LMFDB - Embedded newform 21.7.f.b.19.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,7,Mod(10,21)]

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([0, 1]))

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

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

chi := DirichletCharacter("21.10");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	21.f (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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 212x^{6} - 787x^{5} + 38792x^{4} - 92833x^{3} + 1563109x^{2} + 3107772x + 38787984 $ x^8 - x^7 + 212x^6 - 787x^5 + 38792x^4 - 92833x^3 + 1563109x^2 + 3107772x + 38787984
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3\cdot 7^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.1
Root			$5.73828 - 9.93899i$ of defining polynomial
Character	$\chi$	$=$	21.19
Dual form			21.7.f.b.10.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-6.23828 + 10.8050i) q^{2} +(13.5000 - 7.79423i) q^{3} +(-45.8323 - 79.3839i) q^{4} +(-175.367 - 101.248i) q^{5} +194.490i q^{6} +(284.280 - 191.921i) q^{7} +345.159 q^{8} +(121.500 - 210.444i) q^{9} +O(q^{10})$	\(q+(-6.23828 + 10.8050i) q^{2} +(13.5000 - 7.79423i) q^{3} +(-45.8323 - 79.3839i) q^{4} +(-175.367 - 101.248i) q^{5} +194.490i q^{6} +(284.280 - 191.921i) q^{7} +345.159 q^{8} +(121.500 - 210.444i) q^{9} +(2187.98 - 1263.23i) q^{10} +(-437.884 - 758.438i) q^{11} +(-1237.47 - 714.455i) q^{12} +275.049i q^{13} +(300.287 + 4268.91i) q^{14} -3156.61 q^{15} +(780.069 - 1351.12i) q^{16} +(-3799.10 + 2193.41i) q^{17} +(1515.90 + 2625.62i) q^{18} +(-11697.8 - 6753.75i) q^{19} +18561.8i q^{20} +(2341.91 - 4806.68i) q^{21} +10926.6 q^{22} +(6367.61 - 11029.0i) q^{23} +(4659.64 - 2690.25i) q^{24} +(12689.9 + 21979.6i) q^{25} +(-2971.91 - 1715.83i) q^{26} -3788.00i q^{27} +(-28264.6 - 13771.1i) q^{28} +6262.53 q^{29} +(19691.8 - 34107.2i) q^{30} +(-17689.7 + 10213.2i) q^{31} +(20777.7 + 35988.0i) q^{32} +(-11822.9 - 6825.94i) q^{33} -54732.5i q^{34} +(-69285.1 + 4873.70i) q^{35} -22274.5 q^{36} +(-7862.08 + 13617.5i) q^{37} +(145949. - 84263.6i) q^{38} +(2143.79 + 3713.16i) q^{39} +(-60529.5 - 34946.7i) q^{40} +69941.8i q^{41} +(37326.8 + 55289.8i) q^{42} +113322. q^{43} +(-40138.5 + 69521.9i) q^{44} +(-42614.2 + 24603.3i) q^{45} +(79445.9 + 137604. i) q^{46} +(-40116.2 - 23161.1i) q^{47} -24320.1i q^{48} +(43981.8 - 109119. i) q^{49} -316653. q^{50} +(-34191.9 + 59222.2i) q^{51} +(21834.4 - 12606.1i) q^{52} +(-64013.2 - 110874. i) q^{53} +(40929.4 + 23630.6i) q^{54} +177340. i q^{55} +(98121.9 - 66243.2i) q^{56} -210561. q^{57} +(-39067.4 + 67666.8i) q^{58} +(242870. - 140221. i) q^{59} +(144675. + 250584. i) q^{60} +(84759.3 + 48935.8i) q^{61} -254850. i q^{62} +(-5848.55 - 83143.6i) q^{63} -418619. q^{64} +(27848.2 - 48234.5i) q^{65} +(147509. - 85164.3i) q^{66} +(-87278.8 - 151171. i) q^{67} +(348243. + 201058. i) q^{68} -198522. i q^{69} +(379559. - 779030. i) q^{70} +345712. q^{71} +(41936.8 - 72636.7i) q^{72} +(-104589. + 60384.4i) q^{73} +(-98091.8 - 169900. i) q^{74} +(342627. + 197816. i) q^{75} +1.23816e6i q^{76} +(-270042. - 131570. i) q^{77} -53494.3 q^{78} +(-381933. + 661527. i) q^{79} +(-273597. + 157961. i) q^{80} +(-29524.5 - 51137.9i) q^{81} +(-755722. - 436316. i) q^{82} -859402. i q^{83} +(-488908. + 34391.1i) q^{84} +888317. q^{85} +(-706933. + 1.22444e6i) q^{86} +(84544.2 - 48811.6i) q^{87} +(-151140. - 261781. i) q^{88} +(-155778. - 89938.3i) q^{89} -613930. i q^{90} +(52787.6 + 78190.9i) q^{91} -1.16737e6 q^{92} +(-159207. + 275755. i) q^{93} +(500512. - 288971. i) q^{94} +(1.36761e6 + 2.36877e6i) q^{95} +(560997. + 323892. i) q^{96} -340171. i q^{97} +(904659. + 1.15594e6i) q^{98} -212812. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 5 q^{2} + 108 q^{3} - 173 q^{4} - 42 q^{5} + 748 q^{7} - 454 q^{8} + 972 q^{9}+O(q^{10}) $ 8 * q - 5 * q^2 + 108 * q^3 - 173 * q^4 - 42 * q^5 + 748 * q^7 - 454 * q^8 + 972 * q^9	\( 8 q - 5 q^{2} + 108 q^{3} - 173 q^{4} - 42 q^{5} + 748 q^{7} - 454 q^{8} + 972 q^{9} + 261 q^{10} - 1070 q^{11} - 4671 q^{12} + 6070 q^{14} - 756 q^{15} + 3911 q^{16} + 7212 q^{17} + 1215 q^{18} - 24606 q^{19} + 8154 q^{21} - 78 q^{22} - 15224 q^{23} - 6129 q^{24} + 22274 q^{25} - 19044 q^{26} - 3415 q^{28} + 32524 q^{29} + 2349 q^{30} + 40200 q^{31} + 70203 q^{32} - 28890 q^{33} - 242436 q^{35} - 84078 q^{36} - 45670 q^{37} + 503310 q^{38} + 93366 q^{39} - 94941 q^{40} + 55161 q^{42} - 445660 q^{43} - 188829 q^{44} - 10206 q^{45} + 525804 q^{46} + 82884 q^{47} + 24116 q^{49} - 1218884 q^{50} + 64908 q^{51} + 722856 q^{52} - 13034 q^{53} + 32805 q^{54} + 127061 q^{56} - 442908 q^{57} - 159501 q^{58} + 1810362 q^{59} + 429705 q^{60} - 392856 q^{61} + 38394 q^{63} - 1410446 q^{64} - 389004 q^{65} - 1053 q^{66} + 384094 q^{67} - 1616346 q^{68} + 406005 q^{70} + 225688 q^{71} - 55161 q^{72} + 903078 q^{73} + 1185530 q^{74} + 601398 q^{75} - 327674 q^{77} - 342792 q^{78} - 559592 q^{79} + 847713 q^{80} - 236196 q^{81} + 347634 q^{82} - 879444 q^{84} + 1953576 q^{85} - 2302402 q^{86} + 439074 q^{87} + 304887 q^{88} - 1770036 q^{89} - 2960718 q^{91} - 113064 q^{92} + 361800 q^{93} - 1837620 q^{94} + 1160112 q^{95} + 1895481 q^{96} + 5732467 q^{98} - 520020 q^{99}+O(q^{100}) \) 8 * q - 5 * q^2 + 108 * q^3 - 173 * q^4 - 42 * q^5 + 748 * q^7 - 454 * q^8 + 972 * q^9 + 261 * q^10 - 1070 * q^11 - 4671 * q^12 + 6070 * q^14 - 756 * q^15 + 3911 * q^16 + 7212 * q^17 + 1215 * q^18 - 24606 * q^19 + 8154 * q^21 - 78 * q^22 - 15224 * q^23 - 6129 * q^24 + 22274 * q^25 - 19044 * q^26 - 3415 * q^28 + 32524 * q^29 + 2349 * q^30 + 40200 * q^31 + 70203 * q^32 - 28890 * q^33 - 242436 * q^35 - 84078 * q^36 - 45670 * q^37 + 503310 * q^38 + 93366 * q^39 - 94941 * q^40 + 55161 * q^42 - 445660 * q^43 - 188829 * q^44 - 10206 * q^45 + 525804 * q^46 + 82884 * q^47 + 24116 * q^49 - 1218884 * q^50 + 64908 * q^51 + 722856 * q^52 - 13034 * q^53 + 32805 * q^54 + 127061 * q^56 - 442908 * q^57 - 159501 * q^58 + 1810362 * q^59 + 429705 * q^60 - 392856 * q^61 + 38394 * q^63 - 1410446 * q^64 - 389004 * q^65 - 1053 * q^66 + 384094 * q^67 - 1616346 * q^68 + 406005 * q^70 + 225688 * q^71 - 55161 * q^72 + 903078 * q^73 + 1185530 * q^74 + 601398 * q^75 - 327674 * q^77 - 342792 * q^78 - 559592 * q^79 + 847713 * q^80 - 236196 * q^81 + 347634 * q^82 - 879444 * q^84 + 1953576 * q^85 - 2302402 * q^86 + 439074 * q^87 + 304887 * q^88 - 1770036 * q^89 - 2960718 * q^91 - 113064 * q^92 + 361800 * q^93 - 1837620 * q^94 + 1160112 * q^95 + 1895481 * q^96 + 5732467 * q^98 - 520020 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$8$	$10$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−6.23828	+	10.8050i	−0.779785	+	1.35063i	0.152280	+	0.988337i	$0.451338\pi$
$2$	−6.23828	+	10.8050i	−0.779785	+	1.35063i	−0.932065	+	0.362290i	$0.881995\pi$
$3$	13.5000	−	7.79423i	0.500000	−	0.288675i
$3$	13.5000	−	7.79423i	0.500000	−	0.288675i
$4$	−45.8323	−	79.3839i	−0.716130	−	1.24037i
$5$	−175.367	−	101.248i	−1.40294	−	0.809986i	−0.408243	−	0.912873i	$-0.633859\pi$
$5$	−175.367	−	101.248i	−1.40294	−	0.809986i	−0.994693	+	0.102887i	$0.967192\pi$
$6$			194.490i			0.900418i
$7$	284.280	−	191.921i	0.828806	−	0.559536i
$7$	284.280	−	191.921i	0.828806	−	0.559536i
$8$	345.159			0.674138
$9$	121.500	−	210.444i	0.166667	−	0.288675i
$10$	2187.98	−	1263.23i	2.18798	−	1.26323i
$11$	−437.884	−	758.438i	−0.328989	−	0.569826i	0.653323	−	0.757080i	$-0.273375\pi$
$11$	−437.884	−	758.438i	−0.328989	−	0.569826i	−0.982312	+	0.187254i	$0.940041\pi$
$12$	−1237.47	−	714.455i	−0.716130	−	0.413458i
$13$			275.049i			0.125193i	0.998039	+	0.0625964i	$0.0199381\pi$
$13$			275.049i			0.125193i	−0.998039	+	0.0625964i	$0.980062\pi$
$14$	300.287	+	4268.91i	0.109434	+	1.55573i
$15$	−3156.61			−0.935291
$16$	780.069	−	1351.12i	0.190447	−	0.329863i
$17$	−3799.10	+	2193.41i	−0.773276	+	0.446451i	−0.834042	−	0.551701i	$-0.813979\pi$
$17$	−3799.10	+	2193.41i	−0.773276	+	0.446451i	0.0607662	+	0.998152i	$0.480646\pi$
$18$	1515.90	+	2625.62i	0.259928	+	0.450209i
$19$	−11697.8	−	6753.75i	−1.70547	−	0.984655i	−0.939992	−	0.341198i	$-0.889167\pi$
$19$	−11697.8	−	6753.75i	−1.70547	−	0.984655i	−0.765482	−	0.643458i	$-0.777499\pi$
$20$			18561.8i			2.32022i
$21$	2341.91	−	4806.68i	0.252879	−	0.519024i
$22$	10926.6			1.02616
$23$	6367.61	−	11029.0i	0.523351	−	0.906470i	−0.476280	−	0.879294i	$-0.658015\pi$
$23$	6367.61	−	11029.0i	0.523351	−	0.906470i	0.999631	−	0.0271766i	$-0.00865163\pi$
$24$	4659.64	−	2690.25i	0.337069	−	0.194607i
$25$	12689.9	+	21979.6i	0.812154	+	1.40669i
$26$	−2971.91	−	1715.83i	−0.169089	−	0.0976235i
$27$		−	3788.00i		−	0.192450i
$28$	−28264.6	−	13771.1i	−1.28757	−	0.627328i
$29$	6262.53			0.256777			0.128388	−	0.991724i	$-0.459020\pi$
$29$	6262.53			0.256777			0.128388	+	0.991724i	$0.459020\pi$
$30$	19691.8	−	34107.2i	0.729326	−	1.26323i
$31$	−17689.7	+	10213.2i	−0.593793	+	0.342827i	−0.766596	−	0.642130i	$-0.778051\pi$
$31$	−17689.7	+	10213.2i	−0.593793	+	0.342827i	0.172803	+	0.984956i	$0.444718\pi$
$32$	20777.7	+	35988.0i	0.634084	+	1.09827i
$33$	−11822.9	−	6825.94i	−0.328989	−	0.189942i
$34$		−	54732.5i		−	1.39254i
$35$	−69285.1	+	4873.70i	−1.61598	+	0.113672i
$36$	−22274.5			−0.477420
$37$	−7862.08	+	13617.5i	−0.155215	+	0.268840i	−0.933137	−	0.359521i	$-0.882940\pi$
$37$	−7862.08	+	13617.5i	−0.155215	+	0.268840i	0.777923	+	0.628360i	$0.216274\pi$
$38$	145949.	−	84263.6i	2.65981	−	1.53564i
$39$	2143.79	+	3713.16i	0.0361400	+	0.0625964i
$40$	−60529.5	−	34946.7i	−0.945773	−	0.546042i
$41$			69941.8i			1.01481i	0.861707	+	0.507405i	$0.169395\pi$
$41$			69941.8i			1.01481i	−0.861707	+	0.507405i	$0.830605\pi$
$42$	37326.8	+	55289.8i	0.503816	+	0.746272i
