LMFDB - Embedded newform 21.7.f.a.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} + 473x^{5} + 39800x^{4} + 36821x^{3} + 985651x^{2} - 601290x + 21068100 $ x^8 - x^7 + 212x^6 + 473x^5 + 39800x^4 + 36821x^3 + 985651x^2 - 601290x + 21068100
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3\cdot 7 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.1
Root			$7.29767 - 12.6399i$ of defining polynomial
Character	$\chi$	$=$	21.19
Dual form			21.7.f.a.10.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.79767 + 13.5060i) q^{2} +(-13.5000 + 7.79423i) q^{3} +(-89.6073 - 155.204i) q^{4} +(22.3721 + 12.9165i) q^{5} -243.107i q^{6} +(-203.121 + 276.389i) q^{7} +1796.81 q^{8} +(121.500 - 210.444i) q^{9} +O(q^{10})$	\(q+(-7.79767 + 13.5060i) q^{2} +(-13.5000 + 7.79423i) q^{3} +(-89.6073 - 155.204i) q^{4} +(22.3721 + 12.9165i) q^{5} -243.107i q^{6} +(-203.121 + 276.389i) q^{7} +1796.81 q^{8} +(121.500 - 210.444i) q^{9} +(-348.901 + 201.438i) q^{10} +(-311.967 - 540.343i) q^{11} +(2419.40 + 1396.84i) q^{12} -3257.26i q^{13} +(-2149.03 - 4898.53i) q^{14} -402.698 q^{15} +(-8276.07 + 14334.6i) q^{16} +(275.246 - 158.913i) q^{17} +(1894.83 + 3281.95i) q^{18} +(-5196.73 - 3000.33i) q^{19} -4629.67i q^{20} +(587.891 - 5314.42i) q^{21} +9730.47 q^{22} +(21.0083 - 36.3874i) q^{23} +(-24256.9 + 14004.8i) q^{24} +(-7478.83 - 12953.7i) q^{25} +(43992.4 + 25399.0i) q^{26} +3788.00i q^{27} +(61097.9 + 6758.77i) q^{28} -24273.4 q^{29} +(3140.11 - 5438.82i) q^{30} +(-17547.8 + 10131.2i) q^{31} +(-71570.2 - 123963. i) q^{32} +(8423.12 + 4863.09i) q^{33} +4956.62i q^{34} +(-8114.24 + 3559.79i) q^{35} -43549.2 q^{36} +(8688.57 - 15049.0i) q^{37} +(81044.8 - 46791.2i) q^{38} +(25387.8 + 43973.0i) q^{39} +(40198.5 + 23208.6i) q^{40} +100535. i q^{41} +(67192.2 + 49380.2i) q^{42} -67873.7 q^{43} +(-55909.1 + 96837.4i) q^{44} +(5436.42 - 3138.72i) q^{45} +(327.631 + 567.474i) q^{46} +(57039.5 + 32931.8i) q^{47} -258022. i q^{48} +(-35132.9 - 112281. i) q^{49} +233270. q^{50} +(-2477.21 + 4290.66i) q^{51} +(-505541. + 291874. i) q^{52} +(-49611.0 - 85928.8i) q^{53} +(-51160.5 - 29537.5i) q^{54} -16118.2i q^{55} +(-364970. + 496619. i) q^{56} +93541.1 q^{57} +(189276. - 327835. i) q^{58} +(87190.7 - 50339.6i) q^{59} +(36084.7 + 62500.5i) q^{60} +(-201092. - 116101. i) q^{61} -315999. i q^{62} +(33485.3 + 76326.9i) q^{63} +1.17299e6 q^{64} +(42072.6 - 72871.8i) q^{65} +(-131361. + 75841.5i) q^{66} +(-20544.0 - 35583.3i) q^{67} +(-49328.1 - 28479.6i) q^{68} +654.974i q^{69} +(15193.8 - 137349. i) q^{70} -400361. q^{71} +(218313. - 378128. i) q^{72} +(479106. - 276612. i) q^{73} +(135501. + 234695. i) q^{74} +(201928. + 116583. i) q^{75} +1.07541e6i q^{76} +(212712. + 23530.6i) q^{77} -791864. q^{78} +(5240.77 - 9077.28i) q^{79} +(-370306. + 213797. i) q^{80} +(-29524.5 - 51137.9i) q^{81} +(-1.35782e6 - 783939. i) q^{82} +712797. i q^{83} +(-877501. + 384968. i) q^{84} +8210.45 q^{85} +(529257. - 916700. i) q^{86} +(327691. - 189192. i) q^{87} +(-560546. - 970895. i) q^{88} +(-164942. - 95229.2i) q^{89} +97898.8i q^{90} +(900271. + 661617. i) q^{91} -7529.99 q^{92} +(157930. - 273543. i) q^{93} +(-889550. + 513582. i) q^{94} +(-77507.9 - 134248. i) q^{95} +(1.93239e6 + 1.11567e6i) q^{96} +1.07270e6i q^{97} +(1.79041e6 + 401025. i) q^{98} -151616. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 5 q^{2} - 108 q^{3} - 173 q^{4} - 294 q^{5} - 656 q^{7} + 3326 q^{8} + 972 q^{9}+O(q^{10}) $ 8 * q - 5 * q^2 - 108 * q^3 - 173 * q^4 - 294 * q^5 - 656 * q^7 + 3326 * q^8 + 972 * q^9	\( 8 q - 5 q^{2} - 108 q^{3} - 173 q^{4} - 294 q^{5} - 656 q^{7} + 3326 q^{8} + 972 q^{9} - 3411 q^{10} - 314 q^{11} + 4671 q^{12} - 5360 q^{14} + 5292 q^{15} - 12721 q^{16} - 5532 q^{17} + 1215 q^{18} - 18234 q^{19} + 9342 q^{21} + 86106 q^{22} + 3928 q^{23} - 44901 q^{24} - 17038 q^{25} + 12366 q^{26} + 85037 q^{28} - 8300 q^{29} + 30699 q^{30} - 89508 q^{31} - 186207 q^{32} + 8478 q^{33} - 25860 q^{35} - 84078 q^{36} + 64706 q^{37} - 77136 q^{38} + 29106 q^{39} + 221823 q^{40} + 173583 q^{42} + 45740 q^{43} + 92529 q^{44} - 71442 q^{45} - 111504 q^{46} + 483276 q^{47} - 310684 q^{49} + 967216 q^{50} + 49788 q^{51} - 1673988 q^{52} - 540974 q^{53} - 32805 q^{54} - 241885 q^{56} + 328212 q^{57} + 539799 q^{58} - 181770 q^{59} - 146367 q^{60} + 418224 q^{61} - 92826 q^{63} + 2378626 q^{64} - 414204 q^{65} - 1162431 q^{66} - 1158902 q^{67} - 821250 q^{68} + 1087917 q^{70} + 1442344 q^{71} + 404109 q^{72} - 378666 q^{73} - 432940 q^{74} + 460026 q^{75} + 1065994 q^{77} - 222588 q^{78} + 611452 q^{79} - 2094945 q^{80} - 236196 q^{81} - 1561266 q^{82} - 1579716 q^{84} - 275112 q^{85} + 816224 q^{86} + 112050 q^{87} - 366441 q^{88} - 989196 q^{89} + 304446 q^{91} + 678720 q^{92} + 805572 q^{93} - 716148 q^{94} - 591792 q^{95} + 5027589 q^{96} + 3509629 q^{98} - 152604 q^{99}+O(q^{100}) \) 8 * q - 5 * q^2 - 108 * q^3 - 173 * q^4 - 294 * q^5 - 656 * q^7 + 3326 * q^8 + 972 * q^9 - 3411 * q^10 - 314 * q^11 + 4671 * q^12 - 5360 * q^14 + 5292 * q^15 - 12721 * q^16 - 5532 * q^17 + 1215 * q^18 - 18234 * q^19 + 9342 * q^21 + 86106 * q^22 + 3928 * q^23 - 44901 * q^24 - 17038 * q^25 + 12366 * q^26 + 85037 * q^28 - 8300 * q^29 + 30699 * q^30 - 89508 * q^31 - 186207 * q^32 + 8478 * q^33 - 25860 * q^35 - 84078 * q^36 + 64706 * q^37 - 77136 * q^38 + 29106 * q^39 + 221823 * q^40 + 173583 * q^42 + 45740 * q^43 + 92529 * q^44 - 71442 * q^45 - 111504 * q^46 + 483276 * q^47 - 310684 * q^49 + 967216 * q^50 + 49788 * q^51 - 1673988 * q^52 - 540974 * q^53 - 32805 * q^54 - 241885 * q^56 + 328212 * q^57 + 539799 * q^58 - 181770 * q^59 - 146367 * q^60 + 418224 * q^61 - 92826 * q^63 + 2378626 * q^64 - 414204 * q^65 - 1162431 * q^66 - 1158902 * q^67 - 821250 * q^68 + 1087917 * q^70 + 1442344 * q^71 + 404109 * q^72 - 378666 * q^73 - 432940 * q^74 + 460026 * q^75 + 1065994 * q^77 - 222588 * q^78 + 611452 * q^79 - 2094945 * q^80 - 236196 * q^81 - 1561266 * q^82 - 1579716 * q^84 - 275112 * q^85 + 816224 * q^86 + 112050 * q^87 - 366441 * q^88 - 989196 * q^89 + 304446 * q^91 + 678720 * q^92 + 805572 * q^93 - 716148 * q^94 - 591792 * q^95 + 5027589 * q^96 + 3509629 * q^98 - 152604 * 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 $

$2$	−7.79767	+	13.5060i	−0.974709	+	1.68825i	−0.293816	+	0.955862i	$0.594925\pi$
$2$	−7.79767	+	13.5060i	−0.974709	+	1.68825i	−0.680893	+	0.732383i	$0.738408\pi$
$3$	−13.5000	+	7.79423i	−0.500000	+	0.288675i
$3$	−13.5000	+	7.79423i	−0.500000	+	0.288675i
$4$	−89.6073	−	155.204i	−1.40011	−	2.42507i
$5$	22.3721	+	12.9165i	0.178977	+	0.103332i	0.586812	−	0.809723i	$-0.300383\pi$
$5$	22.3721	+	12.9165i	0.178977	+	0.103332i	−0.407835	+	0.913056i	$0.633716\pi$
$6$		−	243.107i		−	1.12550i
$7$	−203.121	+	276.389i	−0.592189	+	0.805799i
$7$	−203.121	+	276.389i	−0.592189	+	0.805799i
$8$	1796.81			3.50940
$9$	121.500	−	210.444i	0.166667	−	0.288675i
$10$	−348.901	+	201.438i	−0.348901	+	0.201438i
$11$	−311.967	−	540.343i	−0.234386	−	0.405968i	0.724708	−	0.689056i	$-0.241975\pi$
$11$	−311.967	−	540.343i	−0.234386	−	0.405968i	−0.959094	+	0.283088i	$0.908641\pi$
$12$	2419.40	+	1396.84i	1.40011	+	0.808356i
$13$		−	3257.26i		−	1.48259i	−0.671177	−	0.741297i	$-0.734211\pi$
$13$		−	3257.26i		−	1.48259i	0.671177	−	0.741297i	$-0.265789\pi$
$14$	−2149.03	−	4898.53i	−0.783175	−	1.78518i
$15$	−402.698			−0.119318
$16$	−8276.07	+	14334.6i	−2.02053	+	3.49965i
$17$	275.246	−	158.913i	0.0560240	−	0.0323455i	−0.471726	−	0.881745i	$-0.656369\pi$
$17$	275.246	−	158.913i	0.0560240	−	0.0323455i	0.527750	+	0.849400i	$0.323036\pi$
$18$	1894.83	+	3281.95i	0.324903	+	0.562748i
$19$	−5196.73	−	3000.33i	−0.757651	−	0.437430i	0.0708006	−	0.997490i	$-0.477445\pi$
$19$	−5196.73	−	3000.33i	−0.757651	−	0.437430i	−0.828452	+	0.560060i	$0.810778\pi$
$20$		−	4629.67i		−	0.578709i
$21$	587.891	−	5314.42i	0.0634803	−	0.573850i
$22$	9730.47			0.913831
$23$	21.0083	−	36.3874i	0.00172666	−	0.00299067i	−0.865161	−	0.501495i	$-0.832784\pi$
$23$	21.0083	−	36.3874i	0.00172666	−	0.00299067i	0.866887	+	0.498504i	$0.166117\pi$
$24$	−24256.9	+	14004.8i	−1.75470	+	1.01308i
$25$	−7478.83	−	12953.7i	−0.478645	−	0.829037i
$26$	43992.4	+	25399.0i	2.50298	+	1.44510i
$27$			3788.00i			0.192450i
$28$	61097.9	+	6758.77i	2.78325	+	0.307888i
$29$	−24273.4			−0.995260			−0.497630	−	0.867389i	$-0.665796\pi$
$29$	−24273.4			−0.995260			−0.497630	+	0.867389i	$0.665796\pi$
$30$	3140.11	−	5438.82i	0.116300	−	0.201438i
$31$	−17547.8	+	10131.2i	−0.589030	+	0.340076i	−0.764714	−	0.644370i	$-0.777120\pi$
$31$	−17547.8	+	10131.2i	−0.589030	+	0.340076i	0.175684	+	0.984447i	$0.443786\pi$
$32$	−71570.2	−	123963.i	−2.18415	−	3.78306i
$33$	8423.12	+	4863.09i	0.234386	+	0.135323i
$34$			4956.62i			0.126110i
$35$	−8114.24	+	3559.79i	−0.189253	+	0.0830272i
$36$	−43549.2			−0.933409
$37$	8688.57	−	15049.0i	0.171531	−	0.297101i	−0.767424	−	0.641140i	$-0.778462\pi$
$37$	8688.57	−	15049.0i	0.171531	−	0.297101i	0.938955	+	0.344039i	$0.111795\pi$
$38$	81044.8	−	46791.2i	1.47698	−	0.852734i
$39$	25387.8	+	43973.0i	0.427988	+	0.741297i
$40$	40198.5	+	23208.6i	0.628101	+	0.362634i
$41$			100535.i			1.45870i	0.684141	+	0.729350i	$0.260177\pi$
$41$			100535.i			1.45870i	−0.684141	+	0.729350i	$0.739823\pi$
$42$	67192.2	+	49380.2i	0.906924	+	0.666507i
$43$	−67873.7			−0.853682			−0.426841	−	0.904327i	$-0.640374\pi$
$43$	−67873.7			−0.853682			−0.426841	+	0.904327i	$0.640374\pi$
$44$	−55909.1	+	96837.4i	−0.656333	+	1.13680i
$45$	5436.42	−	3138.72i	0.0596590	−	0.0344441i
$46$	327.631	+	567.474i	0.00336598	+	0.00583006i
$47$	57039.5	+	32931.8i	0.549392	+	0.317191i	0.748877	−	0.662709i	$-0.230594\pi$
