LMFDB - Embedded newform 69.7.b.a.47.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [69,7,Mod(47,69)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(69, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("69.47");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 69 = 3 \cdot 23 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	69.b (of order $2$, degree $1$, 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:	$15.8737317698$
Analytic rank:	$0$
Dimension:	$44$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			47.3
Character	$\chi$	$=$	69.47
Dual form			69.7.b.a.47.42

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-14.4029i q^{2} +(25.1960 + 9.70372i) q^{3} -143.443 q^{4} +103.914i q^{5} +(139.762 - 362.895i) q^{6} +470.752 q^{7} +1144.21i q^{8} +(540.676 + 488.990i) q^{9} +O(q^{10})$	\(q-14.4029i q^{2} +(25.1960 + 9.70372i) q^{3} -143.443 q^{4} +103.914i q^{5} +(139.762 - 362.895i) q^{6} +470.752 q^{7} +1144.21i q^{8} +(540.676 + 488.990i) q^{9} +1496.66 q^{10} -2592.07i q^{11} +(-3614.19 - 1391.93i) q^{12} -326.916 q^{13} -6780.19i q^{14} +(-1008.35 + 2618.22i) q^{15} +7299.58 q^{16} -1603.05i q^{17} +(7042.86 - 7787.29i) q^{18} +13151.4 q^{19} -14905.8i q^{20} +(11861.1 + 4568.05i) q^{21} -37333.2 q^{22} -2536.99i q^{23} +(-11103.1 + 28829.5i) q^{24} +4826.84 q^{25} +4708.53i q^{26} +(8877.84 + 17567.1i) q^{27} -67526.2 q^{28} -9239.71i q^{29} +(37709.9 + 14523.2i) q^{30} -31725.4 q^{31} -31905.5i q^{32} +(25152.7 - 65309.7i) q^{33} -23088.5 q^{34} +48917.9i q^{35} +(-77556.2 - 70142.2i) q^{36} +58979.1 q^{37} -189418. i q^{38} +(-8236.97 - 3172.30i) q^{39} -118900. q^{40} +66916.1i q^{41} +(65793.1 - 170834. i) q^{42} -82745.5 q^{43} +371814. i q^{44} +(-50813.0 + 56183.9i) q^{45} -36540.1 q^{46} +25142.4i q^{47} +(183920. + 70833.1i) q^{48} +103959. q^{49} -69520.4i q^{50} +(15555.5 - 40390.4i) q^{51} +46893.9 q^{52} -214386. i q^{53} +(253018. - 127867. i) q^{54} +269352. q^{55} +538640. i q^{56} +(331363. + 127618. i) q^{57} -133079. q^{58} +49051.5i q^{59} +(144642. - 375566. i) q^{60} +90082.7 q^{61} +456938. i q^{62} +(254524. + 230193. i) q^{63} +7641.58 q^{64} -33971.2i q^{65} +(-940648. - 362271. i) q^{66} -315985. q^{67} +229946. i q^{68} +(24618.3 - 63922.1i) q^{69} +704558. q^{70} +26014.7i q^{71} +(-559507. + 618647. i) q^{72} +23544.7 q^{73} -849469. i q^{74} +(121617. + 46838.3i) q^{75} -1.88648e6 q^{76} -1.22022e6i q^{77} +(-45690.3 + 118636. i) q^{78} -387709. q^{79} +758530. i q^{80} +(53219.3 + 528770. i) q^{81} +963786. q^{82} +548672. i q^{83} +(-1.70139e6 - 655256. i) q^{84} +166579. q^{85} +1.19177e6i q^{86} +(89659.6 - 232804. i) q^{87} +2.96587e6 q^{88} -170207. i q^{89} +(809210. + 731853. i) q^{90} -153896. q^{91} +363915. i q^{92} +(-799354. - 307855. i) q^{93} +362123. q^{94} +1.36662e6i q^{95} +(309602. - 803891. i) q^{96} -608773. q^{97} -1.49731e6i q^{98} +(1.26749e6 - 1.40147e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 20 q^{3} - 1408 q^{4} + 95 q^{6} + 568 q^{7} - 548 q^{9}+O(q^{10}) $ 44 * q + 20 * q^3 - 1408 * q^4 + 95 * q^6 + 568 * q^7 - 548 * q^9	$ 44 q + 20 q^{3} - 1408 q^{4} + 95 q^{6} + 568 q^{7} - 548 q^{9} + 1752 q^{10} + 4075 q^{12} + 808 q^{13} + 7696 q^{15} + 36776 q^{16} + 12149 q^{18} + 28936 q^{19} - 6416 q^{21} - 7764 q^{22} - 11792 q^{24} - 129172 q^{25} - 27172 q^{27} - 25988 q^{28} - 54658 q^{30} - 72248 q^{31} + 25968 q^{33} - 32100 q^{34} - 217125 q^{36} + 260968 q^{37} + 133440 q^{39} - 227880 q^{40} + 63332 q^{42} - 187304 q^{43} + 455472 q^{45} - 164849 q^{48} + 959652 q^{49} - 218832 q^{51} - 410102 q^{52} + 882504 q^{54} + 517392 q^{55} - 572600 q^{57} - 197334 q^{58} - 854196 q^{60} + 914248 q^{61} + 885136 q^{63} - 312634 q^{64} - 816874 q^{66} - 310856 q^{67} - 395040 q^{70} + 205764 q^{72} - 227912 q^{73} + 1167580 q^{75} - 1438412 q^{76} - 6065 q^{78} + 841384 q^{79} + 1019636 q^{81} - 291126 q^{82} - 2787738 q^{84} - 2823120 q^{85} - 2899120 q^{87} - 2657340 q^{88} + 1478966 q^{90} - 2848288 q^{91} - 1992952 q^{93} + 6985482 q^{94} + 1309665 q^{96} + 1079608 q^{97} + 3251880 q^{99}+O(q^{100}) $ 44 * q + 20 * q^3 - 1408 * q^4 + 95 * q^6 + 568 * q^7 - 548 * q^9 + 1752 * q^10 + 4075 * q^12 + 808 * q^13 + 7696 * q^15 + 36776 * q^16 + 12149 * q^18 + 28936 * q^19 - 6416 * q^21 - 7764 * q^22 - 11792 * q^24 - 129172 * q^25 - 27172 * q^27 - 25988 * q^28 - 54658 * q^30 - 72248 * q^31 + 25968 * q^33 - 32100 * q^34 - 217125 * q^36 + 260968 * q^37 + 133440 * q^39 - 227880 * q^40 + 63332 * q^42 - 187304 * q^43 + 455472 * q^45 - 164849 * q^48 + 959652 * q^49 - 218832 * q^51 - 410102 * q^52 + 882504 * q^54 + 517392 * q^55 - 572600 * q^57 - 197334 * q^58 - 854196 * q^60 + 914248 * q^61 + 885136 * q^63 - 312634 * q^64 - 816874 * q^66 - 310856 * q^67 - 395040 * q^70 + 205764 * q^72 - 227912 * q^73 + 1167580 * q^75 - 1438412 * q^76 - 6065 * q^78 + 841384 * q^79 + 1019636 * q^81 - 291126 * q^82 - 2787738 * q^84 - 2823120 * q^85 - 2899120 * q^87 - 2657340 * q^88 + 1478966 * q^90 - 2848288 * q^91 - 1992952 * q^93 + 6985482 * q^94 + 1309665 * q^96 + 1079608 * q^97 + 3251880 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/69\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$1$	$-1$

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 $

$2$		−	14.4029i		−	1.80036i	−0.435517	−	0.900180i	$-0.643434\pi$
$2$		−	14.4029i		−	1.80036i	0.435517	−	0.900180i	$-0.356566\pi$
$3$	25.1960	+	9.70372i	0.933185	+	0.359397i
$3$	25.1960	+	9.70372i	0.933185	+	0.359397i
$4$	−143.443			−2.24130
$5$			103.914i			0.831314i	0.909522	+	0.415657i	$0.136448\pi$
$5$			103.914i			0.831314i	−0.909522	+	0.415657i	$0.863552\pi$
$6$	139.762	−	362.895i	0.647044	−	1.68007i
$7$	470.752			1.37246			0.686228	−	0.727386i	$-0.259265\pi$
$7$	470.752			1.37246			0.686228	+	0.727386i	$0.259265\pi$
$8$			1144.21i			2.23479i
$9$	540.676	+	488.990i	0.741668	+	0.670768i
$10$	1496.66			1.49666
$11$		−	2592.07i		−	1.94746i	−0.227711	−	0.973729i	$-0.573124\pi$
$11$		−	2592.07i		−	1.94746i	0.227711	−	0.973729i	$-0.426876\pi$
$12$	−3614.19	−	1391.93i	−2.09155	−	0.805516i
$13$	−326.916			−0.148801			−0.0744005	−	0.997228i	$-0.523704\pi$
$13$	−326.916			−0.148801			−0.0744005	+	0.997228i	$0.523704\pi$
$14$		−	6780.19i		−	2.47092i
$15$	−1008.35	+	2618.22i	−0.298772	+	0.775769i
$16$	7299.58			1.78212
$17$		−	1603.05i		−	0.326287i	−0.986602	−	0.163143i	$-0.947837\pi$
$17$		−	1603.05i		−	0.326287i	0.986602	−	0.163143i	$-0.0521633\pi$
$18$	7042.86	−	7787.29i	1.20762	−	1.33527i
$19$	13151.4			1.91739			0.958697	−	0.284429i	$-0.0918038\pi$
$19$	13151.4			1.91739			0.958697	+	0.284429i	$0.0918038\pi$
$20$		−	14905.8i		−	1.86322i
$21$	11861.1	+	4568.05i	1.28076	+	0.493257i
$22$	−37333.2			−3.50613
$23$		−	2536.99i		−	0.208514i
$23$		−	2536.99i		−	0.208514i
$24$	−11103.1	+	28829.5i	−0.803176	+	2.08547i
$25$	4826.84			0.308918
$26$			4708.53i			0.267896i
$27$	8877.84	+	17567.1i	0.451041	+	0.892503i
$28$	−67526.2			−3.07609
$29$		−	9239.71i		−	0.378848i	−0.981895	−	0.189424i	$-0.939338\pi$
$29$		−	9239.71i		−	0.378848i	0.981895	−	0.189424i	$-0.0606620\pi$
$30$	37709.9	+	14523.2i	1.39666	+	0.537897i
$31$	−31725.4			−1.06493			−0.532467	−	0.846451i	$-0.678735\pi$
$31$	−31725.4			−1.06493			−0.532467	+	0.846451i	$0.678735\pi$
$32$		−	31905.5i		−	0.973679i
$33$	25152.7	−	65309.7i	0.699910	−	1.81734i
$34$	−23088.5			−0.587434
$35$			48917.9i			1.14094i
$36$	−77556.2	−	70142.2i	−1.66230	−	1.50339i
$37$	58979.1			1.16437			0.582187	−	0.813055i	$-0.302197\pi$
$37$	58979.1			1.16437			0.582187	+	0.813055i	$0.302197\pi$
$38$		−	189418.i		−	3.45200i
$39$	−8236.97	−	3172.30i	−0.138859	−	0.0534787i
$40$	−118900.			−1.85781
$41$			66916.1i			0.970911i	0.874261	+	0.485455i	$0.161346\pi$
$41$			66916.1i			0.970911i	−0.874261	+	0.485455i	$0.838654\pi$
$42$	65793.1	−	170834.i	0.888040	−	2.30582i
$43$	−82745.5			−1.04073			−0.520366	−	0.853943i	$-0.674204\pi$
$43$	−82745.5			−1.04073			−0.520366	+	0.853943i	$0.674204\pi$
$44$			371814.i			4.36484i
