LMFDB - Embedded newform 21.7.h.a.2.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,7,Mod(2,21)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(21, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("21.2");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	21.h (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.83113575602$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			2.13
Character	$\chi$	$=$	21.2
Dual form			21.7.h.a.11.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(11.1103 + 6.41456i) q^{2} +(26.9925 - 0.635931i) q^{3} +(50.2932 + 87.1103i) q^{4} +(-38.4659 - 22.2083i) q^{5} +(303.975 + 166.080i) q^{6} +(-244.854 - 240.199i) q^{7} +469.371i q^{8} +(728.191 - 34.3307i) q^{9} +O(q^{10})$	\(q+(11.1103 + 6.41456i) q^{2} +(26.9925 - 0.635931i) q^{3} +(50.2932 + 87.1103i) q^{4} +(-38.4659 - 22.2083i) q^{5} +(303.975 + 166.080i) q^{6} +(-244.854 - 240.199i) q^{7} +469.371i q^{8} +(728.191 - 34.3307i) q^{9} +(-284.913 - 493.483i) q^{10} +(-1976.59 + 1141.18i) q^{11} +(1412.94 + 2319.34i) q^{12} +1632.89 q^{13} +(-1179.65 - 4239.32i) q^{14} +(-1052.41 - 574.996i) q^{15} +(207.957 - 360.192i) q^{16} +(565.551 - 326.521i) q^{17} +(8310.67 + 4289.60i) q^{18} +(1432.18 - 2480.60i) q^{19} -4467.70i q^{20} +(-6761.98 - 6327.85i) q^{21} -29280.8 q^{22} +(-5700.94 - 3291.44i) q^{23} +(298.487 + 12669.5i) q^{24} +(-6826.08 - 11823.1i) q^{25} +(18141.9 + 10474.3i) q^{26} +(19633.9 - 1389.75i) q^{27} +(8609.27 - 33409.7i) q^{28} +31946.0i q^{29} +(-8004.33 - 13139.2i) q^{30} +(23450.7 + 40617.8i) q^{31} +(30636.1 - 17687.8i) q^{32} +(-52627.4 + 32060.4i) q^{33} +8377.96 q^{34} +(4084.14 + 14677.2i) q^{35} +(39613.6 + 61706.4i) q^{36} +(12837.6 - 22235.3i) q^{37} +(31824.0 - 18373.6i) q^{38} +(44075.7 - 1038.40i) q^{39} +(10423.9 - 18054.8i) q^{40} +90943.6i q^{41} +(-34537.6 - 113680. i) q^{42} -87735.6 q^{43} +(-198818. - 114788. i) q^{44} +(-28772.9 - 14851.3i) q^{45} +(-42226.3 - 73138.0i) q^{46} +(-14076.8 - 8127.24i) q^{47} +(5384.22 - 9854.73i) q^{48} +(2258.34 + 117627. i) q^{49} -175145. i q^{50} +(15058.0 - 9173.27i) q^{51} +(82123.1 + 142241. i) q^{52} +(-54963.5 + 31733.2i) q^{53} +(227054. + 110502. i) q^{54} +101375. q^{55} +(112742. - 114927. i) q^{56} +(37080.6 - 67868.5i) q^{57} +(-204919. + 354931. i) q^{58} +(57358.9 - 33116.2i) q^{59} +(-2841.15 - 120594. i) q^{60} +(226744. - 392733. i) q^{61} +601704. i q^{62} +(-186547. - 166504. i) q^{63} +427218. q^{64} +(-62810.4 - 36263.6i) q^{65} +(-790362. + 18620.6i) q^{66} +(22352.1 + 38714.9i) q^{67} +(56886.7 + 32843.6i) q^{68} +(-155976. - 85218.8i) q^{69} +(-48771.8 + 189267. i) q^{70} +133341. i q^{71} +(16113.8 + 341792. i) q^{72} +(-259235. - 449009. i) q^{73} +(285260. - 164695. i) q^{74} +(-191772. - 314795. i) q^{75} +288115. q^{76} +(758088. + 195350. i) q^{77} +(496357. + 271189. i) q^{78} +(-73802.1 + 127829. i) q^{79} +(-15998.5 + 9236.73i) q^{80} +(529084. - 49998.7i) q^{81} +(-583363. + 1.01041e6i) q^{82} -281251. i q^{83} +(211140. - 907286. i) q^{84} -29005.9 q^{85} +(-974772. - 562785. i) q^{86} +(20315.4 + 862302. i) q^{87} +(-535639. - 927753. i) q^{88} +(-469964. - 271334. i) q^{89} +(-224413. - 349569. i) q^{90} +(-399819. - 392217. i) q^{91} -662148. i q^{92} +(658823. + 1.08146e6i) q^{93} +(-104265. - 180593. i) q^{94} +(-110180. + 63612.4i) q^{95} +(815697. - 496920. i) q^{96} +89556.3 q^{97} +(-729437. + 1.32137e6i) q^{98} +(-1.40016e6 + 898858. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - q^{3} + 382 q^{4} - 356 q^{6} + 1120 q^{7} + 1031 q^{9}+O(q^{10}) $ 28 * q - q^3 + 382 * q^4 - 356 * q^6 + 1120 * q^7 + 1031 * q^9	$ 28 q - q^{3} + 382 q^{4} - 356 q^{6} + 1120 q^{7} + 1031 q^{9} - 930 q^{10} - 404 q^{12} + 3632 q^{13} + 5450 q^{15} - 13706 q^{16} + 1612 q^{18} + 6830 q^{19} - 11333 q^{21} - 27348 q^{22} - 54498 q^{24} - 7640 q^{25} + 13268 q^{27} + 88522 q^{28} + 32380 q^{30} + 69410 q^{31} - 85459 q^{33} - 31344 q^{34} + 399028 q^{36} - 71830 q^{37} + 104570 q^{39} + 230250 q^{40} - 467782 q^{42} - 498904 q^{43} - 85375 q^{45} - 342660 q^{46} - 324728 q^{48} + 395668 q^{49} + 42177 q^{51} + 218000 q^{52} - 402122 q^{54} + 231660 q^{55} + 786782 q^{57} + 459522 q^{58} + 1021150 q^{60} + 153158 q^{61} + 179011 q^{63} - 1399412 q^{64} + 80896 q^{66} - 977098 q^{67} - 1520742 q^{69} - 139650 q^{70} - 1001352 q^{72} - 488350 q^{73} + 1434610 q^{75} + 6196280 q^{76} + 245176 q^{78} + 380762 q^{79} + 893531 q^{81} - 3665004 q^{82} + 1231496 q^{84} - 912540 q^{85} + 1452416 q^{87} - 1522482 q^{88} - 11713820 q^{90} - 1529416 q^{91} - 1690071 q^{93} - 3034044 q^{94} + 7549346 q^{96} + 7212176 q^{97} + 435866 q^{99}+O(q^{100}) $ 28 * q - q^3 + 382 * q^4 - 356 * q^6 + 1120 * q^7 + 1031 * q^9 - 930 * q^10 - 404 * q^12 + 3632 * q^13 + 5450 * q^15 - 13706 * q^16 + 1612 * q^18 + 6830 * q^19 - 11333 * q^21 - 27348 * q^22 - 54498 * q^24 - 7640 * q^25 + 13268 * q^27 + 88522 * q^28 + 32380 * q^30 + 69410 * q^31 - 85459 * q^33 - 31344 * q^34 + 399028 * q^36 - 71830 * q^37 + 104570 * q^39 + 230250 * q^40 - 467782 * q^42 - 498904 * q^43 - 85375 * q^45 - 342660 * q^46 - 324728 * q^48 + 395668 * q^49 + 42177 * q^51 + 218000 * q^52 - 402122 * q^54 + 231660 * q^55 + 786782 * q^57 + 459522 * q^58 + 1021150 * q^60 + 153158 * q^61 + 179011 * q^63 - 1399412 * q^64 + 80896 * q^66 - 977098 * q^67 - 1520742 * q^69 - 139650 * q^70 - 1001352 * q^72 - 488350 * q^73 + 1434610 * q^75 + 6196280 * q^76 + 245176 * q^78 + 380762 * q^79 + 893531 * q^81 - 3665004 * q^82 + 1231496 * q^84 - 912540 * q^85 + 1452416 * q^87 - 1522482 * q^88 - 11713820 * q^90 - 1529416 * q^91 - 1690071 * q^93 - 3034044 * q^94 + 7549346 * q^96 + 7212176 * q^97 + 435866 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$.

$n$	$8$	$10$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	11.1103	+	6.41456i	1.38879	+	0.801820i	0.993179	−	0.116597i	$-0.0371986\pi$
$2$	11.1103	+	6.41456i	1.38879	+	0.801820i	0.395614	+	0.918417i	$0.370532\pi$
$3$	26.9925	−	0.635931i	0.999723	−	0.0235530i
$3$	26.9925	−	0.635931i	0.999723	−	0.0235530i
$4$	50.2932	+	87.1103i	0.785831	+	1.36110i
$5$	−38.4659	−	22.2083i	−0.307727	−	0.177666i	0.338182	−	0.941081i	$-0.390188\pi$
$5$	−38.4659	−	22.2083i	−0.307727	−	0.177666i	−0.645909	+	0.763414i	$0.723521\pi$
$6$	303.975	+	166.080i	1.40729	+	0.768887i
$7$	−244.854	−	240.199i	−0.713861	−	0.700287i
$7$	−244.854	−	240.199i	−0.713861	−	0.700287i
$8$			469.371i			0.916739i
$9$	728.191	−	34.3307i	0.998891	−	0.0470929i
$10$	−284.913	−	493.483i	−0.284913	−	0.493483i
$11$	−1976.59	+	1141.18i	−1.48504	+	0.857389i	−0.999855	−	0.0170219i	$-0.994581\pi$
$11$	−1976.59	+	1141.18i	−1.48504	+	0.857389i	−0.485186	+	0.874411i	$0.661248\pi$
$12$	1412.94	+	2319.34i	0.817671	+	1.34221i
$13$	1632.89			0.743235			0.371617	−	0.928386i	$-0.378803\pi$
$13$	1632.89			0.743235			0.371617	+	0.928386i	$0.378803\pi$
$14$	−1179.65	−	4239.32i	−0.429901	−	1.54494i
$15$	−1052.41	−	574.996i	−0.311826	−	0.170369i
$16$	207.957	−	360.192i	0.0507707	−	0.0879374i
$17$	565.551	−	326.521i	0.115113	−	0.0664606i	−0.441338	−	0.897341i	$-0.645496\pi$
$17$	565.551	−	326.521i	0.115113	−	0.0664606i	0.556451	+	0.830880i	$0.312163\pi$
$18$	8310.67	+	4289.60i	1.42501	+	0.735528i
$19$	1432.18	−	2480.60i	0.208803	−	0.361657i	−0.742535	−	0.669807i	$-0.766377\pi$
$19$	1432.18	−	2480.60i	0.208803	−	0.361657i	0.951338	+	0.308151i	$0.0997101\pi$
$20$		−	4467.70i		−	0.558463i
$21$	−6761.98	−	6327.85i	−0.730157	−	0.683279i
$22$	−29280.8			−2.74989
$23$	−5700.94	−	3291.44i	−0.468558	−	0.270522i	0.247078	−	0.968996i	$-0.420530\pi$
$23$	−5700.94	−	3291.44i	−0.468558	−	0.270522i	−0.715636	+	0.698474i	$0.753863\pi$
$24$	298.487	+	12669.5i	0.0215920	+	0.916485i
$25$	−6826.08	−	11823.1i	−0.436869	−	0.756680i
$26$	18141.9	+	10474.3i	1.03220	+	0.595941i
$27$	19633.9	−	1389.75i	0.997504	−	0.0706067i
$28$	8609.27	−	33409.7i	0.392186	−	1.52194i
$29$			31946.0i			1.30985i	0.755693	+	0.654926i	$0.227300\pi$
$29$			31946.0i			1.30985i	−0.755693	+	0.654926i	$0.772700\pi$
$30$	−8004.33	−	13139.2i	−0.296457	−	0.486636i
$31$	23450.7	+	40617.8i	0.787174	+	1.36343i	0.927692	+	0.373347i	$0.121790\pi$
$31$	23450.7	+	40617.8i	0.787174	+	1.36343i	−0.140518	+	0.990078i	$0.544877\pi$
$32$	30636.1	−	17687.8i	0.934940	−	0.539788i
$33$	−52627.4	+	32060.4i	−1.46444	+	0.892128i
$34$	8377.96			0.213158
$35$	4084.14	+	14677.2i	0.0952570	+	0.342326i
$36$	39613.6	+	61706.4i	0.849057	+	1.32258i
$37$	12837.6	−	22235.3i	0.253442	−	0.438974i	−0.711029	−	0.703162i	$-0.751771\pi$
$37$	12837.6	−	22235.3i	0.253442	−	0.438974i	0.964471	+	0.264188i	$0.0851041\pi$
$38$	31824.0	−	18373.6i	0.579967	−	0.334844i
$39$	44075.7	−	1038.40i	0.743029	−	0.0175054i
$40$	10423.9	−	18054.8i	0.162874	−	0.282106i
$41$			90943.6i			1.31953i	0.751470	+	0.659767i	$0.229345\pi$
$41$			90943.6i			1.31953i	−0.751470	+	0.659767i	$0.770655\pi$
$42$	−34537.6	−	113680.i	−0.466170	−	1.53439i
$43$	−87735.6			−1.10350			−0.551748	−	0.834011i	$-0.686039\pi$
$43$	−87735.6			−1.10350			−0.551748	+	0.834011i	$0.686039\pi$
$44$	−198818.	−	114788.i	−2.33398	−	1.34753i
$45$	−28772.9	−	14851.3i	−0.315752	−	0.162977i
$46$	−42226.3	−	73138.0i	−0.433820	−	0.751398i
$47$	−14076.8	−	8127.24i	−0.135585	−	0.0782798i	0.430673	−	0.902508i	$-0.358276\pi$
$47$	−14076.8	−	8127.24i	−0.135585	−	0.0782798i	−0.566258	+	0.824228i	$0.691609\pi$
$48$	5384.22	−	9854.73i	0.0486854	−	0.0891089i
$49$	2258.34	+	117627.i	0.0191956	+	0.999816i
$50$		−	175145.i		−	1.40116i
$51$	15058.0	−	9173.27i	0.113516	−	0.0691534i
$52$	82123.1	+	142241.i	0.584057	+	1.01162i
$53$	−54963.5	+	31733.2i	−0.369187	+	0.213150i	−0.673103	−	0.739548i	$-0.735039\pi$
$53$	−54963.5	+	31733.2i	−0.369187	+	0.213150i	0.303916	+	0.952699i	$0.401706\pi$
$54$	227054.	+	110502.i	1.44194	+	0.701761i