$47$	57039.5	+	32931.8i	0.549392	+	0.317191i	−0.199485	+	0.979901i	$0.563927\pi$
$48$		−	258022.i		−	2.33310i
$49$	−35132.9	−	112281.i	−0.298624	−	0.954371i
$50$	233270.			1.86616
$51$	−2477.21	+	4290.66i	−0.0186747	+	0.0323455i
$52$	−505541.	+	291874.i	−3.59539	+	2.07580i
$53$	−49611.0	−	85928.8i	−0.333235	−	0.577180i	0.649909	−	0.760012i	$-0.274807\pi$
$53$	−49611.0	−	85928.8i	−0.333235	−	0.577180i	−0.983144	+	0.182832i	$0.941474\pi$
$54$	−51160.5	−	29537.5i	−0.324903	−	0.187583i
$55$		−	16118.2i		−	0.0968785i
$56$	−364970.	+	496619.i	−2.07823	+	2.82787i
$57$	93541.1			0.505101
$58$	189276.	−	327835.i	0.970088	−	1.68024i
$59$	87190.7	−	50339.6i	0.424536	−	0.245106i	−0.272480	−	0.962161i	$-0.587844\pi$
$59$	87190.7	−	50339.6i	0.424536	−	0.245106i	0.697016	+	0.717055i	$0.254511\pi$
$60$	36084.7	+	62500.5i	0.167059	+	0.289354i
$61$	−201092.	−	116101.i	−0.885943	−	0.511499i	−0.0133295	−	0.999911i	$-0.504243\pi$
$61$	−201092.	−	116101.i	−0.885943	−	0.511499i	−0.872613	+	0.488412i	$0.837576\pi$
$62$		−	315999.i		−	1.32590i
$63$	33485.3	+	76326.9i	0.133916	+	0.305250i
$64$	1.17299e6			4.47458
$65$	42072.6	−	72871.8i	0.153200	−	0.265350i
$66$	−131361.	+	75841.5i	−0.456916	+	0.263800i
$67$	−20544.0	−	35583.3i	−0.0683063	−	0.118310i	0.829850	−	0.557987i	$-0.188426\pi$
$67$	−20544.0	−	35583.3i	−0.0683063	−	0.118310i	−0.898156	+	0.439677i	$0.855093\pi$
$68$	−49328.1	−	28479.6i	−0.156880	−	0.0905747i
$69$			654.974i			0.00199378i
$70$	15193.8	−	137349.i	0.0442967	−	0.400433i
$71$	−400361.			−1.11861			−0.559303	−	0.828963i	$-0.688931\pi$
$71$	−400361.			−1.11861			−0.559303	+	0.828963i	$0.688931\pi$
$72$	218313.	−	378128.i	0.584899	−	1.01308i
$73$	479106.	−	276612.i	1.23158	−	0.711054i	0.264223	−	0.964462i	$-0.414885\pi$
$73$	479106.	−	276612.i	1.23158	−	0.711054i	0.967360	+	0.253407i	$0.0815513\pi$
$74$	135501.	+	234695.i	0.334386	+	0.579173i
$75$	201928.	+	116583.i	0.478645	+	0.276346i
$76$			1.07541e6i			2.44981i
$77$	212712.	+	23530.6i	0.465929	+	0.0515420i
$78$	−791864.			−1.66866
$79$	5240.77	−	9077.28i	0.0106295	−	0.0184109i	−0.860662	−	0.509177i	$-0.829950\pi$
$79$	5240.77	−	9077.28i	0.0106295	−	0.0184109i	0.871291	+	0.490766i	$0.163283\pi$
$80$	−370306.	+	213797.i	−0.723255	+	0.417571i
$81$	−29524.5	−	51137.9i	−0.0555556	−	0.0962250i
$82$	−1.35782e6	−	783939.i	−2.46264	−	1.42181i
$83$			712797.i			1.24661i	0.781978	+	0.623306i	$0.214211\pi$
$83$			712797.i			1.24661i	−0.781978	+	0.623306i	$0.785789\pi$
$84$	−877501.	+	384968.i	−1.48050	+	0.649511i
$85$	8210.45			0.0133693
$86$	529257.	−	916700.i	0.832091	−	1.44122i
$87$	327691.	−	189192.i	0.497630	−	0.287307i
$88$	−560546.	−	970895.i	−0.822552	−	1.42470i
$89$	−164942.	−	95229.2i	−0.233970	−	0.135083i	0.378432	−	0.925629i	$-0.376463\pi$
$89$	−164942.	−	95229.2i	−0.233970	−	0.135083i	−0.612402	+	0.790546i	$0.709797\pi$
$90$			97898.8i			0.134292i
$91$	900271.	+	661617.i	1.19467	+	0.877976i
$92$	−7529.99			−0.00967009
$93$	157930.	−	273543.i	0.196343	−	0.340076i
$94$	−889550.	+	513582.i	−1.07099	+	0.618339i
$95$	−77507.9	−	134248.i	−0.0904014	−	0.156580i
$96$	1.93239e6	+	1.11567e6i	2.18415	+	1.26102i
$97$			1.07270e6i			1.17533i	0.809103	+	0.587667i	$0.199954\pi$
$97$			1.07270e6i			1.17533i	−0.809103	+	0.587667i	$0.800046\pi$
$98$	1.79041e6	+	401025.i	1.90228	+	0.426082i
$99$	−151616.			−0.156257
$100$	−1.34031e6	+	2.32149e6i	−1.34031	+	2.32149i
$101$	−461204.	+	266276.i	−0.447640	+	0.258445i	−0.706833	−	0.707380i	$-0.749877\pi$
$101$	−461204.	+	266276.i	−0.447640	+	0.258445i	0.259193	+	0.965826i	$0.416544\pi$
$102$	−38633.0	−	66914.3i	−0.0364047	−	0.0630548i
$103$	904654.	+	522302.i	0.827886	+	0.477980i	0.853128	−	0.521701i	$-0.174702\pi$
$103$	904654.	+	522302.i	0.827886	+	0.477980i	−0.0252420	+	0.999681i	$0.508036\pi$
$104$		−	5.85268e6i		−	5.20301i
$105$	81796.4	−	111301.i	0.0706588	−	0.0961463i
$106$	1.54740e6			1.29923
$107$	−179422.	+	310767.i	−0.146461	+	0.253679i	−0.929917	−	0.367769i	$-0.880122\pi$
$107$	−179422.	+	310767.i	−0.146461	+	0.253679i	0.783456	+	0.621448i	$0.213455\pi$
$108$	587914.	−	339432.i	0.466705	−	0.269452i
$109$	−376187.	−	651575.i	−0.290485	−	0.503136i	0.683439	−	0.730007i	$-0.260483\pi$
$109$	−376187.	−	651575.i	−0.290485	−	0.503136i	−0.973925	+	0.226872i	$0.927150\pi$
$110$	217691.	+	125684.i	0.163555	+	0.0944283i
$111$			270883.i			0.198067i
$112$	−2.28088e6	−	5.19907e6i	−1.62348	−	3.70059i
$113$	−2.37249e6			−1.64425			−0.822126	−	0.569306i	$-0.807212\pi$
$113$	−2.37249e6			−1.64425			−0.822126	+	0.569306i	$0.807212\pi$
$114$	−729403.	+	1.26336e6i	−0.492326	+	0.852734i
$115$	940.000	−	542.709i	0.000618065	−	0.000356840i
$116$	2.17507e6	+	3.76734e6i	1.39348	+	2.41357i
$117$	−685471.	−	395757.i	−0.427988	−	0.247099i
$118$			1.57013e6i			0.955627i
$119$	−11986.3	+	108354.i	−0.00711285	+	0.0642987i
$120$	−723572.			−0.418734
$121$	691133.	−	1.19708e6i	0.390127	−	0.675719i
$122$	3.13610e6	−	1.81063e6i	1.72707	−	0.997126i
$123$	−783593.	−	1.35722e6i	−0.421090	−	0.729350i
$124$	3.14482e6	+	1.81566e6i	1.64942	+	0.952291i
$125$		−	790045.i		−	0.404503i
$126$	−1.29197e6	−	142921.i	−0.645866	−	0.0714469i
$127$	−1.06403e6			−0.519447			−0.259724	−	0.965683i	$-0.583631\pi$
$127$	−1.06403e6			−0.519447			−0.259724	+	0.965683i	$0.583631\pi$
$128$	−4.56606e6	+	7.90865e6i	−2.17727	+	3.77114i
$129$	916295.	−	529023.i	0.426841	−	0.246437i
$130$	656136.	+	1.13646e6i	0.298651	+	0.517278i
$131$	−565054.	−	326234.i	−0.251348	−	0.145116i	0.369033	−	0.929416i	$-0.379689\pi$
$131$	−565054.	−	326234.i	−0.251348	−	0.145116i	−0.620382	+	0.784300i	$0.713022\pi$
$132$		−	1.74307e6i		−	0.757869i
$133$	1.88482e6	−	826889.i	0.801153	−	0.351473i
$134$	640782.			0.266315
$135$	−48927.8	+	84745.5i	−0.0198863	+	0.0344441i
$136$	494565.	−	285537.i	0.196610	−	0.113513i
$137$	−2.29875e6	−	3.98155e6i	−0.893985	−	1.54843i	−0.835056	−	0.550165i	$-0.814565\pi$
$137$	−2.29875e6	−	3.98155e6i	−0.893985	−	1.54843i	−0.0589291	−	0.998262i	$-0.518769\pi$
$138$	−8846.05	−	5107.27i	−0.00336598	−	0.00194335i
$139$			1.96781e6i			0.732720i	0.930473	+	0.366360i	$0.119396\pi$
$139$			1.96781e6i			0.732720i	−0.930473	+	0.366360i	$0.880604\pi$
$140$	1.27959e6	+	940382.i	0.466323	+	0.342705i
$141$	−1.02671e6			−0.366261
$142$	3.12189e6	−	5.40726e6i	1.09031	−	1.88848i
$143$	−1.76004e6	+	1.01616e6i	−0.601886	+	0.347499i
$144$	2.01109e6	+	3.48330e6i	0.673508	+	1.16655i
$145$	−543047.	−	313528.i	−0.178129	−	0.102843i
$146$			8.62772e6i			2.77228i
$147$	1.34944e6	+	1.24196e6i	0.424815	+	0.390980i
$148$	−3.11424e6			−0.960653
$149$	1.55562e6	−	2.69442e6i	0.470268	−	0.814529i	−0.529154	−	0.848526i	$-0.677490\pi$
$149$	1.55562e6	−	2.69442e6i	0.470268	−	0.814529i	0.999422	+	0.0339975i	$0.0108238\pi$
$150$	−3.14914e6	+	1.81816e6i	−0.933079	+	0.538713i
$151$	869607.	+	1.50620e6i	0.252576	+	0.437475i	0.964234	−	0.265051i	$-0.0853889\pi$
$151$	869607.	+	1.50620e6i	0.252576	+	0.437475i	−0.711658	+	0.702526i	$0.752056\pi$
$152$	−9.33754e6	−	5.39103e6i	−2.65890	−	1.53512i
$153$		−	77231.9i		−	0.0215637i
$154$	−1.97646e6	+	2.68940e6i	−0.541161	+	0.736364i
$155$	−523441.			−0.140564
$156$	4.54987e6	−	7.88061e6i	1.19846	−	2.07580i
$157$	−735252.	+	424498.i	−0.189993	+	0.109692i	−0.591979	−	0.805953i	$-0.701653\pi$
$157$	−735252.	+	424498.i	−0.189993	+	0.109692i	0.401986	+	0.915646i	$0.368320\pi$
$158$	81731.6	+	141563.i	0.0207214	+	0.0358905i
$159$	1.33950e6	+	773359.i	0.333235	+	0.192393i
$160$		−	3.69776e6i		−	0.902773i
$161$	5789.87	+	13197.5i	0.00138737	+	0.00316238i
$162$	920889.			0.216602
$163$	−671609.	+	1.16326e6i	−0.155079	+	0.268605i	−0.933088	−	0.359648i	$-0.882897\pi$
$163$	−671609.	+	1.16326e6i	−0.155079	+	0.268605i	0.778009	+	0.628254i	$0.216230\pi$
$164$	1.56035e7	−	9.00868e6i	3.53745	−	2.04235i
$165$	125629.	+	217595.i	0.0279664	+	0.0484393i
$166$	−9.62701e6	−	5.55815e6i	−2.10459	−	1.21508i
$167$			6.60321e6i			1.41777i	0.705324	+	0.708885i	$0.250801\pi$
$167$			6.60321e6i			1.41777i	−0.705324	+	0.708885i	$0.749199\pi$
$168$	1.05633e6	−	9.54901e6i	0.222778	−	2.01387i
$169$	−5.78293e6			−1.19809
$170$	−64022.4	+	110890.i	−0.0130312	+	0.0225707i
$171$	−1.26281e6	+	729081.i	−0.252550	+	0.145810i
$172$	6.08198e6	+	1.05343e7i	1.19525	+	2.07024i
$173$	8.15811e6	+	4.71008e6i	1.57562	+	0.909684i	0.995460	+	0.0951797i	$0.0303426\pi$
$173$	8.15811e6	+	4.71008e6i	1.57562	+	0.909684i	0.580158	+	0.814504i	$0.302991\pi$
$174$			5.90104e6i			1.12016i
$175$	5.09937e6	+	564102.i	0.951486	+	0.105255i
$176$	1.03275e7			1.89433
$177$	−784717.	+	1.35917e6i	−0.141512	+	0.245106i
$178$	2.57232e6	−	1.48513e6i	0.456106	−	0.263333i
$179$	1.50382e6	+	2.60470e6i	0.262203	+	0.454149i	0.966827	−	0.255432i	$-0.0822176\pi$
$179$	1.50382e6	+	2.60470e6i	0.262203	+	0.454149i	−0.704624	+	0.709581i	$0.748884\pi$
$180$	−974287.	−	562505.i	−0.167059	−	0.0964514i
$181$		−	8.77281e6i		−	1.47946i	−0.672904	−	0.739730i	$-0.734953\pi$
$181$		−	8.77281e6i		−	1.47946i	0.672904	−	0.739730i	$-0.265047\pi$
$182$	−1.59558e7	+	6.99995e6i	−2.64670	+	1.16113i
$183$	3.61966e6			0.590628
$184$	37747.9	−	65381.3i	0.00605954	−	0.0104954i
$185$	388763.	−	224453.i	0.0614002	−	0.0354494i
$186$	2.46297e6	+	4.26599e6i	0.382755	+	0.662951i
$187$	−171736.	−	99151.6i	−0.0262625	−	0.0151626i
$188$		−	1.18037e7i		−	1.77642i
$189$	−1.04696e6	−	769421.i	−0.155076	−	0.113967i
$190$	2.41752e6			0.352460
$191$	−720715.	+	1.24831e6i	−0.103434	+	0.179153i	−0.913097	−	0.407742i	$-0.866316\pi$
$191$	−720715.	+	1.24831e6i	−0.103434	+	0.179153i	0.809663	+	0.586895i	$0.199650\pi$
$192$	−1.58353e7	+	9.14252e6i	−2.23729	+	1.29170i
$193$	−851094.	−	1.47414e6i	−0.118387	−	0.205053i	0.800741	−	0.599010i	$-0.204439\pi$
$193$	−851094.	−	1.47414e6i	−0.118387	−	0.205053i	−0.919129	+	0.393957i	$0.871106\pi$
