LMFDB - Embedded newform 150.6.g.a.61.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [150,6,Mod(31,150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(150, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("150.31");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 150 = 2 \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	150.g (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$24.0575729719$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 10 x^{19} + 67300 x^{18} - 605415 x^{17} + 1505002471 x^{16} - 12026298320 x^{15} + \cdots + 45\!\cdots\!05 $ x^20 - 10x^19 + 67300x^18 - 605415x^17 + 1505002471x^16 - 12026298320x^15 + 15161344295580x^14 - 105918997871590x^13 + 72521519492275041x^12 - 433752716999522710x^11 + 150954604904063839080x^10 - 750799480917962811625x^9 + 100084099910299358028076x^8 - 395836369710607771806480x^7 + 22144208384329171616972475x^6 - 65050346450081546072582845x^5 + 865137734840778899106150416x^4 - 1622318535480468844324766865x^3 + 11299132807307021058314145735x^2 - 10498749516125580450644510315*x + 45940690246932155189634577205
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8}\cdot 5^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			61.1
Root			$0.500000 - 22.2192i$ of defining polynomial
Character	$\chi$	$=$	150.61
Dual form			150.6.g.a.91.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.23607 - 2.35114i) q^{2} +(-2.78115 + 8.55951i) q^{3} +(4.94427 - 15.2169i) q^{4} +(-41.6409 - 37.2966i) q^{5} +(11.1246 + 34.2380i) q^{6} -58.1692 q^{7} +(-19.7771 - 60.8676i) q^{8} +(-65.5304 - 47.6106i) q^{9} +O(q^{10})$	\(q+(3.23607 - 2.35114i) q^{2} +(-2.78115 + 8.55951i) q^{3} +(4.94427 - 15.2169i) q^{4} +(-41.6409 - 37.2966i) q^{5} +(11.1246 + 34.2380i) q^{6} -58.1692 q^{7} +(-19.7771 - 60.8676i) q^{8} +(-65.5304 - 47.6106i) q^{9} +(-222.442 - 22.7907i) q^{10} +(-75.5060 + 54.8583i) q^{11} +(116.498 + 84.6411i) q^{12} +(756.886 + 549.910i) q^{13} +(-188.239 + 136.764i) q^{14} +(435.050 - 252.698i) q^{15} +(-207.108 - 150.473i) q^{16} +(665.326 + 2047.66i) q^{17} -324.000 q^{18} +(-315.787 - 971.893i) q^{19} +(-773.423 + 449.241i) q^{20} +(161.777 - 497.900i) q^{21} +(-115.363 + 355.050i) q^{22} +(-270.239 + 196.340i) q^{23} +576.000 q^{24} +(342.927 + 3106.13i) q^{25} +3742.25 q^{26} +(589.773 - 428.495i) q^{27} +(-287.604 + 885.155i) q^{28} +(-1972.31 + 6070.15i) q^{29} +(813.724 - 1840.61i) q^{30} +(1520.23 + 4678.80i) q^{31} -1024.00 q^{32} +(-259.566 - 798.863i) q^{33} +(6967.38 + 5062.10i) q^{34} +(2422.22 + 2169.51i) q^{35} +(-1048.49 + 761.770i) q^{36} +(-4103.26 - 2981.19i) q^{37} +(-3306.97 - 2402.65i) q^{38} +(-6811.97 + 4949.19i) q^{39} +(-1446.62 + 3272.20i) q^{40} +(-2940.87 - 2136.67i) q^{41} +(-647.110 - 1991.60i) q^{42} +12768.6 q^{43} +(461.451 + 1420.20i) q^{44} +(953.029 + 4426.61i) q^{45} +(-412.888 + 1270.74i) q^{46} +(-6800.92 + 20931.1i) q^{47} +(1863.98 - 1354.26i) q^{48} -13423.3 q^{49} +(8412.68 + 9245.37i) q^{50} -19377.4 q^{51} +(12110.2 - 8798.55i) q^{52} +(3437.97 - 10581.0i) q^{53} +(901.094 - 2773.28i) q^{54} +(5190.16 + 531.768i) q^{55} +(1150.42 + 3540.62i) q^{56} +9197.18 q^{57} +(7889.24 + 24280.6i) q^{58} +(39236.5 + 28507.0i) q^{59} +(-1694.27 - 7869.53i) q^{60} +(14156.9 - 10285.6i) q^{61} +(15920.1 + 11566.6i) q^{62} +(3811.85 + 2769.47i) q^{63} +(-3313.73 + 2407.57i) q^{64} +(-11007.6 - 51128.0i) q^{65} +(-2718.21 - 1974.90i) q^{66} +(-3545.22 - 10911.1i) q^{67} +34448.6 q^{68} +(-928.998 - 2859.16i) q^{69} +(12939.3 + 1325.72i) q^{70} +(16765.2 - 51598.0i) q^{71} +(-1601.94 + 4930.28i) q^{72} +(-23773.1 + 17272.2i) q^{73} -20287.6 q^{74} +(-27540.7 - 5703.33i) q^{75} -16350.5 q^{76} +(4392.12 - 3191.06i) q^{77} +(-10407.8 + 32031.8i) q^{78} +(-3995.93 + 12298.2i) q^{79} +(3012.04 + 13990.3i) q^{80} +(2027.46 + 6239.88i) q^{81} -14540.5 q^{82} +(22693.5 + 69843.4i) q^{83} +(-6776.62 - 4923.50i) q^{84} +(48666.1 - 110081. i) q^{85} +(41320.0 - 30020.7i) q^{86} +(-46472.2 - 33764.0i) q^{87} +(4832.38 + 3510.93i) q^{88} +(-83147.1 + 60409.9i) q^{89} +(13491.6 + 12084.1i) q^{90} +(-44027.4 - 31987.8i) q^{91} +(1651.55 + 5082.95i) q^{92} -44276.2 q^{93} +(27203.7 + 83724.3i) q^{94} +(-23098.6 + 52248.3i) q^{95} +(2847.90 - 8764.94i) q^{96} +(26326.7 - 81025.3i) q^{97} +(-43438.9 + 31560.2i) q^{98} +7559.77 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 20 q^{2} + 45 q^{3} - 80 q^{4} - 55 q^{5} - 180 q^{6} + 180 q^{7} + 320 q^{8} - 405 q^{9}+O(q^{10}) $ 20 * q + 20 * q^2 + 45 * q^3 - 80 * q^4 - 55 * q^5 - 180 * q^6 + 180 * q^7 + 320 * q^8 - 405 * q^9	\( 20 q + 20 q^{2} + 45 q^{3} - 80 q^{4} - 55 q^{5} - 180 q^{6} + 180 q^{7} + 320 q^{8} - 405 q^{9} + 220 q^{10} + 380 q^{11} + 720 q^{12} - 230 q^{13} - 920 q^{14} - 630 q^{15} - 1280 q^{16} + 2870 q^{17} - 6480 q^{18} + 1560 q^{19} + 1120 q^{20} + 2880 q^{21} - 720 q^{22} + 760 q^{23} + 11520 q^{24} + 1725 q^{25} + 7320 q^{26} + 3645 q^{27} - 5120 q^{28} + 12000 q^{29} + 5220 q^{30} - 1710 q^{31} - 20480 q^{32} - 1620 q^{33} + 20620 q^{34} - 22440 q^{35} - 6480 q^{36} - 5595 q^{37} - 5240 q^{38} + 2070 q^{39} - 9280 q^{40} - 2820 q^{41} - 11520 q^{42} + 66020 q^{43} + 2880 q^{44} - 8505 q^{45} + 21960 q^{46} - 19630 q^{47} + 11520 q^{48} - 61780 q^{49} + 100 q^{50} - 41130 q^{51} - 3680 q^{52} + 62735 q^{53} - 14580 q^{54} + 66590 q^{55} + 20480 q^{56} + 51660 q^{57} - 48000 q^{58} + 105100 q^{59} + 15120 q^{60} + 34790 q^{61} - 28560 q^{62} + 18630 q^{63} - 20480 q^{64} - 44345 q^{65} + 13680 q^{66} - 19470 q^{67} + 73120 q^{68} + 49410 q^{69} - 81240 q^{70} - 111720 q^{71} + 25920 q^{72} - 198830 q^{73} - 104120 q^{74} + 60975 q^{75} - 91840 q^{76} + 144740 q^{77} + 41220 q^{78} + 71210 q^{79} - 26880 q^{80} - 32805 q^{81} + 166680 q^{82} - 288690 q^{83} - 33120 q^{84} + 338735 q^{85} + 39920 q^{86} + 108225 q^{87} - 24320 q^{88} + 114225 q^{89} + 17820 q^{90} - 155800 q^{91} - 87840 q^{92} + 97740 q^{93} + 78520 q^{94} - 416900 q^{95} - 46080 q^{96} - 446970 q^{97} - 123380 q^{98} - 90720 q^{99}+O(q^{100}) \) 20 * q + 20 * q^2 + 45 * q^3 - 80 * q^4 - 55 * q^5 - 180 * q^6 + 180 * q^7 + 320 * q^8 - 405 * q^9 + 220 * q^10 + 380 * q^11 + 720 * q^12 - 230 * q^13 - 920 * q^14 - 630 * q^15 - 1280 * q^16 + 2870 * q^17 - 6480 * q^18 + 1560 * q^19 + 1120 * q^20 + 2880 * q^21 - 720 * q^22 + 760 * q^23 + 11520 * q^24 + 1725 * q^25 + 7320 * q^26 + 3645 * q^27 - 5120 * q^28 + 12000 * q^29 + 5220 * q^30 - 1710 * q^31 - 20480 * q^32 - 1620 * q^33 + 20620 * q^34 - 22440 * q^35 - 6480 * q^36 - 5595 * q^37 - 5240 * q^38 + 2070 * q^39 - 9280 * q^40 - 2820 * q^41 - 11520 * q^42 + 66020 * q^43 + 2880 * q^44 - 8505 * q^45 + 21960 * q^46 - 19630 * q^47 + 11520 * q^48 - 61780 * q^49 + 100 * q^50 - 41130 * q^51 - 3680 * q^52 + 62735 * q^53 - 14580 * q^54 + 66590 * q^55 + 20480 * q^56 + 51660 * q^57 - 48000 * q^58 + 105100 * q^59 + 15120 * q^60 + 34790 * q^61 - 28560 * q^62 + 18630 * q^63 - 20480 * q^64 - 44345 * q^65 + 13680 * q^66 - 19470 * q^67 + 73120 * q^68 + 49410 * q^69 - 81240 * q^70 - 111720 * q^71 + 25920 * q^72 - 198830 * q^73 - 104120 * q^74 + 60975 * q^75 - 91840 * q^76 + 144740 * q^77 + 41220 * q^78 + 71210 * q^79 - 26880 * q^80 - 32805 * q^81 + 166680 * q^82 - 288690 * q^83 - 33120 * q^84 + 338735 * q^85 + 39920 * q^86 + 108225 * q^87 - 24320 * q^88 + 114225 * q^89 + 17820 * q^90 - 155800 * q^91 - 87840 * q^92 + 97740 * q^93 + 78520 * q^94 - 416900 * q^95 - 46080 * q^96 - 446970 * q^97 - 123380 * q^98 - 90720 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	3.23607	−	2.35114i	0.572061	−	0.415627i
$2$	3.23607	−	2.35114i	0.572061	−	0.415627i
$3$	−2.78115	+	8.55951i	−0.178411	+	0.549093i
$3$	−2.78115	+	8.55951i	−0.178411	+	0.549093i
$4$	4.94427	−	15.2169i	0.154508	−	0.475528i
$5$	−41.6409	−	37.2966i	−0.744895	−	0.667182i
$5$	−41.6409	−	37.2966i	−0.744895	−	0.667182i
$6$	11.1246	+	34.2380i	0.126156	+	0.388267i
$7$	−58.1692			−0.448692			−0.224346	−	0.974510i	$-0.572025\pi$
$7$	−58.1692			−0.448692			−0.224346	+	0.974510i	$0.572025\pi$
$8$	−19.7771	−	60.8676i	−0.109254	−	0.336249i
$9$	−65.5304	−	47.6106i	−0.269672	−	0.195928i
$10$	−222.442	−	22.7907i	−0.703424	−	0.0720707i
$11$	−75.5060	+	54.8583i	−0.188148	+	0.136697i	−0.677872	−	0.735180i	$-0.737098\pi$
$11$	−75.5060	+	54.8583i	−0.188148	+	0.136697i	0.489724	+	0.871878i	$0.337098\pi$
$12$	116.498	+	84.6411i	0.233543	+	0.169679i
$13$	756.886	+	549.910i	1.24214	+	0.902470i	0.997739	−	0.0672032i	$-0.0214076\pi$
$13$	756.886	+	549.910i	1.24214	+	0.902470i	0.244404	+	0.969673i	$0.421408\pi$
$14$	−188.239	+	136.764i	−0.256679	+	0.186488i
$15$	435.050	−	252.698i	0.499242	−	0.289984i
$16$	−207.108	−	150.473i	−0.202254	−	0.146946i
$17$	665.326	+	2047.66i	0.558357	+	1.71845i	0.686909	+	0.726744i	$0.258967\pi$
$17$	665.326	+	2047.66i	0.558357	+	1.71845i	−0.128551	+	0.991703i	$0.541033\pi$
$18$	−324.000			−0.235702
$19$	−315.787	−	971.893i	−0.200683	−	0.617639i	−0.999863	−	0.0165470i	$-0.994733\pi$
$19$	−315.787	−	971.893i	−0.200683	−	0.617639i	0.799180	−	0.601092i	$-0.205267\pi$
$20$	−773.423	+	449.241i	−0.432356	+	0.251133i
$21$	161.777	−	497.900i	0.0800515	−	0.246373i
$22$	−115.363	+	355.050i	−0.0508170	+	0.156399i
$23$	−270.239	+	196.340i	−0.106519	+	0.0773907i	−0.639770	−	0.768567i	$-0.720970\pi$
$23$	−270.239	+	196.340i	−0.106519	+	0.0773907i	0.533251	+	0.845957i	$0.320970\pi$
$24$	576.000			0.204124
$25$	342.927	+	3106.13i	0.109737	+	0.993961i
$26$	3742.25			1.08567
$27$	589.773	−	428.495i	0.155695	−	0.113119i
$28$	−287.604	+	885.155i	−0.0693267	+	0.213366i
$29$	−1972.31	+	6070.15i	−0.435492	+	1.34031i	0.457089	+	0.889421i	$0.348892\pi$
$29$	−1972.31	+	6070.15i	−0.435492	+	1.34031i	−0.892581	+	0.450886i	$0.851108\pi$
$30$	813.724	−	1840.61i	0.165072	−	0.373387i
$31$	1520.23	+	4678.80i	0.284123	+	0.874440i	0.986660	+	0.162793i	$0.0520503\pi$
$31$	1520.23	+	4678.80i	0.284123	+	0.874440i	−0.702538	+	0.711647i	$0.747950\pi$
$32$	−1024.00			−0.176777
$33$	−259.566	−	798.863i	−0.0414919	−	0.127699i