$45$	−50813.0	+	56183.9i	−0.557618	+	0.616558i
$46$	−36540.1			−0.375401
$47$			25142.4i			0.242166i	0.992642	+	0.121083i	$0.0386367\pi$
$47$			25142.4i			0.242166i	−0.992642	+	0.121083i	$0.961363\pi$
$48$	183920.	+	70833.1i	1.66305	+	0.640490i
$49$	103959.			0.883636
$50$		−	69520.4i		−	0.556163i
$51$	15555.5	−	40390.4i	0.117267	−	0.304486i
$52$	46893.9			0.333508
$53$		−	214386.i		−	1.44002i	−0.693964	−	0.720010i	$-0.744137\pi$
$53$		−	214386.i		−	1.44002i	0.693964	−	0.720010i	$-0.255863\pi$
$54$	253018.	−	127867.i	1.60683	−	0.812037i
$55$	269352.			1.61895
$56$			538640.i			3.06715i
$57$	331363.	+	127618.i	1.78928	+	0.689106i
$58$	−133079.			−0.682062
$59$			49051.5i			0.238834i	0.992844	+	0.119417i	$0.0381025\pi$
$59$			49051.5i			0.238834i	−0.992844	+	0.119417i	$0.961897\pi$
$60$	144642.	−	375566.i	0.669637	−	1.73873i
$61$	90082.7			0.396874			0.198437	−	0.980114i	$-0.436414\pi$
$61$	90082.7			0.396874			0.198437	+	0.980114i	$0.436414\pi$
$62$			456938.i			1.91727i
$63$	254524.	+	230193.i	1.01791	+	0.920599i
$64$	7641.58			0.0291503
$65$		−	33971.2i		−	0.123700i
$66$	−940648.	−	362271.i	−3.27186	−	1.26009i
$67$	−315985.			−1.05061			−0.525305	−	0.850914i	$-0.676049\pi$
$67$	−315985.			−1.05061			−0.525305	+	0.850914i	$0.676049\pi$
$68$			229946.i			0.731307i
$69$	24618.3	−	63922.1i	0.0749395	−	0.194582i
$70$	704558.			2.05411
$71$			26014.7i			0.0726847i	0.999339	+	0.0363423i	$0.0115707\pi$
$71$			26014.7i			0.0726847i	−0.999339	+	0.0363423i	$0.988429\pi$
$72$	−559507.	+	618647.i	−1.49902	+	1.65747i
$73$	23544.7			0.0605235			0.0302617	−	0.999542i	$-0.490366\pi$
$73$	23544.7			0.0605235			0.0302617	+	0.999542i	$0.490366\pi$
$74$		−	849469.i		−	2.09630i
$75$	121617.	+	46838.3i	0.288277	+	0.111024i
$76$	−1.88648e6			−4.29746
$77$		−	1.22022e6i		−	2.67280i
$78$	−45690.3	+	118636.i	−0.0962809	+	0.249996i
$79$	−387709.			−0.786366			−0.393183	−	0.919460i	$-0.628626\pi$
$79$	−387709.			−0.786366			−0.393183	+	0.919460i	$0.628626\pi$
$80$			758530.i			1.48150i
$81$	53219.3	+	528770.i	0.100142	+	0.994973i
$82$	963786.			1.74799
$83$			548672.i			0.959575i	0.877385	+	0.479787i	$0.159286\pi$
$83$			548672.i			0.959575i	−0.877385	+	0.479787i	$0.840714\pi$
$84$	−1.70139e6	−	655256.i	−2.87056	−	1.10554i
$85$	166579.			0.271247
$86$			1.19177e6i			1.87369i
$87$	89659.6	−	232804.i	0.136157	−	0.353535i
$88$	2.96587e6			4.35215
$89$		−	170207.i		−	0.241438i	−0.992687	−	0.120719i	$-0.961480\pi$
$89$		−	170207.i		−	0.241438i	0.992687	−	0.120719i	$-0.0385201\pi$
$90$	809210.	+	731853.i	1.11003	+	1.00391i
$91$	−153896.			−0.204223
$92$			363915.i			0.467343i
$93$	−799354.	−	307855.i	−0.993780	−	0.382734i
$94$	362123.			0.435986
$95$			1.36662e6i			1.59396i
$96$	309602.	−	803891.i	0.349937	−	0.908622i
$97$	−608773.			−0.667022			−0.333511	−	0.942746i	$-0.608233\pi$
$97$	−608773.			−0.667022			−0.333511	+	0.942746i	$0.608233\pi$
$98$		−	1.49731e6i		−	1.59086i
$99$	1.26749e6	−	1.40147e6i	1.30629	−	1.44437i
$100$	−692377.			−0.692377
$101$			340623.i			0.330605i	0.986243	+	0.165303i	$0.0528601\pi$
$101$			340623.i			0.330605i	−0.986243	+	0.165303i	$0.947140\pi$
$102$	−581738.	−	224045.i	−0.548185	−	0.211122i
$103$	963610.			0.881839			0.440920	−	0.897547i	$-0.354652\pi$
$103$	963610.			0.881839			0.440920	+	0.897547i	$0.354652\pi$
$104$		−	374061.i		−	0.332539i
$105$	−474685.	+	1.23253e6i	−0.410051	+	1.06471i
$106$	−3.08777e6			−2.59256
$107$			1.42443e6i			1.16276i	0.813632	+	0.581380i	$0.197487\pi$
$107$			1.42443e6i			1.16276i	−0.813632	+	0.581380i	$0.802513\pi$
$108$	−1.27347e6	−	2.51989e6i	−1.01092	−	2.00037i
$109$	330544.			0.255241			0.127620	−	0.991823i	$-0.459266\pi$
$109$	330544.			0.255241			0.127620	+	0.991823i	$0.459266\pi$
$110$		−	3.87945e6i		−	2.91469i
$111$	1.48604e6	+	572317.i	1.08658	+	0.418473i
$112$	3.43629e6			2.44589
$113$			533126.i			0.369483i	0.982787	+	0.184742i	$0.0591448\pi$
$113$			533126.i			0.369483i	−0.982787	+	0.184742i	$0.940855\pi$
$114$	1.83806e6	−	4.77258e6i	1.24064	−	3.22136i
$115$	263630.			0.173341
$116$			1.32537e6i			0.849111i
$117$	−176755.	−	159858.i	−0.110361	−	0.0998109i
$118$	706483.			0.429987
$119$		−	754639.i		−	0.447815i
$120$	−2.99580e6	−	1.15377e6i	−1.73368	−	0.667691i
$121$	−4.94724e6			−2.79259
$122$		−	1.29745e6i		−	0.714516i
$123$	−649335.	+	1.68602e6i	−0.348942	+	0.906039i
$124$	4.55080e6			2.38684
$125$			2.12524e6i			1.08812i
$126$	3.31544e6	−	3.66589e6i	1.65741	−	1.83260i
$127$	−3.24663e6			−1.58497			−0.792486	−	0.609891i	$-0.791213\pi$
$127$	−3.24663e6			−1.58497			−0.792486	+	0.609891i	$0.791213\pi$
$128$		−	2.15201e6i		−	1.02616i
$129$	−2.08485e6	−	802939.i	−0.971195	−	0.374036i
$130$	−489283.			−0.222705
$131$			2.18747e6i			0.973034i	0.873671	+	0.486517i	$0.161733\pi$
$131$			2.18747e6i			0.973034i	−0.873671	+	0.486517i	$0.838267\pi$
$132$	−3.60798e6	+	9.36822e6i	−1.56871	+	4.07320i
$133$	6.19106e6			2.63154
$134$			4.55109e6i			1.89148i
$135$	−1.82548e6	+	922534.i	−0.741950	+	0.374956i
$136$	1.83422e6			0.729182
$137$			2.06312e6i			0.802346i	0.916002	+	0.401173i	$0.131397\pi$
$137$			2.06312e6i			0.802346i	−0.916002	+	0.401173i	$0.868603\pi$
$138$	−920663.	−	354574.i	−0.350319	−	0.134918i
$139$	−513910.			−0.191356			−0.0956781	−	0.995412i	$-0.530502\pi$
$139$	−513910.			−0.191356			−0.0956781	+	0.995412i	$0.530502\pi$
$140$		−	7.01693e6i		−	2.55719i
$141$	−243974.	+	633487.i	−0.0870336	+	0.225985i
$142$	374686.			0.130859
$143$			847388.i			0.289784i
$144$	3.94670e6	+	3.56942e6i	1.32174	+	1.19539i
$145$	960137.			0.314941
$146$		−	339111.i		−	0.108964i
$147$	2.61935e6	+	1.00879e6i	0.824596	+	0.317576i
$148$	−8.46015e6			−2.60971
$149$		−	762177.i		−	0.230408i	−0.993342	−	0.115204i	$-0.963248\pi$
$149$		−	762177.i		−	0.230408i	0.993342	−	0.115204i	$-0.0367521\pi$
$150$	674607.	−	1.75164e6i	0.199883	−	0.519003i
$151$	−3.36167e6			−0.976393			−0.488197	−	0.872734i	$-0.662345\pi$
$151$	−3.36167e6			−0.976393			−0.488197	+	0.872734i	$0.662345\pi$
$152$			1.50480e7i			4.28497i
$153$	783874.	−	866729.i	0.218863	−	0.241996i
$154$	−1.75747e7			−4.81200
$155$		−	3.29672e6i		−	0.885294i
$156$	1.18154e6	+	455045.i	0.311224	+	0.119862i
$157$	3.23991e6			0.837210			0.418605	−	0.908168i	$-0.362519\pi$
$157$	3.23991e6			0.837210			0.418605	+	0.908168i	$0.362519\pi$
$158$			5.58413e6i			1.41574i
$159$	2.08034e6	−	5.40166e6i	0.517539	−	1.34380i
$160$	3.31544e6			0.809432
$161$		−	1.19430e6i		−	0.286177i
$162$	7.61581e6	−	766512.i	1.79131	−	0.180291i
$163$	−5.04417e6			−1.16473			−0.582367	−	0.812926i	$-0.697873\pi$
$163$	−5.04417e6			−1.16473			−0.582367	+	0.812926i	$0.697873\pi$
$164$		−	9.59866e6i		−	2.17610i
$165$	6.78660e6	+	2.61372e6i	1.51078	+	0.581845i
$166$	7.90246e6			1.72758
$167$		−	1.40330e6i		−	0.301302i	−0.988587	−	0.150651i	$-0.951863\pi$
$167$		−	1.40330e6i		−	0.301302i	0.988587	−	0.150651i	$-0.0481370\pi$
$168$	−5.22681e6	+	1.35716e7i	−1.10232	+	2.86221i
$169$	−4.71993e6			−0.977858
$170$		−	2.39922e6i		−	0.488342i
$171$	7.11065e6	+	6.43090e6i	1.42207	+	1.28613i
$172$	1.18693e7			2.33259
$173$		−	8.74212e6i		−	1.68841i	−0.536019	−	0.844206i	$-0.680072\pi$
$173$		−	8.74212e6i		−	1.68841i	0.536019	−	0.844206i	$-0.319928\pi$
$174$	−3.35305e6	−	1.29136e6i	−0.636490	−	0.245131i
$175$	2.27225e6			0.423976
$176$		−	1.89210e7i		−	3.47061i
$177$	−475982.	+	1.23590e6i	−0.0858362	+	0.222876i
$178$	−2.45147e6			−0.434676
$179$		−	3.45560e6i		−	0.602510i	−0.953544	−	0.301255i	$-0.902594\pi$
$179$		−	3.45560e6i		−	0.602510i	0.953544	−	0.301255i	$-0.0974055\pi$
$180$	7.28877e6	−	8.05919e6i	1.24979	−	1.38189i
$181$	−6.62457e6			−1.11718			−0.558589	−	0.829445i	$-0.688657\pi$
$181$	−6.62457e6			−1.11718			−0.558589	+	0.829445i	$0.688657\pi$
$182$			2.21655e6i			0.367675i
$183$	2.26972e6	+	874138.i	0.370356	+	0.142635i
$184$	2.90286e6			0.465985
$185$			6.12876e6i			0.967961i
$186$	−4.43400e6	+	1.15130e7i	−0.689059	+	1.78916i
$187$	−4.15521e6			−0.635430
$188$		−	3.60650e6i		−	0.542766i
$189$	4.17926e6	+	8.26977e6i	0.619034	+	1.22492i
$190$	1.96832e7			2.86970
