LMFDB - Embedded newform 48.7.l.a.19.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,7,Mod(19,48)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(48, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

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

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

chi := DirichletCharacter("48.19");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	48.l (of order $4$, 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:	$11.0425960138$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			19.11
Character	$\chi$	$=$	48.19
Dual form			48.7.l.a.43.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.382617 + 7.99085i) q^{2} +(-11.0227 + 11.0227i) q^{3} +(-63.7072 - 6.11486i) q^{4} +(122.335 - 122.335i) q^{5} +(-83.8632 - 92.2982i) q^{6} +392.292 q^{7} +(73.2383 - 506.735i) q^{8} -243.000i q^{9} +O(q^{10})$	\(q+(-0.382617 + 7.99085i) q^{2} +(-11.0227 + 11.0227i) q^{3} +(-63.7072 - 6.11486i) q^{4} +(122.335 - 122.335i) q^{5} +(-83.8632 - 92.2982i) q^{6} +392.292 q^{7} +(73.2383 - 506.735i) q^{8} -243.000i q^{9} +(930.754 + 1024.37i) q^{10} +(469.716 + 469.716i) q^{11} +(769.628 - 634.823i) q^{12} +(284.024 + 284.024i) q^{13} +(-150.098 + 3134.75i) q^{14} +2696.93i q^{15} +(4021.22 + 779.121i) q^{16} -4543.37 q^{17} +(1941.78 + 92.9758i) q^{18} +(2142.85 - 2142.85i) q^{19} +(-8541.70 + 7045.57i) q^{20} +(-4324.12 + 4324.12i) q^{21} +(-3933.15 + 3573.71i) q^{22} +23403.6 q^{23} +(4778.30 + 6392.87i) q^{24} -14306.8i q^{25} +(-2378.26 + 2160.92i) q^{26} +(2678.52 + 2678.52i) q^{27} +(-24991.8 - 2398.81i) q^{28} +(29793.3 + 29793.3i) q^{29} +(-21550.7 - 1031.89i) q^{30} +6957.76i q^{31} +(-7764.42 + 31834.8i) q^{32} -10355.1 q^{33} +(1738.37 - 36305.4i) q^{34} +(47991.2 - 47991.2i) q^{35} +(-1485.91 + 15480.9i) q^{36} +(42880.6 - 42880.6i) q^{37} +(16303.3 + 17943.1i) q^{38} -6261.42 q^{39} +(-53031.9 - 70951.1i) q^{40} -51071.1i q^{41} +(-32898.9 - 36207.9i) q^{42} +(-56561.8 - 56561.8i) q^{43} +(-27052.1 - 32796.6i) q^{44} +(-29727.5 - 29727.5i) q^{45} +(-8954.62 + 187015. i) q^{46} -62130.0i q^{47} +(-52912.7 + 35736.7i) q^{48} +36244.2 q^{49} +(114324. + 5474.03i) q^{50} +(50080.3 - 50080.3i) q^{51} +(-16357.6 - 19831.1i) q^{52} +(-175135. + 175135. i) q^{53} +(-22428.5 + 20378.8i) q^{54} +114926. q^{55} +(28730.8 - 198788. i) q^{56} +47240.0i q^{57} +(-249473. + 226675. i) q^{58} +(147653. + 147653. i) q^{59} +(16491.4 - 171814. i) q^{60} +(-189596. - 189596. i) q^{61} +(-55598.4 - 2662.15i) q^{62} -95327.0i q^{63} +(-251416. - 74224.8i) q^{64} +69492.2 q^{65} +(3962.03 - 82745.9i) q^{66} +(59250.9 - 59250.9i) q^{67} +(289446. + 27782.1i) q^{68} +(-257971. + 257971. i) q^{69} +(365128. + 401852. i) q^{70} +575576. q^{71} +(-123137. - 17796.9i) q^{72} +377493. i q^{73} +(326245. + 359059. i) q^{74} +(157700. + 157700. i) q^{75} +(-149618. + 123412. i) q^{76} +(184266. + 184266. i) q^{77} +(2395.72 - 50034.0i) q^{78} -605647. i q^{79} +(587250. - 396622. i) q^{80} -59049.0 q^{81} +(408101. + 19540.6i) q^{82} +(-644721. + 644721. i) q^{83} +(301919. - 249036. i) q^{84} +(-555815. + 555815. i) q^{85} +(473618. - 430335. i) q^{86} -656806. q^{87} +(272423. - 203620. i) q^{88} -651468. i q^{89} +(248922. - 226173. i) q^{90} +(111420. + 111420. i) q^{91} +(-1.49098e6 - 143110. i) q^{92} +(-76693.3 - 76693.3i) q^{93} +(496471. + 23772.0i) q^{94} -524293. i q^{95} +(-265321. - 436491. i) q^{96} -463699. q^{97} +(-13867.6 + 289622. i) q^{98} +(114141. - 114141. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 180 q^{4} - 1932 q^{8}+O(q^{10}) $ 48 * q - 180 * q^4 - 1932 * q^8	\( 48 q - 180 q^{4} - 1932 q^{8} + 744 q^{10} - 2720 q^{11} - 1944 q^{12} - 15388 q^{14} + 3744 q^{16} + 4860 q^{18} - 3936 q^{19} - 14000 q^{20} - 41184 q^{22} + 26240 q^{23} + 18468 q^{24} - 5300 q^{26} - 96120 q^{28} + 66400 q^{29} - 33048 q^{30} - 52960 q^{32} + 122208 q^{34} + 162336 q^{35} + 32076 q^{36} - 7200 q^{37} + 16968 q^{38} - 309072 q^{40} - 231660 q^{42} + 340704 q^{43} - 193192 q^{44} - 450264 q^{46} + 299376 q^{48} + 806736 q^{49} + 537764 q^{50} + 80352 q^{51} + 1126224 q^{52} + 443680 q^{53} + 78732 q^{54} + 232704 q^{55} - 420448 q^{56} - 1295664 q^{58} - 886144 q^{59} - 627912 q^{60} - 326496 q^{61} - 719652 q^{62} - 192024 q^{64} - 372832 q^{65} + 775656 q^{66} - 962112 q^{67} + 3197632 q^{68} + 541728 q^{69} + 642816 q^{70} + 534016 q^{71} + 82620 q^{72} - 4894836 q^{74} - 1073088 q^{75} - 3162552 q^{76} - 932960 q^{77} - 337284 q^{78} + 4668072 q^{80} - 2834352 q^{81} + 5077560 q^{82} - 2497760 q^{83} + 1312200 q^{84} - 372000 q^{85} + 4142928 q^{86} - 2794272 q^{88} - 507384 q^{90} + 775008 q^{91} - 9470992 q^{92} - 5050728 q^{94} + 1879200 q^{96} + 12708584 q^{98} - 660960 q^{99}+O(q^{100}) \) 48 * q - 180 * q^4 - 1932 * q^8 + 744 * q^10 - 2720 * q^11 - 1944 * q^12 - 15388 * q^14 + 3744 * q^16 + 4860 * q^18 - 3936 * q^19 - 14000 * q^20 - 41184 * q^22 + 26240 * q^23 + 18468 * q^24 - 5300 * q^26 - 96120 * q^28 + 66400 * q^29 - 33048 * q^30 - 52960 * q^32 + 122208 * q^34 + 162336 * q^35 + 32076 * q^36 - 7200 * q^37 + 16968 * q^38 - 309072 * q^40 - 231660 * q^42 + 340704 * q^43 - 193192 * q^44 - 450264 * q^46 + 299376 * q^48 + 806736 * q^49 + 537764 * q^50 + 80352 * q^51 + 1126224 * q^52 + 443680 * q^53 + 78732 * q^54 + 232704 * q^55 - 420448 * q^56 - 1295664 * q^58 - 886144 * q^59 - 627912 * q^60 - 326496 * q^61 - 719652 * q^62 - 192024 * q^64 - 372832 * q^65 + 775656 * q^66 - 962112 * q^67 + 3197632 * q^68 + 541728 * q^69 + 642816 * q^70 + 534016 * q^71 + 82620 * q^72 - 4894836 * q^74 - 1073088 * q^75 - 3162552 * q^76 - 932960 * q^77 - 337284 * q^78 + 4668072 * q^80 - 2834352 * q^81 + 5077560 * q^82 - 2497760 * q^83 + 1312200 * q^84 - 372000 * q^85 + 4142928 * q^86 - 2794272 * q^88 - 507384 * q^90 + 775008 * q^91 - 9470992 * q^92 - 5050728 * q^94 + 1879200 * q^96 + 12708584 * q^98 - 660960 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

$n$	$17$	$31$	$37$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.382617	+	7.99085i	−0.0478271	+	0.998856i
$2$	−0.382617	+	7.99085i	−0.0478271	+	0.998856i
$3$	−11.0227	+	11.0227i	−0.408248	+	0.408248i
$3$	−11.0227	+	11.0227i	−0.408248	+	0.408248i
$4$	−63.7072	−	6.11486i	−0.995425	−	0.0955447i
$5$	122.335	−	122.335i	0.978682	−	0.978682i	−0.0210956	−	0.999777i	$-0.506715\pi$
$5$	122.335	−	122.335i	0.978682	−	0.978682i	0.999777	+	0.0210956i	$0.00671545\pi$
$6$	−83.8632	−	92.2982i	−0.388256	−	0.427306i
$7$	392.292			1.14371			0.571855	−	0.820355i	$-0.306224\pi$
$7$	392.292			1.14371			0.571855	+	0.820355i	$0.306224\pi$
$8$	73.2383	−	506.735i	0.143044	−	0.989716i
$9$		−	243.000i		−	0.333333i
$10$	930.754	+	1024.37i	0.930754	+	1.02437i
$11$	469.716	+	469.716i	0.352905	+	0.352905i	0.861189	−	0.508285i	$-0.169720\pi$
$11$	469.716	+	469.716i	0.352905	+	0.352905i	−0.508285	+	0.861189i	$0.669720\pi$
$12$	769.628	−	634.823i	0.445387	−	0.367375i
$13$	284.024	+	284.024i	0.129278	+	0.129278i	0.768785	−	0.639507i	$-0.220862\pi$
$13$	284.024	+	284.024i	0.129278	+	0.129278i	−0.639507	+	0.768785i	$0.720862\pi$
$14$	−150.098	+	3134.75i	−0.0547003	+	1.14240i
$15$			2696.93i			0.799090i
$16$	4021.22	+	779.121i	0.981742	+	0.190215i
$17$	−4543.37			−0.924766			−0.462383	−	0.886680i	$-0.653005\pi$
$17$	−4543.37			−0.924766			−0.462383	+	0.886680i	$0.653005\pi$
$18$	1941.78	+	92.9758i	0.332952	+	0.0159424i
$19$	2142.85	−	2142.85i	0.312415	−	0.312415i	−0.533430	−	0.845844i	$-0.679097\pi$
$19$	2142.85	−	2142.85i	0.312415	−	0.312415i	0.845844	+	0.533430i	$0.179097\pi$
$20$	−8541.70	+	7045.57i	−1.06771	+	0.880697i
$21$	−4324.12	+	4324.12i	−0.466917	+	0.466917i
$22$	−3933.15	+	3573.71i	−0.369379	+	0.335622i
$23$	23403.6			1.92353			0.961766	−	0.273871i	$-0.0883042\pi$
$23$	23403.6			1.92353			0.961766	+	0.273871i	$0.0883042\pi$
$24$	4778.30	+	6392.87i	0.345653	+	0.462447i
$25$		−	14306.8i		−	0.915636i
$26$	−2378.26	+	2160.92i	−0.135313	+	0.122947i
$27$	2678.52	+	2678.52i	0.136083	+	0.136083i
$28$	−24991.8	−	2398.81i	−1.13848	−	0.109275i
$29$	29793.3	+	29793.3i	1.22159	+	1.22159i	0.967067	+	0.254522i	$0.0819183\pi$
$29$	29793.3	+	29793.3i	1.22159	+	1.22159i	0.254522	+	0.967067i	$0.418082\pi$
$30$	−21550.7	−	1031.89i	−0.798176	−	0.0382182i
$31$			6957.76i			0.233552i	0.993158	+	0.116776i	$0.0372560\pi$
$31$			6957.76i			0.233552i	−0.993158	+	0.116776i	$0.962744\pi$
$32$	−7764.42	+	31834.8i	−0.236951	+	0.971522i
$33$	−10355.1			−0.288145
$34$	1738.37	−	36305.4i	0.0442289	−	0.923708i
$35$	47991.2	−	47991.2i	1.11933	−	1.11933i
$36$	−1485.91	+	15480.9i	−0.0318482	+	0.331808i
$37$	42880.6	−	42880.6i	0.846556	−	0.846556i	−0.143146	−	0.989702i	$-0.545722\pi$
$37$	42880.6	−	42880.6i	0.846556	−	0.846556i	0.989702	+	0.143146i	$0.0457218\pi$
$38$	16303.3	+	17943.1i	0.297115	+	0.326999i
$39$	−6261.42			−0.105555
$40$	−53031.9	−	70951.1i	−0.828623	−	1.10861i
$41$		−	51071.1i		−	0.741009i	−0.928831	−	0.370504i	$-0.879185\pi$
$41$		−	51071.1i		−	0.741009i	0.928831	−	0.370504i	$-0.120815\pi$
$42$	−32898.9	−	36207.9i	−0.444052	−	0.488714i
$43$	−56561.8	−	56561.8i	−0.711406	−	0.711406i	0.255423	−	0.966829i	$-0.417785\pi$
$43$	−56561.8	−	56561.8i	−0.711406	−	0.711406i	−0.966829	+	0.255423i	$0.917785\pi$
$44$	−27052.1	−	32796.6i	−0.317572	−	0.385008i
$45$	−29727.5	−	29727.5i	−0.326227	−	0.326227i
$46$	−8954.62	+	187015.i	−0.0919970	+	1.92133i
$47$		−	62130.0i		−	0.598422i	−0.954187	−	0.299211i	$-0.903277\pi$
$47$		−	62130.0i		−	0.598422i	0.954187	−	0.299211i	$-0.0967234\pi$
$48$	−52912.7	+	35736.7i	−0.478450	+	0.323140i
$49$	36244.2			0.308070
$50$	114324.	+	5474.03i	0.914588	+	0.0437922i
