LMFDB - Embedded newform 150.6.g.a.121.2

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			121.2
Root			$0.500000 + 187.698i$ of defining polynomial
Character	$\chi$	$=$	150.121
Dual form			150.6.g.a.31.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.23607 + 3.80423i) q^{2} +(7.28115 + 5.29007i) q^{3} +(-12.9443 - 9.40456i) q^{4} +(-49.2840 + 26.3835i) q^{5} +(-29.1246 + 21.1603i) q^{6} +255.057 q^{7} +(51.7771 - 37.6183i) q^{8} +(25.0304 + 77.0356i) q^{9} +O(q^{10})$	\(q+(-1.23607 + 3.80423i) q^{2} +(7.28115 + 5.29007i) q^{3} +(-12.9443 - 9.40456i) q^{4} +(-49.2840 + 26.3835i) q^{5} +(-29.1246 + 21.1603i) q^{6} +255.057 q^{7} +(51.7771 - 37.6183i) q^{8} +(25.0304 + 77.0356i) q^{9} +(-39.4504 - 220.099i) q^{10} +(149.137 - 458.997i) q^{11} +(-44.4984 - 136.952i) q^{12} +(-307.729 - 947.092i) q^{13} +(-315.268 + 970.296i) q^{14} +(-498.415 - 68.6134i) q^{15} +(79.1084 + 243.470i) q^{16} +(87.9029 - 63.8652i) q^{17} -324.000 q^{18} +(673.270 - 489.159i) q^{19} +(886.071 + 121.979i) q^{20} +(1857.11 + 1349.27i) q^{21} +(1561.79 + 1134.70i) q^{22} +(-343.025 + 1055.72i) q^{23} +576.000 q^{24} +(1732.82 - 2600.57i) q^{25} +3983.33 q^{26} +(-225.273 + 693.320i) q^{27} +(-3301.53 - 2398.70i) q^{28} +(5867.46 + 4262.96i) q^{29} +(877.095 - 1811.27i) q^{30} +(3328.16 - 2418.05i) q^{31} -1024.00 q^{32} +(3514.02 - 2553.08i) q^{33} +(134.304 + 413.344i) q^{34} +(-12570.2 + 6729.30i) q^{35} +(400.486 - 1232.57i) q^{36} +(2350.31 + 7233.51i) q^{37} +(1028.67 + 3165.91i) q^{38} +(2769.56 - 8523.83i) q^{39} +(-1559.28 + 3220.04i) q^{40} +(-1151.94 - 3545.30i) q^{41} +(-7428.45 + 5397.08i) q^{42} +5702.64 q^{43} +(-6247.14 + 4538.81i) q^{44} +(-3266.06 - 3136.23i) q^{45} +(-3592.20 - 2609.89i) q^{46} +(-19949.3 - 14494.0i) q^{47} +(-711.975 + 2191.23i) q^{48} +48247.3 q^{49} +(7751.26 + 9806.53i) q^{50} +977.886 q^{51} +(-4923.66 + 15153.5i) q^{52} +(19254.4 + 13989.2i) q^{53} +(-2359.09 - 1713.98i) q^{54} +(4759.87 + 26556.0i) q^{55} +(13206.1 - 9594.82i) q^{56} +7489.87 q^{57} +(-23469.8 + 17051.8i) q^{58} +(5402.53 + 16627.3i) q^{59} +(5806.34 + 5575.52i) q^{60} +(-6698.62 + 20616.2i) q^{61} +(5084.98 + 15650.0i) q^{62} +(6384.18 + 19648.5i) q^{63} +(1265.73 - 3895.53i) q^{64} +(40153.7 + 38557.5i) q^{65} +(5368.94 + 16523.9i) q^{66} +(40806.3 - 29647.5i) q^{67} -1738.46 q^{68} +(-8082.46 + 5872.25i) q^{69} +(-10062.1 - 56137.9i) q^{70} +(-14425.4 - 10480.6i) q^{71} +(4193.94 + 3047.08i) q^{72} +(1963.96 - 6044.46i) q^{73} -30423.0 q^{74} +(26374.1 - 9768.38i) q^{75} -13315.3 q^{76} +(38038.6 - 117071. i) q^{77} +(29003.2 + 21072.1i) q^{78} +(-78631.1 - 57128.8i) q^{79} +(-10322.4 - 9912.04i) q^{80} +(-5307.96 + 3856.46i) q^{81} +14911.0 q^{82} +(-97382.0 + 70752.2i) q^{83} +(-11349.7 - 34930.7i) q^{84} +(-2647.22 + 5466.72i) q^{85} +(-7048.86 + 21694.2i) q^{86} +(20170.5 + 62078.5i) q^{87} +(-9544.78 - 29375.8i) q^{88} +(-18216.4 + 56064.3i) q^{89} +(15968.0 - 8548.25i) q^{90} +(-78488.5 - 241563. i) q^{91} +(14368.8 - 10439.6i) q^{92} +37024.5 q^{93} +(79797.1 - 57976.0i) q^{94} +(-20275.7 + 41870.9i) q^{95} +(-7455.90 - 5417.03i) q^{96} +(-80972.3 - 58829.8i) q^{97} +(-59636.9 + 183544. i) q^{98} +39092.1 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 $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−1.23607	+	3.80423i	−0.218508	+	0.672499i
$2$	−1.23607	+	3.80423i	−0.218508	+	0.672499i
$3$	7.28115	+	5.29007i	0.467086	+	0.339358i
$3$	7.28115	+	5.29007i	0.467086	+	0.339358i
$4$	−12.9443	−	9.40456i	−0.404508	−	0.293893i
$5$	−49.2840	+	26.3835i	−0.881619	+	0.471962i
$5$	−49.2840	+	26.3835i	−0.881619	+	0.471962i
$6$	−29.1246	+	21.1603i	−0.330280	+	0.239962i
$7$	255.057			1.96740			0.983700	−	0.179815i	$-0.0575499\pi$
$7$	255.057			1.96740			0.983700	+	0.179815i	$0.0575499\pi$
$8$	51.7771	−	37.6183i	0.286031	−	0.207813i
$9$	25.0304	+	77.0356i	0.103006	+	0.317019i
$10$	−39.4504	−	220.099i	−0.124753	−	0.696015i
$11$	149.137	−	458.997i	0.371625	−	1.14374i	−0.574103	−	0.818783i	$-0.694649\pi$
$11$	149.137	−	458.997i	0.371625	−	1.14374i	0.945728	−	0.324960i	$-0.105351\pi$
$12$	−44.4984	−	136.952i	−0.0892055	−	0.274546i
$13$	−307.729	−	947.092i	−0.505021	−	1.55430i	−0.800735	−	0.599019i	$-0.795557\pi$
$13$	−307.729	−	947.092i	−0.505021	−	1.55430i	0.295713	−	0.955277i	$-0.404443\pi$
$14$	−315.268	+	970.296i	−0.429893	+	1.32307i
$15$	−498.415	−	68.6134i	−0.571956	−	0.0787374i
$16$	79.1084	+	243.470i	0.0772542	+	0.237764i
$17$	87.9029	−	63.8652i	0.0737702	−	0.0535972i	−0.550289	−	0.834974i	$-0.685482\pi$
$17$	87.9029	−	63.8652i	0.0737702	−	0.0535972i	0.624059	+	0.781377i	$0.285482\pi$
$18$	−324.000			−0.235702
$19$	673.270	−	489.159i	0.427864	−	0.310861i	−0.352930	−	0.935650i	$-0.614815\pi$
$19$	673.270	−	489.159i	0.427864	−	0.310861i	0.780794	+	0.624788i	$0.214815\pi$
$20$	886.071	+	121.979i	0.495328	+	0.0681885i
$21$	1857.11	+	1349.27i	0.918946	+	0.667653i
$22$	1561.79	+	1134.70i	0.687962	+	0.499834i
$23$	−343.025	+	1055.72i	−0.135209	+	0.416131i	−0.995622	−	0.0934658i	$-0.970205\pi$
$23$	−343.025	+	1055.72i	−0.135209	+	0.416131i	0.860413	+	0.509597i	$0.170205\pi$
$24$	576.000			0.204124
$25$	1732.82	−	2600.57i	0.554503	−	0.832181i
$26$	3983.33			1.15561
$27$	−225.273	+	693.320i	−0.0594703	+	0.183031i
$28$	−3301.53	−	2398.70i	−0.795830	−	0.578205i
$29$	5867.46	+	4262.96i	1.29555	+	0.941274i	0.999902	−	0.0140221i	$-0.00446352\pi$
$29$	5867.46	+	4262.96i	1.29555	+	0.941274i	0.295651	+	0.955296i	$0.404464\pi$
$30$	877.095	−	1811.27i	0.177928	−	0.367435i
$31$	3328.16	−	2418.05i	0.622014	−	0.451920i	−0.231610	−	0.972809i	$-0.574399\pi$
$31$	3328.16	−	2418.05i	0.622014	−	0.451920i	0.853625	+	0.520889i	$0.174399\pi$
$32$	−1024.00			−0.176777
$33$	3514.02	−	2553.08i	0.561719	−	0.408113i
$34$	134.304	+	413.344i	0.0199247	+	0.0613218i
$35$	−12570.2	+	6729.30i	−1.73450	+	0.928539i
$36$	400.486	−	1232.57i	0.0515028	−	0.158509i
$37$	2350.31	+	7233.51i	0.282241	+	0.868650i	0.987212	+	0.159413i	$0.0509602\pi$
$37$	2350.31	+	7233.51i	0.282241	+	0.868650i	−0.704971	+	0.709236i	$0.749040\pi$
$38$	1028.67	+	3165.91i	0.115562	+	0.355663i
$39$	2769.56	−	8523.83i	0.291574	−	0.897373i
$40$	−1559.28	+	3220.04i	−0.154090	+	0.318208i
$41$	−1151.94	−	3545.30i	−0.107021	−	0.329377i	0.883178	−	0.469037i	$-0.155399\pi$
$41$	−1151.94	−	3545.30i	−0.107021	−	0.329377i	−0.990199	+	0.139660i	$0.955399\pi$
$42$	−7428.45	+	5397.08i	−0.649793	+	0.472102i
$43$	5702.64			0.470333			0.235166	−	0.971955i	$-0.424437\pi$
$43$	5702.64			0.470333			0.235166	+	0.971955i	$0.424437\pi$
$44$	−6247.14	+	4538.81i	−0.486463	+	0.353436i
$45$	−3266.06	−	3136.23i	−0.240433	−	0.230875i
$46$	−3592.20	−	2609.89i	−0.250303	−	0.181856i
$47$	−19949.3	−	14494.0i	−1.31729	−	0.957070i	−0.999962	−	0.00875553i	$-0.997213\pi$
$47$	−19949.3	−	14494.0i	−1.31729	−	0.957070i	−0.317332	−	0.948314i	$-0.602787\pi$
$48$	−711.975	+	2191.23i	−0.0446028	+	0.137273i
$49$	48247.3			2.87067
$50$	7751.26	+	9806.53i	0.438477	+	0.554741i
$51$	977.886			0.0526457
$52$	−4923.66	+	15153.5i	−0.252511	+	0.777148i
$53$	19254.4	+	13989.2i	0.941544	+	0.684072i	0.948792	−	0.315902i	$-0.102307\pi$
$53$	19254.4	+	13989.2i	0.941544	+	0.684072i	−0.00724781	+	0.999974i	$0.502307\pi$
$54$	−2359.09	−	1713.98i	−0.110093	−	0.0799874i
$55$	4759.87	+	26556.0i	0.212172	+	1.18374i
$56$	13206.1	−	9594.82i	0.562737	−	0.408852i
$57$	7489.87			0.305342
$58$	−23469.8	+	17051.8i	−0.916094	+	0.665581i
$59$	5402.53	+	16627.3i	0.202054	+	0.621857i	0.999822	+	0.0188926i	$0.00601407\pi$
$59$	5402.53	+	16627.3i	0.202054	+	0.621857i	−0.797768	+	0.602965i	$0.793986\pi$
$60$	5806.34	+	5575.52i	0.208221	+	0.199944i
$61$	−6698.62	+	20616.2i	−0.230495	+	0.709390i	0.767193	+	0.641417i	$0.221653\pi$
$61$	−6698.62	+	20616.2i	−0.230495	+	0.709390i	−0.997687	+	0.0679727i	$0.978347\pi$
$62$	5084.98	+	15650.0i	0.168000	+	0.517052i
$63$	6384.18	+	19648.5i	0.202653	+	0.623703i
$64$	1265.73	−	3895.53i	0.0386271	−	0.118882i
$65$	40153.7	+	38557.5i	1.17881	+	1.13195i
$66$	5368.94	+	16523.9i	0.151715	+	0.466931i
$67$	40806.3	−	29647.5i	1.11056	−	0.806866i	0.127804	−	0.991799i	$-0.459207\pi$
$67$	40806.3	−	29647.5i	1.11056	−	0.806866i	0.982751	+	0.184934i	$0.0592070\pi$
$68$	−1738.46			−0.0455925
$69$	−8082.46	+	5872.25i	−0.204372	+	0.148485i
$70$	−10062.1	−	56137.9i	−0.245439	−	1.36934i
$71$	−14425.4	−	10480.6i	−0.339610	−	0.246741i	0.404887	−	0.914367i	$-0.367311\pi$
$71$	−14425.4	−	10480.6i	−0.339610	−	0.246741i	−0.744497	+	0.667625i	$0.767311\pi$
$72$	4193.94	+	3047.08i	0.0953436	+	0.0692712i
$73$	1963.96	−	6044.46i	0.0431346	−	0.132755i	−0.927170	−	0.374641i	$-0.877766\pi$
$73$	1963.96	−	6044.46i	0.0431346	−	0.132755i	0.970305	+	0.241886i	$0.0777660\pi$
$74$	−30423.0			−0.645837
$75$	26374.1	−	9768.38i	0.541408	−	0.200525i
$76$	−13315.3			−0.264434
$77$	38038.6	−	117071.i	0.731134	−	2.25020i
$78$	29003.2	+	21072.1i	0.539771	+	0.392166i
$79$	−78631.1	−	57128.8i	−1.41751	−	1.02988i	−0.992176	−	0.124846i	$-0.960156\pi$
$79$	−78631.1	−	57128.8i	−1.41751	−	1.02988i	−0.425335	−	0.905036i	$-0.639844\pi$
$80$	−10322.4	−	9912.04i	−0.180324	−	0.173156i
