1.92951	+	1.32850i
$211$	8.15619e6	+	3.37841e6i	0.868241	+	0.359637i	0.771925	−	0.635714i	$-0.219294\pi$
$211$	8.15619e6	+	3.37841e6i	0.868241	+	0.359637i	0.0963158	+	0.995351i	$0.469294\pi$
$212$	−2.84012e6	+	2.68614e6i	−0.298078	+	0.281917i
$213$	−1.35408e7	+	5.60877e6i	−1.40121	+	0.580402i
$214$	−7.38685e6	−	1.13956e7i	−0.753734	−	1.16278i
$215$	6.01742e6	−	6.01742e6i	0.605473	−	0.605473i
$216$	1.86309e6	−	2.55082e6i	0.184873	−	0.253115i
$217$	−1.20449e6	+	1.20449e6i	−0.117876	+	0.117876i
$218$	1.45738e6	−	6.82831e6i	0.140671	−	0.659088i
$219$	−1.69754e7	+	7.03144e6i	−1.61617	+	0.669441i
$220$	6.99848e6	−	1.56482e7i	0.657257	−	1.46959i
$221$	5.43521e6	+	2.25134e6i	0.503547	+	0.208576i
$222$	1.71551e7	−	3.16464e6i	1.56795	−	0.289244i
$223$		−	1.07187e7i		−	0.966556i	−0.875467	−	0.483278i	$-0.839446\pi$
$223$		−	1.07187e7i		−	0.966556i	0.875467	−	0.483278i	$-0.160554\pi$
$224$	−1.52999e7	+	1.94911e6i	−1.36127	+	0.173417i
$225$	5.67458e6			0.498179
$226$	−282852.	−	1.53330e6i	−0.0245038	−	0.132832i
$227$	4.84199e6	−	1.16896e7i	0.413949	−	0.999361i	−0.570118	−	0.821563i	$-0.693103\pi$
$227$	4.84199e6	−	1.16896e7i	0.413949	−	0.999361i	0.984067	−	0.177798i	$-0.0568974\pi$
$228$	1.00010e6	−	2.23617e6i	0.0843800	−	0.188669i
$229$	−892585.	−	2.15489e6i	−0.0743264	−	0.179440i	0.882350	−	0.470595i	$-0.155961\pi$
$229$	−892585.	−	2.15489e6i	−0.0743264	−	0.179440i	−0.956676	+	0.291155i	$0.905961\pi$
$230$	−2.76243e7	−	5.89592e6i	−2.27043	−	0.484583i
$231$	1.98971e7	+	1.98971e7i	1.61419	+	1.61419i
$232$	4.46586e6	−	695822.i	0.357636	−	0.0557229i
$233$	1.54524e7	+	1.54524e7i	1.22160	+	1.22160i	0.967063	+	0.254537i	$0.0819231\pi$
$233$	1.54524e7	+	1.54524e7i	1.22160	+	1.22160i	0.254537	+	0.967063i	$0.418077\pi$
$234$	−1.39608e7	+	9.04962e6i	−1.08959	+	0.706290i
$235$	−5.51717e6	−	1.33196e7i	−0.425121	−	1.02633i
$236$	7.07863e6	−	6.69487e6i	0.538534	−	0.509338i
$237$	1.80903e6	−	4.36737e6i	0.135894	−	0.328077i
$238$	−3.36445e6	+	4.88653e6i	−0.249565	+	0.362468i
$239$	−1.00244e7			−0.734282			−0.367141	−	0.930165i	$-0.619663\pi$
$239$	−1.00244e7			−0.734282			−0.367141	+	0.930165i	$0.619663\pi$
$240$	−1.75904e7	+	1.57321e7i	−1.27246	+	1.13803i
$241$			9.00782e6i			0.643530i	0.946820	+	0.321765i	$0.104276\pi$
$241$			9.00782e6i			0.643530i	−0.946820	+	0.321765i	$0.895724\pi$
$242$	4.57120e6	−	6.63921e6i	0.322540	−	0.468457i
$243$	1.66263e7	+	6.88685e6i	1.15872	+	0.479957i
$244$	2.27866e7	+	634898.i	1.56859	+	0.0437054i
$245$	−1.54226e7	+	6.38825e6i	−1.04872	+	0.434394i
$246$	2.87399e6	−	1.86297e6i	0.193055	−	0.125141i
$247$	2.81813e6	−	2.81813e6i	0.187012	−	0.187012i
$248$	−964165.	−	1.58229e6i	−0.0632115	−	0.103736i
$249$	933369.	−	933369.i	0.0604582	−	0.0604582i
$250$	−6.83375e6	−	1.45854e6i	−0.437360	−	0.0933468i
$251$	1.45198e7	−	6.01431e6i	0.918206	−	0.380333i	0.127014	−	0.991901i	$-0.459461\pi$
$251$	1.45198e7	−	6.01431e6i	0.918206	−	0.380333i	0.791192	+	0.611568i	$0.209461\pi$
$252$	−5.98642e6	−	1.56736e7i	−0.374081	−	0.979416i
$253$	−3.38471e7	−	1.40199e7i	−2.09007	−	0.865734i
$254$	4.51869e6	+	2.44952e7i	0.275747	+	1.49479i
$255$			9.07755e6i			0.547454i
$256$	1.86549e6	−	1.66732e7i	0.111192	−	0.993799i
$257$	1.88052e7			1.10784			0.553922	−	0.832568i	$-0.313130\pi$
$257$	1.88052e7			1.10784			0.553922	+	0.832568i	$0.313130\pi$
$258$	−1.49430e7	+	2.75658e6i	−0.870121	+	0.160513i
$259$	−1.09529e7	+	2.64427e7i	−0.630422	+	1.52197i
$260$	−3.58677e7	+	1.36994e7i	−2.04072	+	0.779438i
$261$	1.88151e6	+	4.54237e6i	0.105824	+	0.255482i
$262$	−804192.	+	3.76790e6i	−0.0447153	+	0.209506i
$263$	5.57498e6	+	5.57498e6i	0.306461	+	0.306461i	0.843535	−	0.537074i	$-0.180470\pi$
$263$	5.57498e6	+	5.57498e6i	0.306461	+	0.306461i	−0.537074	+	0.843535i	$0.680470\pi$
$264$	−2.61380e7	+	1.59272e7i	−1.42056	+	0.865618i
$265$	−6.93927e6	−	6.93927e6i	−0.372886	−	0.372886i
$266$	2.18615e6	+	3.37256e6i	0.116154	+	0.179190i
$267$	−8.50797e6	−	2.05400e7i	−0.446984	−	1.07911i
$268$	62630.8	−	2.24783e6i	0.00325374	−	0.116777i
$269$	8.66495e6	−	2.09190e7i	0.445153	−	1.07469i	−0.528963	−	0.848645i	$-0.677419\pi$
$269$	8.66495e6	−	2.09190e7i	0.445153	−	1.07469i	0.974116	−	0.226049i	$-0.0725811\pi$
$270$	6.53136e6	+	4.49694e6i	0.331828	+	0.228468i
$271$	−2.05838e7			−1.03423			−0.517117	−	0.855915i	$-0.672995\pi$
$271$	−2.05838e7			−1.03423			−0.517117	+	0.855915i	$0.672995\pi$
$272$	−4.30210e6	−	4.81029e6i	−0.213783	−	0.239037i
$273$		−	6.30259e7i		−	3.09764i
$274$	5.85241e6	+	4.02947e6i	0.284500	+	0.195883i
$275$	1.56921e7	+	6.49989e6i	0.754543	+	0.312542i
$276$	3.46568e7	+	3.66434e7i	1.64839	+	1.74288i
$277$	−5.06142e6	+	2.09651e6i	−0.238140	+	0.0986410i	−0.498562	−	0.866854i	$-0.666138\pi$
$277$	−5.06142e6	+	2.09651e6i	−0.238140	+	0.0986410i	0.260422	+	0.965495i	$0.416138\pi$
$278$	−2.20264e7	−	3.39800e7i	−1.02520	−	1.58157i
$279$	1.42525e6	−	1.42525e6i	0.0656263	−	0.0656263i
$280$	−5.96092e6	−	3.82578e7i	−0.271543	−	1.74280i
$281$	2.62473e7	−	2.62473e7i	1.18295	−	1.18295i	0.203971	−	0.978977i	$-0.434615\pi$
$281$	2.62473e7	−	2.62473e7i	1.18295	−	1.18295i	0.978977	−	0.203971i	$-0.0653849\pi$
$282$	−5.37334e6	+	2.51758e7i	−0.239605	+	1.12263i
$283$	−3.11560e7	+	1.29052e7i	−1.37462	+	0.569385i	−0.943037	−	0.332689i	$-0.892044\pi$
$283$	−3.11560e7	+	1.29052e7i	−1.37462	+	0.569385i	−0.431581	+	0.902074i	$0.642044\pi$
$284$	2.38781e7	+	1.06792e7i	1.04243	+	0.466212i
$285$	5.68144e6	+	2.35333e6i	0.245428	+	0.101660i
$286$	−4.89721e7	+	9.03402e6i	−2.09339	+	0.386174i
$287$			5.61940e6i			0.237708i
$288$	1.81041e7	−	2.30634e6i	0.757878	−	0.0965485i
$289$	2.16552e7			0.897158
$290$	2.05837e6	+	1.11581e7i	0.0843974	+	0.457506i
$291$	1.32543e7	−	3.19986e7i	0.537869	−	1.29853i
$292$	2.99348e7	+	1.33880e7i	1.20234	+	0.537733i
$293$	1.51153e7	+	3.64917e7i	0.600918	+	1.45074i	0.872638	+	0.488368i	$0.162407\pi$
$293$	1.51153e7	+	3.64917e7i	0.600918	+	1.45074i	−0.271720	+	0.962376i	$0.587593\pi$
$294$	2.91507e7	+	6.22170e6i	1.14712	+	0.244831i
$295$	1.72952e7	+	1.72952e7i	0.673690	+	0.673690i
$296$	−2.51413e7	−	1.83629e7i	−0.969421	−	0.708055i
$297$	7.27257e6	+	7.27257e6i	0.277599	+	0.277599i
$298$	4.24049e7	−	2.74876e7i	1.60239	−	1.03869i
$299$	3.14022e7	+	7.58116e7i	1.17475	+	2.83610i
$300$	−1.60675e7	−	1.69885e7i	−0.595092	−	0.629205i
$301$	9.54063e6	−	2.30331e7i	0.349847	−	0.844604i
$302$	−4.50221e6	+	6.53901e6i	−0.163457	+	0.237406i
$303$	1.86324e7			0.669794
$304$	−4.12597e6	+	1.44554e6i	−0.146860	+	0.0514528i
$305$			5.72258e7i			2.01694i
$306$	3.98108e6	−	5.78213e6i	0.138943	−	0.201801i
$307$	−2.39699e7	−	9.92865e6i	−0.828420	−	0.343143i	−0.0721429	−	0.997394i	$-0.522984\pi$
$307$	−2.39699e7	−	9.92865e6i	−0.828420	−	0.343143i	−0.756277	+	0.654252i	$0.772984\pi$
$308$	1.39871e6	−	5.01999e7i	0.0478713	−	1.71811i
$309$	−1.92864e7	+	7.98871e6i	−0.653697	+	0.270770i
$310$	3.90323e6	−	2.53014e6i	0.131020	−	0.0849296i
$311$	−6.78614e6	+	6.78614e6i	−0.225601	+	0.225601i	−0.810852	−	0.585251i	$-0.800996\pi$
$311$	−6.78614e6	+	6.78614e6i	−0.225601	+	0.225601i	0.585251	+	0.810852i	$0.300996\pi$
$312$	6.66225e7	+	1.61719e7i	2.19360	+	0.532471i
$313$	−286924.	+	286924.i	−0.00935693	+	0.00935693i	−0.711770	−	0.702413i	$-0.752106\pi$
$313$	−286924.	+	286924.i	−0.00935693	+	0.00935693i	0.702413	+	0.711770i	$0.252106\pi$
