LMFDB - Embedded newform 150.6.g.a.91.1

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			91.1
Root			$0.500000 + 22.2192i$ of defining polynomial
Character	$\chi$	$=$	150.91
Dual form			150.6.g.a.61.1

$q$-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 $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

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

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	0.489724	−	0.871878i	$-0.337098\pi$
$11$	−75.5060	−	54.8583i	−0.188148	−	0.136697i	−0.677872	+	0.735180i	$0.737098\pi$
$12$	116.498	−	84.6411i	0.233543	−	0.169679i
$13$	756.886	−	549.910i	1.24214	−	0.902470i	0.244404	−	0.969673i	$-0.421408\pi$
$13$	756.886	−	549.910i	1.24214	−	0.902470i	0.997739	+	0.0672032i	$0.0214076\pi$
$14$	−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	−0.128551	−	0.991703i	$-0.541033\pi$
$17$	665.326	−	2047.66i	0.558357	−	1.71845i	0.686909	−	0.726744i	$-0.258967\pi$
$18$	−324.000			−0.235702
$19$	−315.787	+	971.893i	−0.200683	+	0.617639i	0.799180	+	0.601092i	$0.205267\pi$
$19$	−315.787	+	971.893i	−0.200683	+	0.617639i	−0.999863	+	0.0165470i	$0.994733\pi$
$20$	−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	0.533251	−	0.845957i	$-0.320970\pi$
$23$	−270.239	−	196.340i	−0.106519	−	0.0773907i	−0.639770	+	0.768567i	$0.720970\pi$
$24$	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	−0.892581	−	0.450886i	$-0.851108\pi$
$29$	−1972.31	−	6070.15i	−0.435492	−	1.34031i	0.457089	−	0.889421i	$-0.348892\pi$
$30$	813.724	+	1840.61i	0.165072	+	0.373387i
$31$	1520.23	−	4678.80i	0.284123	−	0.874440i	−0.702538	−	0.711647i	$-0.747950\pi$
$31$	1520.23	−	4678.80i	0.284123	−	0.874440i	0.986660	−	0.162793i	$-0.0520503\pi$
$32$	−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	−0.806240	−	0.591588i	$-0.798501\pi$
$37$	−4103.26	+	2981.19i	−0.492748	+	0.358002i	0.313492	+	0.949591i	$0.398501\pi$
$38$	−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	−0.715956	−	0.698146i	$-0.754009\pi$
$41$	−2940.87	+	2136.67i	−0.273222	+	0.198508i	0.442733	+	0.896653i	$0.354009\pi$
$42$	−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	−0.877948	−	0.478757i	$-0.841088\pi$
$47$	−6800.92	−	20931.1i	−0.449079	−	1.38212i	0.428868	−	0.903367i	$-0.358912\pi$
$48$	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	0.999252	−	0.0386587i	$-0.0123085\pi$
$53$	3437.97	+	10581.0i	0.168117	+	0.517412i	−0.831135	+	0.556070i	$0.812309\pi$
$54$	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	0.486094	−	0.873906i	$-0.338421\pi$
$59$	39236.5	−	28507.0i	1.46744	−	1.06616i	0.981346	−	0.192251i	$-0.0615788\pi$
$60$	−1694.27	+	7869.53i	−0.0607583	+	0.282209i
$61$	14156.9	+	10285.6i	0.487129	+	0.353920i	0.804079	−	0.594522i	$-0.202659\pi$
$61$	14156.9	+	10285.6i	0.487129	+	0.353920i	−0.316950	+	0.948442i	$0.602659\pi$
$62$	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	−0.987638	−	0.156754i	$-0.949897\pi$
$67$	−3545.22	+	10911.1i	−0.0964841	+	0.296947i	0.891154	+	0.453702i	$0.149897\pi$
$68$	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	0.929198	+	0.369583i	$0.120499\pi$
$71$	16765.2	+	51598.0i	0.394696	+	1.21475i	−0.534501	+	0.845168i	$0.679501\pi$
$72$	−1601.94	−	4930.28i	−0.0364180	−	0.112083i