$81$	−5307.96	+	3856.46i	−0.0898908	+	0.0653095i
$82$	14911.0			0.244890
$83$	−97382.0	+	70752.2i	−1.55161	+	1.12731i	−0.609126	+	0.793074i	$0.708480\pi$
$83$	−97382.0	+	70752.2i	−1.55161	+	1.12731i	−0.942488	+	0.334240i	$0.891520\pi$
$84$	−11349.7	−	34930.7i	−0.175503	−	0.540143i
$85$	−2647.22	+	5466.72i	−0.0397414	+	0.0820691i
$86$	−7048.86	+	21694.2i	−0.102771	+	0.316298i
$87$	20170.5	+	62078.5i	0.285706	+	0.879312i
$88$	−9544.78	−	29375.8i	−0.131389	−	0.404374i
$89$	−18216.4	+	56064.3i	−0.243774	+	0.750259i	0.752062	+	0.659093i	$0.229059\pi$
$89$	−18216.4	+	56064.3i	−0.243774	+	0.750259i	−0.995836	+	0.0911663i	$0.970941\pi$
$90$	15968.0	−	8548.25i	0.207800	−	0.111243i
$91$	−78488.5	−	241563.i	−0.993579	−	3.05792i
$92$	14368.8	−	10439.6i	0.176991	−	0.128592i
$93$	37024.5			0.443897
$94$	79797.1	−	57976.0i	0.931467	−	0.676751i
$95$	−20275.7	+	41870.9i	−0.230498	+	0.475996i
$96$	−7455.90	−	5417.03i	−0.0825700	−	0.0599906i
$97$	−80972.3	−	58829.8i	−0.873790	−	0.634846i	0.0578113	−	0.998328i	$-0.481588\pi$
$97$	−80972.3	−	58829.8i	−0.873790	−	0.634846i	−0.931601	+	0.363482i	$0.881588\pi$
$98$	−59636.9	+	183544.i	−0.627264	+	1.93052i
$99$	39092.1			0.400867
$100$	−46887.3	+	17366.0i	−0.468873	+	0.173660i
$101$	118908.			1.15987			0.579934	−	0.814663i	$-0.303078\pi$
$101$	118908.			1.15987			0.579934	+	0.814663i	$0.303078\pi$
$102$	−1208.73	+	3720.10i	−0.0115035	+	0.0354041i
$103$	130806.	+	95036.4i	1.21489	+	0.882667i	0.995665	−	0.0930081i	$-0.0296483\pi$
$103$	130806.	+	95036.4i	1.21489	+	0.882667i	0.219222	+	0.975675i	$0.429648\pi$
$104$	−51561.2	−	37461.4i	−0.467455	−	0.339626i
$105$	−127124.	−	17500.4i	−1.12527	−	0.154908i
$106$	−77017.7	+	55956.6i	−0.665772	+	0.483712i
$107$	88341.6			0.745944			0.372972	−	0.927843i	$-0.378339\pi$
$107$	88341.6			0.745944			0.372972	+	0.927843i	$0.378339\pi$
$108$	9436.37	−	6855.93i	0.0778477	−	0.0565597i
$109$	−56773.5	−	174731.i	−0.457698	−	1.40865i	−0.867938	−	0.496673i	$-0.834555\pi$
$109$	−56773.5	−	174731.i	−0.457698	−	1.40865i	0.410239	−	0.911978i	$-0.365445\pi$
$110$	−106908.	−	14717.4i	−0.842423	−	0.115971i
$111$	−21152.8	+	65101.6i	−0.162952	+	0.501515i
$112$	20177.2	+	62098.9i	0.151990	+	0.467777i
$113$	−60992.5	−	187716.i	−0.449345	−	1.38294i	−0.877647	−	0.479307i	$-0.840888\pi$
$113$	−60992.5	−	187716.i	−0.449345	−	1.38294i	0.428302	−	0.903636i	$-0.359112\pi$
$114$	−9257.99	+	28493.2i	−0.0667198	+	0.205342i
$115$	−10948.0	−	61080.4i	−0.0771952	−	0.430683i
$116$	−35858.7	−	110362.i	−0.247429	−	0.761507i
$117$	65257.2	−	47412.1i	0.440721	−	0.320203i
$118$	−69931.8			−0.462349
$119$	22420.3	−	16289.3i	0.145136	−	0.105447i
$120$	−28387.6	+	15196.9i	−0.179960	+	0.0963389i
$121$	−58143.5	−	42243.7i	−0.361026	−	0.262300i
$122$	−70148.9	−	50966.1i	−0.426699	−	0.310015i
$123$	10367.4	−	31907.7i	0.0617886	−	0.190166i
$124$	−65821.4			−0.384426
$125$	−16788.4	+	173884.i	−0.0961024	+	0.995371i
$126$	−82638.6			−0.463721
$127$	31515.2	−	96993.8i	0.173385	−	0.533623i	−0.826171	−	0.563419i	$-0.809486\pi$
$127$	31515.2	−	96993.8i	0.173385	−	0.533623i	0.999556	+	0.0297957i	$0.00948568\pi$
$128$	13254.9	+	9630.27i	0.0715077	+	0.0519534i
$129$	41521.8	+	30167.4i	0.219686	+	0.159611i
$130$	−196314.	+	105094.i	−1.01881	+	0.545406i
$131$	180264.	−	130970.i	0.917765	−	0.666795i	−0.0252019	−	0.999682i	$-0.508023\pi$
$131$	180264.	−	130970.i	0.917765	−	0.666795i	0.942967	+	0.332887i	$0.108023\pi$
$132$	−69497.0			−0.347161
$133$	171723.	−	124764.i	0.841779	−	0.611589i
$134$	62346.5	+	191883.i	0.299951	+	0.923154i
$135$	−7189.83	−	40113.1i	−0.0339535	−	0.189431i
$136$	2148.86	−	6613.51i	0.00996233	−	0.0306609i
$137$	34043.8	+	104776.i	0.154966	+	0.476937i	0.998157	−	0.0606766i	$-0.0193258\pi$
$137$	34043.8	+	104776.i	0.154966	+	0.476937i	−0.843191	+	0.537614i	$0.819326\pi$
$138$	−12348.9	−	38006.0i	−0.0551989	−	0.169885i
$139$	−0.00695366	+	0.0214012i	−3.05265e−8	+	9.39508e-8i	−0.951057	−	0.309017i	$-0.900000\pi$
$139$	−0.00695366	+	0.0214012i	−3.05265e−8	+	9.39508e-8i	0.951057	+	0.309017i	$0.100000\pi$
$140$	225999.	+	31111.7i	0.974510	+	0.134154i
$141$	−68579.5	−	211066.i	−0.290500	−	0.894068i
$142$	57701.4	−	41922.5i	0.240141	−	0.174472i
$143$	−480606.			−1.96539
$144$	−16775.8	+	12188.3i	−0.0674181	+	0.0489821i
$145$	−401643.	−	55291.6i	−1.58643	−	0.218393i
$146$	20566.9	+	14942.7i	0.0798521	+	0.0580160i
$147$	351296.	+	255231.i	1.34085	+	0.974183i
$148$	37604.9	−	115736.i	0.141121	−	0.434325i
$149$	75186.2			0.277442			0.138721	−	0.990332i	$-0.455701\pi$
$149$	75186.2			0.277442			0.138721	+	0.990332i	$0.455701\pi$
$150$	4560.90	+	112408.i	0.0165509	+	0.407913i
$151$	155775.			0.555974			0.277987	−	0.960585i	$-0.410333\pi$
$151$	155775.			0.555974			0.277987	+	0.960585i	$0.410333\pi$
$152$	16458.6	−	50654.5i	0.0577810	−	0.177832i
$153$	7120.14	+	5173.08i	0.0245901	+	0.0178657i
$154$	398345.	+	289415.i	1.35350	+	0.983374i
$155$	−100229.	+	206980.i	−0.335091	+	0.691988i
$156$	−116013.	+	84288.2i	−0.381676	+	0.277304i
$157$	108387.			0.350936			0.175468	−	0.984485i	$-0.443856\pi$
$157$	108387.			0.350936			0.175468	+	0.984485i	$0.443856\pi$
$158$	314524.	−	228515.i	1.00233	−	0.728237i
$159$	66190.8	+	203714.i	0.207637	+	0.639041i
$160$	50466.8	−	27016.7i	0.155850	−	0.0834319i
$161$	−87491.1	+	269270.i	−0.266011	+	0.818697i
$162$	−8109.84	−	24959.5i	−0.0242787	−	0.0747221i
$163$	87232.3	+	268473.i	0.257163	+	0.791466i	0.993396	+	0.114738i	$0.0366027\pi$
$163$	87232.3	+	268473.i	0.257163	+	0.791466i	−0.736233	+	0.676728i	$0.763397\pi$
$164$	−18431.0	+	56724.7i	−0.0535105	+	0.164688i
$165$	−105826.	+	218538.i	−0.302608	+	0.624910i
$166$	−148787.	−	457918.i	−0.419077	−	1.28978i
$167$	101127.	−	73473.4i	0.280594	−	0.203863i	−0.438583	−	0.898691i	$-0.644519\pi$
$167$	101127.	−	73473.4i	0.280594	−	0.203863i	0.719176	+	0.694828i	$0.244519\pi$
$168$	146913.			0.401594
$169$	−501904.	+	364654.i	−1.35177	+	0.982120i
$170$	−17524.5	−	16827.9i	−0.0465075	−	0.0446588i
$171$	54534.9	+	39621.9i	0.142621	+	0.103620i
$172$	−73816.6	−	53630.9i	−0.190254	−	0.138227i
$173$	−49906.1	+	153595.i	−0.126776	+	0.390177i	−0.994221	−	0.107357i	$-0.965761\pi$
$173$	−49906.1	+	153595.i	−0.126776	+	0.390177i	0.867444	+	0.497534i	$0.165761\pi$
$174$	−261093.			−0.653765
$175$	441969.	−	663294.i	1.09093	−	1.63723i
$176$	123550.			0.300651
$177$	−48622.7	+	149645.i	−0.116656	+	0.359030i
$178$	−190764.	−	138598.i	−0.451281	−	0.327875i
$179$	−68284.8	−	49611.8i	−0.159291	−	0.115732i	0.505284	−	0.862953i	$-0.331388\pi$
$179$	−68284.8	−	49611.8i	−0.159291	−	0.115732i	−0.664576	+	0.747221i	$0.731388\pi$
$180$	12781.9	+	71312.1i	0.0294046	+	0.164052i
$181$	−187420.	+	136169.i	−0.425226	+	0.308944i	−0.779737	−	0.626107i	$-0.784647\pi$
$181$	−187420.	+	136169.i	−0.425226	+	0.308944i	0.354511	+	0.935052i	$0.384647\pi$
$182$	1.01598e6			2.27355
$183$	−157835.	+	114674.i	−0.348398	+	0.253126i
$184$	21953.6	+	67566.2i	0.0478037	+	0.147125i
$185$	−306678.	−	294487.i	−0.658799	−	0.632610i
$186$	−45764.8	+	140850.i	−0.0969951	+	0.298520i
$187$	−16204.4	−	49871.9i	−0.0338866	−	0.104292i
$188$	121919.	+	375229.i	0.251581	+	0.774286i
$189$	−57457.6	+	176836.i	−0.117002	+	0.360095i
$190$	−134224.	−	128889.i	−0.269741	−	0.259019i
$191$	−229806.	−	707271.i	−0.455804	−	1.40282i	−0.870188	−	0.492719i	$-0.836003\pi$
$191$	−229806.	−	707271.i	−0.455804	−	1.40282i	0.414384	−	0.910102i	$-0.363997\pi$
$192$	29823.6	−	21668.1i	0.0583858	−	0.0424197i
$193$	256420.			0.495517			0.247758	−	0.968822i	$-0.420306\pi$
$193$	256420.			0.495517			0.247758	+	0.968822i	$0.420306\pi$
$194$	323889.	−	235319.i	0.617863	−	0.448904i
$195$	88393.4	+	493159.i	0.166469	+	0.928753i
$196$	−624526.	−	453745.i	−1.16121	−	0.843668i
$197$	258064.	+	187495.i	0.473764	+	0.344210i	0.798907	−	0.601455i	$-0.205412\pi$
$197$	258064.	+	187495.i	0.473764	+	0.344210i	−0.325142	+	0.945665i	$0.605412\pi$
$198$	−48320.5	+	148715.i	−0.0875927	+	0.269583i
$199$	−720400.			−1.28956			−0.644779	−	0.764369i	$-0.723051\pi$
$199$	−720400.			−1.28956			−0.644779	+	0.764369i	$0.723051\pi$
$200$	−8108.27	−	199836.i	−0.0143335	−	0.353263i
$201$	453954.			0.792541
$202$	−146979.	+	452354.i	−0.253441	+	0.780010i
$203$	1.49654e6	+	1.08730e6i	2.54887	+	1.85186i
$204$	−12658.0	−	9196.59i	−0.0212956	−	0.0154722i
$205$	150309.	+	144334.i	0.249805	+	0.239875i
$206$	−523225.	+	380146.i	−0.859055	+	0.624140i
$207$	−89914.2			−0.145849
$208$	206245.	−	149846.i	0.330541	−	0.240152i
$209$	−124113.	−	381981.i	−0.196541	−	0.604890i
$210$	223710.	−	461978.i	0.350055	−	0.722892i
$211$	32637.0	−	100446.i	0.0504666	−	0.155320i	−0.922647	−	0.385645i	$-0.873979\pi$
$211$	32637.0	−	100446.i	0.0504666	−	0.155320i	0.973114	+	0.230325i	$0.0739789\pi$
$212$	−117673.	−	362159.i	−0.179819	−	0.553426i
$213$	−49590.0	−	152622.i	−0.0748936	−	0.230499i
$214$	−109196.	+	336072.i	−0.162995	+	0.501646i
$215$	−281049.	+	150456.i	−0.414654	+	0.221979i
$216$	14417.5	+	44372.5i	0.0210259	+	0.0647112i
$217$	848873.	−	616742.i	1.22375	−	0.889108i
$218$	734892.			1.04733
$219$	46275.5	−	33621.1i	0.0651990	−	0.0473698i