$314$	1.94897e7	+	4.15973e6i	0.629530	+	0.134362i
$315$	3.89132e7	−	1.61184e7i	1.24499	−	0.515691i
$316$	−7.88137e6	+	3.01023e6i	−0.249770	+	0.0953979i
$317$	−2.21626e7	−	9.18003e6i	−0.695732	−	0.288182i	0.00665379	−	0.999978i	$-0.497882\pi$
$317$	−2.21626e7	−	9.18003e6i	−0.695732	−	0.288182i	−0.702386	+	0.711796i	$0.747882\pi$
$318$	3.17888e6	+	1.72323e7i	0.0988536	+	0.535872i
$319$			1.47163e7i			0.453344i
$320$	4.19706e7	+	3.51553e6i	1.28084	+	0.107285i
$321$	−6.08744e7			−1.84043
$322$	−8.13785e7	+	1.50121e7i	−2.43749	+	0.449649i
$323$	−643543.	+	1.55365e6i	−0.0190972	+	0.0461048i
$324$	−1.43238e7	−	3.75024e7i	−0.421136	−	1.10261i
$325$	−1.45586e7	−	3.51476e7i	−0.424102	−	1.02387i
$326$	−3.25610e6	+	1.52559e7i	−0.0939822	+	0.440337i
$327$	−2.21307e7	−	2.21307e7i	−0.632924	−	0.632924i
$328$	−5.94008e6	−	1.44189e6i	−0.168334	−	0.0408611i
$329$	−2.98658e7	−	2.98658e7i	−0.838661	−	0.838661i
$330$	−4.17956e7	−	6.44778e7i	−1.16302	−	1.79419i
$331$	−1.10767e7	−	2.67416e7i	−0.305441	−	0.737401i	−0.999841	−	0.0178115i	$-0.994330\pi$
$331$	−1.10767e7	−	2.67416e7i	−0.305441	−	0.737401i	0.694400	−	0.719589i	$-0.255670\pi$
$332$	−2.35487e6	−	65613.1i	−0.0643505	−	0.00179298i
$333$	1.29604e7	−	3.12891e7i	0.350982	−	0.847346i
$334$	−2.76261e7	−	1.90210e7i	−0.741448	−	0.510499i
$335$	5.64515e6			0.150155
$336$	−2.99731e7	+	6.23017e7i	−0.790158	+	1.64241i
$337$			603331.i			0.0157640i	0.999969	+	0.00788199i	$0.00250894\pi$
$337$			603331.i			0.0157640i	−0.999969	+	0.00788199i	$0.997491\pi$
$338$	6.00650e7	+	4.13556e7i	1.55550	+	1.07099i
$339$	−6.45703e6	−	2.67459e6i	−0.165743	−	0.0686528i
$340$	1.17703e7	−	1.11322e7i	0.299468	−	0.283232i
$341$	5.57383e6	−	2.30876e6i	0.140569	−	0.0582257i
$342$	−2.58683e6	−	3.99068e6i	−0.0646679	−	0.0997627i
$343$	4.57581e6	−	4.57581e6i	0.113393	−	0.113393i
$344$	2.18995e7	+	1.59952e7i	0.537971	+	0.392928i
$345$	−8.95308e7	+	8.95308e7i	−2.18030	+	2.18030i
$346$	−5.35094e6	+	2.50709e7i	−0.129182	+	0.605259i
$347$	−1.35211e6	+	560063.i	−0.0323611	+	0.0134044i	−0.398805	−	0.917036i	$-0.630575\pi$
$347$	−1.35211e6	+	560063.i	−0.0323611	+	0.0134044i	0.366444	+	0.930440i	$0.380575\pi$
$348$	8.27145e6	−	1.84945e7i	0.196265	−	0.438839i
$349$	2.58034e7	+	1.06881e7i	0.607018	+	0.251435i	0.664953	−	0.746885i	$-0.268452\pi$
$349$	2.58034e7	+	1.06881e7i	0.607018	+	0.251435i	−0.0579351	+	0.998320i	$0.518452\pi$
$350$	3.77285e7	−	6.95988e6i	0.879965	−	0.162329i
$351$		−	2.30365e7i		−	0.532716i
$352$	5.27058e7	+	1.43594e7i	1.20845	+	0.329236i
$353$	−2.71220e7			−0.616591			−0.308296	−	0.951291i	$-0.599759\pi$
$353$	−2.71220e7			−0.616591			−0.308296	+	0.951291i	$0.599759\pi$
$354$	−7.92294e6	−	4.29492e7i	−0.178598	−	0.968155i
$355$	−2.51291e7	+	6.06671e7i	−0.561685	+	1.35603i
$356$	−1.61993e7	+	3.62208e7i	−0.359043	+	0.802801i
$357$	1.01770e7	+	2.45695e7i	0.223674	+	0.539997i
$358$	5.73821e7	+	1.22472e7i	1.25062	+	0.266924i
$359$	−3.68079e7	−	3.68079e7i	−0.795531	−	0.795531i	0.186856	−	0.982387i	$-0.440170\pi$
$359$	−3.68079e7	−	3.68079e7i	−0.795531	−	0.795531i	−0.982387	+	0.186856i	$0.940170\pi$
$360$	7.05343e6	+	4.52697e7i	0.151179	+	0.970287i
$361$	−3.24609e7	−	3.24609e7i	−0.689984	−	0.689984i
$362$	−7.40032e7	+	4.79702e7i	−1.56000	+	1.01122i
$363$	−1.38273e7	−	3.33819e7i	−0.289079	−	0.697898i
$364$	−8.17216e7	+	7.72911e7i	−1.69447	+	1.60260i
$365$	−3.15032e7	+	7.60554e7i	−0.647852	+	1.56405i
$366$	5.79467e7	−	8.41619e7i	1.18191	−	1.71661i
$367$	3.20572e7			0.648526			0.324263	−	0.945967i	$-0.394884\pi$
$367$	3.20572e7			0.648526			0.324263	+	0.945967i	$0.394884\pi$
$368$	5.01219e6	−	8.98745e7i	0.100574	−	1.80340i
$369$		−	6.64932e6i		−	0.132342i
$370$	4.43227e7	−	6.43743e7i	0.875025	−	1.27089i
$371$	−2.65617e7	−	1.10022e7i	−0.520157	−	0.215456i
$372$	−8.30247e6	−	231330.i	−0.161279	−	0.00449369i
$373$	8.89865e7	−	3.68594e7i	1.71474	−	0.710268i	0.714797	−	0.699332i	$-0.246519\pi$
$373$	8.89865e7	−	3.68594e7i	1.71474	−	0.710268i	0.999940	−	0.0109358i	$-0.00348105\pi$
$374$	1.76321e7	−	1.14295e7i	0.337047	−	0.218479i
$375$	−2.21483e7	+	2.21483e7i	−0.419998	+	0.419998i
$376$	3.92334e7	−	2.39068e7i	0.738062	−	0.449737i
$377$	2.33077e7	−	2.33077e7i	0.434985	−	0.434985i
$378$	2.27195e7	+	4.84909e6i	0.420653	+	0.0897810i
$379$	−2.17755e7	+	9.01972e6i	−0.399992	+	0.165682i	−0.573605	−	0.819132i	$-0.694456\pi$
$379$	−2.17755e7	+	9.01972e6i	−0.399992	+	0.165682i	0.173614	+	0.984814i	$0.444456\pi$
$380$	−3.91596e6	−	1.02527e7i	−0.0713654	−	0.186848i
$381$	1.03154e8	+	4.27278e7i	1.86514	+	0.772565i
$382$	−2.43385e6	−	1.31935e7i	−0.0436619	−	0.236685i
$383$		−	3.35055e6i		−	0.0596376i	−0.999555	−	0.0298188i	$-0.990507\pi$
$383$		−	3.35055e6i		−	0.0596376i	0.999555	−	0.0298188i	$-0.00949302\pi$
$384$	−5.81662e7	−	4.76696e7i	−1.02725	−	0.841876i
$385$	1.26071e8			2.20919
$386$	−8.65602e6	+	1.59680e6i	−0.150507	+	0.0277644i
$387$	−1.12892e7	+	2.72546e7i	−0.194774	+	0.470226i
$388$	−5.77448e7	+	2.20552e7i	−0.988593	+	0.377586i
$389$	−2.27224e7	−	5.48568e7i	−0.386017	−	0.931926i	−0.990775	−	0.135517i	$-0.956730\pi$
$389$	−2.27224e7	−	5.48568e7i	−0.386017	−	0.931926i	0.604758	−	0.796409i	$-0.293270\pi$
$390$	−3.59239e7	+	1.68315e8i	−0.605606	+	2.83746i
$391$	−2.44831e7	−	2.44831e7i	−0.409578	−	0.409578i
$392$	−2.76814e7	−	4.54278e7i	−0.459546	−	0.754160i
$393$	1.22118e7	+	1.22118e7i	0.201189	+	0.201189i
$394$	−5.78167e6	−	8.91935e6i	−0.0945290	−	0.145829i
$395$	−8.10503e6	−	1.95673e7i	−0.131511	−	0.317497i
$396$	−1.65506e6	+	5.94005e7i	−0.0266519	+	0.956543i
$397$	−2.33507e7	+	5.63736e7i	−0.373189	+	0.900958i	0.620017	+	0.784588i	$0.287126\pi$
$397$	−2.33507e7	+	5.63736e7i	−0.373189	+	0.900958i	−0.993206	+	0.116370i	$0.962874\pi$
$398$	−4.08359e6	−	2.81161e6i	−0.0647729	−	0.0445971i
$399$	1.80159e7			0.283620
$400$	−2.32374e6	+	4.16674e7i	−0.0363085	+	0.651053i
$401$			3.11826e7i			0.483592i	0.970327	+	0.241796i	$0.0777365\pi$
$401$			3.11826e7i			0.483592i	−0.970327	+	0.241796i	$0.922263\pi$
$402$	−8.30231e6	−	5.71627e6i	−0.127797	−	0.0879902i
$403$	−1.24844e7	−	5.17121e6i	−0.190745	−	0.0790091i
$404$	−2.28496e7	−	2.41594e7i	−0.346526	−	0.366389i
$405$	9.31080e7	−	3.85666e7i	1.40159	−	0.580559i
$406$	1.80808e7	+	2.78931e7i	0.270172	+	0.416792i
$407$	7.16797e7	−	7.16797e7i	1.06320	−	1.06320i
$408$	−2.85829e7	+	4.45347e6i	−0.420849	+	0.0655720i
$409$	6.33002e7	−	6.33002e7i	0.925199	−	0.925199i	−0.0721922	−	0.997391i	$-0.523000\pi$
$409$	6.33002e7	−	6.33002e7i	0.925199	−	0.925199i	0.997391	+	0.0721922i	$0.0229995\pi$
$410$	3.20299e6	−	1.50070e7i	0.0464733	−	0.217743i
$411$	2.94259e7	−	1.21886e7i	0.423842	−	0.175561i
$412$	3.40102e7	+	1.52106e7i	0.486314	+	0.217498i
$413$	6.62017e7	+	2.74216e7i	0.939764	+	0.389263i
$414$	9.62935e7	−	1.77635e7i	1.35705	−	0.250338i
$415$		−	5.91396e6i		−	0.0827435i
$416$	−6.07328e7	−	1.06217e8i	−0.843613	−	1.47542i
$417$	−1.81518e8			−2.50329
$418$	−2.58236e6	−	1.39986e7i	−0.0353581	−	0.191671i
$419$	3.51286e7	−	8.48079e7i	0.477550	−	1.15291i	−0.483205	−	0.875507i	$-0.660527\pi$
$419$	3.51286e7	−	8.48079e7i	0.477550	−	1.15291i	0.960755	−	0.277400i	$-0.0894726\pi$
$420$	−1.58438e8	−	7.08593e7i	−2.13850	−	0.956420i
$421$	−1.90436e7	−	4.59753e7i	−0.255213	−	0.616139i	0.743397	−	0.668851i	$-0.233213\pi$