$191$			7.62747e6i			1.09466i	0.836916	+	0.547331i	$0.184356\pi$
$191$			7.62747e6i			1.09466i	−0.836916	+	0.547331i	$0.815644\pi$
$192$	192537.	+	74151.8i	0.0272026	+	0.0104765i
$193$	6.96603e6			0.968977			0.484488	−	0.874798i	$-0.339006\pi$
$193$	6.96603e6			0.968977			0.484488	+	0.874798i	$0.339006\pi$
$194$			8.76808e6i			1.20088i
$195$	329647.	−	855938.i	0.0444575	−	0.115435i
$196$	−1.49122e7			−1.98049
$197$			7.12687e6i			0.932181i	0.884737	+	0.466091i	$0.154338\pi$
$197$			7.12687e6i			0.932181i	−0.884737	+	0.466091i	$0.845662\pi$
$198$	−2.01852e7	−	1.82556e7i	−2.60038	−	2.35180i
$199$	−5.62679e6			−0.714005			−0.357003	−	0.934103i	$-0.616201\pi$
$199$	−5.62679e6			−0.714005			−0.357003	+	0.934103i	$0.616201\pi$
$200$			5.52292e6i			0.690365i
$201$	−7.96155e6	−	3.06623e6i	−0.980414	−	0.377586i
$202$	4.90596e6			0.595209
$203$		−	4.34962e6i		−	0.519952i
$204$	−2.23133e6	+	5.79372e6i	−0.262829	+	0.682444i
$205$	−6.95354e6			−0.807131
$206$		−	1.38788e7i		−	1.58763i
$207$	1.24056e6	−	1.37169e6i	0.139865	−	0.154648i
$208$	−2.38635e6			−0.265182
$209$		−	3.40893e7i		−	3.73404i
$210$	1.77520e7	+	6.83684e6i	1.91686	+	0.738240i
$211$	1.40652e7			1.49727			0.748633	−	0.662985i	$-0.230711\pi$
$211$	1.40652e7			1.49727			0.748633	+	0.662985i	$0.230711\pi$
$212$			3.07522e7i			3.22752i
$213$	−252439.	+	655465.i	−0.0261227	+	0.0678282i
$214$	2.05159e7			2.09339
$215$		−	8.59843e6i		−	0.865175i
$216$	−2.01005e7	+	1.01581e7i	−1.99455	+	1.00798i
$217$	−1.49348e7			−1.46158
$218$		−	4.76079e6i		−	0.459526i
$219$	593231.	+	228471.i	0.0564796	+	0.0217519i
$220$	−3.86368e7			−3.62855
$221$			524062.i			0.0485518i
$222$	8.24301e6	−	2.14032e7i	0.753402	−	1.95623i
$223$	1.24846e7			1.12580			0.562900	−	0.826525i	$-0.309686\pi$
$223$	1.24846e7			1.12580			0.562900	+	0.826525i	$0.309686\pi$
$224$		−	1.50196e7i		−	1.33633i
$225$	2.60975e6	+	2.36027e6i	0.229114	+	0.207212i
$226$	7.67856e6			0.665203
$227$			5.84215e6i			0.499453i	0.968316	+	0.249727i	$0.0803408\pi$
$227$			5.84215e6i			0.499453i	−0.968316	+	0.249727i	$0.919659\pi$
$228$	−4.75317e7	−	1.83059e7i	−4.01032	−	1.54449i
$229$	1.86993e7			1.55711			0.778555	−	0.627577i	$-0.215953\pi$
$229$	1.86993e7			1.55711			0.778555	+	0.627577i	$0.215953\pi$
$230$		−	3.79703e6i		−	0.312076i
$231$	1.18407e7	−	3.07447e7i	0.960596	−	2.49422i
$232$	1.05722e7			0.846643
$233$			1.08711e7i			0.859422i	0.902966	+	0.429711i	$0.141385\pi$
$233$			1.08711e7i			0.859422i	−0.902966	+	0.429711i	$0.858615\pi$
$234$	−2.30242e6	+	2.54579e6i	−0.179696	+	0.198689i
$235$	−2.61265e6			−0.201316
$236$		−	7.03610e6i		−	0.535298i
$237$	−9.76871e6	−	3.76222e6i	−0.733825	−	0.282618i
$238$	−1.08690e7			−0.806228
$239$		−	4.94120e6i		−	0.361942i	−0.983488	−	0.180971i	$-0.942076\pi$
$239$		−	4.94120e6i		−	0.361942i	0.983488	−	0.180971i	$-0.0579240\pi$
$240$	−7.36056e6	+	1.91119e7i	−0.532448	+	1.38252i
$241$	−1.27041e7			−0.907594			−0.453797	−	0.891105i	$-0.649931\pi$
$241$	−1.27041e7			−0.907594			−0.453797	+	0.891105i	$0.649931\pi$
$242$			7.12546e7i			5.02767i
$243$	−3.79012e6	+	1.38393e7i	−0.264140	+	0.964484i
$244$	−1.29218e7			−0.889512
$245$			1.08028e7i			0.734579i
$246$	2.42835e7	+	9.35231e6i	1.63120	+	0.628222i
$247$	−4.29940e6			−0.285310
$248$		−	3.63006e7i		−	2.37990i
$249$	−5.32416e6	+	1.38243e7i	−0.344868	+	0.895460i
$250$	3.06095e7			1.95901
$251$		−	1.10258e7i		−	0.697254i	−0.937262	−	0.348627i	$-0.886648\pi$
$251$		−	1.10258e7i		−	0.697254i	0.937262	−	0.348627i	$-0.113352\pi$
$252$	−3.65098e7	−	3.30196e7i	−2.28143	−	2.06334i
$253$	−6.57606e6			−0.406073
$254$			4.67608e7i			2.85352i
$255$	4.19713e6	+	1.61644e6i	0.253123	+	0.0974853i
$256$	−3.05061e7			−1.81831
$257$		−	2.36374e7i		−	1.39252i	−0.717791	−	0.696259i	$-0.754847\pi$
$257$		−	2.36374e7i		−	1.39252i	0.717791	−	0.696259i	$-0.245153\pi$
$258$	−1.15646e7	+	3.00279e7i	−0.673400	+	1.74850i
$259$	2.77645e7			1.59805
$260$			4.87294e6i			0.277249i
$261$	4.51812e6	−	4.99569e6i	0.254119	−	0.280979i
$262$	3.15059e7			1.75181
$263$		−	1.31703e7i		−	0.723984i	−0.932181	−	0.361992i	$-0.882097\pi$
$263$		−	1.31703e7i		−	0.723984i	0.932181	−	0.361992i	$-0.117903\pi$
$264$	7.47280e7	+	2.87800e7i	4.06136	+	1.56415i
$265$	2.22777e7			1.19711
$266$		−	8.91691e7i		−	4.73772i
$267$	1.65164e6	−	4.28852e6i	0.0867723	−	0.225307i
$268$	4.53259e7			2.35473
$269$			1.14662e7i			0.589066i	0.955641	+	0.294533i	$0.0951640\pi$
$269$			1.14662e7i			0.589066i	−0.955641	+	0.294533i	$0.904836\pi$
$270$	1.32871e7	+	2.62921e7i	0.675057	+	1.33578i
$271$	−2.60681e7			−1.30979			−0.654894	−	0.755721i	$-0.727287\pi$
$271$	−2.60681e7			−1.30979			−0.654894	+	0.755721i	$0.727287\pi$
$272$		−	1.17016e7i		−	0.581484i
$273$	−3.87757e6	−	1.49337e6i	−0.190578	−	0.0733971i
$274$	2.97148e7			1.44451
$275$		−	1.25115e7i		−	0.601604i
$276$	−3.53132e6	+	9.16919e6i	−0.167962	+	0.436118i
$277$	−1.86866e6			−0.0879206			−0.0439603	−	0.999033i	$-0.513998\pi$
$277$	−1.86866e6			−0.0879206			−0.0439603	+	0.999033i	$0.513998\pi$
$278$			7.40179e6i			0.344510i
$279$	−1.71532e7	−	1.55134e7i	−0.789827	−	0.714323i
$280$	−5.59724e7			−2.54976
$281$		−	1.21368e7i		−	0.546998i	−0.961872	−	0.273499i	$-0.911819\pi$
$281$		−	1.21368e7i		−	0.546998i	0.961872	−	0.273499i	$-0.0881810\pi$
$282$	9.12404e6	+	3.51394e6i	0.406855	+	0.156692i
$283$	−1.56496e7			−0.690469			−0.345235	−	0.938516i	$-0.612201\pi$
$283$	−1.56496e7			−0.690469			−0.345235	+	0.938516i	$0.612201\pi$
$284$		−	3.73162e6i		−	0.162908i
$285$	−1.32613e7	+	3.44333e7i	−0.572863	+	1.48746i
$286$	1.22048e7			0.521715
$287$			3.15009e7i			1.33253i
$288$	1.56015e7	−	1.72505e7i	0.653112	−	0.722146i
$289$	2.15678e7			0.893537
$290$		−	1.38287e7i		−	0.567008i
$291$	−1.53386e7	−	5.90736e6i	−0.622454	−	0.239726i
$292$	−3.37732e6			−0.135651
$293$		−	1.25973e7i		−	0.500813i	−0.968141	−	0.250406i	$-0.919436\pi$
$293$		−	1.25973e7i		−	0.500813i	0.968141	−	0.250406i	$-0.0805642\pi$
$294$	1.45295e7	−	3.77262e7i	0.571752	−	1.48457i
$295$	−5.09714e6			−0.198546
$296$			6.74845e7i			2.60213i
$297$	4.55352e7	−	2.30119e7i	1.73811	−	0.878383i
$298$	−1.09775e7			−0.414817
$299$			829384.i			0.0310272i
$300$	−1.74451e7	−	6.71863e6i	−0.646116	−	0.248838i
$301$	−3.89526e7			−1.42836
$302$			4.84178e7i			1.75786i
$303$	−3.30531e6	+	8.58234e6i	−0.118819	+	0.308516i
$304$	9.59997e7			3.41703
$305$			9.36088e6i			0.329926i
$306$	−1.24834e7	−	1.12900e7i	−0.435681	−	0.394032i
$307$	−4.58517e7			−1.58468			−0.792338	−	0.610083i	$-0.791136\pi$
$307$	−4.58517e7			−1.58468			−0.792338	+	0.610083i	$0.791136\pi$
$308$			1.75032e8i			5.99055i
$309$	2.42791e7	+	9.35060e6i	0.822919	+	0.316930i
$310$	−4.74823e7			−1.59385
$311$			1.66104e7i			0.552204i	0.961128	+	0.276102i	$0.0890428\pi$
$311$			1.66104e7i			0.552204i	−0.961128	+	0.276102i	$0.910957\pi$
$312$	3.62978e6	−	9.42483e6i	0.119513	−	0.310320i
$313$	9.84835e6			0.321167			0.160583	−	0.987022i	$-0.448662\pi$
$313$	9.84835e6			0.321167			0.160583	+	0.987022i	$0.448662\pi$
$314$		−	4.66641e7i		−	1.50728i
$315$	−2.39203e7	+	2.64487e7i	−0.765307	+	0.846199i
$316$	5.56142e7			1.76248
$317$		−	2.62049e7i		−	0.822629i	−0.911494	−	0.411314i	$-0.865070\pi$
$317$		−	2.62049e7i		−	0.822629i	0.911494	−	0.411314i	$-0.134930\pi$
$318$	−7.77995e7	−	2.99629e7i	−2.41933	−	0.931757i
$319$	−2.39499e7			−0.737789
$320$			794069.i			0.0242331i
$321$	−1.38223e7	+	3.58900e7i	−0.417893	+	1.08507i
$322$	−1.72013e7			−0.515222
$323$		−	2.10823e7i		−	0.625621i
$324$	−7.63395e6	−	7.58484e7i	−0.224447	−	2.23003i
$325$	−1.57797e6			−0.0459673
$326$			7.26506e7i			2.09694i
$327$	8.32839e6	+	3.20751e6i	0.238187	+	0.0917328i
$328$	−7.65662e7			−2.16978
$329$			1.18358e7i			0.332362i
$330$	3.76451e7	−	9.77467e7i	1.04753	−	2.71994i
$331$	2.95037e6			0.0813565			0.0406783	−	0.999172i	$-0.487048\pi$
$331$	2.95037e6			0.0813565			0.0406783	+	0.999172i	$0.487048\pi$
$332$		−	7.87033e7i		−	2.15069i
$333$	3.18886e7	+	2.88402e7i	0.863579	+	0.781025i
$334$	−2.02116e7			−0.542453
$335$		−	3.28353e7i		−	0.873387i
$336$	8.65808e7	+	3.33448e7i	2.28246	+	0.879044i
