LMFDB - Embedded newform 48.7.l.a.43.18

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			43.18
Character	$\chi$	$=$	48.43
Dual form			48.7.l.a.19.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5.00967 - 6.23724i) q^{2} +(-11.0227 - 11.0227i) q^{3} +(-13.8064 - 62.4931i) q^{4} +(45.7781 + 45.7781i) q^{5} +(-123.971 + 13.5312i) q^{6} -565.544 q^{7} +(-458.950 - 226.956i) q^{8} +243.000i q^{9} +O(q^{10})$	\(q+(5.00967 - 6.23724i) q^{2} +(-11.0227 - 11.0227i) q^{3} +(-13.8064 - 62.4931i) q^{4} +(45.7781 + 45.7781i) q^{5} +(-123.971 + 13.5312i) q^{6} -565.544 q^{7} +(-458.950 - 226.956i) q^{8} +243.000i q^{9} +(514.863 - 56.1959i) q^{10} +(1291.95 - 1291.95i) q^{11} +(-536.659 + 841.026i) q^{12} +(-2882.93 + 2882.93i) q^{13} +(-2833.19 + 3527.44i) q^{14} -1009.20i q^{15} +(-3714.77 + 1725.61i) q^{16} -662.555 q^{17} +(1515.65 + 1217.35i) q^{18} +(1940.19 + 1940.19i) q^{19} +(2228.79 - 3492.85i) q^{20} +(6233.83 + 6233.83i) q^{21} +(-1585.96 - 14530.4i) q^{22} -15879.3 q^{23} +(2557.20 + 7560.54i) q^{24} -11433.7i q^{25} +(3539.01 + 32424.1i) q^{26} +(2678.52 - 2678.52i) q^{27} +(7808.12 + 35342.6i) q^{28} +(11555.8 - 11555.8i) q^{29} +(-6294.61 - 5055.75i) q^{30} -39097.9i q^{31} +(-7846.73 + 31814.6i) q^{32} -28481.5 q^{33} +(-3319.18 + 4132.52i) q^{34} +(-25889.6 - 25889.6i) q^{35} +(15185.8 - 3354.95i) q^{36} +(-51336.5 - 51336.5i) q^{37} +(21821.2 - 2381.73i) q^{38} +63555.4 q^{39} +(-10620.3 - 31399.5i) q^{40} +66520.0i q^{41} +(70111.3 - 7652.47i) q^{42} +(68923.6 - 68923.6i) q^{43} +(-98574.8 - 62900.6i) q^{44} +(-11124.1 + 11124.1i) q^{45} +(-79550.2 + 99043.2i) q^{46} -107734. i q^{47} +(59967.6 + 21925.9i) q^{48} +202191. q^{49} +(-71314.9 - 57279.2i) q^{50} +(7303.15 + 7303.15i) q^{51} +(219966. + 140360. i) q^{52} +(-108477. - 108477. i) q^{53} +(-3288.07 - 30125.0i) q^{54} +118286. q^{55} +(259556. + 128354. i) q^{56} -42772.3i q^{57} +(-14185.5 - 129967. i) q^{58} +(-67889.1 + 67889.1i) q^{59} +(-63067.9 + 13933.4i) q^{60} +(-99209.6 + 99209.6i) q^{61} +(-243863. - 195868. i) q^{62} -137427. i q^{63} +(159126. + 208323. i) q^{64} -263951. q^{65} +(-142683. + 177646. i) q^{66} +(-105403. - 105403. i) q^{67} +(9147.50 + 41405.1i) q^{68} +(175033. + 175033. i) q^{69} +(-291178. + 31781.3i) q^{70} +266114. q^{71} +(55150.3 - 111525. i) q^{72} +267965. i q^{73} +(-577377. + 63019.2i) q^{74} +(-126031. + 126031. i) q^{75} +(94461.5 - 148036. i) q^{76} +(-730653. + 730653. i) q^{77} +(318392. - 396411. i) q^{78} +557984. i q^{79} +(-249050. - 91060.0i) q^{80} -59049.0 q^{81} +(414901. + 333243. i) q^{82} +(-236224. - 236224. i) q^{83} +(303504. - 475638. i) q^{84} +(-30330.5 - 30330.5i) q^{85} +(-84608.7 - 775178. i) q^{86} -254751. q^{87} +(-886153. + 299724. i) q^{88} +419786. i q^{89} +(13655.6 + 125112. i) q^{90} +(1.63043e6 - 1.63043e6i) q^{91} +(219236. + 992347. i) q^{92} +(-430964. + 430964. i) q^{93} +(-671966. - 539714. i) q^{94} +177637. i q^{95} +(437175. - 264191. i) q^{96} +393308. q^{97} +(1.01291e6 - 1.26112e6i) q^{98} +(313943. + 313943. 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 $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

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

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 $

$2$	5.00967	−	6.23724i	0.626209	−	0.779655i
$2$	5.00967	−	6.23724i	0.626209	−	0.779655i
$3$	−11.0227	−	11.0227i	−0.408248	−	0.408248i
$3$	−11.0227	−	11.0227i	−0.408248	−	0.408248i
$4$	−13.8064	−	62.4931i	−0.215725	−	0.976454i
$5$	45.7781	+	45.7781i	0.366225	+	0.366225i	0.866098	−	0.499873i	$-0.166620\pi$
$5$	45.7781	+	45.7781i	0.366225	+	0.366225i	−0.499873	+	0.866098i	$0.666620\pi$
$6$	−123.971	+	13.5312i	−0.573942	+	0.0626443i
$7$	−565.544			−1.64882			−0.824408	−	0.565995i	$-0.808492\pi$
$7$	−565.544			−1.64882			−0.824408	+	0.565995i	$0.808492\pi$
$8$	−458.950	−	226.956i	−0.896387	−	0.443273i
$9$			243.000i			0.333333i
$10$	514.863	−	56.1959i	0.514863	−	0.0561959i
$11$	1291.95	−	1291.95i	0.970658	−	0.970658i	−0.0289233	−	0.999582i	$-0.509208\pi$
$11$	1291.95	−	1291.95i	0.970658	−	0.970658i	0.999582	+	0.0289233i	$0.00920786\pi$
$12$	−536.659	+	841.026i	−0.310566	+	0.486705i
$13$	−2882.93	+	2882.93i	−1.31221	+	1.31221i	−0.392433	+	0.919781i	$0.628366\pi$
$13$	−2882.93	+	2882.93i	−1.31221	+	1.31221i	−0.919781	+	0.392433i	$0.871634\pi$
$14$	−2833.19	+	3527.44i	−1.03250	+	1.28551i
$15$		−	1009.20i		−	0.299022i
$16$	−3714.77	+	1725.61i	−0.906926	+	0.421291i
$17$	−662.555			−0.134858			−0.0674288	−	0.997724i	$-0.521480\pi$
$17$	−662.555			−0.134858			−0.0674288	+	0.997724i	$0.521480\pi$
$18$	1515.65	+	1217.35i	0.259885	+	0.208736i
$19$	1940.19	+	1940.19i	0.282868	+	0.282868i	0.834252	−	0.551384i	$-0.185900\pi$
$19$	1940.19	+	1940.19i	0.282868	+	0.282868i	−0.551384	+	0.834252i	$0.685900\pi$
$20$	2228.79	−	3492.85i	0.278598	−	0.436606i
$21$	6233.83	+	6233.83i	0.673127	+	0.673127i
$22$	−1585.96	−	14530.4i	−0.148944	−	1.36461i
$23$	−15879.3			−1.30511			−0.652557	−	0.757740i	$-0.726304\pi$
$23$	−15879.3			−1.30511			−0.652557	+	0.757740i	$0.726304\pi$
$24$	2557.20	+	7560.54i	0.184983	+	0.546914i
$25$		−	11433.7i		−	0.731758i
$26$	3539.01	+	32424.1i	0.201355	+	1.84479i
$27$	2678.52	−	2678.52i	0.136083	−	0.136083i
$28$	7808.12	+	35342.6i	0.355691	+	1.60999i
$29$	11555.8	−	11555.8i	0.473810	−	0.473810i	−0.429335	−	0.903145i	$-0.641252\pi$
$29$	11555.8	−	11555.8i	0.473810	−	0.473810i	0.903145	+	0.429335i	$0.141252\pi$
$30$	−6294.61	−	5055.75i	−0.233134	−	0.187250i
$31$		−	39097.9i		−	1.31241i	−0.754585	−	0.656203i	$-0.772162\pi$
$31$		−	39097.9i		−	1.31241i	0.754585	−	0.656203i	$-0.227838\pi$
$32$	−7846.73	+	31814.6i	−0.239463	+	0.970905i
$33$	−28481.5			−0.792539
$34$	−3319.18	+	4132.52i	−0.0844490	+	0.105142i
$35$	−25889.6	−	25889.6i	−0.603838	−	0.603838i
$36$	15185.8	−	3354.95i	0.325485	−	0.0719083i
$37$	−51336.5	−	51336.5i	−1.01349	−	1.01349i	−0.999908	−	0.0135861i	$-0.995675\pi$
$37$	−51336.5	−	51336.5i	−1.01349	−	1.01349i	−0.0135861	−	0.999908i	$-0.504325\pi$
$38$	21821.2	−	2381.73i	0.397674	−	0.0434051i
$39$	63555.4			1.07142
$40$	−10620.3	−	31399.5i	−0.165941	−	0.490617i
$41$			66520.0i			0.965163i	0.875851	+	0.482582i	$0.160301\pi$
$41$			66520.0i			0.965163i	−0.875851	+	0.482582i	$0.839699\pi$
$42$	70111.3	−	7652.47i	0.946325	−	0.103289i
$43$	68923.6	−	68923.6i	0.866887	−	0.866887i	−0.125239	−	0.992127i	$-0.539970\pi$
$43$	68923.6	−	68923.6i	0.866887	−	0.866887i	0.992127	+	0.125239i	$0.0399699\pi$
$44$	−98574.8	−	62900.6i	−1.15720	−	0.738408i
$45$	−11124.1	+	11124.1i	−0.122075	+	0.122075i
$46$	−79550.2	+	99043.2i	−0.817274	+	1.01754i
$47$		−	107734.i		−	1.03767i	−0.854873	−	0.518837i	$-0.826365\pi$
$47$		−	107734.i		−	1.03767i	0.854873	−	0.518837i	$-0.173635\pi$
$48$	59967.6	+	21925.9i	0.542242	+	0.198260i
$49$	202191.			1.71860
$50$	−71314.9	−	57279.2i	−0.570519	−	0.458234i
$51$	7303.15	+	7303.15i	0.0550554	+	0.0550554i
$52$	219966.	+	140360.i	1.56439	+	0.998239i
$53$	−108477.	−	108477.i	−0.728637	−	0.728637i	0.241711	−	0.970348i	$-0.422291\pi$
$53$	−108477.	−	108477.i	−0.728637	−	0.728637i	−0.970348	+	0.241711i	$0.922291\pi$
$54$	−3288.07	−	30125.0i	−0.0208814	−	0.191314i
$55$	118286.			0.710959
$56$	259556.	+	128354.i	1.47798	+	0.730876i
$57$		−	42772.3i		−	0.230961i
$58$	−14185.5	−	129967.i	−0.0727045	−	0.666113i
$59$	−67889.1	+	67889.1i	−0.330555	+	0.330555i	−0.852797	−	0.522242i	$-0.825096\pi$
$59$	−67889.1	+	67889.1i	−0.330555	+	0.330555i	0.522242	+	0.852797i	$0.325096\pi$
$60$	−63067.9	+	13933.4i	−0.291981	+	0.0645064i
$61$	−99209.6	+	99209.6i	−0.437083	+	0.437083i	−0.891029	−	0.453946i	$-0.850016\pi$
$61$	−99209.6	+	99209.6i	−0.437083	+	0.437083i	0.453946	+	0.891029i	$0.350016\pi$
$62$	−243863.	−	195868.i	−1.02322	−	0.821840i
$63$		−	137427.i		−	0.549606i
$64$	159126.	+	208323.i	0.607018	+	0.794688i
$65$	−263951.			−0.961131
$66$	−142683.	+	177646.i	−0.496295	+	0.617907i
$67$	−105403.	−	105403.i	−0.350451	−	0.350451i	0.509826	−	0.860277i	$-0.329710\pi$
$67$	−105403.	−	105403.i	−0.350451	−	0.350451i	−0.860277	+	0.509826i	$0.829710\pi$
$68$	9147.50	+	41405.1i	0.0290921	+	0.131682i
$69$	175033.	+	175033.i	0.532810	+	0.532810i
$70$	−291178.	+	31781.3i	−0.848914	+	0.0926568i
$71$	266114.			0.743520			0.371760	−	0.928329i	$-0.378754\pi$
$71$	266114.			0.743520			0.371760	+	0.928329i	$0.378754\pi$
$72$	55150.3	−	111525.i	0.147758	−	0.298796i
$73$			267965.i			0.688826i	0.938818	+	0.344413i	$0.111922\pi$
$73$			267965.i			0.688826i	−0.938818	+	0.344413i	$0.888078\pi$
$74$	−577377.	+	63019.2i	−1.42483	+	0.155517i
$75$	−126031.	+	126031.i	−0.298739	+	0.298739i
$76$	94461.5	−	148036.i	0.215186	−	0.337229i
$77$	−730653.	+	730653.i	−1.60044	+	1.60044i
$78$	318392.	−	396411.i	0.670931	−	0.835337i
$79$			557984.i			1.13172i	0.824500	+	0.565862i	$0.191456\pi$
$79$			557984.i			1.13172i	−0.824500	+	0.565862i	$0.808544\pi$
$80$	−249050.	−	91060.0i	−0.486426	−	0.177852i
$81$	−59049.0			−0.111111