$43$	113322.			1.42530			0.712652	−	0.701517i	$-0.247494\pi$
$43$	113322.			1.42530			0.712652	+	0.701517i	$0.247494\pi$
$44$	−40138.5	+	69521.9i	−0.471197	+	0.816138i
$45$	−42614.2	+	24603.3i	−0.467645	+	0.269995i
$46$	79445.9	+	137604.i	0.816202	+	1.41370i
$47$	−40116.2	−	23161.1i	−0.386390	−	0.223083i	0.294205	−	0.955742i	$-0.404945\pi$
$47$	−40116.2	−	23161.1i	−0.386390	−	0.223083i	−0.680595	+	0.732660i	$0.738279\pi$
$48$		−	24320.1i		−	0.219909i
$49$	43981.8	−	109119.i	0.373839	−	0.927494i
$50$	−316653.			−2.53322
$51$	−34191.9	+	59222.2i	−0.257759	+	0.446451i
$52$	21834.4	−	12606.1i	0.155286	−	0.0896543i
$53$	−64013.2	−	110874.i	−0.429973	−	0.744736i	0.566897	−	0.823789i	$-0.308144\pi$
$53$	−64013.2	−	110874.i	−0.429973	−	0.744736i	−0.996870	+	0.0790529i	$0.974810\pi$
$54$	40929.4	+	23630.6i	0.259928	+	0.150070i
$55$			177340.i			1.06591i
$56$	98121.9	−	66243.2i	0.558730	−	0.377205i
$57$	−210561.			−1.13698
$58$	−39067.4	+	67666.8i	−0.200231	+	0.346810i
$59$	242870.	−	140221.i	1.18254	−	0.682742i	0.225942	−	0.974141i	$-0.427454\pi$
$59$	242870.	−	140221.i	1.18254	−	0.682742i	0.956602	+	0.291398i	$0.0941205\pi$
$60$	144675.	+	250584.i	0.669789	+	1.16011i
$61$	84759.3	+	48935.8i	0.373420	+	0.215594i	0.674952	−	0.737862i	$-0.264164\pi$
$61$	84759.3	+	48935.8i	0.373420	+	0.215594i	−0.301531	+	0.953456i	$0.597498\pi$
$62$		−	254850.i		−	1.06932i
$63$	−5848.55	−	83143.6i	−0.0233898	−	0.332512i
$64$	−418619.			−1.59690
$65$	27848.2	−	48234.5i	0.101404	−	0.175638i
$66$	147509.	−	85164.3i	0.513081	−	0.296228i
$67$	−87278.8	−	151171.i	−0.290191	−	0.502626i	0.683663	−	0.729797i	$-0.260386\pi$
$67$	−87278.8	−	151171.i	−0.290191	−	0.502626i	−0.973855	+	0.227171i	$0.927052\pi$
$68$	348243.	+	201058.i	1.10753	+	0.639433i
$69$		−	198522.i		−	0.604314i
$70$	379559.	−	779030.i	1.10659	−	2.27122i
$71$	345712.			0.965915			0.482957	−	0.875644i	$-0.339563\pi$
$71$	345712.			0.965915			0.482957	+	0.875644i	$0.339563\pi$
$72$	41936.8	−	72636.7i	0.112356	−	0.194607i
$73$	−104589.	+	60384.4i	−0.268854	+	0.155223i	−0.628367	−	0.777917i	$-0.716276\pi$
$73$	−104589.	+	60384.4i	−0.268854	+	0.155223i	0.359513	+	0.933140i	$0.382943\pi$
$74$	−98091.8	−	169900.i	−0.242068	−	0.419274i
$75$	342627.	+	197816.i	0.812154	+	0.468897i
$76$			1.23816e6i			2.82056i
$77$	−270042.	−	131570.i	−0.591506	−	0.288194i
$78$	−53494.3			−0.112726
$79$	−381933.	+	661527.i	−0.774650	+	1.34173i	0.160341	+	0.987062i	$0.448741\pi$
$79$	−381933.	+	661527.i	−0.774650	+	1.34173i	−0.934991	+	0.354671i	$0.884593\pi$
$80$	−273597.	+	157961.i	−0.534369	+	0.308518i
$81$	−29524.5	−	51137.9i	−0.0555556	−	0.0962250i
$82$	−755722.	−	436316.i	−1.37063	−	0.791334i
$83$		−	859402.i		−	1.50301i	−0.659727	−	0.751505i	$-0.729328\pi$
$83$		−	859402.i		−	1.50301i	0.659727	−	0.751505i	$-0.270672\pi$
$84$	−488908.	+	34391.1i	−0.824877	+	0.0580241i
$85$	888317.			1.44648
$86$	−706933.	+	1.22444e6i	−1.11143	+	1.92506i
$87$	84544.2	−	48811.6i	0.128388	−	0.0741251i
$88$	−151140.	−	261781.i	−0.221784	−	0.384141i
$89$	−155778.	−	89938.3i	−0.220971	−	0.127578i	0.385429	−	0.922738i	$-0.374054\pi$
$89$	−155778.	−	89938.3i	−0.220971	−	0.127578i	−0.606400	+	0.795160i	$0.707387\pi$
$90$		−	613930.i		−	0.842153i
$91$	52787.6	+	78190.9i	0.0700499	+	0.103761i
$92$	−1.16737e6			−1.49915
$93$	−159207.	+	275755.i	−0.197931	+	0.342827i
$94$	500512.	−	288971.i	0.602603	−	0.347913i
$95$	1.36761e6	+	2.36877e6i	1.59511	+	2.76282i
$96$	560997.	+	323892.i	0.634084	+	0.366088i
$97$		−	340171.i		−	0.372720i	−0.982482	−	0.186360i	$-0.940331\pi$
$97$		−	340171.i		−	0.372720i	0.982482	−	0.186360i	$-0.0596690\pi$
$98$	904659.	+	1.15594e6i	0.961184	+	1.22816i
$99$	−212812.			−0.219326
$100$	1.16321e6	−	2.01475e6i	1.16321	−	2.01475i
$101$	903587.	−	521686.i	0.877013	−	0.506344i	0.00734043	−	0.999973i	$-0.497663\pi$
$101$	903587.	−	521686.i	0.877013	−	0.506344i	0.869672	+	0.493630i	$0.164330\pi$
$102$	−426598.	−	738889.i	−0.401993	−	0.696272i
$103$	−675522.	−	390013.i	−0.618198	−	0.356917i	0.157969	−	0.987444i	$-0.449505\pi$
$103$	−675522.	−	390013.i	−0.618198	−	0.356917i	−0.776167	+	0.630527i	$0.782839\pi$
$104$			94935.5i			0.0843973i
$105$	−897362.	+	605819.i	−0.775175	+	0.523329i
$106$	1.59733e6			1.34115
$107$	498844.	−	864024.i	0.407205	−	0.705301i	−0.587370	−	0.809319i	$-0.699837\pi$
$107$	498844.	−	864024.i	0.407205	−	0.705301i	0.994575	+	0.104018i	$0.0331700\pi$
$108$	−300706.	+	173612.i	−0.238710	+	0.137819i
$109$	−727835.	−	1.26065e6i	−0.562023	−	0.973452i	−0.997320	−	0.0731648i	$-0.976690\pi$
$109$	−727835.	−	1.26065e6i	−0.562023	−	0.973452i	0.435297	−	0.900287i	$-0.356643\pi$
$110$	−1.91616e6	−	1.10630e6i	−1.43964	−	0.831177i
$111$			245116.i			0.179226i
$112$	−37549.5	−	533808.i	−0.0267270	−	0.379954i
$113$	177612.			0.123094			0.0615469	−	0.998104i	$-0.480397\pi$
$113$	177612.			0.123094			0.0615469	+	0.998104i	$0.480397\pi$
$114$	1.31354e6	−	2.27512e6i	0.886602	−	1.53564i
$115$	−2.23334e6	+	1.28942e6i	−1.46846	+	0.847814i
$116$	−287026.	−	497144.i	−0.183886	−	0.318499i
$117$	57882.4	+	33418.4i	0.0361400	+	0.0208655i
$118$			3.49895e6i			2.12957i
$119$	−659049.	+	1.35267e6i	−0.391090	+	0.802697i
$120$	−1.08953e6			−0.630516
$121$	502295.	−	870001.i	0.283533	−	0.491093i
$122$	−1.05750e6	+	610551.i	−0.582375	+	0.336234i
$123$	545142.	+	944214.i	0.292951	+	0.507405i
$124$	1.62152e6	+	936184.i	0.850466	+	0.491017i
$125$		−	1.97531e6i		−	1.01136i
$126$	934853.	+	455479.i	0.467338	+	0.227697i
$127$	924373.			0.451269			0.225635	−	0.974212i	$-0.427554\pi$
$127$	924373.			0.451269			0.225635	+	0.974212i	$0.427554\pi$
$128$	1.28169e6	−	2.21995e6i	0.611158	−	1.05856i
$129$	1.52984e6	−	883255.i	0.712652	−	0.411450i
$130$	347450.	+	601800.i	0.158147	+	0.273919i
$131$	837624.	+	483602.i	0.372593	+	0.215117i	0.674591	−	0.738192i	$-0.264320\pi$
$131$	837624.	+	483602.i	0.372593	+	0.215117i	−0.301997	+	0.953309i	$0.597653\pi$
$132$			1.25139e6i			0.544092i
$133$	−4.62165e6	+	325100.i	−1.96446	+	0.138185i
$134$	2.17788e6			0.905148
$135$	−383528.	+	664290.i	−0.155882	+	0.269995i
$136$	−1.31129e6	+	757076.i	−0.521295	+	0.300970i
$137$	−2.35006e6	−	4.07043e6i	−0.913940	−	1.58299i	−0.808446	−	0.588570i	$-0.799691\pi$
$137$	−2.35006e6	−	4.07043e6i	−0.913940	−	1.58299i	−0.105493	−	0.994420i	$-0.533642\pi$
$138$	2.14504e6	+	1.23844e6i	0.816202	+	0.471235i
$139$		−	1.64306e6i		−	0.611798i	−0.952064	−	0.305899i	$-0.901043\pi$
$139$		−	1.64306e6i		−	0.611798i	0.952064	−	0.305899i	$-0.0989570\pi$
$140$	3.56239e6	+	5.27674e6i	1.29825	+	1.92301i
$141$	−722092.			−0.257594
$142$	−2.15665e6	+	3.73542e6i	−0.753206	+	1.30459i
$143$	208607.	−	120439.i	0.0713381	−	0.0411870i
$144$	−189557.	−	328322.i	−0.0634822	−	0.109954i
$145$	−1.09824e6	−	634070.i	−0.360242	−	0.207986i
$146$		−	1.50678e6i		−	0.484162i
$147$	−256742.	−	1.81591e6i	−0.0808249	−	0.571665i
$148$	1.44135e6			0.444615
$149$	−2.31369e6	+	4.00743e6i	−0.699433	+	1.21145i	0.269230	+	0.963076i	$0.413231\pi$
$149$	−2.31369e6	+	4.00743e6i	−0.699433	+	1.21145i	−0.968663	+	0.248378i	$0.920103\pi$
$150$	−4.27481e6	+	2.46806e6i	−1.26661	+	0.731278i
$151$	2.24610e6	+	3.89036e6i	0.652377	+	1.12995i	0.982545	+	0.186028i	$0.0595614\pi$
$151$	2.24610e6	+	3.89036e6i	0.652377	+	1.12995i	−0.330168	+	0.943922i	$0.607105\pi$
$152$	−4.03761e6	−	2.33112e6i	−1.14972	−	0.663794i
$153$			1.06600e6i			0.297634i
$154$	3.10621e6	−	2.09704e6i	0.850490	−	0.574175i
$155$	4.13625e6			1.11074
$156$	196510.	−	340365.i	0.0517619	−	0.0896543i
$157$	−4.17859e6	+	2.41251e6i	−1.07977	+	0.623405i	−0.930834	−	0.365442i	$-0.880918\pi$
$157$	−4.17859e6	+	2.41251e6i	−1.07977	+	0.623405i	−0.148935	+	0.988847i	$0.547584\pi$
$158$	−4.76521e6	−	8.25358e6i	−1.20812	−	2.09253i
$159$	−1.72836e6	−	997866.i	−0.429973	−	0.248245i
$160$		−	8.41480e6i		−	2.05440i
$161$	−306513.	−	4.35741e6i	−0.0734464	−	1.04412i
$162$	736728.			0.173286
$163$	1.69763e6	−	2.94038e6i	0.391994	−	0.678954i	−0.600718	−	0.799461i	$-0.705119\pi$
$163$	1.69763e6	−	2.94038e6i	0.391994	−	0.678954i	0.992713	+	0.120507i	$0.0384519\pi$
$164$	5.55225e6	−	3.20559e6i	1.25874	−	0.726736i
$165$	1.38223e6	+	2.39409e6i	0.307700	+	0.532953i
$166$	9.28585e6	+	5.36119e6i	2.03001	+	1.17203i
$167$			2.04579e6i			0.439249i	0.975584	+	0.219625i	$0.0704832\pi$
$167$			2.04579e6i			0.439249i	−0.975584	+	0.219625i	$0.929517\pi$
$168$	808331.	−	1.65907e6i	0.170475	−	0.349894i
$169$	4.75116e6			0.984327
$170$	−5.54157e6	+	9.59828e6i	−1.12794	+	1.95365i
$171$	−2.84258e6	+	1.64116e6i	−0.568491	+	0.328218i
$172$	−5.19379e6	−	8.99591e6i	−1.02070	−	1.76791i
$173$	−272758.	−	157477.i	−0.0526792	−	0.0304144i	0.473429	−	0.880832i	$-0.343016\pi$
$173$	−272758.	−	157477.i	−0.0526792	−	0.0304144i	−0.526108	+	0.850418i	$0.676349\pi$
$174$			1.21800e6i			0.231207i
$175$	7.82583e6	+	3.81290e6i	1.46021	+	0.711445i
$176$	−1.36632e6			−0.250619
$177$	2.18583e6	−	3.78596e6i	0.394181	−	0.682742i
$178$	1.94357e6	−	1.12212e6i	0.344620	−	0.198966i
$179$	2.01204e6	+	3.48495e6i	0.350814	+	0.607627i	0.986392	−	0.164409i	$-0.0525717\pi$
$179$	2.01204e6	+	3.48495e6i	0.350814	+	0.607627i	−0.635579	+	0.772036i	$0.719238\pi$
$180$	3.90621e6	+	2.25525e6i	0.669789	+	0.386703i
$181$		−	1.53820e6i		−	0.259405i	−0.991553	−	0.129703i	$-0.958598\pi$
$181$		−	1.53820e6i		−	0.259405i	0.991553	−	0.129703i	$-0.0414022\pi$
$182$	−1.17416e6	+	82593.5i	−0.194766	+	0.0137004i
$183$	1.52567e6			0.248947
$184$	2.19784e6	−	3.80677e6i	0.352811	−	0.611086i
$185$	2.75750e6	−	1.59204e6i	0.435512	−	0.251443i
$186$	−1.98636e6	−	3.44047e6i	−0.308687	−	0.534662i
$187$	3.32714e6	+	1.92092e6i	0.508798	+	0.293755i
$188$			4.24611e6i			0.639024i
$189$	−726995.	−	1.07685e6i	−0.107683	−	0.159504i
$190$	−3.41262e7			−4.97538