$421$	−1.90436e7	−	4.59753e7i	−0.255213	−	0.616139i	−0.998610	+	0.0527120i	$0.983213\pi$
$422$	−6.90699e7	−	1.47418e7i	−0.919076	−	0.196161i
$423$	3.53396e7	+	3.53396e7i	0.466917	+	0.466917i
$424$	1.84456e7	−	2.52544e7i	0.241989	−	0.331314i
$425$	1.13508e7	+	1.13508e7i	0.147863	+	0.147863i
$426$	9.83887e7	−	6.37773e7i	1.27267	−	0.824968i
$427$	6.41570e7	+	1.54889e8i	0.824062	+	1.98946i
$428$	7.46527e7	+	7.89320e7i	0.952170	+	1.00675i
$429$	−8.54238e7	+	2.06231e8i	−1.08195	+	2.61206i
$430$	−3.86075e7	+	5.60736e7i	−0.485587	+	0.705267i
$431$	6.31392e7			0.788619			0.394309	−	0.918978i	$-0.370984\pi$
$431$	6.31392e7			0.788619			0.394309	+	0.918978i	$0.370984\pi$
$432$	−1.09554e7	+	2.27718e7i	−0.135887	+	0.282453i
$433$		−	3.76887e7i		−	0.464245i	−0.972687	−	0.232123i	$-0.925433\pi$
$433$		−	3.76887e7i		−	0.464245i	0.972687	−	0.232123i	$-0.0745670\pi$
$434$	7.72797e6	−	1.12241e7i	0.0945357	−	0.137304i
$435$	4.69890e7	+	1.94635e7i	0.570859	+	0.236457i
$436$	−1.55572e6	+	5.58351e7i	−0.0187704	+	0.673672i
$437$	−2.16707e7	+	8.97629e6i	−0.259674	+	0.107560i
$438$	1.23345e8	−	7.99545e7i	1.46791	−	0.951525i
$439$	−7.35383e7	+	7.35383e7i	−0.869201	+	0.869201i	−0.992384	−	0.123183i	$-0.960690\pi$
$439$	−7.35383e7	+	7.35383e7i	−0.869201	+	0.869201i	0.123183	+	0.992384i	$0.460690\pi$
$440$	−3.23487e7	+	1.33265e8i	−0.379750	+	1.56444i
$441$	4.09191e7	−	4.09191e7i	0.477101	−	0.477101i
$442$	−4.60276e7	−	9.82378e6i	−0.533030	−	0.113766i
$443$	−4.56717e7	+	1.89178e7i	−0.525334	+	0.217601i	−0.629558	−	0.776953i	$-0.716764\pi$
$443$	−4.56717e7	+	1.89178e7i	−0.525334	+	0.217601i	0.104224	+	0.994554i	$0.466764\pi$
$444$	−1.30370e8	+	4.97940e7i	−1.48946	+	0.568890i
$445$	−9.20262e7	−	3.81185e7i	−1.04431	−	0.432569i
$446$	1.55560e7	+	8.43267e7i	0.175345	+	0.950519i
$447$		−	2.26523e8i		−	2.53624i
$448$	1.17540e8	−	3.75388e7i	1.30723	−	0.417491i
$449$	3.67541e7			0.406038			0.203019	−	0.979175i	$-0.434925\pi$
$449$	3.67541e7			0.406038			0.203019	+	0.979175i	$0.434925\pi$
$450$	−4.46434e7	+	8.23547e6i	−0.489913	+	0.0903756i
$451$	7.61641e6	−	1.83876e7i	0.0830272	−	0.200445i
$452$	4.45054e6	+	1.16524e7i	0.0481945	+	0.126183i
$453$	1.36186e7	+	3.28782e7i	0.146500	+	0.353682i
$454$	−2.11282e7	+	9.89923e7i	−0.225785	+	1.05787i
$455$	−1.99670e8	−	1.99670e8i	−2.11973	−	2.11973i
$456$	−4.62271e6	+	1.90440e7i	−0.0487531	+	0.200846i
$457$	1.09517e8	+	1.09517e8i	1.14744	+	1.14744i	0.987054	+	0.160391i	$0.0512755\pi$
$457$	1.09517e8	+	1.09517e8i	1.14744	+	1.14744i	0.160391	+	0.987054i	$0.448724\pi$
$458$	1.01496e7	+	1.56577e7i	0.105646	+	0.162979i
$459$	3.71979e6	+	8.98036e6i	0.0384663	+	0.0928658i
$460$	2.25884e8	+	6.29376e6i	2.32066	+	0.0646601i
$461$	5.69623e7	−	1.37519e8i	0.581413	−	1.40365i	−0.310119	−	0.950698i	$-0.600369\pi$
$461$	5.69623e7	−	1.37519e8i	0.581413	−	1.40365i	0.891532	−	0.452957i	$-0.149631\pi$
$462$	−1.85412e8	−	1.27659e8i	−1.88024	−	1.29457i
$463$	9.12154e7			0.919021			0.459510	−	0.888172i	$-0.348025\pi$
$463$	9.12154e7			0.919021			0.459510	+	0.888172i	$0.348025\pi$
$464$	−3.41243e7	+	1.19555e7i	−0.341593	+	0.119678i
$465$		−	2.08506e7i		−	0.207377i
$466$	−1.43994e8	−	9.91423e7i	−1.42294	−	0.979718i
$467$	−1.15882e8	−	4.79998e7i	−1.13780	−	0.471291i	−0.267373	−	0.963593i	$-0.586155\pi$
$467$	−1.15882e8	−	4.79998e7i	−1.13780	−	0.471291i	−0.870424	+	0.492302i	$0.836155\pi$
$468$	9.66995e7	−	9.14569e7i	0.943380	−	0.892234i
$469$	1.52793e7	−	6.32889e6i	0.148110	−	0.0613492i
$470$	6.27357e7	+	9.67820e7i	0.604256	+	0.932182i
$471$	6.31665e7	−	6.31665e7i	0.604539	−	0.604539i
$472$	−4.59732e7	+	6.29434e7i	−0.437199	+	0.598583i
$473$	−6.24371e7	+	6.24371e7i	−0.590010	+	0.590010i
$474$	−7.89373e6	+	3.69847e7i	−0.0741220	+	0.347286i
$475$	1.00469e7	−	4.16157e6i	0.0937458	−	0.0388308i
$476$	1.93772e7	−	4.33264e7i	0.179668	−	0.401728i
$477$	3.14299e7	+	1.30187e7i	0.289593	+	0.119953i
$478$	7.88642e7	−	1.45483e7i	0.722098	−	0.133207i
$479$			1.34211e8i			1.22118i	0.791946	+	0.610591i	$0.209068\pi$
$479$			1.34211e8i			1.22118i	−0.791946	+	0.610591i	$0.790932\pi$
$480$	1.15557e8	−	1.49297e8i	1.04489	−	1.34998i
$481$	−2.27052e8			−2.04028
$482$	−1.30730e7	−	7.08668e7i	−0.116744	−	0.632852i
$483$	−1.41951e8	+	3.42701e8i	−1.25979	+	3.04140i
$484$	−2.63273e7	+	5.88665e7i	−0.232205	+	0.519197i
$485$	−5.93835e7	−	1.43364e8i	−0.520523	−	1.25665i
$486$	−1.40798e8	−	3.00510e7i	−1.22656	−	0.261788i
$487$	2.20996e7	+	2.20996e7i	0.191336	+	0.191336i	0.796273	−	0.604937i	$-0.206802\pi$
$487$	2.20996e7	+	2.20996e7i	0.191336	+	0.191336i	−0.604937	+	0.796273i	$0.706802\pi$
$488$	−1.80190e8	+	2.80752e7i	−1.55049	+	0.241581i
$489$	4.94447e7	+	4.94447e7i	0.422857	+	0.422857i
$490$	1.12062e8	−	7.26407e7i	0.952514	−	0.617436i
$491$	−3.60544e7	−	8.70429e7i	−0.304588	−	0.735341i	−0.999862	−	0.0165965i	$-0.994717\pi$
$491$	−3.60544e7	−	8.70429e7i	−0.304588	−	0.735341i	0.695274	−	0.718745i	$-0.255283\pi$
$492$	−1.99067e7	+	1.88275e7i	−0.167149	+	0.158087i
$493$	−5.32249e6	+	1.28496e7i	−0.0444196	+	0.107238i
$494$	−1.80810e7	+	2.62609e7i	−0.149983	+	0.217836i
$495$	−1.49177e8			−1.22995
$496$	9.88170e6	+	1.10490e7i	0.0809816	+	0.0905476i
$497$			1.92376e8i			1.56704i
$498$	−5.98846e6	+	8.69765e6i	−0.0484872	+	0.0704229i
$499$	1.19906e8	+	4.96668e7i	0.965029	+	0.399728i	0.808859	−	0.588002i	$-0.200085\pi$
$499$	1.19906e8	+	4.96668e7i	0.965029	+	0.399728i	0.156170	+	0.987730i	$0.450085\pi$
$500$	5.58796e7	+	1.55696e6i	0.447037	+	0.0124557i
$501$	−1.38904e8	+	5.75361e7i	−1.10459	+	0.457538i
$502$	−1.05503e8	+	6.83886e7i	−0.833973	+	0.540596i
$503$	2.82660e7	−	2.82660e7i	0.222106	−	0.222106i	−0.587279	−	0.809385i	$-0.699801\pi$
$503$	2.82660e7	−	2.82660e7i	0.222106	−	0.222106i	0.809385	+	0.587279i	$0.199801\pi$
$504$	6.98437e7	+	1.14620e8i	0.545551	+	0.895302i
$505$	5.90288e7	−	5.90288e7i	0.458342	−	0.458342i
$506$	2.86631e8	+	6.11764e7i	2.21244	+	0.472207i
$507$	3.02007e8	−	1.25095e8i	2.31736	−	0.959880i
$508$	−7.10994e7	−	1.86152e8i	−0.542344	−	1.41996i
$509$	−1.67812e8	−	6.95098e7i	−1.27253	−	0.527100i	−0.358799	−	0.933415i	$-0.616814\pi$
$509$	−1.67812e8	−	6.95098e7i	−1.27253	−	0.527100i	−0.913733	+	0.406315i	$0.866814\pi$
$510$	−1.31742e7	−	7.14154e7i	−0.0993146	−	0.538371i
$511$			2.41172e8i			1.80744i
$512$	9.52139e6	+	1.33880e8i	0.0709399	+	0.997481i
$513$	6.58497e6			0.0487755
$514$	−1.47945e8	+	2.72919e7i	−1.08946	+	0.200976i
$515$	−3.57920e7	+	8.64096e7i	−0.262038	+	0.632617i
$516$	1.13560e8	−	4.33734e7i	0.826564	−	0.315700i
$517$	5.72465e7	+	1.38205e8i	0.414264	+	1.00012i
$518$	4.77934e7	−	2.23928e8i	0.343858	−	1.61109i
$519$	8.12552e7	+	8.12552e7i	0.581231	+	0.581231i
$520$	2.62299e8	−	1.59831e8i	1.86546	−	1.13672i
$521$	−7.21617e7	−	7.21617e7i	−0.510263	−	0.510263i	0.404344	−	0.914607i	$-0.367500\pi$
$521$	−7.21617e7	−	7.21617e7i	−0.510263	−	0.510263i	−0.914607	+	0.404344i	$0.867500\pi$
$522$	−2.13946e7	−	3.30053e7i	−0.150416	−	0.232045i
$523$	−5.02478e7	−	1.21309e8i	−0.351246	−	0.847984i	−0.996467	−	0.0839873i	$-0.973234\pi$
$523$	−5.02478e7	−	1.21309e8i	−0.351246	−	0.847984i	0.645220	−	0.763996i	$-0.276766\pi$
$524$	858456.	−	3.08102e7i	0.00596656	−	0.214141i
$525$	6.58111e7	−	1.58882e8i	0.454801	−	1.09799i
$526$	−5.19507e7	−	3.57689e7i	−0.356972	−	0.245781i
$527$	5.70183e6			0.0389567
$528$	1.82519e8	−	1.63237e8i	1.23996	−	1.10896i