$194$	−1.44878e7	−	8.36453e6i	−1.98425	−	1.14561i
$195$			1.31169e6i			0.176900i
$196$	−1.42783e7	+	1.55140e7i	−1.89631	+	2.06041i
$197$	6.42619e6			0.840534			0.420267	−	0.907401i	$-0.361936\pi$
$197$	6.42619e6			0.840534			0.420267	+	0.907401i	$0.361936\pi$
$198$	1.18225e6	−	2.04772e6i	0.152305	−	0.263800i
$199$	−5.77106e6	+	3.33192e6i	−0.732312	+	0.422801i	−0.819267	−	0.573412i	$-0.805620\pi$
$199$	−5.77106e6	+	3.33192e6i	−0.732312	+	0.422801i	0.0869554	+	0.996212i	$0.472286\pi$
$200$	−1.34380e7	−	2.32754e7i	−1.67975	−	2.90942i
$201$	554689.	+	320250.i	0.0683063	+	0.0394367i
$202$		−	8.30534e6i		−	1.00764i
$203$	4.93043e6	−	6.70890e6i	0.589382	−	0.801979i
$204$	887906.			0.104587
$205$	−1.29857e6	+	2.24918e6i	−0.150731	+	0.261074i
$206$	−1.41084e7	+	8.14548e6i	−1.61390	+	0.931783i
$207$	−5105.01	−	8842.14i	−0.000575554	−	0.000996888i
$208$	4.66914e7	+	2.69573e7i	5.18856	+	2.99562i
$209$			3.74402e6i			0.410109i
$210$	865411.	+	1.97263e6i	0.0934468	+	0.213004i
$211$	1.06742e6			0.113629			0.0568144	−	0.998385i	$-0.481906\pi$
$211$	1.06742e6			0.113629			0.0568144	+	0.998385i	$0.481906\pi$
$212$	−8.89102e6	+	1.53997e7i	−0.933134	+	1.61624i
$213$	5.40488e6	−	3.12051e6i	0.559303	−	0.322914i
$214$	−2.79814e6	−	4.84652e6i	−0.285515	−	0.494526i
$215$	−1.51848e6	−	876694.i	−0.152789	−	0.0882130i
$216$			6.80631e6i			0.675384i
$217$	764162.	−	6.90788e6i	0.0747836	−	0.676029i
$218$	1.17335e7			1.13255
$219$	−4.31196e6	+	7.46853e6i	−0.410527	+	0.711054i
$220$	−2.50161e6	+	1.44431e6i	−0.234937	+	0.135641i
$221$	−517622.	−	896548.i	−0.0479552	−	0.0830609i
$222$	−3.65853e6	−	2.11225e6i	−0.334386	−	0.193058i
$223$		−	1.67396e7i		−	1.50949i	−0.656016	−	0.754747i	$-0.727760\pi$
$223$		−	1.67396e7i		−	1.50949i	0.656016	−	0.754747i	$-0.272240\pi$
$224$	4.87995e7	+	5.39829e6i	4.34181	+	0.480299i
$225$	−3.63471e6			−0.319097
$226$	1.84999e7	−	3.20427e7i	1.60267	−	2.77590i
$227$	1.64212e7	−	9.48080e6i	1.40387	−	0.810527i	0.409086	−	0.912496i	$-0.365847\pi$
$227$	1.64212e7	−	9.48080e6i	1.40387	−	0.810527i	0.994788	+	0.101969i	$0.0325141\pi$
$228$	−8.38197e6	−	1.45180e7i	−0.707199	−	1.22490i
$229$	−3.68706e6	−	2.12872e6i	−0.307025	−	0.177261i	0.338569	−	0.940941i	$-0.390057\pi$
$229$	−3.68706e6	−	2.12872e6i	−0.307025	−	0.177261i	−0.645594	+	0.763680i	$0.723390\pi$
$230$			16927.5i			0.00139126i
$231$	−3.05502e6	+	1.34026e6i	−0.247844	+	0.108731i
$232$	−4.36147e7			−3.49276
$233$	−6.08975e6	+	1.05478e7i	−0.481429	+	0.833859i	−0.999773	−	0.0213134i	$-0.993215\pi$
$233$	−6.08975e6	+	1.05478e7i	−0.481429	+	0.833859i	0.518344	+	0.855172i	$0.326549\pi$
$234$	1.06902e7	−	6.17197e6i	0.834328	−	0.481699i
$235$	850730.	+	1.47351e6i	0.0655523	+	0.113540i
$236$	−1.56259e7	−	9.02159e6i	−1.18880	−	0.686352i
$237$			163391.i			0.0122739i
$238$	−1.36995e6	−	1.00679e6i	−0.101619	−	0.0746808i
$239$	−1.03799e7			−0.760328			−0.380164	−	0.924919i	$-0.624132\pi$
$239$	−1.03799e7			−0.760328			−0.380164	+	0.924919i	$0.624132\pi$
$240$	3.33276e6	−	5.77251e6i	0.241085	−	0.417571i
$241$	−9.70985e6	+	5.60598e6i	−0.693683	+	0.400498i	−0.804990	−	0.593288i	$-0.797830\pi$
$241$	−9.70985e6	+	5.60598e6i	−0.693683	+	0.400498i	0.111307	+	0.993786i	$0.464496\pi$
$242$	1.07785e7	+	1.86688e7i	0.760520	+	1.31726i
$243$	797162.	+	460241.i	0.0555556	+	0.0320750i
$244$			4.16139e7i			2.86463i
$245$	664283.	−	2.96575e6i	0.0451705	−	0.201668i
$246$	2.44408e7			1.64176
$247$	−9.77286e6	+	1.69271e7i	−0.648531	+	1.12329i
$248$	−3.15300e7	+	1.82039e7i	−2.06714	+	1.19346i
$249$	−5.55570e6	−	9.62276e6i	−0.359866	−	0.623306i
$250$	1.06703e7	+	6.16051e6i	0.682900	+	0.394272i
$251$		−	2.63644e7i		−	1.66724i	−0.552341	−	0.833618i	$-0.686265\pi$
$251$		−	2.63644e7i		−	1.66724i	0.552341	−	0.833618i	$-0.313735\pi$
$252$	8.84574e6	−	1.20365e7i	0.552755	−	0.752140i
$253$	−26215.6			−0.00161882
$254$	8.29693e6	−	1.43707e7i	0.506310	−	0.876954i
$255$	−110841.	+	63994.1i	−0.00668467	+	0.00385940i
$256$	−3.36737e7	−	5.83246e7i	−2.00711	−	3.47642i
$257$	2.22833e7	+	1.28653e7i	1.31274	+	0.757913i	0.982550	−	0.186000i	$-0.0595525\pi$
$257$	2.22833e7	+	1.28653e7i	1.31274	+	0.757913i	0.330194	+	0.943913i	$0.392886\pi$
$258$			1.65006e7i			0.960816i
$259$	2.39456e6	+	5.45820e6i	0.137825	+	0.314159i
$260$	−1.50800e7			−0.857990
$261$	−2.94922e6	+	5.10819e6i	−0.165877	+	0.287307i
$262$	8.81221e6	−	5.08773e6i	0.489983	−	0.282892i
$263$	−8.45919e6	−	1.46517e7i	−0.465009	−	0.805420i	0.534193	−	0.845363i	$-0.320616\pi$
$263$	−8.45919e6	−	1.46517e7i	−0.465009	−	0.805420i	−0.999202	+	0.0399431i	$0.987282\pi$
$264$	1.51348e7	+	8.73805e6i	0.822552	+	0.474901i
$265$		−	2.56321e6i		−	0.137736i
$266$	−3.52930e6	+	3.19042e7i	−0.187518	+	1.69513i
$267$	2.96895e6			0.155980
$268$	−3.68179e6	+	6.37705e6i	−0.191273	+	0.331295i
$269$	−2.28580e7	+	1.31971e7i	−1.17431	+	0.677987i	−0.954691	−	0.297599i	$-0.903814\pi$
$269$	−2.28580e7	+	1.31971e7i	−1.17431	+	0.677987i	−0.219617	+	0.975586i	$0.570481\pi$
$270$	−763046.	−	1.32163e6i	−0.0387668	−	0.0671460i
$271$	5.51435e6	+	3.18371e6i	0.277068	+	0.159965i	0.632095	−	0.774891i	$-0.282195\pi$
$271$	5.51435e6	+	3.18371e6i	0.277068	+	0.159965i	−0.355027	+	0.934856i	$0.615528\pi$
$272$			5.26071e6i			0.261419i
$273$	−1.73105e7	−	1.91491e6i	−0.850786	−	0.0941156i
$274$	7.16996e7			3.48550
$275$	−4.66630e6	+	8.08227e6i	−0.224375	+	0.388629i
$276$	101655.	−	58690.4i	0.00483505	−	0.00279152i
$277$	1.72556e7	+	2.98876e7i	0.811878	+	1.40621i	0.911548	+	0.411194i	$0.134888\pi$
$277$	1.72556e7	+	2.98876e7i	0.811878	+	1.40621i	−0.0996696	+	0.995021i	$0.531779\pi$
$278$	−2.65771e7	−	1.53443e7i	−1.23701	−	0.714189i
$279$			4.92377e6i			0.226718i
$280$	−1.45797e7	+	6.39627e6i	−0.664165	+	0.291375i
$281$	4.02256e7			1.81294			0.906470	−	0.422270i	$-0.138767\pi$
$281$	4.02256e7			1.81294			0.906470	+	0.422270i	$0.138767\pi$
$282$	8.00595e6	−	1.38667e7i	0.356998	−	0.618339i
$283$	−2.53348e6	+	1.46270e6i	−0.111778	+	0.0645352i	−0.554847	−	0.831953i	$-0.687223\pi$
$283$	−2.53348e6	+	1.46270e6i	−0.111778	+	0.0645352i	0.443069	+	0.896488i	$0.353890\pi$
$284$	3.58753e7	+	6.21378e7i	1.56618	+	2.71270i
$285$	2.09271e6	+	1.20823e6i	0.0904014	+	0.0521933i
$286$		−	3.16947e7i		−	1.35484i
$287$	−2.77868e7	−	2.04208e7i	−1.17542	−	0.863826i
$288$	−3.47831e7			−1.45610
$289$	−1.20183e7	+	2.08163e7i	−0.497908	+	0.862401i
$290$	8.46900e6	−	4.88958e6i	0.347247	−	0.200483i
$291$	−8.36084e6	−	1.44814e7i	−0.339290	−	0.587667i
$292$	−8.58629e7	−	4.95730e7i	−3.44871	−	1.99111i
$293$			1.16741e7i			0.464109i	0.972703	+	0.232054i	$0.0745448\pi$
$293$			1.16741e7i			0.464109i	−0.972703	+	0.232054i	$0.925455\pi$
$294$	−2.72963e7	+	8.54105e6i	−1.07414	+	0.336101i
$295$	2.60086e6			0.101309
$296$	1.56117e7	−	2.70403e7i	0.601971	−	1.04264i
$297$	2.04682e6	−	1.18173e6i	0.0781286	−	0.0451075i
$298$	2.42605e7	+	4.20204e7i	0.916749	+	1.58786i
$299$	−118523.	−	68429.5i	−0.00443394	−	0.00255994i
$300$		−	4.17869e7i		−	1.54766i
$301$	1.37866e7	−	1.87596e7i	0.505541	−	0.687896i
$302$	−2.71236e7			−0.984753
$303$	4.15084e6	−	7.18947e6i	0.149213	−	0.258445i
$304$	8.60170e7	−	4.96619e7i	3.06171	−	1.76768i
$305$	−2.99924e6	−	5.19483e6i	−0.105709	−	0.183093i
$306$	1.04309e6	+	602229.i	0.0364047	+	0.0210183i
$307$		−	3.20193e7i		−	1.10661i	−0.832977	−	0.553307i	$-0.813366\pi$
$307$		−	3.20193e7i		−	1.10661i	0.832977	−	0.553307i	$-0.186634\pi$
$308$	−1.54085e7	−	3.51224e7i	−0.527361	−	1.20208i
$309$	−1.62838e7			−0.551924
$310$	4.08162e6	−	7.06958e6i	0.137009	−	0.237306i
$311$	2.10086e6	−	1.21293e6i	0.0698418	−	0.0403232i	−0.464672	−	0.885483i	$-0.653828\pi$
$311$	2.10086e6	−	1.21293e6i	0.0698418	−	0.0403232i	0.534514	+	0.845159i	$0.320495\pi$
$312$	4.56171e7	+	7.90112e7i	1.50198	+	2.60151i
$313$	2.43110e7	+	1.40359e7i	0.792810	+	0.457729i	0.840951	−	0.541112i	$-0.181996\pi$
$313$	2.43110e7	+	1.40359e7i	0.792810	+	0.457729i	−0.0481409	+	0.998841i	$0.515330\pi$
$314$		−	1.32404e7i		−	0.427673i
$315$	−236743.	+	2.14011e6i	−0.00757434	+	0.0684706i
$316$	−1.87845e6			−0.0595302
$317$	−3.84108e6	+	6.65294e6i	−0.120580	+	0.208851i	−0.919997	−	0.391927i	$-0.871809\pi$
$317$	−3.84108e6	+	6.65294e6i	−0.120580	+	0.208851i	0.799417	+	0.600777i	$0.205142\pi$
$318$	−2.08899e7	+	1.20608e7i	−0.649614	+	0.375055i
$319$	7.57251e6	+	1.31160e7i	0.233275	+	0.404044i
$320$	2.62422e7	+	1.51509e7i	0.800847	+	0.462369i
$321$		−	5.59381e6i		−	0.169119i
$322$	−223392.	−	24712.1i	−0.00669115	−	0.000740188i
$323$	−1.90717e6			−0.0565955
$324$	−5.29122e6	+	9.16466e6i	−0.155568	+	0.269452i
$325$	−4.21936e7	+	2.43605e7i	−1.22913	+	0.709636i
$326$	−1.04740e7	−	1.81414e7i	−0.302314	−	0.523624i
$327$	1.01571e7	+	5.86418e6i	0.290485	+	0.167712i
$328$			1.80642e8i			5.11916i
$329$	−2.06879e7	+	9.07597e6i	−0.580936	+	0.254862i
$330$	−3.91844e6			−0.109036
$331$	2.56402e7	−	4.44102e7i	0.707031	−	1.22461i	−0.258923	−	0.965898i	$-0.583368\pi$
$331$	2.56402e7	−	4.44102e7i	0.707031	−	1.22461i	0.965954	−	0.258715i	$-0.0832990\pi$
$332$	1.10629e8	−	6.38718e7i	3.02312	−	1.74540i
$333$	−2.11132e6	−	3.65692e6i	−0.0571770	−	0.0990335i
$334$	−8.91827e7	−	5.14896e7i	−2.39354	−	1.38191i
$335$		−	1.06143e6i		−	0.0282330i
$336$	7.13146e7	+	5.24097e7i	1.88001	+	1.38164i
$337$	1.62829e7			0.425443			0.212721	−	0.977113i	$-0.431767\pi$
$337$	1.62829e7			0.425443			0.212721	+	0.977113i	$0.431767\pi$
$338$	4.50934e7	−	7.81041e7i	1.16778	−	2.02266i
$339$	3.20286e7	−	1.84917e7i	0.822126	−	0.474655i
$340$	−735716.	−	1.27430e6i	−0.0187186	−	0.0324216i
$341$	1.09487e7	+	6.32122e6i	0.276120	+	0.159418i
$342$		−	2.27405e7i		−	0.568489i
$343$	3.81694e7	+	1.30962e7i	0.945873	+	0.324537i
$344$	−1.21956e8			−2.99591
