LMFDB - Embedded newform 9.7.d.a.5.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [9,7,Mod(2,9)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("9.2"); S:= CuspForms(chi, 7); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(9, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 7, names="a")

Level:	$ N $	$=$	$ 9 = 3^{2} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	9.d (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$2.07048675258$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 75 x^{8} - 2 x^{7} + 4610 x^{6} - 2412 x^{5} + 66932 x^{4} - 174032 x^{3} + \cdots + 1982464 $ x^10 - x^9 + 75x^8 - 2x^7 + 4610x^6 - 2412x^5 + 66932x^4 - 174032x^3 + 870720x^2 - 1272832x + 1982464
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			5.1
Root			$4.07727 - 7.06203i$ of defining polynomial
Character	$\chi$	$=$	9.5
Dual form			9.7.d.a.2.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-12.2318 + 7.06203i) q^{2} +(9.56099 - 25.2505i) q^{3} +(67.7447 - 117.337i) q^{4} +(-103.839 - 59.9512i) q^{5} +(61.3717 + 376.379i) q^{6} +(-128.891 - 223.245i) q^{7} +1009.72i q^{8} +(-546.175 - 482.840i) q^{9} +1693.51 q^{10} +(518.417 - 299.308i) q^{11} +(-2315.12 - 2832.45i) q^{12} +(-968.088 + 1676.78i) q^{13} +(3153.13 + 1820.46i) q^{14} +(-2506.60 + 2048.78i) q^{15} +(-2795.02 - 4841.12i) q^{16} -4874.12i q^{17} +(10090.5 + 2048.89i) q^{18} +7688.70 q^{19} +(-14069.0 + 8122.75i) q^{20} +(-6869.37 + 1120.11i) q^{21} +(-4227.45 + 7322.16i) q^{22} +(-594.548 - 343.263i) q^{23} +(25495.9 + 9653.93i) q^{24} +(-624.198 - 1081.14i) q^{25} -27346.7i q^{26} +(-17413.9 + 9174.76i) q^{27} -34926.6 q^{28} +(29972.2 - 17304.5i) q^{29} +(16191.6 - 42762.0i) q^{30} +(-1387.88 + 2403.88i) q^{31} +(12411.9 + 7166.00i) q^{32} +(-2601.10 - 15952.0i) q^{33} +(34421.2 + 59619.2i) q^{34} +30908.6i q^{35} +(-93655.5 + 31376.8i) q^{36} +17175.3 q^{37} +(-94046.7 + 54297.9i) q^{38} +(33083.6 + 40476.4i) q^{39} +(60534.0 - 104848. i) q^{40} +(71583.2 + 41328.6i) q^{41} +(76114.5 - 62212.6i) q^{42} +(-63212.6 - 109487. i) q^{43} -81106.2i q^{44} +(27767.2 + 82881.2i) q^{45} +9696.53 q^{46} +(-72025.6 + 41584.0i) q^{47} +(-148964. + 24289.7i) q^{48} +(25599.0 - 44338.7i) q^{49} +(15270.1 + 8816.21i) q^{50} +(-123074. - 46601.4i) q^{51} +(131166. + 227185. i) q^{52} +40017.8i q^{53} +(148211. - 235201. i) q^{54} -71775.6 q^{55} +(225415. - 130143. i) q^{56} +(73511.6 - 194144. i) q^{57} +(-244410. + 423330. i) q^{58} +(-57614.7 - 33263.9i) q^{59} +(70589.7 + 432911. i) q^{60} +(-184662. - 319843. i) q^{61} -39205.0i q^{62} +(-37394.7 + 184164. i) q^{63} +155336. q^{64} +(201050. - 116076. i) q^{65} +(144470. + 176752. i) q^{66} +(-127954. + 221623. i) q^{67} +(-571915. - 330195. i) q^{68} +(-14352.0 + 11730.7i) q^{69} +(-218277. - 378068. i) q^{70} +269837. i q^{71} +(487533. - 551484. i) q^{72} +551862. q^{73} +(-210085. + 121292. i) q^{74} +(-33267.3 + 5424.50i) q^{75} +(520869. - 902171. i) q^{76} +(-133638. - 77156.0i) q^{77} +(-690517. - 261461. i) q^{78} +(355021. + 614915. i) q^{79} +670259. i q^{80} +(65172.8 + 527430. i) q^{81} -1.16746e6 q^{82} +(301612. - 174136. i) q^{83} +(-333933. + 881913. i) q^{84} +(-292209. + 506121. i) q^{85} +(1.54641e6 + 892818. i) q^{86} +(-150382. - 922262. i) q^{87} +(302218. + 523456. i) q^{88} -836103. i q^{89} +(-924953. - 817694. i) q^{90} +499109. q^{91} +(-80554.9 + 46508.4i) q^{92} +(47429.6 + 58028.1i) q^{93} +(587335. - 1.01729e6i) q^{94} +(-798384. - 460947. i) q^{95} +(299615. - 244892. i) q^{96} +(-47014.3 - 81431.2i) q^{97} +723123. i q^{98} +(-427664. - 86837.8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 3 q^{2} + 24 q^{3} + 127 q^{4} - 219 q^{5} + 333 q^{6} - 121 q^{7} - 1980 q^{9} - 132 q^{10} + 483 q^{11} - 1830 q^{12} - 841 q^{13} + 12174 q^{14} + 7965 q^{15} - 1985 q^{16} - 7884 q^{18} + 6176 q^{19}+ \cdots - 432567 q^{99}+O(q^{100}) $ 10 * q - 3 * q^2 + 24 * q^3 + 127 * q^4 - 219 * q^5 + 333 * q^6 - 121 * q^7 - 1980 * q^9 - 132 * q^10 + 483 * q^11 - 1830 * q^12 - 841 * q^13 + 12174 * q^14 + 7965 * q^15 - 1985 * q^16 - 7884 * q^18 + 6176 * q^19 - 63186 * q^20 - 25845 * q^21 + 3471 * q^22 + 53565 * q^23 + 111519 * q^24 + 8452 * q^25 - 101034 * q^27 - 22660 * q^28 - 80679 * q^29 - 37782 * q^30 - 24601 * q^31 + 218295 * q^32 + 229995 * q^33 + 7425 * q^34 - 274977 * q^36 + 12764 * q^37 - 371877 * q^38 - 112749 * q^39 + 54150 * q^40 + 232251 * q^41 + 270540 * q^42 - 93271 * q^43 + 63801 * q^45 + 112512 * q^46 - 142887 * q^47 - 143283 * q^48 + 86238 * q^49 + 318459 * q^50 + 57078 * q^51 + 186920 * q^52 + 13851 * q^54 - 419982 * q^55 + 342546 * q^56 - 1086 * q^57 - 380658 * q^58 - 995061 * q^59 - 1011402 * q^60 - 59305 * q^61 + 526455 * q^63 + 403066 * q^64 + 1642029 * q^65 + 1610586 * q^66 + 158513 * q^67 - 1693791 * q^68 - 851715 * q^69 - 304788 * q^70 + 1469907 * q^72 + 933896 * q^73 + 595182 * q^74 - 757524 * q^75 + 666641 * q^76 - 2198883 * q^77 - 3481884 * q^78 + 468707 * q^79 + 1774548 * q^81 - 2038470 * q^82 + 3008337 * q^83 + 1543746 * q^84 - 1189944 * q^85 + 1905549 * q^86 - 615591 * q^87 - 349773 * q^88 + 84294 * q^90 - 211778 * q^91 - 973788 * q^92 - 2954553 * q^93 + 809124 * q^94 - 2562954 * q^95 - 1022112 * q^96 + 336029 * q^97 - 432567 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/9\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−12.2318	+	7.06203i	−1.52898	+	0.882754i	−0.529570	+	0.848266i	$0.677647\pi$
$2$	−12.2318	+	7.06203i	−1.52898	+	0.882754i	−0.999405	+	0.0344882i	$0.989020\pi$
$3$	9.56099	−	25.2505i	0.354111	−	0.935203i
$3$	9.56099	−	25.2505i	0.354111	−	0.935203i
$4$	67.7447	−	117.337i	1.05851	−	1.83339i
$5$	−103.839	−	59.9512i	−0.830709	−	0.479610i	0.0233865	−	0.999726i	$-0.492555\pi$
$5$	−103.839	−	59.9512i	−0.830709	−	0.479610i	−0.854095	+	0.520117i	$0.825888\pi$
$6$	61.3717	+	376.379i	0.284128	+	1.74250i
$7$	−128.891	−	223.245i	−0.375774	−	0.650860i	0.614668	−	0.788786i	$-0.289290\pi$
$7$	−128.891	−	223.245i	−0.375774	−	0.650860i	−0.990443	+	0.137926i	$0.955956\pi$
$8$			1009.72i			1.97211i
$9$	−546.175	−	482.840i	−0.749211	−	0.662331i
$10$	1693.51			1.69351
$11$	518.417	−	299.308i	0.389495	−	0.224875i	−0.292447	−	0.956282i	$-0.594469\pi$
$11$	518.417	−	299.308i	0.389495	−	0.224875i	0.681941	+	0.731407i	$0.261136\pi$
$12$	−2315.12	−	2832.45i	−1.33977	−	1.63915i
$13$	−968.088	+	1676.78i	−0.440641	+	0.763212i	−0.997737	−	0.0672356i	$-0.978582\pi$
$13$	−968.088	+	1676.78i	−0.440641	+	0.763212i	0.557096	+	0.830448i	$0.311915\pi$
$14$	3153.13	+	1820.46i	1.14910	+	0.663432i
$15$	−2506.60	+	2048.78i	−0.742696	+	0.607047i
$16$	−2795.02	−	4841.12i	−0.682378	−	1.18191i
$17$		−	4874.12i		−	0.992085i	−0.868298	−	0.496043i	$-0.834786\pi$
$17$		−	4874.12i		−	0.992085i	0.868298	−	0.496043i	$-0.165214\pi$
$18$	10090.5	+	2048.89i	1.73020	+	0.351319i
$19$	7688.70			1.12097			0.560483	−	0.828166i	$-0.310616\pi$
$19$	7688.70			1.12097			0.560483	+	0.828166i	$0.310616\pi$
$20$	−14069.0	+	8122.75i	−1.75863	+	1.01534i
$21$	−6869.37	+	1120.11i	−0.741752	+	0.120949i
$22$	−4227.45	+	7322.16i	−0.397018	+	0.687656i
$23$	−594.548	−	343.263i	−0.0488656	−	0.0282126i	0.475368	−	0.879787i	$-0.342315\pi$
$23$	−594.548	−	343.263i	−0.0488656	−	0.0282126i	−0.524234	+	0.851574i	$0.675648\pi$
$24$	25495.9	+	9653.93i	1.84432	+	0.698345i
$25$	−624.198	−	1081.14i	−0.0399486	−	0.0691931i
$26$		−	27346.7i		−	1.55591i
$27$	−17413.9	+	9174.76i	−0.884718	+	0.466126i
$28$	−34926.6			−1.59104
$29$	29972.2	−	17304.5i	1.22892	−	0.709520i	0.262119	−	0.965036i	$-0.415579\pi$
$29$	29972.2	−	17304.5i	1.22892	−	0.709520i	0.966805	+	0.255516i	$0.0822453\pi$
$30$	16191.6	−	42762.0i	0.599691	−	1.58378i
$31$	−1387.88	+	2403.88i	−0.0465872	+	0.0806915i	−0.888379	−	0.459111i	$-0.848168\pi$
$31$	−1387.88	+	2403.88i	−0.0465872	+	0.0806915i	0.841791	+	0.539803i	$0.181501\pi$
$32$	12411.9	+	7166.00i	0.378780	+	0.218689i
$33$	−2601.10	−	15952.0i	−0.0723794	−	0.443887i
$34$	34421.2	+	59619.2i	0.875768	+	1.51687i
$35$			30908.6i			0.720900i
$36$	−93655.5	+	31376.8i	−2.00736	+	0.672514i
$37$	17175.3			0.339077			0.169539	−	0.985524i	$-0.445772\pi$
$37$	17175.3			0.339077			0.169539	+	0.985524i	$0.445772\pi$
$38$	−94046.7	+	54297.9i	−1.71393	+	0.989537i
$39$	33083.6	+	40476.4i	0.557723	+	0.682351i
$40$	60534.0	−	104848.i	0.945843	−	1.63825i
$41$	71583.2	+	41328.6i	1.03863	+	0.599652i	0.919444	−	0.393221i	$-0.128639\pi$
$41$	71583.2	+	41328.6i	1.03863	+	0.599652i	0.119183	+	0.992872i	$0.461973\pi$
$42$	76114.5	−	62212.6i	1.02735	−	0.839712i
$43$	−63212.6	−	109487.i	−0.795056	−	1.37708i	−0.922803	−	0.385271i	$-0.874108\pi$
$43$	−63212.6	−	109487.i	−0.795056	−	1.37708i	0.127747	−	0.991807i	$-0.459225\pi$
$44$		−	81106.2i		−	0.952129i
$45$	27767.2	+	82881.2i	0.304715	+	0.909534i
$46$	9696.53			0.0996191
$47$	−72025.6	+	41584.0i	−0.693734	+	0.400528i	−0.805009	−	0.593262i	$-0.797840\pi$
$47$	−72025.6	+	41584.0i	−0.693734	+	0.400528i	0.111275	+	0.993790i	$0.464506\pi$
$48$	−148964.	+	24289.7i	−1.34697	+	0.219634i
$49$	25599.0	−	44338.7i	0.217588	−	0.376873i
$50$	15270.1	+	8816.21i	0.122161	+	0.0705297i
$51$	−123074.	−	46601.4i	−0.927802	−	0.351308i
$52$	131166.	+	227185.i	0.932846	+	1.61574i
$53$			40017.8i			0.268798i	0.990927	+	0.134399i	$0.0429103\pi$
$53$			40017.8i			0.268798i	−0.990927	+	0.134399i	$0.957090\pi$
$54$	148211.	−	235201.i	0.941238	−	1.49368i
$55$	−71775.6			−0.431409
$56$	225415.	−	130143.i	1.28357	−	0.741068i
$57$	73511.6	−	194144.i	0.396946	−	1.04833i
$58$	−244410.	+	423330.i	−1.25266	+	2.16968i