$529$		−	3.34913e8i		−	2.26238i
$530$	6.46640e7	+	4.45221e7i	0.434345	+	0.299053i
$531$	−7.83350e7	−	3.24474e7i	−0.523206	−	0.216719i
$532$	−2.20936e7	−	2.33600e7i	−0.146734	−	0.155145i
$533$	−4.11851e7	+	1.70594e7i	−0.271993	+	0.112663i
$534$	9.67440e7	+	1.49246e8i	0.635331	+	0.980121i
$535$	−1.92855e8	+	1.92855e8i	−1.25941	+	1.25941i
$536$	2.76953e6	+	1.77752e7i	0.0179850	+	0.115430i
$537$	1.85976e8	−	1.85976e8i	1.20098	−	1.20098i
$538$	−3.78097e7	+	1.77151e8i	−0.242805	+	1.13762i
$539$	1.60026e8	−	6.62848e7i	1.02194	−	0.423300i
$540$	−5.79103e7	−	2.58997e7i	−0.367769	−	0.164480i
$541$	2.55649e8	+	1.05893e8i	1.61456	+	0.668771i	0.993377	−	0.114899i	$-0.0366544\pi$
$541$	2.55649e8	+	1.05893e8i	1.61456	+	0.668771i	0.621178	+	0.783669i	$0.286654\pi$
$542$	1.61938e8	−	2.98732e7i	1.01707	−	0.187622i
$543$			3.95318e8i			2.46915i
$544$	4.08269e7	+	3.16002e7i	0.253600	+	0.196287i
$545$	−1.40223e8			−0.866224
$546$	9.14690e7	+	4.95841e8i	0.561948	+	3.04624i
$547$	4.25638e7	−	1.02758e8i	0.260063	−	0.627848i	−0.738879	−	0.673838i	$-0.764644\pi$
$547$	4.25638e7	−	1.02758e8i	0.260063	−	0.627848i	0.998942	+	0.0459904i	$0.0146444\pi$
$548$	−5.18903e7	−	2.32073e7i	−0.315315	−	0.141021i
$549$	−7.59156e7	−	1.83276e8i	−0.458790	−	1.10762i
$550$	−1.32887e8	−	2.83625e7i	−0.798721	−	0.170473i
$551$	6.66247e6	+	6.66247e6i	0.0398273	+	0.0398273i
$552$	−3.25834e8	−	2.37986e8i	−1.93722	−	1.41493i
$553$	−4.38745e7	−	4.38745e7i	−0.259440	−	0.259440i
$554$	3.67769e7	−	2.38394e7i	0.216294	−	0.140206i
$555$	−1.34070e8	−	3.23674e8i	−0.784247	−	1.89334i
$556$	2.22603e8	+	2.35363e8i	1.29511	+	1.36935i
$557$	−1.47539e7	+	3.56190e7i	−0.0853769	+	0.206118i	−0.960802	−	0.277236i	$-0.910582\pi$
$557$	−1.47539e7	+	3.56190e7i	−0.0853769	+	0.206118i	0.875425	+	0.483354i	$0.160582\pi$
$558$	−9.14434e6	+	1.32812e7i	−0.0526320	+	0.0764427i
$559$	1.97775e8			1.13223
$560$	1.02419e8	+	2.92333e8i	0.583201	+	1.66462i
$561$		−	9.41891e7i		−	0.533473i
$562$	−1.68402e8	+	2.44587e8i	−0.948719	+	1.37792i
$563$	−1.81323e7	−	7.51066e6i	−0.101608	−	0.0420875i	0.331300	−	0.943525i	$-0.392513\pi$
$563$	−1.81323e7	−	7.51066e6i	−0.101608	−	0.0420875i	−0.432908	+	0.901438i	$0.642513\pi$
$564$	5.73591e6	−	2.05863e8i	0.0319717	−	1.14747i
$565$	−2.89296e7	+	1.19831e7i	−0.160398	+	0.0664389i
$566$	2.26383e8	−	1.46745e8i	1.24852	−	0.809309i
$567$	2.08770e8	−	2.08770e8i	1.14530	−	1.14530i
$568$	−2.03354e8	−	4.93618e7i	−1.10970	−	0.269368i
$569$	−8.86486e7	+	8.86486e7i	−0.481211	+	0.481211i	−0.905518	−	0.424308i	$-0.860518\pi$
$569$	−8.86486e7	+	8.86486e7i	−0.481211	+	0.481211i	0.424308	+	0.905518i	$0.360518\pi$
$570$	−4.81128e7	−	1.02688e7i	−0.259798	−	0.0554493i
$571$	−2.92097e8	+	1.20991e8i	−1.56899	+	0.649896i	−0.986621	−	0.163030i	$-0.947873\pi$
$571$	−2.92097e8	+	1.20991e8i	−1.56899	+	0.649896i	−0.582367	+	0.812926i	$0.697873\pi$
$572$	3.72165e8	−	1.42146e8i	1.98860	−	0.759532i
$573$	−5.55606e7	−	2.30139e7i	−0.295327	−	0.122328i
$574$	−8.15541e6	−	4.42093e7i	−0.0431231	−	0.233764i
$575$			2.23904e8i			1.17776i
$576$	−1.39082e8	+	4.44189e7i	−0.727788	+	0.232434i
$577$	1.39596e8			0.726683			0.363342	−	0.931656i	$-0.381636\pi$
$577$	1.39596e8			0.726683			0.363342	+	0.931656i	$0.381636\pi$
$578$	−1.70367e8	+	3.14281e7i	−0.882272	+	0.162755i
$579$	−1.50990e7	+	3.64522e7i	−0.0777879	+	0.187797i
$580$	−3.23874e7	−	8.47965e7i	−0.165994	−	0.434604i
$581$	−6.63025e6	−	1.60068e7i	−0.0338066	−	0.0816164i
$582$	−5.78353e7	+	2.70977e8i	−0.293376	+	1.37456i
$583$	7.20023e7	+	7.20023e7i	0.363363	+	0.363363i
$584$	−2.54935e8	−	6.18826e7i	−1.27994	−	0.310692i
$585$	2.36266e8	+	2.36266e8i	1.18014	+	1.18014i
$586$	−1.71876e8	−	2.65152e8i	−0.854129	−	1.31766i
$587$	−1.22401e7	−	2.95501e7i	−0.0605158	−	0.146098i	0.890729	−	0.454534i	$-0.150194\pi$
$587$	−1.22401e7	−	2.95501e7i	−0.0605158	−	0.146098i	−0.951245	+	0.308436i	$0.900194\pi$
$588$	−2.38366e8	−	6.64152e6i	−1.17250	−	0.0326690i
$589$	1.47818e6	−	3.56865e6i	0.00723407	−	0.0174646i
$590$	−1.61167e8	−	1.10966e8i	−0.784727	−	0.540297i
$591$	−4.76463e7			−0.230816
$592$	2.24443e8	+	1.07979e8i	1.08179	+	0.520442i
$593$			2.69309e8i			1.29148i	0.763559	+	0.645738i	$0.223450\pi$
$593$			2.69309e8i			1.29148i	−0.763559	+	0.645738i	$0.776550\pi$
$594$	−6.77698e7	−	4.66606e7i	−0.323353	−	0.222634i
$595$	1.10079e8	+	4.55964e7i	0.522583	+	0.216461i
$596$	−2.93718e8	+	2.77794e8i	−1.38737	+	1.31215i
$597$	−2.05323e7	+	8.50476e6i	−0.0964972	+	0.0399704i
$598$	−3.57074e8	−	5.50856e8i	−1.66976	−	2.57593i
$599$	−7.63048e7	+	7.63048e7i	−0.355035	+	0.355035i	−0.861979	−	0.506944i	$-0.830775\pi$
$599$	−7.63048e7	+	7.63048e7i	−0.355035	+	0.355035i	0.506944	+	0.861979i	$0.330775\pi$
$600$	1.51062e8	+	1.10334e8i	0.699363	+	0.510808i
$601$	1.48654e8	−	1.48654e8i	0.684782	−	0.684782i	−0.276292	−	0.961074i	$-0.589106\pi$
$601$	1.48654e8	−	1.48654e8i	0.684782	−	0.684782i	0.961074	+	0.276292i	$0.0891056\pi$
$602$	−4.16308e7	+	1.95054e8i	−0.190821	+	0.894056i
$603$	−1.80797e7	+	7.48884e6i	−0.0824590	+	0.0341556i
$604$	2.59300e7	−	5.79781e7i	0.117677	−	0.263120i
$605$	−1.49562e8	−	6.19507e7i	−0.675392	−	0.279756i
$606$	−1.46586e8	+	2.70411e7i	−0.658680	+	0.121508i
$607$		−	2.01527e8i		−	0.901088i	−0.892754	−	0.450544i	$-0.851230\pi$
$607$		−	2.01527e8i		−	0.901088i	0.892754	−	0.450544i	$-0.148770\pi$
$608$	3.03621e7	−	1.73604e7i	0.135089	−	0.0772412i
$609$	1.49002e8			0.659692
$610$	−8.30515e7	−	4.50210e8i	−0.365896	−	1.98347i
$611$	1.28222e8	−	3.09555e8i	0.562133	−	1.35711i
$612$	−2.29286e7	+	5.12672e7i	−0.100029	+	0.223658i
$613$	−8.20577e7	−	1.98105e8i	−0.356236	−	0.860030i	−0.995822	−	0.0913108i	$-0.970894\pi$
$613$	−8.20577e7	−	1.98105e8i	−0.356236	−	0.860030i	0.639586	−	0.768719i	$-0.279106\pi$
$614$	2.02987e8	+	4.33239e7i	0.876924	+	0.187164i
$615$	−4.86381e7	−	4.86381e7i	−0.209099	−	0.209099i
$616$	6.18508e7	+	3.96966e8i	0.264608	+	1.69829i
$617$	6.24861e7	+	6.24861e7i	0.266028	+	0.266028i	0.827498	−	0.561469i	$-0.189764\pi$
$617$	6.24861e7	+	6.24861e7i	0.266028	+	0.266028i	−0.561469	+	0.827498i	$0.689764\pi$
$618$	1.40137e8	−	9.08395e7i	0.593730	−	0.384866i
$619$	8.65095e7	+	2.08852e8i	0.364747	+	0.880578i	0.994592	+	0.103857i	$0.0331184\pi$
$619$	8.65095e7	+	2.08852e8i	0.364747	+	0.880578i	−0.629845	+	0.776721i	$0.716882\pi$
$620$	−2.70357e7	+	2.55700e7i	−0.113439	+	0.107289i
$621$	−5.18845e7	+	1.25260e8i	−0.216652	+	0.523044i
$622$	4.35396e7	−	6.32370e7i	0.180931	−	0.262785i
$623$	−2.91815e8			−1.20682
$624$	−5.47607e8	−	3.05394e7i	−2.25380	−	0.125692i
$625$			2.99530e8i			1.22688i
$626$	1.84089e6	−	2.67371e6i	0.00750422	−	0.0108991i
$627$	−5.89510e7	−	2.44183e7i	−0.239160	−	0.0990633i
$628$	−1.59368e8	−	4.44042e6i	−0.643459	−	0.0179285i
$629$	8.85120e7	−	3.66629e7i	0.355672	−	0.147324i
$630$	−2.82748e8	+	1.83282e8i	−1.13078	+	0.732990i
$631$	1.58404e8	−	1.58404e8i	0.630489	−	0.630489i	−0.317702	−	0.948191i	$-0.602911\pi$
$631$	1.58404e8	−	1.58404e8i	0.630489	−	0.630489i	0.948191	+	0.317702i	$0.102911\pi$
$632$	5.76361e7	−	3.51205e7i	0.228320	−	0.139126i
$633$	−2.23857e8	+	2.23857e8i	−0.882591	+	0.882591i
$634$	1.87682e8	+	4.00573e7i	0.736468	+	0.157186i
$635$	4.62164e8	−	1.91435e8i	1.80499	−	0.747651i
$636$	−5.00181e7	−	1.30957e8i	−0.194427	−	0.509047i
$637$	−3.58429e8	−	1.48466e8i	−1.38671	−	0.574394i
