LMFDB - Embedded newform 150.6.g.a.121.5

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			121.5
Root			$0.500000 - 62.0735i$ of defining polynomial
Character	$\chi$	$=$	150.121
Dual form			150.6.g.a.31.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.23607 + 3.80423i) q^{2} +(7.28115 + 5.29007i) q^{3} +(-12.9443 - 9.40456i) q^{4} +(51.5150 - 21.7074i) q^{5} +(-29.1246 + 21.1603i) q^{6} -38.5661 q^{7} +(51.7771 - 37.6183i) q^{8} +(25.0304 + 77.0356i) q^{9} +O(q^{10})$	\(q+(-1.23607 + 3.80423i) q^{2} +(7.28115 + 5.29007i) q^{3} +(-12.9443 - 9.40456i) q^{4} +(51.5150 - 21.7074i) q^{5} +(-29.1246 + 21.1603i) q^{6} -38.5661 q^{7} +(51.7771 - 37.6183i) q^{8} +(25.0304 + 77.0356i) q^{9} +(18.9037 + 222.806i) q^{10} +(100.280 - 308.629i) q^{11} +(-44.4984 - 136.952i) q^{12} +(52.3555 + 161.134i) q^{13} +(47.6703 - 146.714i) q^{14} +(489.922 + 114.463i) q^{15} +(79.1084 + 243.470i) q^{16} +(620.318 - 450.687i) q^{17} -324.000 q^{18} +(591.765 - 429.943i) q^{19} +(-870.972 - 203.490i) q^{20} +(-280.805 - 204.017i) q^{21} +(1050.14 + 762.973i) q^{22} +(991.484 - 3051.47i) q^{23} +576.000 q^{24} +(2182.58 - 2236.51i) q^{25} -677.703 q^{26} +(-225.273 + 693.320i) q^{27} +(499.210 + 362.697i) q^{28} +(1560.31 + 1133.63i) q^{29} +(-1041.02 + 1722.29i) q^{30} +(2392.36 - 1738.15i) q^{31} -1024.00 q^{32} +(2362.82 - 1716.69i) q^{33} +(947.761 + 2916.91i) q^{34} +(-1986.73 + 837.167i) q^{35} +(400.486 - 1232.57i) q^{36} +(1967.15 + 6054.26i) q^{37} +(904.137 + 2782.65i) q^{38} +(-471.199 + 1450.20i) q^{39} +(1850.70 - 3061.85i) q^{40} +(1195.20 + 3678.46i) q^{41} +(1123.22 - 816.068i) q^{42} +13101.2 q^{43} +(-4200.57 + 3051.89i) q^{44} +(2961.68 + 3425.14i) q^{45} +(10383.0 + 7543.65i) q^{46} +(12781.3 + 9286.13i) q^{47} +(-711.975 + 2191.23i) q^{48} -15319.7 q^{49} +(5810.36 + 11067.5i) q^{50} +6900.79 q^{51} +(837.688 - 2578.14i) q^{52} +(-2225.62 - 1617.01i) q^{53} +(-2359.09 - 1713.98i) q^{54} +(-1533.62 - 18075.8i) q^{55} +(-1996.84 + 1450.79i) q^{56} +6583.16 q^{57} +(-6241.23 + 4534.52i) q^{58} +(9933.45 + 30572.0i) q^{59} +(-5265.20 - 6089.14i) q^{60} +(-6576.87 + 20241.5i) q^{61} +(3655.19 + 11249.5i) q^{62} +(-965.323 - 2970.96i) q^{63} +(1265.73 - 3895.53i) q^{64} +(6194.87 + 7164.29i) q^{65} +(3610.07 + 11110.6i) q^{66} +(18518.7 - 13454.6i) q^{67} -12268.1 q^{68} +(23361.6 - 16973.2i) q^{69} +(-729.041 - 8592.76i) q^{70} +(27483.3 + 19967.8i) q^{71} +(4193.94 + 3047.08i) q^{72} +(24741.0 - 76144.9i) q^{73} -25463.3 q^{74} +(27723.0 - 4738.34i) q^{75} -11703.4 q^{76} +(-3867.39 + 11902.6i) q^{77} +(-4934.46 - 3585.10i) q^{78} +(12993.3 + 9440.18i) q^{79} +(9360.36 + 10825.1i) q^{80} +(-5307.96 + 3856.46i) q^{81} -15471.1 q^{82} +(6591.75 - 4789.18i) q^{83} +(1716.13 + 5281.70i) q^{84} +(22172.4 - 36682.6i) q^{85} +(-16194.0 + 49840.0i) q^{86} +(5363.86 + 16508.3i) q^{87} +(-6417.90 - 19752.3i) q^{88} +(-5302.75 + 16320.2i) q^{89} +(-16690.8 + 7033.18i) q^{90} +(-2019.14 - 6214.29i) q^{91} +(-41531.8 + 30174.6i) q^{92} +26614.0 q^{93} +(-51125.1 + 37144.5i) q^{94} +(21151.8 - 34994.1i) q^{95} +(-7455.90 - 5417.03i) q^{96} +(-125295. - 91032.3i) q^{97} +(18936.1 - 58279.4i) q^{98} +26285.5 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
$5$	51.5150	−	21.7074i	0.921528	−	0.388313i
$5$	51.5150	−	21.7074i	0.921528	−	0.388313i
$6$	−29.1246	+	21.1603i	−0.330280	+	0.239962i
$7$	−38.5661			−0.297482			−0.148741	−	0.988876i	$-0.547522\pi$
$7$	−38.5661			−0.297482			−0.148741	+	0.988876i	$0.547522\pi$
$8$	51.7771	−	37.6183i	0.286031	−	0.207813i
$9$	25.0304	+	77.0356i	0.103006	+	0.317019i
$10$	18.9037	+	222.806i	0.0597787	+	0.704575i
$11$	100.280	−	308.629i	0.249880	−	0.769051i	−0.744916	−	0.667159i	$-0.767510\pi$
$11$	100.280	−	308.629i	0.249880	−	0.769051i	0.994795	−	0.101892i	$-0.0324897\pi$
$12$	−44.4984	−	136.952i	−0.0892055	−	0.274546i
$13$	52.3555	+	161.134i	0.0859219	+	0.264440i	0.984782	−	0.173796i	$-0.0556033\pi$
$13$	52.3555	+	161.134i	0.0859219	+	0.264440i	−0.898860	+	0.438236i	$0.855603\pi$
$14$	47.6703	−	146.714i	0.0650021	−	0.200056i
$15$	489.922	+	114.463i	0.562210	+	0.131352i
$16$	79.1084	+	243.470i	0.0772542	+	0.237764i
$17$	620.318	−	450.687i	0.520585	−	0.378227i	−0.296239	−	0.955114i	$-0.595733\pi$
$17$	620.318	−	450.687i	0.520585	−	0.378227i	0.816824	+	0.576887i	$0.195733\pi$
$18$	−324.000			−0.235702
$19$	591.765	−	429.943i	0.376067	−	0.273229i	−0.383655	−	0.923476i	$-0.625335\pi$
$19$	591.765	−	429.943i	0.376067	−	0.273229i	0.759722	+	0.650248i	$0.225335\pi$
$20$	−870.972	−	203.490i	−0.486888	−	0.113754i
$21$	−280.805	−	204.017i	−0.138950	−	0.100953i
$22$	1050.14	+	762.973i	0.462585	+	0.336088i
$23$	991.484	−	3051.47i	0.390810	−	1.20279i	−0.541367	−	0.840787i	$-0.682093\pi$
$23$	991.484	−	3051.47i	0.390810	−	1.20279i	0.932177	−	0.362003i	$-0.117907\pi$
$24$	576.000			0.204124
$25$	2182.58	−	2236.51i	0.698426	−	0.715682i
$26$	−677.703			−0.196610
$27$	−225.273	+	693.320i	−0.0594703	+	0.183031i
$28$	499.210	+	362.697i	0.120334	+	0.0874277i
$29$	1560.31	+	1133.63i	0.344521	+	0.250309i	0.746567	−	0.665311i	$-0.231701\pi$
$29$	1560.31	+	1133.63i	0.344521	+	0.250309i	−0.402046	+	0.915619i	$0.631701\pi$
$30$	−1041.02	+	1722.29i	−0.211181	+	0.349384i
$31$	2392.36	−	1738.15i	0.447117	−	0.324850i	−0.341339	−	0.939940i	$-0.610880\pi$
$31$	2392.36	−	1738.15i	0.447117	−	0.324850i	0.788457	+	0.615090i	$0.210880\pi$
$32$	−1024.00			−0.176777
$33$	2362.82	−	1716.69i	0.377699	−	0.274414i
$34$	947.761	+	2916.91i	0.140605	+	0.432738i
$35$	−1986.73	+	837.167i	−0.274138	+	0.115516i
$36$	400.486	−	1232.57i	0.0515028	−	0.158509i
$37$	1967.15	+	6054.26i	0.236229	+	0.727037i	0.996956	+	0.0779657i	$0.0248425\pi$
$37$	1967.15	+	6054.26i	0.236229	+	0.727037i	−0.760727	+	0.649072i	$0.775158\pi$
$38$	904.137	+	2782.65i	0.101572	+	0.312607i
$39$	−471.199	+	1450.20i	−0.0496070	+	0.152675i
$40$	1850.70	−	3061.85i	0.182889	−	0.302575i
$41$	1195.20	+	3678.46i	0.111041	+	0.341749i	0.991101	−	0.133114i	$-0.0424977\pi$
$41$	1195.20	+	3678.46i	0.111041	+	0.341749i	−0.880060	+	0.474863i	$0.842498\pi$
$42$	1123.22	−	816.068i	0.0982522	−	0.0713844i
$43$	13101.2			1.08054			0.540269	−	0.841492i	$-0.318322\pi$
$43$	13101.2			1.08054			0.540269	+	0.841492i	$0.318322\pi$
$44$	−4200.57	+	3051.89i	−0.327097	+	0.237650i
$45$	2961.68	+	3425.14i	0.218025	+	0.252143i
$46$	10383.0	+	7543.65i	0.723479	+	0.525639i
$47$	12781.3	+	9286.13i	0.843974	+	0.613183i	0.923478	−	0.383651i	$-0.125334\pi$
$47$	12781.3	+	9286.13i	0.843974	+	0.613183i	−0.0795038	+	0.996835i	$0.525334\pi$
$48$	−711.975	+	2191.23i	−0.0446028	+	0.137273i
$49$	−15319.7			−0.911505
$50$	5810.36	+	11067.5i	0.328683	+	0.626073i
$51$	6900.79			0.371513
$52$	837.688	−	2578.14i	0.0429609	−	0.132220i
$53$	−2225.62	−	1617.01i	−0.108833	−	0.0790719i	0.532037	−	0.846721i	$-0.321427\pi$
$53$	−2225.62	−	1617.01i	−0.108833	−	0.0790719i	−0.640871	+	0.767649i	$0.721427\pi$
$54$	−2359.09	−	1713.98i	−0.110093	−	0.0799874i
$55$	−1533.62	−	18075.8i	−0.0683613	−	0.805733i
$56$	−1996.84	+	1450.79i	−0.0850889	+	0.0618207i
$57$	6583.16			0.268378
$58$	−6241.23	+	4534.52i	−0.243613	+	0.176995i
$59$	9933.45	+	30572.0i	0.371510	+	1.14339i	0.945803	+	0.324740i	$0.105277\pi$
$59$	9933.45	+	30572.0i	0.371510	+	1.14339i	−0.574294	+	0.818649i	$0.694723\pi$
$60$	−5265.20	−	6089.14i	−0.188815	−	0.218362i
$61$	−6576.87	+	20241.5i	−0.226305	+	0.696496i	0.771851	+	0.635803i	$0.219331\pi$
$61$	−6576.87	+	20241.5i	−0.226305	+	0.696496i	−0.998157	+	0.0606926i	$0.980669\pi$
$62$	3655.19	+	11249.5i	0.120762	+	0.371668i
$63$	−965.323	−	2970.96i	−0.0306423	−	0.0943073i
$64$	1265.73	−	3895.53i	0.0386271	−	0.118882i
$65$	6194.87	+	7164.29i	0.181865	+	0.210324i
$66$	3610.07	+	11110.6i	0.102013	+	0.313964i
$67$	18518.7	−	13454.6i	0.503992	−	0.366172i	−0.306548	−	0.951855i	$-0.599174\pi$
$67$	18518.7	−	13454.6i	0.503992	−	0.366172i	0.810540	+	0.585684i	$0.199174\pi$
$68$	−12268.1			−0.321739
$69$	23361.6	−	16973.2i	0.590718	−	0.429182i
$70$	−729.041	−	8592.76i	−0.0177831	−	0.209598i
$71$	27483.3	+	19967.8i	0.647029	+	0.470094i	0.862258	−	0.506470i	$-0.169050\pi$
$71$	27483.3	+	19967.8i	0.647029	+	0.470094i	−0.215229	+	0.976564i	$0.569050\pi$
$72$	4193.94	+	3047.08i	0.0953436	+	0.0692712i
$73$	24741.0	−	76144.9i	0.543388	−	1.67238i	−0.181404	−	0.983409i	$-0.558064\pi$
$73$	24741.0	−	76144.9i	0.543388	−	1.67238i	0.724792	−	0.688968i	$-0.241936\pi$
$74$	−25463.3			−0.540549
$75$	27723.0	−	4738.34i	0.569098	−	0.0972687i
$76$	−11703.4			−0.232422
$77$	−3867.39	+	11902.6i	−0.0743346	+	0.228779i
$78$	−4934.46	−	3585.10i	−0.0918340	−	0.0667213i
$79$	12993.3	+	9440.18i	0.234235	+	0.170182i	0.698711	−	0.715404i	$-0.253757\pi$
$79$	12993.3	+	9440.18i	0.234235	+	0.170182i	−0.464476	+	0.885586i	$0.653757\pi$
$80$	9360.36	+	10825.1i	0.163519	+	0.189107i
$81$	−5307.96	+	3856.46i	−0.0898908	+	0.0653095i
$82$	−15471.1			−0.254089
$83$	6591.75	−	4789.18i	0.105028	−	0.0763074i	−0.534032	−	0.845465i	$-0.679324\pi$
$83$	6591.75	−	4789.18i	0.105028	−	0.0763074i	0.639060	+	0.769157i	$0.279324\pi$