$55$	101375.			0.609316
$56$	112742.	−	114927.i	0.641981	−	0.654425i
$57$	37080.6	−	67868.5i	0.200227	−	0.366474i
$58$	−204919.	+	354931.i	−1.05027	+	1.81911i
$59$	57358.9	−	33116.2i	0.279283	−	0.161244i	−0.353816	−	0.935315i	$-0.615116\pi$
$59$	57358.9	−	33116.2i	0.279283	−	0.161244i	0.633099	+	0.774071i	$0.281783\pi$
$60$	−2841.15	−	120594.i	−0.0131535	−	0.558308i
$61$	226744.	−	392733.i	0.998957	−	1.73024i	0.459935	−	0.887953i	$-0.347873\pi$
$61$	226744.	−	392733.i	0.998957	−	1.73024i	0.539022	−	0.842291i	$-0.318794\pi$
$62$			601704.i			2.52469i
$63$	−186547.	−	166504.i	−0.746048	−	0.665892i
$64$	427218.			1.62971
$65$	−62810.4	−	36263.6i	−0.228713	−	0.132048i
$66$	−790362.	+	18620.6i	−2.74912	+	0.0647681i
$67$	22352.1	+	38714.9i	0.0743179	+	0.128722i	0.900789	−	0.434256i	$-0.142989\pi$
$67$	22352.1	+	38714.9i	0.0743179	+	0.128722i	−0.826472	+	0.562979i	$0.809655\pi$
$68$	56886.7	+	32843.6i	0.180919	+	0.104454i
$69$	−155976.	−	85218.8i	−0.474799	−	0.259411i
$70$	−48771.8	+	189267.i	−0.142192	+	0.551799i
$71$			133341.i			0.372554i	0.982497	+	0.186277i	$0.0596422\pi$
$71$			133341.i			0.372554i	−0.982497	+	0.186277i	$0.940358\pi$
$72$	16113.8	+	341792.i	0.0431719	+	0.915722i
$73$	−259235.	−	449009.i	−0.666385	−	1.15421i	−0.978908	−	0.204303i	$-0.934507\pi$
$73$	−259235.	−	449009.i	−0.666385	−	1.15421i	0.312523	−	0.949910i	$-0.398826\pi$
$74$	285260.	−	164695.i	0.703956	−	0.406429i
$75$	−191772.	−	314795.i	−0.454570	−	0.746180i
$76$	288115.			0.656334
$77$	758088.	+	195350.i	1.66053	+	0.427899i
$78$	496357.	+	271189.i	1.04595	+	0.571464i
$79$	−73802.1	+	127829.i	−0.149688	+	0.259267i	−0.931112	−	0.364733i	$-0.881160\pi$
$79$	−73802.1	+	127829.i	−0.149688	+	0.259267i	0.781424	+	0.624000i	$0.214494\pi$
$80$	−15998.5	+	9236.73i	−0.0312470	+	0.0180405i
$81$	529084.	−	49998.7i	0.995565	−	0.0940813i
$82$	−583363.	+	1.01041e6i	−1.05803	+	1.83256i
$83$		−	281251.i		−	0.491881i	−0.969285	−	0.245941i	$-0.920903\pi$
$83$		−	281251.i		−	0.491881i	0.969285	−	0.245941i	$-0.0790968\pi$
$84$	211140.	−	907286.i	0.356231	−	1.53076i
$85$	−29005.9			−0.0472312
$86$	−974772.	−	562785.i	−1.53253	−	0.884804i
$87$	20315.4	+	862302.i	0.0308509	+	1.30949i
$88$	−535639.	−	927753.i	−0.786002	−	1.36140i
$89$	−469964.	−	271334.i	−0.666644	−	0.384887i	0.128160	−	0.991754i	$-0.459093\pi$
$89$	−469964.	−	271334.i	−0.666644	−	0.384887i	−0.794804	+	0.606866i	$0.792426\pi$
$90$	−224413.	−	349569.i	−0.307836	−	0.479519i
$91$	−399819.	−	392217.i	−0.530566	−	0.520478i
$92$		−	662148.i		−	0.850337i
$93$	658823.	+	1.08146e6i	0.819068	+	1.34451i
$94$	−104265.	−	180593.i	−0.125533	−	0.217429i
$95$	−110180.	+	63612.4i	−0.128508	+	0.0741944i
$96$	815697.	−	496920.i	0.921967	−	0.561659i
$97$	89556.3			0.0981253			0.0490627	−	0.998796i	$-0.484377\pi$
$97$	89556.3			0.0981253			0.0490627	+	0.998796i	$0.484377\pi$
$98$	−729437.	+	1.32137e6i	−0.775014	+	1.40393i
$99$	−1.40016e6	+	898858.i	−1.44302	+	0.926373i
$100$	686611.	−	1.18924e6i	0.686611	−	1.18924i
$101$	896691.	−	517705.i	0.870320	−	0.502479i	0.00286511	−	0.999996i	$-0.499088\pi$
$101$	896691.	−	517705.i	0.870320	−	0.502479i	0.867454	+	0.497517i	$0.165755\pi$
$102$	226142.	−	5327.80i	0.213099	−	0.00502050i
$103$	228566.	−	395888.i	0.209170	−	0.362294i	−0.742283	−	0.670086i	$-0.766257\pi$
$103$	228566.	−	395888.i	0.209170	−	0.362294i	0.951453	+	0.307793i	$0.0995903\pi$
$104$			766429.i			0.681353i
$105$	119575.	+	393578.i	0.103293	+	0.339988i
$106$	−814218.			−0.683633
$107$	−1.08784e6	−	628062.i	−0.887998	−	0.512686i	−0.0147107	−	0.999892i	$-0.504683\pi$
$107$	−1.08784e6	−	628062.i	−0.887998	−	0.512686i	−0.873287	+	0.487206i	$0.838016\pi$
$108$	1.10851e6	+	1.64042e6i	0.879972	+	1.30222i
$109$	747136.	+	1.29408e6i	0.576926	+	0.999265i	0.995829	+	0.0912340i	$0.0290811\pi$
$109$	747136.	+	1.29408e6i	0.576926	+	0.999265i	−0.418904	+	0.908031i	$0.637586\pi$
$110$	1.12631e6	+	650276.i	0.846214	+	0.488562i
$111$	332378.	−	608351.i	0.243032	−	0.444821i
$112$	−137437.	+	38243.6i	−0.0978247	+	0.0272211i
$113$		−	127575.i		−	0.0884161i	−0.999022	−	0.0442081i	$-0.985924\pi$
$113$		−	127575.i		−	0.0884161i	0.999022	−	0.0442081i	$-0.0140765\pi$
$114$	847324.	−	516187.i	0.571920	−	0.348411i
$115$	146194.	+	253216.i	0.0961252	+	0.166494i
$116$	−2.78283e6	+	1.60667e6i	−1.78284	+	1.02932i
$117$	1.18905e6	−	56058.2i	0.742410	−	0.0350011i
$118$	849703.			0.517155
$119$	−216908.	−	55894.4i	−0.128716	−	0.0331686i
$120$	269886.	−	493972.i	0.156184	−	0.285863i
$121$	1.71882e6	−	2.97709e6i	0.970232	−	1.68049i
$122$	5.03841e6	−	2.90893e6i	2.77469	−	1.60197i
$123$	57833.8	+	2.45480e6i	0.0310790	+	1.31917i
$124$	−2.35882e6	+	4.08560e6i	−1.23717	+	2.14284i
$125$			1.30039e6i			0.665800i
$126$	−1.00455e6	−	3.04654e6i	−0.502180	−	1.52298i
$127$	−1.98508e6			−0.969095			−0.484548	−	0.874765i	$-0.661016\pi$
$127$	−1.98508e6			−0.969095			−0.484548	+	0.874765i	$0.661016\pi$
$128$	2.78583e6	+	1.60840e6i	1.32839	+	0.766946i
$129$	−2.36820e6	+	55793.7i	−1.10319	+	0.0259906i
$130$	−465230.	−	805803.i	−0.211757	−	0.366774i
$131$	−2.98659e6	−	1.72431e6i	−1.32850	−	0.767010i	−0.343432	−	0.939178i	$-0.611590\pi$
$131$	−2.98659e6	−	1.72431e6i	−1.32850	−	0.767010i	−0.985068	+	0.172168i	$0.944923\pi$
$132$	−5.43959e6	−	2.97197e6i	−2.36507	−	1.29218i
$133$	−946512.	+	263380.i	−0.402320	+	0.111951i
$134$			573515.i			0.238358i
$135$	−786098.	−	382577.i	−0.319503	−	0.155495i
$136$	153259.	+	265453.i	0.0609271	+	0.105529i
$137$	2.05544e6	−	1.18671e6i	0.799363	−	0.461512i	−0.0438856	−	0.999037i	$-0.513974\pi$
$137$	2.05544e6	−	1.18671e6i	0.799363	−	0.461512i	0.843248	+	0.537524i	$0.180640\pi$
$138$	−1.18630e6	−	1.94733e6i	−0.451397	−	0.740971i
$139$	3.27319e6			1.21878			0.609392	−	0.792869i	$-0.291414\pi$
$139$	3.27319e6			1.21878			0.609392	+	0.792869i	$0.291414\pi$
$140$	−1.07314e6	+	1.09394e6i	−0.391084	+	0.398665i
$141$	−385136.	−	210423.i	−0.137391	−	0.0750647i
$142$	−855326.	+	1.48147e6i	−0.298721	+	0.517401i
$143$	−3.22755e6	+	1.86343e6i	−1.10373	+	0.637241i
$144$	139067.	−	269428.i	0.0465731	−	0.0902308i
$145$	709466.	−	1.22883e6i	0.232717	−	0.403077i
$146$		−	6.65152e6i		−	2.13728i
$147$	135761.	+	3.17362e6i	0.0427389	+	0.999086i
$148$	2.58257e6			0.796649
$149$	3.09917e6	+	1.78931e6i	0.936885	+	0.540911i	0.888983	−	0.457941i	$-0.151413\pi$
$149$	3.09917e6	+	1.78931e6i	0.936885	+	0.540911i	0.0479027	+	0.998852i	$0.484746\pi$
$150$	−111380.	−	4.72761e6i	−0.0330016	−	1.40077i
$151$	−370170.	−	641153.i	−0.107515	−	0.186222i	0.807248	−	0.590213i	$-0.200956\pi$
$151$	−370170.	−	641153.i	−0.107515	−	0.186222i	−0.914763	+	0.403991i	$0.867623\pi$
$152$	1.16432e6	+	672222.i	0.331545	+	0.191418i
$153$	400620.	−	257186.i	0.111856	−	0.0718079i
$154$	7.16953e6	+	7.03320e6i	1.96304	+	1.92571i
$155$		−	2.08320e6i		−	0.559417i
$156$	2.30716e6	+	3.78723e6i	0.607721	+	0.997579i
$157$	−186635.	−	323262.i	−0.0482275	−	0.0835325i	0.840904	−	0.541184i	$-0.182024\pi$
$157$	−186635.	−	323262.i	−0.0482275	−	0.0835325i	−0.889131	+	0.457652i	$0.848691\pi$
$158$	−1.63993e6	+	946815.i	−0.415772	+	0.240046i
$159$	−1.46342e6	+	891512.i	−0.364065	+	0.221787i
$160$	−1.57126e6			−0.383608
$161$	605301.	+	2.17528e6i	0.145042	+	0.521240i
$162$	6.19902e6	+	2.83834e6i	1.45807	+	0.667604i
$163$	−1.48642e6	+	2.57456e6i	−0.343225	+	0.594484i	−0.985030	−	0.172385i	$-0.944853\pi$
$163$	−1.48642e6	+	2.57456e6i	−0.343225	+	0.594484i	0.641804	+	0.766868i	$0.278186\pi$
$164$	−7.92213e6	+	4.57384e6i	−1.79602	+	1.03693i
$165$	2.73637e6	−	64467.5i	0.609147	−	0.0143512i
$166$	1.80410e6	−	3.12480e6i	0.394400	−	0.683121i
$167$		−	176945.i		−	0.0379917i	−0.999820	−	0.0189958i	$-0.993953\pi$
$167$		−	176945.i		−	0.0379917i	0.999820	−	0.0189958i	$-0.00604693\pi$
$168$	2.97011e6	−	3.17388e6i	0.626389	−	0.669364i
$169$	−2.16049e6			−0.447602
$170$	−322265.	−	186060.i	−0.0655944	−	0.0378710i
$171$	957738.	−	1.85552e6i	0.191539	−	0.371089i
$172$	−4.41250e6	−	7.64267e6i	−0.867160	−	1.50197i
$173$	739743.	+	427091.i	0.142871	+	0.0824864i	0.569731	−	0.821831i	$-0.307047\pi$
$173$	739743.	+	427091.i	0.142871	+	0.0824864i	−0.426861	+	0.904317i	$0.640381\pi$
$174$	−5.30558e6	+	9.71079e6i	−1.00713	+	1.84335i
$175$	−1.16850e6	+	4.53456e6i	−0.218029	+	0.846098i
$176$			949269.i			0.174121i
$177$	1.52720e6	−	930365.i	0.275408	−	0.167777i
$178$	−3.48097e6	−	6.02922e6i	−0.617221	−	1.06906i
$179$	−723180.	+	417528.i	−0.126092	+	0.0727992i	−0.561719	−	0.827328i	$-0.689860\pi$
$179$	−723180.	+	417528.i	−0.126092	+	0.0727992i	0.435627	+	0.900127i	$0.356527\pi$
$180$	−153379.	−	3.25334e6i	−0.0262996	−	0.557843i
$181$	865510.			0.145961			0.0729804	−	0.997333i	$-0.476749\pi$
$181$	865510.			0.145961			0.0729804	+	0.997333i	$0.476749\pi$
$182$	−1.92623e6	−	6.92233e6i	−0.319517	−	1.14825i
$183$	5.87065e6	−	1.07450e7i	0.957927	−	1.75329i
$184$	1.54490e6	−	2.67585e6i	0.247998	−	0.429545i
$185$	−987617.	+	570201.i	−0.155982	+	0.0900561i
$186$	382642.	+	1.62415e7i	0.0594639	+	2.52399i
$187$	−745242.	+	1.29080e6i	−0.113965	+	0.197394i
$188$		−	1.63498e6i		−	0.246059i
$189$	−5.14126e6	−	4.37574e6i	−0.761525	−	0.648136i
$190$	−1.63218e6			−0.237962
$191$	5.67532e6	+	3.27665e6i	0.814499	+	0.470251i	0.848516	−	0.529170i	$-0.177497\pi$
$191$	5.67532e6	+	3.27665e6i	0.814499	+	0.470251i	−0.0340169	+	0.999421i	$0.510830\pi$
$192$	1.15317e7	−	271681.i	1.62926	−	0.0383845i
$193$	603080.	+	1.04457e6i	0.0838887	+	0.145299i	0.904917	−	0.425588i	$-0.139933\pi$
$193$	603080.	+	1.04457e6i	0.0838887	+	0.145299i	−0.821028	+	0.570887i	$0.806599\pi$
$194$	995002.	+	574464.i	0.136276	+	0.0786788i
$195$	−1.71847e6	−	938903.i	−0.231760	−	0.126624i
$196$	−1.01330e7	+	6.11258e6i	−1.34576	+	0.811813i
$197$		−	2.27517e6i		−	0.297588i	−0.988868	−	0.148794i	$-0.952461\pi$
$197$		−	2.27517e6i		−	0.297588i	0.988868	−	0.148794i	$-0.0475392\pi$