$51$	50080.3	−	50080.3i	0.377534	−	0.377534i
$52$	−16357.6	−	19831.1i	−0.116335	−	0.141038i
$53$	−175135.	+	175135.i	−1.17638	+	1.17638i	−0.195715	+	0.980661i	$0.562703\pi$
$53$	−175135.	+	175135.i	−1.17638	+	1.17638i	−0.980661	+	0.195715i	$0.937297\pi$
$54$	−22428.5	+	20378.8i	−0.142435	+	0.129419i
$55$	114926.			0.690763
$56$	28730.8	−	198788.i	0.163600	−	1.13195i
$57$			47240.0i			0.255085i
$58$	−249473.	+	226675.i	−1.27862	+	1.16177i
$59$	147653.	+	147653.i	0.718929	+	0.718929i	0.968386	−	0.249457i	$-0.0802522\pi$
$59$	147653.	+	147653.i	0.718929	+	0.718929i	−0.249457	+	0.968386i	$0.580252\pi$
$60$	16491.4	−	171814.i	0.0763488	−	0.795435i
$61$	−189596.	−	189596.i	−0.835294	−	0.835294i	0.152941	−	0.988235i	$-0.451126\pi$
$61$	−189596.	−	189596.i	−0.835294	−	0.835294i	−0.988235	+	0.152941i	$0.951126\pi$
$62$	−55598.4	−	2662.15i	−0.233285	−	0.0111701i
$63$		−	95327.0i		−	0.381236i
$64$	−251416.	−	74224.8i	−0.959077	−	0.283145i
$65$	69492.2			0.253044
$66$	3962.03	−	82745.9i	0.0137812	−	0.287816i
$67$	59250.9	−	59250.9i	0.197002	−	0.197002i	−0.601711	−	0.798714i	$-0.705514\pi$
$67$	59250.9	−	59250.9i	0.197002	−	0.197002i	0.798714	+	0.601711i	$0.205514\pi$
$68$	289446.	+	27782.1i	0.920535	+	0.0883565i
$69$	−257971.	+	257971.i	−0.785279	+	0.785279i
$70$	365128.	+	401852.i	1.06451	+	1.17158i
$71$	575576.			1.60815			0.804077	−	0.594525i	$-0.202660\pi$
$71$	575576.			1.60815			0.804077	+	0.594525i	$0.202660\pi$
$72$	−123137.	−	17796.9i	−0.329905	−	0.0476812i
$73$			377493.i			0.970377i	0.874409	+	0.485189i	$0.161249\pi$
$73$			377493.i			0.970377i	−0.874409	+	0.485189i	$0.838751\pi$
$74$	326245.	+	359059.i	0.805099	+	0.886075i
$75$	157700.	+	157700.i	0.373807	+	0.373807i
$76$	−149618.	+	123412.i	−0.340835	+	0.281136i
$77$	184266.	+	184266.i	0.403620	+	0.403620i
$78$	2395.72	−	50034.0i	0.00504839	−	0.105434i
$79$		−	605647.i		−	1.22840i	−0.789152	−	0.614198i	$-0.789480\pi$
$79$		−	605647.i		−	1.22840i	0.789152	−	0.614198i	$-0.210520\pi$
$80$	587250.	−	396622.i	1.14697	−	0.774653i
$81$	−59049.0			−0.111111
$82$	408101.	+	19540.6i	0.740161	+	0.0354403i
$83$	−644721.	+	644721.i	−1.12755	+	1.12755i	−0.136980	+	0.990574i	$0.543740\pi$
$83$	−644721.	+	644721.i	−1.12755	+	1.12755i	−0.990574	+	0.136980i	$0.956260\pi$
$84$	301919.	−	249036.i	0.509393	−	0.420170i
$85$	−555815.	+	555815.i	−0.905052	+	0.905052i
$86$	473618.	−	430335.i	0.744617	−	0.676568i
$87$	−656806.			−0.997423
$88$	272423.	−	203620.i	0.399756	−	0.298795i
$89$		−	651468.i		−	0.924109i	−0.886852	−	0.462054i	$-0.847113\pi$
$89$		−	651468.i		−	0.924109i	0.886852	−	0.462054i	$-0.152887\pi$
$90$	248922.	−	226173.i	0.341456	−	0.310251i
$91$	111420.	+	111420.i	0.147856	+	0.147856i
$92$	−1.49098e6	−	143110.i	−1.91473	−	0.183783i
$93$	−76693.3	−	76693.3i	−0.0953474	−	0.0953474i
$94$	496471.	+	23772.0i	0.597737	+	0.0286208i
$95$		−	524293.i		−	0.611509i
$96$	−265321.	−	436491.i	−0.299887	−	0.493357i
$97$	−463699.			−0.508067			−0.254034	−	0.967195i	$-0.581757\pi$
$97$	−463699.			−0.508067			−0.254034	+	0.967195i	$0.581757\pi$
$98$	−13867.6	+	289622.i	−0.0147341	+	0.307718i
$99$	114141.	−	114141.i	0.117635	−	0.117635i
$100$	−87484.2	+	911447.i	−0.0874842	+	0.911447i
$101$	−942349.	+	942349.i	−0.914635	+	0.914635i	−0.996633	−	0.0819976i	$-0.973870\pi$
$101$	−942349.	+	942349.i	−0.914635	+	0.914635i	0.0819976	+	0.996633i	$0.473870\pi$
$102$	381022.	+	419345.i	0.359046	+	0.395158i
$103$	96429.5			0.0882467			0.0441233	−	0.999026i	$-0.485951\pi$
$103$	96429.5			0.0882467			0.0441233	+	0.999026i	$0.485951\pi$
$104$	164726.	−	123123.i	0.146441	−	0.109456i
$105$			1.05798e6i			0.913927i
$106$	−1.33247e6	−	1.46649e6i	−1.11877	−	1.23129i
$107$	753107.	+	753107.i	0.614759	+	0.614759i	0.944182	−	0.329423i	$-0.106854\pi$
$107$	753107.	+	753107.i	0.614759	+	0.614759i	−0.329423	+	0.944182i	$0.606854\pi$
$108$	−154262.	−	187020.i	−0.122458	−	0.148462i
$109$	−1.35137e6	−	1.35137e6i	−1.04351	−	1.04351i	−0.999010	−	0.0444959i	$-0.985832\pi$
$109$	−1.35137e6	−	1.35137e6i	−1.04351	−	1.04351i	−0.0444959	−	0.999010i	$-0.514168\pi$
$110$	−43972.5	+	918353.i	−0.0330372	+	0.689972i
$111$			945320.i			0.691210i
$112$	1.57749e6	+	305643.i	1.12283	+	0.217551i
$113$	−1.17677e6			−0.815562			−0.407781	−	0.913080i	$-0.633697\pi$
$113$	−1.17677e6			−0.815562			−0.407781	+	0.913080i	$0.633697\pi$
$114$	−377488.	−	18074.8i	−0.254794	−	0.0122000i
$115$	2.86309e6	−	2.86309e6i	1.88253	−	1.88253i
$116$	−1.71587e6	−	2.08023e6i	−1.09928	−	1.33272i
$117$	69017.8	−	69017.8i	0.0430927	−	0.0430927i
$118$	−1.23637e6	+	1.12338e6i	−0.752490	+	0.683722i
$119$	−1.78233e6			−1.05766
$120$	1.36663e6	+	197519.i	0.790873	+	0.114305i
$121$		−	1.33029e6i		−	0.750917i
$122$	1.58757e6	−	1.44249e6i	0.874288	−	0.794389i
$123$	562941.	+	562941.i	0.302516	+	0.302516i
$124$	42545.7	−	443259.i	0.0223147	−	0.232484i
$125$	161260.	+	161260.i	0.0825653	+	0.0825653i
$126$	761743.	+	36473.7i	0.380800	+	0.0182334i
$127$		−	2.87183e6i		−	1.40200i	−0.713163	−	0.700998i	$-0.752738\pi$
$127$		−	2.87183e6i		−	1.40200i	0.713163	−	0.700998i	$-0.247262\pi$
$128$	689315.	−	1.98063e6i	0.328691	−	0.944437i
$129$	1.24693e6			0.580861
$130$	−26588.9	+	555302.i	−0.0121024	+	0.252754i
$131$	−1.89500e6	+	1.89500e6i	−0.842935	+	0.842935i	−0.989240	−	0.146304i	$-0.953262\pi$
$131$	−1.89500e6	+	1.89500e6i	−0.842935	+	0.842935i	0.146304	+	0.989240i	$0.453262\pi$
$132$	659693.	+	63319.9i	0.286827	+	0.0275308i
$133$	840624.	−	840624.i	0.357311	−	0.357311i
$134$	450795.	+	496135.i	0.187355	+	0.206199i
$135$	655354.			0.266363
$136$	−332749.	+	2.30229e6i	−0.132282	+	0.915256i
$137$		−	679679.i		−	0.264327i	−0.991228	−	0.132164i	$-0.957808\pi$
$137$		−	679679.i		−	0.264327i	0.991228	−	0.132164i	$-0.0421925\pi$
$138$	−1.96270e6	−	2.16011e6i	−0.746823	−	0.821938i
$139$	2.58234e6	+	2.58234e6i	0.961545	+	0.961545i	0.999287	−	0.0377425i	$-0.0120167\pi$
$139$	2.58234e6	+	2.58234e6i	0.961545	+	0.961545i	−0.0377425	+	0.999287i	$0.512017\pi$
$140$	−3.35084e6	+	2.76392e6i	−1.22115	+	1.00726i
$141$	684840.	+	684840.i	0.244305	+	0.244305i
$142$	−220225.	+	4.59934e6i	−0.0769133	+	1.60631i
$143$			266821.i			0.0912456i
$144$	189327.	−	977156.i	0.0634051	−	0.327247i
$145$	7.28955e6			2.39109
$146$	−3.01649e6	−	144435.i	−0.969267	−	0.0464103i
$147$	−399509.	+	399509.i	−0.125769	+	0.125769i
$148$	−2.99401e6	+	2.46959e6i	−0.923567	+	0.761799i
$149$	767862.	−	767862.i	0.232126	−	0.232126i	−0.581453	−	0.813580i	$-0.697516\pi$
$149$	767862.	−	767862.i	0.232126	−	0.232126i	0.813580	+	0.581453i	$0.197516\pi$
$150$	−1.32049e6	+	1.19982e6i	−0.391257	+	0.355501i
$151$	−3.97625e6			−1.15490			−0.577448	−	0.816428i	$-0.695951\pi$
$151$	−3.97625e6			−1.15490			−0.577448	+	0.816428i	$0.695951\pi$
$152$	−928919.	−	1.24280e6i	−0.264513	−	0.353891i
$153$			1.10404e6i			0.308255i
$154$	−1.54294e6	+	1.40194e6i	−0.422462	+	0.383854i
$155$	851179.	+	851179.i	0.228573	+	0.228573i
$156$	398898.	+	38287.7i	0.105072	+	0.0100852i
$157$	2.77632e6	+	2.77632e6i	0.717416	+	0.717416i	0.968075	−	0.250659i	$-0.0806473\pi$
$157$	2.77632e6	+	2.77632e6i	0.717416	+	0.717416i	−0.250659	+	0.968075i	$0.580647\pi$
$158$	4.83963e6	+	231731.i	1.22699	+	0.0587506i
$159$		−	3.86093e6i		−	0.960507i
$160$	2.94466e6	+	4.84438e6i	0.718910	+	1.18271i
$161$	9.18106e6			2.19996
$162$	22593.1	−	471851.i	0.00531412	−	0.110984i
$163$	−4.29755e6	+	4.29755e6i	−0.992335	+	0.992335i	−0.999971	−	0.00763542i	$-0.997570\pi$
$163$	−4.29755e6	+	4.29755e6i	−0.992335	+	0.992335i	0.00763542	+	0.999971i	$0.497570\pi$
$164$	−312292.	+	3.25359e6i	−0.0707994	+	0.737619i
$165$	−1.26679e6	+	1.26679e6i	−0.282003	+	0.282003i
$166$	−4.90518e6	−	5.39854e6i	−1.07234	−	1.18019i
$167$	−1.20746e6			−0.259254			−0.129627	−	0.991563i	$-0.541378\pi$
$167$	−1.20746e6			−0.259254			−0.129627	+	0.991563i	$0.541378\pi$
$168$	1.87449e6	+	2.50787e6i	0.395326	+	0.528905i
$169$		−	4.66547e6i		−	0.966574i
$170$	−4.22877e6	−	4.65409e6i	−0.860730	−	0.947302i
$171$	−520713.	−	520713.i	−0.104138	−	0.104138i
$172$	3.25753e6	+	3.94926e6i	0.640181	+	0.776123i
$173$	−4.65046e6	−	4.65046e6i	−0.898169	−	0.898169i	0.0971053	−	0.995274i	$-0.469042\pi$
$173$	−4.65046e6	−	4.65046e6i	−0.898169	−	0.898169i	−0.995274	+	0.0971053i	$0.969042\pi$
$174$	251305.	−	5.24844e6i	0.0477039	−	0.996282i
$175$		−	5.61245e6i		−	1.04722i
$176$	1.52286e6	+	2.25480e6i	0.279334	+	0.413589i
$177$	−3.25507e6			−0.587003
$178$	5.20578e6	+	249262.i	0.923051	+	0.0441974i
$179$	−4.55728e6	+	4.55728e6i	−0.794597	+	0.794597i	−0.982238	−	0.187641i	$-0.939916\pi$
$179$	−4.55728e6	+	4.55728e6i	−0.794597	+	0.794597i	0.187641	+	0.982238i	$0.439916\pi$
$180$	1.71207e6	+	2.07563e6i	0.293566	+	0.355904i
$181$	−7.25174e6	+	7.25174e6i	−1.22294	+	1.22294i	−0.256363	+	0.966580i	$0.582524\pi$
$181$	−7.25174e6	+	7.25174e6i	−1.22294	+	1.22294i	−0.966580	+	0.256363i	$0.917476\pi$
$182$	−932974.	+	847711.i	−0.154759	+	0.140616i
$183$	4.17972e6			0.682015
$184$	1.71404e6	−	1.18594e7i	0.275149	−	1.90375i
$185$		−	1.04916e7i		−	1.65702i
$186$	642189.	−	583500.i	0.0997984	−	0.0906781i
$187$	−2.13410e6	−	2.13410e6i	−0.326354	−	0.326354i
$188$	−379916.	+	3.95813e6i	−0.0571760	+	0.595684i
$189$	1.05076e6	+	1.05076e6i	0.155639	+	0.155639i
$190$	4.18954e6	+	200603.i	0.610809	+	0.0292467i
$191$			1.78504e6i			0.256182i	0.991762	+	0.128091i	$0.0408850\pi$
$191$			1.78504e6i			0.256182i	−0.991762	+	0.128091i	$0.959115\pi$
$192$	3.58945e6	−	1.95313e6i	0.507135	−	0.275948i
$193$	7.57123e6			1.05316			0.526580	−	0.850125i	$-0.323474\pi$
$193$	7.57123e6			1.05316			0.526580	+	0.850125i	$0.323474\pi$
$194$	177419.	−	3.70535e6i	0.0242994	−	0.507486i