$84$	1716.13	+	5281.70i	0.0265370	+	0.0816725i
$85$	22172.4	−	36682.6i	0.332863	−	0.550697i
$86$	−16194.0	+	49840.0i	−0.236106	+	0.726661i
$87$	5363.86	+	16508.3i	0.0759765	+	0.233832i
$88$	−6417.90	−	19752.3i	−0.0883458	−	0.271901i
$89$	−5302.75	+	16320.2i	−0.0709620	+	0.218399i	−0.980248	−	0.197774i	$-0.936629\pi$
$89$	−5302.75	+	16320.2i	−0.0709620	+	0.218399i	0.909286	+	0.416173i	$0.136629\pi$
$90$	−16690.8	+	7033.18i	−0.217206	+	0.0915262i
$91$	−2019.14	−	6214.29i	−0.0255602	−	0.0786661i
$92$	−41531.8	+	30174.6i	−0.511577	+	0.371683i
$93$	26614.0			0.319083
$94$	−51125.1	+	37144.5i	−0.596780	+	0.433586i
$95$	21151.8	−	34994.1i	0.240458	−	0.397820i
$96$	−7455.90	−	5417.03i	−0.0825700	−	0.0599906i
$97$	−125295.	−	91032.3i	−1.35209	−	0.982350i	−0.998904	−	0.0467961i	$-0.985099\pi$
$97$	−125295.	−	91032.3i	−1.35209	−	0.982350i	−0.353184	−	0.935554i	$-0.614901\pi$
$98$	18936.1	−	58279.4i	0.199171	−	0.612986i
$99$	26285.5			0.269543
$100$	−49285.3	+	8423.72i	−0.492853	+	0.0842372i
$101$	−75903.5			−0.740386			−0.370193	−	0.928955i	$-0.620708\pi$
$101$	−75903.5			−0.740386			−0.370193	+	0.928955i	$0.620708\pi$
$102$	−8529.85	+	26252.2i	−0.0811785	+	0.249842i
$103$	−70891.1	−	51505.4i	−0.658413	−	0.478365i	0.207714	−	0.978190i	$-0.433398\pi$
$103$	−70891.1	−	51505.4i	−0.658413	−	0.478365i	−0.866127	+	0.499825i	$0.833398\pi$
$104$	8772.38	+	6373.51i	0.0795305	+	0.0577823i
$105$	−18894.3	−	4414.39i	−0.167247	−	0.0390749i
$106$	8902.48	−	6468.03i	0.0769567	−	0.0559123i
$107$	−158396.			−1.33747			−0.668734	−	0.743502i	$-0.733164\pi$
$107$	−158396.			−1.33747			−0.668734	+	0.743502i	$0.733164\pi$
$108$	9436.37	−	6855.93i	0.0778477	−	0.0565597i
$109$	−59521.4	−	183188.i	−0.479852	−	1.47683i	−0.839301	−	0.543667i	$-0.817036\pi$
$109$	−59521.4	−	183188.i	−0.479852	−	1.47683i	0.359450	−	0.933164i	$-0.382964\pi$
$110$	70660.1	+	16508.7i	0.556792	+	0.130086i
$111$	−17704.3	+	54488.3i	−0.136387	+	0.419755i
$112$	−3050.90	−	9389.70i	−0.0229817	−	0.0707305i
$113$	−34227.3	−	105341.i	−0.252160	−	0.776070i	−0.994376	−	0.105909i	$-0.966225\pi$
$113$	−34227.3	−	105341.i	−0.252160	−	0.776070i	0.742215	−	0.670161i	$-0.233775\pi$
$114$	−8137.23	+	25043.8i	−0.0586428	+	0.180484i
$115$	−15163.2	−	178719.i	−0.106917	−	1.26016i
$116$	−9535.75	−	29348.0i	−0.0657976	−	0.202504i
$117$	−11102.5	+	8066.47i	−0.0749821	+	0.0544777i
$118$	−128581.			−0.850105
$119$	−23923.2	+	17381.2i	−0.154865	+	0.112516i
$120$	29672.6	−	12503.4i	0.188106	−	0.0792640i
$121$	45097.1	+	32765.0i	0.280018	+	0.203445i
$122$	−68873.8	−	50039.8i	−0.418943	−	0.304380i
$123$	−10756.8	+	33106.2i	−0.0641095	+	0.197309i
$124$	−47313.8			−0.276334
$125$	63887.0	−	162592.i	0.365710	−	0.930729i
$126$	12495.4			0.0701171
$127$	−33286.6	+	102446.i	−0.183130	+	0.563617i	−0.999911	−	0.0133310i	$-0.995756\pi$
$127$	−33286.6	+	102446.i	−0.183130	+	0.563617i	0.816781	+	0.576948i	$0.195756\pi$
$128$	13254.9	+	9630.27i	0.0715077	+	0.0519534i
$129$	95391.9	+	69306.3i	0.504705	+	0.366689i
$130$	−34911.9	+	14711.1i	−0.181182	+	0.0763463i
$131$	56170.3	−	40810.1i	0.285975	−	0.207773i	−0.435544	−	0.900167i	$-0.643444\pi$
$131$	56170.3	−	40810.1i	0.285975	−	0.207773i	0.721519	+	0.692394i	$0.243444\pi$
$132$	−46729.7			−0.233431
$133$	−22822.1	+	16581.2i	−0.111873	+	0.0812806i
$134$	28294.1	+	87080.2i	0.136124	+	0.418945i
$135$	3445.20	+	40606.4i	0.0162697	+	0.191761i
$136$	15164.2	−	46670.5i	0.0703026	−	0.216369i
$137$	82803.3	+	254842.i	0.376917	+	1.16003i	0.942176	+	0.335119i	$0.108776\pi$
$137$	82803.3	+	254842.i	0.376917	+	1.16003i	−0.565258	+	0.824914i	$0.691224\pi$
$138$	35693.4	+	109853.i	0.159548	+	0.491037i
$139$	12228.0	−	37634.0i	0.0536809	−	0.165213i	−0.920622	−	0.390456i	$-0.872318\pi$
$139$	12228.0	−	37634.0i	0.0536809	−	0.165213i	0.974303	+	0.225243i	$0.0723175\pi$
$140$	33590.0	+	7847.80i	0.144840	+	0.0338398i
$141$	43938.1	+	135227.i	0.186120	+	0.572819i
$142$	−109933.	+	79871.3i	−0.457518	+	0.332407i
$143$	54980.7			0.224838
$144$	−16775.8	+	12188.3i	−0.0674181	+	0.0489821i
$145$	104987.	+	24528.8i	0.414684	+	0.0968848i
$146$	259091.	+	188241.i	1.00594	+	0.730855i
$147$	−111545.	−	81042.0i	−0.425751	−	0.309326i
$148$	31474.4	−	96868.2i	0.118114	−	0.363519i
$149$	−48720.6			−0.179782			−0.0898911	−	0.995952i	$-0.528652\pi$
$149$	−48720.6			−0.179782			−0.0898911	+	0.995952i	$0.528652\pi$
$150$	−16241.8	+	111321.i	−0.0589393	+	0.403971i
$151$	163079.			0.582045			0.291023	−	0.956716i	$-0.406005\pi$
$151$	163079.			0.582045			0.291023	+	0.956716i	$0.406005\pi$
$152$	14466.2	−	44522.4i	0.0507861	−	0.156304i
$153$	50245.7	+	36505.7i	0.173528	+	0.126076i
$154$	−40499.8	−	29424.9i	−0.137610	−	0.0999799i
$155$	85511.5	−	141472.i	0.285888	−	0.472980i
$156$	19737.8	−	14340.4i	0.0649364	−	0.0471791i
$157$	−80633.3			−0.261075			−0.130537	−	0.991443i	$-0.541670\pi$
$157$	−80633.3			−0.261075			−0.130537	+	0.991443i	$0.541670\pi$
$158$	−51973.2	+	37760.7i	−0.165629	+	0.120337i
$159$	−7651.00	−	23547.4i	−0.0240008	−	0.0738668i
$160$	−52751.3	+	22228.3i	−0.162905	+	0.0686447i
$161$	−38237.6	+	117683.i	−0.116259	+	0.357808i
$162$	−8109.84	−	24959.5i	−0.0242787	−	0.0747221i
$163$	−52095.2	−	160332.i	−0.153578	−	0.472664i	0.844436	−	0.535656i	$-0.179936\pi$
$163$	−52095.2	−	160332.i	−0.153578	−	0.472664i	−0.998014	+	0.0629923i	$0.979936\pi$
$164$	19123.3	−	58855.4i	0.0555204	−	0.170874i
$165$	84455.8	−	139726.i	0.241501	−	0.399546i
$166$	10071.3	+	30996.3i	0.0283671	+	0.0873050i
$167$	−291223.	+	211586.i	−0.808042	+	0.587077i	−0.913262	−	0.407372i	$-0.866445\pi$
$167$	−291223.	+	211586.i	−0.808042	+	0.587077i	0.105220	+	0.994449i	$0.466445\pi$
$168$	−22214.1			−0.0607232
$169$	277159.	−	201368.i	0.746471	−	0.542343i
$170$	112142.	+	129691.i	0.297610	+	0.344182i
$171$	47933.0	+	34825.4i	0.125356	+	0.0910763i
$172$	−169586.	−	123211.i	−0.437087	−	0.317562i
$173$	5519.44	−	16987.1i	0.0140210	−	0.0431523i	−0.943801	−	0.330514i	$-0.892778\pi$
$173$	5519.44	−	16987.1i	0.0140210	−	0.0431523i	0.957822	+	0.287361i	$0.0927780\pi$
$174$	−69431.3			−0.173853
$175$	−84173.6	+	86253.3i	−0.207769	+	0.212902i
$176$	83075.0			0.202157
$177$	−89401.0	+	275148.i	−0.214491	+	0.660136i
$178$	−55531.1	−	40345.7i	−0.131367	−	0.0954437i
$179$	171509.	+	124609.i	0.400087	+	0.290680i	0.769576	−	0.638555i	$-0.220467\pi$
$179$	171509.	+	124609.i	0.400087	+	0.290680i	−0.369490	+	0.929235i	$0.620467\pi$
$180$	−6124.79	−	72189.2i	−0.0140900	−	0.166070i
$181$	−122265.	+	88830.6i	−0.277399	+	0.201542i	−0.717782	−	0.696268i	$-0.754843\pi$
$181$	−122265.	+	88830.6i	−0.277399	+	0.201542i	0.440383	+	0.897810i	$0.354843\pi$
$182$	26136.4			0.0584880
$183$	−154966.	+	112589.i	−0.342065	+	0.248525i
$184$	−63454.9	−	195294.i	−0.138172	−	0.425251i
$185$	232760.	+	269183.i	0.500009	+	0.578254i
$186$	−32896.8	+	101246.i	−0.0697221	+	0.214583i
$187$	−76889.9	−	236643.i	−0.160792	−	0.494868i
$188$	−78112.1	−	240404.i	−0.161185	−	0.496076i
$189$	8687.91	−	26738.6i	0.0176913	−	0.0544483i
$190$	106980.	+	123722.i	0.214991	+	0.248634i
$191$	161211.	+	496155.i	0.319750	+	0.984088i	0.973755	+	0.227598i	$0.0730873\pi$
$191$	161211.	+	496155.i	0.319750	+	0.984088i	−0.654006	+	0.756490i	$0.726913\pi$
$192$	29823.6	−	21668.1i	0.0583858	−	0.0424197i
$193$	−451530.			−0.872556			−0.436278	−	0.899812i	$-0.643704\pi$
$193$	−451530.			−0.872556			−0.436278	+	0.899812i	$0.643704\pi$
$194$	501181.	−	364129.i	0.956071	−	0.694626i
$195$	7206.24	+	84935.6i	0.0135713	+	0.159957i
$196$	198302.	+	144075.i	0.368711	+	0.267884i
$197$	−76516.1	−	55592.2i	−0.140471	−	0.102058i	0.515330	−	0.856992i	$-0.327669\pi$
$197$	−76516.1	−	55592.2i	−0.140471	−	0.102058i	−0.655802	+	0.754933i	$0.727669\pi$
$198$	−32490.6	+	99995.8i	−0.0588972	+	0.181267i
$199$	418289.			0.748762			0.374381	−	0.927275i	$-0.377855\pi$
$199$	418289.			0.748762			0.374381	+	0.927275i	$0.377855\pi$
$200$	28874.3	−	197905.i	0.0510429	−	0.349849i
$201$	206013.			0.359671
$202$	93821.9	−	288754.i	0.161780	−	0.497909i
$203$	−60174.9	−	43719.6i	−0.102489	−	0.0744623i
$204$	−89325.7	−	64898.9i	−0.150280	−	0.109185i
$205$	141421.	+	163551.i	0.235033	+	0.271812i
$206$	283564.	−	206021.i	0.465568	−	0.338255i
$207$	259889.			0.421563
$208$	−35089.5	+	25494.0i	−0.0562366	+	0.0408583i
$209$	−73350.8	−	225750.i	−0.116155	−	0.357489i
$210$	40148.0	−	66421.9i	0.0628226	−	0.103935i
$211$	−278809.	+	858087.i	−0.431123	+	1.32686i	0.465885	+	0.884845i	$0.345736\pi$
$211$	−278809.	+	858087.i	−0.431123	+	1.32686i	−0.897008	+	0.442014i	$0.854264\pi$
$212$	13601.8	+	41862.0i	0.0207853	+	0.0639706i
$213$	94479.3	+	290777.i	0.142688	+	0.439149i
$214$	195788.	−	602572.i	0.292248	−	0.899445i
$215$	674908.	−	284393.i	0.995746	−	0.419587i
$216$	14417.5	+	44372.5i	0.0210259	+	0.0647112i
$217$	−92263.7	+	67033.5i	−0.133009	+	0.0966369i
$218$	770461.			1.09802
$219$	582955.	−	423542.i	0.821343	−	0.596741i
$220$	−150144.	+	248401.i	−0.209146	+	0.346017i
$221$	105098.	+	76358.0i	0.144748	+	0.105166i
$222$	−185402.	−	134703.i	−0.252483	−	0.183440i