$34$	6967.38	+	5062.10i	1.03365	+	0.750989i
$35$	2422.22	+	2169.51i	0.334228	+	0.299359i
$36$	−1048.49	+	761.770i	−0.134836	+	0.0979642i
$37$	−4103.26	−	2981.19i	−0.492748	−	0.358002i	0.313492	−	0.949591i	$-0.398501\pi$
$37$	−4103.26	−	2981.19i	−0.492748	−	0.358002i	−0.806240	+	0.591588i	$0.798501\pi$
$38$	−3306.97	−	2402.65i	−0.371510	−	0.269918i
$39$	−6811.97	+	4949.19i	−0.717152	+	0.521041i
$40$	−1446.62	+	3272.20i	−0.142957	+	0.323363i
$41$	−2940.87	−	2136.67i	−0.273222	−	0.198508i	0.442733	−	0.896653i	$-0.354009\pi$
$41$	−2940.87	−	2136.67i	−0.273222	−	0.198508i	−0.715956	+	0.698146i	$0.754009\pi$
$42$	−647.110	−	1991.60i	−0.0566050	−	0.174212i
$43$	12768.6			1.05310			0.526552	−	0.850143i	$-0.323484\pi$
$43$	12768.6			1.05310			0.526552	+	0.850143i	$0.323484\pi$
$44$	461.451	+	1420.20i	0.0359331	+	0.110591i
$45$	953.029	+	4426.61i	0.0701576	+	0.325867i
$46$	−412.888	+	1270.74i	−0.0287699	+	0.0885445i
$47$	−6800.92	+	20931.1i	−0.449079	+	1.38212i	0.428868	+	0.903367i	$0.358912\pi$
$47$	−6800.92	+	20931.1i	−0.449079	+	1.38212i	−0.877948	+	0.478757i	$0.841088\pi$
$48$	1863.98	−	1354.26i	0.116772	−	0.0848395i
$49$	−13423.3			−0.798676
$50$	8412.68	+	9245.37i	0.475893	+	0.522997i
$51$	−19377.4			−1.04320
$52$	12110.2	−	8798.55i	0.621072	−	0.451235i
$53$	3437.97	−	10581.0i	0.168117	−	0.517412i	−0.831135	−	0.556070i	$-0.812309\pi$
$53$	3437.97	−	10581.0i	0.168117	−	0.517412i	0.999252	+	0.0386587i	$0.0123085\pi$
$54$	901.094	−	2773.28i	0.0420519	−	0.129422i
$55$	5190.16	+	531.768i	0.231353	+	0.0237037i
$56$	1150.42	+	3540.62i	0.0490214	+	0.150872i
$57$	9197.18			0.374945
$58$	7889.24	+	24280.6i	0.307939	+	0.947740i
$59$	39236.5	+	28507.0i	1.46744	+	1.06616i	0.981346	+	0.192251i	$0.0615788\pi$
$59$	39236.5	+	28507.0i	1.46744	+	1.06616i	0.486094	+	0.873906i	$0.338421\pi$
$60$	−1694.27	−	7869.53i	−0.0607583	−	0.282209i
$61$	14156.9	−	10285.6i	0.487129	−	0.353920i	−0.316950	−	0.948442i	$-0.602659\pi$
$61$	14156.9	−	10285.6i	0.487129	−	0.353920i	0.804079	+	0.594522i	$0.202659\pi$
$62$	15920.1	+	11566.6i	0.525976	+	0.382144i
$63$	3811.85	+	2769.47i	0.121000	+	0.0879114i
$64$	−3313.73	+	2407.57i	−0.101127	+	0.0734732i
$65$	−11007.6	−	51128.0i	−0.323155	−	1.50098i
$66$	−2718.21	−	1974.90i	−0.0768111	−	0.0558065i
$67$	−3545.22	−	10911.1i	−0.0964841	−	0.296947i	0.891154	−	0.453702i	$-0.149897\pi$
$67$	−3545.22	−	10911.1i	−0.0964841	−	0.296947i	−0.987638	+	0.156754i	$0.949897\pi$
$68$	34448.6			0.903441
$69$	−928.998	−	2859.16i	−0.0234905	−	0.0722963i
$70$	12939.3	+	1325.72i	0.315621	+	0.0323375i
$71$	16765.2	−	51598.0i	0.394696	−	1.21475i	−0.534501	−	0.845168i	$-0.679501\pi$
$71$	16765.2	−	51598.0i	0.394696	−	1.21475i	0.929198	−	0.369583i	$-0.120499\pi$
$72$	−1601.94	+	4930.28i	−0.0364180	+	0.112083i
$73$	−23773.1	+	17272.2i	−0.522131	+	0.379350i	−0.817406	−	0.576062i	$-0.804589\pi$
$73$	−23773.1	+	17272.2i	−0.522131	+	0.379350i	0.295275	+	0.955412i	$0.404589\pi$
$74$	−20287.6			−0.430678
$75$	−27540.7	−	5703.33i	−0.565355	−	0.117078i
$76$	−16350.5			−0.324712
$77$	4392.12	−	3191.06i	0.0844204	−	0.0613350i
$78$	−10407.8	+	32031.8i	−0.193696	+	0.596135i
$79$	−3995.93	+	12298.2i	−0.0720360	+	0.221704i	−0.980592	−	0.196059i	$-0.937186\pi$
$79$	−3995.93	+	12298.2i	−0.0720360	+	0.221704i	0.908556	+	0.417763i	$0.137186\pi$
$80$	3012.04	+	13990.3i	0.0526182	+	0.244400i
$81$	2027.46	+	6239.88i	0.0343352	+	0.105673i
$82$	−14540.5			−0.238805
$83$	22693.5	+	69843.4i	0.361581	+	1.11283i	0.952094	+	0.305805i	$0.0989255\pi$
$83$	22693.5	+	69843.4i	0.361581	+	1.11283i	−0.590513	+	0.807028i	$0.701075\pi$
$84$	−6776.62	−	4923.50i	−0.104789	−	0.0761335i
$85$	48666.1	−	110081.i	0.730599	−	1.65259i
$86$	41320.0	−	30020.7i	0.602440	−	0.437699i
$87$	−46472.2	−	33764.0i	−0.658256	−	0.478251i
$88$	4832.38	+	3510.93i	0.0665204	+	0.0483299i
$89$	−83147.1	+	60409.9i	−1.11268	+	0.808412i	−0.983084	−	0.183154i	$-0.941369\pi$
$89$	−83147.1	+	60409.9i	−1.11268	+	0.808412i	−0.129600	+	0.991566i	$0.541369\pi$
$90$	13491.6	+	12084.1i	0.175573	+	0.157256i
$91$	−44027.4	−	31987.8i	−0.557339	−	0.404931i
$92$	1651.55	+	5082.95i	0.0203434	+	0.0626104i
$93$	−44276.2			−0.530839
$94$	27203.7	+	83724.3i	0.317547	+	0.977309i
$95$	−23098.6	+	52248.3i	−0.262590	+	0.593968i
$96$	2847.90	−	8764.94i	0.0315389	−	0.0970668i
$97$	26326.7	−	81025.3i	0.284097	−	0.874362i	−0.702570	−	0.711614i	$-0.747964\pi$
$97$	26326.7	−	81025.3i	0.284097	−	0.874362i	0.986668	−	0.162748i	$-0.0520357\pi$
$98$	−43438.9	+	31560.2i	−0.456892	+	0.331951i
$99$	7559.77			0.0775212
$100$	48961.2	+	10139.3i	0.489612	+	0.101393i
$101$	−184406.			−1.79875			−0.899377	−	0.437174i	$-0.855980\pi$
$101$	−184406.			−1.79875			−0.899377	+	0.437174i	$0.855980\pi$
$102$	−62706.4	+	45558.9i	−0.596777	+	0.433584i
$103$	29506.1	−	90810.4i	0.274043	−	0.843417i	−0.715428	−	0.698686i	$-0.753768\pi$
$103$	29506.1	−	90810.4i	0.274043	−	0.843417i	0.989471	−	0.144731i	$-0.0462316\pi$
$104$	18502.7	−	56945.4i	0.167746	−	0.516268i
$105$	−25306.5	+	14699.2i	−0.224006	+	0.130113i
$106$	−13751.9	−	42323.9i	−0.118877	−	0.365865i
$107$	−150313.			−1.26922			−0.634612	−	0.772831i	$-0.718840\pi$
$107$	−150313.			−1.26922			−0.634612	+	0.772831i	$0.718840\pi$
$108$	−3604.37	−	11093.1i	−0.0297352	−	0.0915155i
$109$	42367.9	+	30782.0i	0.341563	+	0.248160i	0.745321	−	0.666706i	$-0.232296\pi$
$109$	42367.9	+	30782.0i	0.341563	+	0.248160i	−0.403758	+	0.914866i	$0.632296\pi$
$110$	18046.0	−	10482.0i	0.142200	−	0.0825964i
$111$	36929.4	−	26830.7i	0.284488	−	0.206693i
$112$	12047.3	+	8752.89i	0.0907498	+	0.0659336i
$113$	27590.7	+	20045.8i	0.203267	+	0.147682i	0.684762	−	0.728767i	$-0.259906\pi$
$113$	27590.7	+	20045.8i	0.203267	+	0.147682i	−0.481495	+	0.876449i	$0.659906\pi$
$114$	29762.7	−	21623.9i	0.214492	−	0.155837i
$115$	18575.8	+	1903.22i	0.130979	+	0.0134197i
$116$	82617.2	+	60024.9i	0.570067	+	0.414178i
$117$	−23417.5	−	72071.6i	−0.158152	−	0.486742i
$118$	193996.			1.28259
$119$	−38701.5	−	119111.i	−0.250530	−	0.771053i
$120$	−23985.2	−	21482.8i	−0.152051	−	0.136188i
$121$	−47075.8	+	144884.i	−0.292304	+	0.899618i
$122$	21629.8	−	66569.8i	0.131569	−	0.404928i
$123$	26467.8	−	19230.0i	0.157745	−	0.114608i
$124$	78713.2			0.459720
$125$	101568.	−	142132.i	0.581410	−	0.813610i
$126$	18846.8			0.105758
$127$	−33620.5	+	24426.7i	−0.184967	+	0.134387i	−0.676416	−	0.736520i	$-0.736468\pi$
$127$	−33620.5	+	24426.7i	−0.184967	+	0.134387i	0.491448	+	0.870907i	$0.336468\pi$
$128$	−5062.93	+	15582.1i	−0.0273135	+	0.0840623i
$129$	−35511.4	+	109293.i	−0.187885	+	0.578252i
$130$	−155831.	−	139573.i	−0.808712	−	0.724342i
$131$	2058.87	+	6336.54i	0.0104821	+	0.0322607i	0.956161	−	0.292842i	$-0.0946011\pi$
$131$	2058.87	+	6336.54i	0.0104821	+	0.0322607i	−0.945679	+	0.325103i	$0.894601\pi$
$132$	−13439.6			−0.0671353
$133$	18369.1	+	56534.2i	0.0900448	+	0.277129i
$134$	−37126.0	−	26973.6i	−0.178614	−	0.129771i
$135$	−40540.1	−	4153.61i	−0.191448	−	0.0196151i
$136$	111478.	−	80993.6i	0.516824	−	0.375494i
$137$	−334446.	−	242989.i	−1.52238	−	1.10608i	−0.960290	−	0.279003i	$-0.909996\pi$
$137$	−334446.	−	242989.i	−1.52238	−	1.10608i	−0.562093	−	0.827074i	$-0.690004\pi$
$138$	−9728.59	−	7068.24i	−0.0434863	−	0.0315946i
$139$	124893.	−	90740.0i	0.548278	−	0.398347i	−0.278872	−	0.960328i	$-0.589961\pi$
$139$	124893.	−	90740.0i	0.548278	−	0.398347i	0.827150	+	0.561981i	$0.189961\pi$
$140$	44989.4	−	26132.0i	0.193995	−	0.112681i
$141$	−160245.	−	116425.i	−0.678793	−	0.493172i
$142$	−67060.9	−	206392.i	−0.279093	−	0.858959i
$143$	−87316.5			−0.357072
$144$	6407.78	+	19721.1i	0.0257514	+	0.0792547i
$145$	308525.	−	179206.i	1.21862	−	0.707835i
$146$	−36322.1	+	111788.i	−0.141023	+	0.434023i
$147$	37332.4	−	114897.i	0.142493	−	0.438547i
$148$	−65652.2	+	47699.1i	−0.246374	+	0.179001i
$149$	−369017.			−1.36170			−0.680849	−	0.732424i	$-0.738389\pi$
$149$	−369017.			−1.36170			−0.680849	+	0.732424i	$0.738389\pi$
$150$	−102533.	+	46295.6i	−0.372078	+	0.168001i
$151$	461082.			1.64564			0.822821	−	0.568301i	$-0.192399\pi$
$151$	461082.			1.64564			0.822821	+	0.568301i	$0.192399\pi$
$152$	−52911.5	+	38442.4i	−0.185755	+	0.134959i
$153$	53891.4	−	165861.i	0.186119	−	0.572816i
$154$	6710.56	−	20653.0i	0.0228012	−	0.0701748i
$155$	111199.	−	251529.i	0.371769	−	0.840927i
$156$	41631.1	+	128127.i	0.136964	+	0.421531i
$157$	70227.3			0.227382			0.113691	−	0.993516i	$-0.463733\pi$
$157$	70227.3			0.227382			0.113691	+	0.993516i	$0.463733\pi$
$158$	15983.7	+	49192.8i	0.0509372	+	0.156768i
$159$	81006.5	+	58854.6i	0.254113	+	0.184624i
$160$	42640.3	+	38191.7i	0.131680	+	0.117942i
$161$	15719.6	−	11420.9i	0.0477943	−	0.0347246i
$162$	21231.8	+	15425.8i	0.0635624	+	0.0461808i
$163$	64680.2	+	46992.9i	0.190679	+	0.138536i	0.679029	−	0.734112i	$-0.262401\pi$
$163$	64680.2	+	46992.9i	0.190679	+	0.138536i	−0.488350	+	0.872648i	$0.662401\pi$
$164$	−47053.9	+	34186.7i	−0.136611	+	0.0992539i
$165$	−18986.3	+	42946.3i	−0.0542914	+	0.122805i
$166$	237649.	+	172662.i	0.669370	+	0.486326i
$167$	95145.6	+	292828.i	0.263996	+	0.812496i	0.991923	+	0.126841i	$0.0404840\pi$
$167$	95145.6	+	292828.i	0.263996	+	0.812496i	−0.727927	+	0.685655i	$0.759516\pi$
$168$	−33505.5			−0.0915888
$169$	155739.	+	479316.i	0.419451	+	1.29094i
$170$	−101329.	−	470650.i	−0.268912	−	1.24904i
$171$	−25578.8	+	78723.3i	−0.0668943	+	0.205880i
$172$	63131.3	−	194298.i	0.162714	−	0.500781i
$173$	−35326.6	+	25666.3i	−0.0897401	+	0.0652000i	−0.631751	−	0.775172i	$-0.717663\pi$
$173$	−35326.6	+	25666.3i	−0.0897401	+	0.0652000i	0.542010	+	0.840372i	$0.317663\pi$
$174$	−229771.			−0.575337
$175$	−19947.8	−	180681.i	−0.0492379	−	0.445982i
$176$	23892.6			0.0581409
$177$	−353129.	+	256563.i	−0.847227	+	0.615546i
$178$	−127037.	+	390981.i	−0.300526	+	0.924923i
$179$	−123155.	+	379032.i	−0.287289	+	0.884185i	0.698414	+	0.715694i	$0.253889\pi$
$179$	−123155.	+	379032.i	−0.287289	+	0.884185i	−0.985703	+	0.168491i	$0.946111\pi$
$180$	72071.3	+	7384.20i	0.165799	+	0.0169872i
$181$	131424.	+	404482.i	0.298180	+	0.917703i	0.982135	+	0.188179i	$0.0602585\pi$