$345$	−8460.00	+	14653.1i	−0.000206022	+	0.000356840i
$346$	−1.27228e8	+	7.34554e7i	−3.07154	+	1.77335i
$347$	−3.79000e7	−	6.56447e7i	−0.907091	−	1.57113i	−0.818086	−	0.575096i	$-0.804965\pi$
$347$	−3.79000e7	−	6.56447e7i	−0.907091	−	1.57113i	−0.0890043	−	0.996031i	$-0.528368\pi$
$348$	−5.87270e7	−	3.39060e7i	−1.39348	−	0.804524i
$349$		−	2.89740e7i		−	0.681605i	−0.940135	−	0.340802i	$-0.889301\pi$
$349$		−	2.89740e7i		−	0.681605i	0.940135	−	0.340802i	$-0.110699\pi$
$350$	−4.73819e7	+	6.44732e7i	−1.10512	+	1.50375i
$351$	1.23385e7			0.285325
$352$	−4.46551e7	+	7.73449e7i	−1.02387	+	1.77339i
$353$	5.10415e7	−	2.94688e7i	1.16038	−	0.669945i	0.208984	−	0.977919i	$-0.432984\pi$
$353$	5.10415e7	−	2.94688e7i	1.16038	−	0.669945i	0.951395	+	0.307974i	$0.0996511\pi$
$354$	−1.22379e7	−	2.11967e7i	−0.275866	−	0.477814i
$355$	−8.95693e6	−	5.17129e6i	−0.200205	−	0.115588i
$356$			3.41329e7i			0.756525i
$357$	−682718.	−	1.55620e6i	−0.0150050	−	0.0342027i
$358$	−4.69053e7			−1.02229
$359$	−3.87579e7	+	6.71306e7i	−0.837677	+	1.45090i	0.0541559	+	0.998532i	$0.482753\pi$
$359$	−3.87579e7	+	6.71306e7i	−0.837677	+	1.45090i	−0.891832	+	0.452366i	$0.850580\pi$
$360$	9.76823e6	−	5.63969e6i	0.209367	−	0.120878i
$361$	−5.51894e6	−	9.55909e6i	−0.117310	−	0.203187i
$362$	1.18485e8	+	6.84075e7i	2.49769	+	1.44204i
$363$			2.15474e7i			0.450479i
$364$	2.20151e7	−	1.99012e8i	0.456474	−	4.12643i
$365$	1.42915e7			0.293900
$366$	−2.82249e7	+	4.88870e7i	−0.575691	+	0.997126i
$367$	−3.58541e7	+	2.07004e7i	−0.725338	+	0.418774i	−0.816714	−	0.577042i	$-0.804207\pi$
$367$	−3.58541e7	+	2.07004e7i	−0.725338	+	0.418774i	0.0913764	+	0.995816i	$0.470873\pi$
$368$	347732.	+	602290.i	0.00697753	+	0.0120854i
$369$	2.11570e7	+	1.22150e7i	0.421090	+	0.243117i
$370$			7.00083e6i			0.138212i
$371$	3.38268e7	+	3.74199e6i	0.662429	+	0.0732791i
$372$	−5.66067e7			−1.09961
$373$	2.39688e7	−	4.15152e7i	0.461871	−	0.799983i	−0.537184	−	0.843465i	$-0.680512\pi$
$373$	2.39688e7	−	4.15152e7i	0.461871	−	0.799983i	0.999054	+	0.0434819i	$0.0138451\pi$
$374$	2.67827e6	−	1.54630e6i	0.0511965	−	0.0295583i
$375$	6.15779e6	+	1.06656e7i	0.116770	+	0.202251i
$376$	1.02489e8	+	5.91722e7i	1.92803	+	1.11315i
$377$			7.90647e7i			1.47557i
$378$	1.85556e7	−	8.14052e6i	0.343558	−	0.150722i
$379$	−1.73029e7			−0.317835			−0.158917	−	0.987292i	$-0.550800\pi$
$379$	−1.73029e7			−0.317835			−0.158917	+	0.987292i	$0.550800\pi$
$380$	−1.38905e7	+	2.40591e7i	−0.253145	+	0.438459i
$381$	1.43644e7	−	8.29327e6i	0.259724	−	0.149952i
$382$	−1.12398e7	−	1.94679e7i	−0.201636	−	0.349244i
$383$	−5.60339e7	−	3.23512e7i	−0.997365	−	0.575829i	−0.0898976	−	0.995951i	$-0.528654\pi$
$383$	−5.60339e7	−	3.23512e7i	−0.997365	−	0.575829i	−0.907468	+	0.420122i	$0.861987\pi$
$384$		−	1.42356e8i		−	2.51409i
$385$	4.45489e6	+	3.27394e6i	0.0780646	+	0.0573704i
$386$	2.65462e7			0.461573
$387$	−8.24665e6	+	1.42836e7i	−0.142280	+	0.246437i
$388$	1.66487e8	−	9.61214e7i	2.85027	−	1.64560i
$389$	3.97139e7	+	6.87865e7i	0.674673	+	1.16857i	0.976564	+	0.215226i	$0.0690488\pi$
$389$	3.97139e7	+	6.87865e7i	0.674673	+	1.16857i	−0.301891	+	0.953342i	$0.597618\pi$
$390$	−1.77157e7	−	1.02281e7i	−0.298651	−	0.172426i
$391$		−	13354.0i		−	0.000223399i
$392$	−6.31271e7	−	2.01747e8i	−1.04799	−	3.34927i
$393$	1.01710e7			0.167566
$394$	−5.01093e7	+	8.67919e7i	−0.819276	+	1.41903i
$395$	234494.	−	135385.i	0.00380488	−	0.00219675i
$396$	1.35859e7	+	2.35315e7i	0.218778	+	0.378934i
$397$	−2.19165e7	−	1.26535e7i	−0.350267	−	0.202227i	0.314536	−	0.949246i	$-0.398151\pi$
$397$	−2.19165e7	−	1.26535e7i	−0.350267	−	0.202227i	−0.664803	+	0.747019i	$0.731484\pi$
$398$		−	1.03925e8i		−	1.64843i
$399$	−1.90002e7	+	2.58537e7i	−0.299115	+	0.407010i
$400$	2.47581e8			3.86846
$401$	−5.65920e6	+	9.80202e6i	−0.0877651	+	0.152014i	−0.906566	−	0.422064i	$-0.861306\pi$
$401$	−5.65920e6	+	9.80202e6i	−0.0877651	+	0.152014i	0.818801	+	0.574077i	$0.194639\pi$
$402$	−8.65056e6	+	4.99440e6i	−0.133158	+	0.0768786i
$403$	3.30000e7	+	5.71577e7i	0.504195	+	0.873292i
$404$	8.26546e7	+	4.77206e7i	1.25350	+	0.723706i
$405$		−	1.52542e6i		−	0.0229628i
$406$	5.21643e7	+	1.18904e8i	0.779462	+	1.77672i
$407$	−1.08422e7			−0.160818
$408$	−4.45109e6	+	7.70951e6i	−0.0655368	+	0.113513i
$409$	−3.32964e7	+	1.92237e7i	−0.486661	+	0.280974i	−0.723188	−	0.690651i	$-0.757324\pi$
$409$	−3.32964e7	+	1.92237e7i	−0.486661	+	0.280974i	0.236527	+	0.971625i	$0.423991\pi$
$410$	−2.02516e7	−	3.50768e7i	−0.293838	−	0.508942i
$411$	6.20663e7	+	3.58340e7i	0.893985	+	0.516142i
$412$		−	1.87208e8i		−	2.67691i
$413$	−3.79694e6	+	3.43236e7i	−0.0538994	+	0.487240i
$414$	159229.			0.00224399
$415$	−9.20688e6	+	1.59468e7i	−0.128815	+	0.223115i
$416$	−4.03780e8	+	2.33123e8i	−5.60874	+	3.23821i
$417$	−1.53375e7	−	2.65654e7i	−0.211518	−	0.366360i
$418$	−5.05666e7	−	2.91947e7i	−0.692365	−	0.399737i
$419$			5.55673e7i			0.755401i	0.925928	+	0.377701i	$0.123285\pi$
$419$			5.55673e7i			0.755401i	−0.925928	+	0.377701i	$0.876715\pi$
$420$	−2.46040e7	−	2.72174e6i	−0.332092	−	0.0367366i
$421$	−9.27660e7			−1.24320			−0.621602	−	0.783333i	$-0.713518\pi$
$421$	−9.27660e7			−1.24320			−0.621602	+	0.783333i	$0.713518\pi$
$422$	−8.32339e6	+	1.44165e7i	−0.110755	+	0.191833i
$423$	1.38606e7	−	8.00242e6i	0.183131	−	0.105730i
$424$	−8.91416e7	−	1.54398e8i	−1.16945	−	2.02555i
$425$	−4.11703e6	−	2.37697e6i	−0.0536312	−	0.0309640i
$426$			9.73308e7i			1.25899i
$427$	7.29349e7	−	3.19972e7i	0.936811	−	0.410988i
$428$	6.43099e7			0.820251
$429$	1.58403e7	−	2.74363e7i	0.200629	−	0.347499i
$430$	2.36812e7	−	1.36723e7i	0.297850	−	0.171964i
$431$	−6.58699e7	−	1.14090e8i	−0.822726	−	1.42500i	−0.903645	−	0.428282i	$-0.859119\pi$
$431$	−6.58699e7	−	1.14090e8i	−0.822726	−	1.42500i	0.0809190	−	0.996721i	$-0.474215\pi$
$432$	−5.42993e7	−	3.13497e7i	−0.673508	−	0.388850i
$433$		−	9.64602e7i		−	1.18819i	−0.804396	−	0.594093i	$-0.797511\pi$
$433$		−	9.64602e7i		−	1.18819i	0.804396	−	0.594093i	$-0.202489\pi$
$434$	8.73388e7	+	6.41861e7i	1.06841	+	0.785184i
$435$	9.77485e6			0.118752
$436$	−6.74182e7	+	1.16772e8i	−0.813426	+	1.40889i
$437$	−218349.	+	126064.i	−0.00261641	+	0.00151059i
$438$	−6.72465e7	−	1.16474e8i	−0.800289	−	1.38614i
$439$	−8.41958e7	−	4.86105e7i	−0.995169	−	0.574561i	−0.0883535	−	0.996089i	$-0.528161\pi$
$439$	−8.41958e7	−	4.86105e7i	−0.995169	−	0.574561i	−0.906815	+	0.421528i	$0.861494\pi$
$440$		−	2.89613e7i		−	0.339985i
$441$	−2.78975e7	−	6.24861e6i	−0.325274	−	0.0728564i
$442$	1.61450e7			0.186970
$443$	8.31985e7	−	1.44104e8i	0.956983	−	1.65754i	0.227219	−	0.973844i	$-0.427037\pi$
$443$	8.31985e7	−	1.44104e8i	0.956983	−	1.65754i	0.729764	−	0.683699i	$-0.239630\pi$
$444$	4.20422e7	−	2.42731e7i	0.480326	−	0.277317i
$445$	−2.46006e6	−	4.26096e6i	−0.0279168	−	0.0483534i
$446$	2.26085e8	+	1.30530e8i	2.54840	+	1.47132i
$447$			4.84995e7i			0.543019i
$448$	−2.38258e8	+	3.24200e8i	−2.64980	+	3.60562i
$449$	−1.03969e8			−1.14859			−0.574294	−	0.818649i	$-0.694723\pi$
$449$	−1.03969e8			−1.14859			−0.574294	+	0.818649i	$0.694723\pi$
$450$	2.83423e7	−	4.90902e7i	0.311026	−	0.538713i
$451$	5.43234e7	−	3.13637e7i	0.592185	−	0.341898i
$452$	2.12592e8	+	3.68220e8i	2.30214	+	3.98742i
$453$	−2.34794e7	−	1.35558e7i	−0.252576	−	0.145825i
$454$			2.95713e8i			3.16011i
$455$	1.15952e7	+	2.64302e7i	0.123096	+	0.280586i
$456$	1.68076e8			1.77260
$457$	3.54494e7	−	6.14002e7i	0.371416	−	0.643311i	−0.618368	−	0.785889i	$-0.712206\pi$
$457$	3.54494e7	−	6.14002e7i	0.371416	−	0.643311i	0.989784	+	0.142578i	$0.0455391\pi$
$458$	5.75009e7	−	3.31982e7i	0.598520	−	0.345556i
$459$	601963.	+	1.04263e6i	0.00622489	+	0.0107818i
$460$	−168462.	−	97261.4i	−0.00173072	−	0.000999234i
$461$			2.94715e7i			0.300815i	0.988624	+	0.150408i	$0.0480586\pi$
$461$			2.94715e7i			0.300815i	−0.988624	+	0.150408i	$0.951941\pi$
$462$	5.72046e6	−	5.17119e7i	0.0580103	−	0.524402i
$463$	−7.67219e7			−0.772994			−0.386497	−	0.922291i	$-0.626315\pi$
$463$	−7.67219e7			−0.772994			−0.386497	+	0.922291i	$0.626315\pi$
$464$	2.00888e8	−	3.47949e8i	2.01095	−	3.48306i
$465$	7.06646e6	−	4.07982e6i	0.0702818	−	0.0405772i
$466$	−9.49717e7	−	1.64496e8i	−0.938505	−	1.62554i
$467$	−1.69532e8	−	9.78791e7i	−1.66456	−	0.961035i	−0.970494	−	0.241126i	$-0.922483\pi$
$467$	−1.69532e8	−	9.78791e7i	−1.66456	−	0.961035i	−0.694068	−	0.719910i	$-0.744183\pi$
$468$			1.41851e8i			1.38387i
$469$	1.40078e7	+	1.54956e6i	0.135784	+	0.0150207i
$470$	−2.65348e7			−0.255578
$471$	6.61727e6	−	1.14614e7i	0.0633310	−	0.109692i
$472$	1.56665e8	−	9.04507e7i	1.48986	−	0.860174i
$473$	2.11744e7	+	3.66751e7i	0.200091	+	0.346568i
$474$	−2.20675e6	−	1.27407e6i	−0.0207214	−	0.0119635i
$475$			8.97559e7i			0.837495i
$476$	1.78910e7	−	7.84895e6i	0.165888	−	0.0727764i
$477$	−2.41110e7			−0.222157
$478$	8.09393e7	−	1.40191e8i	0.741098	−	1.28362i
$479$	−2.78233e7	+	1.60638e7i	−0.253164	+	0.146164i	−0.621212	−	0.783642i	$-0.713360\pi$
$479$	−2.78233e7	+	1.60638e7i	−0.253164	+	0.146164i	0.368048	+	0.929807i	$0.380026\pi$
$480$	2.88212e7	+	4.99197e7i	0.260608	+	0.451387i
$481$	−4.90186e7	−	2.83009e7i	−0.440480	−	0.254311i
$482$		−	1.74854e8i		−	1.56148i
$483$	−181028.	−	133039.i	−0.00160658	−	0.00118069i
$484$	−2.47722e8			−2.18489
$485$	−1.38555e7	+	2.39985e7i	−0.121450	+	0.210358i
$486$	−1.24320e7	+	7.17762e6i	−0.108301	+	0.0625276i
$487$	8.66229e7	+	1.50035e8i	0.749973	+	1.29899i	0.947835	+	0.318762i	$0.103267\pi$
$487$	8.66229e7	+	1.50035e8i	0.749973	+	1.29899i	−0.197862	+	0.980230i	$0.563400\pi$
$488$	−3.61325e8	−	2.08611e8i	−3.10912	−	1.79505i
$489$		−	2.09387e7i		−	0.179070i
$490$	3.48755e7	+	3.20978e7i	0.296437	+	0.272826i
$491$	2.27726e7			0.192383			0.0961917	−	0.995363i	$-0.469334\pi$