$73$	−23773.1	−	17272.2i	−0.522131	−	0.379350i	0.295275	−	0.955412i	$-0.404589\pi$
$73$	−23773.1	−	17272.2i	−0.522131	−	0.379350i	−0.817406	+	0.576062i	$0.804589\pi$
$74$	−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	0.908556	−	0.417763i	$-0.137186\pi$
$79$	−3995.93	−	12298.2i	−0.0720360	−	0.221704i	−0.980592	+	0.196059i	$0.937186\pi$
$80$	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	−0.590513	−	0.807028i	$-0.701075\pi$
$83$	22693.5	−	69843.4i	0.361581	−	1.11283i	0.952094	−	0.305805i	$-0.0989255\pi$
$84$	−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	−0.129600	−	0.991566i	$-0.541369\pi$
$89$	−83147.1	−	60409.9i	−1.11268	−	0.808412i	−0.983084	+	0.183154i	$0.941369\pi$
$90$	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	0.986668	+	0.162748i	$0.0520357\pi$
$97$	26326.7	+	81025.3i	0.284097	+	0.874362i	−0.702570	+	0.711614i	$0.747964\pi$
$98$	−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	0.989471	+	0.144731i	$0.0462316\pi$
$103$	29506.1	+	90810.4i	0.274043	+	0.843417i	−0.715428	+	0.698686i	$0.753768\pi$
$104$	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	−0.403758	−	0.914866i	$-0.632296\pi$
$109$	42367.9	−	30782.0i	0.341563	−	0.248160i	0.745321	+	0.666706i	$0.232296\pi$
$110$	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	−0.481495	−	0.876449i	$-0.659906\pi$
$113$	27590.7	−	20045.8i	0.203267	−	0.147682i	0.684762	+	0.728767i	$0.259906\pi$
$114$	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	0.491448	−	0.870907i	$-0.336468\pi$
$127$	−33620.5	−	24426.7i	−0.184967	−	0.134387i	−0.676416	+	0.736520i	$0.736468\pi$
$128$	−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	−0.945679	−	0.325103i	$-0.894601\pi$
$131$	2058.87	−	6336.54i	0.0104821	−	0.0322607i	0.956161	+	0.292842i	$0.0946011\pi$
$132$	−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	−0.562093	+	0.827074i	$0.690004\pi$
$137$	−334446.	+	242989.i	−1.52238	+	1.10608i	−0.960290	+	0.279003i	$0.909996\pi$
$138$	−9728.59	+	7068.24i	−0.0434863	+	0.0315946i
$139$	124893.	+	90740.0i	0.548278	+	0.398347i	0.827150	−	0.561981i	$-0.189961\pi$
$139$	124893.	+	90740.0i	0.548278	+	0.398347i	−0.278872	+	0.960328i	$0.589961\pi$
$140$	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	−0.488350	−	0.872648i	$-0.662401\pi$
$163$	64680.2	−	46992.9i	0.190679	−	0.138536i	0.679029	+	0.734112i	$0.262401\pi$
$164$	−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	−0.727927	−	0.685655i	$-0.759516\pi$
$167$	95145.6	−	292828.i	0.263996	−	0.812496i	0.991923	−	0.126841i	$-0.0404840\pi$
$168$	−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	0.542010	−	0.840372i	$-0.317663\pi$
$173$	−35326.6	−	25666.3i	−0.0897401	−	0.0652000i	−0.631751	+	0.775172i	$0.717663\pi$
$174$	−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	−0.985703	−	0.168491i	$-0.946111\pi$
$179$	−123155.	−	379032.i	−0.287289	−	0.884185i	0.698414	−	0.715694i	$-0.253889\pi$
$180$	72071.3	−	7384.20i	0.165799	−	0.0169872i
$181$	131424.	−	404482.i	0.298180	−	0.917703i	−0.683955	−	0.729524i	$-0.739742\pi$
$181$	131424.	−	404482.i	0.298180	−	0.917703i	0.982135	−	0.188179i	$-0.0602585\pi$
$182$	−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	−0.130485	−	0.991450i	$-0.541654\pi$
$191$	389284.	−	282832.i	0.772118	−	0.560976i	0.902603	+	0.430474i	$0.141654\pi$