$638$	−2.13577e7	−	1.15777e8i	−0.0822419	−	0.445822i
$639$		−	2.27634e8i		−	0.872438i
$640$	−3.35296e8	+	3.32541e7i	−1.27905	+	0.126854i
$641$	4.20312e8			1.59587			0.797935	−	0.602743i	$-0.205926\pi$
$641$	4.20312e8			1.59587			0.797935	+	0.602743i	$0.205926\pi$
$642$	4.78915e8	−	8.83467e7i	1.80989	−	0.333876i
$643$	3.45739e7	−	8.34689e7i	0.130052	−	0.313972i	−0.845418	−	0.534105i	$-0.820649\pi$
$643$	3.45739e7	−	8.34689e7i	0.130052	−	0.313972i	0.975470	+	0.220132i	$0.0706488\pi$
$644$	6.18439e8	−	2.36208e8i	2.31547	−	0.884377i
$645$	1.16783e8	+	2.81938e8i	0.435210	+	1.05069i
$646$	2.80812e6	−	1.31569e7i	0.0104164	−	0.0488042i
$647$	1.82345e8	+	1.82345e8i	0.673256	+	0.673256i	0.958465	−	0.285210i	$-0.0920632\pi$
$647$	1.82345e8	+	1.82345e8i	0.673256	+	0.673256i	−0.285210	+	0.958465i	$0.592063\pi$
$648$	1.67116e8	+	2.74253e8i	0.614175	+	1.00792i
$649$	−1.79456e8	−	1.79456e8i	−0.656485	−	0.656485i
$650$	1.65546e8	+	2.55386e8i	0.602807	+	0.929946i
$651$	−2.33761e7	−	5.64348e7i	−0.0847283	−	0.204552i
$652$	3.47582e6	−	1.24748e8i	0.0125405	−	0.450080i
$653$	−1.33838e8	+	3.23113e8i	−0.480661	+	1.16042i	0.478634	+	0.878015i	$0.341132\pi$
$653$	−1.33838e8	+	3.23113e8i	−0.480661	+	1.16042i	−0.959295	+	0.282405i	$0.908868\pi$
$654$	2.06226e8	+	1.41990e8i	0.737242	+	0.507602i
$655$	7.73760e7			0.275348
$656$	4.88248e7	+	2.72290e6i	0.172953	+	0.00964540i
$657$		−	2.85374e8i		−	1.00628i
$658$	2.78306e8	+	1.91618e8i	0.976888	+	0.672602i
$659$	1.42938e8	+	5.92070e7i	0.499451	+	0.206879i	0.618164	−	0.786049i	$-0.287877\pi$
$659$	1.42938e8	+	5.92070e7i	0.499451	+	0.206879i	−0.118713	+	0.992929i	$0.537877\pi$
$660$	4.22393e8	+	4.46606e8i	1.46921	+	1.55343i
$661$	8.22858e7	−	3.40839e7i	0.284918	−	0.118017i	−0.235647	−	0.971839i	$-0.575721\pi$
$661$	8.22858e7	−	3.40839e7i	0.284918	−	0.118017i	0.520566	+	0.853822i	$0.325721\pi$
$662$	1.25953e8	+	1.94308e8i	0.434146	+	0.669755i
$663$	−1.49176e8	+	1.49176e8i	−0.511869	+	0.511869i
$664$	1.86216e7	−	2.90141e6i	0.0636080	−	0.00991070i
$665$	5.70756e7	−	5.70756e7i	0.194082	−	0.194082i
$666$	−5.65529e7	+	2.64969e8i	−0.191440	+	0.896958i
$667$	−1.79230e8	+	7.42394e7i	−0.603994	+	0.250182i
$668$	2.44947e8	+	1.09550e8i	0.821756	+	0.367521i
$669$	3.55116e8	+	1.47094e8i	1.18602	+	0.491266i
$670$	−4.44119e7	+	8.19277e6i	−0.147664	+	0.0272400i
$671$		−	5.93778e8i		−	1.96543i
$672$	1.45388e8	−	5.33644e8i	0.479094	−	1.75850i
$673$	−4.47426e8			−1.46783			−0.733915	−	0.679241i	$-0.762309\pi$
$673$	−4.47426e8			−1.46783			−0.733915	+	0.679241i	$0.762309\pi$
$674$	−875611.	−	4.74656e6i	−0.00285977	−	0.0155024i
$675$	2.40546e7	−	5.80728e7i	0.0782143	−	0.188826i
$676$	−5.32566e8	−	2.38184e8i	−1.72398	−	0.771031i
$677$	4.18468e7	+	1.01027e8i	0.134864	+	0.325591i	0.976856	−	0.213900i	$-0.0686167\pi$
$677$	4.18468e7	+	1.01027e8i	0.134864	+	0.325591i	−0.841991	+	0.539491i	$0.818617\pi$
$678$	5.46808e7	+	1.16706e7i	0.175447	+	0.0374460i
$679$	−3.21457e8	−	3.21457e8i	−1.02687	−	1.02687i
$680$	−7.64438e7	+	1.04662e8i	−0.243117	+	0.332859i
$681$	3.20836e8	+	3.20836e8i	1.01588	+	1.01588i
$682$	−4.05001e7	+	2.62528e7i	−0.127674	+	0.0827605i
$683$	−3.04049e7	−	7.34040e7i	−0.0954293	−	0.230387i	0.868955	−	0.494891i	$-0.164792\pi$
$683$	−3.04049e7	−	7.34040e7i	−0.0954293	−	0.230387i	−0.964385	+	0.264504i	$0.914792\pi$
$684$	2.61429e7	+	2.76414e7i	0.0816930	+	0.0863759i
$685$	5.46090e7	−	1.31838e8i	0.169900	−	0.410174i
$686$	−2.93583e7	+	4.26400e7i	−0.0909406	+	0.132082i
$687$	8.36418e7			0.257961
$688$	−1.95503e8	−	9.40555e7i	−0.600326	−	0.288815i
$689$		−	2.28074e8i		−	0.697296i
$690$	5.74427e8	−	8.34298e8i	1.74859	−	2.53965i
$691$	−2.39692e8	−	9.92839e7i	−0.726474	−	0.300915i	−0.0113720	−	0.999935i	$-0.503620\pi$
$691$	−2.39692e8	−	9.92839e7i	−0.726474	−	0.300915i	−0.715102	+	0.699020i	$0.753620\pi$
$692$	5.71200e6	−	2.05005e8i	0.0172373	−	0.618651i
$693$	−4.03766e8	+	1.67245e8i	−1.21319	+	0.502521i
$694$	9.82459e6	−	6.36847e6i	0.0293925	−	0.0190527i
$695$	−5.75062e8	+	5.75062e8i	−1.71301	+	1.71301i
$696$	−3.82327e7	+	1.57505e8i	−0.113398	+	0.467162i
$697$	1.33006e7	−	1.33006e7i	0.0392801	−	0.0392801i
$698$	−2.18514e8	−	4.66380e7i	−0.642559	−	0.137143i
$699$	−7.24003e8	+	2.99892e8i	−2.11987	+	0.878079i
$700$	−2.86719e8	+	1.09510e8i	−0.835916	+	0.319272i
$701$	−2.20907e8	−	9.15026e7i	−0.641291	−	0.265631i	0.0382509	−	0.999268i	$-0.487821\pi$
$701$	−2.20907e8	−	9.15026e7i	−0.641291	−	0.265631i	−0.679542	+	0.733637i	$0.737821\pi$
$702$	3.34327e7	+	1.81234e8i	0.0966408	+	0.523876i
$703$		−	6.49025e7i		−	0.186808i
$704$	−4.35489e8	−	3.64774e7i	−1.24813	−	0.104545i
$705$	5.17000e8			1.47545
$706$	2.13376e8	−	3.93620e7i	0.606360	−	0.111857i
$707$	9.35903e7	−	2.25947e8i	0.264833	−	0.639364i
$708$	1.24664e8	+	3.26394e8i	0.351269	+	0.919691i
$709$	9.24222e6	+	2.23127e7i	0.0259321	+	0.0626056i	0.936315	−	0.351161i	$-0.114213\pi$
$709$	9.24222e6	+	2.23127e7i	0.0259321	+	0.0626056i	−0.910383	+	0.413767i	$0.864213\pi$
$710$	1.09652e8	−	5.13754e8i	0.306366	−	1.43542i
$711$	5.19158e7	+	5.19158e7i	0.144441	+	0.144441i
$712$	7.48772e7	−	3.08468e8i	0.207448	−	0.854615i
$713$	5.62365e7	+	5.62365e7i	0.155149	+	0.155149i
$714$	−1.15723e8	−	1.78525e8i	−0.317924	−	0.490460i
$715$	3.82727e8	+	9.23984e8i	1.04706	+	2.52782i
$716$	−4.69214e8	−	1.30736e7i	−1.27830	−	0.0356169i
$717$	1.37566e8	−	3.32113e8i	0.373209	−	0.901006i
$718$	3.42996e8	+	2.36158e8i	0.926650	+	0.638013i
$719$	−2.11121e8			−0.567994			−0.283997	−	0.958825i	$-0.591661\pi$
$719$	−2.11121e8			−0.567994			−0.283997	+	0.958825i	$0.591661\pi$
$720$	−1.21191e8	−	3.45912e8i	−0.324692	−	0.926761i
$721$			2.74005e8i			0.731060i
$722$	3.02489e8	+	2.08268e8i	0.803706	+	0.553364i
$723$	−2.98434e8	−	1.23615e8i	−0.789648	−	0.327083i
$724$	5.12584e8	−	4.84794e8i	1.35067	−	1.27744i
$725$	8.30941e7	−	3.44187e7i	0.218050	−	0.0903193i
$726$	1.57230e8	+	2.42557e8i	0.410889	+	0.633875i
$727$	−2.19024e8	+	2.19024e8i	−0.570019	+	0.570019i	−0.932133	−	0.362115i	$-0.882055\pi$
$727$	−2.19024e8	+	2.19024e8i	−0.570019	+	0.570019i	0.362115	+	0.932133i	$0.382055\pi$
$728$	5.30753e8	−	7.26671e8i	1.37562	−	1.88340i
$729$	−1.32989e8	+	1.32989e8i	−0.343269	+	0.343269i
$730$	1.37465e8	−	6.44068e8i	0.353365	−	1.65563i
$731$	−7.70990e7	+	3.19354e7i	−0.197377	+	0.0817562i
$732$	−3.33738e8	+	7.46221e8i	−0.850889	+	1.90254i
$733$	3.93787e8	+	1.63112e8i	0.999884	+	0.414165i	0.821755	−	0.569842i	$-0.192995\pi$
$733$	3.93787e8	+	1.63112e8i	0.999884	+	0.414165i	0.178129	+	0.984007i	$0.442995\pi$
$734$	−2.52202e8	+	4.65244e7i	−0.637765	+	0.117650i
$735$		−	5.98626e8i		−	1.50763i
$736$	9.10020e7	+	7.14340e8i	0.228254	+	1.79173i
$737$	−5.85744e7			−0.146321
$738$	9.65012e6	+	5.23119e7i	0.0240084	+	0.130146i
$739$	1.65373e8	−	3.99247e8i	0.409763	−	0.989255i	−0.575437	−	0.817846i	$-0.695168\pi$
$739$	1.65373e8	−	3.99247e8i	0.409763	−	0.989255i	0.985200	−	0.171409i	$-0.0548319\pi$
$740$	−2.55272e8	+	5.70774e8i	−0.629952	+	1.40854i
$741$	5.46927e7	+	1.32040e8i	0.134423	+	0.324527i
$742$	2.24935e8	+	4.80085e7i	0.550613	+	0.117519i
$743$	2.59817e8	+	2.59817e8i	0.633434	+	0.633434i	0.948928	−	0.315494i	$-0.102170\pi$
$743$	2.59817e8	+	2.59817e8i	0.633434	+	0.633434i	−0.315494	+	0.948928i	$0.602170\pi$
$744$	6.56534e7	−	1.02294e7i	0.159418	−	0.0248388i