$181$	131424.	+	404482.i	0.298180	+	0.917703i	−0.683955	+	0.729524i	$0.739742\pi$
$182$	−217684.			−0.487132
$183$	48667.1	+	149782.i	0.107426	+	0.330622i
$184$	17295.3	+	12565.8i	0.0376602	+	0.0273618i
$185$	59675.1	+	277177.i	0.128193	+	0.595427i
$186$	−143281.	+	104100.i	−0.303673	+	0.220631i
$187$	−162567.	−	118112.i	−0.339961	−	0.246996i
$188$	284881.	+	206978.i	0.587852	+	0.427100i
$189$	−34306.6	+	24925.2i	−0.0698592	+	0.0507557i
$190$	48094.3	+	223387.i	0.0966517	+	0.448925i
$191$	389284.	+	282832.i	0.772118	+	0.560976i	0.902603	−	0.430474i	$-0.141654\pi$
$191$	389284.	+	282832.i	0.772118	+	0.560976i	−0.130485	+	0.991450i	$0.541654\pi$
$192$	−11391.6	−	35059.7i	−0.0223014	−	0.0686366i
$193$	638055.			1.23300			0.616502	−	0.787353i	$-0.288549\pi$
$193$	638055.			1.23300			0.616502	+	0.787353i	$0.288549\pi$
$194$	−105307.	−	324101.i	−0.200887	−	0.618267i
$195$	468244.	+	47974.8i	0.881832	+	0.0903498i
$196$	−66368.7	+	204262.i	−0.123402	+	0.379793i
$197$	−106085.	+	326497.i	−0.194756	+	0.599396i	0.805224	+	0.592971i	$0.202045\pi$
$197$	−106085.	+	326497.i	−0.194756	+	0.599396i	−0.999979	+	0.00642489i	$0.997955\pi$
$198$	24463.9	−	17774.1i	0.0443469	−	0.0322199i
$199$	316013.			0.565683			0.282841	−	0.959167i	$-0.408723\pi$
$199$	316013.			0.565683			0.282841	+	0.959167i	$0.408723\pi$
$200$	182280.	−	82303.3i	0.322229	−	0.145493i
$201$	103253.			0.180265
$202$	−596751.	+	433565.i	−1.02900	+	0.747611i
$203$	114728.	−	353096.i	0.195402	−	0.601384i
$204$	−95806.9	+	294863.i	−0.161184	+	0.496073i
$205$	42770.0	+	198657.i	0.0710812	+	0.330156i
$206$	−118024.	−	363241.i	−0.193778	−	0.596386i
$207$	27056.7			0.0438883
$208$	−74010.8	−	227782.i	−0.118614	−	0.365057i
$209$	77160.2	+	56060.2i	0.122188	+	0.0887746i
$210$	−47333.6	+	107067.i	−0.0740665	+	0.167536i
$211$	−945090.	+	686648.i	−1.46139	+	1.06176i	−0.478395	+	0.878145i	$0.658781\pi$
$211$	−945090.	+	686648.i	−1.46139	+	1.06176i	−0.982997	+	0.183619i	$0.941219\pi$
$212$	−144011.	−	104630.i	−0.220068	−	0.159889i
$213$	395027.	+	287004.i	0.596593	+	0.433450i
$214$	−486424.	+	353408.i	−0.726074	+	0.527524i
$215$	−531695.	−	476225.i	−0.784452	−	0.702612i
$216$	−37745.5	−	27423.7i	−0.0550466	−	0.0399937i
$217$	−88430.7	−	272162.i	−0.127483	−	0.392354i
$218$	209478.			0.298537
$219$	−81724.8	−	251523.i	−0.115145	−	0.354379i
$220$	33753.4	−	76349.0i	0.0470177	−	0.106352i
$221$	−622454.	+	1.91572e6i	−0.857287	+	2.63846i
$222$	56423.0	−	173652.i	0.0768376	−	0.236482i
$223$	736992.	−	535456.i	0.992432	−	0.721044i	0.0319796	−	0.999489i	$-0.489819\pi$
$223$	736992.	−	535456.i	0.992432	−	0.721044i	0.960452	+	0.278445i	$0.0898188\pi$
$224$	59565.3			0.0793182
$225$	125412.	−	219873.i	0.165152	−	0.289544i
$226$	136416.			0.177662
$227$	59300.2	−	43084.1i	0.0763821	−	0.0554948i	−0.548939	−	0.835862i	$-0.684968\pi$
$227$	59300.2	−	43084.1i	0.0763821	−	0.0554948i	0.625321	+	0.780368i	$0.284968\pi$
$228$	45473.4	−	139953.i	0.0579322	−	0.178297i
$229$	−13088.2	+	40281.2i	−0.0164926	+	0.0507591i	−0.958964	−	0.283527i	$-0.908495\pi$
$229$	−13088.2	+	40281.2i	−0.0164926	+	0.0507591i	0.942472	+	0.334287i	$0.108495\pi$
$230$	64587.2	−	37515.4i	0.0805058	−	0.0467616i
$231$	15098.8	+	46469.2i	0.0186171	+	0.0572975i
$232$	408482.			0.498257
$233$	−29211.7	−	89904.3i	−0.0352506	−	0.108490i	0.931883	−	0.362759i	$-0.118165\pi$
$233$	−29211.7	−	89904.3i	−0.0352506	−	0.108490i	−0.967134	+	0.254269i	$0.918165\pi$
$234$	−245231.	−	178171.i	−0.292776	−	0.212714i
$235$	1.06385e6	−	617937.i	1.25664	−	0.729919i
$236$	627784.	−	456112.i	0.733720	−	0.533079i
$237$	−94153.2	−	68406.3i	−0.108884	−	0.0791089i
$238$	−405287.	−	294458.i	−0.463789	−	0.336962i
$239$	−547470.	+	397760.i	−0.619963	+	0.450429i	−0.852909	−	0.522060i	$-0.825164\pi$
$239$	−547470.	+	397760.i	−0.619963	+	0.450429i	0.232946	+	0.972490i	$0.425164\pi$
$240$	−128127.	−	13127.5i	−0.143586	−	0.0147114i
$241$	102845.	+	74721.5i	0.114062	+	0.0828710i	0.643354	−	0.765569i	$-0.277542\pi$
$241$	102845.	+	74721.5i	0.114062	+	0.0828710i	−0.529292	+	0.848440i	$0.677542\pi$
$242$	188303.	+	579537.i	0.206690	+	0.636126i
$243$	−59049.0			−0.0641500
$244$	−86519.3	−	266279.i	−0.0930334	−	0.286327i
$245$	558960.	+	500645.i	0.594930	+	0.532862i
$246$	40439.3	−	124459.i	0.0426055	−	0.131126i
$247$	295438.	−	909266.i	0.308123	−	0.948306i
$248$	254721.	−	185066.i	0.262988	−	0.191072i
$249$	−660939.			−0.675559
$250$	−5490.52	−	698750.i	−0.00555602	−	0.707085i
$251$	1.17857e6			1.18078			0.590392	−	0.807116i	$-0.298973\pi$
$251$	1.17857e6			1.18078			0.590392	+	0.807116i	$0.298973\pi$
$252$	60989.6	−	44311.5i	0.0604999	−	0.0439557i
$253$	9633.76	−	29649.7i	0.00946225	−	0.0291218i
$254$	−51367.6	+	158093.i	−0.0499580	+	0.153755i
$255$	806890.	+	722710.i	0.777077	+	0.696007i
$256$	20251.7	+	62328.4i	0.0193136	+	0.0594410i
$257$	−1.48597e6			−1.40339			−0.701695	−	0.712478i	$-0.747573\pi$
$257$	−1.48597e6			−1.40339			−0.701695	+	0.712478i	$0.747573\pi$
$258$	142046.	+	437171.i	0.132855	+	0.408886i
$259$	238683.	+	173414.i	0.221092	+	0.160633i
$260$	−832434.	−	85288.6i	−0.763689	−	0.0782452i
$261$	418250.	−	303876.i	0.380044	−	0.276118i
$262$	21560.7	+	15664.8i	0.0194048	+	0.0140984i
$263$	953688.	+	692895.i	0.850192	+	0.617701i	0.925199	−	0.379482i	$-0.123898\pi$
$263$	953688.	+	692895.i	0.850192	+	0.617701i	−0.0750069	+	0.997183i	$0.523898\pi$
$264$	−43491.4	+	31598.4i	−0.0384055	+	0.0279033i
$265$	−537795.	+	312377.i	−0.470437	+	0.273252i
$266$	192364.	+	139760.i	0.166694	+	0.121110i
$267$	−285834.	−	879707.i	−0.245378	−	0.755197i
$268$	−183561.			−0.156114
$269$	−274612.	−	845170.i	−0.231387	−	0.712137i	−0.997580	−	0.0695260i	$-0.977851\pi$
$269$	−274612.	−	845170.i	−0.231387	−	0.712137i	0.766193	−	0.642611i	$-0.222149\pi$
$270$	−140956.	+	81874.1i	−0.117673	+	0.0683498i
$271$	−225504.	+	694028.i	−0.186522	+	0.574056i	−0.999971	−	0.00758016i	$-0.997587\pi$
$271$	−225504.	+	694028.i	−0.186522	+	0.574056i	0.813449	+	0.581636i	$0.197587\pi$
$272$	170323.	−	524202.i	0.139589	−	0.429612i
$273$	396247.	−	287890.i	0.321780	−	0.233787i
$274$	−1.65359e6			−1.33061
$275$	−196290.	−	215719.i	−0.156519	−	0.172011i
$276$	−48100.8			−0.0380084
$277$	1.70131e6	−	1.23608e6i	1.33225	−	0.967934i	0.332556	−	0.943083i	$-0.392089\pi$
$277$	1.70131e6	−	1.23608e6i	1.33225	−	0.967934i	0.999691	−	0.0248509i	$-0.00791111\pi$
$278$	190819.	−	587281.i	0.148085	−	0.455758i
$279$	123139.	−	378982.i	0.0947076	−	0.291480i
$280$	84148.7	−	190341.i	0.0641435	−	0.145090i
$281$	−129971.	−	400008.i	−0.0981927	−	0.302206i	0.889880	−	0.456195i	$-0.150788\pi$
$281$	−129971.	−	400008.i	−0.0981927	−	0.302206i	−0.988073	+	0.153989i	$0.950788\pi$
$282$	−792297.			−0.593287
$283$	−462253.	−	1.42267e6i	−0.343094	−	1.05594i	−0.962596	−	0.270941i	$-0.912665\pi$
$283$	−462253.	−	1.42267e6i	−0.343094	−	1.05594i	0.619502	−	0.784995i	$-0.287335\pi$
$284$	−702270.	−	510229.i	−0.516664	−	0.375379i
$285$	−382979.	−	343024.i	−0.279295	−	0.250156i
$286$	−282562.	+	205293.i	−0.204267	+	0.148409i
$287$	171068.	+	124288.i	0.122593	+	0.0890687i
$288$	67103.1	+	48753.3i	0.0476718	+	0.0346356i
$289$	−2.60157e6	+	1.89015e6i	−1.83228	+	1.33123i
$290$	577069.	−	1.30531e6i	0.402933	−	0.911418i
$291$	620318.	+	450688.i	0.429420	+	0.311992i
$292$	145288.	+	447152.i	0.0997181	+	0.306901i
$293$	2.17441e6			1.47970			0.739849	−	0.672773i	$-0.234897\pi$
$293$	2.17441e6			1.47970			0.739849	+	0.672773i	$0.234897\pi$
$294$	−149330.	−	459589.i	−0.100757	−	0.310100i
$295$	−570629.	−	2.65044e6i	−0.381767	−	1.77322i
$296$	−100308.	+	308715.i	−0.0665433	+	0.204799i
$297$	−21024.9	+	64707.9i	−0.0138306	+	0.0425663i
$298$	−1.19416e6	+	867611.i	−0.778975	+	0.565958i
$299$	−312509.			−0.202155
$300$	−222955.	+	390885.i	−0.143026	+	0.250753i
$301$	−742738.			−0.472519
$302$	1.49209e6	−	1.08407e6i	0.941408	−	0.683973i
$303$	512862.	−	1.57843e6i	0.320918	−	0.987683i
$304$	−80841.5	+	248805.i	−0.0501707	+	0.154410i
$305$	−973124.	−	99703.3i	−0.598989	−	0.0613705i
$306$	−215566.	−	663443.i	−0.131606	−	0.405042i
$307$	−2.06176e6			−1.24851			−0.624255	−	0.781221i	$-0.714597\pi$
$307$	−2.06176e6			−1.24851			−0.624255	+	0.781221i	$0.714597\pi$
$308$	−26842.3	−	82612.0i	−0.0161229	−	0.0496211i
$309$	695231.	+	505115.i	0.414222	+	0.300950i
$310$	−231531.	−	1.07541e6i	−0.136837	−	0.635579i
$311$	−1.78709e6	+	1.29840e6i	−1.04772	+	0.761212i	−0.971777	−	0.235900i	$-0.924196\pi$
$311$	−1.78709e6	+	1.29840e6i	−1.04772	+	0.761212i	−0.0759417	+	0.997112i	$0.524196\pi$
$312$	435966.	+	316748.i	0.253552	+	0.184216i
$313$	−1.61064e6	−	1.17020e6i	−0.929262	−	0.675148i	0.0165503	−	0.999863i	$-0.494732\pi$
$313$	−1.61064e6	−	1.17020e6i	−0.929262	−	0.675148i	−0.945812	+	0.324715i	$0.894732\pi$
$314$	227260.	−	165114.i	0.130077	−	0.0945063i
$315$	−55436.9	−	257492.i	−0.0314791	−	0.146214i
$316$	167384.	+	121611.i	0.0942964	+	0.0685103i
$317$	251916.	+	775316.i	0.140801	+	0.433342i	0.996447	−	0.0842198i	$-0.0268398\pi$
$317$	251916.	+	775316.i	0.140801	+	0.433342i	−0.855646	+	0.517562i	$0.826840\pi$
$318$	400518.			0.222103
$319$	−184077.	−	566530.i	−0.101280	−	0.311707i
$320$	227781.	+	23337.7i	0.124349	+	0.0127404i
$321$	418045.	−	1.28661e6i	0.226444	−	0.696922i
$322$	24017.4	−	73917.8i	0.0129088	−	0.0397292i
$323$	1.78001e6	−	1.29325e6i	0.949326	−	0.689726i
$324$	104976.			0.0555556
$325$	−1.44853e6	+	2.53956e6i	−0.760711	+	1.33368i
$326$	319796.			0.166659
$327$	−381311.	+	277038.i	−0.197201	+	0.143275i
$328$	−71892.0	+	221261.i	−0.0368974	+	0.113559i
$329$	395604.	−	1.21754e6i	0.201498	−	0.620147i
$330$	39531.9	+	183617.i	0.0199831	+	0.0928170i
$331$	624446.	+	1.92185e6i	0.313274	+	0.964159i	0.976459	+	0.215703i	$0.0692044\pi$
$331$	624446.	+	1.92185e6i	0.313274	+	0.964159i	−0.663185	+	0.748456i	$0.730796\pi$
$332$	1.17500e6			0.585051
$333$	126952.	+	390718.i	0.0627377	+	0.193087i
$334$	996377.	+	723910.i	0.488717	+	0.355074i
$335$	−259319.	+	586570.i	−0.126247	+	0.285567i