$59$	−57614.7	−	33263.9i	−0.280529	−	0.161963i	0.353134	−	0.935573i	$-0.385116\pi$
$59$	−57614.7	−	33263.9i	−0.280529	−	0.161963i	−0.633663	+	0.773609i	$0.718449\pi$
$60$	70589.7	+	432911.i	0.326804	+	2.00422i
$61$	−184662.	−	319843.i	−0.813555	−	1.40912i	−0.910361	−	0.413815i	$-0.864196\pi$
$61$	−184662.	−	319843.i	−0.813555	−	1.40912i	0.0968060	−	0.995303i	$-0.469137\pi$
$62$		−	39205.0i		−	0.164500i
$63$	−37394.7	+	184164.i	−0.149551	+	0.736518i
$64$	155336.			0.592561
$65$	201050.	−	116076.i	0.732088	−	0.422671i
$66$	144470.	+	176752.i	0.502510	+	0.614800i
$67$	−127954.	+	221623.i	−0.425432	+	0.736870i	−0.996461	−	0.0840603i	$-0.973211\pi$
$67$	−127954.	+	221623.i	−0.425432	+	0.736870i	0.571029	+	0.820930i	$0.306545\pi$
$68$	−571915.	−	330195.i	−1.81888	−	1.05013i
$69$	−14352.0	+	11730.7i	−0.0436884	+	0.0357089i
$70$	−218277.	−	378068.i	−0.636377	−	1.10224i
$71$			269837.i			0.753923i	0.926229	+	0.376961i	$0.123031\pi$
$71$			269837.i			0.753923i	−0.926229	+	0.376961i	$0.876969\pi$
$72$	487533.	−	551484.i	1.30619	−	1.47753i
$73$	551862.			1.41861			0.709303	−	0.704903i	$-0.249010\pi$
$73$	551862.			1.41861			0.709303	+	0.704903i	$0.249010\pi$
$74$	−210085.	+	121292.i	−0.518441	+	0.299322i
$75$	−33267.3	+	5424.50i	−0.0788559	+	0.0128581i
$76$	520869.	−	902171.i	1.18655	−	2.05517i
$77$	−133638.	−	77156.0i	−0.292724	−	0.169004i
$78$	−690517.	−	261461.i	−1.45509	−	0.550965i
$79$	355021.	+	614915.i	0.720068	+	1.24719i	0.960972	+	0.276645i	$0.0892226\pi$
$79$	355021.	+	614915.i	0.720068	+	1.24719i	−0.240905	+	0.970549i	$0.577444\pi$
$80$			670259.i			1.30910i
$81$	65172.8	+	527430.i	0.122634	+	0.992452i
$82$	−1.16746e6			−2.11738
$83$	301612.	−	174136.i	0.527490	−	0.304547i	−0.212503	−	0.977160i	$-0.568162\pi$
$83$	301612.	−	174136.i	0.527490	−	0.304547i	0.739994	+	0.672614i	$0.234828\pi$
$84$	−333933.	+	881913.i	−0.563406	+	1.48795i
$85$	−292209.	+	506121.i	−0.475814	+	0.824134i
$86$	1.54641e6	+	892818.i	2.43124	+	1.40368i
$87$	−150382.	−	922262.i	−0.228370	−	1.40054i
$88$	302218.	+	523456.i	0.443478	+	0.768126i
$89$		−	836103.i		−	1.18601i	−0.805197	−	0.593007i	$-0.797941\pi$
$89$		−	836103.i		−	1.18601i	0.805197	−	0.593007i	$-0.202059\pi$
$90$	−924953.	−	817694.i	−1.26880	−	1.12167i
$91$	499109.			0.662326
$92$	−80554.9	+	46508.4i	−0.103450	+	0.0597266i
$93$	47429.6	+	58028.1i	0.0589659	+	0.0721423i
$94$	587335.	−	1.01729e6i	0.707135	−	1.22479i
$95$	−798384.	−	460947.i	−0.931196	−	0.537626i
$96$	299615.	−	244892.i	0.338649	−	0.276797i
$97$	−47014.3	−	81431.2i	−0.0515128	−	0.0892227i	0.839119	−	0.543948i	$-0.183071\pi$
$97$	−47014.3	−	81431.2i	−0.0515128	−	0.0892227i	−0.890632	+	0.454725i	$0.849738\pi$
$98$			723123.i			0.768306i
$99$	−427664.	−	86837.8i	−0.440755	−	0.0894959i
$100$	−169144.			−0.169144
$101$	−233315.	+	134704.i	−0.226453	+	0.130743i	−0.608935	−	0.793220i	$-0.708403\pi$
$101$	−233315.	+	134704.i	−0.226453	+	0.130743i	0.382482	+	0.923963i	$0.375070\pi$
$102$	1.83452e6	−	299133.i	1.72870	−	0.281879i
$103$	128429.	−	222446.i	0.117531	−	0.203569i	−0.801258	−	0.598319i	$-0.795835\pi$
$103$	128429.	−	222446.i	0.117531	−	0.203569i	0.918789	+	0.394750i	$0.129169\pi$
$104$	−1.69308e6	−	977498.i	−1.50514	−	0.868992i
$105$	780457.	+	295517.i	0.674188	+	0.255279i
$106$	−282607.	−	489490.i	−0.237282	−	0.410985i
$107$			983414.i			0.802759i	0.915912	+	0.401379i	$0.131469\pi$
$107$			983414.i			0.802759i	−0.915912	+	0.401379i	$0.868531\pi$
$108$	−103160.	+	2.66484e6i	−0.0818914	+	2.11544i
$109$	−1.19797e6			−0.925053			−0.462526	−	0.886606i	$-0.653057\pi$
$109$	−1.19797e6			−0.925053			−0.462526	+	0.886606i	$0.653057\pi$
$110$	877945.	−	506882.i	0.659613	−	0.380828i
$111$	164213.	−	433684.i	0.120071	−	0.317106i
$112$	−720503.	+	1.24795e6i	−0.512840	+	0.888264i
$113$	−246875.	−	142533.i	−0.171097	−	0.0987827i	0.412006	−	0.911181i	$-0.364828\pi$
$113$	−246875.	−	142533.i	−0.171097	−	0.0987827i	−0.583103	+	0.812398i	$0.698162\pi$
$114$	471868.	+	2.89387e6i	0.318498	+	1.95328i
$115$	41158.0	+	71287.8i	0.0270621	+	0.0468729i
$116$		−	4.68914e6i		−	3.00414i
$117$	1.33836e6	−	448382.i	0.835632	−	0.279957i
$118$	939643.			0.571896
$119$	−1.08812e6	+	628227.i	−0.645709	+	0.372800i
$120$	−2.06870e6	−	2.53096e6i	−1.19716	−	1.46468i
$121$	−706609.	+	1.22388e6i	−0.398863	+	0.690850i
$122$	4.51749e6	+	2.60817e6i	2.48781	+	1.43634i
$123$	1.72797e6	−	1.41237e6i	0.928585	−	0.758984i
$124$	188043.	+	325700.i	0.0986261	+	0.170825i
$125$			2.02316e6i			1.03586i
$126$	−843169.	−	2.51674e6i	−0.421505	−	1.25813i
$127$	359846.			0.175673			0.0878365	−	0.996135i	$-0.472005\pi$
$127$	359846.			0.175673			0.0878365	+	0.996135i	$0.472005\pi$
$128$	−2.69440e6	+	1.55561e6i	−1.28479	+	0.741775i
$129$	−3.36898e6	+	549340.i	−1.56939	+	0.255901i
$130$	−1.63947e6	+	2.83964e6i	−0.746230	+	1.29251i
$131$	−1.24110e6	−	716547.i	−0.552066	−	0.318736i	0.197889	−	0.980225i	$-0.436592\pi$
$131$	−1.24110e6	−	716547.i	−0.552066	−	0.318736i	−0.749955	+	0.661489i	$0.769925\pi$
$132$	−2.04797e6	−	775456.i	−0.890435	−	0.337159i
$133$	−991001.	−	1.71646e6i	−0.421230	−	0.729591i
$134$		−	3.61447e6i		−	1.50221i
$135$	2.35827e6	+	91292.0i	0.958502	+	0.0371049i
$136$	4.92149e6			1.95650
$137$	3.36619e6	−	1.94347e6i	1.30911	−	0.755816i	0.327164	−	0.944968i	$-0.393907\pi$
$137$	3.36619e6	−	1.94347e6i	1.30911	−	0.755816i	0.981948	+	0.189152i	$0.0605738\pi$
$138$	92708.4	−	244842.i	0.0352762	−	0.0931642i
$139$	2.53995e6	−	4.39933e6i	0.945760	−	1.63810i	0.191538	−	0.981485i	$-0.438652\pi$
$139$	2.53995e6	−	4.39933e6i	0.945760	−	1.63810i	0.754222	−	0.656620i	$-0.228014\pi$
$140$	3.62673e6	+	2.09389e6i	1.32169	+	0.763080i
$141$	361380.	+	2.21627e6i	0.128916	+	0.790614i
$142$	−1.90560e6	−	3.30060e6i	−0.665529	−	1.15273i
$143$			1.15903e6i			0.396356i
$144$	−810913.	+	3.99364e6i	−0.271573	+	1.33746i
$145$	−4.14970e6			−1.36117
$146$	−6.75027e6	+	3.89727e6i	−2.16902	+	1.25228i
$147$	−874823.	−	1.07031e6i	−0.275403	−	0.336944i
$148$	1.16353e6	−	2.01530e6i	0.358917	−	0.621662i
$149$	−842550.	−	486446.i	−0.254705	−	0.147054i	0.367212	−	0.930137i	$-0.380312\pi$
$149$	−842550.	−	486446.i	−0.254705	−	0.147054i	−0.621917	+	0.783084i	$0.713646\pi$
$150$	368611.	−	301286.i	0.109218	−	0.0892700i
$151$	3.13402e6	+	5.42828e6i	0.910271	+	1.57663i	0.813682	+	0.581310i	$0.197460\pi$
$151$	3.13402e6	+	5.42828e6i	0.910271	+	1.57663i	0.0965886	+	0.995324i	$0.469207\pi$
$152$			7.76344e6i			2.21067i
$153$	−2.35342e6	+	2.66212e6i	−0.657089	+	0.743281i
$154$	2.17951e6			0.596757
$155$	288231.	−	166410.i	0.0774008	−	0.0446874i
$156$	6.99062e6	−	1.13988e6i	1.84137	−	0.300251i
$157$	832183.	−	1.44138e6i	0.215040	−	0.372461i	−0.738245	−	0.674533i	$-0.764345\pi$
$157$	832183.	−	1.44138e6i	0.215040	−	0.372461i	0.953285	+	0.302072i	$0.0976783\pi$
$158$	−8.68510e6	−	5.01435e6i	−2.20193	−	1.27129i
$159$	1.01047e6	+	382610.i	0.251381	+	0.0951842i
$160$	−859221.	−	1.48822e6i	−0.209771	−	0.363334i
$161$			176973.i			0.0424062i
$162$	−4.52191e6	−	5.99116e6i	−1.06360	−	1.40918i
$163$	2.47297e6			0.571025			0.285513	−	0.958375i	$-0.407836\pi$
$163$	2.47297e6			0.571025			0.285513	+	0.958375i	$0.407836\pi$
$164$	9.69876e6	−	5.59958e6i	2.19879	−	1.26947i
$165$	−686246.	+	1.81237e6i	−0.152767	+	0.403455i
$166$	−2.45951e6	+	4.25999e6i	−0.537680	+	0.931289i
$167$	5.00452e6	+	2.88936e6i	1.07452	+	0.620373i	0.929412	−	0.369044i	$-0.120315\pi$
$167$	5.00452e6	+	2.88936e6i	1.07452	+	0.620373i	0.145105	+	0.989416i	$0.453648\pi$
$168$	−1.13099e6	−	6.93614e6i	−0.238524	−	1.46282i
$169$	539017.	+	933604.i	0.111671	+	0.193421i
$170$		−	8.25437e6i		−	1.68011i
$171$	−4.19938e6	−	3.71241e6i	−0.839840	−	0.742451i
$172$	−1.71293e7			−3.36630
$173$	6.80297e6	−	3.92770e6i	1.31389	−	0.758577i	0.331156	−	0.943576i	$-0.392562\pi$
$173$	6.80297e6	−	3.92770e6i	1.31389	−	0.758577i	0.982739	+	0.184999i	$0.0592282\pi$
$174$	8.35249e6	+	1.02189e7i	1.58551	+	1.93980i
$175$	−160906.	+	278698.i	−0.0300233	+	0.0520019i
$176$	−2.89797e6	−	1.67315e6i	−0.531565	−	0.306899i
$177$	−1.39078e6	+	1.13676e6i	−0.250807	+	0.204999i
$178$	5.90459e6	+	1.02270e7i	1.04696	+	1.81339i
$179$		−	1.71905e6i		−	0.299730i	−0.988706	−	0.149865i	$-0.952116\pi$
$179$		−	1.71905e6i		−	0.299730i	0.988706	−	0.149865i	$-0.0478839\pi$
$180$	1.16061e7	+	2.35664e6i	1.99008	+	0.404087i
$181$	−4.16259e6			−0.701985			−0.350993	−	0.936378i	$-0.614156\pi$
$181$	−4.16259e6			−0.701985			−0.350993	+	0.936378i	$0.614156\pi$
$182$	−6.10501e6	+	3.52473e6i	−1.01268	+	0.584671i
$183$	−9.84174e6	+	1.60478e6i	−1.60590	+	0.261855i
$184$	346599.	−	600327.i	0.0556383	−	0.0963684i
$185$	−1.78346e6	−	1.02968e6i	−0.281674	−	0.162625i
$186$	−989946.	−	374839.i	−0.153841	−	0.0582514i
$187$	−1.45886e6	−	2.52683e6i	−0.223095	−	0.386412i
$188$			1.12684e7i			1.69585i
$189$	4.29271e6	+	2.70503e6i	0.635837	+	0.400670i
$190$	1.30209e7			1.89837
$191$	−7.35905e6	+	4.24875e6i	−1.05614	+	0.609763i	−0.924362	−	0.381516i	$-0.875402\pi$
$191$	−7.35905e6	+	4.24875e6i	−1.05614	+	0.609763i	−0.131778	+	0.991279i	$0.542069\pi$
$192$	1.48517e6	−	3.92232e6i	0.209832	−	0.554165i
$193$	1.99176e6	−	3.44984e6i	0.277055	−	0.479873i	−0.693597	−	0.720364i	$-0.743975\pi$
$193$	1.99176e6	−	3.44984e6i	0.277055	−	0.479873i	0.970651	+	0.240490i	$0.0773083\pi$
$194$	1.15014e6	+	664033.i	0.157523	+	0.0909462i
$195$	−1.00874e6	−	6.18641e6i	−0.136043	−	0.834324i
$196$	−3.46839e6	−	6.00742e6i	−0.460638	−	0.797848i
$197$		−	5.45308e6i		−	0.713252i	−0.934247	−	0.356626i	$-0.883927\pi$
$197$		−	5.45308e6i		−	0.713252i	0.934247	−	0.356626i	$-0.116073\pi$
