LMFDB - Embedded newform 21.7.f.a.10.3

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			10.3
Root			$-2.75320 - 4.76869i$ of defining polynomial
Character	$\chi$	$=$	21.10
Dual form			21.7.f.a.19.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.25320 + 3.90266i) q^{2} +(-13.5000 - 7.79423i) q^{3} +(21.8461 - 37.8386i) q^{4} +(53.9244 - 31.1333i) q^{5} -70.2479i q^{6} +(218.833 - 264.124i) q^{7} +485.305 q^{8} +(121.500 + 210.444i) q^{9} +O(q^{10})$	\(q+(2.25320 + 3.90266i) q^{2} +(-13.5000 - 7.79423i) q^{3} +(21.8461 - 37.8386i) q^{4} +(53.9244 - 31.1333i) q^{5} -70.2479i q^{6} +(218.833 - 264.124i) q^{7} +485.305 q^{8} +(121.500 + 210.444i) q^{9} +(243.005 + 140.299i) q^{10} +(-9.71675 + 16.8299i) q^{11} +(-589.846 + 340.548i) q^{12} -1642.65i q^{13} +(1523.86 + 258.906i) q^{14} -970.639 q^{15} +(-304.661 - 527.689i) q^{16} +(-186.054 - 107.418i) q^{17} +(-547.529 + 948.347i) q^{18} +(-8237.53 + 4755.94i) q^{19} -2720.57i q^{20} +(-5012.88 + 1860.04i) q^{21} -87.5753 q^{22} +(7223.90 + 12512.2i) q^{23} +(-6551.62 - 3782.58i) q^{24} +(-5873.94 + 10174.0i) q^{25} +(6410.70 - 3701.22i) q^{26} -3788.00i q^{27} +(-5213.43 - 14050.4i) q^{28} +43016.4 q^{29} +(-2187.05 - 3788.08i) q^{30} +(-7799.62 - 4503.11i) q^{31} +(16902.7 - 29276.3i) q^{32} +(262.352 - 151.469i) q^{33} -968.141i q^{34} +(3577.38 - 21055.7i) q^{35} +10617.2 q^{36} +(16564.6 + 28690.7i) q^{37} +(-37121.7 - 21432.2i) q^{38} +(-12803.2 + 22175.8i) q^{39} +(26169.8 - 15109.1i) q^{40} +73712.4i q^{41} +(-18554.1 - 15372.5i) q^{42} +4761.19 q^{43} +(424.547 + 735.337i) q^{44} +(13103.6 + 7565.38i) q^{45} +(-32553.9 + 56384.9i) q^{46} +(-63760.5 + 36812.2i) q^{47} +9498.40i q^{48} +(-21873.6 - 115598. i) q^{49} -52940.7 q^{50} +(1674.48 + 2900.29i) q^{51} +(-62155.6 - 35885.5i) q^{52} +(-119317. + 206663. i) q^{53} +(14783.3 - 8535.13i) q^{54} +1210.06i q^{55} +(106201. - 128181. i) q^{56} +148275. q^{57} +(96924.8 + 167879. i) q^{58} +(-282811. - 163281. i) q^{59} +(-21204.7 + 36727.6i) q^{60} +(350517. - 202371. i) q^{61} -40585.7i q^{62} +(82171.4 + 13961.0i) q^{63} +113344. q^{64} +(-51141.0 - 88578.8i) q^{65} +(1182.27 + 682.582i) q^{66} +(-109982. + 190494. i) q^{67} +(-8129.12 + 4693.35i) q^{68} -225219. i q^{69} +(90233.8 - 33481.4i) q^{70} +350228. q^{71} +(58964.6 + 102130. i) q^{72} +(-174606. - 100809. i) q^{73} +(-74646.7 + 129292. i) q^{74} +(158596. - 91565.7i) q^{75} +415596. i q^{76} +(2318.83 + 6249.36i) q^{77} -115393. q^{78} +(-197745. - 342505. i) q^{79} +(-32857.4 - 18970.2i) q^{80} +(-29524.5 + 51137.9i) q^{81} +(-287675. + 166089. i) q^{82} -13229.0i q^{83} +(-39130.8 + 230315. i) q^{84} -13377.1 q^{85} +(10727.9 + 18581.3i) q^{86} +(-580722. - 335280. i) q^{87} +(-4715.59 + 8167.65i) q^{88} +(-199460. + 115158. i) q^{89} +68185.4i q^{90} +(-433862. - 359465. i) q^{91} +631258. q^{92} +(70196.6 + 121584. i) q^{93} +(-287331. - 165891. i) q^{94} +(-296136. + 512922. i) q^{95} +(-456373. + 263487. i) q^{96} +662517. i q^{97} +(401853. - 345831. i) q^{98} -4722.34 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 $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$.

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

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 $

$2$	2.25320	+	3.90266i	0.281650	+	0.487833i	0.971791	−	0.235842i	$-0.0757848\pi$
$2$	2.25320	+	3.90266i	0.281650	+	0.487833i	−0.690141	+	0.723675i	$0.742451\pi$
$3$	−13.5000	−	7.79423i	−0.500000	−	0.288675i
$3$	−13.5000	−	7.79423i	−0.500000	−	0.288675i
$4$	21.8461	−	37.8386i	0.341346	−	0.591229i
$5$	53.9244	−	31.1333i	0.431395	−	0.249066i	−0.268546	−	0.963267i	$-0.586543\pi$
$5$	53.9244	−	31.1333i	0.431395	−	0.249066i	0.699941	+	0.714201i	$0.253210\pi$
$6$		−	70.2479i		−	0.325222i
$7$	218.833	−	264.124i	0.637996	−	0.770040i
$7$	218.833	−	264.124i	0.637996	−	0.770040i
$8$	485.305			0.947862
$9$	121.500	+	210.444i	0.166667	+	0.288675i
$10$	243.005	+	140.299i	0.243005	+	0.140299i
$11$	−9.71675	+	16.8299i	−0.00730034	+	0.0126446i	−0.869652	−	0.493664i	$-0.835657\pi$
$11$	−9.71675	+	16.8299i	−0.00730034	+	0.0126446i	0.862352	+	0.506309i	$0.168990\pi$
$12$	−589.846	+	340.548i	−0.341346	+	0.197076i
$13$		−	1642.65i		−	0.747678i	−0.927494	−	0.373839i	$-0.878041\pi$
$13$		−	1642.65i		−	0.747678i	0.927494	−	0.373839i	$-0.121959\pi$
$14$	1523.86	+	258.906i	0.555343	+	0.0943533i
$15$	−970.639			−0.287597
$16$	−304.661	−	527.689i	−0.0743802	−	0.128830i
$17$	−186.054	−	107.418i	−0.0378697	−	0.0218641i	0.480946	−	0.876750i	$-0.340293\pi$
$17$	−186.054	−	107.418i	−0.0378697	−	0.0218641i	−0.518815	+	0.854886i	$0.673627\pi$
$18$	−547.529	+	948.347i	−0.0938835	+	0.162611i
$19$	−8237.53	+	4755.94i	−1.20098	+	0.693387i	−0.960773	−	0.277335i	$-0.910549\pi$
$19$	−8237.53	+	4755.94i	−1.20098	+	0.693387i	−0.240208	+	0.970722i	$0.577215\pi$
$20$		−	2720.57i		−	0.340071i
$21$	−5012.88	+	1860.04i	−0.541289	+	0.200846i
$22$	−87.5753			−0.00822458
$23$	7223.90	+	12512.2i	0.593729	+	1.02837i	0.993725	+	0.111852i	$0.0356783\pi$
$23$	7223.90	+	12512.2i	0.593729	+	1.02837i	−0.399996	+	0.916517i	$0.630988\pi$
$24$	−6551.62	−	3782.58i	−0.473931	−	0.273624i
$25$	−5873.94	+	10174.0i	−0.375932	+	0.651134i
$26$	6410.70	−	3701.22i	0.364742	−	0.210584i
$27$		−	3788.00i		−	0.192450i
$28$	−5213.43	−	14050.4i	−0.237492	−	0.640051i
$29$	43016.4			1.76376			0.881882	−	0.471471i	$-0.156277\pi$
$29$	43016.4			1.76376			0.881882	+	0.471471i	$0.156277\pi$
$30$	−2187.05	−	3788.08i	−0.0810017	−	0.140299i
$31$	−7799.62	−	4503.11i	−0.261811	−	0.151157i	0.363349	−	0.931653i	$-0.381633\pi$
$31$	−7799.62	−	4503.11i	−0.261811	−	0.151157i	−0.625161	+	0.780496i	$0.714967\pi$
$32$	16902.7	−	29276.3i	0.515829	−	0.893443i
$33$	262.352	−	151.469i	0.00730034	−	0.00421485i
$34$		−	968.141i		−	0.0246321i
$35$	3577.38	−	21055.7i	0.0834375	−	0.491094i
$36$	10617.2			0.227564
$37$	16564.6	+	28690.7i	0.327020	+	0.566416i	0.981919	−	0.189301i	$-0.0606221\pi$
$37$	16564.6	+	28690.7i	0.327020	+	0.566416i	−0.654899	+	0.755717i	$0.727289\pi$
$38$	−37121.7	−	21432.2i	−0.676514	−	0.390585i
$39$	−12803.2	+	22175.8i	−0.215836	+	0.373839i
$40$	26169.8	−	15109.1i	0.408903	−	0.236080i
$41$			73712.4i			1.06952i	0.845004	+	0.534760i	$0.179598\pi$
$41$			73712.4i			1.06952i	−0.845004	+	0.534760i	$0.820402\pi$
$42$	−18554.1	−	15372.5i	−0.250434	−	0.207490i
$43$	4761.19			0.0598839			0.0299420	−	0.999552i	$-0.490468\pi$
$43$	4761.19			0.0598839			0.0299420	+	0.999552i	$0.490468\pi$
$44$	424.547	+	735.337i	0.00498388	+	0.00863234i
$45$	13103.6	+	7565.38i	0.143798	+	0.0830220i
$46$	−32553.9	+	56384.9i	−0.334448	+	0.579281i
$47$	−63760.5	+	36812.2i	−0.614127	+	0.354567i	−0.774579	−	0.632477i	$-0.782038\pi$
$47$	−63760.5	+	36812.2i	−0.614127	+	0.354567i	0.160452	+	0.987044i	$0.448705\pi$
$48$			9498.40i			0.0858869i
$49$	−21873.6	−	115598.i	−0.185922	−	0.982564i
$50$	−52940.7			−0.423526
$51$	1674.48	+	2900.29i	0.0126232	+	0.0218641i
$52$	−62155.6	−	35885.5i	−0.442049	−	0.255217i
$53$	−119317.	+	206663.i	−0.801447	+	1.38815i	0.117216	+	0.993106i	$0.462603\pi$
$53$	−119317.	+	206663.i	−0.801447	+	1.38815i	−0.918664	+	0.395041i	$0.870730\pi$
$54$	14783.3	−	8535.13i	0.0938835	−	0.0542037i
$55$			1210.06i			0.00727307i
$56$	106201.	−	128181.i	0.604732	−	0.729891i
$57$	148275.			0.800654
$58$	96924.8	+	167879.i	0.496765	+	0.860422i
$59$	−282811.	−	163281.i	−1.37702	−	0.795023i	−0.385221	−	0.922824i	$-0.625875\pi$
$59$	−282811.	−	163281.i	−1.37702	−	0.795023i	−0.991800	+	0.127801i	$0.959208\pi$
$60$	−21204.7	+	36727.6i	−0.0981700	+	0.170035i
$61$	350517.	−	202371.i	1.54426	−	0.891578i	0.545696	−	0.837983i	$-0.316265\pi$
$61$	350517.	−	202371.i	1.54426	−	0.891578i	0.998563	−	0.0535954i	$-0.0170681\pi$
$62$		−	40585.7i		−	0.170294i
$63$	82171.4	+	13961.0i	0.328624	+	0.0558336i
$64$	113344.			0.432374
$65$	−51141.0	−	88578.8i	−0.186221	−	0.322545i
$66$	1182.27	+	682.582i	0.00411229	+	0.00237423i
$67$	−109982.	+	190494.i	−0.365676	+	0.633369i	−0.988884	−	0.148687i	$-0.952495\pi$
$67$	−109982.	+	190494.i	−0.365676	+	0.633369i	0.623209	+	0.782056i	$0.285829\pi$
$68$	−8129.12	+	4693.35i	−0.0258533	+	0.0149264i
$69$		−	225219.i		−	0.685579i
$70$	90233.8	−	33481.4i	0.263072	−	0.0976134i
$71$	350228.			0.978535			0.489267	−	0.872134i	$-0.337264\pi$
$71$	350228.			0.978535			0.489267	+	0.872134i	$0.337264\pi$
$72$	58964.6	+	102130.i	0.157977	+	0.273624i
$73$	−174606.	−	100809.i	−0.448838	−	0.259137i	0.258501	−	0.966011i	$-0.416771\pi$
$73$	−174606.	−	100809.i	−0.448838	−	0.259137i	−0.707339	+	0.706874i	$0.750105\pi$
$74$	−74646.7	+	129292.i	−0.184211	+	0.319063i
$75$	158596.	−	91565.7i	0.375932	−	0.217045i
$76$			415596.i			0.946739i
$77$	2318.83	+	6249.36i	0.00507923	+	0.0136887i
$78$	−115393.			−0.243161
$79$	−197745.	−	342505.i	−0.401074	−	0.694681i	0.592782	−	0.805363i	$-0.298030\pi$
$79$	−197745.	−	342505.i	−0.401074	−	0.694681i	−0.993856	+	0.110682i	$0.964696\pi$
$80$	−32857.4	−	18970.2i	−0.0641745	−	0.0370512i
$81$	−29524.5	+	51137.9i	−0.0555556	+	0.0962250i