$336$	−108426.	+	78776.0i	−0.0523944	+	0.0380668i
$337$	−1.57889e6	−	1.14713e6i	−0.757314	−	0.550221i	0.140772	−	0.990042i	$-0.455042\pi$
$337$	−1.57889e6	−	1.14713e6i	−0.757314	−	0.550221i	−0.898085	+	0.439822i	$0.855042\pi$
$338$	1.63092e6	+	1.18494e6i	0.776501	+	0.564161i
$339$	−248316.	+	180412.i	−0.117356	+	0.0852642i
$340$	−1.43447e6	−	1.28482e6i	−0.672968	−	0.602759i
$341$	−371457.	−	269880.i	−0.172991	−	0.125685i
$342$	102315.	+	314893.i	0.0473014	+	0.145579i
$343$	1.75847e6			0.807051
$344$	−252525.	−	777193.i	−0.115056	−	0.354106i
$345$	−67952.7	+	153706.i	−0.0307368	+	0.0695255i
$346$	−53974.2	+	166116.i	−0.0242380	+	0.0745968i
$347$	1.03583e6	−	3.18797e6i	0.461814	−	1.42132i	−0.401132	−	0.916020i	$-0.631383\pi$
$347$	1.03583e6	−	3.18797e6i	0.461814	−	1.42132i	0.862946	−	0.505296i	$-0.168617\pi$
$348$	−743555.	+	540224.i	−0.329128	+	0.239126i
$349$	2.46965e6			1.08535			0.542676	−	0.839942i	$-0.317411\pi$
$349$	2.46965e6			1.08535			0.542676	+	0.839942i	$0.317411\pi$
$350$	−489359.	−	537796.i	−0.213529	−	0.234664i
$351$	682025.			0.295483
$352$	77318.1	−	56174.9i	0.0332602	−	0.0241649i
$353$	353156.	−	1.08690e6i	0.150845	−	0.464252i	−0.846871	−	0.531798i	$-0.821517\pi$
$353$	353156.	−	1.08690e6i	0.150845	−	0.464252i	0.997716	+	0.0675452i	$0.0215167\pi$
$354$	−539532.	+	1.66051e6i	−0.228828	+	0.704261i
$355$	−2.62255e6	+	1.52330e6i	−1.10447	+	0.641527i
$356$	508150.	+	1.56392e6i	0.212504	+	0.654019i
$357$	1.12717e6			0.468077
$358$	492620.	+	1.51613e6i	0.203144	+	0.625213i
$359$	524574.	+	381125.i	0.214818	+	0.156074i	0.689991	−	0.723818i	$-0.257614\pi$
$359$	524574.	+	381125.i	0.214818	+	0.156074i	−0.475173	+	0.879892i	$0.657614\pi$
$360$	250589.	−	145554.i	0.101907	−	0.0591927i
$361$	1.15835e6	−	841592.i	0.467813	−	0.339886i
$362$	1.37629e6	+	999933.i	0.551999	+	0.401051i
$363$	−1.10921e6	−	805891.i	−0.441823	−	0.321004i
$364$	−704439.	+	511805.i	−0.278670	+	0.202465i
$365$	1.63413e6	+	167428.i	0.642028	+	0.0657802i
$366$	509649.	+	370282.i	0.198870	+	0.144487i
$367$	−878185.	−	2.70278e6i	−0.340346	−	1.04748i	−0.964028	−	0.265800i	$-0.914364\pi$
$367$	−878185.	−	2.70278e6i	−0.340346	−	1.04748i	0.623682	−	0.781678i	$-0.285636\pi$
$368$	85512.5			0.0329162
$369$	90988.3	+	280033.i	0.0347872	+	0.107064i
$370$	844795.	+	756660.i	0.320810	+	0.287340i
$371$	−199984.	+	615487.i	−0.0754328	+	0.232158i
$372$	−218914.	+	673747.i	−0.0820191	+	0.252429i
$373$	−2.37656e6	+	1.72667e6i	−0.884457	+	0.642595i	−0.934427	−	0.356155i	$-0.884087\pi$
$373$	−2.37656e6	+	1.72667e6i	−0.884457	+	0.642595i	0.0499701	+	0.998751i	$0.484087\pi$
$374$	−803777.			−0.297137
$375$	934103.	+	1.26466e6i	0.343018	+	0.464405i
$376$	1.40853e6			0.513802
$377$	−4.83085e6	+	3.50981e6i	−1.75053	+	1.27184i
$378$	−52415.9	+	161320.i	−0.0188683	+	0.0580707i
$379$	−599640.	+	1.84550e6i	−0.214433	+	0.659958i	0.784760	+	0.619800i	$0.212786\pi$
$379$	−599640.	+	1.84550e6i	−0.214433	+	0.659958i	−0.999193	+	0.0401583i	$0.987214\pi$
$380$	680851.	+	609820.i	0.241876	+	0.216642i
$381$	−115577.	−	355709.i	−0.0407905	−	0.125540i
$382$	1.92473e6			0.674856
$383$	1.08113e6	+	3.32737e6i	0.376600	+	1.15906i	0.942393	+	0.334508i	$0.108570\pi$
$383$	1.08113e6	+	3.32737e6i	0.376600	+	1.15906i	−0.565793	+	0.824547i	$0.691430\pi$
$384$	−119294.	−	86672.5i	−0.0412850	−	0.0299953i
$385$	−301908.	−	30932.5i	−0.103806	−	0.0106356i
$386$	2.06479e6	−	1.50016e6i	0.705354	−	0.512470i
$387$	−836730.	−	607920.i	−0.283993	−	0.206333i
$388$	−1.10279e6	−	801222.i	−0.371888	−	0.270193i
$389$	975806.	−	708965.i	0.326956	−	0.237548i	−0.412182	−	0.911102i	$-0.635233\pi$
$389$	975806.	−	708965.i	0.326956	−	0.237548i	0.739138	+	0.673554i	$0.235233\pi$
$390$	1.62807e6	−	945658.i	0.542014	−	0.314828i
$391$	−581835.	−	422728.i	−0.192468	−	0.139836i
$392$	265475.	+	817047.i	0.0872585	+	0.268554i
$393$	−59963.7			−0.0195842
$394$	424341.	+	1.30599e6i	0.137713	+	0.423837i
$395$	625075.	−	363073.i	0.201576	−	0.117085i
$396$	37377.6	−	115036.i	0.0119777	−	0.0368635i
$397$	450034.	−	1.38506e6i	0.143308	−	0.441055i	−0.853482	−	0.521122i	$-0.825513\pi$
$397$	450034.	−	1.38506e6i	0.143308	−	0.441055i	0.996789	+	0.0800671i	$0.0255135\pi$
$398$	1.02264e6	−	742992.i	0.323605	−	0.235113i
$399$	−534992.			−0.168235
$400$	396365.	−	694906.i	0.123864	−	0.217158i
$401$	−3.81269e6			−1.18405			−0.592025	−	0.805919i	$-0.701671\pi$
$401$	−3.81269e6			−1.18405			−0.592025	+	0.805919i	$0.701671\pi$
$402$	334134.	−	242762.i	0.103123	−	0.0749232i
$403$	−1.42227e6	+	4.37730e6i	−0.436235	+	1.34259i
$404$	−911754.	+	2.80609e6i	−0.277923	+	0.855358i
$405$	148301.	−	335452.i	0.0449269	−	0.101623i
$406$	−458911.	−	1.41238e6i	−0.138170	−	0.425243i
$407$	473364.			0.141648
$408$	383228.	+	1.17945e6i	0.113974	+	0.350776i
$409$	−777797.	−	565103.i	−0.229910	−	0.167040i	0.466866	−	0.884328i	$-0.345383\pi$
$409$	−777797.	−	565103.i	−0.229910	−	0.167040i	−0.696776	+	0.717288i	$0.745383\pi$
$410$	605478.	+	542310.i	0.177885	+	0.159326i
$411$	3.01001e6	−	2.18690e6i	0.878949	−	0.638594i
$412$	−1.23597e6	−	897982.i	−0.358727	−	0.260630i
$413$	−2.28236e6	−	1.65823e6i	−0.658428	−	0.478376i
$414$	87557.3	−	63614.1i	0.0251068	−	0.0182412i
$415$	1.65994e6	−	3.75473e6i	0.473122	−	1.07018i
$416$	−775051.	−	563107.i	−0.219582	−	0.159536i
$417$	429343.	+	1.32138e6i	0.120911	+	0.372125i
$418$	381501.			0.106796
$419$	−429671.	−	1.32239e6i	−0.119564	−	0.367981i	0.873307	−	0.487170i	$-0.161971\pi$
$419$	−429671.	−	1.32239e6i	−0.119564	−	0.367981i	−0.992872	+	0.119189i	$0.961971\pi$
$420$	98554.6	+	457764.i	0.0272617	+	0.126625i
$421$	−1.96008e6	+	6.03249e6i	−0.538974	+	1.65879i	0.195929	+	0.980618i	$0.437228\pi$
$421$	−1.96008e6	+	6.03249e6i	−0.538974	+	1.65879i	−0.734903	+	0.678173i	$0.762772\pi$
$422$	−1.44397e6	+	4.44408e6i	−0.394709	+	1.21479i
$423$	1.44221e6	−	1.04783e6i	0.391902	−	0.284733i
$424$	−712032.			−0.192347
$425$	−6.13214e6	+	2.76879e6i	−1.64680	+	0.743562i
$426$	1.95312e6			0.521441
$427$	−823496.	+	598305.i	−0.218571	+	0.158801i
$428$	−743190.	+	2.28731e6i	−0.196106	+	0.603552i
$429$	242840.	−	747386.i	0.0637056	−	0.196066i
$430$	−2.84027e6	−	291005.i	−0.740779	−	0.0758979i
$431$	−1.01266e6	−	3.11664e6i	−0.262585	−	0.808152i	−0.992240	−	0.124337i	$-0.960319\pi$
$431$	−1.01266e6	−	3.11664e6i	−0.262585	−	0.808152i	0.729655	−	0.683815i	$-0.239681\pi$
$432$	−186624.			−0.0481125
$433$	−219911.	−	676818.i	−0.0563674	−	0.173481i	0.918909	−	0.394470i	$-0.129072\pi$
$433$	−219911.	−	676818.i	−0.0563674	−	0.173481i	−0.975276	+	0.220989i	$0.929072\pi$
$434$	−926058.	−	672821.i	−0.236001	−	0.171465i
$435$	675860.	+	3.13922e6i	0.171251	+	0.795423i
$436$	677886.	−	492513.i	0.170781	−	0.124080i
$437$	276159.	+	200641.i	0.0691761	+	0.0502594i
$438$	−855833.	−	621799.i	−0.213159	−	0.154869i
$439$	5.70111e6	−	4.14210e6i	1.41188	−	1.02579i	0.418835	−	0.908062i	$-0.362438\pi$
$439$	5.70111e6	−	4.14210e6i	1.41188	−	1.02579i	0.993046	−	0.117730i	$-0.0375616\pi$
$440$	−70278.9	−	326430.i	−0.0173059	−	0.0803818i
$441$	879637.	+	639094.i	0.215381	+	0.156483i
$442$	2.48981e6	+	7.66286e6i	0.606194	+	1.86567i
$443$	5.38678e6			1.30413			0.652064	−	0.758164i	$-0.273903\pi$
$443$	5.38678e6			1.30413			0.652064	+	0.758164i	$0.273903\pi$
$444$	−225692.	−	694609.i	−0.0543324	−	0.167218i
$445$	5.71540e6	+	585582.i	1.36819	+	0.140181i
$446$	1.12602e6	−	3.46555e6i	0.268047	−	0.824963i
$447$	1.02629e6	−	3.15861e6i	0.242942	−	0.747699i
$448$	192757.	−	140046.i	0.0453749	−	0.0329668i
$449$	8.20332e6			1.92032			0.960160	−	0.279449i	$-0.0901519\pi$
$449$	8.20332e6			1.92032			0.960160	+	0.279449i	$0.0901519\pi$
$450$	−111108.	−	1.00639e6i	−0.0258652	−	0.234279i
$451$	339267.			0.0785417
$452$	441451.	−	320733.i	0.101633	−	0.0738410i
$453$	−1.28234e6	+	3.94663e6i	−0.293601	+	0.903610i
$454$	90602.6	−	278846.i	0.0206301	−	0.0634929i
$455$	640305.	+	2.97407e6i	0.144997	+	0.673478i
$456$	−181893.	−	559810.i	−0.0409642	−	0.126075i
$457$	1.03674e6			0.232209			0.116104	−	0.993237i	$-0.462959\pi$
$457$	1.03674e6			0.232209			0.116104	+	0.993237i	$0.462959\pi$
$458$	52352.7	+	161125.i	0.0116621	+	0.0358921i
$459$	1.26981e6	+	922568.i	0.281323	+	0.204393i
$460$	120805.	−	273256.i	0.0266189	−	0.0602109i
$461$	−5.40060e6	+	3.92376e6i	−1.18356	+	0.859905i	−0.992569	−	0.121687i	$-0.961170\pi$
$461$	−5.40060e6	+	3.92376e6i	−1.18356	+	0.859905i	−0.190989	+	0.981592i	$0.561170\pi$
$462$	158116.	+	114878.i	0.0344645	+	0.0250399i
$463$	−4.98147e6	−	3.61925e6i	−1.07995	−	0.784632i	−0.102279	−	0.994756i	$-0.532613\pi$
$463$	−4.98147e6	−	3.61925e6i	−1.07995	−	0.784632i	−0.977675	+	0.210124i	$0.932613\pi$
$464$	1.32188e6	−	960399.i	0.285033	−	0.207089i
$465$	1.84370e6	+	1.65135e6i	0.395419	+	0.354166i
$466$	−305908.	−	222256.i	−0.0652569	−	0.0474119i
$467$	314603.	+	968249.i	0.0667530	+	0.205445i	0.978869	−	0.204487i	$-0.0655526\pi$
$467$	314603.	+	968249.i	0.0667530	+	0.205445i	−0.912116	+	0.409932i	$0.865553\pi$
$468$	−1.21249e6			−0.255896
$469$	206222.	+	634687.i	0.0432916	+	0.133238i
$470$	1.98985e6	−	4.50096e6i	0.415504	−	0.939854i
$471$	−195313.	+	601111.i	−0.0405675	+	0.124854i
$472$	959169.	−	2.95202e6i	0.198171	−	0.609908i
$473$	−964104.	+	700463.i	−0.198139	+	0.143957i
$474$	−465519.			−0.0951682
$475$	2.91053e6	−	1.31416e6i	0.591886	−	0.267249i
$476$	−2.00385e6			−0.405366
$477$	−729058.	+	529692.i	−0.146712	+	0.106593i
$478$	−836460.	+	2.57436e6i	−0.167446	+	0.515347i
$479$	1.68267e6	−	5.17872e6i	0.335089	−	1.03130i	−0.631590	−	0.775303i	$-0.717597\pi$
$479$	1.68267e6	−	5.17872e6i	0.335089	−	1.03130i	0.966678	−	0.255994i	$-0.0824027\pi$
$480$	−445491.	+	258763.i	−0.0882544	+	0.0512624i
$481$	−1.46631e6	−	4.51285e6i	−0.288977	−	0.889381i
$482$	508495.			0.0996940
$483$	54039.1	+	166315.i	0.0105400	+	0.0324387i
$484$	1.97194e6	+	1.43270e6i	0.382630	+	0.277997i
$485$	−4.11824e6	+	2.39207e6i	−0.794981	+	0.461763i
$486$	−191087.	+	138833.i	−0.0366978	+	0.0266625i
$487$	1.01226e6	+	735448.i	0.193405	+	0.140517i	0.680274	−	0.732958i	$-0.261861\pi$