$191$	−2.13865e6	+	3.70425e6i	−0.306931	+	0.531619i	−0.977689	−	0.210056i	$-0.932635\pi$
$191$	−2.13865e6	+	3.70425e6i	−0.306931	+	0.531619i	0.670759	+	0.741676i	$0.265969\pi$
$192$	−5.65135e6	+	3.26281e6i	−0.798452	+	0.460986i
$193$	3.22312e6	+	5.58261e6i	0.448337	+	0.776543i	0.998278	−	0.0586609i	$-0.0186831\pi$
$193$	3.22312e6	+	5.58261e6i	0.448337	+	0.776543i	−0.549941	+	0.835204i	$0.685350\pi$
$194$	3.67556e6	+	2.12208e6i	0.503406	+	0.290641i
$195$		−	868220.i		−	0.117092i
$196$	−1.06780e7	+	1.50972e6i	−1.41815	+	0.200506i
$197$	−2.73215e6			−0.357359			−0.178680	−	0.983907i	$-0.557183\pi$
$197$	−2.73215e6			−0.357359			−0.178680	+	0.983907i	$0.557183\pi$
$198$	1.32758e6	−	2.29943e6i	0.171027	−	0.296228i
$199$	517231.	−	298623.i	0.0656334	−	0.0378935i	−0.466824	−	0.884350i	$-0.654602\pi$
$199$	517231.	−	298623.i	0.0656334	−	0.0378935i	0.532458	+	0.846457i	$0.321269\pi$
$200$	4.38003e6	+	7.58644e6i	0.547504	+	0.948305i
$201$	−2.35653e6	−	1.36054e6i	−0.290191	−	0.167542i
$202$			1.30177e7i			1.57936i
$203$	1.78032e6	−	1.20191e6i	0.212818	−	0.143676i
$204$	6.26838e6			0.738354
$205$	7.08148e6	−	1.22655e7i	0.821982	−	1.42372i
$206$	8.42819e6	−	4.86602e6i	0.964123	−	0.556637i
$207$	−1.54733e6	−	2.68005e6i	−0.174450	−	0.302157i
$208$	371623.	+	214557.i	0.0412965	+	0.0238425i
$209$			1.18294e7i			1.29576i
$210$	−947888.	−	1.34753e7i	−0.102353	−	1.45506i
$211$	−3.67602e6			−0.391319			−0.195659	−	0.980672i	$-0.562685\pi$
$211$	−3.67602e6			−0.391319			−0.195659	+	0.980672i	$0.562685\pi$
$212$	−5.86774e6	+	1.01632e7i	−0.615833	+	1.06665i
$213$	4.66711e6	−	2.69455e6i	0.482957	−	0.278836i
$214$	6.22386e6	+	1.07800e7i	0.635066	+	1.09997i
$215$	−1.98729e7	−	1.14736e7i	−1.99961	−	1.15448i
$216$		−	1.30746e6i		−	0.129738i
$217$	−3.06872e6	+	6.29842e6i	−0.300316	+	0.616386i
$218$	1.81618e7			1.75303
$219$	−941299.	+	1.63038e6i	−0.0896180	+	0.155223i
$220$	1.40779e7	−	8.12790e6i	1.32212	−	0.763326i
$221$	−603295.	−	1.04494e6i	−0.0558924	−	0.0968086i
$222$	−2.64848e6	−	1.52910e6i	−0.242068	−	0.139758i
$223$		−	1.43225e7i		−	1.29153i	−0.763535	−	0.645766i	$-0.776538\pi$
$223$		−	1.43225e7i		−	1.29153i	0.763535	−	0.645766i	$-0.223462\pi$
$224$	1.28135e7	+	6.24301e6i	1.14005	+	0.555456i
$225$	6.16729e6			0.541436
$226$	−1.10799e6	+	1.91910e6i	−0.0959867	+	0.166254i
$227$	−2.62502e6	+	1.51555e6i	−0.224416	+	0.129567i	−0.607994	−	0.793942i	$-0.708025\pi$
$227$	−2.62502e6	+	1.51555e6i	−0.224416	+	0.129567i	0.383577	+	0.923509i	$0.374692\pi$
$228$	9.65050e6	+	1.67152e7i	0.814227	+	1.41028i
$229$	−5.42194e6	−	3.13036e6i	−0.451490	−	0.260668i	0.256969	−	0.966420i	$-0.417276\pi$
$229$	−5.42194e6	−	3.13036e6i	−0.451490	−	0.260668i	−0.708459	+	0.705752i	$0.750609\pi$
$230$		−	3.21750e7i		−	2.64445i
$231$	−4.67105e6	+	328575.i	−0.378947	+	0.0266562i
$232$	2.16157e6			0.173103
$233$	5.92360e6	−	1.02600e7i	0.468293	−	0.811107i	−0.531050	−	0.847340i	$-0.678203\pi$
$233$	5.92360e6	−	1.02600e7i	0.468293	−	0.811107i	0.999343	+	0.0362330i	$0.0115359\pi$
$234$	−722173.	+	416947.i	−0.0563629	+	0.0325412i
$235$	4.69004e6	+	8.12339e6i	0.361387	+	0.625941i
$236$	−2.22626e7	−	1.28533e7i	−1.69371	−	0.977864i
$237$			1.19075e7i			0.894489i
$238$	−1.05043e7	−	1.55594e7i	−0.779178	−	1.15415i
$239$	4.29229e6			0.314410			0.157205	−	0.987566i	$-0.449752\pi$
$239$	4.29229e6			0.314410			0.157205	+	0.987566i	$0.449752\pi$
$240$	−2.46237e6	+	4.26495e6i	−0.178123	+	0.308518i
$241$	1.37366e7	−	7.93085e6i	0.981362	−	0.566589i	0.0786807	−	0.996900i	$-0.474929\pi$
$241$	1.37366e7	−	7.93085e6i	0.981362	−	0.566589i	0.902681	+	0.430310i	$0.141596\pi$
$242$	6.26692e6	+	1.08546e7i	0.442189	+	0.765894i
$243$	−797162.	−	460241.i	−0.0555556	−	0.0320750i
$244$		−	8.97136e6i		−	0.617574i
$245$	−1.87610e7	+	1.46827e7i	−1.27573	+	0.998410i
$246$	−1.36030e7			−0.913754
$247$	1.85761e6	−	3.21747e6i	0.123272	−	0.213513i
$248$	−6.10575e6	+	3.52516e6i	−0.400299	+	0.231113i
$249$	−6.69838e6	−	1.16019e7i	−0.433882	−	0.751505i
$250$	2.13433e7	+	1.23226e7i	1.36597	+	0.788644i
$251$			7.11752e6i			0.450099i	0.974347	+	0.225049i	$0.0722543\pi$
$251$			7.11752e6i			0.450099i	−0.974347	+	0.225049i	$0.927746\pi$
$252$	−6.33220e6	+	4.27494e6i	−0.395688	+	0.267134i
$253$	−1.11531e7			−0.688707
$254$	−5.76650e6	+	9.98786e6i	−0.351893	+	0.609497i
$255$	1.19923e7	−	6.92374e6i	0.723238	−	0.417562i
$256$	2.59529e6	+	4.49518e6i	0.154692	+	0.267934i
$257$	−6.24715e6	−	3.60680e6i	−0.368030	−	0.212482i	0.304568	−	0.952491i	$-0.401488\pi$
$257$	−6.24715e6	−	3.60680e6i	−0.368030	−	0.212482i	−0.672597	+	0.740009i	$0.734821\pi$
$258$			2.20400e7i			1.28337i
$259$	378451.	+	5.38010e6i	0.0217826	+	0.309664i
$260$	−5.10538e6			−0.290475
$261$	760898.	−	1.31791e6i	0.0427962	−	0.0741251i
$262$	−1.04507e7	+	6.03370e6i	−0.581086	+	0.335490i
$263$	8.28046e6	+	1.43422e7i	0.455184	+	0.788402i	0.998699	−	0.0509974i	$-0.0162400\pi$
$263$	8.28046e6	+	1.43422e7i	0.455184	+	0.788402i	−0.543514	+	0.839400i	$0.682907\pi$
$264$	−4.08077e6	−	2.35603e6i	−0.221784	−	0.128047i
$265$			2.59249e7i			1.39309i
$266$	2.53185e7	−	5.19651e7i	1.34522	−	2.76100i
$267$	−2.80400e6			−0.147314
$268$	−8.00038e6	+	1.38571e7i	−0.415629	+	0.719891i
$269$	4.73497e6	−	2.73374e6i	0.243254	−	0.140443i	−0.373417	−	0.927663i	$-0.621814\pi$
$269$	4.73497e6	−	2.73374e6i	0.243254	−	0.140443i	0.616671	+	0.787221i	$0.288481\pi$
$270$	−4.78511e6	−	8.28805e6i	−0.243109	−	0.421077i
$271$	−1.61594e7	−	9.32961e6i	−0.811925	−	0.468765i	0.0356988	−	0.999363i	$-0.488634\pi$
$271$	−1.61594e7	−	9.32961e6i	−0.811925	−	0.468765i	−0.847624	+	0.530597i	$0.821968\pi$
$272$			6.84405e6i			0.340100i
$273$	1.32207e6	+	644139.i	0.0649780	+	0.0316586i
$274$	5.86414e7			2.85071
$275$	1.11134e7	−	1.92490e7i	0.534379	−	0.925572i
$276$	−1.57595e7	+	9.09874e6i	−0.749574	+	0.432767i
$277$	3.81751e6	+	6.61212e6i	0.179614	+	0.311101i	0.941748	−	0.336318i	$-0.109182\pi$
$277$	3.81751e6	+	6.61212e6i	0.179614	+	0.311101i	−0.762134	+	0.647419i	$0.775848\pi$
$278$	1.77532e7	+	1.02498e7i	0.826311	+	0.477071i
$279$			4.96359e6i			0.228551i
$280$	−2.39144e7	+	1.68220e6i	−1.08939	+	0.0766309i
$281$	−2.86272e7			−1.29021			−0.645103	−	0.764095i	$-0.723186\pi$
$281$	−2.86272e7			−1.29021			−0.645103	+	0.764095i	$0.723186\pi$
$282$	4.50461e6	−	7.80221e6i	0.200868	−	0.347913i
$283$	−1.84385e7	+	1.06455e7i	−0.813518	+	0.469685i	−0.848176	−	0.529714i	$-0.822299\pi$
$283$	−1.84385e7	+	1.06455e7i	−0.813518	+	0.469685i	0.0346580	+	0.999399i	$0.488966\pi$
$284$	−1.58448e7	−	2.74439e7i	−0.691720	−	1.19809i
$285$	3.69255e7	+	2.13189e7i	1.59511	+	0.920939i
$286$			3.00534e6i			0.128468i
$287$	1.34233e7	+	1.98831e7i	0.567823	+	0.841081i
$288$	1.00979e7			0.422723
$289$	−2.44666e6	+	4.23774e6i	−0.101363	+	0.175566i
$290$	1.37023e7	−	7.91102e6i	0.561822	−	0.324368i
$291$	−2.65137e6	−	4.59231e6i	−0.107595	−	0.186360i
$292$	9.58709e6	+	5.53511e6i	0.385069	+	0.222319i
$293$			1.72102e7i			0.684199i	0.939664	+	0.342100i	$0.111138\pi$
$293$			1.72102e7i			0.684199i	−0.939664	+	0.342100i	$0.888862\pi$
$294$	2.12225e7	+	8.55403e6i	0.835132	+	0.336611i
$295$	−5.67885e7			−2.21205
$296$	−2.71367e6	+	4.70021e6i	−0.104636	+	0.181235i
$297$	−2.87296e6	+	1.65870e6i	−0.109663	+	0.0633139i
$298$	−2.88669e7	−	4.99989e7i	−1.09082	−	1.88935i
$299$	3.03352e6	+	1.75140e6i	0.113484	+	0.0655198i
$300$		−	3.62654e7i		−	1.34316i
$301$	3.22151e7	−	2.17488e7i	1.18130	−	0.797509i
$302$	−5.60472e7			−2.03485
$303$	8.13228e6	−	1.40855e7i	0.292338	−	0.506344i
$304$	−1.82502e7	+	1.05368e7i	−0.649603	+	0.375048i
$305$	−9.90933e6	−	1.71635e7i	−0.349257	−	0.604930i
$306$	−1.15181e7	−	6.65000e6i	−0.401993	−	0.232091i
$307$		−	4.11253e7i		−	1.42133i	−0.703533	−	0.710663i	$-0.748395\pi$
$307$		−	4.11253e7i		−	1.42133i	0.703533	−	0.710663i	$-0.251605\pi$
$308$	1.93211e6	+	2.74671e7i	0.0661272	+	0.940072i
$309$	−1.21594e7			−0.412132
$310$	−2.58031e7	+	4.46923e7i	−0.866138	+	1.50019i
$311$	9.88085e6	−	5.70471e6i	0.328483	−	0.189650i	−0.326684	−	0.945133i	$-0.605931\pi$
$311$	9.88085e6	−	5.70471e6i	0.328483	−	0.189650i	0.655167	+	0.755484i	$0.272598\pi$
$312$	739949.	+	1.28163e6i	0.0243634	+	0.0421986i
$313$	−930200.	−	537051.i	−0.0303350	−	0.0175139i	0.484756	−	0.874650i	$-0.338908\pi$
$313$	−930200.	−	537051.i	−0.0303350	−	0.0175139i	−0.515091	+	0.857136i	$0.672242\pi$
$314$		−	6.01997e7i		−	1.94449i
$315$	−7.39249e6	+	1.51728e7i	−0.236515	+	0.485438i
$316$	7.00194e7			2.21900
$317$	9.89978e6	−	1.71469e7i	0.310776	−	0.538280i	−0.667754	−	0.744382i	$-0.732744\pi$
$317$	9.89978e6	−	1.71469e7i	0.310776	−	0.538280i	0.978531	+	0.206101i	$0.0660777\pi$
$318$	2.15639e7	−	1.24499e7i	0.670574	−	0.387156i
$319$	−2.74226e6	−	4.74974e6i	−0.0844768	−	0.146318i
$320$	7.34119e7	+	4.23844e7i	2.24035	+	1.29347i
$321$		−	1.55524e7i		−	0.470200i
$322$	4.89940e7	+	2.38709e7i	1.46749	+	0.714992i
$323$	5.92551e7			1.75840
$324$	−2.70635e6	+	4.68754e6i	−0.0795699	+	0.137819i
$325$	−6.04545e6	+	3.49034e6i	−0.176108	+	0.101676i
$326$	2.11806e7	+	3.66858e7i	0.611343	+	1.05888i
$327$	−1.96516e7	−	1.13458e7i	−0.562023	−	0.324484i
$328$			2.41410e7i			0.684123i
$329$	−1.58494e7	+	1.11489e6i	−0.445065	+	0.0313071i
$330$	−3.44909e7			−0.959761
$331$	9.56610e6	−	1.65690e7i	0.263785	−	0.456890i	−0.703459	−	0.710736i	$-0.748362\pi$
$331$	9.56610e6	−	1.65690e7i	0.263785	−	0.456890i	0.967245	+	0.253846i	$0.0816956\pi$
$332$	−6.82226e7	+	3.93884e7i	−1.86429	+	1.07635i
$333$	1.91049e6	+	3.30906e6i	0.0517382	+	0.0896132i
$334$	−2.21048e7	−	1.27622e7i	−0.593262	−	0.342520i
$335$			3.53473e7i			0.940204i
$336$	−4.66754e6	−	6.91374e6i	−0.123047	−	0.182262i
$337$	6.12984e7			1.60162			0.800810	−	0.598919i	$-0.204403\pi$
$337$	6.12984e7			1.60162			0.800810	+	0.598919i	$0.204403\pi$
$338$	−2.96391e7	+	5.13363e7i	−0.767563	+	1.32946i