$337$	−3.91238e7			−1.02224			−0.511119	−	0.859510i	$-0.670769\pi$
$337$	−3.91238e7			−1.02224			−0.511119	+	0.859510i	$0.670769\pi$
$338$			6.79807e7i			1.76050i
$339$	−5.17331e6	+	1.34326e7i	−0.132791	+	0.344796i
$340$	−2.38947e7			−0.607945
$341$			8.22344e7i			2.07391i
$342$	9.26236e7	−	1.02414e8i	2.31549	−	2.56024i
$343$	−6.44466e6			−0.159705
$344$		−	9.46783e7i		−	2.32581i
$345$	6.64241e6	+	2.55819e6i	0.161759	+	0.0622982i
$346$	−1.25912e8			−3.03975
$347$		−	3.82490e7i		−	0.915443i	−0.889096	−	0.457722i	$-0.848666\pi$
$347$		−	3.82490e7i		−	0.915443i	0.889096	−	0.457722i	$-0.151334\pi$
$348$	−1.28611e7	+	3.33941e7i	−0.305168	+	0.792377i
$349$	−7.65865e6			−0.180167			−0.0900837	−	0.995934i	$-0.528713\pi$
$349$	−7.65865e6			−0.180167			−0.0900837	+	0.995934i	$0.528713\pi$
$350$		−	3.27269e7i		−	0.763310i
$351$	−2.90231e6	−	5.74298e6i	−0.0671154	−	0.132805i
$352$	−8.27012e7			−1.89620
$353$			2.48365e7i			0.564632i	0.959321	+	0.282316i	$0.0911027\pi$
$353$			2.48365e7i			0.564632i	−0.959321	+	0.282316i	$0.908897\pi$
$354$	1.78005e7	+	6.85551e6i	0.401257	+	0.154536i
$355$	−2.70329e6			−0.0604238
$356$			2.44150e7i			0.541136i
$357$	7.32280e6	−	1.90139e7i	0.160943	−	0.417894i
$358$	−4.97706e7			−1.08474
$359$		−	4.50861e7i		−	0.974450i	−0.873276	−	0.487225i	$-0.838009\pi$
$359$		−	4.50861e7i		−	0.974450i	0.873276	−	0.487225i	$-0.161991\pi$
$360$	−6.42862e7	−	5.81407e7i	−1.37788	−	1.24616i
$361$	1.25914e8			2.67640
$362$			9.54130e7i			2.01132i
$363$	−1.24651e8	−	4.80067e7i	−2.60600	−	1.00365i
$364$	2.20754e7			0.457725
$365$			2.44662e6i			0.0503140i
$366$	1.25901e7	−	3.26906e7i	0.256795	−	0.666775i
$367$	6.88134e7			1.39211			0.696057	−	0.717986i	$-0.254936\pi$
$367$	6.88134e7			1.39211			0.696057	+	0.717986i	$0.254936\pi$
$368$		−	1.85190e7i		−	0.371598i
$369$	−3.27213e7	+	3.61799e7i	−0.651256	+	0.720093i
$370$	8.82719e7			1.74268
$371$		−	1.00923e8i		−	1.97636i
$372$	1.14662e8	+	4.41597e7i	2.22736	+	0.857822i
$373$	6.59517e7			1.27087			0.635433	−	0.772156i	$-0.280822\pi$
$373$	6.59517e7			1.27087			0.635433	+	0.772156i	$0.280822\pi$
$374$			5.98470e7i			1.14400i
$375$	−2.06227e7	+	5.35474e7i	−0.391067	+	1.01542i
$376$	−2.87682e7			−0.541189
$377$			3.02061e6i			0.0563729i
$378$	1.19109e8	−	6.01935e7i	2.20530	−	1.11448i
$379$	−7.69716e7			−1.41388			−0.706940	−	0.707273i	$-0.749925\pi$
$379$	−7.69716e7			−1.41388			−0.706940	+	0.707273i	$0.749925\pi$
$380$		−	1.96032e8i		−	3.57253i
$381$	−8.18020e7	−	3.15044e7i	−1.47907	−	0.569634i
$382$	1.09858e8			1.97079
$383$		−	1.06922e8i		−	1.90314i	−0.307435	−	0.951569i	$-0.599471\pi$
$383$		−	1.06922e8i		−	1.90314i	0.307435	−	0.951569i	$-0.400529\pi$
$384$	2.08825e7	−	5.42221e7i	0.368799	−	0.957597i
$385$	1.26798e8			2.22193
$386$		−	1.00331e8i		−	1.74451i
$387$	−4.47385e7	−	4.04617e7i	−0.771877	−	0.698089i
$388$	8.73243e7			1.49500
$389$			1.00045e8i			1.69961i	0.527101	+	0.849803i	$0.323279\pi$
$389$			1.00045e8i			1.69961i	−0.527101	+	0.849803i	$0.676721\pi$
$390$	−1.23280e7	−	4.74787e6i	−0.207825	−	0.0800396i
$391$	−4.06692e6			−0.0680355
$392$			1.18951e8i			1.97474i
$393$	−2.12266e7	+	5.51155e7i	−0.349706	+	0.908021i
$394$	1.02648e8			1.67826
$395$		−	4.02885e7i		−	0.653717i
$396$	−1.81813e8	+	2.01031e8i	−2.92779	+	3.23726i
$397$	−2.01092e7			−0.321383			−0.160692	−	0.987005i	$-0.551372\pi$
$397$	−2.01092e7			−0.321383			−0.160692	+	0.987005i	$0.551372\pi$
$398$			8.10420e7i			1.28547i
$399$	1.55990e8	+	6.00763e7i	2.45571	+	0.945768i
$400$	3.52339e7			0.550530
$401$			1.17456e8i			1.82155i	0.412906	+	0.910774i	$0.364514\pi$
$401$			1.17456e8i			1.82155i	−0.412906	+	0.910774i	$0.635486\pi$
$402$	−4.41625e7	+	1.14669e8i	−0.679792	+	1.76510i
$403$	1.03716e7			0.158463
$404$		−	4.88601e7i		−	0.740986i
$405$	−5.49467e7	+	5.53024e6i	−0.827135	+	0.0832490i
$406$	−6.26470e7			−0.936101
$407$		−	1.52878e8i		−	2.26757i
$408$	4.62151e7	+	1.77988e7i	0.680461	+	0.262066i
$409$	5.90651e7			0.863298			0.431649	−	0.902042i	$-0.357932\pi$
$409$	5.90651e7			0.863298			0.431649	+	0.902042i	$0.357932\pi$
$410$			1.00151e8i			1.45313i
$411$	−2.00199e7	+	5.19822e7i	−0.288361	+	0.748738i
$412$	−1.38223e8			−1.97647
$413$			2.30911e7i			0.327789i
$414$	−1.97563e7	−	1.78677e7i	−0.278423	−	0.251807i
$415$	−5.70148e7			−0.797707
$416$			1.04304e7i			0.144884i
$417$	−1.29485e7	−	4.98684e6i	−0.178571	−	0.0687729i
$418$	−4.90985e8			−6.72263
$419$			5.31750e7i			0.722879i	0.932396	+	0.361440i	$0.117715\pi$
$419$			5.31750e7i			0.722879i	−0.932396	+	0.361440i	$0.882285\pi$
$420$	6.80904e7	−	1.76799e8i	0.919047	−	2.38633i
$421$	5.20180e7			0.697119			0.348560	−	0.937287i	$-0.386671\pi$
$421$	5.20180e7			0.697119			0.348560	+	0.937287i	$0.386671\pi$
$422$		−	2.02580e8i		−	2.69562i
$423$	−1.22944e7	+	1.35939e7i	−0.162437	+	0.179606i
$424$	2.45303e8			3.21814
$425$		−	7.73766e6i		−	0.100796i
$426$	9.44059e6	+	3.63585e6i	0.122115	+	0.0470302i
$427$	4.24067e7			0.544692
$428$		−	2.04325e8i		−	2.60609i
$429$	−8.22281e6	+	2.13508e7i	−0.104147	+	0.270422i
$430$	−1.23842e8			−1.55763
$431$		−	1.92896e6i		−	0.0240931i	−0.999927	−	0.0120465i	$-0.996165\pi$
$431$		−	1.92896e6i		−	0.0240931i	0.999927	−	0.0120465i	$-0.00383462\pi$
$432$	6.48045e7	+	1.28233e8i	0.803811	+	1.59055i
$433$	1.23082e8			1.51611			0.758056	−	0.652189i	$-0.226149\pi$
$433$	1.23082e8			1.51611			0.758056	+	0.652189i	$0.226149\pi$
$434$			2.15105e8i			2.63136i
$435$	2.41916e7	+	9.31690e6i	0.293898	+	0.113189i
$436$	−4.74143e7			−0.572071
$437$		−	3.33651e7i		−	0.399804i
$438$	3.29064e6	−	8.54424e6i	0.0391614	−	0.101684i
$439$	1.65101e7			0.195144			0.0975722	−	0.995228i	$-0.468892\pi$
$439$	1.65101e7			0.195144			0.0975722	+	0.995228i	$0.468892\pi$
$440$			3.08196e8i			3.61800i
$441$	5.62080e7	+	5.08348e7i	0.655364	+	0.592714i
$442$	7.54800e6			0.0874108
$443$			7.48999e7i			0.861530i	0.902464	+	0.430765i	$0.141756\pi$
$443$			7.48999e7i			0.861530i	−0.902464	+	0.430765i	$0.858244\pi$
$444$	−2.13162e8	−	8.20949e7i	−2.43534	−	0.937923i
$445$	1.76869e7			0.200711
$446$		−	1.79815e8i		−	2.02685i
$447$	7.39595e6	−	1.92038e7i	0.0828078	−	0.215013i
$448$	3.59729e6			0.0400075
$449$			8.27993e7i			0.914719i	0.889282	+	0.457359i	$0.151205\pi$
$449$			8.27993e7i			0.914719i	−0.889282	+	0.457359i	$0.848795\pi$
$450$	3.39948e7	−	3.75880e7i	0.373056	−	0.412488i
$451$	1.73451e8			1.89081
$452$		−	7.64733e7i		−	0.828123i
$453$	−8.47007e7	−	3.26207e7i	−0.911155	−	0.350913i
$454$	8.41438e7			0.899196
$455$		−	1.59920e7i		−	0.169773i
$456$	−1.46021e8	+	3.79149e8i	−1.54000	+	3.99867i
$457$	−7.52915e7			−0.788856			−0.394428	−	0.918927i	$-0.629057\pi$
$457$	−7.52915e7			−0.788856			−0.394428	+	0.918927i	$0.629057\pi$
$458$		−	2.69324e8i		−	2.80336i
$459$	2.81610e7	−	1.42316e7i	0.291212	−	0.147169i
$460$	−3.78159e7			−0.388509
$461$		−	5.33363e7i		−	0.544402i	−0.962240	−	0.272201i	$-0.912248\pi$
$461$		−	5.33363e7i		−	0.544402i	0.962240	−	0.272201i	$-0.0877516\pi$
$462$	−4.42812e8	−	1.70540e8i	−4.49049	−	1.72942i
$463$	−6.14717e7			−0.619344			−0.309672	−	0.950843i	$-0.600219\pi$
$463$	−6.14717e7			−0.619344			−0.309672	+	0.950843i	$0.600219\pi$
$464$		−	6.74460e7i		−	0.675153i
$465$	3.19905e7	−	8.30642e7i	0.318172	−	0.826143i
$466$	1.56576e8			1.54727
$467$			6.28651e7i			0.617247i	0.951184	+	0.308624i	$0.0998683\pi$
$467$			6.28651e7i			0.617247i	−0.951184	+	0.308624i	$0.900132\pi$
$468$	2.53544e7	+	2.29306e7i	0.247352	+	0.223706i
$469$	−1.48751e8			−1.44192
$470$			3.76297e7i			0.362441i
$471$	8.16328e7	+	3.14392e7i	0.781272	+	0.300891i
$472$	−5.61252e7			−0.533743
$473$			2.14482e8i			2.02678i
$474$	−5.41868e7	+	1.40698e8i	−0.508814	+	1.32115i
$475$	6.34797e7			0.592317
$476$			1.08248e8i			1.00369i
$477$	1.04832e8	−	1.15913e8i	0.965919	−	1.06802i
$478$	−7.11676e7			−0.651626
$479$			4.12005e7i			0.374883i	0.982276	+	0.187441i	$0.0600195\pi$
$479$			4.12005e7i			0.374883i	−0.982276	+	0.187441i	$0.939981\pi$
$480$	8.35357e7	+	3.21721e7i	0.755350	+	0.290908i
$481$	−1.92812e7			−0.173260
$482$			1.82975e8i			1.63400i