$223$	180211.	−	554633.i	0.242672	−	0.746867i	−0.753339	−	0.657633i	$-0.771558\pi$
$223$	180211.	−	554633.i	0.242672	−	0.746867i	0.996011	−	0.0892347i	$-0.0284421\pi$
$224$	39491.6			0.0525878
$225$	226921.	+	112156.i	0.298827	+	0.147695i
$226$	443048.			0.577005
$227$	−391483.	+	1.20486e6i	−0.504253	+	1.55193i	0.297769	+	0.954638i	$0.403757\pi$
$227$	−391483.	+	1.20486e6i	−0.504253	+	1.55193i	−0.802022	+	0.597294i	$0.796243\pi$
$228$	−85214.2	−	61911.7i	−0.108561	−	0.0788744i
$229$	−962707.	−	699448.i	−1.21313	−	0.881387i	−0.217614	−	0.976035i	$-0.569828\pi$
$229$	−962707.	−	699448.i	−1.21313	−	0.881387i	−0.995511	+	0.0946478i	$0.969828\pi$
$230$	698630.	+	163225.i	0.870818	+	0.203454i
$231$	−91124.7	+	66205.9i	−0.112359	+	0.0816332i
$232$	123433.			0.150561
$233$	−647307.	+	470296.i	−0.781125	+	0.567520i	−0.905316	−	0.424738i	$-0.860366\pi$
$233$	−647307.	+	470296.i	−0.781125	+	0.567520i	0.124192	+	0.992258i	$0.460366\pi$
$234$	−16963.2	−	52207.3i	−0.0202520	−	0.0623292i
$235$	860004.	+	200927.i	1.01585	+	0.237339i
$236$	158935.	−	489152.i	0.185755	−	0.571695i
$237$	44667.0	+	137471.i	0.0516554	+	0.158979i
$238$	−36551.4	−	112494.i	−0.0418275	−	0.128732i
$239$	167039.	−	514094.i	0.189158	−	0.582167i	−0.810838	−	0.585271i	$-0.800988\pi$
$239$	167039.	−	514094.i	0.189158	−	0.582167i	0.999995	+	0.00310395i	$0.000988018\pi$
$240$	10888.5	+	128336.i	0.0122023	+	0.143821i
$241$	212735.	+	654731.i	0.235937	+	0.726140i	0.996996	+	0.0774570i	$0.0246800\pi$
$241$	212735.	+	654731.i	0.235937	+	0.726140i	−0.761058	+	0.648683i	$0.775320\pi$
$242$	−180389.	+	131060.i	−0.198002	+	0.143857i
$243$	−59049.0			−0.0641500
$244$	275495.	−	200159.i	0.296237	−	0.215229i
$245$	−789192.	+	332549.i	−0.839977	+	0.353949i
$246$	−112647.	−	81842.9i	−0.118681	−	0.0862270i
$247$	100260.	+	72843.4i	0.104565	+	0.0759710i
$248$	58483.1	−	179993.i	0.0603811	−	0.185834i
$249$	73330.6			0.0749527
$250$	539567.	+	444015.i	0.546003	+	0.449311i
$251$	−800739.			−0.802244			−0.401122	−	0.916025i	$-0.631380\pi$
$251$	−800739.			−0.802244			−0.401122	+	0.916025i	$0.631380\pi$
$252$	−15445.2	+	47535.3i	−0.0153211	+	0.0471536i
$253$	−842347.	−	612001.i	−0.827351	−	0.601106i
$254$	−348582.	−	253260.i	−0.339016	−	0.246310i
$255$	355494.	−	149798.i	0.342359	−	0.144263i
$256$	−53019.7	+	38521.1i	−0.0505636	+	0.0367366i
$257$	−274035.			−0.258805			−0.129403	−	0.991592i	$-0.541306\pi$
$257$	−274035.			−0.258805			−0.129403	+	0.991592i	$0.541306\pi$
$258$	−381568.	+	277225.i	−0.356880	+	0.259289i
$259$	−75865.2	−	233489.i	−0.0702737	−	0.216280i
$260$	−12811.1	−	150997.i	−0.0117531	−	0.138527i
$261$	−48274.8	+	148574.i	−0.0438651	+	0.135003i
$262$	85820.6	+	264129.i	0.0772393	+	0.237718i
$263$	−547709.	−	1.68567e6i	−0.488270	−	1.50274i	−0.827188	−	0.561925i	$-0.810061\pi$
$263$	−547709.	−	1.68567e6i	−0.488270	−	1.50274i	0.338918	−	0.940816i	$-0.389939\pi$
$264$	57761.1	−	177770.i	0.0510065	−	0.156982i
$265$	−149754.	−	34987.8i	−0.130997	−	0.0306056i
$266$	−34869.0	−	107316.i	−0.0302159	−	0.0929950i
$267$	−124945.	+	90777.8i	−0.107261	+	0.0779295i
$268$	−366246.			−0.311484
$269$	371232.	−	269716.i	0.312799	−	0.227262i	−0.420298	−	0.907386i	$-0.638074\pi$
$269$	371232.	−	269716.i	0.312799	−	0.227262i	0.733097	+	0.680125i	$0.238074\pi$
$270$	−158735.	−	37086.0i	−0.132514	−	0.0309600i
$271$	1.18473e6	+	860755.i	0.979930	+	0.711961i	0.957693	−	0.287792i	$-0.0929212\pi$
$271$	1.18473e6	+	860755.i	0.979930	+	0.711961i	0.0222370	+	0.999753i	$0.492921\pi$
$272$	158801.	+	115376.i	0.130146	+	0.0945568i
$273$	18172.3	−	55928.6i	0.0147572	−	0.0454179i
$274$	−1.07183e6			−0.862480
$275$	−471382.	−	897884.i	−0.375873	−	0.715960i
$276$	−462025.			−0.365084
$277$	58050.8	−	178662.i	0.0454579	−	0.139905i	−0.925752	−	0.378132i	$-0.876566\pi$
$277$	58050.8	−	178662.i	0.0454579	−	0.139905i	0.971209	+	0.238228i	$0.0765664\pi$
$278$	128054.	+	93036.4i	0.0993757	+	0.0722006i
$279$	193781.	+	140790.i	0.149039	+	0.108283i
$280$	−71374.3	+	118083.i	−0.0544060	+	0.0900106i
$281$	−1.93470e6	+	1.40564e6i	−1.46166	+	1.06196i	−0.478739	+	0.877958i	$0.658906\pi$
$281$	−1.93470e6	+	1.40564e6i	−1.46166	+	1.06196i	−0.982926	+	0.184004i	$0.941094\pi$
$282$	−568746.			−0.425888
$283$	−1.13791e6	+	826743.i	−0.844585	+	0.613627i	−0.923648	−	0.383243i	$-0.874807\pi$
$283$	−1.13791e6	+	826743.i	−0.844585	+	0.613627i	0.0790626	+	0.996870i	$0.474807\pi$
$284$	−167963.	−	516938.i	−0.123572	−	0.380314i
$285$	339131.	−	142903.i	0.247318	−	0.104215i
$286$	−67959.9	+	209159.i	−0.0491289	+	0.151203i
$287$	−46094.3	−	141864.i	−0.0330326	−	0.101664i
$288$	−25631.1	−	78884.4i	−0.0182090	−	0.0560415i
$289$	−257085.	+	791226.i	−0.181064	+	0.557258i
$290$	−223084.	+	369076.i	−0.155767	+	0.257704i
$291$	−430727.	−	1.32564e6i	−0.298174	−	0.917684i
$292$	−1.03636e6	+	752963.i	−0.711304	+	0.516793i
$293$	−2.56378e6			−1.74466			−0.872331	−	0.488916i	$-0.837393\pi$
$293$	−2.56378e6			−1.74466			−0.872331	+	0.488916i	$0.837393\pi$
$294$	446179.	−	324168.i	0.301052	−	0.218727i
$295$	1.17536e6	+	1.35929e6i	0.786349	+	0.909403i
$296$	329604.	+	239471.i	0.218657	+	0.158863i
$297$	191388.	+	139052.i	0.125900	+	0.0914714i
$298$	60221.9	−	185344.i	0.0392838	−	0.120903i
$299$	543604.			0.351645
$300$	−403416.	−	199388.i	−0.258791	−	0.127908i
$301$	−505262.			−0.321440
$302$	−201577.	+	620391.i	−0.127182	+	0.391425i
$303$	−552665.	−	401535.i	−0.345824	−	0.251256i
$304$	151492.	+	110065.i	0.0940168	+	0.0683072i
$305$	100583.	+	1.18551e6i	0.0619118	+	0.729717i
$306$	−200983.	+	146023.i	−0.122703	+	0.0891490i
$307$	3.12092e6			1.88989			0.944946	−	0.327227i	$-0.106114\pi$
$307$	3.12092e6			1.88989			0.944946	+	0.327227i	$0.106114\pi$
$308$	161999.	−	117699.i	0.0973053	−	0.0706965i
$309$	−243702.	−	750037.i	−0.145199	−	0.446875i
$310$	432495.	+	500175.i	0.255609	+	0.295609i
$311$	5437.00	−	16733.4i	0.00318756	−	0.00981030i	−0.949450	−	0.313918i	$-0.898358\pi$
$311$	5437.00	−	16733.4i	0.00318756	−	0.00981030i	0.952638	+	0.304108i	$0.0983583\pi$
$312$	30156.8	+	92812.9i	0.0175387	+	0.0539787i
$313$	−491439.	−	1.51249e6i	−0.283536	−	0.872635i	−0.986834	−	0.161739i	$-0.948290\pi$
$313$	−491439.	−	1.51249e6i	−0.283536	−	0.872635i	0.703297	−	0.710896i	$-0.251710\pi$
$314$	99668.2	−	306747.i	0.0570469	−	0.175572i
$315$	−114220.	−	132094.i	−0.0648585	−	0.0750080i
$316$	−79407.9	−	244392.i	−0.0447349	−	0.137680i
$317$	−2.06872e6	+	1.50301e6i	−1.15625	+	0.840068i	−0.989300	−	0.145897i	$-0.953393\pi$
$317$	−2.06872e6	+	1.50301e6i	−1.15625	+	0.840068i	−0.166954	+	0.985965i	$0.553393\pi$
$318$	99036.6			0.0549197
$319$	506338.	−	367876.i	0.278589	−	0.202407i
$320$	−19357.4	−	228154.i	−0.0105675	−	0.124553i
$321$	−1.15330e6	−	837923.i	−0.624713	−	0.453881i
$322$	−400429.	−	290929.i	−0.215222	−	0.156368i
$323$	173313.	−	533402.i	0.0924324	−	0.284478i
$324$	104976.			0.0555556
$325$	474646.	+	234594.i	0.249265	+	0.123199i
$326$	674334.			0.351424
$327$	535693.	−	1.64869e6i	0.277042	−	0.852649i
$328$	200262.	+	145499.i	0.102781	+	0.0746748i
$329$	−492923.	−	358130.i	−0.251067	−	0.182411i
$330$	427155.	+	493999.i	0.215924	+	0.249713i
$331$	−427731.	+	310765.i	−0.214586	+	0.155906i	−0.689886	−	0.723918i	$-0.742339\pi$
$331$	−427731.	+	310765.i	−0.214586	+	0.155906i	0.475300	+	0.879824i	$0.342339\pi$
$332$	−130366.			−0.0649109
$333$	−417155.	+	303081.i	−0.206152	+	0.149778i
$334$	−444948.	−	1.36941e6i	−0.218245	−	0.671688i
$335$	661926.	−	1.09511e6i	0.322253	−	0.533144i
$336$	27458.1	−	84507.3i	0.0132685	−	0.0408363i
$337$	193376.	+	595149.i	0.0927527	+	0.285464i	0.986662	−	0.162785i	$-0.0520478\pi$
$337$	193376.	+	595149.i	0.0927527	+	0.285464i	−0.893909	+	0.448249i	$0.852048\pi$
$338$	423462.	+	1.30328e6i	0.201615	+	0.620507i
$339$	308046.	−	948068.i	0.145585	−	0.448064i
$340$	−631989.	+	266307.i	−0.296492	+	0.124936i
$341$	−296538.	−	912651.i	−0.138100	−	0.425029i
$342$	−191732.	+	139301.i	−0.0886399	+	0.0644007i
$343$	1.23900e6			0.568638
$344$	678343.	−	492845.i	0.309067	−	0.224550i
$345$	835030.	−	1.38149e6i	0.377706	−	0.624887i
$346$	57800.3	+	41994.4i	0.0259561	+	0.0188582i
$347$	−1.13554e6	−	825020.i	−0.506267	−	0.367825i	0.305139	−	0.952308i	$-0.401297\pi$
$347$	−1.13554e6	−	825020.i	−0.506267	−	0.367825i	−0.811406	+	0.584483i	$0.801297\pi$
$348$	85821.8	−	264132.i	0.0379883	−	0.116916i
$349$	−211885.			−0.0931189			−0.0465594	−	0.998916i	$-0.514826\pi$
$349$	−211885.			−0.0931189			−0.0465594	+	0.998916i	$0.514826\pi$
$350$	−224083.	−	426830.i	−0.0977773	−	0.186245i
$351$	−123511.			−0.0535106
$352$	−102686.	+	316036.i	−0.0441729	+	0.135950i
$353$	−1.96235e6	−	1.42573e6i	−0.838186	−	0.608978i	0.0836770	−	0.996493i	$-0.473334\pi$
$353$	−1.96235e6	−	1.42573e6i	−0.838186	−	0.608978i	−0.921863	+	0.387515i	$0.873334\pi$
$354$	−936220.	−	680204.i	−0.397072	−	0.288490i
$355$	1.84925e6	+	432051.i	0.778798	+	0.181955i
$356$	222124.	−	161383.i	0.0928905	−	0.0674889i
$357$	−266136.			−0.110518
$358$	−686036.	+	498434.i	−0.282904	+	0.205542i
$359$	1.09905e6	+	3.38254e6i	0.450073	+	1.38518i	0.876823	+	0.480813i	$0.159658\pi$
