LMFDB - Embedded newform 62.7.f.a.15.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [62,7,Mod(15,62)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(62, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([7])) N = Newforms(chi, 7, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("62.15"); S:= CuspForms(chi, 7); N := Newforms(S);

Level:	$ N $	$=$	$ 62 = 2 \cdot 31 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	62.f (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$14.2633531844$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			15.10
Character	$\chi$	$=$	62.15
Dual form			62.7.f.a.29.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(4.57649 - 3.32502i) q^{2} +(-22.4820 + 30.9438i) q^{3} +(9.88854 - 30.4338i) q^{4} -120.991 q^{5} +216.367i q^{6} +(61.2460 - 188.496i) q^{7} +(-55.9381 - 172.160i) q^{8} +(-226.806 - 698.038i) q^{9} +(-553.716 + 402.298i) q^{10} +(1158.64 + 376.466i) q^{11} +(719.424 + 990.202i) q^{12} +(1458.90 - 2008.01i) q^{13} +(-346.459 - 1066.29i) q^{14} +(2720.13 - 3743.94i) q^{15} +(-828.433 - 601.892i) q^{16} +(1003.09 - 325.922i) q^{17} +(-3358.96 - 2440.43i) q^{18} +(5991.79 - 4353.29i) q^{19} +(-1196.43 + 3682.23i) q^{20} +(4455.84 + 6132.94i) q^{21} +(6554.27 - 2129.61i) q^{22} +(12414.8 - 4033.81i) q^{23} +(6584.88 + 2139.56i) q^{24} -986.079 q^{25} -14040.5i q^{26} +(180.456 + 58.6337i) q^{27} +(-5131.01 - 3727.90i) q^{28} +(-11108.5 - 15289.5i) q^{29} -26178.6i q^{30} +(-22672.6 - 19325.0i) q^{31} -5792.62 q^{32} +(-37697.9 + 27389.1i) q^{33} +(3506.91 - 4826.85i) q^{34} +(-7410.23 + 22806.4i) q^{35} -23486.7 q^{36} -10441.1i q^{37} +(12946.6 - 39845.6i) q^{38} +(29336.3 + 90288.0i) q^{39} +(6768.02 + 20829.8i) q^{40} +(27622.5 - 20068.9i) q^{41} +(40784.3 + 13251.6i) q^{42} +(-73377.9 - 100996. i) q^{43} +(22914.6 - 31539.2i) q^{44} +(27441.6 + 84456.6i) q^{45} +(43403.7 - 59740.1i) q^{46} +(147331. + 107042. i) q^{47} +(37249.7 - 12103.2i) q^{48} +(63400.5 + 46063.2i) q^{49} +(-4512.78 + 3278.73i) q^{50} +(-12466.1 + 38366.7i) q^{51} +(-46684.8 - 64256.2i) q^{52} +(16360.2 - 5315.74i) q^{53} +(1020.81 - 331.682i) q^{54} +(-140186. - 45549.1i) q^{55} -35877.3 q^{56} +283280. i q^{57} +(-101676. - 33036.4i) q^{58} +(7445.84 + 5409.72i) q^{59} +(-87044.1 - 119806. i) q^{60} +86281.9i q^{61} +(-168017. - 13054.1i) q^{62} -145468. q^{63} +(-26509.9 + 19260.5i) q^{64} +(-176515. + 242951. i) q^{65} +(-81454.8 + 250692. i) q^{66} -163227. q^{67} -33750.6i q^{68} +(-154288. + 474849. i) q^{69} +(41918.6 + 129012. i) q^{70} +(-156621. - 482029. i) q^{71} +(-107487. + 78093.8i) q^{72} +(142451. + 46285.3i) q^{73} +(-34716.9 - 47783.7i) q^{74} +(22169.0 - 30513.1i) q^{75} +(-73237.2 - 225401. i) q^{76} +(141924. - 195342. i) q^{77} +(434466. + 315658. i) q^{78} +(278645. - 90537.3i) q^{79} +(100233. + 72823.8i) q^{80} +(426999. - 310233. i) q^{81} +(59684.7 - 183691. i) q^{82} +(-376456. - 518147. i) q^{83} +(230711. - 74962.4i) q^{84} +(-121365. + 39433.8i) q^{85} +(-671627. - 218225. i) q^{86} +722856. q^{87} -220530. i q^{88} +(626258. + 203484. i) q^{89} +(406406. + 295271. i) q^{90} +(-289148. - 397979. i) q^{91} -417718. i q^{92} +(1.10772e6 - 267112. i) q^{93} +1.03018e6 q^{94} +(-724956. + 526711. i) q^{95} +(130230. - 179246. i) q^{96} +(-230565. + 709605. i) q^{97} +443312. q^{98} -894161. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 512 q^{4} - 288 q^{5} - 692 q^{7} + 3248 q^{9} + 1344 q^{10} + 3200 q^{11} - 3600 q^{13} + 4560 q^{14} + 9520 q^{15} - 16384 q^{16} - 1400 q^{17} - 11200 q^{18} + 2912 q^{19} - 9216 q^{20} + 4860 q^{21}+ \cdots + 13577088 q^{98}+O(q^{100}) $ 64 * q - 512 * q^4 - 288 * q^5 - 692 * q^7 + 3248 * q^9 + 1344 * q^10 + 3200 * q^11 - 3600 * q^13 + 4560 * q^14 + 9520 * q^15 - 16384 * q^16 - 1400 * q^17 - 11200 * q^18 + 2912 * q^19 - 9216 * q^20 + 4860 * q^21 + 6720 * q^22 - 26240 * q^23 + 241592 * q^25 - 206100 * q^27 + 16896 * q^28 - 48160 * q^29 + 142924 * q^31 + 291360 * q^33 + 123840 * q^34 + 16728 * q^35 - 518144 * q^36 - 89856 * q^38 - 169400 * q^39 - 64512 * q^40 - 291056 * q^41 + 220320 * q^42 + 145600 * q^43 - 44412 * q^45 - 213120 * q^46 + 596760 * q^47 - 163840 * q^48 + 481596 * q^49 - 295744 * q^50 + 1117652 * q^51 + 115200 * q^52 - 1276880 * q^53 + 290880 * q^55 - 97280 * q^56 - 367200 * q^58 + 469780 * q^59 - 304640 * q^60 - 963152 * q^62 - 1359328 * q^63 - 524288 * q^64 + 934760 * q^65 - 789792 * q^66 + 1470992 * q^67 - 933024 * q^69 + 515232 * q^70 - 906672 * q^71 - 358400 * q^72 + 1236840 * q^73 - 126400 * q^74 - 2881620 * q^75 - 139776 * q^76 + 3063520 * q^77 + 2374288 * q^78 + 4375280 * q^79 + 442368 * q^80 - 3676208 * q^81 + 1386144 * q^82 + 4922820 * q^83 - 601600 * q^84 - 1012320 * q^85 - 2054800 * q^86 - 5911600 * q^87 - 1219900 * q^89 - 2696992 * q^90 + 163640 * q^91 - 248320 * q^93 + 290592 * q^94 + 2034328 * q^95 - 1078884 * q^97 + 13577088 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/62\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{7}{10}\right)$

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 $

$2$	4.57649	−	3.32502i	0.572061	−	0.415627i
$2$	4.57649	−	3.32502i	0.572061	−	0.415627i
$3$	−22.4820	+	30.9438i	−0.832667	+	1.14607i	0.154754	+	0.987953i	$0.450542\pi$
$3$	−22.4820	+	30.9438i	−0.832667	+	1.14607i	−0.987421	+	0.158115i	$0.949458\pi$
$4$	9.88854	−	30.4338i	0.154508	−	0.475528i
$5$	−120.991			−0.967931			−0.483966	−	0.875087i	$-0.660804\pi$
$5$	−120.991			−0.967931			−0.483966	+	0.875087i	$0.660804\pi$
$6$			216.367i			1.00170i
$7$	61.2460	−	188.496i	0.178560	−	0.549550i	−0.821219	−	0.570614i	$-0.806705\pi$
$7$	61.2460	−	188.496i	0.178560	−	0.549550i	0.999778	+	0.0210638i	$0.00670532\pi$
$8$	−55.9381	−	172.160i	−0.109254	−	0.336249i
$9$	−226.806	−	698.038i	−0.311120	−	0.957528i
$10$	−553.716	+	402.298i	−0.553716	+	0.402298i
$11$	1158.64	+	376.466i	0.870505	+	0.282844i	0.710009	−	0.704192i	$-0.248691\pi$
$11$	1158.64	+	376.466i	0.870505	+	0.282844i	0.160496	+	0.987037i	$0.448691\pi$
$12$	719.424	+	990.202i	0.416333	+	0.573034i
$13$	1458.90	−	2008.01i	0.664042	−	0.913976i	−0.335564	−	0.942017i	$-0.608927\pi$
$13$	1458.90	−	2008.01i	0.664042	−	0.913976i	0.999607	+	0.0280413i	$0.00892700\pi$
$14$	−346.459	−	1066.29i	−0.126261	−	0.388591i
$15$	2720.13	−	3743.94i	0.805964	−	1.10931i
$16$	−828.433	−	601.892i	−0.202254	−	0.146946i
$17$	1003.09	−	325.922i	0.204170	−	0.0663387i	−0.205147	−	0.978731i	$-0.565767\pi$
$17$	1003.09	−	325.922i	0.204170	−	0.0663387i	0.409316	+	0.912392i	$0.365767\pi$
$18$	−3358.96	−	2440.43i	−0.575954	−	0.418455i
$19$	5991.79	−	4353.29i	0.873567	−	0.634683i	−0.0579748	−	0.998318i	$-0.518464\pi$
$19$	5991.79	−	4353.29i	0.873567	−	0.634683i	0.931542	+	0.363635i	$0.118464\pi$
$20$	−1196.43	+	3682.23i	−0.149554	+	0.460279i
$21$	4455.84	+	6132.94i	0.481141	+	0.662233i
$22$	6554.27	−	2129.61i	0.615540	−	0.200001i
$23$	12414.8	−	4033.81i	1.02037	−	0.331537i	0.249391	−	0.968403i	$-0.419770\pi$
$23$	12414.8	−	4033.81i	1.02037	−	0.331537i	0.770975	+	0.636866i	$0.219770\pi$
$24$	6584.88	+	2139.56i	0.476337	+	0.154771i
$25$	−986.079			−0.0631091
$26$		−	14040.5i		−	0.798844i
$27$	180.456	+	58.6337i	0.00916811	+	0.00297890i
$28$	−5131.01	−	3727.90i	−0.233738	−	0.169820i
$29$	−11108.5	−	15289.5i	−0.455470	−	0.626901i	0.518091	−	0.855325i	$-0.326643\pi$
$29$	−11108.5	−	15289.5i	−0.455470	−	0.626901i	−0.973562	+	0.228424i	$0.926643\pi$
$30$		−	26178.6i		−	0.969577i
$31$	−22672.6	−	19325.0i	−0.761055	−	0.648687i
$31$	−22672.6	−	19325.0i	−0.761055	−	0.648687i
$32$	−5792.62			−0.176777
$33$	−37697.9	+	27389.1i	−1.04900	+	0.762143i
$34$	3506.91	−	4826.85i	0.0892254	−	0.122808i
$35$	−7410.23	+	22806.4i	−0.172833	+	0.531927i
$36$	−23486.7			−0.503402
$37$		−	10441.1i		−	0.206130i	−0.994675	−	0.103065i	$-0.967135\pi$
$37$		−	10441.1i		−	0.206130i	0.994675	−	0.103065i	$-0.0328650\pi$
$38$	12946.6	−	39845.6i	0.235942	−	0.726156i
$39$	29336.3	+	90288.0i	0.494552	+	1.52207i
$40$	6768.02	+	20829.8i	0.105750	+	0.325466i
$41$	27622.5	−	20068.9i	0.400785	−	0.291188i	−0.369075	−	0.929399i	$-0.620326\pi$
$41$	27622.5	−	20068.9i	0.400785	−	0.291188i	0.769861	+	0.638212i	$0.220326\pi$
$42$	40784.3	+	13251.6i	0.550484	+	0.178863i
$43$	−73377.9	−	100996.i	−0.922911	−	1.27028i	−0.962561	−	0.271065i	$-0.912624\pi$
$43$	−73377.9	−	100996.i	−0.922911	−	1.27028i	0.0396497	−	0.999214i	$-0.487376\pi$
$44$	22914.6	−	31539.2i	0.269001	−	0.370248i
$45$	27441.6	+	84456.6i	0.301143	+	0.926822i
$46$	43403.7	−	59740.1i	0.445916	−	0.613751i
$47$	147331.	+	107042.i	1.41906	+	1.03101i	0.991926	+	0.126822i	$0.0404777\pi$
$47$	147331.	+	107042.i	1.41906	+	1.03101i	0.427137	+	0.904187i	$0.359522\pi$
$48$	37249.7	−	12103.2i	0.336821	−	0.109440i
$49$	63400.5	+	46063.2i	0.538895	+	0.391530i
$50$	−4512.78	+	3278.73i	−0.0361023	+	0.0262298i
$51$	−12466.1	+	38366.7i	−0.0939766	+	0.289230i
$52$	−46684.8	−	64256.2i	−0.332021	−	0.456988i
$53$	16360.2	−	5315.74i	0.109891	−	0.0357056i	−0.253556	−	0.967321i	$-0.581600\pi$
$53$	16360.2	−	5315.74i	0.109891	−	0.0357056i	0.363446	+	0.931615i	$0.381600\pi$
$54$	1020.81	−	331.682i	0.00648283	−	0.00210640i
$55$	−140186.	−	45549.1i	−0.842589	−	0.273774i
$56$	−35877.3			−0.204294
$57$			283280.i			1.52965i
$58$	−101676.	−	33036.4i	−0.521114	−	0.169320i
$59$	7445.84	+	5409.72i	0.0362542	+	0.0263402i	0.605765	−	0.795644i	$-0.292867\pi$
$59$	7445.84	+	5409.72i	0.0362542	+	0.0263402i	−0.569511	+	0.821984i	$0.692867\pi$
$60$	−87044.1	−	119806.i	−0.402982	−	0.554657i
$61$			86281.9i			0.380128i	0.981772	+	0.190064i	$0.0608696\pi$
