LMFDB - Embedded newform 72.7.j.a.5.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [72,7,Mod(5,72)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(72, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

N = Newforms(chi, 7, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("72.5");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 72 = 2^{3} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	72.j (of order $6$, degree $2$, 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:	$16.5638940206$
Analytic rank:	$0$
Dimension:	$140$
Relative dimension:	$70$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			5.4
Character	$\chi$	$=$	72.5
Dual form			72.7.j.a.29.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.93602 - 1.00978i) q^{2} +(-16.2129 - 21.5903i) q^{3} +(61.9607 + 16.0272i) q^{4} +(92.8213 - 160.771i) q^{5} +(106.864 + 187.713i) q^{6} +(288.471 + 499.646i) q^{7} +(-475.537 - 189.758i) q^{8} +(-203.285 + 700.083i) q^{9} +O(q^{10})$	\(q+(-7.93602 - 1.00978i) q^{2} +(-16.2129 - 21.5903i) q^{3} +(61.9607 + 16.0272i) q^{4} +(92.8213 - 160.771i) q^{5} +(106.864 + 187.713i) q^{6} +(288.471 + 499.646i) q^{7} +(-475.537 - 189.758i) q^{8} +(-203.285 + 700.083i) q^{9} +(-898.975 + 1182.15i) q^{10} +(-35.7086 - 61.8492i) q^{11} +(-658.530 - 1597.60i) q^{12} +(-500.678 - 289.067i) q^{13} +(-1784.78 - 4256.49i) q^{14} +(-4976.01 + 602.523i) q^{15} +(3582.26 + 1986.11i) q^{16} +5352.51i q^{17} +(2320.20 - 5350.60i) q^{18} +13199.1i q^{19} +(8327.99 - 8473.84i) q^{20} +(6110.58 - 14328.9i) q^{21} +(220.931 + 526.894i) q^{22} +(8898.34 + 5137.46i) q^{23} +(3612.89 + 13343.5i) q^{24} +(-9419.10 - 16314.4i) q^{25} +(3681.50 + 2799.61i) q^{26} +(18410.9 - 6961.39i) q^{27} +(9865.93 + 35581.8i) q^{28} +(7785.84 + 13485.5i) q^{29} +(40098.1 + 243.014i) q^{30} +(17808.1 - 30844.5i) q^{31} +(-26423.3 - 19379.1i) q^{32} +(-756.404 + 1773.71i) q^{33} +(5404.83 - 42477.6i) q^{34} +107105. q^{35} +(-23816.0 + 40119.6i) q^{36} +7327.20i q^{37} +(13328.1 - 104748. i) q^{38} +(1876.39 + 15496.4i) q^{39} +(-74647.7 + 58839.1i) q^{40} +(22239.4 + 12839.9i) q^{41} +(-62962.6 + 107544. i) q^{42} +(-30439.0 + 17574.0i) q^{43} +(-1221.26 - 4404.53i) q^{44} +(93684.1 + 97665.0i) q^{45} +(-65429.7 - 49756.3i) q^{46} +(86527.4 - 49956.6i) q^{47} +(-15198.0 - 109543. i) q^{48} +(-107606. + 186379. i) q^{49} +(58276.3 + 138982. i) q^{50} +(115562. - 86779.7i) q^{51} +(-26389.5 - 25935.2i) q^{52} -210300. q^{53} +(-153138. + 36654.9i) q^{54} -13258.1 q^{55} +(-42366.6 - 292340. i) q^{56} +(284973. - 213996. i) q^{57} +(-48171.3 - 114883. i) q^{58} +(189669. - 328517. i) q^{59} +(-317974. - 42418.6i) q^{60} +(102615. - 59244.5i) q^{61} +(-172471. + 226800. i) q^{62} +(-408435. + 100383. i) q^{63} +(190127. + 180474. i) q^{64} +(-92947.3 + 53663.1i) q^{65} +(7793.89 - 13312.4i) q^{66} +(160838. + 92859.9i) q^{67} +(-85785.7 + 331645. i) q^{68} +(-33348.3 - 275411. i) q^{69} +(-849987. - 108152. i) q^{70} +527264. i q^{71} +(229516. - 294341. i) q^{72} -287298. q^{73} +(7398.83 - 58148.8i) q^{74} +(-199522. + 467864. i) q^{75} +(-211545. + 817827. i) q^{76} +(20601.8 - 35683.3i) q^{77} +(756.801 - 124875. i) q^{78} +(347641. + 602132. i) q^{79} +(651820. - 391571. i) q^{80} +(-448792. - 284632. i) q^{81} +(-163527. - 124355. i) q^{82} +(-145784. - 252505. i) q^{83} +(608267. - 789892. i) q^{84} +(860530. + 496827. i) q^{85} +(259310. - 108731. i) q^{86} +(164925. - 386737. i) q^{87} +(5244.39 + 36187.6i) q^{88} -567422. i q^{89} +(-644859. - 869671. i) q^{90} -333549. i q^{91} +(469008. + 460936. i) q^{92} +(-954663. + 115596. i) q^{93} +(-737128. + 309083. i) q^{94} +(2.12204e6 + 1.22516e6i) q^{95} +(9997.64 + 884680. i) q^{96} +(237627. + 411582. i) q^{97} +(1.04217e6 - 1.37045e6i) q^{98} +(50558.6 - 12426.0i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 140 q - 3 q^{2} - q^{4} + 317 q^{6} - 2 q^{7} - 4 q^{9}+O(q^{10}) $ 140 * q - 3 * q^2 - q^4 + 317 * q^6 - 2 * q^7 - 4 * q^9	$ 140 q - 3 q^{2} - q^{4} + 317 q^{6} - 2 q^{7} - 4 q^{9} + 124 q^{10} - 6946 q^{12} - 7428 q^{14} + 1454 q^{15} - q^{16} + 20878 q^{18} - 35346 q^{20} + 127 q^{22} - 6 q^{23} + 50209 q^{24} - 193752 q^{25} + 8188 q^{28} - 21344 q^{30} - 2 q^{31} - 180093 q^{32} + 45534 q^{33} + 20061 q^{34} + 39831 q^{36} + 274239 q^{38} + 125738 q^{39} - 58376 q^{40} + 31314 q^{41} - 213688 q^{42} - 22560 q^{46} - 6 q^{47} - 114411 q^{48} - 974808 q^{49} + 723249 q^{50} - 79338 q^{52} - 231173 q^{54} + 62492 q^{55} + 1294542 q^{56} + 125032 q^{57} - 221138 q^{58} - 1156344 q^{60} + 275294 q^{63} - 804478 q^{64} - 6 q^{65} + 1782258 q^{66} + 2100195 q^{68} - 86464 q^{70} + 1113091 q^{72} - 8 q^{73} - 1886976 q^{74} + 432081 q^{76} + 1658428 q^{78} - 2 q^{79} + 597124 q^{81} - 965382 q^{82} + 4997288 q^{84} - 1041879 q^{86} - 1337970 q^{87} - 536717 q^{88} - 4261994 q^{90} - 737184 q^{92} - 72534 q^{94} + 93744 q^{95} + 1053622 q^{96} - 2 q^{97}+O(q^{100}) $ 140 * q - 3 * q^2 - q^4 + 317 * q^6 - 2 * q^7 - 4 * q^9 + 124 * q^10 - 6946 * q^12 - 7428 * q^14 + 1454 * q^15 - q^16 + 20878 * q^18 - 35346 * q^20 + 127 * q^22 - 6 * q^23 + 50209 * q^24 - 193752 * q^25 + 8188 * q^28 - 21344 * q^30 - 2 * q^31 - 180093 * q^32 + 45534 * q^33 + 20061 * q^34 + 39831 * q^36 + 274239 * q^38 + 125738 * q^39 - 58376 * q^40 + 31314 * q^41 - 213688 * q^42 - 22560 * q^46 - 6 * q^47 - 114411 * q^48 - 974808 * q^49 + 723249 * q^50 - 79338 * q^52 - 231173 * q^54 + 62492 * q^55 + 1294542 * q^56 + 125032 * q^57 - 221138 * q^58 - 1156344 * q^60 + 275294 * q^63 - 804478 * q^64 - 6 * q^65 + 1782258 * q^66 + 2100195 * q^68 - 86464 * q^70 + 1113091 * q^72 - 8 * q^73 - 1886976 * q^74 + 432081 * q^76 + 1658428 * q^78 - 2 * q^79 + 597124 * q^81 - 965382 * q^82 + 4997288 * q^84 - 1041879 * q^86 - 1337970 * q^87 - 536717 * q^88 - 4261994 * q^90 - 737184 * q^92 - 72534 * q^94 + 93744 * q^95 + 1053622 * q^96 - 2 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/72\mathbb{Z}\right)^\times$.

$n$	$37$	$55$	$65$
$\chi(n)$	$-1$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−7.93602	−	1.00978i	−0.992002	−	0.126222i
$2$	−7.93602	−	1.00978i	−0.992002	−	0.126222i
$3$	−16.2129	−	21.5903i	−0.600477	−	0.799642i
$3$	−16.2129	−	21.5903i	−0.600477	−	0.799642i
$4$	61.9607	+	16.0272i	0.968136	+	0.250425i
$5$	92.8213	−	160.771i	0.742571	−	1.28617i	−0.208750	−	0.977969i	$-0.566940\pi$
$5$	92.8213	−	160.771i	0.742571	−	1.28617i	0.951321	−	0.308201i	$-0.0997270\pi$
$6$	106.864	+	187.713i	0.494742	+	0.869040i
$7$	288.471	+	499.646i	0.841022	+	1.45669i	0.889031	+	0.457847i	$0.151379\pi$
$7$	288.471	+	499.646i	0.841022	+	1.45669i	−0.0480088	+	0.998847i	$0.515288\pi$
$8$	−475.537	−	189.758i	−0.928784	−	0.370622i
$9$	−203.285	+	700.083i	−0.278854	+	0.960333i
$10$	−898.975	+	1182.15i	−0.898975	+	1.18215i
$11$	−35.7086	−	61.8492i	−0.0268284	−	0.0464682i	0.852299	−	0.523054i	$-0.175207\pi$
$11$	−35.7086	−	61.8492i	−0.0268284	−	0.0464682i	−0.879128	+	0.476586i	$0.841874\pi$
$12$	−658.530	−	1597.60i	−0.381094	−	0.924536i
$13$	−500.678	−	289.067i	−0.227892	−	0.131573i	0.381707	−	0.924283i	$-0.375336\pi$
$13$	−500.678	−	289.067i	−0.227892	−	0.131573i	−0.609599	+	0.792710i	$0.708670\pi$
$14$	−1784.78	−	4256.49i	−0.650429	−	1.55120i
$15$	−4976.01	+	602.523i	−1.47437	+	0.178525i
$16$	3582.26	+	1986.11i	0.874575	+	0.484891i
$17$			5352.51i			1.08946i	0.838612	+	0.544729i	$0.183368\pi$
$17$			5352.51i			1.08946i	−0.838612	+	0.544729i	$0.816632\pi$
$18$	2320.20	−	5350.60i	0.397839	−	0.917455i
$19$			13199.1i			1.92435i	0.272432	+	0.962175i	$0.412172\pi$
$19$			13199.1i			1.92435i	−0.272432	+	0.962175i	$0.587828\pi$
$20$	8327.99	−	8473.84i	1.04100	−	1.05923i
$21$	6110.58	−	14328.9i	0.659818	−	1.54723i
$22$	220.931	+	526.894i	0.0207485	+	0.0494829i
$23$	8898.34	+	5137.46i	0.731350	+	0.422245i	0.818916	−	0.573914i	$-0.194575\pi$
$23$	8898.34	+	5137.46i	0.731350	+	0.422245i	−0.0875657	+	0.996159i	$0.527909\pi$
$24$	3612.89	+	13343.5i	0.261349	+	0.965244i
$25$	−9419.10	−	16314.4i	−0.602823	−	1.04412i
$26$	3681.50	+	2799.61i	0.209462	+	0.159286i
$27$	18410.9	−	6961.39i	0.935368	−	0.353675i
$28$	9865.93	+	35581.8i	0.449432	+	1.62089i
$29$	7785.84	+	13485.5i	0.319236	+	0.552933i	0.980329	−	0.197371i	$-0.0632404\pi$
$29$	7785.84	+	13485.5i	0.319236	+	0.552933i	−0.661093	+	0.750304i	$0.729907\pi$
$30$	40098.1	+	243.014i	1.48511	+	0.00900052i
$31$	17808.1	−	30844.5i	0.597767	−	1.03536i	−0.395383	−	0.918516i	$-0.629388\pi$
$31$	17808.1	−	30844.5i	0.597767	−	1.03536i	0.993150	−	0.116846i	$-0.0372785\pi$
$32$	−26423.3	−	19379.1i	−0.806376	−	0.591403i
$33$	−756.404	+	1773.71i	−0.0210481	+	0.0493562i
$34$	5404.83	−	42477.6i	0.137514	−	1.08075i
$35$	107105.			2.49807
$36$	−23816.0	+	40119.6i	−0.510460	+	0.859902i
$37$			7327.20i			0.144655i	0.997381	+	0.0723274i	$0.0230427\pi$
$37$			7327.20i			0.144655i	−0.997381	+	0.0723274i	$0.976957\pi$
$38$	13328.1	−	104748.i	0.242895	−	1.90896i
$39$	1876.39	+	15496.4i	0.0316323	+	0.261239i
$40$	−74647.7	+	58839.1i	−1.16637	+	0.919361i
$41$	22239.4	+	12839.9i	0.322680	+	0.186299i	0.652586	−	0.757714i	$-0.273684\pi$
$41$	22239.4	+	12839.9i	0.322680	+	0.186299i	−0.329907	+	0.944014i	$0.607017\pi$
$42$	−62962.6	+	107544.i	−0.849835	+	1.45157i
$43$	−30439.0	+	17574.0i	−0.382847	+	0.221037i	−0.679056	−	0.734086i	$-0.737611\pi$
$43$	−30439.0	+	17574.0i	−0.382847	+	0.221037i	0.296209	+	0.955123i	$0.404277\pi$
$44$	−1221.26	−	4404.53i	−0.0143368	−	0.0517060i
$45$	93684.1	+	97665.0i	1.02808	+	1.07177i
$46$	−65429.7	−	49756.3i	−0.672204	−	0.511181i
$47$	86527.4	−	49956.6i	0.833413	−	0.481171i	−0.0216070	−	0.999767i	$-0.506878\pi$
$47$	86527.4	−	49956.6i	0.833413	−	0.481171i	0.855020	+	0.518595i	$0.173545\pi$
$48$	−15198.0	−	109543.i	−0.137424	−	0.990512i
$49$	−107606.	+	186379.i	−0.914637	+	1.58420i
$50$	58276.3	+	138982.i	0.466211	+	1.11186i
$51$	115562.	−	86779.7i	0.871177	−	0.654195i
$52$	−26389.5	−	25935.2i	−0.187681	−	0.184451i
$53$	−210300.			−1.41257			−0.706286	−	0.707926i	$-0.749631\pi$