$359$	1.09905e6	+	3.38254e6i	0.450073	+	1.38518i	−0.426750	+	0.904370i	$0.640342\pi$
$360$	282195.	+	65930.7i	0.114761	+	0.0268121i
$361$	−599821.	+	1.84606e6i	−0.242244	+	0.745552i
$362$	−186804.	−	574924.i	−0.0749229	−	0.230589i
$363$	155030.	+	477134.i	0.0617518	+	0.190052i
$364$	−32306.3	+	99428.6i	−0.0127801	+	0.0393331i
$365$	−378374.	−	4.45967e6i	−0.148658	−	1.75215i
$366$	−236767.	−	728694.i	−0.0923887	−	0.284343i
$367$	3.35933e6	−	2.44069e6i	1.30193	−	0.945906i	0.301956	−	0.953322i	$-0.402361\pi$
$367$	3.35933e6	−	2.44069e6i	1.30193	−	0.945906i	0.999973	+	0.00741589i	$0.00236057\pi$
$368$	821378.			0.316172
$369$	−253456.	+	184147.i	−0.0969029	+	0.0704041i
$370$	−1.31174e6	+	552741.i	−0.498131	+	0.209902i
$371$	85833.4	+	62361.6i	0.0323759	+	0.0235225i
$372$	−344499.	−	250293.i	−0.129072	−	0.0937761i
$373$	174617.	−	537417.i	0.0649853	−	0.200004i	−0.913292	−	0.407306i	$-0.866468\pi$
$373$	174617.	−	537417.i	0.0649853	−	0.200004i	0.978277	+	0.207302i	$0.0664682\pi$
$374$	995284.			0.367932
$375$	1.32529e6	−	845888.i	0.486668	−	0.310624i
$376$	1.01110e6			0.368830
$377$	−100975.	+	310770.i	−0.0365899	+	0.112612i
$378$	90980.9	+	66101.5i	0.0327507	+	0.0237948i
$379$	−117987.	−	85722.5i	−0.0421926	−	0.0306547i	0.566489	−	0.824069i	$-0.308301\pi$
$379$	−117987.	−	85722.5i	−0.0421926	−	0.0306547i	−0.608682	+	0.793415i	$0.708301\pi$
$380$	−602900.	+	254050.i	−0.214184	+	0.0902526i
$381$	−784309.	+	569834.i	−0.276806	+	0.201111i
$382$	−2.08675e6			−0.731666
$383$	668313.	−	485558.i	0.232800	−	0.169139i	−0.465270	−	0.885169i	$-0.654043\pi$
$383$	668313.	−	485558.i	0.232800	−	0.169139i	0.698070	+	0.716030i	$0.254043\pi$
$384$	45566.4	+	140239.i	0.0157695	+	0.0485334i
$385$	59145.6	+	697113.i	0.0203362	+	0.239691i
$386$	558122.	−	1.71772e6i	0.190661	−	0.586793i
$387$	327928.	+	1.00926e6i	0.111302	+	0.342551i
$388$	765736.	+	2.35669e6i	0.258226	+	0.794738i
$389$	−1.02000e6	+	3.13923e6i	−0.341763	+	1.05184i	0.621531	+	0.783389i	$0.286511\pi$
$389$	−1.02000e6	+	3.13923e6i	−0.341763	+	1.05184i	−0.963294	+	0.268448i	$0.913489\pi$
$390$	−332022.	−	77572.0i	−0.110536	−	0.0258252i
$391$	−760225.	−	2.33973e6i	−0.251478	−	0.773970i
$392$	−793207.	+	576299.i	−0.260718	+	0.189423i
$393$	624873.			0.204085
$394$	306065.	−	222369.i	0.0993282	−	0.0721662i
$395$	874270.	+	204260.i	0.281938	+	0.0658706i
$396$	−340246.	−	247203.i	−0.109032	−	0.0792166i
$397$	3.76947e6	+	2.73868e6i	1.20034	+	0.872096i	0.994318	−	0.106451i	$-0.0339488\pi$
$397$	3.76947e6	+	2.73868e6i	1.20034	+	0.872096i	0.206020	+	0.978548i	$0.433949\pi$
$398$	−517034.	+	1.59127e6i	−0.163611	+	0.503541i
$399$	−253887.			−0.0798376
$400$	717184.	+	354468.i	0.224120	+	0.110771i
$401$	5.08432e6			1.57896			0.789481	−	0.613775i	$-0.210350\pi$
$401$	5.08432e6			1.57896			0.789481	+	0.613775i	$0.210350\pi$
$402$	−254647.	+	783722.i	−0.0785910	+	0.241878i
$403$	405327.	+	294487.i	0.124321	+	0.0903242i
$404$	982516.	+	713839.i	0.299493	+	0.217594i
$405$	−189726.	+	313887.i	−0.0574763	+	0.0950902i
$406$	240700.	−	174879.i	0.0724704	−	0.0526528i
$407$	2.06579e6			0.618158
$408$	357303.	−	259596.i	0.106264	−	0.0772053i
$409$	814949.	+	2.50815e6i	0.240892	+	0.741389i	0.996285	+	0.0861170i	$0.0274459\pi$
$409$	814949.	+	2.50815e6i	0.240892	+	0.741389i	−0.755393	+	0.655272i	$0.772554\pi$
$410$	−796991.	+	335836.i	−0.234150	+	0.0986659i
$411$	−745230.	+	2.29358e6i	−0.217613	+	0.669745i
$412$	433248.	+	1.33340e6i	0.125746	+	0.387005i
$413$	−383094.	−	1.17904e6i	−0.110517	−	0.340137i
$414$	−321241.	+	988677.i	−0.0921149	+	0.283500i
$415$	235613.	−	389804.i	0.0671551	−	0.111103i
$416$	−53612.0	−	165001.i	−0.0151890	−	0.0467469i
$417$	288121.	−	209332.i	0.0811399	−	0.0589516i
$418$	949472.			0.265792
$419$	2.70692e6	−	1.96669e6i	0.753252	−	0.547270i	−0.143581	−	0.989639i	$-0.545862\pi$
$419$	2.70692e6	−	1.96669e6i	0.753252	−	0.547270i	0.896833	+	0.442369i	$0.145862\pi$
$420$	203058.	+	234834.i	0.0561691	+	0.0649588i
$421$	1.19235e6	+	866294.i	0.327868	+	0.238210i	0.739525	−	0.673129i	$-0.235050\pi$
$421$	1.19235e6	+	866294.i	0.327868	+	0.238210i	−0.411657	+	0.911339i	$0.635050\pi$
$422$	−2.91973e6	−	2.12131e6i	−0.798107	−	0.579859i
$423$	−395443.	+	1.21705e6i	−0.107456	+	0.330717i
$424$	−176065.			−0.0475619
$425$	345929.	−	2.37101e6i	0.0928998	−	0.636737i
$426$	−1.22297e6			−0.326505
$427$	253644.	−	780635.i	0.0673216	−	0.207195i
$428$	2.05032e6	+	1.48964e6i	0.541017	+	0.393072i
$429$	400323.	+	290852.i	0.105019	+	0.0763006i
$430$	247661.	+	2.91903e6i	0.0645932	+	0.761321i
$431$	926248.	−	672958.i	0.240178	−	0.174500i	−0.461184	−	0.887304i	$-0.652575\pi$
$431$	926248.	−	672958.i	0.240178	−	0.174500i	0.701363	+	0.712805i	$0.252575\pi$
$432$	−186624.			−0.0481125
$433$	−2.91441e6	+	2.11744e6i	−0.747018	+	0.542741i	−0.894901	−	0.446264i	$-0.852754\pi$
$433$	−2.91441e6	+	2.11744e6i	−0.747018	+	0.542741i	0.147883	+	0.989005i	$0.452754\pi$
$434$	−140966.	−	433850.i	−0.0359246	−	0.110564i
$435$	634670.	+	733987.i	0.160814	+	0.185980i
$436$	−952342.	+	2.93101e6i	−0.239926	+	0.738416i
$437$	−725233.	−	2.23204e6i	−0.181666	−	0.559111i
$438$	890676.	+	2.74122e6i	0.221837	+	0.682745i
$439$	−1.33711e6	+	4.11519e6i	−0.331135	+	1.01913i	0.637460	+	0.770483i	$0.279985\pi$
$439$	−1.33711e6	+	4.11519e6i	−0.331135	+	1.01913i	−0.968595	+	0.248644i	$0.920015\pi$
$440$	−759387.	−	878221.i	−0.186996	−	0.216258i
$441$	−383457.	−	1.18016e6i	−0.0938901	−	0.288964i
$442$	−420391.	+	305432.i	−0.102352	+	0.0743634i
$443$	5.36861e6			1.29973			0.649865	−	0.760050i	$-0.274826\pi$
$443$	5.36861e6			1.29973			0.649865	+	0.760050i	$0.274826\pi$
$444$	741609.	−	538810.i	0.178533	−	0.129712i
$445$	81097.1	+	955842.i	0.0194136	+	0.228816i
$446$	1.88720e6	+	1.37113e6i	0.449241	+	0.326393i
$447$	−354742.	−	257735.i	−0.0839738	−	0.0610105i
$448$	−48814.4	+	150235.i	−0.0114909	+	0.0353652i
$449$	−1.62171e6			−0.379628			−0.189814	−	0.981820i	$-0.560788\pi$
$449$	−1.62171e6			−0.379628			−0.189814	+	0.981820i	$0.560788\pi$
$450$	−707156.	+	724628.i	−0.164621	+	0.168688i
$451$	1.25513e6			0.290569
$452$	−547637.	+	1.68545e6i	−0.126080	+	0.388035i
$453$	1.18741e6	+	862701.i	0.271865	+	0.197522i
$454$	−4.09967e6	−	2.97858e6i	−0.933489	−	0.678219i
$455$	−238912.	−	276298.i	−0.0541015	−	0.0625677i
$456$	340857.	−	247647.i	0.0767644	−	0.0557726i
$457$	1.61866e6			0.362548			0.181274	−	0.983433i	$-0.441978\pi$
$457$	1.61866e6			0.362548			0.181274	+	0.983433i	$0.441978\pi$
$458$	3.85083e6	−	2.79779e6i	0.857809	−	0.623235i
$459$	172729.	+	531606.i	0.0382679	+	0.117776i
$460$	−1.48450e6	+	2.45599e6i	−0.327103	+	0.541168i
$461$	298352.	−	918232.i	0.0653847	−	0.201233i	−0.913027	−	0.407899i	$-0.866261\pi$
$461$	298352.	−	918232.i	0.0653847	−	0.201233i	0.978412	+	0.206666i	$0.0662614\pi$
$462$	−139226.	−	428494.i	−0.0303470	−	0.0933984i
$463$	−642603.	−	1.97773e6i	−0.139312	−	0.428760i	0.856923	−	0.515444i	$-0.172373\pi$
$463$	−642603.	−	1.97773e6i	−0.139312	−	0.428760i	−0.996236	+	0.0866841i	$0.972373\pi$
$464$	−152572.	+	469568.i	−0.0328988	+	0.101252i
$465$	1.37102e6	−	577720.i	0.294044	−	0.123904i
$466$	−988997.	−	3.04382e6i	−0.210975	−	0.649313i
$467$	−1.85893e6	+	1.35059e6i	−0.394430	+	0.286570i	−0.767269	−	0.641326i	$-0.778385\pi$
$467$	−1.85893e6	+	1.35059e6i	−0.394430	+	0.286570i	0.372838	+	0.927896i	$0.378385\pi$
$468$	219576.			0.0463415
$469$	−714194.	+	518892.i	−0.149928	+	0.108929i
$470$	−1.82740e6	+	3.02329e6i	−0.381582	+	0.631299i
$471$	−587103.	−	426555.i	−0.121944	−	0.0885978i
$472$	1.66439e6	+	1.20925e6i	0.343875	+	0.249840i
$473$	1.31378e6	−	4.04341e6i	0.270005	−	0.830989i
$474$	−578181.			−0.118200
$475$	330007.	−	2.26187e6i	0.0671102	−	0.459975i
$476$	473131.			0.0957115
$477$	68859.0	−	211926.i	0.0138569	−	0.0426470i
$478$	1.74926e6	+	1.27091e6i	0.350174	+	0.254416i
$479$	4.35473e6	+	3.16390e6i	0.867206	+	0.630062i	0.929836	−	0.367975i	$-0.119949\pi$
$479$	4.35473e6	+	3.16390e6i	0.867206	+	0.630062i	−0.0626297	+	0.998037i	$0.519949\pi$
$480$	−501680.	−	117210.i	−0.0993856	−	0.0232200i
$481$	−872554.	+	633947.i	−0.171961	+	0.124937i
$482$	−2.75370e6			−0.539883
$483$	−900966.	+	654590.i	−0.175728	+	0.127674i
$484$	−275609.	−	848238.i	−0.0534786	−	0.164590i
$485$	−8.43065e6	−	1.96970e6i	−1.62745	−	0.380229i
$486$	72988.6	−	224636.i	0.0140173	−	0.0431408i
$487$	−1.53692e6	−	4.73015e6i	−0.293649	−	0.903758i	−0.983672	−	0.179971i	$-0.942400\pi$
$487$	−1.53692e6	−	4.73015e6i	−0.293649	−	0.903758i	0.690023	−	0.723787i	$-0.257600\pi$
$488$	420919.	+	1.29546e6i	0.0800109	+	0.246248i
$489$	468856.	−	1.44299e6i	0.0886682	−	0.272893i
$490$	−289598.	−	3.41332e6i	−0.0544886	−	0.642224i
$491$	34162.8	+	105142.i	0.00639514	+	0.0196822i	0.954203	−	0.299159i	$-0.0967062\pi$
$491$	34162.8	+	105142.i	0.00639514	+	0.0196822i	−0.947808	+	0.318842i	$0.896706\pi$
$492$	450588.	−	327372.i	0.0839204	−	0.0609717i
$493$	1.47880e6			0.274026
$494$	−401041.	+	291374.i	−0.0739387	+	0.0537196i
$495$	1.35409e6	−	570588.i	0.248391	−	0.104667i
$496$	612443.	+	444966.i	0.111779	+	0.0812125i
$497$	−1.05992e6	−	770080.i	−0.192479	−	0.139844i