$487$	1.01226e6	+	735448.i	0.193405	+	0.140517i	−0.486868	+	0.873475i	$0.661861\pi$
$488$	−906042.	−	658278.i	−0.172226	−	0.125130i
$489$	−582122.	+	422936.i	−0.110088	+	0.0799839i
$490$	2.98592e6	+	305928.i	0.561808	+	0.0575611i
$491$	−3.16650e6	−	2.30060e6i	−0.592756	−	0.430662i	0.250544	−	0.968105i	$-0.419390\pi$
$491$	−3.16650e6	−	2.30060e6i	−0.592756	−	0.430662i	−0.843300	+	0.537443i	$0.819390\pi$
$492$	−161757.	−	497837.i	−0.0301266	−	0.0927202i
$493$	−1.37418e7			−2.54641
$494$	−1.18175e6	−	3.63706e6i	−0.217876	−	0.670554i
$495$	−314796.	−	281954.i	−0.0577452	−	0.0517208i
$496$	389180.	−	1.19777e6i	0.0710307	−	0.218610i
$497$	−975219.	+	3.00142e6i	−0.177097	+	0.545048i
$498$	−2.13884e6	+	1.55396e6i	−0.386461	+	0.280780i
$499$	5.10834e6			0.918393			0.459196	−	0.888335i	$-0.348137\pi$
$499$	5.10834e6			0.918393			0.459196	+	0.888335i	$0.348137\pi$
$500$	−1.66063e6	−	2.24829e6i	−0.297062	−	0.402187i
$501$	−2.77108e6			−0.493236
$502$	3.81393e6	−	2.77098e6i	0.675481	−	0.490766i
$503$	2.84045e6	−	8.74199e6i	0.500572	−	1.54060i	−0.307518	−	0.951542i	$-0.599498\pi$
$503$	2.84045e6	−	8.74199e6i	0.500572	−	1.54060i	0.808090	−	0.589060i	$-0.200502\pi$
$504$	93183.8	−	286790.i	0.0163405	−	0.0502907i
$505$	7.67883e6	+	6.87772e6i	1.33988	+	1.20010i
$506$	−38535.0	−	118599.i	−0.00669082	−	0.0205922i
$507$	−4.53585e6			−0.783680
$508$	205470.	+	632372.i	0.0353256	+	0.108721i
$509$	2.64162e6	+	1.91925e6i	0.451934	+	0.328349i	0.790359	−	0.612644i	$-0.209894\pi$
$509$	2.64162e6	+	1.91925e6i	0.451934	+	0.328349i	−0.338425	+	0.940993i	$0.609894\pi$
$510$	4.31034e6	+	441624.i	0.733815	+	0.0751844i
$511$	1.38286e6	−	1.00471e6i	0.234276	−	0.170211i
$512$	212079.	+	154084.i	0.0357538	+	0.0259767i
$513$	−602695.	−	437883.i	−0.101112	−	0.0734624i
$514$	−4.80871e6	+	3.49373e6i	−0.802825	+	0.583286i
$515$	−4.61558e6	+	2.68095e6i	−0.766846	+	0.445421i
$516$	1.48752e6	+	1.08075e6i	0.245945	+	0.178690i
$517$	−634733.	−	1.95351e6i	−0.104440	−	0.321432i
$518$	1.18012e6			0.193241
$519$	−121442.	−	373760.i	−0.0197902	−	0.0609080i
$520$	−2.89434e6	+	1.68117e6i	−0.469398	+	0.272649i
$521$	841610.	−	2.59021e6i	0.135837	−	0.418062i	−0.859883	−	0.510492i	$-0.829463\pi$
$521$	841610.	−	2.59021e6i	0.135837	−	0.418062i	0.995719	+	0.0924298i	$0.0294634\pi$
$522$	639029.	−	1.96673e6i	0.102646	−	0.315913i
$523$	5.09615e6	−	3.70257e6i	0.814682	−	0.591901i	−0.100502	−	0.994937i	$-0.532045\pi$
$523$	5.09615e6	−	3.70257e6i	0.814682	−	0.591901i	0.915184	+	0.403036i	$0.132045\pi$
$524$	106602.			0.0169605
$525$	1.60202e6	+	331758.i	0.253670	+	0.0525319i
$526$	4.71529e6			0.743095
$527$	−8.56914e6	+	6.22585e6i	−1.34404	+	0.976499i
$528$	−66449.0	+	204509.i	−0.0103730	+	0.0319248i
$529$	−1.95446e6	+	6.01521e6i	−0.303660	+	0.934569i
$530$	−1.00590e6	+	2.27530e6i	−0.155548	+	0.351844i
$531$	−1.21395e6	−	3.73615e6i	−0.186837	−	0.575026i
$532$	951098.			0.145695
$533$	−1.05093e6	−	3.23443e6i	−0.160234	−	0.493150i
$534$	−2.99329e6	−	2.17476e6i	−0.454251	−	0.330033i
$535$	6.25918e6	+	5.60618e6i	0.945439	+	0.846803i
$536$	−594016.	+	431578.i	−0.0893071	+	0.0648854i
$537$	−2.90181e6	−	2.10829e6i	−0.434244	−	0.315497i
$538$	−2.87578e6	−	2.08937e6i	−0.428351	−	0.311215i
$539$	1.01354e6	−	736382.i	0.150269	−	0.109177i
$540$	−263646.	+	596358.i	−0.0389079	+	0.0880082i
$541$	−8.11191e6	−	5.89365e6i	−1.19160	−	0.865747i	−0.198166	−	0.980168i	$-0.563499\pi$
$541$	−8.11191e6	−	5.89365e6i	−1.19160	−	0.865747i	−0.993432	+	0.114421i	$0.963499\pi$
$542$	902014.	+	2.77611e6i	0.131891	+	0.405919i
$543$	−3.82767e6			−0.557103
$544$	−681294.	−	2.09681e6i	−0.0987045	−	0.303781i
$545$	−616169.	−	2.86197e6i	−0.0888605	−	0.412737i
$546$	605411.	−	1.86326e6i	0.0869098	−	0.267481i
$547$	−735698.	+	2.26425e6i	−0.105131	+	0.323560i	−0.989761	−	0.142733i	$-0.954411\pi$
$547$	−735698.	+	2.26425e6i	−0.105131	+	0.323560i	0.884630	+	0.466294i	$0.154411\pi$
$548$	−5.35113e6	+	3.88782e6i	−0.761192	+	0.553038i
$549$	−1.41741e6			−0.200708
$550$	−1.14239e6	−	236575.i	−0.161031	−	0.0333475i
$551$	6.52237e6			0.915221
$552$	−155657.	+	113092.i	−0.0217431	+	0.0157973i
$553$	232440.	−	715376.i	0.0323220	−	0.0994767i
$554$	2.59938e6	−	8.00005e6i	0.359828	−	1.10744i
$555$	−2.53847e6	−	260083.i	−0.349816	−	0.0358410i
$556$	−763277.	−	2.34913e6i	−0.104712	−	0.322270i
$557$	8.76310e6			1.19680			0.598398	−	0.801199i	$-0.295804\pi$
$557$	8.76310e6			1.19680			0.598398	+	0.801199i	$0.295804\pi$
$558$	−492555.	−	1.51593e6i	−0.0669684	−	0.206107i
$559$	9.66435e6	+	7.02156e6i	1.30811	+	0.950395i
$560$	−175208.	−	813803.i	−0.0236094	−	0.109660i
$561$	1.46311e6	−	1.06301e6i	0.196277	−	0.142603i
$562$	−1.36107e6	−	988875.i	−0.181777	−	0.132069i
$563$	−5.61376e6	−	4.07863e6i	−0.746419	−	0.542305i	0.148296	−	0.988943i	$-0.452621\pi$
$563$	−5.61376e6	−	4.07863e6i	−0.746419	−	0.542305i	−0.894715	+	0.446638i	$0.852621\pi$
$564$	−2.56393e6	+	1.86280e6i	−0.339397	+	0.246586i
$565$	−401260.	−	1.86376e6i	−0.0528816	−	0.245623i
$566$	−4.84078e6	−	3.51703e6i	−0.635147	−	0.461461i
$567$	−117936.	−	362969.i	−0.0154059	−	0.0474146i
$568$	−3.47222e6			−0.451581
$569$	−4.16905e6	−	1.28310e7i	−0.539829	−	1.66142i	−0.732977	−	0.680253i	$-0.761870\pi$
$569$	−4.16905e6	−	1.28310e7i	−0.539829	−	1.66142i	0.193148	−	0.981170i	$-0.438130\pi$
$570$	−2.04584e6	−	209611.i	−0.263745	−	0.0270225i
$571$	2.15894e6	−	6.64453e6i	0.277108	−	0.852852i	−0.711545	−	0.702640i	$-0.752004\pi$
$571$	2.15894e6	−	6.64453e6i	0.277108	−	0.852852i	0.988654	−	0.150212i	$-0.0479956\pi$
$572$	−431716.	+	1.32869e6i	−0.0551707	+	0.169798i
$573$	−3.50356e6	+	2.54548e6i	−0.445782	+	0.323880i
$574$	845807.			0.107150
$575$	−702529.	−	772065.i	−0.0886124	−	0.0973833i
$576$	331776.			0.0416667
$577$	1.80205e6	−	1.30926e6i	0.225334	−	0.163715i	−0.469391	−	0.882991i	$-0.655526\pi$
$577$	1.80205e6	−	1.30926e6i	0.225334	−	0.163715i	0.694724	+	0.719276i	$0.255526\pi$
$578$	−3.97485e6	+	1.22333e7i	−0.494882	+	1.52309i
$579$	−1.77453e6	+	5.46143e6i	−0.219982	+	0.677034i
$580$	−1.20153e6	−	5.58083e6i	−0.148308	−	0.688857i
$581$	−1.32006e6	−	4.06273e6i	−0.162238	−	0.499319i
$582$	3.06702e6			0.375327
$583$	320867.	+	987528.i	0.0390980	+	0.120331i
$584$	1.52148e6	+	1.10542e6i	0.184601	+	0.134121i
$585$	−1.71290e6	+	3.87452e6i	−0.206939	+	0.468088i
$586$	7.03655e6	−	5.11235e6i	0.846478	−	0.615002i
$587$	9.77787e6	+	7.10404e6i	1.17125	+	0.850962i	0.991158	−	0.132688i	$-0.0423610\pi$
$587$	9.77787e6	+	7.10404e6i	1.17125	+	0.850962i	0.180090	+	0.983650i	$0.442361\pi$
$588$	−1.56380e6	−	1.13617e6i	−0.186525	−	0.135519i
$589$	4.06722e6	−	2.95501e6i	0.483069	−	0.350970i
$590$	−8.07816e6	−	7.23539e6i	−0.955394	−	0.855721i
$591$	−2.49962e6	−	1.81608e6i	−0.294377	−	0.213878i
$592$	401230.	+	1.23486e6i	0.0470533	+	0.144815i
$593$	1.10005e7			1.28462			0.642310	−	0.766445i	$-0.277976\pi$
$593$	1.10005e7			1.28462			0.642310	+	0.766445i	$0.277976\pi$
$594$	84099.5	+	258832.i	0.00977974	+	0.0300989i
$595$	−2.83087e6	+	6.40332e6i	−0.327814	+	0.741502i
$596$	−1.82452e6	+	5.61530e6i	−0.210394	+	0.647526i
$597$	−878882.	+	2.70492e6i	−0.100924	+	0.310612i
$598$	−1.01130e6	+	734752.i	−0.115645	+	0.0840210i
$599$	4.94047e6			0.562602			0.281301	−	0.959620i	$-0.409234\pi$
$599$	4.94047e6			0.562602			0.281301	+	0.959620i	$0.409234\pi$
$600$	197526.	+	1.78913e6i	0.0223999	+	0.202891i
$601$	9.24203e6			1.04371			0.521857	−	0.853033i	$-0.325240\pi$
$601$	9.24203e6			1.04371			0.521857	+	0.853033i	$0.325240\pi$
$602$	−2.40355e6	+	1.74628e6i	−0.270310	+	0.196392i
$603$	−287162.	+	883795.i	−0.0321614	+	0.0989825i
$604$	2.27971e6	−	7.01623e6i	0.254266	−	0.782549i
$605$	7.36397e6	−	4.27735e6i	0.817944	−	0.475101i
$606$	−2.05145e6	−	6.31370e6i	−0.226923	−	0.698397i
$607$	1.25674e7			1.38444			0.692221	−	0.721686i	$-0.256632\pi$
$607$	1.25674e7			1.38444			0.692221	+	0.721686i	$0.256632\pi$
$608$	323366.	+	995218.i	0.0354761	+	0.109184i
$609$	2.70325e6	+	1.96403e6i	0.295354	+	0.214587i
$610$	−3.38351e6	+	1.96531e6i	−0.368166	+	0.213848i
$611$	−1.66577e7	+	1.21025e7i	−1.80515	+	1.31152i
$612$	−2.25743e6	−	1.64012e6i	−0.243633	−	0.177010i
$613$	5.38642e6	+	3.91347e6i	0.578961	+	0.420640i	0.838349	−	0.545133i	$-0.183521\pi$
$613$	5.38642e6	+	3.91347e6i	0.578961	+	0.420640i	−0.259388	+	0.965773i	$0.583521\pi$
$614$	−6.67199e6	+	4.84749e6i	−0.714224	+	0.518914i
$615$	−1.81936e6	−	186406.i	−0.193968	−	0.0198734i
$616$	−281096.	−	204228.i	−0.0298471	−	0.0216852i
$617$	926178.	+	2.85048e6i	0.0979449	+	0.301443i	0.988010	−	0.154390i	$-0.0493413\pi$
$617$	926178.	+	2.85048e6i	0.0979449	+	0.301443i	−0.890065	+	0.455833i	$0.849341\pi$
$618$	3.43741e6			0.362043
$619$	−3.99729e6	−	1.23024e7i	−0.419313	−	1.29051i	−0.908335	−	0.418242i	$-0.862646\pi$
$619$	−3.99729e6	−	1.23024e7i	−0.419313	−	1.29051i	0.489022	−	0.872271i	$-0.337354\pi$
$620$	−3.27769e6	−	2.93574e6i	−0.342443	−	0.306717i
$621$	−75248.8	+	231592.i	−0.00783016	+	0.0240988i
$622$	−2.73043e6	+	8.40339e6i	−0.282979	+	0.870921i
$623$	4.83660e6	−	3.51399e6i	0.499252	−	0.362728i
$624$	2.15553e6			0.221612
$625$	−9.53043e6	+	2.13035e6i	−0.975916	+	0.218148i
$626$	−7.96345e6			−0.812204
$627$	−694442.	+	504542.i	−0.0705451	+	0.0512540i
$628$	347223.	−	1.06864e6i	0.0351325	−	0.108127i
$629$	3.37447e6	−	1.03856e7i	0.340079	−	1.04665i
$630$	−784798.	−	702922.i	−0.0787783	−	0.0705596i
$631$	−104627.	−	322009.i	−0.0104609	−	0.0321955i	0.945690	−	0.325070i	$-0.105388\pi$
$631$	−104627.	−	322009.i	−0.0104609	−	0.0321955i	−0.956151	+	0.292875i	$0.905388\pi$
$632$	827590.			0.0824180
$633$	−3.24893e6	−	9.99918e6i	−0.322278	−	0.991871i
$634$	2.63809e6	+	1.91669e6i	0.260656	+	0.189377i
$635$	2.31102e6	+	236780.i	0.227441	+	0.0233029i
$636$	1.29610e6	−	941674.i	0.127056	−	0.0923119i
$637$	−1.01599e7	−	7.38163e6i	−0.992070	−	0.720781i
$638$	−1.92768e6	−	1.40054e6i	−0.187492	−	0.136221i
$639$	−3.55524e6	+	2.58304e6i	−0.344443	+	0.250252i
$640$	791985.	−	460023.i	0.0764305	−	0.0443945i
$641$	−2.28309e6	−	1.65876e6i	−0.219471	−	0.159455i	0.472618	−	0.881268i	$-0.343309\pi$