$198$	−2.13220e7	+	1.00523e6i	−2.74684	+	0.129500i
$199$	222272.	+	384987.i	0.0282050	+	0.0488525i	0.879783	−	0.475375i	$-0.157688\pi$
$199$	222272.	+	384987.i	0.0282050	+	0.0488525i	−0.851578	+	0.524227i	$0.824354\pi$
$200$	5.54943e6	−	3.20396e6i	0.693678	−	0.400495i
$201$	627959.	+	1.03080e6i	0.0773291	+	0.126936i
$202$	1.32834e7			1.61159
$203$	7.67338e6	−	7.82212e6i	0.917273	−	0.935053i
$204$	1.55640e6	+	850354.i	0.183329	+	0.100163i
$205$	2.01970e6	−	3.49823e6i	0.234437	−	0.406056i
$206$	5.07890e6	−	2.93230e6i	0.580989	−	0.335434i
$207$	−4.26437e6	−	2.20108e6i	−0.480777	−	0.248156i
$208$	339570.	−	588152.i	0.0377346	−	0.0653582i
$209$			6.53751e6i			0.716100i
$210$	−1.19611e6	+	5.13981e6i	−0.129156	+	0.554995i
$211$	−5.36127e6			−0.570716			−0.285358	−	0.958421i	$-0.592113\pi$
$211$	−5.36127e6			−0.570716			−0.285358	+	0.958421i	$0.592113\pi$
$212$	−5.52858e6	−	3.19193e6i	−0.580238	−	0.335000i
$213$	84795.8	+	3.59922e6i	0.00877477	+	0.372451i
$214$	−8.05748e6	−	1.39560e7i	−0.822163	−	1.42403i
$215$	3.37483e6	+	1.94846e6i	0.339575	+	0.196054i
$216$	652309.	+	9.21556e6i	0.0647280	+	0.914451i
$217$	4.01433e6	−	1.55783e7i	0.392856	−	1.52454i
$218$			1.91702e7i			1.85036i
$219$	−7.28295e6	−	1.19550e7i	−0.693386	−	1.13820i
$220$	5.09847e6	+	8.83081e6i	0.478820	+	0.829340i
$221$	923481.	−	533172.i	0.0855561	−	0.0493958i
$222$	7.59514e6	−	4.62693e6i	0.694188	−	0.422897i
$223$	−8.56544e6			−0.772387			−0.386194	−	0.922418i	$-0.626210\pi$
$223$	−8.56544e6			−0.772387			−0.386194	+	0.922418i	$0.626210\pi$
$224$	−1.17500e7	−	3.02782e6i	−1.04542	−	0.269393i
$225$	−5.37659e6	−	8.37515e6i	−0.472019	−	0.735267i
$226$	818340.	−	1.41741e6i	0.0708938	−	0.122792i
$227$	−1.35487e7	+	7.82235e6i	−1.15830	+	0.668744i	−0.950896	−	0.309512i	$-0.899834\pi$
$227$	−1.35487e7	+	7.82235e6i	−1.15830	+	0.668744i	−0.207403	+	0.978256i	$0.566501\pi$
$228$	7.77694e6	−	183221.i	0.656152	−	0.0154586i
$229$	−7.34810e6	+	1.27273e7i	−0.611883	+	1.05981i	0.379040	+	0.925380i	$0.376254\pi$
$229$	−7.34810e6	+	1.27273e7i	−0.611883	+	1.05981i	−0.990923	+	0.134432i	$0.957079\pi$
$230$			3.75109e6i			0.308300i
$231$	2.05869e7	+	4.79089e6i	1.67015	+	0.388670i
$232$	−1.49945e7			−1.20079
$233$	−2.41055e6	−	1.39173e6i	−0.190567	−	0.110024i	0.401681	−	0.915780i	$-0.368426\pi$
$233$	−2.41055e6	−	1.39173e6i	−0.190567	−	0.110024i	−0.592248	+	0.805756i	$0.701759\pi$
$234$	1.35704e7	+	7.00443e6i	1.05912	+	0.546670i
$235$	360984.	+	625243.i	0.0278154	+	0.0481776i
$236$	5.76952e6	+	3.33103e6i	0.438939	+	0.253421i
$237$	−1.91081e6	+	3.49736e6i	−0.143540	+	0.262721i
$238$	−2.05138e6	−	2.01237e6i	−0.152165	−	0.149272i
$239$			1.08371e7i			0.793816i	0.917858	+	0.396908i	$0.129917\pi$
$239$			1.08371e7i			0.793816i	−0.917858	+	0.396908i	$0.870083\pi$
$240$	−425965.	+	259496.i	−0.0308135	+	0.0187714i
$241$	1.09990e7	+	1.90508e7i	0.785779	+	1.36101i	0.928533	+	0.371251i	$0.121071\pi$
$241$	1.09990e7	+	1.90508e7i	0.785779	+	1.36101i	−0.142753	+	0.989758i	$0.545596\pi$
$242$	3.81935e7	−	2.20510e7i	2.69490	−	1.55590i
$243$	1.42495e7	−	1.68605e6i	0.993072	−	0.117504i
$244$	4.56148e7			3.14004
$245$	2.52543e6	−	4.57479e6i	0.171727	−	0.311081i
$246$	−1.51039e7	+	2.76446e7i	−1.01457	+	1.85697i
$247$	2.33858e6	−	4.05054e6i	0.155189	−	0.268796i
$248$	−1.90648e7	+	1.10071e7i	−1.24991	+	0.721633i
$249$	−178856.	−	7.59168e6i	−0.0115853	−	0.491745i
$250$	−8.34144e6	+	1.44478e7i	−0.533852	+	0.924659i
$251$		−	1.63397e7i		−	1.03329i	−0.856199	−	0.516646i	$-0.827180\pi$
$251$		−	1.63397e7i		−	1.03329i	0.856199	−	0.516646i	$-0.172820\pi$
$252$	5.12221e6	−	2.46242e7i	0.320078	−	1.53872i
$253$	1.50246e7			0.927770
$254$	−2.20549e7	−	1.27334e7i	−1.34587	−	0.777040i
$255$	−782942.	+	18445.7i	−0.0472181	+	0.00111244i
$256$	6.96339e6	+	1.20609e7i	0.415050	+	0.718888i
$257$	−1.72309e7	−	9.94827e6i	−1.01510	−	0.586068i	−0.102419	−	0.994741i	$-0.532658\pi$
$257$	−1.72309e7	−	9.94827e6i	−1.01510	−	0.586068i	−0.912681	+	0.408673i	$0.865992\pi$
$258$	−2.66694e7	−	1.45711e7i	−1.55294	−	0.848463i
$259$	−8.48423e6	+	2.36085e6i	−0.488330	+	0.135884i
$260$		−	7.29525e6i		−	0.415069i
$261$	1.09673e6	+	2.32628e7i	0.0616848	+	1.30840i
$262$	−2.21213e7	−	3.83153e7i	−1.23001	−	2.13044i
$263$	−3.02923e7	+	1.74893e7i	−1.66519	+	0.961400i	−0.695020	+	0.718991i	$0.744604\pi$
$263$	−3.02923e7	+	1.74893e7i	−1.66519	+	0.961400i	−0.970174	+	0.242409i	$0.922062\pi$
$264$	−1.50482e7	−	2.47018e7i	−0.817849	−	1.34251i
$265$	2.81896e6			0.151479
$266$	−1.22055e7	−	3.14522e6i	−0.648503	−	0.167111i
$267$	−1.28580e7	−	7.02511e6i	−0.675525	−	0.369079i
$268$	−2.24831e6	+	3.89419e6i	−0.116803	+	0.202308i
$269$	9.63851e6	−	5.56480e6i	0.495169	−	0.285886i	−0.231547	−	0.972824i	$-0.574379\pi$
$269$	9.63851e6	−	5.56480e6i	0.495169	−	0.285886i	0.726716	+	0.686938i	$0.241046\pi$
$270$	−6.27976e6	−	9.29303e6i	−0.319045	−	0.472135i
$271$	−1.17083e7	+	2.02794e7i	−0.588284	+	1.01894i	0.406173	+	0.913796i	$0.366863\pi$
$271$	−1.17083e7	+	2.02794e7i	−0.588284	+	1.01894i	−0.994457	+	0.105142i	$0.966470\pi$
$272$		−	271609.i		−	0.0134970i
$273$	−1.10416e7	−	1.03327e7i	−0.542678	−	0.507837i
$274$	3.04489e7			1.48020
$275$	2.69847e7	+	1.55796e7i	1.29754	+	0.749134i
$276$	−421080.	−	1.78730e7i	−0.0200280	−	0.850102i
$277$	−1.91825e6	−	3.32251e6i	−0.0902540	−	0.156324i	0.817364	−	0.576122i	$-0.195435\pi$
$277$	−1.91825e6	−	3.32251e6i	−0.0902540	−	0.156324i	−0.907618	+	0.419797i	$0.862101\pi$
$278$	3.63663e7	+	2.09961e7i	1.69264	+	0.977245i
$279$	1.84710e7	+	2.87724e7i	0.850508	+	1.32484i
$280$	−6.88907e6	+	1.91698e6i	−0.313824	+	0.0873258i
$281$		−	2.63996e7i		−	1.18981i	−0.803794	−	0.594907i	$-0.797189\pi$
$281$		−	2.63996e7i		−	1.18981i	0.803794	−	0.594907i	$-0.202811\pi$
$282$	−2.92923e6	−	4.80835e6i	−0.130619	−	0.214412i
$283$	3.21025e6	+	5.56031e6i	0.141638	+	0.245324i	0.928113	−	0.372297i	$-0.121430\pi$
$283$	3.21025e6	+	5.56031e6i	0.141638	+	0.245324i	−0.786476	+	0.617621i	$0.788097\pi$
$284$	−1.16154e7	+	6.70616e6i	−0.507083	+	0.292765i
$285$	−2.93358e6	+	1.78712e6i	−0.126725	+	0.0772005i
$286$	−4.78122e7			−2.04381
$287$	2.18445e7	−	2.22679e7i	0.924053	−	0.941964i
$288$	2.17017e7	−	1.39318e7i	0.908482	−	0.583218i
$289$	−1.18556e7	+	2.05344e7i	−0.491166	+	0.850724i
$290$	1.57648e7	−	9.10182e6i	0.646390	−	0.373194i
$291$	2.41735e6	−	56951.6i	0.0980981	−	0.00231114i
$292$	2.60755e7	−	4.51641e7i	1.04733	−	1.81403i
$293$			3.45100e7i			1.37196i	0.727619	+	0.685982i	$0.240627\pi$
$293$			3.45100e7i			1.37196i	−0.727619	+	0.685982i	$0.759373\pi$
$294$	−1.88490e7	+	3.61309e7i	−0.741732	+	1.42179i
$295$	−2.94181e6			−0.114591
$296$	1.04366e7	+	6.02558e6i	0.402425	+	0.232340i
$297$	−3.72222e7	+	2.51528e7i	−1.42080	+	0.960103i
$298$	2.29552e7	+	3.97596e7i	0.867426	+	1.50243i
$299$	−9.30899e6	−	5.37455e6i	−0.348248	−	0.201061i
$300$	1.77771e7	−	3.25373e7i	0.658410	−	1.20509i
$301$	2.14824e7	+	2.10740e7i	0.787742	+	0.772763i
$302$		−	9.49790e6i		−	0.344831i
$303$	2.38747e7	−	1.45444e7i	0.858243	−	0.522838i
$304$	−595662.	−	1.03172e6i	−0.0212021	−	0.0367231i
$305$	−1.74438e7	+	1.00712e7i	−0.614812	+	0.354962i
$306$	6.10075e6	−	287621.i	0.212921	−	0.0100382i
$307$	6.11502e6			0.211341			0.105670	−	0.994401i	$-0.466301\pi$
$307$	6.11502e6			0.211341			0.105670	+	0.994401i	$0.466301\pi$
$308$	2.11096e7	+	7.58620e7i	0.722485	+	2.59640i
$309$	5.91782e6	−	1.08314e7i	0.200579	−	0.367120i
$310$	1.33628e7	−	2.31451e7i	0.448552	−	0.776915i
$311$	2.75173e7	−	1.58871e7i	0.914798	−	0.528159i	0.0328262	−	0.999461i	$-0.489549\pi$
$311$	2.75173e7	−	1.58871e7i	0.914798	−	0.528159i	0.881972	+	0.471302i	$0.156216\pi$
$312$	487396.	+	2.06878e7i	0.0160479	+	0.681164i
$313$	1.03822e7	−	1.79825e7i	0.338577	−	0.586432i	−0.645588	−	0.763686i	$-0.723388\pi$
$313$	1.03822e7	−	1.79825e7i	0.338577	−	0.586432i	0.984165	+	0.177253i	$0.0567212\pi$
$314$		−	4.78874e6i		−	0.154679i
$315$	3.47792e6	+	1.05476e7i	0.111272	+	0.337461i
$316$	−1.48470e7			−0.470518
$317$	−9.73777e6	−	5.62211e6i	−0.305690	−	0.176490i	0.339306	−	0.940676i	$-0.389808\pi$
$317$	−9.73777e6	−	5.62211e6i	−0.305690	−	0.176490i	−0.644996	+	0.764186i	$0.723141\pi$
$318$	−2.19778e7	+	517786.i	−0.683444	+	0.0161016i
$319$	−3.64563e7	−	6.31441e7i	−1.12305	−	1.94518i
$320$	−1.64333e7	−	9.48779e6i	−0.501506	−	0.289544i
$321$	−2.97628e7	−	1.62612e7i	−0.899827	−	0.491628i
$322$	−7.22836e6	+	2.80509e7i	−0.216507	+	0.840192i
$323$		−	1.87054e6i		−	0.0555086i
$324$	3.09647e7	+	4.35741e7i	0.910399	+	1.28113i
$325$	−1.11462e7	−	1.93058e7i	−0.324696	−	0.562391i
$326$	−3.30293e7	+	1.90695e7i	−0.953338	+	0.550410i
$327$	2.09900e7	+	3.44553e7i	0.600301	+	0.985399i
$328$	−4.26863e7			−1.20967
$329$	1.49461e6	+	5.37122e6i	0.0419702	+	0.150829i
$330$	3.08155e7	+	1.68363e7i	0.857487	+	0.468496i
$331$	1.21424e7	−	2.10313e7i	0.334827	−	0.579938i	−0.648624	−	0.761109i	$-0.724655\pi$
$331$	1.21424e7	−	2.10313e7i	0.334827	−	0.579938i	0.983452	+	0.181171i	$0.0579887\pi$
$332$	2.44999e7	−	1.41450e7i	0.669499	−	0.386535i
$333$	8.58485e6	−	1.66323e7i	0.232488	−	0.450422i
$334$	1.13502e6	−	1.96592e6i	0.0304625	−	0.0527626i
$335$		−	1.98561e6i		−	0.0528152i
$336$	−3.68544e6	+	1.11969e6i	−0.0971564	+	0.0295176i
$337$	1.16537e7			0.304491			0.152246	−	0.988343i	$-0.451350\pi$
$337$	1.16537e7			0.304491			0.152246	+	0.988343i	$0.451350\pi$
$338$	−2.40038e7	−	1.38586e7i	−0.621627	−	0.358896i
$339$	−81129.1	−	3.44358e6i	−0.00208246	−	0.0883916i
$340$	−1.45880e6	−	2.52671e6i	−0.0371158	−	0.0642864i
$341$	−9.27048e7	−	5.35232e7i	−2.33797	−	1.34983i
$342$	2.25431e7	−	1.44720e7i	0.563555	−	0.361785i
$343$	2.77009e7	−	2.93440e7i	0.686455	−	0.727172i
$344$		−	4.11805e7i		−	1.01162i
$345$	4.10718e6	+	6.74197e6i	0.100020	+	0.164184i
$346$	5.47920e6	+	9.49026e6i	0.132278	+	0.229113i