$82$	−287675.	+	166089.i	−0.521747	+	0.301231i
$83$		−	13229.0i		−	0.0231362i	−0.999933	−	0.0115681i	$-0.996318\pi$
$83$		−	13229.0i		−	0.0231362i	0.999933	−	0.0115681i	$-0.00368232\pi$
$84$	−39130.8	+	230315.i	−0.0660208	+	0.388584i
$85$	−13377.1			−0.0217824
$86$	10727.9	+	18581.3i	0.0168663	+	0.0292134i
$87$	−580722.	−	335280.i	−0.881882	−	0.509155i
$88$	−4715.59	+	8167.65i	−0.00691972	+	0.0119853i
$89$	−199460.	+	115158.i	−0.282934	+	0.163352i	−0.634751	−	0.772717i	$-0.718897\pi$
$89$	−199460.	+	115158.i	−0.282934	+	0.163352i	0.351817	+	0.936069i	$0.385564\pi$
$90$			68185.4i			0.0935328i
$91$	−433862.	−	359465.i	−0.575742	−	0.477015i
$92$	631258.			0.810668
$93$	70196.6	+	121584.i	0.0872705	+	0.151157i
$94$	−287331.	−	165891.i	−0.345939	−	0.199728i
$95$	−296136.	+	512922.i	−0.345398	+	0.598247i
$96$	−456373.	+	263487.i	−0.515829	+	0.297814i
$97$			662517.i			0.725909i	0.931807	+	0.362954i	$0.118232\pi$
$97$			662517.i			0.725909i	−0.931807	+	0.362954i	$0.881768\pi$
$98$	401853.	−	345831.i	0.426962	−	0.367439i
$99$	−4722.34			−0.00486689
$100$	256646.	+	444524.i	0.256646	+	0.444524i
$101$	1.62606e6	+	938803.i	1.57823	+	0.911193i	0.995106	+	0.0988126i	$0.0315044\pi$
$101$	1.62606e6	+	938803.i	1.57823	+	0.911193i	0.583127	+	0.812381i	$0.301829\pi$
$102$	−7545.91	+	13069.9i	−0.00711068	+	0.0123161i
$103$	782887.	−	452000.i	0.716452	−	0.413644i	−0.0969931	−	0.995285i	$-0.530922\pi$
$103$	782887.	−	452000.i	0.716452	−	0.413644i	0.813446	+	0.581641i	$0.197589\pi$
$104$		−	797186.i		−	0.708696i
$105$	−212407.	+	256369.i	−0.183485	+	0.221461i
$106$	−1.07538e6			−0.902912
$107$	−423106.	−	732842.i	−0.345381	−	0.598217i	0.640042	−	0.768340i	$-0.278917\pi$
$107$	−423106.	−	732842.i	−0.345381	−	0.598217i	−0.985423	+	0.170123i	$0.945584\pi$
$108$	−143333.	−	82753.1i	−0.113782	−	0.0656921i
$109$	847674.	−	1.46821e6i	0.654560	−	1.13373i	−0.327444	−	0.944871i	$-0.606187\pi$
$109$	847674.	−	1.46821e6i	0.654560	−	1.13373i	0.982004	−	0.188861i	$-0.0604794\pi$
$110$	−4722.44	+	2726.50i	−0.00354804	+	0.00204846i
$111$		−	516432.i		−	0.377611i
$112$	−206045.	−	35007.3i	−0.146659	−	0.0249175i
$113$	−152753.			−0.105866			−0.0529328	−	0.998598i	$-0.516857\pi$
$113$	−152753.			−0.105866			−0.0529328	+	0.998598i	$0.516857\pi$
$114$	334095.	+	578669.i	0.225505	+	0.390585i
$115$	779089.	+	449807.i	0.512264	+	0.295756i
$116$	939743.	−	1.62768e6i	0.602054	−	1.04279i
$117$	345686.	−	199582.i	0.215836	−	0.124613i
$118$		−	1.47162e6i		−	0.895675i
$119$	−69086.3	+	25634.6i	−0.0409969	+	0.0152120i
$120$	−471056.			−0.272602
$121$	885592.	+	1.53389e6i	0.499893	+	0.865841i
$122$	1.57957e6	+	911968.i	0.869883	+	0.502227i
$123$	574531.	−	995117.i	0.308744	−	0.534760i
$124$	−340783.	+	196751.i	−0.178737	+	0.103194i
$125$			1.70441e6i			0.872660i
$126$	130664.	+	352145.i	0.0653196	+	0.176039i
$127$	−2.82114e6			−1.37725			−0.688627	−	0.725116i	$-0.741786\pi$
$127$	−2.82114e6			−1.37725			−0.688627	+	0.725116i	$0.741786\pi$
$128$	−826385.	−	1.43134e6i	−0.394051	−	0.682517i
$129$	−64276.1	−	37109.8i	−0.0299420	−	0.0172870i
$130$	230462.	−	399172.i	0.104899	−	0.181690i
$131$	−3.86131e6	+	2.22933e6i	−1.71759	+	0.991654i	−0.794333	+	0.607482i	$0.792180\pi$
$131$	−3.86131e6	+	2.22933e6i	−1.71759	+	0.991654i	−0.923262	+	0.384171i	$0.874487\pi$
$132$		−	13236.1i		−	0.00575489i
$133$	−546484.	+	3.21648e6i	−0.232286	+	1.36718i
$134$	−991245.			−0.411971
$135$	−117933.	−	204265.i	−0.0479328	−	0.0830220i
$136$	−90292.9	−	52130.6i	−0.0358952	−	0.0207241i
$137$	−649623.	+	1.12518e6i	−0.252639	+	0.437583i	−0.964252	−	0.264989i	$-0.914632\pi$
$137$	−649623.	+	1.12518e6i	−0.252639	+	0.437583i	0.711613	+	0.702572i	$0.247965\pi$
$138$	878954.	−	507464.i	0.334448	−	0.193094i
$139$			119566.i			0.0445207i	0.999752	+	0.0222603i	$0.00708627\pi$
$139$			119566.i			0.0445207i	−0.999752	+	0.0222603i	$0.992914\pi$
$140$	−718566.	−	595349.i	−0.261868	−	0.216964i
$141$	1.14769e6			0.409418
$142$	789136.	+	1.36682e6i	0.275605	+	0.477361i
$143$	27645.6	+	15961.2i	0.00945406	+	0.00545830i
$144$	74032.7	−	128228.i	0.0247934	−	0.0429434i
$145$	2.31963e6	−	1.33924e6i	0.760879	−	0.439293i
$146$		−	908570.i		−	0.291944i
$147$	−605702.	+	1.73106e6i	−0.190681	+	0.544953i
$148$	1.44749e6			0.446509
$149$	−3.12914e6	−	5.41983e6i	−0.945946	−	1.63843i	−0.753845	−	0.657052i	$-0.771803\pi$
$149$	−3.12914e6	−	5.41983e6i	−0.945946	−	1.63843i	−0.192101	−	0.981375i	$-0.561530\pi$
$150$	714700.	+	412632.i	0.211763	+	0.122261i
$151$	753969.	−	1.30591e6i	0.218989	−	0.379300i	−0.735510	−	0.677514i	$-0.763057\pi$
$151$	753969.	−	1.30591e6i	0.218989	−	0.379300i	0.954499	+	0.298213i	$0.0963907\pi$
$152$	−3.99772e6	+	2.30808e6i	−1.13836	+	0.657235i
$153$		−	52205.3i		−	0.0145761i
$154$	−19164.3	+	23130.7i	−0.00524725	+	0.00633325i
$155$	−560786.			−0.150592
$156$	559400.	+	968910.i	0.147350	+	0.255217i
$157$	2.14761e6	+	1.23992e6i	0.554954	+	0.320403i	0.751118	−	0.660169i	$-0.229515\pi$
$157$	2.14761e6	+	1.23992e6i	0.554954	+	0.320403i	−0.196164	+	0.980571i	$0.562848\pi$
$158$	891121.	−	1.54347e6i	0.225925	−	0.391314i
$159$	3.22156e6	−	1.85997e6i	0.801447	−	0.462716i
$160$		−	2.10494e6i		−	0.513902i
$161$	4.88558e6	+	830066.i	1.17068	+	0.198900i
$162$	−266099.			−0.0625890
$163$	−3.29510e6	−	5.70727e6i	−0.760861	−	1.31785i	−0.942407	−	0.334468i	$-0.891444\pi$
$163$	−3.29510e6	−	5.70727e6i	−0.760861	−	1.31785i	0.181546	−	0.983382i	$-0.441890\pi$
$164$	2.78918e6	+	1.61033e6i	0.632331	+	0.365076i
$165$	9431.46	−	16335.8i	0.00209955	−	0.00363653i
$166$	51628.2	−	29807.5i	0.0112866	−	0.00651631i
$167$			5.45006e6i			1.17018i	0.810969	+	0.585089i	$0.198941\pi$
$167$			5.45006e6i			1.17018i	−0.810969	+	0.585089i	$0.801059\pi$
$168$	−2.43278e6	+	902686.i	−0.513068	+	0.190375i
$169$	2.12851e6			0.440978
$170$	−30141.4	−	52206.4i	−0.00613502	−	0.0106262i
$171$	−2.00172e6	−	1.15569e6i	−0.400327	−	0.231129i
$172$	104014.	−	180157.i	0.0204411	−	0.0354051i
$173$	2.39148e6	−	1.38072e6i	0.461879	−	0.266666i	−0.250955	−	0.967999i	$-0.580745\pi$
$173$	2.39148e6	−	1.38072e6i	0.461879	−	0.266666i	0.712834	+	0.701333i	$0.247411\pi$
$174$		−	3.02182e6i		−	0.573615i
$175$	1.40177e6	+	3.77784e6i	0.261556	+	0.704903i
$176$	11841.3			0.00217200
$177$	2.54530e6	+	4.40859e6i	0.459007	+	0.795023i
$178$	−898847.	−	518949.i	−0.159377	−	0.0920164i
$179$	743863.	−	1.28841e6i	0.129698	−	0.224644i	−0.793861	−	0.608099i	$-0.791932\pi$
$179$	743863.	−	1.28841e6i	0.129698	−	0.224644i	0.923560	+	0.383455i	$0.125266\pi$
$180$	572527.	−	330549.i	0.0981700	−	0.0566785i
$181$		−	6.01679e6i		−	1.01468i	−0.861746	−	0.507340i	$-0.830629\pi$
$181$		−	6.01679e6i		−	1.01468i	0.861746	−	0.507340i	$-0.169371\pi$
$182$	425291.	−	2.50317e6i	0.0705459	−	0.415217i
$183$	−6.30931e6			−1.02951
$184$	3.50580e6	+	6.07222e6i	0.562773	+	0.974752i
$185$	1.78647e6	+	1.03142e6i	0.282150	+	0.162899i
$186$	−316334.	+	547907.i	−0.0491595	+	0.0851468i
$187$	3615.68	−	2087.51i	0.000552923	−	0.000319230i
$188$			3.21682e6i			0.484120i
$189$	−1.00050e6	−	828937.i	−0.148194	−	0.122782i
$190$	−2.66902e6			−0.389126
$191$	−3.20172e6	−	5.54554e6i	−0.459498	−	0.795874i	0.539437	−	0.842026i	$-0.318637\pi$
$191$	−3.20172e6	−	5.54554e6i	−0.459498	−	0.795874i	−0.998934	+	0.0461527i	$0.985304\pi$
$192$	−1.53015e6	−	883431.i	−0.216187	−	0.124816i
$193$	−4.92592e6	+	8.53194e6i	−0.685197	+	1.18680i	0.288178	+	0.957577i	$0.406951\pi$
$193$	−4.92592e6	+	8.53194e6i	−0.685197	+	1.18680i	−0.973375	+	0.229219i	$0.926383\pi$
$194$	−2.58558e6	+	1.49279e6i	−0.354122	+	0.204453i
$195$			1.59442e6i			0.215030i
$196$	−4.85191e6	−	1.69770e6i	−0.644384	−	0.225472i
$197$	2.38883e6			0.312454			0.156227	−	0.987721i	$-0.450067\pi$
$197$	2.38883e6			0.312454			0.156227	+	0.987721i	$0.450067\pi$
$198$	−10640.4	−	18429.7i	−0.00137076	−	0.00237423i
$199$	−1.36103e7	−	7.85789e6i	−1.72706	−	0.997118i	−0.901464	−	0.432854i	$-0.857507\pi$
$199$	−1.36103e7	−	7.85789e6i	−1.72706	−	0.997118i	−0.825594	−	0.564264i	$-0.809160\pi$
$200$	−2.85066e6	+	4.93748e6i	−0.356332	+	0.617185i
$201$	2.96951e6	−	1.71445e6i	0.365676	−	0.211123i
$202$			8.46126e6i			1.02655i
$203$	9.41339e6	−	1.13617e7i	1.12527	−	1.35817i
$204$	146324.			0.0172356
$205$	2.29491e6	+	3.97490e6i	0.266381	+	0.461386i
$206$	3.52801e6	+	2.03690e6i	0.403578	+	0.233006i
$207$	−1.75541e6	+	3.04046e6i	−0.197910	+	0.342790i
$208$	−866808.	+	500452.i	−0.0963236	+	0.0556125i
$209$		−	184849.i		−	0.0202478i
$210$	−1.47912e6	−	251304.i	−0.159715	−	0.0271357i
$211$	1.46740e6			0.156207			0.0781034	−	0.996945i	$-0.475114\pi$
$211$	1.46740e6			0.156207			0.0781034	+	0.996945i	$0.475114\pi$
$212$	5.21324e6	+	9.02959e6i	0.547142	+	0.947677i
$213$	−4.72808e6	−	2.72976e6i	−0.489267	−	0.282479i
$214$	1.90669e6	−	3.30248e6i	0.194553	−	0.336976i
$215$	256744.	−	148231.i	0.0258336	−	0.0149151i
$216$		−	1.83833e6i		−	0.182416i
$217$	−2.89619e6	+	1.07464e6i	−0.283431	+	0.105168i
$218$	7.63993e6			0.737429
$219$	1.57145e6	+	2.72183e6i	0.149613	+	0.259137i
