LMFDB - Embedded newform 150.6.g.a.121.1

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			121.1
Root			$0.500000 - 105.104i$ of defining polynomial
Character	$\chi$	$=$	150.121
Dual form			150.6.g.a.31.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.23607 + 3.80423i) q^{2} +(7.28115 + 5.29007i) q^{3} +(-12.9443 - 9.40456i) q^{4} +(-55.7220 - 4.47850i) q^{5} +(-29.1246 + 21.1603i) q^{6} -89.1519 q^{7} +(51.7771 - 37.6183i) q^{8} +(25.0304 + 77.0356i) q^{9} +O(q^{10})$	\(q+(-1.23607 + 3.80423i) q^{2} +(7.28115 + 5.29007i) q^{3} +(-12.9443 - 9.40456i) q^{4} +(-55.7220 - 4.47850i) q^{5} +(-29.1246 + 21.1603i) q^{6} -89.1519 q^{7} +(51.7771 - 37.6183i) q^{8} +(25.0304 + 77.0356i) q^{9} +(85.9134 - 206.443i) q^{10} +(-234.045 + 720.316i) q^{11} +(-44.4984 - 136.952i) q^{12} +(-137.908 - 424.438i) q^{13} +(110.198 - 339.154i) q^{14} +(-382.029 - 327.382i) q^{15} +(79.1084 + 243.470i) q^{16} +(484.961 - 352.345i) q^{17} -324.000 q^{18} +(1874.18 - 1361.67i) q^{19} +(679.163 + 582.012i) q^{20} +(-649.129 - 471.620i) q^{21} +(-2450.95 - 1780.72i) q^{22} +(1250.69 - 3849.23i) q^{23} +576.000 q^{24} +(3084.89 + 499.102i) q^{25} +1785.12 q^{26} +(-225.273 + 693.320i) q^{27} +(1154.01 + 838.435i) q^{28} +(-2866.44 - 2082.59i) q^{29} +(1717.65 - 1048.66i) q^{30} +(-1135.73 + 825.153i) q^{31} -1024.00 q^{32} +(-5514.63 + 4006.62i) q^{33} +(740.954 + 2280.42i) q^{34} +(4967.72 + 399.267i) q^{35} +(400.486 - 1232.57i) q^{36} +(-4114.64 - 12663.5i) q^{37} +(2863.49 + 8812.93i) q^{38} +(1241.17 - 3819.94i) q^{39} +(-3053.60 + 1864.28i) q^{40} +(-2344.43 - 7215.42i) q^{41} +(2596.51 - 1886.48i) q^{42} +5609.41 q^{43} +(9803.79 - 7122.87i) q^{44} +(-1049.74 - 4404.68i) q^{45} +(13097.4 + 9515.81i) q^{46} +(16588.0 + 12051.9i) q^{47} +(-711.975 + 2191.23i) q^{48} -8858.94 q^{49} +(-5711.82 + 11118.7i) q^{50} +5395.00 q^{51} +(-2206.53 + 6791.00i) q^{52} +(29423.7 + 21377.6i) q^{53} +(-2359.09 - 1713.98i) q^{54} +(16267.4 - 39089.3i) q^{55} +(-4616.03 + 3353.74i) q^{56} +20849.5 q^{57} +(11465.8 - 8330.36i) q^{58} +(-644.865 - 1984.69i) q^{59} +(1866.20 + 7830.54i) q^{60} +(15286.1 - 47045.9i) q^{61} +(-1735.23 - 5340.50i) q^{62} +(-2231.51 - 6867.87i) q^{63} +(1265.73 - 3895.53i) q^{64} +(5783.68 + 24268.1i) q^{65} +(-8425.61 - 25931.4i) q^{66} +(-38948.9 + 28298.0i) q^{67} -9591.12 q^{68} +(29469.1 - 21410.6i) q^{69} +(-7659.34 + 18404.8i) q^{70} +(-25294.2 - 18377.3i) q^{71} +(4193.94 + 3047.08i) q^{72} +(-1847.34 + 5685.52i) q^{73} +53261.0 q^{74} +(19821.2 + 19953.3i) q^{75} -37065.8 q^{76} +(20865.5 - 64217.5i) q^{77} +(12997.7 + 9443.41i) q^{78} +(-2944.61 - 2139.38i) q^{79} +(-3317.69 - 13921.0i) q^{80} +(-5307.96 + 3856.46i) q^{81} +30347.0 q^{82} +(-40094.0 + 29130.0i) q^{83} +(3967.12 + 12209.5i) q^{84} +(-28601.0 + 17461.5i) q^{85} +(-6933.62 + 21339.5i) q^{86} +(-9853.94 - 30327.3i) q^{87} +(14978.9 + 46100.2i) q^{88} +(10172.3 - 31307.0i) q^{89} +(18053.9 + 1451.03i) q^{90} +(12294.8 + 37839.4i) q^{91} +(-52389.5 + 38063.2i) q^{92} -12634.5 q^{93} +(-66352.1 + 48207.6i) q^{94} +(-110531. + 67481.6i) q^{95} +(-7455.90 - 5417.03i) q^{96} +(-122153. - 88749.4i) q^{97} +(10950.2 - 33701.4i) q^{98} -61348.2 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
$5$	−55.7220	−	4.47850i	−0.996786	−	0.0801138i
$5$	−55.7220	−	4.47850i	−0.996786	−	0.0801138i
$6$	−29.1246	+	21.1603i	−0.330280	+	0.239962i
$7$	−89.1519			−0.687679			−0.343839	−	0.939028i	$-0.611728\pi$
$7$	−89.1519			−0.687679			−0.343839	+	0.939028i	$0.611728\pi$
$8$	51.7771	−	37.6183i	0.286031	−	0.207813i
$9$	25.0304	+	77.0356i	0.103006	+	0.317019i
$10$	85.9134	−	206.443i	0.271682	−	0.652831i
$11$	−234.045	+	720.316i	−0.583200	+	1.79490i	0.0231838	+	0.999731i	$0.492620\pi$
$11$	−234.045	+	720.316i	−0.583200	+	1.79490i	−0.606383	+	0.795172i	$0.707380\pi$
$12$	−44.4984	−	136.952i	−0.0892055	−	0.274546i
$13$	−137.908	−	424.438i	−0.226325	−	0.696555i	−0.998154	−	0.0607262i	$-0.980658\pi$
$13$	−137.908	−	424.438i	−0.226325	−	0.696555i	0.771830	−	0.635829i	$-0.219342\pi$
$14$	110.198	−	339.154i	0.150263	−	0.462463i
$15$	−382.029	−	327.382i	−0.438398	−	0.375687i
$16$	79.1084	+	243.470i	0.0772542	+	0.237764i
$17$	484.961	−	352.345i	0.406991	−	0.295696i	−0.365392	−	0.930854i	$-0.619065\pi$
$17$	484.961	−	352.345i	0.406991	−	0.295696i	0.772382	+	0.635158i	$0.219065\pi$
$18$	−324.000			−0.235702
$19$	1874.18	−	1361.67i	1.19104	−	0.865344i	0.197669	−	0.980269i	$-0.436663\pi$
$19$	1874.18	−	1361.67i	1.19104	−	0.865344i	0.993374	+	0.114925i	$0.0366628\pi$
$20$	679.163	+	582.012i	0.379663	+	0.325355i
$21$	−649.129	−	471.620i	−0.321205	−	0.233369i
$22$	−2450.95	−	1780.72i	−1.07964	−	0.784402i
$23$	1250.69	−	3849.23i	0.492981	−	1.51724i	−0.327100	−	0.944990i	$-0.606071\pi$
$23$	1250.69	−	3849.23i	0.492981	−	1.51724i	0.820080	−	0.572248i	$-0.193929\pi$
$24$	576.000			0.204124
$25$	3084.89	+	499.102i	0.987164	+	0.159713i
$26$	1785.12			0.517886
$27$	−225.273	+	693.320i	−0.0594703	+	0.183031i
$28$	1154.01	+	838.435i	0.278172	+	0.202104i
$29$	−2866.44	−	2082.59i	−0.632919	−	0.459842i	0.224492	−	0.974476i	$-0.427928\pi$
$29$	−2866.44	−	2082.59i	−0.632919	−	0.459842i	−0.857410	+	0.514634i	$0.827928\pi$
$30$	1717.65	−	1048.66i	0.348442	−	0.212731i
$31$	−1135.73	+	825.153i	−0.212261	+	0.154216i	−0.688836	−	0.724917i	$-0.741878\pi$
$31$	−1135.73	+	825.153i	−0.212261	+	0.154216i	0.476575	+	0.879134i	$0.341878\pi$
$32$	−1024.00			−0.176777
$33$	−5514.63	+	4006.62i	−0.881519	+	0.640461i
$34$	740.954	+	2280.42i	0.109924	+	0.338313i
$35$	4967.72	+	399.267i	0.685468	+	0.0550925i
$36$	400.486	−	1232.57i	0.0515028	−	0.158509i
$37$	−4114.64	−	12663.5i	−0.494114	−	1.52073i	−0.818333	−	0.574744i	$-0.805101\pi$
$37$	−4114.64	−	12663.5i	−0.494114	−	1.52073i	0.324219	−	0.945982i	$-0.394899\pi$
$38$	2863.49	+	8812.93i	0.321690	+	0.990059i
$39$	1241.17	−	3819.94i	0.130669	−	0.402156i
$40$	−3053.60	+	1864.28i	−0.301760	+	0.184230i
$41$	−2344.43	−	7215.42i	−0.217810	−	0.670351i	−0.998942	−	0.0459849i	$-0.985357\pi$
$41$	−2344.43	−	7215.42i	−0.217810	−	0.670351i	0.781132	−	0.624366i	$-0.214643\pi$
$42$	2596.51	−	1886.48i	0.227126	−	0.165017i
$43$	5609.41			0.462643			0.231322	−	0.972877i	$-0.425695\pi$
$43$	5609.41			0.462643			0.231322	+	0.972877i	$0.425695\pi$
$44$	9803.79	−	7122.87i	0.763418	−	0.554656i
$45$	−1049.74	−	4404.68i	−0.0772770	−	0.324252i
$46$	13097.4	+	9515.81i	0.912620	+	0.663057i
$47$	16588.0	+	12051.9i	1.09534	+	0.795813i	0.980293	−	0.197547i	$-0.0632976\pi$
$47$	16588.0	+	12051.9i	1.09534	+	0.795813i	0.115049	+	0.993360i	$0.463298\pi$
$48$	−711.975	+	2191.23i	−0.0446028	+	0.137273i
$49$	−8858.94			−0.527098
$50$	−5711.82	+	11118.7i	−0.323110	+	0.628968i
$51$	5395.00			0.290447
$52$	−2206.53	+	6791.00i	−0.113162	+	0.348278i
$53$	29423.7	+	21377.6i	1.43883	+	1.04537i	0.988286	+	0.152611i	$0.0487683\pi$
$53$	29423.7	+	21377.6i	1.43883	+	1.04537i	0.450539	+	0.892757i	$0.351232\pi$
$54$	−2359.09	−	1713.98i	−0.110093	−	0.0799874i
$55$	16267.4	−	39089.3i	0.725122	−	1.74241i
$56$	−4616.03	+	3353.74i	−0.196697	+	0.142909i
$57$	20849.5			0.849981
$58$	11465.8	−	8330.36i	0.447541	−	0.325158i
$59$	−644.865	−	1984.69i	−0.0241179	−	0.0742272i	0.938273	−	0.345895i	$-0.112425\pi$
$59$	−644.865	−	1984.69i	−0.0241179	−	0.0742272i	−0.962391	+	0.271668i	$0.912425\pi$
$60$	1866.20	+	7830.54i	0.0669238	+	0.280810i
$61$	15286.1	−	47045.9i	0.525985	−	1.61881i	−0.236376	−	0.971662i	$-0.575960\pi$
$61$	15286.1	−	47045.9i	0.525985	−	1.61881i	0.762360	−	0.647153i	$-0.224040\pi$
$62$	−1735.23	−	5340.50i	−0.0573296	−	0.176442i
$63$	−2231.51	−	6867.87i	−0.0708348	−	0.218007i
$64$	1265.73	−	3895.53i	0.0386271	−	0.118882i
$65$	5783.68	+	24268.1i	0.169793	+	0.712448i
$66$	−8425.61	−	25931.4i	−0.238090	−	0.732766i
$67$	−38948.9	+	28298.0i	−1.06000	+	0.770138i	−0.974089	−	0.226164i	$-0.927381\pi$
$67$	−38948.9	+	28298.0i	−1.06000	+	0.770138i	−0.0859152	+	0.996302i	$0.527381\pi$
$68$	−9591.12			−0.251534
$69$	29469.1	−	21410.6i	0.745151	−	0.541384i
$70$	−7659.34	+	18404.8i	−0.186830	+	0.448938i
$71$	−25294.2	−	18377.3i	−0.595490	−	0.432649i	0.248785	−	0.968559i	$-0.419969\pi$
$71$	−25294.2	−	18377.3i	−0.595490	−	0.432649i	−0.844275	+	0.535910i	$0.819969\pi$
$72$	4193.94	+	3047.08i	0.0953436	+	0.0692712i
$73$	−1847.34	+	5685.52i	−0.0405732	+	0.124871i	−0.969291	−	0.245915i	$-0.920912\pi$
$73$	−1847.34	+	5685.52i	−0.0405732	+	0.124871i	0.928718	+	0.370786i	$0.120912\pi$
$74$	53261.0			1.13065
$75$	19821.2	+	19953.3i	0.406891	+	0.409601i
$76$	−37065.8			−0.736105
$77$	20865.5	−	64217.5i	0.401054	−	1.23432i
$78$	12997.7	+	9443.41i	0.241897	+	0.175749i
$79$	−2944.61	−	2139.38i	−0.0530835	−	0.0385674i	0.560927	−	0.827865i	$-0.310445\pi$
$79$	−2944.61	−	2139.38i	−0.0530835	−	0.0385674i	−0.614011	+	0.789298i	$0.710445\pi$
$80$	−3317.69	−	13921.0i	−0.0579577	−	0.243189i
$81$	−5307.96	+	3856.46i	−0.0898908	+	0.0653095i
$82$	30347.0			0.498403
$83$	−40094.0	+	29130.0i	−0.638829	+	0.464136i	−0.859448	−	0.511224i	$-0.829192\pi$
$83$	−40094.0	+	29130.0i	−0.638829	+	0.464136i	0.220619	+	0.975360i	$0.429192\pi$