$82$	414901.	+	333243.i	0.752495	+	0.604394i
$83$	−236224.	−	236224.i	−0.413133	−	0.413133i	0.469695	−	0.882829i	$-0.344364\pi$
$83$	−236224.	−	236224.i	−0.413133	−	0.413133i	−0.882829	+	0.469695i	$0.844364\pi$
$84$	303504.	−	475638.i	0.512067	−	0.802487i
$85$	−30330.5	−	30330.5i	−0.0493882	−	0.0493882i
$86$	−84608.7	−	775178.i	−0.133021	−	1.21873i
$87$	−254751.			−0.386864
$88$	−886153.	+	299724.i	−1.30035	+	0.439818i
$89$			419786.i			0.595467i	0.954649	+	0.297733i	$0.0962307\pi$
$89$			419786.i			0.595467i	−0.954649	+	0.297733i	$0.903769\pi$
$90$	13655.6	+	125112.i	0.0187320	+	0.171621i
$91$	1.63043e6	−	1.63043e6i	2.16360	−	2.16360i
$92$	219236.	+	992347.i	0.281546	+	1.27438i
$93$	−430964.	+	430964.i	−0.535787	+	0.535787i
$94$	−671966.	−	539714.i	−0.809028	−	0.649801i
$95$			177637.i			0.207187i
$96$	437175.	−	264191.i	0.494131	−	0.298610i
$97$	393308.			0.430940			0.215470	−	0.976510i	$-0.430872\pi$
$97$	393308.			0.430940			0.215470	+	0.976510i	$0.430872\pi$
$98$	1.01291e6	−	1.26112e6i	1.07620	−	1.33991i
$99$	313943.	+	313943.i	0.323553	+	0.323553i
$100$	−714529.	+	157858.i	−0.714529	+	0.157858i
$101$	670944.	+	670944.i	0.651212	+	0.651212i	0.953285	−	0.302073i	$-0.0976787\pi$
$101$	670944.	+	670944.i	0.651212	+	0.651212i	−0.302073	+	0.953285i	$0.597679\pi$
$102$	82137.9	−	8965.14i	0.0774004	−	0.00844805i
$103$	456775.			0.418013			0.209007	−	0.977914i	$-0.432977\pi$
$103$	456775.			0.418013			0.209007	+	0.977914i	$0.432977\pi$
$104$	1.97742e6	−	668823.i	1.75792	−	0.594581i
$105$			570746.i			0.493032i
$106$	−1.22004e6	+	133164.i	−1.02436	+	0.111807i
$107$	−498780.	+	498780.i	−0.407153	+	0.407153i	−0.880745	−	0.473592i	$-0.842957\pi$
$107$	−498780.	+	498780.i	−0.407153	+	0.407153i	0.473592	+	0.880745i	$0.342957\pi$
$108$	−204369.	−	130408.i	−0.162235	−	0.103522i
$109$	−686021.	+	686021.i	−0.529734	+	0.529734i	−0.920493	−	0.390759i	$-0.872213\pi$
$109$	−686021.	+	686021.i	−0.529734	+	0.529734i	0.390759	+	0.920493i	$0.372213\pi$
$110$	592573.	−	737777.i	0.445209	−	0.554303i
$111$			1.13173e6i			0.827514i
$112$	2.10086e6	−	975907.i	1.49535	−	0.694632i
$113$	1.76590e6			1.22386			0.611930	−	0.790912i	$-0.290394\pi$
$113$	1.76590e6			1.22386			0.611930	+	0.790912i	$0.290394\pi$
$114$	−266781.	−	214275.i	−0.180070	−	0.144630i
$115$	−726926.	−	726926.i	−0.477965	−	0.477965i
$116$	−881698.	−	562611.i	−0.564866	−	0.360441i
$117$	−700553.	−	700553.i	−0.437404	−	0.437404i
$118$	83338.8	+	763543.i	0.0507226	+	0.464716i
$119$	374704.			0.222355
$120$	−229043.	+	463171.i	−0.132548	+	0.268039i
$121$		−	1.56669e6i		−	0.884355i
$122$	121787.	+	1.11580e6i	0.0670689	+	0.614480i
$123$	733230.	−	733230.i	0.394026	−	0.394026i
$124$	−2.44335e6	+	539801.i	−1.28150	+	0.283119i
$125$	1.23870e6	−	1.23870e6i	0.634213	−	0.634213i
$126$	−857167.	−	688465.i	−0.428503	−	0.344168i
$127$		−	2.52519e6i		−	1.23277i	−0.787445	−	0.616385i	$-0.788596\pi$
$127$		−	2.52519e6i		−	1.23277i	0.787445	−	0.616385i	$-0.211404\pi$
$128$	2.09653e6	+	51120.8i	0.999703	+	0.0243763i
$129$	−1.51945e6			−0.707810
$130$	−1.32231e6	+	1.64632e6i	−0.601869	+	0.749351i
$131$	−2.20532e6	−	2.20532e6i	−0.980976	−	0.980976i	0.0188466	−	0.999822i	$-0.494001\pi$
$131$	−2.20532e6	−	2.20532e6i	−0.980976	−	0.980976i	−0.999822	+	0.0188466i	$0.994001\pi$
$132$	393227.	+	1.77990e6i	0.170970	+	0.773878i
$133$	−1.09726e6	−	1.09726e6i	−0.466398	−	0.466398i
$134$	−1.18546e6	+	129389.i	−0.492687	+	0.0537755i
$135$	245235.			0.0996738
$136$	304080.	+	150371.i	0.120885	+	0.0597788i
$137$		−	210985.i		−	0.0820520i	−0.999158	−	0.0410260i	$-0.986937\pi$
$137$		−	210985.i		−	0.0820520i	0.999158	−	0.0410260i	$-0.0130626\pi$
$138$	1.96858e6	−	214866.i	0.749059	−	0.0817579i
$139$	−678952.	+	678952.i	−0.252810	+	0.252810i	−0.822122	−	0.569312i	$-0.807210\pi$
$139$	−678952.	+	678952.i	−0.252810	+	0.252810i	0.569312	+	0.822122i	$0.307210\pi$
$140$	−1.26048e6	+	1.97536e6i	−0.459357	+	0.719883i
$141$	−1.18752e6	+	1.18752e6i	−0.423629	+	0.423629i
$142$	1.33314e6	−	1.65982e6i	0.465599	−	0.579690i
$143$			7.44919e6i			2.54742i
$144$	−419323.	−	902688.i	−0.140430	−	0.302309i
$145$	1.05800e6			0.347042
$146$	1.67136e6	+	1.34242e6i	0.537047	+	0.431349i
$147$	−2.22869e6	−	2.22869e6i	−0.701614	−	0.701614i
$148$	−2.49940e6	+	3.91695e6i	−0.770994	+	1.20827i
$149$	−2.62816e6	−	2.62816e6i	−0.794497	−	0.794497i	0.187724	−	0.982222i	$-0.439889\pi$
$149$	−2.62816e6	−	2.62816e6i	−0.794497	−	0.794497i	−0.982222	+	0.187724i	$0.939889\pi$
$150$	154712.	+	1.41745e6i	0.0458405	+	0.419987i
$151$	2.88045e6			0.836622			0.418311	−	0.908304i	$-0.362622\pi$
$151$	2.88045e6			0.836622			0.418311	+	0.908304i	$0.362622\pi$
$152$	−450113.	−	1.33079e6i	−0.128171	−	0.378947i
$153$		−	161001.i		−	0.0449525i
$154$	896928.	+	8.21759e6i	0.245581	+	2.25000i
$155$	1.78983e6	−	1.78983e6i	0.480636	−	0.480636i
$156$	−877471.	−	3.97177e6i	−0.231131	−	1.04619i
$157$	−501498.	+	501498.i	−0.129590	+	0.129590i	−0.768927	−	0.639337i	$-0.779209\pi$
$157$	−501498.	+	501498.i	−0.129590	+	0.129590i	0.639337	+	0.768927i	$0.279209\pi$
$158$	3.48028e6	+	2.79531e6i	0.882354	+	0.708695i
$159$			2.39143e6i			0.594930i
$160$	−1.81562e6	+	1.09721e6i	−0.443267	+	0.267873i
$161$	8.98046e6			2.15189
$162$	−295816.	+	368303.i	−0.0695788	+	0.0866284i
$163$	1.30009e6	+	1.30009e6i	0.300199	+	0.300199i	0.841092	−	0.540893i	$-0.181913\pi$
$163$	1.30009e6	+	1.30009e6i	0.300199	+	0.300199i	−0.540893	+	0.841092i	$0.681913\pi$
$164$	4.15704e6	−	918401.i	0.942438	−	0.208210i
$165$	−1.30383e6	−	1.30383e6i	−0.290248	−	0.290248i
$166$	−2.65679e6	+	289982.i	−0.580809	+	0.0633938i
$167$	−8.60262e6			−1.84706			−0.923531	−	0.383524i	$-0.874710\pi$
$167$	−8.60262e6			−1.84706			−0.923531	+	0.383524i	$0.874710\pi$
$168$	−1.44621e6	−	4.27582e6i	−0.305003	−	0.901761i
$169$		−	1.17958e7i		−	2.44381i
$170$	−341125.	+	37232.9i	−0.0694331	+	0.00757845i
$171$	−471467.	+	471467.i	−0.0942894	+	0.0942894i
$172$	−5.25883e6	−	3.35566e6i	−1.03348	−	0.659466i
$173$	−891920.	+	891920.i	−0.172261	+	0.172261i	−0.787972	−	0.615711i	$-0.788869\pi$
$173$	−891920.	+	891920.i	−0.172261	+	0.172261i	0.615711	+	0.787972i	$0.288869\pi$
$174$	−1.27622e6	+	1.58895e6i	−0.242258	+	0.301621i
$175$			6.46628e6i			1.20654i
$176$	−2.56989e6	+	7.02867e6i	−0.471385	+	1.28924i
$177$	1.49664e6			0.269897
$178$	2.61831e6	+	2.10299e6i	0.464259	+	0.372887i
$179$	−2.89580e6	−	2.89580e6i	−0.504904	−	0.504904i	0.408054	−	0.912958i	$-0.366208\pi$
$179$	−2.89580e6	−	2.89580e6i	−0.504904	−	0.504904i	−0.912958	+	0.408054i	$0.866208\pi$
$180$	848762.	+	541595.i	0.145535	+	0.0928661i
$181$	2.14643e6	+	2.14643e6i	0.361977	+	0.361977i	0.864541	−	0.502563i	$-0.167610\pi$
$181$	2.14643e6	+	2.14643e6i	0.361977	+	0.361977i	−0.502563	+	0.864541i	$0.667610\pi$
$182$	−2.00146e6	−	1.83373e7i	−0.331997	−	3.04173i
$183$	2.18712e6			0.356877
$184$	7.28781e6	+	3.60391e6i	1.16989	+	0.578522i
$185$		−	4.70018e6i		−	0.742334i
$186$	529040.	+	4.84702e6i	0.0822147	+	0.753244i
$187$	−855986.	+	855986.i	−0.130901	+	0.130901i
$188$	−6.73265e6	+	1.48742e6i	−1.01324	+	0.223852i
$189$	−1.51482e6	+	1.51482e6i	−0.224376	+	0.224376i
$190$	1.10796e6	+	889902.i	0.161534	+	0.129742i
$191$		−	1.12449e6i		−	0.161382i	−0.996739	−	0.0806912i	$-0.974287\pi$
$191$		−	1.12449e6i		−	0.161382i	0.996739	−	0.0806912i	$-0.0257128\pi$
$192$	542281.	−	4.05028e6i	0.0766162	−	0.572244i
$193$	6.65489e6			0.925697			0.462848	−	0.886437i	$-0.346827\pi$
$193$	6.65489e6			0.925697			0.462848	+	0.886437i	$0.346827\pi$
$194$	1.97034e6	−	2.45316e6i	0.269859	−	0.335985i
$195$	2.90945e6	+	2.90945e6i	0.392380	+	0.392380i
$196$	−2.79153e6	−	1.26355e7i	−0.370744	−	1.67813i
$197$	1.01919e6	+	1.01919e6i	0.133307	+	0.133307i	0.770612	−	0.637305i	$-0.219951\pi$
$197$	1.01919e6	+	1.01919e6i	0.133307	+	0.133307i	−0.637305	+	0.770612i	$0.719951\pi$
$198$	3.53089e6	−	385387.i	0.454871	−	0.0496480i
$199$	889727.			0.112901			0.0564505	−	0.998405i	$-0.482022\pi$
$199$	889727.			0.112901			0.0564505	+	0.998405i	$0.482022\pi$
$200$	−2.59495e6	+	5.24751e6i	−0.324369	+	0.655938i
$201$			2.32365e6i			0.286142i
$202$	7.54605e6	−	823632.i	0.915515	−	0.0999261i
$203$	−6.53529e6	+	6.53529e6i	−0.781226	+	0.781226i
$204$	355566.	−	557226.i	0.0418822	−	0.0656359i
$205$	−3.04516e6	+	3.04516e6i	−0.353467	+	0.353467i
$206$	2.28829e6	−	2.84901e6i	0.261764	−	0.325906i
$207$		−	3.85867e6i		−	0.435038i
$208$	5.73461e6	−	1.56842e7i	0.637256	−	1.74290i
$209$	5.01325e6			0.549137
$210$	3.55988e6	+	2.85925e6i	0.384395	+	0.308741i
$211$	−6.10371e6	−	6.10371e6i	−0.649750	−	0.649750i	0.303182	−	0.952933i	$-0.401951\pi$
$211$	−6.10371e6	−	6.10371e6i	−0.649750	−	0.649750i	−0.952933	+	0.303182i	$0.901951\pi$
$212$	−5.28140e6	+	8.27676e6i	−0.554296	+	0.868666i
$213$	−2.93330e6	−	2.93330e6i	−0.303541	−	0.303541i
$214$	612288.	+	5.60973e6i	0.0624762	+	0.572402i
$215$	6.31039e6			0.634952
$216$	−1.83721e6	+	621400.i	−0.182305	+	0.0616609i
$217$			2.21116e7i			2.16392i
$218$	842139.	+	7.71561e6i	0.0812858	+	0.744734i