$198$	5.84436e6	−	1.95800e6i	0.752907	−	0.252242i
$199$	3.95878e6			0.502345			0.251172	−	0.967942i	$-0.419184\pi$
$199$	3.95878e6			0.502345			0.251172	+	0.967942i	$0.419184\pi$
$200$	1.09165e6	−	630265.i	0.136456	−	0.0787831i
$201$	4.37273e6	+	5.34984e6i	0.538473	+	0.658799i
$202$	1.90257e6	−	3.29535e6i	0.230827	−	0.399805i
$203$	−7.72627e6	−	4.46077e6i	−0.923596	−	0.533238i
$204$	−1.38057e7	+	1.12841e7i	−1.62617	+	1.32916i
$205$	−4.95540e6	−	8.58300e6i	−0.575198	−	0.996272i
$206$			3.62788e6i			0.415003i
$207$	158986.	+	474553.i	0.0179246	+	0.0535024i
$208$	1.08233e7			1.20273
$209$	3.98596e6	−	2.30129e6i	0.436610	−	0.252077i
$210$	−1.16333e7	+	1.89691e6i	−1.25617	+	0.204828i
$211$	−4.70148e6	+	8.14320e6i	−0.500481	+	0.866858i	0.499519	+	0.866303i	$0.333510\pi$
$211$	−4.70148e6	+	8.14320e6i	−0.500481	+	0.866858i	−1.00000		0.000555034i	$0.999823\pi$
$212$	4.69558e6	+	2.71099e6i	0.492812	+	0.284525i
$213$	6.81353e6	+	2.57991e6i	0.705071	+	0.266972i
$214$	−6.94490e6	−	1.20289e7i	−0.708639	−	1.22740i
$215$			1.51587e7i			1.52527i
$216$	−9.26393e6	−	1.75832e7i	−0.919251	−	1.74476i
$217$	715538.			0.0700251
$218$	1.46533e7	−	8.46010e6i	1.41438	−	0.816594i
$219$	5.27635e6	−	1.39348e7i	0.502344	−	1.32669i
$220$	−4.86242e6	+	8.42195e6i	−0.456651	+	0.790942i
$221$	8.17281e6	+	4.71857e6i	0.757172	+	0.437153i
$222$	1.05408e6	+	6.46442e6i	0.0963413	+	0.590841i
$223$	795234.	+	1.37739e6i	0.0717101	+	0.124205i	0.899651	−	0.436610i	$-0.143821\pi$
$223$	795234.	+	1.37739e6i	0.0717101	+	0.124205i	−0.827941	+	0.560816i	$0.810488\pi$
$224$		−	3.69452e6i		−	0.328711i
$225$	−181097.	+	891880.i	−0.0158988	+	0.0782995i
$226$	4.02630e6			0.348803
$227$	−6.81870e6	+	3.93678e6i	−0.582940	+	0.336561i	−0.762301	−	0.647223i	$-0.775930\pi$
$227$	−6.81870e6	+	3.93678e6i	−0.582940	+	0.336561i	0.179361	+	0.983783i	$0.442597\pi$
$228$	−1.78002e7	−	2.17778e7i	−1.50183	−	1.83743i
$229$	−1.97961e6	+	3.42878e6i	−0.164844	+	0.285518i	−0.936600	−	0.350401i	$-0.886045\pi$
$229$	−1.97961e6	+	3.42878e6i	−0.164844	+	0.285518i	0.771756	+	0.635919i	$0.219379\pi$
$230$	−1.00687e6	−	581319.i	−0.0827545	−	0.0477783i
$231$	−3.22594e6	+	2.63674e6i	−0.261710	+	0.213910i
$232$	1.74727e7	+	3.02636e7i	1.39925	+	2.42357i
$233$			2.89646e6i			0.228981i	0.993424	+	0.114491i	$0.0365236\pi$
$233$			2.89646e6i			0.228981i	−0.993424	+	0.114491i	$0.963476\pi$
$234$	−1.32041e7	+	1.49361e7i	−1.03053	+	1.16570i
$235$	9.97205e6			0.768388
$236$	−7.80618e6	+	4.50690e6i	−0.593885	+	0.342880i
$237$	1.89213e7	−	3.08527e6i	1.42136	−	0.231765i
$238$	8.87313e6	−	1.53687e7i	0.658182	−	1.14000i
$239$	576101.	+	332612.i	0.0421992	+	0.0243637i	0.520951	−	0.853586i	$-0.325577\pi$
$239$	576101.	+	332612.i	0.0421992	+	0.0243637i	−0.478752	+	0.877950i	$0.658911\pi$
$240$	1.69244e7	+	6.40835e6i	1.22428	+	0.463567i
$241$	−413009.	−	715353.i	−0.0295059	−	0.0511057i	0.850895	−	0.525335i	$-0.176060\pi$
$241$	−413009.	−	715353.i	−0.0295059	−	0.0511057i	−0.880401	+	0.474229i	$0.842727\pi$
$242$		−	1.99604e7i		−	1.40839i
$243$	1.39410e7	+	3.39711e6i	0.971571	+	0.236750i
$244$	−5.00393e7			−3.44462
$245$	−5.31632e6	+	3.06938e6i	−0.361504	+	0.208714i
$246$	−1.11620e7	+	2.94788e7i	−0.749787	+	1.98018i
$247$	−7.44334e6	+	1.28922e7i	−0.493943	+	0.855535i
$248$	−2.42724e6	−	1.40137e6i	−0.159132	−	0.0918751i
$249$	−1.51330e6	−	9.28077e6i	−0.0980231	−	0.601154i
$250$	−1.42876e7	−	2.47469e7i	−0.914409	−	1.58380i
$251$		−	1.12048e7i		−	0.708568i	−0.935138	−	0.354284i	$-0.884725\pi$
$251$		−	1.12048e7i		−	0.708568i	0.935138	−	0.354284i	$-0.115275\pi$
$252$	1.90760e7	+	1.68639e7i	1.19203	+	1.05380i
$253$	−410965.			−0.0253772
$254$	−4.40156e6	+	2.54124e6i	−0.268600	+	0.155076i
$255$	9.98600e6	+	1.22175e7i	0.602242	+	0.736818i
$256$	1.70008e7	−	2.94463e7i	1.01333	−	1.75514i
$257$	−6.71894e6	−	3.87918e6i	−0.395823	−	0.228529i	0.288857	−	0.957372i	$-0.406725\pi$
$257$	−6.71894e6	−	3.87918e6i	−0.395823	−	0.228529i	−0.684680	+	0.728844i	$0.740058\pi$
$258$	3.73293e7	−	3.05113e7i	2.17366	−	1.77665i
$259$	−2.21373e6	−	3.83429e6i	−0.127416	−	0.220692i
$260$		−	3.14542e7i		−	1.78961i
$261$	−2.47254e7	−	5.02051e6i	−1.39066	−	0.282375i
$262$	2.02411e7			1.12546
$263$	−1.56666e7	+	9.04514e6i	−0.861209	+	0.497219i	−0.864417	−	0.502776i	$-0.832312\pi$
$263$	−1.56666e7	+	9.04514e6i	−0.861209	+	0.497219i	0.00320789	+	0.999995i	$0.498979\pi$
$264$	1.61070e7	−	2.62638e6i	0.875394	−	0.142740i
$265$	2.39912e6	−	4.15539e6i	0.128918	−	0.223293i
$266$	2.42435e7	+	1.39970e7i	1.28810	+	0.743685i
$267$	−2.11120e7	−	7.99397e6i	−1.10916	−	0.419980i
$268$	1.73364e7	+	3.00276e7i	0.900648	+	1.55997i
$269$		−	2.74843e7i		−	1.41198i	−0.708222	−	0.705990i	$-0.750502\pi$
$269$		−	2.74843e7i		−	1.41198i	0.708222	−	0.705990i	$-0.249498\pi$
$270$	−2.94907e7	+	1.55375e7i	−1.49828	+	0.789389i
$271$	3.70982e6			0.186400			0.0931999	−	0.995647i	$-0.470290\pi$
$271$	3.70982e6			0.186400			0.0931999	+	0.995647i	$0.470290\pi$
$272$	−2.35962e7	+	1.36232e7i	−1.17256	+	0.676977i
$273$	4.77198e6	−	1.26028e7i	0.234537	−	0.619409i
$274$	−2.74497e7	+	4.75443e7i	−1.33440	+	2.31125i
$275$	−647190.	−	373655.i	−0.0311196	−	0.0179669i
$276$	404175.	+	2.47872e6i	0.0192239	+	0.117896i
$277$	1.29022e7	+	2.23472e7i	0.607049	+	1.05144i	0.991724	+	0.128387i	$0.0409801\pi$
$277$	1.29022e7	+	2.23472e7i	0.607049	+	1.05144i	−0.384675	+	0.923052i	$0.625687\pi$
$278$			7.17489e7i			3.33950i
$279$	1.91871e6	−	642815.i	0.0883482	−	0.0295987i
$280$	−3.12090e7			−1.42169
$281$	1.85887e7	−	1.07322e7i	0.837781	−	0.483693i	−0.0187281	−	0.999825i	$-0.505962\pi$
$281$	1.85887e7	−	1.07322e7i	0.837781	−	0.483693i	0.856509	+	0.516131i	$0.172628\pi$
$282$	−2.00717e7	−	2.45568e7i	−0.895027	−	1.09503i
$283$	4.29799e6	−	7.44434e6i	0.189630	−	0.328448i	−0.755497	−	0.655152i	$-0.772605\pi$
$283$	4.29799e6	−	7.44434e6i	0.189630	−	0.328448i	0.945127	+	0.326704i	$0.105938\pi$
$284$	3.16620e7	+	1.82800e7i	1.38224	+	0.798035i
$285$	−1.92725e7	+	1.57525e7i	−0.832537	+	0.680478i
$286$	−8.18509e6	−	1.41770e7i	−0.349885	−	0.606019i
$287$		−	2.13074e7i		−	0.901334i
$288$	−3.31903e6	−	9.90684e6i	−0.138942	−	0.414722i
$289$	380565.			0.0157665
$290$	5.07583e7	−	2.93053e7i	2.08120	−	1.20158i
$291$	−2.50568e6	+	408571.i	−0.101683	+	0.0165802i
$292$	3.73857e7	−	6.47540e7i	1.50161	−	2.60086i
$293$	−2.62704e6	−	1.51672e6i	−0.104439	−	0.0602980i	0.446871	−	0.894599i	$-0.352538\pi$
$293$	−2.62704e6	−	1.51672e6i	−0.104439	−	0.0602980i	−0.551310	+	0.834301i	$0.685872\pi$
$294$	1.82592e7	+	6.91378e6i	0.718522	+	0.272065i
$295$	3.98842e6	+	6.90815e6i	0.155359	+	0.269089i
$296$			1.73422e7i			0.668697i
$297$	−6.28159e6	+	9.96848e6i	−0.239773	+	0.380504i
$298$	1.37412e7			0.519249
$299$	1.15115e6	−	664617.i	0.0430644	−	0.0248632i
$300$	−1.61719e6	+	4.27097e6i	−0.0598958	+	0.158184i
$301$	−1.62950e7	+	2.82238e7i	−0.597523	+	1.03494i
$302$	−7.66693e7	−	4.42651e7i	−2.78356	−	1.60709i
$303$	1.17063e6	+	7.17922e6i	0.0420815	+	0.258077i
$304$	−2.14901e7	−	3.72219e7i	−0.764922	−	1.32488i
$305$			4.42827e7i			1.56076i
$306$	9.98655e6	−	4.91824e7i	0.348539	−	1.71651i
$307$	1.14414e7			0.395426			0.197713	−	0.980260i	$-0.436649\pi$
$307$	1.14414e7			0.395426			0.197713	+	0.980260i	$0.436649\pi$
$308$	−1.81065e7	+	1.04538e7i	−0.619703	+	0.357786i
$309$	−4.38895e6	−	5.36970e6i	−0.148760	−	0.182001i
$310$	−2.35039e6	+	4.07100e6i	−0.0788960	+	0.136652i
$311$	2.38167e7	+	1.37506e7i	0.791771	+	0.457129i	0.840586	−	0.541679i	$-0.182211\pi$
$311$	2.38167e7	+	1.37506e7i	0.791771	+	0.457129i	−0.0488146	+	0.998808i	$0.515544\pi$
$312$	−4.08698e7	+	3.34051e7i	−1.34567	+	1.09989i
$313$	−1.26080e7	−	2.18377e7i	−0.411163	−	0.712155i	0.583854	−	0.811858i	$-0.301544\pi$
$313$	−1.26080e7	−	2.18377e7i	−0.411163	−	0.712155i	−0.995017	+	0.0997035i	$0.968211\pi$
$314$			2.35076e7i			0.759311i
$315$	1.49239e7	−	1.68815e7i	0.477475	−	0.540106i
$316$	9.62032e7			3.04880
$317$	−2.38960e7	+	1.37964e7i	−0.750150	+	0.433099i	−0.825748	−	0.564039i	$-0.809247\pi$
$317$	−2.38960e7	+	1.37964e7i	−0.750150	+	0.433099i	0.0755979	+	0.997138i	$0.475913\pi$
$318$	−1.50619e7	+	2.45596e6i	−0.468379	+	0.0763730i
$319$	1.03587e7	−	1.79419e7i	0.319106	−	0.552708i
$320$	−1.61299e7	−	9.31260e6i	−0.492245	−	0.284198i
$321$	2.48317e7	+	9.40241e6i	0.750743	+	0.284266i
$322$	−1.24979e6	−	2.16470e6i	−0.0374343	−	0.0648381i
$323$		−	3.74756e7i		−	1.11209i
$324$	6.63022e7	+	2.80834e7i	1.94936	+	0.825684i
$325$	2.41711e6			0.0704120
$326$	−3.02488e7	+	1.74642e7i	−0.873083	+	0.504075i
$327$	−1.14538e7	+	3.02493e7i	−0.327571	+	0.865112i
$328$	−4.17303e7	+	7.22790e7i	−1.18258	+	2.04829i
$329$	1.85668e7	+	1.07196e7i	0.521375	+	0.301016i
$330$	−4.40499e6	−	2.70149e7i	−0.122575	−	0.751728i
$331$	−2.48940e7	−	4.31176e7i	−0.686452	−	1.18897i	−0.972978	−	0.230897i	$-0.925834\pi$
$331$	−2.48940e7	−	4.31176e7i	−0.686452	−	1.18897i	0.286527	−	0.958072i	$-0.407499\pi$
$332$		−	4.71871e7i		−	1.28946i
$333$	−9.38070e6	−	8.29291e6i	−0.254040	−	0.224582i
$334$	−8.16191e7			−2.19055
$335$	2.65732e7	−	1.53420e7i	0.706820	−	0.408083i
$336$	2.46226e7	+	3.01247e7i	0.649106	+	0.794154i
$337$	1.25640e7	−	2.17615e7i	0.328275	−	0.568589i	−0.653895	−	0.756586i	$-0.726866\pi$
$337$	1.25640e7	−	2.17615e7i	0.328275	−	0.568589i	0.982170	+	0.187997i	$0.0601994\pi$
$338$	−1.31863e7	−	7.61311e6i	−0.341486	−	0.197157i
$339$	−5.95940e6	+	4.87095e6i	−0.152969	+	0.125030i
$340$	3.95912e7	+	6.85740e7i	1.00731	+	1.74471i
$341$			1.66162e6i			0.0419052i
$342$	7.75831e7	+	1.57533e7i	1.93950	+	0.393817i
$343$	−4.35255e7			−1.07860