$84$	3967.12	+	12209.5i	0.0613447	+	0.188800i
$85$	−28601.0	+	17461.5i	−0.429372	+	0.262140i
$86$	−6933.62	+	21339.5i	−0.101091	+	0.311127i
$87$	−9853.94	−	30327.3i	−0.139576	−	0.429572i
$88$	14978.9	+	46100.2i	0.206192	+	0.634594i
$89$	10172.3	−	31307.0i	0.136126	−	0.418954i	−0.859637	−	0.510905i	$-0.829310\pi$
$89$	10172.3	−	31307.0i	0.136126	−	0.418954i	0.995764	+	0.0919512i	$0.0293104\pi$
$90$	18053.9	+	1451.03i	0.234945	+	0.0188830i
$91$	12294.8	+	37839.4i	0.155639	+	0.479006i
$92$	−52389.5	+	38063.2i	−0.645320	+	0.468852i
$93$	−12634.5			−0.151478
$94$	−66352.1	+	48207.6i	−0.774524	+	0.562724i
$95$	−110531.	+	67481.6i	−1.25654	+	0.767143i
$96$	−7455.90	−	5417.03i	−0.0825700	−	0.0599906i
$97$	−122153.	−	88749.4i	−1.31818	−	0.957714i	−0.999953	−	0.00970015i	$-0.996912\pi$
$97$	−122153.	−	88749.4i	−1.31818	−	0.957714i	−0.318228	−	0.948014i	$-0.603088\pi$
$98$	10950.2	−	33701.4i	0.115175	−	0.354473i
$99$	−61348.2			−0.629091
$100$	−35237.8	−	35472.5i	−0.352378	−	0.354725i
$101$	−1956.27			−0.0190821			−0.00954105	−	0.999954i	$-0.503037\pi$
$101$	−1956.27			−0.0190821			−0.00954105	+	0.999954i	$0.503037\pi$
$102$	−6668.59	+	20523.8i	−0.0634649	+	0.195325i
$103$	−58000.2	−	42139.6i	−0.538686	−	0.391379i	0.284910	−	0.958554i	$-0.408036\pi$
$103$	−58000.2	−	42139.6i	−0.538686	−	0.391379i	−0.823597	+	0.567175i	$0.808036\pi$
$104$	−23107.1	−	16788.3i	−0.209489	−	0.152203i
$105$	34058.6	+	29186.7i	0.301477	+	0.258352i
$106$	−117695.	+	85510.4i	−1.01740	+	0.739187i
$107$	134740.			1.13772			0.568862	−	0.822433i	$-0.307384\pi$
$107$	134740.			1.13772			0.568862	+	0.822433i	$0.307384\pi$
$108$	9436.37	−	6855.93i	0.0778477	−	0.0565597i
$109$	−39994.2	−	123089.i	−0.322426	−	0.992326i	−0.972589	−	0.232531i	$-0.925299\pi$
$109$	−39994.2	−	123089.i	−0.322426	−	0.992326i	0.650163	−	0.759795i	$-0.274701\pi$
$110$	128597.	+	110202.i	1.01332	+	0.868374i
$111$	37031.7	−	113972.i	0.285277	−	0.877992i
$112$	−7052.66	−	21705.9i	−0.0531261	−	0.163505i
$113$	67622.3	+	208120.i	0.498189	+	1.53327i	0.811928	+	0.583758i	$0.198418\pi$
$113$	67622.3	+	208120.i	0.498189	+	1.53327i	−0.313739	+	0.949509i	$0.601582\pi$
$114$	−25771.4	+	79316.4i	−0.185728	+	0.571611i
$115$	−86929.7	+	208885.i	−0.612948	+	1.47287i
$116$	17518.1	+	53915.2i	0.120877	+	0.372020i
$117$	29244.9	−	21247.7i	0.197508	−	0.143498i
$118$	8347.31			0.0551876
$119$	−43235.2	+	31412.2i	−0.279879	+	0.203344i
$120$	−32095.9	−	2579.61i	−0.203468	−	0.0163532i
$121$	−333785.	−	242509.i	−2.07254	−	1.50579i
$122$	160078.	+	116304.i	0.973719	+	0.707448i
$123$	21099.9	−	64938.8i	0.125753	−	0.387027i
$124$	22461.3			0.131184
$125$	−169661.	−	41626.6i	−0.971195	−	0.238285i
$126$	28885.2			0.162087
$127$	27217.7	−	83767.3i	0.149741	−	0.460856i	−0.847849	−	0.530238i	$-0.822103\pi$
$127$	27217.7	−	83767.3i	0.149741	−	0.460856i	0.997590	+	0.0693817i	$0.0221026\pi$
$128$	13254.9	+	9630.27i	0.0715077	+	0.0519534i
$129$	40843.0	+	29674.2i	0.216094	+	0.157002i
$130$	−99470.5	−	7994.66i	−0.516221	−	0.0414898i
$131$	163559.	−	118833.i	0.832716	−	0.605004i	−0.0876104	−	0.996155i	$-0.527923\pi$
$131$	163559.	−	118833.i	0.832716	−	0.605004i	0.920326	+	0.391151i	$0.127923\pi$
$132$	109063.			0.544809
$133$	−167087.	+	121396.i	−0.819055	+	0.595078i
$134$	−59508.6	−	183148.i	−0.286297	−	0.881133i
$135$	15657.7	−	37624.3i	0.0739425	−	0.177678i
$136$	11855.3	−	36486.8i	0.0549622	−	0.169156i
$137$	−86675.9	−	266761.i	−0.394545	−	1.21429i	−0.929315	−	0.369288i	$-0.879602\pi$
$137$	−86675.9	−	266761.i	−0.394545	−	1.21429i	0.534770	−	0.844998i	$-0.320398\pi$
$138$	45024.8	+	138572.i	0.201258	+	0.619410i
$139$	−68386.0	+	210470.i	−0.300214	+	0.923962i	0.681207	+	0.732091i	$0.261456\pi$
$139$	−68386.0	+	210470.i	−0.300214	+	0.923962i	−0.981420	+	0.191871i	$0.938544\pi$
$140$	−60548.6	−	51887.5i	−0.261086	−	0.223739i
$141$	57024.5	+	175503.i	0.241554	+	0.743426i
$142$	101177.	−	73509.2i	0.421075	−	0.305929i
$143$	338006.			1.38224
$144$	−16775.8	+	12188.3i	−0.0674181	+	0.0489821i
$145$	150397.	+	128883.i	0.594044	+	0.509070i
$146$	−19345.6	−	14055.4i	−0.0751103	−	0.0545708i
$147$	−64503.3	−	46864.4i	−0.246200	−	0.178875i
$148$	−65834.2	+	202617.i	−0.247057	+	0.760363i
$149$	−276617.			−1.02074			−0.510369	−	0.859956i	$-0.670491\pi$
$149$	−276617.			−1.02074			−0.510369	+	0.859956i	$0.670491\pi$
$150$	−100407.	+	50740.9i	−0.364365	+	0.184132i
$151$	−295364.			−1.05418			−0.527091	−	0.849809i	$-0.676717\pi$
$151$	−295364.			−1.05418			−0.527091	+	0.849809i	$0.676717\pi$
$152$	45815.9	−	141007.i	0.160845	−	0.495030i
$153$	39281.8	+	28539.9i	0.135664	+	0.0985653i
$154$	218507.	+	158754.i	0.742443	+	0.539416i
$155$	66980.4	−	40892.8i	0.223933	−	0.136716i
$156$	−51990.9	+	37773.6i	−0.171047	+	0.124273i
$157$	471191.			1.52563			0.762813	−	0.646620i	$-0.223818\pi$
$157$	471191.			1.52563			0.762813	+	0.646620i	$0.223818\pi$
$158$	11778.4	−	8557.53i	0.0375357	−	0.0272713i
$159$	101150.	+	311307.i	0.317302	+	0.976554i
$160$	57059.3	+	4585.98i	0.176208	+	0.0141623i
$161$	−111501.	+	343166.i	−0.339012	+	1.04337i
$162$	−8109.84	−	24959.5i	−0.0242787	−	0.0747221i
$163$	−64579.5	−	198755.i	−0.190382	−	0.585935i	0.809618	−	0.586958i	$-0.199675\pi$
$163$	−64579.5	−	198755.i	−0.190382	−	0.585935i	−0.999999	+	0.00102237i	$0.999675\pi$
$164$	−37510.9	+	115447.i	−0.108905	+	0.335175i
$165$	325230.	−	198559.i	0.929996	−	0.567781i
$166$	−61258.2	−	188533.i	−0.172542	−	0.531029i
$167$	291242.	−	211599.i	0.808095	−	0.587115i	−0.105183	−	0.994453i	$-0.533543\pi$
$167$	291242.	−	211599.i	0.808095	−	0.587115i	0.913278	+	0.407338i	$0.133543\pi$
$168$	−51351.5			−0.140372
$169$	139254.	−	101174.i	0.375051	−	0.272490i
$170$	−31074.6	−	130388.i	−0.0824676	−	0.346032i
$171$	151809.	+	110295.i	0.397014	+	0.288448i
$172$	−72609.8	−	52754.1i	−0.187143	−	0.135967i
$173$	79264.0	−	243949.i	0.201354	−	0.619704i	−0.798489	−	0.602009i	$-0.794367\pi$
$173$	79264.0	−	243949.i	0.201354	−	0.619704i	0.999843	−	0.0176952i	$-0.00563286\pi$
$174$	127552.			0.319385
$175$	−275023.	−	44495.9i	−0.678851	−	0.109831i
$176$	−193890.			−0.471818
$177$	5803.79	−	17862.2i	0.0139245	−	0.0428551i
$178$	106525.	+	77395.1i	0.252001	+	0.183090i
$179$	129500.	+	94087.1i	0.302090	+	0.219481i	0.728495	−	0.685051i	$-0.240220\pi$
$179$	129500.	+	94087.1i	0.302090	+	0.219481i	−0.426405	+	0.904532i	$0.640220\pi$
$180$	−27835.9	+	66887.7i	−0.0640361	+	0.153874i
$181$	−269311.	+	195666.i	−0.611023	+	0.443934i	−0.849775	−	0.527146i	$-0.823262\pi$
$181$	−269311.	+	195666.i	−0.611023	+	0.443934i	0.238751	+	0.971081i	$0.423262\pi$
$182$	−159147.			−0.356139
$183$	360177.	−	261684.i	0.795038	−	0.577629i
$184$	−80044.1	−	246350.i	−0.174295	−	0.536425i
$185$	172562.	+	724066.i	0.370695	+	1.55542i
$186$	15617.1	−	48064.5i	0.0330993	−	0.101869i
$187$	140297.	+	431789.i	0.293389	+	0.902959i
$188$	−101377.	−	312006.i	−0.209192	−	0.643826i
$189$	20083.6	−	61810.8i	0.0408965	−	0.125866i
$190$	−120091.	−	503898.i	−0.241338	−	1.01265i
$191$	−239358.	−	736669.i	−0.474750	−	1.46113i	−0.846295	−	0.532715i	$-0.821172\pi$
$191$	−239358.	−	736669.i	−0.474750	−	1.46113i	0.371545	−	0.928415i	$-0.378828\pi$
$192$	29823.6	−	21668.1i	0.0583858	−	0.0424197i
$193$	327082.			0.632068			0.316034	−	0.948748i	$-0.397649\pi$
$193$	327082.			0.632068			0.316034	+	0.948748i	$0.397649\pi$
$194$	488612.	−	354998.i	0.932095	−	0.677206i
$195$	−86268.3	+	207296.i	−0.162467	+	0.390395i
$196$	114672.	+	83314.4i	0.213216	+	0.154910i
$197$	−332092.	−	241279.i	−0.609667	−	0.442949i	0.239630	−	0.970864i	$-0.422974\pi$
$197$	−332092.	−	241279.i	−0.609667	−	0.442949i	−0.849297	+	0.527915i	$0.822974\pi$
$198$	75830.5	−	233382.i	0.137461	−	0.423063i
$199$	−97800.2			−0.175068			−0.0875341	−	0.996162i	$-0.527899\pi$
$199$	−97800.2			−0.175068			−0.0875341	+	0.996162i	$0.527899\pi$
$200$	178502.	−	90206.0i	0.315550	−	0.159463i
$201$	−433291.			−0.756466
$202$	2418.09	−	7442.11i	0.00416959	−	0.0128327i
$203$	255549.	+	185667.i	0.435245	+	0.316224i
$204$	−69834.4	−	50737.6i	−0.117488	−	0.0853601i
$205$	98322.3	+	412558.i	0.163406	+	0.685646i
$206$	232001.	−	168558.i	0.380909	−	0.276746i
$207$	327833.			0.531773
$208$	92428.4	−	67153.1i	0.148131	−	0.107624i
$209$	542192.	+	1.66869e6i	0.858592	+	2.64248i
$210$	−153132.	+	93489.9i	−0.239616	+	0.146291i
$211$	334706.	−	1.03012e6i	0.517556	−	1.59287i	−0.261026	−	0.965332i	$-0.584061\pi$
$211$	334706.	−	1.03012e6i	0.517556	−	1.59287i	0.778582	−	0.627542i	$-0.215939\pi$
$212$	−179822.	−	553435.i	−0.274791	−	0.845720i
$213$	−86953.7	−	267616.i	−0.131322	−	0.404169i
$214$	−166548.	+	512582.i	−0.248602	+	0.765118i
$215$	−312568.	−	25121.7i	−0.461156	−	0.0370641i
$216$	14417.5	+	44372.5i	0.0210259	+	0.0647112i
$217$	101252.	−	73564.0i	0.145967	−	0.106051i
$218$	517695.			0.737790
$219$	−43527.5	+	31624.6i	−0.0613273	+	0.0445569i
$220$	−578187.	+	352995.i	−0.805400	+	0.491713i
$221$	−216428.	−	157244.i	−0.298081	−	0.216568i
$222$	387801.	+	281754.i	0.528113	+	0.383697i
$223$	179902.	−	553682.i	0.242256	−	0.745587i	−0.753820	−	0.657081i	$-0.771791\pi$