$347$	2.46675e7	−	1.42418e7i	0.590388	−	0.340860i	−0.174863	−	0.984593i	$-0.555948\pi$
$347$	2.46675e7	−	1.42418e7i	0.590388	−	0.340860i	0.765251	+	0.643732i	$0.222615\pi$
$348$	−7.40937e7	+	4.51376e7i	−1.75810	+	1.07103i
$349$	−4.18490e7			−0.984485			−0.492243	−	0.870458i	$-0.663823\pi$
$349$	−4.18490e7			−0.984485			−0.492243	+	0.870458i	$0.663823\pi$
$350$	−4.20696e7	+	4.28851e7i	−0.981216	+	1.00024i
$351$	3.20599e7	−	2.26931e6i	0.741380	−	0.0524774i
$352$	−4.03700e7	+	6.99229e7i	−0.925616	+	1.60321i
$353$	4.00412e7	−	2.31178e7i	0.910297	−	0.525560i	0.0297702	−	0.999557i	$-0.490522\pi$
$353$	4.00412e7	−	2.31178e7i	0.910297	−	0.525560i	0.880527	+	0.473997i	$0.157189\pi$
$354$	2.29356e7	−	540352.i	0.517012	−	0.0121806i
$355$	2.96128e6	−	5.12909e6i	0.0661903	−	0.114645i
$356$		−	5.45849e7i		−	1.20983i
$357$	−5.89042e6	−	1.37079e6i	−0.129462	−	0.0301278i
$358$	−1.07130e7			−0.233488
$359$	9.42345e6	+	5.44063e6i	0.203670	+	0.117589i	0.598366	−	0.801223i	$-0.295817\pi$
$359$	9.42345e6	+	5.44063e6i	0.203670	+	0.117589i	−0.394696	+	0.918812i	$0.629150\pi$
$360$	6.97077e6	−	1.35052e7i	0.149408	−	0.289463i
$361$	1.94207e7	+	3.36376e7i	0.412803	+	0.714996i
$362$	9.61611e6	+	5.55187e6i	0.202709	+	0.117034i
$363$	4.45022e7	−	8.14522e7i	0.930382	−	1.70288i
$364$	1.40580e7	−	5.45542e7i	0.291486	−	1.13116i
$365$			2.30287e7i			0.473577i
$366$	1.34150e8	−	8.17234e7i	2.73619	−	1.66688i
$367$	2.55253e7	+	4.42111e7i	0.516384	+	0.894403i	0.999819	+	0.0190228i	$0.00605551\pi$
$367$	2.55253e7	+	4.42111e7i	0.516384	+	0.894403i	−0.483435	+	0.875380i	$0.660611\pi$
$368$	−2.37110e6	+	1.36895e6i	−0.0475780	+	0.0274692i
$369$	3.12216e6	+	6.62243e7i	0.0621407	+	1.31807i
$370$	−1.46304e7			−0.288835
$371$	2.10803e7	+	5.43214e6i	0.412815	+	0.106377i
$372$	−6.10723e7	+	1.11781e8i	−1.18636	+	2.17139i
$373$	2.55721e7	−	4.42922e7i	0.492765	−	0.853494i	−0.507200	−	0.861828i	$-0.669320\pi$
$373$	2.55721e7	−	4.42922e7i	0.492765	−	0.853494i	0.999965	+	0.00833438i	$0.00265295\pi$
$374$	−1.65598e7	+	9.56080e6i	−0.316548	+	0.182759i
$375$	826959.	+	3.51008e7i	0.0156816	+	0.665616i
$376$	3.81469e6	−	6.60724e6i	0.0717622	−	0.124296i
$377$			5.21642e7i			0.973528i
$378$	−2.90527e7	−	8.15949e7i	−0.537911	−	1.51073i
$379$	−9.30768e7			−1.70972			−0.854858	−	0.518862i	$-0.826356\pi$
$379$	−9.30768e7			−1.70972			−0.854858	+	0.518862i	$0.826356\pi$
$380$	−1.10826e7	−	6.39854e6i	−0.201972	−	0.116608i
$381$	−5.35822e7	+	1.26237e6i	−0.968826	+	0.0228251i
$382$	4.20365e7	+	7.28094e7i	0.754114	+	1.30616i
$383$	6.95337e7	+	4.01453e7i	1.23765	+	0.714559i	0.968614	−	0.248570i	$-0.0799607\pi$
$383$	6.95337e7	+	4.01453e7i	1.23765	+	0.714559i	0.269039	+	0.963129i	$0.413294\pi$
$384$	7.62195e7	+	4.16432e7i	1.34608	+	0.735445i
$385$	−2.48221e7	−	2.43501e7i	−0.434967	−	0.426697i
$386$			1.54740e7i			0.269054i
$387$	−6.38883e7	+	3.01203e6i	−1.10227	+	0.0519668i
$388$	4.50407e6	+	7.80128e6i	0.0771099	+	0.133558i
$389$	−5.39859e6	+	3.11688e6i	−0.0917132	+	0.0529506i	−0.545155	−	0.838335i	$-0.683529\pi$
$389$	−5.39859e6	+	3.11688e6i	−0.0917132	+	0.0529506i	0.453442	+	0.891286i	$0.350196\pi$
$390$	−1.30702e7	−	2.14548e7i	−0.220337	−	0.361685i
$391$	−4.29890e6			−0.0719162
$392$	−5.52108e7	+	1.06000e6i	−0.916571	+	0.0175973i
$393$	−8.17121e7	−	4.46441e7i	−1.34620	−	0.735507i
$394$	1.45942e7	−	2.52780e7i	0.238612	−	0.413289i
$395$	5.67772e6	−	3.27803e6i	0.0921261	−	0.0531890i
$396$	−1.48718e8	−	7.67617e7i	−2.39485	−	1.23612i
$397$	3.87684e7	−	6.71488e7i	0.619592	−	1.07317i	−0.369968	−	0.929045i	$-0.620631\pi$
$397$	3.87684e7	−	6.71488e7i	0.619592	−	1.07317i	0.989560	−	0.144121i	$-0.0460354\pi$
$398$			5.70312e6i			0.0904613i
$399$	−2.53812e7	+	7.71120e6i	−0.399571	+	0.121396i
$400$	−5.67812e6			−0.0887207
$401$	4.39274e7	+	2.53615e7i	0.681243	+	0.393316i	0.800323	−	0.599569i	$-0.204661\pi$
$401$	4.39274e7	+	2.53615e7i	0.681243	+	0.393316i	−0.119080	+	0.992885i	$0.537995\pi$
$402$	364716.	+	1.54806e7i	0.00561405	+	0.238292i
$403$	3.82923e7	+	6.63243e7i	0.585055	+	1.01335i
$404$	9.01949e7	+	5.20740e7i	1.36785	+	0.789727i
$405$	−2.14621e7	−	9.82680e6i	−0.323077	−	0.147927i
$406$	1.35429e8	−	3.76850e7i	2.02365	−	0.563107i
$407$			5.86002e7i			0.869192i
$408$	4.30567e6	+	7.06778e6i	0.0633957	+	0.104065i
$409$	3.65408e7	+	6.32904e7i	0.534082	+	0.925056i	0.999207	+	0.0398118i	$0.0126758\pi$
$409$	3.65408e7	+	6.32904e7i	0.534082	+	0.925056i	−0.465126	+	0.885245i	$0.653991\pi$
$410$	4.48792e7	−	2.59110e7i	0.651168	−	0.375952i
$411$	5.47269e7	−	3.33394e7i	0.788271	−	0.480212i
$412$	4.59813e7			0.657490
$413$	−2.19990e7	−	5.66888e6i	−0.312287	−	0.0804724i
$414$	−3.32597e7	−	5.18088e7i	−0.468724	−	0.730134i
$415$	−6.24611e6	+	1.08186e7i	−0.0873907	+	0.151365i
$416$	5.00253e7	−	2.88821e7i	0.694880	−	0.401189i
$417$	8.83516e7	−	2.08152e6i	1.21845	−	0.0287060i
$418$	−4.19353e7	+	7.26340e7i	−0.574183	+	0.994515i
$419$		−	107271.i		−	0.00145828i	−1.00000		0.000729142i	$-0.999768\pi$
$419$		−	107271.i		−	0.00145828i	1.00000		0.000729142i	$-0.000232093\pi$
$420$	−2.82709e7	+	3.02105e7i	−0.381586	+	0.407765i
$421$	1.00991e8			1.35343			0.676716	−	0.736244i	$-0.263403\pi$
$421$	1.00991e8			1.35343			0.676716	+	0.736244i	$0.263403\pi$
$422$	−5.95656e7	−	3.43902e7i	−0.792607	−	0.457612i
$423$	−1.05296e7	−	5.43492e6i	−0.139121	−	0.0718079i
$424$	−1.48946e7	−	2.57983e7i	−0.195403	−	0.338449i
$425$	−7.72100e6	−	4.45772e6i	−0.100579	−	0.0580692i
$426$	−2.21453e7	+	4.05325e7i	−0.286452	+	0.524293i
$427$	−1.49853e8	+	4.16987e7i	−1.92478	+	0.535597i
$428$		−	1.26349e8i		−	1.61154i
$429$	−8.59346e7	+	5.23510e7i	−1.08842	+	0.663061i
$430$	2.49970e7	+	4.32961e7i	0.314400	+	0.544556i
$431$	−8.86295e7	+	5.11703e7i	−1.10700	+	0.639125i	−0.938050	−	0.346500i	$-0.887370\pi$
$431$	−8.86295e7	+	5.11703e7i	−1.10700	+	0.639125i	−0.168947	+	0.985625i	$0.554037\pi$
$432$	3.58242e6	−	7.36097e6i	0.0444350	−	0.0913027i
$433$	5.17987e7			0.638050			0.319025	−	0.947746i	$-0.396645\pi$
$433$	5.17987e7			0.638050			0.319025	+	0.947746i	$0.396645\pi$
$434$	1.44528e8	−	1.47330e8i	1.76801	−	1.80228i
$435$	1.83688e7	−	3.36204e7i	0.223158	−	0.408446i
$436$	−7.51516e7	+	1.30166e8i	−0.906732	+	1.57051i
$437$	−1.63295e7	+	9.42785e6i	−0.195672	+	0.112971i
$438$	−4.22991e6	−	1.79541e8i	−0.0503394	−	2.13669i
$439$	5.26595e6	−	9.12089e6i	0.0622419	−	0.107806i	−0.833225	−	0.552934i	$-0.813508\pi$
$439$	5.26595e6	−	9.12089e6i	0.0622419	−	0.107806i	0.895467	+	0.445127i	$0.146842\pi$
$440$			4.75825e7i			0.558584i
$441$	5.68273e6	+	8.55776e7i	0.0662585	+	0.997802i
$442$	1.36803e7			0.158426
$443$	−8.18071e7	−	4.72313e7i	−0.940979	−	0.543274i	−0.0507116	−	0.998713i	$-0.516149\pi$
$443$	−8.18071e7	−	4.72313e7i	−0.940979	−	0.543274i	−0.890267	+	0.455439i	$0.849482\pi$
$444$	6.97100e7	−	1.64234e6i	0.796428	−	0.0187635i
$445$	1.20517e7	+	2.08742e7i	0.136763	+	0.236880i
$446$	−9.51650e7	−	5.49435e7i	−1.07269	−	0.619316i
$447$	8.47922e7	+	4.63270e7i	0.949365	+	0.518694i
$448$	−1.04606e8	−	1.02617e8i	−1.16339	−	1.14126i
$449$			1.56966e8i			1.73407i	0.498245	+	0.867036i	$0.333978\pi$
$449$			1.56966e8i			1.73407i	−0.498245	+	0.867036i	$0.666022\pi$
$450$	−6.01287e6	−	1.27539e8i	−0.0659848	−	1.39961i
$451$	−1.03783e8	−	1.79758e8i	−1.13135	−	1.95956i
$452$	1.11131e7	−	6.41617e6i	0.120343	−	0.0694801i
$453$	−1.03995e7	−	1.70709e7i	−0.111871	−	0.183638i
$454$	−2.00708e8			−2.14485
$455$	6.66894e6	+	2.39663e7i	0.0707983	+	0.254429i
$456$	3.18555e7	+	1.74045e7i	0.335961	+	0.183556i
$457$	5.48042e7	−	9.49237e7i	0.574203	−	0.994548i	−0.421925	−	0.906631i	$-0.638645\pi$
$457$	5.48042e7	−	9.49237e7i	0.574203	−	0.994548i	0.996128	−	0.0879177i	$-0.0280212\pi$
$458$	−1.63280e8	+	9.42697e7i	−1.69956	+	0.981241i
$459$	1.06502e7	−	7.19685e6i	0.110133	−	0.0744225i
$460$	−1.47052e7	+	2.54701e7i	−0.151076	+	0.261672i
$461$		−	1.59203e8i		−	1.62498i	−0.582975	−	0.812490i	$-0.698111\pi$
$461$		−	1.59203e8i		−	1.62498i	0.582975	−	0.812490i	$-0.301889\pi$
$462$	1.97996e8	+	1.85284e8i	2.00785	+	1.87894i
$463$	1.14258e8			1.15118			0.575591	−	0.817738i	$-0.304772\pi$
$463$	1.14258e8			1.15118			0.575591	+	0.817738i	$0.304772\pi$
$464$	1.15067e7	+	6.64339e6i	0.115185	+	0.0665021i
$465$	−1.32477e6	−	5.62308e7i	−0.0131759	−	0.559262i
$466$	−1.78547e7	−	3.09252e7i	−0.176439	−	0.305601i
$467$	−1.52263e8	−	8.79092e7i	−1.49501	−	0.863145i	−0.495028	−	0.868877i	$-0.664842\pi$
$467$	−1.52263e8	−	8.79092e7i	−1.49501	−	0.863145i	−0.999984	+	0.00573225i	$0.998175\pi$
$468$	6.46845e7	+	1.00760e8i	0.631049	+	0.982989i
$469$	3.82627e6	−	1.48485e7i	0.0370900	−	0.143934i
$470$			9.26222e6i			0.0892117i
$471$	−5.24333e6	−	8.60696e6i	−0.0501816	−	0.0823735i
$472$	1.55438e7	+	2.69226e7i	0.147819	+	0.256030i
$473$	1.73417e8	−	1.00122e8i	1.63874	−	0.946124i
$474$	−4.36638e7	+	2.65998e7i	−0.410002	+	0.249772i
$475$	−3.91046e7			−0.364878
$476$	−6.03999e6	−	2.17060e7i	−0.0560035	−	0.201261i
$477$	−3.89345e7	+	2.49948e7i	−0.358740	+	0.230300i
$478$	−6.95153e7	+	1.20404e8i	−0.636497	+	1.10245i
$479$	−8.54411e7	+	4.93295e7i	−0.777428	+	0.448848i	−0.835518	−	0.549463i	$-0.814832\pi$
$479$	−8.54411e7	+	4.93295e7i	−0.777428	+	0.448848i	0.0580898	+	0.998311i	$0.481499\pi$
$480$	−4.24122e7	+	999212.i	−0.383502	+	0.00903512i
$481$	2.09623e7	−	3.63078e7i	0.188367	−	0.326261i
$482$			2.82214e8i			2.52021i
$483$	1.77219e7	+	5.83313e7i	0.157279	+	0.517679i
$484$	3.45781e8			3.04975
$485$	−3.44486e6	−	1.98889e6i	−0.0301958	−	0.0174336i
$486$	1.69132e8	+	7.26717e7i	1.47339	+	0.633077i
$487$	2.31500e7	+	4.00971e7i	0.200431	+	0.347157i	0.948667	−	0.316276i	$-0.102432\pi$
$487$	2.31500e7	+	4.00971e7i	0.200431	+	0.347157i	−0.748236	+	0.663432i	$0.769099\pi$
$488$	1.84337e8	+	1.06427e8i	1.58618	+	0.915783i
$489$	−3.84850e7	+	7.04391e7i	−0.329128	+	0.602403i
$490$	5.74037e7	−	3.46280e7i	0.487923	−	0.294333i