$53$	−210300.			−1.41257			−0.706286	+	0.707926i	$0.749631\pi$
$54$	−153138.	+	36654.9i	−0.972529	+	0.232782i
$55$	−13258.1			−0.0796880
$56$	−42366.6	−	292340.i	−0.241246	−	1.66465i
$57$	284973.	−	213996.i	1.53879	−	1.15553i
$58$	−48171.3	−	114883.i	−0.246890	−	0.588805i
$59$	189669.	−	328517.i	0.923508	−	1.59956i	0.129565	−	0.991571i	$-0.458642\pi$
$59$	189669.	−	328517.i	0.923508	−	1.59956i	0.793943	−	0.607992i	$-0.208025\pi$
$60$	−317974.	−	42418.6i	−1.47210	−	0.196382i
$61$	102615.	−	59244.5i	0.452084	−	0.261011i	−0.256626	−	0.966511i	$-0.582611\pi$
$61$	102615.	−	59244.5i	0.452084	−	0.261011i	0.708710	+	0.705500i	$0.249277\pi$
$62$	−172471.	+	226800.i	−0.723671	+	0.951631i
$63$	−408435.	+	100383.i	−1.63343	+	0.401457i
$64$	190127.	+	180474.i	0.725279	+	0.688455i
$65$	−92947.3	+	53663.1i	−0.338452	+	0.195405i
$66$	7793.89	−	13312.4i	0.0271095	−	0.0463048i
$67$	160838.	+	92859.9i	0.534767	+	0.308748i	0.742955	−	0.669341i	$-0.233423\pi$
$67$	160838.	+	92859.9i	0.534767	+	0.308748i	−0.208189	+	0.978089i	$0.566757\pi$
$68$	−85785.7	+	331645.i	−0.272828	+	1.05474i
$69$	−33348.3	−	275411.i	−0.101514	−	0.838367i
$70$	−849987.	−	108152.i	−2.47809	−	0.315312i
$71$			527264.i			1.47317i	0.676345	+	0.736585i	$0.263563\pi$
$71$			527264.i			1.47317i	−0.676345	+	0.736585i	$0.736437\pi$
$72$	229516.	−	294341.i	0.614916	−	0.788593i
$73$	−287298.			−0.738524			−0.369262	−	0.929325i	$-0.620390\pi$
$73$	−287298.			−0.738524			−0.369262	+	0.929325i	$0.620390\pi$
$74$	7398.83	−	58148.8i	0.0182586	−	0.143498i
$75$	−199522.	+	467864.i	−0.472940	+	1.10901i
$76$	−211545.	+	817827.i	−0.481905	+	1.86303i
$77$	20601.8	−	35683.3i	0.0451266	−	0.0781616i
$78$	756.801	−	124875.i	0.00159477	−	0.263142i
$79$	347641.	+	602132.i	0.705098	+	1.22127i	0.966656	+	0.256078i	$0.0824303\pi$
$79$	347641.	+	602132.i	0.705098	+	1.22127i	−0.261558	+	0.965188i	$0.584236\pi$
$80$	651820.	−	391571.i	1.27309	−	0.764787i
$81$	−448792.	−	284632.i	−0.844481	−	0.535586i
$82$	−163527.	−	124355.i	−0.296584	−	0.225538i
$83$	−145784.	−	252505.i	−0.254962	−	0.441607i	0.709923	−	0.704279i	$-0.248730\pi$
$83$	−145784.	−	252505.i	−0.254962	−	0.441607i	−0.964885	+	0.262672i	$0.915396\pi$
$84$	608267.	−	789892.i	1.02626	−	1.33269i
$85$	860530.	+	496827.i	1.40123	+	0.809000i
$86$	259310.	−	108731.i	0.407685	−	0.170945i
$87$	164925.	−	386737.i	0.250454	−	0.587298i
$88$	5244.39	+	36187.6i	0.00769568	+	0.0531021i
$89$		−	567422.i		−	0.804889i	−0.915444	−	0.402444i	$-0.868161\pi$
$89$		−	567422.i		−	0.804889i	0.915444	−	0.402444i	$-0.131839\pi$
$90$	−644859.	−	869671.i	−0.884580	−	1.19296i
$91$		−	333549.i		−	0.442625i
$92$	469008.	+	460936.i	0.602306	+	0.591939i
$93$	−954663.	+	115596.i	−1.18686	+	0.143712i
$94$	−737128.	+	309083.i	−0.887481	+	0.372128i
$95$	2.12204e6	+	1.22516e6i	2.47504	+	1.42897i
$96$	9997.64	+	884680.i	0.0113001	+	0.999936i
$97$	237627.	+	411582.i	0.260364	+	0.450963i	0.966339	−	0.257274i	$-0.0828242\pi$
$97$	237627.	+	411582.i	0.260364	+	0.450963i	−0.705975	+	0.708237i	$0.749491\pi$
$98$	1.04217e6	−	1.37045e6i	1.10728	−	1.45608i
$99$	50558.6	−	12426.0i	0.0521062	−	0.0128064i
$100$	−322141.	−	1.16181e6i	−0.322141	−	1.16181i
$101$	350051.	+	606306.i	0.339756	+	0.588475i	0.984387	−	0.176020i	$-0.0563222\pi$
$101$	350051.	+	606306.i	0.339756	+	0.588475i	−0.644631	+	0.764494i	$0.722989\pi$
$102$	−1.00473e6	+	571993.i	−0.946783	+	0.539001i
$103$	454651.	−	787478.i	0.416070	−	0.720654i	−0.579470	−	0.814993i	$-0.696741\pi$
$103$	454651.	−	787478.i	0.416070	−	0.720654i	0.995540	+	0.0943394i	$0.0300739\pi$
$104$	183238.	+	232470.i	0.162898	+	0.206665i
$105$	−1.73648e6	−	2.31243e6i	−1.50004	−	1.99756i
$106$	1.66894e6	+	212355.i	1.40127	+	0.178298i
$107$	65771.6			0.0536892			0.0268446	−	0.999640i	$-0.491454\pi$
$107$	65771.6			0.0536892			0.0268446	+	0.999640i	$0.491454\pi$
$108$	1.25232e6	−	136258.i	0.994133	−	0.108166i
$109$			7988.54i			0.00616862i	0.999995	+	0.00308431i	$0.000981768\pi$
$109$			7988.54i			0.00616862i	−0.999995	+	0.00308431i	$0.999018\pi$
$110$	105216.	+	13387.7i	0.0790507	+	0.0100584i
$111$	158197.	−	118795.i	0.115672	−	0.0868620i
$112$	41024.1	+	2.36280e6i	0.0292002	+	1.68179i
$113$	−280505.	−	161950.i	−0.194404	−	0.112239i	0.399639	−	0.916673i	$-0.369136\pi$
$113$	−280505.	−	161950.i	−0.194404	−	0.112239i	−0.594043	+	0.804434i	$0.702469\pi$
$114$	−2.47764e6	+	1.41052e6i	−1.67234	+	0.952057i
$115$	1.65191e6	−	953731.i	1.08616	−	0.627094i
$116$	266282.	+	960355.i	0.170596	+	0.615259i
$117$	304151.	−	291754.i	0.189903	−	0.182162i
$118$	−1.83695e6	+	2.41559e6i	−1.11802	+	1.47020i
$119$	−2.67436e6	+	1.54404e6i	−1.58701	+	0.916259i
$120$	2.48061e6	+	657717.i	1.43554	+	0.380623i
$121$	883230.	−	1.52980e6i	0.498560	−	0.863532i
$122$	−874174.	+	366548.i	−0.481414	+	0.201860i
$123$	−83346.7	−	688328.i	−0.0447892	−	0.369896i
$124$	1.59775e6	−	1.62573e6i	0.838000	−	0.852676i
$125$	−596508.			−0.305412
$126$	3.34271e6	−	384214.i	1.67104	−	0.192071i
$127$	−1.22976e6			−0.600356			−0.300178	−	0.953883i	$-0.597046\pi$
$127$	−1.22976e6			−0.600356			−0.300178	+	0.953883i	$0.597046\pi$
$128$	−1.32662e6	−	1.62423e6i	−0.632580	−	0.774495i
$129$	872932.	+	372263.i	0.406641	+	0.173413i
$130$	791819.	−	332016.i	0.360409	−	0.151122i
$131$	−1.10217e6	+	1.90902e6i	−0.490271	+	0.849174i	−0.999937	−	0.0111980i	$-0.996436\pi$
$131$	−1.10217e6	+	1.90902e6i	−0.490271	+	0.849174i	0.509666	+	0.860372i	$0.329769\pi$
$132$	−75295.0	+	97777.6i	−0.0327374	+	0.0425126i
$133$	−6.59488e6	+	3.80756e6i	−2.80319	+	1.61842i
$134$	−1.18265e6	−	899347.i	−0.491519	−	0.373777i
$135$	589729.	−	3.60610e6i	0.239691	−	1.46567i
$136$	1.01568e6	−	2.54532e6i	0.403777	−	1.01187i
$137$	−430159.	+	248352.i	−0.167289	+	0.0965843i	−0.581307	−	0.813684i	$-0.697458\pi$
$137$	−430159.	+	248352.i	−0.167289	+	0.0965843i	0.414018	+	0.910269i	$0.364125\pi$
$138$	−13450.3	+	2.21934e6i	−0.00511793	+	0.844475i
$139$	−232236.	−	134082.i	−0.0864740	−	0.0499258i	0.456139	−	0.889908i	$-0.349232\pi$
$139$	−232236.	−	134082.i	−0.0864740	−	0.0499258i	−0.542613	+	0.839983i	$0.682565\pi$
$140$	6.63630e6	+	1.71659e6i	2.41848	+	0.625580i
$141$	−2.48144e6	−	1.05821e6i	−0.885210	−	0.377499i
$142$	532418.	−	4.18437e6i	0.185946	−	1.46139i
$143$			41288.7i			0.0141196i
$144$	−2.11866e6	+	2.10413e6i	−0.709535	+	0.704670i
$145$	2.89077e6			0.948221
$146$	2.28001e6	+	290107.i	0.732617	+	0.0932179i
$147$	5.76860e6	−	698495.i	1.81601	−	0.219893i
$148$	−117434.	+	453999.i	−0.0362252	+	0.140046i
$149$	−890239.	+	1.54194e6i	−0.269121	+	0.466132i	−0.968635	−	0.248487i	$-0.920067\pi$
$149$	−890239.	+	1.54194e6i	−0.269121	+	0.466132i	0.699514	+	0.714619i	$0.253400\pi$
$150$	2.05585e6	−	3.51151e6i	0.609139	−	1.04045i
$151$	3.28424e6	+	5.68848e6i	0.953904	+	1.65221i	0.736857	+	0.676049i	$0.236309\pi$
$151$	3.28424e6	+	5.68848e6i	0.953904	+	1.65221i	0.217048	+	0.976161i	$0.430357\pi$
$152$	2.50464e6	−	6.27667e6i	0.713206	−	1.78731i
$153$	−3.74720e6	−	1.08808e6i	−1.04624	−	0.303800i
$154$	−199528.	+	262380.i	−0.0546314	+	0.0718405i
$155$	−3.30594e6	−	5.72605e6i	−0.887768	−	1.53766i
$156$	−132101.	+	990242.i	−0.0347963	+	0.260836i
$157$	−1.84275e6	−	1.06391e6i	−0.476175	−	0.274920i	0.242646	−	0.970115i	$-0.421985\pi$
$157$	−1.84275e6	−	1.06391e6i	−0.476175	−	0.274920i	−0.718821	+	0.695195i	$0.755318\pi$
$158$	−2.15087e6	−	5.12956e6i	−0.545308	−	1.30050i
$159$	3.40956e6	+	4.54044e6i	0.848218	+	1.12955i
$160$	−5.56825e6	+	2.44932e6i	−1.35944	+	0.597979i
$161$			5.92802e6i			1.42047i
$162$	3.27420e6	+	2.71202e6i	0.770124	+	0.637894i
$163$			3.78468e6i			0.873908i	0.899484	+	0.436954i	$0.143943\pi$
$163$			3.78468e6i			0.873908i	−0.899484	+	0.436954i	$0.856057\pi$
$164$	1.17218e6	+	1.15201e6i	0.265744	+	0.261170i
$165$	214952.	+	286247.i	0.0478508	+	0.0637219i
$166$	901969.	+	2.15109e6i	0.197182	+	0.470256i
$167$	−1.38746e6	−	801050.i	−0.297900	−	0.171993i	0.343599	−	0.939116i	$-0.388354\pi$
$167$	−1.38746e6	−	801050.i	−0.297900	−	0.171993i	−0.641499	+	0.767124i	$0.721687\pi$
$168$	−5.62483e6	+	5.65438e6i	−1.18627	+	1.19250i
$169$	−2.24629e6	−	3.89068e6i	−0.465377	−	0.806056i
$170$	−6.32750e6	−	4.81177e6i	−1.28791	−	0.979396i
$171$	−9.24048e6	−	2.68318e6i	−1.84802	−	0.536613i
$172$	−2.16768e6	+	601044.i	−0.426001	+	0.118119i
$173$	−1.75647e6	−	3.04229e6i	−0.339236	−	0.587574i	0.645053	−	0.764138i	$-0.276835\pi$
$173$	−1.75647e6	−	3.04229e6i	−0.339236	−	0.587574i	−0.984289	+	0.176564i	$0.943502\pi$
$174$	−1.69936e6	+	2.90262e6i	−0.322581	+	0.550988i
$175$	5.43427e6	−	9.41243e6i	1.01397	−	1.75626i
$176$	−5078.21	−	292481.i	−0.000931479	−	0.0536488i
$177$	−1.01679e7	+	1.23118e6i	−1.83362	+	0.222026i
$178$	−572968.	+	4.50307e6i	−0.101595	+	0.798451i
$179$	3.82790e6			0.667424			0.333712	−	0.942675i	$-0.391699\pi$
$179$	3.82790e6			0.667424			0.333712	+	0.942675i	$0.391699\pi$
$180$	4.23944e6	+	7.55288e6i	0.726927	+	1.29508i
$181$		−	4.75768e6i		−	0.802342i	−0.916003	−	0.401171i	$-0.868603\pi$
$181$		−	4.75768e6i		−	0.802342i	0.916003	−	0.401171i	$-0.131397\pi$
$182$	−336810.	+	2.64705e6i	−0.0558689	+	0.439085i
$183$	−2.94279e6	−	1.25496e6i	−0.480182	−	0.204774i
$184$	−3.25662e6	−	4.13159e6i	−0.522773	−	0.663229i
$185$	1.17800e6	+	680121.i	0.186051	+	0.107416i
$186$	7.69295e6	+	46623.0i	1.19551	+	0.00724539i
$187$	331048.	−	191131.i	0.0506252	−	0.0292285i
$188$	6.16196e6	−	1.70856e6i	0.927354	−	0.257132i
$189$	8.78922e6	+	7.19075e6i	1.30186	+	1.06510i
$190$	−1.56034e7	−	1.18657e7i	−2.27488	−	1.72994i
$191$	−8.02678e6	+	4.63426e6i	−1.15197	+	0.665090i	−0.949366	−	0.314171i	$-0.898274\pi$
$191$	−8.02678e6	+	4.63426e6i	−1.15197	+	0.665090i	−0.202603	+	0.979261i	$0.564940\pi$
$192$	813986.	−	7.03093e6i	0.115004	−	0.993365i
$193$	2.02148e6	−	3.50131e6i	0.281189	−	0.487033i	−0.690489	−	0.723343i	$-0.742605\pi$
$193$	2.02148e6	−	3.50131e6i	0.281189	−	0.487033i	0.971678	+	0.236310i	$0.0759380\pi$
$194$	−1.47021e6	−	3.50627e6i	−0.201360	−	0.480220i
$195$	2.66555e6	+	1.13673e6i	0.359487	+	0.153304i
$196$	−9.65449e6	+	9.82357e6i	−1.28222	+	1.30467i
