LMFDB - Embedded newform 72.7.j.a.5.7

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			5.7
Character	$\chi$	$=$	72.5
Dual form			72.7.j.a.29.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.59729 + 2.50624i) q^{2} +(-12.5996 - 23.8799i) q^{3} +(51.4376 - 38.0812i) q^{4} +(-40.6546 + 70.4159i) q^{5} +(155.572 + 149.845i) q^{6} +(-158.685 - 274.850i) q^{7} +(-295.345 + 418.229i) q^{8} +(-411.498 + 601.756i) q^{9} +O(q^{10})$	\(q+(-7.59729 + 2.50624i) q^{2} +(-12.5996 - 23.8799i) q^{3} +(51.4376 - 38.0812i) q^{4} +(-40.6546 + 70.4159i) q^{5} +(155.572 + 149.845i) q^{6} +(-158.685 - 274.850i) q^{7} +(-295.345 + 418.229i) q^{8} +(-411.498 + 601.756i) q^{9} +(132.386 - 636.860i) q^{10} +(-562.279 - 973.896i) q^{11} +(-1557.47 - 748.513i) q^{12} +(-1390.56 - 802.842i) q^{13} +(1894.41 + 1690.41i) q^{14} +(2193.76 + 83.6127i) q^{15} +(1195.64 - 3917.61i) q^{16} +3494.04i q^{17} +(1618.12 - 5603.03i) q^{18} -5672.81i q^{19} +(590.348 + 5170.20i) q^{20} +(-4564.01 + 7252.38i) q^{21} +(6712.61 + 5989.76i) q^{22} +(6686.11 + 3860.23i) q^{23} +(13708.5 + 1783.28i) q^{24} +(4506.90 + 7806.18i) q^{25} +(12576.6 + 2614.34i) q^{26} +(19554.6 + 2244.61i) q^{27} +(-18629.0 - 8094.70i) q^{28} +(7494.17 + 12980.3i) q^{29} +(-16876.2 + 4862.85i) q^{30} +(-26792.2 + 46405.4i) q^{31} +(734.809 + 32759.8i) q^{32} +(-16172.0 + 25697.9i) q^{33} +(-8756.89 - 26545.2i) q^{34} +25805.1 q^{35} +(1749.16 + 46623.2i) q^{36} +14062.0i q^{37} +(14217.4 + 43098.0i) q^{38} +(-1651.17 + 43322.0i) q^{39} +(-17442.8 - 37799.9i) q^{40} +(59282.1 + 34226.5i) q^{41} +(16497.9 - 66536.9i) q^{42} +(122400. - 70667.6i) q^{43} +(-66009.4 - 28682.6i) q^{44} +(-25643.9 - 53440.2i) q^{45} +(-60470.9 - 12570.3i) q^{46} +(87962.2 - 50785.0i) q^{47} +(-108617. + 20808.7i) q^{48} +(8462.89 - 14658.2i) q^{49} +(-53804.3 - 48010.4i) q^{50} +(83437.2 - 44023.6i) q^{51} +(-102100. + 11658.1i) q^{52} +57803.3 q^{53} +(-154187. + 31955.5i) q^{54} +91437.0 q^{55} +(161817. + 14809.2i) q^{56} +(-135466. + 71475.4i) q^{57} +(-89467.1 - 79832.8i) q^{58} +(-146382. + 253541. i) q^{59} +(116026. - 79240.1i) q^{60} +(-59185.8 + 34170.9i) q^{61} +(87245.0 - 419703. i) q^{62} +(230691. + 17610.7i) q^{63} +(-87686.3 - 247044. i) q^{64} +(113066. - 65278.5i) q^{65} +(58458.3 - 235765. i) q^{66} +(-292503. - 168877. i) q^{67} +(133057. + 179725. i) q^{68} +(7939.16 - 208301. i) q^{69} +(-196048. + 64673.6i) q^{70} +519322. i q^{71} +(-130138. - 349826. i) q^{72} -298483. q^{73} +(-35242.7 - 106833. i) q^{74} +(129625. - 205979. i) q^{75} +(-216028. - 291796. i) q^{76} +(-178450. + 309085. i) q^{77} +(-96030.8 - 333268. i) q^{78} +(299658. + 519022. i) q^{79} +(227253. + 243461. i) q^{80} +(-192780. - 495243. i) q^{81} +(-536163. - 111454. i) q^{82} +(-168958. - 292644. i) q^{83} +(41417.8 + 546848. i) q^{84} +(-246036. - 142049. i) q^{85} +(-752797. + 843645. i) q^{86} +(215544. - 342507. i) q^{87} +(573378. + 52474.4i) q^{88} +523754. i q^{89} +(328758. + 341731. i) q^{90} +509595. i q^{91} +(490919. - 56054.5i) q^{92} +(1.44573e6 + 55102.4i) q^{93} +(-540995. + 606282. i) q^{94} +(399456. + 230626. i) q^{95} +(773041. - 430309. i) q^{96} +(-229224. - 397028. i) q^{97} +(-27558.2 + 132572. i) q^{98} +(817425. + 62401.2i) 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 $

$2$	−7.59729	+	2.50624i	−0.949661	+	0.313280i
$2$	−7.59729	+	2.50624i	−0.949661	+	0.313280i
$3$	−12.5996	−	23.8799i	−0.466654	−	0.884440i
$3$	−12.5996	−	23.8799i	−0.466654	−	0.884440i
$4$	51.4376	−	38.0812i	0.803712	−	0.595019i
$5$	−40.6546	+	70.4159i	−0.325237	+	0.563327i	−0.981560	−	0.191153i	$-0.938777\pi$
$5$	−40.6546	+	70.4159i	−0.325237	+	0.563327i	0.656323	+	0.754480i	$0.272111\pi$
$6$	155.572	+	149.845i	0.720240	+	0.693725i
$7$	−158.685	−	274.850i	−0.462637	−	0.801311i	0.536454	−	0.843930i	$-0.319763\pi$
$7$	−158.685	−	274.850i	−0.462637	−	0.801311i	−0.999091	+	0.0426181i	$0.986430\pi$
$8$	−295.345	+	418.229i	−0.576846	+	0.816853i
$9$	−411.498	+	601.756i	−0.564469	+	0.825454i
$10$	132.386	−	636.860i	0.132386	−	0.636860i
$11$	−562.279	−	973.896i	−0.422449	−	0.731703i	0.573730	−	0.819045i	$-0.305496\pi$
$11$	−562.279	−	973.896i	−0.422449	−	0.731703i	−0.996178	+	0.0873421i	$0.972163\pi$
$12$	−1557.47	−	748.513i	−0.901314	−	0.433167i
$13$	−1390.56	−	802.842i	−0.632937	−	0.365427i	0.148951	−	0.988845i	$-0.452410\pi$
$13$	−1390.56	−	802.842i	−0.632937	−	0.365427i	−0.781889	+	0.623418i	$0.785744\pi$
$14$	1894.41	+	1690.41i	0.690383	+	0.616039i
$15$	2193.76	+	83.6127i	0.650002	+	0.0247741i
$16$	1195.64	−	3917.61i	0.291905	−	0.956447i
$17$			3494.04i			0.711182i	0.934642	+	0.355591i	$0.115720\pi$
$17$			3494.04i			0.711182i	−0.934642	+	0.355591i	$0.884280\pi$
$18$	1618.12	−	5603.03i	0.277456	−	0.960738i
$19$		−	5672.81i		−	0.827061i	−0.910490	−	0.413530i	$-0.864296\pi$
$19$		−	5672.81i		−	0.827061i	0.910490	−	0.413530i	$-0.135704\pi$
$20$	590.348	+	5170.20i	0.0737934	+	0.646275i
$21$	−4564.01	+	7252.38i	−0.492821	+	0.783110i
$22$	6712.61	+	5989.76i	0.630411	+	0.562525i
$23$	6686.11	+	3860.23i	0.549528	+	0.317270i	0.748932	−	0.662647i	$-0.230567\pi$
$23$	6686.11	+	3860.23i	0.549528	+	0.317270i	−0.199404	+	0.979917i	$0.563900\pi$
$24$	13708.5	+	1783.28i	0.991645	+	0.128999i
$25$	4506.90	+	7806.18i	0.288442	+	0.499595i
$26$	12576.6	+	2614.34i	0.715557	+	0.148745i
$27$	19554.6	+	2244.61i	0.993476	+	0.114038i
$28$	−18629.0	−	8094.70i	−0.848622	−	0.368745i
$29$	7494.17	+	12980.3i	0.307277	+	0.532219i	0.977766	−	0.209701i	$-0.0672489\pi$
$29$	7494.17	+	12980.3i	0.307277	+	0.532219i	−0.670489	+	0.741920i	$0.733916\pi$
$30$	−16876.2	+	4862.85i	−0.625043	+	0.180105i
$31$	−26792.2	+	46405.4i	−0.899338	+	1.55770i	−0.0709969	+	0.997477i	$0.522618\pi$
$31$	−26792.2	+	46405.4i	−0.899338	+	1.55770i	−0.828342	+	0.560223i	$0.810715\pi$
$32$	734.809	+	32759.8i	0.0224246	+	0.999749i
$33$	−16172.0	+	25697.9i	−0.450010	+	0.715082i
$34$	−8756.89	−	26545.2i	−0.222799	−	0.675382i
$35$	25805.1			0.601867
$36$	1749.16	+	46623.2i	0.0374906	+	0.999297i
$37$			14062.0i			0.277615i	0.990319	+	0.138807i	$0.0443269\pi$
$37$			14062.0i			0.277615i	−0.990319	+	0.138807i	$0.955673\pi$
$38$	14217.4	+	43098.0i	0.259101	+	0.785428i
$39$	−1651.17	+	43322.0i	−0.0278355	+	0.730323i
$40$	−17442.8	−	37799.9i	−0.272544	−	0.590624i
$41$	59282.1	+	34226.5i	0.860145	+	0.496605i	0.864061	−	0.503387i	$-0.167913\pi$
$41$	59282.1	+	34226.5i	0.860145	+	0.496605i	−0.00391564	+	0.999992i	$0.501246\pi$
$42$	16497.9	−	66536.9i	0.222680	−	0.898080i
$43$	122400.	−	70667.6i	1.53949	−	0.888822i	0.540617	−	0.841269i	$-0.318191\pi$
$43$	122400.	−	70667.6i	1.53949	−	0.888822i	0.998869	−	0.0475531i	$-0.0151423\pi$
$44$	−66009.4	−	28682.6i	−0.774904	−	0.336713i
$45$	−25643.9	−	53440.2i	−0.281415	−	0.586449i
$46$	−60470.9	−	12570.3i	−0.621259	−	0.129143i
$47$	87962.2	−	50785.0i	0.847232	−	0.489150i	−0.0124839	−	0.999922i	$-0.503974\pi$
$47$	87962.2	−	50785.0i	0.847232	−	0.489150i	0.859716	+	0.510772i	$0.170641\pi$
$48$	−108617.	+	20808.7i	−0.982139	+	0.188157i
$49$	8462.89	−	14658.2i	0.0719334	−	0.124592i
$50$	−53804.3	−	48010.4i	−0.430435	−	0.384083i
$51$	83437.2	−	44023.6i	0.628998	−	0.331876i
$52$	−102100.	+	11658.1i	−0.726135	+	0.0829121i
$53$	57803.3			0.388262			0.194131	−	0.980976i	$-0.437811\pi$
$53$	57803.3			0.388262			0.194131	+	0.980976i	$0.437811\pi$
$54$	−154187.	+	31955.5i	−0.979191	+	0.202939i
$55$	91437.0			0.549584
$56$	161817.	+	14809.2i	0.921424	+	0.0843270i
$57$	−135466.	+	71475.4i	−0.731486	+	0.385951i
$58$	−89467.1	−	79832.8i	−0.458542	−	0.409164i
$59$	−146382.	+	253541.i	−0.712741	+	1.23450i	0.251083	+	0.967966i	$0.419213\pi$
$59$	−146382.	+	253541.i	−0.712741	+	1.23450i	−0.963824	+	0.266539i	$0.914120\pi$
$60$	116026.	−	79240.1i	0.537156	−	0.366852i
$61$	−59185.8	+	34170.9i	−0.260752	+	0.150545i	−0.624678	−	0.780883i	$-0.714770\pi$
$61$	−59185.8	+	34170.9i	−0.260752	+	0.150545i	0.363925	+	0.931428i	$0.381436\pi$
$62$	87245.0	−	419703.i	0.366071	−	1.76103i
$63$	230691.	+	17610.7i	0.922590	+	0.0704294i
$64$	−87686.3	−	247044.i	−0.334497	−	0.942397i
$65$	113066.	−	65278.5i	0.411709	−	0.237701i
$66$	58458.3	−	235765.i	0.203336	−	0.820065i
$67$	−292503.	−	168877.i	−0.972538	−	0.561495i	−0.0725289	−	0.997366i	$-0.523107\pi$
$67$	−292503.	−	168877.i	−0.972538	−	0.561495i	−0.900009	+	0.435871i	$0.856440\pi$
$68$	133057.	+	179725.i	0.423167	+	0.571586i
$69$	7939.16	−	208301.i	0.0241673	−	0.634080i
$70$	−196048.	+	64673.6i	−0.571570	+	0.188553i
$71$			519322.i			1.45098i	0.688232	+	0.725490i	$0.258387\pi$
$71$			519322.i			1.45098i	−0.688232	+	0.725490i	$0.741613\pi$
$72$	−130138.	−	349826.i	−0.348663	−	0.937248i
$73$	−298483.			−0.767275			−0.383638	−	0.923484i	$-0.625329\pi$
$73$	−298483.			−0.767275			−0.383638	+	0.923484i	$0.625329\pi$
$74$	−35242.7	−	106833.i	−0.0869710	−	0.263640i
$75$	129625.	−	205979.i	0.307260	−	0.488247i
$76$	−216028.	−	291796.i	−0.492117	−	0.664719i
$77$	−178450.	+	309085.i	−0.390881	+	0.677026i
$78$	−96030.8	−	333268.i	−0.202361	−	0.702279i
$79$	299658.	+	519022.i	0.607777	+	1.05270i	0.991606	+	0.129296i	$0.0412717\pi$
$79$	299658.	+	519022.i	0.607777	+	1.05270i	−0.383829	+	0.923404i	$0.625395\pi$
$80$	227253.	+	243461.i	0.443854	+	0.475510i
$81$	−192780.	−	495243.i	−0.362750	−	0.931887i
$82$	−536163.	−	111454.i	−0.972423	−	0.202140i
$83$	−168958.	−	292644.i	−0.295491	−	0.511806i	0.679608	−	0.733576i	$-0.262150\pi$