$498$	−90641.6	+	278966.i	−0.0163778	+	0.0504056i
$499$	−3.83387e6			−0.689265			−0.344632	−	0.938738i	$-0.611996\pi$
$499$	−3.83387e6			−0.689265			−0.344632	+	0.938738i	$0.611996\pi$
$500$	−2.35607e6	+	1.50380e6i	−0.421467	+	0.269008i
$501$	−3.23974e6			−0.576654
$502$	989768.	−	3.04619e6i	0.175297	−	0.539508i
$503$	1.54462e6	+	1.12223e6i	0.272208	+	0.197771i	0.715512	−	0.698601i	$-0.246194\pi$
$503$	1.54462e6	+	1.12223e6i	0.272208	+	0.197771i	−0.443303	+	0.896372i	$0.646194\pi$
$504$	−161744.	−	117514.i	−0.0283630	−	0.0206069i
$505$	−3.91017e6	+	1.64766e6i	−0.682286	+	0.287502i
$506$	3.36939e6	−	2.44800e6i	0.585026	−	0.425046i
$507$	3.08329e6			0.532715
$508$	1.39433e6	−	1.01304e6i	0.239721	−	0.174167i
$509$	3.29847e6	+	1.01516e7i	0.564310	+	1.73677i	0.669993	+	0.742367i	$0.266297\pi$
$509$	3.29847e6	+	1.01516e7i	0.564310	+	1.73677i	−0.105683	+	0.994400i	$0.533703\pi$
$510$	130450.	+	1.53754e6i	0.0222085	+	0.261759i
$511$	−954163.	+	2.93661e6i	−0.161648	+	0.497501i
$512$	−81007.0	−	249314.i	−0.0136568	−	0.0420312i
$513$	164779.	+	507137.i	0.0276445	+	0.0850809i
$514$	338726.	−	1.04249e6i	0.0565511	−	0.174046i
$515$	−4.77000e6	−	1.11444e6i	−0.792501	−	0.185156i
$516$	−582984.	−	1.79424e6i	−0.0963900	−	0.296658i
$517$	4.14767e6	−	3.01346e6i	0.682461	−	0.495837i
$518$	982019.			0.160804
$519$	130051.	−	94487.3i	0.0211931	−	0.0153977i
$520$	590261.	+	137906.i	0.0957272	+	0.0223653i
$521$	6.36720e6	+	4.62604e6i	1.02767	+	0.746646i	0.967841	−	0.251562i	$-0.0809443\pi$
$521$	6.36720e6	+	4.62604e6i	1.02767	+	0.746646i	0.0598295	+	0.998209i	$0.480944\pi$
$522$	−505540.	−	367296.i	−0.0812043	−	0.0589984i
$523$	2.24131e6	−	6.89803e6i	0.358300	−	1.10273i	−0.595771	−	0.803154i	$-0.703153\pi$
$523$	2.24131e6	−	6.89803e6i	0.358300	−	1.10273i	0.954071	−	0.299580i	$-0.0968465\pi$
$524$	−1.11088e6			−0.176742
$525$	−1.06917e6	+	182739.i	−0.169296	+	0.0289357i
$526$	7.08969e6			1.11728
$527$	700659.	−	2.15641e6i	0.109896	−	0.338224i
$528$	604882.	+	439472.i	0.0944247	+	0.0686036i
$529$	−3.12133e6	−	2.26778e6i	−0.484955	−	0.352340i
$530$	318207.	−	526450.i	0.0492062	−	0.0814080i
$531$	−2.10649e6	+	1.53046e6i	−0.324208	+	0.235551i
$532$	451354.			0.0691414
$533$	−530148.	+	385175.i	−0.0808312	+	0.0587273i
$534$	−190899.	−	587527.i	−0.0289701	−	0.0891609i
$535$	−8.15974e6	+	3.43835e6i	−1.23251	+	0.519356i
$536$	452705.	−	1.39328e6i	0.0680618	−	0.209473i
$537$	589595.	+	1.81459e6i	0.0882304	+	0.271545i
$538$	567193.	+	1.74564e6i	0.0844841	+	0.260015i
$539$	−1.53625e6	+	4.72809e6i	−0.227767	+	0.700993i
$540$	337290.	−	558021.i	0.0497760	−	0.0823506i
$541$	−2.22108e6	−	6.83577e6i	−0.326265	−	1.00414i	−0.970866	−	0.239621i	$-0.922977\pi$
$541$	−2.22108e6	−	6.83577e6i	−0.326265	−	1.00414i	0.644602	−	0.764519i	$-0.277023\pi$
$542$	−4.73891e6	+	3.44302e6i	−0.692915	+	0.503432i
$543$	−1.36015e6			−0.197964
$544$	−635205.	+	461504.i	−0.0920273	+	0.0668618i
$545$	−7.04277e6	−	8.14487e6i	−1.01567	−	1.17461i
$546$	190303.	+	138263.i	0.0273189	+	0.0198484i
$547$	−8.33552e6	−	6.05611e6i	−1.19114	−	0.865417i	−0.197760	−	0.980251i	$-0.563367\pi$
$547$	−8.33552e6	−	6.05611e6i	−1.19114	−	0.865417i	−0.993385	+	0.114834i	$0.963367\pi$
$548$	1.32485e6	−	4.07748e6i	0.188459	−	0.580016i
$549$	−1.72394e6			−0.244113
$550$	3.99842e6	−	683399.i	0.563613	−	0.0963313i
$551$	1.41073e6			0.197955
$552$	571095.	−	1.75765e6i	0.0797738	−	0.245519i
$553$	−501100.	−	364071.i	−0.0696806	−	0.0506259i
$554$	607916.	+	441677.i	0.0841530	+	0.0611407i
$555$	270759.	+	3.19128e6i	0.0373122	+	0.439777i
$556$	−512215.	+	372146.i	−0.0702692	+	0.0510536i
$557$	7.26105e6			0.991656			0.495828	−	0.868421i	$-0.334865\pi$
$557$	7.26105e6			0.991656			0.495828	+	0.868421i	$0.334865\pi$
$558$	−775123.	+	563160.i	−0.105387	+	0.0765678i
$559$	685920.	+	2.11104e6i	0.0928419	+	0.285738i
$560$	−360992.	−	417483.i	−0.0486438	−	0.0562560i
$561$	692009.	−	2.12978e6i	0.0928335	−	0.285712i
$562$	−2.95596e6	−	9.09750e6i	−0.394782	−	1.21501i
$563$	1.78482e6	+	5.49310e6i	0.237313	+	0.730376i	0.996806	+	0.0798598i	$0.0254473\pi$
$563$	1.78482e6	+	5.49310e6i	0.237313	+	0.730376i	−0.759493	+	0.650516i	$0.774553\pi$
$564$	703009.	−	2.16364e6i	0.0930600	−	0.286409i
$565$	−4.04989e6	−	4.68365e6i	−0.533731	−	0.617253i
$566$	−1.73858e6	−	5.35079e6i	−0.228115	−	0.702065i
$567$	204707.	−	148728.i	0.0267409	−	0.0194284i
$568$	2.17416e6			0.282762
$569$	−1.00949e7	+	7.33434e6i	−1.30713	+	0.949687i	−0.999998	−	0.00198000i	$-0.999370\pi$
$569$	−1.00949e7	+	7.33434e6i	−1.30713	+	0.949687i	−0.307133	+	0.951667i	$0.599370\pi$
$570$	124446.	+	1.46677e6i	0.0160433	+	0.189093i
$571$	−8.61935e6	−	6.26232e6i	−1.10633	−	0.803795i	−0.124247	−	0.992251i	$-0.539652\pi$
$571$	−8.61935e6	−	6.26232e6i	−1.10633	−	0.803795i	−0.982082	+	0.188456i	$0.939652\pi$
$572$	−711685.	−	517069.i	−0.0909490	−	0.0660783i
$573$	−1.45089e6	+	4.46539e6i	−0.184607	+	0.568163i
$574$	596658.			0.0755867
$575$	−4.66064e6	−	8.87755e6i	−0.587863	−	1.11976i
$576$	331776.			0.0416667
$577$	1.27931e6	−	3.93733e6i	0.159970	−	0.492336i	−0.838661	−	0.544654i	$-0.816661\pi$
$577$	1.27931e6	−	3.93733e6i	0.159970	−	0.492336i	0.998630	+	0.0523180i	$0.0166609\pi$
$578$	−2.69223e6	−	1.95602e6i	−0.335191	−	0.243530i
$579$	−3.28766e6	−	2.38862e6i	−0.407559	−	0.296109i
$580$	−1.12830e6	−	1.30487e6i	−0.139269	−	0.161063i
$581$	−254218.	+	184700.i	−0.0312439	+	0.0227000i
$582$	5.57544e6			0.682295
$583$	−722240.	+	524738.i	−0.0880056	+	0.0639398i
$584$	−1.58342e6	−	4.87328e6i	−0.192117	−	0.591274i
$585$	−396845.	+	656551.i	−0.0479437	+	0.0793192i
$586$	3.16900e6	−	9.75319e6i	0.381223	−	1.17328i
$587$	1.33469e6	+	4.10775e6i	0.159877	+	0.492050i	0.998622	−	0.0524738i	$-0.0167106\pi$
$587$	1.33469e6	+	4.10775e6i	0.159877	+	0.492050i	−0.838746	+	0.544523i	$0.816711\pi$
$588$	681701.	+	2.09806e6i	0.0813112	+	0.250250i
$589$	668409.	−	2.05715e6i	0.0793879	−	0.244331i
$590$	−6.62386e6	+	2.79116e6i	−0.783395	+	0.330107i
$591$	−263039.	−	809551.i	−0.0309779	−	0.0953401i
$592$	−1.31842e6	+	957885.i	−0.154614	+	0.112333i
$593$	5.02836e6			0.587204			0.293602	−	0.955928i	$-0.405146\pi$
$593$	5.02836e6			0.587204			0.293602	+	0.955928i	$0.405146\pi$
$594$	−765554.	+	556207.i	−0.0890245	+	0.0646801i
$595$	−855102.	+	1.41470e6i	−0.0990206	+	0.163822i
$596$	630652.	+	458196.i	0.0727234	+	0.0528367i
$597$	3.04563e6	+	2.21278e6i	0.349736	+	0.254098i
$598$	−671932.	+	2.06799e6i	−0.0768373	+	0.236481i
$599$	2.66581e6			0.303573			0.151786	−	0.988413i	$-0.451497\pi$
$599$	2.66581e6			0.303573			0.151786	+	0.988413i	$0.451497\pi$
$600$	1.25717e6	−	1.28823e6i	0.142566	−	0.146088i
$601$	−1.50698e7			−1.70185			−0.850924	−	0.525289i	$-0.823957\pi$
$601$	−1.50698e7			−1.70185			−0.850924	+	0.525289i	$0.823957\pi$
$602$	624538.	−	1.92213e6i	0.0702373	−	0.216168i
$603$	1.50002e6	+	1.08983e6i	0.167997	+	0.122057i
$604$	−2.11094e6	−	1.53369e6i	−0.235442	−	0.171059i
$605$	3.03442e6	+	708947.i	0.337044	+	0.0787455i
$606$	2.21066e6	−	1.60614e6i	0.244535	−	0.177665i
$607$	1.35007e7			1.48726			0.743629	−	0.668593i	$-0.233103\pi$
$607$	1.35007e7			1.48726			0.743629	+	0.668593i	$0.233103\pi$
$608$	−605968.	+	440261.i	−0.0664799	+	0.0483005i
$609$	−206863.	−	636659.i	−0.0226016	−	0.0695606i
$610$	−4.63426e6	−	1.08273e6i	−0.504262	−	0.117813i
$611$	−827139.	+	2.54567e6i	−0.0896345	+	0.275867i
$612$	−307075.	−	945078.i	−0.0331410	−	0.101997i
$613$	4.59560e6	+	1.41438e7i	0.493959	+	1.52025i	0.818573	+	0.574403i	$0.194766\pi$
$613$	4.59560e6	+	1.41438e7i	0.493959	+	1.52025i	−0.324614	+	0.945847i	$0.605234\pi$
$614$	−3.85767e6	+	1.18727e7i	−0.412956	+	1.27095i
$615$	164509.	+	1.93896e6i	0.0175388	+	0.206720i
$616$	247513.	+	761767.i	0.0262813	+	0.0808854i
$617$	−8.63189e6	+	6.27143e6i	−0.912836	+	0.663214i	−0.941731	−	0.336368i	$-0.890801\pi$
$617$	−8.63189e6	+	6.27143e6i	−0.912836	+	0.663214i	0.0288943	+	0.999582i	$0.490801\pi$
$618$	3.15454e6			0.332250
$619$	−1.07307e7	+	7.79630e6i	−1.12564	+	0.817827i	−0.985055	−	0.172241i	$-0.944899\pi$
$619$	−1.07307e7	+	7.79630e6i	−1.12564	+	0.817827i	−0.140588	+	0.990068i	$0.544899\pi$
$620$	−2.43737e6	+	1.02706e6i	−0.254649	+	0.107304i
$621$	1.89229e6	+	1.37483e6i	0.196906	+	0.143061i
$622$	56937.0	+	41367.2i	0.00590091	+	0.00428726i
$623$	204506.	−	629405.i	0.0211099	−	0.0649696i
$624$	−390357.			−0.0401329
$625$	−238298.	−	9.76272e6i	−0.0244018	−	0.999702i
$626$	6.36132e6			0.648801
$627$	660157.	−	2.03175e6i	0.0670623	−	0.206396i
$628$	1.04374e6	+	758321.i	0.105607	+	0.0767280i
$629$	3.94883e6	+	2.86900e6i	0.397963	+	0.289137i
$630$	643700.	−	271242.i	0.0646148	−	0.0272274i
$631$	−1.06892e7	+	7.76616e6i	−1.06874	+	0.776485i	−0.975685	−	0.219176i	$-0.929663\pi$
$631$	−1.06892e7	+	7.76616e6i	−1.06874	+	0.776485i	−0.0930545	+	0.995661i	$0.529663\pi$
$632$	1.02788e6			0.102364
$633$	−6.56939e6	+	4.77294e6i	−0.651652	+	0.473453i
$634$	−3.16072e6	−	9.72770e6i	−0.312293	−	0.961140i
$635$	509065.	+	6.00005e6i	0.0501002	+	0.590501i
$636$	−122416.	+	376758.i	−0.0120004	+	0.0369334i