$195$	−765992.	+	765992.i	−0.103305	+	0.103305i
$196$	−2.30902e6	−	221628.i	−0.306661	−	0.0294345i
$197$	4.33545e6	−	4.33545e6i	0.567069	−	0.567069i	−0.364237	−	0.931306i	$-0.618670\pi$
$197$	4.33545e6	−	4.33545e6i	0.567069	−	0.567069i	0.931306	+	0.364237i	$0.118670\pi$
$198$	868411.	+	955755.i	0.111874	+	0.123126i
$199$	−982494.			−0.124673			−0.0623363	−	0.998055i	$-0.519855\pi$
$199$	−982494.			−0.124673			−0.0623363	+	0.998055i	$0.519855\pi$
$200$	−7.24976e6	−	1.04781e6i	−0.906220	−	0.130976i
$201$			1.30621e6i			0.160852i
$202$	−7.16961e6	−	7.89073e6i	−0.869844	−	0.957333i
$203$	1.16877e7	+	1.16877e7i	1.39714	+	1.39714i
$204$	−3.49671e6	+	2.88424e6i	−0.411878	+	0.339736i
$205$	−6.24779e6	−	6.24779e6i	−0.725212	−	0.725212i
$206$	−36895.5	+	770553.i	−0.00422058	+	0.0881457i
$207$		−	5.68708e6i		−	0.641178i
$208$	920832.	+	1.36341e6i	0.102327	+	0.151508i
$209$	2.01306e6			0.220505
$210$	−8.45419e6	−	404803.i	−0.912881	−	0.0437105i
$211$	−1.85086e6	+	1.85086e6i	−0.197027	+	0.197027i	−0.798724	−	0.601697i	$-0.794491\pi$
$211$	−1.85086e6	+	1.85086e6i	−0.197027	+	0.197027i	0.601697	+	0.798724i	$0.294491\pi$
$212$	1.22283e7	−	1.00865e7i	1.28339	−	1.05860i
$213$	−6.34441e6	+	6.34441e6i	−0.656526	+	0.656526i
$214$	−6.30611e6	+	5.72981e6i	−0.643458	+	0.584654i
$215$	−1.38390e7			−1.39248
$216$	1.55347e6	−	1.16113e6i	0.154149	−	0.115218i
$217$			2.72947e6i			0.267116i
$218$	1.13156e7	−	1.02815e7i	1.09222	−	0.992404i
$219$	−4.16100e6	−	4.16100e6i	−0.396155	−	0.396155i
$220$	−7.32159e6	−	702754.i	−0.687603	−	0.0659987i
$221$	−1.29043e6	−	1.29043e6i	−0.119552	−	0.119552i
$222$	−7.55391e6	−	361695.i	−0.690419	−	0.0330585i
$223$			1.05662e7i			0.952809i	0.879226	+	0.476405i	$0.158060\pi$
$223$			1.05662e7i			0.952809i	−0.879226	+	0.476405i	$0.841940\pi$
$224$	−3.04592e6	+	1.24886e7i	−0.271003	+	1.11114i
$225$	−3.47656e6			−0.305212
$226$	450252.	−	9.40340e6i	0.0390059	−	0.814628i
$227$	−2.21227e6	+	2.21227e6i	−0.189130	+	0.189130i	−0.795320	−	0.606190i	$-0.792697\pi$
$227$	−2.21227e6	+	2.21227e6i	−0.189130	+	0.189130i	0.606190	+	0.795320i	$0.292697\pi$
$228$	288866.	−	3.00953e6i	0.0243721	−	0.253918i
$229$	−3.44055e6	+	3.44055e6i	−0.286498	+	0.286498i	−0.835694	−	0.549196i	$-0.814934\pi$
$229$	−3.44055e6	+	3.44055e6i	−0.286498	+	0.286498i	0.549196	+	0.835694i	$0.314934\pi$
$230$	2.17830e7	+	2.39740e7i	1.79034	+	1.97041i
$231$	−4.06222e6			−0.329555
$232$	1.72793e7	−	1.29153e7i	1.38377	−	1.03429i
$233$			6.61595e6i			0.523028i	0.965200	+	0.261514i	$0.0842217\pi$
$233$			6.61595e6i			0.523028i	−0.965200	+	0.261514i	$0.915778\pi$
$234$	525103.	+	577918.i	0.0409824	+	0.0451044i
$235$	−7.60068e6	−	7.60068e6i	−0.585665	−	0.585665i
$236$	−8.50367e6	−	1.03094e7i	−0.646950	−	0.784330i
$237$	6.67587e6	+	6.67587e6i	0.501491	+	0.501491i
$238$	681949.	−	1.42423e7i	0.0505849	−	1.05645i
$239$			1.57243e7i			1.15180i	0.817520	+	0.575900i	$0.195348\pi$
$239$			1.57243e7i			1.15180i	−0.817520	+	0.575900i	$0.804652\pi$
$240$	−2.10124e6	+	1.08449e7i	−0.151999	+	0.784501i
$241$	−1.86091e7			−1.32946			−0.664728	−	0.747086i	$-0.731452\pi$
$241$	−1.86091e7			−1.32946			−0.664728	+	0.747086i	$0.731452\pi$
$242$	1.06302e7	+	508993.i	0.750057	+	0.0359141i
$243$	650880.	−	650880.i	0.0453609	−	0.0453609i
$244$	1.09193e7	+	1.32380e7i	0.751665	+	0.911281i
$245$	4.43394e6	−	4.43394e6i	0.301503	−	0.301503i
$246$	−4.71377e6	+	4.28298e6i	−0.316638	+	0.287701i
$247$	1.21724e6			0.0807767
$248$	3.52574e6	+	509575.i	0.231151	+	0.0334082i
$249$		−	1.42131e7i		−	0.920644i
$250$	−1.35031e6	+	1.22691e6i	−0.0864197	+	0.0785220i
$251$	−4.73120e6	−	4.73120e6i	−0.299192	−	0.299192i	0.541505	−	0.840697i	$-0.317855\pi$
$251$	−4.73120e6	−	4.73120e6i	−0.299192	−	0.299192i	−0.840697	+	0.541505i	$0.817855\pi$
$252$	−582911.	+	6.07302e6i	−0.0364251	+	0.379492i
$253$	1.09931e7	+	1.09931e7i	0.678824	+	0.678824i
$254$	2.29483e7	+	1.09881e6i	1.40039	+	0.0670534i
$255$		−	1.22532e7i		−	0.738972i
$256$	1.55632e7	+	6.26603e6i	0.927636	+	0.373485i
$257$	8.83798e6			0.520659			0.260330	−	0.965520i	$-0.416169\pi$
$257$	8.83798e6			0.520659			0.260330	+	0.965520i	$0.416169\pi$
$258$	−477095.	+	9.96400e6i	−0.0277809	+	0.580196i
$259$	1.68217e7	−	1.68217e7i	0.968213	−	0.968213i
$260$	−4.42716e6	−	424935.i	−0.251886	−	0.0241770i
$261$	7.23978e6	−	7.23978e6i	0.407196	−	0.407196i
$262$	−1.44176e7	−	1.58677e7i	−0.801656	−	0.882286i
$263$	5.35689e6			0.294473			0.147236	−	0.989101i	$-0.452962\pi$
$263$	5.35689e6			0.294473			0.147236	+	0.989101i	$0.452962\pi$
$264$	−758389.	+	5.24728e6i	−0.0412174	+	0.285182i
$265$			4.28504e7i			2.30260i
$266$	6.39566e6	+	7.03893e6i	0.339813	+	0.373992i
$267$	7.18094e6	+	7.18094e6i	0.377266	+	0.377266i
$268$	−4.13702e6	+	3.41240e6i	−0.214923	+	0.177278i
$269$	−386471.	−	386471.i	−0.0198546	−	0.0198546i	0.697110	−	0.716964i	$-0.254469\pi$
$269$	−386471.	−	386471.i	−0.0198546	−	0.0198546i	−0.716964	+	0.697110i	$0.754469\pi$
$270$	−250749.	+	5.23683e6i	−0.0127394	+	0.266059i
$271$			6.79350e6i			0.341339i	0.985328	+	0.170669i	$0.0545930\pi$
$271$			6.79350e6i			0.341339i	−0.985328	+	0.170669i	$0.945407\pi$
$272$	−1.82699e7	−	3.53984e6i	−0.907882	−	0.175905i
$273$	−2.45631e6			−0.120724
$274$	5.43121e6	+	260057.i	0.264025	+	0.0126420i
$275$	6.72014e6	−	6.72014e6i	0.323132	−	0.323132i
$276$	1.80121e7	−	1.48572e7i	0.856716	−	0.706657i
$277$	−1.70039e7	+	1.70039e7i	−0.800035	+	0.800035i	−0.983101	−	0.183066i	$-0.941398\pi$
$277$	−1.70039e7	+	1.70039e7i	−0.800035	+	0.800035i	0.183066	+	0.983101i	$0.441398\pi$
$278$	−2.16232e7	+	1.96471e7i	−1.00643	+	0.914457i
$279$	1.69074e6			0.0778508
$280$	−2.08040e7	−	2.78336e7i	−0.947704	−	1.26793i
$281$		−	2.72409e7i		−	1.22773i	−0.789411	−	0.613865i	$-0.789614\pi$
$281$		−	2.72409e7i		−	1.22773i	0.789411	−	0.613865i	$-0.210386\pi$
$282$	−5.73448e6	+	5.21042e6i	−0.255710	+	0.232341i
$283$	5.17450e6	+	5.17450e6i	0.228302	+	0.228302i	0.811983	−	0.583681i	$-0.198388\pi$
$283$	5.17450e6	+	5.17450e6i	0.228302	+	0.228302i	−0.583681	+	0.811983i	$0.698388\pi$
$284$	−3.66684e7	−	3.51957e6i	−1.60080	−	0.153651i
$285$	5.77912e6	+	5.77912e6i	0.249648	+	0.249648i
$286$	−2.13213e6	−	102090.i	−0.0911412	−	0.00436401i
$287$		−	2.00348e7i		−	0.847498i
$288$	7.73586e6	+	1.88675e6i	0.323841	+	0.0789838i
$289$	−3.49531e6			−0.144808
$290$	−2.78910e6	+	5.82497e7i	−0.114359	+	2.38836i
$291$	5.11122e6	−	5.11122e6i	0.207418	−	0.207418i
$292$	2.30832e6	−	2.40490e7i	0.0927144	−	0.965938i
$293$	2.63628e7	−	2.63628e7i	1.04807	−	1.04807i	0.0492814	−	0.998785i	$-0.484307\pi$
$293$	2.63628e7	−	2.63628e7i	1.04807	−	1.04807i	0.998785	−	0.0492814i	$-0.0156931\pi$
$294$	−3.03955e6	−	3.34527e6i	−0.119610	−	0.131640i
$295$	3.61263e7			1.40720
$296$	−1.85886e7	−	2.48696e7i	−0.716756	−	0.958944i
$297$			2.51629e6i			0.0960485i
$298$	5.84207e6	+	6.42966e6i	0.220759	+	0.242963i
$299$	6.64719e6	+	6.64719e6i	0.248670	+	0.248670i
$300$	−9.08230e6	−	1.10109e7i	−0.336382	−	0.407812i
$301$	−2.21887e7	−	2.21887e7i	−0.813642	−	0.813642i
$302$	1.52138e6	−	3.17736e7i	0.0552353	−	1.15357i
$303$		−	2.07745e7i		−	0.746796i
$304$	1.02864e7	−	6.94733e6i	0.366137	−	0.247285i
$305$	−4.63885e7			−1.63498
$306$	−8.82221e6	−	422424.i	−0.307903	−	0.0147430i
$307$	8.78516e6	−	8.78516e6i	0.303623	−	0.303623i	−0.538807	−	0.842430i	$-0.681125\pi$
$307$	8.78516e6	−	8.78516e6i	0.303623	−	0.303623i	0.842430	+	0.538807i	$0.181125\pi$
$308$	−1.06123e7	−	1.28658e7i	−0.363210	−	0.440338i
$309$	−1.06291e6	+	1.06291e6i	−0.0360266	+	0.0360266i
$310$	−7.12732e6	+	6.47596e6i	−0.239244	+	0.217380i
$311$	2.89046e7			0.960915			0.480458	−	0.877018i	$-0.340471\pi$
$311$	2.89046e7			0.960915			0.480458	+	0.877018i	$0.340471\pi$
$312$	−458576.	+	3.17288e6i	−0.0150990	+	0.104470i
$313$			2.10369e7i			0.686037i	0.939329	+	0.343019i	$0.111449\pi$
$313$			2.10369e7i			0.686037i	−0.939329	+	0.343019i	$0.888551\pi$
$314$	−2.32474e7	+	2.11229e7i	−0.750907	+	0.682284i
$315$	−1.16619e7	−	1.16619e7i	−0.373109	−	0.373109i
$316$	−3.70345e6	+	3.85841e7i	−0.117367	+	1.22278i
$317$	−5.24343e6	−	5.24343e6i	−0.164603	−	0.164603i	0.619999	−	0.784602i	$-0.287133\pi$
$317$	−5.24343e6	−	5.24343e6i	−0.164603	−	0.164603i	−0.784602	+	0.619999i	$0.787133\pi$
$318$	3.08521e7	+	1.47726e6i	0.959408	+	0.0459382i
$319$			2.79888e7i			0.862209i
$320$	−3.98374e7	+	2.16768e7i	−1.21574	+	0.661522i
$321$	−1.66025e7			−0.501949
$322$	−3.51283e6	+	7.33644e7i	−0.105218	+	2.19744i
$323$	−9.73578e6	+	9.73578e6i	−0.288910	+	0.288910i
$324$	3.76185e6	+	361076.i	0.110603	+	0.0106161i
$325$	4.06348e6	−	4.06348e6i	0.118372	−	0.118372i
$326$	−3.26968e7	−	3.59854e7i	−0.943739	−	1.03866i
$327$	2.97915e7			0.852019
$328$	−2.58795e7	−	3.74036e6i	−0.733388	−	0.105997i
$329$		−	2.43731e7i		−	0.684421i
$330$	−9.63804e6	−	1.06074e7i	−0.268193	−	0.295167i
$331$	−1.54918e7	−	1.54918e7i	−0.427186	−	0.427186i	0.460483	−	0.887669i	$-0.347676\pi$
$331$	−1.54918e7	−	1.54918e7i	−0.427186	−	0.427186i	−0.887669	+	0.460483i	$0.847676\pi$
$332$	4.50157e7	−	3.71310e7i	1.23013	−	1.01466i
$333$	−1.04200e7	−	1.04200e7i	−0.282185	−	0.282185i
$334$	461996.	−	9.64866e6i	0.0123993	−	0.258957i
$335$		−	1.44970e7i		−	0.385605i
$336$	−2.07572e7	+	1.40192e7i	−0.547207	+	0.369578i
$337$	3.73868e7			0.976853			0.488426	−	0.872605i	$-0.337571\pi$
$337$	3.73868e7			0.976853			0.488426	+	0.872605i	$0.337571\pi$
$338$	3.72810e7	+	1.78509e6i	0.965468	+	0.0462284i
$339$	1.29712e7	−	1.29712e7i	0.332952	−	0.332952i
$340$	3.88081e7	−	3.20107e7i	0.987384	−	0.814438i
$341$	−3.26817e6	+	3.26817e6i	−0.0824217	+	0.0824217i
$342$	4.36017e6	−	3.96170e6i	0.109000	−	0.0990384i
$343$	−3.19345e7			−0.791366