$745$	−7.17641e8	−	7.17641e8i	−1.73556	−	1.73556i
$746$	−6.46586e8	+	4.19128e8i	−1.55743	+	1.00956i
$747$	7.84544e6	+	1.89406e7i	0.0188216	+	0.0454392i
$748$	−1.22129e8	+	1.15508e8i	−0.291819	+	0.275998i
$749$	−3.05771e8	+	7.38197e8i	−0.727698	+	1.75682i
$750$	1.42103e8	−	2.06390e8i	0.336836	−	0.489221i
$751$	1.75421e8			0.414154			0.207077	−	0.978325i	$-0.433605\pi$
$751$	1.75421e8			0.414154			0.207077	+	0.978325i	$0.433605\pi$
$752$	−2.73964e8	+	2.45020e8i	−0.644228	+	0.576168i
$753$			5.63585e8i			1.32000i
$754$	−1.49541e8	+	2.17194e8i	−0.348856	+	0.506679i
$755$	1.47305e8	+	6.10157e7i	0.342276	+	0.141775i
$756$	−1.85778e8	−	5.17629e6i	−0.429961	−	0.0119799i
$757$	5.46370e8	−	2.26314e8i	1.25950	−	0.521703i	0.349746	−	0.936844i	$-0.386268\pi$
$757$	5.46370e8	−	2.26314e8i	1.25950	−	0.521703i	0.909757	+	0.415141i	$0.136268\pi$
$758$	1.58223e8	−	1.02563e8i	0.363298	−	0.235496i
$759$	9.28977e8	−	9.28977e8i	2.12461	−	2.12461i
$760$	4.56876e7	+	7.49778e7i	0.104078	+	0.170802i
$761$	1.19497e8	−	1.19497e8i	0.271146	−	0.271146i	−0.558415	−	0.829562i	$-0.688590\pi$
$761$	1.19497e8	−	1.19497e8i	0.271146	−	0.271146i	0.829562	+	0.558415i	$0.188590\pi$
$762$	−8.73549e8	−	1.86444e8i	−1.97434	−	0.421389i
$763$	−3.79531e8	+	1.57207e8i	−0.854424	+	0.353914i
$764$	3.82954e7	+	1.00265e8i	0.0858749	+	0.224837i
$765$	−1.30255e8	−	5.39532e7i	−0.290944	−	0.120513i
$766$	4.86263e6	+	2.63596e7i	0.0108190	+	0.0586480i
$767$			5.68444e8i			1.25980i
$768$	5.26791e8	+	2.90613e8i	1.16293	+	0.641551i
$769$	2.17776e8			0.478885			0.239443	−	0.970911i	$-0.423035\pi$
$769$	2.17776e8			0.478885			0.239443	+	0.970911i	$0.423035\pi$
$770$	−9.91833e8	+	1.82966e8i	−2.17253	+	0.400773i
$771$	−2.58066e8	+	6.23027e8i	−0.563078	+	1.35939i
$772$	6.57817e7	−	2.51248e7i	0.142973	−	0.0546074i
$773$	−2.19524e8	−	5.29977e8i	−0.475273	−	1.14741i	−0.961802	−	0.273746i	$-0.911737\pi$
$773$	−2.19524e8	−	5.29977e8i	−0.475273	−	1.14741i	0.486529	−	0.873664i	$-0.338263\pi$
$774$	4.92608e7	−	2.30803e8i	0.106238	−	0.497758i
$775$	−2.60722e7	−	2.60722e7i	−0.0560110	−	0.0560110i
$776$	4.22284e8	−	2.57319e8i	0.903691	−	0.550663i
$777$	−7.25754e8	−	7.25754e8i	−1.54713	−	1.54713i
$778$	2.58377e8	+	3.98596e8i	0.548674	+	0.846435i
$779$	−4.87642e6	−	1.17727e7i	−0.0103155	−	0.0249037i
$780$	3.83480e7	−	1.37632e9i	0.0808088	−	2.90024i
$781$	2.60741e8	−	6.29485e8i	0.547340	−	1.32139i
$782$	2.28147e8	+	1.57083e8i	0.477085	+	0.328480i
$783$	5.44617e7			0.113450
$784$	2.83705e8	+	3.17218e8i	0.588734	+	0.658279i
$785$		−	4.00232e8i		−	0.827376i
$786$	−1.13797e8	−	7.83507e7i	−0.234348	−	0.161352i
$787$	−2.56291e8	−	1.06159e8i	−0.525787	−	0.217788i	0.103970	−	0.994580i	$-0.466845\pi$
$787$	−2.56291e8	−	1.06159e8i	−0.525787	−	0.217788i	−0.629757	+	0.776792i	$0.716845\pi$
$788$	5.84305e7	+	6.17799e7i	0.119416	+	0.126261i
$789$	−2.61208e8	+	1.08196e8i	−0.531809	+	0.220283i
$790$	9.21622e7	+	1.42178e8i	0.186927	+	0.288371i
$791$	−6.48672e7	+	6.48672e7i	−0.131068	+	0.131068i
$792$	−7.31868e7	−	4.69721e8i	−0.147318	−	0.945506i
$793$	−9.40423e8	+	9.40423e8i	−1.88583	+	1.88583i
$794$	1.01891e8	−	4.77395e8i	0.203552	−	0.953709i
$795$	3.25130e8	−	1.34673e8i	0.647077	−	0.268028i
$796$	3.62071e7	+	1.61932e7i	0.0717885	+	0.0321066i
$797$	−3.16978e8	−	1.31297e8i	−0.626115	−	0.259345i	0.0469862	−	0.998896i	$-0.485038\pi$
$797$	−3.16978e8	−	1.31297e8i	−0.626115	−	0.259345i	−0.673102	+	0.739550i	$0.735038\pi$
$798$	−1.41736e8	+	2.61463e7i	−0.278914	+	0.0514520i
$799$			1.41379e8i			0.277169i
$800$	−4.21901e7	−	3.31181e8i	−0.0824026	−	0.646837i
$801$	3.45299e8			0.671889
$802$	−4.52551e7	−	2.45322e8i	−0.0877293	−	0.475568i
$803$	3.26879e8	−	7.89155e8i	0.631306	−	1.52411i
$804$	7.36124e7	+	3.29223e7i	0.141639	+	0.0633463i
$805$	6.35989e8	+	1.53541e9i	1.21916	+	2.94332i
$806$	1.05723e8	+	2.25647e7i	0.201913	+	0.0430948i
$807$	5.74149e8	+	5.74149e8i	1.09246	+	1.09246i
$808$	2.14826e8	+	1.56907e8i	0.407243	+	0.297446i
$809$	−2.47346e8	−	2.47346e8i	−0.467154	−	0.467154i	0.433837	−	0.900991i	$-0.357159\pi$
$809$	−2.47346e8	−	2.47346e8i	−0.467154	−	0.467154i	−0.900991	+	0.433837i	$0.857159\pi$
$810$	−6.76533e8	+	4.38541e8i	−1.27302	+	0.825191i
$811$	−3.79875e8	−	9.17098e8i	−0.712160	−	1.71931i	−0.694531	−	0.719462i	$-0.744388\pi$
$811$	−3.79875e8	−	9.17098e8i	−0.712160	−	1.71931i	−0.0176288	−	0.999845i	$-0.505612\pi$
$812$	−1.82727e8	−	1.93202e8i	−0.341299	−	0.360864i
$813$	2.82475e8	−	6.81954e8i	0.525664	−	1.26906i
$814$	−4.59894e8	+	6.67951e8i	−0.852678	+	1.23843i
$815$	3.13289e8			0.578725
$816$	2.18406e8	−	7.65188e7i	0.401970	−	0.140831i
$817$			5.65338e7i			0.103667i
$818$	−4.06132e8	+	5.89866e8i	−0.742005	+	1.07769i
$819$	9.04364e8	+	3.74600e8i	1.64623	+	0.681893i
$820$	−3.41912e6	+	1.22713e8i	−0.00620115	+	0.222561i
$821$	7.95309e8	−	3.29428e8i	1.43716	−	0.595293i	0.478055	−	0.878330i	$-0.341342\pi$
$821$	7.95309e8	−	3.29428e8i	1.43716	−	0.595293i	0.959109	+	0.283037i	$0.0913419\pi$
$822$	−2.13812e8	+	1.38597e8i	−0.384961	+	0.249538i
$823$	5.04531e8	−	5.04531e8i	0.905083	−	0.905083i	−0.0907876	−	0.995870i	$-0.528938\pi$
$823$	5.04531e8	−	5.04531e8i	0.905083	−	0.905083i	0.995870	+	0.0907876i	$0.0289384\pi$
$824$	−2.89642e8	−	7.03073e7i	−0.517702	−	0.125666i
$825$	−4.30690e8	+	4.30690e8i	−0.767014	+	0.767014i
$826$	−5.60622e8	−	1.19655e8i	−0.994787	−	0.212320i
$827$	−2.67300e7	+	1.10719e7i	−0.0472587	+	0.0195752i	−0.406188	−	0.913790i	$-0.633142\pi$
$827$	−2.67300e7	+	1.10719e7i	−0.0472587	+	0.0195752i	0.358929	+	0.933365i	$0.383142\pi$
$828$	−7.31785e8	+	2.79500e8i	−1.28912	+	0.492369i
$829$	7.58577e8	+	3.14213e8i	1.33148	+	0.551519i	0.931078	−	0.364819i	$-0.118869\pi$
$829$	7.58577e8	+	3.14213e8i	1.33148	+	0.551519i	0.400406	+	0.916338i	$0.368869\pi$
$830$	8.58289e6	+	4.65267e7i	0.0150106	+	0.0813706i
$831$		−	1.96458e8i		−	0.342348i
$832$	6.31953e8	+	7.47498e8i	1.09727	+	1.29790i
$833$	1.63701e8			0.283214
$834$	1.42805e9	−	2.63436e8i	2.46176	−	0.454127i
$835$	−2.57781e8	+	6.22337e8i	−0.442783	+	1.06897i
$836$	4.06323e7	+	1.06383e8i	0.0695428	+	0.182076i
$837$	−8.54416e6	−	2.06274e7i	−0.0145711	−	0.0351778i
$838$	−1.53284e8	+	7.18188e8i	−0.260475	+	1.22041i
$839$	−2.80687e8	−	2.80687e8i	−0.475266	−	0.475266i	0.428348	−	0.903614i	$-0.359096\pi$
$839$	−2.80687e8	−	2.80687e8i	−0.475266	−	0.475266i	−0.903614	+	0.428348i	$0.859096\pi$
$840$	1.34931e9	+	3.27529e8i	2.27653	+	0.552601i
$841$	−3.65501e8	−	3.65501e8i	−0.614470	−	0.614470i
$842$	2.16545e8	+	3.34062e8i	0.362753	+	0.559617i
$843$	5.09393e8	+	1.22978e9i	0.850296	+	2.05280i
$844$	5.64786e8	+	1.57365e7i	0.939412	+	0.0261746i
$845$	5.60468e8	−	1.35309e9i	0.928925	−	2.24262i
$846$	−3.29314e8	−	2.26737e8i	−0.543874	−	0.374466i
$847$	−4.74262e8			−0.780492
$848$	−1.08465e8	+	2.25453e8i	−0.177869	+	0.369716i
$849$		−	1.20931e9i		−	1.97613i
$850$	−1.05773e8	−	7.28264e7i	−0.172234	−	0.118586i
$851$	1.23459e9	+	5.11382e8i	2.00324	+	0.829768i
$852$	−6.81490e8	+	6.44543e8i	−1.10190	+	1.04216i
$853$	−4.19978e8	+	1.73961e8i	−0.676674	+	0.280288i	−0.694436	−	0.719555i	$-0.744346\pi$
$853$	−4.19978e8	+	1.73961e8i	−0.676674	+	0.280288i	0.0177618	+	0.999842i	$0.494346\pi$
$854$	−7.29528e8	−	1.12544e9i	−1.17130	−	1.80696i
$855$	−6.75364e7	+	6.75364e7i	−0.108054	+	0.108054i
$856$	−7.01866e8	−	5.12635e8i	−1.11901	−	0.817311i