$641$	−2.28309e6	−	1.65876e6i	−0.219471	−	0.159455i	−0.692089	+	0.721813i	$0.743309\pi$
$642$	−1.67218e6	−	5.14644e6i	−0.160120	−	0.492798i
$643$	−261614.			−0.0249537			−0.0124768	−	0.999922i	$-0.503972\pi$
$643$	−261614.			−0.0249537			−0.0124768	+	0.999922i	$0.503972\pi$
$644$	−96069.4	−	295671.i	−0.00912789	−	0.0280928i
$645$	5.55497e6	−	3.22659e6i	0.525754	−	0.305383i
$646$	2.71961e6	−	8.37010e6i	0.256404	−	0.789131i
$647$	−657729.	+	2.02428e6i	−0.0617713	+	0.190112i	−0.977180	−	0.212413i	$-0.931868\pi$
$647$	−657729.	+	2.02428e6i	−0.0617713	+	0.190112i	0.915409	+	0.402526i	$0.131868\pi$
$648$	339709.	−	246813.i	0.0317812	−	0.0230904i
$649$	−4.52644e6			−0.421837
$650$	1.28332e6	+	1.16239e7i	0.119138	+	1.07912i
$651$	2.57551e6			0.238183
$652$	1.03488e6	−	751887.i	0.0953394	−	0.0692681i
$653$	−5.13776e6	+	1.58124e7i	−0.471510	+	1.45116i	0.379097	+	0.925357i	$0.376235\pi$
$653$	−5.13776e6	+	1.58124e7i	−0.471510	+	1.45116i	−0.850607	+	0.525802i	$0.823765\pi$
$654$	−582591.	+	1.79303e6i	−0.0532622	+	0.163924i
$655$	150598.	−	340648.i	0.0137157	−	0.0310243i
$656$	287568.	+	885043.i	0.0260904	+	0.0802981i
$657$	2.38020e6			0.215130
$658$	−1.58242e6	−	4.87018e6i	−0.142481	−	0.438510i
$659$	1.57669e7	+	1.14553e7i	1.41427	+	1.02753i	0.992684	+	0.120739i	$0.0385265\pi$
$659$	1.57669e7	+	1.14553e7i	1.41427	+	1.02753i	0.421586	+	0.906788i	$0.361474\pi$
$660$	559637.	+	501251.i	0.0500088	+	0.0447915i
$661$	4.42168e6	−	3.21254e6i	0.393626	−	0.285986i	−0.373314	−	0.927705i	$-0.621778\pi$
$661$	4.42168e6	−	3.21254e6i	0.393626	−	0.285986i	0.766940	+	0.641719i	$0.221778\pi$
$662$	6.53928e6	+	4.75107e6i	0.579943	+	0.421353i
$663$	−1.46664e7	−	1.06558e7i	−1.29581	−	0.941460i
$664$	3.80239e6	−	2.76260e6i	0.334685	−	0.243163i
$665$	1.34363e6	−	3.03924e6i	0.117822	−	0.266508i
$666$	1.32946e6	+	965907.i	0.116142	+	0.0843820i
$667$	−658818.	−	2.02763e6i	−0.0573391	−	0.176471i
$668$	4.92636e6			0.427154
$669$	2.53355e6	+	7.79748e6i	0.218859	+	0.673579i
$670$	539935.	+	2.50788e6i	0.0464680	+	0.215834i
$671$	−504681.	+	1.55325e6i	−0.0432724	+	0.133179i
$672$	−165660.	+	509849.i	−0.0141512	+	0.0435531i
$673$	1.18406e6	−	860272.i	0.100771	−	0.0732147i	−0.536259	−	0.844054i	$-0.680163\pi$
$673$	1.18406e6	−	860272.i	0.100771	−	0.0732147i	0.637030	+	0.770839i	$0.280163\pi$
$674$	−7.80644e6			−0.661916
$675$	1.53321e6	+	1.68497e6i	0.129522	+	0.142342i
$676$	8.06373e6			0.678687
$677$	8.27561e6	−	6.01258e6i	0.693950	−	0.504184i	−0.184006	−	0.982925i	$-0.558907\pi$
$677$	8.27561e6	−	6.01258e6i	0.693950	−	0.504184i	0.877956	+	0.478741i	$0.158907\pi$
$678$	−379393.	+	1.16765e6i	−0.0316968	+	0.0975527i
$679$	−1.53140e6	+	4.71318e6i	−0.127472	+	0.392319i
$680$	−7.66283e6	−	785110.i	−0.635502	−	0.0651116i
$681$	203856.	+	627404.i	0.0168444	+	0.0518417i
$682$	−1.83659e6			−0.151200
$683$	503829.	+	1.55063e6i	0.0413268	+	0.127191i	0.969591	−	0.244730i	$-0.0786993\pi$
$683$	503829.	+	1.55063e6i	0.0413268	+	0.127191i	−0.928265	+	0.371921i	$0.878699\pi$
$684$	1.07146e6	+	778459.i	0.0875658	+	0.0636203i
$685$	4.86395e6	+	2.25920e7i	0.396062	+	1.83962i
$686$	5.69054e6	−	4.13442e6i	0.461683	−	0.335432i
$687$	−308387.	−	224057.i	−0.0249290	−	0.0181120i
$688$	−2.64448e6	−	1.92133e6i	−0.212995	−	0.154750i
$689$	8.42073e6	−	6.11802e6i	0.675774	−	0.490979i
$690$	141486.	+	657171.i	0.0113133	+	0.0525479i
$691$	−443078.	−	321915.i	−0.0353009	−	0.0256476i	0.569995	−	0.821648i	$-0.306945\pi$
$691$	−443078.	−	321915.i	−0.0353009	−	0.0256476i	−0.605296	+	0.796001i	$0.706945\pi$
$692$	215897.	+	664462.i	0.0171388	+	0.0527479i
$693$	−439746.			−0.0347831
$694$	−4.14334e6	−	1.27519e7i	−0.326552	−	1.00502i
$695$	−8.58494e6	−	879586.i	−0.674179	−	0.0690743i
$696$	−1.13605e6	+	3.49641e6i	−0.0888945	+	0.273589i
$697$	2.41854e6	−	7.44349e6i	0.188569	−	0.580356i
$698$	7.99194e6	−	5.80648e6i	0.620888	−	0.451102i
$699$	850778.			0.0658603
$700$	−2.84803e6	−	589792.i	−0.219685	−	0.0454940i
$701$	−1.12995e7			−0.868489			−0.434245	−	0.900795i	$-0.642985\pi$
$701$	−1.12995e7			−0.868489			−0.434245	+	0.900795i	$0.642985\pi$
$702$	2.20708e6	−	1.60354e6i	0.169034	−	0.122811i
$703$	−1.60164e6	+	4.92935e6i	−0.122230	+	0.376185i
$704$	118132.	−	363572.i	0.00898327	−	0.0276476i
$705$	2.33050e6	+	1.08246e7i	0.176594	+	0.820240i
$706$	−1.41263e6	−	4.34761e6i	−0.106663	−	0.328276i
$707$	1.07268e7			0.807086
$708$	2.15813e6	+	6.64204e6i	0.161806	+	0.497987i
$709$	1.71087e7	+	1.24302e7i	1.27821	+	0.928675i	0.999497	−	0.0316993i	$-0.0100919\pi$
$709$	1.71087e7	+	1.24302e7i	1.27821	+	0.928675i	0.278714	+	0.960374i	$0.410092\pi$
$710$	−4.90525e6	+	1.10955e7i	−0.365187	+	0.826039i
$711$	847379.	−	615657.i	0.0628642	−	0.0456735i
$712$	5.32141e6	+	3.86623e6i	0.393393	+	0.285817i
$713$	−1.32946e6	−	965909.i	−0.0979380	−	0.0711561i
$714$	3.64758e6	−	2.65012e6i	0.267769	−	0.194545i
$715$	3.63594e6	+	3.25661e6i	0.265981	+	0.238232i
$716$	5.15878e6	+	3.74807e6i	0.376066	+	0.273228i
$717$	−1.88203e6	−	5.79231e6i	−0.136719	−	0.420779i
$718$	2.59364e6			0.187758
$719$	−3.46387e6	−	1.06607e7i	−0.249885	−	0.769066i	−0.994795	−	0.101901i	$-0.967508\pi$
$719$	−3.46387e6	−	1.06607e7i	−0.249885	−	0.769066i	0.744910	−	0.667165i	$-0.232492\pi$
$720$	468705.	−	1.06019e6i	0.0336952	−	0.0762173i
$721$	−1.71634e6	+	5.28237e6i	−0.122961	+	0.378434i
$722$	1.76980e6	−	5.44690e6i	0.126352	−	0.388871i
$723$	−925608.	+	672493.i	−0.0658538	+	0.0478456i
$724$	6.80475e6			0.482465
$725$	−1.95310e7	−	4.04463e6i	−1.38000	−	0.285781i
$726$	−5.48426e6			−0.386168
$727$	−3.02885e6	+	2.20059e6i	−0.212540	+	0.154420i	−0.688962	−	0.724797i	$-0.741933\pi$
$727$	−3.02885e6	+	2.20059e6i	−0.212540	+	0.154420i	0.476422	+	0.879217i	$0.341933\pi$
$728$	−1.07629e6	+	3.31247e6i	−0.0752661	+	0.231645i
$729$	164224.	−	505430.i	0.0114451	−	0.0352243i
$730$	5.68180e6	−	3.30026e6i	0.394620	−	0.229214i
$731$	8.49527e6	+	2.61457e7i	0.588008	+	1.80970i
$732$	2.51984e6			0.173818
$733$	−800978.	−	2.46516e6i	−0.0550631	−	0.169467i	0.919743	−	0.392522i	$-0.128397\pi$
$733$	−800978.	−	2.46516e6i	−0.0550631	−	0.169467i	−0.974806	+	0.223055i	$0.928397\pi$
$734$	−9.19647e6	−	6.68163e6i	−0.630059	−	0.457765i
$735$	−5.83983e6	+	3.39205e6i	−0.398733	+	0.231603i
$736$	276724.	−	201052.i	0.0188301	−	0.0136809i
$737$	866246.	+	629365.i	0.0587452	+	0.0426809i
$738$	952842.	+	692280.i	0.0643991	+	0.0467887i
$739$	−1.97501e7	+	1.43493e7i	−1.33033	+	0.966538i	−0.330585	+	0.943776i	$0.607246\pi$
$739$	−1.97501e7	+	1.43493e7i	−1.33033	+	0.966538i	−0.999741	+	0.0227620i	$0.992754\pi$
$740$	4.51283e6	+	462370.i	0.302949	+	0.0310392i
$741$	6.96121e6	+	5.05762e6i	0.465736	+	0.338377i
$742$	799935.	+	2.46195e6i	0.0533390	+	0.164161i
$743$	1.19103e7			0.791503			0.395751	−	0.918358i	$-0.370484\pi$
$743$	1.19103e7			0.791503			0.395751	+	0.918358i	$0.370484\pi$
$744$	875654.	+	2.69499e6i	0.0579963	+	0.178494i
$745$	1.53662e7	+	1.37631e7i	1.01432	+	0.908500i
$746$	−3.63106e6	+	1.11753e7i	−0.238884	+	0.735208i
$747$	1.83817e6	−	5.65731e6i	0.120527	−	0.370944i
$748$	−2.60108e6	+	1.88979e6i	−0.169981	+	0.123498i
$749$	8.74361e6			0.569490
$750$	5.99622e6	+	1.89633e6i	0.389246	+	0.123101i
$751$	−1.15422e7			−0.746774			−0.373387	−	0.927676i	$-0.621804\pi$
$751$	−1.15422e7			−0.746774			−0.373387	+	0.927676i	$0.621804\pi$
$752$	4.55809e6	−	3.31165e6i	0.293926	−	0.213550i
$753$	−3.27778e6	+	1.00880e7i	−0.210665	+	0.648360i
$754$	−7.38088e6	+	2.27160e7i	−0.472802	+	1.45514i
$755$	−1.91998e7	−	1.71968e7i	−1.22583	−	1.09794i
$756$	209664.	+	645278.i	0.0133419	+	0.0410622i
$757$	1.32731e7			0.841844			0.420922	−	0.907097i	$-0.361707\pi$
$757$	1.32731e7			0.841844			0.420922	+	0.907097i	$0.361707\pi$
$758$	2.39856e6	+	7.38201e6i	0.151627	+	0.466661i
$759$	226994.	+	164920.i	0.0143024	+	0.0103913i
$760$	3.63705e6	+	372641.i	0.228410	+	0.0234022i
$761$	7.70910e6	−	5.60099e6i	0.482550	−	0.350593i	−0.319762	−	0.947498i	$-0.603603\pi$
$761$	7.70910e6	−	5.60099e6i	0.482550	−	0.350593i	0.802312	+	0.596905i	$0.203603\pi$
$762$	−1.21034e6	−	879362.i	−0.0755126	−	0.0548631i
$763$	−2.46450e6	−	1.79057e6i	−0.153256	−	0.111347i
$764$	6.22855e6	−	4.52531e6i	0.386059	−	0.280488i
$765$	−8.43012e6	+	4.89662e6i	−0.520811	+	0.302512i
$766$	1.13217e7	+	8.22571e6i	0.697173	+	0.506526i
$767$	1.40213e7	+	4.31531e7i	0.860596	+	2.64864i
$768$	−589824.			−0.0360844
$769$	−4.71332e6	−	1.45061e7i	−0.287416	−	0.884576i	−0.985664	−	0.168720i	$-0.946037\pi$
$769$	−4.71332e6	−	1.45061e7i	−0.287416	−	0.884576i	0.698248	−	0.715856i	$-0.253963\pi$
$770$	−1.04972e6	+	609728.i	−0.0638038	+	0.0370603i
$771$	4.13272e6	−	1.27192e7i	0.250380	−	0.770591i
$772$	3.15472e6	−	9.70922e6i	0.190510	−	0.586328i
$773$	5.22952e6	−	3.79947e6i	0.314784	−	0.228704i	−0.419163	−	0.907911i	$-0.637676\pi$
$773$	5.22952e6	−	3.79947e6i	0.314784	−	0.228704i	0.733947	+	0.679207i	$0.237676\pi$
$774$	−4.13702e6			−0.248219
$775$	−1.40116e7	+	6.32652e6i	−0.837980	+	0.378365i
$776$	−5.45248e6			−0.325042
$777$	−2.14815e6	+	1.56072e6i	−0.127647	+	0.0927413i
$778$	1.49090e6	−	4.58852e6i	0.0883079	−	0.271784i
$779$	−1.14792e6	+	3.53294e6i	−0.0677749	+	0.208590i
$780$	3.04516e6	−	6.88803e6i	0.179214	−	0.405376i
$781$	1.56471e6	+	4.81567e6i	0.0917921	+	0.282507i
$782$	−2.87675e6			−0.168223
$783$	1.43781e6	+	4.42514e6i	0.0838105	+	0.257942i
$784$	2.78009e6	+	2.01985e6i	0.161536	+	0.117362i
$785$	−2.92433e6	−	2.61924e6i	−0.169376	−	0.151705i
$786$	−194047.	+	140983.i	−0.0112034	+	0.00813974i
$787$	−4.84242e6	−	3.51822e6i	−0.278693	−	0.202482i	0.439654	−	0.898167i	$-0.355101\pi$
$787$	−4.84242e6	−	3.51822e6i	−0.278693	−	0.202482i	−0.718347	+	0.695685i	$0.755101\pi$
$788$	4.44376e6	+	3.22858e6i	0.254938	+	0.185224i
$789$	−8.58319e6	+	6.23606e6i	−0.490859	+	0.356630i
$790$	1.16915e6	−	2.64457e6i	0.0666502	−	0.150760i
$791$	−1.60493e6	−	1.16605e6i	−0.0912041	−	0.0662636i
$792$	−149510.	−	460145.i	−0.00846950	−	0.0260665i
$793$	1.63713e7			0.924486
$794$	−1.80014e6	−	5.54025e6i	−0.101334	−	0.311873i
$795$	−1.17810e6	−	5.47202e6i	−0.0661097	−	0.307065i