$491$	2.27726e7			0.192383			0.0961917	+	0.995363i	$0.469334\pi$
$492$	−1.40431e8	+	2.43234e8i	−1.17915	+	2.04235i
$493$	−6.68115e6	+	3.85737e6i	−0.0557584	+	0.0321922i
$494$	−1.52411e8	−	2.63984e8i	−1.26426	−	2.18976i
$495$	−3.39197e6	−	1.95836e6i	−0.0279664	−	0.0161464i
$496$		−	3.35387e8i		−	2.74853i
$497$	8.13217e7	−	1.10656e8i	0.662426	−	0.901372i
$498$	1.73286e8			1.40306
$499$	7.15586e7	−	1.23943e8i	0.575917	−	0.997518i	−0.420024	−	0.907513i	$-0.637978\pi$
$499$	7.15586e7	−	1.23943e8i	0.575917	−	0.997518i	0.995941	−	0.0900050i	$-0.0286883\pi$
$500$	−1.22618e8	+	7.07938e7i	−0.980947	+	0.566350i
$501$	−5.14669e7	−	8.91433e7i	−0.409275	−	0.708885i
$502$	3.56077e8	+	2.05581e8i	2.81470	+	1.62507i
$503$			1.94323e8i			1.52693i	0.645848	+	0.763466i	$0.276504\pi$
$503$			1.94323e8i			1.52693i	−0.645848	+	0.763466i	$0.723496\pi$
$504$	6.01667e7	+	1.37145e8i	0.469964	+	1.07124i
$505$	−1.37575e7			−0.106823
$506$	204421.	−	354067.i	0.00157788	−	0.00273296i
$507$	7.80696e7	−	4.50735e7i	0.599043	−	0.345858i
$508$	9.53446e7	+	1.65142e8i	0.727286	+	1.25970i
$509$	−1.45925e7	−	8.42496e6i	−0.110656	−	0.0638873i	0.443651	−	0.896200i	$-0.353683\pi$
$509$	−1.45925e7	−	8.42496e6i	−0.110656	−	0.0638873i	−0.554307	+	0.832313i	$0.687016\pi$
$510$		−	1.99602e6i		−	0.0150472i
$511$	−2.08639e7	+	1.88606e8i	−0.156363	+	1.41349i
$512$	4.65851e8			3.47086
$513$	1.13652e7	−	1.96852e7i	0.0841835	−	0.145810i
$514$	−3.47515e8	+	2.00638e8i	−2.55909	+	1.47749i
$515$	1.34927e7	+	2.33700e7i	0.0987817	+	0.171095i
$516$	−1.64213e8	−	9.48087e7i	−1.19525	−	0.690079i
$517$		−	4.10946e7i		−	0.297381i
$518$	−9.23902e7	−	1.02204e7i	−0.664717	−	0.0735322i
$519$	−1.46846e8			−1.05041
$520$	7.55964e7	−	1.30937e8i	0.537640	−	0.931219i
$521$	5.01224e7	−	2.89382e7i	0.354421	−	0.204625i	−0.312210	−	0.950013i	$-0.601069\pi$
$521$	5.01224e7	−	2.89382e7i	0.354421	−	0.204625i	0.666631	+	0.745388i	$0.267736\pi$
$522$	−4.59940e7	−	7.96640e7i	−0.323363	−	0.560081i
$523$	2.20396e8	+	1.27246e8i	1.54063	+	0.889483i	0.998799	+	0.0489961i	$0.0156022\pi$
$523$	2.20396e8	+	1.27246e8i	1.54063	+	0.889483i	0.541831	+	0.840487i	$0.317731\pi$
$524$			1.16932e8i			0.812716i
$525$	−7.32382e7	+	3.21303e7i	−0.506127	+	0.222043i
$526$	2.63848e8			1.81299
$527$	−3.21997e6	+	5.57715e6i	−0.0219999	+	0.0381049i
$528$	−1.39421e8	+	8.04946e7i	−0.947164	+	0.546846i
$529$	7.40171e7	+	1.28201e8i	0.499994	+	0.866015i
$530$	3.46186e7	+	1.99871e7i	0.232532	+	0.134252i
$531$		−	2.44650e7i		−	0.163404i
$532$	−2.97231e8	−	2.18438e8i	−1.97405	−	1.45075i
$533$	3.27469e8			2.16266
$534$	−2.31509e7	+	4.00985e7i	−0.152035	+	0.263333i
$535$	−8.02808e6	+	4.63501e6i	−0.0524264	+	0.0302684i
$536$	−3.69137e7	−	6.39364e7i	−0.239714	−	0.415197i
$537$	−4.06033e7	−	2.34423e7i	−0.262203	−	0.151383i
$538$		−	4.11626e8i		−	2.64336i
$539$	−4.97099e7	+	5.40117e7i	−0.317451	+	0.344923i
$540$	1.75372e7			0.111373
$541$	3.10487e7	−	5.37779e7i	0.196088	−	0.339635i	−0.751168	−	0.660111i	$-0.770509\pi$
$541$	3.10487e7	−	5.37779e7i	0.196088	−	0.339635i	0.947257	+	0.320476i	$0.103843\pi$
$542$	−8.59981e7	+	4.96510e7i	−0.540121	+	0.311839i
$543$	6.83773e7	+	1.18433e8i	0.427083	+	0.739730i
$544$	−3.93988e7	−	2.27469e7i	−0.244730	−	0.141295i
$545$		−	1.94362e7i		−	0.120066i
$546$	1.60844e8	−	2.18862e8i	0.988159	−	1.34460i
$547$	7.72887e6			0.0472230			0.0236115	−	0.999721i	$-0.492484\pi$
$547$	7.72887e6			0.0472230			0.0236115	+	0.999721i	$0.492484\pi$
$548$	−4.11970e8	+	7.13553e8i	−2.50336	+	4.33595i
$549$	−4.88654e7	+	2.82124e7i	−0.295314	+	0.170500i
$550$	−7.27725e7	−	1.26046e8i	−0.437401	−	0.757600i
$551$	1.26142e8	+	7.28282e7i	0.754060	+	0.435357i
$552$			1.17686e6i			0.00699695i
$553$	1.44435e6	+	3.29228e6i	0.00854078	+	0.0194680i
$554$	−5.38214e8			−3.16538
$555$	−3.49887e6	+	6.06022e6i	−0.0204667	+	0.0354494i
$556$	3.05412e8	−	1.76330e8i	1.77690	−	1.02589i
$557$	−1.26683e7	−	2.19422e7i	−0.0733083	−	0.126974i	0.827041	−	0.562142i	$-0.190022\pi$
$557$	−1.26683e7	−	2.19422e7i	−0.0733083	−	0.126974i	−0.900349	+	0.435168i	$0.856689\pi$
$558$	−6.65003e7	−	3.83939e7i	−0.382755	−	0.220984i
$559$			2.21082e8i			1.26566i
$560$	1.61259e7	−	1.45775e8i	0.0918249	−	0.830079i
$561$	3.09124e6			0.0175083
$562$	−3.13666e8	+	5.43285e8i	−1.76709	+	3.06069i
$563$	6.59556e7	−	3.80795e7i	0.369596	−	0.213386i	−0.303686	−	0.952772i	$-0.598217\pi$
$563$	6.59556e7	−	3.80795e7i	0.369596	−	0.213386i	0.673282	+	0.739386i	$0.264884\pi$
$564$	9.20008e7	+	1.59350e8i	0.512807	+	0.888209i
$565$	−5.30775e7	−	3.06443e7i	−0.294283	−	0.169904i
$566$		−	4.56227e7i		−	0.251612i
$567$	2.01310e7	+	2.22693e6i	0.110437	+	0.0122168i
$568$	−7.19374e8			−3.92563
$569$	2.66483e7	−	4.61562e7i	0.144655	−	0.250549i	−0.784589	−	0.620016i	$-0.787126\pi$
$569$	2.66483e7	−	4.61562e7i	0.144655	−	0.250549i	0.929244	+	0.369466i	$0.120460\pi$
$570$	−3.26366e7	+	1.88427e7i	−0.176230	+	0.101746i
$571$	−2.05691e7	−	3.56267e7i	−0.110486	−	0.191367i	0.805480	−	0.592622i	$-0.201907\pi$
$571$	−2.05691e7	−	3.56267e7i	−0.110486	−	0.191367i	−0.915966	+	0.401255i	$0.868574\pi$
$572$	3.15425e8	+	1.82110e8i	1.68542	+	0.973076i
$573$		−	2.24697e7i		−	0.119435i
$574$	4.92474e8	−	2.16053e8i	2.60404	−	1.14242i
$575$	−628469.			−0.00330583
$576$	1.42518e8	−	2.46848e8i	0.745764	−	1.29170i
$577$	−7.59861e7	+	4.38706e7i	−0.395555	+	0.228374i	−0.684564	−	0.728953i	$-0.740007\pi$
$577$	−7.59861e7	+	4.38706e7i	−0.395555	+	0.228374i	0.289009	+	0.957326i	$0.406674\pi$
$578$	−1.87429e8	−	3.24637e8i	−0.970630	−	1.68118i
$579$	2.29795e7	+	1.32672e7i	0.118387	+	0.0683510i
$580$			1.12378e8i			0.575965i
$581$	−1.97009e8	−	1.44784e8i	−1.00452	−	0.738230i
$582$	2.60780e8			1.32284
$583$	−3.09540e7	+	5.36140e7i	−0.156211	+	0.270565i
$584$	8.60864e8	−	4.97020e8i	4.32211	−	2.49537i
$585$	−1.02236e7	−	1.77078e7i	−0.0510667	−	0.0884501i
$586$	−1.57670e8	−	9.10307e7i	−0.783530	−	0.452371i
$587$		−	4.55880e7i		−	0.225391i	−0.993630	−	0.112695i	$-0.964052\pi$
$587$		−	4.55880e7i		−	0.225391i	0.993630	−	0.112695i	$-0.0359485\pi$
$588$	7.18379e7	−	3.20727e8i	0.353363	−	1.57762i
$589$	1.21588e8			0.595039
$590$	−2.02806e7	+	3.51270e7i	−0.0987473	+	0.171035i
$591$	−8.67536e7	+	5.00872e7i	−0.420267	+	0.242641i
$592$	1.43814e8	+	2.49094e8i	0.693166	+	1.20060i
$593$	−1.25860e8	−	7.26654e7i	−0.603565	−	0.348468i	0.166878	−	0.985978i	$-0.446631\pi$
$593$	−1.25860e8	−	7.26654e7i	−0.603565	−	0.348468i	−0.770443	+	0.637509i	$0.779965\pi$
$594$			3.68590e7i			0.175867i
$595$	−1.66771e6	+	2.26928e6i	−0.00791718	+	0.0107730i
$596$	−5.57581e8			−2.63372
$597$	5.19395e7	−	8.99619e7i	0.244104	−	0.422801i
$598$	1.84841e6	−	1.06718e6i	0.00864361	−	0.00499039i
$599$	−2.81542e7	−	4.87645e7i	−0.130998	−	0.226894i	0.793064	−	0.609139i	$-0.208485\pi$
$599$	−2.81542e7	−	4.87645e7i	−0.130998	−	0.226894i	−0.924061	+	0.382244i	$0.875151\pi$
$600$	3.62827e8	+	2.09478e8i	1.67975	+	0.969807i
$601$		−	2.39440e8i		−	1.10299i	−0.834177	−	0.551497i	$-0.814057\pi$
$601$		−	2.39440e8i		−	1.10299i	0.834177	−	0.551497i	$-0.185943\pi$
$602$	1.45863e8	+	3.32482e8i	0.668582	+	1.52398i
$603$	−9.98439e6			−0.0455376
$604$	1.55846e8	−	2.69934e8i	0.707271	−	1.22503i
$605$	3.09242e7	−	1.78541e7i	0.139647	−	0.0806254i
$606$	6.47338e7	+	1.12122e8i	0.290879	+	0.503818i
$607$	−2.54893e8	−	1.47163e8i	−1.13970	−	0.658008i	−0.193347	−	0.981130i	$-0.561934\pi$
$607$	−2.54893e8	−	1.47163e8i	−1.13970	−	0.658008i	−0.946357	+	0.323122i	$0.895268\pi$
$608$			8.58938e8i			3.82165i
$609$	−1.42701e7	+	1.28999e8i	−0.0631794	+	0.571130i
$610$	9.35483e7			0.412141
$611$	1.07267e8	−	1.85792e8i	0.470266	−	0.814525i
$612$	−1.19867e7	+	6.92054e6i	−0.0522933	+	0.0301916i
$613$	−1.10391e8	−	1.91204e8i	−0.479241	−	0.830070i	0.520475	−	0.853877i	$-0.325755\pi$
$613$	−1.10391e8	−	1.91204e8i	−0.479241	−	0.830070i	−0.999717	+	0.0238066i	$0.992421\pi$
$614$	4.32451e8	+	2.49676e8i	1.86824	+	1.07863i
$615$		−	4.04853e7i		−	0.174049i
$616$	3.82203e8	+	4.22801e7i	1.63513	+	0.180881i
$617$	3.86786e8			1.64670			0.823352	−	0.567531i	$-0.192101\pi$
$617$	3.86786e8			1.64670			0.823352	+	0.567531i	$0.192101\pi$
$618$	1.26975e8	−	2.19928e8i	0.537965	−	0.931783i
$619$	1.13096e8	−	6.52959e7i	0.476842	−	0.275305i	−0.242257	−	0.970212i	$-0.577888\pi$
$619$	1.13096e8	−	6.52959e7i	0.476842	−	0.275305i	0.719100	+	0.694907i	$0.244554\pi$
$620$	4.69042e7	+	8.12404e7i	0.196805	+	0.340876i
$621$	137835.	+	79579.3i	0.000575554	+	0.000332296i
$622$			3.78321e7i			0.157213i
$623$	5.98234e7	−	2.62451e7i	0.247404	−	0.108538i
$624$	−8.40446e8			−3.45904
$625$	−1.06652e8	+	1.84727e8i	−0.436847	+	0.756641i
$626$	−3.79138e8	+	2.18895e8i	−1.54552	+	0.892305i
$627$	−2.91818e7	−	5.05443e7i	−0.118388	−	0.205055i
$628$	1.31768e8	+	7.60762e7i	0.532023	+	0.307164i
$629$		−	5.52292e6i		−	0.0221930i
$630$	−2.70582e7	−	1.98853e7i	−0.108212	−	0.0795262i
$631$	−1.10414e8			−0.439475			−0.219738	−	0.975559i	$-0.570520\pi$
$631$	−1.10414e8			−0.439475			−0.219738	+	0.975559i	$0.570520\pi$
$632$	9.41667e6	−	1.63102e7i	0.0373032	−	0.0646111i
$633$	−1.44102e7	+	8.31972e6i	−0.0568144	+	0.0328018i
$634$	−5.99029e7	−	1.03755e8i	−0.235061	−	0.407137i
$635$	−2.38045e7	−	1.37436e7i	−0.0929691	−	0.0536757i
$636$		−	2.77195e8i		−	1.07749i
$637$	−3.65728e8	+	1.14437e8i	−1.41494	+	0.442739i
$638$	−2.36192e8			−0.909499
$639$	−4.86439e7	+	8.42537e7i	−0.186434	+	0.322914i
$640$	−2.04305e8	+	1.17956e8i	−0.779362	+	0.449965i
$641$	2.56393e7	+	4.44085e7i	0.0973491	+	0.168614i	0.910587	−	0.413318i	$-0.135630\pi$
$641$	2.56393e7	+	4.44085e7i	0.0973491	+	0.168614i	−0.813238	+	0.581932i	$0.802297\pi$
$642$	7.55498e7	+	4.36187e7i	0.285515	+	0.164842i
$643$		−	2.95342e8i		−	1.11094i	−0.831535	−	0.555472i	$-0.812537\pi$