$220$	188134.	−	388512.i	0.262066	−	0.541188i
$221$	−87536.5	−	63599.0i	−0.120561	−	0.0875930i
$222$	−221515.	−	160940.i	−0.301662	−	0.219170i
$223$	−332066.	+	1.02199e6i	−0.447159	+	1.37621i	0.432939	+	0.901423i	$0.357476\pi$
$223$	−332066.	+	1.02199e6i	−0.447159	+	1.37621i	−0.880098	+	0.474791i	$0.842524\pi$
$224$	−261179.			−0.347791
$225$	243709.	+	68395.9i	0.320934	+	0.0900686i
$226$	789504.			1.02821
$227$	191977.	−	590843.i	0.247277	−	0.761040i	−0.747977	−	0.663725i	$-0.768975\pi$
$227$	191977.	−	590843.i	0.247277	−	0.761040i	0.995254	−	0.0973150i	$-0.0310254\pi$
$228$	−96950.9	−	70439.0i	−0.123514	−	0.0897379i
$229$	501761.	+	364550.i	0.632278	+	0.459377i	0.857189	−	0.515003i	$-0.172209\pi$
$229$	501761.	+	364550.i	0.632278	+	0.459377i	−0.224911	+	0.974379i	$0.572209\pi$
$230$	245896.	+	33850.9i	0.306501	+	0.0421940i
$231$	896276.	−	651183.i	1.10513	−	0.802921i
$232$	464165.			0.566177
$233$	66508.1	−	48321.0i	0.0802574	−	0.0583104i	−0.546933	−	0.837176i	$-0.684205\pi$
$233$	66508.1	−	48321.0i	0.0802574	−	0.0583104i	0.627190	+	0.778866i	$0.284205\pi$
$234$	99704.1	+	306858.i	0.119035	+	0.366351i
$235$	1.36558e6	+	187991.i	1.61305	+	0.222058i
$236$	86440.4	−	266036.i	0.101027	−	0.310929i
$237$	−270310.	−	831927.i	−0.312601	−	0.962088i
$238$	34255.2	+	105427.i	0.0391998	+	0.120645i
$239$	−365149.	+	1.12381e6i	−0.413500	+	1.27262i	0.500085	+	0.865976i	$0.333302\pi$
$239$	−365149.	+	1.12381e6i	−0.413500	+	1.27262i	−0.913586	+	0.406647i	$0.866698\pi$
$240$	−22723.4	−	126777.i	−0.0254651	−	0.142073i
$241$	−284001.	−	874066.i	−0.314976	−	0.969397i	−0.975764	−	0.218824i	$-0.929778\pi$
$241$	−284001.	−	874066.i	−0.314976	−	0.969397i	0.660788	−	0.750572i	$-0.270222\pi$
$242$	232574.	−	168975.i	0.255284	−	0.185474i
$243$	−59049.0			−0.0641500
$244$	280595.	−	203865.i	0.301721	−	0.219213i
$245$	−2.37782e6	+	1.27293e6i	−2.53083	+	1.35485i
$246$	108569.	+	78880.1i	0.114385	+	0.0831055i
$247$	−670464.	−	487120.i	−0.699250	−	0.508035i
$248$	81359.7	−	250399.i	0.0840002	−	0.258526i
$249$	−1.08334e6			−1.10730
$250$	−640743.	−	278800.i	−0.648387	−	0.282125i
$251$	−914847.			−0.916567			−0.458283	−	0.888806i	$-0.651536\pi$
$251$	−914847.			−0.916567			−0.458283	+	0.888806i	$0.651536\pi$
$252$	102147.	−	314376.i	0.101327	−	0.311852i
$253$	433416.	+	314895.i	0.425700	+	0.309289i
$254$	330031.	+	239782.i	0.320975	+	0.233202i
$255$	−48194.1	+	25800.0i	−0.0464134	+	0.0248468i
$256$	−53019.7	+	38521.1i	−0.0505636	+	0.0367366i
$257$	243122.			0.229610			0.114805	−	0.993388i	$-0.463376\pi$
$257$	243122.			0.229610			0.114805	+	0.993388i	$0.463376\pi$
$258$	−166087.	+	120669.i	−0.155341	+	0.112862i
$259$	599464.	+	1.84496e6i	0.555282	+	1.70898i
$260$	−157144.	−	876727.i	−0.144166	−	0.804324i
$261$	−181535.	+	558706.i	−0.164952	+	0.507671i
$262$	275419.	+	847653.i	0.247880	+	0.762896i
$263$	2723.23	+	8381.26i	0.00242770	+	0.00747170i	0.952263	−	0.305279i	$-0.0987496\pi$
$263$	2723.23	+	8381.26i	0.00242770	+	0.00747170i	−0.949835	+	0.312750i	$0.898750\pi$
$264$	85903.0	−	264382.i	0.0758575	−	0.233465i
$265$	−1.31802e6	−	181443.i	−1.15294	−	0.158717i
$266$	262369.	+	807488.i	0.227357	+	0.699732i
$267$	−429220.	+	311847.i	−0.368470	+	0.267709i
$268$	−807030.			−0.686361
$269$	−714657.	+	519229.i	−0.602167	+	0.437500i	−0.846647	−	0.532154i	$-0.821383\pi$
$269$	−714657.	+	519229.i	−0.602167	+	0.437500i	0.244480	+	0.969654i	$0.421383\pi$
$270$	161486.	+	22230.7i	0.134811	+	0.0185586i
$271$	−503345.	−	365702.i	−0.416335	−	0.302485i	0.359827	−	0.933019i	$-0.382836\pi$
$271$	−503345.	−	365702.i	−0.416335	−	0.302485i	−0.776162	+	0.630534i	$0.782836\pi$
$272$	22503.2	+	16349.5i	0.0184426	+	0.0133993i
$273$	706397.	−	2.17407e6i	0.573643	−	1.76549i
$274$	−440673.			−0.354601
$275$	−935225.	−	1.18320e6i	−0.745734	−	0.943468i
$276$	159847.			0.126309
$277$	−81291.7	+	250190.i	−0.0636571	+	0.195916i	−0.977827	−	0.209415i	$-0.932844\pi$
$277$	−81291.7	+	250190.i	−0.0636571	+	0.195916i	0.914170	+	0.405332i	$0.132844\pi$
$278$	−0.0728197	−	0.0529066i	−5.65115e−8	−	4.10580e-8i
$279$	269581.	+	195862.i	0.207338	+	0.150640i
$280$	−397706.	+	821295.i	−0.303157	+	0.626043i
$281$	−970542.	+	705140.i	−0.733244	+	0.532733i	−0.890588	−	0.454811i	$-0.849707\pi$
$281$	−970542.	+	705140.i	−0.733244	+	0.532733i	0.157344	+	0.987544i	$0.449707\pi$
$282$	887712.			0.664736
$283$	41376.4	−	30061.7i	0.0307105	−	0.0223125i	−0.572324	−	0.820028i	$-0.693958\pi$
$283$	41376.4	−	30061.7i	0.0307105	−	0.0223125i	0.603035	+	0.797715i	$0.293958\pi$
$284$	88159.9	+	271328.i	0.0648598	+	0.199618i
$285$	−369131.	+	197609.i	−0.269196	+	0.144110i
$286$	594062.	−	1.82834e6i	0.429454	−	1.32172i
$287$	−293810.	−	904254.i	−0.210553	−	0.648016i
$288$	−25631.1	−	78884.4i	−0.0182090	−	0.0560415i
$289$	−435112.	+	1.33914e6i	−0.306448	+	0.943149i
$290$	706800.	−	1.45960e6i	0.493516	−	1.01915i
$291$	−278358.	−	856698.i	−0.192695	−	0.593055i
$292$	−82267.6	+	59770.9i	−0.0564640	+	0.0410235i
$293$	972204.			0.661589			0.330795	−	0.943703i	$-0.392683\pi$
$293$	972204.			0.661589			0.330795	+	0.943703i	$0.392683\pi$
$294$	−1.40518e6	+	1.02093e6i	−0.948123	+	0.688852i
$295$	−704943.	−	676921.i	−0.471628	−	0.452879i
$296$	393804.	+	286115.i	0.261247	+	0.189807i
$297$	284635.	+	206800.i	0.187240	+	0.136038i
$298$	−92935.2	+	286025.i	−0.0606233	+	0.186579i
$299$	1.10542e6			0.715074
$300$	−433261.	−	121593.i	−0.277937	−	0.0780017i
$301$	1.45450e6			0.925333
$302$	−192548.	+	592602.i	−0.121485	+	0.373892i
$303$	865789.	+	629033.i	0.541758	+	0.393611i
$304$	172357.	+	125225.i	0.106966	+	0.0777153i
$305$	−213793.	−	1.19278e6i	−0.131597	−	0.734196i
$306$	−28480.6	+	20692.3i	−0.0173878	+	0.0126330i
$307$	−3.04446e6			−1.84359			−0.921794	−	0.387679i	$-0.873277\pi$
$307$	−3.04446e6			−1.84359			−0.921794	+	0.387679i	$0.873277\pi$
$308$	−1.59338e6	+	1.15766e6i	−0.957067	+	0.695350i
$309$	449672.	+	1.38395e6i	0.267917	+	0.824563i
$310$	−663509.	−	637133.i	−0.392141	−	0.376553i
$311$	870782.	−	2.67999e6i	0.510515	−	1.57120i	−0.280782	−	0.959772i	$-0.590594\pi$
$311$	870782.	−	2.67999e6i	0.510515	−	1.57120i	0.791297	−	0.611432i	$-0.209406\pi$
$312$	−177252.	−	545525.i	−0.103087	−	0.317269i
$313$	530163.	+	1.63167e6i	0.305878	+	0.941397i	0.979348	+	0.202182i	$0.0648032\pi$
$313$	530163.	+	1.63167e6i	0.305878	+	0.941397i	−0.673470	+	0.739215i	$0.735197\pi$
$314$	−133974.	+	412329.i	−0.0766824	+	0.236004i
$315$	−833034.	−	799919.i	−0.473027	−	0.454224i
$316$	480550.	+	1.47898e6i	0.270721	+	0.833192i
$317$	−2.57555e6	+	1.87125e6i	−1.43953	+	1.04588i	−0.451393	+	0.892325i	$0.649073\pi$
$317$	−2.57555e6	+	1.87125e6i	−1.43953	+	1.04588i	−0.988140	+	0.153556i	$0.950927\pi$
$318$	−856792.			−0.475124
$319$	2.83174e6	−	2.05738e6i	1.55803	−	1.13198i
$320$	40397.2	+	225382.i	0.0220534	+	0.123039i
$321$	643229.	+	467333.i	0.348420	+	0.253142i
$322$	−916218.	−	665672.i	−0.492447	−	0.357783i
$323$	27942.2	−	85997.1i	0.0149023	−	0.0458646i
$324$	104976.			0.0555556
$325$	−2.99622e6	−	840873.i	−1.57349	−	0.441593i
$326$	−1.12916e6			−0.588452
$327$	510962.	−	1.57258e6i	0.264252	−	0.813285i
$328$	−193012.	−	140231.i	−0.0990602	−	0.0719715i
$329$	−5.08821e6	−	3.69680e6i	−2.59165	−	1.88294i
$330$	−700561.	−	672712.i	−0.354129	−	0.340051i
$331$	1.62014e6	−	1.17710e6i	0.812798	−	0.590532i	−0.101842	−	0.994801i	$-0.532474\pi$
$331$	1.62014e6	−	1.17710e6i	0.812798	−	0.590532i	0.914641	+	0.404268i	$0.132474\pi$
$332$	1.92593e6			0.958950
$333$	−498408.	+	362115.i	−0.246306	+	0.178952i
$334$	154509.	+	475530.i	0.0757858	+	0.233245i
$335$	−1.22889e6	+	2.53776e6i	−0.598276	+	1.23549i
$336$	−181595.	+	558891.i	−0.0877515	+	0.270071i
$337$	337875.	+	1.03987e6i	0.162062	+	0.498775i	0.998808	−	0.0488163i	$-0.0155449\pi$
$337$	337875.	+	1.03987e6i	0.162062	+	0.498775i	−0.836746	+	0.547591i	$0.815545\pi$
$338$	−766840.	−	2.36009e6i	−0.365101	−	1.12367i
$339$	548933.	−	1.68944e6i	0.259430	−	0.798443i
$340$	85678.4	−	45866.7i	0.0401952	−	0.0215179i
$341$	−613526.	−	1.88824e6i	−0.285724	−	0.879369i
$342$	−218140.	+	158488.i	−0.100848	+	0.0732707i
$343$	8.01908e6			3.68035
$344$	295266.	−	214524.i	0.134530	−	0.0977415i
$345$	243405.	−	502651.i	0.110099	−	0.227363i
$346$	−522623.	−	379708.i	−0.234692	−	0.170514i
$347$	801418.	+	582264.i	0.357302	+	0.259595i	0.751926	−	0.659248i	$-0.229125\pi$
$347$	801418.	+	582264.i	0.357302	+	0.259595i	−0.394624	+	0.918843i	$0.629125\pi$
$348$	322728.	−	993256.i	0.142853	−	0.439656i
$349$	760571.			0.334253			0.167127	−	0.985935i	$-0.446551\pi$
$349$	760571.			0.334253			0.167127	+	0.985935i	$0.446551\pi$
$350$	1.97702e6	+	2.50123e6i	0.862661	+	1.09140i
$351$	725961.			0.314518
$352$	−152717.	+	470013.i	−0.0656946	+	0.202187i
$353$	−448599.	−	325926.i	−0.191611	−	0.139214i	0.487844	−	0.872931i	$-0.337784\pi$
$353$	−448599.	−	325926.i	−0.191611	−	0.139214i	−0.679455	+	0.733717i	$0.737784\pi$
$354$	−509184.	−	369944.i	−0.215957	−	0.156902i
$355$	987455.	+	135936.i	0.415859	+	0.0572485i
$356$	763058.	−	554394.i	0.319104	−	0.231843i
$357$	249417.			0.103575
$358$	273139.	−	198447.i	0.112636	−	0.0818347i