$197$	−80548.4			−0.0105356			−0.00526779	−	0.999986i	$-0.501677\pi$
$197$	−80548.4			−0.0105356			−0.00526779	+	0.999986i	$0.501677\pi$
$198$	−413781.	+	47560.4i	−0.0533059	+	0.00612702i
$199$	7.96394e6			1.01057			0.505287	−	0.862951i	$-0.331386\pi$
$199$	7.96394e6			1.01057			0.505287	+	0.862951i	$0.331386\pi$
$200$	1.38335e6	+	9.54544e6i	0.172918	+	1.19318i
$201$	−602773.	−	4.97807e6i	−0.0742277	−	0.613018i
$202$	−2.16578e6	−	5.16513e6i	−0.262760	−	0.626653i
$203$	−4.49198e6	+	7.78033e6i	−0.536969	+	0.930058i
$204$	8.55117e6	−	3.52479e6i	1.00724	−	0.415186i
$205$	4.12858e6	−	2.38364e6i	0.479225	−	0.276681i
$206$	−4.40329e6	+	5.79034e6i	−0.503704	+	0.662373i
$207$	−5.40554e6	+	5.18521e6i	−0.609436	+	0.584595i
$208$	−1.21944e6	−	2.02991e6i	−0.135510	−	0.225573i
$209$	816354.	−	471322.i	0.0894211	−	0.0516273i
$210$	1.14457e7	+	2.01049e7i	1.23590	+	2.17093i
$211$	1.50611e7	+	8.69551e6i	1.60328	+	0.925652i	0.990826	+	0.135144i	$0.0431496\pi$
$211$	1.50611e7	+	8.69551e6i	1.60328	+	0.925652i	0.612451	+	0.790509i	$0.290184\pi$
$212$	−1.30303e7	−	3.37051e6i	−1.36756	−	0.353743i
$213$	1.13838e7	−	8.54847e6i	1.17801	−	0.884605i
$214$	−521964.	−	66414.5i	−0.0532598	−	0.00677675i
$215$			6.52496e6i			0.656542i
$216$	−1.00760e7	−	183215.i	−0.999835	−	0.0181802i
$217$	2.05484e7			2.01094
$218$	8066.63	−	63397.2i	0.000778615	−	0.00611928i
$219$	4.65794e6	+	6.20287e6i	0.443467	+	0.590555i
$220$	−821481.	−	212490.i	−0.0771488	−	0.0199559i
$221$	1.54723e6	−	2.67989e6i	0.143344	−	0.248279i
$222$	−1.37541e6	+	783017.i	−0.125711	+	0.0715669i
$223$	−4.52718e6	−	7.84130e6i	−0.408237	−	0.707088i	0.586455	−	0.809982i	$-0.300523\pi$
$223$	−4.52718e6	−	7.84130e6i	−0.408237	−	0.707088i	−0.994692	+	0.102894i	$0.967190\pi$
$224$	2.06032e6	−	1.87926e7i	0.183312	−	1.67203i
$225$	1.33362e7	−	3.27770e6i	1.17080	−	0.287754i
$226$	2.06256e6	+	1.56848e6i	0.178682	+	0.135880i
$227$	−8.35175e6	−	1.44656e7i	−0.714002	−	1.23669i	−0.963343	−	0.268273i	$-0.913547\pi$
$227$	−8.35175e6	−	1.44656e7i	−0.714002	−	1.23669i	0.249341	−	0.968416i	$-0.419786\pi$
$228$	2.10869e7	−	8.69201e6i	1.77913	−	0.733357i
$229$	1.05099e7	+	6.06791e6i	0.875172	+	0.505281i	0.869064	−	0.494700i	$-0.164722\pi$
$229$	1.05099e7	+	6.06791e6i	0.875172	+	0.505281i	0.00610873	+	0.999981i	$0.498056\pi$
$230$	−1.40726e7	+	5.90077e6i	−1.15662	+	0.484981i
$231$	−1.10443e6	+	133731.i	−0.0895988	+	0.0108491i
$232$	−1.14348e6	−	7.89028e6i	−0.0915722	−	0.631871i
$233$			9.44982e6i			0.747061i	0.927618	+	0.373530i	$0.121853\pi$
$233$			9.44982e6i			0.747061i	−0.927618	+	0.373530i	$0.878147\pi$
$234$	−2.70835e6	+	2.00824e6i	−0.211377	+	0.156736i
$235$		−	1.85482e7i		−	1.42921i
$236$	1.70172e7	−	1.73153e7i	1.29465	−	1.31733i
$237$	7.36396e6	−	1.72680e7i	0.553180	−	1.29717i
$238$	2.27829e7	−	9.55304e6i	1.68997	−	0.708616i
$239$	−5.98010e6	−	3.45261e6i	−0.438041	−	0.252903i	0.264725	−	0.964324i	$-0.414719\pi$
$239$	−5.98010e6	−	3.45261e6i	−0.438041	−	0.252903i	−0.702766	+	0.711421i	$0.748052\pi$
$240$	−1.90220e7	−	7.72451e6i	−1.37601	−	0.558775i
$241$	9.10166e6	+	1.57645e7i	0.650233	+	1.12624i	0.983066	+	0.183251i	$0.0586622\pi$
$241$	9.10166e6	+	1.57645e7i	0.650233	+	1.12624i	−0.332833	+	0.942986i	$0.608004\pi$
$242$	−8.55408e6	+	1.12487e7i	−0.603570	+	0.793696i
$243$	1.13091e6	+	1.43043e7i	0.0788148	+	0.996889i
$244$	7.30759e6	−	2.02621e6i	0.503043	−	0.139481i
$245$	1.99763e7	+	3.46000e7i	1.35837	+	2.35276i
$246$	−33616.0	+	5.54674e6i	−0.00225809	+	0.372591i
$247$	3.81543e6	−	6.60851e6i	0.253193	−	0.438544i
$248$	−1.43214e7	+	1.12885e7i	−0.938924	+	0.740083i
$249$	−3.08809e6	+	7.24135e6i	−0.200028	+	0.469053i
$250$	4.73390e6	+	602339.i	0.302970	+	0.0385497i
$251$	3.34537e6			0.211555			0.105777	−	0.994390i	$-0.466267\pi$
$251$	3.34537e6			0.211555			0.105777	+	0.994390i	$0.466267\pi$
$252$	−2.69158e7	−	326258.i	−1.68192	−	0.0203873i
$253$		−	733806.i		−	0.0453127i
$254$	9.75939e6	+	1.24178e6i	0.595555	+	0.0757781i
$255$	−3.22501e6	−	2.66341e7i	−0.194496	−	1.60627i
$256$	8.88794e6	+	1.42295e7i	0.529762	+	0.848146i
$257$	−1.78214e7	−	1.02892e7i	−1.04989	−	0.606152i	−0.127268	−	0.991868i	$-0.540621\pi$
$257$	−1.78214e7	−	1.02892e7i	−1.04989	−	0.606152i	−0.922617	+	0.385716i	$0.873954\pi$
$258$	−6.55170e6	−	3.83575e6i	−0.381500	−	0.223353i
$259$	−3.66101e6	+	2.11368e6i	−0.210718	+	0.121658i
$260$	−6.61915e6	+	1.83532e6i	−0.376601	+	0.104422i
$261$	−1.10237e7	+	2.70935e6i	−0.620020	+	0.152385i
$262$	1.06746e7	−	1.40371e7i	0.593534	−	0.780500i
$263$	−1.79290e7	+	1.03513e7i	−0.985573	+	0.569021i	−0.903948	−	0.427643i	$-0.859344\pi$
$263$	−1.79290e7	+	1.03513e7i	−0.985573	+	0.569021i	−0.0816246	+	0.996663i	$0.526011\pi$
$264$	696276.	−	699934.i	0.0378416	−	0.0380404i
$265$	−1.95203e7	+	3.38101e7i	−1.04893	+	1.81681i
$266$	5.61819e7	−	2.35575e7i	2.98505	−	1.25165i
$267$	−1.22508e7	+	9.19954e6i	−0.643623	+	0.483317i
$268$	8.47735e6	+	8.33144e6i	0.440409	+	0.432828i
$269$	1.37460e7			0.706188			0.353094	−	0.935588i	$-0.385130\pi$
$269$	1.37460e7			0.706188			0.353094	+	0.935588i	$0.385130\pi$
$270$	−8.32145e6	+	2.80226e7i	−0.422774	+	1.42370i
$271$	−342824.			−0.0172251			−0.00861257	−	0.999963i	$-0.502742\pi$
$271$	−342824.			−0.0172251			−0.00861257	+	0.999963i	$0.502742\pi$
$272$	−1.06307e7	+	1.91741e7i	−0.528268	+	0.952813i
$273$	−7.20143e6	+	5.40779e6i	−0.353941	+	0.265786i
$274$	3.66453e6	−	1.53656e6i	0.178142	−	0.0746963i
$275$	−672687.	+	1.16513e6i	−0.0323456	+	0.0560242i
$276$	2.34778e6	−	1.75991e7i	0.111668	−	0.837075i
$277$	−2.68895e7	+	1.55247e7i	−1.26515	+	0.730437i	−0.974067	−	0.226260i	$-0.927350\pi$
$277$	−2.68895e7	+	1.55247e7i	−1.26515	+	0.730437i	−0.291087	+	0.956697i	$0.594017\pi$
$278$	1.70764e6	+	1.29858e6i	0.0794807	+	0.0604414i
$279$	1.79736e7	+	1.87373e7i	0.827604	+	0.862771i
$280$	−5.09324e7	−	2.03241e7i	−2.32017	−	0.925841i
$281$	2.39904e7	−	1.38509e7i	1.08123	−	0.624250i	0.150004	−	0.988685i	$-0.452071\pi$
$281$	2.39904e7	−	1.38509e7i	1.08123	−	0.624250i	0.931229	+	0.364436i	$0.118738\pi$
$282$	1.86242e7	+	1.09037e7i	0.830481	+	0.486213i
$283$	−1.43855e7	−	8.30546e6i	−0.634695	−	0.366441i	0.147873	−	0.989006i	$-0.452757\pi$
$283$	−1.43855e7	−	8.30546e6i	−0.634695	−	0.366441i	−0.782568	+	0.622565i	$0.786091\pi$
$284$	−8.45056e6	+	3.26696e7i	−0.368918	+	1.42623i
$285$	−7.95277e6	−	6.56789e7i	−0.343545	−	2.83721i
$286$	41692.3	−	327668.i	0.00178221	−	0.0140067i
$287$			1.48158e7i			0.626727i
$288$	1.89384e7	−	1.45591e7i	0.792805	−	0.609475i
$289$	−4.51181e6			−0.186921
$290$	−2.29412e7	−	2.91903e6i	−0.940637	−	0.119686i
$291$	5.03357e6	−	1.18034e7i	0.204267	−	0.478991i
$292$	−1.78012e7	−	4.60459e6i	−0.714992	−	0.184945i
$293$	7.22005e6	−	1.25055e7i	0.287037	−	0.497162i	−0.686064	−	0.727541i	$-0.740663\pi$
$293$	7.22005e6	−	1.25055e7i	0.287037	−	0.497162i	0.973101	+	0.230379i	$0.0739966\pi$
$294$	−4.64850e7	−	281722.i	−1.82924	−	0.0110861i
$295$	−3.52107e7	−	6.09867e7i	−1.37154	−	2.37558i
$296$	1.39040e6	−	3.48436e6i	0.0536123	−	0.134353i
$297$	−1.08798e6	−	890115.i	−0.0415291	−	0.0339763i
$298$	8.62197e6	−	1.13379e7i	0.325805	−	0.428435i
$299$	−2.97014e6	−	5.14443e6i	−0.111112	−	0.192452i
$300$	−1.98611e7	+	2.57914e7i	−0.735595	+	0.955239i
$301$	−1.75615e7	−	1.01392e7i	−0.643966	−	0.371794i
$302$	−2.03197e7	−	4.84602e7i	−0.737730	−	1.75940i
$303$	7.41501e6	−	1.73877e7i	0.266553	−	0.625049i
$304$	−2.62149e7	+	4.72826e7i	−0.933099	+	1.68299i
$305$		−	2.19966e7i		−	0.775276i
$306$	2.86391e7	+	1.24189e7i	0.999530	+	0.433429i
$307$			1.15342e7i			0.398633i	0.979935	+	0.199316i	$0.0638721\pi$
$307$			1.15342e7i			0.398633i	−0.979935	+	0.199316i	$0.936128\pi$
$308$	1.84841e6	−	1.88078e6i	0.0632623	−	0.0643702i
$309$	−2.43731e7	+	2.95124e6i	−0.826105	+	0.100030i
$310$	2.04540e7	+	4.87803e7i	0.686582	+	1.63742i
$311$	2.23576e7	+	1.29082e7i	0.743265	+	0.429124i	0.823255	−	0.567671i	$-0.192156\pi$
$311$	2.23576e7	+	1.29082e7i	0.743265	+	0.429124i	−0.0799901	+	0.996796i	$0.525489\pi$
$312$	2.04828e6	−	7.72518e6i	0.0674412	−	0.254358i
$313$	2.86139e7	+	4.95608e7i	0.933135	+	1.61624i	0.777927	+	0.628355i	$0.216272\pi$
$313$	2.86139e7	+	4.95608e7i	0.933135	+	1.61624i	0.155208	+	0.987882i	$0.450395\pi$
$314$	1.35498e7	+	1.03040e7i	0.437666	+	0.332825i
$315$	−2.17728e7	+	7.49824e7i	−0.696598	+	2.39898i
$316$	1.18896e7	+	4.28802e7i	0.376796	+	1.35893i
$317$	−6.62026e6	−	1.14666e7i	−0.207825	−	0.359963i	0.743204	−	0.669064i	$-0.233305\pi$
$317$	−6.62026e6	−	1.14666e7i	−0.207825	−	0.359963i	−0.951029	+	0.309102i	$0.899972\pi$
$318$	−2.24735e7	−	3.94759e7i	−0.698859	−	1.22758i
$319$	556044.	−	963096.i	0.0171292	−	0.0296686i
$320$	4.66630e7	−	1.38152e7i	1.42404	−	0.421605i
$321$	−1.06635e6	−	1.42003e6i	−0.0322391	−	0.0429321i
$322$	5.98597e6	−	4.70449e7i	0.179295	−	1.40911i
$323$	−7.06484e7			−2.09650
$324$	−2.32456e7	−	2.48289e7i	−0.683448	−	0.729999i
$325$			1.08910e7i			0.317262i
$326$	3.82167e6	−	3.00352e7i	0.110306	−	0.866919i
$327$	172475.	−	129517.i	0.00493268	−	0.00370412i
$328$	−8.13918e6	−	1.03260e7i	−0.230653	−	0.292624i
$329$	4.99212e7	+	2.88220e7i	1.40184	+	0.809351i
$330$	−1.41682e6	−	2.48871e6i	−0.0394250	−	0.0692521i
$331$	2.36579e7	−	1.36589e7i	0.652367	−	0.376644i	−0.136996	−	0.990572i	$-0.543745\pi$
$331$	2.36579e7	−	1.36589e7i	0.652367	−	0.376644i	0.789362	+	0.613928i	$0.210411\pi$
$332$	−4.98592e6	−	1.79819e7i	−0.136248	−	0.491384i
$333$	−5.12965e6	−	1.48951e6i	−0.138917	−	0.0403376i
$334$	1.02020e7	+	7.75816e6i	0.273808	+	0.208219i
$335$	2.98584e7	−	1.72388e7i	0.794204	−	0.458534i
$336$	5.03484e7	−	3.91935e7i	1.32730	−	1.03323i
$337$	1.75112e7	−	3.03303e7i	0.457537	−	0.792477i	−0.541294	−	0.840834i	$-0.682065\pi$
$337$	1.75112e7	−	3.03303e7i	0.457537	−	0.792477i	0.998830	+	0.0483571i	$0.0153985\pi$
$338$	1.38978e7	+	3.31447e7i	0.359913	+	0.858350i
$339$	1.05125e6	+	8.68186e6i	0.0269840	+	0.222851i
$340$	4.53563e7	+	4.45756e7i	1.15399	+	1.13412i
$341$	−2.54361e6			−0.0641486
$342$	7.06232e7	+	3.06245e7i	1.76551	+	0.765581i
$343$	−5.62883e7			−1.39488