$220$	45786.9	+	26435.1i	0.00430005	+	0.00248263i
$221$	−176450.	+	305621.i	−0.0163473	+	0.0283143i
$222$	2.01546e6	−	1.16363e6i	0.184211	−	0.106354i
$223$		−	3.63341e6i		−	0.327642i	−0.986490	−	0.163821i	$-0.947618\pi$
$223$		−	3.63341e6i		−	0.327642i	0.986490	−	0.163821i	$-0.0523820\pi$
$224$	−4.03371e6	−	1.08710e7i	−0.358889	−	0.967222i
$225$	−2.85474e6			−0.250621
$226$	−344184.	−	596144.i	−0.0298171	−	0.0516447i
$227$	5.14121e6	+	2.96828e6i	0.439529	+	0.253762i	0.703398	−	0.710796i	$-0.251665\pi$
$227$	5.14121e6	+	2.96828e6i	0.439529	+	0.253762i	−0.263869	+	0.964559i	$0.584999\pi$
$228$	3.23925e6	−	5.61054e6i	0.273300	−	0.473370i
$229$	1.05964e7	−	6.11784e6i	0.882373	−	0.509438i	0.0109329	−	0.999940i	$-0.496520\pi$
$229$	1.05964e7	−	6.11784e6i	0.882373	−	0.509438i	0.871440	+	0.490502i	$0.163187\pi$
$230$			4.05403e6i			0.333199i
$231$	17404.6	−	102440.i	0.00141198	−	0.00831061i
$232$	2.08761e7			1.67180
$233$	−6.06046e6	−	1.04970e7i	−0.479113	−	0.829848i	0.520600	−	0.853801i	$-0.325708\pi$
$233$	−6.06046e6	−	1.04970e7i	−0.479113	−	0.829848i	−0.999713	+	0.0239524i	$0.992375\pi$
$234$	1.55780e6	+	899397.i	0.121581	+	0.0701946i
$235$	−2.29216e6	+	3.97015e6i	−0.176621	+	0.305917i
$236$	−1.23567e7	+	7.13413e6i	−0.940081	+	0.542756i
$237$			6.16509e6i			0.463121i
$238$	−255709.	−	211861.i	−0.0189677	−	0.0157152i
$239$	1.19016e7			0.871790			0.435895	−	0.899998i	$-0.356432\pi$
$239$	1.19016e7			0.871790			0.435895	+	0.899998i	$0.356432\pi$
$240$	295716.	+	512195.i	0.0213915	+	0.0370512i
$241$	−8.62117e6	−	4.97743e6i	−0.615907	−	0.355594i	0.159367	−	0.987219i	$-0.449055\pi$
$241$	−8.62117e6	−	4.97743e6i	−0.615907	−	0.355594i	−0.775274	+	0.631625i	$0.782388\pi$
$242$	−3.99084e6	+	6.91233e6i	−0.281590	+	0.487729i
$243$	797162.	−	460241.i	0.0555556	−	0.0320750i
$244$		−	1.76841e7i		−	1.21735i
$245$	−4.77845e6	−	5.55254e6i	−0.324929	−	0.377566i
$246$	5.17814e6			0.347831
$247$	7.81234e6	+	1.35314e7i	0.518430	+	0.897947i
$248$	−3.78520e6	−	2.18539e6i	−0.248161	−	0.143276i
$249$	−103109.	+	178591.i	−0.00667883	+	0.0115681i
$250$	−6.65175e6	+	3.84039e6i	−0.425712	+	0.245785i
$251$			4.57737e6i			0.289464i	0.989471	+	0.144732i	$0.0462320\pi$
$251$			4.57737e6i			0.289464i	−0.989471	+	0.144732i	$0.953768\pi$
$252$	2.32340e6	−	2.80426e6i	0.145185	−	0.175233i
$253$	−280772.			−0.0173377
$254$	−6.35661e6	−	1.10100e7i	−0.387904	−	0.671870i
$255$	180591.	+	104264.i	0.0108912	+	0.00628804i
$256$	7.35104e6	−	1.27324e7i	0.438156	−	0.758909i
$257$	−3.50429e6	+	2.02320e6i	−0.206443	+	0.119190i	−0.599657	−	0.800257i	$-0.704696\pi$
$257$	−3.50429e6	+	2.02320e6i	−0.206443	+	0.119190i	0.393214	+	0.919447i	$0.371363\pi$
$258$		−	334464.i		−	0.0194756i
$259$	1.12028e7	+	1.90336e6i	0.644801	+	0.109552i
$260$	−4.46893e6			−0.254263
$261$	5.22650e6	+	9.05256e6i	0.293961	+	0.509155i
$262$	−1.74006e7	−	1.00463e7i	−0.967523	−	0.558600i
$263$	−1.48379e7	+	2.56999e7i	−0.815651	+	1.41275i	0.0932094	+	0.995647i	$0.470287\pi$
$263$	−1.48379e7	+	2.56999e7i	−0.815651	+	1.41275i	−0.908860	+	0.417102i	$0.863046\pi$
$264$	127321.	−	73508.8i	0.00691972	−	0.00399510i
$265$			1.48589e7i			0.798453i
$266$	−1.37842e7	+	5.11464e6i	−0.732379	+	0.271751i
$267$	3.59027e6			0.188623
$268$	4.80535e6	+	8.32312e6i	0.249644	+	0.432396i
$269$	−1.77285e7	−	1.02355e7i	−0.910783	−	0.525841i	−0.0300997	−	0.999547i	$-0.509582\pi$
$269$	−1.77285e7	−	1.02355e7i	−0.910783	−	0.525841i	−0.880683	+	0.473706i	$0.842916\pi$
$270$	531452.	−	920503.i	0.0270006	−	0.0467664i
$271$	2.19287e6	−	1.26606e6i	0.110181	−	0.0636128i	−0.443897	−	0.896078i	$-0.646404\pi$
$271$	2.19287e6	−	1.26606e6i	0.110181	−	0.0636128i	0.554078	+	0.832465i	$0.313071\pi$
$272$			130905.i			0.00650502i
$273$	3.05539e6	+	8.23440e6i	0.150168	+	0.404710i
$274$	−5.85494e6			−0.284623
$275$	−114151.	−	197716.i	−0.00548887	−	0.00950700i
$276$	−8.52198e6	−	4.92017e6i	−0.405334	−	0.234020i
$277$	−1.52864e7	+	2.64769e7i	−0.719229	+	1.24574i	0.242077	+	0.970257i	$0.422171\pi$
$277$	−1.52864e7	+	2.64769e7i	−0.719229	+	1.24574i	−0.961306	+	0.275484i	$0.911162\pi$
$278$	−466624.	+	269405.i	−0.0217186	+	0.0125393i
$279$		−	2.18851e6i		−	0.100771i
$280$	1.73612e6	−	1.02184e7i	0.0790872	−	0.465490i
$281$	−2.27089e7			−1.02348			−0.511738	−	0.859142i	$-0.670998\pi$
$281$	−2.27089e7			−1.02348			−0.511738	+	0.859142i	$0.670998\pi$
$282$	2.58598e6	+	4.47905e6i	0.115313	+	0.199728i
$283$	3.54922e7	+	2.04914e7i	1.56593	+	0.904092i	0.996636	+	0.0819595i	$0.0261178\pi$
$283$	3.54922e7	+	2.04914e7i	1.56593	+	0.904092i	0.569297	+	0.822132i	$0.307216\pi$
$284$	7.65114e6	−	1.32522e7i	0.334019	−	0.578538i
$285$	7.99566e6	−	4.61630e6i	0.345398	−	0.199416i
$286$			143855.i			0.00614934i
$287$	1.94692e7	+	1.61307e7i	0.823573	+	0.682349i
$288$	8.21471e6			0.343886
$289$	−1.20457e7	−	2.08638e7i	−0.499044	−	0.864369i
$290$	1.04532e7	+	6.03517e6i	0.428604	+	0.247454i
$291$	5.16381e6	−	8.94398e6i	0.209552	−	0.362954i
$292$	−7.62892e6	+	4.40456e6i	−0.306418	+	0.176911i
$293$		−	2.94333e7i		−	1.17014i	−0.810984	−	0.585069i	$-0.801068\pi$
$293$		−	2.94333e7i		−	1.17014i	0.810984	−	0.585069i	$-0.198932\pi$
$294$	−8.12050e6	+	1.53658e6i	−0.319552	+	0.0604661i
$295$	−2.03339e7			−0.792053
$296$	8.03887e6	+	1.39237e7i	0.309970	+	0.536884i
$297$	63751.6	+	36807.0i	0.00243345	+	0.00140495i
$298$	1.41012e7	−	2.44240e7i	0.532853	−	0.922928i
$299$	2.05531e7	−	1.18663e7i	0.768889	−	0.443918i
$300$		−	8.00143e6i		−	0.296349i
$301$	1.04190e6	−	1.25754e6i	0.0382057	−	0.0461130i
$302$	6.79538e6			0.246714
$303$	−1.46345e7	−	2.53477e7i	−0.526078	−	0.911193i
$304$	5.01931e6	+	2.89790e6i	0.178658	+	0.103148i
$305$	1.26010e7	−	2.18255e7i	0.444124	−	0.769245i
$306$	203740.	−	117629.i	0.00711068	−	0.00410535i
$307$		−	4.67295e6i		−	0.161501i	−0.996734	−	0.0807506i	$-0.974268\pi$
$307$		−	4.67295e6i		−	0.161501i	0.996734	−	0.0807506i	$-0.0257317\pi$
$308$	287125.	+	48782.8i	0.00982694	+	0.00166961i
$309$	−1.40920e7			−0.477635
$310$	−1.26357e6	−	2.18856e6i	−0.0424143	−	0.0734638i
$311$	2.77399e7	+	1.60156e7i	0.922196	+	0.532430i	0.884335	−	0.466853i	$-0.154612\pi$
$311$	2.77399e7	+	1.60156e7i	0.922196	+	0.532430i	0.0378610	+	0.999283i	$0.487946\pi$
$312$	−6.21345e6	+	1.07620e7i	−0.204583	+	0.354348i
$313$	1.88804e7	−	1.09006e7i	0.615714	−	0.355483i	−0.159484	−	0.987200i	$-0.550983\pi$
$313$	1.88804e7	−	1.09006e7i	0.615714	−	0.355483i	0.775199	+	0.631718i	$0.217650\pi$
$314$			1.11752e7i			0.360966i
$315$	4.86570e6	−	1.80542e6i	0.155673	−	0.0577627i
$316$	−1.72799e7			−0.547620
$317$	−5.26241e6	−	9.11476e6i	−0.165199	−	0.286133i	0.771527	−	0.636196i	$-0.219493\pi$
$317$	−5.26241e6	−	9.11476e6i	−0.165199	−	0.286133i	−0.936726	+	0.350064i	$0.886160\pi$
$318$	1.45177e7	+	8.38178e6i	0.451456	+	0.260648i
$319$	−417980.	+	723962.i	−0.0128761	+	0.0223020i
$320$	6.11202e6	−	3.52878e6i	0.186524	−	0.107690i
$321$			1.31911e7i			0.398811i
$322$	7.76875e6	+	2.09371e7i	0.232693	+	0.627117i
$323$	2.04350e6			0.0606410
$324$	1.28999e6	+	2.23433e6i	0.0379273	+	0.0656921i
$325$	1.67122e7	+	9.64882e6i	0.486838	+	0.281076i
$326$	1.48490e7	−	2.57193e7i	0.428594	−	0.742346i
$327$	−2.28872e7	+	1.32139e7i	−0.654560	+	0.377910i
$328$			3.57730e7i			1.01376i
$329$	−4.22992e6	+	2.48964e7i	−0.118780	+	0.699114i
$330$	85004.0			0.00236536
$331$	−2.03472e7	−	3.52425e7i	−0.561076	−	0.971812i	−0.997403	−	0.0720239i	$-0.977054\pi$
$331$	−2.03472e7	−	3.52425e7i	−0.561076	−	0.971812i	0.436327	−	0.899788i	$-0.356279\pi$
$332$	−500566.	−	289002.i	−0.0136788	−	0.00789744i
$333$	−4.02519e6	+	6.97183e6i	−0.109007	+	0.188805i
$334$	−2.12698e7	+	1.22801e7i	−0.570852	+	0.329581i
$335$			1.36964e7i			0.364310i
$336$	2.50875e6	+	2.07856e6i	0.0661363	+	0.0547955i
$337$	−4.05258e7			−1.05887			−0.529434	−	0.848351i	$-0.677596\pi$
$337$	−4.05258e7			−1.05887			−0.529434	+	0.848351i	$0.677596\pi$
$338$	4.79598e6	+	8.30688e6i	0.124202	+	0.215123i
$339$	2.06217e6	+	1.19059e6i	0.0529328	+	0.0305607i
$340$	−292238.	+	506172.i	−0.00743533	+	0.0128784i
$341$	151574.	−	87511.3i	0.00382262	−	0.00220699i
$342$		−	1.04160e7i		−	0.260390i
$343$	−3.53187e7	−	1.95192e7i	−0.875231	−	0.483704i
$344$	2.31063e6			0.0567617
$345$	−7.01180e6	−	1.21448e7i	−0.170755	−	0.295756i
$346$	1.07770e7	+	6.22209e6i	0.260177	+	0.150213i
$347$	8.26775e6	−	1.43202e7i	0.197879	−	0.342736i	−0.749962	−	0.661481i	$-0.769928\pi$
$347$	8.26775e6	−	1.43202e7i	0.197879	−	0.342736i	0.947840	+	0.318745i	$0.103262\pi$
$348$	−2.53731e7	+	1.46491e7i	−0.602054	+	0.347596i
$349$		−	5.07209e6i		−	0.119319i	−0.998219	−	0.0596597i	$-0.980998\pi$
$349$		−	5.07209e6i		−	0.119319i	0.998219	−	0.0596597i	$-0.0190015\pi$
$350$	−1.15852e7	+	1.39829e7i	−0.270208	+	0.326132i
$351$	−6.22234e6			−0.143891
$352$	328479.	+	568942.i	0.00753146	+	0.0130449i
$353$	−3.94332e7	−	2.27668e7i	−0.896475	−	0.517580i	−0.0204200	−	0.999791i	$-0.506500\pi$
$353$	−3.94332e7	−	2.27668e7i	−0.896475	−	0.517580i	−0.876055	+	0.482211i	$0.839834\pi$
$354$	−1.14702e7	+	1.98669e7i	−0.258559	+	0.447837i