$344$	−3.28043e7	+	2.45193e7i	−0.805853	+	0.602328i
$345$			6.31179e7i			1.53708i
$346$	3.89405e7	−	3.53818e7i	0.940098	−	0.854184i
$347$	−1.15709e7	−	1.15709e7i	−0.276937	−	0.276937i	0.554948	−	0.831885i	$-0.312738\pi$
$347$	−1.15709e7	−	1.15709e7i	−0.276937	−	0.276937i	−0.831885	+	0.554948i	$0.812738\pi$
$348$	4.18433e7	+	4.01628e6i	0.992860	+	0.0952985i
$349$	−2.40972e7	−	2.40972e7i	−0.566879	−	0.566879i	0.364374	−	0.931253i	$-0.381283\pi$
$349$	−2.40972e7	−	2.40972e7i	−0.566879	−	0.566879i	−0.931253	+	0.364374i	$0.881283\pi$
$350$	4.48482e7	+	2.14742e6i	1.04602	+	0.0500855i
$351$			1.52153e6i			0.0351850i
$352$	−1.86004e7	+	1.13063e7i	−0.426476	+	0.259233i
$353$	−5.11973e7			−1.16392			−0.581960	−	0.813217i	$-0.697714\pi$
$353$	−5.11973e7			−1.16392			−0.581960	+	0.813217i	$0.697714\pi$
$354$	1.24544e6	−	2.60107e7i	0.0280746	−	0.586331i
$355$	7.04132e7	−	7.04132e7i	1.57387	−	1.57387i
$356$	−3.98364e6	+	4.15032e7i	−0.0882937	+	0.919881i
$357$	1.96461e7	−	1.96461e7i	0.431789	−	0.431789i
$358$	−3.46728e7	−	3.81602e7i	−0.755684	−	0.831691i
$359$	2.43606e7			0.526507			0.263253	−	0.964727i	$-0.415204\pi$
$359$	2.43606e7			0.526507			0.263253	+	0.964727i	$0.415204\pi$
$360$	−1.72411e7	+	1.28867e7i	−0.369537	+	0.276208i
$361$			3.78623e7i			0.804794i
$362$	−5.51729e7	−	6.07222e7i	−1.16305	−	1.28003i
$363$	1.46634e7	+	1.46634e7i	0.306560	+	0.306560i
$364$	−6.41696e6	−	7.77960e6i	−0.133053	−	0.161307i
$365$	4.61807e7	+	4.61807e7i	0.949691	+	0.949691i
$366$	−1.59923e6	+	3.33995e7i	−0.0326188	+	0.681235i
$367$			5.41348e7i			1.09516i	0.836752	+	0.547581i	$0.184451\pi$
$367$			5.41348e7i			1.09516i	−0.836752	+	0.547581i	$0.815549\pi$
$368$	9.41110e7	+	1.82343e7i	1.88841	+	0.365885i
$369$	−1.24103e7			−0.247003
$370$	8.38368e7	+	4.01427e6i	1.65512	+	0.0792503i
$371$	−6.87042e7	+	6.87042e7i	−1.34543	+	1.34543i
$372$	4.41695e6	+	5.35489e6i	0.0858012	+	0.104021i
$373$	2.83469e7	−	2.83469e7i	0.546234	−	0.546234i	−0.379116	−	0.925349i	$-0.623772\pi$
$373$	2.83469e7	−	2.83469e7i	0.546234	−	0.546234i	0.925349	+	0.379116i	$0.123772\pi$
$374$	1.78698e7	−	1.62367e7i	0.341589	−	0.310372i
$375$	−3.55505e6			−0.0674143
$376$	−3.14834e7	−	4.55030e6i	−0.592268	−	0.0856005i
$377$			1.69240e7i			0.315849i
$378$	−8.79851e6	+	7.99443e6i	−0.162905	+	0.148017i
$379$	−2.70551e7	−	2.70551e7i	−0.496971	−	0.496971i	0.413523	−	0.910494i	$-0.364298\pi$
$379$	−2.70551e7	−	2.70551e7i	−0.496971	−	0.496971i	−0.910494	+	0.413523i	$0.864298\pi$
$380$	−3.20598e6	+	3.34012e7i	−0.0584264	+	0.608711i
$381$	3.16553e7	+	3.16553e7i	0.572363	+	0.572363i
$382$	−1.42640e7	−	682987.i	−0.255889	−	0.0122524i
$383$			9.57861e7i			1.70493i	0.522785	+	0.852464i	$0.324893\pi$
$383$			9.57861e7i			1.70493i	−0.522785	+	0.852464i	$0.675107\pi$
$384$	1.42338e7	+	2.94300e7i	0.251377	+	0.519753i
$385$	4.50844e7			0.790032
$386$	−2.89688e6	+	6.05006e7i	−0.0503696	+	1.05196i
$387$	−1.37445e7	+	1.37445e7i	−0.237135	+	0.237135i
$388$	2.95410e7	+	2.83546e6i	0.505743	+	0.0485431i
$389$	2.36188e6	−	2.36188e6i	0.0401244	−	0.0401244i	−0.686760	−	0.726884i	$-0.740968\pi$
$389$	2.36188e6	−	2.36188e6i	0.0401244	−	0.0401244i	0.726884	+	0.686760i	$0.240968\pi$
$390$	−5.82784e6	−	6.41401e6i	−0.0982458	−	0.108127i
$391$	−1.06331e8			−1.77882
$392$	2.65446e6	−	1.83662e7i	0.0440675	−	0.304902i
$393$		−	4.17759e7i		−	0.688254i
$394$	3.29851e7	+	3.63027e7i	0.539299	+	0.593541i
$395$	−7.40920e7	−	7.40920e7i	−1.20221	−	1.20221i
$396$	−7.96956e6	+	6.57365e6i	−0.128336	+	0.105857i
$397$	1.85501e7	+	1.85501e7i	0.296466	+	0.296466i	0.839628	−	0.543162i	$-0.182773\pi$
$397$	1.85501e7	+	1.85501e7i	0.296466	+	0.296466i	−0.543162	+	0.839628i	$0.682773\pi$
$398$	375919.	−	7.85096e6i	0.00596272	−	0.124530i
$399$			1.85319e7i			0.291744i
$400$	1.11467e7	−	5.75308e7i	0.174168	−	0.898919i
$401$	−1.08332e8			−1.68006			−0.840029	−	0.542541i	$-0.817462\pi$
$401$	−1.08332e8			−1.68006			−0.840029	+	0.542541i	$0.817462\pi$
$402$	−1.04377e7	−	499778.i	−0.160667	−	0.00769306i
$403$	−1.97617e6	+	1.97617e6i	−0.0301932	+	0.0301932i
$404$	6.57968e7	−	5.42721e7i	0.997839	−	0.823062i
$405$	−7.22377e6	+	7.22377e6i	−0.108742	+	0.108742i
$406$	−9.78665e7	+	8.89227e7i	−1.46237	+	1.32872i
$407$	4.02834e7			0.597507
$408$	−2.17096e7	−	2.90452e7i	−0.319648	−	0.427656i
$409$		−	1.21757e8i		−	1.77960i	−0.456350	−	0.889800i	$-0.650844\pi$
$409$		−	1.21757e8i		−	1.77960i	0.456350	−	0.889800i	$-0.349156\pi$
$410$	5.23156e7	−	4.75346e7i	0.759067	−	0.689697i
$411$	7.49190e6	+	7.49190e6i	0.107911	+	0.107911i
$412$	−6.14326e6	−	589653.i	−0.0878430	−	0.00843150i
$413$	5.79231e7	+	5.79231e7i	0.822245	+	0.822245i
$414$	4.54446e7	+	2.17597e6i	0.640444	+	0.0306657i
$415$			1.57744e8i			2.20703i
$416$	−1.12471e7	+	6.83656e6i	−0.156229	+	0.0949638i
$417$	−5.69288e7			−0.785098
$418$	−770232.	+	1.60861e7i	−0.0105461	+	0.220253i
$419$	3.41913e6	−	3.41913e6i	0.0464808	−	0.0464808i	−0.683484	−	0.729965i	$-0.739536\pi$
$419$	3.41913e6	−	3.41913e6i	0.0464808	−	0.0464808i	0.729965	+	0.683484i	$0.239536\pi$
$420$	6.46943e6	−	6.74012e7i	0.0873209	−	0.909746i
$421$	−3.98449e6	+	3.98449e6i	−0.0533981	+	0.0533981i	−0.733302	−	0.679903i	$-0.762022\pi$
$421$	−3.98449e6	+	3.98449e6i	−0.0533981	+	0.0533981i	0.679903	+	0.733302i	$0.262022\pi$
$422$	−1.40817e7	−	1.54981e7i	−0.187378	−	0.206225i
$423$	−1.50976e7			−0.199474
$424$	7.59205e7	+	1.01574e8i	0.996005	+	1.33255i
$425$			6.50012e7i			0.846749i
$426$	−4.82697e7	−	5.31246e7i	−0.624375	−	0.687175i
$427$	−7.43770e7	−	7.43770e7i	−0.955334	−	0.955334i
$428$	−4.33732e7	−	5.25835e7i	−0.553210	−	0.670684i
$429$	−2.94109e6	−	2.94109e6i	−0.0372509	−	0.0372509i
$430$	5.29503e6	−	1.10585e8i	0.0665983	−	1.39089i
$431$		−	8.79481e7i		−	1.09849i	−0.835663	−	0.549243i	$-0.814916\pi$
$431$		−	8.79481e7i		−	1.09849i	0.835663	−	0.549243i	$-0.185084\pi$
$432$	8.68401e6	+	1.28578e7i	0.107713	+	0.159483i
$433$	3.25160e7			0.400529			0.200264	−	0.979742i	$-0.435820\pi$
$433$	3.25160e7			0.400529			0.200264	+	0.979742i	$0.435820\pi$
$434$	−2.18108e7	−	1.04434e6i	−0.266810	−	0.0127754i
$435$	−8.03506e7	+	8.03506e7i	−0.976160	+	0.976160i
$436$	7.78286e7	+	9.43554e7i	0.939030	+	1.13843i
$437$	5.01505e7	−	5.01505e7i	0.600940	−	0.600940i
$438$	3.48419e7	−	3.16578e7i	0.414648	−	0.376755i
$439$	5.94225e7			0.702356			0.351178	−	0.936309i	$-0.385781\pi$
$439$	5.94225e7			0.702356			0.351178	+	0.936309i	$0.385781\pi$
$440$	8.41696e6	−	5.82368e7i	0.0988092	−	0.683659i
$441$		−	8.80734e6i		−	0.102690i
$442$	1.08053e7	−	9.81786e6i	0.125133	−	0.113697i
$443$	2.61766e7	+	2.61766e7i	0.301094	+	0.301094i	0.841442	−	0.540348i	$-0.181707\pi$
$443$	2.61766e7	+	2.61766e7i	0.301094	+	0.301094i	−0.540348	+	0.841442i	$0.681707\pi$
$444$	5.78050e6	−	6.02237e7i	0.0660414	−	0.688048i
$445$	−7.96975e7	−	7.96975e7i	−0.904408	−	0.904408i
$446$	−8.44332e7	−	4.04282e6i	−0.951719	−	0.0455701i
$447$			1.69278e7i			0.189530i
$448$	−9.86287e7	−	2.91178e7i	−1.09691	−	0.323836i
$449$	9.68147e7			1.06955			0.534776	−	0.844994i	$-0.320396\pi$
$449$	9.68147e7			1.06955			0.534776	+	0.844994i	$0.320396\pi$
$450$	1.33019e6	−	2.77806e7i	0.0145974	−	0.304863i
$451$	2.39889e7	−	2.39889e7i	0.261505	−	0.261505i
$452$	7.49688e7	+	7.19579e6i	0.811831	+	0.0779226i
$453$	4.38290e7	−	4.38290e7i	0.471484	−	0.471484i
$454$	−1.68315e7	−	1.85244e7i	−0.179868	−	0.197959i
$455$	2.72613e7			0.289409
$456$	2.39382e7	+	3.45978e6i	0.252462	+	0.0364884i
$457$		−	4.64453e7i		−	0.486623i	−0.969948	−	0.243312i	$-0.921766\pi$
$457$		−	4.64453e7i		−	0.486623i	0.969948	−	0.243312i	$-0.0782338\pi$
$458$	−2.61765e7	−	2.88093e7i	−0.272468	−	0.299872i
$459$	−1.21695e7	−	1.21695e7i	−0.125845	−	0.125845i
$460$	−1.99907e8	+	1.64892e8i	−2.05378	+	1.69405i
$461$	7.14679e7	+	7.14679e7i	0.729471	+	0.729471i	0.970514	−	0.241043i	$-0.0774896\pi$
$461$	7.14679e7	+	7.14679e7i	0.729471	+	0.729471i	−0.241043	+	0.970514i	$0.577490\pi$
$462$	1.55427e6	−	3.24606e7i	0.0157616	−	0.329177i
$463$		−	1.26013e8i		−	1.26961i	−0.772671	−	0.634807i	$-0.781080\pi$
$463$		−	1.26013e8i		−	1.26961i	0.772671	−	0.634807i	$-0.218920\pi$
$464$	9.65929e7	+	1.43018e8i	0.966921	+	1.43165i
$465$	−1.87646e7			−0.186629
$466$	−5.28671e7	−	2.53137e6i	−0.522429	−	0.0250149i
$467$	3.02706e7	−	3.02706e7i	0.297215	−	0.297215i	−0.542707	−	0.839922i	$-0.682601\pi$
$467$	3.02706e7	−	3.02706e7i	0.297215	−	0.297215i	0.839922	+	0.542707i	$0.182601\pi$
$468$	−4.81896e6	+	3.97490e6i	−0.0470128	+	0.0387782i
$469$	2.32437e7	−	2.32437e7i	0.225313	−	0.225313i
$470$	6.36440e7	−	5.78277e7i	0.613005	−	0.556984i
$471$	−6.12052e7			−0.585768
$472$	8.56347e7	−	6.40070e7i	0.814374	−	0.608697i
$473$		−	5.31360e7i		−	0.502117i
$474$	−5.59001e7	+	5.07915e7i	−0.524902	+	0.476932i
$475$	−3.06574e7	−	3.06574e7i	−0.286058	−	0.286058i
$476$	1.13547e8	+	1.08987e7i	1.05282	+	0.101054i
$477$	4.25579e7	+	4.25579e7i	0.392125	+	0.392125i
$478$	−1.25650e8	−	6.01637e6i	−1.15048	−	0.0550872i
$479$		−	1.11145e8i		−	1.01131i	−0.862737	−	0.505653i	$-0.831252\pi$
$479$		−	1.11145e8i		−	1.01131i	0.862737	−	0.505653i	$-0.168748\pi$
$480$	−8.58563e7	−	2.09401e7i	−0.776333	−	0.189346i
$481$	2.43582e7			0.218882
$482$	7.12014e6	−	1.48702e8i	0.0635840	−	1.32793i
$483$	−1.01200e8	+	1.01200e8i	−0.898131	+	0.898131i
$484$	−8.13457e6	+	8.47494e7i	−0.0717461	+	0.747481i
$485$	−5.67268e7	+	5.67268e7i	−0.497236	+	0.497236i
$486$	4.95204e6	+	5.45012e6i	0.0431395	+	0.0474785i
$487$	−5.86613e7			−0.507885			−0.253942	−	0.967219i	$-0.581727\pi$
$487$	−5.86613e7			−0.507885			−0.253942	+	0.967219i	$0.581727\pi$
$488$	−1.09961e8	+	8.21892e7i	−0.946188	+	0.707221i
$489$		−	9.47413e7i		−	0.810238i
$490$	3.37344e7	+	3.71274e7i	0.286738	+	0.315578i