$223$	179902.	−	553682.i	0.242256	−	0.745587i	0.996076	−	0.0885055i	$-0.0282091\pi$
$224$	91291.6			0.121566
$225$	38767.3	+	250139.i	0.0510515	+	0.329401i
$226$	−875321.			−1.13998
$227$	195640.	−	602117.i	0.251995	−	0.775562i	−0.742411	−	0.669944i	$-0.766318\pi$
$227$	195640.	−	602117.i	0.251995	−	0.775562i	0.994407	−	0.105618i	$-0.0336820\pi$
$228$	−269882.	−	196081.i	−0.343825	−	0.249803i
$229$	445772.	+	323872.i	0.561725	+	0.408117i	0.832090	−	0.554641i	$-0.187144\pi$
$229$	445772.	+	323872.i	0.561725	+	0.408117i	−0.270365	+	0.962758i	$0.587144\pi$
$230$	−687196.	−	588897.i	−0.856567	−	0.734040i
$231$	491640.	−	357197.i	0.606202	−	0.440432i
$232$	−226759.			−0.276596
$233$	−672667.	+	488721.i	−0.811727	+	0.589754i	−0.914331	−	0.404968i	$-0.867283\pi$
$233$	−672667.	+	488721.i	−0.811727	+	0.589754i	0.102604	+	0.994722i	$0.467283\pi$
$234$	44682.2	+	137518.i	0.0533452	+	0.164180i
$235$	−870343.	−	745845.i	−1.02807	−	0.881007i
$236$	−10317.8	+	31755.1i	−0.0120589	+	0.0371136i
$237$	−10122.7	−	31154.3i	−0.0117064	−	0.0360286i
$238$	−66057.5	−	203304.i	−0.0755927	−	0.232650i
$239$	161932.	−	498374.i	0.183374	−	0.564366i	−0.816543	−	0.577285i	$-0.804112\pi$
$239$	161932.	−	498374.i	0.183374	−	0.564366i	0.999917	+	0.0129186i	$0.00411223\pi$
$240$	49486.1	−	118911.i	0.0554569	−	0.133259i
$241$	−252983.	−	778601.i	−0.280575	−	0.863520i	−0.987690	−	0.156422i	$-0.950004\pi$
$241$	−252983.	−	778601.i	−0.280575	−	0.863520i	0.707116	−	0.707098i	$-0.249996\pi$
$242$	1.33514e6	−	970035.i	1.46551	−	1.06475i
$243$	−59049.0			−0.0641500
$244$	−640314.	+	465215.i	−0.688523	+	0.500241i
$245$	493638.	+	39674.7i	0.525404	+	0.0422278i
$246$	220961.	+	160538.i	0.232797	+	0.169137i
$247$	−836410.	−	607687.i	−0.872322	−	0.633779i
$248$	−27763.8	+	85448.0i	−0.0286648	+	0.0882212i
$249$	−446030.			−0.455896
$250$	368069.	−	593975.i	0.372460	−	0.601060i
$251$	753920.			0.755338			0.377669	−	0.925941i	$-0.376726\pi$
$251$	753920.			0.755338			0.377669	+	0.925941i	$0.376726\pi$
$252$	−35704.1	+	109886.i	−0.0354174	+	0.109004i
$253$	2.47994e6	+	1.80178e6i	2.43579	+	1.76971i
$254$	285027.	+	207084.i	0.277205	+	0.201402i
$255$	−300620.	−	24161.5i	−0.289513	−	0.0232688i
$256$	−53019.7	+	38521.1i	−0.0505636	+	0.0367366i
$257$	−246738.			−0.233026			−0.116513	−	0.993189i	$-0.537172\pi$
$257$	−246738.			−0.233026			−0.116513	+	0.993189i	$0.537172\pi$
$258$	−163372.	+	118697.i	−0.152802	+	0.111017i
$259$	366828.	+	1.12898e6i	0.339792	+	1.04577i
$260$	153366.	−	368526.i	0.140700	−	0.338092i
$261$	88685.5	−	272946.i	0.0805845	−	0.248013i
$262$	249896.	+	769102.i	0.224909	+	0.692198i
$263$	512302.	+	1.57670e6i	0.456706	+	1.40560i	0.869121	+	0.494600i	$0.164685\pi$
$263$	512302.	+	1.57670e6i	0.456706	+	1.40560i	−0.412415	+	0.910996i	$0.635315\pi$
$264$	−134810.	+	414902.i	−0.119045	+	0.366383i
$265$	−1.54381e6	−	1.32298e6i	−1.35045	−	1.15728i
$266$	−255286.	−	785689.i	−0.221219	−	0.680843i
$267$	239682.	−	174139.i	0.205758	−	0.149492i
$268$	770295.			0.655119
$269$	−1.06046e6	+	770466.i	−0.893535	+	0.649191i	−0.936797	−	0.349873i	$-0.886225\pi$
$269$	−1.06046e6	+	770466.i	−0.893535	+	0.649191i	0.0432623	+	0.999064i	$0.486225\pi$
$270$	123777.	+	106072.i	0.103331	+	0.0885503i
$271$	761664.	+	553382.i	0.630000	+	0.457722i	0.856400	−	0.516313i	$-0.172696\pi$
$271$	761664.	+	553382.i	0.630000	+	0.457722i	−0.226400	+	0.974034i	$0.572696\pi$
$272$	124150.	+	90200.3i	0.101748	+	0.0739240i
$273$	−110653.	+	340555.i	−0.0898579	+	0.276554i
$274$	1.12196e6			0.902817
$275$	−1.08151e6	+	2.10528e6i	−0.862382	+	1.67872i
$276$	−582813.			−0.460529
$277$	−205707.	+	633102.i	−0.161083	+	0.495763i	−0.998726	−	0.0504548i	$-0.983933\pi$
$277$	−205707.	+	633102.i	−0.161083	+	0.495763i	0.837643	+	0.546218i	$0.183933\pi$
$278$	−716148.	−	520312.i	−0.555764	−	0.403786i
$279$	−91993.8	−	66837.4i	−0.0707535	−	0.0514054i
$280$	272234.	−	166204.i	0.207514	−	0.126691i
$281$	−497315.	+	361321.i	−0.375721	+	0.272978i	−0.759579	−	0.650415i	$-0.774595\pi$
$281$	−497315.	+	361321.i	−0.375721	+	0.272978i	0.383858	+	0.923392i	$0.374595\pi$
$282$	−738141.			−0.552734
$283$	745016.	−	541286.i	0.552968	−	0.401754i	−0.275911	−	0.961183i	$-0.588979\pi$
$283$	745016.	−	541286.i	0.552968	−	0.401754i	0.828878	+	0.559429i	$0.188979\pi$
$284$	154584.	+	475761.i	0.113729	+	0.350020i
$285$	−1.16178e6	−	93374.6i	−0.847249	−	0.0680952i
$286$	−417798.	+	1.28585e6i	−0.302031	+	0.929556i
$287$	209011.	+	643269.i	0.149783	+	0.460986i
$288$	−25631.1	−	78884.4i	−0.0182090	−	0.0560415i
$289$	−327720.	+	1.00862e6i	−0.230812	+	0.710365i
$290$	−676203.	+	412835.i	−0.472152	+	0.288258i
$291$	−419925.	−	1.29240e6i	−0.290696	−	0.894670i
$292$	77382.3	−	56221.5i	0.0531110	−	0.0385874i
$293$	1.46935e6			0.999897			0.499949	−	0.866055i	$-0.333352\pi$
$293$	1.46935e6			0.999897			0.499949	+	0.866055i	$0.333352\pi$
$294$	258013.	−	187457.i	0.174090	−	0.126484i
$295$	27044.8	+	113479.i	0.0180937	+	0.0759208i
$296$	−689425.	−	500896.i	−0.457359	−	0.332291i
$297$	−446685.	−	324536.i	−0.293840	−	0.213487i
$298$	341918.	−	1.05232e6i	0.223039	−	0.686444i
$299$	−1.80624e6			−1.16841
$300$	−68919.6	−	444691.i	−0.0442119	−	0.285269i
$301$	−500090.			−0.318150
$302$	365090.	−	1.12363e6i	0.230347	−	0.708935i
$303$	−14243.9	−	10348.8i	−0.00891299	−	0.00647566i
$304$	479790.	+	348588.i	0.297761	+	0.216336i
$305$	−1.06247e6	+	2.55303e6i	−0.653983	+	1.57147i
$306$	−157127.	+	114160.i	−0.0959286	+	0.0696962i
$307$	−1.31520e6			−0.796429			−0.398214	−	0.917292i	$-0.630370\pi$
$307$	−1.31520e6			−0.796429			−0.398214	+	0.917292i	$0.630370\pi$
$308$	−874027.	+	635018.i	−0.524986	+	0.381425i
$309$	−199387.	−	613649.i	−0.118796	−	0.365615i
$310$	72773.3	+	305355.i	0.0430099	+	0.180468i
$311$	−692358.	+	2.13086e6i	−0.405910	+	1.24926i	0.514223	+	0.857657i	$0.328080\pi$
$311$	−692358.	+	2.13086e6i	−0.405910	+	1.24926i	−0.920133	+	0.391606i	$0.871920\pi$
$312$	−79435.1	−	244476.i	−0.0461983	−	0.142184i
$313$	15584.5	+	47964.0i	0.00899147	+	0.0276729i	0.955452	−	0.295148i	$-0.0953689\pi$
$313$	15584.5	+	47964.0i	0.00899147	+	0.0276729i	−0.946460	+	0.322821i	$0.895369\pi$
$314$	−582424.	+	1.79252e6i	−0.333361	+	1.02598i
$315$	93586.3	+	392685.i	0.0531417	+	0.222981i
$316$	17995.8	+	55385.5i	0.0101380	+	0.0312017i
$317$	−2.08686e6	+	1.51619e6i	−1.16639	+	0.847434i	−0.990573	−	0.136988i	$-0.956258\pi$
$317$	−2.08686e6	+	1.51619e6i	−1.16639	+	0.847434i	−0.175821	+	0.984422i	$0.556258\pi$
$318$	−1.30931e6			−0.726064
$319$	2.17100e6	−	1.57732e6i	1.19449	−	0.867848i
$320$	−87975.3	+	211398.i	−0.0480271	+	0.115405i
$321$	981063.	+	712784.i	0.531416	+	0.386096i
$322$	−1.16766e6	−	848352.i	−0.627589	−	0.455970i
$323$	429127.	−	1.32072e6i	0.228865	−	0.704374i
$324$	104976.			0.0555556
$325$	−213593.	−	1.37817e6i	−0.112171	−	0.723761i
$326$	835935.			0.435641
$327$	359947.	−	1.10780e6i	0.186153	−	0.572920i
$328$	−392820.	−	285400.i	−0.201608	−	0.146477i
$329$	−1.47885e6	−	1.07445e6i	−0.753243	−	0.547263i
$330$	353358.	+	1.48268e6i	0.178620	+	0.749485i
$331$	755405.	−	548834.i	0.378974	−	0.275341i	−0.381948	−	0.924184i	$-0.624747\pi$
$331$	755405.	−	548834.i	0.378974	−	0.275341i	0.760923	+	0.648843i	$0.224747\pi$
$332$	792943.			0.394818
$333$	872553.	−	633947.i	0.431202	−	0.313287i
$334$	444977.	+	1.36950e6i	0.218259	+	0.671732i
$335$	2.29704e6	−	1.40239e6i	1.11830	−	0.682742i
$336$	63473.9	−	195353.i	0.0306724	−	0.0943998i
$337$	110809.	+	341035.i	0.0531496	+	0.163578i	0.974108	−	0.226083i	$-0.0725922\pi$
$337$	110809.	+	341035.i	0.0531496	+	0.163578i	−0.920958	+	0.389661i	$0.872592\pi$
$338$	212761.	+	654810.i	0.101298	+	0.311762i
$339$	−608601.	+	1.87308e6i	−0.287629	+	0.885232i
$340$	534436.	+	42953.8i	0.250726	+	0.0201513i
$341$	−328560.	−	1.01120e6i	−0.153013	−	0.470926i
$342$	−607235.	+	441182.i	−0.280732	+	0.203963i
$343$	2.28817e6			1.05015
$344$	290439.	−	211016.i	0.132330	−	0.0961435i
$345$	−1.73797e6	+	1.06106e6i	−0.786128	+	0.479947i
$346$	830063.	+	603076.i	0.372753	+	0.270821i
$347$	−2.86454e6	−	2.08121e6i	−1.27712	−	0.927880i	−0.277655	−	0.960681i	$-0.589557\pi$
$347$	−2.86454e6	−	2.08121e6i	−1.27712	−	0.927880i	−0.999462	+	0.0328010i	$0.989557\pi$
$348$	−157663.	+	485237.i	−0.0697882	+	0.214786i
$349$	3.01901e6			1.32679			0.663394	−	0.748270i	$-0.269115\pi$
$349$	3.01901e6			1.32679			0.663394	+	0.748270i	$0.269115\pi$
$350$	509220.	−	991252.i	0.222196	−	0.432528i
$351$	325338.			0.140951
$352$	239662.	−	737603.i	0.103096	−	0.317297i
$353$	−819319.	−	595270.i	−0.349958	−	0.254260i	0.398893	−	0.916997i	$-0.369394\pi$
$353$	−819319.	−	595270.i	−0.349958	−	0.254260i	−0.748852	+	0.662738i	$0.769394\pi$
$354$	60778.1	+	44157.8i	0.0257774	+	0.0187284i
$355$	1.32714e6	+	1.13730e6i	0.558915	+	0.478965i
$356$	−426101.	+	309580.i	−0.178192	+	0.129464i
$357$	−480975.			−0.199734
$358$	−517999.	+	376349.i	−0.213610	+	0.155197i
$359$	−1.22769e6	−	3.77845e6i	−0.502752	−	1.54731i	−0.804517	−	0.593930i	$-0.797576\pi$
$359$	−1.22769e6	−	3.77845e6i	−0.502752	−	1.54731i	0.301765	−	0.953382i	$-0.402424\pi$
$360$	−220049.	−	188572.i	−0.0894875	−	0.0766868i