$355$	1.88858e7	−	1.09037e7i	0.422135	−	0.243720i
$356$			1.00630e7i			0.223038i
$357$	1.13247e6	+	192408.i	0.0248898	+	0.00422880i
$358$	6.70430e6			0.146118
$359$	2.00085e7	+	3.46558e7i	0.432446	+	0.749018i	0.997083	−	0.0763210i	$-0.0243174\pi$
$359$	2.00085e7	+	3.46558e7i	0.432446	+	0.749018i	−0.564638	+	0.825339i	$0.690984\pi$
$360$	6.35926e6	+	3.67152e6i	0.136301	+	0.0786934i
$361$	2.17150e7	−	3.76114e7i	0.461570	−	0.799463i
$362$	2.34815e7	−	1.35570e7i	0.494994	−	0.285785i
$363$		−	2.76100e7i		−	0.577227i
$364$	−2.30799e7	+	8.56383e6i	−0.478552	+	0.177568i
$365$	−1.25540e7			−0.258169
$366$	−1.42162e7	−	2.46231e7i	−0.289961	−	0.502227i
$367$	1.53736e7	+	8.87597e6i	0.311013	+	0.179563i	0.647380	−	0.762168i	$-0.275865\pi$
$367$	1.53736e7	+	8.87597e6i	0.311013	+	0.179563i	−0.336367	+	0.941731i	$0.609198\pi$
$368$	4.40169e6	−	7.62395e6i	0.0883234	−	0.152981i
$369$	−1.55123e7	+	8.95606e6i	−0.308744	+	0.178253i
$370$			9.29598e6i			0.183523i
$371$	2.84742e7	+	7.67391e7i	0.557609	+	1.50278i
$372$	6.13410e6			0.119158
$373$	2.69790e6	+	4.67291e6i	0.0519876	+	0.0900452i	0.890848	−	0.454301i	$-0.150111\pi$
$373$	2.69790e6	+	4.67291e6i	0.0519876	+	0.0900452i	−0.838860	+	0.544346i	$0.816778\pi$
$374$	16293.7	+	9407.18i	0.000311462	+	0.000179823i
$375$	1.32846e7	−	2.30096e7i	0.251915	−	0.436330i
$376$	−3.09433e7	+	1.78651e7i	−0.582108	+	0.336080i
$377$		−	7.06609e7i		−	1.31873i
$378$	980733.	−	5.77237e6i	0.0181583	−	0.106876i
$379$	3.47845e7			0.638951			0.319475	−	0.947595i	$-0.396493\pi$
$379$	3.47845e7			0.638951			0.319475	+	0.947595i	$0.396493\pi$
$380$	1.29388e7	+	2.24107e7i	0.235801	+	0.408418i
$381$	3.80854e7	+	2.19886e7i	0.688627	+	0.397579i
$382$	1.44283e7	−	2.49905e7i	0.258836	−	0.448316i
$383$	−4.90000e7	+	2.82902e7i	−0.872168	+	0.503546i	−0.868068	−	0.496445i	$-0.834638\pi$
$383$	−4.90000e7	+	2.82902e7i	−0.872168	+	0.503546i	−0.00409994	+	0.999992i	$0.501305\pi$
$384$			2.57641e7i			0.455011i
$385$	319605.	+	264800.i	0.00560055	+	0.00464019i
$386$	−4.43964e7			−0.771944
$387$	578485.	+	1.00196e6i	0.00998065	+	0.0172870i
$388$	2.50688e7	+	1.44735e7i	0.429178	+	0.247786i
$389$	1.30039e7	−	2.25234e7i	0.220915	−	0.382636i	−0.734171	−	0.678964i	$-0.762429\pi$
$389$	1.30039e7	−	2.25234e7i	0.220915	−	0.382636i	0.955086	+	0.296329i	$0.0957624\pi$
$390$	−6.22248e6	+	3.59255e6i	−0.104899	+	0.0605632i
$391$		−	3.10392e6i		−	0.0519254i
$392$	−1.06154e7	−	5.61002e7i	−0.176229	−	0.931336i
$393$	6.95036e7			1.14506
$394$	5.38252e6	+	9.32280e6i	0.0880029	+	0.152425i
$395$	−2.13266e7	−	1.23129e7i	−0.346043	−	0.199788i
$396$	−103165.	+	178687.i	−0.00166129	+	0.00287745i
$397$	−1.18039e7	+	6.81496e6i	−0.188648	+	0.108916i	−0.591350	−	0.806415i	$-0.701405\pi$
$397$	−1.18039e7	+	6.81496e6i	−0.188648	+	0.108916i	0.402701	+	0.915331i	$0.368071\pi$
$398$		−	7.08217e7i		−	1.12335i
$399$	3.24475e7	−	3.91631e7i	0.510814	−	0.616535i
$400$	7.15825e6			0.111848
$401$	2.00929e7	+	3.48019e7i	0.311609	+	0.539722i	0.978711	−	0.205244i	$-0.0657988\pi$
$401$	2.00929e7	+	3.48019e7i	0.311609	+	0.539722i	−0.667102	+	0.744966i	$0.732465\pi$
$402$	1.33818e7	+	7.72599e6i	0.205986	+	0.118926i
$403$	−7.39703e6	+	1.28120e7i	−0.113017	+	0.195751i
$404$	7.10461e7	−	4.10185e7i	1.07745	−	0.622064i
$405$			3.67677e6i			0.0553480i
$406$	6.55510e7	+	1.11372e7i	0.979493	+	0.166417i
$407$	−643815.			−0.00954944
$408$	812636.	+	1.40753e6i	0.0119651	+	0.0207241i
$409$	6.55577e6	+	3.78497e6i	0.0958194	+	0.0553214i	0.547144	−	0.837038i	$-0.315715\pi$
$409$	6.55577e6	+	3.78497e6i	0.0958194	+	0.0553214i	−0.451325	+	0.892360i	$0.649048\pi$
$410$	−1.03418e7	+	1.79125e7i	−0.150053	+	0.259899i
$411$	1.75398e7	−	1.01266e7i	0.252639	−	0.145861i
$412$		−	3.94978e7i		−	0.564783i
$413$	−1.05015e8	+	3.89659e7i	−1.49073	+	0.553139i
$414$	−1.58212e7			−0.222965
$415$	−411860.	−	713363.i	−0.00576243	−	0.00998082i
$416$	−4.80907e7	−	2.77652e7i	−0.668008	−	0.385674i
$417$	931921.	−	1.61413e6i	0.0128520	−	0.0222603i
$418$	721404.	−	416503.i	0.00987756	−	0.00570281i
$419$			3.12413e7i			0.424705i	0.977193	+	0.212353i	$0.0681125\pi$
$419$			3.12413e7i			0.424705i	−0.977193	+	0.212353i	$0.931887\pi$
$420$	5.06036e6	+	1.36379e7i	0.0683020	+	0.184077i
$421$	5.98978e7			0.802721			0.401361	−	0.915920i	$-0.368537\pi$
$421$	5.98978e7			0.802721			0.401361	+	0.915920i	$0.368537\pi$
$422$	3.30634e6	+	5.72675e6i	0.0439957	+	0.0762029i
$423$	−1.54938e7	−	8.94536e6i	−0.204709	−	0.118189i
$424$	−5.79052e7	+	1.00295e8i	−0.759661	+	1.31577i
$425$	2.18574e6	−	1.26194e6i	0.0284729	−	0.0164388i
$426$		−	2.46028e7i		−	0.318241i
$427$	2.32536e7	−	1.36865e8i	0.298680	−	1.75796i
$428$	−3.69730e7			−0.471577
$429$	−248811.	−	430953.i	−0.00315135	−	0.00545830i
$430$	1.15699e6	+	667991.i	0.0145521	+	0.00840166i
$431$	−4.81510e7	+	8.33999e7i	−0.601414	+	1.04168i	0.391194	+	0.920308i	$0.372062\pi$
$431$	−4.81510e7	+	8.33999e7i	−0.601414	+	1.04168i	−0.992607	+	0.121371i	$0.961271\pi$
$432$	−1.99888e6	+	1.15406e6i	−0.0247934	+	0.0143145i
$433$			1.11186e8i			1.36958i	0.728741	+	0.684790i	$0.240106\pi$
$433$			1.11186e8i			1.36958i	−0.728741	+	0.684790i	$0.759894\pi$
$434$	−1.07197e7	−	8.88148e6i	−0.131133	−	0.108647i
$435$	−4.17534e7			−0.507252
$436$	−3.70368e7	−	6.41497e7i	−0.446863	−	0.773989i
$437$	−1.19014e8	−	6.87129e7i	−1.42611	−	0.823368i
$438$	−7.08160e6	+	1.22657e7i	−0.0842770	+	0.145972i
$439$	−7.90517e7	+	4.56405e7i	−0.934367	+	0.539457i	−0.888190	−	0.459476i	$-0.848037\pi$
$439$	−7.90517e7	+	4.56405e7i	−0.934367	+	0.539457i	−0.0461770	+	0.998933i	$0.514704\pi$
$440$			587247.i			0.00689386i
$441$	2.16692e7	−	1.86483e7i	0.252655	−	0.217432i
$442$	−1.59031e6			−0.0184169
$443$	5.31635e7	+	9.20820e7i	0.611509	+	1.05916i	0.990986	+	0.133963i	$0.0427705\pi$
$443$	5.31635e7	+	9.20820e7i	0.611509	+	1.05916i	−0.379477	+	0.925201i	$0.623896\pi$
$444$	−1.95411e7	−	1.12821e7i	−0.223254	−	0.128896i
$445$	−7.17049e6	+	1.24197e7i	−0.0813709	+	0.140939i
$446$	1.41800e7	−	8.18681e6i	0.159835	−	0.0922806i
$447$			9.75570e7i			1.09228i
$448$	2.48034e7	−	2.99369e7i	0.275853	−	0.332945i
$449$	7.74221e7			0.855315			0.427657	−	0.903941i	$-0.359339\pi$
$449$	7.74221e7			0.855315			0.427657	+	0.903941i	$0.359339\pi$
$450$	−6.43230e6	−	1.11411e7i	−0.0705877	−	0.122261i
$451$	−1.24057e6	−	716245.i	−0.0135236	−	0.00780786i
$452$	−3.33707e6	+	5.77997e6i	−0.0361368	+	0.0625907i
$453$	−2.03572e7	+	1.17532e7i	−0.218989	+	0.126433i
$454$			2.67525e7i			0.285889i
$455$	−3.45871e7	−	5.87638e6i	−0.367180	−	0.0623844i
$456$	7.19589e7			0.758909
$457$	−9.50468e6	−	1.64626e7i	−0.0995838	−	0.172484i	0.811929	−	0.583757i	$-0.198418\pi$
$457$	−9.50468e6	−	1.64626e7i	−0.0995838	−	0.172484i	−0.911512	+	0.411272i	$0.865084\pi$
$458$	4.77517e7	+	2.75695e7i	0.497042	+	0.286967i
$459$	−406900.	+	704771.i	−0.00420774	+	0.00728803i
$460$	3.40402e7	−	1.96531e7i	0.349718	−	0.201910i
$461$			1.05709e8i			1.07897i	0.841996	+	0.539483i	$0.181380\pi$
$461$			1.05709e8i			1.07897i	−0.841996	+	0.539483i	$0.818620\pi$
$462$	439004.	−	162893.i	0.00445188	−	0.00165188i
$463$	−2.82212e7			−0.284336			−0.142168	−	0.989843i	$-0.545407\pi$
$463$	−2.82212e7			−0.284336			−0.142168	+	0.989843i	$0.545407\pi$
$464$	−1.31054e7	−	2.26993e7i	−0.131189	−	0.227226i
$465$	7.57062e6	+	4.37090e6i	0.0752961	+	0.0434722i
$466$	2.73109e7	−	4.73039e7i	0.269885	−	0.467454i
$467$	1.49701e8	−	8.64297e7i	1.46985	−	0.848619i	0.470423	−	0.882441i	$-0.344101\pi$
$467$	1.49701e8	−	8.64297e7i	1.46985	−	0.848619i	0.999428	+	0.0338227i	$0.0107681\pi$
$468$		−	1.74404e7i		−	0.170145i
$469$	2.62464e7	+	7.07351e7i	0.254420	+	0.685672i
$470$	−2.06589e7			−0.198982
$471$	−1.93285e7	−	3.34779e7i	−0.184985	−	0.320403i
$472$	−1.37250e8	−	7.92412e7i	−1.30523	−	0.753572i
$473$	−46263.3	+	80130.4i	−0.000437173	+	0.000757206i
$474$	−2.40603e7	+	1.38912e7i	−0.225925	+	0.130438i
$475$		−	1.11744e8i		−	1.04267i
$476$	−539292.	+	3.17415e6i	−0.00500038	+	0.0294311i
$477$	−5.79881e7			−0.534298
$478$	2.68167e7	+	4.64480e7i	0.245540	+	0.425288i
$479$	−2.41808e7	−	1.39608e7i	−0.220021	−	0.127029i	0.385939	−	0.922524i	$-0.373878\pi$
$479$	−2.41808e7	−	1.39608e7i	−0.220021	−	0.127029i	−0.605960	+	0.795495i	$0.707211\pi$
$480$	−1.64064e7	+	2.84167e7i	−0.148351	+	0.256951i
$481$	4.71287e7	−	2.72098e7i	0.423497	−	0.244506i
$482$		−	4.48607e7i		−	0.400613i
$483$	−5.94857e7	−	4.92853e7i	−0.527923	−	0.437397i
$484$	7.73871e7			0.682546
$485$	2.06263e7	+	3.57258e7i	0.180799	+	0.313153i
$486$	3.59233e6	+	2.07404e6i	0.0312945	+	0.0180679i
$487$	−2.68794e7	+	4.65566e7i	−0.232720	+	0.403082i	−0.958608	−	0.284731i	$-0.908096\pi$
$487$	−2.68794e7	+	4.65566e7i	−0.232720	+	0.403082i	0.725888	+	0.687813i	$0.241429\pi$
$488$	1.70108e8	−	9.82119e7i	1.46374	−	0.845093i
$489$			1.02731e8i			0.878567i
$490$	1.09029e7	−	3.11597e7i	0.0926728	−	0.264853i
$491$	9.34867e7			0.789779			0.394889	−	0.918729i	$-0.370783\pi$
$491$	9.34867e7			0.789779			0.394889	+	0.918729i	$0.370783\pi$
$492$	−2.51026e7	−	4.34790e7i	−0.210777	−	0.365076i