$359$	−580999.	−	1.78813e6i	−0.237924	−	0.732256i	−0.996720	−	0.0809272i	$-0.974212\pi$
$359$	−580999.	−	1.78813e6i	−0.237924	−	0.732256i	0.758796	−	0.651329i	$-0.225788\pi$
$360$	−287087.	−	39521.3i	−0.116750	−	0.0160722i
$361$	−551141.	+	1.69624e6i	−0.222584	+	0.685044i
$362$	−286352.	−	881301.i	−0.114849	−	0.353470i
$363$	−199880.	−	615166.i	−0.0796163	−	0.245034i
$364$	−1.25582e6	+	3.86500e6i	−0.496790	+	1.52896i
$365$	62681.9	+	349711.i	0.0246269	+	0.137397i
$366$	−241150.	−	742185.i	−0.0940990	−	0.289607i
$367$	−938925.	+	682169.i	−0.363886	+	0.264379i	−0.754671	−	0.656103i	$-0.772204\pi$
$367$	−938925.	+	682169.i	−0.363886	+	0.264379i	0.390785	+	0.920482i	$0.372204\pi$
$368$	−284173.			−0.109387
$369$	244281.	−	177480.i	0.0933949	−	0.0678553i
$370$	1.49937e6	−	802666.i	0.569382	−	0.304811i
$371$	4.91098e6	+	3.56804e6i	1.85239	+	1.34584i
$372$	−479256.	−	348200.i	−0.179560	−	0.130458i
$373$	−998713.	+	3.07372e6i	−0.371680	+	1.14391i	0.574012	+	0.818847i	$0.305386\pi$
$373$	−998713.	+	3.07372e6i	−0.371680	+	1.14391i	−0.945692	+	0.325065i	$0.894614\pi$
$374$	209754.			0.0775408
$375$	−1.04210e6	+	1.17727e6i	−0.382675	+	0.432311i
$376$	−1.57815e6			−0.575679
$377$	2.23183e6	−	6.86886e6i	0.808737	−	2.48904i
$378$	−601704.	−	437164.i	−0.216598	−	0.157367i
$379$	2.03964e6	+	1.48189e6i	0.729383	+	0.529928i	0.889368	−	0.457192i	$-0.151145\pi$
$379$	2.03964e6	+	1.48189e6i	0.729383	+	0.529928i	−0.159985	+	0.987119i	$0.551145\pi$
$380$	656232.	−	351305.i	0.233130	−	0.124803i
$381$	742571.	−	539509.i	0.262075	−	0.190409i
$382$	2.97468e6			1.04299
$383$	−2.90419e6	+	2.11002e6i	−1.01165	+	0.735003i	−0.964554	−	0.263887i	$-0.914995\pi$
$383$	−2.90419e6	+	2.11002e6i	−1.01165	+	0.735003i	−0.0470917	+	0.998891i	$0.514995\pi$
$384$	45566.4	+	140239.i	0.0157695	+	0.0485334i
$385$	1.21404e6	+	6.77330e6i	0.417428	+	2.32889i
$386$	−316953.	+	975479.i	−0.108274	+	0.333234i
$387$	142739.	+	439307.i	0.0484469	+	0.149104i
$388$	494859.	+	1.52302e6i	0.166879	+	0.513601i
$389$	309857.	−	953641.i	0.103821	−	0.319529i	−0.885631	−	0.464390i	$-0.846273\pi$
$389$	309857.	−	953641.i	0.103821	−	0.319529i	0.989452	+	0.144861i	$0.0462735\pi$
$390$	−1.98535e6	−	273309.i	−0.660960	−	0.0909899i
$391$	37271.0	+	114708.i	0.0123290	+	0.0379449i
$392$	2.49810e6	−	1.81498e6i	0.821099	−	0.596563i
$393$	2.00537e6			0.654957
$394$	−1.03226e6	+	749979.i	−0.335002	+	0.243393i
$395$	5.38251e6	+	740974.i	1.73577	+	0.238952i
$396$	−506018.	−	367644.i	−0.162154	−	0.117812i
$397$	−765301.	−	556024.i	−0.243700	−	0.177059i	0.459230	−	0.888317i	$-0.348125\pi$
$397$	−765301.	−	556024.i	−0.243700	−	0.177059i	−0.702930	+	0.711259i	$0.748125\pi$
$398$	890463.	−	2.74056e6i	0.281779	−	0.867226i
$399$	1.91035e6			0.600731
$400$	770242.	+	216165.i	0.240701	+	0.0675515i
$401$	−5.48843e6			−1.70446			−0.852230	−	0.523167i	$-0.824750\pi$
$401$	−5.48843e6			−1.70446			−0.852230	+	0.523167i	$0.824750\pi$
$402$	−561118.	+	1.72694e6i	−0.173177	+	0.532983i
$403$	−3.31429e6	−	2.40797e6i	−1.01655	−	0.738565i
$404$	−1.53918e6	−	1.11828e6i	−0.469177	−	0.340877i
$405$	159851.	−	330104.i	0.0484258	−	0.100003i
$406$	−5.98616e6	+	4.34920e6i	−1.80232	+	1.30947i
$407$	3.67068e6			1.09840
$408$	50632.1	−	36786.4i	0.0150583	−	0.0109405i
$409$	−1.71920e6	−	5.29116e6i	−0.508182	−	1.56402i	−0.795355	−	0.606144i	$-0.792716\pi$
$409$	−1.71920e6	−	5.29116e6i	−0.508182	−	1.56402i	0.287173	−	0.957879i	$-0.407284\pi$
$410$	−734873.	+	393404.i	−0.215900	+	0.115579i
$411$	−306395.	+	942986.i	−0.0894698	+	0.275360i
$412$	−799417.	−	2.46035e6i	−0.232023	−	0.714093i
$413$	1.37795e6	+	4.24091e6i	0.397521	+	1.22344i
$414$	111140.	−	342054.i	0.0318691	−	0.0980830i
$415$	2.93269e6	−	6.05623e6i	0.835883	−	1.72616i
$416$	315114.	+	969822.i	0.0892760	+	0.274763i
$417$	−0.163844	+	0.119040i	−4.61415e−8	+	3.35237e-8i
$418$	1.60655e6			0.449733
$419$	−404463.	+	293859.i	−0.112549	+	0.0817719i	−0.642636	−	0.766171i	$-0.722159\pi$
$419$	−404463.	+	293859.i	−0.112549	+	0.0817719i	0.530087	+	0.847943i	$0.322159\pi$
$420$	1.48095e6	+	1.42208e6i	0.409654	+	0.393369i
$421$	2.33624e6	+	1.69738e6i	0.642411	+	0.466739i	0.860677	−	0.509151i	$-0.170040\pi$
$421$	2.33624e6	+	1.69738e6i	0.642411	+	0.466739i	−0.218267	+	0.975889i	$0.570040\pi$
$422$	341779.	+	248317.i	0.0934253	+	0.0678775i
$423$	617216.	−	1.89959e6i	0.167720	−	0.516191i
$424$	1.52318e6			0.411470
$425$	−13765.6	−	339265.i	−0.00369676	−	0.0911100i
$426$	641906.			0.171375
$427$	−1.70853e6	+	5.25832e6i	−0.453475	+	1.39565i
$428$	−1.14352e6	−	830814.i	−0.301740	−	0.219227i
$429$	−3.49937e6	−	2.54244e6i	−0.918008	−	0.666972i
$430$	−224972.	−	1.25515e6i	−0.0586755	−	0.327359i
$431$	2.28050e6	−	1.65688e6i	0.591340	−	0.429634i	−0.251455	−	0.967869i	$-0.580909\pi$
$431$	2.28050e6	−	1.65688e6i	0.591340	−	0.429634i	0.842794	+	0.538236i	$0.180909\pi$
$432$	−186624.			−0.0481125
$433$	−1.72492e6	+	1.25322e6i	−0.442128	+	0.321225i	−0.786480	−	0.617616i	$-0.788099\pi$
$433$	−1.72492e6	+	1.25322e6i	−0.442128	+	0.321225i	0.344352	+	0.938841i	$0.388099\pi$
$434$	1.29696e6	+	3.99164e6i	0.330524	+	1.01725i
$435$	−2.63193e6	−	2.52731e6i	−0.666886	−	0.640376i
$436$	−908376.	+	2.79569e6i	−0.228849	+	0.704326i
$437$	285468.	+	878580.i	0.0715079	+	0.220079i
$438$	70702.7	+	217600.i	0.0176096	+	0.0541969i
$439$	−538119.	+	1.65616e6i	−0.133265	+	0.410148i	−0.995316	−	0.0966734i	$-0.969180\pi$
$439$	−538119.	+	1.65616e6i	−0.133265	+	0.410148i	0.862051	+	0.506822i	$0.169180\pi$
$440$	1.24544e6	+	1.19593e6i	0.306684	+	0.294493i
$441$	1.20765e6	+	3.71676e6i	0.295695	+	0.910055i
$442$	350146.	−	254396.i	0.0852498	−	0.0619376i
$443$	−4.03755e6			−0.977482			−0.488741	−	0.872429i	$-0.662544\pi$
$443$	−4.03755e6			−0.977482			−0.488741	+	0.872429i	$0.662544\pi$
$444$	886059.	−	643760.i	0.213307	−	0.154977i
$445$	−581395.	−	3.24368e6i	−0.139178	−	0.776494i
$446$	−3.47744e6	−	2.52651e6i	−0.827794	−	0.601428i
$447$	547442.	+	397740.i	0.129589	+	0.0941522i
$448$	322835.	−	993583.i	0.0759950	−	0.233889i
$449$	−578767.			−0.135484			−0.0677420	−	0.997703i	$-0.521579\pi$
$449$	−578767.			−0.135484			−0.0677420	+	0.997703i	$0.521579\pi$
$450$	−561435.	+	842584.i	−0.130698	+	0.196147i
$451$	−1.79908e6			−0.416494
$452$	−975880.	+	3.00345e6i	−0.224673	+	0.691472i
$453$	1.13422e6	+	824058.i	0.259688	+	0.188674i
$454$	2.01040e6	+	1.46064e6i	0.457766	+	0.332587i
$455$	1.02415e7	+	9.83438e6i	2.31918	+	2.22699i
$456$	387804.	−	281756.i	0.0873373	−	0.0634543i
$457$	−2.15691e6			−0.483106			−0.241553	−	0.970388i	$-0.577657\pi$
$457$	−2.15691e6			−0.483106			−0.241553	+	0.970388i	$0.577657\pi$
$458$	−2.00704e6	+	1.45820e6i	−0.447088	+	0.324828i
$459$	24476.9	+	75332.0i	0.00542280	+	0.0166897i
$460$	−432721.	+	893602.i	−0.0953483	+	0.196902i
$461$	880900.	−	2.71113e6i	0.193052	−	0.594153i	−0.806942	−	0.590631i	$-0.798879\pi$
$461$	880900.	−	2.71113e6i	0.193052	−	0.594153i	0.999994	−	0.00352190i	$-0.00112106\pi$
$462$	1.36939e6	+	4.21454e6i	0.298484	+	0.918640i
$463$	681733.	+	2.09816e6i	0.147796	+	0.454869i	0.997360	−	0.0726166i	$-0.0231350\pi$
$463$	681733.	+	2.09816e6i	0.147796	+	0.454869i	−0.849564	+	0.527485i	$0.823135\pi$
$464$	−573739.	+	1.76579e6i	−0.123714	+	0.380753i
$465$	−1.82472e6	+	976836.i	−0.391348	+	0.209503i
$466$	101615.	+	312740.i	0.0216768	+	0.0667143i
$467$	736135.	−	534834.i	0.156194	−	0.113482i	−0.506943	−	0.861980i	$-0.669225\pi$
$467$	736135.	−	534834.i	0.156194	−	0.113482i	0.663137	+	0.748498i	$0.269225\pi$
$468$	−1.29060e6			−0.272381
$469$	1.04080e7	−	7.56182e6i	2.18491	−	1.58743i
$470$	−2.40311e6	+	4.96262e6i	−0.501798	+	1.03625i
$471$	789182.	+	573375.i	0.163917	+	0.119093i
$472$	905216.	+	657678.i	0.187024	+	0.135881i
$473$	850477.	−	2.61750e6i	0.174787	−	0.537940i
$474$	3.49896e6			0.715308
$475$	−105434.	−	2.59851e6i	−0.0214410	−	0.528434i
$476$	−443408.			−0.0896987
$477$	−595717.	+	1.83343e6i	−0.119879	+	0.368950i
$478$	−3.82389e6	−	2.77822e6i	−0.765484	−	0.556156i
$479$	380965.	+	276788.i	0.0758659	+	0.0551198i	0.625072	−	0.780567i	$-0.285070\pi$
$479$	380965.	+	276788.i	0.0758659	+	0.0551198i	−0.549206	+	0.835687i	$0.685070\pi$
$480$	510377.	+	70260.1i	0.101109	+	0.0139189i
$481$	6.12754e6	−	4.45192e6i	1.20760	−	0.877373i
$482$	3.67619e6			0.720743
$483$	−2.06149e6	+	1.49776e6i	−0.402081	+	0.292129i
$484$	355342.	+	1.09363e6i	0.0689497	+	0.212205i
$485$	5.54277e6	+	763036.i	1.06997	+	0.147296i
$486$	72988.6	−	224636.i	0.0140173	−	0.0431408i
$487$	3.02689e6	+	9.31580e6i	0.578327	+	1.77991i	0.624559	+	0.780977i	$0.285279\pi$
$487$	3.02689e6	+	9.31580e6i	0.578327	+	1.77991i	−0.0462321	+	0.998931i	$0.514721\pi$
$488$	428712.	+	1.31944e6i	0.0814922	+	0.250807i
$489$	−785090.	+	2.41626e6i	−0.148473	+	0.456953i
$490$	−1.90337e6	−	1.06192e7i	−0.358125	−	1.99803i
$491$	−576075.	−	1.77298e6i	−0.107839	−	0.331894i	0.882547	−	0.470224i	$-0.155827\pi$
$491$	−576075.	−	1.77298e6i	−0.107839	−	0.331894i	−0.990386	+	0.138329i	$0.955827\pi$
$492$	−434277.	+	315520.i	−0.0808823	+	0.0587644i
$493$	788022.			0.146023
$494$	2.68185e6	−	1.94848e6i	0.494445	−	0.359235i