$361$	893247.	−	2.74913e6i	0.360748	−	1.11027i
$362$	−411471.	−	1.26638e6i	−0.165032	−	0.507916i
$363$	−1.14745e6	−	3.53149e6i	−0.457054	−	1.40667i
$364$	196716.	−	605431.i	0.0778193	−	0.239503i
$365$	128400.	−	308535.i	0.0504467	−	0.121220i
$366$	550301.	+	1.69365e6i	0.214732	+	0.660878i
$367$	−287692.	+	209020.i	−0.111497	+	0.0810071i	−0.642136	−	0.766590i	$-0.721952\pi$
$367$	−287692.	+	209020.i	−0.111497	+	0.0810071i	0.530640	+	0.847598i	$0.321952\pi$
$368$	1.03611e6			0.398830
$369$	497162.	−	361210.i	0.190078	−	0.138100i
$370$	−2.96781e6	−	238529.i	−1.12702	−	0.0905810i
$371$	−2.62318e6	−	1.90585e6i	−0.989450	−	0.718877i
$372$	163545.	+	118822.i	0.0612743	+	0.0445184i
$373$	23750.8	−	73097.6i	0.00883908	−	0.0272039i	−0.946540	−	0.322587i	$-0.895447\pi$
$373$	23750.8	−	73097.6i	0.00883908	−	0.0272039i	0.955379	+	0.295383i	$0.0954474\pi$
$374$	−1.81604e6			−0.671346
$375$	−1.01512e6	−	1.20061e6i	−0.372768	−	0.440882i
$376$	1.31225e6			0.478682
$377$	−488624.	+	1.50383e6i	−0.177061	+	0.544936i
$378$	210318.	+	152805.i	0.0757088	+	0.0550057i
$379$	−3.21242e6	−	2.33396e6i	−1.14877	−	0.834632i	−0.160455	−	0.987043i	$-0.551296\pi$
$379$	−3.21242e6	−	2.33396e6i	−1.14877	−	0.834632i	−0.988317	+	0.152411i	$0.951296\pi$
$380$	2.06538e6	+	165999.i	0.733739	+	0.0589722i
$381$	641311.	−	465939.i	0.226337	−	0.164444i
$382$	3.09832e6			1.08634
$383$	−492741.	+	357998.i	−0.171641	+	0.124705i	−0.670289	−	0.742100i	$-0.733830\pi$
$383$	−492741.	+	357998.i	−0.171641	+	0.124705i	0.498648	+	0.866805i	$0.333830\pi$
$384$	45566.4	+	140239.i	0.0157695	+	0.0485334i
$385$	−1.45027e6	+	3.48488e6i	−0.498651	+	1.19822i
$386$	−404296.	+	1.24430e6i	−0.138112	+	0.425065i
$387$	140406.	+	432124.i	0.0476549	+	0.146667i
$388$	746533.	+	2.29759e6i	0.251750	+	0.774807i
$389$	−714457.	+	2.19887e6i	−0.239388	+	0.736760i	0.757121	+	0.653275i	$0.226605\pi$
$389$	−714457.	+	2.19887e6i	−0.239388	+	0.736760i	−0.996509	+	0.0834857i	$0.973395\pi$
$390$	−681968.	−	584416.i	−0.227040	−	0.194563i
$391$	−749719.	−	2.30740e6i	−0.248003	−	0.763274i
$392$	−458690.	+	333258.i	−0.150766	+	0.109538i
$393$	1.81953e6			0.594263
$394$	1.32837e6	−	965116.i	0.431100	−	0.313212i
$395$	154498.	+	132398.i	0.0498231	+	0.0426962i
$396$	794107.	+	576953.i	0.254473	+	0.184885i
$397$	4.15823e6	+	3.02113e6i	1.32414	+	0.962041i	0.999871	+	0.0160748i	$0.00511698\pi$
$397$	4.15823e6	+	3.02113e6i	1.32414	+	0.962041i	0.324265	+	0.945966i	$0.394883\pi$
$398$	120888.	−	372054.i	0.0382538	−	0.117733i
$399$	−1.85878e6			−0.584514
$400$	122524.	+	790562.i	0.0382887	+	0.247051i
$401$	4.56282e6			1.41701			0.708504	−	0.705707i	$-0.249370\pi$
$401$	4.56282e6			1.41701			0.708504	+	0.705707i	$0.249370\pi$
$402$	535577.	−	1.64834e6i	0.165294	−	0.508722i
$403$	506852.	+	368249.i	0.155460	+	0.112948i
$404$	25322.5	+	18397.9i	0.00771887	+	0.00560809i
$405$	313041.	−	191118.i	0.0948340	−	0.0578981i
$406$	−1.02219e6	+	742668.i	−0.307764	+	0.223604i
$407$	1.00848e7			3.01772
$408$	279338.	−	202951.i	0.0830766	−	0.0603587i
$409$	7245.72	+	22300.0i	0.00214177	+	0.00659169i	0.952122	−	0.305719i	$-0.0988969\pi$
$409$	7245.72	+	22300.0i	0.00214177	+	0.00659169i	−0.949980	+	0.312311i	$0.898897\pi$
$410$	−1.69100e6	−	135909.i	−0.496801	−	0.0399290i
$411$	780083.	−	2.40085e6i	0.227791	−	0.701068i
$412$	354465.	+	1.09093e6i	0.102880	+	0.316632i
$413$	57491.0	+	176939.i	0.0165853	+	0.0510444i
$414$	−405223.	+	1.24715e6i	−0.116197	+	0.357616i
$415$	2.36458e6	−	1.44362e6i	0.673959	−	0.411465i
$416$	141218.	+	434624.i	0.0400089	+	0.123135i
$417$	−1.61133e6	+	1.17070e6i	−0.453780	+	0.329690i
$418$	−7.01828e6			−1.96467
$419$	2.32598e6	−	1.68993e6i	0.647249	−	0.470254i	−0.215084	−	0.976596i	$-0.569002\pi$
$419$	2.32598e6	−	1.68993e6i	0.647249	−	0.470254i	0.862333	+	0.506341i	$0.169002\pi$
$420$	−166376.	−	698107.i	−0.0460221	−	0.193107i
$421$	−1.63474e6	−	1.18771e6i	−0.449513	−	0.326591i	0.339890	−	0.940465i	$-0.389610\pi$
$421$	−1.63474e6	−	1.18771e6i	−0.449513	−	0.326591i	−0.789404	+	0.613875i	$0.789610\pi$
$422$	3.50509e6	+	2.54660e6i	0.958115	+	0.696112i
$423$	−513221.	+	1.57953e6i	−0.139461	+	0.429217i
$424$	2.32766e6			0.628790
$425$	1.67191e6	−	844899.i	0.448993	−	0.226899i
$426$	1.12555e6			0.300498
$427$	−1.36279e6	+	4.19423e6i	−0.361708	+	1.11322i
$428$	−1.74411e6	−	1.26717e6i	−0.460219	−	0.334369i
$429$	2.46107e6	+	1.78807e6i	0.645626	+	0.469075i
$430$	481924.	−	1.15803e6i	0.125692	−	0.302028i
$431$	−3.51203e6	+	2.55164e6i	−0.910679	+	0.661647i	−0.941187	−	0.337887i	$-0.890288\pi$
$431$	−3.51203e6	+	2.55164e6i	−0.910679	+	0.661647i	0.0305073	+	0.999535i	$0.490288\pi$
$432$	−186624.			−0.0481125
$433$	1.41545e6	−	1.02839e6i	0.362807	−	0.263595i	−0.391415	−	0.920214i	$-0.628014\pi$
$433$	1.41545e6	−	1.02839e6i	0.362807	−	0.263595i	0.754222	+	0.656620i	$0.228014\pi$
$434$	154699.	+	476116.i	0.0394243	+	0.121336i
$435$	413261.	+	1.73403e6i	0.104713	+	0.439373i
$436$	−639907.	+	1.96943e6i	−0.161213	+	0.496163i
$437$	−2.89737e6	−	8.91717e6i	−0.725771	−	2.23369i
$438$	−66504.1	−	204679.i	−0.0165639	−	0.0509785i
$439$	1.48226e6	−	4.56192e6i	0.367081	−	1.12976i	−0.581586	−	0.813485i	$-0.697568\pi$
$439$	1.48226e6	−	4.56192e6i	0.367081	−	1.12976i	0.948667	−	0.316275i	$-0.102432\pi$
$440$	−628193.	−	2.63588e6i	−0.154690	−	0.649073i
$441$	−221743.	−	682453.i	−0.0542941	−	0.167100i
$442$	865714.	−	628978.i	0.210775	−	0.153137i
$443$	4.01536e6			0.972110			0.486055	−	0.873928i	$-0.338435\pi$
$443$	4.01536e6			0.972110			0.486055	+	0.873928i	$0.338435\pi$
$444$	−1.55121e6	+	1.12702e6i	−0.373432	+	0.271314i
$445$	−707027.	+	1.69893e6i	−0.169253	+	0.406702i
$446$	1.88396e6	+	1.36878e6i	0.448471	+	0.325833i
$447$	−2.01409e6	−	1.46333e6i	−0.476772	−	0.346395i
$448$	−112843.	+	347294.i	−0.0265630	+	0.0817527i
$449$	−2.02883e6			−0.474931			−0.237465	−	0.971396i	$-0.576317\pi$
$449$	−2.02883e6			−0.474931			−0.237465	+	0.971396i	$0.576317\pi$
$450$	−999503.	−	161709.i	−0.232677	−	0.0376446i
$451$	5.74609e6			1.33024
$452$	1.08196e6	−	3.32992e6i	0.249094	−	0.766633i
$453$	−2.15059e6	−	1.56250e6i	−0.492393	−	0.357745i
$454$	2.04877e6	+	1.48852e6i	0.466501	+	0.338933i
$455$	−515626.	−	2.16355e6i	−0.116763	−	0.489935i
$456$	1.07953e6	−	784323.i	0.243121	−	0.176638i
$457$	−4.99871e6			−1.11961			−0.559806	−	0.828624i	$-0.689124\pi$
$457$	−4.99871e6			−1.11961			−0.559806	+	0.828624i	$0.689124\pi$
$458$	−1.78309e6	+	1.29549e6i	−0.397200	+	0.288582i
$459$	135039.	+	415607.i	0.0299176	+	0.0920770i
$460$	3.08972e6	−	1.88633e6i	0.680807	−	0.415646i
$461$	−1.77799e6	+	5.47208e6i	−0.389651	+	1.19922i	0.543399	+	0.839475i	$0.317137\pi$
$461$	−1.77799e6	+	5.47208e6i	−0.389651	+	1.19922i	−0.933050	+	0.359748i	$0.882863\pi$
$462$	751159.	+	2.31183e6i	0.163730	+	0.503908i
$463$	522209.	+	1.60719e6i	0.113212	+	0.348430i	0.991570	−	0.129573i	$-0.0413607\pi$
$463$	522209.	+	1.60719e6i	0.113212	+	0.348430i	−0.878358	+	0.478003i	$0.841361\pi$
$464$	280290.	−	862644.i	0.0604383	−	0.186010i
$465$	704020.	+	56583.6i	0.150992	+	0.0121355i
$466$	−1.02774e6	−	3.16307e6i	−0.219240	−	0.674751i
$467$	−208198.	+	151265.i	−0.0441759	+	0.0320956i	−0.609654	−	0.792668i	$-0.708692\pi$
$467$	−208198.	+	151265.i	−0.0441759	+	0.0320956i	0.565478	+	0.824763i	$0.308692\pi$
$468$	−578379.			−0.122067
$469$	3.47236e6	−	2.52282e6i	0.728942	−	0.529608i
$470$	3.91317e6	−	2.38907e6i	0.817116	−	0.498866i
$471$	3.43081e6	+	2.49263e6i	0.712598	+	0.517733i
$472$	−108050.	−	78502.8i	−0.0223239	−	0.0162192i
$473$	−1.31285e6	+	4.04055e6i	−0.269813	+	0.830400i
$474$	131030.			0.0267871
$475$	6.46125e6	−	3.26520e6i	1.31396	−	0.664011i
$476$	855066.			0.172975
$477$	−910348.	+	2.80176e6i	−0.183194	+	0.563814i
$478$	1.69577e6	+	1.23205e6i	0.339467	+	0.246637i
$479$	−5.28911e6	−	3.84276e6i	−1.05328	−	0.765253i	−0.0804468	−	0.996759i	$-0.525635\pi$
$479$	−5.28911e6	−	3.84276e6i	−1.05328	−	0.765253i	−0.972833	+	0.231506i	$0.925635\pi$
$480$	391198.	+	335239.i	0.0774985	+	0.0664127i
$481$	−4.80745e6	+	3.49281e6i	−0.947440	+	0.688355i
$482$	3.27468e6			0.642024
$483$	−2.62723e6	+	1.90879e6i	−0.512425	+	0.372298i
$484$	2.03991e6	+	6.27820e6i	0.395820	+	1.21821i
$485$	6.40915e6	+	5.49236e6i	1.23722	+	1.06024i
$486$	72988.6	−	224636.i	0.0140173	−	0.0431408i
$487$	−1.42372e6	−	4.38176e6i	−0.272021	−	0.837194i	−0.989992	−	0.141121i	$-0.954929\pi$
$487$	−1.42372e6	−	4.38176e6i	−0.272021	−	0.837194i	0.717972	−	0.696072i	$-0.245071\pi$
$488$	−978313.	−	3.01094e6i	−0.185964	−	0.572337i
$489$	581216.	−	1.78880e6i	0.109917	−	0.338290i
$490$	−761102.	+	1.82887e6i	−0.143203	+	0.344106i
$491$	−1.75700e6	−	5.40750e6i	−0.328904	−	1.01226i	−0.969647	−	0.244507i	$-0.921374\pi$
$491$	−1.75700e6	−	5.40750e6i	−0.328904	−	1.01226i	0.640744	−	0.767755i	$-0.278626\pi$
$492$	−883844.	+	642150.i	−0.164613	+	0.119598i
$493$	−2.12390e6			−0.393565
$494$	3.34564e6	−	2.43075e6i	0.616825	−	0.448149i
$495$	3.41844e6	+	274748.i	0.627069	+	0.0503989i
$496$	−290746.	−	211239.i	−0.0530651	−	0.0385541i
$497$	2.25502e6	+	1.63837e6i	0.409506	+	0.297524i
$498$	551324.	−	1.69680e6i	0.0996170	−	0.306590i