$339$	2.39776e6	−	1.38435e6i	0.0615469	−	0.0355341i
$340$	−4.07136e7	−	7.05180e7i	−1.03586	−	1.79417i
$341$	1.54921e7	+	8.94435e6i	0.390703	+	0.225572i
$342$		−	4.09521e7i		−	1.02376i
$343$	−8.43899e6	−	3.94613e7i	−0.209126	−	0.977889i
$344$	3.91140e7			0.960853
$345$	−2.01000e7	+	3.48143e7i	−0.489485	+	0.847814i
$346$	3.40308e6	−	1.96477e6i	0.0821569	−	0.0474333i
$347$	−3.87907e7	−	6.71875e7i	−0.928409	−	1.60805i	−0.785985	−	0.618246i	$-0.787844\pi$
$347$	−3.87907e7	−	6.71875e7i	−0.928409	−	1.60805i	−0.142424	−	0.989806i	$-0.545490\pi$
$348$	−7.74971e6	−	4.47430e6i	−0.183886	−	0.106166i
$349$			3.32443e7i			0.782061i	0.920378	+	0.391031i	$0.127881\pi$
$349$			3.32443e7i			0.782061i	−0.920378	+	0.391031i	$0.872119\pi$
$350$	−9.00182e7	+	6.07723e7i	−2.09955	+	1.41743i
$351$	1.04188e6			0.0240934
$352$	1.81964e7	−	3.15171e7i	0.417213	−	0.722634i
$353$	−1.68383e7	+	9.72160e6i	−0.382802	+	0.221011i	−0.679037	−	0.734104i	$-0.737602\pi$
$353$	−1.68383e7	+	9.72160e6i	−0.382802	+	0.221011i	0.296235	+	0.955115i	$0.404269\pi$
$354$	2.72716e7	+	4.72358e7i	0.614754	+	1.06478i
$355$	−6.06264e7	−	3.50027e7i	−1.35512	−	0.782377i
$356$			1.64883e7i			0.365448i
$357$	1.64587e6	+	2.33979e7i	0.0361735	+	0.514246i
$358$	−5.02066e7			−1.09424
$359$	−1.27237e7	+	2.20381e7i	−0.274999	+	0.476311i	−0.970135	−	0.242567i	$-0.922011\pi$
$359$	−1.27237e7	+	2.20381e7i	−0.274999	+	0.476311i	0.695136	+	0.718878i	$0.255344\pi$
$360$	−1.47087e7	+	8.49205e6i	−0.315258	+	0.182014i
$361$	6.77034e7	+	1.17266e8i	1.43909	+	2.49258i
$362$	1.66203e7	+	9.59575e6i	0.350360	+	0.202280i
$363$		−	1.56600e7i		−	0.327395i
$364$	3.78772e6	−	7.77415e6i	0.0785370	−	0.161194i
$365$	2.44552e7			0.502914
$366$	−9.51754e6	+	1.64849e7i	−0.194125	+	0.336234i
$367$	−7.02719e6	+	4.05715e6i	−0.142162	+	0.0820773i	−0.569394	−	0.822065i	$-0.692822\pi$
$367$	−7.02719e6	+	4.05715e6i	−0.142162	+	0.0820773i	0.427232	+	0.904142i	$0.359489\pi$
$368$	−9.93435e6	−	1.72068e7i	−0.199341	−	0.345268i
$369$	1.47188e7	+	8.49793e6i	0.292951	+	0.169135i
$370$			3.97265e7i			0.784287i
$371$	−3.94767e7	−	1.92339e7i	−0.773071	−	0.376656i
$372$	2.91873e7			0.566977
$373$	3.60324e7	−	6.24099e7i	0.694330	−	1.20262i	−0.276076	−	0.961136i	$-0.589034\pi$
$373$	3.60324e7	−	6.24099e7i	0.694330	−	1.20262i	0.970406	−	0.241480i	$-0.0776327\pi$
$374$	−4.15112e7	+	2.39665e7i	−0.793507	+	0.458131i
$375$	−1.53960e7	−	2.66667e7i	−0.291955	−	0.505680i
$376$	−1.38465e7	−	7.99426e6i	−0.260481	−	0.150389i
$377$			1.72250e6i			0.0321466i
$378$	1.61706e7	−	1.13749e6i	0.299400	−	0.0210606i
$379$	4.53715e7			0.833423			0.416711	−	0.909039i	$-0.363183\pi$
$379$	4.53715e7			0.833423			0.416711	+	0.909039i	$0.363183\pi$
$380$	1.25361e8	−	2.17132e8i	2.28462	−	3.95707i
$381$	1.24790e7	−	7.20477e6i	0.225635	−	0.130270i
$382$	−2.66830e7	−	4.62164e7i	−0.478680	−	0.829098i
$383$	6.55862e7	+	3.78662e7i	1.16739	+	0.673994i	0.953064	−	0.302768i	$-0.0979108\pi$
$383$	6.55862e7	+	3.78662e7i	1.16739	+	0.673994i	0.214327	+	0.976762i	$0.431244\pi$
$384$		−	3.99592e7i		−	0.705704i
$385$	3.40352e7	+	5.04143e7i	0.596412	+	0.883429i
$386$	−8.04269e7			−1.39843
$387$	1.37686e7	−	2.38479e7i	0.237551	−	0.411450i
$388$	−2.70041e7	+	1.55908e7i	−0.462311	+	0.266916i
$389$	−4.41471e6	−	7.64649e6i	−0.0749986	−	0.129901i	0.826087	−	0.563542i	$-0.190562\pi$
$389$	−4.41471e6	−	7.64649e6i	−0.0749986	−	0.129901i	−0.901086	+	0.433641i	$0.857229\pi$
$390$	9.38114e6	+	5.41620e6i	0.158147	+	0.0913064i
$391$			5.58672e7i			0.934602i
$392$	1.51807e7	−	3.76633e7i	0.252019	−	0.625259i
$393$	1.50772e7			0.248396
$394$	1.70439e7	−	2.95209e7i	0.278664	−	0.482659i
$395$	1.33957e8	−	7.73400e7i	2.17357	−	1.25491i
$396$	9.75365e6	+	1.68938e7i	0.157066	+	0.272046i
$397$	−3.45140e7	−	1.99267e7i	−0.551599	−	0.318466i	0.198167	−	0.980168i	$-0.436501\pi$
$397$	−3.45140e7	−	1.99267e7i	−0.551599	−	0.318466i	−0.749767	+	0.661702i	$0.769834\pi$
$398$			7.45158e6i			0.118195i
$399$	−5.98584e7	+	4.04111e7i	−0.942338	+	0.636182i
$400$	3.95960e7			0.618687
$401$	1.65566e6	−	2.86769e6i	0.0256767	−	0.0444733i	−0.852902	−	0.522072i	$-0.825159\pi$
$401$	1.65566e6	−	2.86769e6i	0.0256767	−	0.0444733i	0.878578	+	0.477599i	$0.158493\pi$
$402$	2.94014e7	−	1.69749e7i	0.452574	−	0.261294i
$403$	−2.80911e6	−	4.86553e6i	−0.0429194	−	0.0743386i
$404$	−8.28269e7	−	4.78202e7i	−1.25611	−	0.725215i
$405$			1.19572e7i			0.179997i
$406$	1.88056e6	+	2.67342e7i	0.0281001	+	0.399475i
$407$	1.37707e7			0.204255
$408$	−1.18016e7	+	2.04411e7i	−0.173765	+	0.300970i
$409$	−8.98031e7	+	5.18478e7i	−1.31257	+	0.757811i	−0.982521	−	0.186154i	$-0.940398\pi$
$409$	−8.98031e7	+	5.18478e7i	−1.31257	+	0.757811i	−0.330046	+	0.943965i	$0.607064\pi$
$410$	8.83525e7	+	1.53031e8i	1.28194	+	2.22038i
$411$	−6.34517e7	−	3.66338e7i	−0.913940	−	0.527663i
$412$			7.15007e7i			1.02239i
$413$	4.21318e7	−	8.64738e7i	0.598081	−	1.22754i
$414$	3.86107e7			0.544135
$415$	−8.70129e7	+	1.50711e8i	−1.21742	+	2.10863i
$416$	−9.89844e6	+	5.71487e6i	−0.137495	+	0.0793827i
$417$	−1.28064e7	−	2.21813e7i	−0.176611	−	0.305899i
$418$	−1.27817e8	−	7.37954e7i	−1.75009	−	1.01042i
$419$		−	2.42723e7i		−	0.329965i	−0.986296	−	0.164983i	$-0.947243\pi$
$419$		−	2.42723e7i		−	0.329965i	0.986296	−	0.164983i	$-0.0527568\pi$
$420$	8.92204e7	+	4.34700e7i	1.20425	+	0.586734i
$421$	−8.03195e7			−1.07640			−0.538201	−	0.842816i	$-0.680896\pi$
$421$	−8.03195e7			−1.07640			−0.538201	+	0.842816i	$0.680896\pi$
$422$	2.29321e7	−	3.97195e7i	0.305145	−	0.528526i
$423$	−9.74824e6	+	5.62815e6i	−0.128797	+	0.0743609i
$424$	−2.20947e7	−	3.82692e7i	−0.289862	−	0.502055i
$425$	−9.64205e7	−	5.56684e7i	−1.25604	−	0.725174i
$426$			6.72376e7i			0.869727i
$427$	3.34872e7	−	2.35558e6i	0.430126	−	0.0302562i
$428$	−9.14527e7			−1.16645
$429$	1.87747e6	−	3.25186e6i	0.0237794	−	0.0411870i
$430$	2.47945e8	−	1.43151e8i	3.11854	−	1.80049i
$431$	2.93452e7	+	5.08273e7i	0.366526	+	0.634841i	0.989020	−	0.147783i	$-0.0472138\pi$
$431$	2.93452e7	+	5.08273e7i	0.366526	+	0.634841i	−0.622494	+	0.782625i	$0.713880\pi$
$432$	−5.11803e6	−	2.95490e6i	−0.0634822	−	0.0366514i
$433$		−	1.51707e8i		−	1.86871i	−0.356344	−	0.934355i	$-0.615977\pi$
$433$		−	1.51707e8i		−	1.86871i	0.356344	−	0.934355i	$-0.384023\pi$
$434$	−4.89110e7	−	7.24489e7i	−0.598326	−	0.886263i
$435$	−1.97684e7			−0.240161
$436$	−6.67167e7	+	1.15557e8i	−0.804962	+	1.39423i
$437$	−1.48975e8	+	8.60105e7i	−1.78512	+	1.03064i
$438$	−1.17442e7	−	2.03415e7i	−0.139766	−	0.242081i
$439$	1.05336e8	+	6.08155e7i	1.24504	+	0.718821i	0.970115	−	0.242646i	$-0.0780152\pi$
$439$	1.05336e8	+	6.08155e7i	1.24504	+	0.718821i	0.274920	+	0.961467i	$0.411349\pi$
$440$			6.12105e7i			0.718568i
$441$	−1.76196e7	−	2.25136e7i	−0.205438	−	0.262500i
$442$	1.50541e7			0.174336
$443$	−4.63310e7	+	8.02476e7i	−0.532918	+	0.923041i	0.466343	+	0.884604i	$0.345571\pi$
$443$	−4.63310e7	+	8.02476e7i	−0.532918	+	0.923041i	−0.999261	+	0.0384371i	$0.987762\pi$
$444$	1.94582e7	−	1.12342e7i	0.222307	−	0.128349i
$445$	1.82122e7	+	3.15444e7i	0.206672	+	0.357967i
$446$	1.54755e8	+	8.93480e7i	1.74438	+	1.00712i
$447$			7.21337e7i			0.807636i
$448$	−1.19005e8	+	8.03417e7i	−1.32352	+	0.893525i
$449$	−2.40772e7			−0.265991			−0.132996	−	0.991117i	$-0.542460\pi$
$449$	−2.40772e7			−0.265991			−0.132996	+	0.991117i	$0.542460\pi$
$450$	−3.84733e7	+	6.66377e7i	−0.422204	+	0.731278i
$451$	5.30465e7	−	3.06264e7i	0.578265	−	0.333862i
$452$	−8.14035e6	−	1.40995e7i	−0.0881511	−	0.152682i
$453$	6.06447e7	+	3.50133e7i	0.652377	+	0.376650i
$454$		−	3.78178e7i		−	0.404137i
$455$	−1.34051e6	−	1.90568e7i	−0.0142310	−	0.202309i
$456$	−7.26770e7			−0.766483
$457$	3.25397e7	−	5.63605e7i	0.340930	−	0.590509i	−0.643675	−	0.765299i	$-0.722591\pi$
$457$	3.25397e7	−	5.63605e7i	0.340930	−	0.590509i	0.984606	+	0.174790i	$0.0559247\pi$
$458$	6.76471e7	−	3.90561e7i	0.704130	−	0.406530i
$459$	8.30864e6	+	1.43910e7i	0.0859195	+	0.148817i
$460$	2.04718e8	+	1.18194e8i	2.10321	+	1.21429i
$461$		−	1.22022e8i		−	1.24548i	−0.782429	−	0.622740i	$-0.786020\pi$
$461$		−	1.22022e8i		−	1.24548i	0.782429	−	0.622740i	$-0.213980\pi$
$462$	2.55891e7	−	5.25206e7i	0.259495	−	0.532603i
$463$	2.62985e7			0.264965			0.132482	−	0.991185i	$-0.457705\pi$
$463$	2.62985e7			0.264965			0.132482	+	0.991185i	$0.457705\pi$
$464$	4.88521e6	−	8.46143e6i	0.0489023	−	0.0847012i
$465$	5.58394e7	−	3.22389e7i	0.555369	−	0.320643i
$466$	7.39061e7	+	1.28009e8i	0.730336	+	1.26498i
$467$	5.31512e7	+	3.06869e7i	0.521870	+	0.301302i	0.737699	−	0.675129i	$-0.235912\pi$
$467$	5.31512e7	+	3.06869e7i	0.521870	+	0.301302i	−0.215829	+	0.976431i	$0.569245\pi$
$468$		−	6.12657e6i		−	0.0597695i
$469$	−5.38246e7	−	2.62244e7i	−0.521750	−	0.254207i
$470$	−1.17031e8			−1.12722
$471$	−3.76073e7	+	6.51378e7i	−0.359923	+	0.623405i
$472$	8.38286e7	−	4.83985e7i	0.797198	−	0.460263i
$473$	−4.96218e7	−	8.59475e7i	−0.468909	−	0.812175i
$474$	−1.28661e8	−	7.42822e7i	−1.20812	−	0.697509i
$475$		−	3.42818e8i		−	3.19877i
$476$	1.37586e8	−	9.67818e6i	1.27571	−	0.0897373i
$477$	−3.11104e7			−0.286649
$478$	−2.67765e7	+	4.63783e7i	−0.245172	+	0.424650i
$479$	−1.67375e8	+	9.66342e7i	−1.52295	+	0.879274i	−0.523315	+	0.852139i	$0.675305\pi$
$479$	−1.67375e8	+	9.66342e7i	−1.52295	+	0.879274i	−0.999632	+	0.0271349i	$0.991362\pi$
$480$	−6.55869e7	−	1.13600e8i	−0.593053	−	1.02720i
$481$	−3.74548e6	−	2.16246e6i	−0.0336568	−	0.0194317i
$482$			1.97899e8i			1.76727i
$483$	−3.81006e7	−	5.64361e7i	−0.338135	−	0.500859i
$484$	−9.20854e7			−0.812184
$485$	−3.44417e7	+	5.96548e7i	−0.301898	+	0.522902i
$486$	9.94583e6	−	5.74223e6i	0.0866428	−	0.0500232i
$487$	−741867.	−	1.28495e6i	−0.00642302	−	0.0111250i	0.862796	−	0.505552i	$-0.168711\pi$