$495$	−1.92661e6	+	1.03139e6i	−0.353412	+	0.189194i
$496$	852010.	+	619021.i	0.155504	+	0.112980i
$497$	−3.67929e6	−	2.67316e6i	−0.668149	−	0.485439i
$498$	1.33908e6	−	4.12126e6i	0.241954	−	0.744658i
$499$	−7.16774e6			−1.28864			−0.644319	−	0.764757i	$-0.722859\pi$
$499$	−7.16774e6			−1.28864			−0.644319	+	0.764757i	$0.722859\pi$
$500$	1.85262e6	−	2.09292e6i	0.331407	−	0.374392i
$501$	1.12500e6			0.200244
$502$	1.13081e6	−	3.48028e6i	0.200277	−	0.616390i
$503$	1.52728e6	+	1.10963e6i	0.269152	+	0.195551i	0.714172	−	0.699970i	$-0.246803\pi$
$503$	1.52728e6	+	1.10963e6i	0.269152	+	0.195551i	−0.445020	+	0.895521i	$0.646803\pi$
$504$	1.06970e6	+	777180.i	0.187579	+	0.136284i
$505$	−5.86027e6	+	3.13722e6i	−1.02256	+	0.547414i
$506$	−1.73366e6	+	1.25958e6i	−0.301015	+	0.218700i
$507$	−5.58348e6			−0.964684
$508$	−1.32013e6	+	959128.i	−0.226964	+	0.164899i
$509$	−51910.3	−	159763.i	−0.00888094	−	0.0273327i	0.946518	−	0.322651i	$-0.104574\pi$
$509$	−51910.3	−	159763.i	−0.00888094	−	0.0273327i	−0.955399	+	0.295319i	$0.904574\pi$
$510$	−38578.0	−	215232.i	−0.00656771	−	0.0366422i
$511$	500923.	−	1.54168e6i	0.0848631	−	0.261182i
$512$	−81007.0	−	249314.i	−0.0136568	−	0.0420312i
$513$	187474.	+	576986.i	0.0314520	+	0.0967993i
$514$	−300515.	+	924889.i	−0.0501716	+	0.154412i
$515$	−8.95405e6	−	1.23264e6i	−1.48765	−	0.204795i
$516$	−253759.	−	780989.i	−0.0419563	−	0.129128i
$517$	−9.62789e6	+	6.99507e6i	−1.58418	+	1.15097i
$518$	−7.75962e6			−1.27062
$519$	−1.17590e6	+	854343.i	−0.191625	+	0.139224i
$520$	3.52951e6	+	485884.i	0.572408	+	0.0787996i
$521$	−5.65178e6	−	4.10626e6i	−0.912201	−	0.662753i	0.0293694	−	0.999569i	$-0.490650\pi$
$521$	−5.65178e6	−	4.10626e6i	−0.912201	−	0.662753i	−0.941571	+	0.336816i	$0.890650\pi$
$522$	−1.90106e6	−	1.38120e6i	−0.305365	−	0.221860i
$523$	1.07955e6	−	3.32253e6i	0.172580	−	0.531146i	−0.826935	−	0.562298i	$-0.809917\pi$
$523$	1.07955e6	−	3.32253e6i	0.172580	−	0.531146i	0.999515	+	0.0311514i	$0.00991742\pi$
$524$	−3.56510e6			−0.567210
$525$	6.72692e6	−	2.49150e6i	1.06517	−	0.394514i
$526$	−35250.3			−0.00555518
$527$	138126.	−	425108.i	0.0216645	−	0.0666765i
$528$	899588.	+	653589.i	0.140430	+	0.102028i
$529$	4.21023e6	+	3.05891e6i	0.654133	+	0.475256i
$530$	2.31941e6	−	4.78976e6i	0.358664	−	0.740669i
$531$	−1.14566e6	+	832374.i	−0.176328	+	0.128110i
$532$	−3.39617e6			−0.520248
$533$	−3.00324e6	+	2.18198e6i	−0.457901	+	0.332685i
$534$	−655790.	−	2.01831e6i	−0.0995203	−	0.306292i
$535$	−4.35383e6	+	2.33076e6i	−0.657638	+	0.352057i
$536$	997544.	−	3.07012e6i	0.149975	−	0.461577i
$537$	−234742.	−	722463.i	−0.0351282	−	0.108113i
$538$	−1.09190e6	−	3.36052e6i	−0.162640	−	0.500554i
$539$	7.19547e6	−	2.21454e7i	1.06681	−	3.28330i
$540$	−284179.	+	586852.i	−0.0419380	+	0.0866052i
$541$	−3.48511e6	−	1.07261e7i	−0.511946	−	1.57561i	−0.788772	−	0.614686i	$-0.789283\pi$
$541$	−3.48511e6	−	1.07261e7i	−0.511946	−	1.57561i	0.276826	−	0.960920i	$-0.410717\pi$
$542$	2.01338e6	−	1.46281e6i	0.294393	−	0.213889i
$543$	−2.08497e6			−0.303460
$544$	−90012.6	+	65398.0i	−0.0130409	+	0.00947474i
$545$	7.40803e6	+	7.11355e6i	1.06835	+	1.02588i
$546$	7.39748e6	+	5.37458e6i	1.06195	+	0.771549i
$547$	−3.24295e6	−	2.35614e6i	−0.463416	−	0.336692i	0.331454	−	0.943472i	$-0.392461\pi$
$547$	−3.24295e6	−	2.35614e6i	−0.463416	−	0.336692i	−0.794870	+	0.606780i	$0.792461\pi$
$548$	544702.	−	1.67642e6i	0.0774831	−	0.238469i
$549$	−1.75585e6			−0.248632
$550$	5.65717e6	−	2.09529e6i	0.797430	−	0.295350i
$551$	6.03565e6			0.846925
$552$	−197582.	+	608096.i	−0.0275995	+	0.0849424i
$553$	−2.00554e7	−	1.45711e7i	−2.78881	−	2.02619i
$554$	−851298.	−	618504.i	−0.117844	−	0.0856186i
$555$	−675113.	−	3.76655e6i	−0.0930345	−	0.519052i
$556$	0.291279	−	0.211626i	3.99597e−8	−	2.90324e-8i
$557$	1.08803e6			0.148594			0.0742971	−	0.997236i	$-0.476329\pi$
$557$	1.08803e6			0.148594			0.0742971	+	0.997236i	$0.476329\pi$
$558$	−1.07833e6	+	783449.i	−0.146610	+	0.106519i
$559$	−1.75487e6	−	5.40093e6i	−0.237528	−	0.731036i
$560$	−2.63280e6	−	2.52814e6i	−0.354771	−	0.340668i
$561$	145839.	−	448847.i	0.0195644	−	0.0602131i
$562$	−1.48286e6	−	4.56376e6i	−0.198042	−	0.609512i
$563$	−1.96525e6	−	6.04840e6i	−0.261304	−	0.804211i	−0.992522	−	0.122067i	$-0.961048\pi$
$563$	−1.96525e6	−	6.04840e6i	−0.261304	−	0.804211i	0.731218	−	0.682144i	$-0.238952\pi$
$564$	−1.09727e6	+	3.37706e6i	−0.145250	+	0.447034i
$565$	7.95855e6	+	7.64218e6i	1.04885	+	1.00715i
$566$	63217.6	+	194564.i	0.00829462	+	0.0255282i
$567$	−1.35383e6	+	983618.i	−0.176851	+	0.128490i
$568$	−1.14117e6			−0.148415
$569$	−64605.4	+	46938.5i	−0.00836542	+	0.00607784i	−0.591960	−	0.805967i	$-0.701646\pi$
$569$	−64605.4	+	46938.5i	−0.00836542	+	0.00607784i	0.583595	+	0.812045i	$0.301646\pi$
$570$	−295478.	−	1.64851e6i	−0.0380924	−	0.212523i
$571$	6.72896e6	+	4.88888e6i	0.863690	+	0.627508i	0.928886	−	0.370365i	$-0.120767\pi$
$571$	6.72896e6	+	4.88888e6i	0.863690	+	0.627508i	−0.0651963	+	0.997872i	$0.520767\pi$
$572$	6.22110e6	+	4.51989e6i	0.795018	+	0.577614i
$573$	2.06826e6	−	6.36544e6i	0.263159	−	0.809920i
$574$	3.80316e6			0.481797
$575$	2.15107e6	+	2.72144e6i	0.271323	+	0.343265i
$576$	331776.			0.0416667
$577$	−2.70053e6	+	8.31139e6i	−0.337684	+	1.03928i	0.627701	+	0.778454i	$0.283996\pi$
$577$	−2.70053e6	+	8.31139e6i	−0.337684	+	1.03928i	−0.965385	+	0.260829i	$0.916004\pi$
$578$	−4.55655e6	−	3.31053e6i	−0.567305	−	0.412171i
$579$	1.86703e6	+	1.35648e6i	0.231449	+	0.168158i
$580$	4.67899e6	+	4.49299e6i	0.577540	+	0.554582i
$581$	−2.48380e7	+	1.80459e7i	−3.05265	+	2.21788i
$582$	3.60314e6			0.440934
$583$	9.29253e6	−	6.75142e6i	1.13230	−	0.822666i
$584$	−125694.	−	386845.i	−0.0152504	−	0.0469359i
$585$	−1.96524e6	+	4.05837e6i	−0.237424	+	0.490300i
$586$	−1.20171e6	+	3.69848e6i	−0.144563	+	0.444918i
$587$	−1.11235e6	−	3.42346e6i	−0.133244	−	0.410082i	0.862069	−	0.506791i	$-0.169168\pi$
$587$	−1.11235e6	−	3.42346e6i	−0.133244	−	0.410082i	−0.995313	+	0.0967091i	$0.969168\pi$
$588$	−2.14693e6	−	6.60757e6i	−0.256079	−	0.788131i
$589$	1.05794e6	−	3.25601e6i	0.125653	−	0.386720i
$590$	3.44652e6	−	1.84504e6i	0.407615	−	0.218211i
$591$	887146.	+	2.73035e6i	0.104478	+	0.321551i
$592$	−1.57522e6	+	1.14446e6i	−0.184729	+	0.134214i
$593$	4.91380e6			0.573827			0.286913	−	0.957957i	$-0.407371\pi$
$593$	4.91380e6			0.573827			0.286913	+	0.957957i	$0.407371\pi$
$594$	−1.13854e6	+	827199.i	−0.132398	+	0.0961931i
$595$	−675193.	+	1.39433e6i	−0.0781872	+	0.161463i
$596$	−973230.	−	707093.i	−0.112228	−	0.0815382i
$597$	−5.24534e6	−	3.81096e6i	−0.602335	−	0.437622i
$598$	−1.36638e6	+	4.20528e6i	−0.156249	+	0.480886i
$599$	−7.27884e6			−0.828887			−0.414443	−	0.910075i	$-0.636024\pi$
$599$	−7.27884e6			−0.828887			−0.414443	+	0.910075i	$0.636024\pi$
$600$	998106.	−	1.49793e6i	0.113188	−	0.169868i
$601$	1.98630e6			0.224315			0.112157	−	0.993690i	$-0.464224\pi$
$601$	1.98630e6			0.224315			0.112157	+	0.993690i	$0.464224\pi$
$602$	−1.79786e6	+	5.53325e6i	−0.202193	+	0.622285i
$603$	3.30531e6	+	2.40145e6i	0.370185	+	0.268955i
$604$	−2.01639e6	−	1.46499e6i	−0.224896	−	0.163397i
$605$	3.98008e6	+	547911.i	0.442083	+	0.0608586i
$606$	−3.46316e6	+	2.51613e6i	−0.383081	+	0.278325i
$607$	−25599.6			−0.00282008			−0.00141004	−	0.999999i	$-0.500449\pi$
$607$	−25599.6			−0.00282008			−0.00141004	+	0.999999i	$0.500449\pi$
$608$	−689429.	+	500899.i	−0.0756363	+	0.0549530i
$609$	5.14464e6	+	1.58336e7i	0.562098	+	1.72996i
$610$	4.80188e6	+	661043.i	0.522501	+	0.0719291i
$611$	−7.58818e6	+	2.33540e7i	−0.822308	+	2.53081i
$612$	−43514.4	−	133924.i	−0.00469629	−	0.0144537i
$613$	1.75770e6	+	5.40965e6i	0.188927	+	0.581458i	0.999994	−	0.00349569i	$-0.00111271\pi$
$613$	1.75770e6	+	5.40965e6i	0.188927	+	0.581458i	−0.811067	+	0.584954i	$0.801113\pi$
$614$	3.76316e6	−	1.15818e7i	0.402839	−	1.23981i
$615$	330887.	+	1.84607e6i	0.0352771	+	0.196816i
$616$	−2.43447e6	−	7.49252e6i	−0.258495	−	0.795566i
$617$	−5.45699e6	+	3.96474e6i	−0.577086	+	0.419277i	−0.837672	−	0.546173i	$-0.816084\pi$
$617$	−5.45699e6	+	3.96474e6i	−0.577086	+	0.419277i	0.260587	+	0.965450i	$0.416084\pi$
$618$	−5.82068e6			−0.613059
$619$	−294865.	+	214232.i	−0.0309312	+	0.0224729i	−0.603143	−	0.797633i	$-0.706085\pi$
$619$	−294865.	+	214232.i	−0.0309312	+	0.0224729i	0.572212	+	0.820106i	$0.306085\pi$
$620$	3.24394e6	−	1.73660e6i	0.338917	−	0.181435i
$621$	−654679.	−	475652.i	−0.0681239	−	0.0494949i
$622$	9.11895e6	+	6.62530e6i	0.945080	+	0.686641i
$623$	−4.64622e6	+	1.42996e7i	−0.479601	+	1.47606i
$624$	2.29440e6			0.235888
$625$	−3.76027e6	−	9.01265e6i	−0.385052	−	0.922895i
$626$	−6.86258e6			−0.699925
$627$	1.11702e6	−	3.43783e6i	0.113473	−	0.349233i
$628$	−1.40299e6	−	1.01933e6i	−0.141957	−	0.103138i
$629$	668569.	+	485744.i	0.0673782	+	0.0489531i
$630$	4.07276e6	−	2.18029e6i	0.408825	−	0.218859i
$631$	4.64600e6	−	3.37552e6i	0.464522	−	0.337495i	−0.330781	−	0.943708i	$-0.607312\pi$
$631$	4.64600e6	−	3.37552e6i	0.464522	−	0.337495i	0.795303	+	0.606213i	$0.207312\pi$
$632$	−6.22038e6			−0.619475
$633$	769003.	−	558714.i	0.0762815	−	0.0554217i
$634$	−3.93509e6	−	1.21110e7i	−0.388804	−	1.19662i