$344$	1.78097e7	−	2.58102e6i	0.437503	−	0.0634039i
$345$	−4.73736e7	−	2.02026e7i	−1.15366	−	0.491982i
$346$	1.08673e7	+	2.59173e7i	0.262358	+	0.625694i
$347$	1.32795e7	−	2.30008e7i	0.317829	−	0.550497i	−0.662205	−	0.749322i	$-0.730379\pi$
$347$	1.32795e7	−	2.30008e7i	0.317829	−	0.550497i	0.980035	+	0.198826i	$0.0637127\pi$
$348$	1.64172e7	−	2.13192e7i	0.389548	−	0.505864i
$349$	−3.93401e7	+	2.27130e7i	−0.925463	+	0.534316i	−0.885374	−	0.464880i	$-0.846098\pi$
$349$	−3.93401e7	+	2.27130e7i	−0.925463	+	0.534316i	−0.0400893	+	0.999196i	$0.512764\pi$
$350$	−5.26309e7	+	6.92098e7i	−1.22754	+	1.61422i
$351$	−1.12302e7	−	1.83655e6i	−0.259697	−	0.0424699i
$352$	−255039.	+	2.32626e6i	−0.00584762	+	0.0533373i
$353$	5.94887e7	−	3.43458e7i	1.35242	−	0.780818i	0.363829	−	0.931466i	$-0.381469\pi$
$353$	5.94887e7	−	3.43458e7i	1.35242	−	0.780818i	0.988588	+	0.150647i	$0.0481358\pi$
$354$	8.19356e7	+	496570.i	1.84698	+	0.0111936i
$355$	8.47689e7	+	4.89413e7i	1.89475	+	1.09393i
$356$	9.09417e6	−	3.51578e7i	0.201564	−	0.779242i
$357$	7.66955e7	+	3.27069e7i	1.68564	+	0.718845i
$358$	−3.03783e7	−	3.86532e6i	−0.662086	−	0.0842435i
$359$		−	3.77834e7i		−	0.816615i	−0.912844	−	0.408308i	$-0.866119\pi$
$359$		−	3.77834e7i		−	0.816615i	0.912844	−	0.408308i	$-0.133881\pi$
$360$	−2.60175e7	−	6.42207e7i	−0.557646	−	1.37647i
$361$	−1.27171e8			−2.70312
$362$	−4.80419e6	+	3.77570e7i	−0.101273	+	0.795925i
$363$	−4.73486e7	+	5.73324e6i	−0.989891	+	0.119862i
$364$	5.34585e6	−	2.06669e7i	0.110844	−	0.428521i
$365$	−2.66674e7	+	4.61893e7i	−0.548406	+	0.949868i
$366$	2.20868e7	+	1.29309e7i	0.450494	+	0.263746i
$367$	3.04785e7	+	5.27902e7i	0.616587	+	1.06796i	0.990104	+	0.140337i	$0.0448187\pi$
$367$	3.04785e7	+	5.27902e7i	0.616587	+	1.06796i	−0.373516	+	0.927624i	$0.621848\pi$
$368$	2.16726e7	+	3.60768e7i	0.434878	+	0.723910i
$369$	−1.35099e7	+	1.29593e7i	−0.268890	+	0.257930i
$370$	−8.66189e6	−	6.58697e6i	−0.171004	−	0.130041i
$371$	−6.06653e7	−	1.05075e8i	−1.18801	−	2.05769i
$372$	−6.10043e7	−	8.13815e6i	−1.18504	−	0.158087i
$373$	−1.90195e7	−	1.09809e7i	−0.366500	−	0.211599i	0.305429	−	0.952215i	$-0.401200\pi$
$373$	−1.90195e7	−	1.09809e7i	−0.366500	−	0.211599i	−0.671928	+	0.740616i	$0.734534\pi$
$374$	−2.82020e6	+	1.18253e6i	−0.0539096	+	0.0226047i
$375$	9.67112e6	+	1.28788e7i	0.183393	+	0.244220i
$376$	−5.06267e7	+	7.33694e6i	−0.952393	+	0.138023i
$377$		−	9.00251e6i		−	0.168012i
$378$	−6.24903e7	−	6.59411e7i	−1.15701	−	1.22090i
$379$		−	6.88495e7i		−	1.26469i	−0.774688	−	0.632343i	$-0.782093\pi$
$379$		−	6.88495e7i		−	1.26469i	0.774688	−	0.632343i	$-0.217907\pi$
$380$	1.11847e8	+	1.09922e8i	2.03833	+	2.00325i
$381$	1.99380e7	+	2.65509e7i	0.360500	+	0.480070i
$382$	6.83802e7	−	2.86723e7i	1.22671	−	0.514367i
$383$	−8.37713e7	−	4.83654e7i	−1.49107	−	0.860872i	−0.491126	−	0.871089i	$-0.663414\pi$
$383$	−8.37713e7	−	4.83654e7i	−1.49107	−	0.860872i	−0.999948	+	0.0102168i	$0.996748\pi$
$384$	−1.35595e7	+	5.49756e7i	−0.239469	+	0.970904i
$385$	−3.82457e6	−	6.62435e6i	−0.0670194	−	0.116081i
$386$	−1.95780e7	+	2.57452e7i	−0.340414	+	0.447646i
$387$	−6.11546e6	−	2.48824e7i	−0.105511	−	0.429298i
$388$	8.12703e6	+	2.93104e7i	0.139135	+	0.501795i
$389$	602187.	+	1.04302e6i	0.0102302	+	0.0177192i	0.871095	−	0.491114i	$-0.163410\pi$
$389$	602187.	+	1.04302e6i	0.0102302	+	0.0177192i	−0.860865	+	0.508833i	$0.830077\pi$
$390$	−2.00060e7	−	1.17127e7i	−0.337261	−	0.197453i
$391$	−2.74983e7	+	4.76285e7i	−0.460019	+	0.796776i
$392$	8.65378e7	−	6.82112e7i	1.43664	−	1.13239i
$393$	5.90858e7	−	7.15445e6i	0.973432	−	0.117869i
$394$	639234.	+	81335.8i	0.0104513	+	0.00132982i
$395$	1.29074e8			2.09434
$396$	3.33180e6	+	40386.2i	0.0536529	+	0.000650350i
$397$		−	5.86929e7i		−	0.938023i	−0.883192	−	0.469012i	$-0.844610\pi$
$397$		−	5.86929e7i		−	0.938023i	0.883192	−	0.469012i	$-0.155390\pi$
$398$	−6.32019e7	−	8.04179e6i	−1.00249	−	0.127557i
$399$	1.89129e8	+	8.06542e7i	2.97741	+	1.26972i
$400$	−1.33951e6	−	7.71497e7i	−0.0209299	−	1.20546i
$401$	−5.29739e7	−	3.05845e7i	−0.821540	−	0.474316i	0.0294074	−	0.999568i	$-0.490638\pi$
$401$	−5.29739e7	−	3.05845e7i	−0.821540	−	0.474316i	−0.850947	+	0.525251i	$0.823971\pi$
$402$	−243115.	+	4.01147e7i	−0.00374225	+	0.617484i
$403$	−1.78322e7	+	1.02954e7i	−0.272452	+	0.157300i
$404$	1.19720e7	+	4.31775e7i	0.181561	+	0.654807i
$405$	−8.74181e7	+	4.57329e7i	−1.31594	+	0.688436i
$406$	4.35048e7	−	5.72089e7i	0.650068	−	0.854842i
$407$	453181.	−	261644.i	0.00672185	−	0.00388086i
$408$	−7.14214e7	+	1.93380e7i	−1.05159	+	0.284729i
$409$	−2.24409e7	+	3.88688e7i	−0.327998	+	0.568109i	−0.982114	−	0.188285i	$-0.939707\pi$
$409$	−2.24409e7	+	3.88688e7i	−0.327998	+	0.568109i	0.654117	+	0.756394i	$0.273041\pi$
$410$	−3.51714e7	+	1.47476e7i	−0.510315	+	0.213979i
$411$	1.23361e7	+	5.26076e6i	0.177686	+	0.0757745i
$412$	4.07915e7	−	4.15059e7i	0.583282	−	0.593497i
$413$	2.18856e8			3.10676
$414$	4.81344e7	−	3.56915e7i	0.678351	−	0.502996i
$415$	−5.41274e7			−0.757309
$416$	7.62774e6	+	1.73408e7i	0.105954	+	0.240874i
$417$	870353.	+	7.18791e6i	0.0120029	+	0.0991276i
$418$	−6.95453e6	+	2.91609e6i	−0.0952224	+	0.0399275i
$419$	−3.74082e7	+	6.47928e7i	−0.508539	+	0.880815i	0.491412	+	0.870927i	$0.336481\pi$
$419$	−3.74082e7	+	6.47928e7i	−0.508539	+	0.880815i	−0.999951	+	0.00988821i	$0.996852\pi$
$420$	−7.05318e7	−	1.71111e8i	−0.952000	−	2.30956i
$421$	−9.70720e6	+	5.60446e6i	−0.130091	+	0.0751082i	−0.563633	−	0.826025i	$-0.690597\pi$
$421$	−9.70720e6	+	5.60446e6i	−0.130091	+	0.0751082i	0.433542	+	0.901133i	$0.357264\pi$
$422$	−1.10744e8	−	8.42160e7i	−1.47362	−	1.12062i
$423$	1.73841e7	+	7.07318e7i	0.229684	+	0.934531i
$424$	1.00005e8	+	3.99061e7i	1.31197	+	0.523530i
$425$	8.73228e7	−	5.04159e7i	1.13753	−	0.656750i
$426$	−9.89741e7	+	5.63457e7i	−1.28024	+	0.728840i
$427$	5.92026e7	+	3.41806e7i	0.760426	+	0.439032i
$428$	4.07525e6	+	1.05413e6i	0.0519784	+	0.0134451i
$429$	891437.	−	669409.i	0.0112906	−	0.00847852i
$430$	6.58874e6	−	5.17822e7i	0.0828700	−	0.651291i
$431$			8.43201e7i			1.05317i	0.850122	+	0.526586i	$0.176528\pi$
$431$			8.43201e7i			1.05317i	−0.850122	+	0.526586i	$0.823472\pi$
$432$	7.97785e7	+	1.16285e7i	0.989543	+	0.144236i
$433$	3.44719e7			0.424622			0.212311	−	0.977202i	$-0.431901\pi$
$433$	3.44719e7			0.424622			0.212311	+	0.977202i	$0.431901\pi$
$434$	−1.63073e8	−	2.07493e7i	−1.99486	−	0.253825i
$435$	−4.68677e7	−	6.24127e7i	−0.569385	−	0.758237i
$436$	−128034.	+	494976.i	−0.00154477	+	0.00597206i
$437$	−6.78099e7	+	1.17450e8i	−0.812548	+	1.40737i
$438$	−3.07020e7	−	5.39295e7i	−0.365379	−	0.641807i
$439$	2.91520e7	+	5.04927e7i	0.344567	+	0.596808i	0.985275	−	0.170977i	$-0.0546923\pi$
$439$	2.91520e7	+	5.04927e7i	0.344567	+	0.596808i	−0.640708	+	0.767785i	$0.721359\pi$
$440$	6.30472e6	+	2.51583e6i	0.0740129	+	0.0295341i
$441$	−1.08606e8	−	1.13221e8i	−1.26631	−	1.32012i
$442$	−1.49849e7	+	1.97053e7i	−0.173536	+	0.228200i
$443$	3.91676e7	+	6.78402e7i	0.450521	+	0.780326i	0.998418	−	0.0562201i	$-0.0179048\pi$
$443$	3.91676e7	+	6.78402e7i	0.450521	+	0.780326i	−0.547897	+	0.836546i	$0.684572\pi$
$444$	1.17059e7	−	4.82518e6i	0.133739	−	0.0551270i
$445$	−9.12251e7	−	5.26688e7i	−1.03522	−	0.597687i
$446$	2.80098e7	+	6.68001e7i	0.315722	+	0.752961i
$447$	4.77243e7	−	5.77874e6i	0.534340	−	0.0647009i
$448$	−3.53271e7	+	1.47058e8i	−0.392892	+	1.63552i
$449$		−	1.12014e8i		−	1.23746i	−0.785602	−	0.618732i	$-0.787647\pi$
$449$		−	1.12014e8i		−	1.23746i	0.785602	−	0.618732i	$-0.212353\pi$
$450$	−1.09146e8	+	1.25453e7i	−1.19776	+	0.137671i
$451$		−	1.83398e6i		−	0.0199925i
$452$	−1.47847e7	−	1.45302e7i	−0.160102	−	0.157346i
$453$	6.95690e7	−	1.63135e8i	0.748379	−	1.75490i
$454$	5.16725e7	+	1.23233e8i	0.552195	+	1.31692i
$455$	−5.36251e7	−	3.09605e7i	−0.569291	−	0.328680i
$456$	−1.76123e8	+	4.76869e7i	−1.85747	+	0.502927i
$457$	−3.24779e7	−	5.62534e7i	−0.340282	−	0.589386i	0.644203	−	0.764855i	$-0.277189\pi$
$457$	−3.24779e7	−	5.62534e7i	−0.340282	−	0.589386i	−0.984485	+	0.175469i	$0.943856\pi$
$458$	−7.72798e7	−	5.87677e7i	−0.804395	−	0.611706i
$459$	3.72609e7	+	9.85443e7i	0.385314	+	1.01905i
$460$	1.17639e8	−	3.26184e7i	1.20859	−	0.335111i
$461$	−2.80400e7	−	4.85667e7i	−0.286204	−	0.495719i	0.686697	−	0.726944i	$-0.259060\pi$
$461$	−2.80400e7	−	4.85667e7i	−0.286204	−	0.495719i	−0.972900	+	0.231225i	$0.925727\pi$
$462$	8.89981e6	+	53937.2i	0.0902516	+	0.000546969i
$463$	7.18732e7	−	1.24488e8i	0.724143	−	1.25425i	−0.235183	−	0.971951i	$-0.575569\pi$
$463$	7.18732e7	−	1.24488e8i	0.724143	−	1.25425i	0.959326	−	0.282301i	$-0.0910977\pi$
$464$	1.10724e6	+	6.37720e7i	0.0110838	+	0.638376i
$465$	−7.00286e7	+	1.64212e8i	−0.696492	+	1.63323i
$466$	9.54220e6	−	7.49940e7i	0.0942954	−	0.741086i
$467$	−3.12828e7			−0.307154			−0.153577	−	0.988137i	$-0.549079\pi$
$467$	−3.12828e7			−0.307154			−0.153577	+	0.988137i	$0.549079\pi$
$468$	2.35214e7	−	1.32026e7i	0.229470	−	0.128802i
$469$			1.07149e8i			1.03865i
$470$	−1.87295e7	+	1.47199e8i	−0.180398	+	1.41778i
$471$	6.90607e6	+	5.70346e7i	0.0660950	+	0.545853i
$472$	−1.52534e8	+	1.20231e8i	−1.45057	+	1.14338i
$473$	2.17387e6	+	1.25509e6i	0.0205424	+	0.0118601i
$474$	−7.58772e7	+	1.29603e8i	−0.712486	+	1.21697i
$475$	2.15335e8	−	1.24324e8i	2.00925	−	1.16004i
$476$	−1.90452e8	+	5.28075e7i	−1.76589	+	0.489638i
$477$	4.27507e7	−	1.47227e8i	0.393902	−	1.35654i
$478$	4.39718e7	+	3.34385e7i	0.402616	+	0.306171i
$479$	4.01174e7	−	2.31618e7i	0.365028	−	0.210749i	−0.306256	−	0.951949i	$-0.599076\pi$
$479$	4.01174e7	−	2.31618e7i	0.365028	−	0.210749i	0.671284	+	0.741200i	$0.265743\pi$
$480$	1.43159e8	+	8.05098e7i	1.29448	+	0.727989i
$481$	2.11805e6	−	3.66857e6i	0.0190327	−	0.0329657i
$482$	−5.63123e7	−	1.34298e8i	−0.502877	−	1.19930i
$483$	1.27988e8	−	9.61104e7i	1.13587	−	0.852960i
$484$	7.92440e7	−	8.06318e7i	0.698924	−	0.711165i
$485$	8.82274e7			0.773354
$486$	5.46921e6	−	1.14661e8i	0.0476448	−	0.998864i
$487$	1.65866e7			0.143605			0.0718026	−	0.997419i	$-0.477125\pi$
$487$	1.65866e7			0.143605			0.0718026	+	0.997419i	$0.477125\pi$