$487$	−741867.	−	1.28495e6i	−0.00642302	−	0.0111250i	−0.869219	+	0.494427i	$0.835378\pi$
$488$	2.92554e7	+	1.68906e7i	0.251737	+	0.145340i
$489$		−	5.29268e7i		−	0.452636i
$490$	−4.16108e7	−	2.94308e8i	−0.353686	−	2.50158i
$491$	1.33332e8			1.12639			0.563195	−	0.826324i	$-0.309572\pi$
$491$	1.33332e8			1.12639			0.563195	+	0.826324i	$0.309572\pi$
$492$	4.99702e7	−	8.65510e7i	0.419581	−	0.726736i
$493$	−2.37920e7	+	1.37363e7i	−0.198559	+	0.114638i
$494$	2.31766e7	+	4.01430e7i	0.192251	+	0.332988i
$495$	3.73202e7	+	2.15468e7i	0.307700	+	0.177651i
$496$			3.18678e7i			0.261161i
$497$	9.82790e7	−	6.63493e7i	0.800556	−	0.540464i
$498$	1.67145e8			1.35334
$499$	−7.54918e7	+	1.30756e8i	−0.607573	+	1.05235i	0.384066	+	0.923306i	$0.374523\pi$
$499$	−7.54918e7	+	1.30756e8i	−0.607573	+	1.05235i	−0.991639	+	0.129042i	$0.958810\pi$
$500$	−1.56808e8	+	9.05331e7i	−1.25446	+	0.724265i
$501$	1.59453e7	+	2.76181e7i	0.126800	+	0.219625i
$502$	−7.69050e7	−	4.44011e7i	−0.607915	−	0.350980i
$503$			9.92575e7i			0.779937i	0.920828	+	0.389968i	$0.127514\pi$
$503$			9.92575e7i			0.779937i	−0.920828	+	0.389968i	$0.872486\pi$
$504$	−2.01868e6	−	2.86977e7i	−0.0157680	−	0.224159i
$505$	−2.11279e8			−1.64052
$506$	6.95762e7	−	1.20510e8i	0.537043	−	0.930186i
$507$	6.41406e7	−	3.70316e7i	0.492163	−	0.284151i
$508$	−4.23661e7	−	7.33803e7i	−0.323167	−	0.559742i
$509$	1.07059e8	+	6.18103e7i	0.811835	+	0.468713i	0.847593	−	0.530647i	$-0.178051\pi$
$509$	1.07059e8	+	6.18103e7i	0.811835	+	0.468713i	−0.0357576	+	0.999360i	$0.511384\pi$
$510$			1.72769e8i			1.30243i
$511$	−1.81435e7	+	3.72389e7i	−0.135975	+	0.279083i
$512$	9.92957e7			0.739811
$513$	−2.55832e7	+	4.43114e7i	−0.189497	+	0.328218i
$514$	7.79430e7	−	4.50004e7i	0.573968	−	0.331381i
$515$	7.89762e7	+	1.36791e8i	0.578195	+	1.00146i
$516$	−1.40232e8	−	8.09632e7i	−1.02070	−	0.589303i
$517$			4.05675e7i			0.293567i
$518$	−6.04929e7	−	2.94734e7i	−0.435226	−	0.212051i
$519$	−4.90965e6			−0.0351195
$520$	9.61205e6	−	1.66486e7i	0.0683606	−	0.118404i
$521$	1.41733e8	−	8.18296e7i	1.00221	−	0.578625i	0.0933071	−	0.995637i	$-0.470256\pi$
$521$	1.41733e8	−	8.18296e7i	1.00221	−	0.578625i	0.908901	+	0.417012i	$0.136923\pi$
$522$	9.49339e6	+	1.64430e7i	0.0667436	+	0.115603i
$523$	2.21384e8	+	1.27816e8i	1.54754	+	0.893471i	0.998329	+	0.0577847i	$0.0184037\pi$
$523$	2.21384e8	+	1.27816e8i	1.54754	+	0.893471i	0.549208	+	0.835686i	$0.314930\pi$
$524$		−	8.86584e7i		−	0.616206i
$525$	1.35367e8	−	9.52211e6i	0.935483	−	0.0658044i
$526$	−2.06623e8			−1.41978
$527$	4.48033e7	−	7.76016e7i	0.306111	−	0.530199i
$528$	−1.84453e7	+	1.06494e7i	−0.125310	+	0.0723475i
$529$	−7.07498e6	−	1.22542e7i	−0.0477924	−	0.0827788i
$530$	−2.80119e8	−	1.61727e8i	−1.88154	−	1.08631i
$531$		−	6.81474e7i		−	0.455161i
$532$	2.37629e8	+	3.51985e8i	1.57821	+	2.33770i
$533$	−1.92374e7			−0.127047
$534$	1.74921e7	−	3.02973e7i	0.114873	−	0.198966i
$535$	−1.74962e8	+	1.01014e8i	−1.14257	+	0.659661i
$536$	−3.01251e7	−	5.21781e7i	−0.195629	−	0.338840i
$537$	5.43250e7	+	3.13645e7i	0.350814	+	0.202542i
$538$			6.82152e7i			0.438061i
$539$	−1.02019e8	+	1.44239e7i	−0.651498	+	0.0921122i
$540$	7.03118e7			0.446526
$541$	1.21035e8	−	2.09639e8i	0.764398	−	1.32398i	−0.176166	−	0.984361i	$-0.556369\pi$
$541$	1.21035e8	−	2.09639e8i	0.764398	−	1.32398i	0.940564	−	0.339616i	$-0.110297\pi$
$542$	2.01613e8	−	1.16401e8i	1.26625	−	0.731072i
$543$	−1.19891e7	−	2.07658e7i	−0.0748838	−	0.129703i
$544$	−1.57873e8	−	9.11480e7i	−0.980643	−	0.566175i
$545$			2.94768e8i			1.82092i
$546$	−1.52074e7	+	1.02667e7i	−0.0934279	+	0.0630742i
$547$	−3.05715e7			−0.186790			−0.0933952	−	0.995629i	$-0.529772\pi$
$547$	−3.05715e7			−0.186790			−0.0933952	+	0.995629i	$0.529772\pi$
$548$	−2.15417e8	+	3.73114e8i	−1.30900	+	2.26725i
$549$	2.05965e7	−	1.18914e7i	0.124473	−	0.0718648i
$550$	1.38657e8	+	2.40161e8i	0.833402	+	1.44349i
$551$	−7.32581e7	−	4.22956e7i	−0.437926	−	0.252837i
$552$		−	6.85218e7i		−	0.407391i
$553$	1.83848e7	+	2.61360e8i	0.108713	+	1.54548i
$554$	−9.52587e7			−0.560242
$555$	2.48175e7	−	4.29852e7i	0.145171	−	0.251443i
$556$	−1.30432e8	+	7.53050e7i	−0.758857	+	0.438126i
$557$	−1.16542e8	−	2.01856e8i	−0.674396	−	1.16809i	−0.976645	−	0.214860i	$-0.931071\pi$
$557$	−1.16542e8	−	2.01856e8i	−0.674396	−	1.16809i	0.302249	−	0.953229i	$-0.402263\pi$
$558$	−5.36317e7	−	3.09643e7i	−0.308687	−	0.178221i
$559$			3.11690e7i			0.178438i
$560$	−4.74622e7	+	9.74142e7i	−0.270261	+	0.554700i
$561$	5.98884e7			0.339199
$562$	1.78584e8	−	3.09317e8i	1.00608	−	1.74259i
$563$	1.95271e8	−	1.12740e8i	1.09424	−	0.631758i	0.159536	−	0.987192i	$-0.449000\pi$
$563$	1.95271e8	−	1.12740e8i	1.09424	−	0.631758i	0.934702	+	0.355434i	$0.115667\pi$
$564$	3.30951e7	+	5.73224e7i	0.184470	+	0.319512i
$565$	−3.11472e7	−	1.79829e7i	−0.172693	−	0.0997042i
$566$		−	2.65638e8i		−	1.46501i
$567$	−1.82077e7	−	8.87115e6i	−0.0998862	−	0.0486666i
$568$	1.19325e8			0.651160
$569$	−1.07390e8	+	1.86004e8i	−0.582943	+	1.00969i	0.412186	+	0.911100i	$0.364765\pi$
$569$	−1.07390e8	+	1.86004e8i	−0.582943	+	1.00969i	−0.995128	+	0.0985864i	$0.968568\pi$
$570$	−4.60703e8	+	2.65987e8i	−2.48769	+	1.43627i
$571$	−1.71362e8	−	2.96807e8i	−0.920460	−	1.59428i	−0.798704	−	0.601724i	$-0.794481\pi$
$571$	−1.71362e8	−	2.96807e8i	−0.920460	−	1.59428i	−0.121757	−	0.992560i	$-0.538853\pi$
$572$	−1.91219e7	−	1.10400e7i	−0.102175	−	0.0589905i
$573$			6.66766e7i			0.354413i
$574$	−2.98575e8	+	2.10026e7i	−1.57877	+	0.111055i
$575$	3.23217e8			1.70017
$576$	−5.08622e7	+	8.80959e7i	−0.266151	+	0.460986i
$577$	2.42646e8	−	1.40092e8i	1.26312	−	0.729263i	0.289444	−	0.957195i	$-0.406530\pi$
$577$	2.42646e8	−	1.40092e8i	1.26312	−	0.729263i	0.973677	+	0.227931i	$0.0731962\pi$
$578$	−3.05259e7	−	5.28724e7i	−0.158083	−	0.273807i
$579$	8.70243e7	+	5.02435e7i	0.448337	+	0.258848i
$580$			1.16244e8i			0.595779i
$581$	−1.64937e8	−	2.44311e8i	−0.840989	−	1.24570i
$582$	6.61600e7			0.335604
$583$	−5.60607e7	+	9.71000e7i	−0.282913	+	0.490020i
$584$	−3.60997e7	+	2.08422e7i	−0.181245	+	0.104642i
$585$	−6.76711e6	−	1.17210e7i	−0.0338015	−	0.0585458i
$586$	−1.85956e8	−	1.07362e8i	−0.924098	−	0.533528i
$587$			2.73172e8i			1.35059i	0.737549	+	0.675293i	$0.235983\pi$
$587$			2.73172e8i			1.35059i	−0.737549	+	0.675293i	$0.764017\pi$
$588$	−1.32387e8	+	1.03608e8i	−0.651196	+	0.509639i
$589$	2.75908e8			1.35026
$590$	3.54262e8	−	6.13600e8i	1.72492	−	2.98765i
$591$	−3.68840e7	+	2.12950e7i	−0.178680	+	0.103161i
$592$	1.22659e7	+	2.12452e7i	0.0591201	+	0.102399i
$593$	−3.17713e8	−	1.83432e8i	−1.52360	−	0.879651i	−0.999610	−	0.0279272i	$-0.991109\pi$
$593$	−3.17713e8	−	1.83432e8i	−1.52360	−	0.879651i	−0.523991	−	0.851724i	$-0.675557\pi$
$594$		−	4.13898e7i		−	0.197485i
$595$	2.52531e8	−	1.70487e8i	1.19885	−	0.809355i
$596$	4.24167e8			2.00354
$597$	4.65507e6	−	8.06283e6i	0.0218778	−	0.0378935i
$598$	−3.78479e7	+	2.18515e7i	−0.176986	+	0.102183i
$599$	8.45253e7	+	1.46402e8i	0.393284	+	0.681188i	0.992881	−	0.119114i	$-0.0380055\pi$
$599$	8.45253e7	+	1.46402e8i	0.393284	+	0.681188i	−0.599596	+	0.800303i	$0.704672\pi$
$600$	1.18261e8	+	6.82779e7i	0.547504	+	0.316102i
$601$		−	1.61411e8i		−	0.743551i	−0.928323	−	0.371775i	$-0.878749\pi$
$601$		−	1.61411e8i		−	0.743551i	0.928323	−	0.371775i	$-0.121251\pi$
$602$	3.40290e7	+	4.83760e8i	0.155977	+	2.21738i
$603$	−4.24175e7			−0.193461
$604$	2.05888e8	−	3.56608e8i	0.934373	−	1.61838i
$605$	−1.76172e8	+	1.01713e8i	−0.795556	+	0.459315i
$606$	1.01463e8	+	1.75739e8i	0.455921	+	0.789678i
$607$	1.67933e8	+	9.69564e7i	0.750881	+	0.433521i	0.826012	−	0.563652i	$-0.190604\pi$
$607$	1.67933e8	+	9.69564e7i	0.750881	+	0.433521i	−0.0751313	+	0.997174i	$0.523938\pi$
$608$		−	5.61309e8i		−	2.49742i
$609$	1.46663e7	−	3.01020e7i	0.0649335	−	0.133273i
$610$	2.47269e8			1.08938
$611$	6.37043e6	−	1.10339e7i	0.0279283	−	0.0483733i
$612$	8.46231e7	−	4.88572e7i	0.369177	−	0.213144i
$613$	5.21774e7	+	9.03739e7i	0.226517	+	0.392339i	0.956773	−	0.290834i	$-0.0939328\pi$
$613$	5.21774e7	+	9.03739e7i	0.226517	+	0.392339i	−0.730256	+	0.683173i	$0.760599\pi$
$614$	4.44359e8	+	2.56551e8i	1.91968	+	1.10833i
$615$		−	2.20779e8i		−	0.949143i
$616$	−9.32074e7	−	4.54125e7i	−0.398757	−	0.194282i
$617$	−3.99769e8			−1.70198			−0.850989	−	0.525183i	$-0.823997\pi$
$617$	−3.99769e8			−1.70198			−0.850989	+	0.525183i	$0.823997\pi$
$618$	7.58537e7	−	1.31382e8i	0.321374	−	0.556637i
$619$	−2.11757e8	+	1.22258e8i	−0.892822	+	0.515471i	−0.874865	−	0.484368i	$-0.839050\pi$
$619$	−2.11757e8	+	1.22258e8i	−0.892822	+	0.515471i	−0.0179577	+	0.999839i	$0.505716\pi$
$620$	−1.89574e8	−	3.28352e8i	−0.795433	−	1.37773i
$621$	−4.17779e7	−	2.41205e7i	−0.174450	−	0.100719i
$622$			1.42350e8i			0.591544i
$623$	−6.15456e7	+	4.32929e6i	−0.254526	+	0.0179041i
$624$	6.68922e6			0.0275310
$625$	−1.71720e6	+	2.97427e6i	−0.00703363	+	0.0121826i
$626$	1.16057e7	−	6.70056e6i	0.0473095	−	0.0273142i
$627$	9.22014e7	+	1.59698e8i	0.374055	+	0.647881i
$628$	3.83029e8	+	2.21142e8i	1.54651	+	0.892877i
$629$		−	6.89792e7i		−	0.277183i
$630$	−1.17826e8	−	1.74528e8i	−0.471215	−	0.697982i
$631$	−2.46592e8			−0.981500			−0.490750	−	0.871301i	$-0.663277\pi$
$631$	−2.46592e8			−0.981500			−0.490750	+	0.871301i	$0.663277\pi$
$632$	−1.31827e8	+	2.28332e8i	−0.522221	+	0.904514i
$633$	−4.96263e7	+	2.86517e7i	−0.195659	+	0.112964i
$634$	1.23515e8	+	2.13935e8i	0.484677	+	0.839486i
$635$	−1.62105e8	−	9.35911e7i	−0.633102	−	0.365522i
$636$			1.82938e8i			0.711103i
$637$	3.00129e7	+	1.20971e7i	0.116116	+	0.0468019i
$638$	6.84281e7			0.263495
$639$	4.20040e7	−	7.27530e7i	0.160986	−	0.278836i
$640$	−4.49533e8	+	2.59538e8i	−1.71483	+	0.990058i
$641$	−1.80422e8	−	3.12501e8i	−0.685040	−	1.18652i	−0.973424	−	0.229010i	$-0.926451\pi$