$483$	1.15891e7	−	3.00915e7i	0.102851	−	0.267056i
$484$	7.09648e8			6.25903
$485$		−	6.32601e7i		−	0.554504i
$486$	1.99326e8	+	5.45886e7i	1.73642	+	0.475547i
$487$	1.12339e8			0.972623			0.486311	−	0.873786i	$-0.338342\pi$
$487$	1.12339e8			0.972623			0.486311	+	0.873786i	$0.338342\pi$
$488$			1.03074e8i			0.886928i
$489$	−1.27093e8	−	4.89472e7i	−1.08691	−	0.418602i
$490$	1.55592e8			1.32251
$491$			1.02001e8i			0.861705i	0.902422	+	0.430852i	$0.141787\pi$
$491$			1.02001e8i			0.861705i	−0.902422	+	0.430852i	$0.858213\pi$
$492$	9.31427e7	−	2.41848e8i	0.782084	−	2.03070i
$493$	−1.48117e7			−0.123613
$494$			6.19238e7i			0.513662i
$495$	1.45632e8	+	1.31711e8i	1.20072	+	1.08594i
$496$	−2.31582e8			−1.89784
$497$			1.22465e7i			0.0997565i
$498$	1.99110e8	+	7.66833e7i	1.61215	+	0.620887i
$499$	−9.35647e7			−0.753027			−0.376514	−	0.926411i	$-0.622877\pi$
$499$	−9.35647e7			−0.753027			−0.376514	+	0.926411i	$0.622877\pi$
$500$		−	3.04851e8i		−	2.43881i
$501$	1.36173e7	−	3.53577e7i	0.108287	−	0.281171i
$502$	−1.58804e8			−1.25531
$503$		−	1.16655e8i		−	0.916645i	−0.888786	−	0.458322i	$-0.848451\pi$
$503$		−	1.16655e8i		−	0.916645i	0.888786	−	0.458322i	$-0.151549\pi$
$504$	−2.63389e8	+	2.91230e8i	−2.05734	+	2.27480i
$505$	−3.53956e7			−0.274837
$506$			9.47142e7i			0.731078i
$507$	−1.18923e8	−	4.58009e7i	−0.912522	−	0.351439i
$508$	4.65707e8			3.55240
$509$		−	7.57879e7i		−	0.574707i	−0.957825	−	0.287354i	$-0.907225\pi$
$509$		−	7.57879e7i		−	0.574707i	0.957825	−	0.287354i	$-0.0927755\pi$
$510$	2.32814e7	−	6.04508e7i	0.175509	−	0.455713i
$511$	1.10837e7			0.0830658
$512$			3.01648e8i			2.24745i
$513$	1.16756e8	+	2.31033e8i	0.864823	+	1.71128i
$514$	−3.40447e8			−2.50703
$515$			1.00133e8i			0.733085i
$516$	2.99058e8	+	1.15176e8i	2.17674	+	0.838327i
$517$	6.51707e7			0.471607
$518$		−	3.99890e8i		−	2.87707i
$519$	8.48311e7	−	2.20266e8i	0.606810	−	1.57560i
$520$	3.88702e7			0.276444
$521$		−	1.76520e8i		−	1.24819i	−0.781348	−	0.624095i	$-0.785468\pi$
$521$		−	1.76520e8i		−	1.24819i	0.781348	−	0.624095i	$-0.214532\pi$
$522$	−7.19523e7	−	6.50740e7i	−0.505863	−	0.457505i
$523$	−1.89640e8			−1.32564			−0.662818	−	0.748781i	$-0.730640\pi$
$523$	−1.89640e8			−1.32564			−0.662818	+	0.748781i	$0.730640\pi$
$524$		−	3.13778e8i		−	2.18086i
$525$	5.72515e7	+	2.20492e7i	0.395648	+	0.152376i
$526$	−1.89691e8			−1.30343
$527$			5.08574e7i			0.347474i
$528$	1.83604e8	−	4.76733e8i	1.24733	−	3.23872i
$529$	−6.43634e6			−0.0434783
$530$		−	3.20864e8i		−	2.15523i
$531$	−2.39857e7	+	2.65209e7i	−0.160202	+	0.177135i
$532$	−8.88065e8			−5.89807
$533$		−	2.18760e7i		−	0.144473i
$534$	−6.17671e7	−	2.37883e7i	−0.405633	−	0.156221i
$535$	−1.48019e8			−0.966619
$536$		−	3.61553e8i		−	2.34789i
$537$	3.35322e7	−	8.70672e7i	0.216540	−	0.562253i
$538$	1.65147e8			1.06053
$539$		−	2.69468e8i		−	1.72084i
$540$	2.61852e8	−	1.32331e8i	1.66293	−	0.840390i
$541$	2.30087e7			0.145312			0.0726558	−	0.997357i	$-0.476853\pi$
$541$	2.30087e7			0.145312			0.0726558	+	0.997357i	$0.476853\pi$
$542$			3.75455e8i			2.35809i
$543$	−1.66913e8	−	6.42830e7i	−1.04253	−	0.401510i
$544$	−5.11461e7			−0.317699
$545$			3.43483e7i			0.212185i
$546$	−2.15088e7	+	5.58483e7i	−0.132141	+	0.343109i
$547$	9.13848e6			0.0558357			0.0279179	−	0.999610i	$-0.491112\pi$
$547$	9.13848e6			0.0558357			0.0279179	+	0.999610i	$0.491112\pi$
$548$		−	2.95940e8i		−	1.79830i
$549$	4.87055e7	+	4.40495e7i	0.294348	+	0.266210i
$550$	−1.80202e8			−1.08310
$551$		−	1.21515e8i		−	0.726400i
$552$	7.31404e7	+	2.81685e7i	0.434850	+	0.167474i
$553$	−1.82515e8			−1.07925
$554$			2.69141e7i			0.158289i
$555$	−5.94718e7	+	1.54420e8i	−0.347882	+	0.903286i
$556$	7.37169e7			0.428887
$557$			1.97109e7i			0.114062i	0.998372	+	0.0570310i	$0.0181634\pi$
$557$			1.97109e7i			0.114062i	−0.998372	+	0.0570310i	$0.981837\pi$
$558$	−2.23438e8	+	2.47055e8i	−1.28604	+	1.42197i
$559$	2.70508e7			0.154862
$560$			3.57080e8i			2.03330i
$561$	−1.04695e8	−	4.03210e7i	−0.592974	−	0.228372i
$562$	−1.74805e8			−0.984794
$563$		−	1.17928e8i		−	0.660835i	−0.943835	−	0.330418i	$-0.892810\pi$
$563$		−	1.17928e8i		−	0.660835i	0.943835	−	0.330418i	$-0.107190\pi$
$564$	3.49965e7	−	9.08693e7i	0.195068	−	0.506501i
$565$	−5.53994e7			−0.307156
$566$			2.25400e8i			1.24309i
$567$	2.50531e7	+	2.48920e8i	0.137440	+	1.36556i
$568$	−2.97662e7			−0.162435
$569$			2.64636e8i			1.43652i	0.695773	+	0.718261i	$0.255062\pi$
$569$			2.64636e8i			1.43652i	−0.695773	+	0.718261i	$0.744938\pi$
$570$	4.95939e8	+	1.91001e8i	2.67796	+	1.03136i
$571$	2.22381e8			1.19451			0.597255	−	0.802052i	$-0.296258\pi$
$571$	2.22381e8			1.19451			0.597255	+	0.802052i	$0.296258\pi$
$572$		−	1.21552e8i		−	0.649492i
$573$	−7.40148e7	+	1.92182e8i	−0.393419	+	1.02152i
$574$	4.53704e8			2.39904
$575$		−	1.22457e7i		−	0.0644138i
$576$	4.13162e6	+	3.73665e6i	0.0216198	+	0.0195531i
$577$	4.88721e7			0.254410			0.127205	−	0.991876i	$-0.459399\pi$
$577$	4.88721e7			0.254410			0.127205	+	0.991876i	$0.459399\pi$
$578$		−	3.10639e8i		−	1.60869i
$579$	1.75516e8	+	6.75964e7i	0.904235	+	0.348247i
$580$	−1.37725e8			−0.705877
$581$			2.58289e8i			1.31697i
$582$	−8.50830e7	+	2.20921e8i	−0.431593	+	1.12064i
$583$	−5.55702e8			−2.80438
$584$			2.69400e7i			0.135257i
$585$	1.66116e7	−	1.83674e7i	0.0829742	−	0.0917445i
$586$	−1.81438e8			−0.901644
$587$			2.54706e8i			1.25929i	0.776884	+	0.629644i	$0.216799\pi$
$587$			2.54706e8i			1.25929i	−0.776884	+	0.629644i	$0.783201\pi$
$588$	−3.75727e8	−	1.44704e8i	−1.84817	−	0.711783i
$589$	−4.17234e8			−2.04190
$590$			7.34136e7i			0.357454i
$591$	−6.91572e7	+	1.79569e8i	−0.335023	+	0.869897i
$592$	4.30522e8			2.07506
$593$			3.18368e8i			1.52674i	0.645960	+	0.763371i	$0.276457\pi$
$593$			3.18368e8i			1.52674i	−0.645960	+	0.763371i	$0.723543\pi$
$594$	−3.31438e8	−	6.55838e8i	−1.58141	−	3.12923i
$595$	7.84177e7			0.372274
$596$			1.09329e8i			0.516412i
$597$	−1.41772e8	−	5.46008e7i	−0.666299	−	0.256611i
$598$	1.19455e7			0.0558601
$599$		−	8.07411e7i		−	0.375677i	−0.982200	−	0.187838i	$-0.939852\pi$
$599$		−	8.07411e7i		−	0.375677i	0.982200	−	0.187838i	$-0.0601481\pi$
$600$	−5.35929e7	+	1.39155e8i	−0.248115	+	0.644238i
$601$	−2.05403e8			−0.946203			−0.473101	−	0.881008i	$-0.656866\pi$
$601$	−2.05403e8			−0.946203			−0.473101	+	0.881008i	$0.656866\pi$
$602$			5.61030e8i			2.57156i
$603$	−1.70845e8	−	1.54513e8i	−0.779204	−	0.704716i
$604$	4.82209e8			2.18839
$605$		−	5.14089e8i		−	2.32152i
$606$	1.23610e8	+	4.76060e7i	0.555440	+	0.213916i
$607$	4.18123e8			1.86955			0.934777	−	0.355235i	$-0.115599\pi$
$607$	4.18123e8			1.86955			0.934777	+	0.355235i	$0.115599\pi$
$608$		−	4.19602e8i		−	1.86693i
$609$	4.22075e7	−	1.09593e8i	0.186869	−	0.485211i
$610$	1.34824e8			0.593987
$611$		−	8.21944e6i		−	0.0360345i
$612$	−1.12441e8	+	1.24326e8i	−0.490537	+	0.542387i
$613$	1.76806e7			0.0767564			0.0383782	−	0.999263i	$-0.487781\pi$
$613$	1.76806e7			0.0767564			0.0383782	+	0.999263i	$0.487781\pi$
$614$			6.60397e8i			2.85299i
$615$	−1.75201e8	−	6.74752e7i	−0.753203	−	0.290081i
$616$	1.39619e9			5.97314
$617$		−	9.88297e7i		−	0.420758i	−0.977620	−	0.210379i	$-0.932530\pi$
$617$		−	9.88297e7i		−	0.420758i	0.977620	−	0.210379i	$-0.0674697\pi$
$618$	1.34676e8	−	3.49689e8i	0.570589	−	1.48155i
$619$	−1.98810e8			−0.838236			−0.419118	−	0.907932i	$-0.637661\pi$
$619$	−1.98810e8			−0.838236			−0.419118	+	0.907932i	$0.637661\pi$
$620$			4.72893e8i			1.98421i
$621$	4.45677e7	−	2.25230e7i	0.186100	−	0.0940485i
$622$	2.39238e8			0.994167
$623$		−	8.01252e7i		−	0.331364i
$624$	−6.01264e7	−	2.31565e7i	−0.247464	−	0.0953056i
$625$	−1.45423e8			−0.595652
$626$		−	1.41845e8i		−	0.578216i
$627$	3.30793e8	−	8.58914e8i	1.34200	−	3.48455i
$628$	−4.64743e8			−1.87644
$629$		−	9.45463e7i		−	0.379920i
$630$	3.80938e8	+	3.44522e8i	1.52346	+	1.37783i
$631$	−2.40252e7			−0.0956267			−0.0478134	−	0.998856i	$-0.515225\pi$
$631$	−2.40252e7			−0.0956267			−0.0478134	+	0.998856i	$0.515225\pi$
$632$		−	4.43621e8i		−	1.75736i
$633$	3.54387e8	+	1.36485e8i	1.39723	+	0.538113i