$83$	−168958.	−	292644.i	−0.295491	−	0.511806i	−0.975099	+	0.221770i	$0.928817\pi$
$84$	41417.8	+	546848.i	0.0698794	+	0.922632i
$85$	−246036.	−	142049.i	−0.400628	−	0.231303i
$86$	−752797.	+	843645.i	−1.18354	+	1.32637i
$87$	215544.	−	342507.i	0.327324	−	0.520130i
$88$	573378.	+	52474.4i	0.841381	+	0.0770016i
$89$			523754.i			0.742946i	0.928444	+	0.371473i	$0.121147\pi$
$89$			523754.i			0.742946i	−0.928444	+	0.371473i	$0.878853\pi$
$90$	328758.	+	341731.i	0.450971	+	0.468766i
$91$			509595.i			0.676240i
$92$	490919.	−	56054.5i	0.630444	−	0.0719858i
$93$	1.44573e6	+	55102.4i	1.79737	+	0.0685049i
$94$	−540995.	+	606282.i	−0.651343	+	0.729947i
$95$	399456.	+	230626.i	0.465906	+	0.268991i
$96$	773041.	−	430309.i	0.873753	−	0.486369i
$97$	−229224.	−	397028.i	−0.251157	−	0.435017i	0.712687	−	0.701482i	$-0.247478\pi$
$97$	−229224.	−	397028.i	−0.251157	−	0.435017i	−0.963845	+	0.266465i	$0.914144\pi$
$98$	−27558.2	+	132572.i	−0.0292801	+	0.140856i
$99$	817425.	+	62401.2i	0.842446	+	0.0643113i
$100$	529093.	+	229903.i	0.529093	+	0.229903i
$101$	4947.46	+	8569.25i	0.00480196	+	0.00831723i	0.868416	−	0.495836i	$-0.165138\pi$
$101$	4947.46	+	8569.25i	0.00480196	+	0.00831723i	−0.863614	+	0.504153i	$0.831805\pi$
$102$	−523563.	+	543574.i	−0.493365	+	0.512222i
$103$	−518797.	+	898582.i	−0.474772	+	0.822330i	−0.999583	−	0.0288893i	$-0.990803\pi$
$103$	−518797.	+	898582.i	−0.474772	+	0.822330i	0.524810	+	0.851219i	$0.324136\pi$
$104$	746468.	−	344458.i	0.663607	−	0.306222i
$105$	−325135.	−	616222.i	−0.280864	−	0.532316i
$106$	−439148.	+	144869.i	−0.368717	+	0.121635i
$107$	−457115.			−0.373142			−0.186571	−	0.982442i	$-0.559737\pi$
$107$	−457115.			−0.373142			−0.186571	+	0.982442i	$0.559737\pi$
$108$	1.09132e6	−	629206.i	0.866323	−	0.499484i
$109$			612831.i			0.473218i	0.971605	+	0.236609i	$0.0760360\pi$
$109$			612831.i			0.473218i	−0.971605	+	0.236609i	$0.923964\pi$
$110$	−694674.	+	229163.i	−0.521918	+	0.172173i
$111$	335799.	−	177176.i	0.245533	−	0.129550i
$112$	−1.26648e6	+	293042.i	−0.901458	+	0.208581i
$113$	−1.76572e6	−	1.01944e6i	−1.22373	−	0.706523i	−0.258021	−	0.966139i	$-0.583071\pi$
$113$	−1.76572e6	−	1.01944e6i	−1.22373	−	0.706523i	−0.965712	+	0.259616i	$0.916404\pi$
$114$	850040.	−	882529.i	0.573753	−	0.595682i
$115$	−543643.	+	313872.i	−0.357454	+	0.206376i
$116$	879787.	+	382287.i	0.563642	+	0.244915i
$117$	1.05533e6	−	506412.i	0.658916	−	0.316189i
$118$	476673.	−	2.29309e6i	0.290118	−	1.39565i
$119$	960336.	−	554450.i	0.569878	−	0.329019i
$120$	−682885.	+	892798.i	−0.395188	+	0.516665i
$121$	253465.	−	439014.i	0.143074	−	0.247812i
$122$	364011.	−	407940.i	0.200463	−	0.224655i
$123$	70392.3	−	1.84689e6i	0.0378277	−	0.992490i
$124$	389050.	+	3.40726e6i	0.204052	+	1.78707i
$125$	−2.00336e6			−1.02572
$126$	−1.79676e6	+	444373.i	−0.898212	+	0.222145i
$127$	3.70460e6			1.80855			0.904275	−	0.426951i	$-0.140412\pi$
$127$	3.70460e6			1.80855			0.904275	+	0.426951i	$0.140412\pi$
$128$	1.28533e6	+	1.65710e6i	0.612892	+	0.790167i
$129$	−3.22973e6	−	2.03251e6i	−1.50452	−	0.946811i
$130$	−695389.	+	779309.i	−0.316518	+	0.354715i
$131$	−345673.	+	598724.i	−0.153763	+	0.266326i	−0.932608	−	0.360891i	$-0.882473\pi$
$131$	−345673.	+	598724.i	−0.153763	+	0.266326i	0.778845	+	0.627217i	$0.215806\pi$
$132$	146759.	+	1.93769e6i	0.0638091	+	0.842484i
$133$	−1.55917e6	+	900188.i	−0.662733	+	0.382629i
$134$	2.64548e6	+	549924.i	1.09949	+	0.228554i
$135$	−953041.	+	1.28570e6i	−0.387356	+	0.522563i
$136$	−1.46131e6	−	1.03195e6i	−0.580931	−	0.410243i
$137$	95667.9	−	55233.9i	0.0372053	−	0.0214805i	−0.481282	−	0.876566i	$-0.659829\pi$
$137$	95667.9	−	55233.9i	0.0372053	−	0.0214805i	0.518487	+	0.855085i	$0.326495\pi$
$138$	461735.	+	1.60242e6i	0.175694	+	0.609732i
$139$	3.78717e6	+	2.18653e6i	1.41017	+	0.814161i	0.995404	−	0.0957683i	$-0.0305308\pi$
$139$	3.78717e6	+	2.18653e6i	1.41017	+	0.814161i	0.414764	+	0.909929i	$0.363864\pi$
$140$	1.32735e6	−	982688.i	0.483728	−	0.358122i
$141$	−2.32103e6	−	1.46065e6i	−0.827987	−	0.521063i
$142$	−1.30154e6	−	3.94544e6i	−0.454563	−	1.37794i
$143$			1.80569e6i			0.617496i
$144$	1.86544e6	+	2.33157e6i	0.624732	+	0.780839i
$145$	−1.21869e6			−0.399751
$146$	2.26766e6	−	748070.i	0.728651	−	0.240372i
$147$	−456664.	−	17405.3i	−0.143762	−	0.00547935i
$148$	535498.	+	723315.i	0.165186	+	0.223122i
$149$	−2.53644e6	+	4.39324e6i	−0.766770	+	1.32809i	0.172535	+	0.985003i	$0.444804\pi$
$149$	−2.53644e6	+	4.39324e6i	−0.766770	+	1.32809i	−0.939306	+	0.343082i	$0.888529\pi$
$150$	−468568.	+	1.88976e6i	−0.138835	+	0.559928i
$151$	−2.44560e6	−	4.23591e6i	−0.710322	−	1.23031i	−0.964736	−	0.263219i	$-0.915216\pi$
$151$	−2.44560e6	−	4.23591e6i	−0.710322	−	1.23031i	0.254414	−	0.967095i	$-0.418117\pi$
$152$	2.37253e6	+	1.67544e6i	0.675587	+	0.477087i
$153$	−2.10256e6	−	1.43779e6i	−0.587048	−	0.401440i
$154$	581097.	−	2.79544e6i	0.159106	−	0.765400i
$155$	−2.17845e6	−	3.77319e6i	−0.584997	−	1.01324i
$156$	1.56482e6	+	2.29126e6i	0.412184	+	0.603532i
$157$	2.13884e6	+	1.23486e6i	0.552688	+	0.319094i	0.750205	−	0.661205i	$-0.229955\pi$
$157$	2.13884e6	+	1.23486e6i	0.552688	+	0.319094i	−0.197518	+	0.980299i	$0.563288\pi$
$158$	−3.57738e6	−	3.19215e6i	−0.906971	−	0.809304i
$159$	−728301.	−	1.38034e6i	−0.181184	−	0.343395i
$160$	−2.33668e6	−	1.28009e6i	−0.570479	−	0.312523i
$161$		−	2.45023e6i		−	0.587124i
$162$	2.70580e6	+	3.27935e6i	0.636430	+	0.771334i
$163$		−	1.25007e6i		−	0.288650i	−0.989530	−	0.144325i	$-0.953899\pi$
$163$		−	1.25007e6i		−	0.288650i	0.989530	−	0.144325i	$-0.0461010\pi$
$164$	4.35271e6	−	497005.i	0.986798	−	0.112675i
$165$	−1.15207e6	−	2.18351e6i	−0.256465	−	0.486074i
$166$	2.01706e6	+	1.79985e6i	0.440955	+	0.393471i
$167$	2.04212e6	+	1.17902e6i	0.438462	+	0.253146i	0.702945	−	0.711244i	$-0.251868\pi$
$167$	2.04212e6	+	1.17902e6i	0.438462	+	0.253146i	−0.264483	+	0.964390i	$0.585201\pi$
$168$	−1.68519e6	−	4.05076e6i	−0.355404	−	0.854296i
$169$	−1.12429e6	−	1.94733e6i	−0.232927	−	0.403441i
$170$	2.22521e6	+	462562.i	0.452924	+	0.0941506i
$171$	3.41365e6	+	2.33435e6i	0.682701	+	0.466850i
$172$	3.60484e6	−	8.29610e6i	0.708436	−	1.63038i
$173$	−2.65695e6	−	4.60196e6i	−0.513150	−	0.888802i	−0.999884	−	0.0152515i	$-0.995145\pi$
$173$	−2.65695e6	−	4.60196e6i	−0.513150	−	0.888802i	0.486734	−	0.873550i	$-0.338188\pi$
$174$	−779145.	+	3.14233e6i	−0.147901	+	0.596491i
$175$	1.43035e6	−	2.47744e6i	0.266888	−	0.462263i
$176$	−4.48763e6	+	1.03836e6i	−0.823150	+	0.190462i
$177$	7.89890e6	+	301058.i	1.42445	+	0.0542913i
$178$	−1.31265e6	−	3.97911e6i	−0.232750	−	0.705547i
$179$	−9.51962e6			−1.65982			−0.829909	−	0.557899i	$-0.811608\pi$
$179$	−9.51962e6			−1.65982			−0.829909	+	0.557899i	$0.811608\pi$
$180$	−3.35413e6	−	1.77228e6i	−0.575125	−	0.303889i
$181$			9.78145e6i			1.64956i	0.565455	+	0.824779i	$0.308700\pi$
$181$			9.78145e6i			1.64956i	−0.565455	+	0.824779i	$0.691300\pi$
$182$	−1.27717e6	−	3.87154e6i	−0.211852	−	0.642199i
$183$	1.56172e6	+	982808.i	0.254829	+	0.160367i
$184$	−3.58917e6	+	1.65622e6i	−0.576156	+	0.265867i
$185$	−990189.	−	571686.i	−0.156388	−	0.0902906i
$186$	−1.11217e7	+	3.20471e6i	−1.72836	+	0.498024i
$187$	3.40283e6	−	1.96463e6i	0.520374	−	0.300438i
$188$	2.59061e6	−	5.96196e6i	0.389877	−	0.897254i
$189$	−2.48608e6	−	5.73076e6i	−0.368240	−	0.848842i
$190$	−3.61279e6	−	751001.i	−0.526722	−	0.109491i
$191$	−2.99470e6	+	1.72899e6i	−0.429787	+	0.248138i	−0.699256	−	0.714871i	$-0.746485\pi$
$191$	−2.99470e6	+	1.72899e6i	−0.429787	+	0.248138i	0.269469	+	0.963009i	$0.413152\pi$
$192$	−4.79456e6	+	5.20660e6i	−0.677400	+	0.735615i
$193$	209158.	−	362273.i	0.0290940	−	0.0503922i	−0.851112	−	0.524984i	$-0.824071\pi$
$193$	209158.	−	362273.i	0.0290940	−	0.0503922i	0.880206	+	0.474592i	$0.157404\pi$
$194$	2.73653e6	+	2.44185e6i	0.374796	+	0.334436i
$195$	−2.98343e6	−	1.87751e6i	−0.402358	−	0.253209i
$196$	−122890.	−	1.07626e6i	−0.0163210	−	0.142938i
$197$	1.12875e7			1.47639			0.738193	−	0.674589i	$-0.235679\pi$
$197$	1.12875e7			1.47639			0.738193	+	0.674589i	$0.235679\pi$
$198$	−6.36660e6	+	1.57458e6i	−0.820186	+	0.202847i
$199$	5.11399e6			0.648934			0.324467	−	0.945897i	$-0.394815\pi$
$199$	5.11399e6			0.648934			0.324467	+	0.945897i	$0.394815\pi$
$200$	−4.59586e6	−	420604.i	−0.574482	−	0.0525755i
$201$	−347322.	+	9.11274e6i	−0.0427705	+	1.12218i
$202$	−59063.8	−	52703.6i	−0.00716585	−	0.00639419i
$203$	2.37842e6	−	4.11954e6i	0.284315	−	0.492449i
$204$	2.61533e6	−	5.44186e6i	0.308061	−	0.640998i
$205$	−4.82018e6	+	2.78293e6i	−0.559502	+	0.323029i
$206$	1.68939e6	−	8.12702e6i	0.193254	−	0.929671i
$207$	−5.07423e6	+	2.43493e6i	−0.572083	+	0.274521i
$208$	−4.80784e6	+	4.48777e6i	−0.534269	+	0.498701i
$209$	−5.52473e6	+	3.18970e6i	−0.605163	+	0.349391i
$210$	4.01454e6	+	3.86675e6i	0.433489	+	0.417531i
$211$	1.29675e7	+	7.48679e6i	1.38041	+	0.796981i	0.992208	−	0.124592i	$-0.0397623\pi$
$211$	1.29675e7	+	7.48679e6i	1.38041	+	0.796981i	0.388204	+	0.921574i	$0.373096\pi$
$212$	2.97326e6	−	2.20122e6i	0.312051	−	0.231023i
$213$	1.24013e7	−	6.54327e6i	1.28331	−	0.677105i
$214$	3.47283e6	−	1.14564e6i	0.354358	−	0.116898i
$215$			1.14919e7i			1.15631i
$216$	−6.71412e6	+	7.51536e6i	−0.666235	+	0.745742i
$217$	1.70060e7			1.66427
$218$	−1.53590e6	−	4.65585e6i	−0.148250	−	0.449397i
$219$	3.76078e6	+	7.12774e6i	0.358052	+	0.678609i
$220$	4.70330e6	−	3.48203e6i	0.441707	−	0.327013i