$857$	−2.79481e8	+	2.79481e8i	−0.444028	+	0.444028i	−0.893363	−	0.449335i	$-0.851661\pi$
$857$	−2.79481e8	+	2.79481e8i	−0.444028	+	0.444028i	0.449335	+	0.893363i	$0.351661\pi$
$858$	3.72749e8	−	1.74645e9i	0.590139	−	2.76499i
$859$	5.46039e8	−	2.26177e8i	0.861477	−	0.356836i	0.0921922	−	0.995741i	$-0.470613\pi$
$859$	5.46039e8	−	2.26177e8i	0.861477	−	0.356836i	0.769285	+	0.638906i	$0.220613\pi$
$860$	2.22356e8	−	4.97177e8i	0.349586	−	0.781655i
$861$	−1.86174e8	−	7.71158e7i	−0.291682	−	0.120819i
$862$	−4.96732e8	+	9.16335e7i	−0.775533	+	0.143065i
$863$			4.62990e8i			0.720343i	0.932886	+	0.360171i	$0.117282\pi$
$863$			4.62990e8i			0.720343i	−0.932886	+	0.360171i	$0.882718\pi$
$864$	5.31406e7	−	1.95051e8i	0.0823920	−	0.302418i
$865$	5.14844e8			0.795477
$866$	5.46974e7	+	2.96507e8i	0.0842195	+	0.456542i
$867$	−2.97177e8	+	7.17450e8i	−0.455993	+	1.10087i
$868$	−4.45084e7	+	9.95185e7i	−0.0680586	+	0.152175i
$869$	8.40983e7	+	2.03031e8i	0.128153	+	0.309388i
$870$	−3.97922e8	−	8.49294e7i	−0.604283	−	0.128973i
$871$	9.27698e7	+	9.27698e7i	0.140395	+	0.140395i
$872$	−6.87939e7	−	4.41527e8i	−0.103753	−	0.665899i
$873$	3.80373e8	+	3.80373e8i	0.571699	+	0.571699i
$874$	1.57462e8	−	1.02069e8i	0.235852	−	0.152884i
$875$	1.57332e8	+	3.79833e8i	0.234851	+	0.566982i
$876$	−8.54351e8	+	8.08032e8i	−1.27094	+	1.20203i
$877$	2.01679e8	−	4.86897e8i	0.298994	−	0.721836i	−0.700968	−	0.713192i	$-0.747249\pi$
$877$	2.01679e8	−	4.86897e8i	0.298994	−	0.721836i	0.999963	−	0.00864377i	$-0.00275143\pi$
$878$	4.71819e8	−	6.85271e8i	0.697095	−	1.01246i
$879$	−1.41642e9			−2.08557
$880$	6.10881e7	−	1.09538e9i	0.0896414	−	1.60737i
$881$			4.12392e8i			0.603090i	0.953452	+	0.301545i	$0.0975024\pi$
$881$			4.12392e8i			0.603090i	−0.953452	+	0.301545i	$0.902498\pi$
$882$	−2.62536e8	+	3.81307e8i	−0.382633	+	0.555737i
$883$	−2.22033e8	−	9.19692e7i	−0.322505	−	0.133586i	0.215557	−	0.976491i	$-0.430843\pi$
$883$	−2.22033e8	−	9.19692e7i	−0.322505	−	0.133586i	−0.538062	+	0.842905i	$0.680843\pi$
$884$	3.76368e8	+	1.04867e7i	0.544824	+	0.0151803i
$885$	−8.10345e8	+	3.35656e8i	−1.16907	+	0.484244i
$886$	3.31856e8	−	2.15114e8i	0.477142	−	0.309292i
$887$	−3.04747e8	+	3.04747e8i	−0.436686	+	0.436686i	−0.890895	−	0.454209i	$-0.849922\pi$
$887$	−3.04747e8	+	3.04747e8i	−0.436686	+	0.436686i	0.454209	+	0.890895i	$0.349922\pi$
$888$	9.53392e8	−	5.80948e8i	1.36155	−	0.829657i
$889$	1.03628e9	−	1.03628e9i	1.47493	−	1.47493i
$890$	7.79315e8	+	1.66331e8i	1.10546	+	0.235941i
$891$	−9.66094e8	+	4.00169e8i	−1.36580	+	0.565732i
$892$	−2.44766e8	−	6.40844e8i	−0.344870	−	0.902937i
$893$	8.84861e7	+	3.66522e7i	0.124257	+	0.0514689i
$894$	3.28751e8	+	1.78211e9i	0.460103	+	2.49415i
$895$		−	1.17837e9i		−	1.64367i
$896$	−8.70236e8	+	4.65913e8i	−1.20980	+	0.647710i
$897$	−2.94262e9			−4.07715
$898$	−2.89154e8	+	5.33410e7i	−0.399301	+	0.0736601i
$899$	1.22255e7	−	2.95149e7i	0.0168262	−	0.0406222i
$900$	3.39269e8	−	1.29581e8i	0.465389	−	0.177752i
$901$	3.68279e7	+	8.89103e7i	0.0503503	+	0.121556i
$902$	−3.32344e7	+	1.55714e8i	−0.0452864	+	0.212182i
$903$	6.32173e8	+	6.32173e8i	0.858564	+	0.858564i
$904$	−5.19246e7	−	8.52132e7i	−0.0702858	−	0.115346i
$905$	1.25240e9	+	1.25240e9i	1.68965	+	1.68965i
$906$	−1.54857e8	−	2.38896e8i	−0.208231	−	0.321237i
$907$	−1.38911e8	−	3.35362e8i	−0.186173	−	0.449461i	0.803044	−	0.595920i	$-0.203212\pi$
$907$	−1.38911e8	−	3.35362e8i	−0.186173	−	0.449461i	−0.989217	+	0.146459i	$0.953212\pi$
$908$	2.25538e7	−	8.09461e8i	0.0301275	−	1.08128i
$909$	−1.10743e8	+	2.67358e8i	−0.147444	+	0.355961i
$910$	1.86064e9	+	1.28108e9i	2.46910	+	1.70001i
$911$	−5.06644e8			−0.670113			−0.335056	−	0.942198i	$-0.608755\pi$
$911$	−5.06644e8			−0.670113			−0.335056	+	0.942198i	$0.608755\pi$
$912$	8.72965e6	−	1.56533e8i	0.0115083	−	0.206358i
$913$			6.13636e7i			0.0806303i
$914$	−1.02054e9	−	7.02655e8i	−1.33657	−	0.920246i
$915$	−1.89592e9	−	7.85317e8i	−2.47490	−	1.02514i
$916$	−1.02573e8	−	1.08453e8i	−0.133459	−	0.141109i
$917$	2.09427e8	−	8.67477e7i	0.271597	−	0.112499i
$918$	−4.22977e7	−	6.52523e7i	−0.0546750	−	0.0843467i
$919$	1.56587e8	−	1.56587e8i	0.201748	−	0.201748i	−0.599001	−	0.800748i	$-0.704435\pi$
$919$	1.56587e8	−	1.56587e8i	0.201748	−	0.201748i	0.800748	+	0.599001i	$0.204435\pi$
$920$	−1.78622e9	+	2.78310e8i	−2.29389	+	0.357408i
$921$	6.57883e8	−	6.57883e8i	0.842112	−	0.842112i
$922$	−2.48556e8	+	1.16457e9i	−0.317126	+	1.48584i
$923$	−1.40994e9	+	5.84015e8i	−1.79306	+	0.742709i
$924$	1.64396e9	+	7.35240e8i	2.08389	+	0.931994i
$925$	−5.72376e8	−	2.37086e8i	−0.723196	−	0.299558i
$926$	−7.17615e8	+	1.32380e8i	−0.903772	+	0.166721i
$927$		−	3.24225e8i		−	0.407012i
$928$	2.51113e8	−	1.43581e8i	0.314214	−	0.179661i
$929$	3.37779e8			0.421294			0.210647	−	0.977562i	$-0.432443\pi$
$929$	3.37779e8			0.421294			0.210647	+	0.977562i	$0.432443\pi$
$930$	3.02604e7	+	1.64037e8i	0.0376206	+	0.203936i
$931$	4.24390e7	−	1.02457e8i	0.0525915	−	0.126967i
$932$	1.27672e9	+	5.71000e8i	1.57706	+	0.705323i
$933$	−1.31702e8	−	3.17956e8i	−0.162161	−	0.391491i
$934$	9.81334e8	+	2.09449e8i	1.20442	+	0.257061i
$935$	−2.98398e8	−	2.98398e8i	−0.365057	−	0.365057i
$936$	−6.28029e8	+	8.59854e8i	−0.765865	+	1.04857i
$937$	−4.75505e8	−	4.75505e8i	−0.578011	−	0.578011i	0.356344	−	0.934355i	$-0.384023\pi$
$937$	−4.75505e8	−	4.75505e8i	−0.578011	−	0.578011i	−0.934355	+	0.356344i	$0.884023\pi$
$938$	−1.11021e8	+	7.19657e7i	−0.134523	+	0.0872001i
$939$	−5.56845e6	−	1.34434e7i	−0.00672570	−	0.0162373i
$940$	−6.34017e8	−	6.70361e8i	−0.763339	−	0.807096i
$941$	−1.31457e8	+	3.17366e8i	−0.157767	+	0.380883i	−0.982922	−	0.184023i	$-0.941088\pi$
$941$	−1.31457e8	+	3.17366e8i	−0.157767	+	0.380883i	0.825155	+	0.564907i	$0.191088\pi$
$942$	−4.05274e8	+	5.88620e8i	−0.484837	+	0.704178i
$943$	2.62365e8			0.312875
$944$	2.70334e8	−	5.61913e8i	0.321355	−	0.667964i
$945$		−	4.66559e8i		−	0.552854i
$946$	4.00594e8	−	5.81823e8i	0.473185	−	0.687255i
$947$	1.18223e9	+	4.89695e8i	1.39204	+	0.576602i	0.947673	−	0.319243i	$-0.103429\pi$
$947$	1.18223e9	+	4.89695e8i	1.39204	+	0.576602i	0.444367	+	0.895845i	$0.353429\pi$
$948$	8.42637e6	−	3.02424e8i	0.00989044	−	0.354970i
$949$	−1.76757e9	+	7.32151e8i	−2.06813	+	0.856647i
$950$	−7.30020e7	+	4.73211e7i	−0.0851459	+	0.0551930i
$951$	6.08279e8	−	6.08279e8i	0.707231	−	0.707231i
$952$	−8.95662e7	+	3.68982e8i	−0.103809	+	0.427656i
$953$	−3.49078e6	+	3.49078e6i	−0.00403314	+	0.00403314i	−0.709120	−	0.705087i	$-0.750908\pi$
$953$	−3.49078e6	+	3.49078e6i	−0.00403314	+	0.00403314i	0.705087	+	0.709120i	$0.250908\pi$
$954$	−2.66161e8	−	5.68074e7i	−0.306549	−	0.0654275i
$955$	−2.48930e8	+	1.03110e8i	−0.285803	+	0.118383i
$956$	−5.99331e8	+	2.28910e8i	−0.685951	+	0.261994i
$957$	−4.87561e8	−	2.01954e8i	−0.556279	−	0.230418i
$958$	−1.94779e8	−	1.05587e9i	−0.221537	−	1.20092i
$959$		−	4.18058e8i		−	0.474003i
$960$	−6.92440e8	+	1.34227e9i	−0.782651	+	1.51714i
$961$	8.74407e8			0.985243
$962$	1.78628e9	−	3.29519e8i	2.00643	−	0.370131i
$963$	3.61813e8	−	8.73493e8i	0.405140	−	0.978094i
$964$	2.05697e8	+	5.38555e8i	0.229613	+	0.601172i
$965$	6.76485e7	+	1.63318e8i	0.0752794	+	0.181740i
$966$	6.19408e8	−	2.90213e9i	0.687141	−	3.21948i
$967$	2.48575e8	+	2.48575e8i	0.274902	+	0.274902i	0.831070	−	0.556168i	$-0.187729\pi$