$637$	−802068.	−	2.46851e6i	−0.0783182	−	0.241039i
$638$	773616.	+	2.38095e6i	0.0752443	+	0.231578i
$639$	−850314.	+	2.61700e6i	−0.0823810	+	0.253543i
$640$	891875.	+	208374.i	0.0860705	+	0.0201091i
$641$	−4.89356e6	−	1.50608e7i	−0.470414	−	1.44778i	−0.852044	−	0.523469i	$-0.824637\pi$
$641$	−4.89356e6	−	1.50608e7i	−0.470414	−	1.44778i	0.381631	−	0.924315i	$-0.375363\pi$
$642$	4.61321e6	−	3.35169e6i	0.441739	−	0.320942i
$643$	137424.			0.0131080			0.00655398	−	0.999979i	$-0.497914\pi$
$643$	137424.			0.0131080			0.00655398	+	0.999979i	$0.497914\pi$
$644$	1.60172e6	−	1.16372e6i	0.152185	−	0.110569i
$645$	6.41857e6	+	1.49960e6i	0.607490	+	0.141931i
$646$	1.81496e6	+	1.31864e6i	0.171114	+	0.124321i
$647$	1.07230e7	+	7.79072e6i	1.00706	+	0.731673i	0.963591	−	0.267382i	$-0.0861584\pi$
$647$	1.07230e7	+	7.79072e6i	1.00706	+	0.731673i	0.0434709	+	0.999055i	$0.486158\pi$
$648$	−129757.	+	399352.i	−0.0121393	+	0.0373610i
$649$	1.04315e7			0.972157
$650$	−1.47914e6	+	1.51569e6i	−0.137318	+	0.140710i
$651$	−1.02640e6			−0.0949213
$652$	−833522.	+	2.56532e6i	−0.0767889	+	0.236332i
$653$	−1.07331e7	−	7.79808e6i	−0.985017	−	0.715657i	−0.0261927	−	0.999657i	$-0.508338\pi$
$653$	−1.07331e7	−	7.79808e6i	−0.985017	−	0.715657i	−0.958824	+	0.284000i	$0.908338\pi$
$654$	5.60985e6	+	4.07579e6i	0.512869	+	0.372621i
$655$	2.00773e6	−	3.32164e6i	0.182853	−	0.302517i
$656$	−801046.	+	581994.i	−0.0726772	+	0.0528030i
$657$	6.48515e6			0.586147
$658$	1.97169e6	−	1.43252e6i	0.177531	−	0.128984i
$659$	5.95170e6	+	1.83174e7i	0.533860	+	1.64305i	0.746100	+	0.665834i	$0.231924\pi$
$659$	5.95170e6	+	1.83174e7i	0.533860	+	1.64305i	−0.212240	+	0.977218i	$0.568076\pi$
$660$	−2.40728e6	+	1.01438e6i	−0.215113	+	0.0906442i
$661$	1.86034e6	−	5.72553e6i	0.165611	−	0.509697i	−0.833470	−	0.552564i	$-0.813649\pi$
$661$	1.86034e6	−	5.72553e6i	0.165611	−	0.509697i	0.999081	+	0.0428676i	$0.0136494\pi$
$662$	−653515.	−	2.01131e6i	−0.0579576	−	0.178375i
$663$	361294.	+	1.11195e6i	0.0319210	+	0.0982429i
$664$	161141.	−	495940.i	0.0141836	−	0.0436525i
$665$	−815743.	+	1.34959e6i	−0.0715319	+	0.118344i
$666$	−637356.	−	1.96158e6i	−0.0556797	−	0.171364i
$667$	5.00626e6	−	3.63726e6i	0.435711	−	0.316563i
$668$	5.75953e6			0.499397
$669$	4.24619e6	−	3.08504e6i	0.366804	−	0.266499i
$670$	3.34785e6	+	3.87174e6i	0.288124	+	0.333211i
$671$	5.58759e6	+	4.05962e6i	0.479091	+	0.348080i
$672$	287545.	+	208913.i	0.0245630	+	0.0178461i
$673$	−1.64736e6	+	5.07005e6i	−0.140201	+	0.431494i	−0.996363	−	0.0852140i	$-0.972843\pi$
$673$	−1.64736e6	+	5.07005e6i	−0.140201	+	0.431494i	0.856162	+	0.516708i	$0.172843\pi$
$674$	−2.50311e6			−0.212241
$675$	1.05894e6	+	2.01705e6i	0.0894563	+	0.170395i
$676$	−5.48141e6			−0.461344
$677$	−5.09121e6	+	1.56691e7i	−0.426923	+	1.31393i	0.474218	+	0.880407i	$0.342731\pi$
$677$	−5.09121e6	+	1.56691e7i	−0.426923	+	1.31393i	−0.901141	+	0.433526i	$0.857269\pi$
$678$	3.22590e6	+	2.34375e6i	0.269511	+	0.195811i
$679$	4.83214e6	+	3.51076e6i	0.402222	+	0.292231i
$680$	−231912.	−	2.73340e6i	−0.0192332	−	0.226690i
$681$	−9.22425e6	+	6.70181e6i	−0.762190	+	0.553764i
$682$	3.83847e6			0.316008
$683$	1.25551e7	−	9.12179e6i	1.02983	−	0.748219i	0.0615589	−	0.998103i	$-0.480393\pi$
$683$	1.25551e7	−	9.12179e6i	1.02983	−	0.748219i	0.968276	+	0.249885i	$0.0803928\pi$
$684$	−292940.	−	901578.i	−0.0239408	−	0.0736823i
$685$	9.79756e6	+	1.13308e7i	0.797796	+	0.922640i
$686$	−1.53149e6	+	4.71343e6i	−0.124252	+	0.382408i
$687$	−3.30949e6	−	1.01856e7i	−0.267528	−	0.823367i
$688$	1.03642e6	+	3.18976e6i	0.0834762	+	0.256913i
$689$	144031.	−	443281.i	0.0115587	−	0.0355739i
$690$	4.22336e6	+	4.88426e6i	0.337704	+	0.390550i
$691$	−6.22860e6	−	1.91697e7i	−0.496244	−	1.52728i	−0.815009	−	0.579448i	$-0.803268\pi$
$691$	−6.22860e6	−	1.91697e7i	−0.496244	−	1.52728i	0.318765	−	0.947834i	$-0.396732\pi$
$692$	−231201.	+	167977.i	−0.0183538	+	0.0133348i
$693$	−1.01373e6			−0.0801840
$694$	4.54217e6	−	3.30008e6i	0.357985	−	0.260091i
$695$	−187008.	−	2.20415e6i	−0.0146858	−	0.173093i
$696$	898737.	+	652971.i	0.0703250	+	0.0510941i
$697$	2.39924e6	+	1.74315e6i	0.187065	+	0.135911i
$698$	261905.	−	806060.i	0.0203472	−	0.0626223i
$699$	−7.20104e6			−0.557445
$700$	1.90074e6	−	324870.i	0.146615	−	0.0250590i
$701$	7.70849e6			0.592481			0.296240	−	0.955113i	$-0.404267\pi$
$701$	7.70849e6			0.592481			0.296240	+	0.955113i	$0.404267\pi$
$702$	152669.	−	469865.i	0.0116925	−	0.0359858i
$703$	3.76707e6	+	2.73694e6i	0.287485	+	0.208870i
$704$	−1.07535e6	−	781284.i	−0.0817742	−	0.0594124i
$705$	5.19890e6	+	6.01246e6i	0.393948	+	0.455595i
$706$	7.84942e6	−	5.70294e6i	0.592687	−	0.430613i
$707$	2.92730e6			0.220251
$708$	3.74488e6	−	2.72081e6i	0.280773	−	0.203993i
$709$	256284.	+	788761.i	0.0191472	+	0.0589291i	0.960174	−	0.279404i	$-0.0901369\pi$
$709$	256284.	+	788761.i	0.0191472	+	0.0589291i	−0.941026	+	0.338333i	$0.890137\pi$
$710$	−3.92942e6	+	6.50093e6i	−0.292538	+	0.483982i
$711$	−402003.	+	1.23724e6i	−0.0298232	+	0.0917865i
$712$	339376.	+	1.04449e6i	0.0250889	+	0.0772156i
$713$	−2.93193e6	−	9.02355e6i	−0.215988	−	0.664743i
$714$	328963.	−	1.01244e6i	0.0241491	−	0.0743233i
$715$	2.83233e6	−	1.19349e6i	0.207195	−	0.0873076i
$716$	−1.04817e6	−	3.22593e6i	−0.0764098	−	0.235165i
$717$	3.93583e6	−	2.85955e6i	0.285916	−	0.207730i
$718$	−1.42265e7			−1.02988
$719$	−584749.	+	424845.i	−0.0421839	+	0.0306484i	−0.608677	−	0.793418i	$-0.708300\pi$
$719$	−584749.	+	424845.i	−0.0421839	+	0.0306484i	0.566493	+	0.824066i	$0.308300\pi$
$720$	−599627.	+	992038.i	−0.0431072	+	0.0713177i
$721$	2.73399e6	+	1.98636e6i	0.195866	+	0.142305i
$722$	−6.28141e6	−	4.56371e6i	−0.448450	−	0.325818i
$723$	−1.91462e6	+	5.89258e6i	−0.136218	+	0.419237i
$724$	2.41804e6			0.171442
$725$	5.94087e6	−	1.01540e6i	0.419764	−	0.0717450i
$726$	−2.00675e6			−0.141303
$727$	−2.93651e6	+	9.03765e6i	−0.206061	+	0.634190i	0.793607	+	0.608430i	$0.208201\pi$
$727$	−2.93651e6	+	9.03765e6i	−0.206061	+	0.634190i	−0.999668	+	0.0257599i	$0.991799\pi$
$728$	−338316.	−	245801.i	−0.0236589	−	0.0171892i
$729$	−429945.	−	312373.i	−0.0299636	−	0.0217698i
$730$	1.74333e7	+	4.07303e6i	1.21080	+	0.282885i
$731$	8.12691e6	−	5.90455e6i	0.562512	−	0.408689i
$732$	3.06478e6			0.211408
$733$	−1.08864e7	+	7.90946e6i	−0.748386	+	0.543735i	−0.895326	−	0.445411i	$-0.853058\pi$
$733$	−1.08864e7	+	7.90946e6i	−0.748386	+	0.543735i	0.146940	+	0.989145i	$0.453058\pi$
$734$	5.13259e6	+	1.57965e7i	0.351639	+	1.08223i
$735$	−7.50543e6	−	1.75353e6i	−0.512457	−	0.119728i
$736$	−1.01528e6	+	3.12471e6i	−0.0690861	+	0.212625i
$737$	−2.29544e6	−	7.06464e6i	−0.155667	−	0.479095i
$738$	−387246.	−	1.19182e6i	−0.0261726	−	0.0805509i
$739$	3.78668e6	−	1.16542e7i	0.255063	−	0.785003i	−0.738754	−	0.673975i	$-0.764586\pi$
$739$	3.78668e6	−	1.16542e7i	0.255063	−	0.785003i	0.993817	−	0.111028i	$-0.0354144\pi$
$740$	−481350.	−	5.67338e6i	−0.0323133	−	0.380858i
$741$	344664.	+	1.06077e6i	0.0230596	+	0.0709700i
$742$	−343334.	+	249446.i	−0.0228932	+	0.0166329i
$743$	2.25508e7			1.49861			0.749307	−	0.662223i	$-0.230387\pi$
$743$	2.25508e7			1.49861			0.749307	+	0.662223i	$0.230387\pi$
$744$	1.37800e6	−	1.00117e6i	0.0912675	−	0.0663097i
$745$	−2.50984e6	+	1.05759e6i	−0.165674	+	0.0698117i
$746$	1.82862e6	+	1.32857e6i	0.120303	+	0.0874050i
$747$	533932.	+	387924.i	0.0350094	+	0.0254358i
$748$	−1.23024e6	+	3.78628e6i	−0.0803961	+	0.247434i
$749$	6.10869e6			0.397872
$750$	1.57980e6	+	6.08728e6i	0.102553	+	0.395158i
$751$	−1.87251e7			−1.21150			−0.605751	−	0.795654i	$-0.707127\pi$
$751$	−1.87251e7			−1.21150			−0.605751	+	0.795654i	$0.707127\pi$
$752$	−1.24979e6	+	3.84647e6i	−0.0805924	+	0.248038i
$753$	−5.83030e6	−	4.23596e6i	−0.374717	−	0.272248i
$754$	−1.05743e6	−	768265.i	−0.0677363	−	0.0492133i
$755$	8.40103e6	−	3.54002e6i	0.536371	−	0.226016i
$756$	−363924.	+	264406.i	−0.0231583	+	0.0168255i
$757$	2.05326e7			1.30228			0.651140	−	0.758958i	$-0.274291\pi$
$757$	2.05326e7			1.30228			0.651140	+	0.758958i	$0.274291\pi$
$758$	471948.	−	342890.i	0.0298346	−	0.0216761i
$759$	−2.89573e6	−	8.91215e6i	−0.182454	−	0.561536i
$760$	−221237.	−	2.60759e6i	−0.0138939	−	0.163759i
$761$	−1.04534e6	+	3.21724e6i	−0.0654331	+	0.201382i	−0.978428	−	0.206589i	$-0.933764\pi$
$761$	−1.04534e6	+	3.21724e6i	−0.0654331	+	0.201382i	0.912995	+	0.407971i	$0.133764\pi$
$762$	−1.19832e6	−	3.68804e6i	−0.0747626	−	0.230096i
$763$	2.29551e6	+	7.06484e6i	0.142747	+	0.439330i
$764$	2.57937e6	−	7.93848e6i	0.159875	−	0.492044i
$765$	3.38085e6	+	789886.i	0.208868	+	0.0487990i
$766$	1.02109e6	+	3.14260e6i	0.0628772	+	0.193516i
$767$	−4.40611e6	+	3.20122e6i	−0.270437	+	0.196484i
$768$	−589824.			−0.0360844
$769$	5.83769e6	−	4.24133e6i	0.355979	−	0.258634i	−0.395394	−	0.918512i	$-0.629392\pi$
$769$	5.83769e6	−	4.24133e6i	0.355979	−	0.258634i	0.751373	+	0.659878i	$0.229392\pi$
$770$	−2.72508e6	−	636676.i	−0.165635	−	0.0386983i
$771$	−1.99529e6	−	1.44966e6i	−0.120884	−	0.0878277i
$772$	5.84473e6	+	4.24644e6i	0.352956	+	0.256438i
$773$	7.26727e6	−	2.23663e7i	0.437444	−	1.34631i	−0.453118	−	0.891451i	$-0.649688\pi$