$219$	2.95370e6	−	2.95370e6i	0.281212	−	0.281212i
$220$	−1.63310e6	−	7.39204e6i	−0.153372	−	0.694219i
$221$	1.91010e6	−	1.91010e6i	0.176962	−	0.176962i
$222$	7.05890e6	+	5.66962e6i	0.645176	+	0.518197i
$223$			8.07405e6i			0.728077i	0.931384	+	0.364038i	$0.118602\pi$
$223$			8.07405e6i			0.728077i	−0.931384	+	0.364038i	$0.881398\pi$
$224$	4.43767e6	−	1.79926e7i	0.394831	−	1.60085i
$225$	2.77840e6			0.243919
$226$	8.84659e6	−	1.10144e7i	0.766391	−	0.954188i
$227$	−4.13774e6	−	4.13774e6i	−0.353741	−	0.353741i	0.507758	−	0.861500i	$-0.330474\pi$
$227$	−4.13774e6	−	4.13774e6i	−0.353741	−	0.353741i	−0.861500	+	0.507758i	$0.830474\pi$
$228$	−2.67297e6	+	590532.i	−0.225523	+	0.0498240i
$229$	−1.19667e7	−	1.19667e7i	−0.996480	−	0.996480i	0.00351356	−	0.999994i	$-0.498882\pi$
$229$	−1.19667e7	−	1.19667e7i	−0.996480	−	0.996480i	−0.999994	+	0.00351356i	$0.998882\pi$
$230$	−8.17567e6	+	892353.i	−0.671954	+	0.0733421i
$231$	1.61075e7			1.30675
$232$	−7.92616e6	+	2.68087e6i	−0.634744	+	0.214690i
$233$			1.46761e6i			0.116023i	0.998316	+	0.0580114i	$0.0184760\pi$
$233$			1.46761e6i			0.116023i	−0.998316	+	0.0580114i	$0.981524\pi$
$234$	−7.87906e6	+	859979.i	−0.614931	+	0.0671182i
$235$	4.93188e6	−	4.93188e6i	0.380022	−	0.380022i
$236$	5.17991e6	+	3.30530e6i	0.394081	+	0.251463i
$237$	6.15049e6	−	6.15049e6i	0.462024	−	0.462024i
$238$	1.87715e6	−	2.33712e6i	0.139241	−	0.173361i
$239$			1.28489e7i			0.941177i	0.882353	+	0.470588i	$0.155958\pi$
$239$			1.28489e7i			0.941177i	−0.882353	+	0.470588i	$0.844042\pi$
$240$	1.74148e6	+	3.74893e6i	0.125975	+	0.271190i
$241$	−1.87104e6			−0.133670			−0.0668348	−	0.997764i	$-0.521290\pi$
$241$	−1.87104e6			−0.133670			−0.0668348	+	0.997764i	$0.521290\pi$
$242$	−9.77182e6	−	7.84860e6i	−0.689492	−	0.553791i
$243$	650880.	+	650880.i	0.0453609	+	0.0453609i
$244$	7.56964e6	+	4.83018e6i	0.521081	+	0.332502i
$245$	9.25593e6	+	9.25593e6i	0.629393	+	0.629393i
$246$	−900093.	−	8.24658e6i	−0.0604619	−	0.553947i
$247$	−1.11869e7			−0.742367
$248$	−8.87349e6	+	1.79440e7i	−0.581754	+	1.17642i
$249$			5.20766e6i			0.337322i
$250$	−1.52059e6	−	1.39315e7i	−0.0973178	−	0.891618i
$251$	−2.06552e7	+	2.06552e7i	−1.30619	+	1.30619i	−0.382052	+	0.924141i	$0.624782\pi$
$251$	−2.06552e7	+	2.06552e7i	−1.30619	+	1.30619i	−0.924141	+	0.382052i	$0.875218\pi$
$252$	−8.58825e6	+	1.89737e6i	−0.536665	+	0.118564i
$253$	−2.05152e7	+	2.05152e7i	−1.26682	+	1.26682i
$254$	−1.57502e7	−	1.26503e7i	−0.961136	−	0.771972i
$255$			668649.i			0.0403253i
$256$	1.08218e7	−	1.28205e7i	0.645028	−	0.764159i
$257$	960591.			0.0565900			0.0282950	−	0.999600i	$-0.490992\pi$
$257$	960591.			0.0565900			0.0282950	+	0.999600i	$0.490992\pi$
$258$	−7.61194e6	+	9.47717e6i	−0.443237	+	0.551848i
$259$	2.90331e7	+	2.90331e7i	1.67107	+	1.67107i
$260$	3.64421e6	+	1.64951e7i	0.207340	+	0.938500i
$261$	2.80805e6	+	2.80805e6i	0.157937	+	0.157937i
$262$	−2.48031e7	+	2.70719e6i	−1.37912	+	0.150527i
$263$	−2.66308e7			−1.46392			−0.731960	−	0.681348i	$-0.761394\pi$
$263$	−2.66308e7			−1.46392			−0.731960	+	0.681348i	$0.761394\pi$
$264$	1.30716e7	+	6.46404e6i	0.710421	+	0.351311i
$265$		−	9.93178e6i		−	0.533690i
$266$	−1.23408e7	+	1.34697e6i	−0.655692	+	0.0715671i
$267$	4.62717e6	−	4.62717e6i	0.243098	−	0.243098i
$268$	−5.13171e6	+	8.04218e6i	−0.266599	+	0.417801i
$269$	2.00276e7	−	2.00276e7i	1.02890	−	1.02890i	0.0293254	−	0.999570i	$-0.490664\pi$
$269$	2.00276e7	−	2.00276e7i	1.02890	−	1.02890i	0.999570	−	0.0293254i	$-0.00933591\pi$
$270$	1.22855e6	−	1.52959e6i	0.0624166	−	0.0777112i
$271$		−	1.33995e7i		−	0.673256i	−0.941638	−	0.336628i	$-0.890714\pi$
$271$		−	1.33995e7i		−	0.673256i	0.941638	−	0.336628i	$-0.109286\pi$
$272$	2.46124e6	−	1.14331e6i	0.122306	−	0.0568143i
$273$	−3.59434e7			−1.76657
$274$	−1.31596e6	−	1.05696e6i	−0.0639723	−	0.0513817i
$275$	−1.47718e7	−	1.47718e7i	−0.710287	−	0.710287i
$276$	8.52178e6	−	1.33549e7i	0.405325	−	0.635206i
$277$	−1.43027e6	−	1.43027e6i	−0.0672942	−	0.0672942i	0.672659	−	0.739953i	$-0.265152\pi$
$277$	−1.43027e6	−	1.43027e6i	−0.0672942	−	0.0672942i	−0.739953	+	0.672659i	$0.765152\pi$
$278$	833462.	+	7.63612e6i	0.0387928	+	0.355417i
$279$	9.50078e6			0.437469
$280$	6.00622e6	+	1.77578e7i	0.273607	+	0.808938i
$281$		−	1.75247e7i		−	0.789825i	−0.918719	−	0.394912i	$-0.870775\pi$
$281$		−	1.75247e7i		−	0.789825i	0.918719	−	0.394912i	$-0.129225\pi$
$282$	1.45777e6	+	1.33560e7i	0.0650043	+	0.595564i
$283$	2.40129e7	−	2.40129e7i	1.05946	−	1.05946i	0.0613460	−	0.998117i	$-0.480461\pi$
$283$	2.40129e7	−	2.40129e7i	1.05946	−	1.05946i	0.998117	−	0.0613460i	$-0.0195393\pi$
$284$	−3.67408e6	−	1.66303e7i	−0.160396	−	0.726014i
$285$	1.95804e6	−	1.95804e6i	0.0845837	−	0.0845837i
$286$	4.64624e7	+	3.73180e7i	1.98611	+	1.59522i
$287$		−	3.76200e7i		−	1.59138i
$288$	−7.73096e6	−	1.90675e6i	−0.323635	−	0.0798210i
$289$	−2.36986e7			−0.981813
$290$	5.30024e6	−	6.59901e6i	0.217321	−	0.270573i
$291$	−4.33531e6	−	4.33531e6i	−0.175931	−	0.175931i
$292$	1.67460e7	−	3.69963e6i	0.672607	−	0.148597i
$293$	2.49680e7	+	2.49680e7i	0.992617	+	0.992617i	0.999973	−	0.00735615i	$-0.00234156\pi$
$293$	2.49680e7	+	2.49680e7i	0.992617	+	0.992617i	−0.00735615	+	0.999973i	$0.502342\pi$
$294$	−2.50659e7	+	2.73588e6i	−0.986374	+	0.107660i
$295$	−6.21568e6			−0.242115
$296$	1.19098e7	+	3.52120e7i	0.459228	+	1.35774i
$297$		−	6.92100e6i		−	0.264180i
$298$	−2.95587e7	+	3.22625e6i	−1.11696	+	0.121913i
$299$	4.57790e7	−	4.57790e7i	1.71259	−	1.71259i
$300$	9.61606e6	+	6.13601e6i	0.356151	+	0.227260i
$301$	−3.89793e7	+	3.89793e7i	−1.42934	+	1.42934i
$302$	1.44301e7	−	1.79661e7i	0.523900	−	0.652277i
$303$		−	1.47912e7i		−	0.531712i
$304$	−1.05554e7	−	3.85935e6i	−0.375710	−	0.137371i
$305$	−9.08326e6			−0.320142
$306$	−1.00420e6	−	806562.i	−0.0350475	−	0.0281497i
$307$	3.13583e6	+	3.13583e6i	0.108377	+	0.108377i	0.759216	−	0.650839i	$-0.225583\pi$
$307$	3.13583e6	+	3.13583e6i	0.108377	+	0.108377i	−0.650839	+	0.759216i	$0.725583\pi$
$308$	5.57484e7	+	3.55730e7i	1.90801	+	1.21750i
$309$	−5.03489e6	−	5.03489e6i	−0.170653	−	0.170653i
$310$	−2.19714e6	−	2.01300e7i	−0.0737519	−	0.675709i
$311$	2.82703e7			0.939830			0.469915	−	0.882712i	$-0.344285\pi$
$311$	2.82703e7			0.939830			0.469915	+	0.882712i	$0.344285\pi$
$312$	−2.91688e7	−	1.44243e7i	−0.960405	−	0.474931i
$313$		−	4.17098e6i		−	0.136021i	−0.997685	−	0.0680104i	$-0.978335\pi$
$313$		−	4.17098e6i		−	0.136021i	0.997685	−	0.0680104i	$-0.0216651\pi$
$314$	615625.	+	5.64030e6i	0.0198851	+	0.182185i
$315$	6.29116e6	−	6.29116e6i	0.201279	−	0.201279i
$316$	3.48701e7	−	7.70374e6i	1.10508	−	0.244141i
$317$	3.49603e7	−	3.49603e7i	1.09748	−	1.09748i	0.102779	−	0.994704i	$-0.467227\pi$
$317$	3.49603e7	−	3.49603e7i	1.09748	−	1.09748i	0.994704	−	0.102779i	$-0.0327733\pi$
$318$	1.49159e7	+	1.19803e7i	0.463840	+	0.372550i
$319$		−	2.98588e7i		−	0.919815i
$320$	−2.25213e6	+	1.68211e7i	−0.0687297	+	0.513340i
$321$	1.09958e7			0.332439
$322$	4.49891e7	−	5.60133e7i	1.34753	−	1.67774i
$323$	−1.28548e6	−	1.28548e6i	−0.0381469	−	0.0381469i
$324$	815254.	+	3.69015e6i	0.0239694	+	0.108495i
$325$	3.29627e7	+	3.29627e7i	0.960223	+	0.960223i
$326$	1.46220e7	−	1.59595e6i	0.422039	−	0.0460645i
$327$	1.51236e7			0.432526
$328$	1.50971e7	−	3.05293e7i	0.427831	−	0.865159i
$329$			6.09286e7i			1.71093i
$330$	−1.46641e7	+	1.60054e6i	−0.408049	+	0.0445375i
$331$	−2.32895e7	+	2.32895e7i	−0.642210	+	0.642210i	−0.951098	−	0.308888i	$-0.900043\pi$
$331$	−2.32895e7	+	2.32895e7i	−0.642210	+	0.642210i	0.308888	+	0.951098i	$0.400043\pi$
$332$	−1.15010e7	+	1.80238e7i	−0.314282	+	0.492529i
$333$	1.24748e7	−	1.24748e7i	0.337831	−	0.337831i
$334$	−4.30963e7	+	5.36566e7i	−1.15665	+	1.44007i
$335$		−	9.65029e6i		−	0.256688i
$336$	−3.39143e7	−	1.24001e7i	−0.894058	−	0.326894i
$337$	−1.28256e7			−0.335110			−0.167555	−	0.985863i	$-0.553587\pi$
$337$	−1.28256e7			−0.335110			−0.167555	+	0.985863i	$0.553587\pi$
$338$	−7.35732e7	−	5.90931e7i	−1.90533	−	1.53033i
$339$	−1.94650e7	−	1.94650e7i	−0.499638	−	0.499638i
$340$	−1.47669e6	+	2.31420e6i	−0.0375711	+	0.0588796i
$341$	−5.05124e7	−	5.05124e7i	−1.27390	−	1.27390i
$342$	578759.	+	5.30255e6i	0.0144684	+	0.132558i
$343$	−4.78123e7			−1.18483
$344$	−4.72751e7	+	1.59899e7i	−1.16133	+	0.392798i
$345$			1.60254e7i			0.390257i
$346$	1.09490e6	+	1.00313e7i	0.0264329	+	0.242176i
$347$	−3.91869e7	+	3.91869e7i	−0.937891	+	0.937891i	−0.998181	−	0.0602903i	$-0.980797\pi$
$347$	−3.91869e7	+	3.91869e7i	−0.937891	+	0.937891i	0.0602903	+	0.998181i	$0.480797\pi$
$348$	3.51720e6	+	1.59202e7i	0.0834563	+	0.377755i
$349$	4.06672e7	−	4.06672e7i	0.956682	−	0.956682i	−0.0424175	−	0.999100i	$-0.513506\pi$
$349$	4.06672e7	−	4.06672e7i	0.956682	−	0.956682i	0.999100	+	0.0424175i	$0.0135060\pi$
$350$	4.03317e7	+	3.23939e7i	0.940682	+	0.755543i
$351$			1.54440e7i			0.357139i
$352$	3.09652e7	+	5.12403e7i	0.709981	+	1.17485i
$353$	−3.01960e7			−0.686475			−0.343237	−	0.939249i	$-0.611524\pi$
$353$	−3.01960e7			−0.686475			−0.343237	+	0.939249i	$0.611524\pi$