$192$	−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	−0.999979	−	0.00642489i	$-0.997955\pi$
$197$	−106085.	−	326497.i	−0.194756	−	0.599396i	0.805224	−	0.592971i	$-0.202045\pi$
$198$	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	−0.982997	−	0.183619i	$-0.941219\pi$
$211$	−945090.	−	686648.i	−1.46139	−	1.06176i	−0.478395	−	0.878145i	$-0.658781\pi$
$212$	−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	0.960452	−	0.278445i	$-0.0898188\pi$
$223$	736992.	+	535456.i	0.992432	+	0.721044i	0.0319796	+	0.999489i	$0.489819\pi$
$224$	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	0.625321	−	0.780368i	$-0.284968\pi$
$227$	59300.2	+	43084.1i	0.0763821	+	0.0554948i	−0.548939	+	0.835862i	$0.684968\pi$
$228$	45473.4	+	139953.i	0.0579322	+	0.178297i
$229$	−13088.2	−	40281.2i	−0.0164926	−	0.0507591i	0.942472	−	0.334287i	$-0.108495\pi$
$229$	−13088.2	−	40281.2i	−0.0164926	−	0.0507591i	−0.958964	+	0.283527i	$0.908495\pi$
$230$	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	−0.967134	−	0.254269i	$-0.918165\pi$
$233$	−29211.7	+	89904.3i	−0.0352506	+	0.108490i	0.931883	+	0.362759i	$0.118165\pi$
$234$	−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	0.232946	−	0.972490i	$-0.425164\pi$
$239$	−547470.	−	397760.i	−0.619963	−	0.450429i	−0.852909	+	0.522060i	$0.825164\pi$
$240$	−128127.	+	13127.5i	−0.143586	+	0.0147114i
$241$	102845.	−	74721.5i	0.114062	−	0.0828710i	−0.529292	−	0.848440i	$-0.677542\pi$
$241$	102845.	−	74721.5i	0.114062	−	0.0828710i	0.643354	+	0.765569i	$0.277542\pi$
$242$	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	−0.0750069	−	0.997183i	$-0.523898\pi$
$263$	953688.	−	692895.i	0.850192	−	0.617701i	0.925199	+	0.379482i	$0.123898\pi$
$264$	−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	0.766193	+	0.642611i	$0.222149\pi$
$269$	−274612.	+	845170.i	−0.231387	+	0.712137i	−0.997580	+	0.0695260i	$0.977851\pi$
$270$	−140956.	−	81874.1i	−0.117673	−	0.0683498i
$271$	−225504.	−	694028.i	−0.186522	−	0.574056i	0.813449	−	0.581636i	$-0.197587\pi$
$271$	−225504.	−	694028.i	−0.186522	−	0.574056i	−0.999971	+	0.00758016i	$0.997587\pi$
$272$	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	0.999691	+	0.0248509i	$0.00791111\pi$
$277$	1.70131e6	+	1.23608e6i	1.33225	+	0.967934i	0.332556	+	0.943083i	$0.392089\pi$
$278$	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	−0.988073	−	0.153989i	$-0.950788\pi$
$281$	−129971.	+	400008.i	−0.0981927	+	0.302206i	0.889880	+	0.456195i	$0.150788\pi$
$282$	−792297.			−0.593287
$283$	−462253.	+	1.42267e6i	−0.343094	+	1.05594i	0.619502	+	0.784995i	$0.287335\pi$
$283$	−462253.	+	1.42267e6i	−0.343094	+	1.05594i	−0.962596	+	0.270941i	$0.912665\pi$
$284$	−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	−0.0759417	−	0.997112i	$-0.524196\pi$
$311$	−1.78709e6	−	1.29840e6i	−1.04772	−	0.761212i	−0.971777	+	0.235900i	$0.924196\pi$
$312$	435966.	−	316748.i	0.253552	−	0.184216i
$313$	−1.61064e6	+	1.17020e6i	−0.929262	+	0.675148i	−0.945812	−	0.324715i	$-0.894732\pi$
$313$	−1.61064e6	+	1.17020e6i	−0.929262	+	0.675148i	0.0165503	+	0.999863i	$0.494732\pi$
$314$	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	−0.855646	−	0.517562i	$-0.826840\pi$
$317$	251916.	−	775316.i	0.140801	−	0.433342i	0.996447	+	0.0842198i	$0.0268398\pi$