$488$	−6.00392e7	+	8.70102e6i	−0.516625	+	0.0748705i
$489$	8.17124e7	−	6.13605e7i	0.698814	−	0.524762i
$490$	−1.23594e8	−	2.94757e8i	−1.05053	−	2.50540i
$491$	2.36432e7	−	4.09512e7i	0.199738	−	0.345957i	−0.748705	−	0.662903i	$-0.769324\pi$
$491$	2.36432e7	−	4.09512e7i	0.199738	−	0.345957i	0.948444	+	0.316946i	$0.102657\pi$
$492$	5.86774e6	−	4.39851e7i	0.0492692	−	0.369326i
$493$	−7.21812e7	+	4.16738e7i	−0.602398	+	0.347794i
$494$	−3.69524e7	+	4.85925e7i	−0.306522	+	0.403078i
$495$	2.69517e6	−	9.28177e6i	0.0222213	−	0.0765271i
$496$	1.25054e8	−	7.51241e7i	1.02483	−	0.615651i
$497$	−2.63445e8	+	1.52100e8i	−2.14596	+	1.23897i
$498$	3.18193e7	−	5.43492e7i	0.257633	−	0.440053i
$499$	−1.50646e8	−	8.69753e7i	−1.21243	−	0.699994i	−0.249139	−	0.968468i	$-0.580147\pi$
$499$	−1.50646e8	−	8.69753e7i	−1.21243	−	0.699994i	−0.963287	+	0.268474i	$0.913481\pi$
$500$	−3.69601e7	−	9.56035e6i	−0.295681	−	0.0764828i
$501$	5.19979e6	+	4.29430e7i	0.0413497	+	0.341491i
$502$	−2.65489e7	−	3.37807e6i	−0.209863	−	0.0267029i
$503$			1.14030e8i			0.896013i	0.894030	+	0.448006i	$0.147866\pi$
$503$			1.14030e8i			0.896013i	−0.894030	+	0.448006i	$0.852134\pi$
$504$	2.13275e8	+	2.97681e7i	1.66590	+	0.232520i
$505$	1.29969e8			1.00917
$506$	−740980.	+	5.82350e6i	−0.00571946	+	0.0449503i
$507$	−4.75823e7	+	1.11577e8i	−0.365108	+	0.856153i
$508$	−7.61968e7	−	1.97096e7i	−0.581227	−	0.150344i
$509$	−1.08221e8	+	1.87444e8i	−0.820649	+	1.42141i	0.0845513	+	0.996419i	$0.473054\pi$
$509$	−1.08221e8	+	1.87444e8i	−0.820649	+	1.42141i	−0.905200	+	0.424986i	$0.860279\pi$
$510$	−1.30074e6	+	2.14625e8i	−0.00980569	+	1.61797i
$511$	−8.28772e7	−	1.43547e8i	−0.621115	−	1.07580i
$512$	−5.61662e7	−	1.21901e8i	−0.418471	−	0.908230i
$513$	9.18842e7	+	2.43007e8i	0.680595	+	1.79998i
$514$	1.31041e8	+	9.96507e7i	0.964979	+	0.733822i
$515$	−8.44026e7	−	1.46190e8i	−0.617922	−	1.07027i
$516$	4.81212e7	+	3.70564e7i	0.350257	+	0.269720i
$517$	−6.17955e6	−	3.56777e6i	−0.0447183	−	0.0258181i
$518$	3.11882e7	−	1.30774e7i	0.224388	−	0.0940878i
$519$	−3.72067e7	+	8.72471e7i	−0.266145	+	0.624092i
$520$	5.43829e7	−	7.88130e6i	0.386770	−	0.0560515i
$521$		−	2.18984e8i		−	1.54846i	−0.632906	−	0.774229i	$-0.718138\pi$
$521$		−	2.18984e8i		−	1.54846i	0.632906	−	0.774229i	$-0.281862\pi$
$522$	9.02201e7	−	1.03700e7i	0.634296	−	0.0729065i
$523$		−	1.86463e7i		−	0.130343i	−0.997874	−	0.0651714i	$-0.979241\pi$
$523$		−	1.86463e7i		−	0.130343i	0.997874	−	0.0651714i	$-0.0207594\pi$
$524$	−9.88877e7	+	1.00620e8i	−0.687303	+	0.699340i
$525$	−2.91323e8	+	3.52750e7i	−2.01324	+	0.243775i
$526$	1.52737e8	−	6.40439e7i	1.04951	−	0.440069i
$527$	1.65095e8	+	9.53179e7i	1.12799	+	0.651242i
$528$	−6.23243e6	+	4.85160e6i	−0.0423405	+	0.0329597i
$529$	−2.12310e7	−	3.67732e7i	−0.143418	−	0.248407i
$530$	1.89054e8	−	2.48607e8i	1.26987	−	1.66988i
$531$	1.91432e8	+	1.99567e8i	1.27859	+	1.33292i
$532$	−4.69648e8	+	1.30222e8i	−3.11916	+	0.864864i
$533$	−7.42319e6	−	1.28573e7i	−0.0490240	−	0.0849121i
$534$	1.06512e8	−	6.06371e7i	0.699480	−	0.398213i
$535$	6.10501e6	−	1.05742e7i	0.0398680	−	0.0690534i
$536$	−5.88635e7	−	7.46787e7i	−0.382254	−	0.484956i
$537$	−6.20614e7	−	8.26457e7i	−0.400773	−	0.533700i
$538$	−1.09089e8	−	1.38804e7i	−0.700540	−	0.0891364i
$539$	1.53699e7			0.0981531
$540$	9.43357e7	−	2.13985e8i	0.599094	−	1.35895i
$541$		−	8.22586e6i		−	0.0519505i	−0.999663	−	0.0259752i	$-0.991731\pi$
$541$		−	8.22586e6i		−	0.0519505i	0.999663	−	0.0259752i	$-0.00826911\pi$
$542$	2.72065e6	+	346175.i	0.0170874	+	0.00217419i
$543$	−1.02720e8	+	7.71358e7i	−0.641586	+	0.481788i
$544$	1.03727e8	−	1.41431e8i	0.644309	−	0.878514i
$545$	1.28433e6	+	741507.i	0.00793389	+	0.00458064i
$546$	6.26114e7	−	3.56445e7i	0.384658	−	0.218985i
$547$	1.47553e8	−	8.51896e7i	0.901540	−	0.520504i	0.0238406	−	0.999716i	$-0.492411\pi$
$547$	1.47553e8	−	8.51896e7i	0.901540	−	0.520504i	0.877700	+	0.479211i	$0.159077\pi$
$548$	−3.06333e7	+	8.49385e6i	−0.186146	+	0.0516135i
$549$	2.06161e7	+	8.38822e7i	0.124592	+	0.506936i
$550$	6.51497e6	−	8.56721e6i	0.0391583	−	0.0514934i
$551$	−1.77996e8	+	1.02766e8i	−1.06404	+	0.614322i
$552$	−3.64032e7	+	1.37296e8i	−0.216432	+	0.816285i
$553$	−2.00568e8	+	3.47395e8i	−1.18601	+	2.05422i
$554$	2.29072e8	−	9.60516e7i	1.34723	−	0.564905i
$555$	−4.41481e6	−	3.64602e7i	−0.0258246	−	0.213275i
$556$	−1.22406e7	−	1.20299e7i	−0.0712160	−	0.0699902i
$557$	−6.75100e7			−0.390663			−0.195331	−	0.980737i	$-0.562578\pi$
$557$	−6.75100e7			−0.390663			−0.195331	+	0.980737i	$0.562578\pi$
$558$	−1.23718e8	−	1.66849e8i	−0.712084	−	0.960332i
$559$	2.03202e7			0.116330
$560$	3.83678e8	+	2.12722e8i	2.18475	+	1.21129i
$561$	−9.49383e6	−	4.04866e6i	−0.0537716	−	0.0229310i
$562$	−2.04375e8	+	8.56959e7i	−1.15138	+	0.482782i
$563$	1.73258e7	−	3.00091e7i	0.0970883	−	0.168162i	−0.813390	−	0.581719i	$-0.802380\pi$
$563$	1.73258e7	−	3.00091e7i	0.0970883	−	0.168162i	0.910478	+	0.413557i	$0.135714\pi$
$564$	−1.36792e8	−	1.05338e8i	−0.762468	−	0.587149i
$565$	−5.20737e7	+	3.00648e7i	−0.288717	+	0.166691i
$566$	1.05777e8	+	8.04383e7i	0.583365	+	0.443623i
$567$	1.27521e7	−	3.06345e8i	0.0699570	−	1.68059i
$568$	1.00053e8	−	2.50734e8i	0.545989	−	1.36826i
$569$	1.67549e8	−	9.67345e7i	0.909505	−	0.525103i	0.0292335	−	0.999573i	$-0.490693\pi$
$569$	1.67549e8	−	9.67345e7i	0.909505	−	0.525103i	0.880272	+	0.474469i	$0.157360\pi$
$570$	−3.20757e6	+	5.29259e8i	−0.0173201	+	2.85788i
$571$	−2.39634e8	−	1.38353e8i	−1.28718	−	0.743155i	−0.309031	−	0.951052i	$-0.600005\pi$
$571$	−2.39634e8	−	1.38353e8i	−1.28718	−	0.743155i	−0.978151	+	0.207897i	$0.933338\pi$
$572$	−661742.	+	2.55828e6i	−0.00353590	+	0.0136697i
$573$	2.30192e8	+	9.81660e7i	1.22357	+	0.521792i
$574$	1.49606e7	−	1.17578e8i	0.0791067	−	0.621714i
$575$		−	1.93561e8i		−	1.01816i
$576$	−1.64997e8	+	9.64174e7i	−0.863394	+	0.504531i
$577$	3.57376e8			1.86037			0.930183	−	0.367097i	$-0.119648\pi$
$577$	3.57376e8			1.86037			0.930183	+	0.367097i	$0.119648\pi$
$578$	3.58058e7	+	4.55592e6i	0.185426	+	0.0235935i
$579$	−1.08368e8	+	1.31219e7i	−0.558299	+	0.0676021i
$580$	1.79114e8	+	4.63309e7i	0.918007	+	0.237458i
$581$	8.41087e7	−	1.45681e8i	0.428857	−	0.742802i
$582$	−5.18652e7	+	8.85890e7i	−0.263092	+	0.449377i
$583$	7.50951e6	+	1.30069e7i	0.0378971	+	0.0656397i
$584$	1.36621e8	+	5.45173e7i	0.685929	+	0.273713i
$585$	−1.86739e7	−	7.59797e7i	−0.0932755	−	0.379516i
$586$	−6.99261e7	+	9.19531e7i	−0.347494	+	0.456955i
$587$	−3.51479e7	−	6.08780e7i	−0.173774	−	0.300986i	0.765962	−	0.642886i	$-0.222263\pi$
$587$	−3.51479e7	−	6.08780e7i	−0.173774	−	0.300986i	−0.939736	+	0.341900i	$0.888930\pi$
$588$	3.68621e8	+	4.91752e7i	1.81321	+	0.241888i
$589$	4.07120e8	+	2.35051e8i	1.99240	+	1.15031i
$590$	2.17850e8	+	5.19546e8i	1.06072	+	2.52970i
$591$	1.30592e6	+	1.73907e6i	0.00632638	+	0.00842469i
$592$	−1.45526e7	+	2.62479e7i	−0.0701418	+	0.126511i
$593$		−	2.27964e7i		−	0.109321i	−0.998505	−	0.0546603i	$-0.982592\pi$
$593$		−	2.27964e7i		−	0.109321i	0.998505	−	0.0546603i	$-0.0174076\pi$
$594$	7.73543e6	+	8.16258e6i	0.0369084	+	0.0389465i
$595$			5.73280e8i			2.72155i
$596$	−7.98728e7	+	8.12717e7i	−0.377277	+	0.383884i
$597$	−1.29118e8	−	1.71944e8i	−0.606827	−	0.808098i
$598$	1.83763e7	+	4.38254e7i	0.0859321	+	0.204938i
$599$	−1.49455e8	−	8.62881e7i	−0.695394	−	0.401486i	0.110235	−	0.993906i	$-0.464840\pi$
$599$	−1.49455e8	−	8.62881e7i	−0.695394	−	0.401486i	−0.805630	+	0.592419i	$0.798173\pi$
$600$	1.83661e8	−	1.84626e8i	0.850283	−	0.854751i
$601$	−8.94517e7	−	1.54935e8i	−0.412064	−	0.713716i	0.583051	−	0.812436i	$-0.301859\pi$
$601$	−8.94517e7	−	1.54935e8i	−0.412064	−	0.713716i	−0.995115	+	0.0987193i	$0.968525\pi$
$602$	1.29130e8	+	9.81977e7i	0.591887	+	0.450103i
$603$	−9.77055e7	+	9.37230e7i	−0.445622	+	0.427459i
$604$	1.12324e8	+	4.05099e8i	0.509754	+	1.83845i
$605$	−1.63965e8	−	2.83996e8i	−0.740433	−	1.28247i
$606$	−7.64033e7	+	1.30501e8i	−0.343316	+	0.586405i
$607$	1.27578e8	−	2.20971e8i	0.570438	−	0.988028i	−0.426083	−	0.904684i	$-0.640107\pi$
$607$	1.27578e8	−	2.20971e8i	0.570438	−	0.988028i	0.996521	−	0.0833437i	$-0.0265599\pi$
$608$	2.55787e8	−	3.48765e8i	1.13807	−	1.55175i
$609$	2.40808e8	−	2.91584e7i	1.06615	−	0.129096i
$610$	−2.22117e7	+	1.74566e8i	−0.0978569	+	0.769076i
$611$	−5.77632e7			−0.253237
$612$	−2.14740e8	−	1.27476e8i	−0.936827	−	0.556125i
$613$		−	2.55774e8i		−	1.11039i	−0.831720	−	0.555195i	$-0.812644\pi$
$613$		−	2.55774e8i		−	1.11039i	0.831720	−	0.555195i	$-0.187356\pi$
$614$	1.16470e7	−	9.15357e7i	0.0503162	−	0.395444i
$615$	−1.18400e8	−	5.04918e7i	−0.509009	−	0.217068i
$616$	−1.65681e7	+	1.30594e7i	−0.0708813	+	0.0558703i
$617$	6.37402e7	+	3.68004e7i	0.271368	+	0.156674i	0.629509	−	0.776993i	$-0.283256\pi$
$617$	6.37402e7	+	3.68004e7i	0.271368	+	0.156674i	−0.358141	+	0.933667i	$0.616589\pi$
$618$	1.96405e8	+	1.19031e6i	0.832124	+	0.00504308i
$619$	−3.96537e8	+	2.28941e8i	−1.67191	+	0.965275i	−0.705335	+	0.708874i	$0.749203\pi$
$619$	−3.96537e8	+	2.28941e8i	−1.67191	+	0.965275i	−0.966570	+	0.256401i	$0.917463\pi$
$620$	−1.13066e8	−	4.07775e8i	−0.474412	−	1.71098i
$621$	1.99590e8	+	3.26402e7i	0.833419	+	0.136294i
$622$	−1.64396e8	−	1.25016e8i	−0.683156	−	0.519509i
$623$	2.83510e8	−	1.63685e8i	1.17248	−	0.676929i
$624$	−2.40559e7	+	5.92389e7i	−0.0990074	+	0.243811i
$625$	9.18048e7	−	1.59011e8i	0.376032	−	0.651307i
$626$	−1.77035e8	−	4.22209e8i	−0.721667	−	1.72109i
$627$	−2.34115e7	−	9.98386e6i	−0.0949787	−	0.0405038i
$628$	−9.71265e7	−	9.54547e7i	−0.392156	−	0.385406i
$629$	−3.92189e7			−0.157596
$630$	2.48505e8	−	5.73076e8i	0.993831	−	2.29187i
$631$	6.78087e7			0.269896			0.134948	−	0.990853i	$-0.456913\pi$
$631$	6.78087e7			0.269896			0.134948	+	0.990853i	$0.456913\pi$
$632$	−5.10567e7	−	3.52304e8i	−0.202256	−	1.39562i
$633$	−5.64444e7	−	4.66153e8i	−0.222541	−	1.83788i
$634$	4.09598e7	+	9.76843e7i	0.160727	+	0.383316i
$635$	−1.14148e8	+	1.97710e8i	−0.445807	+	0.772160i
$636$	1.38489e8	+	3.35974e8i	0.538322	+	1.30597i
$637$	1.07752e8	−	6.22107e7i	0.416877	−	0.240684i