$634$	−3.77426e8			−1.48103
$635$		−	3.37371e8i		−	1.31761i
$636$	−2.98411e8	+	7.74832e8i	−1.15996	+	3.01187i
$637$	−3.39858e7			−0.131486
$638$			3.44948e8i			1.32829i
$639$	−1.27209e7	+	1.40655e7i	−0.0487545	+	0.0539079i
$640$	2.23625e8			0.853061
$641$		−	1.92414e8i		−	0.730573i	−0.930895	−	0.365286i	$-0.880971\pi$
$641$		−	1.92414e8i		−	0.730573i	0.930895	−	0.365286i	$-0.119029\pi$
$642$	5.16919e8	+	1.99081e8i	1.95352	+	0.752358i
$643$	2.18934e8			0.823532			0.411766	−	0.911290i	$-0.364912\pi$
$643$	2.18934e8			0.823532			0.411766	+	0.911290i	$0.364912\pi$
$644$			1.71314e8i			0.641408i
$645$	8.34367e7	−	2.16646e8i	0.310941	−	0.807368i
$646$	−3.03647e8			−1.12634
$647$		−	1.66576e8i		−	0.615035i	−0.951542	−	0.307518i	$-0.900502\pi$
$647$		−	1.66576e8i		−	0.615035i	0.951542	−	0.307518i	$-0.0994983\pi$
$648$	−6.05024e8	+	6.08941e7i	−2.22355	+	0.223795i
$649$	1.27145e8			0.465119
$650$			2.27273e7i			0.0827577i
$651$	−3.76298e8	−	1.44923e8i	−1.36392	−	0.525286i
$652$	7.23551e8			2.61052
$653$		−	4.73288e8i		−	1.69975i	−0.526982	−	0.849876i	$-0.676677\pi$
$653$		−	4.73288e8i		−	1.69975i	0.526982	−	0.849876i	$-0.323323\pi$
$654$	4.61974e7	−	1.19953e8i	0.165152	−	0.428823i
$655$	−2.27309e8			−0.808897
$656$			4.88460e8i			1.73028i
$657$	1.27300e7	+	1.15131e7i	0.0448883	+	0.0405972i
$658$	1.70470e8			0.598371
$659$			2.78636e8i			0.973602i	0.873513	+	0.486801i	$0.161836\pi$
$659$			2.78636e8i			0.973602i	−0.873513	+	0.486801i	$0.838164\pi$
$660$	−9.73492e8	−	3.74920e8i	−3.38610	−	1.30409i
$661$	−9.25988e7			−0.320628			−0.160314	−	0.987066i	$-0.551251\pi$
$661$	−9.25988e7			−0.320628			−0.160314	+	0.987066i	$0.551251\pi$
$662$		−	4.24938e7i		−	0.146471i
$663$	−5.08535e6	+	1.32043e7i	−0.0174494	+	0.0453078i
$664$	−6.27797e8			−2.14444
$665$			6.43339e8i			2.18763i
$666$	4.15382e8	−	4.59287e8i	1.40613	−	1.55475i
$667$	−2.34411e7			−0.0789952
$668$			2.01295e8i			0.675309i
$669$	3.14563e8	+	1.21147e8i	1.05058	+	0.404609i
$670$	−4.72923e8			−1.57241
$671$		−	2.33500e8i		−	0.772894i
$672$	1.45746e8	−	3.78434e8i	0.480274	−	1.24704i
$673$	1.77064e8			0.580879			0.290439	−	0.956893i	$-0.406199\pi$
$673$	1.77064e8			0.580879			0.290439	+	0.956893i	$0.406199\pi$
$674$			5.63496e8i			1.84040i
$675$	4.28519e7	+	8.47938e7i	0.139335	+	0.275710i
$676$	6.77042e8			2.19167
$677$			1.63007e8i			0.525338i	0.964886	+	0.262669i	$0.0846028\pi$
$677$			1.63007e8i			0.525338i	−0.964886	+	0.262669i	$0.915397\pi$
$678$	1.93469e8	+	7.45106e7i	0.620758	+	0.239072i
$679$	−2.86581e8			−0.915458
$680$			1.90602e8i			0.606179i
$681$	−5.66906e7	+	1.47199e8i	−0.179502	+	0.466082i
$682$	1.18441e9			3.73379
$683$			3.86343e8i			1.21258i	0.795243	+	0.606291i	$0.207344\pi$
$683$			3.86343e8i			1.21258i	−0.795243	+	0.606291i	$0.792656\pi$
$684$	−1.01997e9	−	9.22469e8i	−3.18728	−	2.88259i
$685$	−2.14387e8			−0.667002
$686$			9.28217e7i			0.287526i
$687$	4.71148e8	+	1.81453e8i	1.45307	+	0.559620i
$688$	−6.04007e8			−1.85471
$689$			7.00861e7i			0.214276i
$690$	3.68453e7	−	9.56699e7i	0.112159	−	0.291225i
$691$	2.74990e8			0.833457			0.416728	−	0.909031i	$-0.363177\pi$
$691$	2.74990e8			0.833457			0.416728	+	0.909031i	$0.363177\pi$
$692$			1.25400e9i			3.78424i
$693$	5.96676e8	−	6.59744e8i	1.79283	−	1.98233i
$694$	−5.50896e8			−1.64813
$695$		−	5.34026e7i		−	0.159077i
$696$	2.66377e8	+	1.02589e8i	0.790075	+	0.304281i
$697$	1.07270e8			0.316796
$698$			1.10307e8i			0.324366i
$699$	−1.05490e8	+	2.73909e8i	−0.308874	+	0.802000i
$700$	−3.25938e8			−0.950257
$701$		−	7.89676e7i		−	0.229242i	−0.993409	−	0.114621i	$-0.963435\pi$
$701$		−	7.89676e7i		−	0.229242i	0.993409	−	0.114621i	$-0.0365654\pi$
$702$	−8.27155e7	+	4.18016e7i	−0.239098	+	0.120832i
$703$	7.75658e8			2.23257
$704$		−	1.98075e7i		−	0.0567690i
$705$	−6.58283e7	−	2.53524e7i	−0.187865	−	0.0723522i
$706$	3.57717e8			1.01654
$707$			1.60349e8i			0.453742i
$708$	6.82763e7	−	1.77281e8i	0.192385	−	0.499532i
$709$	−1.26101e7			−0.0353818			−0.0176909	−	0.999844i	$-0.505631\pi$
$709$	−1.26101e7			−0.0353818			−0.0176909	+	0.999844i	$0.505631\pi$
$710$			3.89352e7i			0.108785i
$711$	−2.09625e8	−	1.89586e8i	−0.583222	−	0.527469i
$712$	1.94752e8			0.539564
$713$			8.04873e7i			0.222054i
$714$	−2.73855e8	−	1.05470e8i	−0.752360	−	0.289756i
$715$	−8.80556e7			−0.240901
$716$			4.95682e8i			1.35041i
$717$	4.79480e7	−	1.24498e8i	0.130081	−	0.337759i
$718$	−6.49371e8			−1.75436
$719$		−	5.88237e8i		−	1.58258i	−0.611440	−	0.791291i	$-0.709410\pi$
$719$		−	5.88237e8i		−	1.58258i	0.611440	−	0.791291i	$-0.290590\pi$
$720$	−3.70913e8	+	4.10119e8i	−0.993745	+	1.09878i
$721$	4.53622e8			1.21029
$722$		−	1.81352e9i		−	4.81849i
$723$	−3.20091e8	−	1.23277e8i	−0.846953	−	0.326186i
$724$	9.50250e8			2.50393
$725$		−	4.45986e7i		−	0.117033i
$726$	−6.91435e8	+	1.79533e9i	−1.80693	+	4.69175i
$727$	−4.98458e8			−1.29726			−0.648628	−	0.761106i	$-0.724657\pi$
$727$	−4.98458e8			−1.29726			−0.648628	+	0.761106i	$0.724657\pi$
$728$		−	1.76090e8i		−	0.456395i
$729$	−2.29788e8	+	3.11917e8i	−0.593124	+	0.805111i
$730$	3.52384e7			0.0905833
$731$			1.32645e8i			0.339577i
$732$	−3.25576e8	−	1.25389e8i	−0.830079	−	0.319688i
$733$	−5.17456e8			−1.31390			−0.656949	−	0.753935i	$-0.728153\pi$
$733$	−5.17456e8			−1.31390			−0.656949	+	0.753935i	$0.728153\pi$
$734$		−	9.91112e8i		−	2.50631i
$735$	−1.04827e8	+	2.72187e8i	−0.264005	+	0.685497i
$736$	−8.09441e7			−0.203026
$737$			8.19053e8i			2.04602i
$738$	5.21095e8	+	4.71281e8i	1.29643	+	1.17249i
$739$	5.95208e7			0.147481			0.0737404	−	0.997277i	$-0.476506\pi$
$739$	5.95208e7			0.147481			0.0737404	+	0.997277i	$0.476506\pi$
$740$		−	8.79129e8i		−	2.16949i
$741$	−1.08328e8	−	4.17202e7i	−0.266247	−	0.102540i
$742$	−1.45358e9			−3.55817
$743$			1.00177e8i			0.244232i	0.992516	+	0.122116i	$0.0389679\pi$
$743$			1.00177e8i			0.244232i	−0.992516	+	0.122116i	$0.961032\pi$
$744$	3.52251e8	−	9.14630e8i	0.855329	−	2.22089i
$745$	7.92010e7			0.191541
$746$		−	9.49895e8i		−	2.28802i
$747$	−2.68295e8	+	2.96654e8i	−0.643652	+	0.711685i
$748$	5.96036e8			1.42419
$749$			6.70555e8i			1.59584i
$750$	7.71238e8	+	2.97026e8i	1.82812	+	0.704063i
$751$	6.96529e7			0.164445			0.0822223	−	0.996614i	$-0.473798\pi$
$751$	6.96529e7			0.164445			0.0822223	+	0.996614i	$0.473798\pi$
$752$			1.83529e8i			0.431569i
$753$	1.06992e8	−	2.77807e8i	0.250591	−	0.650666i
$754$	4.35055e7			0.101492
$755$		−	3.49326e8i		−	0.811689i
$756$	−5.99487e8	−	1.18624e9i	−1.38744	−	2.74542i
$757$	2.09004e8			0.481801			0.240900	−	0.970550i	$-0.422557\pi$
$757$	2.09004e8			0.481801			0.240900	+	0.970550i	$0.422557\pi$
$758$			1.10861e9i			2.54550i
$759$	−1.65690e8	−	6.38122e7i	−0.378941	−	0.145941i
$760$	−1.56370e9			−3.56215
$761$		−	7.92345e8i		−	1.79788i	−0.438072	−	0.898940i	$-0.644339\pi$
$761$		−	7.92345e8i		−	1.79788i	0.438072	−	0.898940i	$-0.355661\pi$
$762$	−4.53754e8	+	1.17819e9i	−1.02555	+	2.66286i
$763$	1.55605e8			0.350307
$764$		−	1.09411e9i		−	2.45347i
$765$	9.00654e7	+	8.14556e7i	0.201175	+	0.181944i
$766$	−1.53998e9			−3.42634
$767$		−	1.60357e7i		−	0.0355387i
$768$	−7.68632e8	−	2.96023e8i	−1.69682	−	0.653494i
$769$	5.88508e8			1.29412			0.647059	−	0.762440i	$-0.275999\pi$
$769$	5.88508e8			1.29412			0.647059	+	0.762440i	$0.275999\pi$
$770$		−	1.82626e9i		−	4.00028i
$771$	2.29371e8	−	5.95568e8i	0.500467	−	1.29948i
$772$	−9.99230e8			−2.17177
$773$		−	2.99161e7i		−	0.0647690i	−0.999475	−	0.0323845i	$-0.989690\pi$
$773$		−	2.99161e7i		−	0.0647690i	0.999475	−	0.0323845i	$-0.0103101\pi$
$774$	−5.82765e8	+	6.44363e8i	−1.25681	+	1.38966i
$775$	−1.53134e8			−0.328977
$776$		−	6.96564e8i		−	1.49065i
$777$	6.99555e8	+	2.69419e8i	1.49128	+	0.574336i
$778$	1.44094e9			3.05990
$779$			8.80042e8i			1.86162i
$780$	−4.72856e7	+	1.22778e8i	−0.0996426	+	0.258725i
$781$	6.74317e7			0.141550
$782$			5.85755e7i			0.122489i
$783$	1.62315e8	−	8.20287e7i	0.338123	−	0.170876i
$784$	7.58856e8			1.57475
$785$			3.36673e8i			0.695984i
$786$	7.93822e8	+	3.05724e8i	1.63477	+	0.629596i
$787$	3.39232e8			0.695940			0.347970	−	0.937506i	$-0.386871\pi$