$318$	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	−0.663185	−	0.748456i	$-0.730796\pi$
$331$	624446.	−	1.92185e6i	0.313274	−	0.964159i	0.976459	−	0.215703i	$-0.0692044\pi$
$332$	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	−0.898085	−	0.439822i	$-0.855042\pi$
$337$	−1.57889e6	+	1.14713e6i	−0.757314	+	0.550221i	0.140772	+	0.990042i	$0.455042\pi$
$338$	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	0.862946	+	0.505296i	$0.168617\pi$
$347$	1.03583e6	+	3.18797e6i	0.461814	+	1.42132i	−0.401132	+	0.916020i	$0.631383\pi$
$348$	−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	0.997716	−	0.0675452i	$-0.0215167\pi$
$353$	353156.	+	1.08690e6i	0.150845	+	0.464252i	−0.846871	+	0.531798i	$0.821517\pi$
$354$	−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	−0.475173	−	0.879892i	$-0.657614\pi$
$359$	524574.	−	381125.i	0.214818	−	0.156074i	0.689991	+	0.723818i	$0.257614\pi$
$360$	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	0.623682	+	0.781678i	$0.285636\pi$
$367$	−878185.	+	2.70278e6i	−0.340346	+	1.04748i	−0.964028	+	0.265800i	$0.914364\pi$
$368$	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	0.0499701	−	0.998751i	$-0.484087\pi$
$373$	−2.37656e6	−	1.72667e6i	−0.884457	−	0.642595i	−0.934427	+	0.356155i	$0.884087\pi$
$374$	−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	−0.999193	−	0.0401583i	$-0.987214\pi$
$379$	−599640.	−	1.84550e6i	−0.214433	−	0.659958i	0.784760	−	0.619800i	$-0.212786\pi$
$380$	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	−0.565793	−	0.824547i	$-0.691430\pi$
$383$	1.08113e6	−	3.32737e6i	0.376600	−	1.15906i	0.942393	−	0.334508i	$-0.108570\pi$
$384$	−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	0.739138	−	0.673554i	$-0.235233\pi$
$389$	975806.	+	708965.i	0.326956	+	0.237548i	−0.412182	+	0.911102i	$0.635233\pi$
$390$	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	0.996789	−	0.0800671i	$-0.0255135\pi$
$397$	450034.	+	1.38506e6i	0.143308	+	0.441055i	−0.853482	+	0.521122i	$0.825513\pi$
$398$	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	−0.696776	−	0.717288i	$-0.745383\pi$
$409$	−777797.	+	565103.i	−0.229910	+	0.167040i	0.466866	+	0.884328i	$0.345383\pi$
$410$	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	−0.992872	−	0.119189i	$-0.961971\pi$
$419$	−429671.	+	1.32239e6i	−0.119564	+	0.367981i	0.873307	+	0.487170i	$0.161971\pi$
$420$	98554.6	−	457764.i	0.0272617	−	0.126625i
$421$	−1.96008e6	−	6.03249e6i	−0.538974	−	1.65879i	−0.734903	−	0.678173i	$-0.762772\pi$
$421$	−1.96008e6	−	6.03249e6i	−0.538974	−	1.65879i	0.195929	−	0.980618i	$-0.437228\pi$
$422$	−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	0.729655	+	0.683815i	$0.239681\pi$
$431$	−1.01266e6	+	3.11664e6i	−0.262585	+	0.808152i	−0.992240	+	0.124337i	$0.960319\pi$
$432$	−186624.			−0.0481125
$433$	−219911.	+	676818.i	−0.0563674	+	0.173481i	−0.975276	−	0.220989i	$-0.929072\pi$
$433$	−219911.	+	676818.i	−0.0563674	+	0.173481i	0.918909	+	0.394470i	$0.129072\pi$
$434$	−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	0.993046	+	0.117730i	$0.0375616\pi$
$439$	5.70111e6	+	4.14210e6i	1.41188	+	1.02579i	0.418835	+	0.908062i	$0.362438\pi$