$491$		−	1.10518e8i		−	0.933661i	−0.884347	−	0.466830i	$-0.845396\pi$
$491$		−	1.10518e8i		−	0.933661i	0.884347	−	0.466830i	$-0.154604\pi$
$492$	−2.10929e8	+	1.28497e8i	−1.77110	+	1.07894i
$493$	1.04310e7	+	1.80671e7i	0.0870536	+	0.150781i
$494$	5.19649e7	−	3.00020e7i	0.431052	−	0.248868i
$495$	7.38204e7	−	3.48028e6i	0.608640	−	0.0286945i
$496$	1.95069e7			0.159862
$497$	3.20284e7	−	3.26492e7i	0.260895	−	0.265952i
$498$	4.67101e7	−	8.54934e7i	0.378201	−	0.692221i
$499$	−5.24098e7	+	9.07764e7i	−0.421804	+	0.730586i	−0.996116	−	0.0880508i	$-0.971936\pi$
$499$	−5.24098e7	+	9.07764e7i	−0.421804	+	0.730586i	0.574312	+	0.818636i	$0.305270\pi$
$500$	−1.13278e8	+	6.54008e7i	−0.906220	+	0.523206i
$501$	−112525.	−	4.77618e6i	−0.000894817	−	0.0379811i
$502$	1.04812e8	−	1.81540e8i	0.828514	−	1.43503i
$503$			5.65796e7i			0.444586i	0.974980	+	0.222293i	$0.0713542\pi$
$503$			5.65796e7i			0.444586i	−0.974980	+	0.222293i	$0.928646\pi$
$504$	7.81523e7	−	8.75597e7i	0.610450	−	0.683931i
$505$	−4.59893e7			−0.357094
$506$	1.66928e8	+	9.63759e7i	1.28848	+	0.743904i
$507$	−5.83170e7	+	1.37392e6i	−0.447478	+	0.0105424i
$508$	−9.98359e7	−	1.72921e8i	−0.761545	−	1.31903i
$509$	1.57230e8	+	9.07767e7i	1.19229	+	0.688369i	0.958825	−	0.283997i	$-0.0916605\pi$
$509$	1.57230e8	+	9.07767e7i	1.19229	+	0.688369i	0.233464	+	0.972365i	$0.424994\pi$
$510$	−8.81707e6	−	4.81729e6i	−0.0664682	−	0.0363155i
$511$	−4.43763e7	+	1.72210e8i	−0.332574	+	1.29061i
$512$		−	2.72071e7i		−	0.202709i
$513$	2.46718e7	−	5.06942e7i	0.182746	−	0.375497i
$514$	−1.27628e8	−	2.21057e8i	−0.939842	−	1.62785i
$515$	−1.75840e7	+	1.01521e7i	−0.128735	+	0.0743250i
$516$	−1.23965e8	−	2.03489e8i	−0.902296	−	1.48112i
$517$	3.70987e7			0.268465
$518$	−1.09407e8	−	2.81927e7i	−0.787144	−	0.202837i
$519$	2.02391e7	+	1.10578e7i	0.144774	+	0.0790985i
$520$	1.70211e7	−	2.94814e7i	0.121053	−	0.209671i
$521$	6.25687e7	−	3.61241e7i	0.442429	−	0.255437i	−0.262198	−	0.965014i	$-0.584447\pi$
$521$	6.25687e7	−	3.61241e7i	0.442429	−	0.255437i	0.704628	+	0.709577i	$0.251114\pi$
$522$	−1.37036e8	+	2.65493e8i	−0.963433	+	1.86656i
$523$	−4.41162e7	+	7.64114e7i	−0.308385	+	0.534138i	−0.978009	−	0.208562i	$-0.933122\pi$
$523$	−4.41162e7	+	7.64114e7i	−0.308385	+	0.534138i	0.669625	+	0.742700i	$0.266455\pi$
$524$		−	3.46884e8i		−	2.41096i
$525$	−2.86571e7	+	1.23142e8i	−0.198041	+	0.850999i
$526$	−4.48744e8			−3.08348
$527$	2.65251e7	+	1.53143e7i	0.181228	+	0.104632i
$528$	603669.	+	2.56231e7i	0.00410107	+	0.174073i
$529$	−5.23508e7	−	9.06743e7i	−0.353636	−	0.612515i
$530$	3.13196e7	+	1.80824e7i	0.210372	+	0.121459i
$531$	4.06313e7	−	2.60841e7i	0.271380	−	0.174218i
$532$	−7.05462e7	−	6.92048e7i	−0.468531	−	0.459622i
$533$			1.48501e8i			0.980724i
$534$	−9.77943e7	−	1.60530e8i	−0.642229	−	1.05422i
$535$	2.78964e7	+	4.83179e7i	0.182174	+	0.315535i
$536$	−1.81717e7	+	1.04914e7i	−0.118005	+	0.0681302i
$537$	−1.92549e7	+	1.17300e7i	−0.124342	+	0.0757489i
$538$	1.42783e8			0.916916
$539$	−1.38698e8	−	2.29924e8i	−0.885737	−	1.46831i
$540$	−6.20899e6	−	8.77183e7i	−0.0394312	−	0.557069i
$541$	−3.40703e7	+	5.90115e7i	−0.215171	+	0.372687i	−0.953326	−	0.301944i	$-0.902364\pi$
$541$	−3.40703e7	+	5.90115e7i	−0.215171	+	0.372687i	0.738154	+	0.674632i	$0.235698\pi$
$542$	−2.60167e8	+	1.50208e8i	−1.63401	+	0.943396i
$543$	2.33623e7	−	550404.i	0.145920	−	0.00343781i
$544$	1.15509e7	−	2.00067e7i	0.0717493	−	0.124273i
$545$		−	6.63704e7i		−	0.410001i
$546$	−5.63960e7	−	1.85626e8i	−0.346474	−	1.14041i
$547$	−1.33802e8			−0.817522			−0.408761	−	0.912641i	$-0.634039\pi$
$547$	−1.33802e8			−0.817522			−0.408761	+	0.912641i	$0.634039\pi$
$548$	2.06750e8	+	1.19367e8i	1.25633	+	0.725341i
$549$	1.51630e8	−	2.93769e8i	0.916366	−	1.77537i
$550$	1.99873e8	+	3.46190e8i	1.20134	+	2.08078i
$551$	7.92453e7	+	4.57523e7i	0.473717	+	0.273501i
$552$	3.99992e7	−	7.32104e7i	0.237812	−	0.435267i
$553$	4.87751e7	−	1.35723e7i	0.288418	−	0.0802562i
$554$		−	4.92190e7i		−	0.289470i
$555$	−2.62957e7	+	1.60192e7i	−0.153817	+	0.0937049i
$556$	1.64619e8	+	2.85129e8i	0.957758	+	1.65889i
$557$	1.37756e8	−	7.95336e7i	0.797161	−	0.460241i	−0.0453167	−	0.998973i	$-0.514430\pi$
$557$	1.37756e8	−	7.95336e7i	0.797161	−	0.460241i	0.842477	+	0.538732i	$0.181096\pi$
$558$	2.06569e7	+	4.38155e8i	0.118895	+	2.52189i
$559$	−1.43262e8			−0.820156
$560$	6.13595e6	+	1.58116e6i	0.0349396	+	0.00900350i
$561$	−1.92951e7	+	3.53158e7i	−0.109284	+	0.200023i
$562$	1.69342e8	−	2.93309e8i	0.954017	−	1.65241i
$563$	2.27943e8	−	1.31603e8i	1.27732	−	0.737462i	0.300966	−	0.953635i	$-0.402691\pi$
$563$	2.27943e8	−	1.31603e8i	1.27732	−	0.737462i	0.976355	+	0.216173i	$0.0693575\pi$
$564$	−1.03973e6	−	4.41322e7i	−0.00579542	−	0.245990i
$565$	−2.83323e6	+	4.90730e6i	−0.0157086	+	0.0272080i
$566$			8.23693e7i			0.454272i
$567$	−1.41558e8	−	1.14843e8i	−0.776579	−	0.630020i
$568$	−6.25865e7			−0.341535
$569$	−9.09408e7	−	5.25047e7i	−0.493653	−	0.285011i	0.232436	−	0.972612i	$-0.425331\pi$
$569$	−9.09408e7	−	5.25047e7i	−0.493653	−	0.285011i	−0.726089	+	0.687601i	$0.758664\pi$
$570$	−4.40567e7	+	1.03795e6i	−0.237896	+	0.00560472i
$571$	2.45002e7	+	4.24355e7i	0.131601	+	0.227940i	0.924294	−	0.381681i	$-0.124655\pi$
$571$	2.45002e7	+	4.24355e7i	0.131601	+	0.227940i	−0.792693	+	0.609622i	$0.791321\pi$
$572$	−3.24647e8	−	1.87435e8i	−1.73470	−	1.00153i
$573$	1.55275e8	+	8.48359e7i	0.825349	+	0.450937i
$574$	3.85539e8	−	1.07281e8i	2.03860	−	0.567269i
$575$			8.98706e7i			0.472731i
$576$	3.11097e8	−	1.46667e7i	1.62790	−	0.0767477i
$577$	8.86675e7	+	1.53577e8i	0.461570	+	0.799462i	0.999039	−	0.0438210i	$-0.0139531\pi$
$577$	8.86675e7	+	1.53577e8i	0.461570	+	0.799462i	−0.537470	+	0.843283i	$0.680620\pi$
$578$	−2.63439e8	+	1.52096e8i	−1.36426	+	0.787653i
$579$	1.69429e7	+	2.78119e7i	0.0872876	+	0.143283i
$580$	1.42725e8			0.731504
$581$	−6.75561e7	+	6.88656e7i	−0.344458	+	0.351135i
$582$	2.72229e7	+	1.48735e7i	0.138091	+	0.0754473i
$583$	7.24269e7	−	1.25447e8i	0.365506	−	0.633074i
$584$	2.10751e8	−	1.21677e8i	1.05811	−	0.610902i
$585$	−4.69830e7	−	2.42505e7i	−0.234678	−	0.121130i
$586$	−2.21367e8	+	3.83418e8i	−1.10007	+	1.90537i
$587$		−	2.24276e8i		−	1.10884i	−0.832238	−	0.554418i	$-0.812941\pi$
$587$		−	2.24276e8i		−	1.10884i	0.832238	−	0.554418i	$-0.187059\pi$
$588$	−2.69627e8	+	1.71438e8i	−1.32627	+	0.843285i
$589$	1.34342e8			0.657456
$590$	−3.26846e7	−	1.88704e7i	−0.159143	−	0.0918811i
$591$	−1.44685e6	−	6.14126e7i	−0.00700909	−	0.297506i
$592$	−5.33932e6	−	9.24798e6i	−0.0257348	−	0.0445740i
$593$	−1.86239e8	−	1.07525e8i	−0.893112	−	0.515638i	−0.0181527	−	0.999835i	$-0.505779\pi$
$593$	−1.86239e8	−	1.07525e8i	−0.893112	−	0.515638i	−0.874959	+	0.484197i	$0.839112\pi$
$594$	−5.74895e8	+	4.06930e7i	−2.74302	+	0.194160i
$595$	7.10222e6	+	6.96717e6i	0.0337166	+	0.0330754i
$596$			3.59959e8i			1.70026i
$597$	6.24451e6	+	1.02504e7i	0.0293478	+	0.0481746i
$598$	−6.89507e7	−	1.19426e8i	−0.322430	−	0.558465i
$599$	−1.54055e8	+	8.89438e7i	−0.716796	+	0.413842i	−0.813572	−	0.581464i	$-0.802480\pi$
$599$	−1.54055e8	+	8.89438e7i	−0.716796	+	0.413842i	0.0967762	+	0.995306i	$0.469147\pi$
$600$	1.47755e8	−	9.00121e7i	0.684053	−	0.416723i
$601$	−5.02762e7			−0.231600			−0.115800	−	0.993273i	$-0.536943\pi$
$601$	−5.02762e7			−0.231600			−0.115800	+	0.993273i	$0.536943\pi$
$602$	1.03497e8	+	3.71939e8i	0.474394	+	1.70484i
$603$	1.76057e7	+	2.74245e7i	0.0802974	+	0.125080i
$604$	3.72340e7	−	6.44912e7i	0.168978	−	0.292678i
$605$	−1.32232e8	+	7.63443e7i	−0.597133	+	0.344755i
$606$	3.58552e8	−	8.44732e6i	1.61114	−	0.0379578i
$607$	1.44612e8	−	2.50476e8i	0.646605	−	1.11995i	−0.337323	−	0.941389i	$-0.609522\pi$
$607$	1.44612e8	−	2.50476e8i	0.646605	−	1.11995i	0.983928	−	0.178564i	$-0.0571452\pi$
$608$		−	1.01328e8i		−	0.450836i
$609$	2.02149e8	−	2.16018e8i	0.894995	−	0.956398i
$610$	−2.58409e8			−1.13846
$611$	−2.29858e7	−	1.32709e7i	−0.100771	−	0.0581803i
$612$	4.25519e7	+	2.19634e7i	0.185637	+	0.0958177i
$613$	−2.09756e8	−	3.63308e8i	−0.910610	−	1.57722i	−0.813204	−	0.581979i	$-0.802279\pi$
$613$	−2.09756e8	−	3.63308e8i	−0.910610	−	1.57722i	−0.0974066	−	0.995245i	$-0.531055\pi$
$614$	6.79400e7	+	3.92252e7i	0.293508	+	0.169457i
$615$	5.22922e7	−	9.57103e7i	0.224808	−	0.411465i
$616$	−9.16915e7	+	3.55824e8i	−0.392272	+	1.52228i
$617$			2.15704e8i			0.918340i	0.888348	+	0.459170i	$0.151853\pi$
$617$			2.15704e8i			0.918340i	−0.888348	+	0.459170i	$0.848147\pi$
$618$	1.35227e8	−	8.23800e7i	0.572927	−	0.349025i
$619$	1.82813e8	+	3.16642e8i	0.770789	+	1.33505i	0.937131	+	0.348978i	$0.113471\pi$
$619$	1.82813e8	+	3.16642e8i	0.770789	+	1.33505i	−0.166341	+	0.986068i	$0.553195\pi$
$620$	1.81468e8	−	1.04771e8i	0.761422	−	0.439607i
$621$	−1.16506e8	−	5.67008e7i	−0.486489	−	0.236763i
$622$	4.07636e8			1.69395
$623$	4.98987e7	+	1.79322e8i	0.206360	+	0.741599i
$624$	8.79182e6	−	1.60917e7i	0.0361847	−	0.0662288i
$625$	−7.77781e7	+	1.34716e8i	−0.318579	+	0.551795i
$626$	2.30700e8	−	1.33195e8i	0.940426	−	0.542955i
$627$	4.15741e6	+	1.76464e8i	0.0168663	+	0.715901i
$628$	1.87730e7	−	3.25157e7i	0.0757974	−	0.131285i
$629$		−	1.67670e7i		−	0.0673755i
$630$	−2.90175e7	+	1.39497e8i	−0.116048	+	0.557883i
$631$	7.53050e7			0.299734			0.149867	−	0.988706i	$-0.452115\pi$
$631$	7.53050e7			0.299734			0.149867	+	0.988706i	$0.452115\pi$
$632$	−5.99991e7	−	3.46405e7i	−0.237681	−	0.137225i
$633$	−1.44714e8	+	3.40940e6i	−0.570558	+	0.0134421i
$634$	−7.21267e7	−	1.24927e8i	−0.283027	−	0.490217i
$635$	7.63578e7	+	4.40852e7i	0.298217	+	0.172176i
$636$	−1.51260e8	−	8.26423e7i	−0.587967	−	0.321241i
$637$	3.68761e6	+	1.92072e8i	0.0142668	+	0.743098i
$638$		−	9.35404e8i		−	3.60195i
$639$	4.57770e6	+	9.70979e7i	0.0175447	+	0.372141i
$640$	−7.14397e7	−	1.23737e8i	−0.272521	−	0.472020i
$641$	−2.73901e8	+	1.58137e8i	−1.03997	+	0.600424i	−0.919824	−	0.392332i	$-0.871668\pi$