$787$	3.39232e8			0.695940			0.347970	+	0.937506i	$0.386871\pi$
$788$		−	1.02230e9i		−	2.08930i
$789$	1.27801e8	−	3.31839e8i	0.260198	−	0.675611i
$790$	−5.80270e8			−1.17693
$791$			2.50971e8i			0.507100i
$792$	1.60357e9	+	1.45028e9i	3.22785	+	2.91928i
$793$	−2.94495e7			−0.0590552
$794$			2.89631e8i			0.578606i
$795$	5.61309e8	+	2.16177e8i	1.11712	+	0.430237i
$796$	8.07124e8			1.60030
$797$			4.39540e7i			0.0868207i	0.999057	+	0.0434103i	$0.0138223\pi$
$797$			4.39540e7i			0.0868207i	−0.999057	+	0.0434103i	$0.986178\pi$
$798$	8.65272e8	−	2.24670e9i	1.70272	−	4.42117i
$799$	4.03044e7			0.0790155
$800$		−	1.54003e8i		−	0.300787i
$801$	8.32293e7	−	9.20266e7i	0.161949	−	0.179067i
$802$	1.69170e9			3.27944
$803$		−	6.10293e7i		−	0.117867i
$804$	1.14203e9	+	4.39829e8i	2.19740	+	0.846284i
$805$	1.24104e8			0.237903
$806$		−	1.49380e8i		−	0.285291i
$807$	−1.11265e8	+	2.88903e8i	−0.211708	+	0.549707i
$808$	−3.89745e8			−0.738833
$809$		−	8.97665e7i		−	0.169539i	−0.996401	−	0.0847693i	$-0.972985\pi$
$809$		−	8.97665e7i		−	0.169539i	0.996401	−	0.0847693i	$-0.0270153\pi$
$810$	7.96515e7	+	7.91391e8i	0.149878	+	1.48914i
$811$	3.33188e8			0.624635			0.312318	−	0.949978i	$-0.398895\pi$
$811$	3.33188e8			0.624635			0.312318	+	0.949978i	$0.398895\pi$
$812$			6.23923e8i			1.16537i
$813$	−6.56811e8	−	2.52957e8i	−1.22227	−	0.470734i
$814$	−2.20188e9			−4.08245
$815$		−	5.24161e8i		−	0.968259i
$816$	1.13549e8	−	2.94833e8i	0.208984	−	0.542632i
$817$	−1.08822e9			−1.99549
$818$		−	8.50707e8i		−	1.55425i
$819$	−8.32081e7	−	7.52538e7i	−0.151466	−	0.136986i
$820$	9.97437e8			1.80902
$821$		−	8.67479e8i		−	1.56758i	−0.621027	−	0.783789i	$-0.713284\pi$
$821$		−	8.67479e8i		−	1.56758i	0.621027	−	0.783789i	$-0.286716\pi$
$822$	7.48694e8	+	2.88344e8i	1.34800	+	0.519154i
$823$	7.85630e7			0.140935			0.0704674	−	0.997514i	$-0.477551\pi$
$823$	7.85630e7			0.140935			0.0704674	+	0.997514i	$0.477551\pi$
$824$			1.10257e9i			1.97072i
$825$	1.21408e8	−	3.15239e8i	0.216215	−	0.561408i
$826$	3.32578e8			0.590139
$827$			9.55815e8i			1.68989i	0.534857	+	0.844943i	$0.320366\pi$
$827$			9.55815e8i			1.68989i	−0.534857	+	0.844943i	$0.679634\pi$
$828$	−1.77950e8	+	1.96760e8i	−0.313479	+	0.346613i
$829$	−1.17318e8			−0.205921			−0.102961	−	0.994685i	$-0.532832\pi$
$829$	−1.17318e8			−0.205921			−0.102961	+	0.994685i	$0.532832\pi$
$830$			8.21178e8i			1.43616i
$831$	−4.70827e7	−	1.81329e7i	−0.0820462	−	0.0315984i
$832$	−2.49815e6			−0.00433760
$833$		−	1.66651e8i		−	0.288319i
$834$	−7.18249e7	+	1.86495e8i	−0.123816	+	0.321492i
$835$	1.45823e8			0.250477
$836$			4.88988e9i			8.36911i
$837$	−2.81653e8	−	5.57325e8i	−0.480329	−	0.950457i
$838$	7.65874e8			1.30144
$839$			3.54494e8i			0.600238i	0.953902	+	0.300119i	$0.0970264\pi$
$839$			3.54494e8i			0.600238i	−0.953902	+	0.300119i	$0.902974\pi$
$840$	−1.41028e9	−	5.43140e8i	−2.37940	−	0.916377i
$841$	5.09451e8			0.856475
$842$		−	7.49209e8i		−	1.25507i
$843$	1.17772e8	−	3.05799e8i	0.196589	−	0.510450i
$844$	−2.01756e9			−3.35582
$845$		−	4.90468e8i		−	0.812907i
$846$	1.95791e8	+	1.77074e8i	0.323356	+	0.292445i
$847$	−2.32893e9			−3.83271
$848$		−	1.56493e9i		−	2.56629i
$849$	−3.94307e8	−	1.51859e8i	−0.644335	−	0.248153i
$850$	−1.11445e8			−0.181469
$851$		−	1.49630e8i		−	0.242789i
$852$	3.62106e7	−	9.40219e7i	0.0585487	−	0.152023i
$853$	6.61061e8			1.06511			0.532555	−	0.846395i	$-0.321232\pi$
$853$	6.61061e8			1.06511			0.532555	+	0.846395i	$0.321232\pi$
$854$		−	6.10779e8i		−	0.980641i
$855$	−6.68262e8	+	7.38897e8i	−1.06917	+	1.18219i
$856$	−1.62985e9			−2.59852
$857$			1.42055e8i			0.225690i	0.993613	+	0.112845i	$0.0359964\pi$
$857$			1.42055e8i			0.225690i	−0.993613	+	0.112845i	$0.964004\pi$
$858$	3.07513e8	+	1.18432e8i	0.486857	+	0.187503i
$859$	9.90490e8			1.56268			0.781341	−	0.624105i	$-0.214536\pi$
$859$	9.90490e8			1.56268			0.781341	+	0.624105i	$0.214536\pi$
$860$			1.23339e9i			1.93912i
$861$	−3.05676e8	+	7.93697e8i	−0.478908	+	1.24350i
$862$	−2.77826e7			−0.0433762
$863$		−	3.81794e8i		−	0.594014i	−0.954875	−	0.297007i	$-0.904012\pi$
$863$		−	3.81794e8i		−	0.594014i	0.954875	−	0.297007i	$-0.0959884\pi$
$864$	5.60489e8	−	2.83252e8i	0.869012	−	0.439169i
$865$	9.08431e8			1.40360
$866$		−	1.77274e9i		−	2.72955i
$867$	5.43422e8	+	2.09288e8i	0.833835	+	0.321134i
$868$	2.14230e9			3.27583
$869$			1.00497e9i			1.53141i
$870$	1.34190e8	−	3.48429e8i	0.203781	−	0.529123i
$871$	1.03300e8			0.156332
$872$			3.78213e8i			0.570409i
$873$	−3.29149e8	−	2.97683e8i	−0.494708	−	0.447417i
$874$	−4.80553e8			−0.719792
$875$			1.00046e9i			1.49340i
$876$	−8.50949e7	−	3.27726e7i	−0.126588	−	0.0487526i
$877$	−1.00274e9			−1.48658			−0.743291	−	0.668968i	$-0.766736\pi$
$877$	−1.00274e9			−1.48658			−0.743291	+	0.668968i	$0.766736\pi$
$878$		−	2.37793e8i		−	0.351330i
$879$	1.22241e8	−	3.17402e8i	0.179991	−	0.467351i
$880$	1.96616e9			2.88517
$881$			4.14884e8i			0.606735i	0.952874	+	0.303368i	$0.0981110\pi$
$881$			4.14884e8i			0.606735i	−0.952874	+	0.303368i	$0.901889\pi$
$882$	7.32168e8	−	8.09558e8i	1.06710	−	1.17989i
$883$	−4.26502e8			−0.619496			−0.309748	−	0.950819i	$-0.600245\pi$
$883$	−4.26502e8			−0.619496			−0.309748	+	0.950819i	$0.600245\pi$
$884$		−	7.51731e7i		−	0.108819i
$885$	−1.28428e8	−	4.94613e7i	−0.185280	−	0.0713568i
$886$	1.07878e9			1.55106
$887$			2.99278e8i			0.428848i	0.976741	+	0.214424i	$0.0687875\pi$
$887$			2.99278e8i			0.428848i	−0.976741	+	0.214424i	$0.931213\pi$
$888$	−6.54851e8	+	1.70034e9i	−0.935198	+	2.42827i
$889$	−1.52836e9			−2.17530
$890$		−	2.54742e8i		−	0.361352i
$891$	1.37061e9	−	1.37948e8i	1.93767	−	0.195021i
$892$	−1.79084e9			−2.52326
$893$			3.30658e8i			0.464327i
$894$	−2.76590e8	−	1.06523e8i	−0.387101	−	0.149084i
$895$	3.59086e8			0.500875
$896$		−	1.01307e9i		−	1.40836i
$897$	−8.04811e6	+	2.08971e7i	−0.0111511	+	0.0289541i
$898$	1.19255e9			1.64682
$899$			2.93134e8i			0.403448i
$900$	−3.74351e8	−	3.38565e8i	−0.513514	−	0.464424i
$901$	−3.43671e8			−0.469860
$902$		−	2.49820e9i		−	3.40414i
$903$	−9.81450e8	−	3.77985e8i	−1.33292	−	0.513348i
$904$	−6.10009e8			−0.825716
$905$		−	6.88387e8i		−	0.928725i
$906$	−4.69833e8	+	1.21993e9i	−0.631770	+	1.64041i
$907$	−1.00658e9			−1.34905			−0.674524	−	0.738253i	$-0.735651\pi$
$907$	−1.00658e9			−1.34905			−0.674524	+	0.738253i	$0.735651\pi$
$908$		−	8.38016e8i		−	1.11942i
$909$	−1.66561e8	+	1.84167e8i	−0.221759	+	0.245199i
$910$	−2.30331e8			−0.305653
$911$			9.66161e8i			1.27789i	0.769251	+	0.638946i	$0.220629\pi$
$911$			9.66161e8i			1.27789i	−0.769251	+	0.638946i	$0.779371\pi$
$912$	2.41881e9	+	9.31555e8i	3.18872	+	1.22807i
$913$	1.42219e9			1.86873
$914$			1.08442e9i			1.42022i
$915$	−9.08353e7	+	2.35857e8i	−0.118575	+	0.307882i
$916$	−2.68229e9			−3.48995
$917$			1.02976e9i			1.33545i
$918$	−2.04976e8	−	4.05599e8i	−0.264957	−	0.524287i
$919$	3.22195e8			0.415119			0.207559	−	0.978222i	$-0.433448\pi$
$919$	3.22195e8			0.415119			0.207559	+	0.978222i	$0.433448\pi$
$920$			3.01648e8i			0.387380i
$921$	−1.15528e9	−	4.44932e8i	−1.47880	−	0.569528i
$922$	−7.68196e8			−0.980120
$923$		−	8.50460e6i		−	0.0108156i
$924$	−1.69847e9	+	4.41011e9i	−2.15298	+	5.59029i
$925$	2.84683e8			0.359696
$926$			8.85369e8i			1.11504i
$927$	5.21000e8	+	4.71195e8i	0.654032	+	0.591509i
$928$	−2.94798e8			−0.368876
$929$		−	1.38149e9i		−	1.72306i	−0.507709	−	0.861528i	$-0.669508\pi$
$929$		−	1.38149e9i		−	1.72306i	0.507709	−	0.861528i	$-0.330492\pi$
$930$	−1.19636e9	−	4.60755e8i	−1.48736	−	0.572824i
$931$	1.36721e9			1.69428
$932$		−	1.55939e9i		−	1.92622i
$933$	−1.61183e8	+	4.18516e8i	−0.198461	+	0.515309i
$934$	9.05439e8			1.11127
$935$		−	4.31785e8i		−	0.528242i
$936$	1.82912e8	−	2.02246e8i	0.223056	−	0.246633i
$937$	3.20612e8			0.389728			0.194864	−	0.980830i	$-0.437574\pi$
$937$	3.20612e8			0.389728			0.194864	+	0.980830i	$0.437574\pi$
$938$			2.14244e9i			2.59597i
$939$	2.48139e8	+	9.55656e7i	0.299708	+	0.115426i
$940$	3.74767e8			0.451209
$941$			1.56435e9i			1.87744i	0.344681	+	0.938720i	$0.387987\pi$