$499$	−2.42754e6			−0.436430			−0.218215	−	0.975901i	$-0.570023\pi$
$499$	−2.42754e6			−0.436430			−0.218215	+	0.975901i	$0.570023\pi$
$500$	1.80466e6	+	2.13441e6i	0.322827	+	0.381815i
$501$	3.23995e6			0.576692
$502$	−931897.	+	2.86808e6i	−0.165047	+	0.507963i
$503$	−1.02342e6	−	743558.i	−0.180357	−	0.131037i	0.493944	−	0.869494i	$-0.335555\pi$
$503$	−1.02342e6	−	743558.i	−0.180357	−	0.131037i	−0.674301	+	0.738457i	$0.735555\pi$
$504$	−373898.	−	271653.i	−0.0655657	−	0.0476363i
$505$	109008.	+	8761.17i	0.0190208	+	0.00152874i
$506$	−9.91976e6	+	7.20713e6i	−1.72236	+	1.25137i
$507$	1.54914e6			0.267653
$508$	−1.14011e6	+	828337.i	−0.196014	+	0.142412i
$509$	−2.48439e6	−	7.64617e6i	−0.425036	−	1.30813i	−0.902960	−	0.429725i	$-0.858610\pi$
$509$	−2.48439e6	−	7.64617e6i	−0.425036	−	1.30813i	0.477924	−	0.878401i	$-0.341390\pi$
$510$	463503.	−	1.11376e6i	0.0789091	−	0.189613i
$511$	164694.	−	506875.i	0.0279013	−	0.0858714i
$512$	−81007.0	−	249314.i	−0.0136568	−	0.0420312i
$513$	521872.	+	1.60616e6i	0.0875529	+	0.269460i
$514$	304985.	−	938648.i	0.0509180	−	0.156709i
$515$	3.04316e6	+	2.60786e6i	0.505600	+	0.433277i
$516$	−249610.	−	768221.i	−0.0412703	−	0.127017i
$517$	−1.25635e7	+	9.12792e6i	−2.06721	+	1.50192i
$518$	−4.74832e6			−0.777527
$519$	1.86764e6	−	1.35692e6i	0.304351	−	0.221124i
$520$	1.21239e6	+	1.03896e6i	0.196622	+	0.168497i
$521$	−3.78137e6	−	2.74732e6i	−0.610316	−	0.443420i	0.239210	−	0.970968i	$-0.423112\pi$
$521$	−3.78137e6	−	2.74732e6i	−0.610316	−	0.443420i	−0.849525	+	0.527548i	$0.823112\pi$
$522$	928726.	+	674759.i	0.149180	+	0.108386i
$523$	1.45975e6	−	4.49264e6i	0.233358	−	0.718203i	−0.763977	−	0.645244i	$-0.776756\pi$
$523$	1.45975e6	−	4.49264e6i	0.233358	−	0.718203i	0.997335	−	0.0729588i	$-0.0232442\pi$
$524$	−3.23473e6			−0.514647
$525$	−1.76710e6	−	1.77887e6i	−0.279810	−	0.281674i
$526$	−6.63137e6			−1.04506
$527$	−260044.	+	800334.i	−0.0407869	+	0.125529i
$528$	−1.41175e6	−	1.02569e6i	−0.220380	−	0.160115i
$529$	−8.04520e6	−	5.84518e6i	−1.24996	−	0.908152i
$530$	6.94116e6	−	4.23771e6i	1.07335	−	0.655303i
$531$	136751.	−	99355.1i	0.0210471	−	0.0152916i
$532$	3.30449e6			0.506204
$533$	−2.73918e6	+	1.99013e6i	−0.417641	+	0.303434i
$534$	366201.	+	1.12705e6i	0.0555733	+	0.171037i
$535$	−7.50799e6	−	603433.i	−1.13407	−	0.0911475i
$536$	−952137.	+	2.93038e6i	−0.143149	+	0.440566i
$537$	445181.	+	1.37013e6i	0.0666194	+	0.205033i
$538$	−1.62023e6	−	4.98656e6i	−0.241336	−	0.742754i
$539$	2.07339e6	−	6.38123e6i	0.307403	−	0.946090i
$540$	−556518.	+	339765.i	−0.0821287	+	0.0501412i
$541$	1.53510e6	+	4.72454e6i	0.225498	+	0.694011i	0.998241	+	0.0592920i	$0.0188843\pi$
$541$	1.53510e6	+	4.72454e6i	0.225498	+	0.694011i	−0.772743	+	0.634719i	$0.781116\pi$
$542$	−3.04666e6	+	2.21353e6i	−0.445477	+	0.323658i
$543$	−2.99598e6			−0.436053
$544$	−496600.	+	360801.i	−0.0719465	+	0.0522722i
$545$	1.67730e6	+	7.03790e6i	0.241891	+	1.01497i
$546$	−1.15877e6	−	841898.i	−0.166348	−	0.120859i
$547$	4.34209e6	+	3.15471e6i	0.620484	+	0.450808i	0.853090	−	0.521763i	$-0.174725\pi$
$547$	4.34209e6	+	3.15471e6i	0.620484	+	0.450808i	−0.232607	+	0.972571i	$0.574725\pi$
$548$	−1.38681e6	+	4.26818e6i	−0.197273	+	0.607143i
$549$	4.00683e6			0.567374
$550$	−6.67214e6	−	6.71659e6i	−0.940499	−	0.946764i
$551$	−8.20803e6			−1.15175
$552$	720397.	−	2.21715e6i	0.100629	−	0.309705i
$553$	262517.	+	190730.i	0.0365044	+	0.0265220i
$554$	−2.15419e6	−	1.56511e6i	−0.298202	−	0.216656i
$555$	−2.57391e6	+	6.18490e6i	−0.354699	+	0.852315i
$556$	2.86459e6	−	2.08125e6i	0.392985	−	0.285520i
$557$	−3.36692e6			−0.459828			−0.229914	−	0.973211i	$-0.573844\pi$
$557$	−3.36692e6			−0.459828			−0.229914	+	0.973211i	$0.573844\pi$
$558$	367975.	−	267350.i	0.0500303	−	0.0363491i
$559$	−773584.	−	2.38085e6i	−0.104708	−	0.322257i
$560$	295779.	+	1.24108e6i	0.0398563	+	0.167236i
$561$	−1.26267e6	+	3.88610e6i	−0.169388	+	0.521324i
$562$	−759830.	−	2.33852e6i	−0.101479	−	0.312320i
$563$	4.12429e6	+	1.26933e7i	0.548376	+	1.68773i	0.712825	+	0.701342i	$0.247415\pi$
$563$	4.12429e6	+	1.26933e7i	0.548376	+	1.68773i	−0.164449	+	0.986386i	$0.552585\pi$
$564$	912392.	−	2.80805e6i	0.120777	−	0.371713i
$565$	−2.83599e6	−	1.18997e7i	−0.373751	−	1.56825i
$566$	1.13828e6	+	3.50328e6i	0.149351	+	0.459656i
$567$	473215.	−	343811.i	0.0618160	−	0.0449119i
$568$	−2.00098e6			−0.260239
$569$	−8.38561e6	+	6.09250e6i	−1.08581	+	0.788887i	−0.978687	−	0.205358i	$-0.934164\pi$
$569$	−8.38561e6	+	6.09250e6i	−1.08581	+	0.788887i	−0.107123	+	0.994246i	$0.534164\pi$
$570$	1.79125e6	−	4.30425e6i	0.230925	−	0.554894i
$571$	9.70038e6	+	7.04774e6i	1.24508	+	0.904606i	0.997926	−	0.0643697i	$-0.0205037\pi$
$571$	9.70038e6	+	7.04774e6i	1.24508	+	0.904606i	0.247157	+	0.968975i	$0.420504\pi$
$572$	−4.37524e6	−	3.17880e6i	−0.559129	−	0.406231i
$573$	2.15422e6	−	6.63002e6i	0.274097	−	0.843584i
$574$	−2.70549e6			−0.342741
$575$	5.77939e6	−	1.12502e7i	0.728974	−	1.41903i
$576$	331776.			0.0416667
$577$	−2.52417e6	+	7.76859e6i	−0.315630	+	0.971410i	0.659864	+	0.751385i	$0.270614\pi$
$577$	−2.52417e6	+	7.76859e6i	−0.315630	+	0.971410i	−0.975494	+	0.220025i	$0.929386\pi$
$578$	−3.43192e6	−	2.49344e6i	−0.427286	−	0.310441i
$579$	2.38154e6	+	1.73029e6i	0.295230	+	0.214497i
$580$	−734686.	−	3.08272e6i	−0.0906842	−	0.380508i
$581$	3.57446e6	−	2.59700e6i	0.439309	−	0.319176i
$582$	5.43562e6			0.665184
$583$	−2.22851e7	+	1.61911e7i	−2.71546	+	1.97290i
$584$	118230.	+	363873.i	0.0143448	+	0.0441487i
$585$	−1.72474e6	+	1.05299e6i	−0.208370	+	0.127214i
$586$	−1.81621e6	+	5.58973e6i	−0.218486	+	0.672429i
$587$	4.59539e6	+	1.41431e7i	0.550461	+	1.69415i	0.707638	+	0.706575i	$0.249761\pi$
$587$	4.59539e6	+	1.41431e7i	0.550461	+	1.69415i	−0.157177	+	0.987570i	$0.550239\pi$
$588$	394209.	+	1.21325e6i	0.0470201	+	0.144713i
$589$	−1.00497e6	+	3.09297e6i	−0.119361	+	0.367357i
$590$	−465129.	−	37383.4i	−0.0550102	−	0.00442129i
$591$	−1.14163e6	−	3.51358e6i	−0.134449	−	0.413791i
$592$	2.75770e6	−	2.00358e6i	0.323402	−	0.234965i
$593$	−5.57231e6			−0.650727			−0.325364	−	0.945589i	$-0.605487\pi$
$593$	−5.57231e6			−0.650727			−0.325364	+	0.945589i	$0.605487\pi$
$594$	1.78674e6	−	1.29814e6i	0.207776	−	0.150958i
$595$	2.54983e6	−	1.55672e6i	0.295270	−	0.180268i
$596$	3.58061e6	+	2.60147e6i	0.412897	+	0.299987i
$597$	−712099.	−	517370.i	−0.0817719	−	0.0594108i
$598$	2.23263e6	−	6.87133e6i	0.255308	−	0.785756i
$599$	5.58249e6			0.635713			0.317856	−	0.948139i	$-0.397037\pi$
$599$	5.58249e6			0.635713			0.317856	+	0.948139i	$0.397037\pi$
$600$	1.77689e6	+	287483.i	0.201504	+	0.0326012i
$601$	7.49587e6			0.846517			0.423259	−	0.906009i	$-0.360886\pi$
$601$	7.49587e6			0.846517			0.423259	+	0.906009i	$0.360886\pi$
$602$	618145.	−	1.90246e6i	0.0695183	−	0.213955i
$603$	−3.15486e6	−	2.29214e6i	−0.353335	−	0.256713i
$604$	3.82327e6	+	2.77777e6i	0.426425	+	0.309816i
$605$	1.75131e7	+	1.50079e7i	1.94524	+	1.66699i
$606$	56975.7	−	41395.3i	0.00630243	−	0.00457899i
$607$	−5.28434e6			−0.582128			−0.291064	−	0.956704i	$-0.594009\pi$
$607$	−5.28434e6			−0.582128			−0.291064	+	0.956704i	$0.594009\pi$
$608$	−1.91916e6	+	1.39435e6i	−0.210549	+	0.152973i
$609$	878498.	+	2.70374e6i	0.0959837	+	0.295407i
$610$	−8.39903e6	−	7.19760e6i	−0.913912	−	0.783182i
$611$	2.82766e6	−	8.70263e6i	0.306425	−	0.943078i
$612$	−240069.	−	738857.i	−0.0259094	−	0.0797410i
$613$	−3.40671e6	−	1.04848e7i	−0.366171	−	1.12696i	−0.949244	−	0.314539i	$-0.898150\pi$
$613$	−3.40671e6	−	1.04848e7i	−0.366171	−	1.12696i	0.583073	−	0.812420i	$-0.301850\pi$
$614$	1.62568e6	−	5.00333e6i	0.174026	−	0.535597i
$615$	−1.46656e6	+	3.52403e6i	−0.156355	+	0.375709i
$616$	−1.33539e6	−	4.10992e6i	−0.141794	−	0.436397i
$617$	9.17067e6	−	6.66288e6i	0.969813	−	0.704611i	0.0144043	−	0.999896i	$-0.495415\pi$
$617$	9.17067e6	−	6.66288e6i	0.969813	−	0.704611i	0.955409	+	0.295286i	$0.0954148\pi$
$618$	2.58092e6			0.271833
$619$	−1.45822e7	+	1.05946e7i	−1.52966	+	1.11136i	−0.573234	+	0.819392i	$0.694311\pi$
$619$	−1.45822e7	+	1.05946e7i	−1.52966	+	1.11136i	−0.956427	+	0.291972i	$0.905689\pi$
$620$	−1.25159e6	−	100593.i	−0.130763	−	0.0105097i
$621$	2.38700e6	+	1.73426e6i	0.248384	+	0.180461i
$622$	−7.25047e6	−	5.26777e6i	−0.751433	−	0.545948i
$623$	−906876.	+	2.79108e6i	−0.0936112	+	0.288106i
$624$	1.02823e6			0.105713
$625$	9.26742e6	+	3.07934e6i	0.948984	+	0.315325i
$626$	−201729.			−0.0205747
$627$	−4.87972e6	+	1.50182e7i	−0.495709	+	1.52563i
$628$	−6.09922e6	−	4.43135e6i	−0.617128	−	0.448370i
$629$	−6.45737e6	−	4.69156e6i	−0.650773	−	0.472814i
$630$	−1.60954e6	−	129362.i	−0.161566	−	0.0129854i
$631$	8.65564e6	−	6.28869e6i	0.865418	−	0.628763i	−0.0639356	−	0.997954i	$-0.520365\pi$
$631$	8.65564e6	−	6.28869e6i	0.865418	−	0.628763i	0.929353	+	0.369191i	$0.120365\pi$
$632$	−232943.			−0.0231983
$633$	7.88645e6	−	5.72984e6i	0.782298	−	0.568373i
$634$	−3.18844e6	−	9.81300e6i	−0.315032	−	0.969569i
$635$	−1.89177e6	+	4.54579e6i	−0.186181	+	0.447378i
$636$	1.61840e6	−	4.98091e6i	0.158651	−	0.488277i
$637$	1.22172e6	+	3.76007e6i	0.119295	+	0.367153i