$440$	−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	−0.190989	−	0.981592i	$-0.561170\pi$
$461$	−5.40060e6	−	3.92376e6i	−1.18356	−	0.859905i	−0.992569	+	0.121687i	$0.961170\pi$
$462$	158116.	−	114878.i	0.0344645	−	0.0250399i
$463$	−4.98147e6	+	3.61925e6i	−1.07995	+	0.784632i	−0.977675	−	0.210124i	$-0.932613\pi$
$463$	−4.98147e6	+	3.61925e6i	−1.07995	+	0.784632i	−0.102279	+	0.994756i	$0.532613\pi$
$464$	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	−0.912116	−	0.409932i	$-0.865553\pi$
$467$	314603.	−	968249.i	0.0667530	−	0.205445i	0.978869	+	0.204487i	$0.0655526\pi$
$468$	−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	0.966678	+	0.255994i	$0.0824027\pi$
$479$	1.68267e6	+	5.17872e6i	0.335089	+	1.03130i	−0.631590	+	0.775303i	$0.717597\pi$
$480$	−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	−0.486868	−	0.873475i	$-0.661861\pi$
$487$	1.01226e6	−	735448.i	0.193405	−	0.140517i	0.680274	+	0.732958i	$0.261861\pi$
$488$	−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	−0.843300	−	0.537443i	$-0.819390\pi$
$491$	−3.16650e6	+	2.30060e6i	−0.592756	+	0.430662i	0.250544	+	0.968105i	$0.419390\pi$
$492$	−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	0.808090	+	0.589060i	$0.200502\pi$
$503$	2.84045e6	+	8.74199e6i	0.500572	+	1.54060i	−0.307518	+	0.951542i	$0.599498\pi$
$504$	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	−0.338425	−	0.940993i	$-0.609894\pi$
$509$	2.64162e6	−	1.91925e6i	0.451934	−	0.328349i	0.790359	+	0.612644i	$0.209894\pi$
$510$	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	0.995719	−	0.0924298i	$-0.0294634\pi$
$521$	841610.	+	2.59021e6i	0.135837	+	0.418062i	−0.859883	+	0.510492i	$0.829463\pi$
$522$	639029.	+	1.96673e6i	0.102646	+	0.315913i
$523$	5.09615e6	+	3.70257e6i	0.814682	+	0.591901i	0.915184	−	0.403036i	$-0.132045\pi$
$523$	5.09615e6	+	3.70257e6i	0.814682	+	0.591901i	−0.100502	+	0.994937i	$0.532045\pi$
$524$	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	−0.993432	−	0.114421i	$-0.963499\pi$
$541$	−8.11191e6	+	5.89365e6i	−1.19160	+	0.865747i	−0.198166	+	0.980168i	$0.563499\pi$
$542$	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	0.884630	−	0.466294i	$-0.154411\pi$
$547$	−735698.	−	2.26425e6i	−0.105131	−	0.323560i	−0.989761	+	0.142733i	$0.954411\pi$
$548$	−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	−0.894715	−	0.446638i	$-0.852621\pi$
$563$	−5.61376e6	+	4.07863e6i	−0.746419	+	0.542305i	0.148296	+	0.988943i	$0.452621\pi$
$564$	−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	0.193148	+	0.981170i	$0.438130\pi$
$569$	−4.16905e6	+	1.28310e7i	−0.539829	+	1.66142i	−0.732977	+	0.680253i	$0.761870\pi$
$570$	−2.04584e6	+	209611.i	−0.263745	+	0.0270225i
$571$	2.15894e6	+	6.64453e6i	0.277108	+	0.852852i	0.988654	+	0.150212i	$0.0479956\pi$
$571$	2.15894e6	+	6.64453e6i	0.277108	+	0.852852i	−0.711545	+	0.702640i	$0.752004\pi$
$572$	−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	0.694724	−	0.719276i	$-0.255526\pi$
$577$	1.80205e6	+	1.30926e6i	0.225334	+	0.163715i	−0.469391	+	0.882991i	$0.655526\pi$
$578$	−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	0.180090	−	0.983650i	$-0.442361\pi$
$587$	9.77787e6	−	7.10404e6i	1.17125	−	0.850962i	0.991158	+	0.132688i	$0.0423610\pi$