$493$	−8.00337e6	−	4.62075e6i	−0.0667932	−	0.0385631i
$494$	−3.52056e7	+	6.09778e7i	−0.292032	+	0.505814i
$495$	−254649.	+	147022.i	−0.00209955	+	0.00121218i
$496$			5.48770e6i			0.0449723i
$497$	7.66414e7	−	9.25036e7i	0.624301	−	0.753511i
$498$	−929307.			−0.00752439
$499$	−2.51376e6	−	4.35396e6i	−0.0202312	−	0.0350415i	0.855733	−	0.517418i	$-0.173107\pi$
$499$	−2.51376e6	−	4.35396e6i	−0.0202312	−	0.0350415i	−0.875964	+	0.482377i	$0.839774\pi$
$500$	6.44927e7	+	3.72349e7i	0.515941	+	0.297879i
$501$	4.24790e7	−	7.35759e7i	0.337802	−	0.585089i
$502$	−1.78639e7	+	1.03137e7i	−0.141210	+	0.0815277i
$503$		−	1.45016e8i		−	1.13949i	−0.821820	−	0.569747i	$-0.807041\pi$
$503$		−	1.45016e8i		−	1.13949i	0.821820	−	0.569747i	$-0.192959\pi$
$504$	3.98782e7	+	6.77536e6i	0.311490	+	0.0529225i
$505$	1.16912e8			0.907789
$506$	−632635.	−	1.09576e6i	−0.00488317	−	0.00845790i
$507$	−2.87349e7	−	1.65901e7i	−0.220489	−	0.127299i
$508$	−6.16311e7	+	1.06748e8i	−0.470120	+	0.814272i
$509$	1.14421e7	−	6.60609e6i	0.0867665	−	0.0500946i	−0.455989	−	0.889985i	$-0.650714\pi$
$509$	1.14421e7	−	6.60609e6i	0.0867665	−	0.0500946i	0.542755	+	0.839891i	$0.317381\pi$
$510$			939715.i			0.00708411i
$511$	−6.48353e7	+	2.40573e7i	−0.485903	+	0.180295i
$512$	−3.95237e7			−0.294474
$513$	1.80155e7	+	3.12037e7i	0.133442	+	0.231129i
$514$	−1.57918e7	−	9.11737e6i	−0.116290	−	0.0671399i
$515$	2.81445e7	−	4.87476e7i	0.206049	−	0.356888i
$516$	−2.80837e6	+	1.62141e6i	−0.0204411	+	0.0118017i
$517$		−	1.43078e6i		−	0.0103538i
$518$	1.78139e7	+	4.80092e7i	0.128165	+	0.345410i
$519$	−4.30466e7			−0.307919
$520$	−2.48190e7	−	4.29878e7i	−0.176512	−	0.305728i
$521$	−6.70170e7	−	3.86923e7i	−0.473884	−	0.273597i	0.243980	−	0.969780i	$-0.421547\pi$
$521$	−6.70170e7	−	3.86923e7i	−0.473884	−	0.273597i	−0.717864	+	0.696183i	$0.754880\pi$
$522$	−2.35527e7	+	4.07945e7i	−0.165588	+	0.286807i
$523$	−1.16424e8	+	6.72177e7i	−0.813840	+	0.469871i	−0.848288	−	0.529536i	$-0.822366\pi$
$523$	−1.16424e8	+	6.72177e7i	−0.813840	+	0.469871i	0.0344475	+	0.999407i	$0.489033\pi$
$524$			1.94809e8i			1.35399i
$525$	1.05214e7	−	6.19266e7i	0.0727103	−	0.427956i
$526$	−1.33731e8			−0.918913
$527$	967433.	+	1.67564e6i	0.00660981	+	0.0114485i
$528$	−159857.	−	92293.6i	−0.00108600	−	0.000627003i
$529$	−3.03516e7	+	5.25705e7i	−0.205029	+	0.355120i
$530$	−5.79893e7	+	3.34802e7i	−0.389512	+	0.224885i
$531$		−	7.93546e7i		−	0.530016i
$532$	1.09769e8	+	9.09459e7i	0.729027	+	0.604016i
$533$	1.21084e8			0.799657
$534$	8.08962e6	+	1.40116e7i	0.0531257	+	0.0920164i
$535$	−4.56315e7	−	2.63453e7i	−0.297991	−	0.172045i
$536$	−5.33747e7	+	9.24478e7i	−0.346610	+	0.600347i
$537$	−2.00843e7	+	1.15957e7i	−0.129698	+	0.0748813i
$538$		−	9.22511e7i		−	0.592413i
$539$	2.15804e6	+	755104.i	0.0137814	+	0.00482215i
$540$	−1.03055e7			−0.0654467
$541$	7.51469e7	+	1.30158e8i	0.474590	+	0.822015i	0.999577	−	0.0290960i	$-0.00926284\pi$
$541$	7.51469e7	+	1.30158e8i	0.474590	+	0.822015i	−0.524986	+	0.851111i	$0.675930\pi$
$542$	9.88197e6	+	5.70536e6i	0.0620649	+	0.0358332i
$543$	−4.68962e7	+	8.12266e7i	−0.292913	+	0.507340i
$544$	−6.28962e6	+	3.63132e6i	−0.0390686	+	0.0225563i
$545$		−	1.05563e8i		−	0.652115i
$546$	−2.52517e7	+	3.04779e7i	−0.155136	+	0.187244i
$547$	−6.65431e7			−0.406576			−0.203288	−	0.979119i	$-0.565163\pi$
$547$	−6.65431e7			−0.406576			−0.203288	+	0.979119i	$0.565163\pi$
$548$	2.83835e7	+	4.91617e7i	0.172474	+	0.298735i
$549$	8.51757e7	+	4.91762e7i	0.514753	+	0.297193i
$550$	514412.	−	890988.i	0.00309188	−	0.00535530i
$551$	−3.54349e8	+	2.04583e8i	−2.11825	+	1.22297i
$552$		−	1.09300e8i		−	0.649835i
$553$	−1.33737e8	−	2.27220e7i	−0.790816	−	0.134360i
$554$	−1.37774e8			−0.810284
$555$	−1.60782e7	−	2.78483e7i	−0.0940500	−	0.162899i
$556$	4.52420e6	+	2.61205e6i	0.0263219	+	0.0151969i
$557$	1.26843e8	−	2.19698e8i	0.734007	−	1.27134i	−0.221151	−	0.975240i	$-0.570981\pi$
$557$	1.26843e8	−	2.19698e8i	0.734007	−	1.27134i	0.955158	−	0.296097i	$-0.0956852\pi$
$558$	8.54103e6	−	4.93117e6i	0.0491595	−	0.0283823i
$559$		−	7.82096e6i		−	0.0447739i
$560$	−1.22007e7	+	4.52710e6i	−0.0694740	+	0.0257784i
$561$	−65082.2			−0.000368616
$562$	−5.11678e7	−	8.86252e7i	−0.288262	−	0.499285i
$563$	1.43519e8	+	8.28606e7i	0.804236	+	0.464326i	0.844950	−	0.534845i	$-0.179630\pi$
$563$	1.43519e8	+	8.28606e7i	0.804236	+	0.464326i	−0.0407139	+	0.999171i	$0.512963\pi$
$564$	2.50726e7	−	4.34270e7i	0.139753	−	0.242060i
$565$	−8.23711e6	+	4.75570e6i	−0.0456699	+	0.0263675i
$566$			1.84685e8i			1.01855i
$567$	7.04581e6	+	1.89888e7i	0.0386529	+	0.104171i
$568$	1.69968e8			0.927516
$569$	−8.19891e7	−	1.42009e8i	−0.445061	−	0.770868i	0.552996	−	0.833184i	$-0.313485\pi$
$569$	−8.19891e7	−	1.42009e8i	−0.445061	−	0.770868i	−0.998056	+	0.0623160i	$0.980151\pi$
$570$	3.60317e7	+	2.08029e7i	0.194563	+	0.112331i
$571$	1.70285e8	−	2.94942e8i	0.914677	−	1.58427i	0.107305	−	0.994226i	$-0.465778\pi$
$571$	1.70285e8	−	2.94942e8i	0.914677	−	1.58427i	0.807373	−	0.590042i	$-0.200889\pi$
$572$	1.20790e6	−	697382.i	0.00645421	−	0.00372634i
$573$			9.98198e7i			0.530582i
$574$	−1.90846e7	+	1.12327e8i	−0.100913	+	0.593950i
$575$	−1.69731e8			−0.892808
$576$	1.37713e7	+	2.38526e7i	0.0720623	+	0.124816i
$577$	2.37115e8	+	1.36899e8i	1.23433	+	0.712642i	0.967930	−	0.251220i	$-0.0808317\pi$
$577$	2.37115e8	+	1.36899e8i	1.23433	+	0.712642i	0.266402	+	0.963862i	$0.414165\pi$
$578$	5.42829e7	−	9.40207e7i	0.281112	−	0.486900i
$579$	1.33000e8	−	7.67875e7i	0.685197	−	0.395599i
$580$		−	1.17029e8i		−	0.599804i
$581$	−3.49408e6	−	2.89493e6i	−0.0178158	−	0.0147608i
$582$	4.65405e7			0.236081
$583$	−2.31875e6	−	4.01619e6i	−0.0117017	−	0.0202679i
$584$	−8.47371e7	−	4.89230e7i	−0.425437	−	0.245626i
$585$	1.24273e7	−	2.15246e7i	0.0620737	−	0.107515i
$586$	1.14868e8	−	6.63193e7i	0.570831	−	0.329570i
$587$		−	2.96429e8i		−	1.46557i	−0.680460	−	0.732785i	$-0.738220\pi$
$587$		−	2.96429e8i		−	1.46557i	0.680460	−	0.732785i	$-0.261780\pi$
$588$	5.22686e7	+	6.07358e7i	0.257104	+	0.298754i
$589$	8.56661e7			0.419241
$590$	−4.58164e7	−	7.93563e7i	−0.223082	−	0.386390i
$591$	−3.22492e7	−	1.86191e7i	−0.156227	−	0.0901978i
$592$	1.00932e7	−	1.74819e7i	0.0486477	−	0.0842603i
$593$	−1.12529e8	+	6.49684e7i	−0.539633	+	0.311557i	−0.744930	−	0.667142i	$-0.767517\pi$
$593$	−1.12529e8	+	6.49684e7i	−0.539633	+	0.311557i	0.205297	+	0.978700i	$0.434184\pi$
$594$			331735.i			0.00158282i
$595$	−2.92735e6	+	3.53321e6i	−0.0138971	+	0.0167733i
$596$	−2.73439e8			−1.29158
$597$	1.22492e8	+	2.12163e8i	0.575686	+	0.997118i
$598$	9.26206e7	+	5.34745e7i	0.433116	+	0.250060i
$599$	3.82426e7	−	6.62382e7i	0.177937	−	0.308197i	−0.763237	−	0.646119i	$-0.776391\pi$
$599$	3.82426e7	−	6.62382e7i	0.177937	−	0.308197i	0.941174	+	0.337923i	$0.109724\pi$
$600$	7.69677e7	−	4.44373e7i	0.356332	−	0.205728i
$601$			1.12466e8i			0.518080i	0.965867	+	0.259040i	$0.0834061\pi$
$601$			1.12466e8i			0.518080i	−0.965867	+	0.259040i	$0.916594\pi$
$602$	7.25539e6	+	1.23270e6i	0.0332561	+	0.00565025i
$603$	−5.34511e7			−0.243784
$604$	−3.29426e7	−	5.70583e7i	−0.149502	−	0.258945i
$605$	9.55100e7	+	5.51427e7i	0.431303	+	0.249013i
$606$	6.59490e7	−	1.14227e8i	0.296340	−	0.513276i
$607$	−4.03159e6	+	2.32764e6i	−0.0180264	+	0.0104076i	−0.508986	−	0.860775i	$-0.669980\pi$
$607$	−4.03159e6	+	2.32764e6i	−0.0180264	+	0.0104076i	0.490960	+	0.871182i	$0.336646\pi$
$608$			3.21553e8i			1.43068i
$609$	−2.15636e8	+	8.00122e7i	−0.954706	+	0.354245i
$610$	1.13570e8			0.500351
$611$	6.04695e7	+	1.04736e8i	0.265102	+	0.459170i
$612$	−1.97538e6	−	1.14048e6i	−0.00861778	−	0.00497548i
$613$	1.02768e8	−	1.78000e8i	0.446147	−	0.772749i	−0.551984	−	0.833854i	$-0.686129\pi$
$613$	1.02768e8	−	1.78000e8i	0.446147	−	0.772749i	0.998131	+	0.0611054i	$0.0194626\pi$
$614$	1.82369e7	−	1.05291e7i	0.0787856	−	0.0454869i
$615$		−	7.15481e7i		−	0.307590i
$616$	1.12534e6	+	3.03285e6i	0.00481441	+	0.0129750i
$617$	1.85696e8			0.790583			0.395292	−	0.918556i	$-0.370644\pi$
$617$	1.85696e8			0.790583			0.395292	+	0.918556i	$0.370644\pi$
$618$	−3.17521e7	−	5.49962e7i	−0.134526	−	0.233006i
$619$	7.59648e7	+	4.38583e7i	0.320288	+	0.184918i	0.651521	−	0.758631i	$-0.274131\pi$
$619$	7.59648e7	+	4.38583e7i	0.320288	+	0.184918i	−0.331233	+	0.943549i	$0.607465\pi$
$620$	−1.22510e7	+	2.12194e7i	−0.0514040	+	0.0890344i
$621$	4.73960e7	−	2.73641e7i	0.197910	−	0.114263i
$622$			1.44346e8i			0.599837i
$623$	−1.32323e7	+	7.78824e7i	−0.0547232	+	0.322088i
$624$	1.56025e7			0.0642157
$625$	−3.87164e7	−	6.70588e7i	−0.158582	−	0.274673i
$626$	8.50830e7	+	4.91227e7i	0.346832	+	0.200244i
$627$	−1.44076e6	+	2.49546e6i	−0.00584505	+	0.0101239i
$628$	9.38340e7	−	5.41751e7i	0.378862	−	0.218736i
$629$		−	7.11735e6i		−	0.0286000i
$630$	1.80094e7	+	1.49212e7i	0.0720239	+	0.0596735i
$631$	−4.15732e8			−1.65472			−0.827362	−	0.561670i	$-0.810159\pi$
$631$	−4.15732e8			−1.65472			−0.827362	+	0.561670i	$0.810159\pi$
$632$	−9.59668e7	−	1.66219e8i	−0.380163	−	0.658462i
$633$	−1.98099e7	−	1.14372e7i	−0.0781034	−	0.0450930i