$61$			86281.9i			0.380128i	−0.981772	+	0.190064i	$0.939130\pi$
$62$	−168017.	−	13054.1i	−0.704982	−	0.0547736i
$63$	−145468.			−0.581763
$64$	−26509.9	+	19260.5i	−0.101127	+	0.0734732i
$65$	−176515.	+	242951.i	−0.642747	+	0.884666i
$66$	−81454.8	+	250692.i	−0.283325	+	0.871985i
$67$	−163227.			−0.542708			−0.271354	−	0.962480i	$-0.587471\pi$
$67$	−163227.			−0.542708			−0.271354	+	0.962480i	$0.587471\pi$
$68$		−	33750.6i		−	0.107338i
$69$	−154288.	+	474849.i	−0.469661	+	1.44547i
$70$	41918.6	+	129012.i	0.122212	+	0.376129i
$71$	−156621.	−	482029.i	−0.437597	−	1.34678i	−0.890402	−	0.455175i	$-0.849577\pi$
$71$	−156621.	−	482029.i	−0.437597	−	1.34678i	0.452805	−	0.891609i	$-0.350423\pi$
$72$	−107487.	+	78093.8i	−0.287977	+	0.209228i
$73$	142451.	+	46285.3i	0.366183	+	0.118980i	0.486328	−	0.873776i	$-0.338336\pi$
$73$	142451.	+	46285.3i	0.366183	+	0.118980i	−0.120145	+	0.992756i	$0.538336\pi$
$74$	−34716.9	−	47783.7i	−0.0856734	−	0.117919i
$75$	22169.0	−	30513.1i	0.0525488	−	0.0723272i
$76$	−73237.2	−	225401.i	−0.166836	−	0.513470i
$77$	141924.	−	195342.i	0.310874	−	0.427881i
$78$	434466.	+	315658.i	0.915530	+	0.665171i
$79$	278645.	−	90537.3i	0.565158	−	0.183631i	−0.0124826	−	0.999922i	$-0.503973\pi$
$79$	278645.	−	90537.3i	0.565158	−	0.183631i	0.577641	+	0.816291i	$0.303973\pi$
$80$	100233.	+	72823.8i	0.195768	+	0.142234i
$81$	426999.	−	310233.i	0.803474	−	0.583758i
$82$	59684.7	−	183691.i	0.108248	−	0.333154i
$83$	−376456.	−	518147.i	−0.658385	−	0.906189i	0.341042	−	0.940048i	$-0.389220\pi$
$83$	−376456.	−	518147.i	−0.658385	−	0.906189i	−0.999427	+	0.0338592i	$0.989220\pi$
$84$	230711.	−	74962.4i	0.389251	−	0.126475i
$85$	−121365.	+	39433.8i	−0.197622	+	0.0642113i
$86$	−671627.	−	218225.i	−1.05592	−	0.343090i
$87$	722856.			1.09773
$88$		−	220530.i		−	0.323609i
$89$	626258.	+	203484.i	0.888348	+	0.288642i	0.717419	−	0.696642i	$-0.245323\pi$
$89$	626258.	+	203484.i	0.888348	+	0.288642i	0.170929	+	0.985283i	$0.445323\pi$
$90$	406406.	+	295271.i	0.557484	+	0.405036i
$91$	−289148.	−	397979.i	−0.383704	−	0.528124i
$92$		−	417718.i		−	0.536438i
$93$	1.10772e6	−	267112.i	1.37714	−	0.332081i
$94$	1.03018e6			1.24031
$95$	−724956.	+	526711.i	−0.845553	+	0.614330i
$96$	130230.	−	179246.i	0.147196	−	0.202598i
$97$	−230565.	+	709605.i	−0.252626	+	0.777502i	0.741662	+	0.670773i	$0.234038\pi$
$97$	−230565.	+	709605.i	−0.252626	+	0.777502i	−0.994288	+	0.106729i	$0.965962\pi$
$98$	443312.			0.471012
$99$		−	894161.i		−	0.921532i
$100$	−9750.89	+	30010.1i	−0.00975089	+	0.0300101i
$101$	−36610.7	−	112676.i	−0.0355340	−	0.109362i	0.931716	−	0.363187i	$-0.118311\pi$
$101$	−36610.7	−	112676.i	−0.0355340	−	0.109362i	−0.967250	+	0.253825i	$0.918311\pi$
$102$	70518.8	+	217035.i	0.0664515	+	0.204517i
$103$	−414828.	+	301390.i	−0.379627	+	0.275815i	−0.761192	−	0.648527i	$-0.775385\pi$
$103$	−414828.	+	301390.i	−0.379627	+	0.275815i	0.381565	+	0.924342i	$0.375385\pi$
$104$	−427306.	−	138840.i	−0.379873	−	0.123428i
$105$	−539119.	−	742034.i	−0.465711	−	0.640997i
$106$	57197.3	−	78725.3i	0.0480239	−	0.0660993i
$107$	−517550.	−	1.59285e6i	−0.422475	−	1.30024i	−0.905392	−	0.424578i	$-0.860423\pi$
$107$	−517550.	−	1.59285e6i	−0.422475	−	1.30024i	0.482917	−	0.875666i	$-0.339577\pi$
$108$	3568.89	−	4912.16i	0.00283310	−	0.00389943i
$109$	570963.	+	414829.i	0.440888	+	0.320324i	0.785988	−	0.618242i	$-0.212155\pi$
$109$	570963.	+	414829.i	0.440888	+	0.320324i	−0.345100	+	0.938566i	$0.612155\pi$
$110$	−793010.	+	257665.i	−0.595800	+	0.193587i
$111$	323088.	+	234737.i	0.236239	+	0.171638i
$112$	−164192.	+	119293.i	−0.116869	+	0.0849102i
$113$	776200.	−	2.38890e6i	0.537946	−	1.65563i	−0.199251	−	0.979948i	$-0.563851\pi$
$113$	776200.	−	2.38890e6i	0.537946	−	1.65563i	0.737197	−	0.675678i	$-0.236149\pi$
$114$	941910.	+	1.29643e6i	0.635762	+	0.875052i
$115$	−1.50208e6	+	488056.i	−0.987644	+	0.320905i
$116$	−575164.	+	186882.i	−0.368483	+	0.119727i
$117$	−1.73255e6	−	562940.i	−1.08175	−	0.351483i
$118$	52063.2			0.0316873
$119$		−	209039.i		−	0.124047i
$120$	−796713.	−	258868.i	−0.461061	−	0.149808i
$121$	−232498.	−	168920.i	−0.131239	−	0.0953507i
$122$	286889.	+	394868.i	0.157991	+	0.217457i
$123$			1.30594e6i			0.701789i
$124$	−812333.	+	498917.i	−0.426058	+	0.261676i
$125$	2.00980e6			1.02902
$126$	−665734.	+	483684.i	−0.332804	+	0.241796i
$127$	628236.	−	864693.i	0.306699	−	0.422135i	−0.627649	−	0.778496i	$-0.715983\pi$
$127$	628236.	−	864693.i	0.306699	−	0.422135i	0.934348	+	0.356362i	$0.115983\pi$
$128$	−57280.6	+	176291.i	−0.0273135	+	0.0840623i
$129$	4.77489e6			2.22430
$130$			1.69878e6i			0.773226i
$131$	−1.04215e6	+	3.20741e6i	−0.463571	+	1.42672i	0.397200	+	0.917732i	$0.369982\pi$
$131$	−1.04215e6	+	3.20741e6i	−0.463571	+	1.42672i	−0.860771	+	0.508992i	$0.830018\pi$
$132$	460778.	+	1.41813e6i	0.200341	+	0.616586i
$133$	−453604.	−	1.39605e6i	−0.192807	−	0.593398i
$134$	−747005.	+	542731.i	−0.310462	+	0.225564i
$135$	−21833.6	−	7094.17i	−0.00887410	−	0.00288337i
$136$	−112221.	−	154459.i	−0.0446127	−	0.0614041i
$137$	−75874.5	+	104432.i	−0.0295076	+	0.0406137i	−0.823516	−	0.567293i	$-0.807991\pi$
$137$	−75874.5	+	104432.i	−0.0295076	+	0.0406137i	0.794008	+	0.607907i	$0.207991\pi$
$138$	872784.	+	2.68615e6i	0.332100	+	1.02210i
$139$	775427.	−	1.06728e6i	0.288733	−	0.397407i	−0.639869	−	0.768484i	$-0.721011\pi$
$139$	775427.	−	1.06728e6i	0.288733	−	0.397407i	0.928602	+	0.371077i	$0.121011\pi$
$140$	620808.	+	451043.i	0.226242	+	0.164374i
$141$	−6.62461e6	+	2.15246e6i	−2.36321	+	0.767854i
$142$	−2.31953e6	−	1.68523e6i	−0.810092	−	0.588566i
$143$	2.44629e6	−	1.77733e6i	0.836565	−	0.607800i
$144$	−232250.	+	714791.i	−0.0777800	+	0.239382i
$145$	1.34403e6	+	1.84990e6i	0.440864	+	0.606797i
$146$	805827.	−	261829.i	0.258930	−	0.0841316i
$147$	−2.85074e6	+	926262.i	−0.897440	+	0.291596i
$148$	−317763.	−	103248.i	−0.0980209	−	0.0318489i
$149$	−3.39363e6			−1.02590			−0.512951	−	0.858418i	$-0.671448\pi$
$149$	−3.39363e6			−1.02590			−0.512951	+	0.858418i	$0.671448\pi$
$150$		−	213355.i		−	0.0632163i
$151$	−4.22263e6	−	1.37202e6i	−1.22646	−	0.398500i	−0.377027	−	0.926202i	$-0.623054\pi$
$151$	−4.22263e6	−	1.37202e6i	−1.22646	−	0.398500i	−0.849429	+	0.527702i	$0.823054\pi$
$152$	−1.08463e6	−	788030.i	−0.308853	−	0.224394i
$153$	−455012.	−	626270.i	−0.127042	−	0.174859i
$154$		−	1.36588e6i		−	0.373982i
$155$	2.74319e6	+	2.33816e6i	0.736649	+	0.627884i
$156$	3.03790e6			0.800202
$157$	−739575.	+	537332.i	−0.191110	+	0.138849i	−0.679226	−	0.733929i	$-0.737684\pi$
$157$	−739575.	+	537332.i	−0.191110	+	0.138849i	0.488116	+	0.872779i	$0.337684\pi$
$158$	974179.	−	1.34084e6i	0.246983	−	0.339943i
$159$	−203320.	+	625755.i	−0.0505812	+	0.155673i
$160$	700857.			0.171108
$161$		−	2.58719e6i		−	0.619941i
$162$	922628.	−	2.83956e6i	0.217011	−	0.667891i
$163$	2.33199e6	+	7.17714e6i	0.538474	+	1.65725i	0.736021	+	0.676959i	$0.236703\pi$
$163$	2.33199e6	+	7.17714e6i	0.538474	+	1.65725i	−0.197547	+	0.980294i	$0.563297\pi$
$164$	−337628.	−	1.03911e6i	−0.0765432	−	0.235576i
$165$	4.56112e6	−	3.31385e6i	1.01536	−	0.737702i
$166$	−3.44569e6	−	1.11957e6i	−0.753273	−	0.244753i
$167$	4.73922e6	+	6.52297e6i	1.01755	+	1.40054i	0.913905	+	0.405928i	$0.133052\pi$
$167$	4.73922e6	+	6.52297e6i	1.01755	+	1.40054i	0.103648	+	0.994614i	$0.466948\pi$
$168$	806594.	−	1.11018e6i	0.170109	−	0.234135i
$169$	−412126.	−	1.26839e6i	−0.0853828	−	0.262781i
$170$	−424306.	+	584008.i	−0.0863640	+	0.118870i
$171$	−4.39774e6	−	3.19515e6i	−0.879511	−	0.639002i
$172$	−3.79929e6	+	1.23447e6i	−0.746651	+	0.242602i
$173$	4.11021e6	+	2.98624e6i	0.793827	+	0.576749i	0.909097	−	0.416585i	$-0.136773\pi$
$173$	4.11021e6	+	2.98624e6i	0.793827	+	0.576749i	−0.115270	+	0.993334i	$0.536773\pi$
$174$	3.30814e6	−	2.40351e6i	0.627967	−	0.456245i
$175$	−60393.3	+	185872.i	−0.0112687	+	0.0346816i
$176$	−733266.	−	1.00925e6i	−0.134500	−	0.185124i
$177$	−334795.	+	108781.i	−0.0603753	+	0.0196171i
$178$	3.54265e6	−	1.15108e6i	0.628157	−	0.204101i
$179$	−8.86264e6	−	2.87965e6i	−1.54527	−	0.502088i	−0.592444	−	0.805611i	$-0.701837\pi$
$179$	−8.86264e6	−	2.87965e6i	−1.54527	−	0.502088i	−0.952824	+	0.303523i	$0.901837\pi$
$180$	2.84169e6			0.487259
$181$			8.46313e6i			1.42723i	0.700536	+	0.713617i	$0.252944\pi$
$181$			8.46313e6i			1.42723i	−0.700536	+	0.713617i	$0.747056\pi$
$182$	−2.64657e6	−	859923.i	−0.439005	−	0.142641i
$183$	−2.66989e6	−	1.93979e6i	−0.435652	−	0.316520i
$184$	−1.38892e6	−	1.91168e6i	−0.222958	−	0.306875i
$185$			1.26329e6i			0.199520i
$186$	4.18130e6	−	4.90561e6i	0.649789	−	0.762349i
$187$	1.28492e6			0.196494
$188$	4.71460e6	−	3.42536e6i	0.709531	−	0.515504i
$189$	22104.4	−	30424.1i	0.00327411	−	0.00450642i
$190$	−1.56643e6	+	4.82098e6i	−0.228376	+	0.702869i
$191$	9.78402e6			1.40416			0.702081	−	0.712097i	$-0.252254\pi$
$191$	9.78402e6			1.40416			0.702081	+	0.712097i	$0.252254\pi$
$192$		−	1.25333e6i		−	0.177077i
$193$	2.39657e6	−	7.37588e6i	0.333363	−	1.02599i	−0.634159	−	0.773203i	$-0.718654\pi$
$193$	2.39657e6	−	7.37588e6i	0.333363	−	1.02599i	0.967523	−	0.252785i	$-0.0813464\pi$
$194$	1.30427e6	+	4.01413e6i	0.178633	+	0.549777i
$195$	−3.54944e6	−	1.09241e7i	−0.478692	−	1.47326i
$196$	2.02882e6	−	1.47402e6i	0.269448	−	0.195765i
$197$	8.53678e6	+	2.77377e6i	1.11659	+	0.362803i	0.808467	−	0.588542i	$-0.200298\pi$
$197$	8.53678e6	+	2.77377e6i	1.11659	+	0.362803i	0.308127	+	0.951345i	$0.400298\pi$
$198$	−2.97310e6	−	4.09212e6i	−0.383013	−	0.527173i
$199$	−307723.	+	423545.i	−0.0390482	+	0.0537452i	−0.828095	−	0.560588i	$-0.810575\pi$
$199$	−307723.	+	423545.i	−0.0390482	+	0.0537452i	0.789046	+	0.614334i	$0.210575\pi$