$635$	1.00584e6	+	5.61172e6i	0.0989908	+	0.552283i
$636$	1.05905e6	−	3.25943e6i	0.103818	−	0.319520i
$637$	−1.48471e7	−	4.56946e7i	−1.44975	−	4.46186i
$638$	4.32652e6	+	1.33157e7i	0.420811	+	1.29512i
$639$	446310.	−	1.37360e6i	0.0432398	−	0.133079i
$640$	−907336.	−	124907.i	−0.0875625	−	0.0120541i
$641$	−2.35929e6	−	7.26113e6i	−0.226796	−	0.698006i	−0.998104	−	0.0615447i	$-0.980397\pi$
$641$	−2.35929e6	−	7.26113e6i	−0.226796	−	0.698006i	0.771308	−	0.636462i	$-0.219603\pi$
$642$	−2.57292e6	+	1.86933e6i	−0.246370	+	0.178998i
$643$	−1.76515e7			−1.68366			−0.841832	−	0.539740i	$-0.818522\pi$
$643$	−1.76515e7			−1.68366			−0.841832	+	0.539740i	$0.818522\pi$
$644$	3.66487e6	−	2.66269e6i	0.348212	−	0.252991i
$645$	−2.84228e6	−	391278.i	−0.269010	−	0.0370328i
$646$	292614.	+	212597.i	0.0275876	+	0.0200436i
$647$	1.08793e6	+	790430.i	0.102174	+	0.0742340i	0.637699	−	0.770285i	$-0.279886\pi$
$647$	1.08793e6	+	790430.i	0.102174	+	0.0742340i	−0.535525	+	0.844519i	$0.679886\pi$
$648$	−129757.	+	399352.i	−0.0121393	+	0.0373610i
$649$	8.43759e6			0.786333
$650$	6.90240e6	−	1.03589e7i	0.640791	−	0.961680i
$651$	9.44338e6			0.873323
$652$	1.39572e6	−	4.29557e6i	0.128581	−	0.395733i
$653$	1.52787e7	+	1.11007e7i	1.40218	+	1.01875i	0.994402	+	0.105665i	$0.0336972\pi$
$653$	1.52787e7	+	1.11007e7i	1.40218	+	1.01875i	0.407781	+	0.913080i	$0.366303\pi$
$654$	5.35086e6	+	3.88763e6i	0.489192	+	0.355419i
$655$	−5.42871e6	+	1.12107e7i	−0.494417	+	1.02101i
$656$	772047.	−	560925.i	0.0700461	−	0.0508915i
$657$	514797.			0.0465289
$658$	2.03529e7	−	1.47872e7i	1.83257	−	1.33144i
$659$	−3.06747e6	−	9.44069e6i	−0.275148	−	0.846818i	−0.989180	−	0.146706i	$-0.953133\pi$
$659$	−3.06747e6	−	9.44069e6i	−0.275148	−	0.846818i	0.714032	−	0.700113i	$-0.246867\pi$
$660$	3.42509e6	−	1.83357e6i	0.306064	−	0.163847i
$661$	−3.49567e6	+	1.07586e7i	−0.311191	+	0.957747i	0.666103	+	0.745859i	$0.267961\pi$
$661$	−3.49567e6	+	1.07586e7i	−0.311191	+	0.957747i	−0.977294	+	0.211887i	$0.932039\pi$
$662$	2.47535e6	+	7.61836e6i	0.219529	+	0.675642i
$663$	−300924.	−	926148.i	−0.0265872	−	0.0818270i
$664$	−2.38058e6	+	7.32669e6i	−0.209538	+	0.644892i
$665$	−5.17147e6	+	1.06795e7i	−0.453482	+	0.936476i
$666$	−761500.	−	2.34366e6i	−0.0665249	−	0.204743i
$667$	−6.51318e6	+	4.73211e6i	−0.566864	+	0.411851i
$668$	−2.00001e6			−0.173417
$669$	−7.82424e6	+	5.68464e6i	−0.675891	+	0.491064i
$670$	−8.13522e6	−	7.81183e6i	−0.700136	−	0.672304i
$671$	8.46378e6	+	6.14930e6i	0.725702	+	0.527253i
$672$	−1.90168e6	−	1.38165e6i	−0.162448	−	0.118026i
$673$	−192788.	+	593340.i	−0.0164075	+	0.0504971i	−0.958925	−	0.283660i	$-0.908451\pi$
$673$	−192788.	+	593340.i	−0.0164075	+	0.0504971i	0.942518	+	0.334157i	$0.108451\pi$
$674$	−4.37354e6			−0.370837
$675$	1.41267e6	+	1.78724e6i	0.119338	+	0.150981i
$676$	9.92619e6			0.835441
$677$	−5.87597e6	+	1.80844e7i	−0.492729	+	1.51646i	0.327738	+	0.944769i	$0.393714\pi$
$677$	−5.87597e6	+	1.80844e7i	−0.492729	+	1.51646i	−0.820466	+	0.571695i	$0.806286\pi$
$678$	5.74850e6	+	4.17653e6i	0.480264	+	0.348932i
$679$	−2.06526e7	−	1.50050e7i	−1.71910	−	1.24900i
$680$	68583.1	+	382635.i	0.00568781	+	0.0317331i
$681$	4.52341e6	−	3.28645e6i	0.373765	−	0.271556i
$682$	7.94165e6			0.653807
$683$	−1.14494e7	+	8.31846e6i	−0.939140	+	0.682325i	−0.948213	−	0.317634i	$-0.897112\pi$
$683$	−1.14494e7	+	8.31846e6i	−0.939140	+	0.682325i	0.00907370	+	0.999959i	$0.497112\pi$
$684$	−333288.	−	1.02575e6i	−0.0272382	−	0.0838307i
$685$	−4.44218e6	−	4.26559e6i	−0.361717	−	0.347339i
$686$	−9.91213e6	+	3.05064e7i	−0.804186	+	2.47503i
$687$	1.72490e6	+	5.30869e6i	0.139435	+	0.429137i
$688$	451127.	+	1.38843e6i	0.0363352	+	0.111828i
$689$	7.32387e6	−	2.25406e7i	0.587750	−	1.80891i
$690$	1.61133e6	+	1.54728e6i	0.128844	+	0.123722i
$691$	191341.	+	588886.i	0.0152445	+	0.0469176i	0.958389	−	0.285464i	$-0.0921478\pi$
$691$	191341.	+	588886.i	0.0152445	+	0.0469176i	−0.943145	+	0.332382i	$0.892148\pi$
$692$	2.09049e6	−	1.51883e6i	0.165952	−	0.120571i
$693$	9.97072e6			0.788667
$694$	−3.20567e6	+	2.32906e6i	−0.252651	+	0.183561i
$695$	−0.221933	−	1.23820i	−1.74285e−8	−	9.72362e-8i
$696$	3.37966e6	+	2.45546e6i	0.264454	+	0.192137i
$697$	−327680.	−	238073.i	−0.0255486	−	0.0185622i
$698$	−940117.	+	2.89338e6i	−0.0730371	+	0.224785i
$699$	739877.			0.0572752
$700$	−1.19590e7	+	4.42933e6i	−0.922462	+	0.341659i
$701$	2.34039e7			1.79885			0.899423	−	0.437079i	$-0.143987\pi$
$701$	2.34039e7			1.79885			0.899423	+	0.437079i	$0.143987\pi$
$702$	−897337.	+	2.76172e6i	−0.0687247	+	0.211513i
$703$	5.12073e6	+	3.72043e6i	0.390790	+	0.283926i
$704$	−1.59927e6	−	1.16194e6i	−0.121616	−	0.0883590i
$705$	8.94853e6	+	8.59281e6i	0.678077	+	0.651122i
$706$	1.79439e6	−	1.30370e6i	0.135490	−	0.0984390i
$707$	3.03284e7			2.28193
$708$	2.03674e6	−	1.47978e6i	0.152704	−	0.110946i
$709$	3.68325e6	+	1.13359e7i	0.275179	+	0.846915i	0.989172	+	0.146761i	$0.0468850\pi$
$709$	3.68325e6	+	1.13359e7i	0.275179	+	0.846915i	−0.713993	+	0.700153i	$0.753115\pi$
$710$	−1.73769e6	+	3.58847e6i	−0.129368	+	0.267155i
$711$	2.43279e6	−	7.48735e6i	0.180480	−	0.555461i
$712$	1.16585e6	+	3.58811e6i	0.0861871	+	0.265257i
$713$	1.41115e6	+	4.34307e6i	0.103956	+	0.319943i
$714$	−308296.	+	948839.i	−0.0226320	+	0.0696542i
$715$	2.36862e7	−	1.26801e7i	1.73273	−	0.927591i
$716$	417320.	+	1.28438e6i	0.0304219	+	0.0936290i
$717$	−8.60376e6	+	6.25100e6i	−0.625015	+	0.454100i
$718$	7.52060e6			0.544429
$719$	5.69167e6	−	4.13524e6i	0.410599	−	0.298318i	−0.363245	−	0.931694i	$-0.618331\pi$
$719$	5.69167e6	−	4.13524e6i	0.410599	−	0.298318i	0.773844	+	0.633376i	$0.218331\pi$
$720$	505207.	−	1.04329e6i	0.0363193	−	0.0750023i
$721$	3.33631e7	+	2.42397e7i	2.39017	+	1.73656i
$722$	−5.77162e6	−	4.19333e6i	−0.412055	−	0.299375i
$723$	2.55601e6	−	7.86659e6i	0.181852	−	0.559681i
$724$	3.70662e6			0.262804
$725$	2.12534e7	−	7.87177e6i	1.50170	−	0.556195i
$726$	2.58730e6			0.182182
$727$	−5.31795e6	+	1.63670e7i	−0.373171	+	1.14850i	0.571533	+	0.820579i	$0.306349\pi$
$727$	−5.31795e6	+	1.63670e7i	−0.373171	+	1.14850i	−0.944704	+	0.327924i	$0.893651\pi$
$728$	−1.31511e7	−	9.55482e6i	−0.919672	−	0.668181i
$729$	−429945.	−	312373.i	−0.0299636	−	0.0217698i
$730$	−1.40786e6	−	193811.i	−0.0977805	−	0.0134608i
$731$	501279.	−	364201.i	0.0346965	−	0.0252085i
$732$	3.12152e6			0.215322
$733$	3.09587e6	−	2.24928e6i	0.212825	−	0.154626i	−0.476266	−	0.879301i	$-0.658010\pi$
$733$	3.09587e6	−	2.24928e6i	0.212825	−	0.154626i	0.689091	+	0.724675i	$0.258010\pi$
$734$	−1.43455e6	−	4.41509e6i	−0.0982823	−	0.302482i
$735$	−2.40472e7	−	3.31041e6i	−1.64190	−	0.226029i
$736$	351258.	−	1.08106e6i	0.0239018	−	0.0735623i
$737$	−7.52239e6	−	2.31515e7i	−0.510137	−	1.57004i
$738$	373227.	+	1.14868e6i	0.0252251	+	0.0776348i
$739$	−7.05143e6	+	2.17021e7i	−0.474970	+	1.46181i	0.371028	+	0.928622i	$0.379005\pi$
$739$	−7.05143e6	+	2.17021e7i	−0.474970	+	1.46181i	−0.845998	+	0.533186i	$0.820995\pi$
$740$	1.20020e6	+	6.69609e6i	0.0805702	+	0.449512i
$741$	−2.30485e6	−	7.09359e6i	−0.154204	−	0.474592i
$742$	−1.96439e7	+	1.42721e7i	−1.30984	+	0.951655i
$743$	1.54125e7			1.02424			0.512119	−	0.858915i	$-0.328861\pi$
$743$	1.54125e7			1.02424			0.512119	+	0.858915i	$0.328861\pi$
$744$	1.91702e6	−	1.39280e6i	0.126968	−	0.0922478i
$745$	−3.70547e6	+	1.98367e6i	−0.244598	+	0.130942i
$746$	−1.04587e7	−	7.59866e6i	−0.688064	−	0.499908i
$747$	−7.88795e6	−	5.73093e6i	−0.517205	−	0.375771i
$748$	−259270.	+	797950.i	−0.0169433	+	0.0521461i
$749$	2.25322e7			1.46757
$750$	−3.19048e6	−	5.41956e6i	−0.207111	−	0.351812i
$751$	1.95446e7			1.26452			0.632261	−	0.774756i	$-0.282127\pi$
$751$	1.95446e7			1.26452			0.632261	+	0.774756i	$0.282127\pi$
$752$	1.95071e6	−	6.00366e6i	0.125790	−	0.387143i
$753$	−6.66114e6	−	4.83960e6i	−0.428116	−	0.311044i
$754$	2.33720e7	+	1.69807e7i	1.49716	+	1.08775i
$755$	−7.67720e6	+	4.10988e6i	−0.490157	+	0.262399i
$756$	2.40682e6	−	1.74866e6i	0.153158	−	0.111276i
$757$	1.28122e7			0.812615			0.406307	−	0.913736i	$-0.366816\pi$
$757$	1.28122e7			0.812615			0.406307	+	0.913736i	$0.366816\pi$
$758$	−8.15856e6	+	5.92754e6i	−0.515751	+	0.374715i
$759$	1.48995e6	+	4.58560e6i	0.0938788	+	0.288929i
$760$	525295.	+	2.93069e6i	0.0329890	+	0.184050i
$761$	7.46806e6	−	2.29843e7i	0.467462	−	1.43870i	−0.388398	−	0.921492i	$-0.626972\pi$
$761$	7.46806e6	−	2.29843e7i	0.467462	−	1.43870i	0.855860	−	0.517207i	$-0.173028\pi$
$762$	1.13455e6	+	3.49178e6i	0.0707840	+	0.217851i
$763$	−1.44805e7	−	4.45664e7i	−0.900476	−	2.77138i
$764$	−3.67690e6	+	1.13163e7i	−0.227902	+	0.701411i
$765$	−487393.	−	67096.1i	−0.0301110	−	0.00414518i
$766$	−4.43721e6	−	1.36563e7i	−0.273236	−	0.840934i
$767$	1.40850e7	−	1.02334e7i	0.864509	−	0.628103i
$768$	−589824.			−0.0360844
$769$	−2.35693e7	+	1.71241e7i	−1.43725	+	1.04422i	−0.448637	+	0.893714i	$0.648090\pi$
$769$	−2.35693e7	+	1.71241e7i	−1.43725	+	1.04422i	−0.988609	+	0.150506i	$0.951910\pi$
$770$	−2.72678e7	−	3.75377e6i	−1.65738	−	0.228161i
$771$	1.77021e6	+	1.28613e6i	0.107248	+	0.0779200i
$772$	−3.31917e6	−	2.41152e6i	−0.200441	−	0.145629i