$641$	−1.80422e8	−	3.12501e8i	−0.685040	−	1.18652i	0.288384	−	0.957515i	$-0.406882\pi$
$642$	1.68044e8	+	9.70204e7i	0.635066	+	0.366655i
$643$			9.49305e7i			0.357086i	0.983932	+	0.178543i	$0.0571384\pi$
$643$			9.49305e7i			0.357086i	−0.983932	+	0.178543i	$0.942862\pi$
$644$	−3.31860e8	+	2.24042e8i	−1.24250	+	0.838827i
$645$	−3.57712e8			−1.33307
$646$	−3.69650e8	+	6.40252e8i	−1.37118	+	2.37495i
$647$	−1.29149e8	+	7.45642e7i	−0.476846	+	0.275307i	−0.719101	−	0.694905i	$-0.755446\pi$
$647$	−1.29149e8	+	7.45642e7i	−0.476846	+	0.275307i	0.242255	+	0.970213i	$0.422113\pi$
$648$	−1.01906e7	−	1.76507e7i	−0.0374521	−	0.0648690i
$649$	−2.12698e8	−	1.22801e8i	−0.778088	−	0.449229i
$650$		−	8.70949e7i		−	0.317141i
$651$	7.66363e6	+	1.08947e8i	0.0277774	+	0.394886i
$652$	−3.11225e8			−1.12288
$653$	2.54667e6	−	4.41096e6i	0.00914604	−	0.0158414i	−0.861416	−	0.507900i	$-0.830422\pi$
$653$	2.54667e6	−	4.41096e6i	0.00914604	−	0.0158414i	0.870562	+	0.492058i	$0.163755\pi$
$654$	2.45184e8	−	1.41557e8i	0.876514	−	0.506055i
$655$	−9.79278e7	−	1.69616e8i	−0.348483	−	0.603591i
$656$	9.44997e7	+	5.45594e7i	0.334749	+	0.193267i
$657$			2.93468e7i			0.103482i
$658$	8.68263e7	−	1.78208e8i	0.304771	−	0.625530i
$659$	5.76822e6			0.0201551			0.0100776	−	0.999949i	$-0.496792\pi$
$659$	5.76822e6			0.0201551			0.0100776	+	0.999949i	$0.496792\pi$
$660$	1.26701e8	−	2.19453e8i	0.440707	−	0.763326i
$661$	1.29229e7	−	7.46102e6i	0.0447460	−	0.0258341i	−0.477460	−	0.878653i	$-0.658442\pi$
$661$	1.29229e7	−	7.46102e6i	0.0447460	−	0.0258341i	0.522206	+	0.852819i	$0.325109\pi$
$662$	1.19352e8	+	2.06724e8i	0.411392	+	0.712552i
$663$	−1.62890e7	−	9.40444e6i	−0.0558924	−	0.0322695i
$664$		−	2.96630e8i		−	1.01324i
$665$	8.43402e8	+	4.10922e8i	2.86794	+	1.39732i
$666$	−4.76726e7			−0.161379
$667$	3.98774e7	−	6.90696e7i	0.134384	−	0.232761i
$668$	1.62402e8	−	9.37631e7i	0.544833	−	0.314559i
$669$	−1.11633e8	−	1.93354e8i	−0.372833	−	0.645766i
$670$	−3.81928e8	−	2.20506e8i	−1.26986	−	0.733157i
$671$		−	8.57129e7i		−	0.283713i
$672$	2.21642e8	−	1.55909e7i	0.730372	−	0.0513764i
$673$	2.64968e8			0.869257			0.434629	−	0.900610i	$-0.356880\pi$
$673$	2.64968e8			0.869257			0.434629	+	0.900610i	$0.356880\pi$
$674$	−3.82396e8	+	6.62330e8i	−1.24892	+	2.16319i
$675$	8.32584e7	−	4.80693e7i	0.270718	−	0.156299i
$676$	−2.17756e8	−	3.77165e8i	−0.704905	−	1.22093i
$677$	2.64867e8	+	1.52921e8i	0.853615	+	0.492835i	0.861869	−	0.507131i	$-0.169294\pi$
$677$	2.64867e8	+	1.52921e8i	0.853615	+	0.492835i	−0.00825369	+	0.999966i	$0.502627\pi$
$678$			3.45438e7i			0.110836i
$679$	−6.52860e7	−	9.67041e7i	−0.208550	−	0.308912i
$680$	3.06610e8			0.975125
$681$	−2.36252e7	+	4.09200e7i	−0.0748055	+	0.129567i
$682$	−1.93288e8	+	1.11595e8i	−0.609328	+	0.351796i
$683$	−7.48455e7	−	1.29636e8i	−0.234911	−	0.406878i	0.724336	−	0.689447i	$-0.242147\pi$
$683$	−7.48455e7	−	1.29636e8i	−0.234911	−	0.406878i	−0.959247	+	0.282570i	$0.908813\pi$
$684$	2.60563e8	+	1.50436e8i	0.814227	+	0.470094i
$685$			9.51758e8i			2.96111i
$686$	4.79025e8	+	1.54987e8i	1.48384	+	0.480091i
$687$	−9.75949e7			−0.300993
$688$	8.83987e7	−	1.53111e8i	0.271444	−	0.470155i
$689$	3.04957e7	−	1.76067e7i	0.0932356	−	0.0538296i
$690$	−2.50779e8	−	4.34363e8i	−0.763387	−	1.32222i
$691$	2.20972e8	+	1.27578e8i	0.669736	+	0.386672i	0.795977	−	0.605327i	$-0.206958\pi$
$691$	2.20972e8	+	1.27578e8i	0.669736	+	0.386672i	−0.126241	+	0.992000i	$0.540291\pi$
$692$			2.88701e7i			0.0871225i
$693$	−6.04982e7	+	4.08430e7i	−0.181779	+	0.122721i
$694$	9.67949e8			2.89584
$695$	−1.66356e8	+	2.88138e8i	−0.495548	+	0.858313i
$696$	2.91812e7	−	1.68478e7i	0.0865516	−	0.0499706i
$697$	−1.53411e8	−	2.65716e8i	−0.453063	−	0.784729i
$698$	−3.59205e8	−	2.07387e8i	−1.05627	−	0.609840i
$699$		−	1.84679e8i		−	0.540738i
$700$	−5.59927e7	−	7.95998e8i	−0.163244	−	2.32069i
$701$	−2.47105e8			−0.717343			−0.358672	−	0.933464i	$-0.616770\pi$
$701$	−2.47105e8			−0.717343			−0.358672	+	0.933464i	$0.616770\pi$
$702$	−6.49956e6	+	1.12576e7i	−0.0187876	+	0.0325412i
$703$	1.83939e8	−	1.06197e8i	0.529429	−	0.305666i
$704$	1.83307e8	+	3.17496e8i	0.525364	+	0.909956i
$705$	1.26631e8	+	7.31105e7i	0.361387	+	0.208647i
$706$		−	2.42584e8i		−	0.689364i
$707$	1.56750e8	−	3.21722e8i	0.443556	−	0.910381i
$708$	−4.00726e8			−1.12914
$709$	5.21037e7	−	9.02462e7i	0.146194	−	0.253215i	−0.783624	−	0.621236i	$-0.786631\pi$
$709$	5.21037e7	−	9.02462e7i	0.146194	−	0.253215i	0.929818	+	0.368020i	$0.119964\pi$
$710$	7.56409e8	−	4.36713e8i	2.11340	−	1.22017i
$711$	9.28096e7	+	1.60751e8i	0.258217	+	0.447244i
$712$	−5.37680e7	−	3.10430e7i	−0.148965	−	0.0860050i
$713$			2.60133e8i			0.717675i
$714$	−2.63082e8	−	1.28179e8i	−0.722763	−	0.352145i
$715$	−4.87771e7			−0.133444
$716$	1.84432e8	−	3.19446e8i	0.502456	−	0.870279i
$717$	5.79460e7	−	3.34551e7i	0.157205	−	0.0907622i
$718$	−1.58748e8	−	2.74960e8i	−0.428879	−	0.742841i
$719$	−4.11126e8	−	2.37363e8i	−1.10608	−	0.638598i	−0.168271	−	0.985741i	$-0.553818\pi$
$719$	−4.11126e8	−	2.37363e8i	−1.10608	−	0.638598i	−0.937812	+	0.347143i	$0.887152\pi$
$720$			7.67691e7i			0.205679i
$721$	−2.66889e8	+	1.87737e7i	−0.712074	+	0.0500893i
$722$	−1.68941e9			−4.48873
$723$	1.23630e8	−	2.14133e8i	0.327121	−	0.566589i
$724$	−1.22109e8	+	7.04995e7i	−0.321759	+	0.185768i
$725$	7.94709e7	+	1.37648e8i	0.208542	+	0.361206i
$726$	1.69207e8	+	9.76916e7i	0.442189	+	0.255298i
$727$			1.04048e8i			0.270790i	0.990792	+	0.135395i	$0.0432303\pi$
$727$			1.04048e8i			0.270790i	−0.990792	+	0.135395i	$0.956770\pi$
$728$	1.82201e7	+	2.69883e7i	0.0472233	+	0.0699490i
$729$	−1.43489e7			−0.0370370
$730$	−1.52559e8	+	2.64239e8i	−0.392164	+	0.679249i
$731$	−4.30521e8	+	2.48561e8i	−1.10215	+	0.636329i
$732$	−6.99248e7	−	1.21113e8i	−0.178278	−	0.308787i
$733$	5.79355e8	+	3.34491e8i	1.47107	+	0.849322i	0.999472	−	0.0324917i	$-0.0103443\pi$
$733$	5.79355e8	+	3.34491e8i	1.47107	+	0.849322i	0.471597	+	0.881814i	$0.343678\pi$
$734$		−	1.01239e8i		−	0.256010i
$735$	−1.38833e8	+	3.44445e8i	−0.349648	+	0.867476i
$736$	5.29216e8			1.32739
$737$	−7.64361e7	+	1.32391e8i	−0.190940	+	0.330717i
$738$	−1.83641e8	+	1.06025e8i	−0.456877	+	0.263778i
$739$	1.54148e8	+	2.66992e8i	0.381948	+	0.661554i	0.991341	−	0.131315i	$-0.0419200\pi$
$739$	1.54148e8	+	2.66992e8i	0.381948	+	0.661554i	−0.609393	+	0.792869i	$0.708587\pi$
$740$	−2.52765e8	−	1.45934e8i	−0.623767	−	0.360132i
$741$		−	5.79145e7i		−	0.142342i
$742$	4.54089e8	−	3.06561e8i	1.11155	−	0.750420i
$743$	1.83763e8			0.448014			0.224007	−	0.974588i	$-0.428086\pi$
$743$	1.83763e8			0.448014			0.224007	+	0.974588i	$0.428086\pi$
$744$	−5.49518e7	+	9.51793e7i	−0.133433	+	0.231113i
$745$	8.11490e8	−	4.68514e8i	1.96252	−	1.13306i
$746$	4.49560e8	+	7.78661e8i	1.08286	+	1.87556i
$747$	−1.80856e8	−	1.04417e8i	−0.433882	−	0.250502i
$748$		−	3.52161e8i		−	0.841466i
$749$	−2.40125e7	−	3.41364e8i	−0.0571467	−	0.812404i
$750$	3.84179e8			0.910647
$751$	−1.22666e8	+	2.12463e8i	−0.289603	+	0.501608i	−0.973715	−	0.227770i	$-0.926857\pi$
$751$	−1.22666e8	+	2.12463e8i	−0.289603	+	0.501608i	0.684112	+	0.729377i	$0.260190\pi$
$752$	−6.25868e7	+	3.61345e7i	−0.147173	+	0.0849706i
$753$	5.54756e7	+	9.60865e7i	0.129932	+	0.225049i
$754$	−1.86117e7	−	1.07454e7i	−0.0434181	−	0.0250675i
$755$		−	9.09655e8i		−	2.11366i
$756$	−5.21649e7	+	1.07066e8i	−0.120729	+	0.247792i
$757$	−8.44770e8			−1.94738			−0.973690	−	0.227876i	$-0.926822\pi$
$757$	−8.44770e8			−1.94738			−0.973690	+	0.227876i	$0.926822\pi$
$758$	−2.83040e8	+	4.90240e8i	−0.649891	+	1.12564i
$759$	−1.50567e8	+	8.69299e7i	−0.344353	+	0.198812i
$760$	4.72043e8	+	8.17602e8i	1.07533	+	1.86252i
$761$	4.91638e8	+	2.83847e8i	1.11556	+	0.644066i	0.940263	−	0.340450i	$-0.110579\pi$
$761$	4.91638e8	+	2.83847e8i	1.11556	+	0.644066i	0.175293	+	0.984516i	$0.443913\pi$
$762$			1.79782e8i			0.406331i
$763$	−4.48854e8	−	2.18691e8i	−1.01049	−	0.492331i
$764$	3.92077e8			0.879208
$765$	1.07930e8	−	1.86941e8i	0.241079	−	0.417562i
$766$	−8.18291e8	+	4.72440e8i	−1.82063	+	1.05114i
$767$	3.85676e7	+	6.68010e7i	0.0854744	+	0.148046i
$768$	7.00729e7	+	4.04566e7i	0.154692	+	0.0893112i
$769$		−	2.83103e6i		−	0.00622536i	−0.999995	−	0.00311268i	$-0.999009\pi$
$769$		−	2.83103e6i		−	0.00622536i	0.999995	−	0.00311268i	$-0.000990799\pi$
$770$	−7.57049e8	+	5.32529e7i	−1.65826	+	0.116646i
$771$	−1.12449e8			−0.245353
$772$	2.95446e8	−	5.11728e8i	0.642135	−	1.11221i
$773$	3.83914e8	−	2.21653e8i	0.831181	−	0.479883i	−0.0230756	−	0.999734i	$-0.507346\pi$
$773$	3.83914e8	−	2.21653e8i	0.831181	−	0.479883i	0.854257	+	0.519851i	$0.174013\pi$
$774$	1.71785e8	+	2.97540e8i	0.370477	+	0.641685i
$775$	−4.48961e8	−	2.59208e8i	−0.964503	−	0.556856i
$776$		−	1.17413e8i		−	0.251265i
$777$	4.70428e7	+	6.96816e7i	0.100284	+	0.148544i
$778$	1.10161e8			0.233931
$779$	4.72369e8	−	8.18168e8i	0.999239	−	1.73073i
$780$	−6.89227e7	+	3.97925e7i	−0.145237	+	0.0838528i
$781$	−1.51382e8	−	2.62201e8i	−0.317775	−	0.550403i
$782$	−6.03646e8	−	3.48515e8i	−1.26230	−	0.728789i
$783$		−	2.37224e7i		−	0.0494168i
$784$	−1.13124e8	−	1.44545e8i	−0.234750	−	0.299954i
$785$	9.77049e8			2.01980
$786$	−9.40560e7	+	1.62910e8i	−0.193695	+	0.335490i
$787$	6.26836e7	−	3.61904e7i	0.128597	−	0.0742454i	−0.434322	−	0.900758i	$-0.643012\pi$
$787$	6.26836e7	−	3.61904e7i	0.128597	−	0.0742454i	0.562918	+	0.826512i	$0.309679\pi$
$788$	1.25220e8	+	2.16888e8i	0.255916	+	0.443259i
$789$	2.23572e8	+	1.29080e8i	0.455184	+	0.262801i
$790$			1.92987e9i			3.91424i
$791$	5.04915e7	−	3.40874e7i	0.102021	−	0.0688754i
$792$	−7.34539e7			−0.147856
$793$	−1.34597e7	+	2.33129e7i	−0.0269909	+	0.0467495i
$794$	4.30616e8	−	2.48616e8i	0.860258	−	0.496670i
$795$	2.02064e8	+	3.49986e8i	0.402150	+	0.696545i
$796$	−4.74117e7	−	2.73732e7i	−0.0940040	−	0.0542733i