$200$	55159.3	+	169763.i	0.00689492	+	0.0212204i
$201$	3.66966e6	−	5.05085e6i	0.451895	−	0.621980i
$202$	−542199.	−	393930.i	−0.0657816	−	0.0477931i
$203$	−3.56235e6	+	1.15748e6i	−0.425842	+	0.138365i
$204$	1.04437e6	+	758781.i	0.123017	+	0.0893770i
$205$	−3.34209e6	+	2.42817e6i	−0.387933	+	0.281850i
$206$	−896330.	+	2.75862e6i	−0.102534	+	0.315566i
$207$	−5.63151e6	−	7.75110e6i	−0.634912	−	0.873881i
$208$	−2.41720e6	+	785397.i	−0.268611	+	0.0872769i
$209$	8.58121e6	−	2.78820e6i	0.939961	−	0.305412i
$210$	−4.93455e6	−	1.60333e6i	−0.532831	−	0.173127i
$211$	−1.58837e7			−1.69084			−0.845422	−	0.534098i	$-0.820651\pi$
$211$	−1.58837e7			−1.69084			−0.845422	+	0.534098i	$0.820651\pi$
$212$		−	550468.i		−	0.0577729i
$213$	1.84370e7	+	5.99053e6i	1.90788	+	0.619907i
$214$	−7.66483e6	−	5.56882e6i	−0.782098	−	0.568227i
$215$	8.87810e6	+	1.22197e7i	0.893315	+	1.22954i
$216$		−	34347.1i		−	0.00340823i
$217$	−5.03129e6	+	3.09011e6i	−0.492380	+	0.302409i
$218$	3.99232e6			0.385350
$219$	−4.63484e6	+	3.36741e6i	−0.441268	+	0.320600i
$220$	−2.77247e6	+	3.81597e6i	−0.260374	+	0.358374i
$221$	808949.	−	2.48969e6i	0.0749453	−	0.230658i
$222$	2.25912e6			0.206481
$223$		−	1.56446e7i		−	1.41075i	−0.708833	−	0.705376i	$-0.750778\pi$
$223$		−	1.56446e7i		−	1.41075i	0.708833	−	0.705376i	$-0.249222\pi$
$224$	−354774.	+	1.09188e6i	−0.0315652	+	0.0971476i
$225$	223649.	+	688321.i	0.0196345	+	0.0604287i
$226$	−4.39085e6	−	1.35137e7i	−0.380385	−	1.17070i
$227$	−75681.4	+	54985.8i	−0.00647011	+	0.00470081i	−0.591016	−	0.806660i	$-0.701273\pi$
$227$	−75681.4	+	54985.8i	−0.00647011	+	0.00470081i	0.584545	+	0.811361i	$0.301273\pi$
$228$	8.62128e6	+	2.80122e6i	0.727390	+	0.236343i
$229$	5.36313e6	+	7.38171e6i	0.446593	+	0.614682i	0.971661	−	0.236378i	$-0.0759603\pi$
$229$	5.36313e6	+	7.38171e6i	0.446593	+	0.614682i	−0.525068	+	0.851060i	$0.675960\pi$
$230$	−5.25147e6	+	7.22803e6i	−0.431616	+	0.594069i
$231$	2.85389e6	+	8.78336e6i	0.231527	+	0.712565i
$232$	−2.01085e6	+	2.76769e6i	−0.161033	+	0.221643i
$233$	1.03119e7	+	7.49204e6i	0.815213	+	0.592287i	0.915337	−	0.402688i	$-0.131924\pi$
$233$	1.03119e7	+	7.49204e6i	0.815213	+	0.592287i	−0.100124	+	0.994975i	$0.531924\pi$
$234$	−9.80080e6	+	3.18447e6i	−0.764916	+	0.248536i
$235$	−1.78258e7	−	1.29512e7i	−1.37355	−	0.997946i
$236$	238267.	−	173111.i	0.0181271	−	0.0131701i
$237$	−3.46293e6	+	1.06578e7i	−0.260135	+	0.800613i
$238$	−695057.	−	956663.i	−0.0515572	−	0.0709624i
$239$	−8.03208e6	+	2.60978e6i	−0.588348	+	0.191166i	−0.588037	−	0.808834i	$-0.700099\pi$
$239$	−8.03208e6	+	2.60978e6i	−0.588348	+	0.191166i	−0.000311240		1.00000i	$0.500099\pi$
$240$	−4.50689e6	+	1.46438e6i	−0.326019	+	0.105930i
$241$	−1.99480e7	−	6.48150e6i	−1.42511	−	0.463046i	−0.507888	−	0.861423i	$-0.669573\pi$
$241$	−1.99480e7	−	6.48150e6i	−1.42511	−	0.463046i	−0.917222	+	0.398377i	$0.869573\pi$
$242$	−1.62568e6			−0.114707
$243$			2.03260e7i			1.41655i
$244$	2.62589e6	+	853202.i	0.180762	+	0.0587330i
$245$	−7.67091e6	−	5.57325e6i	−0.521614	−	0.378974i
$246$	4.34226e6	+	5.97661e6i	0.291683	+	0.401467i
$247$		−	1.83826e7i		−	1.21988i
$248$	−2.05873e6	+	4.98431e6i	−0.134972	+	0.326776i
$249$	2.44969e7			1.58677
$250$	9.19782e6	−	6.68261e6i	0.588661	−	0.427687i
$251$	−2.61521e6	+	3.59953e6i	−0.165381	+	0.227628i	−0.883662	−	0.468126i	$-0.844929\pi$
$251$	−2.61521e6	+	3.59953e6i	−0.165381	+	0.227628i	0.718281	+	0.695754i	$0.244929\pi$
$252$	−1.43847e6	+	4.42715e6i	−0.0898874	+	0.276645i
$253$	1.59029e7			0.982007
$254$		−	6.04616e6i		−	0.368959i
$255$	1.50829e6	−	4.64204e6i	0.0909629	−	0.279955i
$256$	324028.	+	997255.i	0.0193136	+	0.0594410i
$257$	1.55483e6	+	4.78529e6i	0.0915977	+	0.281909i	0.986352	−	0.164650i	$-0.0526494\pi$
$257$	1.55483e6	+	4.78529e6i	0.0915977	+	0.281909i	−0.894754	+	0.446559i	$0.852649\pi$
$258$	2.18522e7	−	1.58766e7i	1.27244	−	0.924480i
$259$	−1.96811e6	−	639477.i	−0.113279	−	0.0368066i
$260$	5.64846e6	+	7.77444e6i	0.321374	+	0.442333i
$261$	−8.15318e6	+	1.12219e7i	−0.458570	+	0.631167i
$262$	5.89529e6	+	1.81438e7i	0.327794	+	1.00885i
$263$	1.61111e7	−	2.21750e7i	0.885639	−	1.21898i	−0.0891879	−	0.996015i	$-0.528427\pi$
$263$	1.61111e7	−	2.21750e7i	0.885639	−	1.21898i	0.974827	−	0.222963i	$-0.0715728\pi$
$264$	6.82405e6	+	4.95796e6i	0.370877	+	0.269458i
$265$	−1.97944e6	+	643159.i	−0.106367	+	0.0345606i
$266$	−6.71780e6	−	4.88077e6i	−0.356929	−	0.259324i
$267$	−2.03761e7	+	1.48041e7i	−1.07050	+	0.777765i
$268$	−1.61407e6	+	4.96761e6i	−0.0838530	+	0.258073i
$269$	328704.	+	452422.i	0.0168868	+	0.0232427i	0.817377	−	0.576103i	$-0.195427\pi$
$269$	328704.	+	452422.i	0.0168868	+	0.0232427i	−0.800490	+	0.599346i	$0.795427\pi$
$270$	−123510.	+	40130.7i	−0.00627494	+	0.00203885i
$271$	−2.42849e7	+	7.89065e6i	−1.22019	+	0.396465i	−0.847153	−	0.531350i	$-0.821685\pi$
$271$	−2.42849e7	+	7.89065e6i	−1.22019	+	0.396465i	−0.373041	+	0.927815i	$0.621685\pi$
$272$	−1.02716e6	−	333744.i	−0.0510424	−	0.0165847i
$273$	1.88156e7			0.924763
$274$			730217.i			0.0354977i
$275$	−1.14251e6	−	371225.i	−0.0549367	−	0.0178500i
$276$	1.29258e7	+	9.39113e6i	0.614794	+	0.446674i
$277$	6.15910e6	+	8.47728e6i	0.289787	+	0.398857i	0.928945	−	0.370218i	$-0.120717\pi$
$277$	6.15910e6	+	8.47728e6i	0.289787	+	0.398857i	−0.639158	+	0.769075i	$0.720717\pi$
$278$		−	7.46272e6i		−	0.347347i
$279$	−8.34732e6	+	2.02094e7i	−0.384357	+	0.930551i
$280$	4.34085e6			0.197743
$281$	−2.70165e7	+	1.96287e7i	−1.21762	+	0.884650i	−0.995900	−	0.0904606i	$-0.971166\pi$
$281$	−2.70165e7	+	1.96287e7i	−1.21762	+	0.884650i	−0.221717	+	0.975111i	$0.571166\pi$
$282$	−2.31605e7	+	3.18777e7i	−1.03276	+	1.42147i
$283$	9.91274e6	−	3.05083e7i	0.437355	−	1.34604i	−0.453298	−	0.891359i	$-0.649753\pi$
$283$	9.91274e6	−	3.05083e7i	0.437355	−	1.34604i	0.890654	−	0.454682i	$-0.150247\pi$
$284$	−1.62187e7			−0.708046
$285$		−	3.42744e7i		−	1.48059i
$286$	5.28576e6	−	1.62679e7i	0.225948	−	0.695398i
$287$	−2.09114e6	−	6.43587e6i	−0.0884581	−	0.272246i
$288$	1.31380e6	+	4.04347e6i	0.0549987	+	0.169269i
$289$	−1.86277e7	+	1.35339e7i	−0.771733	+	0.560697i
$290$	1.23019e7	+	3.99712e6i	0.504403	+	0.163890i
$291$	−1.67743e7	−	2.30879e7i	−0.680717	−	0.936927i
$292$	2.81727e6	−	3.87764e6i	0.113157	−	0.155747i
$293$	9.54845e6	+	2.93871e7i	0.379603	+	1.16830i	0.940320	+	0.340291i	$0.110526\pi$
$293$	9.54845e6	+	2.93871e7i	0.379603	+	1.16830i	−0.560717	+	0.828008i	$0.689474\pi$
$294$	−9.96655e6	+	1.37178e7i	−0.392196	+	0.539811i
$295$	−900883.	−	654530.i	−0.0350915	−	0.0254955i
$296$	−1.79754e6	+	584056.i	−0.0693112	+	0.0225206i
$297$	187010.	+	135871.i	0.00713832	+	0.00518629i
$298$	−1.55309e7	+	1.12839e7i	−0.586879	+	0.426393i
$299$	1.00120e7	−	3.08139e7i	0.374549	−	1.15274i
$300$	−709409.	−	976418.i	−0.0262744	−	0.0361636i
$301$	−2.35314e7	+	7.64582e6i	−0.862876	+	0.280366i
$302$	−2.38868e7	+	7.76129e6i	−0.867236	+	0.281782i
$303$	4.30971e6	+	1.40031e6i	0.154925	+	0.0503381i
$304$	−7.58402e6			−0.269947
$305$		−	1.04394e7i		−	0.367938i
$306$	−4.16472e6	−	1.35320e6i	−0.145352	−	0.0472278i
$307$	−2.96691e7	−	2.15559e7i	−1.02539	−	0.744991i	−0.0580108	−	0.998316i	$-0.518476\pi$
$307$	−2.96691e7	−	2.15559e7i	−1.02539	−	0.744991i	−0.967381	+	0.253325i	$0.918476\pi$
$308$	−4.54158e6	−	6.25094e6i	−0.155437	−	0.213941i
$309$		−	1.96122e7i		−	0.664740i
$310$	2.03286e7	+	1.57943e6i	0.682374	+	0.0530170i
$311$	5.97586e7			1.98664			0.993321	−	0.115388i	$-0.0368111\pi$
$311$	5.97586e7			1.98664			0.993321	+	0.115388i	$0.0368111\pi$
$312$	1.39029e7	−	1.01011e7i	0.457765	−	0.332586i
$313$	−1.26843e7	+	1.74584e7i	−0.413650	+	0.569341i	−0.964104	−	0.265525i	$-0.914455\pi$
$313$	−1.26843e7	+	1.74584e7i	−0.413650	+	0.569341i	0.550454	+	0.834866i	$0.314455\pi$
$314$	−1.59802e6	+	4.91819e6i	−0.0516170	+	0.158861i
$315$	1.76004e7			0.563107
$316$		−	9.37551e6i		−	0.297121i
$317$	1.23990e7	−	3.81601e7i	0.389231	−	1.19793i	−0.544133	−	0.838999i	$-0.683141\pi$
$317$	1.23990e7	−	3.81601e7i	0.389231	−	1.19793i	0.933364	−	0.358931i	$-0.116859\pi$
$318$	1.15015e6	+	3.53981e6i	0.0357663	+	0.110077i
$319$	−7.11477e6	−	2.18970e7i	−0.219174	−	0.674548i
$320$	3.20747e6	−	2.33036e6i	0.0978841	−	0.0711170i
$321$	6.09246e7	+	1.97956e7i	1.84195	+	0.598485i
$322$	−8.60244e6	−	1.18402e7i	−0.257664	−	0.354644i
$323$	4.59145e6	−	6.31958e6i	0.136252	−	0.187534i
$324$	−5.21917e6	−	1.60630e7i	−0.153450	−	0.472270i
$325$	−1.43859e6	+	1.98005e6i	−0.0419071	+	0.0576802i
$326$	3.45365e7	+	2.50922e7i	0.996839	+	0.724246i
$327$	−2.56728e7	+	8.34159e6i	−0.734226	+	0.238564i
$328$	−5.00021e6	−	3.63287e6i	−0.141699	−	0.102950i
$329$	2.92005e7	−	2.12154e7i	0.819978	−	0.595749i
$330$	9.85533e6	−	3.03316e7i	0.274239	−	0.844021i
$331$	−3.90047e6	−	5.36854e6i	−0.107556	−	0.148038i	0.751846	−	0.659339i	$-0.229164\pi$
$331$	−3.90047e6	−	5.36854e6i	−0.107556	−	0.148038i	−0.859402	+	0.511301i	$0.829164\pi$
$332$	−1.94918e7	+	6.33327e6i	−0.532644	+	0.173067i
$333$	−7.28830e6	+	2.36811e6i	−0.197376	+	0.0641313i
$334$	4.33780e7	+	1.40944e7i	1.16421	+	0.378273i
$335$	1.97490e7			0.525304
$336$		−	7.76267e6i		−	0.204641i
$337$	−2.28671e7	−	7.42997e6i	−0.597477	−	0.194132i	−0.00536218	−	0.999986i	$-0.501707\pi$
$337$	−2.28671e7	−	7.42997e6i	−0.597477	−	0.194132i	−0.592115	+	0.805854i	$0.701707\pi$
$338$	−6.10352e6	−	4.43447e6i	−0.158063	−	0.114840i
$339$	5.64711e7	+	7.77258e7i	1.44953	+	1.99511i
$340$			4.08353e6i			0.103896i
$341$	−1.89942e7	−	3.09262e7i	−0.479025	−	0.779945i
$342$	−3.07501e7			−0.768721
$343$	3.14300e7	−	2.28353e7i	0.778866	−	0.565879i
$344$	−1.32828e7	+	1.82822e7i	−0.326298	+	0.449111i
$345$	1.86675e7	−	5.74527e7i	0.454600	−	1.39911i