$796$	1.56246e6	−	4.80875e6i	0.0874028	−	0.268998i
$797$	−611379.	+	1.88163e6i	−0.0340930	+	0.104927i	−0.966655	−	0.256083i	$-0.917568\pi$
$797$	−611379.	+	1.88163e6i	−0.0340930	+	0.104927i	0.932562	+	0.361010i	$0.117568\pi$
$798$	−1.73127e6	+	1.25784e6i	−0.0962405	+	0.0699229i
$799$	−4.73846e7			−2.62585
$800$	−351157.	−	3.18067e6i	−0.0193989	−	0.175709i
$801$	8.32481e6			0.458451
$802$	−1.23381e7	+	8.96416e6i	−0.677350	+	0.492123i
$803$	847490.	−	2.60831e6i	0.0463816	−	0.142748i
$804$	510511.	−	1.57119e6i	0.0278526	−	0.0857213i
$805$	−1.08054e6	−	110709.i	−0.0587693	−	0.00602132i
$806$	5.68909e6	+	1.75092e7i	0.308464	+	0.949356i
$807$	7.99798e6			0.432311
$808$	3.64702e6	+	1.12244e7i	0.196521	+	0.604830i
$809$	−2.76633e7	−	2.00986e7i	−1.48605	−	1.07968i	−0.975544	−	0.219802i	$-0.929459\pi$
$809$	−2.76633e7	−	2.00986e7i	−1.48605	−	1.07968i	−0.510504	−	0.859875i	$-0.670541\pi$
$810$	−308781.	−	1.43422e6i	−0.0165363	−	0.0768075i
$811$	−1.52709e7	+	1.10949e7i	−0.815288	+	0.592342i	−0.915359	−	0.402639i	$-0.868093\pi$
$811$	−1.52709e7	+	1.10949e7i	−0.815288	+	0.592342i	0.100071	+	0.994980i	$0.468093\pi$
$812$	−4.80578e6	−	3.49160e6i	−0.255784	−	0.185838i
$813$	−5.31338e6	−	3.86040e6i	−0.281932	−	0.204836i
$814$	1.53184e6	−	1.11295e6i	0.0810311	−	0.0588726i
$815$	−940665.	−	4.36918e6i	−0.0496068	−	0.230412i
$816$	4.01321e6	+	2.91577e6i	0.210992	+	0.153295i
$817$	−4.03215e6	−	1.24097e7i	−0.211340	−	0.650438i
$818$	−3.84564e6			−0.200949
$819$	1.36218e6	+	4.19234e6i	0.0709616	+	0.218397i
$820$	3.23441e6	+	331388.i	0.167981	+	0.0172108i
$821$	3.62689e6	−	1.11624e7i	0.187792	−	0.577964i	−0.812194	−	0.583388i	$-0.801727\pi$
$821$	3.62689e6	−	1.11624e7i	0.187792	−	0.577964i	0.999985	+	0.00542454i	$0.00172669\pi$
$822$	4.59889e6	−	1.41539e7i	0.237396	−	0.730629i
$823$	9.28088e6	−	6.74295e6i	0.477628	−	0.347017i	−0.322779	−	0.946474i	$-0.604617\pi$
$823$	9.28088e6	−	6.74295e6i	0.477628	−	0.347017i	0.800407	+	0.599458i	$0.204617\pi$
$824$	−6.11096e6			−0.313539
$825$	2.39236e6	−	1.08020e6i	0.122375	−	0.0552546i
$826$	−1.12846e7			−0.575487
$827$	−4.33176e6	+	3.14721e6i	−0.220242	+	0.160015i	−0.692436	−	0.721480i	$-0.743462\pi$
$827$	−4.33176e6	+	3.14721e6i	−0.220242	+	0.160015i	0.472194	+	0.881495i	$0.343462\pi$
$828$	133776.	−	411719.i	0.00678112	−	0.0208701i
$829$	−1.46447e6	+	4.50717e6i	−0.0740105	+	0.227781i	−0.981218	−	0.192903i	$-0.938210\pi$
$829$	−1.46447e6	+	4.50717e6i	−0.0740105	+	0.227781i	0.907207	+	0.420684i	$0.138210\pi$
$830$	−3.45621e6	−	1.60533e7i	−0.174143	−	0.808853i
$831$	5.84859e6	+	1.80001e7i	0.293798	+	0.904218i
$832$	−3.83206e6			−0.191922
$833$	−8.93090e6	−	2.74865e7i	−0.445946	−	1.37248i
$834$	4.49614e6	+	3.26664e6i	0.223833	+	0.162625i
$835$	6.95954e6	−	1.57422e7i	0.345433	−	0.781358i
$836$	1.23456e6	−	896963.i	0.0610939	−	0.0443873i
$837$	2.90144e6	+	2.10802e6i	0.143153	+	0.104006i
$838$	−4.49958e6	−	3.26913e6i	−0.221341	−	0.160814i
$839$	2.73235e7	−	1.98517e7i	1.34008	−	0.973626i	0.340640	−	0.940194i	$-0.389356\pi$
$839$	2.73235e7	−	1.98517e7i	1.34008	−	0.973626i	0.999441	−	0.0334316i	$-0.0106436\pi$
$840$	1.39520e6	+	1.24964e6i	0.0682240	+	0.0611064i
$841$	−1.63628e7	−	1.18883e7i	−0.797753	−	0.579601i
$842$	7.84030e6	+	2.41300e7i	0.381112	+	1.17294i
$843$	3.78534e6			0.183458
$844$	5.77587e6	+	1.77763e7i	0.279101	+	0.858985i
$845$	1.13918e7	−	2.57677e7i	0.548844	−	1.24146i
$846$	2.20350e6	−	6.78167e6i	0.105849	−	0.325770i
$847$	2.73836e6	−	8.42781e6i	0.131154	−	0.403651i
$848$	−2.30418e6	+	1.67409e6i	−0.110034	+	0.0799445i
$849$	1.34629e7			0.641019
$850$	−1.33342e7	+	2.33775e7i	−0.633024	+	1.10982i
$851$	1.69419e6			0.0801932
$852$	6.32043e6	−	4.59206e6i	0.298296	−	0.216725i
$853$	−5.37146e6	+	1.65317e7i	−0.252767	+	0.777936i	0.741495	+	0.670959i	$0.234117\pi$
$853$	−5.37146e6	+	1.65317e7i	−0.252767	+	0.777936i	−0.994261	+	0.106977i	$0.965883\pi$
$854$	−1.25819e6	+	3.87231e6i	−0.0590339	+	0.181688i
$855$	4.00124e6	−	2.32411e6i	0.187188	−	0.108728i
$856$	2.97276e6	+	9.14922e6i	0.138668	+	0.426776i
$857$	−1.11062e6			−0.0516550			−0.0258275	−	0.999666i	$-0.508222\pi$
$857$	−1.11062e6			−0.0516550			−0.0258275	+	0.999666i	$0.508222\pi$
$858$	−971362.	−	2.98954e6i	−0.0450467	−	0.138639i
$859$	−2.05025e7	−	1.48960e7i	−0.948035	−	0.688788i	0.00230613	−	0.999997i	$-0.499266\pi$
$859$	−2.05025e7	−	1.48960e7i	−0.948035	−	0.688788i	−0.950341	+	0.311209i	$0.899266\pi$
$860$	−9.87551e6	+	5.73617e6i	−0.455317	+	0.264470i
$861$	−1.53961e6	+	1.11859e6i	−0.0707789	+	0.0514239i
$862$	−1.06047e7	−	7.70475e6i	−0.486104	−	0.353176i
$863$	−4.03302e6	−	2.93016e6i	−0.184333	−	0.133926i	0.491792	−	0.870713i	$-0.336342\pi$
$863$	−4.03302e6	−	2.93016e6i	−0.184333	−	0.133926i	−0.676125	+	0.736787i	$0.736342\pi$
$864$	−603928.	+	438779.i	−0.0275233	+	0.0199969i
$865$	2.42829e6	+	248795.i	0.110347	+	0.0113058i
$866$	−2.30294e6	−	1.67319e6i	−0.104349	−	0.0758140i
$867$	−8.94342e6	−	2.75250e7i	−0.404069	−	1.24360i
$868$	−4.57868e6			−0.206273
$869$	−372942.	−	1.14780e6i	−0.0167530	−	0.0515603i
$870$	9.56787e6	+	8.56968e6i	0.428566	+	0.383854i
$871$	3.31677e6	−	1.02080e7i	0.148139	−	0.455925i
$872$	1.03572e6	−	3.18761e6i	0.0461264	−	0.141963i
$873$	−5.58286e6	+	4.05619e6i	−0.247926	+	0.180129i
$874$	1.36541e6			0.0604621
$875$	−5.90814e6	+	8.26770e6i	−0.260874	+	0.365060i
$876$	−4.23147e6			−0.186308
$877$	−1.38212e7	+	1.00417e7i	−0.606803	+	0.440869i	−0.848287	−	0.529536i	$-0.822366\pi$
$877$	−1.38212e7	+	1.00417e7i	−0.606803	+	0.440869i	0.241484	+	0.970405i	$0.422366\pi$
$878$	8.71052e6	−	2.68082e7i	0.381336	−	1.17363i
$879$	−6.04738e6	+	1.86119e7i	−0.263995	+	0.812492i
$880$	−994909.	−	891113.i	−0.0433089	−	0.0387906i
$881$	−7.26397e6	−	2.23562e7i	−0.315307	−	0.970417i	−0.975628	−	0.219432i	$-0.929579\pi$
$881$	−7.26397e6	−	2.23562e7i	−0.315307	−	0.970417i	0.660320	−	0.750984i	$-0.270421\pi$
$882$	4.34916e6			0.188250
$883$	−3.36563e6	−	1.03584e7i	−0.145266	−	0.447084i	0.851779	−	0.523902i	$-0.175524\pi$
$883$	−3.36563e6	−	1.03584e7i	−0.145266	−	0.447084i	−0.997045	+	0.0768176i	$0.975524\pi$
$884$	2.60737e7	+	1.89436e7i	1.12220	+	0.815328i
$885$	2.42735e7	+	2.48699e6i	1.04178	+	0.106737i
$886$	1.74320e7	−	1.26651e7i	0.746041	−	0.542030i
$887$	−3.40773e7	−	2.47586e7i	−1.45431	−	1.05662i	−0.984801	−	0.173688i	$-0.944432\pi$
$887$	−3.40773e7	−	2.47586e7i	−1.45431	−	1.05662i	−0.469507	−	0.882929i	$-0.655568\pi$
$888$	−2.36348e6	−	1.71717e6i	−0.100582	−	0.0730769i
$889$	1.95568e6	−	1.42088e6i	0.0829933	−	0.0602981i
$890$	1.98722e7	−	1.15427e7i	0.840952	−	0.488465i
$891$	−495395.	−	359925.i	−0.0209053	−	0.0151886i
$892$	−4.50410e6	−	1.38622e7i	−0.189538	−	0.583337i
$893$	2.24904e7			0.943776
$894$	−4.10517e6	−	1.26344e7i	−0.171786	−	0.528703i
$895$	1.92649e7	−	1.11900e7i	0.803912	−	0.466951i
$896$	294507.	−	906399.i	0.0122553	−	0.0377181i
$897$	869135.	−	2.67492e6i	0.0360667	−	0.111002i
$898$	2.65465e7	−	1.92872e7i	1.09854	−	0.798137i
$899$	−3.13994e7			−1.29575
$900$	−2.72571e6	−	2.99550e6i	−0.112169	−	0.123272i
$901$	2.39536e7			0.983014
$902$	1.09789e6	−	797665.i	0.0449307	−	0.0326441i
$903$	2.06567e6	−	6.35747e6i	0.0843026	−	0.259457i
$904$	674477.	−	2.07583e6i	0.0274502	−	0.0844831i
$905$	9.61317e6	−	2.17446e7i	0.390162	−	0.882533i
$906$	5.12935e6	+	1.57865e7i	0.207607	+	0.638949i
$907$	−3.88028e7			−1.56619			−0.783095	−	0.621902i	$-0.786360\pi$
$907$	−3.88028e7			−1.56619			−0.783095	+	0.621902i	$0.786360\pi$
$908$	−362410.	−	1.11538e6i	−0.0145877	−	0.0448963i
$909$	1.20842e7	+	8.77969e6i	0.485074	+	0.352427i
$910$	9.06454e6	+	8.11886e6i	0.362862	+	0.325006i
$911$	−1.81907e7	+	1.32163e7i	−0.726194	+	0.527611i	−0.888357	−	0.459153i	$-0.848153\pi$
$911$	−1.81907e7	+	1.32163e7i	−0.726194	+	0.527611i	0.162163	+	0.986764i	$0.448153\pi$
$912$	−1.90481e6	−	1.38393e6i	−0.0758342	−	0.0550968i
$913$	−5.54498e6	−	4.02866e6i	−0.220152	−	0.159950i
$914$	3.35496e6	−	2.43752e6i	0.132838	−	0.0965122i
$915$	3.55982e6	−	8.05218e6i	0.140564	−	0.317951i
$916$	548244.	+	398323.i	0.0215891	+	0.0156854i
$917$	−119763.	−	368591.i	−0.00470325	−	0.0144751i
$918$	6.27826e6			0.245885
$919$	−1.05036e7	−	3.23266e7i	−0.410249	−	1.26262i	−0.916432	−	0.400191i	$-0.868944\pi$
$919$	−1.05036e7	−	3.23266e7i	−0.410249	−	1.26262i	0.506183	−	0.862426i	$-0.331056\pi$
$920$	−251531.	−	1.16830e6i	−0.00979764	−	0.0455078i
$921$	5.73407e6	−	1.76476e7i	0.222748	−	0.685548i
$922$	−8.25138e6	+	2.53951e7i	−0.319668	+	0.983837i
$923$	4.10636e7	−	2.98344e7i	1.58655	−	1.15269i
$924$	781770.			0.0301231
$925$	7.85285e6	−	1.37676e7i	0.301768	−	0.529058i
$926$	−2.46297e7			−0.943914
$927$	−6.25708e6	+	4.54604e6i	−0.239151	+	0.173753i
$928$	2.01965e6	−	6.21583e6i	0.0769849	−	0.236935i
$929$	−9.66482e6	+	2.97453e7i	−0.367413	+	1.13078i	0.581043	+	0.813873i	$0.302645\pi$
$929$	−9.66482e6	+	2.97453e7i	−0.367413	+	1.13078i	−0.948456	+	0.316908i	$0.897355\pi$
$930$	9.84890e6	+	1.00909e6i	0.373405	+	0.0382579i
$931$	4.23892e6	+	1.30461e7i	0.160281	+	0.493293i
$932$	−1.51249e6			−0.0570367
$933$	−6.14346e6	−	1.89076e7i	−0.231052	−	0.711104i
$934$	3.29457e6	+	2.39364e6i	0.123575	+	0.0897826i
$935$	2.36427e6	+	1.09815e7i	0.0884439	+	0.410802i
$936$	−3.92369e6	+	2.85073e6i	−0.146388	+	0.106357i
$937$	−9.48669e6	−	6.89248e6i	−0.352993	−	0.256464i	0.397131	−	0.917762i	$-0.370006\pi$
$937$	−9.48669e6	−	6.89248e6i	−0.352993	−	0.256464i	−0.750123	+	0.661298i	$0.770006\pi$
$938$	2.15959e6	+	1.56903e6i	0.0801427	+	0.0582271i
$939$	1.44958e7	−	1.05318e7i	0.536509	−	0.389797i
$940$	−4.14311e6	−	1.92438e7i	−0.152935	−	0.710349i
$941$	2.32763e7	+	1.69112e7i	0.856919	+	0.622588i	0.927045	−	0.374950i	$-0.122340\pi$
$941$	2.32763e7	+	1.69112e7i	0.856919	+	0.622588i	−0.0701261	+	0.997538i	$0.522340\pi$
$942$	781251.	+	2.40444e6i	0.0286856	+	0.0882851i
$943$	1.21425e6			0.0444661
$944$	−3.83668e6	−	1.18081e7i	−0.140128	−	0.431270i
$945$	2.35819e6	+	241612.i	0.0859010	+	0.00880115i
$946$	−1.47302e6	+	4.53349e6i	−0.0535156	+	0.164704i
$947$	−8.35502e6	+	2.57141e7i	−0.302742	+	0.931744i	0.677768	+	0.735276i	$0.262947\pi$