$643$		−	2.95342e8i		−	1.11094i	0.831535	−	0.555472i	$-0.187463\pi$
$644$	1.52950e6	−	2.08121e6i	0.00572652	−	0.00779215i
$645$	2.73326e7			0.101860
$646$	1.48715e7	−	2.57582e7i	0.0551642	−	0.0955472i
$647$	−2.54170e8	+	1.46745e8i	−0.938449	+	0.541814i	−0.889474	−	0.456986i	$-0.848929\pi$
$647$	−2.54170e8	+	1.46745e8i	−0.938449	+	0.541814i	−0.0489752	+	0.998800i	$0.515596\pi$
$648$	−5.30499e7	−	9.18852e7i	−0.194966	−	0.337692i
$649$	−5.44013e7	−	3.14086e7i	−0.199010	−	0.114899i
$650$		−	7.59820e8i		−	2.76675i
$651$	4.35254e7	+	9.92124e7i	0.157761	+	0.359603i
$652$	2.40724e8			0.868515
$653$	−1.58530e8	+	2.74583e8i	−0.569342	+	0.986129i	0.427289	+	0.904115i	$0.359469\pi$
$653$	−1.58530e8	+	2.74583e8i	−0.569342	+	0.986129i	−0.996631	+	0.0820143i	$0.973865\pi$
$654$	−1.58403e8	+	9.14538e7i	−0.566277	+	0.326940i
$655$	−8.42764e6	−	1.45971e7i	−0.0299904	−	0.0519449i
$656$	−1.44113e9	−	8.32035e8i	−5.10494	−	2.94734i
$657$		−	1.34434e8i		−	0.474036i
$658$	3.87377e7	−	3.50181e8i	0.135974	−	1.22918i
$659$	1.86604e8			0.652026			0.326013	−	0.945365i	$-0.394295\pi$
$659$	1.86604e8			0.652026			0.326013	+	0.945365i	$0.394295\pi$
$660$	2.25145e7	−	3.89962e7i	0.0783124	−	0.135641i
$661$	2.56295e8	−	1.47972e8i	0.887433	−	0.512359i	0.0143307	−	0.999897i	$-0.495438\pi$
$661$	2.56295e8	−	1.47972e8i	0.887433	−	0.512359i	0.873102	+	0.487538i	$0.162105\pi$
$662$	3.99868e8	+	6.92592e8i	1.37830	+	2.38728i
$663$	1.39758e7	+	8.06893e6i	0.0479552	+	0.0276870i
$664$			1.28076e9i			4.37486i
$665$	5.28480e7	+	5.84615e6i	0.179707	+	0.0198795i
$666$	6.58536e7			0.222924
$667$	−509942.	+	883246.i	−0.00171848	+	0.00297649i
$668$	1.02485e9	−	5.91696e8i	3.43819	−	1.98504i
$669$	1.30473e8	+	2.25985e8i	0.435753	+	0.754747i
$670$	1.43356e7	+	8.27669e6i	0.0476643	+	0.0275190i
$671$			1.44878e8i			0.479552i
$672$	−7.00868e8	+	3.07477e8i	−2.30956	+	1.01322i
$673$	1.17111e8			0.384197			0.192098	−	0.981376i	$-0.438471\pi$
$673$	1.17111e8			0.384197			0.192098	+	0.981376i	$0.438471\pi$
$674$	−1.26968e8	+	2.19916e8i	−0.414683	+	0.718252i
$675$	4.90686e7	−	2.83298e7i	0.159548	−	0.0921152i
$676$	5.18193e8	+	8.97537e8i	1.67746	+	2.90544i
$677$	−8.12613e7	−	4.69162e7i	−0.261889	−	0.151202i	0.363307	−	0.931670i	$-0.381648\pi$
$677$	−8.12613e7	−	4.69162e7i	−0.261889	−	0.151202i	−0.625196	+	0.780468i	$0.714981\pi$
$678$			5.76769e8i			1.85060i
$679$	−2.96482e8	−	2.17887e8i	−0.947084	−	0.696020i
$680$	1.47526e7			0.0469183
$681$	−1.47791e8	+	2.55982e8i	−0.467958	+	0.810527i
$682$	−1.70748e8	+	9.85815e7i	−0.538274	+	0.310772i
$683$	1.47967e8	+	2.56287e8i	0.464412	+	0.804385i	0.999175	−	0.0406170i	$-0.0129323\pi$
$683$	1.47967e8	+	2.56287e8i	0.464412	+	0.804385i	−0.534763	+	0.845002i	$0.679599\pi$
$684$	2.26313e8	+	1.30662e8i	0.707199	+	0.408301i
$685$		−	1.18768e8i		−	0.369510i
$686$	−4.74509e8	+	4.13394e8i	−1.46985	+	1.28054i
$687$	6.63671e7			0.204683
$688$	5.61728e8	−	9.72941e8i	1.72489	−	2.98759i
$689$	−2.79892e8	+	1.61596e8i	−0.855723	+	0.494052i
$690$	−131937.	−	228521.i	−0.000401622	−	0.000695630i
$691$	−9.29926e6	−	5.36893e6i	−0.0281848	−	0.0162725i	0.485841	−	0.874047i	$-0.338513\pi$
$691$	−9.29926e6	−	5.36893e6i	−0.0281848	−	0.0162725i	−0.514026	+	0.857774i	$0.671847\pi$
$692$		−	1.68823e9i		−	5.09464i
$693$	3.07964e7	−	4.19050e7i	0.0925338	−	0.125912i
$694$	1.18213e9			3.53660
$695$	−2.54173e7	+	4.40240e7i	−0.0757137	+	0.131140i
$696$	5.88798e8	−	3.39943e8i	1.74638	−	1.00827i
$697$	1.59764e7	+	2.76719e7i	0.0471824	+	0.0817222i
$698$	3.91322e8	+	2.25930e8i	1.15072	+	0.664366i
$699$		−	1.89860e8i		−	0.555906i
$700$	−3.69390e8	−	8.41992e8i	−1.07694	−	2.45479i
$701$	1.38696e8			0.402634			0.201317	−	0.979526i	$-0.435478\pi$
$701$	1.38696e8			0.402634			0.201317	+	0.979526i	$0.435478\pi$
$702$	−9.62114e7	+	1.66643e8i	−0.278109	+	0.481699i
$703$	−9.03043e7	+	5.21372e7i	−0.259922	+	0.150066i
$704$	−3.65933e8	−	6.33815e8i	−1.04878	−	1.81654i
$705$	−2.29697e7	−	1.32616e7i	−0.0655523	−	0.0378466i
$706$			9.19153e8i			2.61200i
$707$	2.00843e7	−	1.81558e8i	0.0568327	−	0.513757i
$708$	2.81265e8			0.792532
$709$	−1.68784e8	+	2.92343e8i	−0.473580	+	0.820264i	−0.999543	−	0.0302432i	$-0.990372\pi$
$709$	−1.68784e8	+	2.92343e8i	−0.473580	+	0.820264i	0.525963	+	0.850508i	$0.323705\pi$
$710$	1.39686e8	−	8.06480e7i	0.390282	−	0.225330i
$711$	−1.27351e6	−	2.20578e6i	−0.00354318	−	0.00613696i
$712$	−2.96369e8	−	1.71109e8i	−0.821094	−	0.474059i
$713$			851358.i			0.00234879i
$714$	2.63415e7	+	2.91395e6i	0.0723680	+	0.00800549i
$715$	−5.25011e7			−0.143632
$716$	2.69507e8	−	4.66800e8i	0.734229	−	1.27172i
$717$	1.40129e8	−	8.09035e7i	0.380164	−	0.219488i
$718$	−6.04442e8	−	1.04692e9i	−1.63298	−	2.82841i
$719$	−9.78596e7	−	5.64993e7i	−0.263279	−	0.152004i	0.362550	−	0.931964i	$-0.381906\pi$
$719$	−9.78596e7	−	5.64993e7i	−0.263279	−	0.152004i	−0.625830	+	0.779960i	$0.715239\pi$
$720$			1.03905e8i			0.278381i
$721$	−3.28113e8	+	1.43946e8i	−0.875421	+	0.384055i
$722$	1.72140e8			0.457372
$723$	8.73886e7	−	1.51362e8i	0.231228	−	0.400498i
$724$	−1.36158e9	+	7.86108e8i	−3.58779	+	2.07141i
$725$	1.81536e8	+	3.14430e8i	0.476376	+	0.825107i
$726$	−2.91018e8	−	1.68020e8i	−0.760520	−	0.439086i
$727$			4.17662e8i			1.08698i	0.839415	+	0.543490i	$0.182898\pi$
$727$			4.17662e8i			1.08698i	−0.839415	+	0.543490i	$0.817102\pi$
$728$	1.61762e9	+	1.18880e9i	4.19258	+	3.08117i
$729$	−1.43489e7			−0.0370370
$730$	−1.11440e8	+	1.93020e8i	−0.286467	+	0.496175i
$731$	−1.86820e7	+	1.07860e7i	−0.0478267	+	0.0276128i
$732$	−3.24348e8	−	5.61787e8i	−0.826947	−	1.43231i
$733$	6.34509e8	+	3.66334e8i	1.61111	+	0.930177i	0.989113	+	0.147159i	$0.0470130\pi$
$733$	6.34509e8	+	3.66334e8i	1.61111	+	0.930177i	0.622000	+	0.783017i	$0.286320\pi$
$734$		−	6.45658e8i		−	1.63273i
$735$	1.41479e7	+	4.52152e7i	0.0356313	+	0.113874i
$736$	−6.01427e6			−0.0150851
$737$	−1.28181e7	+	2.22016e7i	−0.0320201	+	0.0554604i
$738$	−3.29951e8	+	1.90497e8i	−0.820881	+	0.473936i
$739$	−2.93464e8	−	5.08295e8i	−0.727146	−	1.25945i	−0.958084	−	0.286486i	$-0.907513\pi$
$739$	−2.93464e8	−	5.08295e8i	−0.727146	−	1.25945i	0.230938	−	0.972968i	$-0.425820\pi$
$740$	−6.96721e7	−	4.02252e7i	−0.171935	−	0.0992665i
$741$		−	3.04688e8i		−	0.748860i
$742$	−3.14309e8	+	4.27685e8i	−0.769388	+	1.04692i
$743$	−3.73015e8			−0.909411			−0.454705	−	0.890642i	$-0.650255\pi$
$743$	−3.73015e8			−0.909411			−0.454705	+	0.890642i	$0.650255\pi$
$744$	2.83770e8	−	4.91505e8i	0.689046	−	1.19346i
$745$	6.96052e7	−	4.01866e7i	0.168334	−	0.0971879i
$746$	3.73802e8	+	6.47444e8i	0.900379	+	1.55950i
$747$	1.50004e8	+	8.66048e7i	0.359866	+	0.207769i
$748$			3.55388e7i			0.0849177i
$749$	−4.94484e7	−	1.12713e8i	−0.117681	−	0.268244i
$750$	−1.92066e8			−0.455267
$751$	2.73909e8	−	4.74424e8i	0.646675	−	1.12007i	−0.337236	−	0.941420i	$-0.609492\pi$
$751$	2.73909e8	−	4.74424e8i	0.646675	−	1.12007i	0.983912	−	0.178655i	$-0.0571745\pi$
$752$	−9.44126e8	+	5.45091e8i	−2.22012	+	1.28179i
$753$	2.05490e8	+	3.55920e8i	0.481290	+	0.833618i
$754$	−1.06785e9	−	6.16521e8i	−2.49112	−	1.43825i
$755$			4.49293e7i			0.104397i
$756$	−2.56022e7	+	2.31439e8i	−0.0592531	+	0.535637i
$757$	4.01667e8			0.925931			0.462966	−	0.886376i	$-0.346785\pi$
$757$	4.01667e8			0.925931			0.462966	+	0.886376i	$0.346785\pi$
$758$	1.34922e8	−	2.33692e8i	0.309796	−	0.536583i
$759$	353911.	−	204330.i	0.000809410	−	0.000467313i
$760$	−1.39267e8	−	2.41218e8i	−0.317254	−	0.549501i
$761$	−9.49273e7	−	5.48063e7i	−0.215396	−	0.124359i	0.388421	−	0.921482i	$-0.373021\pi$
$761$	−9.49273e7	−	5.48063e7i	−0.215396	−	0.124359i	−0.603816	+	0.797123i	$0.706354\pi$
$762$			2.58673e8i			0.584636i
$763$	2.56500e8	+	2.83745e7i	0.577448	+	0.0638784i
$764$	2.58325e8			0.579278
$765$	997569.	−	1.72784e6i	0.00222822	−	0.00385940i
$766$	8.73867e8	−	5.04527e8i	1.94428	−	1.12253i
$767$	−1.63969e8	−	2.84003e8i	−0.363393	−	0.629414i
$768$	9.09191e8	+	5.24922e8i	2.00711	+	1.15881i
$769$		−	2.51373e8i		−	0.552763i	−0.961048	−	0.276381i	$-0.910865\pi$
$769$		−	2.51373e8i		−	0.552763i	0.961048	−	0.276381i	$-0.0891353\pi$
$770$	−7.89554e7	+	3.46384e7i	−0.172946	+	0.0758728i
$771$	−4.01099e8			−0.875162
$772$	−1.52528e8	+	2.64187e8i	−0.331512	+	0.574195i
$773$	−5.00828e8	+	2.89153e8i	−1.08430	+	0.626022i	−0.932054	−	0.362321i	$-0.881985\pi$
$773$	−5.00828e8	+	2.89153e8i	−1.08430	+	0.626022i	−0.152248	+	0.988342i	$0.548651\pi$
$774$	−1.28609e8	−	2.22758e8i	−0.277364	−	0.480408i
$775$	2.62474e8	+	1.51539e8i	0.563872	+	0.325552i
$776$			1.92743e9i			4.12471i
$777$	−7.48690e7	−	5.50219e7i	−0.159602	−	0.117293i
$778$	−1.23870e9			−2.63044
$779$	3.01639e8	−	5.22453e8i	0.638079	−	1.10519i
$780$	2.03580e8	−	1.17537e8i	0.428995	−	0.247680i
$781$	1.24900e8	+	2.16333e8i	0.262185	+	0.454118i
$782$	180358.	+	104130.i	0.000377152	+	0.000217749i
$783$		−	9.19475e7i		−	0.191538i
$784$	1.90026e9	+	4.25629e8i	3.94334	+	0.883249i
$785$	−2.19322e7			−0.0453391
$786$	−7.93099e7	+	1.37369e8i	−0.163328	+	0.282892i
$787$	5.03438e8	−	2.90660e8i	1.03281	−	0.596296i	0.115025	−	0.993363i	$-0.463305\pi$
$787$	5.03438e8	−	2.90660e8i	1.03281	−	0.596296i	0.917790	+	0.397067i	$0.129972\pi$
$788$	−5.75834e8	−	9.97374e8i	−1.17684	−	2.03835i
$789$	2.28398e8	+	1.31866e8i	0.465009	+	0.268473i
$790$			4.22276e6i			0.00856476i
$791$	4.81901e8	−	6.55729e8i	0.973708	−	1.32494i
$792$	−2.72426e8			−0.548368
$793$	−3.78170e8	+	6.55009e8i	−0.758346	+	1.31349i
$794$	3.41795e8	−	1.97335e8i	0.682817	−	0.394224i
$795$	1.99783e7	+	3.46034e7i	0.0397609	+	0.0688679i
$796$	1.03426e9	+	5.97129e8i	2.05064	+	1.18394i
$797$		−	2.88172e8i		−	0.569215i	−0.958644	−	0.284607i	$-0.908137\pi$
$797$		−	2.88172e8i		−	0.569215i	0.958644	−	0.284607i	$-0.0918632\pi$