$346$	2.87397e7			0.693830
$347$		−	3.92298e7i		−	0.938918i	−0.882954	−	0.469459i	$-0.844449\pi$
$347$		−	3.92298e7i		−	0.938918i	0.882954	−	0.469459i	$-0.155551\pi$
$348$	7.14799e6	−	2.19993e7i	0.169608	−	0.522000i
$349$	−2.13690e7	−	6.57670e7i	−0.502698	−	1.54715i	−0.804606	−	0.593809i	$-0.797623\pi$
$349$	−2.13690e7	−	6.57670e7i	−0.502698	−	1.54715i	0.301907	−	0.953337i	$-0.402377\pi$
$350$	341636.	+	1.05145e6i	0.00796820	+	0.0245236i
$351$	381004.	−	276816.i	0.00881066	−	0.00640132i
$352$	−6.71157e6	−	2.18072e6i	−0.153885	−	0.0500003i
$353$	1.36458e7	+	1.87818e7i	0.310223	+	0.426986i	0.935451	−	0.353457i	$-0.114994\pi$
$353$	1.36458e7	+	1.87818e7i	0.310223	+	0.426986i	−0.625228	+	0.780442i	$0.714994\pi$
$354$	−1.17049e6	+	1.61104e6i	−0.0263850	+	0.0363158i
$355$	1.89498e7	+	5.83214e7i	0.423564	+	1.30359i
$356$	1.23856e7	−	1.70473e7i	0.274515	−	0.377837i
$357$	6.46845e6	+	4.69961e6i	0.142166	+	0.103290i
$358$	−5.01347e7	+	1.62897e7i	−1.09267	+	0.355030i
$359$	5.70391e7	+	4.14413e7i	1.23279	+	0.895674i	0.997096	−	0.0761531i	$-0.0242638\pi$
$359$	5.70391e7	+	4.14413e7i	1.23279	+	0.895674i	0.235694	+	0.971827i	$0.424264\pi$
$360$	1.30050e7	−	9.44868e6i	0.278742	−	0.202518i
$361$	2.41246e6	−	7.42480e6i	0.0512789	−	0.157820i
$362$	2.81400e7	+	3.87314e7i	0.593197	+	0.816465i
$363$	1.04540e7	−	3.39672e6i	0.218557	−	0.0710134i
$364$	−1.49713e7	+	4.86446e6i	−0.310423	+	0.100863i
$365$	−1.72354e7	−	5.60012e6i	−0.354440	−	0.115165i
$366$	−1.86686e7			−0.380774
$367$			7.27771e7i			1.47230i	0.676818	+	0.736150i	$0.263358\pi$
$367$			7.27771e7i			1.47230i	−0.676818	+	0.736150i	$0.736642\pi$
$368$	−1.27127e7	−	4.13062e6i	−0.255091	−	0.0828842i
$369$	−2.02738e7	−	1.47298e7i	−0.403513	−	0.293169i
$370$	4.20045e6	+	5.78142e6i	0.0829259	+	0.114138i
$371$		−	3.40939e6i		−	0.0667660i
$372$	2.82447e6	−	3.63534e7i	0.0548667	−	0.706180i
$373$	−9.61982e6			−0.185370			−0.0926852	−	0.995695i	$-0.529545\pi$
$373$	−9.61982e6			−0.185370			−0.0926852	+	0.995695i	$0.529545\pi$
$374$	5.88040e6	−	4.27236e6i	0.112407	−	0.0816683i
$375$	−4.51843e7	+	6.21908e7i	−0.856828	+	1.17932i
$376$	1.01870e7	−	3.13522e7i	0.191638	−	0.589800i
$377$	−4.69075e7			−0.875424
$378$		−	212733.i		−	0.00393876i
$379$	−1.68580e7	+	5.18835e7i	−0.309662	+	0.953041i	0.668235	+	0.743951i	$0.267050\pi$
$379$	−1.68580e7	+	5.18835e7i	−0.309662	+	0.953041i	−0.977896	+	0.209090i	$0.932950\pi$
$380$	8.86107e6	+	2.72716e7i	0.161486	+	0.497003i
$381$	1.26329e7	+	3.88801e7i	0.228417	+	0.702995i
$382$	4.47765e7	−	3.25320e7i	0.803267	−	0.583608i
$383$	−4.75203e7	−	1.54403e7i	−0.845829	−	0.274827i	−0.146131	−	0.989265i	$-0.546682\pi$
$383$	−4.75203e7	−	1.54403e7i	−0.845829	−	0.274827i	−0.699698	+	0.714439i	$0.746682\pi$
$384$	−4.16735e6	−	5.73586e6i	−0.0735980	−	0.101299i
$385$	−1.71716e7	+	2.36347e7i	−0.300905	+	0.414160i
$386$	−1.35570e7	−	4.17243e7i	−0.235724	−	0.725483i
$387$	−5.38565e7	+	7.41271e7i	−0.929192	+	1.27892i
$388$	1.93160e7	+	1.40339e7i	0.330692	+	0.240261i
$389$	−9.09016e7	+	2.95357e7i	−1.54427	+	0.501763i	−0.952550	−	0.304382i	$-0.901550\pi$
$389$	−9.09016e7	+	2.95357e7i	−1.54427	+	0.501763i	−0.591718	+	0.806145i	$0.701550\pi$
$390$	−5.25667e7	−	3.81919e7i	−0.886170	−	0.643840i
$391$	1.11384e7	−	8.09251e6i	0.186334	−	0.135379i
$392$	4.38372e6	−	1.34917e7i	0.0727753	−	0.223979i
$393$	−7.58198e7	−	1.04357e8i	−1.24912	−	1.71927i
$394$	4.82913e7	−	1.56908e7i	0.789551	−	0.256541i
$395$	−3.37137e7	+	1.09542e7i	−0.547034	+	0.177742i
$396$	−2.72127e7	−	8.84195e6i	−0.438214	−	0.142384i
$397$	−3.33345e7			−0.532748			−0.266374	−	0.963870i	$-0.585826\pi$
$397$	−3.33345e7			−0.532748			−0.266374	+	0.963870i	$0.585826\pi$
$398$			2.96153e6i			0.0469750i
$399$	5.33970e7	+	1.73497e7i	0.840617	+	0.273133i
$400$	816901.	+	593513.i	0.0127641	+	0.00927364i
$401$	4.77350e7	+	6.57016e7i	0.740293	+	1.01893i	0.998602	+	0.0528633i	$0.0168348\pi$
$401$	4.77350e7	+	6.57016e7i	0.740293	+	1.01893i	−0.258309	+	0.966062i	$0.583165\pi$
$402$		−	3.53169e7i		−	0.543631i
$403$	−7.18818e7	+	1.73334e7i	−1.09826	+	0.264831i
$404$	−3.79119e6			−0.0574952
$405$	−5.16632e7	+	3.75355e7i	−0.777708	+	0.565038i
$406$	−1.24544e7	+	1.71421e7i	−0.186100	+	0.256145i
$407$	3.93072e6	−	1.20975e7i	0.0583028	−	0.179438i
$408$	7.30252e6			0.107521
$409$			5.51490e7i			0.806060i	0.915187	+	0.403030i	$0.132043\pi$
$409$			5.51490e7i			0.806060i	−0.915187	+	0.403030i	$0.867957\pi$
$410$	−7.22134e6	+	2.22250e7i	−0.104777	+	0.322471i
$411$	−1.52572e6	−	4.69569e6i	−0.0219761	−	0.0676354i
$412$	5.07041e6	+	1.56051e7i	0.0725022	+	0.223139i
$413$	1.47574e6	−	1.07219e6i	0.0209488	−	0.0152202i
$414$	−5.15451e7	−	1.67480e7i	−0.726417	−	0.236027i
$415$	4.55479e7	+	6.26913e7i	0.637271	+	0.877129i
$416$	−8.45086e6	+	1.16316e7i	−0.117387	+	0.161570i
$417$	1.55927e7	+	4.79894e7i	0.215037	+	0.661815i
$418$	3.00010e7	−	4.12929e7i	0.410778	−	0.565387i
$419$	7.08159e6	+	5.14508e6i	0.0962696	+	0.0699439i	0.634879	−	0.772612i	$-0.281050\pi$
$419$	7.08159e6	+	5.14508e6i	0.0962696	+	0.0699439i	−0.538609	+	0.842556i	$0.681050\pi$
$420$	−2.79140e7	+	9.06981e6i	−0.376768	+	0.122419i
$421$	7.94494e7	+	5.77233e7i	1.06474	+	0.773580i	0.974960	−	0.222382i	$-0.0713831\pi$
$421$	7.94494e7	+	5.77233e7i	1.06474	+	0.773580i	0.0897815	+	0.995961i	$0.471383\pi$
$422$	−7.26915e7	+	5.28135e7i	−0.967267	+	0.702761i
$423$	4.13040e7	−	1.27121e8i	0.545722	−	1.67956i
$424$	−1.83031e6	−	2.51921e6i	−0.0240120	−	0.0330496i
$425$	−989121.	+	321385.i	−0.0128849	+	0.00418657i
$426$	1.04295e8	−	3.38876e7i	1.34907	−	0.438341i
$427$	1.62638e7	+	5.28441e6i	0.208899	+	0.0678755i
$428$	−5.35945e7			−0.683579
$429$			1.15656e8i			1.46486i
$430$	8.12611e7	+	2.64033e7i	1.02206	+	0.332088i
$431$	2.97124e7	+	2.15873e7i	0.371113	+	0.269629i	0.757672	−	0.652635i	$-0.226337\pi$
$431$	2.97124e7	+	2.15873e7i	0.371113	+	0.269629i	−0.386559	+	0.922265i	$0.626337\pi$
$432$	−114205.	−	157189.i	−0.00141655	−	0.00194972i
$433$			1.71431e7i			0.211167i	0.994410	+	0.105584i	$0.0336711\pi$
$433$			1.71431e7i			0.211167i	−0.994410	+	0.105584i	$0.966329\pi$
$434$	−1.27510e7	+	3.08710e7i	−0.155982	+	0.377643i
$435$	−8.74594e7			−1.06252
$436$	1.82708e7	−	1.32745e7i	0.220444	−	0.160162i
$437$	5.68265e7	−	7.82150e7i	0.680937	−	0.937229i
$438$	−1.00146e7	+	3.08218e7i	−0.119182	+	0.366805i
$439$	1.22917e8			1.45284			0.726421	−	0.687250i	$-0.241183\pi$
$439$	1.22917e8			1.45284			0.726421	+	0.687250i	$0.241183\pi$
$440$			2.66823e7i			0.313231i
$441$	1.77742e7	−	5.47034e7i	0.207240	−	0.637820i
$442$	−4.57611e6	−	1.40838e7i	−0.0529943	−	0.163100i
$443$	−1.05683e6	−	3.25257e6i	−0.0121560	−	0.0374124i	0.944795	−	0.327663i	$-0.106261\pi$
$443$	−1.05683e6	−	3.25257e6i	−0.0121560	−	0.0374124i	−0.956951	+	0.290251i	$0.906261\pi$
$444$	1.03388e7	−	7.51160e6i	0.118120	−	0.0858190i
$445$	−7.57718e7	−	2.46198e7i	−0.859860	−	0.279385i
$446$	−5.20186e7	−	7.15975e7i	−0.586347	−	0.807037i
$447$	7.62957e7	−	1.05012e8i	0.854235	−	1.17575i
$448$	2.00691e6	+	6.17663e6i	0.0223200	+	0.0686938i
$449$	−272004.	+	374382.i	−0.00300495	+	0.00413595i	−0.810517	−	0.585715i	$-0.800814\pi$
$449$	−272004.	+	374382.i	−0.00300495	+	0.00413595i	0.807512	+	0.589851i	$0.200814\pi$
$450$	3.31220e6	+	2.40646e6i	0.0363479	+	0.0264083i
$451$	3.95599e7	−	1.28538e7i	0.431246	−	0.140120i
$452$	−6.50278e7	−	4.72455e7i	−0.704180	−	0.511617i
$453$	1.37389e8	−	9.98186e7i	1.47794	−	1.07378i
$454$	−163527.	+	503284.i	−0.00174752	+	0.00537830i
$455$	3.49845e7	+	4.81520e7i	0.371399	+	0.511187i
$456$	4.87693e7	−	1.58461e7i	0.514342	−	0.167120i
$457$	1.33088e8	−	4.32430e7i	1.39441	−	0.453072i	0.487033	−	0.873383i	$-0.338079\pi$
$457$	1.33088e8	−	4.32430e7i	1.39441	−	0.453072i	0.907380	+	0.420311i	$0.138079\pi$
$458$	4.90886e7	+	1.59499e7i	0.510957	+	0.166020i
$459$	200123.			0.00206947
$460$			5.05403e7i			0.519235i
$461$	7.15893e6	+	2.32608e6i	0.0730710	+	0.0237422i	0.345324	−	0.938483i	$-0.387769\pi$
$461$	7.15893e6	+	2.32608e6i	0.0730710	+	0.0237422i	−0.272253	+	0.962226i	$0.587769\pi$
$462$	4.22656e7	+	3.07078e7i	0.428609	+	0.311403i
$463$	−8.95510e7	−	1.23256e8i	−0.902251	−	1.24184i	−0.969744	−	0.244122i	$-0.921500\pi$
$463$	−8.95510e7	−	1.23256e8i	−0.902251	−	1.24184i	0.0674934	−	0.997720i	$-0.478500\pi$
$464$			1.93524e7i			0.193723i
$465$	−1.34024e8	+	3.23182e7i	−1.33298	+	0.321432i
$466$	7.21035e7			0.712522
$467$	4.77776e7	−	3.47125e7i	0.469109	−	0.340828i	−0.327985	−	0.944683i	$-0.606369\pi$
$467$	4.77776e7	−	3.47125e7i	0.469109	−	0.340828i	0.797094	+	0.603855i	$0.206369\pi$
$468$	−3.42648e7	+	4.71615e7i	−0.334281	+	0.460098i
$469$	−9.99697e6	+	3.07675e7i	−0.0969058	+	0.298245i
$470$	−1.24643e8			−1.20053
$471$		−	3.49656e7i		−	0.334640i
$472$	514830.	−	1.58448e6i	0.00489596	−	0.0150682i
$473$	−4.69972e7	−	1.44643e8i	−0.444108	−	1.36682i
$474$	1.95893e7	+	6.02896e7i	0.183943	+	0.566119i
$475$	−5.90838e6	+	4.29269e6i	−0.0551300	+	0.0400543i
$476$	−6.36184e6	−	2.06709e6i	−0.0589878	−	0.0191663i
$477$	−7.42118e6	−	1.02144e7i	−0.0683783	−	0.0941146i
$478$	−2.80812e7	+	3.86504e7i	−0.257118	+	0.353892i
$479$	−3.33535e6	−	1.02652e7i	−0.0303484	−	0.0934026i	0.934735	−	0.355346i	$-0.115637\pi$
$479$	−3.33535e6	−	1.02652e7i	−0.0303484	−	0.0934026i	−0.965083	+	0.261943i	$0.915637\pi$
$480$	−1.57567e7	+	2.16872e7i	−0.142476	+	0.196101i
$481$	−2.09658e7	−	1.52326e7i	−0.188398	−	0.136879i
$482$	−1.12843e8	+	3.66649e7i	−1.00770	+	0.327423i
$483$	8.00575e7	+	5.81652e7i	0.710494	+	0.516204i
$484$	−7.43993e6	+	5.40543e6i	−0.0656195	+	0.0476753i
$485$	2.78964e7	−	8.58562e7i	0.244524	−	0.752569i
$486$	6.75842e7	+	9.30216e7i	0.588757	+	0.810355i