$588$	−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	−0.259388	−	0.965773i	$-0.583521\pi$
$613$	5.38642e6	−	3.91347e6i	0.578961	−	0.420640i	0.838349	+	0.545133i	$0.183521\pi$
$614$	−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	−0.890065	−	0.455833i	$-0.849341\pi$
$617$	926178.	−	2.85048e6i	0.0979449	−	0.301443i	0.988010	+	0.154390i	$0.0493413\pi$
$618$	3.43741e6			0.362043
$619$	−3.99729e6	+	1.23024e7i	−0.419313	+	1.29051i	0.489022	+	0.872271i	$0.337354\pi$
$619$	−3.99729e6	+	1.23024e7i	−0.419313	+	1.29051i	−0.908335	+	0.418242i	$0.862646\pi$
$620$	−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	−0.956151	−	0.292875i	$-0.905388\pi$
$631$	−104627.	+	322009.i	−0.0104609	+	0.0321955i	0.945690	+	0.325070i	$0.105388\pi$
$632$	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	−0.692089	−	0.721813i	$-0.743309\pi$
$641$	−2.28309e6	+	1.65876e6i	−0.219471	+	0.159455i	0.472618	+	0.881268i	$0.343309\pi$
$642$	−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	0.915409	−	0.402526i	$-0.131868\pi$
$647$	−657729.	−	2.02428e6i	−0.0617713	−	0.190112i	−0.977180	+	0.212413i	$0.931868\pi$
$648$	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	−0.850607	−	0.525802i	$-0.823765\pi$
$653$	−5.13776e6	−	1.58124e7i	−0.471510	−	1.45116i	0.379097	−	0.925357i	$-0.376235\pi$
$654$	−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	0.421586	−	0.906788i	$-0.361474\pi$
$659$	1.57669e7	−	1.14553e7i	1.41427	−	1.02753i	0.992684	−	0.120739i	$-0.0385265\pi$
$660$	559637.	−	501251.i	0.0500088	−	0.0447915i
$661$	4.42168e6	+	3.21254e6i	0.393626	+	0.285986i	0.766940	−	0.641719i	$-0.221778\pi$
$661$	4.42168e6	+	3.21254e6i	0.393626	+	0.285986i	−0.373314	+	0.927705i	$0.621778\pi$
$662$	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	0.637030	−	0.770839i	$-0.280163\pi$
$673$	1.18406e6	+	860272.i	0.100771	+	0.0732147i	−0.536259	+	0.844054i	$0.680163\pi$
$674$	−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	0.877956	−	0.478741i	$-0.158907\pi$
$677$	8.27561e6	+	6.01258e6i	0.693950	+	0.504184i	−0.184006	+	0.982925i	$0.558907\pi$
$678$	−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	−0.928265	−	0.371921i	$-0.878699\pi$
$683$	503829.	−	1.55063e6i	0.0413268	−	0.127191i	0.969591	+	0.244730i	$0.0786993\pi$
$684$	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	−0.605296	−	0.796001i	$-0.706945\pi$
$691$	−443078.	+	321915.i	−0.0353009	+	0.0256476i	0.569995	+	0.821648i	$0.306945\pi$
$692$	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	0.278714	−	0.960374i	$-0.410092\pi$
$709$	1.71087e7	−	1.24302e7i	1.27821	−	0.928675i	0.999497	+	0.0316993i	$0.0100919\pi$
$710$	−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	0.744910	+	0.667165i	$0.232492\pi$
$719$	−3.46387e6	+	1.06607e7i	−0.249885	+	0.769066i	−0.994795	+	0.101901i	$0.967508\pi$
$720$	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	0.476422	−	0.879217i	$-0.341933\pi$
$727$	−3.02885e6	−	2.20059e6i	−0.212540	−	0.154420i	−0.688962	+	0.724797i	$0.741933\pi$
$728$	−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	−0.974806	−	0.223055i	$-0.928397\pi$
$733$	−800978.	+	2.46516e6i	−0.0550631	+	0.169467i	0.919743	+	0.392522i	$0.128397\pi$
$734$	−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	−0.999741	−	0.0227620i	$-0.992754\pi$