$221$	2.80516e6	−	4.85868e6i	0.259885	−	0.450134i
$222$	−2.10712e6	+	2.18765e6i	−0.192588	+	0.199949i
$223$	−88052.1	−	152511.i	−0.00794008	−	0.0137526i	0.862028	−	0.506861i	$-0.169194\pi$
$223$	−88052.1	−	152511.i	−0.00794008	−	0.0137526i	−0.869968	+	0.493108i	$0.835861\pi$
$224$	8.88741e6	−	5.40043e6i	0.790735	−	0.480490i
$225$	−6.55200e6	−	500171.i	−0.575210	−	0.0439108i
$226$	1.59696e7	+	3.31966e6i	1.38347	+	0.287586i
$227$	−4.45109e6	−	7.70952e6i	−0.380530	−	0.659098i	0.610608	−	0.791933i	$-0.290925\pi$
$227$	−4.45109e6	−	7.70952e6i	−0.380530	−	0.659098i	−0.991138	+	0.132835i	$0.957592\pi$
$228$	−4.24617e6	+	8.83523e6i	−0.358256	+	0.745441i
$229$	1.11852e7	+	6.45775e6i	0.931399	+	0.537743i	0.887254	−	0.461282i	$-0.152610\pi$
$229$	1.11852e7	+	6.45775e6i	0.931399	+	0.537743i	0.0441451	+	0.999025i	$0.485944\pi$
$230$	3.34357e6	−	3.74707e6i	0.274806	−	0.307970i
$231$	9.62931e6	+	367011.i	0.781195	+	0.0297744i
$232$	−7.64210e6	−	699390.i	−0.611996	−	0.0560087i
$233$			1.57657e7i			1.24636i	0.782077	+	0.623181i	$0.214160\pi$
$233$			1.57657e7i			1.24636i	−0.782077	+	0.623181i	$0.785840\pi$
$234$	−6.74845e6	+	6.49226e6i	−0.526692	+	0.506697i
$235$			8.25858e6i			0.636359i
$236$	2.12562e6	+	1.86160e7i	0.161715	+	1.41628i
$237$	8.61861e6	−	1.36953e7i	0.647429	−	1.02879i
$238$	−5.90636e6	+	6.61915e6i	−0.438116	+	0.490988i
$239$	−1.66096e7	−	9.58956e6i	−1.21665	−	0.702433i	−0.252450	−	0.967610i	$-0.581236\pi$
$239$	−1.66096e7	−	9.58956e6i	−1.21665	−	0.702433i	−0.964200	+	0.265177i	$0.914570\pi$
$240$	2.95051e6	−	8.49431e6i	0.213434	−	0.614461i
$241$	8.23150e6	+	1.42574e7i	0.588069	+	1.01856i	0.994485	+	0.104877i	$0.0334449\pi$
$241$	8.23150e6	+	1.42574e7i	0.588069	+	1.01856i	−0.406417	+	0.913688i	$0.633222\pi$
$242$	−825372.	+	3.97056e6i	−0.0582376	+	0.280159i
$243$	−9.39738e6	+	1.08434e7i	−0.654920	+	0.755699i
$244$	−1.74310e6	+	4.01154e6i	−0.119992	+	0.276148i
$245$	688111.	+	1.19184e6i	0.0467908	+	0.0810441i
$246$	4.09396e6	+	1.42078e7i	0.275003	+	0.954379i
$247$	−4.55437e6	+	7.88840e6i	−0.302230	+	0.523478i
$248$	−1.14951e7	−	2.49109e7i	−0.753631	−	1.63318i
$249$	−4.85949e6	+	7.72191e6i	−0.314770	+	0.500181i
$250$	1.52201e7	−	5.02090e6i	0.974088	−	0.321338i
$251$	−2.77775e7			−1.75660			−0.878299	−	0.478111i	$-0.841322\pi$
$251$	−2.77775e7			−1.75660			−0.878299	+	0.478111i	$0.841322\pi$
$252$	1.25368e7	−	7.87914e6i	0.783404	−	0.492354i
$253$		−	8.68210e6i		−	0.536121i
$254$	−2.81449e7	+	9.28461e6i	−1.71751	+	0.566582i
$255$	−292146.	+	7.66507e6i	−0.0176189	+	0.462270i
$256$	−1.39181e7	−	9.36812e6i	−0.829583	−	0.558384i
$257$	2.04176e7	+	1.17881e7i	1.20284	+	0.694457i	0.961185	−	0.275906i	$-0.0889778\pi$
$257$	2.04176e7	+	1.17881e7i	1.20284	+	0.694457i	0.241651	+	0.970363i	$0.422311\pi$
$258$	2.96311e7	+	7.34708e6i	1.72540	+	0.427815i
$259$	3.86494e6	−	2.23142e6i	0.222456	−	0.128435i
$260$	3.32994e6	−	7.66345e6i	0.189459	−	0.436018i
$261$	−1.08948e7	−	831696.i	−0.612771	−	0.0467781i
$262$	1.12564e6	−	5.41502e6i	0.0625885	−	0.301090i
$263$	−5.25644e6	+	3.03480e6i	−0.288951	+	0.166826i	−0.637469	−	0.770476i	$-0.720018\pi$
$263$	−5.25644e6	+	3.03480e6i	−0.288951	+	0.166826i	0.348518	+	0.937302i	$0.386685\pi$
$264$	−5.97127e6	−	1.43534e7i	−0.324530	−	0.780084i
$265$	−2.34997e6	+	4.07027e6i	−0.126277	+	0.218719i
$266$	9.58939e6	−	1.07466e7i	0.509502	−	0.570989i
$267$	1.25072e7	−	6.59912e6i	0.657092	−	0.346699i
$268$	−2.14767e7	+	2.45227e6i	−1.11574	+	0.127398i
$269$	1.42675e6			0.0732980			0.0366490	−	0.999328i	$-0.488332\pi$
$269$	1.42675e6			0.0732980			0.0366490	+	0.999328i	$0.488332\pi$
$270$	4.01826e6	−	1.21564e7i	0.204149	−	0.617608i
$271$	−8.82369e6			−0.443346			−0.221673	−	0.975121i	$-0.571152\pi$
$271$	−8.82369e6			−0.443346			−0.221673	+	0.975121i	$0.571152\pi$
$272$	1.36883e7	+	4.17762e6i	0.680208	+	0.207598i
$273$	1.21691e7	−	6.42071e6i	0.598094	−	0.315570i
$274$	−588387.	+	659394.i	−0.0286030	+	0.0320548i
$275$	5.06827e6	−	8.77850e6i	0.243704	−	0.422107i
$276$	−7.52398e6	−	1.10168e7i	−0.357866	−	0.523997i
$277$	−3.01159e7	+	1.73874e7i	−1.41696	+	0.818080i	−0.996030	−	0.0890153i	$-0.971628\pi$
$277$	−3.01159e7	+	1.73874e7i	−1.41696	+	0.818080i	−0.420926	+	0.907095i	$0.638295\pi$
$278$	−3.42522e7	−	7.12011e6i	−1.59424	−	0.331400i
$279$	−1.68998e7	−	3.52181e7i	−0.778162	−	1.62164i
$280$	−7.62141e6	+	1.07924e7i	−0.347185	+	0.491637i
$281$	2.62270e7	−	1.51422e7i	1.18203	−	0.682448i	0.225550	−	0.974231i	$-0.427582\pi$
$281$	2.62270e7	−	1.51422e7i	1.18203	−	0.682448i	0.956484	+	0.291783i	$0.0942486\pi$
$282$	2.12943e7	+	5.27995e6i	0.949546	+	0.235441i
$283$	1.76494e7	+	1.01899e7i	0.778700	+	0.449582i	0.835969	−	0.548776i	$-0.184906\pi$
$283$	1.76494e7	+	1.01899e7i	0.778700	+	0.449582i	−0.0572696	+	0.998359i	$0.518239\pi$
$284$	1.97764e7	+	2.67127e7i	0.863361	+	1.16617i
$285$	474319.	−	1.24448e7i	0.0204897	−	0.537592i
$286$	−4.52548e6	−	1.37183e7i	−0.193449	−	0.586412i
$287$		−	2.17249e7i		−	0.918992i
$288$	−2.00158e7	−	1.30384e7i	−0.837905	−	0.545816i
$289$	1.19293e7			0.494220
$290$	9.25875e6	−	3.05433e6i	0.379628	−	0.125234i
$291$	−6.59285e6	+	1.04763e7i	−0.267543	+	0.425136i
$292$	−1.53532e7	+	1.13666e7i	−0.616668	+	0.456543i
$293$	−1.55943e7	+	2.70101e7i	−0.619958	+	1.07380i	0.369534	+	0.929217i	$0.379517\pi$
$293$	−1.55943e7	+	2.70101e7i	−0.619958	+	1.07380i	−0.989493	+	0.144582i	$0.953816\pi$
$294$	3.51303e6	−	1.01228e6i	0.138242	−	0.0398343i
$295$	−1.19022e7	−	2.06153e7i	−0.463620	−	0.803013i
$296$	−5.88113e6	−	4.15315e6i	−0.226770	−	0.160141i
$297$	−8.80913e6	−	2.03062e7i	−0.336251	−	0.775104i
$298$	8.25955e6	−	3.97336e7i	0.312110	−	1.50144i
$299$	−6.19830e6	−	1.07358e7i	−0.231878	−	0.401624i
$300$	−1.17633e6	−	1.55314e7i	−0.0435679	−	0.575236i
$301$	−3.88459e7	−	2.24277e7i	−1.42445	−	0.822405i
$302$	2.91962e7	+	2.60522e7i	1.06000	+	0.945852i
$303$	142296.	−	226114.i	0.00511524	−	0.00812831i
$304$	−2.22239e7	−	6.78266e6i	−0.791040	−	0.241423i
$305$		−	5.55683e6i		−	0.195852i
$306$	1.95772e7	+	5.65379e6i	0.683260	+	0.197322i
$307$		−	4.63259e7i		−	1.60106i	−0.599291	−	0.800532i	$-0.704551\pi$
$307$		−	4.63259e7i		−	1.60106i	0.599291	−	0.800532i	$-0.295449\pi$
$308$	2.59128e6	+	2.26942e7i	0.0886875	+	0.776715i
$309$	2.79947e7	+	1.06699e6i	0.948856	+	0.0361646i
$310$	2.60069e7	+	2.32063e7i	0.872977	+	0.778970i
$311$	−1.89129e7	−	1.09193e7i	−0.628747	−	0.363007i	0.151519	−	0.988454i	$-0.451583\pi$
$311$	−1.89129e7	−	1.09193e7i	−0.628747	−	0.363007i	−0.780267	+	0.625447i	$0.784917\pi$
$312$	−1.76308e7	−	1.34855e7i	−0.580509	−	0.444022i
$313$	−1.85554e7	−	3.21388e7i	−0.605113	−	1.04809i	−0.992034	−	0.125973i	$-0.959795\pi$
$313$	−1.85554e7	−	3.21388e7i	−0.605113	−	1.04809i	0.386921	−	0.922113i	$-0.373539\pi$
$314$	−1.93443e7	−	4.02115e6i	−0.624832	−	0.129886i
$315$	−1.06187e7	+	1.55284e7i	−0.339735	+	0.496814i
$316$	3.51786e7	+	1.52859e7i	1.11485	+	0.484429i
$317$	2.63344e7	+	4.56125e7i	0.826695	+	1.43188i	0.900617	+	0.434614i	$0.143115\pi$
$317$	2.63344e7	+	4.56125e7i	0.826695	+	1.43188i	−0.0739219	+	0.997264i	$0.523552\pi$
$318$	8.99256e6	+	8.66152e6i	0.279642	+	0.269347i
$319$	8.42764e6	−	1.45971e7i	0.259617	−	0.449670i
$320$	2.09607e7	+	3.86896e6i	0.639669	+	0.118071i
$321$	5.75948e6	+	1.09158e7i	0.174128	+	0.330021i
$322$	6.14087e6	+	1.86151e7i	0.183934	+	0.557569i
$323$	1.98210e7			0.588191
$324$	−2.87756e7	−	1.81328e7i	−0.846036	−	0.533125i
$325$		−	1.44733e7i		−	0.421617i
$326$	3.13297e6	+	9.49713e6i	0.0904281	+	0.274119i
$327$	1.46343e7	−	7.72145e6i	0.418533	−	0.220829i
$328$	−3.18232e7	+	1.46848e7i	−0.901825	+	0.416147i
$329$	−2.79165e7	−	1.61176e7i	−0.783922	−	0.452598i
$330$	1.42250e7	+	1.37014e7i	0.395832	+	0.381260i
$331$	2.94516e7	−	1.70039e7i	0.812130	−	0.468883i	−0.0355653	−	0.999367i	$-0.511323\pi$
$331$	2.94516e7	−	1.70039e7i	0.812130	−	0.468883i	0.847695	+	0.530484i	$0.177990\pi$
$332$	−1.98350e7	−	8.61876e6i	−0.542024	−	0.235522i
$333$	−8.46190e6	−	5.78649e6i	−0.229158	−	0.156705i
$334$	−1.84695e7	−	3.83930e6i	−0.495695	−	0.103042i
$335$	2.37832e7	−	1.37313e7i	0.632611	−	0.365238i
$336$	2.29551e7	+	2.65513e7i	0.605146	+	0.699951i
$337$	−3.19650e7	+	5.53650e7i	−0.835190	+	1.44659i	0.0586860	+	0.998276i	$0.481309\pi$
$337$	−3.19650e7	+	5.53650e7i	−0.835190	+	1.44659i	−0.893876	+	0.448315i	$0.852024\pi$
$338$	1.34221e7	+	1.19767e7i	0.347591	+	0.310161i
$339$	−2.09664e6	+	5.50098e7i	−0.0538176	+	1.41202i
$340$	−1.80649e7	+	2.06270e6i	−0.459619	+	0.0524806i
$341$	6.02588e7			1.51970
$342$	−3.17849e7	−	9.17931e6i	−0.794589	−	0.229473i
$343$	−4.27099e7			−1.05839
$344$	−6.59502e6	+	7.20625e7i	−0.162010	+	1.77025i
$345$	1.43449e7	+	9.02744e6i	0.349334	+	0.219840i
$346$	3.17192e7	+	2.83035e7i	0.765762	+	0.683301i
$347$	−1.75610e7	+	3.04166e7i	−0.420302	+	0.727985i	−0.995969	−	0.0896999i	$-0.971409\pi$
$347$	−1.75610e7	+	3.04166e7i	−0.420302	+	0.727985i	0.575667	+	0.817684i	$0.304743\pi$
$348$	−1.95603e6	−	2.58259e7i	−0.0464129	−	0.612798i
$349$	−4.97701e7	+	2.87348e7i	−1.17083	+	0.675977i	−0.953875	−	0.300205i	$-0.902945\pi$
$349$	−4.97701e7	+	2.87348e7i	−1.17083	+	0.675977i	−0.216952	+	0.976182i	$0.569612\pi$
$350$	−4.65773e6	+	2.24066e7i	−0.108635	+	0.522604i
$351$	−2.53898e7	−	1.88205e7i	−0.587136	−	0.435221i
$352$	3.14914e7	−	1.91358e7i	0.722045	−	0.438751i
$353$	3.57062e7	−	2.06150e7i	0.811744	−	0.468661i	−0.0358171	−	0.999358i	$-0.511403\pi$