$491$	1.15069e8	+	1.15069e8i	0.972109	+	0.972109i	0.999621	−	0.0275124i	$-0.00875859\pi$
$491$	1.15069e8	+	1.15069e8i	0.972109	+	0.972109i	−0.0275124	+	0.999621i	$0.508759\pi$
$492$	−3.24211e7	−	3.93057e7i	−0.272228	−	0.330035i
$493$	−1.35362e8	−	1.35362e8i	−1.12968	−	1.12968i
$494$	−465737.	+	9.72679e6i	−0.00386331	+	0.0806842i
$495$		−	2.79269e7i		−	0.230254i
$496$	−5.42094e6	+	2.79787e7i	−0.0444252	+	0.229288i
$497$	2.25794e8			1.83926
$498$	1.13575e8	+	5.43818e6i	0.919590	+	0.0440317i
$499$	1.23014e6	−	1.23014e6i	0.00990039	−	0.00990039i	−0.702139	−	0.712040i	$-0.747772\pi$
$499$	1.23014e6	−	1.23014e6i	0.00990039	−	0.00990039i	0.712040	+	0.702139i	$0.247772\pi$
$500$	−9.28736e6	−	1.12595e7i	−0.0742989	−	0.0900763i
$501$	1.33095e7	−	1.33095e7i	0.105840	−	0.105840i
$502$	3.96165e7	−	3.59960e7i	0.313159	−	0.284540i
$503$	−2.07824e8			−1.63302			−0.816509	−	0.577333i	$-0.804094\pi$
$503$	−2.07824e8			−1.63302			−0.816509	+	0.577333i	$0.804094\pi$
$504$	−4.83055e7	−	6.98159e6i	−0.377316	−	0.0545334i
$505$			2.30565e8i			1.79027i
$506$	−9.20500e7	+	8.36377e7i	−0.710513	+	0.645581i
$507$	5.14261e7	+	5.14261e7i	0.394602	+	0.394602i
$508$	−1.75608e7	+	1.82956e8i	−0.133953	+	1.39558i
$509$	−1.30783e8	−	1.30783e8i	−0.991737	−	0.991737i	0.00822873	−	0.999966i	$-0.497381\pi$
$509$	−1.30783e8	−	1.30783e8i	−0.991737	−	0.991737i	−0.999966	+	0.00822873i	$0.997381\pi$
$510$	9.79131e7	+	4.68826e6i	0.738126	+	0.0353429i
$511$			1.48088e8i			1.10983i
$512$	−5.60256e7	+	1.21965e8i	−0.417423	+	0.908712i
$513$	1.14793e7			0.0850285
$514$	−3.38156e6	+	7.06230e7i	−0.0249016	+	0.520064i
$515$	1.17967e7	−	1.17967e7i	0.0863654	−	0.0863654i
$516$	−7.94383e7	−	7.62479e6i	−0.578203	−	0.0554982i
$517$	2.91834e7	−	2.91834e7i	0.211186	−	0.211186i
$518$	1.27983e8	+	1.40856e8i	0.920799	+	1.01341i
$519$	1.02521e8			0.733352
$520$	5.08950e6	−	3.52141e7i	0.0361963	−	0.250442i
$521$			2.08686e8i			1.47564i	0.674999	+	0.737819i	$0.264144\pi$
$521$			2.08686e8i			1.47564i	−0.674999	+	0.737819i	$0.735856\pi$
$522$	5.50819e7	+	6.06220e7i	0.387255	+	0.426205i
$523$	1.38048e8	+	1.38048e8i	0.964996	+	0.964996i	0.999408	−	0.0344117i	$-0.0109558\pi$
$523$	1.38048e8	+	1.38048e8i	0.964996	+	0.964996i	−0.0344117	+	0.999408i	$0.510956\pi$
$524$	1.32312e8	−	1.09137e8i	0.919617	−	0.758541i
$525$	6.18644e7	+	6.18644e7i	0.427526	+	0.427526i
$526$	−2.04963e6	+	4.28060e7i	−0.0140838	+	0.294136i
$527$		−	3.16117e7i		−	0.215981i
$528$	−4.16400e7	−	8.06787e6i	−0.282885	−	0.0548096i
$529$	3.99694e8			2.69998
$530$	−3.42411e8	−	1.63953e7i	−2.29996	−	0.110126i
$531$	3.58796e7	−	3.58796e7i	0.239643	−	0.239643i
$532$	−5.86941e7	+	4.84135e7i	−0.389816	+	0.321538i
$533$	1.45054e7	−	1.45054e7i	0.0957961	−	0.0957961i
$534$	−6.01293e7	+	5.46342e7i	−0.394878	+	0.358791i
$535$	1.84263e8			1.20331
$536$	−2.56851e7	−	3.43639e7i	−0.166796	−	0.223156i
$537$		−	1.00467e8i		−	0.648785i
$538$	3.23610e6	−	2.94036e6i	0.0207814	−	0.0188822i
$539$	1.70245e7	+	1.70245e7i	0.108720	+	0.108720i
$540$	−4.17508e7	−	4.00740e6i	−0.265145	−	0.0254496i
$541$	−6.07610e7	−	6.07610e7i	−0.383737	−	0.383737i	0.488710	−	0.872446i	$-0.337468\pi$
$541$	−6.07610e7	−	6.07610e7i	−0.383737	−	0.383737i	−0.872446	+	0.488710i	$0.837468\pi$
$542$	−5.42858e7	−	2.59930e6i	−0.340948	−	0.0163252i
$543$		−	1.59868e8i		−	0.998529i
$544$	3.52767e7	−	1.44638e8i	0.219125	−	0.898430i
$545$	−3.30640e8			−2.04252
$546$	939824.	−	1.96280e7i	0.00577389	−	0.120586i
$547$	1.77371e8	−	1.77371e8i	1.08373	−	1.08373i	0.0875704	−	0.996158i	$-0.472090\pi$
$547$	1.77371e8	−	1.77371e8i	1.08373	−	1.08373i	0.996158	−	0.0875704i	$-0.0279103\pi$
$548$	−4.15614e6	+	4.33005e7i	−0.0252551	+	0.263118i
$549$	−4.60718e7	+	4.60718e7i	−0.278431	+	0.278431i
$550$	5.11284e7	+	5.62708e7i	0.307308	+	0.338217i
$551$	1.27685e8			0.763285
$552$	1.11830e8	+	1.49616e8i	0.664874	+	0.889533i
$553$		−	2.37591e8i		−	1.40493i
$554$	−1.29369e8	−	1.42381e8i	−0.760856	−	0.837382i
$555$	1.15646e8	+	1.15646e8i	0.676474	+	0.676474i
$556$	−1.48723e8	−	1.80305e8i	−0.865276	−	1.04902i
$557$	1.20696e8	+	1.20696e8i	0.698435	+	0.698435i	0.964073	−	0.265638i	$-0.0855827\pi$
$557$	1.20696e8	+	1.20696e8i	0.698435	+	0.698435i	−0.265638	+	0.964073i	$0.585583\pi$
$558$	−646904.	+	1.35104e7i	−0.00372338	+	0.0777617i
$559$		−	3.21298e7i		−	0.183938i
$560$	2.30374e8	−	1.55592e8i	1.31180	−	0.885978i
$561$	4.70470e7			0.266467
$562$	2.17678e8	+	1.04228e7i	1.22633	+	0.0587188i
$563$	1.11849e8	−	1.11849e8i	0.626766	−	0.626766i	−0.320487	−	0.947253i	$-0.603847\pi$
$563$	1.11849e8	−	1.11849e8i	0.626766	−	0.626766i	0.947253	+	0.320487i	$0.103847\pi$
$564$	−3.94416e7	−	4.78170e7i	−0.219845	−	0.266529i
$565$	−1.43961e8	+	1.43961e8i	−0.798175	+	0.798175i
$566$	−4.33285e7	+	3.93688e7i	−0.238959	+	0.217121i
$567$	−2.31645e7			−0.127079
$568$	4.21542e7	−	2.91664e8i	0.230036	−	1.59162i
$569$			3.58530e7i			0.194621i	0.995254	+	0.0973104i	$0.0310239\pi$
$569$			3.58530e7i			0.194621i	−0.995254	+	0.0973104i	$0.968976\pi$
$570$	−4.83913e7	+	4.39689e7i	−0.261302	+	0.237422i
$571$	−4.71277e7	−	4.71277e7i	−0.253144	−	0.253144i	0.569114	−	0.822259i	$-0.307286\pi$
$571$	−4.71277e7	−	4.71277e7i	−0.253144	−	0.253144i	−0.822259	+	0.569114i	$0.807286\pi$
$572$	1.63157e6	−	1.69984e7i	0.00871804	−	0.0908282i
$573$	−1.96760e7	−	1.96760e7i	−0.104586	−	0.104586i
$574$	1.60095e8	+	7.66564e6i	0.846528	+	0.0405334i
$575$		−	3.34831e8i		−	1.76126i
$576$	−1.80366e7	+	6.10942e7i	−0.0943818	+	0.319692i
$577$	−2.10659e8			−1.09661			−0.548306	−	0.836278i	$-0.684727\pi$
$577$	−2.10659e8			−1.09661			−0.548306	+	0.836278i	$0.684727\pi$
$578$	1.33737e6	−	2.79305e7i	0.00692575	−	0.144642i
$579$	−8.34555e7	+	8.34555e7i	−0.429951	+	0.429951i
$580$	−4.64397e8	−	4.45746e7i	−2.38016	−	0.228456i
$581$	−2.52919e8	+	2.52919e8i	−1.28959	+	1.28959i
$582$	3.88873e7	+	4.27986e7i	0.197260	+	0.217100i
$583$	−1.64528e8			−0.830297
$584$	1.91289e8	+	2.76470e7i	0.960398	+	0.138806i
$585$		−	1.68866e7i		−	0.0843480i
$586$	2.00574e8	+	2.20748e8i	0.996741	+	1.09699i
$587$	1.88056e8	+	1.88056e8i	0.929762	+	0.929762i	0.997690	−	0.0679282i	$-0.0216389\pi$
$587$	1.88056e8	+	1.88056e8i	0.929762	+	0.929762i	−0.0679282	+	0.997690i	$0.521639\pi$
$588$	2.78945e7	−	2.30087e7i	0.137210	−	0.113177i
$589$	1.49094e7	+	1.49094e7i	0.0729652	+	0.0729652i
$590$	−1.38225e7	+	2.88680e8i	−0.0673025	+	1.40559i
$591$			9.55768e7i			0.463010i
$592$	2.05841e8	−	1.39023e8i	0.992127	−	0.670072i
$593$	−2.06809e8			−0.991759			−0.495880	−	0.868391i	$-0.665154\pi$
$593$	−2.06809e8			−0.991759			−0.495880	+	0.868391i	$0.665154\pi$
$594$	−2.01072e7	−	962773.i	−0.0959386	−	0.00459372i
$595$	−2.18042e8	+	2.18042e8i	−1.03512	+	1.03512i
$596$	−5.36137e7	+	4.42230e7i	−0.253243	+	0.208886i
$597$	1.08297e7	−	1.08297e7i	0.0508974	−	0.0508974i
$598$	−5.56600e7	+	5.05733e7i	−0.260279	+	0.236493i
$599$	−2.50484e8			−1.16547			−0.582733	−	0.812664i	$-0.698017\pi$
$599$	−2.50484e8			−1.16547			−0.582733	+	0.812664i	$0.698017\pi$
$600$	9.14616e7	−	6.83623e7i	0.423434	−	0.316492i
$601$		−	1.30998e7i		−	0.0603449i	−0.999545	−	0.0301724i	$-0.990394\pi$
$601$		−	1.30998e7i		−	0.0603449i	0.999545	−	0.0301724i	$-0.00960564\pi$
$602$	1.85797e8	−	1.68817e8i	0.851625	−	0.773797i
$603$	−1.43980e7	−	1.43980e7i	−0.0656674	−	0.0656674i
$604$	2.53316e8	+	2.43142e7i	1.14961	+	0.110344i
$605$	−1.62742e8	−	1.62742e8i	−0.734908	−	0.734908i
$606$	1.66006e8	+	7.94866e6i	0.745942	+	0.0357171i
$607$			8.45094e7i			0.377867i	0.981990	+	0.188934i	$0.0605031\pi$
$607$			8.45094e7i			0.377867i	−0.981990	+	0.188934i	$0.939497\pi$
$608$	5.15793e7	+	8.48553e7i	0.229490	+	0.377545i
$609$	−2.57660e8			−1.14076
$610$	1.77490e7	−	3.70684e8i	0.0781961	−	1.63310i
$611$	1.76464e7	−	1.76464e7i	0.0773628	−	0.0773628i
$612$	6.75105e6	−	7.03353e7i	0.0294522	−	0.306845i
$613$	−7.07698e7	+	7.07698e7i	−0.307232	+	0.307232i	−0.843835	−	0.536603i	$-0.819707\pi$
$613$	−7.07698e7	+	7.07698e7i	−0.307232	+	0.307232i	0.536603	+	0.843835i	$0.319707\pi$
$614$	6.68395e7	+	7.35622e7i	0.288754	+	0.317797i
$615$	1.37735e8			0.592133
$616$	1.06869e8	−	7.98786e7i	0.457205	−	0.341734i
$617$		−	4.73788e7i		−	0.201711i	−0.994901	−	0.100855i	$-0.967842\pi$
$617$		−	4.73788e7i		−	0.201711i	0.994901	−	0.100855i	$-0.0321579\pi$
$618$	−8.08689e6	−	8.90027e6i	−0.0342623	−	0.0377084i
$619$	−1.85132e8	−	1.85132e8i	−0.780564	−	0.780564i	0.199362	−	0.979926i	$-0.436113\pi$
$619$	−1.85132e8	−	1.85132e8i	−0.780564	−	0.780564i	−0.979926	+	0.199362i	$0.936113\pi$
$620$	−4.90214e7	−	5.94311e7i	−0.205689	−	0.249367i
$621$	6.26870e7	+	6.26870e7i	0.261760	+	0.261760i
$622$	−1.10594e7	+	2.30972e8i	−0.0459578	+	0.959816i
$623$		−	2.55566e8i		−	1.05691i
$624$	−2.51785e7	−	4.87841e6i	−0.103628	−	0.0200782i
$625$	2.63000e8			1.07725
$626$	−1.68102e8	−	8.04905e6i	−0.685252	−	0.0328112i
$627$	−2.21894e7	+	2.21894e7i	−0.0900209	+	0.0900209i
$628$	−1.59895e8	−	1.93849e8i	−0.645589	−	0.782680i
$629$	−1.94823e8	+	1.94823e8i	−0.782866	+	0.782866i
$630$	9.76501e7	−	8.87260e7i	0.390527	−	0.354837i
$631$	−2.58533e8			−1.02903			−0.514516	−	0.857481i	$-0.672028\pi$
$631$	−2.58533e8			−1.02903			−0.514516	+	0.857481i	$0.672028\pi$
$632$	−3.06903e8	−	4.43566e7i	−1.21576	−	0.175714i
$633$		−	4.08029e7i		−	0.160872i
$634$	4.39057e7	−	3.98932e7i	0.172287	−	0.156542i
$635$	−3.51325e8	−	3.51325e8i	−1.37211	−	1.37211i
$636$	−2.36090e7	+	2.45969e8i	−0.0917713	+	0.956113i
$637$	1.02942e7	+	1.02942e7i	0.0398267	+	0.0398267i
$638$	−2.23654e8	−	1.07090e7i	−0.861222	−	0.0412369i
$639$		−	1.39865e8i		−	0.536051i
$640$	−1.57973e8	−	3.26628e8i	−0.602620	−	1.24599i
$641$	2.40142e8			0.911790			0.455895	−	0.890034i	$-0.349319\pi$