$354$	7.49769e6	−	9.33493e6i	0.169012	−	0.210427i
$355$	1.21822e7	+	1.21822e7i	0.272296	+	0.272296i
$356$	2.62337e7	−	5.79573e6i	0.581446	−	0.128457i
$357$	−4.13025e6	−	4.13025e6i	−0.0907762	−	0.0907762i
$358$	−3.25688e7	+	3.55480e6i	−0.709827	+	0.0774757i
$359$	6.27234e7			1.35565			0.677823	−	0.735225i	$-0.262924\pi$
$359$	6.27234e7			1.35565			0.677823	+	0.735225i	$0.262924\pi$
$360$	7.63008e6	−	2.58072e6i	0.163539	−	0.0553138i
$361$		−	3.95172e7i		−	0.839971i
$362$	2.41407e7	−	2.63490e6i	0.508891	−	0.0555442i
$363$	−1.72691e7	+	1.72691e7i	−0.361036	+	0.361036i
$364$	−1.24401e8	−	7.93800e7i	−2.57940	−	1.64591i
$365$	−1.22669e7	+	1.22669e7i	−0.252265	+	0.252265i
$366$	1.09567e7	−	1.36416e7i	0.223479	−	0.278241i
$367$		−	7.63574e7i		−	1.54473i	−0.635179	−	0.772365i	$-0.719073\pi$
$367$		−	7.63574e7i		−	1.54473i	0.635179	−	0.772365i	$-0.280927\pi$
$368$	5.89880e7	−	2.74015e7i	1.18364	−	0.549833i
$369$	−1.61644e7			−0.321721
$370$	−2.93162e7	−	2.35463e7i	−0.578764	−	0.464856i
$371$	6.13487e7	+	6.13487e7i	1.20139	+	1.20139i
$372$	3.28823e7	+	2.09822e7i	0.638755	+	0.407589i
$373$	3.70594e7	+	3.70594e7i	0.714121	+	0.714121i	0.967395	−	0.253274i	$-0.0815073\pi$
$373$	3.70594e7	+	3.70594e7i	0.714121	+	0.714121i	−0.253274	+	0.967395i	$0.581507\pi$
$374$	1.05078e6	+	9.62720e6i	0.0200862	+	0.184029i
$375$	−2.73076e7			−0.517833
$376$	−2.44510e7	+	4.94447e7i	−0.459973	+	0.930157i
$377$			6.66289e7i			1.24348i
$378$	1.85955e6	+	1.70370e7i	0.0344296	+	0.315442i
$379$	−4.65182e7	+	4.65182e7i	−0.854487	+	0.854487i	−0.990682	−	0.136195i	$-0.956513\pi$
$379$	−4.65182e7	+	4.65182e7i	−0.854487	+	0.854487i	0.136195	+	0.990682i	$0.456513\pi$
$380$	1.11011e7	−	2.45252e6i	0.202308	−	0.0446953i
$381$	−2.78344e7	+	2.78344e7i	−0.503276	+	0.503276i
$382$	−7.01373e6	−	5.63334e6i	−0.125823	−	0.101059i
$383$			1.38162e7i			0.245919i	0.992412	+	0.122959i	$0.0392385\pi$
$383$			1.38162e7i			0.245919i	−0.992412	+	0.122959i	$0.960762\pi$
$384$	−2.25459e7	−	2.36729e7i	−0.398175	−	0.418079i
$385$	−6.68958e7			−1.17224
$386$	3.33388e7	−	4.15081e7i	0.579680	−	0.721724i
$387$	1.67484e7	+	1.67484e7i	0.288962	+	0.288962i
$388$	−5.43016e6	−	2.45790e7i	−0.0929646	−	0.420794i
$389$	3.29148e7	+	3.29148e7i	0.559168	+	0.559168i	0.929071	−	0.369902i	$-0.120609\pi$
$389$	3.29148e7	+	3.29148e7i	0.559168	+	0.559168i	−0.369902	+	0.929071i	$0.620609\pi$
$390$	3.27223e7	−	3.57156e6i	0.551633	−	0.0602093i
$391$	1.05209e7			0.176004
$392$	−9.27956e7	−	4.58885e7i	−1.54053	−	0.761808i
$393$			4.86172e7i			0.800963i
$394$	1.14627e7	−	1.25112e6i	0.187412	−	0.0204556i
$395$	−2.55435e7	+	2.55435e7i	−0.414465	+	0.414465i
$396$	1.52848e7	−	2.39537e7i	0.246136	−	0.385733i
$397$	9.09263e6	−	9.09263e6i	0.145318	−	0.145318i	−0.630705	−	0.776023i	$-0.717234\pi$
$397$	9.09263e6	−	9.09263e6i	0.145318	−	0.145318i	0.776023	+	0.630705i	$0.217234\pi$
$398$	4.45724e6	−	5.54944e6i	0.0706996	−	0.0880238i
$399$			2.41896e7i			0.380812i
$400$	1.97301e7	+	4.24736e7i	0.308283	+	0.663650i
$401$	5.10274e7			0.791353			0.395677	−	0.918390i	$-0.370510\pi$
$401$	5.10274e7			0.791353			0.395677	+	0.918390i	$0.370510\pi$
$402$	1.44932e7	+	1.16407e7i	0.223092	+	0.179185i
$403$	1.12717e8	+	1.12717e8i	1.72216	+	1.72216i
$404$	3.26660e7	−	5.11927e7i	0.495396	−	0.776361i
$405$	−2.70315e6	−	2.70315e6i	−0.0406917	−	0.0406917i
$406$	8.02253e6	+	7.35018e7i	0.119876	+	1.09830i
$407$	−1.32648e8			−1.96751
$408$	−1.69429e6	−	5.00927e6i	−0.0249463	−	0.0737555i
$409$		−	8.06130e7i		−	1.17824i	−0.808044	−	0.589122i	$-0.799474\pi$
$409$		−	8.06130e7i		−	1.17824i	0.808044	−	0.589122i	$-0.200526\pi$
$410$	3.73815e6	+	3.42487e7i	0.0542382	+	0.496927i
$411$	−2.32562e6	+	2.32562e6i	−0.0334976	+	0.0334976i
$412$	−6.30641e6	−	2.85452e7i	−0.0901759	−	0.408171i
$413$	3.83943e7	−	3.83943e7i	0.545025	−	0.545025i
$414$	−2.40675e7	−	1.93307e7i	−0.339180	−	0.272425i
$415$		−	2.16278e7i		−	0.302599i
$416$	−6.90979e7	−	1.14341e8i	−0.959809	−	1.58826i
$417$	1.49678e7			0.206419
$418$	2.51147e7	−	3.12688e7i	0.343874	−	0.428137i
$419$	−8.05454e7	−	8.05454e7i	−1.09496	−	1.09496i	−0.994990	−	0.0999711i	$-0.968125\pi$
$419$	−8.05454e7	−	8.05454e7i	−1.09496	−	1.09496i	−0.0999711	−	0.994990i	$-0.531875\pi$
$420$	3.56677e7	−	7.87994e6i	0.481423	−	0.106359i
$421$	−1.99109e7	−	1.99109e7i	−0.266837	−	0.266837i	0.560988	−	0.827824i	$-0.310422\pi$
$421$	−1.99109e7	−	1.99109e7i	−0.266837	−	0.266837i	−0.827824	+	0.560988i	$0.810422\pi$
$422$	−6.86479e7	+	7.49274e6i	−0.913461	+	0.0997019i
$423$	2.61795e7			0.345891
$424$	2.51661e7	+	7.44052e7i	0.330155	+	0.976126i
$425$			7.57548e6i			0.0986832i
$426$	−3.29905e7	+	3.60083e6i	−0.426737	+	0.0465773i
$427$	5.61074e7	−	5.61074e7i	0.720670	−	0.720670i
$428$	3.80566e7	+	2.42839e7i	0.485399	+	0.309733i
$429$	8.21102e7	−	8.21102e7i	1.03998	−	1.03998i
$430$	3.16130e7	−	3.93594e7i	0.397612	−	0.495043i
$431$			5.56500e7i			0.695078i	0.937666	+	0.347539i	$0.112982\pi$
$431$			5.56500e7i			0.695078i	−0.937666	+	0.347539i	$0.887018\pi$
$432$	−5.32800e6	+	1.45721e7i	−0.0660865	+	0.180747i
$433$	1.28922e8			1.58804			0.794022	−	0.607889i	$-0.207984\pi$
$433$	1.28922e8			1.58804			0.794022	+	0.607889i	$0.207984\pi$
$434$	1.37915e8	+	1.10772e8i	1.68711	+	1.35506i
$435$	−1.16620e7	−	1.16620e7i	−0.141679	−	0.141679i
$436$	5.23430e7	+	3.34001e7i	0.631537	+	0.402984i
$437$	−3.08089e7	−	3.08089e7i	−0.369175	−	0.369175i
$438$	−3.62588e6	−	3.32200e7i	−0.0431510	−	0.395346i
$439$	−1.16571e8			−1.37784			−0.688918	−	0.724839i	$-0.741914\pi$
$439$	−1.16571e8			−1.37784			−0.688918	+	0.724839i	$0.741914\pi$
$440$	−5.42872e7	−	2.68457e7i	−0.637294	−	0.315149i
$441$			4.91325e7i			0.572865i
$442$	−2.34479e6	−	2.14828e7i	−0.0271542	−	0.248784i
$443$	−8.56146e7	+	8.56146e7i	−0.984775	+	0.984775i	−0.999886	−	0.0151112i	$-0.995190\pi$
$443$	−8.56146e7	+	8.56146e7i	−0.984775	+	0.984775i	0.0151112	+	0.999886i	$0.495190\pi$
$444$	7.07255e7	−	1.56252e7i	0.808030	−	0.178515i
$445$	−1.92170e7	+	1.92170e7i	−0.218075	+	0.218075i
$446$	5.03598e7	+	4.04484e7i	0.567649	+	0.455928i
$447$			5.79388e7i			0.648704i
$448$	−8.99928e7	−	1.17816e8i	−1.00086	−	1.31030i
$449$	−1.62296e8			−1.79295			−0.896474	−	0.443096i	$-0.853880\pi$
$449$	−1.62296e8			−1.79295			−0.896474	+	0.443096i	$0.853880\pi$
$450$	1.39188e7	−	1.73295e7i	0.152745	−	0.190173i
$451$	8.59403e7	+	8.59403e7i	0.936844	+	0.936844i
$452$	−2.43807e7	−	1.10357e8i	−0.264017	−	1.19504i
$453$	−3.17503e7	−	3.17503e7i	−0.341550	−	0.341550i
$454$	−4.65368e7	+	5.07937e6i	−0.497312	+	0.0542804i
$455$	1.49276e8			1.58473
$456$	−9.70743e6	+	1.96304e7i	−0.102379	+	0.207030i
$457$		−	1.31224e8i		−	1.37488i	−0.726241	−	0.687440i	$-0.758734\pi$
$457$		−	1.31224e8i		−	1.37488i	0.726241	−	0.687440i	$-0.241266\pi$
$458$	−1.34589e8	+	1.46900e7i	−1.40092	+	0.152906i
$459$	−1.77467e6	+	1.77467e6i	−0.0183518	+	0.0183518i
$460$	−3.53916e7	+	5.54640e7i	−0.363602	+	0.569820i
$461$	3.76397e7	−	3.76397e7i	0.384188	−	0.384188i	−0.488421	−	0.872608i	$-0.662427\pi$
$461$	3.76397e7	−	3.76397e7i	0.384188	−	0.384188i	0.872608	+	0.488421i	$0.162427\pi$
$462$	8.06934e7	−	1.00467e8i	0.818300	−	1.01882i
$463$		−	5.50458e6i		−	0.0554602i	−0.999615	−	0.0277301i	$-0.991172\pi$
$463$		−	5.50458e6i		−	0.0554602i	0.999615	−	0.0277301i	$-0.00882789\pi$
$464$	−2.29862e7	+	6.28676e7i	−0.230099	+	0.629322i
$465$	−3.94575e7			−0.392438
$466$	9.15384e6	+	7.35225e6i	0.0904578	+	0.0726545i
$467$	−9.63536e6	−	9.63536e6i	−0.0946057	−	0.0946057i	0.658220	−	0.752826i	$-0.271310\pi$
$467$	−9.63536e6	−	9.63536e6i	−0.0946057	−	0.0946057i	−0.752826	+	0.658220i	$0.771310\pi$
$468$	−3.41076e7	+	5.34518e7i	−0.332746	+	0.521464i
$469$	5.96099e7	+	5.96099e7i	0.577830	+	0.577830i
$470$	−6.05424e6	−	5.54684e7i	−0.0583131	−	0.534260i
$471$	1.10557e7			0.105809
$472$	4.65656e7	−	1.57499e7i	0.442832	−	0.149779i
$473$		−	1.78091e8i		−	1.68290i
$474$	−7.55016e6	−	6.91740e7i	−0.0708959	−	0.649543i
$475$	2.21836e7	−	2.21836e7i	0.206991	−	0.206991i
$476$	−5.17331e6	−	2.34164e7i	−0.0479676	−	0.217120i
$477$	2.63600e7	−	2.63600e7i	0.242879	−	0.242879i
$478$	8.01415e7	+	6.43686e7i	0.733793	+	0.589373i
$479$			3.68794e6i			0.0335566i	0.999859	+	0.0167783i	$0.00534095\pi$
$479$			3.68794e6i			0.0335566i	−0.999859	+	0.0167783i	$0.994659\pi$
$480$	3.21073e7	+	7.91890e6i	0.290322	+	0.0716046i
$481$	2.95999e8			2.65984
$482$	−9.37331e6	+	1.16702e7i	−0.0837051	+	0.104216i
$483$	−9.89889e7	−	9.89889e7i	−0.878507	−	0.878507i
$484$	−9.79072e7	+	2.16303e7i	−0.863532	+	0.190777i
$485$	1.80049e7	+	1.80049e7i	0.157821	+	0.157821i
$486$	7.32039e6	−	799001.i	0.0637713	−	0.00696047i
$487$	−6.06471e7			−0.525077			−0.262539	−	0.964921i	$-0.584560\pi$
$487$	−6.06471e7			−0.525077			−0.262539	+	0.964921i	$0.584560\pi$
$488$	6.80484e7	−	2.30160e7i	0.585543	−	0.198048i
$489$		−	2.86609e7i		−	0.245112i
$490$	1.04101e8	−	1.13623e7i	0.884841	−	0.0965781i
$491$	2.63117e7	−	2.63117e7i	0.222282	−	0.222282i	−0.587177	−	0.809459i	$-0.699761\pi$