$353$	3.57062e7	−	2.06150e7i	0.811744	−	0.468661i	0.847561	+	0.530698i	$0.178070\pi$
$354$	−6.07647e7	+	1.75093e7i	−1.36975	+	0.394692i
$355$	−3.65685e7	−	2.11129e7i	−0.817377	−	0.471913i
$356$	1.99452e7	+	2.69406e7i	0.442067	+	0.597115i
$357$	−2.53401e7	−	1.59468e7i	−0.556934	−	0.350485i
$358$	7.23233e7	−	2.38584e7i	1.57626	−	0.519987i
$359$			3.87055e7i			0.836544i	0.908322	+	0.418272i	$0.137364\pi$
$359$			3.87055e7i			0.836544i	−0.908322	+	0.418272i	$0.862636\pi$
$360$	2.99240e7	+	5.05829e6i	0.641376	+	0.108417i
$361$	1.48651e7			0.315970
$362$	−2.45146e7	−	7.43125e7i	−0.516773	−	1.56652i
$363$	−1.36772e7	−	521290.i	−0.285941	−	0.0108983i
$364$	1.94060e7	+	2.62123e7i	0.402375	+	0.543502i
$365$	1.21347e7	−	2.10180e7i	0.249546	−	0.432227i
$366$	−1.43280e7	−	3.55264e6i	−0.292241	−	0.0724616i
$367$	−5.90975e6	−	1.02360e7i	−0.119556	−	0.207077i	0.800036	−	0.599952i	$-0.204814\pi$
$367$	−5.90975e6	−	1.02360e7i	−0.119556	−	0.207077i	−0.919592	+	0.392875i	$0.871480\pi$
$368$	2.31170e7	−	2.15781e7i	0.463862	−	0.432982i
$369$	−4.49905e7	+	2.15892e7i	−0.895450	+	0.429693i
$370$	8.95553e6	+	1.86161e6i	0.176802	+	0.0367523i
$371$	−9.17249e6	−	1.58872e7i	−0.179625	−	0.311119i
$372$	7.64631e7	−	5.22208e7i	1.48533	−	1.01441i
$373$	−2.73947e7	−	1.58163e7i	−0.527886	−	0.304775i	0.212269	−	0.977211i	$-0.431915\pi$
$373$	−2.73947e7	−	1.58163e7i	−0.527886	−	0.304775i	−0.740155	+	0.672436i	$0.765248\pi$
$374$	−2.09285e7	+	2.34541e7i	−0.400058	+	0.448337i
$375$	2.52417e7	+	4.78401e7i	0.478657	+	0.907190i
$376$	−4.73948e6	+	5.17874e7i	−0.0891595	+	0.974228i
$377$		−	2.40666e7i		−	0.449148i
$378$	3.32501e7	+	3.73075e7i	0.615628	+	0.690750i
$379$		−	3.16823e7i		−	0.581968i	−0.956728	−	0.290984i	$-0.906017\pi$
$379$		−	3.16823e7i		−	0.581968i	0.956728	−	0.290984i	$-0.0939826\pi$
$380$	2.93296e7	−	3.34893e6i	0.534509	−	0.0610317i
$381$	−4.66767e7	−	8.84655e7i	−0.843966	−	1.59955i
$382$	1.84183e7	−	2.06411e7i	0.330416	−	0.370290i
$383$	4.54219e7	+	2.62243e7i	0.808479	+	0.466775i	0.846427	−	0.532504i	$-0.178749\pi$
$383$	4.54219e7	+	2.62243e7i	0.808479	+	0.466775i	−0.0379485	+	0.999280i	$0.512082\pi$
$384$	2.33767e7	−	5.15724e7i	0.412847	−	0.910800i
$385$	−1.45097e7	−	2.51315e7i	−0.254258	−	0.440388i
$386$	−681094.	+	3.27649e6i	−0.0118425	+	0.0569701i
$387$	−7.84262e6	+	1.02734e8i	−0.135309	+	1.77249i
$388$	−2.69101e7	−	1.16930e7i	−0.460701	−	0.200185i
$389$	5.70877e7	+	9.88789e7i	0.969826	+	1.67979i	0.696047	+	0.717996i	$0.254940\pi$
$389$	5.70877e7	+	9.88789e7i	0.969826	+	1.67979i	0.273779	+	0.961793i	$0.411726\pi$
$390$	2.73715e7	+	6.78680e6i	0.461428	+	0.114412i
$391$	−1.34878e7	+	2.33615e7i	−0.225637	+	0.390815i
$392$	3.63098e6	+	7.86864e6i	0.0602790	+	0.130630i
$393$	1.86528e7	+	710932.i	0.307303	+	0.0117125i
$394$	−8.57546e7	+	2.82892e7i	−1.40207	+	0.462522i
$395$	−4.87299e7			−0.790686
$396$	4.44226e7	−	2.79188e7i	0.715350	−	0.449584i
$397$		−	2.42376e7i		−	0.387362i	−0.981065	−	0.193681i	$-0.937957\pi$
$397$		−	2.42376e7i		−	0.387362i	0.981065	−	0.193681i	$-0.0620427\pi$
$398$	−3.88524e7	+	1.28169e7i	−0.616267	+	0.203298i
$399$	4.11414e7	+	2.58908e7i	0.647680	+	0.407593i
$400$	3.59702e7	−	8.32286e6i	0.562034	−	0.130045i
$401$	−3.62598e7	−	2.09346e7i	−0.562331	−	0.324662i	0.191749	−	0.981444i	$-0.438584\pi$
$401$	−3.62598e7	−	2.09346e7i	−0.562331	−	0.324662i	−0.754081	+	0.656782i	$0.771917\pi$
$402$	−2.02000e7	−	7.01026e7i	−0.310937	−	1.07909i
$403$	7.45125e7	−	4.30198e7i	1.13845	−	0.657284i
$404$	580813.	+	252376.i	0.00880830	+	0.00382740i
$405$	4.27104e7	+	6.55914e6i	0.642937	+	0.0987374i
$406$	−7.74498e6	+	3.72582e7i	−0.115729	+	0.556730i
$407$	1.36949e7	−	7.90678e6i	0.203131	−	0.117278i
$408$	−6.23085e6	+	4.78980e7i	−0.0917417	+	0.705240i
$409$	−2.35828e7	+	4.08466e7i	−0.344687	+	0.597016i	−0.985297	−	0.170851i	$-0.945348\pi$
$409$	−2.35828e7	+	4.08466e7i	−0.344687	+	0.597016i	0.640610	+	0.767867i	$0.278682\pi$
$410$	2.96456e7	−	3.32233e7i	0.430139	−	0.482049i
$411$	−2.52436e6	−	1.58861e6i	−0.0363602	−	0.0228819i
$412$	7.53347e6	+	6.59773e7i	0.107722	+	0.943415i
$413$	9.29144e7			1.31896
$414$	3.24479e7	−	3.12161e7i	0.457283	−	0.439924i
$415$	2.74757e7			0.384419
$416$	2.52791e7	−	4.61445e7i	0.351141	−	0.640973i
$417$	4.49694e6	−	1.17987e8i	0.0620167	−	1.62714i
$418$	3.39788e7	−	3.80794e7i	0.465242	−	0.521388i
$419$	376918.	−	652841.i	0.00512395	−	0.00887494i	−0.863452	−	0.504431i	$-0.831702\pi$
$419$	376918.	−	652841.i	0.00512395	−	0.00887494i	0.868576	+	0.495556i	$0.165036\pi$
$420$	−4.01906e7	−	1.93154e7i	−0.542471	−	0.260709i
$421$	−1.00818e7	+	5.82075e6i	−0.135112	+	0.0780068i	−0.566032	−	0.824383i	$-0.691522\pi$
$421$	−1.00818e7	+	5.82075e6i	−0.135112	+	0.0780068i	0.430921	+	0.902390i	$0.358189\pi$
$422$	−1.17281e8	−	2.43797e7i	−1.56060	−	0.324407i
$423$	−5.63607e6	+	7.38297e7i	−0.0744655	+	0.975461i
$424$	−1.70719e7	+	2.41750e7i	−0.223968	+	0.317153i
$425$	−2.72751e7	+	1.57473e7i	−0.355303	+	0.205135i
$426$	−7.78176e7	+	8.07919e7i	−1.00658	+	1.04505i
$427$	1.87837e7	+	1.08448e7i	0.241267	+	0.139296i
$428$	−2.35129e7	+	1.74075e7i	−0.299898	+	0.222026i
$429$	4.31196e7	−	2.27510e7i	0.546138	−	0.288157i
$430$	−2.88013e7	−	8.73070e7i	−0.362249	−	1.09810i
$431$			3.95816e7i			0.494380i	0.968967	+	0.247190i	$0.0795072\pi$
$431$			3.95816e7i			0.494380i	−0.968967	+	0.247190i	$0.920493\pi$
$432$	3.21738e7	−	7.39235e7i	0.399072	−	0.916920i
$433$	−2.20295e7			−0.271356			−0.135678	−	0.990753i	$-0.543321\pi$
$433$	−2.20295e7			−0.271356			−0.135678	+	0.990753i	$0.543321\pi$
$434$	−1.29200e8	+	4.26212e7i	−1.58049	+	0.521382i
$435$	1.53551e7	+	2.91022e7i	0.186545	+	0.353556i
$436$	2.33373e7	+	3.15225e7i	0.281574	+	0.380331i
$437$	2.18983e7	−	3.79290e7i	0.262402	−	0.454493i
$438$	−4.64356e7	−	4.47261e7i	−0.552622	−	0.532278i
$439$	4.96036e7	+	8.59159e7i	0.586299	+	1.01550i	0.994712	+	0.102703i	$0.0327491\pi$
$439$	4.96036e7	+	8.59159e7i	0.586299	+	1.01550i	−0.408413	+	0.912797i	$0.633918\pi$
$440$	−2.70055e7	+	3.82416e7i	−0.317026	+	0.448929i
$441$	5.33817e6	+	1.11244e7i	0.0622411	+	0.129706i
$442$	−9.13461e6	+	4.39432e7i	−0.105785	+	0.508891i
$443$	−7.68289e7	−	1.33072e8i	−0.883718	−	1.53064i	−0.847176	−	0.531312i	$-0.821699\pi$
$443$	−7.68289e7	−	1.33072e8i	−0.883718	−	1.53064i	−0.0365413	−	0.999332i	$-0.511634\pi$
$444$	1.05256e7	−	2.19012e7i	0.120254	−	0.250218i
$445$	−3.68806e7	−	2.12930e7i	−0.418522	−	0.241634i
$446$	1.05118e6	+	937988.i	0.0118488	+	0.0105729i
$447$	1.36868e8	+	5.21658e6i	1.53243	+	0.0584068i
$448$	−5.39855e7	+	6.33026e7i	−0.600403	+	0.704024i
$449$			2.83285e7i			0.312957i	0.987681	+	0.156478i	$0.0500141\pi$
$449$			2.83285e7i			0.312957i	−0.987681	+	0.156478i	$0.949986\pi$
$450$	5.10309e7	−	1.26209e7i	0.560010	−	0.138501i
$451$		−	7.69794e7i		−	0.839161i
$452$	−1.29646e8	+	1.48033e7i	−1.40392	+	0.160304i
$453$	−7.03393e7	+	1.11772e8i	−0.756665	+	1.20237i
$454$	5.31381e7	+	4.74159e7i	0.567856	+	0.506707i
$455$	−3.58836e7	−	2.07174e7i	−0.380944	−	0.219938i
$456$	1.01162e7	−	7.77657e7i	0.106690	−	0.820151i
$457$	2.20848e7	+	3.82521e7i	0.231391	+	0.400780i	0.958218	−	0.286040i	$-0.0923391\pi$
$457$	2.20848e7	+	3.82521e7i	0.231391	+	0.400780i	−0.726827	+	0.686821i	$0.759006\pi$
$458$	−1.01162e8	−	2.10288e7i	−1.05298	−	0.218886i
$459$	−7.84274e6	+	6.83245e7i	−0.0811017	+	0.706543i
$460$	−1.60110e7	+	3.68474e7i	−0.164492	+	0.378559i
$461$	−2.22218e7	−	3.84893e7i	−0.226818	−	0.392860i	0.730046	−	0.683399i	$-0.239499\pi$
$461$	−2.22218e7	−	3.84893e7i	−0.226818	−	0.392860i	−0.956863	+	0.290539i	$0.906166\pi$
$462$	−7.40765e7	+	2.13451e7i	−0.751198	+	0.216457i
$463$	3.92514e7	−	6.79854e7i	0.395469	−	0.684972i	−0.597692	−	0.801726i	$-0.703915\pi$
$463$	3.92514e7	−	6.79854e7i	0.395469	−	0.684972i	0.993161	+	0.116754i	$0.0372488\pi$
$464$	5.98120e7	−	1.38394e7i	0.598735	−	0.138537i
$465$	−6.26557e7	+	9.95621e7i	−0.623163	+	0.990228i
$466$	−3.95125e7	−	1.19776e8i	−0.390460	−	1.18362i
$467$	1.88094e8			1.84682			0.923409	−	0.383817i	$-0.125391\pi$
$467$	1.88094e8			1.84682			0.923409	+	0.383817i	$0.125391\pi$
$468$	3.49987e7	−	6.62368e7i	0.341440	−	0.646192i
$469$			1.07193e8i			1.03907i
$470$	−2.06980e7	−	6.27428e7i	−0.199358	−	0.604325i
$471$	2.53969e6	−	6.66341e7i	0.0243062	−	0.637726i
$472$	−6.28049e7	−	1.36103e8i	−0.597266	−	1.29432i
$473$	−1.37646e8	−	7.94698e7i	−1.30071	−	0.750964i
$474$	−3.11544e7	+	1.25647e8i	−0.292540	+	1.17983i
$475$	4.42830e7	−	2.55668e7i	0.413196	−	0.238559i
$476$	2.82832e7	−	6.50903e7i	0.262245	−	0.603525i
$477$	−2.37859e7	+	3.47835e7i	−0.219162	+	0.320493i
$478$	1.50222e8	+	3.12270e7i	1.37546	+	0.285922i
$479$	5.98810e7	−	3.45723e7i	0.544857	−	0.314574i	−0.202188	−	0.979347i	$-0.564805\pi$
$479$	5.98810e7	−	3.45723e7i	0.544857	−	0.314574i	0.747045	+	0.664773i	$0.231472\pi$
$480$	−1.12714e6	+	7.19284e7i	−0.0101919	+	0.650394i
$481$	1.12896e7	−	1.95541e7i	0.101448	−	0.175713i
$482$	−9.82695e7	−	8.76873e7i	−0.877561	−	0.783061i
$483$	−5.85113e7	+	3.08721e7i	−0.519276	+	0.273983i
$484$	−3.68057e6	−	3.22340e7i	−0.0324623	−	0.284301i
$485$	3.72762e7			0.326743
$486$	4.42183e7	−	1.05933e8i	0.385207	−	0.922830i
$487$	4.50051e7			0.389650			0.194825	−	0.980838i	$-0.437586\pi$
$487$	4.50051e7			0.389650			0.194825	+	0.980838i	$0.437586\pi$
$488$	3.18899e6	−	3.48454e7i	0.0274406	−	0.299838i
$489$	−2.98515e7	+	1.57504e7i	−0.255293	+	0.134699i
$490$	−8.21482e6	−	7.33021e6i	−0.0698249	−	0.0623058i