$487$	1.01759e8	−	3.30636e7i	0.881022	−	0.286261i	0.166640	−	0.986018i	$-0.446708\pi$
$487$	1.01759e8	−	3.30636e7i	0.881022	−	0.286261i	0.714382	+	0.699756i	$0.246708\pi$
$488$	1.48543e7	−	4.82644e6i	0.127818	−	0.0415305i
$489$	−2.74516e8	−	8.91957e7i	−2.34769	−	0.762812i
$490$	−5.36370e7			−0.455907
$491$		−	8.60774e7i		−	0.727185i	−0.931558	−	0.363592i	$-0.881550\pi$
$491$		−	8.60774e7i		−	0.727185i	0.931558	−	0.363592i	$-0.118450\pi$
$492$	3.97446e7	+	1.29138e7i	0.333721	+	0.108432i
$493$	−1.61259e7	−	1.17162e7i	−0.134581	−	0.0977788i
$494$	−6.11224e7	−	8.41277e7i	−0.507013	−	0.697844i
$495$			1.08186e8i			0.891979i
$496$	7.15116e6	+	2.96560e7i	0.0586046	+	0.243034i
$497$	−1.00453e8			−0.818262
$498$	1.12110e8	−	8.14527e7i	0.907729	−	0.659504i
$499$	1.27932e8	−	1.76084e8i	1.02962	−	1.41715i	0.124392	−	0.992233i	$-0.460302\pi$
$499$	1.27932e8	−	1.76084e8i	1.02962	−	1.41715i	0.905230	−	0.424921i	$-0.139698\pi$
$500$	1.98740e7	−	6.11658e7i	0.158992	−	0.489326i
$501$	−3.08393e8			−2.45240
$502$			2.51689e7i			0.198954i
$503$	−3.00303e7	+	9.24238e7i	−0.235970	+	0.726240i	0.761022	+	0.648726i	$0.224698\pi$
$503$	−3.00303e7	+	9.24238e7i	−0.235970	+	0.726240i	−0.996991	+	0.0775134i	$0.975302\pi$
$504$	8.13720e6	+	2.50437e7i	0.0635600	+	0.195617i
$505$	4.42958e6	+	1.36329e7i	0.0343945	+	0.105855i
$506$	7.27794e7	−	5.28773e7i	0.561768	−	0.408148i
$507$	4.85144e7	+	1.57633e7i	0.372260	+	0.120955i
$508$	−2.01036e7	−	2.76702e7i	−0.153349	−	0.211067i
$509$	−7.47171e7	+	1.02839e8i	−0.566587	+	0.779840i	−0.992145	−	0.125091i	$-0.960078\pi$
$509$	−7.47171e7	+	1.02839e8i	−0.566587	+	0.779840i	0.425558	+	0.904931i	$0.360078\pi$
$510$	−8.53217e6	−	2.62593e7i	−0.0643205	−	0.197958i
$511$	1.74491e7	−	2.40167e7i	0.130771	−	0.179991i
$512$	4.79880e6	+	3.48653e6i	0.0357538	+	0.0259767i
$513$	1.33650e6	−	434257.i	0.00989962	−	0.00321658i
$514$	2.30268e7	+	1.67300e7i	0.169568	+	0.123199i
$515$	5.01907e7	−	3.64657e7i	0.367453	−	0.266970i
$516$	4.72167e7	−	1.45318e8i	0.343674	−	1.05772i
$517$	1.30406e8	+	1.79489e8i	0.943686	+	1.29887i
$518$	−1.11333e7	+	3.61743e6i	−0.0801003	+	0.0260262i
$519$	−1.84812e8	+	6.00489e7i	−1.32199	+	0.429540i
$520$	5.17003e7	+	1.67984e7i	0.367691	+	0.119470i
$521$	1.98636e8			1.40458			0.702288	−	0.711893i	$-0.252162\pi$
$521$	1.98636e8			1.40458			0.702288	+	0.711893i	$0.252162\pi$
$522$			7.84663e7i			0.551660i
$523$	1.67485e8	+	5.44191e7i	1.17077	+	0.380405i	0.828929	−	0.559354i	$-0.188951\pi$
$523$	1.67485e8	+	5.44191e7i	1.17077	+	0.380405i	0.341837	+	0.939759i	$0.388951\pi$
$524$	8.73082e7	+	6.34331e7i	0.606822	+	0.440882i
$525$	−4.39381e6	−	6.04757e6i	−0.0303643	−	0.0417929i
$526$		−	1.55053e8i		−	1.06543i
$527$	−2.90410e7	−	1.19951e7i	−0.198417	−	0.0819547i
$528$	4.77155e7			0.324159
$529$	1.80918e7	−	1.31445e7i	0.122212	−	0.0887925i
$530$	−6.92038e6	+	9.52509e6i	−0.0464839	+	0.0639796i
$531$	2.08743e6	−	6.42444e6i	0.0139421	−	0.0429093i
$532$	−4.69726e7			−0.311968
$533$		−	8.47448e7i		−	0.559669i
$534$	−4.40272e7	+	1.35502e8i	−0.289132	+	0.889858i
$535$	6.26191e7	+	1.92722e8i	0.408927	+	1.25855i
$536$	9.13058e6	+	2.81010e7i	0.0592931	+	0.182485i
$537$	2.88357e8	−	2.09504e8i	1.86212	−	1.35291i
$538$	3.00862e6	+	977560.i	0.0193206	+	0.00627764i
$539$	5.61173e7	+	7.72388e7i	0.358369	+	0.493253i
$540$	−431805.	+	594329.i	−0.00274225	+	0.00377438i
$541$	7.94126e7	+	2.44407e8i	0.501531	+	1.54355i	0.806526	+	0.591198i	$0.201345\pi$
$541$	7.94126e7	+	2.44407e8i	0.501531	+	1.54355i	−0.304996	+	0.952354i	$0.598655\pi$
$542$	−8.49032e7	+	1.16859e8i	−0.533244	+	0.733948i
$543$	−2.61881e8	−	1.90268e8i	−1.63571	−	1.18841i
$544$	−5.81049e6	+	1.88794e6i	−0.0360924	+	0.0117271i
$545$	−6.90816e7	−	5.01907e7i	−0.426749	−	0.310051i
$546$	8.61095e7	−	6.25622e7i	0.529021	−	0.384357i
$547$	8.39122e7	−	2.58255e8i	0.512700	−	1.57793i	−0.274728	−	0.961522i	$-0.588588\pi$
$547$	8.39122e7	−	2.58255e8i	0.512700	−	1.57793i	0.787428	−	0.616406i	$-0.211412\pi$
$548$	2.42798e6	+	3.34183e6i	0.0147538	+	0.0203069i
$549$	6.02280e7	−	1.95693e7i	0.363983	−	0.118265i
$550$	−6.46303e6	+	2.09996e6i	−0.0388461	+	0.0126219i
$551$	−1.33119e8	−	4.32531e7i	−0.795768	−	0.258561i
$552$	9.03804e7			0.537350
$553$		−	5.80684e7i		−	0.343372i
$554$	5.63742e7	+	1.83171e7i	0.331551	+	0.107728i
$555$	−3.90909e7	−	2.84012e7i	−0.228664	−	0.166134i
$556$	−2.48137e7	−	3.41531e7i	−0.144367	−	0.198704i
$557$		−	2.38005e7i		−	0.137728i	−0.997626	−	0.0688638i	$-0.978063\pi$
$557$		−	2.38005e7i		−	0.137728i	0.997626	−	0.0688638i	$-0.0219374\pi$
$558$	2.89951e7	+	1.20243e8i	0.166887	+	0.692082i
$559$	−3.09852e8			−1.77386
$560$	1.98659e7	−	1.44334e7i	0.113121	−	0.0821872i
$561$	−2.88875e7	+	3.97602e7i	−0.163614	+	0.225196i
$562$	−5.83753e7	+	1.79661e8i	−0.328867	+	1.01215i
$563$	−2.80148e7			−0.156986			−0.0784932	−	0.996915i	$-0.525011\pi$
$563$	−2.80148e7			−0.156986			−0.0784932	+	0.996915i	$0.525011\pi$
$564$			2.22897e8i			1.24241i
$565$	−9.39136e7	+	2.89036e8i	−0.520694	+	1.60253i
$566$	−5.60749e7	−	1.72581e8i	−0.309257	−	0.951795i
$567$	−3.23256e7	−	9.94880e7i	−0.177336	−	0.545785i
$568$	−7.42249e7	+	5.39275e7i	−0.405046	+	0.294283i
$569$	−8.78236e6	−	2.85356e6i	−0.0476732	−	0.0154900i	0.285083	−	0.958503i	$-0.407979\pi$
$569$	−8.78236e6	−	2.85356e6i	−0.0476732	−	0.0154900i	−0.332757	+	0.943013i	$0.607979\pi$
$570$	−1.13963e8	−	1.56857e8i	−0.615374	−	0.846990i
$571$	1.96532e8	−	2.70503e8i	1.05566	−	1.45300i	0.171870	−	0.985120i	$-0.445019\pi$
$571$	1.96532e8	−	2.70503e8i	1.05566	−	1.45300i	0.883794	−	0.467876i	$-0.154981\pi$
$572$	−2.99008e7	−	9.20251e7i	−0.159770	−	0.491721i
$573$	−2.19964e8	+	3.02755e8i	−1.16920	+	1.60926i
$574$	−3.09694e7	−	2.25006e7i	−0.163756	−	0.118976i
$575$	−1.22420e7	+	3.97765e6i	−0.0643943	+	0.0209230i
$576$	1.94572e7	+	1.41365e7i	0.101815	+	0.0739731i
$577$	−7.37586e7	+	5.35888e7i	−0.383960	+	0.278963i	−0.762976	−	0.646427i	$-0.776262\pi$
$577$	−7.37586e7	+	5.35888e7i	−0.383960	+	0.278963i	0.379016	+	0.925390i	$0.376262\pi$
$578$	−4.02495e7	+	1.23875e8i	−0.208438	+	0.641506i
$579$	1.74358e8	+	2.39984e8i	0.898270	+	1.23636i
$580$	6.95899e7	−	2.26111e7i	0.356667	−	0.115888i
$581$	−1.20725e8	+	3.92259e7i	−0.615557	+	0.200007i
$582$	−1.53535e8	−	4.98866e7i	−0.778824	−	0.253055i
$583$	2.09568e7			0.105759
$584$		−	2.71135e7i		−	0.136128i
$585$	2.09624e8	+	6.81109e7i	1.04706	+	0.340212i
$586$	1.41411e8	+	1.02741e8i	0.702733	+	0.510565i
$587$	1.50169e7	+	2.06690e7i	0.0742450	+	0.102189i	0.844524	−	0.535517i	$-0.179883\pi$
$587$	1.50169e7	+	2.06690e7i	0.0742450	+	0.102189i	−0.770279	+	0.637707i	$0.779883\pi$
$588$			9.59183e7i			0.471812i
$589$	−2.19977e8	−	1.70911e7i	−1.07654	−	0.0836420i
$590$	−6.29920e6			−0.0306711
$591$	−2.77755e8	+	2.01801e8i	−1.34555	+	0.977598i
$592$	−6.28443e6	+	8.64978e6i	−0.0302901	+	0.0416908i
$593$	6.58530e7	−	2.02675e8i	0.315800	−	0.971932i	−0.659624	−	0.751596i	$-0.729285\pi$
$593$	6.58530e7	−	2.02675e8i	0.315800	−	0.971932i	0.975424	−	0.220336i	$-0.0707154\pi$
$594$	1.30762e6			0.00623912
$595$			2.52919e7i			0.120069i
$596$	−3.35581e7	+	1.03281e8i	−0.158511	+	0.487846i
$597$	−6.18786e6	−	1.90443e7i	−0.0290815	−	0.0895037i
$598$	−5.66366e7	−	1.74310e8i	−0.264846	−	0.815113i
$599$	−1.20793e8	+	8.77616e7i	−0.562034	+	0.408342i	−0.832203	−	0.554471i	$-0.812921\pi$
$599$	−1.20793e8	+	8.77616e7i	−0.562034	+	0.408342i	0.270169	+	0.962813i	$0.412921\pi$
$600$	−6.49321e6	−	2.10977e6i	−0.0300611	−	0.00976746i
$601$	−1.81375e8	−	2.49641e8i	−0.835515	−	1.14999i	−0.986871	−	0.161509i	$-0.948364\pi$
$601$	−1.81375e8	−	2.49641e8i	−0.835515	−	1.14999i	0.151356	−	0.988479i	$-0.451636\pi$
$602$	−8.22688e7	+	1.13233e8i	−0.377091	+	0.519021i
$603$	3.70208e7	+	1.13938e8i	0.168847	+	0.519659i
$604$	−8.35113e7	+	1.14943e8i	−0.378996	+	0.521643i
$605$	2.81302e7	+	2.04378e7i	0.127030	+	0.0922929i
$606$	2.43794e7	−	7.92136e6i	0.109548	−	0.0355944i
$607$	3.51828e8	+	2.55618e8i	1.57313	+	1.14294i	0.924081	+	0.382196i	$0.124832\pi$
$607$	3.51828e8	+	2.55618e8i	1.57313	+	1.14294i	0.649047	+	0.760748i	$0.275168\pi$
$608$	−3.47082e7	+	2.52170e7i	−0.154426	+	0.112197i
$609$	4.42720e7	−	1.36255e8i	0.196010	−	0.603256i
$610$	−3.47110e7	−	4.77757e7i	−0.152925	−	0.210483i
$611$	4.29884e8	−	1.39678e8i	1.88463	−	0.612355i
$612$	−2.35592e7	+	7.65485e6i	−0.102779	+	0.0333951i
$613$	1.39620e8	+	4.53653e7i	0.606131	+	0.196944i	0.595973	−	0.803004i	$-0.296766\pi$
$613$	1.39620e8	+	4.53653e7i	0.606131	+	0.196944i	0.0101583	+	0.999948i	$0.496766\pi$
$614$	−2.07454e8			−0.896225
$615$		−	1.58007e8i		−	0.679284i
$616$	−4.15690e7	−	1.35066e7i	−0.177839	−	0.0577834i
$617$	2.81514e8	+	2.04532e8i	1.19852	+	0.870773i	0.994138	−	0.108119i	$-0.0344826\pi$
$617$	2.81514e8	+	2.04532e8i	1.19852	+	0.870773i	0.204379	+	0.978892i	$0.434483\pi$
$618$	−6.52110e7	−	8.97552e7i	−0.276284	−	0.380272i
$619$			5.84470e7i			0.246428i	0.992380	+	0.123214i	$0.0393202\pi$
$619$			5.84470e7i			0.246428i	−0.992380	+	0.123214i	$0.960680\pi$
$620$	9.82853e7	−	6.03647e7i	0.412395	−	0.253284i
$621$	2.47684e6			0.0103424
$622$	2.73485e8	−	1.98698e8i	1.13648	−	0.825702i
$623$	7.67115e7	−	1.05584e8i	0.317246	−	0.436652i
$624$	3.00404e7	−	9.24549e7i	0.123638	−	0.380519i
$625$	−2.27761e8			−0.932908
$626$			1.22074e8i			0.497622i
$627$	−1.06645e8	+	3.28220e8i	−0.432652	+	1.33156i
$628$	9.03976e6	+	2.78215e7i	0.0364987	+	0.112332i
$629$	−3.40299e6	−	1.04733e7i	−0.0136744	−	0.0420856i
$630$	8.05481e7	−	5.85216e7i	0.322132	−	0.234042i
$631$	−1.58887e7	−	5.16256e6i	−0.0632414	−	0.0205484i	0.277225	−	0.960805i	$-0.410585\pi$