$941$			1.56435e9i			1.87744i	−0.344681	+	0.938720i	$0.612013\pi$
$942$	4.52815e8	−	1.17575e9i	0.541712	−	1.40657i
$943$	1.69766e8			0.202449
$944$			3.58055e8i			0.425632i
$945$	−8.59347e8	+	4.34285e8i	−1.01829	+	0.514611i
$946$	3.08916e9			3.64894
$947$		−	1.20490e9i		−	1.41873i	−0.704840	−	0.709367i	$-0.748981\pi$
$947$		−	1.20490e9i		−	1.41873i	0.704840	−	0.709367i	$-0.251019\pi$
$948$	1.40125e9	+	5.39665e8i	1.64472	+	0.633431i
$949$	−7.69712e6			−0.00900595
$950$		−	9.14292e8i		−	1.06638i
$951$	2.54285e8	−	6.60257e8i	0.295650	−	0.767665i
$952$	8.63466e8			1.00077
$953$		−	1.60176e9i		−	1.85063i	−0.379197	−	0.925316i	$-0.623800\pi$
$953$		−	1.60176e9i		−	1.85063i	0.379197	−	0.925316i	$-0.376200\pi$
$954$	−1.66948e9	−	1.50989e9i	−1.92281	−	1.73900i
$955$	−7.92602e8			−0.910008
$956$			7.08782e8i			0.811220i
$957$	−6.03442e8	−	2.32404e8i	−0.688494	−	0.265159i
$958$	5.93406e8			0.674924
$959$			9.71217e8i			1.10119i
$960$	−7.70542e6	+	2.00073e7i	−0.00870929	+	0.0226139i
$961$	1.19000e8			0.134084
$962$			2.77705e8i			0.311931i
$963$	−6.96532e8	+	7.70155e8i	−0.779942	+	0.862382i
$964$	1.82231e9			2.03419
$965$			7.23870e8i			0.805524i
$966$	−4.33404e8	−	1.66917e8i	−0.480797	−	0.185169i
$967$	−2.36198e8			−0.261214			−0.130607	−	0.991434i	$-0.541693\pi$
$967$	−2.36198e8			−0.261214			−0.130607	+	0.991434i	$0.541693\pi$
$968$		−	5.66069e9i		−	6.24085i
$969$	2.04577e8	−	5.31190e8i	0.224846	−	0.583820i
$970$	−9.11128e8			−0.998308
$971$			5.57607e8i			0.609074i	0.952500	+	0.304537i	$0.0985018\pi$
$971$			5.57607e8i			0.609074i	−0.952500	+	0.304537i	$0.901498\pi$
$972$	5.43667e8	−	1.98515e9i	0.592016	−	2.16170i
$973$	−2.41924e8			−0.262628
$974$		−	1.61801e9i		−	1.75107i
$975$	−3.97585e7	−	1.53122e7i	−0.0428960	−	0.0165205i
$976$	6.57566e8			0.707278
$977$			1.50151e9i			1.61007i	0.593225	+	0.805037i	$0.297854\pi$
$977$			1.50151e9i			1.61007i	−0.593225	+	0.805037i	$0.702146\pi$
$978$	−7.04981e8	+	1.83050e9i	−0.753634	+	1.95683i
$979$	−4.41187e8			−0.470191
$980$		−	1.54959e9i		−	1.64641i
$981$	1.78717e8	+	1.61633e8i	0.189304	+	0.171207i
$982$	1.46910e9			1.55138
$983$		−	1.22407e9i		−	1.28868i	−0.764740	−	0.644339i	$-0.777133\pi$
$983$		−	1.22407e9i		−	1.28868i	0.764740	−	0.644339i	$-0.222867\pi$
$984$	−1.92916e9	−	7.42977e8i	−2.02480	−	0.779812i
$985$	−7.40583e8			−0.774935
$986$			2.13331e8i			0.222548i
$987$	−1.14852e8	+	2.98215e8i	−0.119450	+	0.310155i
$988$	6.16720e8			0.639466
$989$			2.09925e8i			0.217008i
$990$	1.89701e9	−	2.09753e9i	1.95508	−	2.16173i
$991$	1.13270e9			1.16384			0.581922	−	0.813245i	$-0.302301\pi$
$991$	1.13270e9			1.16384			0.581922	+	0.813245i	$0.302301\pi$
$992$			1.01222e9i			1.03690i
$993$	7.43374e7	+	2.86295e7i	0.0759206	+	0.0292393i
$994$	1.76384e8			0.179598
$995$		−	5.84703e8i		−	0.593562i
$996$	7.63715e8	−	1.98301e9i	0.772953	−	2.00699i
$997$	−7.99025e8			−0.806260			−0.403130	−	0.915143i	$-0.632078\pi$
$997$	−7.99025e8			−0.806260			−0.403130	+	0.915143i	$0.632078\pi$
$998$			1.34760e9i			1.35572i
$999$	5.23607e8	+	1.03609e9i	0.525181	+	1.03921i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.7.b.a.47.3	✓	44
3.2	odd	2	inner	69.7.b.a.47.42	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.7.b.a.47.3	✓	44	1.1	even	1	trivial
69.7.b.a.47.42	yes	44	3.2	odd	2	inner

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:	\( N \)	\(=\)	\( 69 = 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	69.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-14.4029i q^{2} +(25.1960 + 9.70372i) q^{3} -143.443 q^{4} +103.914i q^{5} +(139.762 - 362.895i) q^{6} +470.752 q^{7} +1144.21i q^{8} +(540.676 + 488.990i) q^{9} +O(q^{10})\)	\(q-14.4029i q^{2} +(25.1960 + 9.70372i) q^{3} -143.443 q^{4} +103.914i q^{5} +(139.762 - 362.895i) q^{6} +470.752 q^{7} +1144.21i q^{8} +(540.676 + 488.990i) q^{9} +1496.66 q^{10} -2592.07i q^{11} +(-3614.19 - 1391.93i) q^{12} -326.916 q^{13} -6780.19i q^{14} +(-1008.35 + 2618.22i) q^{15} +7299.58 q^{16} -1603.05i q^{17} +(7042.86 - 7787.29i) q^{18} +13151.4 q^{19} -14905.8i q^{20} +(11861.1 + 4568.05i) q^{21} -37333.2 q^{22} -2536.99i q^{23} +(-11103.1 + 28829.5i) q^{24} +4826.84 q^{25} +4708.53i q^{26} +(8877.84 + 17567.1i) q^{27} -67526.2 q^{28} -9239.71i q^{29} +(37709.9 + 14523.2i) q^{30} -31725.4 q^{31} -31905.5i q^{32} +(25152.7 - 65309.7i) q^{33} -23088.5 q^{34} +48917.9i q^{35} +(-77556.2 - 70142.2i) q^{36} +58979.1 q^{37} -189418. i q^{38} +(-8236.97 - 3172.30i) q^{39} -118900. q^{40} +66916.1i q^{41} +(65793.1 - 170834. i) q^{42} -82745.5 q^{43} +371814. i q^{44} +(-50813.0 + 56183.9i) q^{45} -36540.1 q^{46} +25142.4i q^{47} +(183920. + 70833.1i) q^{48} +103959. q^{49} -69520.4i q^{50} +(15555.5 - 40390.4i) q^{51} +46893.9 q^{52} -214386. i q^{53} +(253018. - 127867. i) q^{54} +269352. q^{55} +538640. i q^{56} +(331363. + 127618. i) q^{57} -133079. q^{58} +49051.5i q^{59} +(144642. - 375566. i) q^{60} +90082.7 q^{61} +456938. i q^{62} +(254524. + 230193. i) q^{63} +7641.58 q^{64} -33971.2i q^{65} +(-940648. - 362271. i) q^{66} -315985. q^{67} +229946. i q^{68} +(24618.3 - 63922.1i) q^{69} +704558. q^{70} +26014.7i q^{71} +(-559507. + 618647. i) q^{72} +23544.7 q^{73} -849469. i q^{74} +(121617. + 46838.3i) q^{75} -1.88648e6 q^{76} -1.22022e6i q^{77} +(-45690.3 + 118636. i) q^{78} -387709. q^{79} +758530. i q^{80} +(53219.3 + 528770. i) q^{81} +963786. q^{82} +548672. i q^{83} +(-1.70139e6 - 655256. i) q^{84} +166579. q^{85} +1.19177e6i q^{86} +(89659.6 - 232804. i) q^{87} +2.96587e6 q^{88} -170207. i q^{89} +(809210. + 731853. i) q^{90} -153896. q^{91} +363915. i q^{92} +(-799354. - 307855. i) q^{93} +362123. q^{94} +1.36662e6i q^{95} +(309602. - 803891. i) q^{96} -608773. q^{97} -1.49731e6i q^{98} +(1.26749e6 - 1.40147e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 20 q^{3} - 1408 q^{4} + 95 q^{6} + 568 q^{7} - 548 q^{9}+O(q^{10}) \) 44 * q + 20 * q^3 - 1408 * q^4 + 95 * q^6 + 568 * q^7 - 548 * q^9	\( 44 q + 20 q^{3} - 1408 q^{4} + 95 q^{6} + 568 q^{7} - 548 q^{9} + 1752 q^{10} + 4075 q^{12} + 808 q^{13} + 7696 q^{15} + 36776 q^{16} + 12149 q^{18} + 28936 q^{19} - 6416 q^{21} - 7764 q^{22} - 11792 q^{24} - 129172 q^{25} - 27172 q^{27} - 25988 q^{28} - 54658 q^{30} - 72248 q^{31} + 25968 q^{33} - 32100 q^{34} - 217125 q^{36} + 260968 q^{37} + 133440 q^{39} - 227880 q^{40} + 63332 q^{42} - 187304 q^{43} + 455472 q^{45} - 164849 q^{48} + 959652 q^{49} - 218832 q^{51} - 410102 q^{52} + 882504 q^{54} + 517392 q^{55} - 572600 q^{57} - 197334 q^{58} - 854196 q^{60} + 914248 q^{61} + 885136 q^{63} - 312634 q^{64} - 816874 q^{66} - 310856 q^{67} - 395040 q^{70} + 205764 q^{72} - 227912 q^{73} + 1167580 q^{75} - 1438412 q^{76} - 6065 q^{78} + 841384 q^{79} + 1019636 q^{81} - 291126 q^{82} - 2787738 q^{84} - 2823120 q^{85} - 2899120 q^{87} - 2657340 q^{88} + 1478966 q^{90} - 2848288 q^{91} - 1992952 q^{93} + 6985482 q^{94} + 1309665 q^{96} + 1079608 q^{97} + 3251880 q^{99}+O(q^{100}) \) 44 * q + 20 * q^3 - 1408 * q^4 + 95 * q^6 + 568 * q^7 - 548 * q^9 + 1752 * q^10 + 4075 * q^12 + 808 * q^13 + 7696 * q^15 + 36776 * q^16 + 12149 * q^18 + 28936 * q^19 - 6416 * q^21 - 7764 * q^22 - 11792 * q^24 - 129172 * q^25 - 27172 * q^27 - 25988 * q^28 - 54658 * q^30 - 72248 * q^31 + 25968 * q^33 - 32100 * q^34 - 217125 * q^36 + 260968 * q^37 + 133440 * q^39 - 227880 * q^40 + 63332 * q^42 - 187304 * q^43 + 455472 * q^45 - 164849 * q^48 + 959652 * q^49 - 218832 * q^51 - 410102 * q^52 + 882504 * q^54 + 517392 * q^55 - 572600 * q^57 - 197334 * q^58 - 854196 * q^60 + 914248 * q^61 + 885136 * q^63 - 312634 * q^64 - 816874 * q^66 - 310856 * q^67 - 395040 * q^70 + 205764 * q^72 - 227912 * q^73 + 1167580 * q^75 - 1438412 * q^76 - 6065 * q^78 + 841384 * q^79 + 1019636 * q^81 - 291126 * q^82 - 2787738 * q^84 - 2823120 * q^85 - 2899120 * q^87 - 2657340 * q^88 + 1478966 * q^90 - 2848288 * q^91 - 1992952 * q^93 + 6985482 * q^94 + 1309665 * q^96 + 1079608 * q^97 + 3251880 * q^99

Introduction

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