$641$	2.40142e8			0.911790			0.455895	+	0.890034i	$0.349319\pi$
$642$	6.35241e6	−	1.32668e8i	0.0240067	−	0.501374i
$643$	−2.42068e7	+	2.42068e7i	−0.0910552	+	0.0910552i	−0.751167	−	0.660112i	$-0.770509\pi$
$643$	−2.42068e7	+	2.42068e7i	−0.0910552	+	0.0910552i	0.660112	+	0.751167i	$0.270509\pi$
$644$	−5.84900e8	−	5.61409e7i	−2.18990	−	0.210195i
$645$	1.52543e8	−	1.52543e8i	0.568478	−	0.568478i
$646$	−7.40720e7	−	8.15222e7i	−0.274762	−	0.302398i
$647$	2.51381e8			0.928154			0.464077	−	0.885795i	$-0.346386\pi$
$647$	2.51381e8			0.928154			0.464077	+	0.885795i	$0.346386\pi$
$648$	−4.32465e6	+	2.99222e7i	−0.0158937	+	0.109968i
$649$			1.38710e8i			0.507427i
$650$	3.09159e7	+	3.40254e7i	0.112575	+	0.123898i
$651$	−3.00862e7	−	3.00862e7i	−0.109050	−	0.109050i
$652$	3.00064e8	−	2.47506e8i	1.08261	−	0.892983i
$653$	2.56061e8	+	2.56061e8i	0.919610	+	0.919610i	0.997001	−	0.0773910i	$-0.0246590\pi$
$653$	2.56061e8	+	2.56061e8i	0.919610	+	0.919610i	−0.0773910	+	0.997001i	$0.524659\pi$
$654$	−1.13987e7	+	2.38059e8i	−0.0407496	+	0.851044i
$655$			4.63649e8i			1.64993i
$656$	3.97906e7	−	2.05368e8i	0.140951	−	0.727480i
$657$	9.17309e7			0.323459
$658$	1.94762e8	+	9.32555e6i	0.683637	+	0.0327338i
$659$	1.34008e8	−	1.34008e8i	0.468246	−	0.468246i	−0.433100	−	0.901346i	$-0.642580\pi$
$659$	1.34008e8	−	1.34008e8i	0.468246	−	0.468246i	0.901346	+	0.433100i	$0.142580\pi$
$660$	8.84500e7	−	7.29575e7i	0.307656	−	0.253769i
$661$	−3.14983e8	+	3.14983e8i	−1.09064	+	1.09064i	−0.0951823	+	0.995460i	$0.530343\pi$
$661$	−3.14983e8	+	3.14983e8i	−1.09064	+	1.09064i	−0.995460	+	0.0951823i	$0.969657\pi$
$662$	1.29720e8	−	1.17865e8i	0.447128	−	0.406266i
$663$	2.84480e7			0.0976137
$664$	2.79484e8	+	3.73921e8i	0.954669	+	1.27725i
$665$		−	2.05676e8i		−	0.699388i
$666$	8.72513e7	−	7.92776e7i	0.295358	−	0.268366i
$667$	6.97272e8	+	6.97272e8i	2.34977	+	2.34977i
$668$	7.69242e7	+	7.38347e6i	0.258068	+	0.0247703i
$669$	−1.16469e8	−	1.16469e8i	−0.388983	−	0.388983i
$670$	1.15843e8	+	5.54678e6i	0.385163	+	0.0184423i
$671$		−	1.78113e8i		−	0.589559i
$672$	−1.04083e8	−	1.71232e8i	−0.342983	−	0.564257i
$673$	1.47833e8			0.484982			0.242491	−	0.970154i	$-0.422036\pi$
$673$	1.47833e8			0.484982			0.242491	+	0.970154i	$0.422036\pi$
$674$	−1.43048e7	+	2.98752e8i	−0.0467200	+	0.975735i
$675$	3.83210e7	−	3.83210e7i	0.124602	−	0.124602i
$676$	−2.85287e7	+	2.97224e8i	−0.0923511	+	0.962152i
$677$	−9.38178e7	+	9.38178e7i	−0.302357	+	0.302357i	−0.841935	−	0.539579i	$-0.818584\pi$
$677$	−9.38178e7	+	9.38178e7i	−0.302357	+	0.302357i	0.539579	+	0.841935i	$0.318584\pi$
$678$	9.86879e7	+	1.08614e8i	0.316647	+	0.348495i
$679$	−1.81906e8			−0.581081
$680$	2.40944e8	+	3.22358e8i	0.766282	+	1.02521i
$681$		−	4.87704e7i		−	0.154424i
$682$	−2.48650e7	−	2.73659e7i	−0.0783854	−	0.0862694i
$683$	3.04498e7	+	3.04498e7i	0.0955701	+	0.0955701i	0.753275	−	0.657705i	$-0.228473\pi$
$683$	3.04498e7	+	3.04498e7i	0.0955701	+	0.0955701i	−0.657705	+	0.753275i	$0.728473\pi$
$684$	2.99891e7	+	3.63573e7i	0.0937119	+	0.113612i
$685$	−8.31487e7	−	8.31487e7i	−0.258692	−	0.258692i
$686$	1.22187e7	−	2.55183e8i	0.0378487	−	0.790460i
$687$		−	7.58483e7i		−	0.233924i
$688$	−1.83379e8	−	2.71516e8i	−0.563097	−	0.833738i
$689$	−9.94852e7			−0.304159
$690$	−5.04366e8	−	2.41500e7i	−1.53532	−	0.0735139i
$691$	6.78224e7	−	6.78224e7i	0.205560	−	0.205560i	−0.596817	−	0.802377i	$-0.703568\pi$
$691$	6.78224e7	−	6.78224e7i	0.205560	−	0.205560i	0.802377	+	0.596817i	$0.203568\pi$
$692$	2.67831e8	+	3.24705e8i	0.808245	+	0.979875i
$693$	4.47766e7	−	4.47766e7i	0.134540	−	0.134540i
$694$	9.68889e7	−	8.80344e7i	0.289865	−	0.263375i
$695$	6.31823e8			1.88209
$696$	−4.81034e7	+	3.32827e8i	−0.142675	+	0.987166i
$697$			2.32035e8i			0.685260i
$698$	2.01777e8	−	1.83337e8i	0.593342	−	0.539118i
$699$	−7.29257e7	−	7.29257e7i	−0.213525	−	0.213525i
$700$	−3.43194e7	+	3.57554e8i	−0.100056	+	1.04243i
$701$	−2.99902e8	−	2.99902e8i	−0.870614	−	0.870614i	0.121925	−	0.992539i	$-0.461093\pi$
$701$	−2.99902e8	−	2.99902e8i	−0.870614	−	0.870614i	−0.992539	+	0.121925i	$0.961093\pi$
$702$	−1.21583e7	−	582161.i	−0.0351448	−	0.00168280i
$703$		−	1.83773e8i		−	0.528953i
$704$	−8.32297e7	−	1.52959e8i	−0.238539	−	0.438386i
$705$	1.67560e8			0.478193
$706$	1.95890e7	−	4.09110e8i	0.0556669	−	1.16259i
$707$	−3.69676e8	+	3.69676e8i	−1.04608	+	1.04608i
$708$	2.07371e8	+	1.99043e7i	0.584317	+	0.0560850i
$709$	−2.43530e8	+	2.43530e8i	−0.683303	+	0.683303i	−0.960743	−	0.277440i	$-0.910514\pi$
$709$	−2.43530e8	+	2.43530e8i	−0.683303	+	0.683303i	0.277440	+	0.960743i	$0.410514\pi$
$710$	5.35720e8	+	5.89603e8i	1.49680	+	1.64734i
$711$	−1.47172e8			−0.409465
$712$	−3.30121e8	−	4.77124e7i	−0.914605	−	0.132188i
$713$			1.62837e8i			0.449246i
$714$	1.49472e8	+	1.64506e8i	0.410644	+	0.451946i
$715$	3.26416e7	+	3.26416e7i	0.0893004	+	0.0893004i
$716$	3.18199e8	−	2.62465e8i	0.866881	−	0.715042i
$717$	−1.73324e8	−	1.73324e8i	−0.470220	−	0.470220i
$718$	−9.32076e6	+	1.94662e8i	−0.0251813	+	0.525904i
$719$			1.00826e8i			0.271261i	0.990760	+	0.135630i	$0.0433060\pi$
$719$			1.00826e8i			0.271261i	−0.990760	+	0.135630i	$0.956694\pi$
$720$	−9.63793e7	−	1.42702e8i	−0.258218	−	0.382325i
$721$	3.78286e7			0.100929
$722$	−3.02551e8	−	1.44867e7i	−0.803873	−	0.0384910i
$723$	2.05122e8	−	2.05122e8i	0.542748	−	0.542748i
$724$	5.06331e8	−	4.17645e8i	1.33419	−	1.10050i
$725$	4.26248e8	−	4.26248e8i	1.11853	−	1.11853i
$726$	−1.22784e8	+	1.11563e8i	−0.320871	+	0.291548i
$727$	1.53908e8			0.400551			0.200275	−	0.979740i	$-0.435816\pi$
$727$	1.53908e8			0.400551			0.200275	+	0.979740i	$0.435816\pi$
$728$	6.46208e7	−	4.83003e7i	0.167486	−	0.125186i
$729$			1.43489e7i			0.0370370i
$730$	−3.86693e8	+	3.51354e8i	−0.994025	+	0.903183i
$731$	2.56981e8	+	2.56981e8i	0.657884	+	0.657884i
$732$	−2.66278e8	−	2.55584e7i	−0.678895	−	0.0651629i
$733$	−1.98287e8	−	1.98287e8i	−0.503480	−	0.503480i	0.409038	−	0.912518i	$-0.365865\pi$
$733$	−1.98287e8	−	1.98287e8i	−0.503480	−	0.503480i	−0.912518	+	0.409038i	$0.865865\pi$
$734$	−4.32583e8	−	2.07129e7i	−1.09391	−	0.0523784i
$735$			9.77480e7i			0.246176i
$736$	−1.81716e8	+	7.45050e8i	−0.455784	+	1.86875i
$737$	5.56622e7			0.139046
$738$	4.74837e6	−	9.91685e7i	0.0118134	−	0.246720i
$739$	2.46278e8	−	2.46278e8i	0.610229	−	0.610229i	−0.332777	−	0.943006i	$-0.607986\pi$
$739$	2.46278e8	−	2.46278e8i	0.610229	−	0.610229i	0.943006	+	0.332777i	$0.107986\pi$
$740$	−6.41547e7	+	6.68391e8i	−0.158319	+	1.64944i
$741$	−1.34173e7	+	1.34173e7i	−0.0329769	+	0.0329769i
$742$	−5.22717e8	−	5.75292e8i	−1.27954	−	1.40824i
$743$	−1.27551e6			−0.00310970			−0.00155485	−	0.999999i	$-0.500495\pi$
$743$	−1.27551e6			−0.00310970			−0.00155485	+	0.999999i	$0.500495\pi$
$744$	−4.44801e7	+	3.32463e7i	−0.108006	+	0.0807280i
$745$		−	1.87873e8i		−	0.454356i
$746$	2.15669e8	+	2.37361e8i	0.519484	+	0.571733i
$747$	1.56667e8	+	1.56667e8i	0.375851	+	0.375851i
$748$	1.22908e8	+	1.49007e8i	0.293680	+	0.356043i
$749$	2.95438e8	+	2.95438e8i	0.703106	+	0.703106i
$750$	1.36022e6	−	2.84079e7i	0.00322423	−	0.0673372i
$751$		−	3.95051e8i		−	0.932682i	−0.884605	−	0.466341i	$-0.845572\pi$
$751$		−	3.95051e8i		−	0.932682i	0.884605	−	0.466341i	$-0.154428\pi$
$752$	4.84068e7	−	2.49838e8i	0.113829	−	0.587496i
$753$	1.04301e8			0.244289
$754$	−1.35237e8	−	6.47542e6i	−0.315488	−	0.0151061i
$755$	−4.86435e8	+	4.86435e8i	−1.13027	+	1.13027i
$756$	−6.05158e7	−	7.33663e7i	−0.140057	−	0.169798i
$757$	5.73389e7	−	5.73389e7i	0.132179	−	0.132179i	−0.637922	−	0.770101i	$-0.720206\pi$
$757$	5.73389e7	−	5.73389e7i	0.132179	−	0.132179i	0.770101	+	0.637922i	$0.220206\pi$
$758$	2.26545e8	−	2.05841e8i	0.520171	−	0.472634i
$759$	−2.42346e8			−0.554257
$760$	−2.65677e8	−	3.83983e7i	−0.605220	−	0.0874725i
$761$		−	6.32076e8i		−	1.43422i	−0.696961	−	0.717109i	$-0.745465\pi$
$761$		−	6.32076e8i		−	1.43422i	0.696961	−	0.717109i	$-0.254535\pi$
$762$	−2.65064e8	+	2.40841e8i	−0.599082	+	0.544333i
$763$	−5.30132e8	−	5.30132e8i	−1.19347	−	1.19347i
$764$	1.09153e7	−	1.13720e8i	0.0244768	−	0.255010i
$765$	1.35063e8	+	1.35063e8i	0.301684	+	0.301684i
$766$	−7.65412e8	−	3.66494e7i	−1.70298	−	0.0815418i
$767$			8.38738e7i			0.185883i
$768$	−2.40617e8	+	1.02479e8i	−0.531180	+	0.226231i
$769$	−8.81406e7			−0.193819			−0.0969097	−	0.995293i	$-0.530896\pi$
$769$	−8.81406e7			−0.193819			−0.0969097	+	0.995293i	$0.530896\pi$
$770$	−1.72501e7	+	3.60263e8i	−0.0377849	+	0.789128i
$771$	−9.74185e7	+	9.74185e7i	−0.212558	+	0.212558i
$772$	−4.82342e8	−	4.62970e7i	−1.04834	−	0.100624i
$773$	5.56813e8	−	5.56813e8i	1.20551	−	1.20551i	0.233045	−	0.972466i	$-0.425131\pi$
$773$	5.56813e8	−	5.56813e8i	1.20551	−	1.20551i	0.972466	−	0.233045i	$-0.0748689\pi$
$774$	−1.04571e8	−	1.15089e8i	−0.225523	−	0.248206i
$775$	9.95434e7			0.213849
$776$	−3.39606e7	+	2.34973e8i	−0.0726758	+	0.502843i
$777$			3.70842e8i			0.790543i
$778$	1.79697e7	+	1.97771e7i	0.0381594	+	0.0419975i
$779$	−1.09438e8	−	1.09438e8i	−0.231502	−	0.231502i
$780$	5.34832e7	−	4.41153e7i	0.112702	−	0.0929620i
$781$	2.70357e8	+	2.70357e8i	0.567525	+	0.567525i
$782$	4.06842e7	−	8.49678e8i	0.0850757	−	1.77678i
$783$			1.59604e8i			0.332474i
$784$	1.45746e8	+	2.82386e7i	0.302446	+	0.0585997i
$785$	6.79285e8			1.40424
$786$	3.33825e8	+	1.59842e7i	0.687466	+	0.0329172i
$787$	1.10666e8	−	1.10666e8i	0.227034	−	0.227034i	−0.584419	−	0.811452i	$-0.698677\pi$
$787$	1.10666e8	−	1.10666e8i	0.227034	−	0.227034i	0.811452	+	0.584419i	$0.198677\pi$
$788$	−3.02710e8	+	2.49689e8i	−0.618655	+	0.510294i
$789$	−5.90474e7	+	5.90474e7i	−0.120218	+	0.120218i
$790$	6.20407e8	−	5.63709e8i	1.25833	−	1.14334i