$947$	−8.35502e6	+	2.57141e7i	−0.302742	+	0.931744i	−0.980510	+	0.196468i	$0.937053\pi$
$948$	−1.50645e6	+	1.09450e6i	−0.0544420	+	0.0395545i
$949$	−2.74917e7			−0.990914
$950$	6.32889e6	−	1.10958e7i	0.227520	−	0.398886i
$951$	−7.33694e6			−0.263065
$952$	−6.48459e6	+	4.71133e6i	−0.231894	+	0.168481i
$953$	−1.21157e7	+	3.72884e7i	−0.432133	+	1.32997i	0.463863	+	0.885907i	$0.346463\pi$
$953$	−1.21157e7	+	3.72884e7i	−0.432133	+	1.32997i	−0.895996	+	0.444062i	$0.853537\pi$
$954$	−1.11390e6	+	3.42824e6i	−0.0396256	+	0.121955i
$955$	−5.66149e6	−	2.62963e7i	−0.200873	−	0.933011i
$956$	3.34584e6	+	1.02974e7i	0.118402	+	0.364405i
$957$	5.36116e6			0.189225
$958$	−6.73067e6	−	2.07149e7i	−0.236943	−	0.729237i
$959$	1.94544e7	+	1.41345e7i	0.683081	+	0.496287i
$960$	−833253.	+	1.88479e6i	−0.0291809	+	0.0660061i
$961$	3.58145e6	−	2.60208e6i	0.125098	−	0.0908890i
$962$	−1.53554e7	−	1.11564e7i	−0.534963	−	0.388674i
$963$	9.85010e6	+	7.15651e6i	0.342275	+	0.248677i
$964$	1.64552e6	−	1.19554e6i	0.0570311	−	0.0414355i
$965$	−2.65692e7	−	2.37973e7i	−0.918459	−	0.822638i
$966$	565904.	+	411154.i	0.0195119	+	0.0141762i
$967$	−1.39398e7	−	4.29023e7i	−0.479391	−	1.47541i	−0.839943	−	0.542675i	$-0.817412\pi$
$967$	−1.39398e7	−	4.29023e7i	−0.479391	−	1.47541i	0.360552	−	0.932739i	$-0.382588\pi$
$968$	9.74979e6			0.334431
$969$	6.11912e6	+	1.88327e7i	0.209353	+	0.644323i
$970$	−7.70280e6	+	1.74235e7i	−0.262857	+	0.594573i
$971$	−1.11673e7	+	3.43695e7i	−0.380103	+	1.16984i	0.559868	+	0.828582i	$0.310852\pi$
$971$	−1.11673e7	+	3.43695e7i	−0.380103	+	1.16984i	−0.939971	+	0.341254i	$0.889148\pi$
$972$	−291954.	+	898543.i	−0.00991172	+	0.0305052i
$973$	−7.26492e6	+	5.27827e6i	−0.246008	+	0.178735i
$974$	5.00488e6			0.169043
$975$	−1.77088e7	−	1.94616e7i	−0.596593	−	0.655644i
$976$	−4.47972e6			−0.150531
$977$	1.37452e7	−	9.98650e6i	0.460697	−	0.334716i	−0.333107	−	0.942889i	$-0.608097\pi$
$977$	1.37452e7	−	9.98650e6i	0.460697	−	0.334716i	0.793805	+	0.608173i	$0.208097\pi$
$978$	−889403.	+	2.73730e6i	−0.0297339	+	0.0915114i
$979$	2.96412e6	−	9.12261e6i	0.0988413	−	0.304202i
$980$	1.03819e7	−	6.03032e6i	0.345313	−	0.200574i
$981$	−1.31083e6	−	4.03432e6i	−0.0434884	−	0.133844i
$982$	−1.56560e7			−0.518088
$983$	1.29341e7	+	3.98070e7i	0.426925	+	1.31394i	0.901139	+	0.433530i	$0.142732\pi$
$983$	1.29341e7	+	3.98070e7i	0.426925	+	1.31394i	−0.474214	+	0.880409i	$0.657268\pi$
$984$	−1.69394e6	−	1.23072e6i	−0.0557713	−	0.0405202i
$985$	1.65947e7	−	9.63901e6i	0.544978	−	0.316550i
$986$	−4.44695e7	+	3.23090e7i	−1.45670	+	1.05836i
$987$	9.32134e6	+	6.77235e6i	0.304569	+	0.221282i
$988$	−1.23755e7	−	8.99132e6i	−0.403339	−	0.293043i
$989$	−3.45056e6	+	2.50698e6i	−0.112176	+	0.0815005i
$990$	−1.68161e6	−	172293.i	−0.0545303	−	0.00558701i
$991$	2.08744e7	+	1.51662e7i	0.675197	+	0.490560i	0.871761	−	0.489931i	$-0.162978\pi$
$991$	2.08744e7	+	1.51662e7i	0.675197	+	0.490560i	−0.196564	+	0.980491i	$0.562978\pi$
$992$	−1.55672e6	−	4.79109e6i	−0.0502263	−	0.154581i
$993$	−1.81867e7			−0.585304
$994$	3.90088e6	+	1.20057e7i	0.125226	+	0.385407i
$995$	−1.31591e7	−	1.17862e7i	−0.421374	−	0.377413i
$996$	−3.26786e6	+	1.00574e7i	−0.104380	+	0.321247i
$997$	−6.29392e6	+	1.93707e7i	−0.200532	+	0.617174i	0.799335	+	0.600885i	$0.205185\pi$
$997$	−6.29392e6	+	1.93707e7i	−0.200532	+	0.617174i	−0.999867	+	0.0162886i	$0.994815\pi$
$998$	1.65309e7	−	1.20104e7i	0.525377	−	0.381709i
$999$	−3.69742e6			−0.117216

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.6.g.a.61.1	✓	20
25.16	even	5	inner	150.6.g.a.91.1	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.6.g.a.61.1	✓	20	1.1	even	1	trivial
150.6.g.a.91.1	yes	20	25.16	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	150.g (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(3.23607 - 2.35114i) q^{2} +(-2.78115 + 8.55951i) q^{3} +(4.94427 - 15.2169i) q^{4} +(-41.6409 - 37.2966i) q^{5} +(11.1246 + 34.2380i) q^{6} -58.1692 q^{7} +(-19.7771 - 60.8676i) q^{8} +(-65.5304 - 47.6106i) q^{9} +O(q^{10})\)	\(q+(3.23607 - 2.35114i) q^{2} +(-2.78115 + 8.55951i) q^{3} +(4.94427 - 15.2169i) q^{4} +(-41.6409 - 37.2966i) q^{5} +(11.1246 + 34.2380i) q^{6} -58.1692 q^{7} +(-19.7771 - 60.8676i) q^{8} +(-65.5304 - 47.6106i) q^{9} +(-222.442 - 22.7907i) q^{10} +(-75.5060 + 54.8583i) q^{11} +(116.498 + 84.6411i) q^{12} +(756.886 + 549.910i) q^{13} +(-188.239 + 136.764i) q^{14} +(435.050 - 252.698i) q^{15} +(-207.108 - 150.473i) q^{16} +(665.326 + 2047.66i) q^{17} -324.000 q^{18} +(-315.787 - 971.893i) q^{19} +(-773.423 + 449.241i) q^{20} +(161.777 - 497.900i) q^{21} +(-115.363 + 355.050i) q^{22} +(-270.239 + 196.340i) q^{23} +576.000 q^{24} +(342.927 + 3106.13i) q^{25} +3742.25 q^{26} +(589.773 - 428.495i) q^{27} +(-287.604 + 885.155i) q^{28} +(-1972.31 + 6070.15i) q^{29} +(813.724 - 1840.61i) q^{30} +(1520.23 + 4678.80i) q^{31} -1024.00 q^{32} +(-259.566 - 798.863i) q^{33} +(6967.38 + 5062.10i) q^{34} +(2422.22 + 2169.51i) q^{35} +(-1048.49 + 761.770i) q^{36} +(-4103.26 - 2981.19i) q^{37} +(-3306.97 - 2402.65i) q^{38} +(-6811.97 + 4949.19i) q^{39} +(-1446.62 + 3272.20i) q^{40} +(-2940.87 - 2136.67i) q^{41} +(-647.110 - 1991.60i) q^{42} +12768.6 q^{43} +(461.451 + 1420.20i) q^{44} +(953.029 + 4426.61i) q^{45} +(-412.888 + 1270.74i) q^{46} +(-6800.92 + 20931.1i) q^{47} +(1863.98 - 1354.26i) q^{48} -13423.3 q^{49} +(8412.68 + 9245.37i) q^{50} -19377.4 q^{51} +(12110.2 - 8798.55i) q^{52} +(3437.97 - 10581.0i) q^{53} +(901.094 - 2773.28i) q^{54} +(5190.16 + 531.768i) q^{55} +(1150.42 + 3540.62i) q^{56} +9197.18 q^{57} +(7889.24 + 24280.6i) q^{58} +(39236.5 + 28507.0i) q^{59} +(-1694.27 - 7869.53i) q^{60} +(14156.9 - 10285.6i) q^{61} +(15920.1 + 11566.6i) q^{62} +(3811.85 + 2769.47i) q^{63} +(-3313.73 + 2407.57i) q^{64} +(-11007.6 - 51128.0i) q^{65} +(-2718.21 - 1974.90i) q^{66} +(-3545.22 - 10911.1i) q^{67} +34448.6 q^{68} +(-928.998 - 2859.16i) q^{69} +(12939.3 + 1325.72i) q^{70} +(16765.2 - 51598.0i) q^{71} +(-1601.94 + 4930.28i) q^{72} +(-23773.1 + 17272.2i) q^{73} -20287.6 q^{74} +(-27540.7 - 5703.33i) q^{75} -16350.5 q^{76} +(4392.12 - 3191.06i) q^{77} +(-10407.8 + 32031.8i) q^{78} +(-3995.93 + 12298.2i) q^{79} +(3012.04 + 13990.3i) q^{80} +(2027.46 + 6239.88i) q^{81} -14540.5 q^{82} +(22693.5 + 69843.4i) q^{83} +(-6776.62 - 4923.50i) q^{84} +(48666.1 - 110081. i) q^{85} +(41320.0 - 30020.7i) q^{86} +(-46472.2 - 33764.0i) q^{87} +(4832.38 + 3510.93i) q^{88} +(-83147.1 + 60409.9i) q^{89} +(13491.6 + 12084.1i) q^{90} +(-44027.4 - 31987.8i) q^{91} +(1651.55 + 5082.95i) q^{92} -44276.2 q^{93} +(27203.7 + 83724.3i) q^{94} +(-23098.6 + 52248.3i) q^{95} +(2847.90 - 8764.94i) q^{96} +(26326.7 - 81025.3i) q^{97} +(-43438.9 + 31560.2i) q^{98} +7559.77 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 20 q^{2} + 45 q^{3} - 80 q^{4} - 55 q^{5} - 180 q^{6} + 180 q^{7} + 320 q^{8} - 405 q^{9}+O(q^{10}) \) 20 * q + 20 * q^2 + 45 * q^3 - 80 * q^4 - 55 * q^5 - 180 * q^6 + 180 * q^7 + 320 * q^8 - 405 * q^9	\( 20 q + 20 q^{2} + 45 q^{3} - 80 q^{4} - 55 q^{5} - 180 q^{6} + 180 q^{7} + 320 q^{8} - 405 q^{9} + 220 q^{10} + 380 q^{11} + 720 q^{12} - 230 q^{13} - 920 q^{14} - 630 q^{15} - 1280 q^{16} + 2870 q^{17} - 6480 q^{18} + 1560 q^{19} + 1120 q^{20} + 2880 q^{21} - 720 q^{22} + 760 q^{23} + 11520 q^{24} + 1725 q^{25} + 7320 q^{26} + 3645 q^{27} - 5120 q^{28} + 12000 q^{29} + 5220 q^{30} - 1710 q^{31} - 20480 q^{32} - 1620 q^{33} + 20620 q^{34} - 22440 q^{35} - 6480 q^{36} - 5595 q^{37} - 5240 q^{38} + 2070 q^{39} - 9280 q^{40} - 2820 q^{41} - 11520 q^{42} + 66020 q^{43} + 2880 q^{44} - 8505 q^{45} + 21960 q^{46} - 19630 q^{47} + 11520 q^{48} - 61780 q^{49} + 100 q^{50} - 41130 q^{51} - 3680 q^{52} + 62735 q^{53} - 14580 q^{54} + 66590 q^{55} + 20480 q^{56} + 51660 q^{57} - 48000 q^{58} + 105100 q^{59} + 15120 q^{60} + 34790 q^{61} - 28560 q^{62} + 18630 q^{63} - 20480 q^{64} - 44345 q^{65} + 13680 q^{66} - 19470 q^{67} + 73120 q^{68} + 49410 q^{69} - 81240 q^{70} - 111720 q^{71} + 25920 q^{72} - 198830 q^{73} - 104120 q^{74} + 60975 q^{75} - 91840 q^{76} + 144740 q^{77} + 41220 q^{78} + 71210 q^{79} - 26880 q^{80} - 32805 q^{81} + 166680 q^{82} - 288690 q^{83} - 33120 q^{84} + 338735 q^{85} + 39920 q^{86} + 108225 q^{87} - 24320 q^{88} + 114225 q^{89} + 17820 q^{90} - 155800 q^{91} - 87840 q^{92} + 97740 q^{93} + 78520 q^{94} - 416900 q^{95} - 46080 q^{96} - 446970 q^{97} - 123380 q^{98} - 90720 q^{99}+O(q^{100}) \) 20 * q + 20 * q^2 + 45 * q^3 - 80 * q^4 - 55 * q^5 - 180 * q^6 + 180 * q^7 + 320 * q^8 - 405 * q^9 + 220 * q^10 + 380 * q^11 + 720 * q^12 - 230 * q^13 - 920 * q^14 - 630 * q^15 - 1280 * q^16 + 2870 * q^17 - 6480 * q^18 + 1560 * q^19 + 1120 * q^20 + 2880 * q^21 - 720 * q^22 + 760 * q^23 + 11520 * q^24 + 1725 * q^25 + 7320 * q^26 + 3645 * q^27 - 5120 * q^28 + 12000 * q^29 + 5220 * q^30 - 1710 * q^31 - 20480 * q^32 - 1620 * q^33 + 20620 * q^34 - 22440 * q^35 - 6480 * q^36 - 5595 * q^37 - 5240 * q^38 + 2070 * q^39 - 9280 * q^40 - 2820 * q^41 - 11520 * q^42 + 66020 * q^43 + 2880 * q^44 - 8505 * q^45 + 21960 * q^46 - 19630 * q^47 + 11520 * q^48 - 61780 * q^49 + 100 * q^50 - 41130 * q^51 - 3680 * q^52 + 62735 * q^53 - 14580 * q^54 + 66590 * q^55 + 20480 * q^56 + 51660 * q^57 - 48000 * q^58 + 105100 * q^59 + 15120 * q^60 + 34790 * q^61 - 28560 * q^62 + 18630 * q^63 - 20480 * q^64 - 44345 * q^65 + 13680 * q^66 - 19470 * q^67 + 73120 * q^68 + 49410 * q^69 - 81240 * q^70 - 111720 * q^71 + 25920 * q^72 - 198830 * q^73 - 104120 * q^74 + 60975 * q^75 - 91840 * q^76 + 144740 * q^77 + 41220 * q^78 + 71210 * q^79 - 26880 * q^80 - 32805 * q^81 + 166680 * q^82 - 288690 * q^83 - 33120 * q^84 + 338735 * q^85 + 39920 * q^86 + 108225 * q^87 - 24320 * q^88 + 114225 * q^89 + 17820 * q^90 - 155800 * q^91 - 87840 * q^92 + 97740 * q^93 + 78520 * q^94 - 416900 * q^95 - 46080 * q^96 - 446970 * q^97 - 123380 * q^98 - 90720 * q^99

Introduction

L-functions

Modular forms

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