$491$	5.42302e7	−	9.39295e7i	0.458139	−	0.793519i	−0.540724	−	0.841200i	$-0.681850\pi$
$491$	5.42302e7	−	9.39295e7i	0.458139	−	0.793519i	0.998863	+	0.0476806i	$0.0151830\pi$
$492$	−6.67110e7	−	9.76802e7i	−0.560148	−	0.820184i
$493$	−4.53536e7	+	2.61849e7i	−0.378505	+	0.218530i
$494$	1.48307e7	−	7.13448e7i	0.123021	−	0.591809i
$495$	−3.76261e7	+	5.50228e7i	−0.310223	+	0.453657i
$496$	1.49764e8	+	1.60446e8i	1.22734	+	1.31487i
$497$	1.42736e8	−	8.24084e7i	1.16269	−	0.671278i
$498$	1.75660e7	−	7.08446e7i	0.142228	−	0.573613i
$499$	7.32891e7	+	4.23135e7i	0.589844	+	0.340547i	0.765036	−	0.643988i	$-0.222721\pi$
$499$	7.32891e7	+	4.23135e7i	0.589844	+	0.340547i	−0.175192	+	0.984534i	$0.556054\pi$
$500$	−1.03048e8	+	7.62905e7i	−0.824385	+	0.610324i
$501$	2.42484e6	−	6.36208e7i	0.0192828	−	0.505924i
$502$	2.11034e8	−	6.96171e7i	1.66817	−	0.550307i
$503$			1.39503e8i			1.09617i	0.836422	+	0.548086i	$0.184643\pi$
$503$			1.39503e8i			1.09617i	−0.836422	+	0.548086i	$0.815357\pi$
$504$	−7.54988e7	+	9.12803e7i	−0.589723	+	0.712993i
$505$	−804549.			−0.00624710
$506$	2.17594e7	+	6.59604e7i	0.167956	+	0.509133i
$507$	−3.23364e7	+	5.13837e7i	−0.248123	+	0.394277i
$508$	1.90556e8	−	1.41076e8i	1.45355	−	1.07612i
$509$	−5.36095e7	+	9.28544e7i	−0.406526	+	0.704124i	−0.994498	−	0.104758i	$-0.966593\pi$
$509$	−5.36095e7	+	9.28544e7i	−0.406526	+	0.704124i	0.587972	+	0.808881i	$0.299927\pi$
$510$	−1.69910e7	−	5.89660e7i	−0.128088	−	0.444520i
$511$	4.73647e7	+	8.20380e7i	0.354970	+	0.614826i
$512$	1.29218e8	+	3.62903e7i	0.962753	+	0.270384i
$513$	1.27332e7	−	1.10930e8i	0.0943162	−	0.821666i
$514$	−1.84663e8	−	3.83864e7i	−1.35985	−	0.282675i
$515$	−4.21830e7	−	7.30631e7i	−0.308827	−	0.534905i
$516$	−2.43530e8	+	1.84447e7i	−1.77257	+	0.134253i
$517$	−9.89186e7	−	5.71107e7i	−0.715824	−	0.413281i
$518$	−2.37706e7	+	2.66392e7i	−0.171021	+	0.191660i
$519$	−7.64178e7	+	1.21431e8i	−0.546629	+	0.868613i
$520$	−6.09209e6	+	6.65670e7i	−0.0433267	+	0.473423i
$521$			5.43451e7i			0.384280i	0.981368	+	0.192140i	$0.0615427\pi$
$521$			5.43451e7i			0.384280i	−0.981368	+	0.192140i	$0.938457\pi$
$522$	8.48554e7	−	2.09863e7i	0.596579	−	0.147545i
$523$			1.47518e8i			1.03119i	0.856832	+	0.515596i	$0.172430\pi$
$523$			1.47518e8i			1.03119i	−0.856832	+	0.515596i	$0.827570\pi$
$524$	5.01954e6	+	4.39606e7i	0.0348875	+	0.305541i
$525$	−7.71829e7	−	2.94174e6i	−0.533388	−	0.0203295i
$526$	3.23287e7	−	3.62302e7i	0.222142	−	0.248951i
$527$	−1.62142e8	−	9.36130e7i	−1.10781	−	0.639594i
$528$	8.13384e7	+	9.40811e7i	0.552578	+	0.639147i
$529$	−4.42153e7	−	7.65831e7i	−0.298679	−	0.517328i
$530$	7.65235e6	−	3.68126e7i	0.0514005	−	0.247269i
$531$	−9.23341e7	−	1.92418e8i	−0.616707	−	1.28517i
$532$	−4.59197e7	+	1.05679e8i	−0.304975	+	0.701863i
$533$	−5.49570e7	−	9.51883e7i	−0.362945	−	0.628640i
$534$	−7.84818e7	+	8.14814e7i	−0.515401	+	0.535100i
$535$	1.85838e7	−	3.21881e7i	0.121360	−	0.210201i
$536$	1.57019e8	−	7.24563e7i	1.01966	−	0.470524i
$537$	1.19944e8	+	2.27327e8i	0.774560	+	1.46801i
$538$	−1.08395e7	+	3.57578e6i	−0.0696082	+	0.0229628i
$539$	−1.90340e7			−0.121553
$540$	−61055.0	+	1.02426e8i	−0.000387739	+	0.650474i
$541$		−	6.22457e7i		−	0.393113i	−0.980492	−	0.196557i	$-0.937024\pi$
$541$		−	6.22457e7i		−	0.393113i	0.980492	−	0.196557i	$-0.0629760\pi$
$542$	6.70361e7	−	2.21143e7i	0.421028	−	0.138891i
$543$	2.33580e8	−	1.23243e8i	1.45894	−	0.769772i
$544$	−1.14464e8	+	2.56745e6i	−0.711003	+	0.0159480i
$545$	−4.31530e7	−	2.49144e7i	−0.266577	−	0.153908i
$546$	−7.63600e7	+	7.92786e7i	−0.469125	+	0.487055i
$547$	5.96729e7	−	3.44522e7i	0.364599	−	0.210501i	−0.306497	−	0.951872i	$-0.599157\pi$
$547$	5.96729e7	−	3.44522e7i	0.364599	−	0.210501i	0.671096	+	0.741370i	$0.265824\pi$
$548$	2.81755e6	−	6.48424e6i	0.0171210	−	0.0394020i
$549$	3.79225e6	−	4.96767e7i	0.0229182	−	0.300217i
$550$	−1.65041e7	+	7.93951e7i	−0.0991982	+	0.477206i
$551$	7.36347e7	−	4.25130e7i	0.440178	−	0.254137i
$552$	8.47726e7	+	6.48411e7i	0.504009	+	0.385508i
$553$	9.51021e7	−	1.64722e8i	0.562360	−	0.974037i
$554$	1.85222e8	−	2.07575e8i	1.08934	−	1.22080i
$555$	−1.17576e6	+	3.08486e7i	−0.00687766	+	0.180450i
$556$	2.78068e8	−	3.17506e7i	1.61781	−	0.184726i
$557$	6.15930e6			0.0356423			0.0178212	−	0.999841i	$-0.494327\pi$
$557$	6.15930e6			0.0356423			0.0178212	+	0.999841i	$0.494327\pi$
$558$	2.16658e8	+	2.25207e8i	1.24702	+	1.29622i
$559$	−2.26940e8			−1.29920
$560$	3.08537e7	−	1.01094e8i	0.175688	−	0.575654i
$561$	−8.97895e7	−	5.65056e7i	−0.508554	−	0.320039i
$562$	−1.61304e8	+	1.80771e8i	−0.908735	+	1.01840i
$563$	−9.99646e7	+	1.73144e8i	−0.560172	+	0.970246i	0.437309	+	0.899311i	$0.355931\pi$
$563$	−9.99646e7	+	1.73144e8i	−0.560172	+	0.970246i	−0.997481	+	0.0709345i	$0.977402\pi$
$564$	−1.75012e8	+	1.32552e7i	−0.975505	+	0.0738840i
$565$	1.43570e8	−	8.28899e7i	0.796007	−	0.459575i
$566$	−1.59626e8	−	3.31819e7i	−0.880346	−	0.183000i
$567$	−1.05526e8	+	1.31573e8i	−0.578910	+	0.721801i
$568$	−2.17195e8	−	1.53379e8i	−1.18524	−	0.836993i
$569$	−1.91290e7	+	1.10442e7i	−0.103838	+	0.0599509i	−0.551020	−	0.834492i	$-0.685761\pi$
$569$	−1.91290e7	+	1.10442e7i	−0.103838	+	0.0599509i	0.447182	+	0.894443i	$0.352428\pi$
$570$	2.75860e7	+	9.57353e7i	0.148958	+	0.516949i
$571$	1.36899e7	+	7.90386e6i	0.0735345	+	0.0424552i	0.536316	−	0.844017i	$-0.319815\pi$
$571$	1.36899e7	+	7.90386e6i	0.0735345	+	0.0424552i	−0.462782	+	0.886472i	$0.653149\pi$
$572$	6.87627e7	+	9.28801e7i	0.367422	+	0.496289i
$573$	7.90203e7	+	4.97284e7i	0.420025	+	0.264327i
$574$	5.44477e7	+	1.65050e8i	0.287902	+	0.872731i
$575$			6.95906e7i			0.366056i
$576$	1.84743e8	+	4.88922e7i	0.966719	+	0.255842i
$577$	−1.35593e8			−0.705848			−0.352924	−	0.935652i	$-0.614813\pi$
$577$	−1.35593e8			−0.705848			−0.352924	+	0.935652i	$0.614813\pi$
$578$	−9.06300e7	+	2.98976e7i	−0.469341	+	0.154829i
$579$	−1.12864e7	−	430167.i	−0.0581457	−	0.00221616i
$580$	−6.26865e7	+	4.64093e7i	−0.321285	+	0.237860i
$581$	−5.36221e7	+	9.28762e7i	−0.273411	+	0.473561i
$582$	2.38317e7	−	9.61145e7i	0.120889	−	0.487551i
$583$	−3.25016e7	−	5.62944e7i	−0.164021	−	0.284092i
$584$	8.81556e7	−	1.24834e8i	0.442600	−	0.626751i
$585$	−7.24454e6	+	9.49000e7i	−0.0361862	+	0.474022i
$586$	5.07806e7	−	2.44286e8i	0.252351	−	1.21397i
$587$	5.56651e7	+	9.64148e7i	0.275213	+	0.476683i	0.970189	−	0.242350i	$-0.0779183\pi$
$587$	5.56651e7	+	9.64148e7i	0.275213	+	0.476683i	−0.694976	+	0.719033i	$0.744585\pi$
$588$	−2.41525e7	+	1.64950e7i	−0.118804	+	0.0811375i
$589$	2.63249e8	+	1.51987e8i	1.28831	+	0.743808i
$590$	1.42091e8	+	1.26790e8i	0.691850	+	0.617348i
$591$	−1.42219e8	−	2.69545e8i	−0.688961	−	1.30578i
$592$	5.50894e7	+	1.68131e7i	0.265524	+	0.0810371i
$593$			3.73382e8i			1.79056i	0.445503	+	0.895281i	$0.353025\pi$
$593$			3.73382e8i			1.79056i	−0.445503	+	0.895281i	$0.646975\pi$
$594$	1.17818e8	+	1.32195e8i	0.562149	+	0.630746i
$595$			9.01639e7i			0.428037i
$596$	3.68317e7	+	3.22568e8i	0.173973	+	1.52364i
$597$	−6.44344e7	−	1.22121e8i	−0.302827	−	0.573943i
$598$	7.39967e7	+	6.60284e7i	0.346026	+	0.308764i
$599$	−2.02253e8	−	1.16771e8i	−0.941053	−	0.543317i	−0.0507624	−	0.998711i	$-0.516165\pi$
$599$	−2.02253e8	−	1.16771e8i	−0.941053	−	0.543317i	−0.890290	+	0.455394i	$0.849498\pi$
$600$	4.78622e7	+	1.15048e8i	0.221584	+	0.532630i
$601$	−7.06159e6	−	1.22310e7i	−0.0325296	−	0.0563429i	0.849302	−	0.527907i	$-0.177023\pi$
$601$	−7.06159e6	−	1.22310e7i	−0.0325296	−	0.0563429i	−0.881832	+	0.471564i	$0.843690\pi$
$602$	3.51333e8	+	7.30327e7i	1.61038	+	0.334755i
$603$	2.21987e8	−	1.06523e8i	1.01246	−	0.485839i
$604$	−2.87105e8	−	1.24753e8i	−1.30295	−	0.566163i
$605$	2.06090e7	+	3.56959e7i	0.0930661	+	0.161195i
$606$	−514371.	+	2.07448e6i	−0.00231131	+	0.00932164i
$607$	1.21302e8	−	2.10102e8i	0.542379	−	0.939427i	−0.456388	−	0.889781i	$-0.650857\pi$
$607$	1.21302e8	−	2.10102e8i	0.542379	−	0.939427i	0.998767	−	0.0496466i	$-0.0158095\pi$
$608$	1.85840e8	−	4.16843e6i	0.826853	−	0.0185465i
$609$	−1.28341e8	−	4.89160e6i	−0.568218	−	0.0216570i
$610$	1.39267e7	+	4.22168e7i	0.0613564	+	0.185993i
$611$	−1.63089e8			−0.714993
$612$	−1.62903e8	+	6.11164e6i	−0.710682	+	0.0266627i
$613$			1.54853e8i			0.672260i	0.941816	+	0.336130i	$0.109118\pi$
$613$			1.54853e8i			0.672260i	−0.941816	+	0.336130i	$0.890882\pi$
$614$	1.16104e8	+	3.51951e8i	0.501580	+	1.52047i
$615$	1.27189e8	+	8.00414e7i	0.546794	+	0.344104i
$616$	−7.65636e7	−	1.65920e8i	−0.327552	−	0.709832i
$617$	8.65649e7	+	4.99783e7i	0.368541	+	0.212777i	0.672821	−	0.739805i	$-0.265082\pi$
$617$	8.65649e7	+	4.99783e7i	0.368541	+	0.212777i	−0.304280	+	0.952583i	$0.598416\pi$
$618$	−2.15358e8	+	6.20551e7i	−0.912421	+	0.262913i
$619$	−1.09077e8	+	6.29757e7i	−0.459898	+	0.265522i	−0.712002	−	0.702178i	$-0.752211\pi$
$619$	−1.09077e8	+	6.29757e7i	−0.459898	+	0.265522i	0.252103	+	0.967700i	$0.418878\pi$
$620$	−2.55742e8	−	1.11126e8i	−1.07307	−	0.466272i
$621$	1.22079e8	+	9.04928e7i	0.509762	+	0.377867i
$622$	1.71053e8	+	3.55573e7i	0.710820	+	0.147760i
$623$	1.43954e8	−	8.31117e7i	0.595331	−	0.343715i
$624$	1.67744e8	+	5.82663e7i	0.690390	+	0.239808i
$625$	1.10257e7	−	1.90971e7i	0.0451613	−	0.0782217i
$626$	2.21518e8	+	1.97664e8i	0.902996	+	0.805757i
$627$	1.45779e8	+	9.17408e7i	0.591417	+	0.372186i
$628$	1.57042e8	−	1.79315e7i	0.634069	−	0.0723997i
$629$	−4.91332e7			−0.197435
$630$	4.17558e7	−	1.44586e8i	0.166992	−	0.578237i
$631$	−1.91725e8			−0.763118			−0.381559	−	0.924344i	$-0.624613\pi$