$344$	1.10552e8	−	6.38270e7i	2.71575	−	1.56794i
$345$	2.19356e6	−	357678.i	0.0534187	−	0.00871034i
$346$	−5.54751e7	+	9.60857e7i	−1.33927	+	2.31969i
$347$	6.77305e7	+	3.91042e7i	1.62105	+	0.935912i	0.986640	+	0.162914i	$0.0520892\pi$
$347$	6.77305e7	+	3.91042e7i	1.62105	+	0.935912i	0.634408	+	0.772999i	$0.281244\pi$
$348$	−1.18403e8	−	4.48329e7i	−2.80948	−	1.06380i
$349$	1.64391e6	+	2.84733e6i	0.0386724	+	0.0669826i	0.884714	−	0.466135i	$-0.154354\pi$
$349$	1.64391e6	+	2.84733e6i	0.0386724	+	0.0669826i	−0.846041	+	0.533117i	$0.821020\pi$
$350$		−	4.54530e6i		−	0.106013i
$351$	1.47418e6	−	3.80812e7i	0.0340901	−	0.880622i
$352$	8.57938e6			0.196711
$353$	−5.41484e7	+	3.12626e7i	−1.23101	+	0.710724i	−0.967241	−	0.253861i	$-0.918299\pi$
$353$	−5.41484e7	+	3.12626e7i	−1.23101	+	0.710724i	−0.263770	+	0.964586i	$0.584966\pi$
$354$	8.98392e6	−	2.37264e7i	0.202514	−	0.534839i
$355$	1.61771e7	−	2.80195e7i	0.361589	−	0.626290i
$356$	−9.81060e7	−	5.66415e7i	−2.17443	−	1.25541i
$357$	5.45952e6	+	3.34821e7i	0.119991	+	0.735881i
$358$	1.21400e7	+	2.10271e7i	0.264588	+	0.458279i
$359$			2.74347e7i			0.592949i	0.955041	+	0.296475i	$0.0958110\pi$
$359$			2.74347e7i			0.592949i	−0.955041	+	0.296475i	$0.904189\pi$
$360$	−8.36868e7	+	2.80371e7i	−1.79370	+	0.600932i
$361$	1.20703e7			0.256564
$362$	5.09160e7	−	2.93964e7i	1.07332	−	0.619680i
$363$	2.41478e7	+	2.95438e7i	0.504844	+	0.617655i
$364$	3.38120e7	−	5.85641e7i	0.701078	−	1.21430i
$365$	−5.73046e7	−	3.30848e7i	−1.17845	−	0.680378i
$366$	1.09049e8	−	8.91320e7i	2.22423	−	1.81799i
$367$	2.15329e7	+	3.72960e7i	0.435616	+	0.754509i	0.997346	−	0.0728120i	$-0.0231973\pi$
$367$	2.15329e7	+	3.72960e7i	0.435616	+	0.754509i	−0.561730	+	0.827321i	$0.689864\pi$
$368$			3.83770e6i			0.0770066i
$369$	−1.91419e7	−	5.71358e7i	−0.380983	−	1.13718i
$370$	2.90865e7			0.574231
$371$	8.93377e6	−	5.15791e6i	0.174950	−	0.101007i
$372$	1.00220e7	−	1.63416e6i	0.194681	−	0.0317443i
$373$	1.92734e7	−	3.33826e7i	0.371392	−	0.643270i	−0.618388	−	0.785873i	$-0.712214\pi$
$373$	1.92734e7	−	3.33826e7i	0.371392	−	0.643270i	0.989780	+	0.142603i	$0.0455472\pi$
$374$	3.56891e7	+	2.06051e7i	0.682214	+	0.393876i
$375$	5.10858e7	+	1.93434e7i	0.968739	+	0.366809i
$376$	−4.19882e7	−	7.27257e7i	−0.789884	−	1.36812i
$377$			6.70090e7i			1.25057i
$378$	−7.16105e7	−	2.77214e6i	−1.32587	−	0.0513263i
$379$	−6.90700e7			−1.26874			−0.634369	−	0.773030i	$-0.718740\pi$
$379$	−6.90700e7			−1.26874			−0.634369	+	0.773030i	$0.718740\pi$
$380$	−1.08173e8	+	6.24534e7i	−1.97136	+	1.13817i
$381$	3.44048e6	−	9.08628e6i	0.0622077	−	0.164290i
$382$	6.00096e7	−	1.03940e8i	1.07654	−	1.86463i
$383$	1.05696e7	+	6.10238e6i	0.188132	+	0.108618i	0.591108	−	0.806592i	$-0.298691\pi$
$383$	1.05696e7	+	6.10238e6i	0.188132	+	0.108618i	−0.402976	+	0.915211i	$0.632024\pi$
$384$	1.35189e7	+	8.29082e7i	0.238752	+	1.46421i
$385$	9.25120e6	+	1.60235e7i	0.162112	+	0.280787i
$386$			5.62636e7i			0.978285i
$387$	−1.83397e7	+	9.03208e7i	−0.316417	+	1.55831i
$388$	−1.27399e7			−0.218107
$389$	4.23039e7	−	2.44242e7i	0.718674	−	0.414926i	−0.0955907	−	0.995421i	$-0.530474\pi$
$389$	4.23039e7	−	2.44242e7i	0.718674	−	0.414926i	0.814264	+	0.580494i	$0.197141\pi$
$390$	5.60274e7	+	6.85471e7i	0.944510	+	1.15557i
$391$	−1.67310e6	+	2.89790e6i	−0.0279893	+	0.0484789i
$392$	4.47697e7	+	2.58478e7i	0.743235	+	0.429107i
$393$	−2.99593e7	+	2.44874e7i	−0.493575	+	0.403427i
$394$	3.85098e7	+	6.67010e7i	0.629626	+	1.09054i
$395$		−	8.51359e7i		−	1.38141i
$396$	−3.91613e7	+	4.42982e7i	−0.630625	+	0.713346i
$397$	−1.99924e7			−0.319516			−0.159758	−	0.987156i	$-0.551071\pi$
$397$	−1.99924e7			−0.319516			−0.159758	+	0.987156i	$0.551071\pi$
$398$	−4.84230e7	+	2.79570e7i	−0.768073	+	0.443447i
$399$	−5.28165e7	+	8.61216e6i	−0.831479	+	0.135579i
$400$	−3.48929e6	+	6.04362e6i	−0.0545201	+	0.0944316i
$401$	−3.74023e7	−	2.15942e7i	−0.580049	−	0.334892i	0.181104	−	0.983464i	$-0.442033\pi$
$401$	−3.74023e7	−	2.15942e7i	−0.580049	−	0.334892i	−0.761153	+	0.648572i	$0.775366\pi$
$402$	−9.12671e7	−	3.45579e7i	−1.40487	−	0.531948i
$403$	−2.68718e6	−	4.65433e6i	−0.0410565	−	0.0711119i
$404$			3.65020e7i			0.553570i
$405$	2.48526e7	−	5.86747e7i	0.374117	−	0.883255i
$406$	1.26008e8			1.88287
$407$	8.90396e6	−	5.14071e6i	0.132069	−	0.0762499i
$408$	4.70544e7	−	1.24270e8i	0.692818	−	1.82973i
$409$	1.84954e7	−	3.20349e7i	0.270329	−	0.468224i	−0.698617	−	0.715496i	$-0.746201\pi$
$409$	1.84954e7	−	3.20349e7i	0.270329	−	0.468224i	0.968946	+	0.247272i	$0.0795341\pi$
$410$	1.21227e8	+	6.99904e7i	1.75893	+	1.01552i
$411$	−1.68895e7	−	1.03579e8i	−0.243271	−	1.49193i
$412$	−1.74008e7	−	3.01390e7i	−0.248815	−	0.430960i
$413$			1.71496e7i			0.243447i
$414$	−5.29600e6	−	4.68187e6i	−0.0746357	−	0.0659809i
$415$	−4.17586e7			−0.584255
$416$	−2.40316e7	+	1.38746e7i	−0.333812	+	0.192727i
$417$	−8.68007e7	−	1.06197e8i	−1.19706	−	1.46455i
$418$	−3.25036e7	+	5.62979e7i	−0.445044	+	0.770839i
$419$	−2.11639e7	−	1.22190e7i	−0.287709	−	0.166109i	0.349199	−	0.937049i	$-0.386454\pi$
$419$	−2.11639e7	−	1.22190e7i	−0.287709	−	0.166109i	−0.636908	+	0.770939i	$0.719787\pi$
$420$	8.75469e7	−	7.15569e7i	1.18166	−	0.965837i
$421$	5.26175e7	+	9.11362e7i	0.705154	+	1.22136i	0.966636	+	0.256154i	$0.0824554\pi$
$421$	5.26175e7	+	9.11362e7i	0.705154	+	1.22136i	−0.261482	+	0.965208i	$0.584211\pi$
$422$		−	1.32808e8i		−	1.76721i
$423$	5.94169e7	+	1.20647e7i	0.785035	+	0.159402i
$424$	−4.04068e7			−0.530099
$425$	−5.26961e6	+	3.04241e6i	−0.0686454	+	0.0396325i
$426$	−1.01561e8	+	1.65604e7i	−1.31371	+	0.214211i
$427$	−4.76022e7	+	8.24495e7i	−0.611426	+	1.05902i
$428$	1.15391e8	+	6.66210e7i	1.47177	+	0.849728i
$429$	2.92660e7	+	1.10815e7i	0.370674	+	0.140354i
$430$	−1.07051e8	−	1.85418e8i	−1.34644	−	2.33210i
$431$		−	1.45082e8i		−	1.81210i	−0.423166	−	0.906052i	$-0.639081\pi$
$431$		−	1.45082e8i		−	1.81210i	0.423166	−	0.906052i	$-0.360919\pi$
$432$	9.30883e7	+	5.86591e7i	1.15463	+	0.727586i
$433$	1.53388e8			1.88941			0.944706	−	0.327920i	$-0.106347\pi$
$433$	1.53388e8			1.88941			0.944706	+	0.327920i	$0.106347\pi$
$434$	−8.75232e6	+	5.05316e6i	−0.107067	+	0.0618150i
$435$	−3.96752e7	+	1.04782e8i	−0.482005	+	1.27297i
$436$	−8.11561e7	+	1.40566e8i	−0.979178	+	1.69599i
$437$	−4.57130e6	−	2.63924e6i	−0.0547767	−	0.0316253i
$438$	3.38687e7	+	2.07709e8i	0.403066	+	2.47192i
$439$	−2.50547e6	−	4.33960e6i	−0.0296139	−	0.0512928i	0.850839	−	0.525427i	$-0.176094\pi$
$439$	−2.50547e6	−	4.33960e6i	−0.0296139	−	0.0512928i	−0.880453	+	0.474134i	$0.842761\pi$
$440$		−	7.24733e7i		−	0.850785i
$441$	−3.53900e7	+	1.18565e7i	−0.412634	+	0.138242i
$442$	−1.33291e8			−1.54360
$443$	−5.63189e7	+	3.25157e7i	−0.647803	+	0.374009i	−0.787614	−	0.616169i	$-0.788684\pi$
$443$	−5.63189e7	+	3.25157e7i	−0.647803	+	0.374009i	0.139811	+	0.990178i	$0.455350\pi$
$444$	−3.97628e7	−	4.86481e7i	−0.454284	−	0.555797i
$445$	−5.01254e7	+	8.68197e7i	−0.568824	+	0.985232i
$446$	−1.94543e7	−	1.12319e7i	−0.219286	−	0.126605i
$447$	−2.03386e7	+	1.66239e7i	−0.227719	+	0.186127i
$448$	−2.00214e7	−	3.46780e7i	−0.222669	−	0.385674i
$449$			7.25149e7i			0.801103i	0.916274	+	0.400551i	$0.131181\pi$
$449$			7.25149e7i			0.801103i	−0.916274	+	0.400551i	$0.868819\pi$
$450$	−4.08334e6	−	1.21882e7i	−0.0448103	−	0.133753i
$451$	4.94800e7			0.539386
$452$	−3.34489e7	+	1.93117e7i	−0.362215	+	0.209125i
$453$	1.67031e8	−	2.72358e7i	1.79681	−	0.292985i
$454$	5.56033e7	−	9.63078e7i	0.594201	−	1.02919i
$455$	−5.18268e7	−	2.99222e7i	−0.550200	−	0.317658i
$456$	1.96031e8	+	7.42262e7i	2.06742	+	0.782821i
$457$	2.85809e7	+	4.95036e7i	0.299452	+	0.518667i	0.976011	−	0.217722i	$-0.0698627\pi$
$457$	2.85809e7	+	4.95036e7i	0.299452	+	0.518667i	−0.676558	+	0.736389i	$0.736529\pi$
$458$		−	5.59202e7i		−	0.582066i
$459$	4.47188e7	+	8.48774e7i	0.462437	+	0.877716i
$460$	1.11529e7			0.114582
$461$	1.35879e8	−	7.84499e7i	1.38692	−	0.800736i	0.393950	−	0.919132i	$-0.371108\pi$
$461$	1.35879e8	−	7.84499e7i	1.38692	−	0.800736i	0.992966	+	0.118396i	$0.0377751\pi$
$462$	2.08383e7	−	5.50338e7i	0.211318	−	0.558089i
$463$	4.63223e7	−	8.02325e7i	0.466710	−	0.808365i	−0.532567	−	0.846388i	$-0.678773\pi$
$463$	4.63223e7	−	8.02325e7i	0.466710	−	0.808365i	0.999277	+	0.0380229i	$0.0121060\pi$
$464$	−1.67546e8	−	9.67327e7i	−1.67718	−	0.968321i
$465$	−1.44617e6	−	8.86902e6i	−0.0143833	−	0.0882098i
$466$	−2.04549e7	−	3.54289e7i	−0.202134	−	0.350107i
$467$			1.48541e8i			1.45846i	0.684269	+	0.729230i	$0.260122\pi$
$467$			1.48541e8i			1.45846i	−0.684269	+	0.729230i	$0.739878\pi$
$468$	3.80548e7	−	1.87415e8i	0.371255	−	1.82838i
$469$	6.59683e7			0.639465
$470$	−1.21976e8	+	7.04229e7i	−1.17485	+	0.678298i
$471$	−2.84392e7	−	3.47941e7i	−0.272179	−	0.332999i
$472$	3.35872e7	−	5.81748e7i	0.319410	−	0.553234i
$473$	−6.55410e7	−	3.78401e7i	−0.619340	−	0.357576i
$474$	−2.09653e8	+	1.71361e8i	−1.96864	+	1.60908i
$475$	−4.79927e6	−	8.31258e6i	−0.0447811	−	0.0775631i
$476$			1.70236e8i			1.57845i
$477$	1.93222e7	−	2.18567e7i	0.178033	−	0.201386i
$478$	−9.39567e6			−0.0860288
$479$	−9.81933e7	+	5.66919e7i	−0.893460	+	0.515839i	−0.875073	−	0.483992i	$-0.839187\pi$
$479$	−9.81933e7	+	5.66919e7i	−0.893460	+	0.515839i	−0.0183874	+	0.999831i	$0.505853\pi$
$480$	−4.57932e7	+	7.46695e6i	−0.414073	+	0.0675180i
$481$	−1.66272e7	+	2.87991e7i	−0.149411	+	0.258788i
$482$	1.01037e7	+	5.83337e6i	0.0902275	+	0.0520929i
$483$	4.46866e6	+	1.69204e6i	0.0396585	+	0.0150165i
$484$	9.57380e7	+	1.65823e8i	0.844400	+	1.46254i
$485$			1.12743e7i			0.0988241i
$486$	−1.94514e8	+	5.68989e7i	−1.69450	+	0.495673i