$638$	3.31699e6	+	1.02086e7i	0.322621	+	0.992925i
$639$	782583.	−	2.40854e6i	0.0758190	−	0.233347i
$640$	−695463.	−	595980.i	−0.0671156	−	0.0575151i
$641$	1.18244e6	+	3.63916e6i	0.113666	+	0.349829i	0.991667	−	0.128831i	$-0.0411225\pi$
$641$	1.18244e6	+	3.63916e6i	0.113666	+	0.349829i	−0.878000	+	0.478660i	$0.841122\pi$
$642$	−3.92425e6	+	2.85114e6i	−0.375768	+	0.273011i
$643$	9.54579e6			0.910510			0.455255	−	0.890361i	$-0.349548\pi$
$643$	9.54579e6			0.910510			0.455255	+	0.890361i	$0.349548\pi$
$644$	4.67063e6	−	3.39341e6i	0.443773	−	0.322420i
$645$	−2.14296e6	−	1.83642e6i	−0.202822	−	0.173809i
$646$	4.49387e6	+	3.26499e6i	0.423681	+	0.307823i
$647$	−8.82061e6	−	6.40855e6i	−0.828396	−	0.601865i	0.0907089	−	0.995877i	$-0.471087\pi$
$647$	−8.82061e6	−	6.40855e6i	−0.828396	−	0.601865i	−0.919105	+	0.394012i	$0.871087\pi$
$648$	−129757.	+	399352.i	−0.0121393	+	0.0373610i
$649$	1.58053e6			0.147296
$650$	5.50689e6	+	890957.i	0.511238	+	0.0827129i
$651$	1.12639e6			0.104169
$652$	−1.03327e6	+	3.18009e6i	−0.0951910	+	0.292968i
$653$	4.24880e6	+	3.08693e6i	0.389927	+	0.283298i	0.765425	−	0.643525i	$-0.222529\pi$
$653$	4.24880e6	+	3.08693e6i	0.389927	+	0.283298i	−0.375499	+	0.926823i	$0.622529\pi$
$654$	3.76942e6	+	2.73864e6i	0.344612	+	0.250375i
$655$	−9.64605e6	+	5.88910e6i	−0.878509	+	0.536347i
$656$	1.57128e6	−	1.14160e6i	0.142559	−	0.103575i
$657$	−484227.			−0.0437659
$658$	5.91541e6	−	4.29780e6i	0.532623	−	0.386974i
$659$	−1.20234e6	−	3.70041e6i	−0.107848	−	0.331922i	0.882540	−	0.470237i	$-0.155831\pi$
$659$	−1.20234e6	−	3.70041e6i	−0.107848	−	0.331922i	−0.990388	+	0.138315i	$0.955831\pi$
$660$	−6.07723e6	−	488440.i	−0.543058	−	0.0436467i
$661$	−3.23424e6	+	9.95398e6i	−0.287918	+	0.886121i	0.697591	+	0.716497i	$0.254256\pi$
$661$	−3.23424e6	+	9.95398e6i	−0.287918	+	0.886121i	−0.985509	+	0.169625i	$0.945744\pi$
$662$	1.15416e6	+	3.55213e6i	0.102357	+	0.315024i
$663$	−744015.	−	2.28984e6i	−0.0657352	−	0.202312i
$664$	−980131.	+	3.01653e6i	−0.0862708	+	0.265514i
$665$	9.85408e6	−	6.01611e6i	0.864096	−	0.527548i
$666$	1.33314e6	+	4.10299e6i	0.116464	+	0.358439i
$667$	−1.16014e7	+	8.42890e6i	−1.00971	+	0.733595i
$668$	−5.75991e6			−0.499430
$669$	4.23891e6	−	3.07975e6i	0.366175	−	0.266042i
$670$	2.49571e6	+	1.04719e7i	0.214786	+	0.901237i
$671$	3.03103e7	+	2.20217e7i	2.59886	+	1.88818i
$672$	664708.	+	482938.i	0.0567816	+	0.0412542i
$673$	3.70936e6	−	1.14162e7i	0.315690	−	0.971594i	−0.659779	−	0.751459i	$-0.729350\pi$
$673$	3.70936e6	−	1.14162e7i	0.315690	−	0.971594i	0.975469	−	0.220135i	$-0.0706498\pi$
$674$	−1.43434e6			−0.121619
$675$	−1.04098e6	+	2.02638e6i	−0.0879393	+	0.171183i
$676$	−2.75403e6			−0.231794
$677$	3.23494e6	−	9.95611e6i	0.271265	−	0.834869i	−0.718918	−	0.695095i	$-0.755362\pi$
$677$	3.23494e6	−	9.95611e6i	0.271265	−	0.834869i	0.990183	−	0.139774i	$-0.0446376\pi$
$678$	−6.37335e6	−	4.63051e6i	−0.532468	−	0.386861i
$679$	1.08902e7	+	7.91218e6i	0.906485	+	0.658600i
$680$	−824005.	+	1.98002e6i	−0.0683373	+	0.164209i
$681$	4.60972e6	−	3.34916e6i	0.380897	−	0.276738i
$682$	4.25297e6			0.350132
$683$	5.04232e6	−	3.66346e6i	0.413598	−	0.300496i	−0.361459	−	0.932388i	$-0.617721\pi$
$683$	5.04232e6	−	3.66346e6i	0.413598	−	0.300496i	0.775057	+	0.631892i	$0.217721\pi$
$684$	−927772.	−	2.85539e6i	−0.0758230	−	0.233359i
$685$	3.63507e6	+	1.52526e7i	0.295996	+	1.24199i
$686$	−2.82833e6	+	8.70471e6i	−0.229467	+	0.706226i
$687$	1.53243e6	+	4.71633e6i	0.123876	+	0.381252i
$688$	443752.	+	1.36573e6i	0.0357412	+	0.110000i
$689$	5.01568e6	−	1.54367e7i	0.402515	−	1.23881i
$690$	−1.88828e6	−	7.92316e6i	−0.150988	−	0.633542i
$691$	−5.64461e6	−	1.73723e7i	−0.449717	−	1.38409i	−0.877227	−	0.480076i	$-0.840609\pi$
$691$	−5.64461e6	−	1.73723e7i	−0.449717	−	1.38409i	0.427510	−	0.904010i	$-0.359391\pi$
$692$	−3.32025e6	+	2.41230e6i	−0.263576	+	0.191499i
$693$	5.46931e6			0.432613
$694$	1.14581e7	−	8.32483e6i	0.903058	−	0.656110i
$695$	4.75320e6	−	1.14216e7i	0.373271	−	0.896941i
$696$	−1.65107e6	−	1.19957e6i	−0.129194	−	0.0938649i
$697$	−3.67928e6	−	2.67315e6i	−0.286867	−	0.208421i
$698$	−3.73171e6	+	1.14850e7i	−0.289914	+	0.892263i
$699$	−7.48316e6			−0.579284
$700$	3.14151e6	+	3.16244e6i	0.242323	+	0.243937i
$701$	−1.46860e7			−1.12878			−0.564389	−	0.825509i	$-0.690888\pi$
$701$	−1.46860e7			−1.12878			−0.564389	+	0.825509i	$0.690888\pi$
$702$	−402140.	+	1.23766e6i	−0.0307989	+	0.0947892i
$703$	−2.49552e7	−	1.81310e7i	−1.90446	−	1.38367i
$704$	2.50977e6	+	1.82346e6i	0.190855	+	0.138664i
$705$	−2.39153e6	−	1.00348e7i	−0.181219	−	0.760388i
$706$	3.27728e6	−	2.38108e6i	0.247458	−	0.179789i
$707$	174406.			0.0131224
$708$	−243112.	+	176631.i	−0.0182274	+	0.0132429i
$709$	−2.07657e6	−	6.39104e6i	−0.155143	−	0.477481i	0.843032	−	0.537863i	$-0.180768\pi$
$709$	−2.07657e6	−	6.39104e6i	−0.155143	−	0.477481i	−0.998175	+	0.0603819i	$0.980768\pi$
$710$	−5.96698e6	+	3.64296e6i	−0.444231	+	0.271212i
$711$	91103.9	−	280389.i	0.00675870	−	0.0208011i
$712$	−651024.	−	2.00365e6i	−0.0481279	−	0.148123i
$713$	1.75576e6	+	5.40367e6i	0.129343	+	0.398075i
$714$	594517.	−	1.82974e6i	0.0436435	−	0.134321i
$715$	−1.88344e7	−	1.51376e6i	−1.37780	−	0.110737i
$716$	−791433.	−	2.43578e6i	−0.0576941	−	0.177564i
$717$	3.81548e6	−	2.77211e6i	0.277174	−	0.201378i
$718$	1.58916e7			1.15042
$719$	7.87064e6	−	5.71836e6i	0.567790	−	0.412524i	−0.266512	−	0.963832i	$-0.585871\pi$
$719$	7.87064e6	−	5.71836e6i	0.567790	−	0.412524i	0.834302	+	0.551308i	$0.185871\pi$
$720$	989365.	−	604027.i	0.0711255	−	0.0434235i
$721$	5.17082e6	+	3.75682e6i	0.370443	+	0.269143i
$722$	9.35420e6	+	6.79622e6i	0.667827	+	0.485204i
$723$	2.27685e6	−	7.00741e6i	0.161990	−	0.498554i
$724$	5.32619e6			0.377633
$725$	−7.80322e6	−	7.85520e6i	−0.551352	−	0.555025i
$726$	1.48529e7			1.04585
$727$	−2.36028e6	+	7.26420e6i	−0.165626	+	0.509744i	−0.999082	−	0.0428419i	$-0.986359\pi$
$727$	−2.36028e6	+	7.26420e6i	−0.165626	+	0.509744i	0.833456	+	0.552586i	$0.186359\pi$
$728$	2.06004e6	+	1.49671e6i	0.144061	+	0.104667i
$729$	−429945.	−	312373.i	−0.0299636	−	0.0217698i
$730$	1.01503e6	+	869833.i	0.0704970	+	0.0604128i
$731$	2.72035e6	−	1.97645e6i	0.188292	−	0.136802i
$732$	−7.12324e6			−0.491360
$733$	1.00322e7	−	7.28884e6i	0.689664	−	0.501070i	−0.186886	−	0.982382i	$-0.559839\pi$
$733$	1.00322e7	−	7.28884e6i	0.689664	−	0.501070i	0.876550	+	0.481311i	$0.159839\pi$
$734$	−439554.	−	1.35281e6i	−0.0301142	−	0.0926821i
$735$	3.38437e6	+	2.90026e6i	0.231079	+	0.198024i
$736$	−1.28071e6	+	3.94161e6i	−0.0871475	+	0.268212i
$737$	−1.12677e7	−	3.46785e7i	−0.764130	−	2.35175i
$738$	759596.	+	2.33780e6i	0.0513384	+	0.158003i
$739$	2.61496e6	−	8.04803e6i	0.176139	−	0.542099i	−0.823545	−	0.567251i	$-0.808007\pi$
$739$	2.61496e6	−	8.04803e6i	0.176139	−	0.542099i	0.999684	+	0.0251521i	$0.00800700\pi$
$740$	4.57583e6	−	1.09954e7i	0.307178	−	0.738127i
$741$	−2.87532e6	−	8.84933e6i	−0.192372	−	0.592059i
$742$	1.04927e7	−	7.62341e6i	0.699647	−	0.508323i
$743$	2.06924e7			1.37511			0.687557	−	0.726130i	$-0.258683\pi$
$743$	2.06924e7			1.37511			0.687557	+	0.726130i	$0.258683\pi$
$744$	−654178.	+	475288.i	−0.0433275	+	0.0314793i
$745$	1.54137e7	+	1.23883e6i	1.01746	+	0.0817751i
$746$	248722.	+	180707.i	0.0163632	+	0.0118885i
$747$	−3.24762e6	−	2.35953e6i	−0.212943	−	0.154712i
$748$	2.24475e6	−	6.90863e6i	0.146695	−	0.451479i
$749$	−1.20123e7			−0.782389
$750$	5.82214e6	−	2.37771e6i	0.377946	−	0.154350i
$751$	1.31510e7			0.850860			0.425430	−	0.904991i	$-0.360123\pi$
$751$	1.31510e7			0.850860			0.425430	+	0.904991i	$0.360123\pi$
$752$	−1.62203e6	+	4.99210e6i	−0.104596	+	0.321913i
$753$	5.48941e6	+	3.98829e6i	0.352808	+	0.256330i
$754$	−5.11694e6	−	3.71768e6i	−0.327780	−	0.238146i
$755$	1.64583e7	+	1.32279e6i	1.05079	+	0.0844545i
$756$	−841271.	+	611219.i	−0.0535342	+	0.0388949i
$757$	1.59333e7			1.01057			0.505284	−	0.862953i	$-0.331388\pi$
$757$	1.59333e7			1.01057			0.505284	+	0.862953i	$0.331388\pi$
$758$	1.28497e7	−	9.33583e6i	0.812305	−	0.590174i
$759$	8.52528e6	+	2.62381e7i	0.537160	+	1.65321i
$760$	−3.18445e6	+	7.65200e6i	−0.199987	+	0.480553i
$761$	−4.98939e6	+	1.53558e7i	−0.312310	+	0.961191i	0.664538	+	0.747255i	$0.268629\pi$
$761$	−4.98939e6	+	1.53558e7i	−0.312310	+	0.961191i	−0.976848	+	0.213936i	$0.931371\pi$
$762$	979836.	+	3.01562e6i	0.0611316	+	0.188144i
$763$	3.56556e6	+	1.09737e7i	0.221726	+	0.682401i
$764$	−3.82973e6	+	1.17867e7i	−0.237375	+	0.730565i
$765$	−2.06105e6	−	1.76623e6i	−0.127331	−	0.109117i
$766$	−752842.	−	2.31701e6i	−0.0463588	−	0.142678i
$767$	−753446.	+	547410.i	−0.0462449	+	0.0335989i
$768$	−589824.			−0.0360844
$769$	−7.11632e6	+	5.17031e6i	−0.433950	+	0.315283i	−0.783226	−	0.621737i	$-0.786427\pi$
$769$	−7.11632e6	+	5.17031e6i	−0.433950	+	0.315283i	0.349276	+	0.937020i	$0.386427\pi$
$770$	−1.14647e7	−	9.82470e6i	−0.696842	−	0.597162i
$771$	−1.79654e6	−	1.30526e6i	−0.108843	−	0.0790791i
$772$	−4.23384e6	−	3.07607e6i	−0.255677	−	0.185760i
$773$	−4.56657e6	+	1.40545e7i	−0.274879	+	0.845990i	0.714373	+	0.699766i	$0.246712\pi$
$773$	−4.56657e6	+	1.40545e7i	−0.274879	+	0.845990i	−0.989251	+	0.146225i	$0.953288\pi$