$634$	2.37146e7	−	4.10748e7i	0.0930566	−	0.161179i
$635$	−1.52128e8	+	8.78313e7i	−0.594140	+	0.343027i
$636$		−	1.62533e8i		−	0.631785i
$637$	−1.89886e8	+	3.59306e7i	−0.734642	+	0.139010i
$638$	−3.76718e6			−0.0145062
$639$	4.25527e7	+	7.37035e7i	0.163089	+	0.282479i
$640$	−8.91246e7	−	5.14561e7i	−0.339983	−	0.196289i
$641$	−8.98600e7	+	1.55642e8i	−0.341187	+	0.590953i	−0.984653	−	0.174521i	$-0.944162\pi$
$641$	−8.98600e7	+	1.55642e8i	−0.341187	+	0.590953i	0.643466	+	0.765474i	$0.277496\pi$
$642$	−5.14806e7	+	2.97223e7i	−0.194553	+	0.112325i
$643$		−	8.10561e7i		−	0.304897i	−0.988311	−	0.152448i	$-0.951284\pi$
$643$		−	8.10561e7i		−	0.304897i	0.988311	−	0.152448i	$-0.0487158\pi$
$644$	1.38140e8	−	1.66730e8i	0.517203	−	0.624247i
$645$	−4.62140e6			−0.0172224
$646$	4.60442e6	+	7.97508e6i	0.0170796	+	0.0295827i
$647$	9.06246e7	+	5.23221e7i	0.334606	+	0.193185i	0.657884	−	0.753119i	$-0.271452\pi$
$647$	9.06246e7	+	5.23221e7i	0.334606	+	0.193185i	−0.323278	+	0.946304i	$0.604785\pi$
$648$	−1.43284e7	+	2.48175e7i	−0.0526590	+	0.0912081i
$649$	5.49601e6	−	3.17312e6i	0.0201054	−	0.0116079i
$650$			8.69630e7i			0.316661i
$651$	4.74745e7	+	8.06598e6i	0.172075	+	0.0292357i
$652$	−2.87941e8			−1.03887
$653$	−2.36179e8	−	4.09074e8i	−0.848206	−	1.46914i	−0.882808	−	0.469734i	$-0.844350\pi$
$653$	−2.36179e8	−	4.09074e8i	−0.848206	−	1.46914i	0.0346020	−	0.999401i	$-0.488984\pi$
$654$	−1.03139e8	−	5.95474e7i	−0.368714	−	0.212877i
$655$	−1.38812e8	+	2.40430e8i	−0.493975	+	0.855589i
$656$	3.88972e7	−	2.24573e7i	0.137787	−	0.0795511i
$657$		−	4.89930e7i		−	0.172758i
$658$	−1.06693e8	+	3.95886e7i	−0.374506	+	0.138961i
$659$	1.73758e8			0.607141			0.303570	−	0.952809i	$-0.401821\pi$
$659$	1.73758e8			0.607141			0.303570	+	0.952809i	$0.401821\pi$
$660$	−412082.	−	713747.i	−0.00143335	−	0.00248263i
$661$	−1.91974e7	−	1.10836e7i	−0.0664720	−	0.0383776i	0.466396	−	0.884576i	$-0.345552\pi$
$661$	−1.91974e7	−	1.10836e7i	−0.0664720	−	0.0383776i	−0.532868	+	0.846199i	$0.678886\pi$
$662$	9.16930e7	−	1.58817e8i	0.316055	−	0.547423i
$663$	4.76416e6	−	2.75059e6i	0.0163473	−	0.00943811i
$664$		−	6.42008e6i		−	0.0219299i
$665$	7.06707e7	+	1.90460e8i	0.240311	+	0.647649i
$666$	−3.62783e7			−0.122807
$667$	3.10746e8	+	5.38229e8i	1.04720	+	1.81380i
$668$	2.06223e8	+	1.19063e8i	0.691843	+	0.399436i
$669$	−2.83196e7	+	4.90510e7i	−0.0945821	+	0.163821i
$670$	−5.34523e7	+	3.08607e7i	−0.177722	+	0.102608i
$671$			7.86557e6i			0.0260353i
$672$	−3.02761e7	+	1.78198e8i	−0.0997682	+	0.587213i
$673$	−4.00045e8			−1.31239			−0.656195	−	0.754591i	$-0.727835\pi$
$673$	−4.00045e8			−1.31239			−0.656195	+	0.754591i	$0.727835\pi$
$674$	−9.13128e7	−	1.58158e8i	−0.298230	−	0.516550i
$675$	3.85389e7	+	2.22505e7i	0.125311	+	0.0723482i
$676$	4.64998e7	−	8.05401e7i	0.150526	−	0.260719i
$677$	−2.51224e8	+	1.45044e8i	−0.809646	+	0.467449i	−0.846833	−	0.531859i	$-0.821494\pi$
$677$	−2.51224e8	+	1.45044e8i	−0.809646	+	0.467449i	0.0371872	+	0.999308i	$0.488160\pi$
$678$			1.07306e7i			0.0344298i
$679$	1.74987e8	+	1.44980e8i	0.558979	+	0.463127i
$680$	−6.49199e6			−0.0206467
$681$	−4.62709e7	−	8.01435e7i	−0.146510	−	0.253762i
$682$	683054.	+	394362.i	0.00215329	+	0.00124320i
$683$	−5.77014e7	+	9.99417e7i	−0.181102	+	0.313678i	−0.942256	−	0.334893i	$-0.891300\pi$
$683$	−5.77014e7	+	9.99417e7i	−0.181102	+	0.313678i	0.761154	+	0.648571i	$0.224633\pi$
$684$	−8.74597e7	+	5.04949e7i	−0.273300	+	0.157790i
$685$			8.08996e7i			0.251695i
$686$	−3.40341e6	−	1.81818e8i	−0.0105425	−	0.563202i
$687$	−1.90735e8			−0.588249
$688$	−1.45055e6	−	2.51243e6i	−0.00445418	−	0.00771487i
$689$	3.39475e8	+	1.95996e8i	1.03789	+	0.599224i
$690$	3.15980e7	−	5.47294e7i	0.0961862	−	0.166599i
$691$	3.59314e8	−	2.07450e8i	1.08903	−	0.628752i	0.155712	−	0.987802i	$-0.450233\pi$
$691$	3.59314e8	−	2.07450e8i	1.08903	−	0.628752i	0.933318	+	0.359051i	$0.116899\pi$
$692$		−	1.20654e8i		−	0.364101i
$693$	−1.03340e6	+	1.24728e6i	−0.00310506	+	0.00374770i
$694$	7.45157e7			0.222930
$695$	3.72246e6	+	6.44750e6i	0.0110886	+	0.0192060i
$696$	−2.81827e8	−	1.62713e8i	−0.835902	−	0.482608i
$697$	7.91806e6	−	1.37145e7i	0.0233841	−	0.0405024i
$698$	1.97947e7	−	1.14285e7i	0.0582079	−	0.0336063i
$699$			1.88947e8i			0.553232i
$700$	1.73572e8	+	2.94900e7i	0.506040	+	0.0859768i
$701$	5.13427e8			1.49047			0.745237	−	0.666800i	$-0.232336\pi$
$701$	5.13427e8			1.49047			0.745237	+	0.666800i	$0.232336\pi$
$702$	−1.40202e7	−	2.42837e7i	−0.0405269	−	0.0701946i
$703$	−2.72902e8	−	1.57560e8i	−0.785491	−	0.453503i
$704$	−1.10134e6	+	1.90757e6i	−0.00315648	+	0.00546718i
$705$	6.18885e7	−	3.57313e7i	0.176621	−	0.101972i
$706$		−	2.05193e8i		−	0.583107i
$707$	6.03794e8	−	2.24039e8i	1.70856	−	0.633965i
$708$	2.22420e8			0.626721
$709$	−1.64200e8	−	2.84402e8i	−0.460716	−	0.797984i	0.538281	−	0.842766i	$-0.319074\pi$
$709$	−1.64200e8	−	2.84402e8i	−0.460716	−	0.797984i	−0.998997	+	0.0447818i	$0.985741\pi$
$710$	8.51073e7	+	4.91367e7i	0.237789	+	0.137288i
$711$	4.80521e7	−	8.32287e7i	0.133691	−	0.231560i
$712$	−9.67989e7	+	5.58869e7i	−0.268182	+	0.154835i
$713$		−	1.30120e8i		−	0.358985i
$714$	1.80078e6	+	4.85317e6i	0.00494727	+	0.0133331i
$715$	1.98770e6			0.00543791
$716$	−3.25011e7	−	5.62935e7i	−0.0885439	−	0.153363i
$717$	−1.60672e8	−	9.27638e7i	−0.435895	−	0.251664i
$718$	−9.01665e7	+	1.56173e8i	−0.243597	+	0.421923i
$719$	9.79686e7	−	5.65622e7i	0.263573	−	0.152174i	−0.362391	−	0.932026i	$-0.618039\pi$
$719$	9.79686e7	−	5.65622e7i	0.263573	−	0.152174i	0.625963	+	0.779853i	$0.284706\pi$
$720$		−	9.21952e6i		−	0.0247008i
$721$	5.19373e7	−	3.05691e8i	0.138571	−	0.815600i
$722$	1.95713e8			0.520006
$723$	7.75905e7	+	1.34391e8i	0.205302	+	0.355594i
$724$	−2.27667e8	−	1.31444e8i	−0.599907	−	0.346357i
$725$	−2.52676e8	+	4.37648e8i	−0.663055	+	1.14845i
$726$	1.07753e8	−	6.22110e7i	0.281590	−	0.162576i
$727$		−	9.97740e7i		−	0.259666i	−0.991536	−	0.129833i	$-0.958556\pi$
$727$		−	9.97740e7i		−	0.259666i	0.991536	−	0.129833i	$-0.0414440\pi$
$728$	−2.10556e8	−	1.74450e8i	−0.545724	−	0.452145i
$729$	−1.43489e7			−0.0370370
$730$	−2.82867e7	−	4.89940e7i	−0.0727133	−	0.125943i
$731$	−885838.	−	511439.i	−0.00226779	−	0.00130931i
$732$	−1.37834e8	+	2.38736e8i	−0.351418	+	0.608673i
$733$	3.13962e8	−	1.81266e8i	0.797197	−	0.460262i	−0.0452931	−	0.998974i	$-0.514422\pi$
$733$	3.13962e8	−	1.81266e8i	0.797197	−	0.460262i	0.842490	+	0.538712i	$0.181089\pi$
$734$			7.99975e7i			0.202296i
$735$	2.12314e7	+	1.12204e8i	0.0534707	+	0.282582i
$736$	4.88414e8			1.22505
$737$	−2.13733e6	−	3.70197e6i	−0.00533912	−	0.00924762i
$738$	−6.99050e7	−	4.03596e7i	−0.173916	−	0.100410i
$739$	1.02140e8	−	1.76912e8i	0.253083	−	0.438352i	−0.711290	−	0.702899i	$-0.751889\pi$
$739$	1.02140e8	−	1.76912e8i	0.253083	−	0.438352i	0.964373	+	0.264546i	$0.0852221\pi$
$740$	7.80549e7	−	4.50650e7i	0.192622	−	0.111210i
$741$		−	2.43565e8i		−	0.598631i
$742$	−2.35329e8	+	2.84034e8i	−0.576054	+	0.695278i
$743$	2.63900e8			0.643389			0.321695	−	0.946844i	$-0.395748\pi$
$743$	2.63900e8			0.643389			0.321695	+	0.946844i	$0.395748\pi$
$744$	3.40668e7	+	5.90054e7i	0.0827203	+	0.143276i
$745$	−3.37474e8	−	1.94841e8i	−0.816153	−	0.471206i
$746$	−1.21579e7	+	2.10580e7i	−0.0292847	+	0.0507226i
$747$	2.78396e6	−	1.60732e6i	0.00667883	−	0.00385603i
$748$		−	182416.i		−	0.000435872i
$749$	−2.86150e8	−	4.86172e7i	−0.681002	−	0.115703i
$750$	1.19732e8			0.283808
$751$	3.68938e8	+	6.39019e8i	0.871031	+	1.50867i	0.860932	+	0.508721i	$0.169881\pi$
$751$	3.68938e8	+	6.39019e8i	0.871031	+	1.50867i	0.0100992	+	0.999949i	$0.496785\pi$
$752$	3.88508e7	+	2.24305e7i	0.0913579	+	0.0527455i
$753$	3.56770e7	−	6.17945e7i	0.0835611	−	0.144732i
$754$	2.75766e8	−	1.59213e8i	0.643318	−	0.371420i
$755$		−	9.38940e7i		−	0.218171i
$756$	−5.32229e7	+	1.97484e7i	−0.123178	+	0.0457054i
$757$	−1.43307e8			−0.330355			−0.165177	−	0.986264i	$-0.552820\pi$
$757$	−1.43307e8			−0.330355			−0.165177	+	0.986264i	$0.552820\pi$
$758$	7.83765e7	+	1.35752e8i	0.179961	+	0.311701i
$759$	3.79042e6	+	2.18840e6i	0.00866885	+	0.00500496i
$760$	−1.43716e8	+	2.48924e8i	−0.327390	+	0.567056i
$761$	−6.67428e8	+	3.85340e8i	−1.51444	+	0.874360i	−0.514578	+	0.857443i	$0.672052\pi$
$761$	−6.67428e8	+	3.85340e8i	−1.51444	+	0.874360i	−0.999857	+	0.0169164i	$0.994615\pi$
$762$			1.98179e8i			0.447913i
$763$	−2.02291e8	−	5.45184e8i	−0.455411	−	1.22735i
$764$	−2.79781e8			−0.627391
$765$	−1.62532e6	−	2.81514e6i	−0.00363040	−	0.00628804i
$766$	−2.20814e8	−	1.27487e8i	−0.491293	−	0.283648i
$767$	−2.68213e8	+	4.64559e8i	−0.594421	+	1.02957i
$768$	−1.98478e8	+	1.14591e8i	−0.438156	+	0.252970i
$769$			6.97335e8i			1.53343i	0.641990	+	0.766713i	$0.278109\pi$
$769$			6.97335e8i			1.53343i	−0.641990	+	0.766713i	$0.721891\pi$
$770$	−313290.	+	1.84396e6i	−0.000686238	+	0.00403904i
$771$	6.30772e7			0.137629
$772$	2.15225e8	+	3.72780e8i	0.467779	+	0.810216i
$773$	−7.04415e8	−	4.06694e8i	−1.52507	−	0.880500i	−0.999558	−	0.0297144i	$-0.990540\pi$