$487$	−1.72741e8			−1.49558			−0.747789	−	0.663937i	$-0.768884\pi$
$487$	−1.72741e8			−1.49558			−0.747789	+	0.663937i	$0.768884\pi$
$488$	3.22952e8	−	1.86456e8i	2.77894	−	1.60442i
$489$	2.36440e7	−	6.24436e7i	0.202206	−	0.534025i
$490$	4.33521e7	−	7.50881e7i	0.368487	−	0.638238i
$491$	1.40807e8	+	8.12949e7i	1.18954	+	0.686782i	0.958202	−	0.286092i	$-0.0923562\pi$
$491$	1.40807e8	+	8.12949e7i	1.18954	+	0.686782i	0.231339	+	0.972873i	$0.425689\pi$
$492$	−4.86624e7	−	2.98436e8i	−0.408600	−	2.50585i
$493$	−8.43440e7	−	1.46088e8i	−0.703904	−	1.21920i
$494$		−	2.10260e8i		−	1.74412i
$495$	3.92020e7	+	3.46561e7i	0.323216	+	0.285736i
$496$	1.55166e7			0.127160
$497$	6.02398e7	−	3.47795e7i	0.490698	−	0.283305i
$498$	8.40515e7	+	1.02834e8i	0.680546	+	0.832620i
$499$	−5.94818e7	+	1.03026e8i	−0.478721	+	0.829169i	−0.999702	−	0.0243990i	$-0.992233\pi$
$499$	−5.94818e7	+	1.03026e8i	−0.478721	+	0.829169i	0.520981	+	0.853568i	$0.325566\pi$
$500$	2.37392e8	+	1.37058e8i	1.89914	+	1.09647i
$501$	1.20806e8	−	9.87415e7i	0.960673	−	0.785211i
$502$	7.91285e7	+	1.37055e8i	0.625492	+	1.08338i
$503$		−	5.21107e7i		−	0.409471i	−0.978817	−	0.204736i	$-0.934367\pi$
$503$		−	5.21107e7i		−	0.409471i	0.978817	−	0.204736i	$-0.0656334\pi$
$504$	−1.85954e8	−	3.77582e7i	−1.45249	−	0.294931i
$505$	3.23028e7			0.250822
$506$	5.02685e6	−	2.90225e6i	0.0388011	−	0.0224018i
$507$	2.87275e7	−	4.68425e6i	0.220432	−	0.0359432i
$508$	2.43776e7	−	4.22233e7i	0.185952	−	0.322078i
$509$	−1.99506e8	−	1.15185e8i	−1.51287	−	0.873458i	−0.999887	−	0.0150611i	$-0.995206\pi$
$509$	−1.99506e8	−	1.15185e8i	−1.51287	−	0.873458i	−0.512987	−	0.858397i	$-0.671461\pi$
$510$	−2.08427e8	−	7.89200e7i	−1.57124	−	0.594944i
$511$	−7.11298e7	−	1.23200e8i	−0.533076	−	0.923314i
$512$			2.81123e8i			2.09453i
$513$	−1.33890e8	+	7.05420e7i	−0.991739	+	0.522511i
$514$	1.09580e8			0.806938
$515$	−2.66718e7	+	1.53990e7i	−0.195268	+	0.112738i
$516$	−1.63773e8	+	4.32522e8i	−1.19204	+	3.14818i
$517$	−2.48929e7	+	4.31157e7i	−0.180137	+	0.312007i
$518$	5.41558e7	+	3.12669e7i	0.389633	+	0.224955i
$519$	−3.41331e7	−	2.09331e8i	−0.244160	−	1.49738i
$520$	1.17204e8	+	2.03004e8i	0.833554	+	1.44376i
$521$			2.01324e8i			1.42358i	0.702392	+	0.711790i	$0.252115\pi$
$521$			2.01324e8i			1.42358i	−0.702392	+	0.711790i	$0.747885\pi$
$522$	3.37891e8	−	1.13201e8i	2.37555	−	0.795867i
$523$	1.15112e8			0.804669			0.402334	−	0.915493i	$-0.368199\pi$
$523$	1.15112e8			0.804669			0.402334	+	0.915493i	$0.368199\pi$
$524$	−1.68155e8	+	9.70844e7i	−1.16874	+	0.674770i
$525$	5.49883e6	+	6.72759e6i	0.0380008	+	0.0464924i
$526$	1.27754e8	−	2.21277e8i	0.877845	−	1.52047i
$527$	1.17168e7	+	6.76469e6i	0.0800528	+	0.0462185i
$528$	−6.99552e7	+	5.71783e7i	−0.475246	+	0.388445i
$529$	−7.37823e7	−	1.27795e8i	−0.498408	−	0.863268i
$530$			6.77706e7i			0.455212i
$531$	1.54066e7	+	4.59866e7i	0.102902	+	0.307148i
$532$	−2.68540e8			−1.78350
$533$	−1.38598e8	+	8.00194e7i	−0.915323	+	0.528462i
$534$	3.14692e8	−	5.13130e7i	2.06662	−	0.336980i
$535$	5.89569e7	−	1.02116e8i	0.385011	−	0.666859i
$536$	−2.23777e8	−	1.29198e8i	−1.45319	−	0.838998i
$537$	−4.34069e7	−	1.64358e7i	−0.280308	−	0.106138i
$538$	1.94095e8	+	3.36183e8i	1.24643	+	2.15888i
$539$		−	3.06480e7i		−	0.195720i
$540$	1.70472e8	−	2.70529e8i	1.08261	−	1.71804i
$541$	−1.95684e8			−1.23584			−0.617921	−	0.786241i	$-0.712025\pi$
$541$	−1.95684e8			−1.23584			−0.617921	+	0.786241i	$0.712025\pi$
$542$	−4.53778e7	+	2.61989e7i	−0.285001	+	0.164545i
$543$	−3.97985e7	+	1.05107e8i	−0.248581	+	0.656499i
$544$	3.49279e7	−	6.04969e7i	0.216958	−	0.375783i
$545$	1.24396e8	+	7.18198e7i	0.768449	+	0.443664i
$546$	3.06312e7	+	1.87854e8i	0.188185	+	1.15410i
$547$	1.66519e7	+	2.88419e7i	0.101742	+	0.176222i	0.912402	−	0.409294i	$-0.134225\pi$
$547$	1.66519e7	+	2.88419e7i	0.101742	+	0.176222i	−0.810660	+	0.585517i	$0.800892\pi$
$548$		−	5.26639e8i		−	3.20016i
$549$	−5.35755e7	+	2.63852e8i	−0.323779	+	1.59457i
$550$	1.05551e7			0.0634414
$551$	2.30448e8	−	1.33049e8i	1.37758	−	0.795347i
$552$	−1.18447e7	−	1.44915e7i	−0.0704219	−	0.0861582i
$553$	9.15178e7	−	1.58513e8i	0.541166	−	0.937326i
$554$	−3.15634e8	−	1.82231e8i	−1.85632	−	1.07175i
$555$	−4.30515e7	+	3.51884e7i	−0.251831	+	0.205836i
$556$	−3.44136e8	−	5.96062e8i	−2.00219	−	3.46790i
$557$			2.14530e7i			0.124143i	0.998072	+	0.0620716i	$0.0197707\pi$
$557$			2.14530e7i			0.124143i	−0.998072	+	0.0620716i	$0.980229\pi$
$558$	−1.89297e7	+	2.14128e7i	−0.108954	+	0.123245i
$559$	2.44781e8			1.40134
$560$	1.49632e8	−	8.63901e7i	0.852041	−	0.491926i
$561$	−7.77518e7	+	1.26781e7i	−0.440374	+	0.0718066i
$562$	−1.51582e8	+	2.62548e8i	−0.853965	+	1.47911i
$563$	−5.21863e7	−	3.01297e7i	−0.292436	−	0.168838i	0.346604	−	0.938012i	$-0.387335\pi$
$563$	−5.21863e7	−	3.01297e7i	−0.292436	−	0.168838i	−0.639040	+	0.769174i	$0.720668\pi$
$564$	2.84532e8	+	1.07737e8i	1.58597	+	0.600519i
$565$	1.70901e7	+	2.96009e7i	0.0947543	+	0.164119i
$566$			1.21410e8i			0.669586i
$567$	1.09346e8	−	8.25302e7i	0.599864	−	0.452755i
$568$	−2.72460e8			−1.48682
$569$	2.39117e8	−	1.38054e8i	1.29800	−	0.749398i	0.317938	−	0.948112i	$-0.397010\pi$
$569$	2.39117e8	−	1.38054e8i	1.29800	−	0.749398i	0.980058	+	0.198714i	$0.0636764\pi$
$570$	1.24493e8	−	3.28784e8i	0.672233	−	1.77536i
$571$	−1.49346e8	+	2.58675e8i	−0.802204	+	1.38946i	0.115958	+	0.993254i	$0.463006\pi$
$571$	−1.49346e8	+	2.58675e8i	−0.802204	+	1.38946i	−0.918162	+	0.396205i	$0.870327\pi$
$572$	1.35997e8	+	7.85179e7i	0.726677	+	0.419547i
$573$	3.69232e7	+	2.26442e8i	0.196262	+	1.20363i
$574$	1.50474e8	+	2.60628e8i	0.795656	+	1.37812i
$575$			857055.i			0.00450822i
$576$	−8.48407e7	−	7.50025e7i	−0.443953	−	0.392472i
$577$	9.68320e7			0.504071			0.252035	−	0.967718i	$-0.418900\pi$
$577$	9.68320e7			0.504071			0.252035	+	0.967718i	$0.418900\pi$
$578$	−4.65499e6	+	2.68756e6i	−0.0241066	+	0.0139179i
$579$	−6.80668e7	−	8.32769e7i	−0.350671	−	0.429031i
$580$	−2.81120e8	+	4.86914e8i	−1.44081	+	2.49556i
$581$	−7.77499e7	−	4.48889e7i	−0.396435	−	0.228882i
$582$	2.77636e7	−	2.26928e7i	0.140834	−	0.115111i
$583$	1.19777e7	+	2.07459e7i	0.0604458	+	0.104695i
$584$			5.57226e8i			2.79765i
$585$	−1.65854e8	−	3.36769e7i	−0.828437	−	0.168215i
$586$	4.28446e7			0.212913
$587$	−8.25319e7	+	4.76498e7i	−0.408044	+	0.235585i	−0.689949	−	0.723858i	$-0.742367\pi$
$587$	−8.25319e7	+	4.76498e7i	−0.408044	+	0.235585i	0.281905	+	0.959442i	$0.409034\pi$
$588$	−1.84852e8	+	3.01416e7i	−0.909267	+	0.148263i
$589$	−1.06710e7	+	1.84827e7i	−0.0522227	+	0.0904523i
$590$	−9.75712e7	−	5.63328e7i	−0.475079	−	0.274287i
$591$	−1.37693e8	−	5.21368e7i	−0.667036	−	0.252570i
$592$	−4.80052e7	−	8.31475e7i	−0.231379	−	0.400760i
$593$		−	5.27042e7i		−	0.252744i	−0.991983	−	0.126372i	$-0.959667\pi$
$593$		−	5.27042e7i		−	0.252744i	0.991983	−	0.126372i	$-0.0403333\pi$
$594$	6.43744e6	−	1.66293e8i	0.0307152	−	0.793443i
$595$	1.50652e8			0.715194
$596$	−1.14156e8	+	6.59083e7i	−0.539215	+	0.311316i
$597$	3.78499e7	−	9.99611e7i	0.177886	−	0.469795i
$598$	−9.38709e6	+	1.62589e7i	−0.0438963	+	0.0760305i
$599$	2.56013e8	+	1.47809e8i	1.19119	+	0.687733i	0.958576	−	0.284836i	$-0.0919391\pi$
$599$	2.56013e8	+	1.47809e8i	1.19119	+	0.687733i	0.232613	+	0.972569i	$0.425272\pi$
$600$	−5.47723e6	−	3.35907e7i	−0.0253575	−	0.155512i
$601$	9.74992e7	+	1.68874e8i	0.449136	+	0.777926i	0.998330	−	0.0577686i	$-0.0183986\pi$
$601$	9.74992e7	+	1.68874e8i	0.449136	+	0.777926i	−0.549194	+	0.835695i	$0.685065\pi$
$602$		−	4.60303e8i		−	2.10986i
$603$	1.76894e8	−	5.92636e7i	0.806790	−	0.270294i
$604$	8.49252e8			3.85412
$605$	1.46747e8	−	8.47242e7i	0.662677	−	0.382597i
$606$	−6.50188e7	−	7.95478e7i	−0.292160	−	0.357446i
$607$	7.29203e7	−	1.26302e8i	0.326049	−	0.564733i	−0.655675	−	0.755043i	$-0.727616\pi$
$607$	7.29203e7	−	1.26302e8i	0.326049	−	0.564733i	0.981724	+	0.190310i	$0.0609493\pi$
$608$	9.54313e7	+	5.50973e7i	0.424600	+	0.245143i
$609$	−1.86507e8	+	1.52443e8i	−0.825741	+	0.674924i
$610$	−3.12726e8	−	5.41658e8i	−1.37776	−	2.38636i
$611$		−	1.61028e8i		−	0.705955i
$612$	1.52934e8	+	4.56488e8i	0.667191	+	1.99147i
$613$	−4.48295e8			−1.94618			−0.973089	−	0.230431i	$-0.925986\pi$
$613$	−4.48295e8			−1.94618			−0.973089	+	0.230431i	$0.925986\pi$
$614$	−1.39949e8	+	8.07997e7i	−0.604596	+	0.349064i
$615$	−2.64104e8	+	4.30642e7i	−1.13540	+	0.185136i
$616$	7.79060e7	−	1.34937e8i	0.333295	−	0.577284i
$617$	1.11067e8	+	6.41247e7i	0.472857	+	0.273004i	0.717435	−	0.696625i	$-0.245316\pi$
$617$	1.11067e8	+	6.41247e7i	0.472857	+	0.273004i	−0.244578	+	0.969630i	$0.578649\pi$
$618$	9.16058e7	+	3.46862e7i	0.388113	+	0.146957i
$619$	2.15337e6	+	3.72975e6i	0.00907919	+	0.0157256i	0.870529	−	0.492117i	$-0.163777\pi$
$619$	2.15337e6	+	3.72975e6i	0.00907919	+	0.0157256i	−0.861450	+	0.507842i	$0.830443\pi$
$620$		−	4.50936e7i		−	0.189208i
$621$	1.35028e7	+	522710.i	0.0563829	+	0.00218266i
$622$	−3.88427e8			−1.61413
$623$	−1.86656e8	+	1.07766e8i	−0.771929	+	0.445673i
$624$	1.03481e8	−	2.73294e8i	0.425901	−	1.12480i
$625$	1.11538e8	−	1.93189e8i	0.456860	−	0.791304i
$626$	3.08438e8	+	1.78077e8i	1.25732	+	0.725912i
$627$	−1.99991e7	−	1.22650e8i	−0.0811348	−	0.497582i
$628$	−1.12752e8	−	1.95292e8i	−0.455245	−	0.788508i
$629$		−	8.37143e7i		−	0.336394i
$630$	−6.33284e7	+	3.11884e8i	−0.253266	+	1.24730i
$631$	2.51870e6			0.0100251			0.00501255	−	0.999987i	$-0.498404\pi$
$631$	2.51870e6			0.0100251			0.00501255	+	0.999987i	$0.498404\pi$
$632$	−6.20892e8	+	3.58472e8i	−2.45960	+	1.42005i
$633$	1.60669e8	+	1.96572e8i	0.633463	+	0.775015i