$739$	−1.97501e7	−	1.43493e7i	−1.33033	−	0.966538i	−0.330585	−	0.943776i	$-0.607246\pi$
$740$	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	0.802312	−	0.596905i	$-0.203603\pi$
$761$	7.70910e6	+	5.60099e6i	0.482550	+	0.350593i	−0.319762	+	0.947498i	$0.603603\pi$
$762$	−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	0.698248	+	0.715856i	$0.253963\pi$
$769$	−4.71332e6	+	1.45061e7i	−0.287416	+	0.884576i	−0.985664	+	0.168720i	$0.946037\pi$
$770$	−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	0.733947	−	0.679207i	$-0.237676\pi$
$773$	5.22952e6	+	3.79947e6i	0.314784	+	0.228704i	−0.419163	+	0.907911i	$0.637676\pi$
$774$	−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	−0.718347	−	0.695685i	$-0.755101\pi$
$787$	−4.84242e6	+	3.51822e6i	−0.278693	+	0.202482i	0.439654	+	0.898167i	$0.355101\pi$
$788$	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	0.932562	−	0.361010i	$-0.117568\pi$
$797$	−611379.	−	1.88163e6i	−0.0340930	−	0.104927i	−0.966655	+	0.256083i	$0.917568\pi$
$798$	−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	−0.510504	+	0.859875i	$0.670541\pi$
$809$	−2.76633e7	+	2.00986e7i	−1.48605	+	1.07968i	−0.975544	+	0.219802i	$0.929459\pi$
$810$	−308781.	+	1.43422e6i	−0.0165363	+	0.0768075i
$811$	−1.52709e7	−	1.10949e7i	−0.815288	−	0.592342i	0.100071	−	0.994980i	$-0.468093\pi$
$811$	−1.52709e7	−	1.10949e7i	−0.815288	−	0.592342i	−0.915359	+	0.402639i	$0.868093\pi$
$812$	−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	0.999985	−	0.00542454i	$-0.00172669\pi$
$821$	3.62689e6	+	1.11624e7i	0.187792	+	0.577964i	−0.812194	+	0.583388i	$0.801727\pi$
$822$	4.59889e6	+	1.41539e7i	0.237396	+	0.730629i
$823$	9.28088e6	+	6.74295e6i	0.477628	+	0.347017i	0.800407	−	0.599458i	$-0.204617\pi$
$823$	9.28088e6	+	6.74295e6i	0.477628	+	0.347017i	−0.322779	+	0.946474i	$0.604617\pi$
$824$	−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	0.472194	−	0.881495i	$-0.343462\pi$
$827$	−4.33176e6	−	3.14721e6i	−0.220242	−	0.160015i	−0.692436	+	0.721480i	$0.743462\pi$
$828$	133776.	+	411719.i	0.00678112	+	0.0208701i
$829$	−1.46447e6	−	4.50717e6i	−0.0740105	−	0.227781i	0.907207	−	0.420684i	$-0.138210\pi$
$829$	−1.46447e6	−	4.50717e6i	−0.0740105	−	0.227781i	−0.981218	+	0.192903i	$0.938210\pi$
$830$	−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	0.999441	+	0.0334316i	$0.0106436\pi$
$839$	2.73235e7	+	1.98517e7i	1.34008	+	0.973626i	0.340640	+	0.940194i	$0.389356\pi$
$840$	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	−0.994261	−	0.106977i	$-0.965883\pi$
$853$	−5.37146e6	−	1.65317e7i	−0.252767	−	0.777936i	0.741495	−	0.670959i	$-0.234117\pi$
$854$	−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	−0.950341	−	0.311209i	$-0.899266\pi$
$859$	−2.05025e7	+	1.48960e7i	−0.948035	+	0.688788i	0.00230613	+	0.999997i	$0.499266\pi$
$860$	−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	−0.676125	−	0.736787i	$-0.736342\pi$
$863$	−4.03302e6	+	2.93016e6i	−0.184333	+	0.133926i	0.491792	+	0.870713i	$0.336342\pi$
$864$	−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	0.241484	−	0.970405i	$-0.422366\pi$
$877$	−1.38212e7	−	1.00417e7i	−0.606803	−	0.440869i	−0.848287	+	0.529536i	$0.822366\pi$
$878$	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	0.660320	+	0.750984i	$0.270421\pi$