$638$	−5.38528e6	+	7.08167e6i	−0.0207370	+	0.0272693i
$639$	−3.69129e8	−	1.07185e8i	−1.41473	−	0.410800i
$640$	−3.84268e8	+	6.25182e7i	−1.46587	+	0.238488i
$641$	−2.19717e8	+	1.26853e8i	−0.834236	+	0.481646i	−0.855301	−	0.518132i	$-0.826628\pi$
$641$	−2.19717e8	+	1.26853e8i	−0.834236	+	0.481646i	0.0210651	+	0.999778i	$0.493294\pi$
$642$	7.02864e6	+	1.23462e7i	0.0265623	+	0.0466580i
$643$	−1.85583e8	−	1.07147e8i	−0.698082	−	0.403038i	0.108551	−	0.994091i	$-0.465379\pi$
$643$	−1.85583e8	−	1.07147e8i	−0.698082	−	0.403038i	−0.806633	+	0.591053i	$0.798712\pi$
$644$	−9.50095e7	+	3.67305e8i	−0.355721	+	1.37521i
$645$	1.40876e8	−	1.05788e8i	0.524998	−	0.394238i
$646$	5.60667e8	+	7.13390e7i	2.07973	+	0.264624i
$647$			4.02056e8i			1.48448i	0.670136	+	0.742238i	$0.266236\pi$
$647$			4.02056e8i			1.48448i	−0.670136	+	0.742238i	$0.733764\pi$
$648$	1.59406e8	+	2.20515e8i	0.585840	+	0.810426i
$649$	−2.70913e7			−0.0991051
$650$	1.09975e7	−	8.64311e7i	0.0400454	−	0.314724i
$651$	−3.33149e8	−	4.43647e8i	−1.20752	−	1.60803i
$652$	−6.06577e7	+	2.34501e8i	−0.218848	+	0.846062i
$653$	−1.03802e8	+	1.79791e8i	−0.372793	+	0.645696i	−0.989994	−	0.141109i	$-0.954933\pi$
$653$	−1.03802e8	+	1.79791e8i	−0.372793	+	0.645696i	0.617201	+	0.786805i	$0.288266\pi$
$654$	−1.49955e6	+	853690.i	−0.00536077	+	0.00305188i
$655$	2.04610e8	+	3.54396e8i	0.728122	+	1.26114i
$656$	5.41658e7	+	9.01659e7i	0.191873	+	0.319397i
$657$	5.84033e7	−	2.01133e8i	0.205940	−	0.709229i
$658$	−3.67072e8	−	2.79141e8i	−1.28847	−	0.979821i
$659$	1.35780e8	+	2.35178e8i	0.474439	+	0.821752i	0.999572	−	0.0292682i	$-0.00931769\pi$
$659$	1.35780e8	+	2.35178e8i	0.474439	+	0.821752i	−0.525133	+	0.851020i	$0.675984\pi$
$660$	8.73085e6	+	2.11811e7i	0.0303686	+	0.0736745i
$661$	−3.21048e8	−	1.85357e8i	−1.11164	−	0.641807i	−0.172388	−	0.985029i	$-0.555148\pi$
$661$	−3.21048e8	−	1.85357e8i	−1.11164	−	0.641807i	−0.939254	+	0.343222i	$0.888482\pi$
$662$	−2.01542e8	+	8.45080e7i	−0.694690	+	0.291289i
$663$	−8.29447e7	+	1.00434e7i	−0.284609	+	0.0344621i
$664$	2.14107e7	+	1.47739e8i	0.0731352	+	0.504652i
$665$			1.41369e9i			4.80717i
$666$	3.92049e7	+	1.70005e7i	0.132714	+	0.0575493i
$667$			1.59998e8i			0.539183i
$668$	−7.31294e7	−	7.18707e7i	−0.245337	−	0.241114i
$669$	−9.58976e7	+	2.24873e8i	−0.320280	+	0.751034i
$670$	−2.54364e8	+	1.06657e8i	−0.845729	+	0.354621i
$671$	−7.32845e6	−	4.23108e6i	−0.0242574	−	0.0140050i
$672$	−4.39142e8	+	2.60199e8i	−1.44710	+	0.857430i
$673$	−1.63162e8	−	2.82605e8i	−0.535271	−	0.927116i	−0.999150	−	0.0412177i	$-0.986876\pi$
$673$	−1.63162e8	−	2.82605e8i	−0.535271	−	0.927116i	0.463880	−	0.885898i	$-0.346457\pi$
$674$	−1.69596e8	+	2.23019e8i	−0.553905	+	0.728387i
$675$	−2.86984e8	−	2.34791e8i	−0.933140	−	0.763433i
$676$	−7.68248e7	−	2.77071e8i	−0.248692	−	0.896914i
$677$	−8.23325e7	−	1.42604e8i	−0.265342	−	0.459585i	0.702312	−	0.711870i	$-0.252151\pi$
$677$	−8.23325e7	−	1.42604e8i	−0.265342	−	0.459585i	−0.967653	+	0.252285i	$0.918818\pi$
$678$	423997.	−	6.99609e7i	0.00136042	−	0.224474i
$679$	−1.37097e8	+	2.37459e8i	−0.437943	+	0.758540i
$680$	−3.14937e8	−	3.99553e8i	−1.00161	−	1.27071i
$681$	−1.76912e8	+	4.14847e8i	−0.560166	+	1.31355i
$682$	2.01861e7	+	2.56847e6i	0.0636355	+	0.00809696i
$683$	2.71379e7			0.0851753			0.0425877	−	0.999093i	$-0.486440\pi$
$683$	2.71379e7			0.0851753			0.0425877	+	0.999093i	$0.486440\pi$
$684$	−5.29543e8	−	3.14350e8i	−1.65475	−	0.982304i
$685$			9.22096e7i			0.286883i
$686$	4.46705e8	+	5.68385e7i	1.38372	+	0.176064i
$687$	−3.93881e7	−	3.25291e8i	−0.121477	−	1.00323i
$688$	−1.43944e8	+	2.49924e6i	−0.442007	+	0.00767436i
$689$	1.05292e8	+	6.07906e7i	0.321914	+	0.185857i
$690$	3.55558e8	+	2.08165e8i	1.08234	+	0.633665i
$691$	3.14333e8	−	1.81480e8i	0.952698	−	0.550040i	0.0587800	−	0.998271i	$-0.481279\pi$
$691$	3.14333e8	−	1.81480e8i	0.952698	−	0.550040i	0.893918	+	0.448230i	$0.147946\pi$
$692$	−6.00726e7	−	2.16654e8i	−0.181284	−	0.653805i
$693$	2.07933e7	+	2.16768e7i	0.0624775	+	0.0651323i
$694$	−1.28612e8	+	1.69125e8i	−0.384772	+	0.505977i
$695$	−4.31130e7	+	2.48913e7i	−0.128426	+	0.0741469i
$696$	−1.51815e8	+	1.52612e8i	−0.450283	+	0.452649i
$697$	−6.87258e7	+	1.19037e8i	−0.202965	+	0.351546i
$698$	3.35139e8	−	1.40526e8i	0.985504	−	0.413229i
$699$	2.04025e8	−	1.53209e8i	0.597381	−	0.448593i
$700$	4.87566e8	−	4.96105e8i	1.42148	−	1.44637i
$701$	1.33952e8			0.388862			0.194431	−	0.980916i	$-0.437714\pi$
$701$	1.33952e8			0.388862			0.194431	+	0.980916i	$0.437714\pi$
$702$	8.72687e7	+	2.59149e7i	0.252259	+	0.0749097i
$703$	−9.67126e7			−0.278367
$704$	4.37300e6	−	1.82037e7i	0.0125332	−	0.0521726i
$705$	−4.00461e8	+	3.00719e8i	−1.14286	+	0.858211i
$706$	−5.06785e8	+	2.12499e8i	−1.44016	+	0.603869i
$707$	−2.01959e8	+	3.49803e8i	−0.571485	+	0.989841i
$708$	−6.49741e8	−	8.66773e7i	−1.83080	−	0.244234i
$709$	5.14103e8	−	2.96817e8i	1.44248	−	0.832819i	0.444470	−	0.895794i	$-0.353392\pi$
$709$	5.14103e8	−	2.96817e8i	1.44248	−	0.832819i	0.998015	+	0.0629750i	$0.0200588\pi$
$710$	−6.23308e8	−	4.73997e8i	−1.74152	−	1.32434i
$711$	−4.92212e8	+	1.20973e8i	−1.36944	+	0.336574i
$712$	−1.07673e8	+	2.69830e8i	−0.298309	+	0.747568i
$713$	3.16925e8	−	1.82976e8i	0.874354	−	0.504808i
$714$	−5.75630e8	−	3.37008e8i	−1.58143	−	0.925860i
$715$	6.63804e6	+	3.83247e6i	0.0181602	+	0.0104848i
$716$	2.37180e8	+	6.13505e7i	0.646157	+	0.167140i
$717$	2.24116e7	+	1.85089e8i	0.0608018	+	0.502138i
$718$	−3.81527e7	+	2.99849e8i	−0.103075	+	0.810084i
$719$		−	3.60984e8i		−	0.971183i	−0.874186	−	0.485591i	$-0.838604\pi$
$719$		−	3.60984e8i		−	0.971183i	0.874186	−	0.485591i	$-0.161396\pi$
$720$	1.41627e8	+	5.35928e8i	0.379445	+	1.43585i
$721$	5.24614e8			1.39970
$722$	1.00923e9	+	1.28414e8i	2.68150	+	0.341193i
$723$	1.92797e8	−	4.52096e8i	0.510136	−	1.19623i
$724$	7.62523e7	−	2.94789e8i	0.200926	−	0.776777i
$725$	1.46671e8	−	2.54042e8i	0.384885	−	0.666641i
$726$	3.81548e8	+	2.31237e6i	0.997103	+	0.00604293i
$727$	1.59873e8	+	2.76908e8i	0.416075	+	0.720663i	0.995541	−	0.0943338i	$-0.0300721\pi$
$727$	1.59873e8	+	2.76908e8i	0.416075	+	0.720663i	−0.579466	+	0.814997i	$0.696739\pi$
$728$	−6.32937e7	+	1.58615e8i	−0.164046	+	0.411103i
$729$	2.90499e8	−	2.56330e8i	0.749828	−	0.661633i
$730$	2.58274e8	−	3.39631e8i	0.663914	−	0.873050i
$731$	−9.40649e7	−	1.62925e8i	−0.240810	−	0.417096i
$732$	−1.62224e8	−	1.24923e8i	−0.413601	−	0.318499i
$733$	9.37184e7	+	5.41083e7i	0.237965	+	0.137389i	0.614241	−	0.789118i	$-0.289462\pi$
$733$	9.37184e7	+	5.41083e7i	0.237965	+	0.137389i	−0.376276	+	0.926508i	$0.622796\pi$
$734$	−1.88571e8	−	4.49720e8i	−0.476856	−	1.13725i
$735$	4.23151e8	−	9.92260e8i	1.06570	−	2.49898i
$736$	−1.35565e8	−	3.08190e8i	−0.340026	−	0.773011i
$737$		−	1.32636e7i		−	0.0331328i
$738$	1.20301e8	−	8.92030e7i	0.299296	−	0.221927i
$739$			1.14446e8i			0.283575i	0.989897	+	0.141788i	$0.0452850\pi$
$739$			1.14446e8i			0.283575i	−0.989897	+	0.141788i	$0.954715\pi$
$740$	6.20895e7	+	6.10208e7i	0.153223	+	0.150585i
$741$	−2.04539e8	+	2.47667e7i	−0.502715	+	0.0608715i
$742$	3.75338e8	+	8.95138e8i	0.918778	+	2.19118i
$743$	−2.23351e8	−	1.28952e8i	−0.544531	−	0.314385i	0.202383	−	0.979307i	$-0.435132\pi$
$743$	−2.23351e8	−	1.28952e8i	−0.544531	−	0.314385i	−0.746913	+	0.664922i	$0.768465\pi$
$744$	4.75913e8	+	1.26185e8i	1.15560	+	0.306400i
$745$	1.65266e8	+	2.86250e8i	0.399683	+	0.692272i
$746$	1.39851e8	+	1.06350e8i	0.336860	+	0.256167i
$747$	2.06410e8	−	5.07304e7i	0.495187	−	0.121704i
$748$	2.35753e7	−	6.53683e6i	0.0563316	−	0.0156193i
$749$	1.89732e7	+	3.28625e7i	0.0451538	+	0.0782087i
$750$	−6.37455e7	−	1.11972e8i	−0.151100	−	0.265415i
$751$	1.50203e8	−	2.60159e8i	0.354616	−	0.614213i	−0.632436	−	0.774613i	$-0.717945\pi$
$751$	1.50203e8	−	2.60159e8i	0.354616	−	0.614213i	0.987052	+	0.160399i	$0.0512782\pi$
$752$	4.09183e8	−	7.10445e6i	0.962197	−	0.0167062i
$753$	−5.42381e7	−	7.22276e7i	−0.127034	−	0.169168i
$754$	−9.09052e6	+	7.14441e7i	−0.0212068	+	0.166668i
$755$	1.21939e9			2.83336
$756$	4.29339e8	+	5.86411e8i	0.993653	+	1.35718i
$757$			1.74595e8i			0.402481i	0.979542	+	0.201240i	$0.0644972\pi$
$757$			1.74595e8i			0.402481i	−0.979542	+	0.201240i	$0.935503\pi$
$758$	−6.95225e7	+	5.46390e8i	−0.159631	+	1.25457i
$759$	−1.58431e7	+	1.18971e7i	−0.0362339	+	0.0272092i
$760$	−7.76624e8	−	9.85284e8i	−1.76917	−	2.24451i
$761$	8.83258e7	+	5.09949e7i	0.200417	+	0.115711i	0.596850	−	0.802353i	$-0.296419\pi$
$761$	8.83258e7	+	5.09949e7i	0.200417	+	0.115711i	−0.396433	+	0.918064i	$0.629752\pi$
$762$	−1.31417e8	−	2.30841e8i	−0.297022	−	0.521733i
$763$	−3.99144e6	+	2.30446e6i	−0.00898579	+	0.00518795i
$764$	−5.71619e8	+	1.58495e8i	−1.28182	+	0.355416i
$765$	−5.22753e8	+	5.01445e8i	−1.16765	+	1.12005i
$766$	6.15972e8	+	4.68419e8i	1.37049	+	1.04219i
$767$	−1.89926e8	+	1.09654e8i	−0.420920	+	0.243018i
$768$	1.63121e8	−	4.22595e8i	0.360103	−	0.932913i
$769$	1.77484e8	−	3.07411e8i	0.390284	−	0.675991i	−0.602203	−	0.798343i	$-0.705710\pi$
$769$	1.77484e8	−	3.07411e8i	0.390284	−	0.675991i	0.992487	+	0.122352i	$0.0390436\pi$
$770$	2.36628e7	+	5.64329e7i	0.0518314	+	0.123612i
$771$	6.67893e7	+	5.51587e8i	0.145728	+	1.20351i
$772$	1.81368e8	−	1.84545e8i	0.394194	−	0.401098i
$773$	−1.63173e7			−0.0353273			−0.0176637	−	0.999844i	$-0.505623\pi$
$773$	−1.63173e7			−0.0353273			−0.0176637	+	0.999844i	$0.505623\pi$
$774$	2.34068e7	+	2.03642e8i	0.0504800	+	0.439182i
$775$	−6.70944e8			−1.44139
$776$	−3.48993e7	−	2.40814e8i	−0.0746848	−	0.515344i
$777$	1.04991e8	+	4.47734e7i	0.223814	+	0.0954459i
$778$	−3.72575e6	−	8.88549e6i	−0.00791180	−	0.0188687i
$779$	−1.69476e8	+	2.93540e8i	−0.358505	+	0.620948i
$780$	1.46941e8	+	1.13154e8i	0.309641	+	0.238443i
$781$	3.26108e7	−	1.88279e7i	0.0684556	−	0.0395228i
$782$	2.66321e8	−	3.50213e8i	0.556910	−	0.732339i
$783$	2.37222e8	+	1.94079e8i	0.494162	+	0.404290i
$784$	−7.55643e8	+	4.53941e8i	−1.56808	+	0.942001i
$785$	−3.42093e8	+	1.97507e8i	−0.707188	+	0.408295i
$786$	−4.76130e8	−	2.88558e6i	−0.980524	−	0.00594245i
$787$	1.84711e8	+	1.06643e8i	0.378939	+	0.218781i	0.677357	−	0.735655i	$-0.263125\pi$