$641$	−2.73901e8	+	1.58137e8i	−1.03997	+	0.600424i	−0.120142	+	0.992757i	$0.538335\pi$
$642$	−2.26367e8	−	3.71583e8i	−0.855475	−	1.40427i
$643$	−4.41742e8			−1.66163			−0.830817	−	0.556546i	$-0.812126\pi$
$643$	−4.41742e8			−1.66163			−0.830817	+	0.556546i	$0.812126\pi$
$644$	−1.59047e8	+	1.62130e8i	−0.595480	+	0.607023i
$645$	9.23341e7	+	5.04476e7i	0.344099	+	0.188001i
$646$	1.19987e7	−	2.07824e7i	0.0445079	−	0.0770900i
$647$	2.77420e8	−	1.60169e8i	1.02429	−	0.591377i	0.108950	−	0.994047i	$-0.465251\pi$
$647$	2.77420e8	−	1.60169e8i	1.02429	−	0.591377i	0.915345	+	0.402670i	$0.131918\pi$
$648$	2.34679e7	+	2.48336e8i	0.0862481	+	0.912673i
$649$	−7.55833e7	+	1.30914e8i	−0.276498	+	0.478909i
$650$		−	2.85992e8i		−	1.04139i
$651$	9.84501e7	−	4.23049e8i	0.356840	−	1.53337i
$652$	−2.99028e8			−1.07887
$653$	6.03095e7	+	3.48197e7i	0.216594	+	0.125050i	0.604372	−	0.796702i	$-0.293424\pi$
$653$	6.03095e7	+	3.48197e7i	0.216594	+	0.125050i	−0.387778	+	0.921753i	$0.626757\pi$
$654$	1.21909e7	+	5.17451e8i	0.0435816	+	1.84985i
$655$	7.65878e7	+	1.32654e8i	0.272544	+	0.472059i
$656$	3.27571e7	+	1.89123e7i	0.116036	+	0.0669937i
$657$	−2.04188e8	−	3.18064e8i	−0.720001	−	1.12155i
$658$	−1.78483e7	+	6.92634e7i	−0.0626498	+	0.243123i
$659$		−	2.37471e8i		−	0.829765i	−0.909875	−	0.414882i	$-0.863823\pi$
$659$		−	2.37471e8i		−	0.829765i	0.909875	−	0.414882i	$-0.136177\pi$
$660$	1.43236e8	+	2.35124e8i	0.498220	+	0.817832i
$661$	3.62613e6	+	6.28064e6i	0.0125556	+	0.0217470i	0.872235	−	0.489087i	$-0.162670\pi$
$661$	3.62613e6	+	6.28064e6i	0.0125556	+	0.0217470i	−0.859679	+	0.510834i	$0.829337\pi$
$662$	2.69813e8	−	1.55776e8i	0.930012	−	0.536943i
$663$	2.45880e7	−	1.49789e7i	0.0843690	−	0.0513972i
$664$	1.32011e8			0.450927
$665$	4.22576e7	+	1.08893e7i	0.143695	+	0.0370283i
$666$	2.02070e8	−	1.29722e8i	0.684035	−	0.439129i
$667$	1.05148e8	−	1.82122e8i	0.354344	−	0.613741i
$668$	1.54137e7	−	8.89911e6i	0.0517104	−	0.0298550i
$669$	−2.31203e8	+	5.44703e6i	−0.772173	+	0.0181920i
$670$	1.27368e7	−	2.20608e7i	0.0423482	−	0.0733493i
$671$			1.03503e9i			3.42598i
$672$	−3.19086e8	−	7.42563e7i	−1.05148	−	0.244695i
$673$	4.94626e8			1.62268			0.811338	−	0.584577i	$-0.198740\pi$
$673$	4.94626e8			1.62268			0.811338	+	0.584577i	$0.198740\pi$
$674$	1.29477e8	+	7.47535e7i	0.422875	+	0.244147i
$675$	−1.50454e8	−	2.22647e8i	−0.489206	−	0.723946i
$676$	−1.08658e8	−	1.88201e8i	−0.351740	−	0.609231i
$677$	3.10383e8	+	1.79200e8i	1.00030	+	0.577526i	0.908338	−	0.418236i	$-0.137352\pi$
$677$	3.10383e8	+	1.79200e8i	1.00030	+	0.577526i	0.0919660	+	0.995762i	$0.470685\pi$
$678$	2.11877e7	−	3.87798e7i	0.0679821	−	0.124427i
$679$	−2.19283e7	−	2.15113e7i	−0.0700479	−	0.0687159i
$680$		−	1.36145e7i		−	0.0432988i
$681$	−3.60739e8	+	2.19761e8i	−1.14223	+	0.695840i
$682$	−6.86655e8	−	1.18932e9i	−2.16464	−	3.74927i
$683$	−8.87610e7	+	5.12462e7i	−0.278586	+	0.160842i	−0.632783	−	0.774329i	$-0.718088\pi$
$683$	−8.87610e7	+	5.12462e7i	−0.278586	+	0.160842i	0.354197	+	0.935171i	$0.384754\pi$
$684$	2.09803e8	−	9.89120e6i	0.655606	−	0.0309087i
$685$	−1.05419e8			−0.327981
$686$	4.95996e8	−	1.48333e8i	1.53641	−	0.459478i
$687$	−1.90250e8	+	3.48214e8i	−0.586752	+	1.07393i
$688$	−1.82452e7	+	3.16016e7i	−0.0560252	+	0.0970385i
$689$	−8.97492e7	+	5.18167e7i	−0.274393	+	0.158421i
$690$	2.38543e6	+	1.01251e8i	0.00726140	+	0.308215i
$691$	−1.77897e8	+	3.08126e8i	−0.539180	+	0.933887i	0.459768	+	0.888039i	$0.347932\pi$
$691$	−1.77897e8	+	3.08126e8i	−0.539180	+	0.933887i	−0.998948	+	0.0458485i	$0.985401\pi$
$692$			8.59191e7i			0.259281i
$693$	5.58739e8	+	1.16226e8i	1.67884	+	0.349225i
$694$	3.65420e8			1.09324
$695$	−1.25906e8	−	7.26919e7i	−0.375053	−	0.216537i
$696$	−4.04739e8	+	9.53547e6i	−1.20046	+	0.0282823i
$697$	2.96950e7	+	5.14332e7i	0.0876971	+	0.151896i
$698$	−4.64957e8	−	2.68443e8i	−1.36725	−	0.789380i
$699$	−6.59518e7	−	3.60334e7i	−0.193106	−	0.105505i
$700$	−4.53775e8	+	1.26269e8i	−1.32296	+	0.368131i
$701$		−	1.69075e8i		−	0.490825i	−0.969419	−	0.245412i	$-0.921077\pi$
$701$		−	1.69075e8i		−	0.490825i	0.969419	−	0.245412i	$-0.0789233\pi$
$702$	3.70753e8	+	1.80437e8i	1.07170	+	0.521573i
$703$	−3.67714e7	−	6.36899e7i	−0.105839	−	0.183318i
$704$	−8.44436e8	+	4.87535e8i	−2.42018	+	1.39729i
$705$	1.01415e7	+	1.66473e7i	0.0289424	+	0.0475091i
$706$	5.93162e8			1.68562
$707$	−3.43911e8	−	8.86216e7i	−0.973167	−	0.250773i
$708$	1.57852e8	+	8.62440e7i	0.444786	+	0.243013i
$709$	2.86163e7	−	4.95648e7i	0.0802924	−	0.139070i	−0.823083	−	0.567921i	$-0.807748\pi$
$709$	2.86163e7	−	4.95648e7i	0.0802924	−	0.139070i	0.903376	+	0.428850i	$0.141081\pi$
$710$	6.58017e7	−	3.79906e7i	0.183849	−	0.106145i
$711$	−4.93535e7	+	9.56176e7i	−0.137312	+	0.266029i
$712$	1.27356e8	−	2.20587e8i	0.352841	−	0.611139i
$713$		−	3.08746e8i		−	0.851791i
$714$	−5.66516e7	−	5.30145e7i	−0.155639	−	0.145646i
$715$	1.65534e8			0.452865
$716$	−7.27420e7	−	4.19976e7i	−0.198174	−	0.114416i
$717$	6.89165e6	+	2.92521e8i	0.0186967	+	0.793596i
$718$	6.97985e7	+	1.20895e8i	0.188570	+	0.326613i
$719$	2.03117e8	+	1.17269e8i	0.546461	+	0.315499i	0.747693	−	0.664044i	$-0.231161\pi$
$719$	2.03117e8	+	1.17269e8i	0.546461	+	0.315499i	−0.201233	+	0.979543i	$0.564495\pi$
$720$	−1.13329e7	+	7.27534e6i	−0.0303628	+	0.0194920i
$721$	−1.51057e8	+	4.20337e7i	−0.403028	+	0.112148i
$722$			4.98300e8i			1.32397i
$723$	3.09004e8	+	5.07233e8i	0.817617	+	1.34212i
$724$	4.35292e7	+	7.53949e7i	0.114701	+	0.198667i
$725$	3.77701e8	−	2.18066e8i	0.991139	−	0.572234i
$726$	1.01691e9	−	6.19500e8i	2.65751	−	1.61894i
$727$	4.40253e8			1.14577			0.572887	−	0.819634i	$-0.305823\pi$
$727$	4.40253e8			1.14577			0.572887	+	0.819634i	$0.305823\pi$
$728$	1.84095e8	−	1.87664e8i	0.477143	−	0.486391i
$729$	3.83558e8	−	5.45724e7i	0.990029	−	0.140861i
$730$	−1.47719e8	+	2.55857e8i	−0.379723	+	0.657700i
$731$	−4.96189e7	+	2.86475e7i	−0.127027	+	0.0733390i
$732$	1.23126e9	−	2.90078e7i	3.13917	−	0.0739574i
$733$	−2.27236e8	+	3.93584e8i	−0.576985	+	0.999367i	0.418838	+	0.908061i	$0.362438\pi$
$733$	−2.27236e8	+	3.93584e8i	−0.576985	+	0.999367i	−0.995823	+	0.0913064i	$0.970896\pi$
$734$			6.54934e8i			1.65619i
$735$	6.52585e7	−	1.25091e8i	0.164352	−	0.315039i
$736$	−2.32873e8			−0.584097
$737$	−8.83618e7	−	5.10157e7i	−0.220730	−	0.127439i
$738$	−3.90112e8	+	7.55802e8i	−0.970554	+	1.88035i
$739$	−3.37304e8	−	5.84227e8i	−0.835772	−	1.44760i	−0.893401	−	0.449261i	$-0.851687\pi$
$739$	−3.37304e8	−	5.84227e8i	−0.835772	−	1.44760i	0.0576292	−	0.998338i	$-0.481646\pi$
$740$	−9.93408e7	−	5.73544e7i	−0.245150	−	0.141538i
$741$	6.05484e7	−	1.10822e8i	0.148815	−	0.272376i
$742$	1.99365e8	+	1.95574e8i	0.488019	+	0.478740i
$743$		−	6.64016e8i		−	1.61887i	−0.587210	−	0.809435i	$-0.699774\pi$
$743$		−	6.64016e8i		−	1.61887i	0.587210	−	0.809435i	$-0.300226\pi$
$744$	−5.07607e8	+	3.09232e8i	−1.23256	+	0.750872i
$745$	−7.94748e7	−	1.37654e8i	−0.192203	−	0.332906i
$746$	5.68229e8	−	3.28067e8i	1.36870	−	0.790217i
$747$	−9.65556e6	−	2.04805e8i	−0.0231641	−	0.491335i
$748$	−1.49922e8			−0.358229
$749$	1.15502e8	+	4.15080e8i	0.274880	+	0.987840i
$750$	−2.15969e8	+	3.95287e8i	−0.511926	+	0.936976i
$751$	3.82313e7	−	6.62185e7i	0.0902607	−	0.156336i	−0.817360	−	0.576127i	$-0.804563\pi$
$751$	3.82313e7	−	6.62185e7i	0.0902607	−	0.156336i	0.907621	+	0.419791i	$0.137897\pi$
$752$	−5.85473e6	+	3.38023e6i	−0.0137675	+	0.00794864i
$753$	−1.03909e7	−	4.41050e8i	−0.0243371	−	1.03301i
$754$	−3.34610e8	+	5.79562e8i	−0.780594	+	1.35203i
$755$			3.28833e7i			0.0764073i
$756$	1.22602e8	−	6.67926e8i	0.283748	−	1.54584i
$757$	−3.64982e8			−0.841364			−0.420682	−	0.907208i	$-0.638209\pi$
$757$	−3.64982e8			−0.841364			−0.420682	+	0.907208i	$0.638209\pi$
$758$	−1.03412e9	−	5.97047e8i	−2.37444	−	1.37088i
$759$	4.05551e8	−	9.55458e6i	0.927512	−	0.0218517i
$760$	−2.98578e7	−	5.17152e7i	−0.0680169	−	0.117809i
$761$	−5.00056e8	−	2.88708e8i	−1.13466	−	0.655095i	−0.189556	−	0.981870i	$-0.560705\pi$
$761$	−5.00056e8	−	2.88708e8i	−1.13466	−	0.655095i	−0.945102	+	0.326775i	$0.894038\pi$
$762$	−6.03415e8	−	3.29681e8i	−1.36380	−	0.745125i
$763$	1.27896e8	−	4.96321e8i	0.287927	−	1.11735i
$764$			6.59172e8i			1.47815i
$765$	−2.11218e7	+	995794.i	−0.0471788	+	0.00222426i
$766$	5.15029e8	+	8.92056e8i	1.14590	+	1.98475i
$767$	9.36606e7	−	5.40750e7i	0.207573	−	0.119842i
$768$	1.95629e8	+	3.21127e8i	0.431867	+	0.708913i
$769$	1.99792e7			0.0439339			0.0219669	−	0.999759i	$-0.493007\pi$
$769$	1.99792e7			0.0439339			0.0219669	+	0.999759i	$0.493007\pi$
$770$	−1.19587e8	−	4.29761e8i	−0.261946	−	0.941359i
$771$	−4.71432e8	−	2.57571e8i	−1.02862	−	0.561997i
$772$	−6.06616e7	+	1.05069e8i	−0.131845	+	0.228362i
$773$	−3.66991e8	+	2.11882e8i	−0.794542	+	0.458729i	−0.841559	−	0.540165i	$-0.818362\pi$
$773$	−3.66991e8	+	2.11882e8i	−0.794542	+	0.458729i	0.0470173	+	0.998894i	$0.485028\pi$
$774$	−7.29142e8	−	3.76351e8i	−1.57249	−	0.811652i
$775$	3.20153e8	−	5.54521e8i	0.687784	−	1.19128i
$776$			4.20351e7i			0.0899553i
$777$	−2.27509e8	+	6.91207e7i	−0.484994	+	0.147348i
$778$	−7.99736e7			−0.169827
$779$	2.25595e8	+	1.30247e8i	0.477218	+	0.275522i
$780$	−4.63927e6	−	1.96917e8i	−0.00977611	−	0.414954i
$781$	−1.52167e8	−	2.63561e8i	−0.319424	−	0.553258i
$782$	−4.77622e7	−	2.75755e7i	−0.0998767	−	0.0576638i
$783$	4.43970e7	+	6.27224e8i	0.0924844	+	1.30658i
$784$	4.28380e7	+	2.36480e7i	0.0888958	+	0.0490733i
$785$			1.65794e7i			0.0342736i
$786$	−6.21477e8	−	1.02016e9i	−1.27984	−	2.10087i
$787$	9.59731e7	+	1.66230e8i	0.196891	+	0.341025i	0.947519	−	0.319700i	$-0.103582\pi$
$787$	9.59731e7	+	1.66230e8i	0.196891	+	0.341025i	−0.750628	+	0.660725i	$0.770249\pi$
$788$	1.98191e8	−	1.14426e8i	0.405047	−	0.233854i
$789$	−8.06543e8	+	4.91343e8i	−1.64209	+	1.00035i
$790$	8.41086e7			0.170592