$631$	−1.91725e8			−0.763118			−0.381559	+	0.924344i	$0.624613\pi$
$632$	−3.05572e8	−	2.79654e7i	−1.21049	−	0.110782i
$633$	1.53978e7	−	4.03993e8i	0.0607081	−	1.59281i
$634$	−3.14386e8	−	2.80531e8i	−1.23366	−	1.10081i
$635$	−1.50609e8	+	2.60863e8i	−0.588207	+	1.01881i
$636$	−9.00269e7	−	4.32665e7i	−0.349946	−	0.168182i
$637$	−2.35364e7	+	1.35887e7i	−0.0910586	+	0.0525727i
$638$	−2.74434e7	+	1.32020e8i	−0.105676	+	0.508367i
$639$	−3.12505e8	−	2.13700e8i	−1.19772	−	0.819034i
$640$	−1.68941e8	+	2.31388e7i	−0.644458	+	0.0882673i
$641$	3.45292e8	−	1.99355e8i	1.31103	−	0.756924i	0.328764	−	0.944412i	$-0.393368\pi$
$641$	3.45292e8	−	1.99355e8i	1.31103	−	0.756924i	0.982267	+	0.187488i	$0.0600347\pi$
$642$	−7.11141e7	−	6.84962e7i	−0.268751	−	0.258858i
$643$	−2.53153e8	−	1.46158e8i	−0.952250	−	0.549782i	−0.0584707	−	0.998289i	$-0.518622\pi$
$643$	−2.53153e8	−	1.46158e8i	−0.952250	−	0.549782i	−0.893779	+	0.448507i	$0.851956\pi$
$644$	−9.33078e7	−	1.26034e8i	−0.349350	−	0.471878i
$645$	2.74424e8	−	1.44793e8i	1.02269	−	0.539597i
$646$	−1.50586e8	+	4.96762e7i	−0.558582	+	0.184268i
$647$		−	1.12436e8i		−	0.415137i	−0.978220	−	0.207569i	$-0.933445\pi$
$647$		−	1.12436e8i		−	0.415137i	0.978220	−	0.207569i	$-0.0665550\pi$
$648$	2.64061e8	+	6.56415e7i	0.970465	+	0.241242i
$649$	3.29231e8			1.20439
$650$	3.62736e7	+	1.09958e8i	0.132084	+	0.400393i
$651$	−2.14270e8	−	4.06102e8i	−0.776638	−	1.47195i
$652$	−4.76041e7	−	6.43005e7i	−0.171752	−	0.231991i
$653$	5.06535e7	−	8.77344e7i	0.181916	−	0.315087i	−0.760617	−	0.649201i	$-0.775104\pi$
$653$	5.06535e7	−	8.77344e7i	0.181916	−	0.315087i	0.942533	+	0.334114i	$0.108437\pi$
$654$	−9.18294e7	+	9.53392e7i	−0.328283	+	0.340830i
$655$	−2.81065e7	−	4.86818e7i	−0.100019	−	0.173238i
$656$	2.04966e8	−	1.91321e8i	0.726057	−	0.677722i
$657$	1.22825e8	−	1.79614e8i	0.433103	−	0.633351i
$658$	2.52484e8	+	5.24846e7i	0.886250	+	0.184228i
$659$	−6.45711e7	−	1.11840e8i	−0.225622	−	0.390789i	0.730884	−	0.682502i	$-0.239108\pi$
$659$	−6.45711e7	−	1.11840e8i	−0.225622	−	0.390789i	−0.956506	+	0.291713i	$0.905775\pi$
$660$	−1.42410e8	−	6.84418e7i	−0.495348	−	0.238062i
$661$	−9.40785e7	−	5.43163e7i	−0.325751	−	0.188073i	0.328202	−	0.944608i	$-0.393557\pi$
$661$	−9.40785e7	−	5.43163e7i	−0.325751	−	0.188073i	−0.653953	+	0.756535i	$0.726891\pi$
$662$	−1.81137e8	+	2.02996e8i	−0.624356	+	0.699704i
$663$	−1.51369e8	−	5.76926e6i	−0.519393	−	0.0197961i
$664$	1.72293e8	+	1.57679e7i	0.588523	+	0.0538605i
$665$		−	1.46387e8i		−	0.497781i
$666$	7.87898e7	+	2.27541e7i	0.266715	+	0.0770258i
$667$			1.15717e8i			0.389959i
$668$	1.49940e8	−	1.71206e7i	0.503023	−	0.0574366i
$669$	−2.53251e6	+	4.02425e6i	−0.00845811	+	0.0134402i
$670$	−1.46274e8	+	1.63927e8i	−0.486344	+	0.545036i
$671$	6.65579e7	+	3.84272e7i	0.220309	+	0.127195i
$672$	−2.40940e8	−	1.44187e8i	−0.793964	−	0.475136i
$673$	2.35447e8	+	4.07806e8i	0.772411	+	1.33785i	0.936238	+	0.351365i	$0.114282\pi$
$673$	2.35447e8	+	4.07806e8i	0.772411	+	1.33785i	−0.163828	+	0.986489i	$0.552384\pi$
$674$	1.04090e8	−	5.00736e8i	0.339960	−	1.63542i
$675$	7.06088e7	+	1.62763e8i	0.229587	+	0.529230i
$676$	−1.31988e8	−	5.73516e7i	−0.427261	−	0.185655i
$677$	−2.98261e8	−	5.16602e8i	−0.961236	−	1.66491i	−0.719406	−	0.694590i	$-0.755586\pi$
$677$	−2.98261e8	−	5.16602e8i	−0.961236	−	1.66491i	−0.241830	−	0.970319i	$-0.577748\pi$
$678$	−1.21939e8	−	4.23180e8i	−0.391249	−	1.35780i
$679$	−7.27488e7	+	1.26005e8i	−0.232389	+	0.402510i
$680$	1.32074e8	−	6.09458e7i	0.420041	−	0.193828i
$681$	−1.28020e8	+	2.03429e8i	−0.405357	+	0.644126i
$682$	−4.57803e8	+	1.51023e8i	−1.44320	+	0.476090i
$683$	−1.54446e8			−0.484748			−0.242374	−	0.970183i	$-0.577926\pi$
$683$	−1.54446e8			−0.484748			−0.242374	+	0.970183i	$0.577926\pi$
$684$	2.64485e8	−	9.92266e6i	0.826480	−	0.0310070i
$685$			8.98206e6i			0.0279450i
$686$	3.24479e8	−	1.07041e8i	1.00511	−	0.331572i
$687$	1.32814e7	−	3.48466e8i	0.0409613	−	1.07471i
$688$	−1.30501e8	−	5.64008e8i	−0.400728	−	1.73189i
$689$	−8.03792e7	−	4.64069e7i	−0.245746	−	0.141881i
$690$	−1.31608e8	−	3.26323e7i	−0.400621	−	0.0993345i
$691$	−4.01815e8	+	2.31988e8i	−1.21785	+	0.703124i	−0.964457	−	0.264241i	$-0.914879\pi$
$691$	−4.01815e8	+	2.31988e8i	−1.21785	+	0.703124i	−0.253389	+	0.967364i	$0.581545\pi$
$692$	−3.11915e8	−	1.35534e8i	−0.941279	−	0.409007i
$693$	−1.12562e8	−	2.34571e8i	−0.338214	−	0.704815i
$694$	5.71850e7	−	2.75096e8i	0.171082	−	0.823011i
$695$	−3.07932e8	+	1.77785e8i	−0.917278	+	0.529591i
$696$	7.95864e7	+	1.91304e8i	0.236054	+	0.567410i
$697$	−1.19589e8	+	2.07134e8i	−0.353177	+	0.611720i
$698$	3.06102e8	−	3.43042e8i	0.900119	−	1.00875i
$699$	3.76482e8	−	1.98642e8i	1.10233	−	0.581620i
$700$	−2.07702e7	−	1.81903e8i	−0.0605545	−	0.530329i
$701$	−5.36570e8			−1.55766			−0.778829	−	0.627236i	$-0.784186\pi$
$701$	−5.36570e8			−1.55766			−0.778829	+	0.627236i	$0.784186\pi$
$702$	2.40063e8	+	7.93519e7i	0.693926	+	0.229375i
$703$	7.97711e7			0.229604
$704$	−1.91291e8	+	2.24305e8i	−0.548247	+	0.642866i
$705$	1.97214e8	−	1.04055e8i	0.562821	−	0.296959i
$706$	−2.19604e8	+	2.46106e8i	−0.624060	+	0.699372i
$707$	1.57017e6	−	2.71962e6i	0.00444313	−	0.00769572i
$708$	4.17765e8	−	2.85314e8i	1.17715	−	0.803939i
$709$	−5.35571e7	+	3.09212e7i	−0.150272	+	0.0867597i	−0.573251	−	0.819380i	$-0.694318\pi$
$709$	−5.35571e7	+	3.09212e7i	−0.150272	+	0.0867597i	0.422979	+	0.906140i	$0.360985\pi$
$710$	3.30735e8	+	6.87510e7i	0.924072	+	0.192090i
$711$	−4.35633e8	−	3.32557e7i	−1.21203	−	0.0925246i
$712$	−2.19049e8	−	1.54688e8i	−0.606878	−	0.428566i
$713$	−3.58271e8	+	2.06848e8i	−0.988423	+	0.570666i
$714$	2.32483e8	+	5.76444e7i	0.638698	+	0.158366i
$715$	−1.27149e8	−	7.34095e7i	−0.347852	−	0.200833i
$716$	−4.89666e8	+	3.62519e8i	−1.33402	+	0.987623i
$717$	−1.97224e7	+	5.17460e8i	−0.0535061	+	1.40385i
$718$	−9.70051e7	−	2.94057e8i	−0.262072	−	0.794434i
$719$			1.85951e7i			0.0500278i	0.999687	+	0.0250139i	$0.00796301\pi$
$719$			1.85951e7i			0.0500278i	−0.999687	+	0.0250139i	$0.992037\pi$
$720$	−2.40019e8	+	3.65674e7i	−0.643054	+	0.0979708i
$721$	3.29300e8			0.878590
$722$	−1.12934e8	+	3.72554e7i	−0.300064	+	0.0989870i
$723$	2.36751e8	−	3.76205e8i	0.626435	−	0.995428i
$724$	3.72489e8	+	5.03134e8i	0.981518	+	1.32577i
$725$	−6.75510e7	+	1.17002e8i	−0.177263	+	0.307028i
$726$	1.05216e8	−	3.03178e7i	0.274961	−	0.0792297i
$727$	3.10897e8	+	5.38490e8i	0.809121	+	1.40144i	0.913473	+	0.406898i	$0.133390\pi$
$727$	3.10897e8	+	5.38490e8i	0.809121	+	1.40144i	−0.104352	+	0.994540i	$0.533277\pi$
$728$	−2.13127e8	−	1.50506e8i	−0.552388	−	0.390086i
$729$	3.77344e8	+	8.77847e7i	0.973991	+	0.226588i
$730$	−3.95150e7	+	1.90092e8i	−0.101577	+	0.488647i
$731$	2.46915e8	+	4.27670e8i	0.632115	+	1.09485i
$732$	1.17757e8	−	8.91886e6i	0.300231	−	0.0227392i
$733$	5.21945e8	+	3.01345e8i	1.32530	+	0.765160i	0.984568	−	0.175002i	$-0.0559931\pi$
$733$	5.21945e8	+	3.01345e8i	1.32530	+	0.765160i	0.340728	+	0.940162i	$0.389326\pi$
$734$	7.05518e7	+	6.29545e7i	0.178410	+	0.159198i
$735$	1.97911e7	−	3.14488e7i	0.0498435	−	0.0792032i
$736$	−1.21547e8	+	2.21872e8i	−0.304867	+	0.556504i
$737$			3.79824e8i			0.948811i
$738$	2.87698e8	−	2.76776e8i	0.715760	−	0.688588i
$739$			5.41016e8i			1.34053i	0.742122	+	0.670265i	$0.233820\pi$
$739$			5.41016e8i			1.34053i	−0.742122	+	0.670265i	$0.766180\pi$
$740$	−7.27034e7	+	8.30147e6i	−0.179415	+	0.0204861i
$741$	2.45758e8	+	9.36679e6i	0.604022	+	0.0230216i
$742$	1.09503e8	+	9.77114e7i	0.268050	+	0.239185i
$743$	3.12661e8	+	1.80515e8i	0.762268	+	0.440096i	0.830110	−	0.557600i	$-0.188278\pi$
$743$	3.12661e8	+	1.80515e8i	0.762268	+	0.440096i	−0.0678412	+	0.997696i	$0.521611\pi$
$744$	−4.50035e8	+	5.88371e8i	−1.09277	+	1.42867i
$745$	−2.06236e8	−	3.57211e8i	−0.498764	−	0.863885i
$746$	2.47765e8	+	5.15037e7i	0.596793	+	0.124057i
$747$	2.45626e8	+	1.87508e7i	0.589268	+	0.0449840i
$748$	1.00218e8	−	2.30639e8i	0.239464	−	0.551098i
$749$	7.25370e7	+	1.25638e8i	0.172629	+	0.299003i
$750$	−3.11667e8	−	3.00193e8i	−0.738766	−	0.711569i
$751$	3.42069e8	−	5.92481e8i	0.807596	−	1.39880i	−0.106929	−	0.994267i	$-0.534102\pi$
$751$	3.42069e8	−	5.92481e8i	0.807596	−	1.39880i	0.914525	−	0.404530i	$-0.132565\pi$
$752$	−9.37843e7	−	4.05322e8i	−0.220534	−	0.953118i
$753$	3.49987e8	+	6.63324e8i	0.819723	+	1.55361i
$754$	6.03165e7	+	1.82840e8i	0.140709	+	0.426539i
$755$	3.97701e8			0.924093
$756$	−3.46112e8	−	2.00103e8i	−0.801035	−	0.463115i
$757$		−	4.56752e8i		−	1.05291i	−0.850202	−	0.526457i	$-0.823520\pi$
$757$		−	4.56752e8i		−	1.05291i	0.850202	−	0.526457i	$-0.176480\pi$
$758$	7.94033e7	+	2.40699e8i	0.182319	+	0.552672i
$759$	−2.07327e8	+	1.09391e8i	−0.474167	+	0.250183i
$760$	−2.14432e8	+	9.89496e7i	−0.488482	+	0.225410i
$761$	3.41980e8	+	1.97442e8i	0.775972	+	0.448008i	0.835001	−	0.550248i	$-0.185467\pi$
$761$	3.41980e8	+	1.97442e8i	0.775972	+	0.448008i	−0.0590285	+	0.998256i	$0.518800\pi$
$762$	5.76332e8	+	5.55115e8i	1.30259	+	1.25464i
$763$	1.68436e8	−	9.72468e7i	0.379195	−	0.218928i
$764$	−8.81980e7	+	2.02977e8i	−0.197778	+	0.455163i
$765$	1.86722e8	−	8.96008e7i	0.417072	−	0.200137i
$766$	−4.10807e8	−	8.53958e7i	−0.914012	−	0.189998i
$767$	4.07107e8	−	2.35043e8i	0.902241	−	0.520909i
$768$	−4.83467e7	+	4.50397e8i	−0.106729	+	0.994288i
$769$	−3.85575e8	+	6.67836e8i	−0.847872	+	1.46856i	0.0352318	+	0.999379i	$0.488783\pi$
$769$	−3.85575e8	+	6.67836e8i	−0.847872	+	1.46856i	−0.883104	+	0.469178i	$0.844550\pi$