$631$	−1.58887e7	−	5.16256e6i	−0.0632414	−	0.0205484i	−0.340467	+	0.940257i	$0.610585\pi$
$632$	−3.11737e7	−	4.29069e7i	−0.123492	−	0.169972i
$633$	3.57097e8	−	4.91502e8i	1.40791	−	1.93782i
$634$	−7.01391e7	−	2.15866e8i	−0.275228	−	0.847065i
$635$	−7.60112e7	+	1.04620e8i	−0.296863	+	0.408597i
$636$	1.70336e7	+	1.23756e7i	0.0662116	+	0.0481056i
$637$	1.84990e8	−	6.01069e7i	0.715699	−	0.232545i
$638$	−1.05369e8	−	7.65548e7i	−0.405741	−	0.294788i
$639$	−3.00952e8	+	2.18654e8i	−1.15344	+	0.838022i
$640$	6.93046e6	−	2.13298e7i	0.0264376	−	0.0813665i
$641$	2.36146e8	+	3.25027e8i	0.896615	+	1.23409i	0.971535	+	0.236896i	$0.0761300\pi$
$641$	2.36146e8	+	3.25027e8i	0.896615	+	1.23409i	−0.0749197	+	0.997190i	$0.523870\pi$
$642$	3.44641e8	−	1.11981e8i	1.30245	−	0.423193i
$643$	−2.79170e8	+	9.07079e7i	−1.05011	+	0.341202i	−0.782713	−	0.622383i	$-0.786165\pi$
$643$	−2.79170e8	+	9.07079e7i	−1.05011	+	0.341202i	−0.267400	+	0.963586i	$0.586165\pi$
$644$	−7.87380e7	−	2.55835e7i	−0.294800	−	0.0957862i
$645$	−5.77720e8			−2.15297
$646$		−	4.41881e7i		−	0.163911i
$647$	−5.16293e6	−	1.67754e6i	−0.0190626	−	0.00619383i	0.299470	−	0.954106i	$-0.403190\pi$
$647$	−5.16293e6	−	1.67754e6i	−0.0190626	−	0.00619383i	−0.318533	+	0.947912i	$0.603190\pi$
$648$	−7.72951e7	−	5.61582e7i	−0.284071	−	0.206390i
$649$	6.59049e6	+	9.07104e6i	0.0241093	+	0.0331835i
$650$			1.38450e7i			0.0504143i
$651$	1.74937e7	−	2.25159e8i	0.0634073	−	0.816106i
$652$	2.41488e8			0.871269
$653$	1.77823e7	−	1.29196e7i	0.0638628	−	0.0463990i	−0.555396	−	0.831586i	$-0.687433\pi$
$653$	1.77823e7	−	1.29196e7i	0.0638628	−	0.0463990i	0.619259	+	0.785187i	$0.287433\pi$
$654$	−8.97553e7	+	1.23538e8i	−0.320868	+	0.441637i
$655$	1.26091e8	−	3.88069e8i	0.448705	−	1.38097i
$656$	−3.49628e7			−0.123849
$657$		−	1.09934e8i		−	0.387648i
$658$	6.30942e7	−	1.94184e8i	0.221469	−	0.681610i
$659$	3.12382e7	+	9.61414e7i	0.109152	+	0.335934i	0.990682	−	0.136192i	$-0.0434865\pi$
$659$	3.12382e7	+	9.61414e7i	0.109152	+	0.335934i	−0.881531	+	0.472127i	$0.843487\pi$
$660$	−5.57502e7	−	1.71581e8i	−0.193916	−	0.596813i
$661$	−4.07959e8	+	2.96400e8i	−1.41258	+	1.02630i	−0.419636	+	0.907692i	$0.637842\pi$
$661$	−4.07959e8	+	2.96400e8i	−1.41258	+	1.02630i	−0.992941	+	0.118605i	$0.962158\pi$
$662$	−3.57010e7	−	1.15999e7i	−0.123057	−	0.0399836i
$663$	5.88537e7	+	8.10052e7i	0.201945	+	0.277953i
$664$	−6.81458e7	+	9.37946e7i	−0.232774	+	0.320386i
$665$	5.48822e7	+	1.68910e8i	0.186623	+	0.574368i
$666$	−2.54808e7	+	3.50714e7i	−0.0862564	+	0.118722i
$667$	−1.99584e8	−	1.45006e8i	−0.672587	−	0.488663i
$668$	2.45383e8	−	7.97297e7i	0.823218	−	0.267480i
$669$	4.84105e8	+	3.51723e8i	1.61682	+	1.17469i
$670$	9.03812e7	−	6.56658e7i	0.300506	−	0.218331i
$671$	−3.24822e7	+	9.99698e7i	−0.107517	+	0.330903i
$672$	−2.58110e7	−	3.55258e7i	−0.0850545	−	0.117067i
$673$	4.30958e8	−	1.40027e8i	1.41381	−	0.459373i	0.500177	−	0.865923i	$-0.333268\pi$
$673$	4.30958e8	−	1.40027e8i	1.41381	−	0.459373i	0.913629	+	0.406550i	$0.133268\pi$
$674$	−1.29356e8	+	4.20303e7i	−0.422480	+	0.137272i
$675$	−177944.	−	57817.4i	−0.000578591	−	0.000187996i
$676$	−4.26774e7			−0.138152
$677$		−	1.48732e8i		−	0.479336i	−0.970855	−	0.239668i	$-0.922961\pi$
$677$		−	1.48732e8i		−	0.479336i	0.970855	−	0.239668i	$-0.0770385\pi$
$678$	5.16879e8	+	1.67944e8i	1.65844	+	0.538860i
$679$	1.19636e8	+	8.69209e7i	0.382168	+	0.277661i
$680$	1.35778e7	+	1.86882e7i	0.0431820	+	0.0594349i
$681$		−	3.57806e6i		−	0.0113294i
$682$	−1.89757e8	−	7.83776e7i	−0.598198	−	0.247081i
$683$	2.37408e8			0.745133			0.372567	−	0.928005i	$-0.378478\pi$
$683$	2.37408e8			0.745133			0.372567	+	0.928005i	$0.378478\pi$
$684$	−1.40728e8	+	1.02245e8i	−0.439756	+	0.319501i
$685$	9.18016e6	−	1.26354e7i	0.0285613	−	0.0393113i
$686$	6.79117e7	−	2.09011e8i	0.210364	−	0.647435i
$687$	−3.48992e8			−1.07633
$688$			1.27834e8i			0.392538i
$689$	1.31938e7	−	4.06065e7i	0.0403379	−	0.124147i
$690$	−1.05599e8	−	3.25001e8i	−0.321450	−	0.989323i
$691$	3.41041e6	+	1.04962e7i	0.0103365	+	0.0318124i	0.956092	−	0.293068i	$-0.0946761\pi$
$691$	3.41041e6	+	1.04962e7i	0.0103365	+	0.0318124i	−0.945755	+	0.324880i	$0.894676\pi$
$692$	1.31527e8	−	9.55598e7i	0.396914	−	0.288375i
$693$	−1.68546e8	−	5.47638e7i	−0.506428	−	0.164548i
$694$	−1.30440e8	−	1.79535e8i	−0.390240	−	0.537119i
$695$	−9.38200e7	+	1.29132e8i	−0.279474	+	0.384663i
$696$	−4.04352e7	−	1.24447e8i	−0.119931	−	0.369110i
$697$	2.11668e7	−	2.91336e7i	0.0625112	−	0.0860392i
$698$	−3.16471e8	−	2.29930e8i	−0.930610	−	0.676128i
$699$	−4.63664e8	+	1.50654e8i	−1.35760	+	0.441111i
$700$	5.05958e6	+	3.67600e6i	0.0147510	+	0.0107172i
$701$	−2.32827e7	+	1.69159e7i	−0.0675896	+	0.0491067i	−0.621067	−	0.783757i	$-0.713301\pi$
$701$	−2.32827e7	+	1.69159e7i	−0.0675896	+	0.0491067i	0.553477	+	0.832864i	$0.313301\pi$
$702$	823245.	−	2.53369e6i	0.00237968	−	0.00732389i
$703$	−4.54533e7	−	6.25611e7i	−0.130828	−	0.180069i
$704$	−3.79664e7	+	1.23360e7i	−0.108813	+	0.0353555i
$705$	8.01520e8	−	2.60430e8i	2.28743	−	0.743230i
$706$	1.24900e8	+	4.05823e7i	0.354934	+	0.115325i
$707$	−2.34812e7			−0.0664451
$708$			1.12648e7i			0.0317412i
$709$	−2.22830e8	−	7.24019e7i	−0.625223	−	0.203147i	−0.0207653	−	0.999784i	$-0.506610\pi$
$709$	−2.22830e8	−	7.24019e7i	−0.625223	−	0.203147i	−0.604458	+	0.796637i	$0.706610\pi$
$710$	2.80643e8	+	2.03899e8i	0.784113	+	0.569692i
$711$	−1.26397e8	−	1.73970e8i	−0.351664	−	0.484024i
$712$		−	1.19199e8i		−	0.330242i
$713$	−3.59429e8	−	1.48459e8i	−0.991618	−	0.409580i
$714$	4.52291e7			0.124258
$715$	−2.95980e8	+	2.15042e8i	−0.809737	+	0.588309i
$716$	−1.75277e8	+	2.41248e8i	−0.477514	+	0.657242i
$717$	9.98207e7	−	3.07216e8i	0.270809	−	0.833464i
$718$	3.98832e8			1.07750
$719$		−	3.15896e8i		−	0.849880i	−0.905221	−	0.424940i	$-0.860295\pi$
$719$		−	3.15896e8i		−	0.849880i	0.905221	−	0.424940i	$-0.139705\pi$
$720$	2.81002e7	−	8.64836e7i	0.0752857	−	0.231705i
$721$	3.14042e7	+	9.66523e7i	0.0837881	+	0.257873i
$722$	−1.36470e7	−	4.20010e7i	−0.0362597	−	0.111596i
$723$	6.49033e8	−	4.71550e8i	1.71732	−	1.24771i
$724$	2.57565e8	+	8.36880e7i	0.678690	+	0.220520i
$725$	1.09538e7	+	1.50766e7i	0.0287443	+	0.0395631i
$726$	3.65486e7	−	5.03049e7i	0.0955127	−	0.131462i
$727$	−4.95291e7	−	1.52435e8i	−0.128901	−	0.396718i	0.865690	−	0.500580i	$-0.166880\pi$
$727$	−4.95291e7	−	1.52435e8i	−0.128901	−	0.396718i	−0.994592	+	0.103862i	$0.966880\pi$
$728$	−5.23415e7	+	7.20418e7i	−0.135660	+	0.186720i
$729$	−3.17681e8	−	2.30809e8i	−0.819990	−	0.595757i
$730$	−9.74981e7	+	3.16791e7i	−0.250627	+	0.0814336i
$731$	−1.06521e8	−	7.73921e7i	−0.272699	−	0.198127i
$732$	−8.54365e7	+	6.20732e7i	−0.217826	+	0.158260i
$733$	4.36193e7	−	1.34246e8i	0.110756	−	0.340872i	−0.880282	−	0.474450i	$-0.842647\pi$
$733$	4.36193e7	−	1.34246e8i	0.110756	−	0.340872i	0.991038	+	0.133579i	$0.0426469\pi$
$734$	2.41985e8	+	3.33064e8i	0.611928	+	0.842246i
$735$	3.44915e8	−	1.12070e8i	0.868661	−	0.282245i
$736$	−7.19141e7	+	2.33663e7i	−0.180377	+	0.0586080i
$737$	−1.89121e8	−	6.14492e7i	−0.472430	−	0.153502i
$738$	−1.41760e8			−0.352683
$739$			5.29741e8i			1.31259i	0.754503	+	0.656297i	$0.227878\pi$
$739$			5.29741e8i			1.31259i	−0.754503	+	0.656297i	$0.772122\pi$
$740$	3.84466e7	+	1.24921e7i	0.0948774	+	0.0308276i
$741$	5.68827e8	+	4.13277e8i	1.39806	+	1.01575i
$742$	−1.13363e7	−	1.56030e7i	−0.0277497	−	0.0381942i
$743$			2.67380e8i			0.651873i	0.945392	+	0.325936i	$0.105680\pi$
$743$			2.67380e8i			0.651873i	−0.945392	+	0.325936i	$0.894320\pi$
$744$	−1.07949e8	−	1.75762e8i	−0.262121	−	0.426783i
$745$	4.10600e8			0.993003
$746$	−4.40250e7	+	3.19860e7i	−0.106043	+	0.0770449i
$747$	−2.76304e8	+	3.80300e8i	−0.662865	+	0.912355i
$748$	1.27059e7	−	3.91049e7i	0.0303600	−	0.0934385i
$749$	−3.31944e8			−0.789986
$750$			4.34854e8i			1.03077i
$751$	−6.26243e6	+	1.92738e7i	−0.0147851	+	0.0455037i	−0.958177	−	0.286177i	$-0.907616\pi$
$751$	−6.26243e6	+	1.92738e7i	−0.0147851	+	0.0455037i	0.943392	+	0.331680i	$0.107616\pi$
$752$	−5.76262e7	−	1.77355e8i	−0.135508	−	0.417052i
$753$	−5.25881e7	−	1.61849e8i	−0.123169	−	0.379076i
$754$	−2.14672e8	+	1.55968e8i	−0.500796	+	0.363850i
$755$	5.10902e8	+	1.66002e8i	1.18713	+	0.385720i
$756$	−707340.	−	973571.i	−0.00163705	−	0.00225321i
$757$	−1.59254e8	+	2.19195e8i	−0.367117	+	0.505293i	−0.952114	−	0.305742i	$-0.901095\pi$
$757$	−1.59254e8	+	2.19195e8i	−0.367117	+	0.505293i	0.584998	+	0.811035i	$0.301095\pi$
$758$	9.53631e7	+	2.93497e8i	0.218964	+	0.673902i
$759$	−3.57529e8	+	4.92096e8i	−0.817684	+	1.12545i
$760$	1.31231e8	+	9.53449e7i	0.298948	+	0.217198i
$761$	7.08602e8	−	2.30239e8i	1.60786	−	0.522425i	0.638825	−	0.769352i	$-0.279421\pi$
$761$	7.08602e8	−	2.30239e8i	1.60786	−	0.522425i	0.969034	+	0.246927i	$0.0794207\pi$
$762$	1.87091e8	+	1.35930e8i	0.422852	+	0.307220i
$763$	1.13163e8	−	8.22174e7i	0.254759	−	0.185093i
$764$	9.67497e7	−	2.97765e8i	0.216955	−	0.667719i
$765$	5.50526e7	+	7.57733e7i	0.122968	+	0.169251i
$766$	−2.68815e8	+	8.73434e7i	−0.598092	+	0.194332i
$767$	2.17255e7	−	7.05904e6i	0.0481486	−	0.0156444i
$768$	−3.81437e7	−	1.23936e7i	−0.0842052	−	0.0273599i
$769$	−1.62109e8			−0.356474			−0.178237	−	0.983988i	$-0.557039\pi$
$769$	−1.62109e8			−0.356474			−0.178237	+	0.983988i	$0.557039\pi$
$770$			1.65260e8i			0.361989i
$771$	−1.83031e8	−	5.94703e7i	−0.399357	−	0.129759i
$772$	−2.00778e8	−	1.45873e8i	−0.436378	−	0.317048i
$773$	8.52517e6	+	1.17339e7i	0.0184572	+	0.0254041i	0.818146	−	0.575011i	$-0.195002\pi$
$773$	8.52517e6	+	1.17339e7i	0.0184572	+	0.0254041i	−0.799689	+	0.600415i	$0.795002\pi$
$774$			5.18316e8i			1.11782i
$775$	2.23570e7	+	1.90560e7i	0.0480295	+	0.0409380i