$791$	−3.06434e7	+	3.12374e7i	−0.0619167	+	0.0631169i
$792$	−4.21898e8	−	6.57193e8i	−0.849242	−	1.32287i
$793$	3.70248e8	−	6.41288e8i	0.742460	−	1.28598i
$794$	8.61460e8	−	4.97364e8i	1.72097	−	0.993603i
$795$	7.60908e7	−	1.79266e6i	0.151437	−	0.00356777i
$796$	−2.23576e7	+	3.87244e7i	−0.0443287	+	0.0767796i
$797$		−	7.53378e8i		−	1.48812i	−0.668113	−	0.744060i	$-0.732898\pi$
$797$		−	7.53378e8i		−	1.48812i	0.668113	−	0.744060i	$-0.267102\pi$
$798$	−3.31458e8	−	7.71355e7i	−0.652259	−	0.151791i
$799$	−1.06149e7			−0.0208101
$800$	−4.18249e8	−	2.41476e8i	−0.816893	−	0.471633i
$801$	−3.51538e8	−	1.81449e8i	−0.684030	−	0.353066i
$802$	3.25365e8	+	5.63549e8i	0.630737	+	1.09247i
$803$	1.02480e9	+	5.91670e8i	1.97922	+	1.14270i
$804$	−5.82112e7	+	1.06544e8i	−0.112005	+	0.205003i
$805$	2.50258e7	−	9.71168e7i	0.0479734	−	0.186169i
$806$			9.82514e8i			1.87644i
$807$	2.56629e8	−	1.56337e8i	0.488298	−	0.297469i
$808$	2.42995e8	+	4.20880e8i	0.460643	+	0.797856i
$809$	2.48907e8	−	1.43707e8i	0.470102	−	0.271413i	−0.246181	−	0.969224i	$-0.579176\pi$
$809$	2.48907e8	−	1.43707e8i	0.470102	−	0.271413i	0.716282	+	0.697811i	$0.245842\pi$
$810$	−1.75416e8	−	2.46849e8i	−0.330077	−	0.464490i
$811$	4.40820e8			0.826417			0.413208	−	0.910636i	$-0.364408\pi$
$811$	4.40820e8			0.826417			0.413208	+	0.910636i	$0.364408\pi$
$812$	1.06731e9	+	2.75032e8i	1.99352	+	0.513706i
$813$	−3.03141e8	+	5.54838e8i	−0.564122	+	1.03251i
$814$	−3.75894e8	+	6.51068e8i	−0.696936	+	1.20713i
$815$	1.14353e8	−	6.60218e7i	0.211240	−	0.121959i
$816$	−172725.	−	7.33141e6i	−0.000317895	−	0.0134933i
$817$	−1.25653e8	+	2.17637e8i	−0.230413	+	0.399086i
$818$			9.37572e8i			1.71295i
$819$	−3.04610e8	−	2.71883e8i	−0.554489	−	0.494914i
$820$	4.06309e8			0.736910
$821$	−7.72518e8	−	4.46013e8i	−1.39598	−	0.805969i	−0.402011	−	0.915635i	$-0.631689\pi$
$821$	−7.72518e8	−	4.46013e8i	−1.39598	−	0.805969i	−0.993969	+	0.109666i	$0.965022\pi$
$822$	8.21893e8	−	1.93634e7i	1.47979	−	0.0348631i
$823$	2.88904e8	+	5.00396e8i	0.518267	+	0.897665i	0.999775	+	0.0212232i	$0.00675606\pi$
$823$	2.88904e8	+	5.00396e8i	0.518267	+	0.897665i	−0.481508	+	0.876442i	$0.659911\pi$
$824$	1.85818e8	+	1.07282e8i	0.332129	+	0.191755i
$825$	7.38293e8	+	4.03373e8i	1.31482	+	0.718365i
$826$	−2.08053e8	−	2.04097e8i	−0.369177	−	0.362157i
$827$		−	5.21430e8i		−	0.921891i	−0.887428	−	0.460945i	$-0.847510\pi$
$827$		−	5.21430e8i		−	0.921891i	0.887428	−	0.460945i	$-0.152490\pi$
$828$	−2.27320e7	−	4.82170e8i	−0.0400449	−	0.849394i
$829$	2.71636e8	+	4.70487e8i	0.476786	+	0.825817i	0.999646	−	0.0266015i	$-0.00846850\pi$
$829$	2.71636e8	+	4.70487e8i	0.476786	+	0.825817i	−0.522861	+	0.852418i	$0.675135\pi$
$830$	−1.38793e8	+	8.01321e7i	−0.242735	+	0.140143i
$831$	−5.38913e7	−	8.84630e7i	−0.0939108	−	0.154155i
$832$	6.97599e8			1.21126
$833$	3.96850e7	+	6.57869e7i	0.0686580	+	0.113816i
$834$	9.94969e8	+	5.43610e8i	1.71519	+	0.937108i
$835$	−3.92964e6	+	6.80634e6i	−0.00674984	+	0.0116911i
$836$	−5.69485e8	+	3.28792e8i	−0.974683	+	0.562734i
$837$	5.16877e8	+	7.64894e8i	0.881476	+	1.30444i
$838$	688099.	−	1.19182e6i	0.00116928	−	0.00202525i
$839$		−	4.18527e8i		−	0.708659i	−0.935121	−	0.354329i	$-0.884709\pi$
$839$		−	4.18527e8i		−	0.708659i	0.935121	−	0.354329i	$-0.115291\pi$
$840$	−1.84734e8	+	5.61250e7i	−0.311680	+	0.0946931i
$841$	−4.25723e8			−0.715713
$842$	1.12204e9	+	6.47813e8i	1.87964	+	1.08521i
$843$	−1.67883e7	−	7.12593e8i	−0.0280237	−	1.18948i
$844$	−2.69635e8	−	4.67022e8i	−0.448487	−	0.776802i
$845$	8.31051e7	+	4.79808e7i	0.137739	+	0.0795238i
$846$	−8.21250e7	−	1.27927e8i	−0.135633	−	0.211276i
$847$	−1.13595e9	+	3.16095e8i	−1.86944	+	0.520196i
$848$			2.63965e7i			0.0432872i
$849$	9.01886e7	+	1.48045e8i	0.147377	+	0.241920i
$850$	−5.71886e7	−	9.90536e7i	−0.0931221	−	0.161292i
$851$	−1.46372e8	+	8.45082e7i	−0.237504	+	0.137123i
$852$	−3.09264e8	+	1.88403e8i	−0.500047	+	0.304627i
$853$	−6.76850e8			−1.09055			−0.545275	−	0.838257i	$-0.683575\pi$
$853$	−6.76850e8			−1.09055			−0.545275	+	0.838257i	$0.683575\pi$
$854$	−1.93240e9	−	4.97955e8i	−3.10258	−	0.799497i
$855$	−7.80482e7	+	5.01045e7i	−0.124872	+	0.0801639i
$856$	2.94794e8	−	5.10598e8i	0.469999	−	0.814063i
$857$	−3.09105e8	+	1.78462e8i	−0.491092	+	0.283532i	−0.725028	−	0.688720i	$-0.758173\pi$
$857$	−3.09105e8	+	1.78462e8i	−0.491092	+	0.283532i	0.233935	+	0.972252i	$0.424840\pi$
$858$	−1.29057e9	+	3.04053e7i	−2.04324	+	0.0481379i
$859$	4.47574e8	−	7.75220e8i	0.706131	−	1.22305i	−0.260151	−	0.965568i	$-0.583773\pi$
$859$	4.47574e8	−	7.75220e8i	0.706131	−	1.22305i	0.966282	−	0.257486i	$-0.0828942\pi$
$860$			3.91976e8i			0.616261i
$861$	5.75478e8	−	6.14959e8i	0.901610	−	0.963467i
$862$	−1.31294e9			−2.04985
$863$	6.58480e8	+	3.80174e8i	1.02450	+	0.591493i	0.915403	−	0.402539i	$-0.131872\pi$
$863$	6.58480e8	+	3.80174e8i	1.02450	+	0.591493i	0.109093	+	0.994032i	$0.465205\pi$
$864$	5.76924e8	−	3.89856e8i	0.894494	−	0.604454i
$865$	−1.89699e7	−	3.28569e7i	−0.0293101	−	0.0507666i
$866$	5.75501e8	+	3.32266e8i	0.886120	+	0.511601i
$867$	−3.06953e8	+	5.61815e8i	−0.470993	+	0.862057i
$868$	1.55892e9	−	4.33791e8i	2.38377	−	0.663317i
$869$		−	3.36887e8i		−	0.513364i
$870$	4.19744e8	−	2.55706e8i	0.637421	−	0.388315i
$871$	3.64984e7	+	6.32171e7i	0.0552357	+	0.0956710i
$872$	−6.07402e8	+	3.50683e8i	−0.916065	+	0.528891i
$873$	6.52141e7	−	3.07453e6i	0.0980164	−	0.00462101i
$874$	−2.41902e8			−0.362331
$875$	3.12352e8	−	3.18407e8i	0.466252	−	0.475289i
$876$	6.75122e8	−	1.23568e9i	1.00432	−	1.83820i
$877$	2.13971e8	−	3.70608e8i	0.317216	−	0.549435i	−0.662690	−	0.748894i	$-0.730585\pi$
$877$	2.13971e8	−	3.70608e8i	0.317216	−	0.549435i	0.979906	+	0.199459i	$0.0639185\pi$
$878$	1.17013e8	−	6.75575e7i	0.172882	−	0.0998136i
$879$	2.19460e7	+	9.31512e8i	0.0323138	+	1.37158i
$880$	2.10816e7	−	3.65145e7i	0.0309354	−	0.0535817i
$881$			5.97818e7i			0.0874261i	0.999044	+	0.0437131i	$0.0139187\pi$
$881$			5.97818e7i			0.0874261i	−0.999044	+	0.0437131i	$0.986081\pi$
$882$	−4.85806e8	+	9.87249e8i	−0.708039	+	1.43887i
$883$	3.12289e8			0.453601			0.226801	−	0.973941i	$-0.427173\pi$
$883$	3.12289e8			0.453601			0.226801	+	0.973941i	$0.427173\pi$
$884$	9.28896e7	+	5.36298e7i	0.134465	+	0.0776336i
$885$	−7.94069e7	+	1.87079e6i	−0.114559	+	0.00269895i
$886$	−6.05937e8	−	1.04951e9i	−0.871216	−	1.50899i
$887$	−4.05964e8	−	2.34384e8i	−0.581724	−	0.335858i	0.180094	−	0.983649i	$-0.442360\pi$
$887$	−4.05964e8	−	2.34384e8i	−0.581724	−	0.335858i	−0.761818	+	0.647791i	$0.775693\pi$
$888$	2.85542e8	+	1.56009e8i	0.407785	+	0.222797i
$889$	4.86055e8	+	4.76813e8i	0.691800	+	0.678645i
$890$			3.09226e8i			0.438637i
$891$	−9.88724e8	+	7.02609e8i	−1.39779	+	0.993301i
$892$	−4.30783e8	−	7.46138e8i	−0.606966	−	1.05130i
$893$	−4.03209e7	+	2.32793e7i	−0.0566208	+	0.0326900i
$894$	6.44903e8	+	1.05861e9i	0.902572	+	1.48158i
$895$	3.70903e7			0.0517359
$896$	−2.95788e8	−	1.06298e9i	−0.411203	−	1.47775i
$897$	−2.54691e8	−	1.39153e8i	−0.352887	−	0.192803i
$898$	−1.00687e9	+	1.74395e9i	−1.39041	+	2.40827i
$899$	−1.29758e9	+	7.49156e8i	−1.78589	+	1.03108i
$900$	4.59156e8	−	8.89569e8i	0.629844	−	1.22026i
$901$	−2.07231e7	+	3.58935e7i	−0.0283322	+	0.0490729i
$902$		−	2.66290e9i		−	3.62857i
$903$	5.93267e8	+	5.55178e8i	0.805725	+	0.753995i
$904$	5.98801e7			0.0810546
$905$	−3.32926e7	−	1.92215e7i	−0.0449161	−	0.0259323i
$906$	−6.04001e6	−	2.56372e8i	−0.00812181	−	0.344736i
$907$	5.90300e8	+	1.02243e9i	0.791136	+	1.37029i	0.925264	+	0.379323i	$0.123843\pi$
$907$	5.90300e8	+	1.02243e9i	0.791136	+	1.37029i	−0.134129	+	0.990964i	$0.542823\pi$
$908$	−1.36282e9	−	7.86822e8i	−1.82045	−	1.05104i
$909$	6.35189e8	−	4.07772e8i	0.845691	−	0.542908i
$910$	−7.96389e7	+	3.09052e8i	−0.105682	+	0.410117i
$911$		−	4.17757e8i		−	0.552546i	−0.961079	−	0.276273i	$-0.910901\pi$
$911$		−	4.17757e8i		−	0.552546i	0.961079	−	0.276273i	$-0.0890994\pi$
$912$	−1.67345e7	−	2.74698e7i	−0.0220612	−	0.0362136i
$913$	3.20960e8	+	5.55918e8i	0.421734	+	0.730464i
$914$	1.21779e9	−	7.03090e8i	1.59490	−	0.920815i
$915$	−4.64448e8	+	2.82940e8i	−0.606281	+	0.369344i
$916$	−1.47824e9			−1.92335
$917$	3.17103e8	+	1.13958e9i	0.411237	+	1.47787i
$918$	1.64492e8	−	1.16433e7i	0.212626	−	0.0150504i
$919$	3.51440e8	−	6.08713e8i	0.452799	−	0.784270i	−0.545760	−	0.837942i	$-0.683759\pi$
$919$	3.51440e8	−	6.08713e8i	0.452799	−	0.784270i	0.998559	+	0.0536712i	$0.0170923\pi$
$920$	−1.18852e8	+	6.86194e7i	−0.152631	+	0.0881218i
$921$	1.65060e8	−	3.88873e6i	0.211282	−	0.00497770i
$922$	1.02122e9	−	1.76880e9i	1.30294	−	2.25676i
$923$			2.17731e8i			0.276895i
$924$	6.18045e8	+	2.03428e9i	0.783437	+	2.57867i
$925$	−3.50522e8			−0.442883
$926$	1.26945e9	+	7.32916e8i	1.59875	+	0.923041i
$927$	1.52849e8	−	2.96129e8i	0.191877	−	0.371742i
$928$	5.65053e8	+	9.78701e8i	0.707042	+	1.22463i
$929$	−2.23231e8	−	1.28883e8i	−0.278425	−	0.160749i	0.354285	−	0.935137i	$-0.384724\pi$
$929$	−2.23231e8	−	1.28883e8i	−0.278425	−	0.160749i	−0.632710	+	0.774389i	$0.718058\pi$
$930$	3.45977e8	−	6.33241e8i	0.430129	−	0.787264i
$931$	2.95021e8	+	1.62861e8i	0.365598	+	0.201822i
$932$		−	2.79978e8i		−	0.345841i
$933$	7.32659e8	−	4.46333e8i	0.902104	−	0.549559i
$934$	−1.12780e9	−	1.95340e9i	−1.38417	−	2.39746i
$935$	5.73328e7	−	3.31011e7i	0.0701404	−	0.0404956i
$936$	2.63121e7	+	5.58107e8i	0.0320869	+	0.680597i
$937$	−1.53063e9			−1.86060			−0.930298	−	0.366806i	$-0.880451\pi$
$937$	−1.53063e9			−1.86060			−0.930298	+	0.366806i	$0.880451\pi$
$938$	1.37757e8	−	1.40428e8i	0.166919	−	0.170155i
$939$	2.68807e8	−	4.91996e8i	0.324671	−	0.594244i
$940$	−3.63101e7	+	6.28909e7i	−0.0437163	+	0.0757189i
$941$	−7.87989e8	+	4.54946e8i	−0.945696	+	0.545998i	−0.891741	−	0.452546i	$-0.850516\pi$
$941$	−7.87989e8	+	4.54946e8i	−0.945696	+	0.545998i	−0.0539544	+	0.998543i	$0.517183\pi$