$491$	2.63117e7	−	2.63117e7i	0.222282	−	0.222282i	0.809459	+	0.587177i	$0.199761\pi$
$492$	−5.59451e7	−	3.56985e7i	−0.469750	−	0.299747i
$493$	−7.65633e6	+	7.65633e6i	−0.0638969	+	0.0638969i
$494$	−5.60426e7	+	6.97753e7i	−0.464877	+	0.578790i
$495$			2.87434e7i			0.236986i
$496$	6.74676e7	+	1.45240e8i	0.552905	+	1.19025i
$497$	−1.50499e8			−1.22593
$498$	3.24814e7	+	2.60887e7i	0.262995	+	0.211234i
$499$	−1.17267e8	−	1.17267e8i	−0.943788	−	0.943788i	0.0547144	−	0.998502i	$-0.482575\pi$
$499$	−1.17267e8	−	1.17267e8i	−0.943788	−	0.943788i	−0.998502	+	0.0547144i	$0.982575\pi$
$500$	−9.45120e7	−	6.03081e7i	−0.756096	−	0.482465i
$501$	9.48241e7	+	9.48241e7i	0.754060	+	0.754060i
$502$	2.53557e7	+	2.32307e8i	0.200431	+	1.83633i
$503$	8.84245e7			0.694814			0.347407	−	0.937714i	$-0.387062\pi$
$503$	8.84245e7			0.694814			0.347407	+	0.937714i	$0.387062\pi$
$504$	−3.11899e7	+	6.30722e7i	−0.243625	+	0.492659i
$505$			6.14291e7i			0.476980i
$506$	2.51839e7	+	2.30733e8i	0.194389	+	1.78098i
$507$	−1.30022e8	+	1.30022e8i	−0.997681	+	0.997681i
$508$	−1.57807e8	+	3.48637e7i	−1.20374	+	0.265939i
$509$	−9.88133e7	+	9.88133e7i	−0.749311	+	0.749311i	−0.974350	−	0.225039i	$-0.927749\pi$
$509$	−9.88133e7	+	9.88133e7i	−0.749311	+	0.749311i	0.225039	+	0.974350i	$0.427749\pi$
$510$	4.17053e6	+	3.34971e6i	0.0314399	+	0.0252521i
$511$		−	1.51546e8i		−	1.13575i
$512$	−2.57508e7	−	1.31724e8i	−0.191858	−	0.981423i
$513$	1.03937e7			0.0769870
$514$	4.81225e6	−	5.99144e6i	0.0354371	−	0.0441207i
$515$	2.09103e7	+	2.09103e7i	0.153087	+	0.153087i
$516$	2.09781e7	+	9.49550e7i	0.152692	+	0.691144i
$517$	−1.39187e8	−	1.39187e8i	−1.00723	−	1.00723i
$518$	3.26532e8	−	3.56402e7i	2.34929	−	0.256419i
$519$	1.96627e7			0.140651
$520$	1.21140e8	+	5.99051e7i	0.861545	+	0.426044i
$521$			1.96978e8i			1.39285i	0.717629	+	0.696425i	$0.245227\pi$
$521$			1.96978e8i			1.39285i	−0.717629	+	0.696425i	$0.754773\pi$
$522$	3.15819e7	−	3.44708e6i	0.222038	−	0.0242348i
$523$	7.96274e7	−	7.96274e7i	0.556618	−	0.556618i	−0.371725	−	0.928343i	$-0.621233\pi$
$523$	7.96274e7	−	7.96274e7i	0.556618	−	0.556618i	0.928343	+	0.371725i	$0.121233\pi$
$524$	−1.07370e8	+	1.68265e8i	−0.746257	+	1.16950i
$525$	7.12758e7	−	7.12758e7i	0.492566	−	0.492566i
$526$	−1.33412e8	+	1.66103e8i	−0.916720	+	1.14135i
$527$			2.59045e7i			0.176988i
$528$	1.05802e8	−	4.91479e7i	0.718774	−	0.333890i
$529$	1.04117e8			0.703322
$530$	−6.19469e7	−	4.97549e7i	−0.416095	−	0.334202i
$531$	−1.64971e7	−	1.64971e7i	−0.110185	−	0.110185i
$532$	−5.34222e7	+	8.37207e7i	−0.354802	+	0.556030i
$533$	−1.91773e8	−	1.91773e8i	−1.26650	−	1.26650i
$534$	−5.68019e6	−	5.20414e7i	−0.0373026	−	0.341763i
$535$	−4.56664e7			−0.298219
$536$	2.44528e7	+	7.22964e7i	0.158794	+	0.469486i
$537$			6.38390e7i			0.412252i
$538$	−2.45853e7	−	2.25248e8i	−0.157880	−	1.44649i
$539$	2.61220e8	−	2.61220e8i	1.66817	−	1.66817i
$540$	−3.38581e6	−	1.53255e7i	−0.0215021	−	0.0973269i
$541$	−1.92069e8	+	1.92069e8i	−1.21302	+	1.21302i	−0.242986	+	0.970030i	$0.578127\pi$
$541$	−1.92069e8	+	1.92069e8i	−1.21302	+	1.21302i	−0.970030	+	0.242986i	$0.921873\pi$
$542$	−8.35758e7	−	6.71270e7i	−0.524908	−	0.421599i
$543$		−	4.73190e7i		−	0.295553i
$544$	5.19889e6	−	2.10790e7i	0.0322934	−	0.130934i
$545$	−6.28095e7			−0.388004
$546$	−1.80065e8	+	2.24188e8i	−1.10624	+	1.37732i
$547$	−7.48181e7	−	7.48181e7i	−0.457135	−	0.457135i	0.440579	−	0.897714i	$-0.354773\pi$
$547$	−7.48181e7	−	7.48181e7i	−0.457135	−	0.457135i	−0.897714	+	0.440579i	$0.854773\pi$
$548$	−1.31851e7	+	2.91294e6i	−0.0801200	+	0.0177007i
$549$	−2.41079e7	−	2.41079e7i	−0.145694	−	0.145694i
$550$	−1.66137e8	+	1.81334e7i	−0.998568	+	0.108991i
$551$	4.48408e7			0.268052
$552$	−4.06066e7	−	1.20056e8i	−0.241424	−	0.713785i
$553$		−	3.15564e8i		−	1.86600i
$554$	−1.60861e7	+	1.75575e6i	−0.0946065	+	0.0103261i
$555$	−5.18087e7	+	5.18087e7i	−0.303056	+	0.303056i
$556$	5.18037e7	+	3.30559e7i	0.301395	+	0.192320i
$557$	−1.38814e8	+	1.38814e8i	−0.803281	+	0.803281i	−0.983607	−	0.180326i	$-0.942285\pi$
$557$	−1.38814e8	+	1.38814e8i	−0.803281	+	0.803281i	0.180326	+	0.983607i	$0.442285\pi$
$558$	4.75958e7	−	5.92587e7i	0.273947	−	0.341075i
$559$			3.97404e8i			2.27508i
$560$	1.40849e8	+	5.14985e7i	0.802028	+	0.293245i
$561$	1.88706e7			0.106880
$562$	−1.09306e8	−	8.77928e7i	−0.615791	−	0.494595i
$563$	−1.37839e8	−	1.37839e8i	−0.772411	−	0.772411i	0.206117	−	0.978527i	$-0.433917\pi$
$563$	−1.37839e8	−	1.37839e8i	−0.772411	−	0.772411i	−0.978527	+	0.206117i	$0.933917\pi$
$564$	9.06075e7	+	5.78166e7i	0.505041	+	0.322267i
$565$	8.08397e7	+	8.08397e7i	0.448208	+	0.448208i
$566$	−2.94776e7	−	2.70071e8i	−0.162571	−	1.48946i
$567$	3.33948e7			0.183202
$568$	−1.22133e8	−	6.03962e7i	−0.666482	−	0.329583i
$569$			1.94110e8i			1.05368i	0.849963	+	0.526842i	$0.176624\pi$
$569$			1.94110e8i			1.05368i	−0.849963	+	0.526842i	$0.823376\pi$
$570$	−2.40363e6	−	2.20219e7i	−0.0129791	−	0.118913i
$571$	5.50758e7	−	5.50758e7i	0.295837	−	0.295837i	−0.543544	−	0.839381i	$-0.682918\pi$
$571$	5.50758e7	−	5.50758e7i	0.295837	−	0.295837i	0.839381	+	0.543544i	$0.182918\pi$
$572$	4.65523e8	−	1.02846e8i	2.48744	−	0.549542i
$573$	−1.23949e7	+	1.23949e7i	−0.0658841	+	0.0658841i
$574$	−2.34645e8	−	1.88464e8i	−1.24073	−	0.996534i
$575$			1.81560e8i			0.955028i
$576$	−5.06224e7	+	3.86676e7i	−0.264896	+	0.202339i
$577$	−1.62355e8			−0.845158			−0.422579	−	0.906326i	$-0.638875\pi$
$577$	−1.62355e8			−0.845158			−0.422579	+	0.906326i	$0.638875\pi$
$578$	−1.18722e8	+	1.47814e8i	−0.614820	+	0.765476i
$579$	−7.33548e7	−	7.33548e7i	−0.377914	−	0.377914i
$580$	−1.46072e7	−	6.61178e7i	−0.0748656	−	0.338871i
$581$	1.33595e8	+	1.33595e8i	0.681181	+	0.681181i
$582$	−4.87589e7	+	5.32191e6i	−0.247335	+	0.0269959i
$583$	−2.80294e8			−1.41452
$584$	6.08162e7	−	1.22982e8i	0.305338	−	0.617454i
$585$		−	6.41400e7i		−	0.320377i
$586$	2.80813e8	−	3.06501e7i	1.39548	−	0.152314i
$587$	1.11238e8	−	1.11238e8i	0.549968	−	0.549968i	−0.376464	−	0.926431i	$-0.622860\pi$
$587$	1.11238e8	−	1.11238e8i	0.549968	−	0.549968i	0.926431	+	0.376464i	$0.122860\pi$
$588$	−1.08508e8	+	1.70048e8i	−0.533738	+	0.836450i
$589$	7.58574e7	−	7.58574e7i	0.371238	−	0.371238i
$590$	−3.11385e7	+	3.87687e7i	−0.151615	+	0.188767i
$591$		−	2.24683e7i		−	0.108845i
$592$	2.79290e8	+	1.02116e8i	1.34614	+	0.492188i
$593$	3.77045e8			1.80813			0.904064	−	0.427397i	$-0.140569\pi$
$593$	3.77045e8			1.80813			0.904064	+	0.427397i	$0.140569\pi$
$594$	−4.31680e7	−	3.46719e7i	−0.205969	−	0.165432i
$595$	1.71533e7	+	1.71533e7i	0.0814321	+	0.0814321i
$596$	−1.27956e8	+	2.00527e8i	−0.604398	+	0.947183i
$597$	−9.80720e6	−	9.80720e6i	−0.0460916	−	0.0460916i
$598$	−5.61970e7	−	5.14873e8i	−0.262791	−	2.40767i
$599$	3.55681e8			1.65493			0.827465	−	0.561517i	$-0.189782\pi$
$599$	3.55681e8			1.65493			0.827465	+	0.561517i	$0.189782\pi$
$600$	8.64451e7	−	2.92383e7i	0.400209	−	0.135363i
$601$			1.48769e8i			0.685313i	0.939461	+	0.342656i	$0.111327\pi$
$601$			1.48769e8i			0.685313i	−0.939461	+	0.342656i	$0.888673\pi$
$602$	4.78499e7	+	4.38397e8i	0.219327	+	2.00946i
$603$	2.56129e7	−	2.56129e7i	0.116817	−	0.116817i
$604$	−3.97686e7	−	1.80008e8i	−0.180480	−	0.816923i
$605$	7.17201e7	−	7.17201e7i	0.323873	−	0.323873i
$606$	−9.22565e7	−	7.40992e7i	−0.414552	−	0.332963i
$607$			2.97217e7i			0.132894i	0.997790	+	0.0664472i	$0.0211664\pi$
$607$			2.97217e7i			0.132894i	−0.997790	+	0.0664472i	$0.978834\pi$
$608$	−7.69507e7	+	4.65023e7i	−0.342375	+	0.206902i
$609$	1.44073e8			0.637868
$610$	−4.55041e7	+	5.66545e7i	−0.200476	+	0.249600i
$611$	3.10591e8	+	3.10591e8i	1.36165	+	1.36165i
$612$	−1.00614e7	+	2.22284e6i	−0.0438941	+	0.00969738i
$613$	1.04355e8	+	1.04355e8i	0.453034	+	0.453034i	0.896360	−	0.443326i	$-0.146202\pi$
$613$	1.04355e8	+	1.04355e8i	0.453034	+	0.453034i	−0.443326	+	0.896360i	$0.646202\pi$
$614$	3.52684e7	−	3.84946e6i	0.152364	−	0.0166301i
$615$	6.71318e7			0.288605
$616$	5.01159e8	−	1.69507e8i	2.14404	−	0.725180i
$617$		−	1.67053e8i		−	0.711213i	−0.934636	−	0.355606i	$-0.884274\pi$
$617$		−	1.67053e8i		−	0.711213i	0.934636	−	0.355606i	$-0.115726\pi$
$618$	−5.66270e7	+	6.18069e6i	−0.239915	+	0.0261861i
$619$	−3.33498e7	+	3.33498e7i	−0.140612	+	0.140612i	−0.773909	−	0.633297i	$-0.781701\pi$
$619$	−3.33498e7	+	3.33498e7i	−0.140612	+	0.140612i	0.633297	+	0.773909i	$0.281701\pi$
$620$	−1.36563e8	−	8.71408e7i	−0.573004	−	0.365634i
$621$	−4.25330e7	+	4.25330e7i	−0.177603	+	0.177603i
$622$	1.41625e8	−	1.76329e8i	0.588530	−	0.732744i
$623$		−	2.37407e8i		−	0.981816i
$624$	−2.36094e8	+	1.09672e8i	−0.971696	+	0.451379i
$625$	−6.52414e7			−0.267229
$626$	−2.60154e7	−	2.08953e7i	−0.106049	−	0.0851775i
$627$	−5.52596e7	−	5.52596e7i	−0.224184	−	0.224184i
$628$	3.82640e7	+	2.44163e7i	0.154494	+	0.0985826i
$629$	3.40133e7	+	3.40133e7i	0.136677	+	0.136677i
$630$	−7.72285e6	−	7.07562e7i	−0.0308856	−	0.282971i
$631$	1.26476e8			0.503408			0.251704	−	0.967804i	$-0.419009\pi$
$631$	1.26476e8			0.503408			0.251704	+	0.967804i	$0.419009\pi$