$774$	−1.81745e6			−0.109046
$775$	−3.91542e6	+	1.97866e6i	−0.234166	+	0.118336i
$776$	−9.66333e6			−0.576066
$777$	−3.30145e6	+	1.01608e7i	−0.196179	+	0.603776i
$778$	−7.48189e6	−	5.43591e6i	−0.443162	−	0.321976i
$779$	−1.42189e7	−	1.03307e7i	−0.839505	−	0.609936i
$780$	3.06621e6	−	1.87198e6i	0.180454	−	0.110170i
$781$	1.91574e7	−	1.39187e7i	1.12385	−	0.816527i
$782$	9.70457e6			0.567491
$783$	2.08963e6	−	1.51821e6i	0.121805	−	0.0884967i
$784$	−700816.	−	2.15689e6i	−0.0407206	−	0.125325i
$785$	−2.62557e7	−	2.11023e6i	−1.52072	−	0.122224i
$786$	−2.24907e6	+	6.92192e6i	−0.129851	+	0.399641i
$787$	−1.91995e6	−	5.90900e6i	−0.110498	−	0.340077i	0.880484	−	0.474076i	$-0.157218\pi$
$787$	−1.91995e6	−	5.90900e6i	−0.110498	−	0.340077i	−0.990981	+	0.134000i	$0.957218\pi$
$788$	2.02957e6	+	6.24636e6i	0.116436	+	0.358353i
$789$	−4.61072e6	+	1.41903e7i	−0.263679	+	0.811521i
$790$	−694643.	+	424093.i	−0.0395999	+	0.0241765i
$791$	−6.02866e6	−	1.85543e7i	−0.342594	−	1.05439i
$792$	−3.17643e6	+	2.30781e6i	−0.179939	+	0.130734i
$793$	−2.20761e7			−1.24664
$794$	−1.66329e7	+	1.20845e7i	−0.936305	+	0.680266i
$795$	−4.24208e6	−	1.77997e7i	−0.238046	−	0.998835i
$796$	1.26595e6	+	919769.i	0.0708166	+	0.0514513i
$797$	−1.86005e7	−	1.35141e7i	−1.03724	−	0.753600i	−0.0674960	−	0.997720i	$-0.521501\pi$
$797$	−1.86005e7	−	1.35141e7i	−1.03724	−	0.753600i	−0.969745	+	0.244120i	$0.921501\pi$
$798$	2.29757e6	−	7.07120e6i	0.127721	−	0.393085i
$799$	1.22910e7			0.681113
$800$	−3.15892e6	−	511080.i	−0.174508	−	0.0282335i
$801$	2.66637e6			0.146838
$802$	−5.63995e6	+	1.73580e7i	−0.309628	+	0.952936i
$803$	−3.66301e6	−	2.66133e6i	−0.200470	−	0.145650i
$804$	5.60863e6	+	4.07491e6i	0.305997	+	0.222320i
$805$	7.74995e6	−	1.86225e7i	0.421511	−	1.01286i
$806$	−2.02741e6	+	1.47300e6i	−0.109927	+	0.0798665i
$807$	−1.17972e7			−0.637666
$808$	−101290.	+	73591.6i	−0.00545807	+	0.00396552i
$809$	2.01942e6	+	6.21514e6i	0.108482	+	0.333872i	0.990532	−	0.137284i	$-0.0438371\pi$
$809$	2.01942e6	+	6.21514e6i	0.108482	+	0.333872i	−0.882050	+	0.471155i	$0.843837\pi$
$810$	340116.	+	1.42712e6i	0.0182144	+	0.0764269i
$811$	2.25094e6	−	6.92768e6i	0.120174	−	0.369859i	−0.872817	−	0.488048i	$-0.837709\pi$
$811$	2.25094e6	−	6.92768e6i	0.120174	−	0.369859i	0.992991	+	0.118189i	$0.0377090\pi$
$812$	−1.56177e6	−	4.80665e6i	−0.0831243	−	0.255830i
$813$	2.61837e6	+	8.05851e6i	0.138933	+	0.427591i
$814$	−1.24655e7	+	3.83647e7i	−0.659397	+	2.02942i
$815$	2.70838e6	+	1.13643e7i	0.142829	+	0.599304i
$816$	426790.	+	1.31352e6i	0.0224382	+	0.0690578i
$817$	1.05131e7	−	7.63818e6i	0.551028	−	0.400346i
$818$	−93790.5			−0.00490090
$819$	−2.60724e6	+	1.89427e6i	−0.135822	+	0.0986807i
$820$	2.60721e6	−	6.26494e6i	0.135407	−	0.325373i
$821$	−942184.	−	684537.i	−0.0487841	−	0.0354437i	0.563126	−	0.826371i	$-0.309599\pi$
$821$	−942184.	−	684537.i	−0.0487841	−	0.0354437i	−0.611910	+	0.790927i	$0.709599\pi$
$822$	8.16914e6	+	5.93522e6i	0.421693	+	0.306378i
$823$	−2.81405e6	+	8.66076e6i	−0.144821	+	0.445714i	−0.996988	−	0.0775563i	$-0.975288\pi$
$823$	−2.81405e6	+	8.66076e6i	−0.144821	+	0.445714i	0.852167	+	0.523270i	$0.175288\pi$
$824$	−4.58830e6			−0.235415
$825$	−1.90117e7	+	9.60759e6i	−0.972493	+	0.491450i
$826$	−744179.			−0.0379513
$827$	−1.32096e6	+	4.06550e6i	−0.0671624	+	0.206705i	−0.979005	−	0.203835i	$-0.934659\pi$
$827$	−1.32096e6	+	4.06550e6i	−0.0671624	+	0.206705i	0.911843	+	0.410539i	$0.134659\pi$
$828$	−4.24355e6	−	3.08312e6i	−0.215107	−	0.156284i
$829$	5.85689e6	+	4.25528e6i	0.295993	+	0.215051i	0.725863	−	0.687839i	$-0.241441\pi$
$829$	5.85689e6	+	4.25528e6i	0.295993	+	0.215051i	−0.429870	+	0.902891i	$0.641441\pi$
$830$	2.56908e6	+	1.07798e7i	0.129444	+	0.543145i
$831$	−4.84694e6	+	3.52151e6i	−0.243481	+	0.176899i
$832$	−1.82796e6			−0.0915502
$833$	−4.29624e6	+	3.12140e6i	−0.214524	+	0.155861i
$834$	−2.46190e6	−	7.57694e6i	−0.122562	−	0.377206i
$835$	−1.71762e7	+	1.04864e7i	−0.852533	+	0.520488i
$836$	8.67507e6	−	2.66991e7i	0.429296	−	1.32124i
$837$	−316246.	−	973307.i	−0.0156031	−	0.0480215i
$838$	3.55379e6	+	1.09374e7i	0.174816	+	0.538028i
$839$	3.85615e6	−	1.18680e7i	0.189125	−	0.582068i	−0.810870	−	0.585227i	$-0.801006\pi$
$839$	3.85615e6	−	1.18680e7i	0.189125	−	0.582068i	0.999995	+	0.00315902i	$0.00100555\pi$
$840$	2.86141e6	+	229978.i	0.139921	+	0.0112457i
$841$	−2.45900e6	−	7.56802e6i	−0.119886	−	0.368971i
$842$	6.53895e6	−	4.75082e6i	0.317854	−	0.230934i
$843$	−5.53244e6			−0.268131
$844$	−1.40204e7	+	1.01864e7i	−0.677490	+	0.492225i
$845$	−8.21260e6	+	5.01396e6i	−0.395675	+	0.241568i
$846$	−5.37452e6	−	3.90481e6i	−0.258175	−	0.187575i
$847$	2.97575e7	+	2.16201e7i	1.42524	+	1.03550i
$848$	−2.87715e6	+	8.85496e6i	−0.137396	+	0.422860i
$849$	8.28802e6			0.394622
$850$	1.14760e6	+	7.40466e6i	0.0544806	+	0.351526i
$851$	−5.38910e7			−2.55089
$852$	−1.39126e6	+	4.28185e6i	−0.0656612	+	0.202084i
$853$	1.95449e7	+	1.42002e7i	0.919730	+	0.668223i	0.943457	−	0.331496i	$-0.107553\pi$
$853$	1.95449e7	+	1.42002e7i	0.919730	+	0.668223i	−0.0237270	+	0.999718i	$0.507553\pi$
$854$	−1.42713e7	−	1.03687e7i	−0.669605	−	0.486497i
$855$	−7.96513e6	−	6.82576e6i	−0.372630	−	0.319327i
$856$	6.97645e6	−	5.06869e6i	0.325424	−	0.236435i
$857$	2.30536e7			1.07223			0.536114	−	0.844146i	$-0.319892\pi$
$857$	2.30536e7			1.07223			0.536114	+	0.844146i	$0.319892\pi$
$858$	−9.84429e6	+	7.15229e6i	−0.456527	+	0.331686i
$859$	1.53700e6	+	4.73040e6i	0.0710707	+	0.218733i	0.980283	−	0.197600i	$-0.0633148\pi$
$859$	1.53700e6	+	4.73040e6i	0.0710707	+	0.218733i	−0.909212	+	0.416334i	$0.863315\pi$
$860$	3.80970e6	+	3.26475e6i	0.175649	+	0.150523i
$861$	−1.88110e6	+	5.78942e6i	−0.0864775	+	0.266150i
$862$	−5.36591e6	−	1.65146e7i	−0.245966	−	0.757006i
$863$	−7.57126e6	−	2.33020e7i	−0.346052	−	1.06504i	−0.961018	−	0.276485i	$-0.910830\pi$
$863$	−7.57126e6	−	2.33020e7i	−0.346052	−	1.06504i	0.614966	−	0.788553i	$-0.289170\pi$
$864$	230680.	−	709960.i	0.0105130	−	0.0323556i
$865$	−5.50927e6	+	1.32384e7i	−0.250354	+	0.601581i
$866$	2.16262e6	+	6.65585e6i	0.0979907	+	0.301585i
$867$	−7.72183e6	+	5.61024e6i	−0.348877	+	0.253474i
$868$	−2.00247e6			−0.0902126
$869$	2.23020e6	−	1.62034e6i	0.100183	−	0.0727873i
$870$	−7.10746e6	−	571242.i	−0.318358	−	0.0255871i
$871$	1.73821e7	+	1.26288e7i	0.776349	+	0.564050i
$872$	−6.70119e6	−	4.86870e6i	−0.298442	−	0.216831i
$873$	3.77932e6	−	1.16316e7i	0.167833	−	0.516538i
$874$	3.75043e7			1.66074
$875$	1.51256e7	+	3.71109e6i	0.667870	+	0.163863i
$876$	860848.			0.0379023
$877$	491387.	−	1.51233e6i	0.0215737	−	0.0663971i	−0.939690	−	0.342027i	$-0.888886\pi$
$877$	491387.	−	1.51233e6i	0.0215737	−	0.0663971i	0.961264	+	0.275630i	$0.0888865\pi$
$878$	1.55224e7	+	1.12777e7i	0.679552	+	0.493723i
$879$	1.06985e7	+	7.77294e6i	0.467038	+	0.339323i
$880$	1.08040e7	+	868338.i	0.470302	+	0.0377992i
$881$	−3.12525e7	+	2.27062e7i	−1.35658	+	0.985611i	−0.357923	+	0.933751i	$0.616515\pi$
$881$	−3.12525e7	+	2.27062e7i	−1.35658	+	0.985611i	−0.998654	+	0.0518597i	$0.983485\pi$
$882$	2.87030e6			0.124238
$883$	1.85956e7	−	1.35105e7i	0.802617	−	0.583135i	−0.109064	−	0.994035i	$-0.534785\pi$
$883$	1.85956e7	−	1.35105e7i	0.802617	−	0.583135i	0.911681	+	0.410900i	$0.134785\pi$
$884$	1.32269e6	+	4.07083e6i	0.0569283	+	0.175207i
$885$	−403395.	+	969327.i	−0.0173130	+	0.0416018i
$886$	−4.96326e6	+	1.52753e7i	−0.212414	+	0.653743i
$887$	−8.73995e6	−	2.68988e7i	−0.372992	−	1.14795i	−0.944823	−	0.327581i	$-0.893767\pi$
$887$	−8.73995e6	−	2.68988e7i	−0.372992	−	1.14795i	0.571831	−	0.820372i	$-0.306233\pi$
$888$	−2.37003e6	−	7.29420e6i	−0.100861	−	0.310417i
$889$	−2.42651e6	+	7.46802e6i	−0.102974	+	0.316921i
$890$	−5.58919e6	−	4.78968e6i	−0.236523	−	0.202690i
$891$	−1.53557e6	−	4.72599e6i	−0.0648000	−	0.199434i
$892$	−7.53584e6	+	5.47511e6i	−0.317117	+	0.230399i
$893$	4.74997e7			1.99325
$894$	8.05638e6	−	5.85330e6i	0.337129	−	0.244938i
$895$	−6.79462e6	−	5.82269e6i	−0.283536	−	0.242978i
$896$	−1.18170e6	−	858557.i	−0.0491743	−	0.0357272i
$897$	−1.31515e7	−	9.55511e6i	−0.545750	−	0.396510i
$898$	2.50777e6	−	7.71814e6i	0.103776	−	0.319390i
$899$	4.97394e6			0.205259
$900$	1.85063e6	−	3.60245e6i	0.0761577	−	0.148249i
$901$	2.18016e7			0.894700
$902$	−7.10255e6	+	2.18594e7i	−0.290669	+	0.894586i
$903$	−3.64123e6	−	2.64551e6i	−0.148603	−	0.107967i
$904$	1.13304e7	+	8.23202e6i	0.461131	+	0.335031i
$905$	1.58828e7	−	9.69679e6i	0.644625	−	0.393556i
$906$	8.60236e6	−	6.24998e6i	0.348175	−	0.252964i
$907$	3.21788e7			1.29883			0.649414	−	0.760435i	$-0.275014\pi$
$907$	3.21788e7			1.29883			0.649414	+	0.760435i	$0.275014\pi$
$908$	−8.19507e6	+	5.95406e6i	−0.329866	+	0.239662i
$909$	−48966.3	−	150703.i	−0.00196556	−	0.00604939i
$910$	8.86799e6	+	712739.i	0.354994	+	0.0285317i
$911$	−2.31611e6	+	7.12824e6i	−0.0924619	+	0.284568i	−0.986584	−	0.163255i	$-0.947801\pi$
$911$	−2.31611e6	+	7.12824e6i	−0.0924619	+	0.284568i	0.894122	+	0.447823i	$0.147801\pi$
$912$	1.64937e6	+	5.07625e6i	0.0656647	+	0.202095i
$913$	−1.15990e7	−	3.56981e7i	−0.460515	−	1.41732i