$967$	2.48575e8	+	2.48575e8i	0.274902	+	0.274902i	−0.556168	+	0.831070i	$0.687729\pi$
$968$	1.21691e8	−	5.01327e8i	0.134163	−	0.552707i
$969$	−4.26419e7	−	4.26419e7i	−0.0468668	−	0.0468668i
$970$	6.75249e8	+	1.04170e9i	0.739858	+	1.14137i
$971$	−4.01905e8	−	9.70285e8i	−0.439001	−	1.05984i	−0.976294	−	0.216447i	$-0.930553\pi$
$971$	−4.01905e8	−	9.70285e8i	−0.439001	−	1.05984i	0.537293	−	0.843396i	$-0.319447\pi$
$972$	1.15131e9	+	3.20787e7i	1.25370	+	0.0349316i
$973$	−9.11763e8	+	2.20119e9i	−0.989790	+	2.38957i
$974$	−2.05936e8	−	1.41790e8i	−0.222872	−	0.153451i
$975$	1.36425e9			1.47191
$976$	1.37685e9	−	4.82383e8i	1.48094	−	0.518850i
$977$			7.94745e8i			0.852205i	0.904675	+	0.426102i	$0.140114\pi$
$977$			7.94745e8i			0.852205i	−0.904675	+	0.426102i	$0.859886\pi$
$978$	−4.60753e8	−	3.17235e8i	−0.492551	−	0.339129i
$979$	9.54869e8	+	3.95520e8i	1.01764	+	0.421522i
$980$	−7.76200e8	+	7.34119e8i	−0.824699	+	0.779988i
$981$	4.49091e8	−	1.86020e8i	0.475694	−	0.197039i
$982$	4.09974e8	+	6.32464e8i	0.432934	+	0.667884i
$983$	−1.04043e9	+	1.04043e9i	−1.09535	+	1.09535i	−0.100404	+	0.994947i	$0.532014\pi$
$983$	−1.04043e9	+	1.04043e9i	−1.09535	+	1.09535i	−0.994947	+	0.100404i	$0.967986\pi$
$984$	1.29287e8	−	1.77011e8i	0.135697	−	0.185787i
$985$	−1.50947e8	+	1.50947e8i	−0.157949	+	0.157949i
$986$	2.32248e7	−	1.08816e8i	0.0242282	−	0.113517i
$987$	1.39932e9	−	5.79618e8i	1.45535	−	0.602824i
$988$	1.04136e8	−	2.32842e8i	0.107977	−	0.241430i
$989$	−1.07539e9	−	4.45443e8i	−1.11168	−	0.460472i
$990$	1.17361e9	−	2.16500e8i	1.20954	−	0.223127i
$991$			4.30598e8i			0.442437i	0.975224	+	0.221218i	$0.0710033\pi$
$991$			4.30598e8i			0.442437i	−0.975224	+	0.221218i	$0.928997\pi$
$992$	−9.37772e7	−	7.25839e7i	−0.0960643	−	0.0743542i
$993$	1.03797e9			1.06008
$994$	−2.79194e8	−	1.51347e9i	−0.284280	−	1.54104i
$995$	−3.81041e7	+	9.19915e7i	−0.0386815	+	0.0933853i
$996$	3.44899e7	−	7.71176e7i	0.0349071	−	0.0780505i
$997$	4.79504e7	+	1.15762e8i	0.0483845	+	0.116811i	0.946224	−	0.323513i	$-0.104864\pi$
$997$	4.79504e7	+	1.15762e8i	0.0483845	+	0.116811i	−0.897839	+	0.440323i	$0.854864\pi$
$998$	−1.01541e9	−	2.16722e8i	−1.02153	−	0.218028i
$999$	−2.65269e8	−	2.65269e8i	−0.266067	−	0.266067i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	32.7.h.a.3.2	✓	92
4.3	odd	2		128.7.h.a.47.21		92
32.11	odd	8	inner	32.7.h.a.11.2	yes	92
32.21	even	8		128.7.h.a.79.21		92

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.7.h.a.3.2	✓	92	1.1	even	1	trivial
32.7.h.a.11.2	yes	92	32.11	odd	8	inner
128.7.h.a.47.21		92	4.3	odd	2
128.7.h.a.79.21		92	32.21	even	8

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 32 = 2^{5} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	32.h (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-7.86726 + 1.45129i) q^{2} +(-13.7231 + 33.1306i) q^{3} +(59.7875 - 22.8354i) q^{4} +(61.4842 + 148.436i) q^{5} +(59.8812 - 280.563i) q^{6} +(332.829 + 332.829i) q^{7} +(-437.223 + 266.421i) q^{8} +(-393.829 - 393.829i) q^{9} +(-699.136 - 1078.55i) q^{10} +(-637.963 - 1540.18i) q^{11} +(-63.9218 + 2294.17i) q^{12} +(-1428.92 + 3449.73i) q^{13} +(-3101.48 - 2135.42i) q^{14} -5761.52 q^{15} +(3053.09 - 2730.54i) q^{16} -1575.55i q^{17} +(3669.92 + 2526.79i) q^{18} +(-986.102 - 408.457i) q^{19} +(7065.58 + 7470.59i) q^{20} +(-15594.2 + 6459.35i) q^{21} +(7254.27 + 11191.1i) q^{22} +(15539.5 - 15539.5i) q^{23} +(-2826.62 - 18141.6i) q^{24} +(-7204.36 + 7204.36i) q^{25} +(6235.15 - 29213.7i) q^{26} +(-5699.84 + 2360.95i) q^{27} +(27499.3 + 12298.7i) q^{28} +(-8155.67 - 3378.19i) q^{29} +(45327.4 - 8361.65i) q^{30} +3618.95i q^{31} +(-20056.6 + 25912.8i) q^{32} +59781.8 q^{33} +(2286.58 + 12395.2i) q^{34} +(-28940.0 + 69867.4i) q^{35} +(-32539.3 - 14552.8i) q^{36} +(23269.9 + 56178.6i) q^{37} +(8350.71 + 1782.31i) q^{38} +(-94682.2 - 94682.2i) q^{39} +(-66428.7 - 48518.9i) q^{40} +(8441.89 + 8441.89i) q^{41} +(113310. - 73449.2i) q^{42} +(-20269.4 - 48934.7i) q^{43} +(-73312.8 - 77515.3i) q^{44} +(34244.1 - 82672.6i) q^{45} +(-99700.6 + 144805. i) q^{46} -89733.3 q^{47} +(48566.5 + 138622. i) q^{48} +103901. i q^{49} +(46222.9 - 67134.2i) q^{50} +(52198.8 + 21621.4i) q^{51} +(-6655.88 + 238881. i) q^{52} +(-56431.4 + 23374.6i) q^{53} +(41415.7 - 26846.3i) q^{54} +(189393. - 189393. i) q^{55} +(-234193. - 56847.7i) q^{56} +(27064.8 - 27064.8i) q^{57} +(69065.5 + 14740.8i) q^{58} +(140648. - 58258.3i) q^{59} +(-344467. + 131567. i) q^{60} +(329067. + 136304. i) q^{61} +(-5252.16 - 28471.2i) q^{62} -262155. i q^{63} +(120184. - 232971. i) q^{64} -599920. q^{65} +(-470319. + 86761.0i) q^{66} +(13446.0 - 32461.4i) q^{67} +(-35978.3 - 94198.0i) q^{68} +(301581. + 728081. i) q^{69} +(126281. - 591665. i) q^{70} +(289001. + 289001. i) q^{71} +(277115. + 67266.6i) q^{72} +(362307. + 362307. i) q^{73} +(-264602. - 408200. i) q^{74} +(-139818. - 337551. i) q^{75} +(-68283.8 - 1902.58i) q^{76} +(300283. - 724948. i) q^{77} +(882301. + 607477. i) q^{78} -131823. q^{79} +(593027. + 285303. i) q^{80} -627261. i q^{81} +(-78666.2 - 54162.9i) q^{82} +(-34007.1 - 14086.2i) q^{83} +(-784839. + 742289. i) q^{84} +(233868. - 96871.2i) q^{85} +(230483. + 355565. i) q^{86} +(223842. - 223842. i) q^{87} +(689268. + 503435. i) q^{88} +(-438387. + 438387. i) q^{89} +(-149425. + 700105. i) q^{90} +(-1.62376e6 + 672582. i) q^{91} +(574215. - 1.28391e6i) q^{92} +(-119898. - 49663.3i) q^{93} +(705955. - 130229. i) q^{94} -171487. i q^{95} +(-583266. - 1.02009e6i) q^{96} -965834. q^{97} +(-150790. - 817414. i) q^{98} +(-355319. + 857816. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 92 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9} + 2996 q^{10} - 4 q^{11} - 3892 q^{12} - 4 q^{13} - 8532 q^{14} - 8 q^{15} + 14096 q^{16} + 24296 q^{18} - 4 q^{19} - 14004 q^{20}+ \cdots + 5967768 q^{99}+O(q^{100}) \) 92 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9 + 2996 * q^10 - 4 * q^11 - 3892 * q^12 - 4 * q^13 - 8532 * q^14 - 8 * q^15 + 14096 * q^16 + 24296 * q^18 - 4 * q^19 - 14004 * q^20 - 4 * q^21 - 19552 * q^22 + 13116 * q^23 - 43568 * q^24 - 4 * q^25 + 5296 * q^26 - 68644 * q^27 + 85496 * q^28 - 4 * q^29 + 102980 * q^30 - 58904 * q^32 - 8 * q^33 - 139248 * q^34 + 162332 * q^35 - 328464 * q^36 - 4 * q^37 + 457684 * q^38 - 254404 * q^39 + 430952 * q^40 - 4 * q^41 - 256504 * q^42 + 145436 * q^43 - 808764 * q^44 - 2920 * q^45 - 197284 * q^46 - 8 * q^47 + 349488 * q^48 + 1254548 * q^50 - 157792 * q^51 - 71644 * q^52 + 443676 * q^53 - 455840 * q^54 - 232708 * q^55 - 619736 * q^56 - 4 * q^57 - 290272 * q^58 + 886140 * q^59 + 803000 * q^60 - 652996 * q^61 + 1415352 * q^62 - 1533928 * q^64 - 8 * q^65 - 308980 * q^66 - 1509604 * q^67 + 447632 * q^68 + 1083452 * q^69 - 676264 * q^70 - 267012 * q^71 - 1219564 * q^72 - 4 * q^73 - 661588 * q^74 + 2083672 * q^75 + 873980 * q^76 - 932964 * q^77 + 1480180 * q^78 - 1721864 * q^79 - 2377928 * q^80 - 1407364 * q^82 + 3074396 * q^83 + 2103584 * q^84 + 62496 * q^85 + 2146368 * q^86 - 2029892 * q^87 + 2855072 * q^88 - 4 * q^89 + 2497832 * q^90 - 3700804 * q^91 - 540888 * q^92 + 2912 * q^93 - 2438936 * q^94 + 3127168 * q^96 - 8 * q^97 + 2073880 * q^98 + 5967768 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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