$791$	−4.61638e8			−0.932765
$792$	−4.94797e7	−	6.61987e7i	−0.0995983	−	0.133252i
$793$		−	1.07700e8i		−	0.215970i
$794$	−1.55329e8	+	1.41134e8i	−0.310306	+	0.281948i
$795$	−4.72328e8	−	4.72328e8i	−0.940031	−	0.940031i
$796$	6.25920e7	+	6.00782e6i	0.124102	+	0.0119118i
$797$	6.10291e8	+	6.10291e8i	1.20549	+	1.20549i	0.972474	+	0.233011i	$0.0748578\pi$
$797$	6.10291e8	+	6.10291e8i	1.20549	+	1.20549i	0.233011	+	0.972474i	$0.425142\pi$
$798$	−1.48086e8	−	7.09061e6i	−0.291410	−	0.0139532i
$799$			2.82280e8i			0.553400i
$800$	4.55455e8	+	1.11084e8i	0.889560	+	0.216961i
$801$	−1.58307e8			−0.308036
$802$	4.14497e7	−	8.65666e8i	0.0803523	−	1.67814i
$803$	−1.77315e8	+	1.77315e8i	−0.342451	+	0.342451i
$804$	7.98730e6	−	8.32151e7i	0.0153685	−	0.160116i
$805$	1.12317e9	−	1.12317e9i	2.15306	−	2.15306i
$806$	−1.50351e7	−	1.65474e7i	−0.0287146	−	0.0316027i
$807$	8.51991e6			0.0162112
$808$	4.08505e8	+	5.46537e8i	0.774396	+	1.03606i
$809$		−	5.80838e8i		−	1.09701i	−0.836148	−	0.548503i	$-0.815198\pi$
$809$		−	5.80838e8i		−	1.09701i	0.836148	−	0.548503i	$-0.184802\pi$
$810$	−5.49601e7	−	6.04880e7i	−0.103417	−	0.113819i
$811$	−5.75654e8	−	5.75654e8i	−1.07919	−	1.07919i	−0.996582	−	0.0826105i	$-0.973674\pi$
$811$	−5.75654e8	−	5.75654e8i	−1.07919	−	1.07919i	−0.0826105	−	0.996582i	$-0.526326\pi$
$812$	−6.73122e8	−	8.16059e8i	−1.25726	−	1.52424i
$813$	−7.48827e7	−	7.48827e7i	−0.139351	−	0.139351i
$814$	−1.54131e7	+	3.21898e8i	−0.0285770	+	0.596823i
$815$			1.05148e9i			1.94236i
$816$	2.40402e8	−	1.62365e8i	0.442454	−	0.298829i
$817$	−2.42407e8			−0.444507
$818$	9.72938e8	+	4.65861e7i	1.77756	+	0.0851131i
$819$	2.70751e7	−	2.70751e7i	0.0492855	−	0.0492855i
$820$	3.59825e8	+	4.36234e8i	0.652604	+	0.791184i
$821$	9.13085e7	−	9.13085e7i	0.164999	−	0.164999i	−0.619778	−	0.784777i	$-0.712777\pi$
$821$	9.13085e7	−	9.13085e7i	0.164999	−	0.164999i	0.784777	+	0.619778i	$0.212777\pi$
$822$	−6.27331e7	+	5.70001e7i	−0.112949	+	0.102627i
$823$	−6.88029e7			−0.123426			−0.0617131	−	0.998094i	$-0.519656\pi$
$823$	−6.88029e7			−0.123426			−0.0617131	+	0.998094i	$0.519656\pi$
$824$	7.06234e6	−	4.88642e7i	0.0126231	−	0.0873392i
$825$			1.48148e8i			0.263836i
$826$	−4.85017e8	+	4.40692e8i	−0.860630	+	0.781979i
$827$	−2.37973e8	−	2.37973e8i	−0.420737	−	0.420737i	0.464720	−	0.885458i	$-0.346155\pi$
$827$	−2.37973e8	−	2.37973e8i	−0.420737	−	0.420737i	−0.885458	+	0.464720i	$0.846155\pi$
$828$	−3.47757e7	+	3.62308e8i	−0.0612611	+	0.638244i
$829$	2.78593e7	+	2.78593e7i	0.0488998	+	0.0488998i	0.731134	−	0.682234i	$-0.238991\pi$
$829$	2.78593e7	+	2.78593e7i	0.0488998	+	0.0488998i	−0.682234	+	0.731134i	$0.738991\pi$
$830$	−1.26051e9	−	6.03555e7i	−2.20451	−	0.105556i
$831$		−	3.74858e8i		−	0.653226i
$832$	−5.03266e7	−	9.24898e7i	−0.0873831	−	0.160592i
$833$	−1.64671e8			−0.284893
$834$	2.17819e7	−	4.54909e8i	0.0375490	−	0.784200i
$835$	−1.47715e8	+	1.47715e8i	−0.253727	+	0.253727i
$836$	−1.28247e8	−	1.23096e7i	−0.219496	−	0.0210681i
$837$	−1.86365e7	+	1.86365e7i	−0.0317825	+	0.0317825i
$838$	2.60135e7	+	2.86300e7i	0.0442046	+	0.0486507i
$839$	−4.20719e8			−0.712371			−0.356186	−	0.934415i	$-0.615923\pi$
$839$	−4.20719e8			−0.712371			−0.356186	+	0.934415i	$0.615923\pi$
$840$	5.36118e8	+	7.74850e7i	0.904528	+	0.130731i
$841$			1.18046e9i			1.98456i
$842$	−3.03149e7	−	3.33639e7i	−0.0507831	−	0.0558909i
$843$	3.00269e8	+	3.00269e8i	0.501219	+	0.501219i
$844$	1.29231e8	−	1.06595e8i	0.214950	−	0.177301i
$845$	−5.70751e8	−	5.70751e8i	−0.945969	−	0.945969i
$846$	5.77659e6	−	1.20642e8i	0.00954026	−	0.199246i
$847$		−	5.21864e8i		−	0.858830i
$848$	−8.40709e8	+	5.67805e8i	−1.37866	+	0.931133i
$849$	−1.14074e8			−0.186408
$850$	−5.19415e8	−	2.48706e7i	−0.845780	−	0.0404975i
$851$	1.00356e9	−	1.00356e9i	1.62838	−	1.62838i
$852$	4.42980e8	−	3.65389e8i	0.716250	−	0.590795i
$853$	−9.20845e7	+	9.20845e7i	−0.148368	+	0.148368i	−0.777388	−	0.629021i	$-0.783456\pi$
$853$	−9.20845e7	+	9.20845e7i	−0.148368	+	0.148368i	0.629021	+	0.777388i	$0.283456\pi$
$854$	6.22793e8	−	5.65877e8i	0.999931	−	0.908550i
$855$	−1.27403e8			−0.203836
$856$	4.36782e8	−	3.26469e8i	0.696375	−	0.520500i
$857$			3.64418e7i			0.0578972i	0.999581	+	0.0289486i	$0.00921591\pi$
$857$			3.64418e7i			0.0578972i	−0.999581	+	0.0289486i	$0.990784\pi$
$858$	2.46271e7	−	2.23765e7i	0.0389898	−	0.0354266i
$859$	2.94227e8	+	2.94227e8i	0.464199	+	0.464199i	0.900029	−	0.435830i	$-0.143545\pi$
$859$	2.94227e8	+	2.94227e8i	0.464199	+	0.464199i	−0.435830	+	0.900029i	$0.643545\pi$
$860$	8.81644e8	+	8.46235e7i	1.38611	+	0.133044i
$861$	2.20837e8	+	2.20837e8i	0.345990	+	0.345990i
$862$	7.02779e8	+	3.36504e7i	1.09723	+	0.0525374i
$863$			8.56113e8i			1.33198i	0.745959	+	0.665992i	$0.231991\pi$
$863$			8.56113e8i			1.33198i	−0.745959	+	0.665992i	$0.768009\pi$
$864$	−1.06067e8	+	6.44730e7i	−0.164452	+	0.0999623i
$865$	−1.13783e9			−1.75804
$866$	−1.24412e7	+	2.59830e8i	−0.0191561	+	0.400070i
$867$	3.85278e7	−	3.85278e7i	0.0591176	−	0.0591176i
$868$	1.66904e7	−	1.73887e8i	0.0255215	−	0.265894i
$869$	2.84482e8	−	2.84482e8i	0.433507	−	0.433507i
$870$	−6.11325e8	−	6.72812e8i	−0.928356	−	1.02173i
$871$	3.36573e7			0.0509361
$872$	−7.83758e8	+	5.85814e8i	−1.18204	+	0.883508i
$873$			1.12679e8i			0.169356i
$874$	3.81556e8	+	4.19933e8i	0.571511	+	0.628993i
$875$	6.32612e7	+	6.32612e7i	0.0944307	+	0.0944307i
$876$	2.39642e8	+	2.90529e8i	0.356492	+	0.432193i
$877$	8.01223e8	+	8.01223e8i	1.18783	+	1.18783i	0.977666	+	0.210165i	$0.0674001\pi$
$877$	8.01223e8	+	8.01223e8i	1.18783	+	1.18783i	0.210165	+	0.977666i	$0.432600\pi$
$878$	−2.27360e7	+	4.74836e8i	−0.0335916	+	0.701552i
$879$			5.81179e8i			0.855743i
$880$	4.62141e8	+	8.95410e7i	0.678151	+	0.131394i
$881$	−8.44013e8			−1.23430			−0.617151	−	0.786845i	$-0.711713\pi$
$881$	−8.44013e8			−1.23430			−0.617151	+	0.786845i	$0.711713\pi$
$882$	7.03781e7	+	3.36983e6i	0.102573	+	0.00491137i
$883$	−5.87807e8	+	5.87807e8i	−0.853794	+	0.853794i	−0.990598	−	0.136805i	$-0.956317\pi$
$883$	−5.87807e8	+	5.87807e8i	−0.853794	+	0.853794i	0.136805	+	0.990598i	$0.456317\pi$
$884$	7.43187e7	+	9.01002e7i	0.107582	+	0.130428i
$885$	−3.98209e8	+	3.98209e8i	−0.574489	+	0.574489i
$886$	−2.19189e8	+	1.99158e8i	−0.315150	+	0.286349i
$887$	−3.68366e8			−0.527848			−0.263924	−	0.964544i	$-0.585017\pi$
$887$	−3.68366e8			−0.527848			−0.263924	+	0.964544i	$0.585017\pi$
$888$	4.79027e8	+	6.92337e7i	0.684102	+	0.0988732i
$889$		−	1.12659e9i		−	1.60348i
$890$	6.67344e8	−	6.06357e8i	0.946629	−	0.860118i
$891$	−2.77363e7	−	2.77363e7i	−0.0392116	−	0.0392116i
$892$	6.46111e7	−	6.73146e8i	0.0910359	−	0.948450i
$893$	−1.33135e8	−	1.33135e8i	−0.186956	−	0.186956i
$894$	−1.35268e8	−	6.47687e6i	−0.189313	−	0.00906468i
$895$			1.11503e9i			1.55531i
$896$	2.70413e8	−	7.76985e8i	0.375927	−	1.08016i
$897$	−1.46540e8			−0.203039
$898$	−3.70429e7	+	7.73631e8i	−0.0511536	+	1.06833i
$899$	−2.07295e8	+	2.07295e8i	−0.285305	+	0.285305i
$900$	2.21482e8	+	2.12587e7i	0.303816	+	0.0291614i
$901$	7.95705e8	−	7.95705e8i	1.08787	−	1.08787i
$902$	1.82513e8	+	2.00870e8i	0.248699	+	0.273713i
$903$	4.89160e8			0.664336
$904$	−8.61848e7	+	5.96311e8i	−0.116661	+	0.807175i
$905$			1.77429e9i			2.39375i
$906$	3.33461e8	+	3.67000e8i	0.448395	+	0.493494i
$907$	−4.57144e8	−	4.57144e8i	−0.612677	−	0.612677i	0.330966	−	0.943643i	$-0.392625\pi$
$907$	−4.57144e8	−	4.57144e8i	−0.612677	−	0.612677i	−0.943643	+	0.330966i	$0.892625\pi$
$908$	1.54465e8	−	1.27410e8i	0.206335	−	0.170195i
$909$	2.28991e8	+	2.28991e8i	0.304878	+	0.304878i
$910$	−1.04306e7	+	2.17840e8i	−0.0138416	+	0.289078i
$911$			8.70276e8i			1.15107i	0.817777	+	0.575536i	$0.195206\pi$
$911$			8.70276e8i			1.15107i	−0.817777	+	0.575536i	$0.804794\pi$
$912$	−3.68057e7	+	1.89962e8i	−0.0485211	+	0.250428i
$913$	−6.05671e8			−0.795838
$914$	3.71137e8	+	1.77707e7i	0.486066	+	0.0232738i
$915$	5.11327e8	−	5.11327e8i	0.667476	−	0.667476i
$916$	2.40226e8	−	1.98149e8i	0.312560	−	0.257814i
$917$	−7.43392e8	+	7.43392e8i	−0.964073	+	0.964073i
$918$	1.01901e8	−	9.25884e7i	0.131719	−	0.119682i
$919$	1.14576e9			1.47620			0.738102	−	0.674689i	$-0.235722\pi$
$919$	1.14576e9			1.47620			0.738102	+	0.674689i	$0.235722\pi$
$920$	−1.24114e9	−	1.66051e9i	−1.59388	−	2.13245i
$921$			1.93672e8i			0.247907i
$922$	−5.98433e8	+	5.43744e8i	−0.763525	+	0.693748i
$923$	1.63477e8	+	1.63477e8i	0.207899	+	0.207899i
$924$	2.58793e8	+	2.48399e7i	0.328047	+	0.0314872i
$925$	−6.13485e8	−	6.13485e8i	−0.775137	−	0.775137i
$926$	1.00695e9	+	4.82146e7i	1.26816	+	0.0607219i
$927$		−	2.34324e7i		−	0.0294156i
$928$	−1.17979e9	+	7.17137e8i	−1.47626	+	0.897343i
$929$	−5.43169e8			−0.677467			−0.338733	−	0.940882i	$-0.609998\pi$
$929$	−5.43169e8			−0.677467			−0.338733	+	0.940882i	$0.609998\pi$
$930$	7.17964e6	−	1.49945e8i	0.00892594	−	0.186416i
$931$	7.76659e7	−	7.76659e7i	0.0962457	−	0.0962457i
$932$	4.04556e7	−	4.21484e8i	0.0499725	−	0.520635i
$933$	−3.18606e8	+	3.18606e8i	−0.392292	+	0.392292i
$934$	2.30306e8	+	2.53470e8i	0.282660	+	0.311090i
$935$	−5.22150e8			−0.638794
$936$	−2.99190e7	−	4.00285e7i	−0.0364854	−	0.0488137i
$937$			4.80996e8i			0.584686i	0.956313	+	0.292343i	$0.0944350\pi$
$937$			4.80996e8i			0.584686i	−0.956313	+	0.292343i	$0.905565\pi$
$938$	1.76843e8	+	1.94630e8i	0.214279	+	0.235831i
$939$	−2.31883e8	−	2.31883e8i	−0.280074	−	0.280074i
$940$	4.37741e8	+	5.30695e8i	0.527028	+	0.638942i
$941$	−8.73738e8	−	8.73738e8i	−1.04861	−	1.04861i	−0.998757	−	0.0498497i	$-0.984126\pi$
$941$	−8.73738e8	−	8.73738e8i	−1.04861	−	1.04861i	−0.0498497	−	0.998757i	$-0.515874\pi$
$942$	2.34181e7	−	4.89081e8i	0.0280156	−	0.585098i
$943$		−	1.19525e9i		−	1.42535i