$881$	−7.26397e6	+	2.23562e7i	−0.315307	+	0.970417i	−0.975628	+	0.219432i	$0.929579\pi$
$882$	4.34916e6			0.188250
$883$	−3.36563e6	+	1.03584e7i	−0.145266	+	0.447084i	−0.997045	−	0.0768176i	$-0.975524\pi$
$883$	−3.36563e6	+	1.03584e7i	−0.145266	+	0.447084i	0.851779	+	0.523902i	$0.175524\pi$
$884$	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	−0.469507	+	0.882929i	$0.655568\pi$
$887$	−3.40773e7	+	2.47586e7i	−1.45431	+	1.05662i	−0.984801	+	0.173688i	$0.944432\pi$
$888$	−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	0.162163	−	0.986764i	$-0.448153\pi$
$911$	−1.81907e7	−	1.32163e7i	−0.726194	−	0.527611i	−0.888357	+	0.459153i	$0.848153\pi$
$912$	−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	0.506183	+	0.862426i	$0.331056\pi$
$919$	−1.05036e7	+	3.23266e7i	−0.410249	+	1.26262i	−0.916432	+	0.400191i	$0.868944\pi$
$920$	−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	−0.948456	−	0.316908i	$-0.897355\pi$
$929$	−9.66482e6	−	2.97453e7i	−0.367413	−	1.13078i	0.581043	−	0.813873i	$-0.302645\pi$
$930$	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	−0.750123	−	0.661298i	$-0.770006\pi$
$937$	−9.48669e6	+	6.89248e6i	−0.352993	+	0.256464i	0.397131	+	0.917762i	$0.370006\pi$
$938$	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	−0.0701261	−	0.997538i	$-0.522340\pi$
$941$	2.32763e7	−	1.69112e7i	0.856919	−	0.622588i	0.927045	+	0.374950i	$0.122340\pi$
$942$	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	−0.980510	−	0.196468i	$-0.937053\pi$
$947$	−8.35502e6	−	2.57141e7i	−0.302742	−	0.931744i	0.677768	−	0.735276i	$-0.262947\pi$
$948$	−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	−0.895996	−	0.444062i	$-0.853537\pi$
$953$	−1.21157e7	−	3.72884e7i	−0.432133	−	1.32997i	0.463863	−	0.885907i	$-0.346463\pi$
$954$	−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	0.360552	+	0.932739i	$0.382588\pi$
$967$	−1.39398e7	+	4.29023e7i	−0.479391	+	1.47541i	−0.839943	+	0.542675i	$0.817412\pi$
$968$	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	−0.939971	−	0.341254i	$-0.889148\pi$
$971$	−1.11673e7	−	3.43695e7i	−0.380103	−	1.16984i	0.559868	−	0.828582i	$-0.310852\pi$
$972$	−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	0.793805	−	0.608173i	$-0.208097\pi$
$977$	1.37452e7	+	9.98650e6i	0.460697	+	0.334716i	−0.333107	+	0.942889i	$0.608097\pi$
$978$	−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	−0.474214	−	0.880409i	$-0.657268\pi$
$983$	1.29341e7	−	3.98070e7i	0.426925	−	1.31394i	0.901139	−	0.433530i	$-0.142732\pi$
$984$	−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	−0.196564	−	0.980491i	$-0.562978\pi$
$991$	2.08744e7	−	1.51662e7i	0.675197	−	0.490560i	0.871761	+	0.489931i	$0.162978\pi$
$992$	−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	−0.999867	−	0.0162886i	$-0.994815\pi$
$997$	−6.29392e6	−	1.93707e7i	−0.200532	−	0.617174i	0.799335	−	0.600885i	$-0.205185\pi$
$998$	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.91.1	yes	20
25.11	even	5	inner	150.6.g.a.61.1	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.6.g.a.61.1	✓	20	25.11	even	5	inner
150.6.g.a.91.1	yes	20	1.1	even	1	trivial

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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