$773$	−7.04415e8	−	4.06694e8i	−1.52507	−	0.880500i	−0.525513	−	0.850786i	$-0.676126\pi$
$774$	−2.60689e6	+	4.51526e6i	−0.00562211	+	0.00973778i
$775$	9.16290e7	−	5.29021e7i	0.196847	−	0.113649i
$776$			3.21523e8i			0.688061i
$777$	−1.36402e8	−	1.13012e8i	−0.290775	−	0.240914i
$778$	1.17202e8			0.248883
$779$	−3.50572e8	−	6.07208e8i	−0.741591	−	1.28447i
$780$	6.03306e7	+	3.48319e7i	0.127132	+	0.0733995i
$781$	−3.40308e6	+	5.89431e6i	−0.00714364	+	0.0123731i
$782$	1.21135e7	−	6.99375e6i	0.0253309	−	0.0146248i
$783$		−	1.62946e8i		−	0.339436i
$784$	−5.43356e7	+	4.67606e7i	−0.112755	+	0.0970358i
$785$	1.54411e8			0.319206
$786$	1.56606e8	+	2.71249e8i	0.322508	+	0.558600i
$787$	3.22928e8	+	1.86443e8i	0.662494	+	0.382491i	0.793227	−	0.608927i	$-0.208400\pi$
$787$	3.22928e8	+	1.86443e8i	0.662494	+	0.382491i	−0.130733	+	0.991418i	$0.541733\pi$
$788$	5.21867e7	−	9.03900e7i	0.106655	−	0.184732i
$789$	4.00622e8	−	2.31299e8i	0.815651	−	0.470916i
$790$		−	1.10974e8i		−	0.225081i
$791$	−3.34273e7	+	4.03457e7i	−0.0675418	+	0.0815207i
$792$	−2.29178e6			−0.00461314
$793$	−3.32425e8	−	5.75777e8i	−0.666614	−	1.15461i
$794$	−5.31930e7	−	3.07110e7i	−0.106266	−	0.0613525i
$795$	1.15814e8	−	2.00595e8i	0.230494	−	0.399227i
$796$	−5.94663e8	+	3.43329e8i	−1.17905	+	0.680724i
$797$			4.15047e8i			0.819827i	0.912124	+	0.409913i	$0.134441\pi$
$797$			4.15047e8i			0.819827i	−0.912124	+	0.409913i	$0.865559\pi$
$798$	2.25951e8	+	3.83894e7i	0.444637	+	0.0755444i
$799$	1.58172e7			0.0310091
$800$	1.98571e8	+	3.43935e8i	0.387834	+	0.671748i
$801$	−4.84687e7	−	2.79834e7i	−0.0943113	−	0.0544507i
$802$	−9.05468e7	+	1.56832e8i	−0.175530	+	0.304026i
$803$	3.39320e6	−	1.95906e6i	0.00655334	−	0.00378357i
$804$		−	1.49816e8i		−	0.288264i
$805$	2.89295e8	−	1.07343e8i	0.554566	−	0.205773i
$806$	−6.66681e7			−0.127325
$807$	1.59556e8	+	2.76360e8i	0.303594	+	0.525841i
$808$	7.89133e8	+	4.55606e8i	1.49595	+	0.863686i
$809$	1.17384e8	−	2.03314e8i	0.221698	−	0.383992i	−0.733626	−	0.679554i	$-0.762173\pi$
$809$	1.17384e8	−	2.03314e8i	0.221698	−	0.383992i	0.955324	+	0.295562i	$0.0955068\pi$
$810$	−1.43492e7	+	8.28452e6i	−0.0270006	+	0.0155888i
$811$			8.08164e7i			0.151508i	0.997127	+	0.0757542i	$0.0241364\pi$
$811$			8.08164e7i			0.151508i	−0.997127	+	0.0757542i	$0.975864\pi$
$812$	−2.24263e8	−	6.04398e8i	−0.418880	−	1.12890i
$813$	−3.94717e7			−0.0734538
$814$	−1.45065e6	−	2.51259e6i	−0.00268961	−	0.00465853i
$815$	−3.55372e8	−	2.05174e8i	−0.656463	−	0.379009i
$816$	1.02030e6	−	1.76721e6i	0.00187784	−	0.00325251i
$817$	−3.92204e7	+	2.26439e7i	−0.0719194	+	0.0415227i
$818$			3.41133e7i			0.0623252i
$819$	2.29331e7	−	1.34979e8i	0.0417455	−	0.245705i
$820$	2.00539e8			0.363713
$821$	3.22564e7	+	5.58697e7i	0.0582890	+	0.100959i	0.893697	−	0.448670i	$-0.148102\pi$
$821$	3.22564e7	+	5.58697e7i	0.0582890	+	0.100959i	−0.835408	+	0.549630i	$0.814769\pi$
$822$	7.90416e7	+	4.56347e7i	0.142312	+	0.0821637i
$823$	7.83609e7	−	1.35725e8i	0.140572	−	0.243478i	−0.787140	−	0.616774i	$-0.788439\pi$
$823$	7.83609e7	−	1.35725e8i	0.140572	−	0.243478i	0.927712	+	0.373296i	$0.121772\pi$
$824$	3.79939e8	−	2.19358e8i	0.679098	−	0.392077i
$825$			3.55888e6i			0.00633800i
$826$	−3.88690e8	−	3.22039e8i	−0.689705	−	0.571437i
$827$	−6.46564e8			−1.14313			−0.571565	−	0.820557i	$-0.693663\pi$
$827$	−6.46564e8			−1.14313			−0.571565	+	0.820557i	$0.693663\pi$
$828$	7.66978e7	+	1.32845e8i	0.135111	+	0.234020i
$829$	−8.11604e8	−	4.68580e8i	−1.42456	−	0.822470i	−0.427875	−	0.903838i	$-0.640738\pi$
$829$	−8.11604e8	−	4.68580e8i	−1.42456	−	0.822470i	−0.996684	+	0.0813680i	$0.974071\pi$
$830$	1.85601e6	−	3.21470e6i	0.00324598	−	0.00562221i
$831$	4.12734e8	−	2.38292e8i	0.719229	−	0.415247i
$832$		−	1.86185e8i		−	0.323277i
$833$	−8.34764e6	+	2.38570e7i	−0.0144420	+	0.0412744i
$834$	8.39923e6			0.0144791
$835$	1.69678e8	+	2.93891e8i	0.291452	+	0.504809i
$836$	−6.99444e6	−	4.03824e6i	−0.0119711	−	0.00691152i
$837$	−1.70578e7	+	2.95449e7i	−0.0290902	+	0.0503856i
$838$	−1.21924e8	+	7.03931e7i	−0.207185	+	0.119618i
$839$		−	7.25284e8i		−	1.22807i	−0.789280	−	0.614034i	$-0.789546\pi$
$839$		−	7.25284e8i		−	1.22807i	0.789280	−	0.614034i	$-0.210454\pi$
$840$	−1.03082e8	+	1.24417e8i	−0.173919	+	0.209914i
$841$	1.25559e9			2.11086
$842$	1.34962e8	+	2.33761e8i	0.226087	+	0.391594i
$843$	3.06570e8	+	1.76998e8i	0.511738	+	0.295452i
$844$	3.20570e7	−	5.55243e7i	0.0533206	−	0.0923540i
$845$	1.14779e8	−	6.62676e7i	0.190236	−	0.109833i
$846$		−	8.06228e7i		−	0.133152i
$847$	5.98933e8	+	1.01759e8i	0.985662	+	0.167465i
$848$	1.45405e8			0.238447
$849$	−3.19429e8	−	5.53268e8i	−0.521978	−	0.904092i
$850$	9.84983e6	+	5.68680e6i	0.0160388	+	0.00926001i
$851$	−2.39322e8	+	4.14517e8i	−0.388323	+	0.672595i
$852$	−2.06581e8	+	1.19269e8i	−0.334019	+	0.192846i
$853$			1.38063e8i			0.222449i	0.993795	+	0.111224i	$0.0354772\pi$
$853$			1.38063e8i			0.222449i	−0.993795	+	0.111224i	$0.964523\pi$
$854$	5.86535e8	−	2.17635e8i	0.941716	−	0.349425i
$855$	−1.43922e8			−0.230265
$856$	−2.05336e8	−	3.55652e8i	−0.327373	−	0.567027i
$857$	6.12238e8	+	3.53476e8i	0.972698	+	0.561588i	0.900058	−	0.435771i	$-0.143524\pi$
$857$	6.12238e8	+	3.53476e8i	0.972698	+	0.561588i	0.0726405	+	0.997358i	$0.476857\pi$
$858$	1.12124e6	−	1.94205e6i	0.00177516	−	0.00307467i
$859$	2.85515e8	−	1.64842e8i	0.450453	−	0.260069i	−0.257569	−	0.966260i	$-0.582921\pi$
$859$	2.85515e8	−	1.64842e8i	0.450453	−	0.260069i	0.708021	+	0.706191i	$0.249588\pi$
$860$		−	1.29531e7i		−	0.0203648i
$861$	−1.37108e8	−	3.69511e8i	−0.214809	−	0.578920i
$862$	−4.33976e8			−0.677554
$863$	4.84152e8	+	8.38576e8i	0.753268	+	1.30470i	0.946231	+	0.323493i	$0.104857\pi$
$863$	4.84152e8	+	8.38576e8i	0.753268	+	1.30470i	−0.192962	+	0.981206i	$0.561810\pi$
$864$	−1.10899e8	−	6.40273e7i	−0.171943	−	0.0992714i
$865$	8.59726e7	−	1.48909e8i	0.132835	−	0.230077i
$866$	−4.33922e8	+	2.50525e8i	−0.668126	+	0.385743i
$867$			3.75548e8i			0.576246i
$868$	−2.26078e7	+	1.33065e8i	−0.0345700	+	0.203471i
$869$	7.68577e6			0.0117119
$870$	−9.40789e7	−	1.62949e8i	−0.142868	−	0.247454i
$871$	3.12915e8	+	1.80661e8i	0.473556	+	0.273408i
$872$	4.11381e8	−	7.12532e8i	0.620433	−	1.07462i
$873$	−1.39423e8	+	8.04959e7i	−0.209552	+	0.120985i
$874$		−	6.19296e8i		−	0.927608i
$875$	4.50176e8	+	3.72981e8i	0.671983	+	0.556753i
$876$	1.37321e8			0.204279
$877$	−1.33382e8	−	2.31025e8i	−0.197742	−	0.342500i	0.750054	−	0.661377i	$-0.230028\pi$
$877$	−1.33382e8	−	2.31025e8i	−0.197742	−	0.342500i	−0.947796	+	0.318877i	$0.896694\pi$
$878$	−3.56239e8	−	2.05675e8i	−0.526330	−	0.303877i
$879$	−2.29410e8	+	3.97350e8i	−0.337790	+	0.585069i
$880$	638534.	−	368657.i	0.000936992	−	0.000540972i
$881$			6.08909e8i			0.890481i	0.895411	+	0.445241i	$0.146882\pi$
$881$			6.08909e8i			0.890481i	−0.895411	+	0.445241i	$0.853118\pi$
$882$	1.21603e8	+	4.25493e7i	0.177231	+	0.0620135i
$883$	−6.56488e8			−0.953553			−0.476777	−	0.879025i	$-0.658195\pi$
$883$	−6.56488e8			−0.953553			−0.476777	+	0.879025i	$0.658195\pi$
$884$	7.70952e6	+	1.33533e7i	0.0111602	+	0.0193300i
$885$	2.74507e8	+	1.58487e8i	0.396027	+	0.228646i
$886$	−2.39577e8	+	4.14959e8i	−0.344464	+	0.596628i
$887$	−6.04195e7	+	3.48832e7i	−0.0865778	+	0.0499857i	−0.542664	−	0.839950i	$-0.682584\pi$
$887$	−6.04195e7	+	3.48832e7i	−0.0865778	+	0.0499857i	0.456086	+	0.889936i	$0.349251\pi$
$888$		−	2.50627e8i		−	0.357923i
$889$	−6.17358e8	+	7.45130e8i	−0.878682	+	1.06054i
$890$	−6.46263e7			−0.0916726
$891$	−573765.	−	993789.i	−0.000811149	−	0.00140495i
$892$	−1.37483e8	−	7.93760e7i	−0.193711	−	0.111839i
$893$	3.50153e8	−	6.06482e8i	0.491703	−	0.851655i
$894$	−3.80732e8	+	2.19816e8i	−0.532853	+	0.307643i
$895$		−	9.26355e7i		−	0.129214i
$896$	−5.58891e8	−	9.49562e7i	−0.776968	−	0.132008i
$897$	−3.69956e8			−0.512593
$898$	1.74448e8	+	3.02152e8i	0.240900	+	0.417251i
$899$	−3.35512e8	−	1.93708e8i	−0.461773	−	0.266605i
$900$	−6.23650e7	+	1.08019e8i	−0.0855486	+	0.148175i
$901$	4.43988e7	−	2.56337e7i	0.0607011	−	0.0350458i
$902$		−	6.45539e6i		−	0.00879635i
$903$	−2.38673e7	+	8.85600e6i	−0.0324145	+	0.0120275i
$904$	−7.41319e7			−0.100346
$905$	−1.87322e8	−	3.24451e8i	−0.252722	−	0.437728i
$906$	−9.17377e7	−	5.29648e7i	−0.123357	−	0.0712201i
$907$	−4.31361e8	+	7.47140e8i	−0.578122	+	1.00134i	0.417573	+	0.908643i	$0.362881\pi$
$907$	−4.31361e8	+	7.47140e8i	−0.578122	+	1.00134i	−0.995695	+	0.0926927i	$0.970453\pi$
$908$	2.24631e8	−	1.29691e8i	0.300063	−	0.173241i
$909$			4.56258e8i			0.607462i
$910$	−5.49982e7	−	1.48222e8i	−0.0729834	−	0.196693i
$911$	−1.41296e8			−0.186885			−0.0934425	−	0.995625i	$-0.529787\pi$
$911$	−1.41296e8			−0.186885			−0.0934425	+	0.995625i	$0.529787\pi$
$912$	−4.51738e7	−	7.82433e7i	−0.0595528	−	0.103148i
$913$	222642.	+	128542.i	0.000292547	+	0.000168902i
$914$	4.28319e7	−	7.41871e7i	0.0560956	−	0.0971605i
$915$	−3.40226e8	+	1.96429e8i	−0.444124	+	0.256415i
$916$		−	5.34605e8i		−	0.695579i
$917$	−2.56162e8	+	1.50771e9i	−0.332206	+	1.95529i
$918$	−3.66731e6			−0.00474045