$798$	−2.01023e8	−	4.58214e8i	−0.395582	−	0.901696i
$799$	2.09332e7			0.0410388
$800$	−1.07052e9	+	1.85420e9i	−2.09086	+	3.62148i
$801$	−4.00808e7	+	2.31407e7i	−0.0779901	+	0.0450276i
$802$	−8.82572e7	−	1.52866e8i	−0.171091	−	0.296338i
$803$	−2.98931e8	−	1.72588e8i	−0.577331	−	0.333322i
$804$		−	1.14787e8i		−	0.220863i
$805$	−40934.7	+	370041.i	−7.84700e−5	+	0.000709353i
$806$	−1.02929e9			−1.96577
$807$	2.05722e8	−	3.56321e8i	0.391436	−	0.677987i
$808$	−8.28697e8	+	4.78449e8i	−1.57095	+	0.906987i
$809$	−2.68679e7	−	4.65365e7i	−0.0507444	−	0.0878918i	0.839537	−	0.543302i	$-0.182826\pi$
$809$	−2.68679e7	−	4.65365e7i	−0.0507444	−	0.0878918i	−0.890282	+	0.455410i	$0.849493\pi$
$810$	2.06022e7	+	1.18947e7i	0.0387668	+	0.0223820i
$811$			1.37731e8i			0.258208i	0.991631	+	0.129104i	$0.0412101\pi$
$811$			1.37731e8i			0.258208i	−0.991631	+	0.129104i	$0.958790\pi$
$812$	−1.48305e9	−	1.64058e8i	−2.77006	−	0.306429i
$813$	−9.92583e7			−0.184712
$814$	8.45439e7	−	1.46434e8i	0.156750	−	0.271500i
$815$	−3.00506e7	+	1.73497e7i	−0.0555112	+	0.0320494i
$816$	−4.10032e7	−	7.10196e7i	−0.0754653	−	0.130710i
$817$	3.52721e8	+	2.03644e8i	0.646793	+	0.373426i
$818$		−	5.99599e8i		−	1.09547i
$819$	2.48616e8	−	1.09070e8i	0.452562	−	0.198543i
$820$	4.65444e8			0.844162
$821$	−2.27200e8	+	3.93522e8i	−0.410563	+	0.711115i	−0.994951	−	0.100359i	$-0.968001\pi$
$821$	−2.27200e8	+	3.93522e8i	−0.410563	+	0.711115i	0.584389	+	0.811474i	$0.301334\pi$
$822$	−9.67945e8	+	5.58843e8i	−1.74275	+	1.00618i
$823$	−1.19151e8	−	2.06376e8i	−0.213747	−	0.370220i	0.739137	−	0.673555i	$-0.235233\pi$
$823$	−1.19151e8	−	2.06376e8i	−0.213747	−	0.370220i	−0.952884	+	0.303335i	$0.901900\pi$
$824$	1.62549e9	+	9.38478e8i	2.90538	+	1.67742i
$825$		−	1.45481e8i		−	0.259086i
$826$	−4.33966e8	−	3.18925e8i	−0.770044	−	0.565912i
$827$	1.39387e8			0.246437			0.123218	−	0.992380i	$-0.460678\pi$
$827$	1.39387e8			0.246437			0.123218	+	0.992380i	$0.460678\pi$
$828$	−914893.	+	1.58464e6i	−0.00161168	+	0.00279152i
$829$	6.84951e8	−	3.95457e8i	1.20225	−	0.694121i	0.241198	−	0.970476i	$-0.422460\pi$
$829$	6.84951e8	−	3.95457e8i	1.20225	−	0.694121i	0.961056	+	0.276355i	$0.0891264\pi$
$830$	−1.43584e8	−	2.48695e8i	−0.251115	−	0.434944i
$831$	−4.65901e8	−	2.68988e8i	−0.811878	−	0.468738i
$832$		−	3.82072e9i		−	6.63399i
$833$	−2.75131e7	−	2.53217e7i	−0.0475997	−	0.0438085i
$834$	4.78388e8			0.824674
$835$	−8.52907e7	+	1.47728e8i	−0.146502	+	0.253748i
$836$	5.81089e8	−	3.35492e8i	0.994544	−	0.574200i
$837$	−3.83770e7	−	6.64709e7i	−0.0654477	−	0.113359i
$838$	−7.50490e8	−	4.33296e8i	−1.27530	−	0.736296i
$839$			8.67968e8i			1.46966i	0.678250	+	0.734832i	$0.262739\pi$
$839$			8.67968e8i			1.46966i	−0.678250	+	0.734832i	$0.737261\pi$
$840$	1.46973e8	−	1.99988e8i	0.247970	−	0.337415i
$841$	−5.62593e6			−0.00945816
$842$	7.23359e8	−	1.25289e9i	1.21176	−	2.09883i
$843$	−5.43045e8	+	3.13527e8i	−0.906470	+	0.523351i
$844$	−9.56487e7	−	1.65668e8i	−0.159093	−	0.275558i
$845$	−1.29376e8	−	7.46955e7i	−0.214430	−	0.123801i
$846$			2.49601e8i			0.412226i
$847$	1.90476e8	+	4.34173e8i	0.313465	+	0.714517i
$848$	1.64234e9			2.69324
$849$	2.28013e7	−	3.94930e7i	0.0372594	−	0.0645352i
$850$	6.42065e7	−	3.70697e7i	0.104550	−	0.0603618i
$851$	−365064.	−	632309.i	−0.000592352	−	0.00102598i
$852$	−9.68633e8	−	5.59241e8i	−1.56618	−	0.904232i
$853$			7.06613e8i			1.13850i	0.822163	+	0.569252i	$0.192767\pi$
$853$			7.06613e8i			1.13850i	−0.822163	+	0.569252i	$0.807233\pi$
$854$	−1.36569e8	+	1.23456e9i	−0.219270	+	1.98216i
$855$	−3.76688e7			−0.0602676
$856$	−3.22387e8	+	5.58390e8i	−0.513991	+	0.890259i
$857$	−4.82285e8	+	2.78447e8i	−0.766233	+	0.442385i	−0.831529	−	0.555481i	$-0.812534\pi$
$857$	−4.82285e8	+	2.78447e8i	−0.766233	+	0.442385i	0.0652960	+	0.997866i	$0.479201\pi$
$858$	2.47036e8	+	4.27878e8i	0.391109	+	0.677420i
$859$	2.54250e8	+	1.46791e8i	0.401127	+	0.231591i	0.686970	−	0.726686i	$-0.258940\pi$
$859$	2.54250e8	+	1.46791e8i	0.401127	+	0.231591i	−0.285843	+	0.958276i	$0.592274\pi$
$860$			3.14233e8i			0.494033i
$861$	5.34286e8	+	5.91037e7i	0.837075	+	0.0925988i
$862$	2.05453e9			3.20767
$863$	−4.51752e8	+	7.82458e8i	−0.702859	+	1.21739i	0.264600	+	0.964358i	$0.414760\pi$
$863$	−4.51752e8	+	7.82458e8i	−0.702859	+	1.21739i	−0.967459	+	0.253029i	$0.918573\pi$
$864$	4.69572e8	−	2.71108e8i	0.728050	−	0.420340i
$865$	1.21676e8	+	2.10749e8i	0.188000	+	0.325625i
$866$	1.30279e9	+	7.52165e8i	2.00595	+	1.15813i
$867$		−	3.74693e8i		−	0.574934i
$868$	−1.14061e9	+	5.00395e8i	−1.74412	+	0.765162i
$869$	−6.53980e6			−0.00996564
$870$	−7.62210e7	+	1.32019e8i	−0.115749	+	0.200483i
$871$	−1.15904e8	+	6.69172e7i	−0.175406	+	0.101271i
$872$	−6.75937e8	−	1.17076e9i	−1.01943	−	1.76570i
$873$	2.25743e8	+	1.30333e8i	0.339290	+	0.195889i
$874$		−	3.93201e6i		−	0.00588953i
$875$	2.18360e8	+	1.60474e8i	0.325948	+	0.239542i
$876$	1.54553e9			2.29914
$877$	−8.98625e7	+	1.55646e8i	−0.133223	+	0.230749i	−0.924917	−	0.380168i	$-0.875866\pi$
$877$	−8.98625e7	+	1.55646e8i	−0.133223	+	0.230749i	0.791694	+	0.610918i	$0.209199\pi$
$878$	1.31306e9	−	7.58097e8i	1.94000	−	1.12006i
$879$	−9.09905e7	−	1.57600e8i	−0.133977	−	0.232054i
$880$	2.31047e8	+	1.33395e8i	0.339041	+	0.195746i
$881$		−	1.07737e9i		−	1.57556i	−0.615954	−	0.787782i	$-0.711229\pi$
$881$		−	1.07737e9i		−	1.57556i	0.615954	−	0.787782i	$-0.288771\pi$
$882$	3.01929e8	−	3.28058e8i	0.440047	−	0.478128i
$883$	−1.25270e9			−1.81955			−0.909775	−	0.415102i	$-0.863746\pi$
$883$	−1.25270e9			−1.81955			−0.909775	+	0.415102i	$0.863746\pi$
$884$	−9.27654e7	+	1.60674e8i	−0.134286	+	0.232589i
$885$	−3.51115e7	+	2.02717e7i	−0.0506547	+	0.0292455i
$886$	1.29751e9	+	2.24735e9i	1.86556	+	3.23124i
$887$	3.29604e8	+	1.90297e8i	0.472304	+	0.272685i	0.717204	−	0.696864i	$-0.245422\pi$
$887$	3.29604e8	+	1.90297e8i	0.472304	+	0.272685i	−0.244900	+	0.969548i	$0.578755\pi$
$888$			4.86725e8i			0.695096i
$889$	2.16126e8	−	2.94085e8i	0.307611	−	0.418570i
$890$	7.67311e7			0.108843
$891$	−1.84214e7	+	3.19067e7i	−0.0260429	+	0.0451075i
$892$	−2.59807e9	+	1.49999e9i	−3.66063	+	2.11346i
$893$	−1.97613e8	−	3.42275e8i	−0.277498	−	0.480641i
$894$	−6.55033e8	−	3.78183e8i	−0.916749	−	0.529285i
$895$			7.76969e7i			0.108376i
$896$	−1.25840e9	−	2.86842e9i	−1.74943	−	3.98767i
$897$	2.13342e6			0.00295596
$898$	8.10714e8	−	1.40420e9i	1.11954	−	1.93910i
$899$	4.25944e8	−	2.45919e8i	0.586237	−	0.338464i
$900$	3.25697e8	+	5.64123e8i	0.446772	+	0.773831i
$901$	−2.73105e7	−	1.57677e7i	−0.0373383	−	0.0215573i
$902$			9.78254e8i			1.33301i
$903$	−3.99024e7	+	3.60710e8i	−0.0541920	+	0.489885i
$904$	−4.26291e9			−5.77033
$905$	1.13314e8	−	1.96266e8i	0.152876	−	0.264789i
$906$	3.66169e8	−	2.11408e8i	0.492376	−	0.284274i
$907$	−3.32531e8	−	5.75961e8i	−0.445667	−	0.771918i	0.552431	−	0.833558i	$-0.313700\pi$
$907$	−3.32531e8	−	5.75961e8i	−0.445667	−	0.771918i	−0.998098	+	0.0616405i	$0.980367\pi$
$908$	−2.94292e9	−	1.69910e9i	−3.93117	−	2.26966i
$909$			1.29410e8i			0.172297i
$910$	−4.47380e8	−	4.94900e7i	−0.593680	−	0.0656740i
$911$	−9.53125e8			−1.26065			−0.630325	−	0.776331i	$-0.717078\pi$
$911$	−9.53125e8			−1.26065			−0.630325	+	0.776331i	$0.717078\pi$
$912$	−7.74153e8	+	1.34087e9i	−1.02057	+	1.76768i
$913$	3.85155e8	−	2.22369e8i	0.506085	−	0.292188i
$914$	5.52846e8	+	9.57557e8i	0.724045	+	1.25408i
$915$	8.09794e7	+	4.67535e7i	0.105709	+	0.0610310i
$916$			7.62997e8i			0.992742i
$917$	2.04942e8	−	8.99099e7i	0.265780	−	0.116600i
$918$	−1.87756e7			−0.0242698
$919$	6.24861e8	−	1.08229e9i	0.805076	−	1.39443i	−0.111164	−	0.993802i	$-0.535458\pi$
$919$	6.24861e8	−	1.08229e9i	0.805076	−	1.39443i	0.916240	−	0.400630i	$-0.131209\pi$
$920$	1.68900e6	−	975146.i	0.00216904	−	0.00125229i
$921$	2.49566e8	+	4.32260e8i	0.319452	+	0.553307i
$922$	−3.98041e8	−	2.29809e8i	−0.507850	−	0.293207i
$923$			1.30408e9i			1.65844i
$924$	4.81767e8	+	3.54055e8i	0.610690	+	0.448801i
$925$	−2.59921e8			−0.328410
$926$	5.98252e8	−	1.03620e9i	0.753444	−	1.30500i
$927$	2.19831e8	−	1.26919e8i	0.275962	−	0.159327i
$928$	1.73725e9	+	3.00901e9i	2.17380	+	3.76512i
$929$	−9.03228e8	−	5.21479e8i	−1.12655	−	0.650414i	−0.183485	−	0.983023i	$-0.558738\pi$
$929$	−9.03228e8	−	5.21479e8i	−1.12655	−	0.650414i	−0.943065	+	0.332609i	$0.892071\pi$
$930$			1.27252e8i			0.158204i
$931$	−1.54304e8	+	6.88903e8i	−0.191217	+	0.853707i
$932$	2.18274e9			2.69622
$933$	−1.89077e7	+	3.27491e7i	−0.0232806	+	0.0403232i
$934$	2.64390e9	−	1.52646e9i	3.24493	−	1.87346i
$935$	−2.56139e6	−	4.43646e6i	−0.00313358	−	0.00542752i
$936$	−1.23166e9	−	7.11101e8i	−1.50198	−	0.867169i
$937$			4.82808e8i			0.586889i	0.955976	+	0.293444i	$0.0948015\pi$
$937$			4.82808e8i			0.586889i	−0.955976	+	0.293444i	$0.905198\pi$
$938$	−1.30156e8	+	1.77105e8i	−0.157709	+	0.214597i
$939$	−4.37597e8			−0.528540
$940$	1.52463e8	−	2.64074e8i	0.183561	−	0.317938i
$941$	−4.90467e8	+	2.83172e8i	−0.588629	+	0.339845i	−0.764555	−	0.644558i	$-0.777041\pi$
$941$	−4.90467e8	+	2.83172e8i	−0.588629	+	0.339845i	0.175926	+	0.984403i	$0.443708\pi$
$942$	1.03199e8	+	1.78745e8i	0.123458	+	0.213836i
$943$	3.65821e6	+	2.11207e6i	0.00436248	+	0.00251868i
$944$			1.66646e9i			1.98097i
$945$	−1.34845e7	−	3.07367e7i	−0.0159786	−	0.0364218i
$946$	−6.60443e8			−0.780121
$947$	1.09258e7	−	1.89240e7i	0.0128648	−	0.0222824i	−0.859521	−	0.511100i	$-0.829238\pi$
$947$	1.09258e7	−	1.89240e7i	0.0128648	−	0.0222824i	0.872386	+	0.488817i	$0.162572\pi$
$948$	2.53590e7	−	1.46410e7i	0.0297651	−	0.0171849i
$949$	−9.00998e8	−	1.56057e9i	−1.05421	−	1.82594i
$950$	−1.21224e9	−	6.99887e8i	−1.41390	−	0.816313i
$951$		−	1.19753e8i		−	0.139234i
$952$	−2.15371e7	+	1.94691e8i	−0.0249618	+	0.225650i