$787$	1.84711e8	+	1.06643e8i	0.378939	+	0.218781i	−0.298417	+	0.954435i	$0.596459\pi$
$788$	−4.99084e6	−	1.29096e6i	−0.0101999	−	0.00263837i
$789$	5.14169e8	+	2.19268e8i	1.04683	+	0.446421i
$790$	−1.02433e9	−	1.30336e8i	−2.07759	−	0.264352i
$791$		−	1.86871e8i		−	0.377583i
$792$	−2.64004e7	−	3.68487e6i	−0.0531417	−	0.00741732i
$793$	−6.85025e7			−0.137368
$794$	−5.92666e7	+	4.65787e8i	−0.118399	+	0.930521i
$795$	1.04645e9	−	1.26710e8i	2.08266	−	0.252180i
$796$	4.93451e8	+	1.27639e8i	0.978374	+	0.253073i
$797$	3.44560e8	−	5.96795e8i	0.680596	−	1.17883i	−0.294203	−	0.955743i	$-0.595054\pi$
$797$	3.44560e8	−	5.96795e8i	0.680596	−	1.17883i	0.974799	−	0.223084i	$-0.0716125\pi$
$798$	−1.41948e9	−	8.31050e8i	−2.79333	−	1.63538i
$799$	2.67393e8	+	4.63139e8i	0.524216	+	0.907969i
$800$	−6.72734e7	+	6.13614e8i	−0.131393	+	1.19846i
$801$	3.97242e8	+	1.15348e8i	0.772962	+	0.224446i
$802$	3.89518e8	+	2.96211e8i	0.755100	+	0.574219i
$803$	1.02590e7	+	1.77692e7i	0.0198134	+	0.0343179i
$804$	4.24362e7	−	3.18106e8i	0.0816523	−	0.612073i
$805$	9.53056e8	+	5.50247e8i	1.82697	+	1.05480i
$806$	1.51913e8	−	6.36983e7i	0.290128	−	0.121653i
$807$	−2.22863e8	−	2.96781e8i	−0.424050	−	0.564697i
$808$	−5.14106e7	−	3.54746e8i	−0.0974583	−	0.672487i
$809$		−	1.06015e8i		−	0.200227i	−0.994976	−	0.100113i	$-0.968079\pi$
$809$		−	1.06015e8i		−	0.200227i	0.994976	−	0.100113i	$-0.0319205\pi$
$810$	7.39932e8	−	2.74664e8i	1.39231	−	0.516829i
$811$		−	1.02602e8i		−	0.192350i	−0.995364	−	0.0961748i	$-0.969339\pi$
$811$		−	1.02602e8i		−	0.192350i	0.995364	−	0.0961748i	$-0.0306608\pi$
$812$	−4.03023e8	+	4.10081e8i	−0.752769	+	0.765952i
$813$	5.55816e6	+	7.40168e6i	0.0103433	+	0.0137739i
$814$	−3.86066e6	+	1.61880e6i	−0.00715794	+	0.00300138i
$815$	6.08467e8	+	3.51299e8i	1.12399	+	0.648939i
$816$	5.86329e8	−	8.13472e7i	1.07912	−	0.149717i
$817$	−2.31961e8	−	4.01768e8i	−0.425352	−	0.736732i
$818$	2.17340e8	−	2.85803e8i	0.397082	−	0.522165i
$819$	2.33512e8	+	6.78054e7i	0.425067	+	0.123428i
$820$	2.94013e8	−	8.15223e7i	0.533243	−	0.147855i
$821$	−3.69695e8	−	6.40330e8i	−0.668057	−	1.15711i	−0.978447	−	0.206500i	$-0.933793\pi$
$821$	−3.69695e8	−	6.40330e8i	−0.668057	−	1.15711i	0.310389	−	0.950609i	$-0.399541\pi$
$822$	−9.25875e7	−	5.42062e7i	−0.166701	−	0.0975964i
$823$	−1.94330e8	+	3.36590e8i	−0.348610	+	0.603811i	−0.986003	−	0.166728i	$-0.946680\pi$
$823$	−1.94330e8	+	3.36590e8i	−0.348610	+	0.603811i	0.637392	+	0.770539i	$0.280013\pi$
$824$	−3.65634e8	+	2.88201e8i	−0.653529	+	0.515127i
$825$	3.60617e7	−	4.36655e6i	0.0642220	−	0.00777637i
$826$	−1.73684e9	−	2.20995e8i	−3.08192	−	0.392142i
$827$	−5.70497e8			−1.00864			−0.504320	−	0.863517i	$-0.668257\pi$
$827$	−5.70497e8			−1.00864			−0.504320	+	0.863517i	$0.668257\pi$
$828$	−4.18036e8	+	2.34644e8i	−0.736414	+	0.413350i
$829$		−	2.24531e8i		−	0.394106i	−0.980393	−	0.197053i	$-0.936863\pi$
$829$		−	2.24531e8i		−	0.394106i	0.980393	−	0.197053i	$-0.0631370\pi$
$830$	4.29556e8	+	5.46565e7i	0.751252	+	0.0955889i
$831$	7.71139e8	+	3.28853e8i	1.34378	+	0.573059i
$832$	−4.30236e7	−	1.45319e8i	−0.0747027	−	0.252321i
$833$	−9.97598e8	−	5.75963e8i	−1.72592	−	0.996460i
$834$	351037.	−	5.79222e7i	0.000605138	−	0.0998498i
$835$	−2.57572e8	+	1.48709e8i	−0.442424	+	0.255434i
$836$	5.81359e7	−	1.61196e7i	0.0995005	−	0.0275890i
$837$	1.13141e8	−	6.91842e8i	0.192950	−	1.17986i
$838$	3.62298e8	−	4.76423e8i	0.615650	−	0.809582i
$839$	6.53690e8	−	3.77408e8i	1.10684	−	0.639036i	0.168833	−	0.985645i	$-0.446000\pi$
$839$	6.53690e8	−	3.77408e8i	1.10684	−	0.639036i	0.938010	+	0.346609i	$0.112667\pi$
$840$	3.86958e8	+	1.42916e9i	0.652869	+	2.41125i
$841$	1.76173e8	−	3.05140e8i	0.296177	−	0.512993i
$842$	8.26958e7	−	3.46750e7i	0.138531	−	0.0580871i
$843$	−6.87999e8	−	2.93398e8i	−1.14843	−	0.489751i
$844$	7.93830e8	+	7.80167e8i	1.32038	+	1.29766i
$845$	−8.34013e8			−1.38230
$846$	−6.65373e7	−	5.78883e8i	−0.109889	−	0.956047i
$847$	1.01914e9			1.67720
$848$	−7.53347e8	−	4.17678e8i	−1.23540	−	0.684943i
$849$	5.39125e7	+	4.45242e8i	0.0880981	+	0.727568i
$850$	−7.43904e8	+	3.11925e8i	−1.21132	+	0.507917i
$851$	−3.76432e7	+	6.51999e7i	−0.0610798	+	0.105793i
$852$	8.42356e8	−	3.47219e8i	1.36200	−	0.561416i
$853$	−7.29775e8	+	4.21336e8i	−1.17582	+	0.678862i	−0.955045	−	0.296462i	$-0.904193\pi$
$853$	−7.29775e8	+	4.21336e8i	−1.17582	+	0.678862i	−0.220779	+	0.975324i	$0.570860\pi$
$854$	−4.35318e8	−	3.31039e8i	−0.698929	−	0.531503i
$855$	−1.28909e9	+	1.23655e9i	−2.06246	+	1.97839i
$856$	−3.12768e7	−	1.24807e7i	−0.0498657	−	0.0198984i
$857$	−6.91715e7	+	3.99362e7i	−0.109897	+	0.0634489i	−0.553941	−	0.832556i	$-0.686877\pi$
$857$	−6.91715e7	+	3.99362e7i	−0.109897	+	0.0634489i	0.444044	+	0.896005i	$0.353543\pi$
$858$	−7.75041e6	+	4.41229e6i	−0.0122705	+	0.00698558i
$859$	−6.90797e7	−	3.98832e7i	−0.108986	−	0.0629232i	0.444516	−	0.895771i	$-0.353376\pi$
$859$	−6.90797e7	−	3.98832e7i	−0.108986	−	0.0629232i	−0.553502	+	0.832848i	$0.686709\pi$
$860$	−1.04577e8	+	4.04291e8i	−0.164414	+	0.635622i
$861$	3.19877e8	−	2.40206e8i	0.501157	−	0.376335i
$862$	8.51443e7	−	6.69166e8i	0.132933	−	1.04475i
$863$			2.15628e8i			0.335485i	0.985831	+	0.167743i	$0.0536478\pi$
$863$			2.15628e8i			0.335485i	−0.985831	+	0.167743i	$0.946352\pi$
$864$	−6.21382e8	−	1.72843e8i	−0.963423	−	0.267984i
$865$	−6.52151e8			−1.00763
$866$	−2.73570e8	−	3.48089e7i	−0.421225	−	0.0535965i
$867$	7.31495e7	+	9.74115e7i	0.112242	+	0.149470i
$868$	1.27320e9	+	3.29333e8i	1.94686	+	0.503590i
$869$	2.48276e7	−	4.30026e7i	0.0378333	−	0.0655293i
$870$	3.08920e8	+	5.42634e8i	0.469125	+	0.824042i
$871$	−5.36854e7	−	9.29858e7i	−0.0812459	−	0.140722i
$872$	1.51589e6	−	3.79885e6i	0.00228622	−	0.00572931i
$873$	−3.36447e8	+	8.26903e7i	−0.505678	+	0.124283i
$874$	6.56739e8	−	8.63614e8i	0.983690	−	1.29356i
$875$	−1.72075e8	−	2.98043e8i	−0.256859	−	0.444892i
$876$	1.89195e8	+	4.58988e8i	0.281447	+	0.682792i
$877$	1.16922e8	+	6.75051e7i	0.173340	+	0.100078i	0.584160	−	0.811639i	$-0.301424\pi$
$877$	1.16922e8	+	6.75051e7i	0.173340	+	0.100078i	−0.410820	+	0.911717i	$0.634758\pi$
$878$	−1.80364e8	−	4.30148e8i	−0.266481	−	0.635527i
$879$	−3.87055e8	+	4.68669e7i	−0.569910	+	0.0690080i
$880$	−4.74939e7	−	2.63321e7i	−0.0696931	−	0.0386400i
$881$		−	5.43889e8i		−	0.795394i	−0.917517	−	0.397697i	$-0.869809\pi$
$881$		−	5.43889e8i		−	0.795394i	0.917517	−	0.397697i	$-0.130191\pi$
$882$	7.47574e8	+	1.00819e9i	1.08955	+	1.46939i
$883$		−	1.16412e9i		−	1.69089i	−0.534061	−	0.845446i	$-0.679335\pi$
$883$		−	1.16412e9i		−	1.69089i	0.534061	−	0.845446i	$-0.320665\pi$
$884$	1.38819e8	−	1.41250e8i	0.200951	−	0.204471i
$885$	−7.45856e8	+	1.74898e9i	−1.07603	+	2.52322i
$886$	−2.42331e8	−	5.77931e8i	−0.348424	−	0.830950i
$887$	4.09889e8	+	2.36650e8i	0.587348	+	0.339106i	0.764048	−	0.645159i	$-0.223209\pi$
$887$	4.09889e8	+	2.36650e8i	0.587348	+	0.339106i	−0.176700	+	0.984265i	$0.556542\pi$
$888$	−9.77708e7	+	2.64724e7i	−0.139627	+	0.0378054i
$889$	−3.54750e8	−	6.14444e8i	−0.504913	−	0.874535i
$890$	6.70780e8	+	5.10098e8i	0.951503	+	0.723575i
$891$	−1.57853e6	+	3.79212e7i	−0.00223161	+	0.0536104i
$892$	−1.54833e8	−	5.58410e8i	−0.218157	−	0.786790i
$893$	6.59383e8	+	1.14209e9i	0.925942	+	1.60378i
$894$	−3.84576e8	−	2.33072e6i	−0.538233	−	0.00326195i
$895$	3.55311e8	−	6.15417e8i	0.495610	−	0.858421i
$896$	4.28852e8	−	1.13138e9i	0.596188	−	1.57284i
$897$	−6.29154e7	+	1.47532e8i	−0.0871725	+	0.204413i
$898$	−1.13109e8	+	8.88944e8i	−0.156195	+	1.22757i
$899$	5.54604e8			0.763315
$900$	8.78851e8	+	1.06529e7i	1.20556	+	0.0146131i
$901$		−	1.12563e9i		−	1.53894i
$902$	−1.85191e6	+	1.45545e7i	−0.00252349	+	0.0198326i
$903$	6.58154e7	+	5.43544e8i	0.0893849	+	0.738196i
$904$	1.02659e8	+	1.30241e8i	0.138961	+	0.176296i
$905$	−7.64899e8	−	4.41614e8i	−1.03195	−	0.595796i
$906$	−7.16830e8	+	1.22439e9i	−0.963900	+	1.64640i
$907$	−9.79694e8	+	5.65627e8i	−1.31301	+	0.758068i	−0.982594	−	0.185767i	$-0.940523\pi$
$907$	−9.79694e8	+	5.65627e8i	−1.31301	+	0.758068i	−0.330418	+	0.943835i	$0.607190\pi$
$908$	−2.85636e8	−	1.03016e9i	−0.381554	−	1.37609i
$909$	−4.95624e8	+	1.21812e8i	−0.659874	+	0.162180i
$910$	3.94307e8	+	2.99852e8i	0.523251	+	0.397908i
$911$	2.64753e8	−	1.52855e8i	0.350176	−	0.202174i	−0.314587	−	0.949229i	$-0.601866\pi$
$911$	2.64753e8	−	1.52855e8i	0.350176	−	0.202174i	0.664763	+	0.747054i	$0.268533\pi$
$912$	1.44587e9	−	2.00600e8i	1.90609	−	0.264451i
$913$	−1.04115e7	+	1.80332e7i	−0.0136804	+	0.0236952i
$914$	2.00942e8	+	4.79223e8i	0.263167	+	0.627623i
$915$	−4.74914e8	+	3.56629e8i	−0.619943	+	0.465536i
$916$	5.53951e8	+	5.44417e8i	0.720751	+	0.708346i
$917$	−1.27178e9			−1.64932
$918$	−1.96196e8	−	8.19674e8i	−0.253607	−	1.05953i
$919$	−9.75198e8			−1.25645			−0.628227	−	0.778030i	$-0.716219\pi$
$919$	−9.75198e8			−1.25645			−0.628227	+	0.778030i	$0.716219\pi$
$920$	−9.66524e8	+	1.40071e8i	−1.24122	+	0.179881i
$921$	2.49027e8	−	1.87003e8i	0.318763	−	0.239370i
$922$	1.73484e8	+	4.13740e8i	0.221344	+	0.527880i
$923$	1.52414e8	−	2.63990e8i	0.193830	−	0.335723i
$924$	−7.05746e7	−	9.41485e6i	−0.0894607	−	0.0119343i
$925$	1.19539e8	−	6.90157e7i	0.151037	−	0.0872012i
$926$	−6.96092e8	+	9.15364e8i	−0.876665	+	1.15282i
$927$	4.58877e8	+	4.78375e8i	0.576045	+	0.600523i
$928$	5.56083e7	−	5.07214e8i	0.0695818	−	0.634669i
$929$	−2.50038e8	+	1.44360e8i	−0.311860	+	0.180052i	−0.647758	−	0.761846i	$-0.724293\pi$
$929$	−2.50038e8	+	1.44360e8i	−0.311860	+	0.180052i	0.335899	+	0.941898i	$0.390960\pi$
$930$	7.21565e8	−	1.23248e9i	0.897071	−	1.53225i
$931$	−2.46004e9	−	1.42031e9i	−3.04855	−	1.76008i
$932$	−1.51454e8	+	5.85518e8i	−0.187083	+	0.723257i
$933$	−8.37897e7	−	6.91986e8i	−0.103168	−	0.852025i
$934$	2.48261e8	+	3.15886e7i	0.304697	+	0.0387695i
$935$		−	7.09641e7i		−	0.0868168i
$936$	−1.99998e8	+	8.10245e7i	−0.243892	+	0.0988073i
$937$	−5.92759e8			−0.720542			−0.360271	−	0.932848i	$-0.617316\pi$
$937$	−5.92759e8			−0.720542			−0.360271	+	0.932848i	$0.617316\pi$
$938$	1.08197e8	−	8.50339e8i	0.131101	−	1.03035i