$634$	1.94861e8	−	3.37509e8i	0.764641	−	1.32440i
$635$	−3.73659e7	−	2.15732e7i	−0.145933	−	0.0842545i
$636$	1.13348e8	−	9.26458e7i	0.440599	−	0.360126i
$637$	4.95641e7	+	8.58475e7i	0.191756	+	0.332131i
$638$			2.92615e8i			1.12677i
$639$	1.30288e8	−	1.47378e8i	0.499347	−	0.564847i
$640$	3.73044e8			1.42305
$641$	−1.94736e8	+	1.12431e8i	−0.739387	+	0.426885i	−0.821846	−	0.569709i	$-0.807056\pi$
$641$	−1.94736e8	+	1.12431e8i	−0.739387	+	0.426885i	0.0824597	+	0.996594i	$0.473722\pi$
$642$	−3.70136e8	+	6.03537e7i	−1.39880	+	0.228086i
$643$	1.85392e8	−	3.21108e8i	0.697360	−	1.20786i	−0.272018	−	0.962292i	$-0.587691\pi$
$643$	1.85392e8	−	3.21108e8i	0.697360	−	1.20786i	0.969378	−	0.245572i	$-0.0789756\pi$
$644$	2.07655e7	+	1.19890e7i	0.0777473	+	0.0448874i
$645$	3.82764e8	+	1.44932e8i	1.42644	+	0.540114i
$646$	2.64654e8	+	4.58394e8i	0.981705	+	1.70036i
$647$		−	1.34128e8i		−	0.495230i	−0.968858	−	0.247615i	$-0.920353\pi$
$647$		−	1.34128e8i		−	0.495230i	0.968858	−	0.247615i	$-0.0796468\pi$
$648$	−5.32556e8	+	6.58063e7i	−1.95722	+	0.241848i
$649$	−3.98246e7			−0.145686
$650$	−2.95656e7	+	1.70697e7i	−0.107658	+	0.0621565i
$651$	6.84126e6	−	1.80677e7i	0.0247967	−	0.0654877i
$652$	1.67530e8	−	2.90171e8i	0.604436	−	1.04691i
$653$	−1.53586e8	−	8.86727e7i	−0.551583	−	0.318457i	0.198177	−	0.980166i	$-0.436498\pi$
$653$	−1.53586e8	−	8.86727e7i	−0.551583	−	0.318457i	−0.749760	+	0.661710i	$0.769831\pi$
$654$	−7.35214e7	−	4.50891e8i	−0.262833	−	1.61190i
$655$	8.59157e7	+	1.48810e8i	0.305738	+	0.529553i
$656$		−	4.62057e8i		−	1.63676i
$657$	−3.01413e8	−	2.66461e8i	−1.06284	−	0.939588i
$658$	−3.02808e8			−1.06289
$659$	−1.53754e8	+	8.87701e7i	−0.537243	+	0.310177i	−0.743961	−	0.668223i	$-0.767055\pi$
$659$	−1.53754e8	+	8.87701e7i	−0.537243	+	0.310177i	0.206718	+	0.978401i	$0.433722\pi$
$660$	1.66169e8	+	2.03301e8i	0.577987	+	0.707142i
$661$	−2.74792e8	+	4.75953e8i	−0.951479	+	1.64801i	−0.209251	+	0.977862i	$0.567103\pi$
$661$	−2.74792e8	+	4.75953e8i	−0.951479	+	1.64801i	−0.742228	+	0.670148i	$0.766231\pi$
$662$	6.08996e8	+	3.51604e8i	2.09914	+	1.21194i
$663$	1.97286e8	−	1.61253e8i	0.676950	−	0.553309i
$664$	1.75828e8	+	3.04544e8i	0.600600	+	1.04027i
$665$			2.37647e8i			0.808104i
$666$	1.73308e8	+	3.51903e7i	0.586672	+	0.119124i
$667$	−2.37599e7			−0.0800695
$668$	6.78059e8	−	3.91478e8i	2.27477	−	1.31334i
$669$	4.23829e7	−	6.91087e6i	0.141551	−	0.0230810i
$670$	−2.16692e8	+	3.75321e8i	−0.720474	+	1.24790i
$671$	−1.91463e8	−	1.10541e8i	−0.633751	−	0.365896i
$672$	−9.32884e7	−	3.53233e7i	−0.307411	−	0.116400i
$673$	−1.22468e8	−	2.12121e8i	−0.401770	−	0.695886i	0.592170	−	0.805813i	$-0.298272\pi$
$673$	−1.22468e8	−	2.12121e8i	−0.401770	−	0.695886i	−0.993940	+	0.109927i	$0.964938\pi$
$674$			3.54909e8i			1.15914i
$675$	2.07889e7	+	1.31000e7i	0.0675960	+	0.0425953i
$676$	1.46062e8			0.472821
$677$	4.25927e8	−	2.45909e8i	1.37268	−	0.792518i	0.381416	−	0.924404i	$-0.375437\pi$
$677$	4.25927e8	−	2.45909e8i	1.37268	−	0.792518i	0.991265	+	0.131886i	$0.0421033\pi$
$678$	3.84954e7	−	1.01666e8i	0.123515	−	0.326202i
$679$	−1.21194e7	+	2.09914e7i	−0.0387143	+	0.0670552i
$680$	−5.11041e8	−	2.95050e8i	−1.62528	−	0.938357i
$681$	3.42120e7	+	2.09815e8i	0.108327	+	0.664347i
$682$	−1.17344e7	−	2.03246e7i	−0.0369920	−	0.0640720i
$683$			5.92974e8i			1.86112i	0.366143	+	0.930559i	$0.380678\pi$
$683$			5.92974e8i			1.86112i	−0.366143	+	0.930559i	$0.619322\pi$
$684$	−7.20089e8	+	2.41247e8i	−2.25018	+	0.753865i
$685$	−4.66054e8			−1.44999
$686$	5.32396e8	−	3.07379e8i	1.64916	−	0.952142i
$687$	6.76514e7	+	8.27686e7i	0.208644	+	0.255267i
$688$	−3.53361e8	+	6.12038e8i	−1.08506	+	1.87937i
$689$	−6.71009e7	−	3.87407e7i	−0.205150	−	0.118443i
$690$	−2.43053e7	+	1.98661e7i	−0.0739867	+	0.0604735i
$691$	1.74226e8	+	3.01769e8i	0.528056	+	0.914620i	0.999465	+	0.0327051i	$0.0104122\pi$
$691$	1.74226e8	+	3.01769e8i	0.528056	+	0.914620i	−0.471409	+	0.881915i	$0.656254\pi$
$692$		−	1.06432e9i		−	3.21185i
$693$	3.57358e7	+	1.06666e8i	0.107375	+	0.320500i
$694$	−1.10462e9			−3.30472
$695$	−5.27490e8	+	3.04546e8i	−1.57130	+	0.907192i
$696$	9.31226e8	−	1.51844e8i	2.76202	−	0.450370i
$697$	2.01440e8	−	3.48905e8i	0.594906	−	1.03041i
$698$	−4.02159e7	−	2.32187e7i	−0.118258	−	0.0682765i
$699$	7.31371e7	+	2.76931e7i	0.214144	+	0.0810848i
$700$	2.18011e7	+	3.77606e7i	0.0635600	+	0.110089i
$701$		−	5.37432e8i		−	1.56016i	−0.625679	−	0.780080i	$-0.715178\pi$
$701$		−	5.37432e8i		−	1.56016i	0.625679	−	0.780080i	$-0.284822\pi$
$702$	2.50899e8	+	4.76213e8i	0.725250	+	1.37654i
$703$	1.32056e8			0.380094
$704$	8.05290e7	−	4.64934e7i	0.230799	−	0.133252i
$705$	9.53427e7	−	2.51799e8i	0.272095	−	0.718599i
$706$	4.41555e8	−	7.64796e8i	1.25479	−	2.17336i
$707$	6.01441e7	+	3.47242e7i	0.170190	+	0.0982594i
$708$	3.91666e7	+	2.40200e8i	0.110361	+	0.676821i
$709$	−7.46671e7	−	1.29327e8i	−0.209503	−	0.362870i	0.742055	−	0.670339i	$-0.233851\pi$
$709$	−7.46671e7	−	1.29327e8i	−0.209503	−	0.362870i	−0.951558	+	0.307469i	$0.900518\pi$
$710$			4.56972e8i			1.27678i
$711$	1.03002e8	−	5.07270e8i	0.286573	−	1.41133i
$712$	8.44230e8			2.33895
$713$	1.65032e6	−	952815.i	0.00455303	−	0.00262869i
$714$	−3.03231e8	−	3.70991e8i	−0.833066	−	1.01922i
$715$	6.94851e7	−	1.20352e8i	0.190096	−	0.329256i
$716$	−2.01709e8	−	1.16457e8i	−0.549522	−	0.317267i
$717$	1.39067e7	−	1.13667e7i	0.0377283	−	0.0308374i
$718$	−1.93745e8	−	3.35576e8i	−0.523429	−	0.906605i
$719$		−	7.89635e7i		−	0.212442i	−0.994343	−	0.106221i	$-0.966125\pi$
$719$		−	7.89635e7i		−	0.212442i	0.994343	−	0.106221i	$-0.0338751\pi$
$720$	3.23628e8	−	3.66079e8i	0.867058	−	0.980792i
$721$	−6.62132e7			−0.176660
$722$	−1.47641e8	+	8.52407e7i	−0.392280	+	0.226483i
$723$	−2.20118e7	+	3.58920e6i	−0.0582426	+	0.00949692i
$724$	−2.81993e8	+	4.88427e8i	−0.743059	+	1.28702i
$725$	−3.74172e7	−	2.16028e7i	−0.0981877	−	0.0566887i
$726$	−5.04010e8	−	1.90841e8i	−1.31713	−	0.498727i
$727$	−4.83494e7	−	8.37436e7i	−0.125831	−	0.217946i	0.796226	−	0.604999i	$-0.206826\pi$
$727$	−4.83494e7	−	8.37436e7i	−0.125831	−	0.217946i	−0.922057	+	0.387053i	$0.873493\pi$
$728$			5.03961e8i			1.30618i
$729$	2.19068e8	−	3.19537e8i	0.565453	−	0.824780i
$730$	9.34585e8			2.40243
$731$	−5.33654e8	+	3.08105e8i	−1.36618	+	0.788764i
$732$	−4.78426e8	+	1.26352e9i	−1.21978	+	3.22143i
$733$	−6.61563e7	+	1.14586e8i	−0.167981	+	0.290951i	−0.937710	−	0.347420i	$-0.887058\pi$
$733$	−6.61563e7	+	1.14586e8i	−0.167981	+	0.290951i	0.769729	+	0.638371i	$0.220391\pi$
$734$	−5.26771e8	−	3.04132e8i	−1.33209	−	0.769083i
$735$	2.66740e7	+	1.63586e8i	0.0671779	+	0.411988i
$736$	−4.91964e6	−	8.52107e6i	−0.0123396	−	0.0213728i
$737$			1.53191e8i			0.382676i
$738$	6.37635e8	+	5.63694e8i	1.58636	+	1.40241i
$739$	−2.72581e7			−0.0675401			−0.0337700	−	0.999430i	$-0.510751\pi$
$739$	−2.72581e7			−0.0675401			−0.0337700	+	0.999430i	$0.510751\pi$
$740$	−2.41639e8	+	1.39511e8i	−0.596311	+	0.344280i
$741$	2.54370e8	+	3.11211e8i	0.625188	+	0.764891i
$742$	−7.28507e7	+	1.26181e8i	−0.178329	+	0.308875i
$743$	1.77637e7	+	1.02559e7i	0.0433078	+	0.0250038i	0.521498	−	0.853253i	$-0.325374\pi$
$743$	1.77637e7	+	1.02559e7i	0.0433078	+	0.0250038i	−0.478190	+	0.878257i	$0.658707\pi$
$744$	−5.85922e7	+	4.78906e7i	−0.142272	+	0.116287i
$745$	5.83261e7	+	1.01024e8i	0.141057	+	0.244318i
$746$			5.44439e8i			1.31139i
$747$	−2.48813e8	−	5.05217e7i	−0.596913	−	0.121204i
$748$	−3.95321e8			−0.944594
$749$	2.19542e8	−	1.26753e8i	0.522483	−	0.301656i
$750$	−7.61476e8	+	1.24165e8i	−1.80498	+	0.294317i
$751$	−3.15842e8	+	5.47054e8i	−0.745676	+	1.29155i	0.204202	+	0.978929i	$0.434540\pi$
$751$	−3.15842e8	+	5.47054e8i	−0.745676	+	1.29155i	−0.949878	+	0.312620i	$0.898793\pi$
$752$	4.02626e8	+	2.32456e8i	0.946778	+	0.546622i
$753$	−2.82926e8	−	1.07129e8i	−0.662656	−	0.250912i
$754$	−4.73220e8	−	8.19641e8i	−1.10395	−	1.91210i
$755$		−	7.51553e8i		−	1.74630i
$756$	6.08208e8	−	3.20443e8i	1.40762	−	0.741626i
$757$	6.20833e8			1.43116			0.715578	−	0.698533i	$-0.246163\pi$
$757$	6.20833e8			1.43116			0.715578	+	0.698533i	$0.246163\pi$
$758$	8.44851e8	−	4.87775e8i	1.93987	−	1.11998i
$759$	−3.92924e6	+	1.03771e7i	−0.00898634	+	0.0237328i
$760$	4.65428e8	−	8.06144e8i	1.06026	−	1.83642i
$761$	7.24053e8	+	4.18032e8i	1.64292	+	0.948540i	0.979789	+	0.200035i	$0.0641057\pi$
$761$	7.24053e8	+	4.18032e8i	1.64292	+	0.948540i	0.663130	+	0.748504i	$0.269228\pi$
$762$	2.20843e7	+	1.35438e8i	0.0499136	+	0.306109i
$763$	1.54407e8	+	2.67441e8i	0.347611	+	0.602080i
$764$			1.15132e9i			2.58176i
$765$	4.03973e8	−	1.35340e8i	0.902335	−	0.302304i
$766$	−1.72381e8			−0.383533
$767$	1.11552e8	−	6.44047e7i	0.247225	−	0.142735i
$768$	−5.80989e8	−	7.10816e8i	−1.28258	−	1.56918i
$769$	−6.70941e7	+	1.16210e8i	−0.147538	+	0.255544i	−0.930317	−	0.366756i	$-0.880468\pi$
$769$	−6.70941e7	+	1.16210e8i	−0.147538	+	0.255544i	0.782779	+	0.622300i	$0.213802\pi$
$770$	−2.26318e8	−	1.30665e8i	−0.495731	−	0.286211i
$771$	−1.62191e8	+	1.32568e8i	−0.353886	+	0.289251i
$772$	−2.69863e8	−	4.67416e8i	−0.586531	−	1.01590i
$773$		−	5.46031e8i		−	1.18217i	−0.806611	−	0.591083i	$-0.798701\pi$
$773$		−	5.46031e8i		−	1.18217i	0.806611	−	0.591083i	$-0.201299\pi$
$774$	−4.13520e8	−	1.23430e9i	−0.891813	−	2.66194i
$775$	3.46525e6			0.00744439
$776$	8.22227e7	−	4.74713e7i	0.175957	−	0.101589i
$777$	−1.17983e8	+	1.92381e7i	−0.251511	+	0.0410109i
$778$	−3.44969e8	+	5.97503e8i	−0.732556	+	1.26882i
$779$	5.50382e8	+	3.17763e8i	1.16427	+	0.672189i
$780$	−7.94233e8	−	3.00733e8i	−1.67365	−	0.633720i
$781$	8.07646e7	+	1.39888e8i	0.169538	+	0.293649i