$776$	1.35063e8			0.289035
$777$	6.40348e7	−	4.65240e7i	0.136506	−	0.0991778i
$778$	−3.17804e8	+	4.37419e8i	−0.674870	+	0.928879i
$779$	7.81425e7	−	2.40498e8i	0.165301	−	0.508744i
$780$	−3.67560e8			−0.774541
$781$		−	6.17461e8i		−	1.29615i
$782$	2.40670e7	−	7.40706e7i	0.0503271	−	0.154891i
$783$	−1.10811e6	−	3.41041e6i	−0.00230833	−	0.00710430i
$784$	−2.47980e7	−	7.63205e7i	−0.0514599	−	0.158377i
$785$	8.94822e7	−	6.50126e7i	0.184981	−	0.134397i
$786$	−6.93977e8	−	2.25487e8i	−1.42915	−	0.464359i
$787$	−1.44224e8	−	1.98508e8i	−0.295879	−	0.407243i	0.635033	−	0.772485i	$-0.280986\pi$
$787$	−1.44224e8	−	1.98508e8i	−0.295879	−	0.407243i	−0.930913	+	0.365242i	$0.880986\pi$
$788$	1.68833e8	−	2.32378e8i	0.345047	−	0.474916i
$789$	3.23969e8	+	9.97075e8i	0.659588	+	2.03000i
$790$	−1.17867e8	+	1.62230e8i	−0.239063	+	0.329042i
$791$	−4.02758e8	−	2.92621e8i	−0.813794	−	0.591256i
$792$	−1.53938e8	+	5.00176e7i	−0.309864	+	0.100681i
$793$	1.73254e8	+	1.25877e8i	0.347428	+	0.252421i
$794$	−1.52555e8	+	1.10838e8i	−0.304765	+	0.221424i
$795$	2.46000e7	−	7.57110e7i	0.0489591	−	0.150681i
$796$	9.84714e6	+	1.35534e7i	0.0195241	+	0.0268726i
$797$	−7.22191e8	+	2.34654e8i	−1.42652	+	0.463504i	−0.917667	−	0.397351i	$-0.869930\pi$
$797$	−7.22191e8	+	2.34654e8i	−1.42652	+	0.463504i	−0.508851	+	0.860855i	$0.669930\pi$
$798$	3.02059e8	−	9.81450e7i	0.594406	−	0.193134i
$799$	1.82673e8	+	5.93542e7i	0.358125	+	0.116362i
$800$	5.71198e6			0.0111562
$801$		−	4.83303e8i		−	0.940421i
$802$	4.36917e8	+	1.41963e8i	0.846986	+	0.275202i
$803$	1.47625e8	+	1.07256e8i	0.285111	+	0.207145i
$804$	−1.17429e8	−	1.61627e8i	−0.225948	−	0.310990i
$805$			3.13028e8i			0.600060i
$806$	−2.71333e8	+	3.18334e8i	−0.518200	+	0.607965i
$807$	−2.13896e7			−0.0406988
$808$	−1.73504e7	+	1.26058e7i	−0.0328908	+	0.0238966i
$809$	−4.61365e8	+	6.35014e8i	−0.871363	+	1.19933i	0.107376	+	0.994218i	$0.465755\pi$
$809$	−4.61365e8	+	6.35014e8i	−0.871363	+	1.19933i	−0.978739	+	0.205109i	$0.934245\pi$
$810$	−1.11630e8	+	3.43562e8i	−0.210052	+	0.646473i
$811$	−5.62598e8			−1.05472			−0.527358	−	0.849643i	$-0.676817\pi$
$811$	−5.62598e8			−1.05472			−0.527358	+	0.849643i	$0.676817\pi$
$812$			1.19862e8i			0.223879i
$813$	3.01807e8	−	9.28866e8i	0.561639	−	1.72855i
$814$	−2.22355e7	−	6.84340e7i	−0.0412263	−	0.126882i
$815$	−2.82151e8	−	8.68373e8i	−0.521206	−	1.60411i
$816$	3.34199e7	−	2.42810e7i	0.0615085	−	0.0446885i
$817$	−8.79331e8	−	2.85712e8i	−1.61245	−	0.523917i
$818$	1.83371e8	+	2.52389e8i	0.335020	+	0.461116i
$819$	−2.12224e8	+	2.92101e8i	−0.386315	+	0.531718i
$820$	4.08501e7	+	1.25724e8i	0.0740885	+	0.228021i
$821$	−5.35049e8	+	7.36432e8i	−0.966861	+	1.33077i	−0.0232442	+	0.999730i	$0.507400\pi$
$821$	−5.35049e8	+	7.36432e8i	−0.966861	+	1.33077i	−0.943617	+	0.331040i	$0.892600\pi$
$822$	−2.25957e7	−	1.64167e7i	−0.0406828	−	0.0295578i
$823$	−3.60894e8	+	1.17261e8i	−0.647410	+	0.210356i	−0.614272	−	0.789094i	$-0.710550\pi$
$823$	−3.60894e8	+	1.17261e8i	−0.647410	+	0.210356i	−0.0331384	+	0.999451i	$0.510550\pi$
$824$	7.50919e7	+	5.45575e7i	0.134218	+	0.0975153i
$825$	3.71731e7	−	2.70078e7i	0.0662013	−	0.0480981i
$826$	3.18866e6	−	9.81370e6i	0.00565807	−	0.0174138i
$827$	5.35798e8	+	7.37462e8i	0.947293	+	1.30384i	0.952719	+	0.303852i	$0.0982728\pi$
$827$	5.35798e8	+	7.37462e8i	0.947293	+	1.30384i	−0.00542598	+	0.999985i	$0.501727\pi$
$828$	−2.91583e8	+	9.47410e7i	−0.513655	+	0.166896i
$829$	1.47671e8	−	4.79813e7i	0.259198	−	0.0842187i	−0.176535	−	0.984294i	$-0.556489\pi$
$829$	1.47671e8	−	4.79813e7i	0.259198	−	0.0842187i	0.435734	+	0.900076i	$0.356489\pi$
$830$	4.16899e8	+	1.35459e8i	0.729117	+	0.236904i
$831$	−4.00788e8			−0.698413
$832$			8.13312e7i			0.141217i
$833$	7.86091e7	+	2.55416e7i	0.136000	+	0.0441890i
$834$	2.30925e8	+	1.67777e8i	0.398083	+	0.289224i
$835$	−5.73405e8	−	7.89224e8i	−0.984922	−	1.35563i
$836$		−	2.88730e8i		−	0.494167i
$837$	−2.95831e6	−	4.81669e6i	−0.00504507	−	0.00821434i
$838$	4.95163e7			0.0841427
$839$	8.84342e7	−	6.42512e7i	0.149739	−	0.108792i	−0.510393	−	0.859941i	$-0.670500\pi$
$839$	8.84342e7	−	6.42512e7i	0.149739	−	0.108792i	0.660132	+	0.751149i	$0.270500\pi$
$840$	−9.75910e7	+	1.34322e8i	−0.164654	+	0.226626i
$841$	7.34399e7	−	2.26025e8i	0.123465	−	0.379987i
$842$	5.55530e8			0.930618
$843$		−	1.27729e9i		−	2.13209i
$844$	−1.57066e8	+	4.83401e8i	−0.261250	+	0.804044i
$845$	4.98637e7	+	1.53465e8i	0.0826446	+	0.254354i
$846$	−2.33651e8	−	7.19104e8i	−0.385884	−	1.18763i
$847$	−4.60801e7	+	3.34792e7i	−0.0758339	+	0.0550966i
$848$	−1.67528e7	−	5.44332e6i	−0.0274726	−	0.00892640i
$849$	7.21185e8	+	9.92625e8i	1.17848	+	1.62204i
$850$	−3.45809e6	+	4.75966e6i	−0.00563093	+	0.00775031i
$851$	−4.21175e7	−	1.29624e8i	−0.0683398	−	0.210328i
$852$	3.64629e8	−	5.01869e8i	0.589567	−	0.811469i
$853$	6.01528e8	+	4.37036e8i	0.969189	+	0.704157i	0.955267	−	0.295746i	$-0.0955682\pi$
$853$	6.01528e8	+	4.37036e8i	0.969189	+	0.704157i	0.0139226	+	0.999903i	$0.495568\pi$
$854$	9.20017e7	−	2.98932e7i	0.147714	−	0.0479953i
$855$	5.32089e8	+	3.86585e8i	0.851307	+	0.618510i
$856$	−2.45275e8	+	1.78202e8i	−0.391049	+	0.284114i
$857$	2.31212e7	−	7.11598e7i	0.0367340	−	0.113056i	−0.931008	−	0.364999i	$-0.881069\pi$
$857$	2.31212e7	−	7.11598e7i	0.0367340	−	0.113056i	0.967742	+	0.251943i	$0.0810695\pi$
$858$	3.84557e8	+	5.29297e8i	0.608833	+	0.837987i
$859$	−1.97614e8	+	6.42087e7i	−0.311773	+	0.101301i	−0.460724	−	0.887543i	$-0.652410\pi$
$859$	−1.97614e8	+	6.42087e7i	−0.311773	+	0.101301i	0.148951	+	0.988845i	$0.452410\pi$
$860$	4.59682e8	−	1.49360e8i	0.722707	−	0.234822i
$861$	2.46163e8	+	7.99833e7i	0.385668	+	0.125311i
$862$	2.07757e8			0.324365
$863$		−	4.94557e8i		−	0.769457i	−0.923030	−	0.384728i	$-0.874295\pi$
$863$		−	4.94557e8i		−	0.769457i	0.923030	−	0.384728i	$-0.125705\pi$
$864$	−1.04531e6	−	339643.i	−0.00162071	−	0.000526600i
$865$	−4.97300e8	−	3.61310e8i	−0.768370	−	0.558254i
$866$	5.70012e7	+	7.84554e7i	0.0877668	+	0.120801i
$867$		−	8.80682e8i		−	1.35133i
$868$	4.42916e7	+	1.83678e8i	0.0677271	+	0.280865i
$869$	3.56934e8			0.543912
$870$	−4.00257e8	+	2.90804e8i	−0.607829	+	0.441613i
$871$	−2.38131e8	+	3.27760e8i	−0.360381	+	0.496022i
$872$	3.94782e7	−	1.21501e8i	0.0595399	−	0.183245i
$873$	5.47625e8			0.823078
$874$		−	5.46899e8i		−	0.819168i
$875$	1.23092e8	−	3.78838e8i	0.183741	−	0.565496i
$876$	5.66512e7	+	1.74354e8i	0.0842746	+	0.259371i
$877$	1.21982e7	+	3.75422e7i	0.0180841	+	0.0556571i	0.959691	−	0.281056i	$-0.0906847\pi$
$877$	1.21982e7	+	3.75422e7i	0.0180841	+	0.0556571i	−0.941607	+	0.336713i	$0.890685\pi$
$878$	5.62528e8	−	4.08701e8i	0.831114	−	0.603840i
$879$	−1.12402e9	−	3.65215e8i	−1.65503	−	0.537753i
$880$	8.87189e7	+	1.22111e8i	0.130187	+	0.179187i
$881$	−4.42188e8	+	6.08619e8i	−0.646665	+	0.890058i	−0.998949	−	0.0458355i	$-0.985405\pi$
$881$	−4.42188e8	+	6.08619e8i	−0.646665	+	0.890058i	0.352284	+	0.935893i	$0.385405\pi$
$882$	−1.00546e8	−	3.09449e8i	−0.146541	−	0.451007i
$883$	−3.14676e8	+	4.33114e8i	−0.457068	+	0.629100i	−0.973898	−	0.226988i	$-0.927112\pi$
$883$	−3.14676e8	+	4.33114e8i	−0.457068	+	0.629100i	0.516829	+	0.856088i	$0.327112\pi$
$884$	−6.77714e7	−	4.92388e7i	−0.0981046	−	0.0712772i
$885$	4.05073e7	−	1.31616e7i	0.0584391	−	0.0189880i
$886$	−1.56514e7	−	1.13714e7i	−0.0225036	−	0.0163498i
$887$	4.30035e8	−	3.12439e8i	0.616216	−	0.447707i	−0.235382	−	0.971903i	$-0.575634\pi$
$887$	4.30035e8	−	3.12439e8i	0.616216	−	0.447707i	0.851598	+	0.524196i	$0.175634\pi$
$888$	2.23394e7	−	6.87535e7i	0.0319030	−	0.0981875i
$889$	−1.24514e8	−	1.71379e8i	−0.177220	−	0.243923i
$890$	−4.28630e8	+	1.39270e8i	−0.608013	+	0.197555i
$891$	6.11531e8	−	1.98699e8i	0.864541	−	0.280906i
$892$	−4.76126e8	−	1.54703e8i	−0.670853	−	0.217973i
$893$	1.34877e9			1.89401
$894$		−	7.34271e8i		−	1.02765i
$895$	1.07230e9	+	3.48412e8i	1.49571	+	0.485987i
$896$	2.97220e7	+	2.15943e7i	0.0413194	+	0.0300203i
$897$	7.28409e8	+	1.00257e9i	1.00925	+	1.38911i
$898$			2.61777e6i			0.00361496i
$899$	−4.36121e7	+	5.61324e8i	−0.0600243	+	0.772564i
$900$	2.31598e7			0.0317693
$901$	1.46781e7	−	1.06643e7i	0.0200676	−	0.0145800i
$902$	1.38306e8	−	1.90362e8i	0.188462	−	0.259395i
$903$	2.92442e8	−	9.00045e8i	0.397171	−	1.22237i
$904$	−4.54691e8			−0.615476
$905$		−	1.02397e9i		−	1.38146i
$906$	2.96859e8	−	9.13638e8i	0.399177	−	1.22854i
$907$	−1.88153e8	−	5.79074e8i	−0.252167	−	0.776090i	−0.994375	−	0.105920i	$-0.966221\pi$
$907$	−1.88153e8	−	5.79074e8i	−0.252167	−	0.776090i	0.742208	−	0.670170i	$-0.233779\pi$
$908$	925047.	+	2.84700e6i	0.00123568	+	0.00380303i
$909$	−7.03487e7	+	5.11114e7i	−0.0936623	+	0.0680496i
$910$	3.20212e8	+	1.04043e8i	0.424927	+	0.138067i
$911$	1.17876e8	+	1.62243e8i	0.155909	+	0.214590i	0.879825	−	0.475298i	$-0.157660\pi$
$911$	1.17876e8	+	1.62243e8i	0.155909	+	0.214590i	−0.723916	+	0.689888i	$0.757660\pi$
$912$	1.70504e8	−	2.34678e8i	0.224776	−	0.309378i
$913$	−2.41113e8	−	7.42070e8i	−0.316817	−	0.975062i
$914$	4.65294e8	−	6.40422e8i	0.609381	−	0.838741i
$915$	3.23034e8	+	2.34698e8i	0.421682	+	0.306370i
$916$	2.77687e8	−	9.02260e7i	0.361301	−	0.117394i
$917$	5.40755e8	+	3.92881e8i	0.701281	+	0.509511i
$918$	915860.	−	665411.i	0.00118386	−	0.000860126i
$919$	−9.29241e7	+	2.85991e8i	−0.119724	+	0.368473i	−0.992903	−	0.118927i	$-0.962055\pi$
$919$	−9.29241e7	+	2.85991e8i	−0.119724	+	0.368473i	0.873179	+	0.487400i	$0.162055\pi$
$920$	1.68047e8	+	2.31297e8i	0.215808	+	0.297034i
$921$	1.33404e9	−	4.33457e8i	1.70762	−	0.554839i
$922$	4.04970e7	−	1.31583e7i	0.0516690	−	0.0167883i
$923$	−1.19641e9	−	3.88737e8i	−1.52151	−	0.494369i
$924$	2.95532e8			0.374618