$914$	6.17875e6	−	1.90162e7i	0.244644	−	0.752937i
$915$	−2.12417e7	+	1.29685e7i	−0.838758	+	0.512079i
$916$	−2.72431e6	−	8.38458e6i	−0.107280	−	0.330174i
$917$	−1.45816e7	+	1.05942e7i	−0.572641	+	0.416048i
$918$	−1.74798e6			−0.0684589
$919$	−3.06287e7	+	2.22530e7i	−1.19630	+	0.869162i	−0.993916	−	0.110145i	$-0.964869\pi$
$919$	−3.06287e7	+	2.22530e7i	−1.19630	+	0.869162i	−0.202383	+	0.979306i	$0.564869\pi$
$920$	3.35694e6	+	1.40856e7i	0.130760	+	0.548664i
$921$	−9.57619e6	−	6.95751e6i	−0.372001	−	0.270274i
$922$	−1.86193e7	−	1.35277e7i	−0.721333	−	0.524079i
$923$	−4.31174e6	+	1.32702e7i	−0.166590	+	0.512711i
$924$	−9.72321e6			−0.374653
$925$	−6.37279e6	−	4.11192e7i	−0.244892	−	1.58012i
$926$	−6.75961e6			−0.259056
$927$	1.79448e6	−	5.52284e6i	0.0685866	−	0.211088i
$928$	2.93523e6	+	2.13257e6i	0.111885	+	0.0812894i
$929$	2.35938e7	+	1.71419e7i	0.896929	+	0.651657i	0.937675	−	0.347512i	$-0.112974\pi$
$929$	2.35938e7	+	1.71419e7i	0.896929	+	0.651657i	−0.0407462	+	0.999170i	$0.512974\pi$
$930$	−1.08547e6	+	2.60831e6i	−0.0411540	+	0.0988899i
$931$	−1.66033e7	+	1.20630e7i	−0.627797	+	0.456121i
$932$	1.33034e7			0.501675
$933$	−1.63136e7	+	1.18525e7i	−0.613542	+	0.445765i
$934$	−318099.	−	979007.i	−0.0119315	−	0.0367214i
$935$	−5.88386e6	−	2.46885e7i	−0.220107	−	0.923561i
$936$	714916.	−	2.20028e6i	0.0266726	−	0.0820898i
$937$	−1.43036e7	−	4.40218e7i	−0.532225	−	1.63802i	−0.749571	−	0.661924i	$-0.769740\pi$
$937$	−1.43036e7	−	4.40218e7i	−0.532225	−	1.63802i	0.217346	−	0.976095i	$-0.430260\pi$
$938$	5.30530e6	+	1.63280e7i	0.196881	+	0.605936i
$939$	−140260.	+	431676.i	−0.00519123	+	0.0159770i
$940$	4.25161e6	+	1.78396e7i	0.156940	+	0.658516i
$941$	−6.24973e6	−	1.92347e7i	−0.230084	−	0.708127i	−0.997736	−	0.0672590i	$-0.978575\pi$
$941$	−6.24973e6	−	1.92347e7i	−0.230084	−	0.708127i	0.767651	−	0.640868i	$-0.221425\pi$
$942$	−1.37233e7	+	9.97053e6i	−0.503883	+	0.366093i
$943$	−3.07059e7			−1.12446
$944$	432200.	−	314011.i	0.0157854	−	0.0114687i
$945$	−1.39592e6	+	3.35428e6i	−0.0508487	+	0.122186i
$946$	−1.37484e7	−	9.98879e6i	−0.499487	−	0.362898i
$947$	1.25721e7	+	9.13417e6i	0.455547	+	0.330974i	0.791782	−	0.610804i	$-0.209154\pi$
$947$	1.25721e7	+	9.13417e6i	0.455547	+	0.330974i	−0.336235	+	0.941778i	$0.609154\pi$
$948$	−161963.	+	498469.i	−0.00585320	+	0.0180143i
$949$	2.66791e6			0.0961625
$950$	4.43500e6	+	2.86161e7i	0.159436	+	1.02873i
$951$	−2.32155e7			−0.832390
$952$	−1.05692e6	+	3.25287e6i	−0.0377963	+	0.116325i
$953$	1.45383e7	+	1.05627e7i	0.518540	+	0.376741i	0.816054	−	0.577976i	$-0.196157\pi$
$953$	1.45383e7	+	1.05627e7i	0.518540	+	0.376741i	−0.297514	+	0.954718i	$0.596157\pi$
$954$	−9.53329e6	−	6.92634e6i	−0.339134	−	0.246396i
$955$	1.00383e7	+	4.21206e7i	0.356167	+	1.49447i
$956$	−6.78308e6	+	4.92820e6i	−0.240039	+	0.174399i
$957$	2.41515e7			0.852441
$958$	2.11564e7	−	1.53711e7i	0.744782	−	0.541116i
$959$	7.72732e6	+	2.37822e7i	0.271320	+	0.835038i
$960$	−1.75887e6	+	1.07383e6i	−0.0615965	+	0.0376059i
$961$	−8.23790e6	+	2.53536e7i	−0.287745	+	0.885588i
$962$	−7.34512e6	−	2.26060e7i	−0.255895	−	0.787563i
$963$	3.37259e6	+	1.03798e7i	0.117192	+	0.360680i
$964$	−4.04773e6	+	1.24576e7i	−0.140287	+	0.431760i
$965$	−1.82257e7	−	1.46484e6i	−0.630036	−	0.0506374i
$966$	−4.01405e6	−	1.23540e7i	−0.138401	−	0.425955i
$967$	−2.25806e7	+	1.64058e7i	−0.776549	+	0.564196i	−0.903941	−	0.427656i	$-0.859339\pi$
$967$	−2.25806e7	+	1.64058e7i	−0.776549	+	0.564196i	0.127392	+	0.991852i	$0.459339\pi$
$968$	−2.64052e7			−0.905733
$969$	1.01112e7	−	7.34622e6i	0.345934	−	0.251336i
$970$	−2.88163e7	+	1.75929e7i	−0.983352	+	0.600356i
$971$	−3.86599e7	−	2.80881e7i	−1.31587	−	0.956035i	−0.999974	−	0.00724154i	$-0.997695\pi$
$971$	−3.86599e7	−	2.80881e7i	−1.31587	−	0.956035i	−0.315896	−	0.948794i	$-0.602305\pi$
$972$	764346.	+	555330.i	0.0259492	+	0.0188532i
$973$	6.09674e6	−	1.87638e7i	0.206450	−	0.635389i
$974$	1.84290e7			0.622450
$975$	5.73542e6	−	1.11646e7i	0.193221	−	0.376125i
$976$	1.26635e7			0.425531
$977$	−6.33025e6	+	1.94825e7i	−0.212170	+	0.652993i	0.787172	+	0.616733i	$0.211544\pi$
$977$	−6.33025e6	+	1.94825e7i	−0.212170	+	0.652993i	−0.999342	+	0.0362597i	$0.988456\pi$
$978$	6.08657e6	+	4.42215e6i	0.203482	+	0.147838i
$979$	2.01701e7	+	1.46545e7i	0.672593	+	0.488667i
$980$	−6.01666e6	−	5.15601e6i	−0.200120	−	0.171494i
$981$	8.48119e6	−	6.16195e6i	0.281374	−	0.204430i
$982$	2.27431e7			0.752613
$983$	−4.60849e7	+	3.34827e7i	−1.52116	+	1.10519i	−0.560253	+	0.828322i	$0.689296\pi$
$983$	−4.60849e7	+	3.34827e7i	−1.52116	+	1.10519i	−0.960908	+	0.276867i	$0.910704\pi$
$984$	−1.35039e6	−	4.15608e6i	−0.0444603	−	0.136835i
$985$	1.74243e7	+	1.49318e7i	0.572221	+	0.490368i
$986$	2.62529e6	−	8.07980e6i	0.0859972	−	0.264672i
$987$	−5.08384e6	−	1.56465e7i	−0.166111	−	0.511238i
$988$	5.11168e6	+	1.57321e7i	0.166599	+	0.512738i
$989$	7.01563e6	−	2.15919e7i	0.228074	−	0.701940i
$990$	−5.27063e6	+	1.26649e7i	−0.170913	+	0.410690i
$991$	−3.73261e6	−	1.14878e7i	−0.120734	−	0.371580i	0.872366	−	0.488853i	$-0.162585\pi$
$991$	−3.73261e6	−	1.14878e7i	−0.120734	−	0.371580i	−0.993100	+	0.117273i	$0.962585\pi$
$992$	1.16298e6	−	844957.i	0.0375227	−	0.0272618i
$993$	8.40359e6			0.270453
$994$	−9.02010e6	+	6.55348e6i	−0.289564	+	0.210381i
$995$	5.44963e6	+	437998.i	0.174505	+	0.0140254i
$996$	5.77354e6	+	4.19472e6i	0.184414	+	0.133985i
$997$	1.21563e7	+	8.83208e6i	0.387315	+	0.281401i	0.764354	−	0.644796i	$-0.223058\pi$
$997$	1.21563e7	+	8.83208e6i	0.387315	+	0.281401i	−0.377039	+	0.926197i	$0.623058\pi$
$998$	3.00060e6	−	9.23490e6i	0.0953635	−	0.293499i
$999$	9.70681e6			0.307725

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.6.g.a.121.1	yes	20
25.6	even	5	inner	150.6.g.a.31.1	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.6.g.a.31.1	✓	20	25.6	even	5	inner
150.6.g.a.121.1	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)

\(f(q)\)	\(=\)	\(q+(-1.23607 + 3.80423i) q^{2} +(7.28115 + 5.29007i) q^{3} +(-12.9443 - 9.40456i) q^{4} +(-55.7220 - 4.47850i) q^{5} +(-29.1246 + 21.1603i) q^{6} -89.1519 q^{7} +(51.7771 - 37.6183i) q^{8} +(25.0304 + 77.0356i) q^{9} +O(q^{10})\)	\(q+(-1.23607 + 3.80423i) q^{2} +(7.28115 + 5.29007i) q^{3} +(-12.9443 - 9.40456i) q^{4} +(-55.7220 - 4.47850i) q^{5} +(-29.1246 + 21.1603i) q^{6} -89.1519 q^{7} +(51.7771 - 37.6183i) q^{8} +(25.0304 + 77.0356i) q^{9} +(85.9134 - 206.443i) q^{10} +(-234.045 + 720.316i) q^{11} +(-44.4984 - 136.952i) q^{12} +(-137.908 - 424.438i) q^{13} +(110.198 - 339.154i) q^{14} +(-382.029 - 327.382i) q^{15} +(79.1084 + 243.470i) q^{16} +(484.961 - 352.345i) q^{17} -324.000 q^{18} +(1874.18 - 1361.67i) q^{19} +(679.163 + 582.012i) q^{20} +(-649.129 - 471.620i) q^{21} +(-2450.95 - 1780.72i) q^{22} +(1250.69 - 3849.23i) q^{23} +576.000 q^{24} +(3084.89 + 499.102i) q^{25} +1785.12 q^{26} +(-225.273 + 693.320i) q^{27} +(1154.01 + 838.435i) q^{28} +(-2866.44 - 2082.59i) q^{29} +(1717.65 - 1048.66i) q^{30} +(-1135.73 + 825.153i) q^{31} -1024.00 q^{32} +(-5514.63 + 4006.62i) q^{33} +(740.954 + 2280.42i) q^{34} +(4967.72 + 399.267i) q^{35} +(400.486 - 1232.57i) q^{36} +(-4114.64 - 12663.5i) q^{37} +(2863.49 + 8812.93i) q^{38} +(1241.17 - 3819.94i) q^{39} +(-3053.60 + 1864.28i) q^{40} +(-2344.43 - 7215.42i) q^{41} +(2596.51 - 1886.48i) q^{42} +5609.41 q^{43} +(9803.79 - 7122.87i) q^{44} +(-1049.74 - 4404.68i) q^{45} +(13097.4 + 9515.81i) q^{46} +(16588.0 + 12051.9i) q^{47} +(-711.975 + 2191.23i) q^{48} -8858.94 q^{49} +(-5711.82 + 11118.7i) q^{50} +5395.00 q^{51} +(-2206.53 + 6791.00i) q^{52} +(29423.7 + 21377.6i) q^{53} +(-2359.09 - 1713.98i) q^{54} +(16267.4 - 39089.3i) q^{55} +(-4616.03 + 3353.74i) q^{56} +20849.5 q^{57} +(11465.8 - 8330.36i) q^{58} +(-644.865 - 1984.69i) q^{59} +(1866.20 + 7830.54i) q^{60} +(15286.1 - 47045.9i) q^{61} +(-1735.23 - 5340.50i) q^{62} +(-2231.51 - 6867.87i) q^{63} +(1265.73 - 3895.53i) q^{64} +(5783.68 + 24268.1i) q^{65} +(-8425.61 - 25931.4i) q^{66} +(-38948.9 + 28298.0i) q^{67} -9591.12 q^{68} +(29469.1 - 21410.6i) q^{69} +(-7659.34 + 18404.8i) q^{70} +(-25294.2 - 18377.3i) q^{71} +(4193.94 + 3047.08i) q^{72} +(-1847.34 + 5685.52i) q^{73} +53261.0 q^{74} +(19821.2 + 19953.3i) q^{75} -37065.8 q^{76} +(20865.5 - 64217.5i) q^{77} +(12997.7 + 9443.41i) q^{78} +(-2944.61 - 2139.38i) q^{79} +(-3317.69 - 13921.0i) q^{80} +(-5307.96 + 3856.46i) q^{81} +30347.0 q^{82} +(-40094.0 + 29130.0i) q^{83} +(3967.12 + 12209.5i) q^{84} +(-28601.0 + 17461.5i) q^{85} +(-6933.62 + 21339.5i) q^{86} +(-9853.94 - 30327.3i) q^{87} +(14978.9 + 46100.2i) q^{88} +(10172.3 - 31307.0i) q^{89} +(18053.9 + 1451.03i) q^{90} +(12294.8 + 37839.4i) q^{91} +(-52389.5 + 38063.2i) q^{92} -12634.5 q^{93} +(-66352.1 + 48207.6i) q^{94} +(-110531. + 67481.6i) q^{95} +(-7455.90 - 5417.03i) q^{96} +(-122153. - 88749.4i) q^{97} +(10950.2 - 33701.4i) q^{98} -61348.2 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

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Representations

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Database

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