$632$	1.26638e8	−	2.56087e8i	0.501663	−	1.01446i
$633$			1.34559e8i			0.530519i
$634$	−4.29163e7	−	3.93196e8i	−0.168405	−	1.54291i
$635$	1.15598e8	−	1.15598e8i	0.451471	−	0.451471i
$636$	1.49448e8	−	3.30170e7i	0.580922	−	0.128341i
$637$	−5.82904e8	+	5.82904e8i	−2.25517	+	2.25517i
$638$	−1.86237e8	−	1.49583e8i	−0.717139	−	0.575997i
$639$			6.46657e7i			0.247840i
$640$	9.36350e7	+	9.83154e7i	0.357189	+	0.375043i
$641$	−3.79771e8			−1.44194			−0.720971	−	0.692965i	$-0.756304\pi$
$641$	−3.79771e8			−1.44194			−0.720971	+	0.692965i	$0.756304\pi$
$642$	5.50854e7	−	6.85835e7i	0.208176	−	0.259188i
$643$	2.19573e8	+	2.19573e8i	0.825937	+	0.825937i	0.986952	−	0.161015i	$-0.0514768\pi$
$643$	2.19573e8	+	2.19573e8i	0.825937	+	0.825937i	−0.161015	+	0.986952i	$0.551477\pi$
$644$	−1.23988e8	−	5.61216e8i	−0.464217	−	2.10123i
$645$	−6.95575e7	−	6.95575e7i	−0.259218	−	0.259218i
$646$	−1.44577e7	+	1.57802e6i	−0.0536294	+	0.00585351i
$647$	1.63625e8			0.604139			0.302069	−	0.953286i	$-0.402323\pi$
$647$	1.63625e8			0.604139			0.302069	+	0.953286i	$0.402323\pi$
$648$	2.71005e7	+	1.34015e7i	0.0995985	+	0.0492526i
$649$			1.75418e8i			0.641713i
$650$	3.70728e8	−	4.04640e7i	1.34994	−	0.147343i
$651$	2.43729e8	−	2.43729e8i	0.883415	−	0.883415i
$652$	6.32969e7	−	9.91959e7i	0.228370	−	0.357891i
$653$	−2.17072e8	+	2.17072e8i	−0.779587	+	0.779587i	−0.979761	−	0.200173i	$-0.935849\pi$
$653$	−2.17072e8	+	2.17072e8i	−0.779587	+	0.779587i	0.200173	+	0.979761i	$0.435849\pi$
$654$	7.57643e7	−	9.43296e7i	0.270851	−	0.337221i
$655$		−	2.01911e8i		−	0.718516i
$656$	−1.14787e8	−	2.47106e8i	−0.406614	−	0.875331i
$657$	−6.51155e7			−0.229609
$658$	3.80026e8	+	3.05232e8i	1.33394	+	1.07140i
$659$	−3.75232e8	−	3.75232e8i	−1.31112	−	1.31112i	−0.920588	−	0.390535i	$-0.872290\pi$
$659$	−3.75232e8	−	3.75232e8i	−1.31112	−	1.31112i	−0.390535	−	0.920588i	$-0.627710\pi$
$660$	−6.34791e7	+	9.94815e7i	−0.220800	+	0.346027i
$661$	−9.25679e7	−	9.25679e7i	−0.320521	−	0.320521i	0.528446	−	0.848967i	$-0.322775\pi$
$661$	−9.25679e7	−	9.25679e7i	−0.320521	−	0.320521i	−0.848967	+	0.528446i	$0.822775\pi$
$662$	2.85896e7	+	2.61936e8i	0.0985448	+	0.902860i
$663$	−4.21090e7			−0.144489
$664$	5.48026e7	+	1.62028e8i	0.187196	+	0.553458i
$665$		−	1.00461e8i		−	0.341613i
$666$	−1.53137e7	−	1.40303e8i	−0.0518390	−	0.474945i
$667$	−1.83498e8	+	1.83498e8i	−0.618376	+	0.618376i
$668$	1.18771e8	+	5.37604e8i	0.398457	+	1.80357i
$669$	8.89979e7	−	8.89979e7i	0.297236	−	0.297236i
$670$	−6.01912e7	−	4.83448e7i	−0.200128	−	0.160740i
$671$			2.56347e8i			0.848517i
$672$	−2.47242e8	+	1.49412e8i	−0.814731	+	0.492353i
$673$	5.35988e8			1.75837			0.879185	−	0.476481i	$-0.158088\pi$
$673$	5.35988e8			1.75837			0.879185	+	0.476481i	$0.158088\pi$
$674$	−6.42520e7	+	7.99964e7i	−0.209849	+	0.261271i
$675$	−3.06254e7	−	3.06254e7i	−0.0995797	−	0.0995797i
$676$	−7.37156e8	+	1.62857e8i	−2.38627	+	0.527190i
$677$	−3.17164e8	−	3.17164e8i	−1.02216	−	1.02216i	−0.999749	−	0.0224072i	$-0.992867\pi$
$677$	−3.17164e8	−	3.17164e8i	−1.02216	−	1.02216i	−0.0224072	−	0.999749i	$-0.507133\pi$
$678$	−2.18921e8	+	2.38947e7i	−0.702424	+	0.0766677i
$679$	−2.22433e8			−0.710542
$680$	7.03651e6	+	2.08039e7i	0.0223785	+	0.0661634i
$681$			9.12182e7i			0.288829i
$682$	−5.68108e8	+	6.20075e7i	−1.79093	+	0.195475i
$683$	−2.38997e8	+	2.38997e8i	−0.750121	+	0.750121i	−0.974502	−	0.224381i	$-0.927964\pi$
$683$	−2.38997e8	+	2.38997e8i	−0.750121	+	0.750121i	0.224381	+	0.974502i	$0.427964\pi$
$684$	3.59727e7	+	2.29541e7i	0.112410	+	0.0717287i
$685$	9.65848e6	−	9.65848e6i	0.0300495	−	0.0300495i
$686$	−2.39524e8	+	2.98217e8i	−0.741953	+	0.923762i
$687$			2.63811e8i			0.813623i
$688$	−1.37100e8	+	3.74970e8i	−0.420990	+	1.15141i
$689$	6.25466e8			1.91226
$690$	9.99541e7	+	8.02818e7i	0.304266	+	0.244382i
$691$	−1.14977e8	−	1.14977e8i	−0.348478	−	0.348478i	0.511065	−	0.859542i	$-0.329251\pi$
$691$	−1.14977e8	−	1.14977e8i	−0.348478	−	0.348478i	−0.859542	+	0.511065i	$0.829251\pi$
$692$	6.80530e7	+	4.34246e7i	0.205366	+	0.131044i
$693$	−1.77549e8	−	1.77549e8i	−0.533479	−	0.533479i
$694$	4.81047e7	+	4.40731e8i	0.143916	+	1.31855i
$695$	−6.21623e7			−0.185171
$696$	1.16918e8	+	5.78173e7i	0.346780	+	0.171487i
$697$		−	4.40732e7i		−	0.130160i
$698$	−4.99219e7	−	4.57380e8i	−0.146800	−	1.34497i
$699$	1.61770e7	−	1.61770e7i	0.0473661	−	0.0473661i
$700$	4.04097e8	−	8.92759e7i	1.17813	−	0.260280i
$701$	1.52614e8	−	1.52614e8i	0.443036	−	0.443036i	−0.449995	−	0.893031i	$-0.648574\pi$
$701$	1.52614e8	−	1.52614e8i	0.443036	−	0.443036i	0.893031	+	0.449995i	$0.148574\pi$
$702$	9.63278e7	+	7.73692e7i	0.278446	+	0.223644i
$703$		−	1.99205e8i		−	0.573370i
$704$	4.74724e8	+	6.35595e7i	1.36058	+	0.182164i
$705$	−1.08725e8			−0.310287
$706$	−1.51272e8	+	1.88339e8i	−0.429877	+	0.535214i
$707$	−3.79448e8	−	3.79448e8i	−1.07373	−	1.07373i
$708$	−2.06633e7	−	9.35299e7i	−0.0582236	−	0.263542i
$709$	2.20534e8	+	2.20534e8i	0.618780	+	0.618780i	0.945218	−	0.326439i	$-0.105849\pi$
$709$	2.20534e8	+	2.20534e8i	0.618780	+	0.618780i	−0.326439	+	0.945218i	$0.605849\pi$
$710$	1.37012e8	−	1.49545e7i	0.382811	−	0.0417828i
$711$	−1.35590e8			−0.377241
$712$	9.52728e7	−	1.92661e8i	0.263955	−	0.533769i
$713$			6.20848e8i			1.71284i
$714$	−4.64526e7	+	5.07018e6i	−0.127619	+	0.0139293i
$715$	−3.41010e8	+	3.41010e8i	−0.932930	+	0.932930i
$716$	−1.40987e8	+	2.20948e8i	−0.384095	+	0.601936i
$717$	1.41629e8	−	1.41629e8i	0.384234	−	0.384234i
$718$	3.14224e8	−	3.91221e8i	0.848917	−	1.05694i
$719$			1.10928e8i			0.298439i	0.988804	+	0.149220i	$0.0476762\pi$
$719$			1.10928e8i			0.298439i	−0.988804	+	0.149220i	$0.952324\pi$
$720$	2.21276e7	−	6.05192e7i	0.0592839	−	0.162142i
$721$	−2.58326e8			−0.689228
$722$	−2.46478e8	−	1.97968e8i	−0.654888	−	0.525997i
$723$	2.06240e7	+	2.06240e7i	0.0545704	+	0.0545704i
$724$	1.04503e8	−	1.63772e8i	0.275367	−	0.431542i
$725$	−1.32125e8	−	1.32125e8i	−0.346714	−	0.346714i
$726$	2.11991e7	+	1.94225e8i	0.0553998	+	0.507568i
$727$	4.40388e8			1.14613			0.573063	−	0.819512i	$-0.305755\pi$
$727$	4.40388e8			1.14613			0.573063	+	0.819512i	$0.305755\pi$
$728$	−1.11832e9	+	3.78249e8i	−2.89849	+	0.980356i
$729$		−	1.43489e7i		−	0.0370370i
$730$	1.50585e7	+	1.37965e8i	0.0387092	+	0.354651i
$731$	−4.56657e7	+	4.56657e7i	−0.116906	+	0.116906i
$732$	−3.01962e7	−	1.36680e8i	−0.0769872	−	0.348474i
$733$	8.77336e7	−	8.77336e7i	0.222769	−	0.222769i	−0.586895	−	0.809663i	$-0.699650\pi$
$733$	8.77336e7	−	8.77336e7i	0.222769	−	0.222769i	0.809663	+	0.586895i	$0.199650\pi$
$734$	−4.76259e8	−	3.82525e8i	−1.20436	−	0.967324i
$735$		−	2.04051e8i		−	0.513897i
$736$	1.24601e8	−	5.05195e8i	0.312527	−	1.26714i
$737$	−2.72349e8			−0.680337
$738$	−8.09781e7	+	1.00821e8i	−0.201465	+	0.250832i
$739$	1.75595e8	+	1.75595e8i	0.435089	+	0.435089i	0.890355	−	0.455266i	$-0.150456\pi$
$739$	1.75595e8	+	1.75595e8i	0.435089	+	0.435089i	−0.455266	+	0.890355i	$0.650456\pi$
$740$	−2.93729e8	+	6.48925e7i	−0.724855	+	0.160140i
$741$	1.23310e8	+	1.23310e8i	0.303070	+	0.303070i
$742$	6.89984e8	−	7.53099e7i	1.68899	−	0.184349i
$743$	1.99950e8			0.487478			0.243739	−	0.969841i	$-0.421626\pi$
$743$	1.99950e8			0.487478			0.243739	+	0.969841i	$0.421626\pi$
$744$	2.95601e8	−	9.99812e7i	0.717773	−	0.242772i
$745$		−	2.40624e8i		−	0.581930i
$746$	4.16804e8	−	4.54931e7i	1.00396	−	0.109579i
$747$	5.74025e7	−	5.74025e7i	0.137711	−	0.137711i
$748$	6.53113e7	+	4.16751e7i	0.156057	+	0.0995800i
$749$	2.82082e8	−	2.82082e8i	0.671320	−	0.671320i
$750$	−1.36802e8	+	1.70324e8i	−0.324272	+	0.403731i
$751$		−	4.31676e7i		−	0.101915i	−0.998701	−	0.0509575i	$-0.983773\pi$
$751$		−	4.31676e7i		−	0.101915i	0.998701	−	0.0509575i	$-0.0162273\pi$
$752$	1.85907e8	+	4.00208e8i	0.437163	+	0.941093i
$753$	4.55351e8			1.06650
$754$	4.15581e8	+	3.33789e8i	0.969486	+	0.778678i
$755$	1.31862e8	+	1.31862e8i	0.306392	+	0.306392i
$756$	1.15580e8	+	7.37515e7i	0.267496	+	0.170689i
$757$	−3.04827e8	−	3.04827e8i	−0.702692	−	0.702692i	0.262295	−	0.964988i	$-0.415521\pi$
$757$	−3.04827e8	−	3.04827e8i	−0.702692	−	0.702692i	−0.964988	+	0.262295i	$0.915521\pi$
$758$	5.71045e7	+	5.23187e8i	0.131118	+	1.20129i
$759$	4.52267e8			1.03435
$760$	4.03157e7	−	8.15264e7i	0.0918404	−	0.185719i
$761$		−	4.91137e8i		−	1.11442i	−0.830372	−	0.557209i	$-0.811872\pi$
$761$		−	4.91137e8i		−	1.11442i	0.830372	−	0.557209i	$-0.188128\pi$
$762$	3.41687e7	+	3.13051e8i	0.0772260	+	0.707538i
$763$	3.87975e8	−	3.87975e8i	0.873434	−	0.873434i
$764$	−7.02730e7	+	1.55252e7i	−0.157583	+	0.0348142i
$765$	7.37032e6	−	7.37032e6i	0.0164627	−	0.0164627i
$766$	8.61748e7	+	6.92145e7i	0.191732	+	0.153996i
$767$		−	3.91440e8i		−	0.867519i
$768$	−2.60601e8	+	2.20309e7i	−0.575298	+	0.0486351i
$769$	−7.18352e8			−1.57964			−0.789820	−	0.613338i	$-0.789826\pi$
$769$	−7.18352e8			−1.57964			−0.789820	+	0.613338i	$0.789826\pi$
$770$	−3.35126e8	+	4.17246e8i	−0.734068	+	0.913944i
$771$	−1.05883e7	−	1.05883e7i	−0.0231028	−	0.0231028i