$797$			8.26919e8i			1.63338i	0.577075	+	0.816691i	$0.304194\pi$
$797$			8.26919e8i			1.63338i	−0.577075	+	0.816691i	$0.695806\pi$
$798$	−6.32288e7	−	8.98867e8i	−0.124425	−	1.76883i
$799$	2.03207e8			0.398382
$800$	−5.27333e8	+	9.13367e8i	−1.02995	+	1.78392i
$801$	−3.78540e7	+	2.18550e7i	−0.0736570	+	0.0425259i
$802$	2.06570e7	+	3.57789e7i	0.0400446	+	0.0693592i
$803$	9.15956e7	+	5.28827e7i	0.176900	+	0.102133i
$804$			2.49427e8i			0.479927i
$805$	−3.87428e8	+	7.95181e8i	−0.742683	+	1.52433i
$806$	7.00961e7			0.133872
$807$	4.26147e7	−	7.38109e7i	0.0810847	−	0.140443i
$808$	3.11881e8	−	1.80065e8i	0.591228	−	0.341346i
$809$	1.39404e8	+	2.41454e8i	0.263287	+	0.456026i	0.967113	−	0.254346i	$-0.0818602\pi$
$809$	1.39404e8	+	2.41454e8i	0.263287	+	0.456026i	−0.703827	+	0.710372i	$0.748527\pi$
$810$	−1.29198e8	−	7.45924e7i	−0.243109	−	0.140359i
$811$		−	8.06633e8i		−	1.51222i	−0.654447	−	0.756108i	$-0.727099\pi$
$811$		−	8.06633e8i		−	1.51222i	0.654447	−	0.756108i	$-0.272901\pi$
$812$	−1.77008e8	−	8.62420e7i	−0.330617	−	0.161083i
$813$	−2.90868e8			−0.541284
$814$	−8.59057e7	+	1.48793e8i	−0.159275	+	0.275873i
$815$	−5.95416e8	+	3.43764e8i	−1.09989	+	0.635020i
$816$	5.33441e7	+	9.23947e7i	0.0981784	+	0.170050i
$817$	−1.32562e9	−	7.65347e8i	−2.43082	−	1.40343i
$818$		−	1.29377e9i		−	2.36372i
$819$	2.28685e7	−	1.60863e6i	0.0416281	−	0.00292823i
$820$	−1.29824e9			−2.35458
$821$	5.29504e8	−	9.17127e8i	0.956840	−	1.65730i	0.226741	−	0.973955i	$-0.427193\pi$
$821$	5.29504e8	−	9.17127e8i	0.956840	−	1.65730i	0.730100	−	0.683341i	$-0.239474\pi$
$822$	7.91658e8	−	4.57064e8i	1.42535	−	0.822928i
$823$	5.41564e8	+	9.38017e8i	0.971517	+	1.68272i	0.690979	+	0.722875i	$0.257180\pi$
$823$	5.41564e8	+	9.38017e8i	0.971517	+	1.68272i	0.280538	+	0.959843i	$0.409487\pi$
$824$	−2.33162e8	−	1.34616e8i	−0.416751	−	0.240611i
$825$		−	3.46482e8i		−	0.617048i
$826$	6.71521e8	+	9.94683e8i	1.19157	+	1.76500i
$827$	−1.33362e8			−0.235785			−0.117892	−	0.993026i	$-0.537614\pi$
$827$	−1.33362e8			−0.235785			−0.117892	+	0.993026i	$0.537614\pi$
$828$	−1.41835e8	+	2.45666e8i	−0.249858	+	0.432767i
$829$	2.16051e8	−	1.24737e8i	0.379221	−	0.218944i	−0.298258	−	0.954485i	$-0.596406\pi$
$829$	2.16051e8	−	1.24737e8i	0.379221	−	0.218944i	0.677479	+	0.735542i	$0.263072\pi$
$830$	−1.08562e9	−	1.88035e9i	−1.89865	−	3.28855i
$831$	1.03073e8	+	5.95090e7i	0.179614	+	0.103700i
$832$		−	1.15140e8i		−	0.199921i
$833$	7.22511e7	+	5.11023e8i	0.125000	+	0.884109i
$834$	3.19558e8			0.550874
$835$	2.07132e8	−	3.58764e8i	0.355786	−	0.616239i
$836$	9.39067e8	−	5.42171e8i	1.60723	−	0.927934i
$837$	3.86874e7	+	6.70085e7i	0.0659770	+	0.114276i
$838$	2.62262e8	+	1.51417e8i	0.445660	+	0.257302i
$839$		−	4.92485e8i		−	0.833887i	−0.908932	−	0.416943i	$-0.863101\pi$
$839$		−	4.92485e8i		−	0.833887i	0.908932	−	0.416943i	$-0.136899\pi$
$840$	−3.09732e8	+	2.09104e8i	−0.522575	+	0.352796i
$841$	−5.55604e8			−0.934066
$842$	5.01056e8	−	8.67854e8i	0.839363	−	1.45382i
$843$	−3.86467e8	+	2.23127e8i	−0.645103	+	0.372450i
$844$	1.68480e8	+	2.91817e8i	0.280235	+	0.485381i
$845$	−8.33196e8	−	4.81046e8i	−1.38095	−	0.797291i
$846$		−	1.40440e8i		−	0.231942i
$847$	−2.41786e7	−	3.43725e8i	−0.0397906	−	0.565667i
$848$	−1.99739e8			−0.327548
$849$	−1.65947e8	+	2.87428e8i	−0.271173	+	0.469685i
$850$	1.20300e9	−	6.94550e8i	1.95888	−	1.13096i
$851$	1.00125e8	+	1.73422e8i	0.162463	+	0.281395i
$852$	−4.27808e8	−	2.46995e8i	−0.691720	−	0.399365i
$853$			6.41660e8i			1.03385i	0.856031	+	0.516925i	$0.172923\pi$
$853$			6.41660e8i			1.03385i	−0.856031	+	0.516925i	$0.827077\pi$
$854$	−1.83451e8	+	3.76525e8i	−0.294541	+	0.604533i
$855$	6.64659e8			1.06341
$856$	1.72180e8	−	2.98225e8i	0.274513	−	0.475470i
$857$	6.22262e8	−	3.59263e8i	0.988623	−	0.570782i	0.0837609	−	0.996486i	$-0.473307\pi$
$857$	6.22262e8	−	3.59263e8i	0.988623	−	0.570782i	0.904863	+	0.425704i	$0.139973\pi$
$858$	2.34243e7	+	4.05721e7i	0.0370856	+	0.0642341i
$859$	6.76979e8	+	3.90854e8i	1.06806	+	0.616645i	0.927651	−	0.373449i	$-0.121825\pi$
$859$	6.76979e8	+	3.90854e8i	1.06806	+	0.616645i	0.140409	+	0.990094i	$0.455158\pi$
$860$			2.10345e9i			3.30702i
$861$	3.36188e8	+	1.63797e8i	0.526711	+	0.256624i
$862$	−7.32253e8			−1.14325
$863$	−5.41290e8	+	9.37542e8i	−0.842166	+	1.45867i	0.0458932	+	0.998946i	$0.485387\pi$
$863$	−5.41290e8	+	9.37542e8i	−0.842166	+	1.45867i	−0.888060	+	0.459729i	$0.847947\pi$
$864$	1.36322e8	−	7.87057e7i	0.211361	−	0.122029i
$865$	3.18885e7	+	5.52325e7i	0.0492704	+	0.0853388i
$866$	1.63920e9	+	9.46391e8i	2.52393	+	1.45719i
$867$			7.62793e7i			0.117044i
$868$	6.40639e8	−	4.50643e7i	0.979613	−	0.0689087i
$869$	6.68969e8			1.01940
$870$	1.23321e8	−	2.13597e8i	0.187274	−	0.324368i
$871$	4.15795e7	−	2.40059e7i	0.0629252	−	0.0363299i
$872$	−2.51219e8	−	4.35124e8i	−0.378881	−	0.656241i
$873$	−7.15871e7	−	4.13308e7i	−0.107595	−	0.0621200i
$874$		−	2.14623e9i		−	3.21471i
$875$	−3.79104e8	−	5.61543e8i	−0.565892	−	0.838221i
$876$	1.72568e8			0.256712
$877$	1.21581e8	−	2.10585e8i	0.180247	−	0.312196i	−0.761718	−	0.647909i	$-0.775644\pi$
$877$	1.21581e8	−	2.10585e8i	0.180247	−	0.312196i	0.941964	+	0.335713i	$0.108977\pi$
$878$	−1.31423e9	+	7.58769e8i	−1.94172	+	1.12105i
$879$	1.34140e8	+	2.32337e8i	0.197511	+	0.342100i
$880$	2.39607e8	+	1.38337e8i	0.351603	+	0.202998i
$881$			1.21869e9i			1.78224i	0.453767	+	0.891120i	$0.350080\pi$
$881$			1.21869e9i			1.78224i	−0.453767	+	0.891120i	$0.649920\pi$
$882$	3.53176e8	−	4.99339e7i	0.514737	−	0.0727762i
$883$	5.63745e8			0.818842			0.409421	−	0.912346i	$-0.365731\pi$
$883$	5.63745e8			0.818842			0.409421	+	0.912346i	$0.365731\pi$
$884$	−5.53008e7	+	9.57838e7i	−0.0800525	+	0.138655i
$885$	−7.66644e8	+	4.42622e8i	−1.10602	+	0.638563i
$886$	−5.78051e8	−	1.00121e9i	−0.831123	−	1.43955i
$887$	−2.33059e8	−	1.34557e8i	−0.333961	−	0.192812i	0.323637	−	0.946181i	$-0.395094\pi$
$887$	−2.33059e8	−	1.34557e8i	−0.333961	−	0.192812i	−0.657598	+	0.753369i	$0.728428\pi$
$888$			8.46038e7i			0.120823i
$889$	2.62781e8	−	1.77406e8i	0.374015	−	0.252502i
$890$	−4.54451e8			−0.644639
$891$	−2.58566e7	+	4.47850e7i	−0.0365543	+	0.0633139i
$892$	−1.13698e9	+	6.56434e8i	−1.60198	+	0.924904i
$893$	3.12849e8	+	5.41870e8i	0.439319	+	0.760923i
$894$	−7.79406e8	−	4.49990e8i	−1.09082	−	0.629782i
$895$		−	8.14860e8i		−	1.13662i
$896$	−6.16957e7	−	8.77072e8i	−0.0857691	−	1.21930i
$897$	5.46033e7			0.0756557
$898$	1.50201e8	−	2.60155e8i	0.207416	−	0.359255i
$899$	−1.10782e8	+	6.39602e7i	−0.152472	+	0.0880300i
$900$	−2.82661e8	−	4.89583e8i	−0.387738	−	0.671582i
$901$	4.86385e8	+	2.80815e8i	0.664976	+	0.383924i
$902$			7.64224e8i			1.04136i
$903$	2.65389e8	−	5.44701e8i	0.360429	−	0.739767i
$904$	6.13042e7			0.0829823
$905$	−1.55741e8	+	2.69750e8i	−0.210114	+	0.363929i
$906$	−7.56638e8	+	4.36845e8i	−1.01743	+	0.587412i
$907$	−3.93227e8	−	6.81089e8i	−0.527013	−	0.912814i	−0.999504	−	0.0314782i	$-0.989979\pi$
$907$	−3.93227e8	−	6.81089e8i	−0.527013	−	0.912814i	0.472491	−	0.881335i	$-0.343355\pi$
$908$	2.40621e8	+	1.38923e8i	0.321423	+	0.185573i
$909$		−	2.53540e8i		−	0.337562i
$910$	2.14271e8	+	1.04397e8i	0.284341	+	0.138537i
$911$	1.05328e9			1.39312			0.696559	−	0.717500i	$-0.254713\pi$
$911$	1.05328e9			1.39312			0.696559	+	0.717500i	$0.254713\pi$
$912$	−1.64252e8	+	2.84493e8i	−0.216534	+	0.375048i
$913$	−6.51803e8	+	3.76319e8i	−0.856454	+	0.494474i
$914$	4.05984e8	+	7.03185e8i	0.531705	+	0.920939i
$915$	−2.67552e8	−	1.54471e8i	−0.349257	−	0.201643i
$916$			5.73886e8i			0.746688i
$917$	3.30934e8	−	2.32788e7i	0.429173	−	0.0301892i
$918$	−2.07327e8			−0.267995
$919$	−5.81563e8	+	1.00730e9i	−0.749290	+	1.29781i	0.198873	+	0.980025i	$0.436272\pi$
$919$	−5.81563e8	+	1.00730e9i	−0.749290	+	1.29781i	−0.948163	+	0.317784i	$0.897061\pi$
$920$	−7.70856e8	+	4.45054e8i	−0.989943	+	0.571544i
$921$	−3.20540e8	−	5.55191e8i	−0.410301	−	0.710663i
$922$	1.31845e9	+	7.61209e8i	1.68218	+	0.971206i
$923$			9.50875e7i			0.120926i
$924$	2.40169e8	+	3.55747e8i	0.304439	+	0.450947i
$925$	−3.99076e8			−0.504232
$926$	−1.64058e8	+	2.84156e8i	−0.206616	+	0.357869i
$927$	−1.64152e8	+	9.47731e7i	−0.206066	+	0.118972i
$928$	1.30121e8	+	2.25376e8i	0.162818	+	0.282009i
$929$	−1.01867e9	−	5.88131e8i	−1.27054	−	0.733545i	−0.295448	−	0.955359i	$-0.595469\pi$
$929$	−1.01867e9	−	5.88131e8i	−1.27054	−	0.733545i	−0.975089	+	0.221814i	$0.928802\pi$
$930$			8.04461e8i			1.00013i
$931$	−1.25145e9	+	9.79411e8i	−1.55083	+	1.21371i
$932$	−1.08597e9			−1.34143
$933$	8.89276e7	−	1.54027e8i	0.109494	−	0.189650i
$934$	−6.63144e8	+	3.82866e8i	−0.813893	+	0.469901i
$935$	−3.88980e8	−	6.73733e8i	−0.475874	−	0.824239i
$936$	1.99786e7	+	1.15347e7i	0.0243634	+	0.0140662i
$937$		−	4.63976e8i		−	0.563997i	−0.959415	−	0.281999i	$-0.909003\pi$
$937$		−	4.63976e8i		−	0.563997i	0.959415	−	0.281999i	$-0.0909974\pi$
$938$	6.19129e8	−	4.17981e8i	0.750192	−	0.506463i
$939$	−1.67436e7			−0.0202233
$940$	4.29911e8	−	7.44627e8i	0.517600	−	0.896510i
$941$	−1.01174e9	+	5.84130e8i	−1.21423	+	0.701036i	−0.963678	−	0.267067i	$-0.913946\pi$
$941$	−1.01174e9	+	5.84130e8i	−1.21423	+	0.701036i	−0.250552	+	0.968103i	$0.580612\pi$
$942$	−4.69210e8	−	8.12695e8i	−0.561325	−	0.972243i
$943$	7.71390e8	+	4.45362e8i	0.919896	+	0.531102i
$944$		−	4.37528e8i		−	0.520103i
$945$	1.84616e7	+	2.62452e8i	0.0218763	+	0.310995i
$946$	1.23822e9			1.46259
$947$	−2.84555e8	+	4.92863e8i	−0.335055	+	0.580332i	−0.983495	−	0.180934i	$-0.942088\pi$
$947$	−2.84555e8	+	4.92863e8i	−0.335055	+	0.580332i	0.648441	+	0.761265i	$0.275421\pi$
$948$	9.45262e8	−	5.45747e8i	1.10950	−	0.640570i
$949$	−1.66086e7	−	2.87670e7i	−0.0194328	−	0.0336586i
$950$	3.70415e9	+	2.13859e9i	4.32034	+	2.49435i
$951$		−	3.08645e8i		−	0.358853i