$953$	1.05425e9			1.21805			0.609023	−	0.793152i	$-0.291562\pi$
$953$	1.05425e9			1.21805			0.609023	+	0.793152i	$0.291562\pi$
$954$	1.88009e8	−	3.25642e8i	0.216538	−	0.375055i
$955$	−3.22478e7	+	1.86183e7i	−0.0370246	+	0.0213762i
$956$	9.30118e8	+	1.61101e9i	1.06455	+	1.84385i
$957$	−2.04458e8	−	1.18044e8i	−0.233275	−	0.134681i
$958$		−	5.01041e8i		−	0.569871i
$959$	1.56738e9	+	1.73387e8i	1.77713	+	0.196589i
$960$	−4.72359e8			−0.533898
$961$	−2.38469e8	+	4.13040e8i	−0.268696	+	0.465395i
$962$	7.64462e8	−	4.41362e8i	0.858679	−	0.495758i
$963$	4.35994e7	+	7.55165e7i	0.0488205	+	0.0845596i
$964$	1.74015e9	+	1.00467e9i	1.94247	+	1.12149i
$965$		−	4.39728e7i		−	0.0489330i
$966$	3.20841e6	−	1.40756e6i	0.00355925	−	0.00156148i
$967$	−7.18604e8			−0.794713			−0.397356	−	0.917664i	$-0.630072\pi$
$967$	−7.18604e8			−0.794713			−0.397356	+	0.917664i	$0.630072\pi$
$968$	1.24184e9	−	2.15092e9i	1.36911	−	2.37137i
$969$	2.57468e7	−	1.48649e7i	0.0282978	−	0.0163377i
$970$	−2.16082e8	−	3.74264e8i	−0.236757	−	0.410075i
$971$	5.48150e8	+	3.16475e8i	0.598745	+	0.345686i	0.768548	−	0.639792i	$-0.220980\pi$
$971$	5.48150e8	+	3.16475e8i	0.598745	+	0.345686i	−0.169803	+	0.985478i	$0.554313\pi$
$972$		−	1.64964e8i		−	0.179635i
$973$	−5.43881e8	−	3.99703e8i	−0.590425	−	0.433909i
$974$	−2.70183e9			−2.92402
$975$	3.79742e8	−	6.57733e8i	0.409709	−	0.709636i
$976$	3.32851e9	−	1.92171e9i	3.58014	−	2.06699i
$977$	−6.59658e8	−	1.14256e9i	−0.707351	−	1.22517i	−0.965836	−	0.259153i	$-0.916557\pi$
$977$	−6.59658e8	−	1.14256e9i	−0.707351	−	1.22517i	0.258485	−	0.966015i	$-0.416777\pi$
$978$	2.82797e8	+	1.63273e8i	0.302314	+	0.174541i
$979$			1.18834e8i			0.126646i
$980$	−5.19823e8	+	1.62653e8i	−0.552302	+	0.172816i
$981$	−1.82827e8			−0.193657
$982$	−1.77573e8	+	3.07566e8i	−0.187518	+	0.324790i
$983$	−6.44167e7	+	3.71910e7i	−0.0678169	+	0.0391541i	−0.533525	−	0.845784i	$-0.679133\pi$
$983$	−6.44167e7	+	3.71910e7i	−0.0678169	+	0.0391541i	0.465708	+	0.884938i	$0.345800\pi$
$984$	−1.40797e9	−	2.43867e9i	−1.47777	−	2.55958i
$985$	1.43768e8	+	8.30042e7i	0.150436	+	0.0868544i
$986$		−	1.20314e8i		−	0.125512i
$987$	2.08546e8	−	2.83772e8i	0.216896	−	0.295133i
$988$	3.50288e9			3.63207
$989$	−1.42591e6	+	2.46975e6i	−0.00147402	+	0.00255308i
$990$	5.28990e7	−	3.05412e7i	0.0545182	−	0.0314761i
$991$	−7.98815e8	−	1.38359e9i	−0.820777	−	1.42163i	−0.905105	−	0.425189i	$-0.860208\pi$
$991$	−7.98815e8	−	1.38359e9i	−0.820777	−	1.42163i	0.0843276	−	0.996438i	$-0.473126\pi$
$992$	2.51180e9	+	1.45019e9i	2.57306	+	1.48555i
$993$			7.99384e8i			0.816409i
$994$	8.60389e8	+	1.96118e9i	0.876064	+	1.99691i
$995$	−1.72148e8			−0.174756
$996$	−9.95663e8	+	1.72454e9i	−1.00771	+	1.74540i
$997$	−1.13154e9	+	6.53297e8i	−1.14179	+	0.659212i	−0.946873	−	0.321608i	$-0.895777\pi$
$997$	−1.13154e9	+	6.53297e8i	−1.14179	+	0.659212i	−0.194916	+	0.980820i	$0.562443\pi$
$998$	1.11598e9	+	1.93293e9i	1.12270	+	1.94458i
$999$	5.70057e7	+	3.29122e7i	0.0571770	+	0.0330112i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.7.f.a.19.1	yes	8
3.2	odd	2		63.7.m.d.19.4		8
4.3	odd	2		336.7.bh.d.145.3		8
7.2	even	3		147.7.d.b.97.7		8
7.3	odd	6	inner	21.7.f.a.10.1	✓	8
7.4	even	3		147.7.f.d.31.1		8
7.5	odd	6		147.7.d.b.97.8		8
7.6	odd	2		147.7.f.d.19.1		8
21.2	odd	6		441.7.d.c.244.2		8
21.5	even	6		441.7.d.c.244.1		8
21.17	even	6		63.7.m.d.10.4		8
28.3	even	6		336.7.bh.d.241.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.7.f.a.10.1	✓	8	7.3	odd	6	inner
21.7.f.a.19.1	yes	8	1.1	even	1	trivial
63.7.m.d.10.4		8	21.17	even	6
63.7.m.d.19.4		8	3.2	odd	2
147.7.d.b.97.7		8	7.2	even	3
147.7.d.b.97.8		8	7.5	odd	6
147.7.f.d.19.1		8	7.6	odd	2
147.7.f.d.31.1		8	7.4	even	3
336.7.bh.d.145.3		8	4.3	odd	2
336.7.bh.d.241.3		8	28.3	even	6
441.7.d.c.244.1		8	21.5	even	6
441.7.d.c.244.2		8	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.f (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-7.79767 + 13.5060i) q^{2} +(-13.5000 + 7.79423i) q^{3} +(-89.6073 - 155.204i) q^{4} +(22.3721 + 12.9165i) q^{5} -243.107i q^{6} +(-203.121 + 276.389i) q^{7} +1796.81 q^{8} +(121.500 - 210.444i) q^{9} +O(q^{10})\)	\(q+(-7.79767 + 13.5060i) q^{2} +(-13.5000 + 7.79423i) q^{3} +(-89.6073 - 155.204i) q^{4} +(22.3721 + 12.9165i) q^{5} -243.107i q^{6} +(-203.121 + 276.389i) q^{7} +1796.81 q^{8} +(121.500 - 210.444i) q^{9} +(-348.901 + 201.438i) q^{10} +(-311.967 - 540.343i) q^{11} +(2419.40 + 1396.84i) q^{12} -3257.26i q^{13} +(-2149.03 - 4898.53i) q^{14} -402.698 q^{15} +(-8276.07 + 14334.6i) q^{16} +(275.246 - 158.913i) q^{17} +(1894.83 + 3281.95i) q^{18} +(-5196.73 - 3000.33i) q^{19} -4629.67i q^{20} +(587.891 - 5314.42i) q^{21} +9730.47 q^{22} +(21.0083 - 36.3874i) q^{23} +(-24256.9 + 14004.8i) q^{24} +(-7478.83 - 12953.7i) q^{25} +(43992.4 + 25399.0i) q^{26} +3788.00i q^{27} +(61097.9 + 6758.77i) q^{28} -24273.4 q^{29} +(3140.11 - 5438.82i) q^{30} +(-17547.8 + 10131.2i) q^{31} +(-71570.2 - 123963. i) q^{32} +(8423.12 + 4863.09i) q^{33} +4956.62i q^{34} +(-8114.24 + 3559.79i) q^{35} -43549.2 q^{36} +(8688.57 - 15049.0i) q^{37} +(81044.8 - 46791.2i) q^{38} +(25387.8 + 43973.0i) q^{39} +(40198.5 + 23208.6i) q^{40} +100535. i q^{41} +(67192.2 + 49380.2i) q^{42} -67873.7 q^{43} +(-55909.1 + 96837.4i) q^{44} +(5436.42 - 3138.72i) q^{45} +(327.631 + 567.474i) q^{46} +(57039.5 + 32931.8i) q^{47} -258022. i q^{48} +(-35132.9 - 112281. i) q^{49} +233270. q^{50} +(-2477.21 + 4290.66i) q^{51} +(-505541. + 291874. i) q^{52} +(-49611.0 - 85928.8i) q^{53} +(-51160.5 - 29537.5i) q^{54} -16118.2i q^{55} +(-364970. + 496619. i) q^{56} +93541.1 q^{57} +(189276. - 327835. i) q^{58} +(87190.7 - 50339.6i) q^{59} +(36084.7 + 62500.5i) q^{60} +(-201092. - 116101. i) q^{61} -315999. i q^{62} +(33485.3 + 76326.9i) q^{63} +1.17299e6 q^{64} +(42072.6 - 72871.8i) q^{65} +(-131361. + 75841.5i) q^{66} +(-20544.0 - 35583.3i) q^{67} +(-49328.1 - 28479.6i) q^{68} +654.974i q^{69} +(15193.8 - 137349. i) q^{70} -400361. q^{71} +(218313. - 378128. i) q^{72} +(479106. - 276612. i) q^{73} +(135501. + 234695. i) q^{74} +(201928. + 116583. i) q^{75} +1.07541e6i q^{76} +(212712. + 23530.6i) q^{77} -791864. q^{78} +(5240.77 - 9077.28i) q^{79} +(-370306. + 213797. i) q^{80} +(-29524.5 - 51137.9i) q^{81} +(-1.35782e6 - 783939. i) q^{82} +712797. i q^{83} +(-877501. + 384968. i) q^{84} +8210.45 q^{85} +(529257. - 916700. i) q^{86} +(327691. - 189192. i) q^{87} +(-560546. - 970895. i) q^{88} +(-164942. - 95229.2i) q^{89} +97898.8i q^{90} +(900271. + 661617. i) q^{91} -7529.99 q^{92} +(157930. - 273543. i) q^{93} +(-889550. + 513582. i) q^{94} +(-77507.9 - 134248. i) q^{95} +(1.93239e6 + 1.11567e6i) q^{96} +1.07270e6i q^{97} +(1.79041e6 + 401025. i) q^{98} -151616. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 5 q^{2} - 108 q^{3} - 173 q^{4} - 294 q^{5} - 656 q^{7} + 3326 q^{8} + 972 q^{9}+O(q^{10}) \) 8 * q - 5 * q^2 - 108 * q^3 - 173 * q^4 - 294 * q^5 - 656 * q^7 + 3326 * q^8 + 972 * q^9	\( 8 q - 5 q^{2} - 108 q^{3} - 173 q^{4} - 294 q^{5} - 656 q^{7} + 3326 q^{8} + 972 q^{9} - 3411 q^{10} - 314 q^{11} + 4671 q^{12} - 5360 q^{14} + 5292 q^{15} - 12721 q^{16} - 5532 q^{17} + 1215 q^{18} - 18234 q^{19} + 9342 q^{21} + 86106 q^{22} + 3928 q^{23} - 44901 q^{24} - 17038 q^{25} + 12366 q^{26} + 85037 q^{28} - 8300 q^{29} + 30699 q^{30} - 89508 q^{31} - 186207 q^{32} + 8478 q^{33} - 25860 q^{35} - 84078 q^{36} + 64706 q^{37} - 77136 q^{38} + 29106 q^{39} + 221823 q^{40} + 173583 q^{42} + 45740 q^{43} + 92529 q^{44} - 71442 q^{45} - 111504 q^{46} + 483276 q^{47} - 310684 q^{49} + 967216 q^{50} + 49788 q^{51} - 1673988 q^{52} - 540974 q^{53} - 32805 q^{54} - 241885 q^{56} + 328212 q^{57} + 539799 q^{58} - 181770 q^{59} - 146367 q^{60} + 418224 q^{61} - 92826 q^{63} + 2378626 q^{64} - 414204 q^{65} - 1162431 q^{66} - 1158902 q^{67} - 821250 q^{68} + 1087917 q^{70} + 1442344 q^{71} + 404109 q^{72} - 378666 q^{73} - 432940 q^{74} + 460026 q^{75} + 1065994 q^{77} - 222588 q^{78} + 611452 q^{79} - 2094945 q^{80} - 236196 q^{81} - 1561266 q^{82} - 1579716 q^{84} - 275112 q^{85} + 816224 q^{86} + 112050 q^{87} - 366441 q^{88} - 989196 q^{89} + 304446 q^{91} + 678720 q^{92} + 805572 q^{93} - 716148 q^{94} - 591792 q^{95} + 5027589 q^{96} + 3509629 q^{98} - 152604 q^{99}+O(q^{100}) \) 8 * q - 5 * q^2 - 108 * q^3 - 173 * q^4 - 294 * q^5 - 656 * q^7 + 3326 * q^8 + 972 * q^9 - 3411 * q^10 - 314 * q^11 + 4671 * q^12 - 5360 * q^14 + 5292 * q^15 - 12721 * q^16 - 5532 * q^17 + 1215 * q^18 - 18234 * q^19 + 9342 * q^21 + 86106 * q^22 + 3928 * q^23 - 44901 * q^24 - 17038 * q^25 + 12366 * q^26 + 85037 * q^28 - 8300 * q^29 + 30699 * q^30 - 89508 * q^31 - 186207 * q^32 + 8478 * q^33 - 25860 * q^35 - 84078 * q^36 + 64706 * q^37 - 77136 * q^38 + 29106 * q^39 + 221823 * q^40 + 173583 * q^42 + 45740 * q^43 + 92529 * q^44 - 71442 * q^45 - 111504 * q^46 + 483276 * q^47 - 310684 * q^49 + 967216 * q^50 + 49788 * q^51 - 1673988 * q^52 - 540974 * q^53 - 32805 * q^54 - 241885 * q^56 + 328212 * q^57 + 539799 * q^58 - 181770 * q^59 - 146367 * q^60 + 418224 * q^61 - 92826 * q^63 + 2378626 * q^64 - 414204 * q^65 - 1162431 * q^66 - 1158902 * q^67 - 821250 * q^68 + 1087917 * q^70 + 1442344 * q^71 + 404109 * q^72 - 378666 * q^73 - 432940 * q^74 + 460026 * q^75 + 1065994 * q^77 - 222588 * q^78 + 611452 * q^79 - 2094945 * q^80 - 236196 * q^81 - 1561266 * q^82 - 1579716 * q^84 - 275112 * q^85 + 816224 * q^86 + 112050 * q^87 - 366441 * q^88 - 989196 * q^89 + 304446 * q^91 + 678720 * q^92 + 805572 * q^93 - 716148 * q^94 - 591792 * q^95 + 5027589 * q^96 + 3509629 * q^98 - 152604 * q^99

Introduction

L-functions

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