$770$	1.73219e8	+	1.54566e8i	0.379424	+	0.338565i
$771$	2.42442e7	−	6.36097e8i	0.0528986	−	1.38791i
$772$	−3.03719e6	−	2.65994e7i	−0.00660117	−	0.0578123i
$773$	−5.02942e8			−1.08888			−0.544439	−	0.838800i	$-0.683258\pi$
$773$	−5.02942e8			−1.08888			−0.544439	+	0.838800i	$0.683258\pi$
$774$	−1.97894e8	−	8.00158e8i	−0.426786	−	1.72565i
$775$	−4.82999e8			−1.03763
$776$	2.33749e8	+	2.13923e7i	0.500224	+	0.0457796i
$777$	−1.01983e8	−	6.41792e7i	−0.217403	−	0.136814i
$778$	−6.81526e8	−	6.08136e8i	−1.44725	−	1.29140i
$779$	1.94161e8	−	3.36296e8i	0.410723	−	0.711393i
$780$	−2.24958e8	+	1.70382e7i	−0.474043	+	0.0359037i
$781$	5.05766e8	−	2.92004e8i	1.06169	−	0.612965i
$782$	4.39210e7	−	2.11288e8i	0.0918443	−	0.441829i
$783$	1.17410e8	+	2.70646e8i	0.244579	+	0.563788i
$784$	−4.73063e7	−	5.06802e7i	−0.0981682	−	0.105170i
$785$	−1.73908e8	+	1.00406e8i	−0.359509	+	0.207563i
$786$	−1.43493e8	+	4.13472e7i	−0.295503	+	0.0851489i
$787$	1.11358e8	+	6.42926e7i	0.228453	+	0.131898i	0.609858	−	0.792510i	$-0.291226\pi$
$787$	1.11358e8	+	6.42926e7i	0.228453	+	0.131898i	−0.381405	+	0.924408i	$0.624560\pi$
$788$	5.80603e8	−	4.29843e8i	1.18659	−	0.878478i
$789$	1.38700e8	+	8.72856e7i	0.282388	+	0.177710i
$790$	3.70215e8	−	1.22129e8i	0.750884	−	0.247706i
$791$			6.47077e8i			1.30746i
$792$	−2.67521e8	+	3.23440e8i	−0.538495	+	0.651057i
$793$	1.09735e8			0.220053
$794$	6.07451e7	+	1.84140e8i	0.121353	+	0.367863i
$795$	1.26806e8	+	4.83309e6i	0.252371	+	0.00961886i
$796$	2.63051e8	−	1.94747e8i	0.521556	−	0.386128i
$797$	−9.64284e7	+	1.67019e8i	−0.190472	+	0.329906i	−0.945407	−	0.325893i	$-0.894335\pi$
$797$	−9.64284e7	+	1.67019e8i	−0.190472	+	0.329906i	0.754935	+	0.655800i	$0.227668\pi$
$798$	−3.77451e8	−	9.35896e7i	−0.742767	−	0.184170i
$799$	1.77445e8	+	3.07343e8i	0.347875	+	0.602536i
$800$	−2.52417e8	+	1.53381e8i	−0.493002	+	0.299572i
$801$	−3.15172e8	−	2.15524e8i	−0.613268	−	0.419370i
$802$	3.27943e8	+	6.81706e7i	0.635734	+	0.132152i
$803$	1.67831e8	+	2.90692e8i	0.324134	+	0.561417i
$804$	3.29159e8	+	4.81963e8i	0.633340	+	0.927355i
$805$	1.72535e8	+	9.96134e7i	0.330743	+	0.190955i
$806$	−4.58275e8	+	5.13580e8i	−0.875227	+	0.980850i
$807$	−1.79766e7	−	3.40707e7i	−0.0342048	−	0.0648277i
$808$	−5.04511e6	−	461719.i	−0.00956394	−	0.000875274i
$809$			6.66117e7i			0.125807i	0.998020	+	0.0629035i	$0.0200360\pi$
$809$			6.66117e7i			0.125807i	−0.998020	+	0.0629035i	$0.979964\pi$
$810$	−3.40922e8	+	5.72107e7i	−0.641504	+	0.107652i
$811$		−	1.12744e7i		−	0.0211364i	−0.999944	−	0.0105682i	$-0.996636\pi$
$811$		−	1.12744e7i		−	0.0211364i	0.999944	−	0.0105682i	$-0.00336402\pi$
$812$	−3.45371e7	−	3.02472e8i	−0.0645087	−	0.564960i
$813$	1.11175e8	+	2.10709e8i	0.206889	+	0.392113i
$814$	−8.42281e7	+	9.43928e7i	−0.156165	+	0.175011i
$815$	8.80247e7	+	5.08211e7i	0.162604	+	0.0938796i
$816$	−7.27062e7	−	3.79511e8i	−0.133814	−	0.698480i
$817$	−4.00884e8	−	6.94351e8i	−0.735110	−	1.27325i
$818$	7.67940e7	−	3.69427e8i	0.140303	−	0.674946i
$819$	−3.06652e8	−	2.09697e8i	−0.558205	−	0.381716i
$820$	−1.41961e8	+	3.26706e8i	−0.257470	+	0.592537i
$821$	−2.33686e8	−	4.04757e8i	−0.422283	−	0.731416i	0.573879	−	0.818940i	$-0.305438\pi$
$821$	−2.33686e8	−	4.04757e8i	−0.422283	−	0.731416i	−0.996162	+	0.0875237i	$0.972105\pi$
$822$	2.31597e7	+	5.74249e6i	0.0416983	+	0.0103391i
$823$	−2.91622e7	+	5.05104e7i	−0.0523143	+	0.0906111i	−0.890997	−	0.454010i	$-0.849993\pi$
$823$	−2.91622e7	+	5.05104e7i	−0.0523143	+	0.0906111i	0.838682	+	0.544621i	$0.183326\pi$
$824$	−2.22589e8	−	4.82368e8i	−0.397852	−	0.862177i
$825$	−2.73488e8	−	1.04237e7i	−0.487053	−	0.0185635i
$826$	−7.05897e8	+	2.32865e8i	−1.25257	+	0.413204i
$827$	8.21555e8			1.45251			0.726257	−	0.687423i	$-0.241258\pi$
$827$	8.21555e8			1.45251			0.726257	+	0.687423i	$0.241258\pi$
$828$	−1.68281e8	+	3.18480e8i	−0.296445	+	0.561036i
$829$			1.34081e8i			0.235345i	0.993052	+	0.117672i	$0.0375433\pi$
$829$			1.34081e8i			0.235345i	−0.993052	+	0.117672i	$0.962457\pi$
$830$	−2.08741e8	+	6.88607e7i	−0.365068	+	0.120431i
$831$	7.94659e8	+	5.00089e8i	1.38477	+	0.871453i
$832$	−7.64038e7	+	4.13928e8i	−0.132661	+	0.718712i
$833$	5.12162e7	+	2.95697e7i	0.0886078	+	0.0511577i
$834$	2.61538e8	+	9.07649e8i	0.450855	+	1.56466i
$835$	−1.66043e8	+	9.58651e7i	−0.285208	+	0.164665i
$836$	−1.62711e8	+	3.74459e8i	−0.278482	+	0.640893i
$837$	−6.28072e8	+	8.47302e8i	−1.07111	+	1.44498i
$838$	−1.22738e6	+	5.90447e6i	−0.00208568	+	0.0100334i
$839$	−4.73215e8	+	2.73211e8i	−0.801258	+	0.462607i	−0.843911	−	0.536483i	$-0.819752\pi$
$839$	−4.73215e8	+	2.73211e8i	−0.801258	+	0.462607i	0.0426526	+	0.999090i	$0.486419\pi$
$840$	3.53749e8	+	4.60177e7i	0.596839	+	0.0776402i
$841$	1.85086e8	−	3.20579e8i	0.311162	−	0.538948i
$842$	6.20064e7	−	6.94894e7i	0.103872	−	0.116408i
$843$	−6.92045e8	−	4.35512e8i	−1.15519	−	0.726972i
$844$	9.52122e8	−	1.08716e8i	1.58367	−	0.180828i
$845$	1.82831e8			0.303026
$846$	−1.42216e8	−	5.75031e8i	−0.234875	−	0.949686i
$847$	−1.60884e8			−0.264766
$848$	6.91121e7	−	2.26451e8i	0.113336	−	0.371352i
$849$	2.09571e7	−	5.49854e8i	0.0342458	−	0.898512i
$850$	1.67750e8	−	1.87994e8i	0.273153	−	0.306118i
$851$	−5.42825e7	+	9.40201e7i	−0.0880788	+	0.152557i
$852$	3.88719e8	−	8.08828e8i	0.628517	−	1.30779i
$853$	8.24626e8	−	4.76098e8i	1.32865	−	0.767095i	0.343557	−	0.939132i	$-0.388368\pi$
$853$	8.24626e8	−	4.76098e8i	1.32865	−	0.767095i	0.985091	+	0.172037i	$0.0550347\pi$
$854$	−1.69885e8	−	3.53146e7i	−0.272761	−	0.0566996i
$855$	−3.03156e8	+	1.45473e8i	−0.485029	+	0.232747i
$856$	1.35007e8	−	1.91178e8i	0.215245	−	0.304802i
$857$	−1.25626e8	+	7.25301e7i	−0.199589	+	0.115233i	−0.596464	−	0.802640i	$-0.703428\pi$
$857$	−1.25626e8	+	7.25301e7i	−0.199589	+	0.115233i	0.396875	+	0.917873i	$0.370095\pi$
$858$	−2.70572e8	+	2.80914e8i	−0.428372	+	0.444745i
$859$	−5.13553e8	−	2.96500e8i	−0.810226	−	0.467784i	0.0368084	−	0.999322i	$-0.488281\pi$
$859$	−5.13553e8	−	2.96500e8i	−0.810226	−	0.467784i	−0.847034	+	0.531538i	$0.821614\pi$
$860$	4.37624e8	+	5.91113e8i	0.688027	+	0.929342i
$861$	−5.18788e8	+	2.73726e8i	−0.812794	+	0.428851i
$862$	−9.92008e7	−	3.00712e8i	−0.154879	−	0.469494i
$863$		−	1.15292e9i		−	1.79377i	−0.442259	−	0.896887i	$-0.645823\pi$
$863$		−	1.15292e9i		−	1.79377i	0.442259	−	0.896887i	$-0.354177\pi$
$864$	−5.91639e7	+	6.42253e8i	−0.0917308	+	0.995784i
$865$	4.32069e8			0.667582
$866$	1.67364e8	−	5.52111e7i	0.257697	−	0.0850105i
$867$	−1.50304e8	−	2.84869e8i	−0.230629	−	0.437108i
$868$	8.74749e8	−	6.47610e8i	1.33759	−	0.990272i
$869$	3.36982e8	−	5.83671e8i	0.513509	−	0.889423i
$870$	−1.89594e8	−	1.82614e8i	−0.287917	−	0.277318i
$871$	2.71163e8	+	4.69668e8i	0.410370	+	0.710782i
$872$	−2.56303e8	−	1.80997e8i	−0.386549	−	0.272974i
$873$	3.33240e8	+	2.54391e7i	0.500857	+	0.0382348i
$874$	−7.13088e7	+	3.43040e8i	−0.106809	+	0.513819i
$875$	3.17903e8	+	5.50624e8i	0.474537	+	0.821923i
$876$	4.64878e8	+	2.23419e8i	0.691556	+	0.332359i
$877$	−4.01556e8	−	2.31839e8i	−0.595316	−	0.343706i	0.171880	−	0.985118i	$-0.445016\pi$
$877$	−4.01556e8	−	2.31839e8i	−0.595316	−	0.343706i	−0.767197	+	0.641412i	$0.778349\pi$
$878$	−5.92178e8	−	5.28410e8i	−0.874921	−	0.780705i
$879$	8.41480e8	+	3.20721e7i	1.23902	+	0.0472238i
$880$	1.09326e8	−	3.58215e8i	0.160426	−	0.525648i
$881$		−	9.25011e8i		−	1.35276i	−0.736555	−	0.676378i	$-0.763549\pi$
$881$		−	9.25011e8i		−	1.35276i	0.736555	−	0.676378i	$-0.236451\pi$
$882$	−6.84360e7	−	7.11365e7i	−0.0997422	−	0.103678i
$883$			8.81659e7i			0.128061i	0.997948	+	0.0640307i	$0.0203956\pi$
$883$			8.81659e7i			0.128061i	−0.997948	+	0.0640307i	$0.979604\pi$
$884$	−4.07338e7	−	3.56743e8i	−0.0589656	−	0.516414i
$885$	−3.42326e8	+	5.43969e8i	−0.493867	+	0.784773i
$886$	9.17200e8	+	8.18432e8i	1.31875	+	1.17674i
$887$	−5.59030e8	−	3.22756e8i	−0.801059	−	0.462492i	0.0427822	−	0.999084i	$-0.486378\pi$
$887$	−5.59030e8	−	3.22756e8i	−0.801059	−	0.462492i	−0.843841	+	0.536593i	$0.819711\pi$
$888$	−2.50765e7	+	1.92769e8i	−0.0358120	+	0.275295i
$889$	−5.87863e8	−	1.01821e9i	−0.836703	−	1.44921i
$890$	3.33558e8	+	6.93377e7i	0.473153	+	0.0983557i
$891$	−3.73919e8	+	4.66212e8i	−0.528621	+	0.659099i
$892$	−1.03370e7	−	4.49165e6i	−0.0145646	−	0.00632865i
$893$	−2.88094e8	−	4.98993e8i	−0.404557	−	0.700713i
$894$	−1.05290e9	+	3.03392e8i	−1.47358	+	0.424612i
$895$	3.87017e8	−	6.70333e8i	0.539834	−	0.935021i
$896$	2.51492e8	−	6.16228e8i	0.349623	−	0.856678i
$897$	−1.78273e8	+	2.83282e8i	−0.247006	+	0.392501i
$898$	−7.09979e7	−	2.15220e8i	−0.0980430	−	0.297203i
$899$	−8.03141e8			−1.10538
$900$	−3.56066e8	+	2.23780e8i	−0.488430	+	0.306969i
$901$			2.01967e8i			0.276125i
$902$	1.92929e8	+	5.84835e8i	0.262892	+	0.796918i
$903$	−4.61261e7	+	1.21022e9i	−0.0626446	+	1.64362i
$904$	9.47856e8	−	4.37388e8i	1.28303	−	0.592055i
$905$	−6.88770e8	−	3.97661e8i	−0.929241	−	0.536497i
$906$	2.54262e8	−	1.02545e9i	0.341898	−	1.37889i
$907$	−8.12927e8	+	4.69343e8i	−1.08951	+	0.629026i	−0.933445	−	0.358721i	$-0.883213\pi$
$907$	−8.12927e8	+	4.69343e8i	−1.08951	+	0.629026i	−0.156061	+	0.987747i	$0.549880\pi$
$908$	−5.22541e8	−	2.27056e8i	−0.698012	−	0.303302i
$909$	−7.19247e6	−	549064.i	−0.00957605	−	0.000731023i
$910$	3.24541e8	+	6.74632e7i	0.430670	+	0.0895247i
$911$	1.09953e9	−	6.34814e8i	1.45429	−	0.839636i	0.455572	−	0.890199i	$-0.349435\pi$
$911$	1.09953e9	−	6.34814e8i	1.45429	−	0.839636i	0.998721	+	0.0505625i	$0.0161014\pi$