$942$	−3.04530e6	−	1.29260e8i	−0.00364316	−	0.154636i
$943$	2.99335e8	−	5.18464e8i	0.356963	−	0.618278i
$944$		−	2.75469e7i		−	0.0327459i
$945$	1.00585e8	+	2.82495e8i	0.119190	+	0.334746i
$946$	2.56897e9			3.03449
$947$	9.07800e8	+	5.24119e8i	1.06891	+	0.617134i	0.927883	−	0.372872i	$-0.121627\pi$
$947$	9.07800e8	+	5.24119e8i	1.06891	+	0.617134i	0.141025	+	0.990006i	$0.454960\pi$
$948$	−4.00757e8	+	9.44164e6i	−0.470387	+	0.0110821i
$949$	−4.23302e8	−	7.33180e8i	−0.495281	−	0.857851i
$950$	−4.34466e8	−	2.50839e8i	−0.506740	−	0.292566i
$951$	−2.66422e8	−	1.45562e8i	−0.309762	−	0.169242i
$952$	2.62352e7	−	1.01810e8i	0.0304070	−	0.117999i
$953$			8.79139e8i			1.01573i	0.861436	+	0.507866i	$0.169565\pi$
$953$			8.79139e8i			1.01573i	−0.861436	+	0.507866i	$0.830435\pi$
$954$	−5.92906e8	+	2.79527e7i	−0.682875	+	0.0321943i
$955$	−1.45538e8	−	2.52078e8i	−0.167096	−	0.289418i
$956$	−9.44024e8	+	5.45033e8i	−1.08046	+	0.623805i
$957$	−1.02420e9	−	1.68123e9i	−1.16856	−	1.91819i
$958$	−1.26571e9			−1.43958
$959$	−7.88331e8	−	2.03143e8i	−0.893825	−	0.230328i
$960$	−4.49610e8	−	2.45649e8i	−0.508186	−	0.277652i
$961$	−6.56119e8	+	1.13643e9i	−0.739286	+	1.28048i
$962$	4.65797e8	−	2.68928e8i	0.523204	−	0.302072i
$963$	−8.13714e8	−	4.20003e8i	−0.911156	−	0.470298i
$964$	−1.10635e9	+	1.91625e9i	−1.23498	+	2.13905i
$965$		−	5.35735e7i		−	0.0596167i
$966$	−1.77273e8	+	7.61760e8i	−0.196658	+	0.845058i
$967$	1.99399e8			0.220518			0.110259	−	0.993903i	$-0.464832\pi$
$967$	1.99399e8			0.220518			0.110259	+	0.993903i	$0.464832\pi$
$968$	1.39736e9	+	8.06766e8i	1.54057	+	0.889450i
$969$	−1.18954e6	−	5.04907e7i	−0.00130739	−	0.0554932i
$970$	−2.55157e7	−	4.41946e7i	−0.0279572	−	0.0484232i
$971$	9.80790e7	+	5.66259e7i	0.107132	+	0.0618526i	0.552609	−	0.833441i	$-0.313632\pi$
$971$	9.80790e7	+	5.66259e7i	0.107132	+	0.0618526i	−0.445477	+	0.895294i	$0.646966\pi$
$972$	8.63525e8	+	1.15648e9i	0.940321	+	1.25933i
$973$	−8.01455e8	−	7.86215e8i	−0.870042	−	0.853499i
$974$			5.93990e8i			0.642839i
$975$	−3.13142e8	−	5.14024e8i	−0.337852	−	0.554587i
$976$	−9.43060e7	−	1.63343e8i	−0.101436	−	0.175691i
$977$	8.45240e8	−	4.87999e8i	0.906350	−	0.523282i	0.0270953	−	0.999633i	$-0.491374\pi$
$977$	8.45240e8	−	4.87999e8i	0.906350	−	0.523282i	0.879255	+	0.476351i	$0.158041\pi$
$978$	−8.79418e8	+	5.35738e8i	−0.940110	+	0.572711i
$979$	1.23857e9			1.31999
$980$	5.25524e8	−	1.00896e7i	0.558360	−	0.0107200i
$981$	5.88484e8	+	9.16686e8i	0.623344	+	0.970987i
$982$	7.08925e8	−	1.22789e9i	0.748628	−	1.29666i
$983$	−2.18031e8	+	1.25880e8i	−0.229540	+	0.132525i	−0.610360	−	0.792124i	$-0.708975\pi$
$983$	−2.18031e8	+	1.25880e8i	−0.229540	+	0.132525i	0.380820	+	0.924649i	$0.375642\pi$
$984$	−1.15221e9	+	2.71455e7i	−1.20933	+	0.0284913i
$985$	−5.05277e7	+	8.75166e7i	−0.0528714	+	0.0915760i
$986$			2.67642e8i			0.279205i
$987$	4.37591e7	+	1.44032e8i	0.0455111	+	0.149799i
$988$	4.70459e8			0.487810
$989$	5.00175e8	+	2.88776e8i	0.517051	+	0.298519i
$990$	8.42495e8	+	4.34858e8i	0.868283	+	0.448169i
$991$	2.12126e8	+	3.67413e8i	0.217958	+	0.377515i	0.954184	−	0.299222i	$-0.0967270\pi$
$991$	2.12126e8	+	3.67413e8i	0.217958	+	0.377515i	−0.736225	+	0.676736i	$0.763394\pi$
$992$	1.43688e9	+	8.29581e8i	1.47192	+	0.849814i
$993$	3.14380e8	−	5.75409e8i	0.321075	−	0.587663i
$994$	5.65277e8	−	1.57296e8i	0.575575	−	0.160161i
$995$		−	1.97451e7i		−	0.0200443i
$996$	6.52318e8	−	3.97390e8i	0.660209	−	0.402197i
$997$	−9.76514e7	−	1.69137e8i	−0.0985356	−	0.170669i	0.812543	−	0.582901i	$-0.198082\pi$
$997$	−9.76514e7	−	1.69137e8i	−0.0985356	−	0.170669i	−0.911079	+	0.412232i	$0.864749\pi$
$998$	−1.16458e9	+	6.72371e8i	−1.17160	+	0.676421i
$999$	2.21150e8	−	4.54407e8i	0.221815	−	0.455773i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.7.h.a.2.13	yes	28
3.2	odd	2	inner	21.7.h.a.2.2	✓	28
7.2	even	3		147.7.b.e.50.2		14
7.4	even	3	inner	21.7.h.a.11.2	yes	28
7.5	odd	6		147.7.b.d.50.2		14
21.2	odd	6		147.7.b.e.50.13		14
21.5	even	6		147.7.b.d.50.13		14
21.11	odd	6	inner	21.7.h.a.11.13	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.7.h.a.2.2	✓	28	3.2	odd	2	inner
21.7.h.a.2.13	yes	28	1.1	even	1	trivial
21.7.h.a.11.2	yes	28	7.4	even	3	inner
21.7.h.a.11.13	yes	28	21.11	odd	6	inner
147.7.b.d.50.2		14	7.5	odd	6
147.7.b.d.50.13		14	21.5	even	6
147.7.b.e.50.2		14	7.2	even	3
147.7.b.e.50.13		14	21.2	odd	6

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:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	21.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(11.1103 + 6.41456i) q^{2} +(26.9925 - 0.635931i) q^{3} +(50.2932 + 87.1103i) q^{4} +(-38.4659 - 22.2083i) q^{5} +(303.975 + 166.080i) q^{6} +(-244.854 - 240.199i) q^{7} +469.371i q^{8} +(728.191 - 34.3307i) q^{9} +O(q^{10})\)	\(q+(11.1103 + 6.41456i) q^{2} +(26.9925 - 0.635931i) q^{3} +(50.2932 + 87.1103i) q^{4} +(-38.4659 - 22.2083i) q^{5} +(303.975 + 166.080i) q^{6} +(-244.854 - 240.199i) q^{7} +469.371i q^{8} +(728.191 - 34.3307i) q^{9} +(-284.913 - 493.483i) q^{10} +(-1976.59 + 1141.18i) q^{11} +(1412.94 + 2319.34i) q^{12} +1632.89 q^{13} +(-1179.65 - 4239.32i) q^{14} +(-1052.41 - 574.996i) q^{15} +(207.957 - 360.192i) q^{16} +(565.551 - 326.521i) q^{17} +(8310.67 + 4289.60i) q^{18} +(1432.18 - 2480.60i) q^{19} -4467.70i q^{20} +(-6761.98 - 6327.85i) q^{21} -29280.8 q^{22} +(-5700.94 - 3291.44i) q^{23} +(298.487 + 12669.5i) q^{24} +(-6826.08 - 11823.1i) q^{25} +(18141.9 + 10474.3i) q^{26} +(19633.9 - 1389.75i) q^{27} +(8609.27 - 33409.7i) q^{28} +31946.0i q^{29} +(-8004.33 - 13139.2i) q^{30} +(23450.7 + 40617.8i) q^{31} +(30636.1 - 17687.8i) q^{32} +(-52627.4 + 32060.4i) q^{33} +8377.96 q^{34} +(4084.14 + 14677.2i) q^{35} +(39613.6 + 61706.4i) q^{36} +(12837.6 - 22235.3i) q^{37} +(31824.0 - 18373.6i) q^{38} +(44075.7 - 1038.40i) q^{39} +(10423.9 - 18054.8i) q^{40} +90943.6i q^{41} +(-34537.6 - 113680. i) q^{42} -87735.6 q^{43} +(-198818. - 114788. i) q^{44} +(-28772.9 - 14851.3i) q^{45} +(-42226.3 - 73138.0i) q^{46} +(-14076.8 - 8127.24i) q^{47} +(5384.22 - 9854.73i) q^{48} +(2258.34 + 117627. i) q^{49} -175145. i q^{50} +(15058.0 - 9173.27i) q^{51} +(82123.1 + 142241. i) q^{52} +(-54963.5 + 31733.2i) q^{53} +(227054. + 110502. i) q^{54} +101375. q^{55} +(112742. - 114927. i) q^{56} +(37080.6 - 67868.5i) q^{57} +(-204919. + 354931. i) q^{58} +(57358.9 - 33116.2i) q^{59} +(-2841.15 - 120594. i) q^{60} +(226744. - 392733. i) q^{61} +601704. i q^{62} +(-186547. - 166504. i) q^{63} +427218. q^{64} +(-62810.4 - 36263.6i) q^{65} +(-790362. + 18620.6i) q^{66} +(22352.1 + 38714.9i) q^{67} +(56886.7 + 32843.6i) q^{68} +(-155976. - 85218.8i) q^{69} +(-48771.8 + 189267. i) q^{70} +133341. i q^{71} +(16113.8 + 341792. i) q^{72} +(-259235. - 449009. i) q^{73} +(285260. - 164695. i) q^{74} +(-191772. - 314795. i) q^{75} +288115. q^{76} +(758088. + 195350. i) q^{77} +(496357. + 271189. i) q^{78} +(-73802.1 + 127829. i) q^{79} +(-15998.5 + 9236.73i) q^{80} +(529084. - 49998.7i) q^{81} +(-583363. + 1.01041e6i) q^{82} -281251. i q^{83} +(211140. - 907286. i) q^{84} -29005.9 q^{85} +(-974772. - 562785. i) q^{86} +(20315.4 + 862302. i) q^{87} +(-535639. - 927753. i) q^{88} +(-469964. - 271334. i) q^{89} +(-224413. - 349569. i) q^{90} +(-399819. - 392217. i) q^{91} -662148. i q^{92} +(658823. + 1.08146e6i) q^{93} +(-104265. - 180593. i) q^{94} +(-110180. + 63612.4i) q^{95} +(815697. - 496920. i) q^{96} +89556.3 q^{97} +(-729437. + 1.32137e6i) q^{98} +(-1.40016e6 + 898858. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - q^{3} + 382 q^{4} - 356 q^{6} + 1120 q^{7} + 1031 q^{9}+O(q^{10}) \) 28 * q - q^3 + 382 * q^4 - 356 * q^6 + 1120 * q^7 + 1031 * q^9	\( 28 q - q^{3} + 382 q^{4} - 356 q^{6} + 1120 q^{7} + 1031 q^{9} - 930 q^{10} - 404 q^{12} + 3632 q^{13} + 5450 q^{15} - 13706 q^{16} + 1612 q^{18} + 6830 q^{19} - 11333 q^{21} - 27348 q^{22} - 54498 q^{24} - 7640 q^{25} + 13268 q^{27} + 88522 q^{28} + 32380 q^{30} + 69410 q^{31} - 85459 q^{33} - 31344 q^{34} + 399028 q^{36} - 71830 q^{37} + 104570 q^{39} + 230250 q^{40} - 467782 q^{42} - 498904 q^{43} - 85375 q^{45} - 342660 q^{46} - 324728 q^{48} + 395668 q^{49} + 42177 q^{51} + 218000 q^{52} - 402122 q^{54} + 231660 q^{55} + 786782 q^{57} + 459522 q^{58} + 1021150 q^{60} + 153158 q^{61} + 179011 q^{63} - 1399412 q^{64} + 80896 q^{66} - 977098 q^{67} - 1520742 q^{69} - 139650 q^{70} - 1001352 q^{72} - 488350 q^{73} + 1434610 q^{75} + 6196280 q^{76} + 245176 q^{78} + 380762 q^{79} + 893531 q^{81} - 3665004 q^{82} + 1231496 q^{84} - 912540 q^{85} + 1452416 q^{87} - 1522482 q^{88} - 11713820 q^{90} - 1529416 q^{91} - 1690071 q^{93} - 3034044 q^{94} + 7549346 q^{96} + 7212176 q^{97} + 435866 q^{99}+O(q^{100}) \) 28 * q - q^3 + 382 * q^4 - 356 * q^6 + 1120 * q^7 + 1031 * q^9 - 930 * q^10 - 404 * q^12 + 3632 * q^13 + 5450 * q^15 - 13706 * q^16 + 1612 * q^18 + 6830 * q^19 - 11333 * q^21 - 27348 * q^22 - 54498 * q^24 - 7640 * q^25 + 13268 * q^27 + 88522 * q^28 + 32380 * q^30 + 69410 * q^31 - 85459 * q^33 - 31344 * q^34 + 399028 * q^36 - 71830 * q^37 + 104570 * q^39 + 230250 * q^40 - 467782 * q^42 - 498904 * q^43 - 85375 * q^45 - 342660 * q^46 - 324728 * q^48 + 395668 * q^49 + 42177 * q^51 + 218000 * q^52 - 402122 * q^54 + 231660 * q^55 + 786782 * q^57 + 459522 * q^58 + 1021150 * q^60 + 153158 * q^61 + 179011 * q^63 - 1399412 * q^64 + 80896 * q^66 - 977098 * q^67 - 1520742 * q^69 - 139650 * q^70 - 1001352 * q^72 - 488350 * q^73 + 1434610 * q^75 + 6196280 * q^76 + 245176 * q^78 + 380762 * q^79 + 893531 * q^81 - 3665004 * q^82 + 1231496 * q^84 - 912540 * q^85 + 1452416 * q^87 - 1522482 * q^88 - 11713820 * q^90 - 1529416 * q^91 - 1690071 * q^93 - 3034044 * q^94 + 7549346 * q^96 + 7212176 * q^97 + 435866 * q^99

Introduction

L-functions

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