$782$		−	4.72620e7i		−	0.0988307i
$783$	−3.63169e8	+	5.76326e8i	−0.756526	+	1.20056i
$784$	−2.86198e8			−0.593908
$785$	−1.72826e8	+	9.97809e7i	−0.357272	+	0.206271i
$786$	1.93525e8	−	5.11098e8i	0.398538	−	1.05254i
$787$	1.03958e8	−	1.80060e8i	0.213272	−	0.369397i	−0.739465	−	0.673195i	$-0.764921\pi$
$787$	1.03958e8	−	1.80060e8i	0.213272	−	0.369397i	0.952736	+	0.303798i	$0.0982548\pi$
$788$	−6.39849e8	−	3.69417e8i	−1.30767	−	0.754984i
$789$	7.86056e7	+	4.82071e8i	0.160038	+	0.981477i
$790$	6.01233e8	+	1.04137e9i	1.21944	+	2.11214i
$791$			7.34847e7i			0.148480i
$792$	8.76818e7	−	4.31821e8i	0.176496	−	0.869218i
$793$	7.15074e8			1.43394
$794$	2.44543e8	−	1.41187e8i	0.488533	−	0.282055i
$795$	−8.19878e7	−	1.00309e8i	−0.163173	−	0.199635i
$796$	2.68186e8	−	4.64512e8i	0.531737	−	0.920996i
$797$	−6.08306e8	−	3.51206e8i	−1.20157	−	0.693724i	−0.240662	−	0.970609i	$-0.577365\pi$
$797$	−6.08306e8	−	3.51206e8i	−1.20157	−	0.693724i	−0.960903	+	0.276885i	$0.910698\pi$
$798$	5.85222e8	−	4.78334e8i	1.15163	−	0.941289i
$799$	2.02685e8	+	3.51061e8i	0.397358	+	0.688244i
$800$		−	1.78920e7i		−	0.0349453i
$801$	−4.03704e8	+	4.56658e8i	−0.785534	+	0.888574i
$802$	6.09996e8			1.18251
$803$	2.86095e8	−	1.65177e8i	0.552540	−	0.319009i
$804$	9.23965e8	−	1.50660e8i	1.77782	−	0.289888i
$805$	1.06098e7	−	1.83766e7i	0.0203385	−	0.0352272i
$806$	6.57381e7	+	3.79539e7i	0.125549	+	0.0724855i
$807$	−6.93993e8	−	2.62778e8i	−1.32049	−	0.499997i
$808$	−1.36014e8	−	2.35583e8i	−0.257839	−	0.446590i
$809$			8.20042e8i			1.54878i	0.632707	+	0.774392i	$0.281944\pi$
$809$			8.20042e8i			1.54878i	−0.632707	+	0.774392i	$0.718056\pi$
$810$	1.10371e8	+	8.93208e8i	0.207682	+	1.68073i
$811$	−6.91041e8			−1.29551			−0.647756	−	0.761848i	$-0.724292\pi$
$811$	−6.91041e8			−1.29551			−0.647756	+	0.761848i	$0.724292\pi$
$812$	−1.04683e9	+	6.04386e8i	−1.95527	+	1.12888i
$813$	3.54696e7	−	9.36748e7i	0.0660062	−	0.174322i
$814$	−7.26077e7	+	1.25760e8i	−0.134620	+	0.233169i
$815$	−2.56789e8	−	1.48257e8i	−0.474356	−	0.273869i
$816$	1.18391e8	+	7.26066e8i	0.217895	+	1.33631i
$817$	−4.86023e8	−	8.41816e8i	−0.891231	−	1.54366i
$818$			5.22459e8i			0.954537i
$819$	−2.72601e8	−	2.40990e8i	−0.496222	−	0.438679i
$820$	−1.34281e9			−2.43541
$821$	6.01769e8	−	3.47432e8i	1.08743	−	0.627827i	0.154538	−	0.987987i	$-0.450611\pi$
$821$	6.01769e8	−	3.47432e8i	1.08743	−	0.627827i	0.932891	+	0.360160i	$0.117278\pi$
$822$	9.38070e8	+	1.14769e9i	1.68896	+	2.06637i
$823$	−7.18960e7	+	1.24528e8i	−0.128975	+	0.223391i	−0.923280	−	0.384128i	$-0.874502\pi$
$823$	−7.18960e7	+	1.24528e8i	−0.128975	+	0.223391i	0.794305	+	0.607519i	$0.207835\pi$
$824$	2.24608e8	+	1.29677e8i	0.401461	+	0.231784i
$825$	−1.56228e7	+	1.27693e7i	−0.0278225	+	0.0227409i
$826$	−1.21111e8	−	2.09770e8i	−0.214904	−	0.372224i
$827$		−	6.36987e8i		−	1.12620i	−0.826390	−	0.563098i	$-0.809609\pi$
$827$		−	6.36987e8i		−	1.12620i	0.826390	−	0.563098i	$-0.190391\pi$
$828$	6.64532e7	+	1.34934e7i	0.117064	+	0.0237701i
$829$	9.52328e7			0.167156			0.0835782	−	0.996501i	$-0.473365\pi$
$829$	9.52328e7			0.167156			0.0835782	+	0.996501i	$0.473365\pi$
$830$	5.10784e8	−	2.94901e8i	0.893311	−	0.515753i
$831$	6.87636e8	−	1.12125e8i	1.19827	−	0.195388i
$832$	−1.50379e8	+	2.60464e8i	−0.261106	+	0.452250i
$833$	−2.16112e8	−	1.24772e8i	−0.373890	−	0.215866i
$834$	1.81170e9	+	6.85991e8i	3.12311	+	1.18255i
$835$	−3.46442e8	−	6.00055e8i	−0.595074	−	1.03070i
$836$		−	6.23601e8i		−	1.06730i
$837$	2.11342e6	−	5.45944e7i	0.00360421	−	0.0931047i
$838$	3.45164e8			0.586534
$839$	−2.46672e8	+	1.42416e8i	−0.417671	+	0.241143i	−0.694081	−	0.719897i	$-0.744189\pi$
$839$	−2.46672e8	+	1.42416e8i	−0.417671	+	0.241143i	0.276409	+	0.961040i	$0.410856\pi$
$840$	−2.98389e8	+	7.88043e8i	−0.503437	+	1.32957i
$841$	3.01478e8	−	5.22175e8i	0.506836	−	0.877866i
$842$	−1.28721e9	−	7.43173e8i	−2.15633	−	1.24496i
$843$	−9.32668e7	−	5.71985e8i	−0.155684	−	0.954777i
$844$	6.37000e8	+	1.10332e9i	1.05953	+	1.83516i
$845$		−	1.29259e8i		−	0.214235i
$846$	−8.11978e8	+	2.72032e8i	−1.34101	+	0.449271i
$847$	3.64301e8			0.599529
$848$	1.93731e8	−	1.11851e8i	0.317695	−	0.183422i
$849$	−1.46880e8	−	1.79702e8i	−0.240016	−	0.293649i
$850$	4.29712e7	−	7.44283e7i	0.0699715	−	0.121194i
$851$	−1.02115e7	−	5.89563e6i	−0.0165692	−	0.00956625i
$852$	7.64300e8	−	6.24705e8i	1.23579	−	1.01008i
$853$	4.56817e7	+	7.91230e7i	0.0736029	+	0.127484i	0.900478	−	0.434902i	$-0.143217\pi$
$853$	4.56817e7	+	7.91230e7i	0.0736029	+	0.127484i	−0.826875	+	0.562386i	$0.809884\pi$
$854$		−	1.34467e9i		−	2.15895i
$855$	2.13494e8	+	6.37249e8i	0.341575	+	1.01956i
$856$	−9.92973e8			−1.58313
$857$	−4.56487e8	+	2.63553e8i	−0.725247	+	0.418721i	−0.816681	−	0.577090i	$-0.804188\pi$
$857$	−4.56487e8	+	2.63553e8i	−0.725247	+	0.418721i	0.0914341	+	0.995811i	$0.470855\pi$
$858$	−4.36234e8	+	7.11314e7i	−0.690649	+	0.112616i
$859$	1.81645e8	−	3.14618e8i	0.286578	−	0.496368i	−0.686413	−	0.727212i	$-0.740816\pi$
$859$	1.81645e8	−	3.14618e8i	0.286578	−	0.496368i	0.972991	+	0.230845i	$0.0741489\pi$
$860$	1.77868e9	+	1.02692e9i	2.79642	+	1.61451i
$861$	−5.38024e8	−	2.03720e8i	−0.842931	−	0.319172i
$862$	1.02458e9	+	1.77462e9i	1.59964	+	2.77066i
$863$			9.96932e8i			1.55108i	0.631300	+	0.775538i	$0.282522\pi$
$863$			9.96932e8i			1.55108i	−0.631300	+	0.775538i	$0.717478\pi$
$864$	−2.81886e8	−	1.09122e7i	−0.437051	−	0.0169188i
$865$	−9.41881e8			−1.45528
$866$	−1.87621e9	+	1.08323e9i	−2.88886	+	1.66789i
$867$	3.63858e6	−	9.60944e6i	0.00558308	−	0.0147449i
$868$	4.84739e7	−	8.39593e7i	0.0741223	−	0.128384i
$869$	3.68099e8	+	2.12522e8i	0.560925	+	0.323850i
$870$	−2.54674e8	−	1.56186e9i	−0.386747	−	2.37183i
$871$	−2.47742e8	−	4.29101e8i	−0.374925	−	0.649390i
$872$		−	1.20961e9i		−	1.82430i
$873$	−1.36402e7	+	6.71760e7i	−0.0205011	+	0.100965i
$874$	7.45537e7			0.111670
$875$	4.51661e8	−	2.60766e8i	0.674199	−	0.389249i
$876$	−1.27762e9	−	1.56312e9i	−1.90060	−	2.32531i
$877$	−4.01845e8	+	6.96015e8i	−0.595744	+	1.03186i	0.397698	+	0.917517i	$0.369809\pi$
$877$	−4.01845e8	+	6.96015e8i	−0.595744	+	1.03186i	−0.993441	+	0.114342i	$0.963524\pi$
$878$	6.12928e7	+	3.53874e7i	0.0905578	+	0.0522836i
$879$	−6.34151e7	+	5.18327e7i	−0.0933740	+	0.0763197i
$880$	2.00614e8	+	3.47474e8i	0.294384	+	0.509888i
$881$			1.05052e8i			0.153630i	0.997045	+	0.0768151i	$0.0244751\pi$
$881$			1.05052e8i			0.153630i	−0.997045	+	0.0768151i	$0.975525\pi$
$882$	3.49153e8	−	3.94952e8i	0.508873	−	0.575623i
$883$	−8.90921e7			−0.129407			−0.0647034	−	0.997905i	$-0.520610\pi$
$883$	−8.90921e7			−0.129407			−0.0647034	+	0.997905i	$0.520610\pi$
$884$	1.10733e9	−	6.39316e8i	1.60295	−	0.925463i
$885$	2.12567e8	−	3.46608e7i	0.306667	−	0.0500045i
$886$	4.59254e8	−	7.95452e8i	0.660316	−	1.14370i
$887$	8.98422e8	+	5.18704e8i	1.28739	+	0.743274i	0.978188	−	0.207722i	$-0.0666051\pi$
$887$	8.98422e8	+	5.18704e8i	1.28739	+	0.743274i	0.309201	+	0.950997i	$0.399938\pi$
$888$	4.37900e8	+	1.65809e8i	0.625368	+	0.236793i
$889$	−4.63807e7	−	8.03337e7i	−0.0660134	−	0.114339i
$890$		−	1.41595e9i		−	2.00853i
$891$	1.91651e8	+	2.53922e8i	0.270943	+	0.358977i
$892$	2.15491e8			0.303623
$893$	−5.53783e8	+	3.19727e8i	−0.777652	+	0.448978i
$894$	1.31380e8	−	3.46972e8i	0.183872	−	0.485604i
$895$	−1.03059e8	+	1.78504e8i	−0.143753	+	0.248988i
$896$	6.94566e8	+	4.01008e8i	0.965582	+	0.557479i
$897$	−5.77576e6	−	3.54215e7i	−0.00800261	−	0.0490783i
$898$	−5.12103e8	−	8.86988e8i	−0.707177	−	1.22487i
$899$			9.60662e7i			0.132218i
$900$	9.23823e7	+	8.16695e7i	0.126725	+	0.112030i
$901$	1.95051e8			0.266670
$902$	−6.05229e8	+	3.49429e8i	−0.824708	+	0.476145i
$903$	5.56868e8	+	6.81304e8i	0.756290	+	0.925289i
$904$	1.43919e8	−	2.49274e8i	0.194810	−	0.337421i
$905$	4.32238e8	+	2.49552e8i	0.583145	+	0.336679i
$906$	−1.85075e9	+	1.51272e9i	−2.48865	+	2.03411i
$907$	−2.83227e8	−	4.90564e8i	−0.379589	−	0.657467i	0.611414	−	0.791311i	$-0.290601\pi$
$907$	−2.83227e8	−	4.90564e8i	−0.379589	−	0.657467i	−0.991002	+	0.133844i	$0.957268\pi$
$908$			1.06678e9i			1.42501i
$909$	1.92471e8	+	3.90815e7i	0.256256	+	0.0520331i
$910$	8.45247e8			1.12166
$911$	7.72892e8	−	4.46229e8i	1.02227	−	0.590205i	0.107506	−	0.994204i	$-0.465714\pi$
$911$	7.72892e8	−	4.46229e8i	1.02227	−	0.590205i	0.914759	+	0.403999i	$0.132380\pi$
$912$	−1.14534e9	+	1.86757e8i	−1.50990	+	0.246202i
$913$	1.04241e8	−	1.80550e8i	0.136970	−	0.237239i
$914$	−6.99193e8	−	4.03679e8i	−0.915711	−	0.528686i
$915$	1.11816e9	+	4.23387e8i	1.45962	+	0.552681i
$916$	2.68216e8	+	4.64563e8i	0.348978	+	0.604447i
$917$			3.69424e8i			0.479090i
$918$	−1.14640e9	−	7.22398e8i	−1.48186	−	0.933789i
$919$	2.10427e8			0.271116			0.135558	−	0.990769i	$-0.456717\pi$
$919$	2.10427e8			0.271116			0.135558	+	0.990769i	$0.456717\pi$
$920$	−7.19807e7	+	4.15581e7i	−0.0924385	+	0.0533694i
$921$	1.09391e8	−	2.88902e8i	0.140025	−	0.369804i
$922$	−1.10803e9	+	1.91917e9i	−1.41371	+	2.44861i
$923$	−4.52457e8	−	2.61226e8i	−0.575403	−	0.332209i
$924$	9.08475e7	+	5.57148e8i	0.115159	+	0.706244i
$925$	−1.07208e7	−	1.85689e7i	−0.0135457	−	0.0234618i
$926$			1.30852e9i			1.64796i
$927$	−1.77550e8	+	5.94836e7i	−0.222886	+	0.0746720i
$928$	4.96016e8			0.620657
$929$	−7.86889e8	+	4.54310e8i	−0.981445	+	0.566638i	−0.902706	−	0.430257i	$-0.858423\pi$
$929$	−7.86889e8	+	4.54310e8i	−0.981445	+	0.566638i	−0.0787392	+	0.996895i	$0.525089\pi$
$930$	8.03226e7	+	9.82713e7i	0.0998594	+	0.122174i
$931$	1.96823e8	−	3.40907e8i	0.243908	−	0.422462i
$932$	3.39863e8	+	1.96220e8i	0.419813	+	0.242379i
$933$	5.74919e8	−	4.69913e8i	0.707884	−	0.578593i