$912$	1.18044e8	+	6.16162e8i	0.155617	+	0.812289i
$913$	−1.90003e8	+	3.29095e8i	−0.249660	+	0.432424i
$914$	−2.63654e8	−	2.35262e8i	−0.345299	−	0.308115i
$915$	−1.32696e8	+	7.00141e7i	−0.173219	+	0.0913949i
$916$	8.21256e8	−	9.37733e7i	1.06854	−	0.122009i
$917$	2.19412e8			0.284546
$918$	−1.11654e8	−	5.38737e8i	−0.144326	−	0.696384i
$919$	−2.71708e8			−0.350070			−0.175035	−	0.984562i	$-0.556004\pi$
$919$	−2.71708e8			−0.350070			−0.175035	+	0.984562i	$0.556004\pi$
$920$	2.92920e7	−	3.20068e8i	0.0376171	−	0.411034i
$921$	−1.10626e9	+	5.83690e8i	−1.41604	+	0.747142i
$922$	2.65289e8	+	2.36721e8i	0.338475	+	0.302026i
$923$	4.16934e8	−	7.22150e8i	0.530227	−	0.918380i
$924$	5.09285e8	−	3.47818e8i	0.645572	−	0.440896i
$925$	−1.09771e8	+	6.33761e7i	−0.138695	+	0.0800756i
$926$	−1.27817e8	+	6.14878e8i	−0.160973	+	0.774383i
$927$	−3.27244e8	−	6.81954e8i	−0.410802	−	0.856083i
$928$	−4.19724e8	+	2.55045e8i	−0.525195	+	0.319134i
$929$	−1.82885e8	+	1.05589e8i	−0.228103	+	0.131695i	−0.609697	−	0.792635i	$-0.708709\pi$
$929$	−1.82885e8	+	1.05589e8i	−0.228103	+	0.131695i	0.381594	+	0.924330i	$0.375375\pi$
$930$	2.26487e8	−	9.13432e8i	0.281575	−	1.13561i
$931$	−8.31529e7	−	4.80084e7i	−0.103045	−	0.0594933i
$932$	6.00375e8	+	8.10947e8i	0.741609	+	1.00172i
$933$	−2.24574e7	+	5.89217e8i	−0.0276512	+	0.725488i
$934$	−1.42900e9	+	4.71408e8i	−1.75385	+	0.578570i
$935$			3.19485e8i			0.390854i
$936$	−9.98904e7	+	5.90935e8i	−0.121814	+	0.720630i
$937$	7.21009e7			0.0876440			0.0438220	−	0.999039i	$-0.486047\pi$
$937$	7.21009e7			0.0876440			0.0438220	+	0.999039i	$0.486047\pi$
$938$	−2.68650e8	−	8.14374e8i	−0.325521	−	0.986768i
$939$	−5.33680e8	+	8.48037e8i	−0.644591	+	1.02428i
$940$	3.14497e8	+	4.24801e8i	0.378645	+	0.511449i
$941$	−4.42845e7	+	7.67031e7i	−0.0531476	+	0.0920543i	−0.891375	−	0.453266i	$-0.850259\pi$
$941$	−4.42845e7	+	7.67031e7i	−0.0531476	+	0.0920543i	0.838228	+	0.545320i	$0.183592\pi$
$942$	1.47706e8	+	5.12604e8i	0.176704	+	0.613238i
$943$	2.64244e8	+	4.57684e8i	0.315116	+	0.545797i
$944$	8.18255e8	+	8.76613e8i	0.972686	+	1.04206i
$945$	5.04608e8	+	5.79222e7i	0.597941	+	0.0686356i
$946$	1.24490e9	+	2.58782e8i	1.47049	+	0.305676i
$947$	8.98301e7	+	1.55590e8i	0.105772	+	0.183203i	0.914053	−	0.405594i	$-0.132935\pi$
$947$	8.98301e7	+	1.55590e8i	0.105772	+	0.183203i	−0.808281	+	0.588797i	$0.799602\pi$
$948$	−7.82128e7	−	1.03266e9i	−0.0918021	−	1.21208i
$949$	4.15060e8	+	2.39635e8i	0.485637	+	0.280383i
$950$	−2.72354e8	+	3.05222e8i	−0.317660	+	0.355996i
$951$	7.57417e8	−	1.20356e9i	0.880630	−	1.39935i
$952$	−5.17438e7	+	5.65394e8i	−0.0599718	+	0.655300i
$953$		−	3.97781e8i		−	0.459585i	−0.973240	−	0.229792i	$-0.926195\pi$
$953$		−	3.97781e8i		−	0.459585i	0.973240	−	0.229792i	$-0.0738047\pi$
$954$	9.35329e7	−	3.23873e8i	0.107726	−	0.373018i
$955$		−	2.81166e8i		−	0.322814i
$956$	−1.21954e9	+	1.39250e8i	−1.39580	+	0.159376i
$957$	−4.54762e8	−	1.73328e7i	−0.518858	−	0.0197757i
$958$	−3.68287e8	+	4.12732e8i	−0.418880	+	0.469431i
$959$	−3.03620e7	−	1.75295e7i	−0.0344251	−	0.0198753i
$960$	−1.71706e8	−	5.49286e8i	−0.194077	−	0.620847i
$961$	−9.91891e8	−	1.71801e9i	−1.11762	−	1.93577i
$962$	−3.67629e7	+	1.76853e8i	−0.0412938	+	0.198649i
$963$	1.88102e8	−	2.75071e8i	0.210627	−	0.308011i
$964$	9.66347e8	+	4.19899e8i	1.07870	+	0.468721i
$965$	1.70065e7	+	2.94561e7i	0.0189249	+	0.0327789i
$966$	3.67154e8	−	3.81187e8i	0.407303	−	0.422870i
$967$	−4.30902e8	+	7.46345e8i	−0.476540	+	0.825392i	−0.999639	−	0.0268805i	$-0.991443\pi$
$967$	−4.30902e8	+	7.46345e8i	−0.476540	+	0.825392i	0.523099	+	0.852272i	$0.324776\pi$
$968$	1.08748e8	+	2.35667e8i	0.119894	+	0.259820i
$969$	−2.49738e8	−	4.73324e8i	−0.274481	−	0.520220i
$970$	−2.83198e8	+	9.34229e7i	−0.310295	+	0.102362i
$971$	5.39697e8			0.589511			0.294756	−	0.955573i	$-0.404762\pi$
$971$	5.39697e8			0.589511			0.294756	+	0.955573i	$0.404762\pi$
$972$	−7.04466e7	+	9.15624e8i	−0.0767116	+	0.997053i
$973$		−	1.38787e9i		−	1.50664i
$974$	−3.41917e8	+	1.12793e8i	−0.370036	+	0.122069i
$975$	−3.45621e8	+	1.82359e8i	−0.372895	+	0.196749i
$976$	6.31032e7	+	2.72723e8i	0.0678738	+	0.293341i
$977$	−1.15258e9	−	6.65441e8i	−1.23591	−	0.713552i	−0.267653	−	0.963515i	$-0.586248\pi$
$977$	−1.15258e9	−	6.65441e8i	−1.23591	−	0.713552i	−0.968255	+	0.249963i	$0.919581\pi$
$978$	1.87316e8	−	1.94475e8i	0.200244	−	0.207897i
$979$	5.10082e8	−	2.94496e8i	0.543616	−	0.313857i
$980$	8.07816e7	+	3.51014e7i	0.0858291	+	0.0372946i
$981$	−3.68775e8	−	2.52179e8i	−0.390620	−	0.267117i
$982$	−1.76593e8	+	8.49523e8i	−0.186483	+	0.897100i
$983$	−3.62807e8	+	2.09467e8i	−0.381958	+	0.220524i	−0.678670	−	0.734443i	$-0.737443\pi$
$983$	−3.62807e8	+	2.09467e8i	−0.381958	+	0.220524i	0.296712	+	0.954967i	$0.404110\pi$
$984$	7.51633e8	+	5.74911e8i	0.788897	+	0.603414i
$985$	−4.58890e8	+	7.94821e8i	−0.480176	+	0.831689i
$986$	2.78939e8	−	3.12601e8i	0.290990	−	0.326107i
$987$	−3.31484e7	+	8.69718e8i	−0.0344755	+	0.904539i
$988$	6.61342e7	+	5.79196e8i	0.0685733	+	0.600558i
$989$	1.09117e9			1.12799
$990$	1.47956e8	−	5.12324e8i	0.152485	−	0.528006i
$991$	7.37758e8			0.758041			0.379021	−	0.925388i	$-0.376261\pi$
$991$	7.37758e8			0.758041			0.379021	+	0.925388i	$0.376261\pi$
$992$	−1.53992e9	−	8.43607e8i	−1.57748	−	0.864182i
$993$	−7.77131e8	−	4.89058e8i	−0.793682	−	0.499474i
$994$	−8.77868e8	+	9.83810e8i	−0.893861	+	1.00173i
$995$	−2.07907e8	+	3.60106e8i	−0.211057	+	0.365562i
$996$	4.40993e7	+	5.82252e8i	0.0446327	+	0.589295i
$997$	−9.53754e8	+	5.50650e8i	−0.962390	+	0.555636i	−0.896908	−	0.442218i	$-0.854192\pi$
$997$	−9.53754e8	+	5.50650e8i	−0.962390	+	0.555636i	−0.0654820	+	0.997854i	$0.520858\pi$
$998$	−6.62846e8	−	1.37788e8i	−0.666839	−	0.138618i
$999$	−3.15637e7	+	2.74977e8i	−0.0316586	+	0.275804i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.7.j.a.5.7	✓	140
8.5	even	2	inner	72.7.j.a.5.18	yes	140
9.2	odd	6	inner	72.7.j.a.29.18	yes	140
72.29	odd	6	inner	72.7.j.a.29.7	yes	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.7.j.a.5.7	✓	140	1.1	even	1	trivial
72.7.j.a.5.18	yes	140	8.5	even	2	inner
72.7.j.a.29.7	yes	140	72.29	odd	6	inner
72.7.j.a.29.18	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)

\(f(q)\)	\(=\)	\(q+(-7.59729 + 2.50624i) q^{2} +(-12.5996 - 23.8799i) q^{3} +(51.4376 - 38.0812i) q^{4} +(-40.6546 + 70.4159i) q^{5} +(155.572 + 149.845i) q^{6} +(-158.685 - 274.850i) q^{7} +(-295.345 + 418.229i) q^{8} +(-411.498 + 601.756i) q^{9} +O(q^{10})\)	\(q+(-7.59729 + 2.50624i) q^{2} +(-12.5996 - 23.8799i) q^{3} +(51.4376 - 38.0812i) q^{4} +(-40.6546 + 70.4159i) q^{5} +(155.572 + 149.845i) q^{6} +(-158.685 - 274.850i) q^{7} +(-295.345 + 418.229i) q^{8} +(-411.498 + 601.756i) q^{9} +(132.386 - 636.860i) q^{10} +(-562.279 - 973.896i) q^{11} +(-1557.47 - 748.513i) q^{12} +(-1390.56 - 802.842i) q^{13} +(1894.41 + 1690.41i) q^{14} +(2193.76 + 83.6127i) q^{15} +(1195.64 - 3917.61i) q^{16} +3494.04i q^{17} +(1618.12 - 5603.03i) q^{18} -5672.81i q^{19} +(590.348 + 5170.20i) q^{20} +(-4564.01 + 7252.38i) q^{21} +(6712.61 + 5989.76i) q^{22} +(6686.11 + 3860.23i) q^{23} +(13708.5 + 1783.28i) q^{24} +(4506.90 + 7806.18i) q^{25} +(12576.6 + 2614.34i) q^{26} +(19554.6 + 2244.61i) q^{27} +(-18629.0 - 8094.70i) q^{28} +(7494.17 + 12980.3i) q^{29} +(-16876.2 + 4862.85i) q^{30} +(-26792.2 + 46405.4i) q^{31} +(734.809 + 32759.8i) q^{32} +(-16172.0 + 25697.9i) q^{33} +(-8756.89 - 26545.2i) q^{34} +25805.1 q^{35} +(1749.16 + 46623.2i) q^{36} +14062.0i q^{37} +(14217.4 + 43098.0i) q^{38} +(-1651.17 + 43322.0i) q^{39} +(-17442.8 - 37799.9i) q^{40} +(59282.1 + 34226.5i) q^{41} +(16497.9 - 66536.9i) q^{42} +(122400. - 70667.6i) q^{43} +(-66009.4 - 28682.6i) q^{44} +(-25643.9 - 53440.2i) q^{45} +(-60470.9 - 12570.3i) q^{46} +(87962.2 - 50785.0i) q^{47} +(-108617. + 20808.7i) q^{48} +(8462.89 - 14658.2i) q^{49} +(-53804.3 - 48010.4i) q^{50} +(83437.2 - 44023.6i) q^{51} +(-102100. + 11658.1i) q^{52} +57803.3 q^{53} +(-154187. + 31955.5i) q^{54} +91437.0 q^{55} +(161817. + 14809.2i) q^{56} +(-135466. + 71475.4i) q^{57} +(-89467.1 - 79832.8i) q^{58} +(-146382. + 253541. i) q^{59} +(116026. - 79240.1i) q^{60} +(-59185.8 + 34170.9i) q^{61} +(87245.0 - 419703. i) q^{62} +(230691. + 17610.7i) q^{63} +(-87686.3 - 247044. i) q^{64} +(113066. - 65278.5i) q^{65} +(58458.3 - 235765. i) q^{66} +(-292503. - 168877. i) q^{67} +(133057. + 179725. i) q^{68} +(7939.16 - 208301. i) q^{69} +(-196048. + 64673.6i) q^{70} +519322. i q^{71} +(-130138. - 349826. i) q^{72} -298483. q^{73} +(-35242.7 - 106833. i) q^{74} +(129625. - 205979. i) q^{75} +(-216028. - 291796. i) q^{76} +(-178450. + 309085. i) q^{77} +(-96030.8 - 333268. i) q^{78} +(299658. + 519022. i) q^{79} +(227253. + 243461. i) q^{80} +(-192780. - 495243. i) q^{81} +(-536163. - 111454. i) q^{82} +(-168958. - 292644. i) q^{83} +(41417.8 + 546848. i) q^{84} +(-246036. - 142049. i) q^{85} +(-752797. + 843645. i) q^{86} +(215544. - 342507. i) q^{87} +(573378. + 52474.4i) q^{88} +523754. i q^{89} +(328758. + 341731. i) q^{90} +509595. i q^{91} +(490919. - 56054.5i) q^{92} +(1.44573e6 + 55102.4i) q^{93} +(-540995. + 606282. i) q^{94} +(399456. + 230626. i) q^{95} +(773041. - 430309. i) q^{96} +(-229224. - 397028. i) q^{97} +(-27558.2 + 132572. i) q^{98} +(817425. + 62401.2i) 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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