$925$			1.02958e7i			0.0130087i
$926$	−8.19659e8	−	2.66323e8i	−1.03229	−	0.335410i
$927$	3.04468e8	+	2.21209e8i	0.382210	+	0.277692i
$928$	6.43471e7	+	8.85662e7i	0.0805166	+	0.110822i
$929$		−	1.13930e9i		−	1.42099i	−0.703704	−	0.710493i	$-0.748472\pi$
$929$		−	1.13930e9i		−	1.42099i	0.703704	−	0.710493i	$-0.251528\pi$
$930$	−5.05902e8	+	5.93536e8i	−0.628952	+	0.737902i
$931$	5.80409e8			0.719259
$932$	3.29981e8	−	2.39745e8i	0.407606	−	0.296143i
$933$	−1.34349e9	+	1.84916e9i	−1.65421	+	2.27682i
$934$	1.03234e8	−	3.17723e8i	0.126702	−	0.389949i
$935$	−1.55464e8			−0.190193
$936$			3.29765e8i			0.402140i
$937$	1.71182e8	−	5.26845e8i	0.208085	−	0.640418i	−0.791488	−	0.611185i	$-0.790693\pi$
$937$	1.71182e8	−	5.26845e8i	0.208085	−	0.640418i	0.999573	−	0.0292338i	$-0.00930674\pi$
$938$	5.65514e7	+	1.74047e8i	0.0685227	+	0.210891i
$939$	−2.55062e8	−	7.85002e8i	−0.308070	−	0.948143i
$940$	−5.70426e8	+	4.14439e8i	−0.686777	+	0.498973i
$941$	−9.19905e8	−	2.98895e8i	−1.10401	−	0.358716i	−0.300367	−	0.953824i	$-0.597109\pi$
$941$	−9.19905e8	−	2.98895e8i	−1.10401	−	0.358716i	−0.803646	+	0.595108i	$0.797109\pi$
$942$	−1.16261e8	−	1.60020e8i	−0.139085	−	0.191435i
$943$	2.61974e8	−	3.60576e8i	0.312408	−	0.429993i
$944$	−2.91232e6	−	8.96319e6i	−0.00346196	−	0.0106548i
$945$	−2.67444e6	+	3.68105e6i	−0.00316911	+	0.00436191i
$946$	−6.96021e8	−	5.05689e8i	−0.822146	−	0.597324i
$947$	−1.42653e9	+	4.63507e8i	−1.67969	+	0.545765i	−0.984852	−	0.173398i	$-0.944525\pi$
$947$	−1.42653e9	+	4.63507e8i	−1.67969	+	0.545765i	−0.694841	+	0.719163i	$0.744525\pi$
$948$	2.90114e8	+	2.10780e8i	0.340521	+	0.247403i
$949$	3.00764e8	−	2.18518e8i	0.351906	−	0.255675i
$950$	−1.27664e7	+	3.92909e7i	−0.0148901	+	0.0458270i
$951$	9.02066e8	+	1.24159e9i	1.04881	+	1.44356i
$952$	−3.59880e7	+	1.16932e7i	−0.0417106	+	0.0135526i
$953$	4.11653e8	−	1.33754e8i	0.475612	−	0.154536i	−0.0613949	−	0.998114i	$-0.519555\pi$
$953$	4.11653e8	−	1.33754e8i	0.475612	−	0.154536i	0.537007	+	0.843578i	$0.319555\pi$
$954$	−6.79260e7	−	2.20705e7i	−0.0782331	−	0.0254195i
$955$	−1.18378e9			−1.35913
$956$			2.70254e8i			0.309313i
$957$	8.37531e8	+	2.72130e8i	0.955576	+	0.310486i
$958$	−4.93960e7	−	3.58883e7i	−0.0561818	−	0.0408184i
$959$	1.50380e7	+	2.06981e7i	0.0170504	+	0.0234679i
$960$			1.51642e8i			0.171399i
$961$	1.40590e8	+	8.76297e8i	0.158411	+	0.987373i
$962$	−1.46598e8			−0.164666
$963$	−9.94490e8	+	7.22539e8i	−1.11358	+	0.809063i
$964$	−3.94513e8	+	5.43001e8i	−0.440383	+	0.606135i
$965$	−2.89964e8	+	8.92418e8i	−0.322673	+	0.993085i
$966$	5.59783e8			0.620995
$967$			5.61420e8i			0.620881i	0.950593	+	0.310440i	$0.100477\pi$
$967$			5.61420e8i			0.620881i	−0.950593	+	0.310440i	$0.899523\pi$
$968$	−1.60756e7	+	4.94758e7i	−0.0177232	+	0.0545464i
$969$	9.23272e7	+	2.84154e8i	0.101475	+	0.312307i
$970$	−1.57806e8	−	4.85676e8i	−0.172905	−	0.532147i
$971$	−4.67754e8	+	3.39843e8i	−0.510928	+	0.371211i	−0.813175	−	0.582019i	$-0.802263\pi$
$971$	−4.67754e8	+	3.39843e8i	−0.510928	+	0.371211i	0.302248	+	0.953229i	$0.402263\pi$
$972$	6.18597e8	+	2.00994e8i	0.673610	+	0.218869i
$973$	−1.53687e8	−	2.11532e8i	−0.166839	−	0.229634i
$974$	3.55763e8	−	4.89666e8i	0.385021	−	0.529936i
$975$	−2.89279e7	−	8.90311e7i	−0.0312107	−	0.0960567i
$976$	5.19324e7	−	7.14788e7i	0.0558584	−	0.0768825i
$977$	7.70513e8	+	5.59811e8i	0.826221	+	0.600285i	0.918488	−	0.395449i	$-0.129411\pi$
$977$	7.70513e8	+	5.59811e8i	0.826221	+	0.600285i	−0.0922665	+	0.995734i	$0.529411\pi$
$978$	−1.55290e9	+	5.04567e8i	−1.66007	+	0.539389i
$979$	6.49004e8	+	4.71529e8i	0.691671	+	0.502528i
$980$	−2.45469e8	+	1.78344e8i	−0.260807	+	0.189487i
$981$	1.60068e8	−	4.92640e8i	0.169550	−	0.521822i
$982$	−2.86209e8	−	3.93933e8i	−0.302238	−	0.415994i
$983$	1.74930e7	−	5.68381e6i	0.0184163	−	0.00598383i	−0.299794	−	0.954004i	$-0.596918\pi$
$983$	1.74930e7	−	5.68381e6i	0.0184163	−	0.00598383i	0.318211	+	0.948020i	$0.396918\pi$
$984$	2.24830e8	−	7.30515e7i	0.235976	−	0.0766733i
$985$	−1.03288e9	−	3.35602e8i	−1.08079	−	0.351169i
$986$	−1.12757e8			−0.117628
$987$			1.38054e9i			1.43581i
$988$	−5.59452e8	−	1.81777e8i	−0.580085	−	0.188481i
$989$	−1.31837e9	−	9.57852e8i	−1.36285	−	0.990169i
$990$	3.59720e8	+	4.95111e8i	0.370731	+	0.510267i
$991$		−	1.08536e9i		−	1.11520i	−0.830110	−	0.557600i	$-0.811722\pi$
$991$		−	1.08536e9i		−	1.11520i	0.830110	−	0.557600i	$-0.188278\pi$
$992$	1.31334e8	+	1.11943e8i	0.134537	+	0.114673i
$993$	2.53814e8			0.259219
$994$	−4.59721e8	+	3.34007e8i	−0.468096	+	0.340092i
$995$	3.72319e7	−	5.12452e7i	0.0377960	−	0.0520217i
$996$	2.42239e8	−	7.45535e8i	0.245169	−	0.754553i
$997$	−4.54183e8			−0.458296			−0.229148	−	0.973392i	$-0.573594\pi$
$997$	−4.54183e8			−0.458296			−0.229148	+	0.973392i	$0.573594\pi$
$998$		−	1.23122e9i		−	1.23864i
$999$	612202.	−	1.88416e6i	0.000614042	−	0.00188983i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	62.7.f.a.15.10	✓	64
31.29	odd	10	inner	62.7.f.a.29.10	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
62.7.f.a.15.10	✓	64	1.1	even	1	trivial
62.7.f.a.29.10	yes	64	31.29	odd	10	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 62 = 2 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	62.f (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(4.57649 - 3.32502i) q^{2} +(-22.4820 + 30.9438i) q^{3} +(9.88854 - 30.4338i) q^{4} -120.991 q^{5} +216.367i q^{6} +(61.2460 - 188.496i) q^{7} +(-55.9381 - 172.160i) q^{8} +(-226.806 - 698.038i) q^{9} +(-553.716 + 402.298i) q^{10} +(1158.64 + 376.466i) q^{11} +(719.424 + 990.202i) q^{12} +(1458.90 - 2008.01i) q^{13} +(-346.459 - 1066.29i) q^{14} +(2720.13 - 3743.94i) q^{15} +(-828.433 - 601.892i) q^{16} +(1003.09 - 325.922i) q^{17} +(-3358.96 - 2440.43i) q^{18} +(5991.79 - 4353.29i) q^{19} +(-1196.43 + 3682.23i) q^{20} +(4455.84 + 6132.94i) q^{21} +(6554.27 - 2129.61i) q^{22} +(12414.8 - 4033.81i) q^{23} +(6584.88 + 2139.56i) q^{24} -986.079 q^{25} -14040.5i q^{26} +(180.456 + 58.6337i) q^{27} +(-5131.01 - 3727.90i) q^{28} +(-11108.5 - 15289.5i) q^{29} -26178.6i q^{30} +(-22672.6 - 19325.0i) q^{31} -5792.62 q^{32} +(-37697.9 + 27389.1i) q^{33} +(3506.91 - 4826.85i) q^{34} +(-7410.23 + 22806.4i) q^{35} -23486.7 q^{36} -10441.1i q^{37} +(12946.6 - 39845.6i) q^{38} +(29336.3 + 90288.0i) q^{39} +(6768.02 + 20829.8i) q^{40} +(27622.5 - 20068.9i) q^{41} +(40784.3 + 13251.6i) q^{42} +(-73377.9 - 100996. i) q^{43} +(22914.6 - 31539.2i) q^{44} +(27441.6 + 84456.6i) q^{45} +(43403.7 - 59740.1i) q^{46} +(147331. + 107042. i) q^{47} +(37249.7 - 12103.2i) q^{48} +(63400.5 + 46063.2i) q^{49} +(-4512.78 + 3278.73i) q^{50} +(-12466.1 + 38366.7i) q^{51} +(-46684.8 - 64256.2i) q^{52} +(16360.2 - 5315.74i) q^{53} +(1020.81 - 331.682i) q^{54} +(-140186. - 45549.1i) q^{55} -35877.3 q^{56} +283280. i q^{57} +(-101676. - 33036.4i) q^{58} +(7445.84 + 5409.72i) q^{59} +(-87044.1 - 119806. i) q^{60} +86281.9i q^{61} +(-168017. - 13054.1i) q^{62} -145468. q^{63} +(-26509.9 + 19260.5i) q^{64} +(-176515. + 242951. i) q^{65} +(-81454.8 + 250692. i) q^{66} -163227. q^{67} -33750.6i q^{68} +(-154288. + 474849. i) q^{69} +(41918.6 + 129012. i) q^{70} +(-156621. - 482029. i) q^{71} +(-107487. + 78093.8i) q^{72} +(142451. + 46285.3i) q^{73} +(-34716.9 - 47783.7i) q^{74} +(22169.0 - 30513.1i) q^{75} +(-73237.2 - 225401. i) q^{76} +(141924. - 195342. i) q^{77} +(434466. + 315658. i) q^{78} +(278645. - 90537.3i) q^{79} +(100233. + 72823.8i) q^{80} +(426999. - 310233. i) q^{81} +(59684.7 - 183691. i) q^{82} +(-376456. - 518147. i) q^{83} +(230711. - 74962.4i) q^{84} +(-121365. + 39433.8i) q^{85} +(-671627. - 218225. i) q^{86} +722856. q^{87} -220530. i q^{88} +(626258. + 203484. i) q^{89} +(406406. + 295271. i) q^{90} +(-289148. - 397979. i) q^{91} -417718. i q^{92} +(1.10772e6 - 267112. i) q^{93} +1.03018e6 q^{94} +(-724956. + 526711. i) q^{95} +(130230. - 179246. i) q^{96} +(-230565. + 709605. i) q^{97} +443312. q^{98} -894161. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 512 q^{4} - 288 q^{5} - 692 q^{7} + 3248 q^{9} + 1344 q^{10} + 3200 q^{11} - 3600 q^{13} + 4560 q^{14} + 9520 q^{15} - 16384 q^{16} - 1400 q^{17} - 11200 q^{18} + 2912 q^{19} - 9216 q^{20} + 4860 q^{21}+ \cdots + 13577088 q^{98}+O(q^{100}) \) 64 * q - 512 * q^4 - 288 * q^5 - 692 * q^7 + 3248 * q^9 + 1344 * q^10 + 3200 * q^11 - 3600 * q^13 + 4560 * q^14 + 9520 * q^15 - 16384 * q^16 - 1400 * q^17 - 11200 * q^18 + 2912 * q^19 - 9216 * q^20 + 4860 * q^21 + 6720 * q^22 - 26240 * q^23 + 241592 * q^25 - 206100 * q^27 + 16896 * q^28 - 48160 * q^29 + 142924 * q^31 + 291360 * q^33 + 123840 * q^34 + 16728 * q^35 - 518144 * q^36 - 89856 * q^38 - 169400 * q^39 - 64512 * q^40 - 291056 * q^41 + 220320 * q^42 + 145600 * q^43 - 44412 * q^45 - 213120 * q^46 + 596760 * q^47 - 163840 * q^48 + 481596 * q^49 - 295744 * q^50 + 1117652 * q^51 + 115200 * q^52 - 1276880 * q^53 + 290880 * q^55 - 97280 * q^56 - 367200 * q^58 + 469780 * q^59 - 304640 * q^60 - 963152 * q^62 - 1359328 * q^63 - 524288 * q^64 + 934760 * q^65 - 789792 * q^66 + 1470992 * q^67 - 933024 * q^69 + 515232 * q^70 - 906672 * q^71 - 358400 * q^72 + 1236840 * q^73 - 126400 * q^74 - 2881620 * q^75 - 139776 * q^76 + 3063520 * q^77 + 2374288 * q^78 + 4375280 * q^79 + 442368 * q^80 - 3676208 * q^81 + 1386144 * q^82 + 4922820 * q^83 - 601600 * q^84 - 1012320 * q^85 - 2054800 * q^86 - 5911600 * q^87 - 1219900 * q^89 - 2696992 * q^90 + 163640 * q^91 - 248320 * q^93 + 290592 * q^94 + 2034328 * q^95 - 1078884 * q^97 + 13577088 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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