$934$	−1.04900e9	−	1.81692e9i	−1.28746	−	2.22995i
$935$			3.49843e8i			0.427994i
$936$	4.52741e8	+	1.35137e9i	0.552105	+	1.64796i
$937$	1.34303e9			1.63255			0.816275	−	0.577663i	$-0.196035\pi$
$937$	1.34303e9			1.63255			0.816275	+	0.577663i	$0.196035\pi$
$938$	−8.06912e8	+	4.65871e8i	−0.977727	+	0.564491i
$939$	−6.71959e8	+	1.09568e8i	−0.811607	+	0.132339i
$940$	6.75553e8	−	1.17009e9i	0.813347	−	1.40876i
$941$	−8.97969e8	−	5.18443e8i	−1.07769	−	0.622202i	−0.147415	−	0.989075i	$-0.547095\pi$
$941$	−8.97969e8	−	5.18443e8i	−1.07769	−	0.622202i	−0.930271	+	0.366872i	$0.880429\pi$
$942$	5.93579e8	+	2.24756e8i	0.710111	+	0.268880i
$943$	−2.83731e7	−	4.91437e7i	−0.0338354	−	0.0586047i
$944$			3.71893e8i			0.442081i
$945$	−2.83579e8	−	5.38239e8i	−0.336030	−	0.637793i
$946$	1.06891e9			1.26261
$947$	2.00750e8	−	1.15903e8i	0.236377	−	0.136472i	−0.377133	−	0.926159i	$-0.623090\pi$
$947$	2.00750e8	−	1.15903e8i	0.236377	−	0.136472i	0.613510	+	0.789687i	$0.289757\pi$
$948$	9.19798e8	−	2.42918e9i	1.07961	−	2.85124i
$949$	−5.34251e8	+	9.25350e8i	−0.625096	+	1.08270i
$950$	1.17407e8	+	6.77852e7i	0.136938	+	0.0790613i
$951$	1.19896e8	+	7.35294e8i	0.139400	+	0.854908i
$952$	−6.34334e8	−	1.09870e9i	−0.735202	−	1.27341i
$953$		−	2.56619e8i		−	0.296490i	−0.988951	−	0.148245i	$-0.952638\pi$
$953$		−	2.56619e8i		−	0.296490i	0.988951	−	0.148245i	$-0.0473625\pi$
$954$	−8.19922e7	+	4.03801e8i	−0.0944338	+	0.465074i
$955$	1.01887e9			1.16979
$956$	7.80555e7	−	4.50654e7i	0.0893367	−	0.0515785i
$957$	−3.54001e8	−	4.33106e8i	−0.403896	−	0.494149i
$958$	8.00720e8	−	1.38689e9i	0.910719	−	1.57741i
$959$	−8.67739e8	−	5.00990e8i	−0.983860	−	0.568032i
$960$	−3.89366e8	+	3.18250e8i	−0.440092	+	0.359712i
$961$	4.39899e8	+	7.61928e8i	0.495659	+	0.858507i
$962$		−	4.69687e8i		−	0.527574i
$963$	4.74831e8	−	5.37116e8i	0.531692	−	0.601436i
$964$	−1.11917e8			−0.124929
$965$	−4.13644e8	+	2.38817e8i	−0.460304	+	0.265757i
$966$	−6.66090e7	+	1.08611e7i	−0.0738927	+	0.0120488i
$967$	1.62366e8	−	2.81225e8i	0.179562	−	0.311010i	−0.762169	−	0.647379i	$-0.775865\pi$
$967$	1.62366e8	−	2.81225e8i	0.179562	−	0.311010i	0.941731	+	0.336368i	$0.109199\pi$
$968$	−1.23578e9	−	7.13478e8i	−1.36243	−	0.786601i
$969$	−9.46278e8	−	3.58304e8i	−1.04003	−	0.393804i
$970$	−7.96192e7	−	1.37905e8i	−0.0872374	−	0.151100i
$971$		−	1.01485e9i		−	1.10852i	−0.832342	−	0.554262i	$-0.813001\pi$
$971$		−	1.01485e9i		−	1.10852i	0.832342	−	0.554262i	$-0.186999\pi$
$972$	1.34303e9	−	1.40566e9i	1.46247	−	1.53067i
$973$	−1.30950e9			−1.42157
$974$	2.11293e9	−	1.21990e9i	2.28670	−	1.32023i
$975$	2.31100e7	−	6.10333e7i	0.0249337	−	0.0658495i
$976$	−1.03226e9	+	1.78794e9i	−1.11030	+	1.92310i
$977$	3.71703e8	+	2.14603e8i	0.398578	+	0.230119i	0.685870	−	0.727724i	$-0.259422\pi$
$977$	3.71703e8	+	2.14603e8i	0.398578	+	0.230119i	−0.287292	+	0.957843i	$0.592755\pi$
$978$	1.51770e8	+	9.30773e8i	0.162244	+	0.995009i
$979$	−2.50253e8	−	4.33450e8i	−0.266705	−	0.461946i
$980$			8.31736e8i			0.883705i
$981$	6.54301e8	+	5.78427e8i	0.693060	+	0.612691i
$982$	−2.29643e9			−2.42504
$983$	1.36423e9	−	7.87641e8i	1.43624	−	0.829216i	0.438658	−	0.898654i	$-0.355454\pi$
$983$	1.36423e9	−	7.87641e8i	1.43624	−	0.829216i	0.997586	+	0.0694381i	$0.0221206\pi$
$984$	1.42610e9	+	1.74477e9i	1.49680	+	1.83127i
$985$	−3.26919e8	+	5.66240e8i	−0.342083	+	0.592505i
$986$	2.06336e9	+	1.19128e9i	2.15250	+	1.24275i
$987$	4.48192e8	−	3.66332e8i	0.466136	−	0.380998i
$988$	1.00849e9	+	1.74676e9i	1.04569	+	1.81118i
$989$			8.67940e7i			0.0897224i
$990$	−7.24254e8	−	1.47061e8i	−0.746424	−	0.151562i
$991$	−1.55480e9			−1.59755			−0.798774	−	0.601631i	$-0.794518\pi$
$991$	−1.55480e9			−1.59755			−0.798774	+	0.601631i	$0.794518\pi$
$992$	−3.44524e7	+	1.98911e7i	−0.0352927	+	0.0203762i
$993$	−1.32675e9	+	2.16338e8i	−1.35501	+	0.220945i
$994$	−4.91228e8	+	8.50831e8i	−0.500177	+	0.866332i
$995$	−4.11074e8	−	2.37334e8i	−0.417302	−	0.240930i
$996$	−1.19150e9	−	4.51156e8i	−1.20591	−	0.456613i
$997$	5.50335e8	+	9.53207e8i	0.555317	+	0.961838i	0.997879	+	0.0650998i	$0.0207366\pi$
$997$	5.50335e8	+	9.53207e8i	0.555317	+	0.961838i	−0.442561	+	0.896738i	$0.645930\pi$
$998$		−	1.68025e9i		−	1.69037i
$999$	−2.99089e8	+	1.57579e8i	−0.299988	+	0.158053i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.7.d.a.5.1	yes	10
3.2	odd	2		27.7.d.a.17.5		10
4.3	odd	2		144.7.q.a.113.2		10
9.2	odd	6	inner	9.7.d.a.2.1	✓	10
9.4	even	3		81.7.b.a.80.1		10
9.5	odd	6		81.7.b.a.80.10		10
9.7	even	3		27.7.d.a.8.5		10
12.11	even	2		432.7.q.a.17.4		10
36.7	odd	6		432.7.q.a.305.4		10
36.11	even	6		144.7.q.a.65.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.7.d.a.2.1	✓	10	9.2	odd	6	inner
9.7.d.a.5.1	yes	10	1.1	even	1	trivial
27.7.d.a.8.5		10	9.7	even	3
27.7.d.a.17.5		10	3.2	odd	2
81.7.b.a.80.1		10	9.4	even	3
81.7.b.a.80.10		10	9.5	odd	6
144.7.q.a.65.2		10	36.11	even	6
144.7.q.a.113.2		10	4.3	odd	2
432.7.q.a.17.4		10	12.11	even	2
432.7.q.a.305.4		10	36.7	odd	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 9 = 3^{2} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	9.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-12.2318 + 7.06203i) q^{2} +(9.56099 - 25.2505i) q^{3} +(67.7447 - 117.337i) q^{4} +(-103.839 - 59.9512i) q^{5} +(61.3717 + 376.379i) q^{6} +(-128.891 - 223.245i) q^{7} +1009.72i q^{8} +(-546.175 - 482.840i) q^{9} +1693.51 q^{10} +(518.417 - 299.308i) q^{11} +(-2315.12 - 2832.45i) q^{12} +(-968.088 + 1676.78i) q^{13} +(3153.13 + 1820.46i) q^{14} +(-2506.60 + 2048.78i) q^{15} +(-2795.02 - 4841.12i) q^{16} -4874.12i q^{17} +(10090.5 + 2048.89i) q^{18} +7688.70 q^{19} +(-14069.0 + 8122.75i) q^{20} +(-6869.37 + 1120.11i) q^{21} +(-4227.45 + 7322.16i) q^{22} +(-594.548 - 343.263i) q^{23} +(25495.9 + 9653.93i) q^{24} +(-624.198 - 1081.14i) q^{25} -27346.7i q^{26} +(-17413.9 + 9174.76i) q^{27} -34926.6 q^{28} +(29972.2 - 17304.5i) q^{29} +(16191.6 - 42762.0i) q^{30} +(-1387.88 + 2403.88i) q^{31} +(12411.9 + 7166.00i) q^{32} +(-2601.10 - 15952.0i) q^{33} +(34421.2 + 59619.2i) q^{34} +30908.6i q^{35} +(-93655.5 + 31376.8i) q^{36} +17175.3 q^{37} +(-94046.7 + 54297.9i) q^{38} +(33083.6 + 40476.4i) q^{39} +(60534.0 - 104848. i) q^{40} +(71583.2 + 41328.6i) q^{41} +(76114.5 - 62212.6i) q^{42} +(-63212.6 - 109487. i) q^{43} -81106.2i q^{44} +(27767.2 + 82881.2i) q^{45} +9696.53 q^{46} +(-72025.6 + 41584.0i) q^{47} +(-148964. + 24289.7i) q^{48} +(25599.0 - 44338.7i) q^{49} +(15270.1 + 8816.21i) q^{50} +(-123074. - 46601.4i) q^{51} +(131166. + 227185. i) q^{52} +40017.8i q^{53} +(148211. - 235201. i) q^{54} -71775.6 q^{55} +(225415. - 130143. i) q^{56} +(73511.6 - 194144. i) q^{57} +(-244410. + 423330. i) q^{58} +(-57614.7 - 33263.9i) q^{59} +(70589.7 + 432911. i) q^{60} +(-184662. - 319843. i) q^{61} -39205.0i q^{62} +(-37394.7 + 184164. i) q^{63} +155336. q^{64} +(201050. - 116076. i) q^{65} +(144470. + 176752. i) q^{66} +(-127954. + 221623. i) q^{67} +(-571915. - 330195. i) q^{68} +(-14352.0 + 11730.7i) q^{69} +(-218277. - 378068. i) q^{70} +269837. i q^{71} +(487533. - 551484. i) q^{72} +551862. q^{73} +(-210085. + 121292. i) q^{74} +(-33267.3 + 5424.50i) q^{75} +(520869. - 902171. i) q^{76} +(-133638. - 77156.0i) q^{77} +(-690517. - 261461. i) q^{78} +(355021. + 614915. i) q^{79} +670259. i q^{80} +(65172.8 + 527430. i) q^{81} -1.16746e6 q^{82} +(301612. - 174136. i) q^{83} +(-333933. + 881913. i) q^{84} +(-292209. + 506121. i) q^{85} +(1.54641e6 + 892818. i) q^{86} +(-150382. - 922262. i) q^{87} +(302218. + 523456. i) q^{88} -836103. i q^{89} +(-924953. - 817694. i) q^{90} +499109. q^{91} +(-80554.9 + 46508.4i) q^{92} +(47429.6 + 58028.1i) q^{93} +(587335. - 1.01729e6i) q^{94} +(-798384. - 460947. i) q^{95} +(299615. - 244892. i) q^{96} +(-47014.3 - 81431.2i) q^{97} +723123. i q^{98} +(-427664. - 86837.8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 3 q^{2} + 24 q^{3} + 127 q^{4} - 219 q^{5} + 333 q^{6} - 121 q^{7} - 1980 q^{9} - 132 q^{10} + 483 q^{11} - 1830 q^{12} - 841 q^{13} + 12174 q^{14} + 7965 q^{15} - 1985 q^{16} - 7884 q^{18} + 6176 q^{19}+ \cdots - 432567 q^{99}+O(q^{100}) \) 10 * q - 3 * q^2 + 24 * q^3 + 127 * q^4 - 219 * q^5 + 333 * q^6 - 121 * q^7 - 1980 * q^9 - 132 * q^10 + 483 * q^11 - 1830 * q^12 - 841 * q^13 + 12174 * q^14 + 7965 * q^15 - 1985 * q^16 - 7884 * q^18 + 6176 * q^19 - 63186 * q^20 - 25845 * q^21 + 3471 * q^22 + 53565 * q^23 + 111519 * q^24 + 8452 * q^25 - 101034 * q^27 - 22660 * q^28 - 80679 * q^29 - 37782 * q^30 - 24601 * q^31 + 218295 * q^32 + 229995 * q^33 + 7425 * q^34 - 274977 * q^36 + 12764 * q^37 - 371877 * q^38 - 112749 * q^39 + 54150 * q^40 + 232251 * q^41 + 270540 * q^42 - 93271 * q^43 + 63801 * q^45 + 112512 * q^46 - 142887 * q^47 - 143283 * q^48 + 86238 * q^49 + 318459 * q^50 + 57078 * q^51 + 186920 * q^52 + 13851 * q^54 - 419982 * q^55 + 342546 * q^56 - 1086 * q^57 - 380658 * q^58 - 995061 * q^59 - 1011402 * q^60 - 59305 * q^61 + 526455 * q^63 + 403066 * q^64 + 1642029 * q^65 + 1610586 * q^66 + 158513 * q^67 - 1693791 * q^68 - 851715 * q^69 - 304788 * q^70 + 1469907 * q^72 + 933896 * q^73 + 595182 * q^74 - 757524 * q^75 + 666641 * q^76 - 2198883 * q^77 - 3481884 * q^78 + 468707 * q^79 + 1774548 * q^81 - 2038470 * q^82 + 3008337 * q^83 + 1543746 * q^84 - 1189944 * q^85 + 1905549 * q^86 - 615591 * q^87 - 349773 * q^88 + 84294 * q^90 - 211778 * q^91 - 973788 * q^92 - 2954553 * q^93 + 809124 * q^94 - 2562954 * q^95 - 1022112 * q^96 + 336029 * q^97 - 432567 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more