$773$	−3.30796e6	+	1.01809e7i	−0.199119	+	0.612824i	0.800785	+	0.598952i	$0.204416\pi$
$773$	−3.30796e6	+	1.01809e7i	−0.199119	+	0.612824i	−0.999904	+	0.0138725i	$0.995584\pi$
$774$	−1.84766e6			−0.110858
$775$	−521189.	−	1.28452e7i	−0.0311703	−	0.768220i
$776$	−6.40558e6			−0.381860
$777$	−5.39517e6	+	1.66046e7i	−0.320592	+	0.986681i
$778$	3.24486e6	+	2.35753e6i	0.192197	+	0.139639i
$779$	−2.50978e6	−	1.82346e6i	−0.148181	−	0.107660i
$780$	3.49376e6	−	7.21488e6i	0.205616	−	0.424612i
$781$	−6.96194e6	+	5.05814e6i	−0.408416	+	0.296731i
$782$	−482446.			−0.0282119
$783$	−4.27738e6	+	3.10770e6i	−0.249329	+	0.181148i
$784$	3.81676e6	+	1.17468e7i	0.221771	+	0.682541i
$785$	−5.34174e6	+	2.85963e6i	−0.309392	+	0.165629i
$786$	−2.47877e6	+	7.62888e6i	−0.143113	+	0.440458i
$787$	9.27087e6	+	2.85328e7i	0.533561	+	1.64213i	0.746739	+	0.665118i	$0.231619\pi$
$787$	9.27087e6	+	2.85328e7i	0.533561	+	1.64213i	−0.213178	+	0.977013i	$0.568381\pi$
$788$	−1.57715e6	−	4.85396e6i	−0.0904809	−	0.278472i
$789$	−24509.1	+	75431.3i	−0.00140164	+	0.00431379i
$790$	−9.47198e6	+	1.95604e7i	−0.539974	+	1.11509i
$791$	−1.55566e7	−	4.78783e7i	−0.884043	−	2.72080i
$792$	2.02407e6	−	1.47058e6i	0.114660	−	0.0833056i
$793$	2.15868e7			1.21901
$794$	3.06120e6	−	2.22410e6i	0.172322	−	0.125199i
$795$	−8.63684e6	−	8.29351e6i	−0.484660	−	0.465394i
$796$	9.32505e6	+	6.77505e6i	0.521637	+	0.378992i
$797$	−1.99201e6	−	1.44728e6i	−0.111083	−	0.0807062i	0.530857	−	0.847461i	$-0.321870\pi$
$797$	−1.99201e6	−	1.44728e6i	−0.111083	−	0.0807062i	−0.641940	+	0.766755i	$0.721870\pi$
$798$	−2.36132e6	+	7.26739e6i	−0.131265	+	0.403991i
$799$	−2.67926e6			−0.148473
$800$	−1.77441e6	+	2.66298e6i	−0.0980233	+	0.147110i
$801$	−4.77491e6			−0.262956
$802$	6.78407e6	−	2.08792e7i	0.372438	−	1.14625i
$803$	−2.48149e6	−	1.80291e6i	−0.135807	−	0.0986699i
$804$	−5.87611e6	−	4.26924e6i	−0.320590	−	0.232922i
$805$	−2.79237e6	−	1.55790e7i	−0.151874	−	0.847325i
$806$	1.32572e7	−	9.63189e6i	0.718808	−	0.522245i
$807$	−7.95028e6			−0.429733
$808$	6.15672e6	−	4.47312e6i	0.331758	−	0.241036i
$809$	1.47710e6	+	4.54604e6i	0.0793483	+	0.244209i	0.982860	−	0.184355i	$-0.0590196\pi$
$809$	1.47710e6	+	4.54604e6i	0.0793483	+	0.244209i	−0.903511	+	0.428564i	$0.859020\pi$
$810$	1.05820e6	+	1.01614e6i	0.0566705	+	0.0544178i
$811$	−1.13087e7	+	3.48047e7i	−0.603756	+	1.85817i	−0.0986274	+	0.995124i	$0.531445\pi$
$811$	−1.13087e7	+	3.48047e7i	−0.603756	+	1.85817i	−0.505128	+	0.863044i	$0.668555\pi$
$812$	−9.14603e6	−	2.81486e7i	−0.486791	−	1.49819i
$813$	−1.73035e6	−	5.32546e6i	−0.0918136	−	0.282573i
$814$	−4.53721e6	+	1.39641e7i	−0.240009	+	0.738672i
$815$	−1.13824e7	−	1.09299e7i	−0.600261	−	0.576400i
$816$	77359.0	+	238086.i	0.00406710	+	0.0125173i
$817$	3.83942e6	−	2.78950e6i	0.201238	−	0.146208i
$818$	2.22538e7			1.16284
$819$	1.66443e7	−	1.20928e7i	0.867075	−	0.629967i
$820$	−588244.	−	3.28190e6i	−0.0305508	−	0.170447i
$821$	−9.02695e6	−	6.55846e6i	−0.467394	−	0.339582i	0.329031	−	0.944319i	$-0.393278\pi$
$821$	−9.02695e6	−	6.55846e6i	−0.467394	−	0.339582i	−0.796425	+	0.604738i	$0.793278\pi$
$822$	−3.20861e6	−	2.33119e6i	−0.165629	−	0.120337i
$823$	5.73292e6	−	1.76441e7i	0.295037	−	0.908030i	−0.688172	−	0.725547i	$-0.741587\pi$
$823$	5.73292e6	−	1.76441e7i	0.295037	−	0.908030i	0.983209	−	0.182483i	$-0.0584133\pi$
$824$	1.03479e7			0.530925
$825$	−550293.	−	1.35625e7i	−0.0281488	−	0.693752i
$826$	−1.78366e7			−0.909625
$827$	−961383.	+	2.95883e6i	−0.0488802	+	0.150438i	−0.972517	−	0.232830i	$-0.925201\pi$
$827$	−961383.	+	2.95883e6i	−0.0488802	+	0.150438i	0.923637	+	0.383268i	$0.125201\pi$
$828$	1.16387e6	+	845604.i	0.0589970	+	0.0428639i
$829$	9.47462e6	+	6.88371e6i	0.478823	+	0.347886i	0.800870	−	0.598838i	$-0.204371\pi$
$829$	9.47462e6	+	6.88371e6i	0.478823	+	0.347886i	−0.322047	+	0.946724i	$0.604371\pi$
$830$	1.94143e7	+	1.86425e7i	0.978196	+	0.939310i
$831$	−1.91542e6	+	1.39163e6i	−0.0962191	+	0.0699073i
$832$	−4.07892e6			−0.204285
$833$	4.24108e6	−	3.08132e6i	0.211770	−	0.153860i
$834$	−0.250332	−	0.770442i	−1.24624e−8	−	3.83553e-8i
$835$	−3.04548e6	+	6.28916e6i	−0.151161	+	0.312159i
$836$	−1.98581e6	+	6.11170e6i	−0.0982703	+	0.302445i
$837$	926738.	+	2.85221e6i	0.0457239	+	0.140724i
$838$	−617964.	−	1.90190e6i	−0.0303986	−	0.0935572i
$839$	−6.17918e6	+	1.90175e7i	−0.303058	+	0.932716i	0.677337	+	0.735673i	$0.263134\pi$
$839$	−6.17918e6	+	1.90175e7i	−0.303058	+	0.932716i	−0.980395	+	0.197043i	$0.936866\pi$
$840$	−7.24046e6	+	3.87608e6i	−0.354053	+	0.189537i
$841$	9.91596e6	+	3.05182e7i	0.483443	+	1.48788i
$842$	−9.34497e6	+	6.78952e6i	−0.454253	+	0.330034i
$843$	−1.07969e7			−0.523275
$844$	−1.36712e6	+	993269.i	−0.0660617	+	0.0479966i
$845$	1.51150e7	−	3.12136e7i	0.728224	−	1.50384i
$846$	6.46357e6	+	4.69606e6i	0.310489	+	0.225584i
$847$	−1.48299e7	−	1.07746e7i	−0.710282	−	0.516050i
$848$	−1.88276e6	+	5.79454e6i	−0.0899095	+	0.276713i
$849$	460297.			0.0219164
$850$	1.30765e6	+	366987.i	0.0620791	+	0.0174222i
$851$	−8.44279e6			−0.399634
$852$	−793439.	+	2.44195e6i	−0.0374468	+	0.115249i
$853$	1.89384e7	+	1.37596e7i	0.891193	+	0.647489i	0.936189	−	0.351498i	$-0.114328\pi$
$853$	1.89384e7	+	1.37596e7i	0.891193	+	0.647489i	−0.0449961	+	0.998987i	$0.514328\pi$
$854$	−1.78920e7	−	1.29993e7i	−0.839487	−	0.609923i
$855$	−3.73306e6	−	513905.i	−0.174642	−	0.0240419i
$856$	4.57407e6	−	3.32326e6i	0.213363	−	0.155017i
$857$	2.44395e7			1.13669			0.568343	−	0.822792i	$-0.307585\pi$
$857$	2.44395e7			1.13669			0.568343	+	0.822792i	$0.307585\pi$
$858$	1.39975e7	−	1.01698e7i	0.649130	−	0.471620i
$859$	−1.02383e7	−	3.15103e7i	−0.473419	−	1.45703i	−0.848078	−	0.529872i	$-0.822240\pi$
$859$	−1.02383e7	−	3.15103e7i	−0.473419	−	1.45703i	0.374659	−	0.927163i	$-0.377760\pi$
$860$	5.05295e6	+	695605.i	0.232969	+	0.0320713i
$861$	2.64429e6	−	8.13829e6i	0.121563	−	0.374132i
$862$	3.48430e6	+	1.07236e7i	0.159715	+	0.491554i
$863$	6.25288e6	+	1.92444e7i	0.285794	+	0.879583i	0.986160	+	0.165799i	$0.0530203\pi$
$863$	6.25288e6	+	1.92444e7i	0.285794	+	0.879583i	−0.700366	+	0.713784i	$0.746980\pi$
$864$	230680.	−	709960.i	0.0105130	−	0.0323556i
$865$	−1.59280e6	−	8.88648e6i	−0.0723806	−	0.403821i
$866$	−2.63544e6	−	8.11104e6i	−0.119415	−	0.367521i
$867$	−1.02522e7	+	7.44869e6i	−0.463202	+	0.336536i
$868$	−1.67882e7			−0.756320
$869$	−3.79488e7	+	2.75714e7i	−1.70470	+	1.23854i
$870$	1.28677e7	−	6.88854e6i	0.576372	−	0.308552i
$871$	−4.06362e7	−	2.95239e7i	−1.81496	−	1.31865i
$872$	−9.51264e6	−	6.91134e6i	−0.423652	−	0.307802i
$873$	2.50522e6	−	7.71028e6i	0.111253	−	0.342401i
$874$	−3.69518e6			−0.163628
$875$	−4.28201e6	+	4.43505e7i	−0.189072	+	1.95829i
$876$	−915195.			−0.0402952
$877$	−1.05288e7	+	3.24043e7i	−0.462253	+	1.42267i	0.400153	+	0.916448i	$0.368957\pi$
$877$	−1.05288e7	+	3.24043e7i	−0.462253	+	1.42267i	−0.862405	+	0.506218i	$0.831043\pi$
$878$	−5.63525e6	−	4.09425e6i	−0.246705	−	0.179241i
$879$	7.07877e6	+	5.14302e6i	0.309019	+	0.224516i
$880$	−6.08905e6	+	3.25969e6i	−0.265059	+	0.141896i
$881$	−6.66115e6	+	4.83961e6i	−0.289141	+	0.210073i	−0.722894	−	0.690958i	$-0.757189\pi$
$881$	−6.66115e6	+	4.83961e6i	−0.289141	+	0.210073i	0.433754	+	0.901031i	$0.357189\pi$
$882$	−1.56321e7			−0.676623
$883$	−1.67043e7	+	1.21364e7i	−0.720985	+	0.523826i	−0.886699	−	0.462348i	$-0.847007\pi$
$883$	−1.67043e7	+	1.21364e7i	−0.720985	+	0.523826i	0.165714	+	0.986174i	$0.447007\pi$
$884$	534975.	+	1.64649e6i	0.0230252	+	0.0708642i
$885$	−1.55185e6	−	8.65796e6i	−0.0666025	−	0.371584i
$886$	4.99069e6	−	1.53598e7i	0.213588	−	0.657355i
$887$	−6.93168e6	−	2.13335e7i	−0.295821	−	0.910444i	−0.982944	−	0.183903i	$-0.941127\pi$
$887$	−6.93168e6	−	2.13335e7i	−0.295821	−	0.910444i	0.687123	−	0.726541i	$-0.258873\pi$
$888$	1.35378e6	+	4.16650e6i	0.0576123	+	0.177312i
$889$	8.03819e6	−	2.47390e7i	0.341117	−	1.04985i
$890$	1.30583e7	+	1.79765e6i	0.552603	+	0.0760731i
$891$	978489.	+	3.01148e6i	0.0412916	+	0.127083i
$892$	1.39098e7	−	1.01060e7i	0.585339	−	0.425274i
$893$	−2.05211e7			−0.861138
$894$	−2.18977e6	+	1.59096e6i	−0.0916335	+	0.0665756i
$895$	4.67428e6	+	643477.i	0.195055	+	0.0268519i
$896$	3.38077e6	+	2.45627e6i	0.140684	+	0.102213i
$897$	8.04877e6	+	5.84777e6i	0.334001	+	0.242666i
$898$	715396.	−	2.20176e6i	0.0296044	−	0.0911128i
$899$	2.98359e7			1.23123
$900$	−2.51141e6	−	3.17732e6i	−0.103350	−	0.130754i
$901$	2.58594e6			0.106122
$902$	2.22378e6	−	6.84410e6i	0.0910072	−	0.280091i
$903$	1.05905e7	+	7.69441e6i	0.432210	+	0.314019i
$904$	−1.02195e7	−	7.42494e6i	−0.415921	−	0.302184i
$905$	5.64420e6	−	1.16557e7i	0.229077	−	0.473062i
$906$	−4.53688e6	+	3.29623e6i	−0.183627	+	0.133413i
$907$	2.22145e7			0.896642			0.448321	−	0.893873i	$-0.352022\pi$
$907$	2.22145e7			0.896642			0.448321	+	0.893873i	$0.352022\pi$
$908$	−8.04162e6	+	5.84258e6i	−0.323690	+	0.235174i
$909$	2.97632e6	+	9.16017e6i	0.119473	+	0.367700i
$910$	−5.00714e7	+	2.68050e7i	−2.00441	+	1.07303i
$911$	−518041.	+	1.59437e6i	−0.0206808	+	0.0636490i	−0.960864	−	0.277019i	$-0.910653\pi$
$911$	−518041.	+	1.59437e6i	−0.0206808	+	0.0636490i	0.940183	+	0.340668i	$0.110653\pi$