$952$	−2.27477e8	+	4.66887e8i	−0.263649	+	0.541129i
$953$	5.61708e8			0.648981			0.324491	−	0.945889i	$-0.394807\pi$
$953$	5.61708e8			0.648981			0.324491	+	0.945889i	$0.394807\pi$
$954$	1.94075e8	−	3.36148e8i	0.223525	−	0.387156i
$955$	7.50098e8	−	4.33069e8i	0.861208	−	0.497219i
$956$	−1.96726e8	−	3.40739e8i	−0.225158	−	0.389985i
$957$	−7.40411e7	−	4.27477e7i	−0.0844768	−	0.0487727i
$958$		−	2.41132e9i		−	2.74258i
$959$	−1.44928e9	−	7.06117e8i	−1.64322	−	0.800609i
$960$	1.32141e9			1.49357
$961$	−2.35135e8	+	4.07266e8i	−0.264940	+	0.458889i
$962$	4.67307e7	−	2.69800e7i	0.0524901	−	0.0303052i
$963$	−1.21219e8	−	2.09958e8i	−0.135735	−	0.235100i
$964$	−1.25916e9	−	7.26978e8i	−1.40556	−	0.811503i
$965$		−	1.30534e9i		−	1.45259i
$966$	8.47475e8	−	5.96137e7i	0.940146	−	0.0661325i
$967$	6.95843e8			0.769541			0.384771	−	0.923012i	$-0.374281\pi$
$967$	6.95843e8			0.769541			0.384771	+	0.923012i	$0.374281\pi$
$968$	1.73372e8	−	3.00289e8i	0.191140	−	0.331065i
$969$	7.99944e8	−	4.61848e8i	0.879201	−	0.507607i
$970$	−4.29714e8	−	7.44287e8i	−0.470831	−	0.815503i
$971$	−7.65735e8	−	4.42097e8i	−0.836413	−	0.482903i	0.0196301	−	0.999807i	$-0.493751\pi$
$971$	−7.65735e8	−	4.42097e8i	−0.836413	−	0.482903i	−0.856043	+	0.516904i	$0.827084\pi$
$972$			8.43757e7i			0.0918795i
$973$	−3.15337e8	−	4.67089e8i	−0.342323	−	0.507062i
$974$	1.85119e7			0.0200343
$975$	−5.44090e7	+	9.42392e7i	−0.0587026	+	0.101676i
$976$	1.32236e8	−	7.63466e7i	0.142233	−	0.0821184i
$977$	1.79936e8	+	3.11659e8i	0.192946	+	0.334192i	0.946225	−	0.323509i	$-0.104863\pi$
$977$	1.79936e8	+	3.11659e8i	0.192946	+	0.334192i	−0.753279	+	0.657701i	$0.771529\pi$
$978$	5.71875e8	+	3.30172e8i	0.611343	+	0.352959i
$979$			1.57530e8i			0.167887i
$980$	2.02543e9	+	8.16379e8i	2.15199	+	0.867388i
$981$	−3.53728e8			−0.374682
$982$	−8.31760e8	+	1.44065e9i	−0.878342	+	1.52133i
$983$	−4.76200e7	+	2.74934e7i	−0.0501336	+	0.0289446i	−0.524857	−	0.851190i	$-0.675881\pi$
$983$	−4.76200e7	+	2.74934e7i	−0.0501336	+	0.0289446i	0.474724	+	0.880135i	$0.342548\pi$
$984$	1.88161e8	+	3.25904e8i	0.197489	+	0.342061i
$985$	4.79128e8	+	2.76625e8i	0.501352	+	0.289456i
$986$		−	3.42764e8i		−	0.357573i
$987$	−2.05277e8	+	1.38584e8i	−0.213495	+	0.144133i
$988$	−3.40554e8			−0.353114
$989$	7.21589e8	−	1.24983e9i	0.745935	−	1.29200i
$990$	−4.65627e8	+	2.68830e8i	−0.479880	+	0.277059i
$991$	−1.53556e8	−	2.65967e8i	−0.157778	−	0.273280i	0.776289	−	0.630377i	$-0.217100\pi$
$991$	−1.53556e8	−	2.65967e8i	−0.157778	−	0.273280i	−0.934067	+	0.357098i	$0.883766\pi$
$992$	−7.35101e8	−	4.24411e8i	−0.753029	−	0.434762i
$993$		−	2.98241e8i		−	0.304593i
$994$	1.03813e8	+	1.47581e9i	0.105704	+	1.50270i
$995$	−1.20940e8			−0.122773
$996$	−6.14004e8	+	1.06349e9i	−0.621431	+	1.07635i
$997$	1.03839e9	−	5.99516e8i	1.04779	−	0.604945i	0.125764	−	0.992060i	$-0.459862\pi$
$997$	1.03839e9	−	5.99516e8i	1.04779	−	0.604945i	0.922031	+	0.387116i	$0.126529\pi$
$998$	−9.41879e8	−	1.63138e9i	−0.947553	−	1.64121i
$999$	5.15831e7	+	2.97815e7i	0.0517382	+	0.0298711i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.7.f.b.19.1	yes	8
3.2	odd	2		63.7.m.c.19.4		8
4.3	odd	2		336.7.bh.b.145.1		8
7.2	even	3		147.7.d.a.97.8		8
7.3	odd	6	inner	21.7.f.b.10.1	✓	8
7.4	even	3		147.7.f.a.31.1		8
7.5	odd	6		147.7.d.a.97.7		8
7.6	odd	2		147.7.f.a.19.1		8
21.2	odd	6		441.7.d.d.244.1		8
21.5	even	6		441.7.d.d.244.2		8
21.17	even	6		63.7.m.c.10.4		8
28.3	even	6		336.7.bh.b.241.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.7.f.b.10.1	✓	8	7.3	odd	6	inner
21.7.f.b.19.1	yes	8	1.1	even	1	trivial
63.7.m.c.10.4		8	21.17	even	6
63.7.m.c.19.4		8	3.2	odd	2
147.7.d.a.97.7		8	7.5	odd	6
147.7.d.a.97.8		8	7.2	even	3
147.7.f.a.19.1		8	7.6	odd	2
147.7.f.a.31.1		8	7.4	even	3
336.7.bh.b.145.1		8	4.3	odd	2
336.7.bh.b.241.1		8	28.3	even	6
441.7.d.d.244.1		8	21.2	odd	6
441.7.d.d.244.2		8	21.5	even	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.f (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-6.23828 + 10.8050i) q^{2} +(13.5000 - 7.79423i) q^{3} +(-45.8323 - 79.3839i) q^{4} +(-175.367 - 101.248i) q^{5} +194.490i q^{6} +(284.280 - 191.921i) q^{7} +345.159 q^{8} +(121.500 - 210.444i) q^{9} +O(q^{10})\)	\(q+(-6.23828 + 10.8050i) q^{2} +(13.5000 - 7.79423i) q^{3} +(-45.8323 - 79.3839i) q^{4} +(-175.367 - 101.248i) q^{5} +194.490i q^{6} +(284.280 - 191.921i) q^{7} +345.159 q^{8} +(121.500 - 210.444i) q^{9} +(2187.98 - 1263.23i) q^{10} +(-437.884 - 758.438i) q^{11} +(-1237.47 - 714.455i) q^{12} +275.049i q^{13} +(300.287 + 4268.91i) q^{14} -3156.61 q^{15} +(780.069 - 1351.12i) q^{16} +(-3799.10 + 2193.41i) q^{17} +(1515.90 + 2625.62i) q^{18} +(-11697.8 - 6753.75i) q^{19} +18561.8i q^{20} +(2341.91 - 4806.68i) q^{21} +10926.6 q^{22} +(6367.61 - 11029.0i) q^{23} +(4659.64 - 2690.25i) q^{24} +(12689.9 + 21979.6i) q^{25} +(-2971.91 - 1715.83i) q^{26} -3788.00i q^{27} +(-28264.6 - 13771.1i) q^{28} +6262.53 q^{29} +(19691.8 - 34107.2i) q^{30} +(-17689.7 + 10213.2i) q^{31} +(20777.7 + 35988.0i) q^{32} +(-11822.9 - 6825.94i) q^{33} -54732.5i q^{34} +(-69285.1 + 4873.70i) q^{35} -22274.5 q^{36} +(-7862.08 + 13617.5i) q^{37} +(145949. - 84263.6i) q^{38} +(2143.79 + 3713.16i) q^{39} +(-60529.5 - 34946.7i) q^{40} +69941.8i q^{41} +(37326.8 + 55289.8i) q^{42} +113322. q^{43} +(-40138.5 + 69521.9i) q^{44} +(-42614.2 + 24603.3i) q^{45} +(79445.9 + 137604. i) q^{46} +(-40116.2 - 23161.1i) q^{47} -24320.1i q^{48} +(43981.8 - 109119. i) q^{49} -316653. q^{50} +(-34191.9 + 59222.2i) q^{51} +(21834.4 - 12606.1i) q^{52} +(-64013.2 - 110874. i) q^{53} +(40929.4 + 23630.6i) q^{54} +177340. i q^{55} +(98121.9 - 66243.2i) q^{56} -210561. q^{57} +(-39067.4 + 67666.8i) q^{58} +(242870. - 140221. i) q^{59} +(144675. + 250584. i) q^{60} +(84759.3 + 48935.8i) q^{61} -254850. i q^{62} +(-5848.55 - 83143.6i) q^{63} -418619. q^{64} +(27848.2 - 48234.5i) q^{65} +(147509. - 85164.3i) q^{66} +(-87278.8 - 151171. i) q^{67} +(348243. + 201058. i) q^{68} -198522. i q^{69} +(379559. - 779030. i) q^{70} +345712. q^{71} +(41936.8 - 72636.7i) q^{72} +(-104589. + 60384.4i) q^{73} +(-98091.8 - 169900. i) q^{74} +(342627. + 197816. i) q^{75} +1.23816e6i q^{76} +(-270042. - 131570. i) q^{77} -53494.3 q^{78} +(-381933. + 661527. i) q^{79} +(-273597. + 157961. i) q^{80} +(-29524.5 - 51137.9i) q^{81} +(-755722. - 436316. i) q^{82} -859402. i q^{83} +(-488908. + 34391.1i) q^{84} +888317. q^{85} +(-706933. + 1.22444e6i) q^{86} +(84544.2 - 48811.6i) q^{87} +(-151140. - 261781. i) q^{88} +(-155778. - 89938.3i) q^{89} -613930. i q^{90} +(52787.6 + 78190.9i) q^{91} -1.16737e6 q^{92} +(-159207. + 275755. i) q^{93} +(500512. - 288971. i) q^{94} +(1.36761e6 + 2.36877e6i) q^{95} +(560997. + 323892. i) q^{96} -340171. i q^{97} +(904659. + 1.15594e6i) q^{98} -212812. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 5 q^{2} + 108 q^{3} - 173 q^{4} - 42 q^{5} + 748 q^{7} - 454 q^{8} + 972 q^{9}+O(q^{10}) \) 8 * q - 5 * q^2 + 108 * q^3 - 173 * q^4 - 42 * q^5 + 748 * q^7 - 454 * q^8 + 972 * q^9	\( 8 q - 5 q^{2} + 108 q^{3} - 173 q^{4} - 42 q^{5} + 748 q^{7} - 454 q^{8} + 972 q^{9} + 261 q^{10} - 1070 q^{11} - 4671 q^{12} + 6070 q^{14} - 756 q^{15} + 3911 q^{16} + 7212 q^{17} + 1215 q^{18} - 24606 q^{19} + 8154 q^{21} - 78 q^{22} - 15224 q^{23} - 6129 q^{24} + 22274 q^{25} - 19044 q^{26} - 3415 q^{28} + 32524 q^{29} + 2349 q^{30} + 40200 q^{31} + 70203 q^{32} - 28890 q^{33} - 242436 q^{35} - 84078 q^{36} - 45670 q^{37} + 503310 q^{38} + 93366 q^{39} - 94941 q^{40} + 55161 q^{42} - 445660 q^{43} - 188829 q^{44} - 10206 q^{45} + 525804 q^{46} + 82884 q^{47} + 24116 q^{49} - 1218884 q^{50} + 64908 q^{51} + 722856 q^{52} - 13034 q^{53} + 32805 q^{54} + 127061 q^{56} - 442908 q^{57} - 159501 q^{58} + 1810362 q^{59} + 429705 q^{60} - 392856 q^{61} + 38394 q^{63} - 1410446 q^{64} - 389004 q^{65} - 1053 q^{66} + 384094 q^{67} - 1616346 q^{68} + 406005 q^{70} + 225688 q^{71} - 55161 q^{72} + 903078 q^{73} + 1185530 q^{74} + 601398 q^{75} - 327674 q^{77} - 342792 q^{78} - 559592 q^{79} + 847713 q^{80} - 236196 q^{81} + 347634 q^{82} - 879444 q^{84} + 1953576 q^{85} - 2302402 q^{86} + 439074 q^{87} + 304887 q^{88} - 1770036 q^{89} - 2960718 q^{91} - 113064 q^{92} + 361800 q^{93} - 1837620 q^{94} + 1160112 q^{95} + 1895481 q^{96} + 5732467 q^{98} - 520020 q^{99}+O(q^{100}) \) 8 * q - 5 * q^2 + 108 * q^3 - 173 * q^4 - 42 * q^5 + 748 * q^7 - 454 * q^8 + 972 * q^9 + 261 * q^10 - 1070 * q^11 - 4671 * q^12 + 6070 * q^14 - 756 * q^15 + 3911 * q^16 + 7212 * q^17 + 1215 * q^18 - 24606 * q^19 + 8154 * q^21 - 78 * q^22 - 15224 * q^23 - 6129 * q^24 + 22274 * q^25 - 19044 * q^26 - 3415 * q^28 + 32524 * q^29 + 2349 * q^30 + 40200 * q^31 + 70203 * q^32 - 28890 * q^33 - 242436 * q^35 - 84078 * q^36 - 45670 * q^37 + 503310 * q^38 + 93366 * q^39 - 94941 * q^40 + 55161 * q^42 - 445660 * q^43 - 188829 * q^44 - 10206 * q^45 + 525804 * q^46 + 82884 * q^47 + 24116 * q^49 - 1218884 * q^50 + 64908 * q^51 + 722856 * q^52 - 13034 * q^53 + 32805 * q^54 + 127061 * q^56 - 442908 * q^57 - 159501 * q^58 + 1810362 * q^59 + 429705 * q^60 - 392856 * q^61 + 38394 * q^63 - 1410446 * q^64 - 389004 * q^65 - 1053 * q^66 + 384094 * q^67 - 1616346 * q^68 + 406005 * q^70 + 225688 * q^71 - 55161 * q^72 + 903078 * q^73 + 1185530 * q^74 + 601398 * q^75 - 327674 * q^77 - 342792 * q^78 - 559592 * q^79 + 847713 * q^80 - 236196 * q^81 + 347634 * q^82 - 879444 * q^84 + 1953576 * q^85 - 2302402 * q^86 + 439074 * q^87 + 304887 * q^88 - 1770036 * q^89 - 2960718 * q^91 - 113064 * q^92 + 361800 * q^93 - 1837620 * q^94 + 1160112 * q^95 + 1895481 * q^96 + 5732467 * q^98 - 520020 * q^99

Introduction

L-functions

Modular forms

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