$944$	4.78705e8	+	7.08784e8i	0.569052	+	0.842554i
$945$	2.57090e8			0.304642
$946$	4.24601e8	+	2.03307e7i	0.501543	+	0.0240148i
$947$	−2.43752e8	+	2.43752e8i	−0.287011	+	0.287011i	−0.835897	−	0.548886i	$-0.815052\pi$
$947$	−2.43752e8	+	2.43752e8i	−0.287011	+	0.287011i	0.548886	+	0.835897i	$0.315052\pi$
$948$	−3.84479e8	−	4.66123e8i	−0.451282	−	0.547111i
$949$	−1.07217e8	+	1.07217e8i	−0.125448	+	0.125448i
$950$	2.56708e8	−	2.33248e8i	0.299412	−	0.272049i
$951$	1.15594e8			0.134398
$952$	−1.30535e8	+	9.03169e8i	−0.151292	+	1.04679i
$953$		−	1.87252e6i		−	0.00216345i	−0.999999	−	0.00108172i	$-0.999656\pi$
$953$		−	1.87252e6i		−	0.00216345i	0.999999	−	0.00108172i	$-0.000344324\pi$
$954$	−3.56357e8	+	3.23790e8i	−0.410431	+	0.372922i
$955$	2.18374e8	+	2.18374e8i	0.250721	+	0.250721i
$956$	9.61518e7	−	1.00175e9i	0.110048	−	1.14653i
$957$	−3.08513e8	−	3.08513e8i	−0.351995	−	0.351995i
$958$	8.88140e8	+	4.25258e7i	1.01015	+	0.0483678i
$959$		−	2.66633e8i		−	0.302314i
$960$	2.00179e8	−	6.78052e8i	0.226259	−	0.766389i
$961$	8.39093e8			0.945453
$962$	−9.31986e6	+	1.94643e8i	−0.0104685	+	0.218632i
$963$	1.83005e8	−	1.83005e8i	0.204920	−	0.204920i
$964$	1.18553e9	+	1.13792e8i	1.32337	+	0.127022i
$965$	9.26229e8	−	9.26229e8i	1.03071	−	1.03071i
$966$	−7.69953e8	−	8.47395e8i	−0.854148	−	0.940058i
$967$	−2.41899e8			−0.267519			−0.133760	−	0.991014i	$-0.542705\pi$
$967$	−2.41899e8			−0.267519			−0.133760	+	0.991014i	$0.542705\pi$
$968$	−6.74107e8	−	9.74286e7i	−0.743194	−	0.107414i
$969$		−	2.14629e8i		−	0.235894i
$970$	−4.31590e8	−	4.74999e8i	−0.472886	−	0.520449i
$971$	−4.30275e8	−	4.30275e8i	−0.469989	−	0.469989i	0.431922	−	0.901911i	$-0.357836\pi$
$971$	−4.30275e8	−	4.30275e8i	−0.469989	−	0.469989i	−0.901911	+	0.431922i	$0.857836\pi$
$972$	−4.54458e7	+	3.74857e7i	−0.0494874	+	0.0408194i
$973$	1.01303e9	+	1.01303e9i	1.09973	+	1.09973i
$974$	2.24448e7	−	4.68754e8i	0.0242906	−	0.507303i
$975$			8.95810e7i			0.0966500i
$976$	−6.14688e8	−	9.10125e8i	−0.661158	−	0.978930i
$977$	1.20501e9			1.29213			0.646065	−	0.763282i	$-0.276413\pi$
$977$	1.20501e9			1.29213			0.646065	+	0.763282i	$0.276413\pi$
$978$	7.57063e8	+	3.62496e7i	0.809311	+	0.0387513i
$979$	3.06005e8	−	3.06005e8i	0.326122	−	0.326122i
$980$	−3.09587e8	+	2.55361e8i	−0.328931	+	0.271317i
$981$	−3.28383e8	+	3.28383e8i	−0.347835	+	0.347835i
$982$	−9.63528e8	+	8.75473e8i	−1.01749	+	0.924503i
$983$	5.23755e8			0.551401			0.275701	−	0.961244i	$-0.411090\pi$
$983$	5.23755e8			0.551401			0.275701	+	0.961244i	$0.411090\pi$
$984$	3.26491e8	−	2.44033e8i	0.342677	−	0.256132i
$985$		−	1.06076e9i		−	1.10996i
$986$	1.13345e9	−	1.02987e9i	1.18242	−	1.07436i
$987$	2.68657e8	+	2.68657e8i	0.279414	+	0.279414i
$988$	−7.75471e7	−	7.44326e6i	−0.0804071	−	0.00771778i
$989$	−1.32375e9	−	1.32375e9i	−1.36841	−	1.36841i
$990$	2.23160e8	+	1.06853e7i	0.229991	+	0.0110124i
$991$		−	1.90803e9i		−	1.96049i	−0.197796	−	0.980243i	$-0.563378\pi$
$991$		−	1.90803e9i		−	1.96049i	0.197796	−	0.980243i	$-0.436622\pi$
$992$	−2.21499e8	−	5.40230e7i	−0.226901	−	0.0553406i
$993$	3.41522e8			0.348796
$994$	−8.63926e7	+	1.80429e9i	−0.0879665	+	1.83716i
$995$	−1.20194e8	+	1.20194e8i	−0.122015	+	0.122015i
$996$	−8.69113e7	+	9.05479e8i	−0.0879627	+	0.916432i
$997$	−8.50935e8	+	8.50935e8i	−0.858640	+	0.858640i	−0.991178	−	0.132538i	$-0.957687\pi$
$997$	−8.50935e8	+	8.50935e8i	−0.858640	+	0.858640i	0.132538	+	0.991178i	$0.457687\pi$
$998$	9.35917e6	+	1.03005e7i	0.00941555	+	0.0103626i
$999$	2.29713e8			0.230403

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.7.l.a.19.11	✓	48
4.3	odd	2		192.7.l.a.175.24		48
8.3	odd	2		384.7.l.a.223.1		48
8.5	even	2		384.7.l.b.223.24		48
16.3	odd	4		384.7.l.b.31.24		48
16.5	even	4		192.7.l.a.79.24		48
16.11	odd	4	inner	48.7.l.a.43.11	yes	48
16.13	even	4		384.7.l.a.31.1		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.7.l.a.19.11	✓	48	1.1	even	1	trivial
48.7.l.a.43.11	yes	48	16.11	odd	4	inner
192.7.l.a.79.24		48	16.5	even	4
192.7.l.a.175.24		48	4.3	odd	2
384.7.l.a.31.1		48	16.13	even	4
384.7.l.a.223.1		48	8.3	odd	2
384.7.l.b.31.24		48	16.3	odd	4
384.7.l.b.223.24		48	8.5	even	2

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:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	48.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.382617 + 7.99085i) q^{2} +(-11.0227 + 11.0227i) q^{3} +(-63.7072 - 6.11486i) q^{4} +(122.335 - 122.335i) q^{5} +(-83.8632 - 92.2982i) q^{6} +392.292 q^{7} +(73.2383 - 506.735i) q^{8} -243.000i q^{9} +O(q^{10})\)	\(q+(-0.382617 + 7.99085i) q^{2} +(-11.0227 + 11.0227i) q^{3} +(-63.7072 - 6.11486i) q^{4} +(122.335 - 122.335i) q^{5} +(-83.8632 - 92.2982i) q^{6} +392.292 q^{7} +(73.2383 - 506.735i) q^{8} -243.000i q^{9} +(930.754 + 1024.37i) q^{10} +(469.716 + 469.716i) q^{11} +(769.628 - 634.823i) q^{12} +(284.024 + 284.024i) q^{13} +(-150.098 + 3134.75i) q^{14} +2696.93i q^{15} +(4021.22 + 779.121i) q^{16} -4543.37 q^{17} +(1941.78 + 92.9758i) q^{18} +(2142.85 - 2142.85i) q^{19} +(-8541.70 + 7045.57i) q^{20} +(-4324.12 + 4324.12i) q^{21} +(-3933.15 + 3573.71i) q^{22} +23403.6 q^{23} +(4778.30 + 6392.87i) q^{24} -14306.8i q^{25} +(-2378.26 + 2160.92i) q^{26} +(2678.52 + 2678.52i) q^{27} +(-24991.8 - 2398.81i) q^{28} +(29793.3 + 29793.3i) q^{29} +(-21550.7 - 1031.89i) q^{30} +6957.76i q^{31} +(-7764.42 + 31834.8i) q^{32} -10355.1 q^{33} +(1738.37 - 36305.4i) q^{34} +(47991.2 - 47991.2i) q^{35} +(-1485.91 + 15480.9i) q^{36} +(42880.6 - 42880.6i) q^{37} +(16303.3 + 17943.1i) q^{38} -6261.42 q^{39} +(-53031.9 - 70951.1i) q^{40} -51071.1i q^{41} +(-32898.9 - 36207.9i) q^{42} +(-56561.8 - 56561.8i) q^{43} +(-27052.1 - 32796.6i) q^{44} +(-29727.5 - 29727.5i) q^{45} +(-8954.62 + 187015. i) q^{46} -62130.0i q^{47} +(-52912.7 + 35736.7i) q^{48} +36244.2 q^{49} +(114324. + 5474.03i) q^{50} +(50080.3 - 50080.3i) q^{51} +(-16357.6 - 19831.1i) q^{52} +(-175135. + 175135. i) q^{53} +(-22428.5 + 20378.8i) q^{54} +114926. q^{55} +(28730.8 - 198788. i) q^{56} +47240.0i q^{57} +(-249473. + 226675. i) q^{58} +(147653. + 147653. i) q^{59} +(16491.4 - 171814. i) q^{60} +(-189596. - 189596. i) q^{61} +(-55598.4 - 2662.15i) q^{62} -95327.0i q^{63} +(-251416. - 74224.8i) q^{64} +69492.2 q^{65} +(3962.03 - 82745.9i) q^{66} +(59250.9 - 59250.9i) q^{67} +(289446. + 27782.1i) q^{68} +(-257971. + 257971. i) q^{69} +(365128. + 401852. i) q^{70} +575576. q^{71} +(-123137. - 17796.9i) q^{72} +377493. i q^{73} +(326245. + 359059. i) q^{74} +(157700. + 157700. i) q^{75} +(-149618. + 123412. i) q^{76} +(184266. + 184266. i) q^{77} +(2395.72 - 50034.0i) q^{78} -605647. i q^{79} +(587250. - 396622. i) q^{80} -59049.0 q^{81} +(408101. + 19540.6i) q^{82} +(-644721. + 644721. i) q^{83} +(301919. - 249036. i) q^{84} +(-555815. + 555815. i) q^{85} +(473618. - 430335. i) q^{86} -656806. q^{87} +(272423. - 203620. i) q^{88} -651468. i q^{89} +(248922. - 226173. i) q^{90} +(111420. + 111420. i) q^{91} +(-1.49098e6 - 143110. i) q^{92} +(-76693.3 - 76693.3i) q^{93} +(496471. + 23772.0i) q^{94} -524293. i q^{95} +(-265321. - 436491. i) q^{96} -463699. q^{97} +(-13867.6 + 289622. i) q^{98} +(114141. - 114141. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 180 q^{4} - 1932 q^{8}+O(q^{10}) \) 48 * q - 180 * q^4 - 1932 * q^8	\( 48 q - 180 q^{4} - 1932 q^{8} + 744 q^{10} - 2720 q^{11} - 1944 q^{12} - 15388 q^{14} + 3744 q^{16} + 4860 q^{18} - 3936 q^{19} - 14000 q^{20} - 41184 q^{22} + 26240 q^{23} + 18468 q^{24} - 5300 q^{26} - 96120 q^{28} + 66400 q^{29} - 33048 q^{30} - 52960 q^{32} + 122208 q^{34} + 162336 q^{35} + 32076 q^{36} - 7200 q^{37} + 16968 q^{38} - 309072 q^{40} - 231660 q^{42} + 340704 q^{43} - 193192 q^{44} - 450264 q^{46} + 299376 q^{48} + 806736 q^{49} + 537764 q^{50} + 80352 q^{51} + 1126224 q^{52} + 443680 q^{53} + 78732 q^{54} + 232704 q^{55} - 420448 q^{56} - 1295664 q^{58} - 886144 q^{59} - 627912 q^{60} - 326496 q^{61} - 719652 q^{62} - 192024 q^{64} - 372832 q^{65} + 775656 q^{66} - 962112 q^{67} + 3197632 q^{68} + 541728 q^{69} + 642816 q^{70} + 534016 q^{71} + 82620 q^{72} - 4894836 q^{74} - 1073088 q^{75} - 3162552 q^{76} - 932960 q^{77} - 337284 q^{78} + 4668072 q^{80} - 2834352 q^{81} + 5077560 q^{82} - 2497760 q^{83} + 1312200 q^{84} - 372000 q^{85} + 4142928 q^{86} - 2794272 q^{88} - 507384 q^{90} + 775008 q^{91} - 9470992 q^{92} - 5050728 q^{94} + 1879200 q^{96} + 12708584 q^{98} - 660960 q^{99}+O(q^{100}) \) 48 * q - 180 * q^4 - 1932 * q^8 + 744 * q^10 - 2720 * q^11 - 1944 * q^12 - 15388 * q^14 + 3744 * q^16 + 4860 * q^18 - 3936 * q^19 - 14000 * q^20 - 41184 * q^22 + 26240 * q^23 + 18468 * q^24 - 5300 * q^26 - 96120 * q^28 + 66400 * q^29 - 33048 * q^30 - 52960 * q^32 + 122208 * q^34 + 162336 * q^35 + 32076 * q^36 - 7200 * q^37 + 16968 * q^38 - 309072 * q^40 - 231660 * q^42 + 340704 * q^43 - 193192 * q^44 - 450264 * q^46 + 299376 * q^48 + 806736 * q^49 + 537764 * q^50 + 80352 * q^51 + 1126224 * q^52 + 443680 * q^53 + 78732 * q^54 + 232704 * q^55 - 420448 * q^56 - 1295664 * q^58 - 886144 * q^59 - 627912 * q^60 - 326496 * q^61 - 719652 * q^62 - 192024 * q^64 - 372832 * q^65 + 775656 * q^66 - 962112 * q^67 + 3197632 * q^68 + 541728 * q^69 + 642816 * q^70 + 534016 * q^71 + 82620 * q^72 - 4894836 * q^74 - 1073088 * q^75 - 3162552 * q^76 - 932960 * q^77 - 337284 * q^78 + 4668072 * q^80 - 2834352 * q^81 + 5077560 * q^82 - 2497760 * q^83 + 1312200 * q^84 - 372000 * q^85 + 4142928 * q^86 - 2794272 * q^88 - 507384 * q^90 + 775008 * q^91 - 9470992 * q^92 - 5050728 * q^94 + 1879200 * q^96 + 12708584 * q^98 - 660960 * q^99

Introduction

L-functions

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