$773$	7.26727e6	−	2.23663e7i	0.437444	−	1.34631i	0.890561	−	0.454863i	$-0.150312\pi$
$774$	−4.24479e6			−0.254685
$775$	1.33413e6	−	9.14417e6i	0.0797893	−	0.546878i
$776$	−9.91190e6			−0.590884
$777$	682786.	−	2.10140e6i	0.0405726	−	0.124869i
$778$	−1.06815e7	−	7.76060e6i	−0.632681	−	0.459670i
$779$	2.28881e6	+	1.66292e6i	0.135134	+	0.0981809i
$780$	705503.	−	1.16720e6i	0.0415205	−	0.0686925i
$781$	8.91867e6	−	6.47979e6i	0.523206	−	0.380131i
$782$	9.84055e6			0.575443
$783$	−1.13746e6	+	826416.i	−0.0663030	+	0.0481720i
$784$	−1.21191e6	−	3.72988e6i	−0.0704176	−	0.216723i
$785$	−4.15382e6	+	1.75033e6i	−0.240588	+	0.101379i
$786$	−772385.	+	2.37716e6i	−0.0445941	+	0.137247i
$787$	−6.54125e6	−	2.01319e7i	−0.376465	−	1.15864i	−0.942485	−	0.334248i	$-0.891518\pi$
$787$	−6.54125e6	−	2.01319e7i	−0.376465	−	1.15864i	0.566021	−	0.824391i	$-0.308482\pi$
$788$	467625.	+	1.43920e6i	0.0268276	+	0.0825669i
$789$	4.92938e6	−	1.51711e7i	0.281903	−	0.867608i
$790$	−1.85771e6	+	3.07344e6i	−0.105903	+	0.175209i
$791$	1.32001e6	+	4.06258e6i	0.0750131	+	0.230867i
$792$	1.36098e6	−	988813.i	0.0770975	−	0.0560146i
$793$	−3.60592e6			−0.203626
$794$	−1.50779e7	+	1.09547e7i	−0.848767	+	0.616665i
$795$	−905292.	−	1.04696e6i	−0.0508008	−	0.0587505i
$796$	−5.41445e6	−	3.93383e6i	−0.302881	−	0.220056i
$797$	5.45172e6	+	3.96090e6i	0.304010	+	0.220876i	0.729322	−	0.684171i	$-0.239836\pi$
$797$	5.45172e6	+	3.96090e6i	0.304010	+	0.220876i	−0.425312	+	0.905047i	$0.639836\pi$
$798$	313821.	−	965842.i	0.0174452	−	0.0536907i
$799$	1.21136e7			0.671283
$800$	−2.23496e6	+	2.29018e6i	−0.123465	+	0.126516i
$801$	−1.38996e6			−0.0765460
$802$	−6.28456e6	+	1.93419e7i	−0.345016	+	1.06185i
$803$	−2.10195e7	−	1.52716e7i	−1.15036	−	0.835786i
$804$	−2.66669e6	−	1.93747e6i	−0.145490	−	0.105705i
$805$	584783.	+	6.89249e6i	0.0318057	+	0.374875i
$806$	−1.62131e6	+	1.17795e6i	−0.0879079	+	0.0638688i
$807$	4.12982e6			0.223227
$808$	−3.93006e6	+	2.85536e6i	−0.211773	+	0.153862i
$809$	−2.86716e6	−	8.82422e6i	−0.154021	−	0.474029i	0.844039	−	0.536282i	$-0.180172\pi$
$809$	−2.86716e6	−	8.82422e6i	−0.154021	−	0.474029i	−0.998060	+	0.0622526i	$0.980172\pi$
$810$	−959583.	−	1.10975e6i	−0.0513890	−	0.0594307i
$811$	−6.92725e6	+	2.13199e7i	−0.369835	+	1.13824i	0.577062	+	0.816700i	$0.304199\pi$
$811$	−6.92725e6	+	2.13199e7i	−0.369835	+	1.13824i	−0.946897	+	0.321536i	$0.895801\pi$
$812$	367756.	+	1.13184e6i	0.0195736	+	0.0602413i
$813$	4.07273e6	+	1.25346e7i	0.216102	+	0.665094i
$814$	−2.55345e6	+	7.85871e6i	−0.135072	+	0.415710i
$815$	−6.16407e6	−	7.12867e6i	−0.325068	−	0.375936i
$816$	545910.	+	1.68014e6i	0.0287009	+	0.0883324i
$817$	7.75284e6	−	5.63277e6i	0.406355	−	0.295234i
$818$	−1.05489e7			−0.551220
$819$	428181.	−	311092.i	0.0223058	−	0.0162061i
$820$	−292460.	−	3.44705e6i	−0.0151891	−	0.179025i
$821$	1.17564e7	+	8.54154e6i	0.608720	+	0.442261i	0.848963	−	0.528452i	$-0.177227\pi$
$821$	1.17564e7	+	8.54154e6i	0.608720	+	0.442261i	−0.240243	+	0.970713i	$0.577227\pi$
$822$	−7.80415e6	−	5.67005e6i	−0.402852	−	0.292689i
$823$	−8.13025e6	+	2.50223e7i	−0.418412	+	1.28774i	0.490751	+	0.871300i	$0.336722\pi$
$823$	−8.13025e6	+	2.50223e7i	−0.418412	+	1.28774i	−0.909163	+	0.416440i	$0.863278\pi$
$824$	−5.60807e6			−0.287737
$825$	1.31766e6	−	9.03128e6i	0.0674014	−	0.461971i
$826$	4.95887e6			0.252891
$827$	−6.23190e6	+	1.91798e7i	−0.316852	+	0.975170i	0.658133	+	0.752901i	$0.271346\pi$
$827$	−6.23190e6	+	1.91798e7i	−0.316852	+	0.975170i	−0.974985	+	0.222269i	$0.928654\pi$
$828$	−3.36408e6	−	2.44414e6i	−0.170526	−	0.123894i
$829$	9.15794e6	+	6.65364e6i	0.462820	+	0.336258i	0.794636	−	0.607086i	$-0.207662\pi$
$829$	9.15794e6	+	6.65364e6i	0.462820	+	0.336258i	−0.331817	+	0.943344i	$0.607662\pi$
$830$	1.19167e6	+	1.37815e6i	0.0600427	+	0.0694386i
$831$	1.36781e6	−	993773.i	0.0687106	−	0.0499212i
$832$	693968.			0.0347561
$833$	−9.50305e6	+	6.90437e6i	−0.474516	+	0.344756i
$834$	440209.	+	1.35483e6i	0.0219151	+	0.0674478i
$835$	−1.04094e7	+	1.72215e7i	−0.516663	+	0.854780i
$836$	−1.17361e6	+	3.61201e6i	−0.0580776	+	0.178745i
$837$	666159.	+	2.05023e6i	0.0328673	+	0.101155i
$838$	4.13581e6	+	1.27287e7i	0.203446	+	0.626144i
$839$	3.47064e6	−	1.06815e7i	0.170218	−	0.523877i	−0.829165	−	0.559004i	$-0.811184\pi$
$839$	3.47064e6	−	1.06815e7i	0.170218	−	0.523877i	0.999383	+	0.0351272i	$0.0111837\pi$
$840$	−1.14436e6	+	482208.i	−0.0559581	+	0.0235796i
$841$	−5.18885e6	−	1.59696e7i	−0.252977	−	0.778583i
$842$	−4.76941e6	+	3.46518e6i	−0.231838	+	0.168440i
$843$	−2.15228e7			−1.04311
$844$	1.16789e7	−	8.48523e6i	0.564347	−	0.410022i
$845$	9.90669e6	−	1.63899e7i	0.477295	−	0.789648i
$846$	−4.14113e6	−	3.00871e6i	−0.198927	−	0.144529i
$847$	−1.73922e6	−	1.26362e6i	−0.0833001	−	0.0605211i
$848$	217628.	−	669792.i	0.0103926	−	0.0319853i
$849$	−1.26589e7			−0.602733
$850$	8.59225e6	+	4.24672e6i	0.407905	+	0.201607i
$851$	2.04248e7			0.966794
$852$	1.51167e6	−	4.65244e6i	0.0713440	−	0.219574i
$853$	1.82589e7	+	1.32658e7i	0.859213	+	0.624255i	0.927671	−	0.373399i	$-0.121808\pi$
$853$	1.82589e7	+	1.32658e7i	0.859213	+	0.624255i	−0.0684576	+	0.997654i	$0.521808\pi$
$854$	2.65619e6	+	1.92984e6i	0.124628	+	0.0905474i
$855$	3.22523e6	+	753528.i	0.150885	+	0.0352521i
$856$	−8.20126e6	+	5.95856e6i	−0.382557	+	0.277944i
$857$	−1.45528e7			−0.676853			−0.338427	−	0.940993i	$-0.609895\pi$
$857$	−1.45528e7			−0.676853			−0.338427	+	0.940993i	$0.609895\pi$
$858$	−1.60129e6	+	1.16341e6i	−0.0742595	+	0.0539527i
$859$	−8.97277e6	−	2.76153e7i	−0.414900	−	1.27693i	−0.912340	−	0.409433i	$-0.865727\pi$
$859$	−8.97277e6	−	2.76153e7i	−0.414900	−	1.27693i	0.497440	−	0.867498i	$-0.334273\pi$
$860$	−1.14108e7	−	2.66596e6i	−0.526101	−	0.122916i
$861$	414849.	−	1.27677e6i	0.0190714	−	0.0586957i
$862$	1.41518e6	+	4.35548e6i	0.0648700	+	0.199649i
$863$	−1.02484e7	−	3.15412e7i	−0.468412	−	1.44162i	−0.854640	−	0.519220i	$-0.826222\pi$
$863$	−1.02484e7	−	3.15412e7i	−0.468412	−	1.44162i	0.386229	−	0.922403i	$-0.373778\pi$
$864$	230680.	−	709960.i	0.0105130	−	0.0323556i
$865$	−84411.0	−	994901.i	−0.00383582	−	0.0452105i
$866$	−4.45283e6	−	1.37044e7i	−0.201763	−	0.620962i
$867$	−6.05751e6	+	4.40104e6i	−0.273682	+	0.198842i
$868$	1.82471e6			0.0822042
$869$	4.21648e6	−	3.06345e6i	0.189409	−	0.137614i
$870$	−3.57675e6	+	1.50717e6i	−0.160210	+	0.0675093i
$871$	3.13755e6	+	2.27956e6i	0.140135	+	0.101814i
$872$	−9.97306e6	−	7.24585e6i	−0.444158	−	0.322699i
$873$	3.87654e6	−	1.19308e7i	0.172151	−	0.529825i
$874$	9.38761e6			0.415697
$875$	−2.46387e6	+	6.27052e6i	−0.108792	+	0.276875i
$876$	−1.15291e7			−0.507618
$877$	−1.26476e7	+	3.89253e7i	−0.555276	+	1.70896i	0.139939	+	0.990160i	$0.455309\pi$
$877$	−1.26476e7	+	3.89253e7i	−0.555276	+	1.70896i	−0.695214	+	0.718802i	$0.744691\pi$
$878$	−1.40024e7	−	1.01733e7i	−0.613006	−	0.445375i
$879$	−1.86673e7	−	1.35626e7i	−0.814908	−	0.592065i
$880$	4.27961e6	−	1.80334e6i	0.186293	−	0.0785002i
$881$	3.51975e7	−	2.55725e7i	1.52782	−	1.11003i	0.570385	−	0.821377i	$-0.306794\pi$
$881$	3.51975e7	−	2.55725e7i	1.52782	−	1.11003i	0.957435	−	0.288649i	$-0.0932060\pi$
$882$	4.96357e6			0.214844
$883$	3.74185e6	−	2.71861e6i	0.161504	−	0.117340i	−0.504098	−	0.863647i	$-0.668175\pi$
$883$	3.74185e6	−	2.71861e6i	0.161504	−	0.117340i	0.665602	+	0.746307i	$0.268175\pi$
$884$	−642301.	−	1.97680e6i	−0.0276444	−	0.0850808i
$885$	1.36725e6	+	1.61149e7i	0.0586798	+	0.691623i
$886$	−6.63597e6	+	2.04234e7i	−0.284001	+	0.874066i
$887$	−1.15564e7	−	3.55668e7i	−0.493187	−	1.51787i	−0.819763	−	0.572703i	$-0.805895\pi$
$887$	−1.15564e7	−	3.55668e7i	−0.493187	−	1.51787i	0.326575	−	0.945171i	$-0.394105\pi$
$888$	1.13308e6	+	3.48725e6i	0.0482200	+	0.148406i
$889$	1.28373e6	−	3.95092e6i	0.0544779	−	0.167666i
$890$	−3.73648e6	−	872974.i	−0.158120	−	0.0369425i
$891$	657935.	+	2.02492e6i	0.0277644	+	0.0854501i
$892$	−7.54878e6	+	5.48451e6i	−0.317662	+	0.230795i
$893$	1.15560e7			0.484930
$894$	1.41897e6	−	1.03094e6i	0.0593784	−	0.0431410i
$895$	1.15402e7	+	2.69620e6i	0.481566	+	0.112511i
$896$	−511191.	−	371402.i	−0.0212722	−	0.0154552i
$897$	3.95807e6	+	2.87570e6i	0.164249	+	0.119334i
$898$	2.00455e6	−	6.16936e6i	0.0829517	−	0.255299i
$899$	5.70323e6			0.235354
$900$	−1.88256e6	−	3.58587e6i	−0.0774714	−	0.147567i
$901$	−2.10936e6			−0.0865641
$902$	−1.55143e6	+	4.77482e6i	−0.0634916	+	0.195407i
$903$	−3.67889e6	−	2.67287e6i	−0.150140	−	0.109083i
$904$	−5.73493e6	−	4.16667e6i	−0.233403	−	0.169578i
$905$	−4.37019e6	+	7.23015e6i	−0.177369	+	0.293444i
$906$	−4.74962e6	+	3.45080e6i	−0.192238	+	0.139669i
$907$	−2.30246e7			−0.929338			−0.464669	−	0.885484i	$-0.653827\pi$
$907$	−2.30246e7			−0.929338			−0.464669	+	0.885484i	$0.653827\pi$
$908$	1.63987e7	−	1.19143e7i	0.660076	−	0.479573i
$909$	−1.89989e6	−	5.84727e6i	−0.0762640	−	0.234716i
$910$	1.34641e6	−	567351.i	0.0538983	−	0.0227116i
$911$	−1.08207e7	+	3.33027e7i	−0.431976	+	1.32949i	0.464177	+	0.885742i	$0.346350\pi$
$911$	−1.08207e7	+	3.33027e7i	−0.431976	+	1.32949i	−0.896154	+	0.443744i	$0.853650\pi$
$912$	520783.	+	1.60280e6i	0.0207334	+	0.0638107i