$772$	−9.18800e7	−	4.15884e8i	−0.199696	−	0.903901i
$773$	4.46865e8	+	4.46865e8i	0.967471	+	0.967471i	0.999487	−	0.0320160i	$-0.0101928\pi$
$773$	4.46865e8	+	4.46865e8i	0.967471	+	0.967471i	−0.0320160	+	0.999487i	$0.510193\pi$
$774$	1.88368e8	−	2.05599e7i	0.406242	−	0.0443403i
$775$	−4.47034e8			−0.960364
$776$	−1.80509e8	−	8.92635e7i	−0.386289	−	0.191024i
$777$		−	6.40046e8i		−	1.36442i
$778$	3.70190e8	−	4.04053e7i	0.786115	−	0.0858024i
$779$	−1.29062e8	+	1.29062e8i	−0.273014	+	0.273014i
$780$	1.41651e8	−	2.21989e8i	0.298495	−	0.467787i
$781$	3.43805e8	−	3.43805e8i	0.721704	−	0.721704i
$782$	5.27064e7	−	6.56216e7i	0.110216	−	0.137223i
$783$		−	6.19046e7i		−	0.128955i
$784$	−7.51093e8	+	3.48903e8i	−1.55864	+	0.724029i
$785$	−4.59153e7			−0.0949179
$786$	3.03238e8	+	2.43556e8i	0.624475	+	0.501570i
$787$	1.27217e8	+	1.27217e8i	0.260989	+	0.260989i	0.825456	−	0.564467i	$-0.190918\pi$
$787$	1.27217e8	+	1.27217e8i	0.260989	+	0.260989i	−0.564467	+	0.825456i	$0.690918\pi$
$788$	4.96207e7	−	7.77633e7i	0.101411	−	0.158926i
$789$	2.93544e8	+	2.93544e8i	0.597643	+	0.597643i
$790$	3.13564e7	+	2.87285e8i	0.0635982	+	0.582682i
$791$	−9.98696e8			−2.01792
$792$	−7.28329e7	−	2.15335e8i	−0.146606	−	0.433451i
$793$		−	5.72029e8i		−	1.14709i
$794$	−1.11619e7	−	1.02264e8i	−0.0222985	−	0.204297i
$795$	−1.09475e8	+	1.09475e8i	−0.217878	+	0.217878i
$796$	−1.22839e7	−	5.56018e7i	−0.0243555	−	0.110243i
$797$	5.09748e7	−	5.09748e7i	0.100689	−	0.100689i	−0.654968	−	0.755657i	$-0.727318\pi$
$797$	5.09748e7	−	5.09748e7i	0.100689	−	0.100689i	0.755657	+	0.654968i	$0.227318\pi$
$798$	1.50877e8	+	1.21182e8i	0.296902	+	0.238468i
$799$			7.13800e7i			0.139938i
$800$	3.63760e8	+	8.97173e7i	0.710468	+	0.175229i
$801$	−1.02008e8			−0.198489
$802$	2.55630e8	−	3.18270e8i	0.495552	−	0.616983i
$803$	3.46196e8	+	3.46196e8i	0.668615	+	0.668615i
$804$	1.45212e8	−	3.20812e7i	0.279405	−	0.0617280i
$805$	4.11109e8	+	4.11109e8i	0.788077	+	0.788077i
$806$	1.26771e9	−	1.38368e8i	2.42112	−	0.264259i
$807$	−4.41516e8			−0.840090
$808$	−1.55655e8	−	4.60204e8i	−0.295073	−	0.872402i
$809$		−	9.47571e8i		−	1.78964i	−0.446424	−	0.894822i	$-0.647303\pi$
$809$		−	9.47571e8i		−	1.78964i	0.446424	−	0.894822i	$-0.352697\pi$
$810$	−3.04021e7	+	3.31831e6i	−0.0572070	+	0.00624399i
$811$	9.22998e7	−	9.22998e7i	0.173037	−	0.173037i	−0.615275	−	0.788312i	$-0.710955\pi$
$811$	9.22998e7	−	9.22998e7i	0.173037	−	0.173037i	0.788312	+	0.615275i	$0.210955\pi$
$812$	4.98639e8	+	3.18181e8i	0.931361	+	0.594301i
$813$	−1.47699e8	+	1.47699e8i	−0.274856	+	0.274856i
$814$	−6.64523e8	+	8.27358e8i	−1.23207	+	1.53398i
$815$			1.19031e8i			0.219881i
$816$	−3.97319e7	−	1.45271e7i	−0.0731255	−	0.0267368i
$817$	2.67450e8			0.490429
$818$	−5.02803e8	−	4.03845e8i	−0.918624	−	0.737827i
$819$	3.96193e8	+	3.96193e8i	0.721200	+	0.721200i
$820$	2.32344e8	+	1.48259e8i	0.421396	+	0.268893i
$821$	−5.05480e8	−	5.05480e8i	−0.913429	−	0.913429i	0.0831113	−	0.996540i	$-0.473514\pi$
$821$	−5.05480e8	−	5.05480e8i	−0.913429	−	0.913429i	−0.996540	+	0.0831113i	$0.973514\pi$
$822$	2.85487e6	+	2.61561e7i	0.00514008	+	0.0470930i
$823$	−3.69057e7			−0.0662055			−0.0331027	−	0.999452i	$-0.510539\pi$
$823$	−3.69057e7			−0.0662055			−0.0331027	+	0.999452i	$0.510539\pi$
$824$	−2.09637e8	−	1.03668e8i	−0.374702	−	0.185294i
$825$			3.25649e8i			0.579947i
$826$	−4.71318e7	−	4.31817e8i	−0.0836322	−	0.766232i
$827$	−1.45689e8	+	1.45689e8i	−0.257579	+	0.257579i	−0.824069	−	0.566490i	$-0.808301\pi$
$827$	−1.45689e8	+	1.45689e8i	−0.257579	+	0.257579i	0.566490	+	0.824069i	$0.308301\pi$
$828$	−2.41140e8	+	5.32744e7i	−0.424795	+	0.0938485i
$829$	6.21154e8	−	6.21154e8i	1.09027	−	1.09027i	0.0947757	−	0.995499i	$-0.469787\pi$
$829$	6.21154e8	−	6.21154e8i	1.09027	−	1.09027i	0.995499	−	0.0947757i	$-0.0302134\pi$
$830$	−1.34898e8	−	1.08348e8i	−0.235923	−	0.189490i
$831$			3.15308e7i			0.0549455i
$832$	−1.05933e9	−	1.41831e8i	−1.83934	−	0.246264i
$833$	−1.33963e8			−0.231766
$834$	7.49836e7	−	9.33577e7i	0.129261	−	0.160935i
$835$	−3.93812e8	−	3.93812e8i	−0.676440	−	0.676440i
$836$	−6.92149e7	−	3.13293e8i	−0.118462	−	0.536207i
$837$	−1.04724e8	−	1.04724e8i	−0.178596	−	0.178596i
$838$	−9.05887e8	+	9.88753e7i	−1.53937	+	0.168018i
$839$	−7.28215e8			−1.23303			−0.616515	−	0.787343i	$-0.711456\pi$
$839$	−7.28215e8			−1.23303			−0.616515	+	0.787343i	$0.711456\pi$
$840$	1.29534e8	−	2.61944e8i	0.218548	−	0.441947i
$841$			3.27752e8i			0.551008i
$842$	−2.23937e8	+	2.44421e7i	−0.375136	+	0.0409451i
$843$	−1.93169e8	+	1.93169e8i	−0.322445	+	0.322445i
$844$	−2.97169e8	+	4.65710e8i	−0.494284	+	0.774619i
$845$	5.39990e8	−	5.39990e8i	0.894984	−	0.894984i
$846$	1.31151e8	−	1.63288e8i	0.216600	−	0.269676i
$847$			8.86032e8i			1.45814i
$848$	5.90157e8	+	2.15779e8i	0.967788	+	0.353851i
$849$	−5.29375e8			−0.865048
$850$	4.72501e7	+	3.79506e7i	0.0769389	+	0.0617963i
$851$	8.15189e8	+	8.15189e8i	1.32272	+	1.32272i
$852$	−1.42813e8	+	2.23809e8i	−0.230913	+	0.361875i
$853$	−3.95707e8	−	3.95707e8i	−0.637568	−	0.637568i	0.312387	−	0.949955i	$-0.398872\pi$
$853$	−3.95707e8	−	3.95707e8i	−0.637568	−	0.637568i	−0.949955	+	0.312387i	$0.898872\pi$
$854$	−6.88758e7	−	6.31035e8i	−0.110584	−	1.01316i
$855$	−4.31657e7			−0.0690623
$856$	3.42116e8	−	1.15714e8i	0.545446	−	0.184486i
$857$			7.60780e8i			1.20870i	0.796721	+	0.604348i	$0.206566\pi$
$857$			7.60780e8i			1.20870i	−0.796721	+	0.604348i	$0.793434\pi$
$858$	−1.00796e8	−	9.23486e8i	−0.159581	−	1.46207i
$859$	2.52493e8	−	2.52493e8i	0.398354	−	0.398354i	−0.479298	−	0.877652i	$-0.659109\pi$
$859$	2.52493e8	−	2.52493e8i	0.398354	−	0.398354i	0.877652	+	0.479298i	$0.159109\pi$
$860$	−8.71237e7	−	3.94355e8i	−0.136975	−	0.620001i
$861$	−4.14674e8	+	4.14674e8i	−0.649677	+	0.649677i
$862$	3.47102e8	+	2.78788e8i	0.541921	+	0.435264i
$863$			7.25728e7i			0.112912i	0.998405	+	0.0564562i	$0.0179801\pi$
$863$			7.25728e7i			0.112912i	−0.998405	+	0.0564562i	$0.982020\pi$
$864$	6.41984e7	+	1.06234e8i	0.0995367	+	0.164710i
$865$	−8.16609e7			−0.126173
$866$	6.45855e8	−	8.04116e8i	0.994447	−	1.23813i
$867$	2.61223e8	+	2.61223e8i	0.400824	+	0.400824i
$868$	1.38182e9	−	3.05281e8i	2.11297	−	0.466811i
$869$	7.20885e8	+	7.20885e8i	1.09852	+	1.09852i
$870$	−1.31162e8	+	1.43160e7i	−0.199182	+	0.0217402i
$871$	6.07738e8			0.919734
$872$	4.70545e8	−	1.59153e8i	0.709663	−	0.240029i
$873$			9.55738e7i			0.143647i
$874$	−3.46505e8	+	3.78202e7i	−0.519010	+	0.0566486i
$875$	−7.00538e8	+	7.00538e8i	−1.04570	+	1.04570i
$876$	−2.25366e8	−	1.43806e8i	−0.335255	−	0.213926i
$877$	5.64497e8	−	5.64497e8i	0.836879	−	0.836879i	−0.151568	−	0.988447i	$-0.548432\pi$
$877$	5.64497e8	−	5.64497e8i	0.836879	−	0.836879i	0.988447	+	0.151568i	$0.0484322\pi$
$878$	−5.83984e8	+	7.27083e8i	−0.862814	+	1.07424i
$879$		−	5.50431e8i		−	0.810468i
$880$	−4.39404e8	+	2.04115e8i	−0.644787	+	0.299521i
$881$	9.73736e7			0.142401			0.0712006	−	0.997462i	$-0.477317\pi$
$881$	9.73736e7			0.142401			0.0712006	+	0.997462i	$0.477317\pi$
$882$	3.06451e8	+	2.46137e8i	0.446638	+	0.358733i
$883$	−6.90645e7	−	6.90645e7i	−0.100317	−	0.100317i	0.655167	−	0.755484i	$-0.272598\pi$
$883$	−6.90645e7	−	6.90645e7i	−0.100317	−	0.100317i	−0.755484	+	0.655167i	$0.772598\pi$
$884$	−1.45740e8	−	9.29965e7i	−0.210970	−	0.134620i
$885$	6.85136e7	+	6.85136e7i	0.0988432	+	0.0988432i
$886$	1.05098e8	+	9.62900e8i	0.151110	+	1.38446i
$887$	−4.66487e8			−0.668450			−0.334225	−	0.942493i	$-0.608474\pi$
$887$	−4.66487e8			−0.668450			−0.334225	+	0.942493i	$0.608474\pi$
$888$	2.56854e8	−	5.19409e8i	0.366815	−	0.741773i
$889$			1.42810e9i			2.03261i
$890$	2.35903e7	+	2.16132e8i	0.0334628	+	0.306584i
$891$	−7.62881e7	+	7.62881e7i	−0.107851	+	0.107851i
$892$	5.04572e8	−	1.11474e8i	0.710933	−	0.157064i
$893$	2.09026e8	−	2.09026e8i	0.293525	−	0.293525i
$894$	3.61378e8	+	2.90254e8i	0.505766	+	0.406225i
$895$		−	2.65128e8i		−	0.369817i
$896$	−1.18568e9	−	2.89111e7i	−1.64833	−	0.0401920i
$897$	−1.00922e9			−1.39832
$898$	−8.13047e8	+	1.01228e9i	−1.12276	+	1.39788i
$899$	−4.51805e8	−	4.51805e8i	−0.621831	−	0.621831i
$900$	−3.83596e7	−	1.73630e8i	−0.0526195	−	0.238176i
$901$	7.18722e7	+	7.18722e7i	0.0982623	+	0.0982623i
$902$	9.66563e8	−	1.05498e8i	1.31707	−	0.143755i
$903$	8.59315e8			1.16705
$904$	−8.10461e8	−	4.00782e8i	−1.09705	−	0.542504i
$905$			1.96519e8i			0.265130i
$906$	−3.57093e8	+	3.89758e7i	−0.480172	+	0.0524096i
$907$	−1.99657e8	+	1.99657e8i	−0.267585	+	0.267585i	−0.828126	−	0.560541i	$-0.810593\pi$
$907$	−1.99657e8	+	1.99657e8i	−0.267585	+	0.267585i	0.560541	+	0.828126i	$0.310593\pi$
$908$	−2.01453e8	+	3.15707e8i	−0.269101	+	0.421723i
$909$	−1.63039e8	+	1.63039e8i	−0.217071	+	0.217071i
$910$	7.47822e8	−	9.31069e8i	0.992371	−	1.23554i
$911$		−	7.71797e8i		−	1.02082i	−0.859932	−	0.510409i	$-0.829494\pi$
$911$		−	7.71797e8i		−	1.02082i	0.859932	−	0.510409i	$-0.170506\pi$
$912$	7.38083e7	+	1.58889e8i	0.0973017	+	0.209464i
$913$	−6.10378e8			−0.802022
$914$	−8.18476e8	−	6.57389e8i	−1.07193	−	0.860962i