$919$	−5.59845e8	−	9.69681e8i	−0.721309	−	1.24934i	−0.960475	−	0.278366i	$-0.910207\pi$
$919$	−5.59845e8	−	9.69681e8i	−0.721309	−	1.24934i	0.239166	−	0.970979i	$-0.423126\pi$
$920$	3.78096e8	+	2.18294e8i	0.485555	+	0.280335i
$921$	−3.64220e7	+	6.30848e7i	−0.0466214	+	0.0807506i
$922$	−4.12546e8	+	2.38183e8i	−0.526356	+	0.303892i
$923$		−	5.75302e8i		−	0.731629i
$924$	−3.49596e6	−	2.89648e6i	−0.00443150	−	0.00367160i
$925$	−3.89197e8			−0.491750
$926$	−6.35881e7	−	1.10138e8i	−0.0800834	−	0.138709i
$927$	1.90242e8	+	1.09836e8i	0.238817	+	0.137881i
$928$	7.27094e8	−	1.25936e9i	0.909801	−	1.57582i
$929$	1.14228e9	−	6.59494e8i	1.42470	−	0.822553i	0.428007	−	0.903775i	$-0.359216\pi$
$929$	1.14228e9	−	6.59494e8i	1.42470	−	0.822553i	0.996696	+	0.0812225i	$0.0258824\pi$
$930$			3.93941e7i			0.0489759i
$931$	7.29960e8	+	8.48210e8i	0.904586	+	1.05112i
$932$	−5.29591e8			−0.654173
$933$	−2.49659e8	−	4.32422e8i	−0.307399	−	0.532430i
$934$	6.74612e8	+	3.89488e8i	0.827968	+	0.478028i
$935$	129982.	−	225136.i	0.000159019	−	0.000275429i
$936$	1.67763e8	−	9.68581e7i	0.204583	−	0.118116i
$937$		−	1.04041e6i		−	0.00126469i	−1.00000		0.000632345i	$-0.999799\pi$
$937$		−	1.04041e6i		−	0.00126469i	1.00000		0.000632345i	$-0.000201282\pi$
$938$	−2.16917e8	+	2.61811e8i	−0.262836	+	0.317234i
$939$	−3.39848e8			−0.410476
$940$	1.00150e8	+	1.73465e8i	0.120578	+	0.208847i
$941$	5.93842e8	+	3.42855e8i	0.712692	+	0.411473i	0.812057	−	0.583578i	$-0.198348\pi$
$941$	5.93842e8	+	3.42855e8i	0.712692	+	0.411473i	−0.0993650	+	0.995051i	$0.531681\pi$
$942$	8.71021e7	−	1.50865e8i	0.104202	−	0.180483i
$943$	−9.22302e8	+	5.32491e8i	−1.09986	+	0.635005i
$944$			1.98982e8i			0.236536i
$945$	−7.97588e7	−	1.35511e7i	−0.0945112	−	0.0160576i
$946$	−416963.			−0.000492520
$947$	−2.67038e8	−	4.62523e8i	−0.314429	−	0.544608i	0.664887	−	0.746944i	$-0.268480\pi$
$947$	−2.67038e8	−	4.62523e8i	−0.314429	−	0.544608i	−0.979316	+	0.202337i	$0.935146\pi$
$948$	2.33278e8	+	1.34683e8i	0.273810	+	0.158084i
$949$	−1.65593e8	+	2.86816e8i	−0.193751	+	0.335586i
$950$	4.36101e8	−	2.51783e8i	0.508647	−	0.293667i
$951$			1.64066e8i			0.190755i
$952$	−3.35280e7	+	1.24406e7i	−0.0388594	+	0.0144189i
$953$	8.66817e8			1.00150			0.500748	−	0.865593i	$-0.333058\pi$
$953$	8.66817e8			1.00150			0.500748	+	0.865593i	$0.333058\pi$
$954$	−1.30659e8	−	2.26308e8i	−0.150485	−	0.260648i
$955$	−3.45302e8	−	1.99360e8i	−0.396450	−	0.228891i
$956$	2.60004e8	−	4.50340e8i	0.297582	−	0.515427i
$957$	1.12855e7	−	6.51566e6i	0.0128761	−	0.00743400i
$958$		−	1.25826e8i		−	0.143112i
$959$	1.55028e8	+	4.17807e8i	0.175774	+	0.473718i
$960$	−1.10016e8			−0.124349
$961$	−4.03196e8	−	6.98356e8i	−0.454303	−	0.786876i
$962$	2.12381e8	+	1.22618e8i	0.238556	+	0.137730i
$963$	1.02815e8	−	1.78080e8i	0.115127	−	0.199406i
$964$	−3.76679e8	+	2.17475e8i	−0.420475	+	0.242761i
$965$			6.13440e8i			0.682637i
$966$	5.83105e7	−	3.43202e8i	0.0646867	−	0.380731i
$967$	1.71422e8			0.189577			0.0947886	−	0.995497i	$-0.469782\pi$
$967$	1.71422e8			0.189577			0.0947886	+	0.995497i	$0.469782\pi$
$968$	4.29782e8	+	7.44405e8i	0.473830	+	0.820698i
$969$	−2.75872e7	−	1.59275e7i	−0.0303205	−	0.0175056i
$970$	−9.29506e7	+	1.60995e8i	−0.101844	+	0.176400i
$971$	9.77273e8	−	5.64229e8i	1.06748	−	0.616308i	0.139985	−	0.990154i	$-0.455294\pi$
$971$	9.77273e8	−	5.64229e8i	1.06748	−	0.616308i	0.927491	+	0.373846i	$0.121961\pi$
$972$		−	4.02180e7i		−	0.0437947i
$973$	3.15801e7	+	2.61648e7i	0.0342827	+	0.0284040i
$974$	−2.42259e8			−0.262183
$975$	−1.50410e8	−	2.60518e8i	−0.162279	−	0.281076i
$976$	−2.13578e8	−	1.23309e8i	−0.229725	−	0.132632i
$977$	2.09709e8	−	3.63227e8i	0.224871	−	0.389488i	−0.731410	−	0.681938i	$-0.761137\pi$
$977$	2.09709e8	−	3.63227e8i	0.224871	−	0.389488i	0.956281	+	0.292450i	$0.0944706\pi$
$978$	−4.00924e8	+	2.31474e8i	−0.428594	+	0.247449i
$979$		−	4.47585e6i		−	0.00477010i
$980$	−3.14491e8	+	5.95086e7i	−0.334141	+	0.0632268i
$981$	4.11970e8			0.436373
$982$	2.10645e8	+	3.64847e8i	0.222442	+	0.385280i
$983$	−5.99335e8	−	3.46026e8i	−0.630971	−	0.364291i	0.150157	−	0.988662i	$-0.452022\pi$
$983$	−5.99335e8	−	3.46026e8i	−0.630971	−	0.364291i	−0.781128	+	0.624371i	$0.785355\pi$
$984$	2.78823e8	−	4.82936e8i	0.292647	−	0.506879i
$985$	1.28816e8	−	7.43720e7i	0.134791	−	0.0778217i
$986$		−	4.16459e7i		−	0.0434452i
$987$	2.51152e8	−	3.03132e8i	0.261207	−	0.315268i
$988$	6.82678e8			0.707856
$989$	3.43944e7	+	5.95728e7i	0.0355548	+	0.0615828i
$990$	−1.14755e6	−	662540.i	−0.00118268	−	0.000682821i
$991$	4.13436e8	−	7.16091e8i	0.424802	−	0.735779i	−0.571600	−	0.820533i	$-0.693677\pi$
$991$	4.13436e8	−	7.16091e8i	0.424802	−	0.735779i	0.996402	+	0.0847535i	$0.0270103\pi$
$992$	−2.63669e8	+	1.52230e8i	−0.270100	+	0.155942i
$993$			6.34364e8i			0.647875i
$994$	5.33699e8	+	9.06761e7i	0.543422	+	0.0923280i
$995$	−9.78566e8			−0.993393
$996$	4.50509e6	+	7.80304e6i	0.00455959	+	0.00789744i
$997$	1.48696e9	+	8.58496e8i	1.50042	+	0.866269i	1.00000		0.000486585i	$0.000154885\pi$
$997$	1.48696e9	+	8.58496e8i	1.50042	+	0.866269i	0.500421	+	0.865782i	$0.333178\pi$
$998$	1.13280e7	−	1.96207e7i	0.0113963	−	0.0197389i
$999$	1.08680e8	−	6.27465e7i	0.109007	−	0.0629351i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.7.f.a.10.3	✓	8
3.2	odd	2		63.7.m.d.10.2		8
4.3	odd	2		336.7.bh.d.241.4		8
7.2	even	3		147.7.f.d.19.3		8
7.3	odd	6		147.7.d.b.97.3		8
7.4	even	3		147.7.d.b.97.4		8
7.5	odd	6	inner	21.7.f.a.19.3	yes	8
7.6	odd	2		147.7.f.d.31.3		8
21.5	even	6		63.7.m.d.19.2		8
21.11	odd	6		441.7.d.c.244.5		8
21.17	even	6		441.7.d.c.244.6		8
28.19	even	6		336.7.bh.d.145.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.7.f.a.10.3	✓	8	1.1	even	1	trivial
21.7.f.a.19.3	yes	8	7.5	odd	6	inner
63.7.m.d.10.2		8	3.2	odd	2
63.7.m.d.19.2		8	21.5	even	6
147.7.d.b.97.3		8	7.3	odd	6
147.7.d.b.97.4		8	7.4	even	3
147.7.f.d.19.3		8	7.2	even	3
147.7.f.d.31.3		8	7.6	odd	2
336.7.bh.d.145.4		8	28.19	even	6
336.7.bh.d.241.4		8	4.3	odd	2
441.7.d.c.244.5		8	21.11	odd	6
441.7.d.c.244.6		8	21.17	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)

\(f(q)\)	\(=\)	\(q+(2.25320 + 3.90266i) q^{2} +(-13.5000 - 7.79423i) q^{3} +(21.8461 - 37.8386i) q^{4} +(53.9244 - 31.1333i) q^{5} -70.2479i q^{6} +(218.833 - 264.124i) q^{7} +485.305 q^{8} +(121.500 + 210.444i) q^{9} +O(q^{10})\)	\(q+(2.25320 + 3.90266i) q^{2} +(-13.5000 - 7.79423i) q^{3} +(21.8461 - 37.8386i) q^{4} +(53.9244 - 31.1333i) q^{5} -70.2479i q^{6} +(218.833 - 264.124i) q^{7} +485.305 q^{8} +(121.500 + 210.444i) q^{9} +(243.005 + 140.299i) q^{10} +(-9.71675 + 16.8299i) q^{11} +(-589.846 + 340.548i) q^{12} -1642.65i q^{13} +(1523.86 + 258.906i) q^{14} -970.639 q^{15} +(-304.661 - 527.689i) q^{16} +(-186.054 - 107.418i) q^{17} +(-547.529 + 948.347i) q^{18} +(-8237.53 + 4755.94i) q^{19} -2720.57i q^{20} +(-5012.88 + 1860.04i) q^{21} -87.5753 q^{22} +(7223.90 + 12512.2i) q^{23} +(-6551.62 - 3782.58i) q^{24} +(-5873.94 + 10174.0i) q^{25} +(6410.70 - 3701.22i) q^{26} -3788.00i q^{27} +(-5213.43 - 14050.4i) q^{28} +43016.4 q^{29} +(-2187.05 - 3788.08i) q^{30} +(-7799.62 - 4503.11i) q^{31} +(16902.7 - 29276.3i) q^{32} +(262.352 - 151.469i) q^{33} -968.141i q^{34} +(3577.38 - 21055.7i) q^{35} +10617.2 q^{36} +(16564.6 + 28690.7i) q^{37} +(-37121.7 - 21432.2i) q^{38} +(-12803.2 + 22175.8i) q^{39} +(26169.8 - 15109.1i) q^{40} +73712.4i q^{41} +(-18554.1 - 15372.5i) q^{42} +4761.19 q^{43} +(424.547 + 735.337i) q^{44} +(13103.6 + 7565.38i) q^{45} +(-32553.9 + 56384.9i) q^{46} +(-63760.5 + 36812.2i) q^{47} +9498.40i q^{48} +(-21873.6 - 115598. i) q^{49} -52940.7 q^{50} +(1674.48 + 2900.29i) q^{51} +(-62155.6 - 35885.5i) q^{52} +(-119317. + 206663. i) q^{53} +(14783.3 - 8535.13i) q^{54} +1210.06i q^{55} +(106201. - 128181. i) q^{56} +148275. q^{57} +(96924.8 + 167879. i) q^{58} +(-282811. - 163281. i) q^{59} +(-21204.7 + 36727.6i) q^{60} +(350517. - 202371. i) q^{61} -40585.7i q^{62} +(82171.4 + 13961.0i) q^{63} +113344. q^{64} +(-51141.0 - 88578.8i) q^{65} +(1182.27 + 682.582i) q^{66} +(-109982. + 190494. i) q^{67} +(-8129.12 + 4693.35i) q^{68} -225219. i q^{69} +(90233.8 - 33481.4i) q^{70} +350228. q^{71} +(58964.6 + 102130. i) q^{72} +(-174606. - 100809. i) q^{73} +(-74646.7 + 129292. i) q^{74} +(158596. - 91565.7i) q^{75} +415596. i q^{76} +(2318.83 + 6249.36i) q^{77} -115393. q^{78} +(-197745. - 342505. i) q^{79} +(-32857.4 - 18970.2i) q^{80} +(-29524.5 + 51137.9i) q^{81} +(-287675. + 166089. i) q^{82} -13229.0i q^{83} +(-39130.8 + 230315. i) q^{84} -13377.1 q^{85} +(10727.9 + 18581.3i) q^{86} +(-580722. - 335280. i) q^{87} +(-4715.59 + 8167.65i) q^{88} +(-199460. + 115158. i) q^{89} +68185.4i q^{90} +(-433862. - 359465. i) q^{91} +631258. q^{92} +(70196.6 + 121584. i) q^{93} +(-287331. - 165891. i) q^{94} +(-296136. + 512922. i) q^{95} +(-456373. + 263487. i) q^{96} +662517. i q^{97} +(401853. - 345831. i) q^{98} -4722.34 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

Modular forms

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