$913$	−817063.	−	2.51466e6i	−0.0324398	−	0.0998396i
$914$	−2.00078e6	+	6.15776e6i	−0.0792197	+	0.243813i
$915$	−5.53905e6	+	9.16395e6i	−0.218717	+	0.361851i
$916$	5.88354e6	+	1.81077e7i	0.231686	+	0.713057i
$917$	−2.16627e6	+	1.57388e6i	−0.0850724	+	0.0618087i
$918$	−2.23586e6			−0.0875663
$919$	−2.00019e7	+	1.45323e7i	−0.781238	+	0.567602i	−0.905350	−	0.424666i	$-0.860392\pi$
$919$	−2.00019e7	+	1.45323e7i	−0.781238	+	0.567602i	0.124112	+	0.992268i	$0.460392\pi$
$920$	−7.50820e6	−	8.68314e6i	−0.292460	−	0.338226i
$921$	2.27239e7	+	1.65099e7i	0.882742	+	0.641350i
$922$	3.12438e6	+	2.26999e6i	0.121042	+	0.0879422i
$923$	−1.77858e6	+	5.47391e6i	−0.0687179	+	0.211492i
$924$	1.80218e6			0.0694414
$925$	1.78339e7	+	8.81438e6i	0.685316	+	0.338717i
$926$	8.31802e6			0.318781
$927$	2.19332e6	−	6.75033e6i	0.0838305	−	0.258004i
$928$	−1.59776e6	−	1.16084e6i	−0.0609032	−	0.0442488i
$929$	−1.72591e7	−	1.25395e7i	−0.656114	−	0.476695i	0.209234	−	0.977866i	$-0.432903\pi$
$929$	−1.72591e7	−	1.25395e7i	−0.656114	−	0.476695i	−0.865348	+	0.501171i	$0.832903\pi$
$930$	503103.	+	5.92977e6i	0.0190743	+	0.224818i
$931$	−9.06564e6	+	6.58657e6i	−0.342787	+	0.249049i
$932$	1.28018e7			0.482762
$933$	128108.	−	93076.1i	0.00481807	−	0.00350053i
$934$	−2.84019e6	−	8.74120e6i	−0.106532	−	0.327872i
$935$	−9.09787e6	−	1.05216e7i	−0.340338	−	0.393597i
$936$	−271411.	+	835316.i	−0.0101260	+	0.0311646i
$937$	−9.00052e6	−	2.77007e7i	−0.334903	−	1.03072i	−0.966770	−	0.255648i	$-0.917711\pi$
$937$	−9.00052e6	−	2.77007e7i	−0.334903	−	1.03072i	0.631867	−	0.775076i	$-0.282289\pi$
$938$	−1.09119e6	−	3.35834e6i	−0.0404943	−	0.124629i
$939$	4.42295e6	−	1.36124e7i	0.163700	−	0.503816i
$940$	−9.24249e6	−	1.06888e7i	−0.341169	−	0.394557i
$941$	−498096.	−	1.53298e6i	−0.0183375	−	0.0564369i	0.941469	−	0.337099i	$-0.109446\pi$
$941$	−498096.	−	1.53298e6i	−0.0183375	−	0.0564369i	−0.959807	+	0.280663i	$0.909446\pi$
$942$	2.34841e6	−	1.70622e6i	0.0862278	−	0.0626481i
$943$	1.24098e7			0.454448
$944$	−6.65756e6	+	4.83700e6i	−0.243156	+	0.176663i
$945$	−132868.	−	1.56603e6i	−0.00483994	−	0.0570454i
$946$	1.37581e7	+	9.99587e6i	0.499841	+	0.363156i
$947$	−3.57454e7	−	2.59706e7i	−1.29523	−	0.941037i	−0.295329	−	0.955396i	$-0.595429\pi$
$947$	−3.57454e7	−	2.59706e7i	−1.29523	−	0.941037i	−0.999897	+	0.0143589i	$0.995429\pi$
$948$	714671.	−	2.19953e6i	0.0258277	−	0.0794895i
$949$	1.35648e7			0.488933
$950$	8.19676e6	+	4.05125e6i	0.294668	+	0.145640i
$951$	−2.30137e7			−0.825154
$952$	−584822.	+	1.79990e6i	−0.0209137	+	0.0643659i
$953$	−1.57676e7	−	1.14558e7i	−0.562383	−	0.408595i	0.269947	−	0.962875i	$-0.412994\pi$
$953$	−1.57676e7	−	1.14558e7i	−0.562383	−	0.408595i	−0.832330	+	0.554280i	$0.812994\pi$
$954$	721101.	+	523911.i	0.0256522	+	0.0186374i
$955$	1.90750e7	+	2.20599e7i	0.676792	+	0.782701i
$956$	−6.99703e6	+	5.08364e6i	−0.247611	+	0.179900i
$957$	5.63282e6			0.198813
$958$	−1.74189e7	+	1.26556e7i	−0.613207	+	0.445521i
$959$	−3.19340e6	−	9.82827e6i	−0.112126	−	0.345088i
$960$	1.06600e6	−	1.76362e6i	0.0373320	−	0.0617629i
$961$	−6.14469e6	+	1.89114e7i	−0.214630	+	0.660565i
$962$	−1.33314e6	−	4.10299e6i	−0.0464450	−	0.142943i
$963$	−3.96470e6	−	1.22021e7i	−0.137767	−	0.424003i
$964$	3.40376e6	−	1.04757e7i	0.117969	−	0.363070i
$965$	−2.32606e7	+	9.80152e6i	−0.804085	+	0.338825i
$966$	−1.37655e6	−	4.23660e6i	−0.0474625	−	0.146075i
$967$	−2.45766e7	+	1.78559e7i	−0.845191	+	0.614067i	−0.923816	−	0.382837i	$-0.874947\pi$
$967$	−2.45766e7	+	1.78559e7i	−0.845191	+	0.614067i	0.0786246	+	0.996904i	$0.474947\pi$
$968$	3.56756e6			0.122372
$969$	4.08365e6	−	2.96694e6i	0.139714	−	0.101508i
$970$	1.79140e7	−	2.96374e7i	0.611313	−	1.01137i
$971$	3.80876e7	+	2.76723e7i	1.29639	+	0.941882i	0.999913	−	0.0131577i	$-0.00418835\pi$
$971$	3.80876e7	+	2.76723e7i	1.29639	+	0.941882i	0.296477	+	0.955040i	$0.404188\pi$
$972$	764346.	+	555330.i	0.0259492	+	0.0188532i
$973$	−471587.	+	1.45140e6i	−0.0159691	+	0.0491478i
$974$	1.98943e7			0.671941
$975$	2.21496e6	+	4.21902e6i	0.0746197	+	0.142135i
$976$	−5.44850e6			−0.183085
$977$	−1.42712e7	+	4.39221e7i	−0.478325	+	1.47213i	0.363096	+	0.931752i	$0.381720\pi$
$977$	−1.42712e7	+	4.39221e7i	−0.478325	+	1.47213i	−0.841421	+	0.540381i	$0.818280\pi$
$978$	4.90993e6	+	3.56727e6i	0.164145	+	0.119258i
$979$	4.50512e6	+	3.27316e6i	0.150228	+	0.109147i
$980$	1.33430e7	+	3.11740e6i	0.443801	+	0.103688i
$981$	1.26222e7	−	9.17053e6i	0.418756	−	0.304244i
$982$	−442213.			−0.0146336
$983$	−1.89036e7	+	1.37343e7i	−0.623965	+	0.453337i	−0.854304	−	0.519773i	$-0.826016\pi$
$983$	−1.89036e7	+	1.37343e7i	−0.623965	+	0.453337i	0.230339	+	0.973110i	$0.426016\pi$
$984$	688438.	+	2.11879e6i	0.0226661	+	0.0697591i
$985$	−5.14849e6	−	1.20287e6i	−0.169079	−	0.0395028i
$986$	−1.82790e6	+	5.62568e6i	−0.0598769	+	0.184282i
$987$	−1.69452e6	−	5.21519e6i	−0.0553673	−	0.170403i
$988$	−612737.	−	1.88581e6i	−0.0199702	−	0.0614618i
$989$	1.29896e7	−	3.99780e7i	0.422286	−	1.29966i
$990$	496892.	+	5.85656e6i	0.0161129	+	0.189913i
$991$	−6.55055e6	−	2.01605e7i	−0.211882	−	0.652105i	−0.999360	−	0.0357628i	$-0.988614\pi$
$991$	−6.55055e6	−	2.01605e7i	−0.211882	−	0.652105i	0.787479	−	0.616342i	$-0.211386\pi$
$992$	−2.44977e6	+	1.77986e6i	−0.0790399	+	0.0574259i
$993$	−4.75834e6			−0.153138
$994$	4.23970e6	−	3.08032e6i	0.136103	−	0.0988849i
$995$	2.15481e7	−	9.07995e6i	0.690005	−	0.290754i
$996$	−949212.	−	689643.i	−0.0303190	−	0.0220280i
$997$	−3.70015e6	−	2.68832e6i	−0.117891	−	0.0856530i	0.527277	−	0.849693i	$-0.323213\pi$
$997$	−3.70015e6	−	2.68832e6i	−0.117891	−	0.0856530i	−0.645169	+	0.764040i	$0.723213\pi$
$998$	4.73892e6	−	1.45849e7i	0.150610	−	0.463529i
$999$	−4.64069e6			−0.147119

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.6.g.a.121.5	yes	20
25.6	even	5	inner	150.6.g.a.31.5	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.6.g.a.31.5	✓	20	25.6	even	5	inner
150.6.g.a.121.5	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)

\(f(q)\)	\(=\)	\(q+(-1.23607 + 3.80423i) q^{2} +(7.28115 + 5.29007i) q^{3} +(-12.9443 - 9.40456i) q^{4} +(51.5150 - 21.7074i) q^{5} +(-29.1246 + 21.1603i) q^{6} -38.5661 q^{7} +(51.7771 - 37.6183i) q^{8} +(25.0304 + 77.0356i) q^{9} +O(q^{10})\)	\(q+(-1.23607 + 3.80423i) q^{2} +(7.28115 + 5.29007i) q^{3} +(-12.9443 - 9.40456i) q^{4} +(51.5150 - 21.7074i) q^{5} +(-29.1246 + 21.1603i) q^{6} -38.5661 q^{7} +(51.7771 - 37.6183i) q^{8} +(25.0304 + 77.0356i) q^{9} +(18.9037 + 222.806i) q^{10} +(100.280 - 308.629i) q^{11} +(-44.4984 - 136.952i) q^{12} +(52.3555 + 161.134i) q^{13} +(47.6703 - 146.714i) q^{14} +(489.922 + 114.463i) q^{15} +(79.1084 + 243.470i) q^{16} +(620.318 - 450.687i) q^{17} -324.000 q^{18} +(591.765 - 429.943i) q^{19} +(-870.972 - 203.490i) q^{20} +(-280.805 - 204.017i) q^{21} +(1050.14 + 762.973i) q^{22} +(991.484 - 3051.47i) q^{23} +576.000 q^{24} +(2182.58 - 2236.51i) q^{25} -677.703 q^{26} +(-225.273 + 693.320i) q^{27} +(499.210 + 362.697i) q^{28} +(1560.31 + 1133.63i) q^{29} +(-1041.02 + 1722.29i) q^{30} +(2392.36 - 1738.15i) q^{31} -1024.00 q^{32} +(2362.82 - 1716.69i) q^{33} +(947.761 + 2916.91i) q^{34} +(-1986.73 + 837.167i) q^{35} +(400.486 - 1232.57i) q^{36} +(1967.15 + 6054.26i) q^{37} +(904.137 + 2782.65i) q^{38} +(-471.199 + 1450.20i) q^{39} +(1850.70 - 3061.85i) q^{40} +(1195.20 + 3678.46i) q^{41} +(1123.22 - 816.068i) q^{42} +13101.2 q^{43} +(-4200.57 + 3051.89i) q^{44} +(2961.68 + 3425.14i) q^{45} +(10383.0 + 7543.65i) q^{46} +(12781.3 + 9286.13i) q^{47} +(-711.975 + 2191.23i) q^{48} -15319.7 q^{49} +(5810.36 + 11067.5i) q^{50} +6900.79 q^{51} +(837.688 - 2578.14i) q^{52} +(-2225.62 - 1617.01i) q^{53} +(-2359.09 - 1713.98i) q^{54} +(-1533.62 - 18075.8i) q^{55} +(-1996.84 + 1450.79i) q^{56} +6583.16 q^{57} +(-6241.23 + 4534.52i) q^{58} +(9933.45 + 30572.0i) q^{59} +(-5265.20 - 6089.14i) q^{60} +(-6576.87 + 20241.5i) q^{61} +(3655.19 + 11249.5i) q^{62} +(-965.323 - 2970.96i) q^{63} +(1265.73 - 3895.53i) q^{64} +(6194.87 + 7164.29i) q^{65} +(3610.07 + 11110.6i) q^{66} +(18518.7 - 13454.6i) q^{67} -12268.1 q^{68} +(23361.6 - 16973.2i) q^{69} +(-729.041 - 8592.76i) q^{70} +(27483.3 + 19967.8i) q^{71} +(4193.94 + 3047.08i) q^{72} +(24741.0 - 76144.9i) q^{73} -25463.3 q^{74} +(27723.0 - 4738.34i) q^{75} -11703.4 q^{76} +(-3867.39 + 11902.6i) q^{77} +(-4934.46 - 3585.10i) q^{78} +(12993.3 + 9440.18i) q^{79} +(9360.36 + 10825.1i) q^{80} +(-5307.96 + 3856.46i) q^{81} -15471.1 q^{82} +(6591.75 - 4789.18i) q^{83} +(1716.13 + 5281.70i) q^{84} +(22172.4 - 36682.6i) q^{85} +(-16194.0 + 49840.0i) q^{86} +(5363.86 + 16508.3i) q^{87} +(-6417.90 - 19752.3i) q^{88} +(-5302.75 + 16320.2i) q^{89} +(-16690.8 + 7033.18i) q^{90} +(-2019.14 - 6214.29i) q^{91} +(-41531.8 + 30174.6i) q^{92} +26614.0 q^{93} +(-51125.1 + 37144.5i) q^{94} +(21151.8 - 34994.1i) q^{95} +(-7455.90 - 5417.03i) q^{96} +(-125295. - 91032.3i) q^{97} +(18936.1 - 58279.4i) q^{98} +26285.5 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

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