$912$	592511.	+	1.82356e6i	0.0235890	+	0.0725995i
$913$	1.79518e7	+	5.52499e7i	0.712739	+	2.19358i
$914$	2.66609e6	−	8.20539e6i	0.105563	−	0.324888i
$915$	4.75324e6	−	9.81582e6i	0.187688	−	0.387591i
$916$	−3.06649e6	−	9.43768e6i	−0.120754	−	0.371643i
$917$	4.59777e7	−	3.34048e7i	1.80561	−	1.31185i
$918$	−316835.			−0.0124087
$919$	−2.90124e7	+	2.10787e7i	−1.13317	+	0.823296i	−0.986153	−	0.165838i	$-0.946967\pi$
$919$	−2.90124e7	+	2.10787e7i	−1.13317	+	0.823296i	−0.147017	+	0.989134i	$0.546967\pi$
$920$	−2.86459e6	−	2.75072e6i	−0.111582	−	0.107146i
$921$	−2.21672e7	−	1.61054e7i	−0.861115	−	0.625637i
$922$	9.22490e6	+	6.70228e6i	0.357383	+	0.259654i
$923$	−5.48702e6	+	1.68873e7i	−0.211998	+	0.652464i
$924$	−1.77257e7			−0.683006
$925$	2.28839e7	+	6.42225e6i	0.879378	+	0.246793i
$926$	−8.82454e6			−0.338193
$927$	−4.04705e6	+	1.24555e7i	−0.154682	+	0.476062i
$928$	−6.00828e6	−	4.36527e6i	−0.229023	−	0.166395i
$929$	−2.92599e7	−	2.12586e7i	−1.11233	−	0.808155i	−0.129301	−	0.991605i	$-0.541273\pi$
$929$	−2.92599e7	−	2.12586e7i	−1.11233	−	0.808155i	−0.983029	+	0.183450i	$0.941273\pi$
$930$	−1.46063e6	−	8.14907e6i	−0.0553775	−	0.308959i
$931$	3.24835e7	−	2.36006e7i	1.22825	−	0.892379i
$932$	−1.31534e6			−0.0496018
$933$	2.05176e7	−	1.49069e7i	0.771655	−	0.560640i
$934$	1.12471e6	+	3.46152e6i	0.0421867	+	0.129837i
$935$	2.11441e6	+	2.03036e6i	0.0790970	+	0.0759528i
$936$	1.59527e6	−	4.90972e6i	0.0595173	−	0.183176i
$937$	−1.59456e7	−	4.90755e7i	−0.593324	−	1.82606i	−0.562897	−	0.826527i	$-0.690313\pi$
$937$	−1.59456e7	−	4.90755e7i	−0.593324	−	1.82606i	−0.0304271	−	0.999537i	$-0.509687\pi$
$938$	1.59019e7	+	4.89411e7i	0.590123	+	1.81621i
$939$	−4.77147e6	+	1.46851e7i	−0.176599	+	0.543516i
$940$	−1.59085e7	−	1.52761e7i	−0.587232	−	0.563888i
$941$	−1.14153e7	−	3.51327e7i	−0.420256	−	1.29341i	−0.907465	−	0.420129i	$-0.861985\pi$
$941$	−1.14153e7	−	3.51327e7i	−0.420256	−	1.29341i	0.487209	−	0.873285i	$-0.338015\pi$
$942$	−3.15673e6	+	2.29350e6i	−0.115907	+	0.0842114i
$943$	4.13799e6			0.151534
$944$	−3.62086e6	+	2.63071e6i	−0.132246	+	0.0960823i
$945$	−1.83382e6	−	1.02311e7i	−0.0668001	−	0.372687i
$946$	8.90631e6	+	6.47081e6i	0.323571	+	0.235088i
$947$	−3.85537e6	−	2.80109e6i	−0.139698	−	0.101497i	0.515741	−	0.856744i	$-0.327517\pi$
$947$	−3.85537e6	−	2.80109e6i	−0.139698	−	0.101497i	−0.655440	+	0.755248i	$0.727517\pi$
$948$	−4.32495e6	+	1.33108e7i	−0.156301	+	0.481044i
$949$	−6.32902e6			−0.228124
$950$	1.00156e7	+	2.81084e6i	0.360056	+	0.101048i
$951$	−2.86520e7			−1.02731
$952$	548083.	−	1.68682e6i	0.0195999	−	0.0603223i
$953$	−3.91816e7	−	2.84671e7i	−1.39749	−	1.01534i	−0.994996	−	0.0999177i	$-0.968142\pi$
$953$	−3.91816e7	−	2.84671e7i	−1.39749	−	1.01534i	−0.402498	−	0.915421i	$-0.631858\pi$
$954$	−6.23843e6	−	4.53248e6i	−0.221924	−	0.161237i
$955$	2.99860e7	+	2.87940e7i	1.06392	+	1.02163i
$956$	1.52956e7	−	1.11129e7i	0.541279	−	0.393262i
$957$	3.15020e7			1.11188
$958$	−1.52386e6	+	1.10715e6i	−0.0536453	+	0.0389756i
$959$	8.68314e6	+	2.67239e7i	0.304881	+	0.938327i
$960$	−898146.	+	1.85474e6i	−0.0314535	+	0.0649539i
$961$	−3.61720e6	+	1.11326e7i	−0.126347	+	0.388855i
$962$	9.36204e6	+	2.88134e7i	0.326162	+	1.00382i
$963$	2.21122e6	+	6.80545e6i	0.0768364	+	0.236478i
$964$	−4.54402e6	+	1.39851e7i	−0.157488	+	0.484698i
$965$	−1.26374e7	+	6.76525e6i	−0.436857	+	0.233865i
$966$	−3.14968e6	−	9.69371e6i	−0.108598	−	0.334231i
$967$	3.47455e7	−	2.52441e7i	1.19490	−	0.868148i	0.201129	−	0.979565i	$-0.435539\pi$
$967$	3.47455e7	−	2.52441e7i	1.19490	−	0.868148i	0.993774	+	0.111417i	$0.0355390\pi$
$968$	−4.59964e6			−0.157774
$969$	658382.	−	478342.i	0.0225252	−	0.0163655i
$970$	−9.75401e6	+	2.01428e7i	−0.332854	+	0.687370i
$971$	9.85827e6	+	7.16245e6i	0.335546	+	0.243789i	0.742780	−	0.669535i	$-0.233507\pi$
$971$	9.85827e6	+	7.16245e6i	0.335546	+	0.243789i	−0.407234	+	0.913324i	$0.633507\pi$
$972$	764346.	+	555330.i	0.0259492	+	0.0188532i
$973$	−1.77358	+	5.45853i	−6.00578e−8	+	1.84839e-7i
$974$	−3.91808e7			−1.32335
$975$	−1.73676e7	−	2.19727e7i	−0.585098	−	0.740239i
$976$	−5.54936e6			−0.186474
$977$	1.08711e7	−	3.34578e7i	0.364366	−	1.12140i	−0.586011	−	0.810303i	$-0.699303\pi$
$977$	1.08711e7	−	3.34578e7i	0.364366	−	1.12140i	0.950377	−	0.311100i	$-0.100697\pi$
$978$	−8.22157e6	−	5.97332e6i	−0.274858	−	0.199696i
$979$	2.30166e7	+	1.67225e7i	0.767511	+	0.557629i
$980$	4.27505e7	+	5.88517e6i	1.42192	+	0.195747i
$981$	1.20394e7	−	8.74716e6i	0.399423	−	0.290198i
$982$	7.45687e6			0.246762
$983$	−1.36830e7	+	9.94128e6i	−0.451645	+	0.328140i	−0.790245	−	0.612791i	$-0.790047\pi$
$983$	−1.36830e7	+	9.94128e6i	−0.451645	+	0.328140i	0.338600	+	0.940931i	$0.390047\pi$
$984$	−663515.	−	2.04209e6i	−0.0218456	−	0.0672337i
$985$	−1.76652e7	−	2.43185e6i	−0.580134	−	0.0798631i
$986$	−974048.	+	2.99781e6i	−0.0319072	+	0.0982002i
$987$	−1.74917e7	−	5.38340e7i	−0.571531	−	1.75899i
$988$	4.09751e6	+	1.26108e7i	0.133545	+	0.411009i
$989$	−1.95615e6	+	6.02041e6i	−0.0635933	+	0.195720i
$990$	−1.54220e6	−	8.60414e6i	−0.0500095	−	0.279010i
$991$	−1.23294e7	−	3.79460e7i	−0.398802	−	1.22739i	−0.925961	−	0.377620i	$-0.876743\pi$
$991$	−1.23294e7	−	3.79460e7i	−0.398802	−	1.22739i	0.527158	−	0.849767i	$-0.323257\pi$
$992$	−3.40804e6	+	2.47609e6i	−0.109958	+	0.0798889i
$993$	1.80234e7			0.580049
$994$	1.47172e7	−	1.06927e7i	0.472453	−	0.343257i
$995$	3.55042e7	−	1.90067e7i	1.13690	−	0.608623i
$996$	1.40230e7	+	1.01883e7i	0.447912	+	0.325427i
$997$	3.74837e7	+	2.72335e7i	1.19428	+	0.867692i	0.993710	−	0.111988i	$-0.0357218\pi$
$997$	3.74837e7	+	2.72335e7i	1.19428	+	0.867692i	0.200566	+	0.979680i	$0.435722\pi$
$998$	8.85981e6	−	2.72677e7i	0.281578	−	0.866607i
$999$	−5.54460e6			−0.175775

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.6.g.a.121.2	yes	20
25.6	even	5	inner	150.6.g.a.31.2	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.6.g.a.31.2	✓	20	25.6	even	5	inner
150.6.g.a.121.2	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)

\(f(q)\)	\(=\)	\(q+(-1.23607 + 3.80423i) q^{2} +(7.28115 + 5.29007i) q^{3} +(-12.9443 - 9.40456i) q^{4} +(-49.2840 + 26.3835i) q^{5} +(-29.1246 + 21.1603i) q^{6} +255.057 q^{7} +(51.7771 - 37.6183i) q^{8} +(25.0304 + 77.0356i) q^{9} +O(q^{10})\)	\(q+(-1.23607 + 3.80423i) q^{2} +(7.28115 + 5.29007i) q^{3} +(-12.9443 - 9.40456i) q^{4} +(-49.2840 + 26.3835i) q^{5} +(-29.1246 + 21.1603i) q^{6} +255.057 q^{7} +(51.7771 - 37.6183i) q^{8} +(25.0304 + 77.0356i) q^{9} +(-39.4504 - 220.099i) q^{10} +(149.137 - 458.997i) q^{11} +(-44.4984 - 136.952i) q^{12} +(-307.729 - 947.092i) q^{13} +(-315.268 + 970.296i) q^{14} +(-498.415 - 68.6134i) q^{15} +(79.1084 + 243.470i) q^{16} +(87.9029 - 63.8652i) q^{17} -324.000 q^{18} +(673.270 - 489.159i) q^{19} +(886.071 + 121.979i) q^{20} +(1857.11 + 1349.27i) q^{21} +(1561.79 + 1134.70i) q^{22} +(-343.025 + 1055.72i) q^{23} +576.000 q^{24} +(1732.82 - 2600.57i) q^{25} +3983.33 q^{26} +(-225.273 + 693.320i) q^{27} +(-3301.53 - 2398.70i) q^{28} +(5867.46 + 4262.96i) q^{29} +(877.095 - 1811.27i) q^{30} +(3328.16 - 2418.05i) q^{31} -1024.00 q^{32} +(3514.02 - 2553.08i) q^{33} +(134.304 + 413.344i) q^{34} +(-12570.2 + 6729.30i) q^{35} +(400.486 - 1232.57i) q^{36} +(2350.31 + 7233.51i) q^{37} +(1028.67 + 3165.91i) q^{38} +(2769.56 - 8523.83i) q^{39} +(-1559.28 + 3220.04i) q^{40} +(-1151.94 - 3545.30i) q^{41} +(-7428.45 + 5397.08i) q^{42} +5702.64 q^{43} +(-6247.14 + 4538.81i) q^{44} +(-3266.06 - 3136.23i) q^{45} +(-3592.20 - 2609.89i) q^{46} +(-19949.3 - 14494.0i) q^{47} +(-711.975 + 2191.23i) q^{48} +48247.3 q^{49} +(7751.26 + 9806.53i) q^{50} +977.886 q^{51} +(-4923.66 + 15153.5i) q^{52} +(19254.4 + 13989.2i) q^{53} +(-2359.09 - 1713.98i) q^{54} +(4759.87 + 26556.0i) q^{55} +(13206.1 - 9594.82i) q^{56} +7489.87 q^{57} +(-23469.8 + 17051.8i) q^{58} +(5402.53 + 16627.3i) q^{59} +(5806.34 + 5575.52i) q^{60} +(-6698.62 + 20616.2i) q^{61} +(5084.98 + 15650.0i) q^{62} +(6384.18 + 19648.5i) q^{63} +(1265.73 - 3895.53i) q^{64} +(40153.7 + 38557.5i) q^{65} +(5368.94 + 16523.9i) q^{66} +(40806.3 - 29647.5i) q^{67} -1738.46 q^{68} +(-8082.46 + 5872.25i) q^{69} +(-10062.1 - 56137.9i) q^{70} +(-14425.4 - 10480.6i) q^{71} +(4193.94 + 3047.08i) q^{72} +(1963.96 - 6044.46i) q^{73} -30423.0 q^{74} +(26374.1 - 9768.38i) q^{75} -13315.3 q^{76} +(38038.6 - 117071. i) q^{77} +(29003.2 + 21072.1i) q^{78} +(-78631.1 - 57128.8i) q^{79} +(-10322.4 - 9912.04i) q^{80} +(-5307.96 + 3856.46i) q^{81} +14911.0 q^{82} +(-97382.0 + 70752.2i) q^{83} +(-11349.7 - 34930.7i) q^{84} +(-2647.22 + 5466.72i) q^{85} +(-7048.86 + 21694.2i) q^{86} +(20170.5 + 62078.5i) q^{87} +(-9544.78 - 29375.8i) q^{88} +(-18216.4 + 56064.3i) q^{89} +(15968.0 - 8548.25i) q^{90} +(-78488.5 - 241563. i) q^{91} +(14368.8 - 10439.6i) q^{92} +37024.5 q^{93} +(79797.1 - 57976.0i) q^{94} +(-20275.7 + 41870.9i) q^{95} +(-7455.90 - 5417.03i) q^{96} +(-80972.3 - 58829.8i) q^{97} +(-59636.9 + 183544. i) q^{98} +39092.1 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

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more