$939$	6.06119e8	−	1.42131e9i	0.732084	−	1.71669i
$940$	2.97275e8	−	1.14926e9i	0.357911	−	1.38367i
$941$	−5.93174e8	+	1.02741e9i	−0.711890	+	1.23303i	0.252257	+	0.967660i	$0.418827\pi$
$941$	−5.93174e8	+	1.02741e9i	−0.711890	+	1.23303i	−0.964147	+	0.265370i	$0.914506\pi$
$942$	2.78541e6	−	4.59601e8i	0.00333224	−	0.549830i
$943$	1.31929e8	+	2.28508e8i	0.157328	+	0.272500i
$944$	1.33191e9	−	8.00127e8i	1.58329	−	0.951137i
$945$	1.97189e9	−	7.45599e8i	2.33662	−	0.883507i
$946$	−1.59845e7	−	1.21555e7i	−0.0188811	−	0.0143582i
$947$	7.66342e8	+	1.32734e9i	0.902345	+	1.56291i	0.824442	+	0.565946i	$0.191489\pi$
$947$	7.66342e8	+	1.32734e9i	0.902345	+	1.56291i	0.0779025	+	0.996961i	$0.475178\pi$
$948$	7.33033e8	−	9.51912e8i	0.860396	−	1.11731i
$949$	1.43844e8	+	8.30484e7i	0.168304	+	0.0971701i
$950$	−1.83444e9	+	7.69196e8i	−2.13960	+	0.897152i
$951$	−1.40235e8	+	3.28841e8i	−0.163047	+	0.382335i
$952$	1.56475e9	−	2.26768e8i	1.81357	−	0.262827i
$953$		−	8.63868e8i		−	0.998087i	−0.866577	−	0.499044i	$-0.833685\pi$
$953$		−	8.63868e8i		−	0.998087i	0.866577	−	0.499044i	$-0.166315\pi$
$954$	−4.87936e8	+	1.12523e9i	−0.561976	+	1.29597i
$955$			1.72063e9i			1.97551i
$956$	−3.15195e8	−	3.09770e8i	−0.360750	−	0.354541i
$957$	−2.98086e7	+	3.60940e6i	−0.0340100	+	0.00411812i
$958$	−3.41761e8	+	1.43303e8i	−0.388710	+	0.162989i
$959$	−2.48176e8	−	1.43285e8i	−0.281387	−	0.162459i
$960$	−1.05482e9	−	7.83486e8i	−1.19224	−	0.885559i
$961$	−1.90503e8	−	3.29961e8i	−0.214650	−	0.371786i
$962$	−2.05133e7	+	2.69751e7i	−0.0230415	+	0.0302996i
$963$	−1.33703e7	+	4.60456e7i	−0.0149714	+	0.0515595i
$964$	3.11284e8	+	1.12266e9i	0.347477	+	1.25319i
$965$	−3.75273e8	−	6.49992e8i	−0.417605	−	0.723313i
$966$	−1.11276e9	+	6.33494e8i	−1.23445	+	0.702767i
$967$	1.04885e8	−	1.81666e8i	0.115993	−	0.200906i	−0.802183	−	0.597078i	$-0.796328\pi$
$967$	1.04885e8	−	1.81666e8i	0.115993	−	0.200906i	0.918176	+	0.396172i	$0.129662\pi$
$968$	−7.10301e8	+	5.59877e8i	−0.783099	+	0.617257i
$969$	1.14541e9	+	1.52532e9i	1.25890	+	1.67645i
$970$	−7.00174e8	−	8.90898e7i	−0.767169	−	0.0976142i
$971$	7.40440e8			0.808784			0.404392	−	0.914586i	$-0.367483\pi$
$971$	7.40440e8			0.808784			0.404392	+	0.914586i	$0.367483\pi$
$972$	−1.59185e8	+	9.04428e8i	−0.173342	+	0.984862i
$973$		−	1.54715e8i		−	0.167955i
$974$	−1.31631e8	−	1.67487e7i	−0.142457	−	0.0181261i
$975$	2.35140e8	−	1.76575e8i	0.253696	−	0.190508i
$976$	4.85258e8	−	8.42531e6i	0.521943	−	0.00906226i
$977$	1.19415e9	+	6.89443e8i	1.28049	+	0.739290i	0.976937	−	0.213526i	$-0.0684947\pi$
$977$	1.19415e9	+	6.89443e8i	1.28049	+	0.739290i	0.303550	+	0.952816i	$0.401828\pi$
$978$	−7.10431e8	+	4.04447e8i	−0.759461	+	0.432359i
$979$	−3.50946e7	+	2.02619e7i	−0.0374017	+	0.0215939i
$980$	6.83205e8	+	2.46400e9i	0.725894	+	2.61796i
$981$	−5.59264e6	−	1.62395e6i	−0.00592393	−	0.00172014i
$982$	−2.28984e8	+	3.01115e8i	−0.241808	+	0.317979i
$983$	−1.55460e9	+	8.97547e8i	−1.63666	+	0.944924i	−0.654682	+	0.755904i	$0.727198\pi$
$983$	−1.55460e9	+	8.97547e8i	−1.63666	+	0.944924i	−0.981973	+	0.189020i	$0.939469\pi$
$984$	−9.09816e7	+	3.43141e8i	−0.0954923	+	0.360154i
$985$	−7.47661e6	+	1.29499e7i	−0.00782341	+	0.0135505i
$986$	6.14912e8	−	2.57837e8i	0.641479	−	0.268977i
$987$	−1.87090e8	−	1.54510e9i	−0.194580	−	1.60696i
$988$	3.42322e8	−	3.48317e8i	0.354948	−	0.361164i
$989$	−3.61142e8			−0.373327
$990$	−3.07614e7	+	7.09387e7i	−0.0317030	+	0.0731102i
$991$	1.12208e8			0.115293			0.0576467	−	0.998337i	$-0.481640\pi$
$991$	1.12208e8			0.115293			0.0576467	+	0.998337i	$0.481640\pi$
$992$	−1.06829e9	+	4.69910e8i	−1.09434	+	0.481371i
$993$	−6.78462e8	−	2.89331e8i	−0.692912	−	0.295493i
$994$	2.24429e9	−	9.41049e8i	2.28518	−	0.958193i
$995$	7.39223e8	−	1.28037e9i	0.750423	−	1.29977i
$996$	−3.07399e8	+	3.99186e8i	−0.311117	+	0.404015i
$997$	−2.63231e8	+	1.51976e8i	−0.265614	+	0.153353i	−0.626893	−	0.779105i	$-0.715674\pi$
$997$	−2.63231e8	+	1.51976e8i	−0.265614	+	0.153353i	0.361279	+	0.932458i	$0.382340\pi$
$998$	1.10770e9	+	8.42356e8i	1.11437	+	0.847430i
$999$	5.10075e7	+	1.34900e8i	0.0511608	+	0.135306i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.7.j.a.5.4	✓	140
8.5	even	2	inner	72.7.j.a.5.27	yes	140
9.2	odd	6	inner	72.7.j.a.29.27	yes	140
72.29	odd	6	inner	72.7.j.a.29.4	yes	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.7.j.a.5.4	✓	140	1.1	even	1	trivial
72.7.j.a.5.27	yes	140	8.5	even	2	inner
72.7.j.a.29.4	yes	140	72.29	odd	6	inner
72.7.j.a.29.27	yes	140	9.2	odd	6	inner

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:	\( N \)	\(=\)	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	72.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-7.93602 - 1.00978i) q^{2} +(-16.2129 - 21.5903i) q^{3} +(61.9607 + 16.0272i) q^{4} +(92.8213 - 160.771i) q^{5} +(106.864 + 187.713i) q^{6} +(288.471 + 499.646i) q^{7} +(-475.537 - 189.758i) q^{8} +(-203.285 + 700.083i) q^{9} +O(q^{10})\)	\(q+(-7.93602 - 1.00978i) q^{2} +(-16.2129 - 21.5903i) q^{3} +(61.9607 + 16.0272i) q^{4} +(92.8213 - 160.771i) q^{5} +(106.864 + 187.713i) q^{6} +(288.471 + 499.646i) q^{7} +(-475.537 - 189.758i) q^{8} +(-203.285 + 700.083i) q^{9} +(-898.975 + 1182.15i) q^{10} +(-35.7086 - 61.8492i) q^{11} +(-658.530 - 1597.60i) q^{12} +(-500.678 - 289.067i) q^{13} +(-1784.78 - 4256.49i) q^{14} +(-4976.01 + 602.523i) q^{15} +(3582.26 + 1986.11i) q^{16} +5352.51i q^{17} +(2320.20 - 5350.60i) q^{18} +13199.1i q^{19} +(8327.99 - 8473.84i) q^{20} +(6110.58 - 14328.9i) q^{21} +(220.931 + 526.894i) q^{22} +(8898.34 + 5137.46i) q^{23} +(3612.89 + 13343.5i) q^{24} +(-9419.10 - 16314.4i) q^{25} +(3681.50 + 2799.61i) q^{26} +(18410.9 - 6961.39i) q^{27} +(9865.93 + 35581.8i) q^{28} +(7785.84 + 13485.5i) q^{29} +(40098.1 + 243.014i) q^{30} +(17808.1 - 30844.5i) q^{31} +(-26423.3 - 19379.1i) q^{32} +(-756.404 + 1773.71i) q^{33} +(5404.83 - 42477.6i) q^{34} +107105. q^{35} +(-23816.0 + 40119.6i) q^{36} +7327.20i q^{37} +(13328.1 - 104748. i) q^{38} +(1876.39 + 15496.4i) q^{39} +(-74647.7 + 58839.1i) q^{40} +(22239.4 + 12839.9i) q^{41} +(-62962.6 + 107544. i) q^{42} +(-30439.0 + 17574.0i) q^{43} +(-1221.26 - 4404.53i) q^{44} +(93684.1 + 97665.0i) q^{45} +(-65429.7 - 49756.3i) q^{46} +(86527.4 - 49956.6i) q^{47} +(-15198.0 - 109543. i) q^{48} +(-107606. + 186379. i) q^{49} +(58276.3 + 138982. i) q^{50} +(115562. - 86779.7i) q^{51} +(-26389.5 - 25935.2i) q^{52} -210300. q^{53} +(-153138. + 36654.9i) q^{54} -13258.1 q^{55} +(-42366.6 - 292340. i) q^{56} +(284973. - 213996. i) q^{57} +(-48171.3 - 114883. i) q^{58} +(189669. - 328517. i) q^{59} +(-317974. - 42418.6i) q^{60} +(102615. - 59244.5i) q^{61} +(-172471. + 226800. i) q^{62} +(-408435. + 100383. i) q^{63} +(190127. + 180474. i) q^{64} +(-92947.3 + 53663.1i) q^{65} +(7793.89 - 13312.4i) q^{66} +(160838. + 92859.9i) q^{67} +(-85785.7 + 331645. i) q^{68} +(-33348.3 - 275411. i) q^{69} +(-849987. - 108152. i) q^{70} +527264. i q^{71} +(229516. - 294341. i) q^{72} -287298. q^{73} +(7398.83 - 58148.8i) q^{74} +(-199522. + 467864. i) q^{75} +(-211545. + 817827. i) q^{76} +(20601.8 - 35683.3i) q^{77} +(756.801 - 124875. i) q^{78} +(347641. + 602132. i) q^{79} +(651820. - 391571. i) q^{80} +(-448792. - 284632. i) q^{81} +(-163527. - 124355. i) q^{82} +(-145784. - 252505. i) q^{83} +(608267. - 789892. i) q^{84} +(860530. + 496827. i) q^{85} +(259310. - 108731. i) q^{86} +(164925. - 386737. i) q^{87} +(5244.39 + 36187.6i) q^{88} -567422. i q^{89} +(-644859. - 869671. i) q^{90} -333549. i q^{91} +(469008. + 460936. i) q^{92} +(-954663. + 115596. i) q^{93} +(-737128. + 309083. i) q^{94} +(2.12204e6 + 1.22516e6i) q^{95} +(9997.64 + 884680. i) q^{96} +(237627. + 411582. i) q^{97} +(1.04217e6 - 1.37045e6i) q^{98} +(50558.6 - 12426.0i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q - 3 q^{2} - q^{4} + 317 q^{6} - 2 q^{7} - 4 q^{9}+O(q^{10}) \) 140 * q - 3 * q^2 - q^4 + 317 * q^6 - 2 * q^7 - 4 * q^9	\( 140 q - 3 q^{2} - q^{4} + 317 q^{6} - 2 q^{7} - 4 q^{9} + 124 q^{10} - 6946 q^{12} - 7428 q^{14} + 1454 q^{15} - q^{16} + 20878 q^{18} - 35346 q^{20} + 127 q^{22} - 6 q^{23} + 50209 q^{24} - 193752 q^{25} + 8188 q^{28} - 21344 q^{30} - 2 q^{31} - 180093 q^{32} + 45534 q^{33} + 20061 q^{34} + 39831 q^{36} + 274239 q^{38} + 125738 q^{39} - 58376 q^{40} + 31314 q^{41} - 213688 q^{42} - 22560 q^{46} - 6 q^{47} - 114411 q^{48} - 974808 q^{49} + 723249 q^{50} - 79338 q^{52} - 231173 q^{54} + 62492 q^{55} + 1294542 q^{56} + 125032 q^{57} - 221138 q^{58} - 1156344 q^{60} + 275294 q^{63} - 804478 q^{64} - 6 q^{65} + 1782258 q^{66} + 2100195 q^{68} - 86464 q^{70} + 1113091 q^{72} - 8 q^{73} - 1886976 q^{74} + 432081 q^{76} + 1658428 q^{78} - 2 q^{79} + 597124 q^{81} - 965382 q^{82} + 4997288 q^{84} - 1041879 q^{86} - 1337970 q^{87} - 536717 q^{88} - 4261994 q^{90} - 737184 q^{92} - 72534 q^{94} + 93744 q^{95} + 1053622 q^{96} - 2 q^{97}+O(q^{100}) \) 140 * q - 3 * q^2 - q^4 + 317 * q^6 - 2 * q^7 - 4 * q^9 + 124 * q^10 - 6946 * q^12 - 7428 * q^14 + 1454 * q^15 - q^16 + 20878 * q^18 - 35346 * q^20 + 127 * q^22 - 6 * q^23 + 50209 * q^24 - 193752 * q^25 + 8188 * q^28 - 21344 * q^30 - 2 * q^31 - 180093 * q^32 + 45534 * q^33 + 20061 * q^34 + 39831 * q^36 + 274239 * q^38 + 125738 * q^39 - 58376 * q^40 + 31314 * q^41 - 213688 * q^42 - 22560 * q^46 - 6 * q^47 - 114411 * q^48 - 974808 * q^49 + 723249 * q^50 - 79338 * q^52 - 231173 * q^54 + 62492 * q^55 + 1294542 * q^56 + 125032 * q^57 - 221138 * q^58 - 1156344 * q^60 + 275294 * q^63 - 804478 * q^64 - 6 * q^65 + 1782258 * q^66 + 2100195 * q^68 - 86464 * q^70 + 1113091 * q^72 - 8 * q^73 - 1886976 * q^74 + 432081 * q^76 + 1658428 * q^78 - 2 * q^79 + 597124 * q^81 - 965382 * q^82 + 4997288 * q^84 - 1041879 * q^86 - 1337970 * q^87 - 536717 * q^88 - 4261994 * q^90 - 737184 * q^92 - 72534 * q^94 + 93744 * q^95 + 1053622 * q^96 - 2 * q^97

Introduction

L-functions

Modular forms

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Database

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