$915$	1.00122e8	+	1.00122e8i	0.130697	+	0.130697i
$916$	−5.82620e8	+	9.13054e8i	−0.758052	+	1.18798i
$917$	1.24721e9	+	1.24721e9i	1.61745	+	1.61745i
$918$	2.17853e6	+	1.99595e7i	0.00281602	+	0.0258001i
$919$	8.94727e8			1.15277			0.576387	−	0.817177i	$-0.304462\pi$
$919$	8.94727e8			1.15277			0.576387	+	0.817177i	$0.304462\pi$
$920$	1.68642e8	+	4.98603e8i	0.216573	+	0.640311i
$921$		−	6.91307e7i		−	0.0884896i
$922$	−4.62055e7	−	4.23331e8i	−0.0589523	−	0.540116i
$923$	−7.67189e8	+	7.67189e8i	−0.975658	+	0.975658i
$924$	−2.22387e8	−	1.00661e9i	−0.281899	−	1.27598i
$925$	−5.86967e8	+	5.86967e8i	−0.741633	+	0.741633i
$926$	−3.43334e7	−	2.75761e7i	−0.0432398	−	0.0347296i
$927$			1.10996e8i			0.139338i
$928$	2.76967e8	+	4.58317e8i	0.346565	+	0.573485i
$929$	5.16188e8			0.643814			0.321907	−	0.946771i	$-0.395676\pi$
$929$	5.16188e8			0.643814			0.321907	+	0.946771i	$0.395676\pi$
$930$	−1.97669e8	+	2.46106e8i	−0.245748	+	0.305966i
$931$	3.92290e8	+	3.92290e8i	0.486136	+	0.486136i
$932$	9.17155e7	−	2.02624e7i	0.113291	−	0.0250290i
$933$	−3.11615e8	−	3.11615e8i	−0.383684	−	0.383684i
$934$	−1.08368e8	+	1.18281e7i	−0.133003	+	0.0145169i
$935$	−7.83709e7			−0.0958782
$936$	1.62524e8	+	4.80513e8i	0.198194	+	0.585973i
$937$			5.89366e8i			0.716418i	0.933641	+	0.358209i	$0.116612\pi$
$937$			5.89366e8i			0.716418i	−0.933641	+	0.358209i	$0.883388\pi$
$938$	6.70428e8	−	7.31755e7i	0.812351	−	0.0886660i
$939$	−4.59755e7	+	4.59755e7i	−0.0555303	+	0.0555303i
$940$	−3.76300e8	−	2.40117e8i	−0.453055	−	0.289094i
$941$	4.11063e7	−	4.11063e7i	0.0493333	−	0.0493333i	−0.682010	−	0.731343i	$-0.738894\pi$
$941$	4.11063e7	−	4.11063e7i	0.0493333	−	0.0493333i	0.731343	+	0.682010i	$0.238894\pi$
$942$	5.53856e7	−	6.89572e7i	0.0662588	−	0.0824949i
$943$		−	1.05629e9i		−	1.25965i
$944$	1.35042e8	−	3.69342e8i	0.160529	−	0.439049i
$945$	−1.38691e8			−0.164344
$946$	−1.11080e9	−	8.92178e8i	−1.31208	−	1.05385i
$947$	−1.82225e8	−	1.82225e8i	−0.214565	−	0.214565i	0.591639	−	0.806203i	$-0.298481\pi$
$947$	−1.82225e8	−	1.82225e8i	−0.214565	−	0.214565i	−0.806203	+	0.591639i	$0.798481\pi$
$948$	−4.69279e8	−	2.99447e8i	−0.550815	−	0.351475i
$949$	−7.72525e8	−	7.72525e8i	−0.903887	−	0.903887i
$950$	−2.72320e7	−	2.49497e8i	−0.0317621	−	0.291001i
$951$	−7.70715e8			−0.896091
$952$	−1.71970e8	−	8.50413e7i	−0.199316	−	0.0985642i
$953$			1.41084e9i			1.63004i	0.579433	+	0.815020i	$0.303274\pi$
$953$			1.41084e9i			1.63004i	−0.579433	+	0.815020i	$0.696726\pi$
$954$	−3.23588e7	−	2.96469e8i	−0.0372689	−	0.341455i
$955$	5.14771e7	−	5.14771e7i	0.0591023	−	0.0591023i
$956$	8.02965e8	−	1.77396e8i	0.919016	−	0.203035i
$957$	−3.29125e8	+	3.29125e8i	−0.375513	+	0.375513i
$958$	2.30026e7	+	1.84754e7i	0.0261626	+	0.0210134i
$959$			1.19321e8i			0.135289i
$960$	2.10239e8	−	1.60590e8i	0.237629	−	0.181511i
$961$	−6.41141e8			−0.722409
$962$	1.48286e9	−	1.84622e9i	1.66562	−	2.07376i
$963$	−1.21203e8	−	1.21203e8i	−0.135718	−	0.135718i
$964$	2.58324e7	+	1.16927e8i	0.0288359	+	0.130522i
$965$	3.04648e8	+	3.04648e8i	0.339013	+	0.339013i
$966$	−1.11332e9	+	1.21516e8i	−1.23506	+	0.134804i
$967$	9.62310e8			1.06423			0.532115	−	0.846672i	$-0.321397\pi$
$967$	9.62310e8			1.06423			0.532115	+	0.846672i	$0.321397\pi$
$968$	−3.55569e8	+	7.19032e8i	−0.392011	+	0.792724i
$969$			2.83390e7i			0.0311468i
$970$	2.02499e8	−	2.21023e7i	0.221875	−	0.0242171i
$971$	8.97286e8	−	8.97286e8i	0.980106	−	0.980106i	−0.0196995	−	0.999806i	$-0.506271\pi$
$971$	8.97286e8	−	8.97286e8i	0.980106	−	0.980106i	0.999806	+	0.0196995i	$0.00627094\pi$
$972$	3.16892e7	−	4.96618e7i	0.0345074	−	0.0540783i
$973$	3.83977e8	−	3.83977e8i	0.416838	−	0.416838i
$974$	−3.03822e8	+	3.78271e8i	−0.328808	+	0.409379i
$975$		−	7.26675e8i		−	0.784019i
$976$	1.97344e8	−	5.39737e8i	0.212263	−	0.580541i
$977$	−1.56733e8			−0.168065			−0.0840324	−	0.996463i	$-0.526780\pi$
$977$	−1.56733e8			−0.168065			−0.0840324	+	0.996463i	$0.526780\pi$
$978$	−1.78765e8	−	1.43582e8i	−0.191103	−	0.153491i
$979$	5.42341e8	+	5.42341e8i	0.577995	+	0.577995i
$980$	4.50641e8	−	7.06223e8i	0.478798	−	0.750349i
$981$	−1.66703e8	−	1.66703e8i	−0.176578	−	0.176578i
$982$	−3.22995e7	−	2.95925e8i	−0.0341084	−	0.312498i
$983$	2.49727e7			0.0262909			0.0131454	−	0.999914i	$-0.495816\pi$
$983$	2.49727e7			0.0262909			0.0131454	+	0.999914i	$0.495816\pi$
$984$	−5.02927e8	+	1.70105e8i	−0.527861	+	0.178539i
$985$			9.33128e7i			0.0976411i
$986$	9.39869e6	+	8.61100e7i	0.00980475	+	0.0898303i
$987$	6.71598e8	−	6.71598e8i	0.698486	−	0.698486i
$988$	1.54451e8	+	6.99103e8i	0.160147	+	0.724887i
$989$	−1.09446e9	+	1.09446e9i	−1.13139	+	1.13139i
$990$	1.79280e8	+	1.43995e8i	0.184768	+	0.148403i
$991$		−	4.63587e8i		−	0.476333i	−0.971224	−	0.238166i	$-0.923454\pi$
$991$		−	4.63587e8i		−	0.476333i	0.971224	−	0.238166i	$-0.0765463\pi$
$992$	1.24388e9	+	3.06790e8i	1.27422	+	0.314273i
$993$	5.13428e8			0.524362
$994$	−7.53952e8	+	9.38701e8i	−0.767688	+	0.955802i
$995$	4.07300e7	+	4.07300e7i	0.0413472	+	0.0413472i
$996$	3.25443e8	−	7.18990e7i	0.329379	−	0.0727687i
$997$	−9.19997e7	−	9.19997e7i	−0.0928327	−	0.0928327i	0.659165	−	0.751998i	$-0.270910\pi$
$997$	−9.19997e7	−	9.19997e7i	−0.0928327	−	0.0928327i	−0.751998	+	0.659165i	$0.770910\pi$
$998$	−1.31889e9	+	1.43954e8i	−1.32684	+	0.144821i
$999$	−2.75011e8			−0.275838

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.7.l.a.43.18	yes	48
4.3	odd	2		192.7.l.a.79.18		48
8.3	odd	2		384.7.l.a.31.7		48
8.5	even	2		384.7.l.b.31.18		48
16.3	odd	4	inner	48.7.l.a.19.18	✓	48
16.5	even	4		384.7.l.a.223.7		48
16.11	odd	4		384.7.l.b.223.18		48
16.13	even	4		192.7.l.a.175.18		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.7.l.a.19.18	✓	48	16.3	odd	4	inner
48.7.l.a.43.18	yes	48	1.1	even	1	trivial
192.7.l.a.79.18		48	4.3	odd	2
192.7.l.a.175.18		48	16.13	even	4
384.7.l.a.31.7		48	8.3	odd	2
384.7.l.a.223.7		48	16.5	even	4
384.7.l.b.31.18		48	8.5	even	2
384.7.l.b.223.18		48	16.11	odd	4

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)

\(f(q)\)	\(=\)	\(q+(5.00967 - 6.23724i) q^{2} +(-11.0227 - 11.0227i) q^{3} +(-13.8064 - 62.4931i) q^{4} +(45.7781 + 45.7781i) q^{5} +(-123.971 + 13.5312i) q^{6} -565.544 q^{7} +(-458.950 - 226.956i) q^{8} +243.000i q^{9} +O(q^{10})\)	\(q+(5.00967 - 6.23724i) q^{2} +(-11.0227 - 11.0227i) q^{3} +(-13.8064 - 62.4931i) q^{4} +(45.7781 + 45.7781i) q^{5} +(-123.971 + 13.5312i) q^{6} -565.544 q^{7} +(-458.950 - 226.956i) q^{8} +243.000i q^{9} +(514.863 - 56.1959i) q^{10} +(1291.95 - 1291.95i) q^{11} +(-536.659 + 841.026i) q^{12} +(-2882.93 + 2882.93i) q^{13} +(-2833.19 + 3527.44i) q^{14} -1009.20i q^{15} +(-3714.77 + 1725.61i) q^{16} -662.555 q^{17} +(1515.65 + 1217.35i) q^{18} +(1940.19 + 1940.19i) q^{19} +(2228.79 - 3492.85i) q^{20} +(6233.83 + 6233.83i) q^{21} +(-1585.96 - 14530.4i) q^{22} -15879.3 q^{23} +(2557.20 + 7560.54i) q^{24} -11433.7i q^{25} +(3539.01 + 32424.1i) q^{26} +(2678.52 - 2678.52i) q^{27} +(7808.12 + 35342.6i) q^{28} +(11555.8 - 11555.8i) q^{29} +(-6294.61 - 5055.75i) q^{30} -39097.9i q^{31} +(-7846.73 + 31814.6i) q^{32} -28481.5 q^{33} +(-3319.18 + 4132.52i) q^{34} +(-25889.6 - 25889.6i) q^{35} +(15185.8 - 3354.95i) q^{36} +(-51336.5 - 51336.5i) q^{37} +(21821.2 - 2381.73i) q^{38} +63555.4 q^{39} +(-10620.3 - 31399.5i) q^{40} +66520.0i q^{41} +(70111.3 - 7652.47i) q^{42} +(68923.6 - 68923.6i) q^{43} +(-98574.8 - 62900.6i) q^{44} +(-11124.1 + 11124.1i) q^{45} +(-79550.2 + 99043.2i) q^{46} -107734. i q^{47} +(59967.6 + 21925.9i) q^{48} +202191. q^{49} +(-71314.9 - 57279.2i) q^{50} +(7303.15 + 7303.15i) q^{51} +(219966. + 140360. i) q^{52} +(-108477. - 108477. i) q^{53} +(-3288.07 - 30125.0i) q^{54} +118286. q^{55} +(259556. + 128354. i) q^{56} -42772.3i q^{57} +(-14185.5 - 129967. i) q^{58} +(-67889.1 + 67889.1i) q^{59} +(-63067.9 + 13933.4i) q^{60} +(-99209.6 + 99209.6i) q^{61} +(-243863. - 195868. i) q^{62} -137427. i q^{63} +(159126. + 208323. i) q^{64} -263951. q^{65} +(-142683. + 177646. i) q^{66} +(-105403. - 105403. i) q^{67} +(9147.50 + 41405.1i) q^{68} +(175033. + 175033. i) q^{69} +(-291178. + 31781.3i) q^{70} +266114. q^{71} +(55150.3 - 111525. i) q^{72} +267965. i q^{73} +(-577377. + 63019.2i) q^{74} +(-126031. + 126031. i) q^{75} +(94461.5 - 148036. i) q^{76} +(-730653. + 730653. i) q^{77} +(318392. - 396411. i) q^{78} +557984. i q^{79} +(-249050. - 91060.0i) q^{80} -59049.0 q^{81} +(414901. + 333243. i) q^{82} +(-236224. - 236224. i) q^{83} +(303504. - 475638. i) q^{84} +(-30330.5 - 30330.5i) q^{85} +(-84608.7 - 775178. i) q^{86} -254751. q^{87} +(-886153. + 299724. i) q^{88} +419786. i q^{89} +(13655.6 + 125112. i) q^{90} +(1.63043e6 - 1.63043e6i) q^{91} +(219236. + 992347. i) q^{92} +(-430964. + 430964. i) q^{93} +(-671966. - 539714. i) q^{94} +177637. i q^{95} +(437175. - 264191. i) q^{96} +393308. q^{97} +(1.01291e6 - 1.26112e6i) q^{98} +(313943. + 313943. 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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