LMFDB - Embedded newform 48.7.l.a.19.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,7,Mod(19,48)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(48, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

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

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

chi := DirichletCharacter("48.19");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	48.l (of order $4$, 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:	$11.0425960138$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			19.7
Character	$\chi$	$=$	48.19
Dual form			48.7.l.a.43.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.50221 + 6.61288i) q^{2} +(11.0227 - 11.0227i) q^{3} +(-23.4602 - 59.5451i) q^{4} +(-9.26689 + 9.26689i) q^{5} +(23.2652 + 122.518i) q^{6} -320.373 q^{7} +(499.387 + 112.945i) q^{8} -243.000i q^{9} +O(q^{10})$	\(q+(-4.50221 + 6.61288i) q^{2} +(11.0227 - 11.0227i) q^{3} +(-23.4602 - 59.5451i) q^{4} +(-9.26689 + 9.26689i) q^{5} +(23.2652 + 122.518i) q^{6} -320.373 q^{7} +(499.387 + 112.945i) q^{8} -243.000i q^{9} +(-19.5593 - 103.002i) q^{10} +(1498.49 + 1498.49i) q^{11} +(-914.943 - 397.753i) q^{12} +(2546.47 + 2546.47i) q^{13} +(1442.39 - 2118.59i) q^{14} +204.292i q^{15} +(-2995.24 + 2793.88i) q^{16} -7232.04 q^{17} +(1606.93 + 1094.04i) q^{18} +(-4865.79 + 4865.79i) q^{19} +(769.201 + 334.394i) q^{20} +(-3531.38 + 3531.38i) q^{21} +(-16655.9 + 3162.82i) q^{22} +12202.6 q^{23} +(6749.55 - 4259.64i) q^{24} +15453.2i q^{25} +(-28304.2 + 5374.75i) q^{26} +(-2678.52 - 2678.52i) q^{27} +(7516.03 + 19076.7i) q^{28} +(9527.74 + 9527.74i) q^{29} +(-1350.96 - 919.767i) q^{30} +13501.8i q^{31} +(-4990.43 - 32385.8i) q^{32} +33034.9 q^{33} +(32560.2 - 47824.6i) q^{34} +(2968.86 - 2968.86i) q^{35} +(-14469.5 + 5700.84i) q^{36} +(-964.122 + 964.122i) q^{37} +(-10270.1 - 54083.7i) q^{38} +56138.0 q^{39} +(-5674.41 + 3581.12i) q^{40} -94673.7i q^{41} +(-7453.56 - 39251.6i) q^{42} +(61457.6 + 61457.6i) q^{43} +(54072.9 - 124383. i) q^{44} +(2251.85 + 2251.85i) q^{45} +(-54938.6 + 80694.2i) q^{46} +125325. i q^{47} +(-2219.44 + 63811.7i) q^{48} -15010.0 q^{49} +(-102190. - 69573.8i) q^{50} +(-79716.7 + 79716.7i) q^{51} +(91889.1 - 211371. i) q^{52} +(92717.8 - 92717.8i) q^{53} +(29771.9 - 5653.46i) q^{54} -27772.7 q^{55} +(-159990. - 36184.5i) q^{56} +107268. i q^{57} +(-105902. + 20109.9i) q^{58} +(-78971.2 - 78971.2i) q^{59} +(12164.6 - 4792.75i) q^{60} +(14025.8 + 14025.8i) q^{61} +(-89285.7 - 60787.9i) q^{62} +77850.7i q^{63} +(236631. + 112806. i) q^{64} -47195.8 q^{65} +(-148730. + 218456. i) q^{66} +(-169382. + 169382. i) q^{67} +(169665. + 430633. i) q^{68} +(134506. - 134506. i) q^{69} +(6266.28 + 32999.2i) q^{70} +239400. q^{71} +(27445.6 - 121351. i) q^{72} -668710. i q^{73} +(-2034.94 - 10716.3i) q^{74} +(170337. + 170337. i) q^{75} +(403887. + 175581. i) q^{76} +(-480077. - 480077. i) q^{77} +(-252745. + 371234. i) q^{78} +572255. i q^{79} +(1865.91 - 53647.1i) q^{80} -59049.0 q^{81} +(626065. + 426241. i) q^{82} +(-360998. + 360998. i) q^{83} +(293123. + 127429. i) q^{84} +(67018.6 - 67018.6i) q^{85} +(-683107. + 129717. i) q^{86} +210043. q^{87} +(579081. + 917575. i) q^{88} +101646. i q^{89} +(-25029.6 + 4752.91i) q^{90} +(-815821. - 815821. i) q^{91} +(-286276. - 726604. i) q^{92} +(148826. + 148826. i) q^{93} +(-828756. - 564238. i) q^{94} -90181.5i q^{95} +(-411987. - 301971. i) q^{96} -1.29911e6 q^{97} +(67578.2 - 99259.3i) q^{98} +(364134. - 364134. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 180 q^{4} - 1932 q^{8}+O(q^{10}) $ 48 * q - 180 * q^4 - 1932 * q^8	\( 48 q - 180 q^{4} - 1932 q^{8} + 744 q^{10} - 2720 q^{11} - 1944 q^{12} - 15388 q^{14} + 3744 q^{16} + 4860 q^{18} - 3936 q^{19} - 14000 q^{20} - 41184 q^{22} + 26240 q^{23} + 18468 q^{24} - 5300 q^{26} - 96120 q^{28} + 66400 q^{29} - 33048 q^{30} - 52960 q^{32} + 122208 q^{34} + 162336 q^{35} + 32076 q^{36} - 7200 q^{37} + 16968 q^{38} - 309072 q^{40} - 231660 q^{42} + 340704 q^{43} - 193192 q^{44} - 450264 q^{46} + 299376 q^{48} + 806736 q^{49} + 537764 q^{50} + 80352 q^{51} + 1126224 q^{52} + 443680 q^{53} + 78732 q^{54} + 232704 q^{55} - 420448 q^{56} - 1295664 q^{58} - 886144 q^{59} - 627912 q^{60} - 326496 q^{61} - 719652 q^{62} - 192024 q^{64} - 372832 q^{65} + 775656 q^{66} - 962112 q^{67} + 3197632 q^{68} + 541728 q^{69} + 642816 q^{70} + 534016 q^{71} + 82620 q^{72} - 4894836 q^{74} - 1073088 q^{75} - 3162552 q^{76} - 932960 q^{77} - 337284 q^{78} + 4668072 q^{80} - 2834352 q^{81} + 5077560 q^{82} - 2497760 q^{83} + 1312200 q^{84} - 372000 q^{85} + 4142928 q^{86} - 2794272 q^{88} - 507384 q^{90} + 775008 q^{91} - 9470992 q^{92} - 5050728 q^{94} + 1879200 q^{96} + 12708584 q^{98} - 660960 q^{99}+O(q^{100}) \) 48 * q - 180 * q^4 - 1932 * q^8 + 744 * q^10 - 2720 * q^11 - 1944 * q^12 - 15388 * q^14 + 3744 * q^16 + 4860 * q^18 - 3936 * q^19 - 14000 * q^20 - 41184 * q^22 + 26240 * q^23 + 18468 * q^24 - 5300 * q^26 - 96120 * q^28 + 66400 * q^29 - 33048 * q^30 - 52960 * q^32 + 122208 * q^34 + 162336 * q^35 + 32076 * q^36 - 7200 * q^37 + 16968 * q^38 - 309072 * q^40 - 231660 * q^42 + 340704 * q^43 - 193192 * q^44 - 450264 * q^46 + 299376 * q^48 + 806736 * q^49 + 537764 * q^50 + 80352 * q^51 + 1126224 * q^52 + 443680 * q^53 + 78732 * q^54 + 232704 * q^55 - 420448 * q^56 - 1295664 * q^58 - 886144 * q^59 - 627912 * q^60 - 326496 * q^61 - 719652 * q^62 - 192024 * q^64 - 372832 * q^65 + 775656 * q^66 - 962112 * q^67 + 3197632 * q^68 + 541728 * q^69 + 642816 * q^70 + 534016 * q^71 + 82620 * q^72 - 4894836 * q^74 - 1073088 * q^75 - 3162552 * q^76 - 932960 * q^77 - 337284 * q^78 + 4668072 * q^80 - 2834352 * q^81 + 5077560 * q^82 - 2497760 * q^83 + 1312200 * q^84 - 372000 * q^85 + 4142928 * q^86 - 2794272 * q^88 - 507384 * q^90 + 775008 * q^91 - 9470992 * q^92 - 5050728 * q^94 + 1879200 * q^96 + 12708584 * q^98 - 660960 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

$n$	$17$	$31$	$37$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−4.50221	+	6.61288i	−0.562776	+	0.826609i
$2$	−4.50221	+	6.61288i	−0.562776	+	0.826609i
$3$	11.0227	−	11.0227i	0.408248	−	0.408248i
$3$	11.0227	−	11.0227i	0.408248	−	0.408248i
$4$	−23.4602	−	59.5451i	−0.366566	−	0.930392i
$5$	−9.26689	+	9.26689i	−0.0741351	+	0.0741351i	−0.743202	−	0.669067i	$-0.766694\pi$
$5$	−9.26689	+	9.26689i	−0.0741351	+	0.0741351i	0.669067	+	0.743202i	$0.266694\pi$
$6$	23.2652	+	122.518i	0.107709	+	0.567214i
$7$	−320.373			−0.934033			−0.467016	−	0.884249i	$-0.654671\pi$
$7$	−320.373			−0.934033			−0.467016	+	0.884249i	$0.654671\pi$
$8$	499.387	+	112.945i	0.975365	+	0.220595i
$9$		−	243.000i		−	0.333333i
$10$	−19.5593	−	103.002i	−0.0195593	−	0.103002i
$11$	1498.49	+	1498.49i	1.12584	+	1.12584i	0.990847	+	0.134993i	$0.0431012\pi$
$11$	1498.49	+	1498.49i	1.12584	+	1.12584i	0.134993	+	0.990847i	$0.456899\pi$
$12$	−914.943	−	397.753i	−0.529481	−	0.230181i
$13$	2546.47	+	2546.47i	1.15907	+	1.15907i	0.984676	+	0.174391i	$0.0557957\pi$
$13$	2546.47	+	2546.47i	1.15907	+	1.15907i	0.174391	+	0.984676i	$0.444204\pi$
$14$	1442.39	−	2118.59i	0.525651	−	0.772080i
$15$			204.292i			0.0605311i
$16$	−2995.24	+	2793.88i	−0.731259	+	0.682100i
$17$	−7232.04			−1.47202			−0.736011	−	0.676970i	$-0.763293\pi$
$17$	−7232.04			−1.47202			−0.736011	+	0.676970i	$0.763293\pi$
$18$	1606.93	+	1094.04i	0.275536	+	0.187592i
$19$	−4865.79	+	4865.79i	−0.709402	+	0.709402i	−0.966410	−	0.257007i	$-0.917264\pi$
$19$	−4865.79	+	4865.79i	−0.709402	+	0.709402i	0.257007	+	0.966410i	$0.417264\pi$
$20$	769.201	+	334.394i	0.0961502	+	0.0417993i
$21$	−3531.38	+	3531.38i	−0.381317	+	0.381317i
$22$	−16655.9	+	3162.82i	−1.56423	+	0.297034i
$23$	12202.6			1.00292			0.501462	−	0.865179i	$-0.332796\pi$
$23$	12202.6			1.00292			0.501462	+	0.865179i	$0.332796\pi$
$24$	6749.55	−	4259.64i	0.488249	−	0.308134i
$25$			15453.2i			0.989008i
$26$	−28304.2	+	5374.75i	−1.61039	+	0.305801i
$27$	−2678.52	−	2678.52i	−0.136083	−	0.136083i
$28$	7516.03	+	19076.7i	0.342385	+	0.869017i
$29$	9527.74	+	9527.74i	0.390657	+	0.390657i	0.874922	−	0.484264i	$-0.160913\pi$
$29$	9527.74	+	9527.74i	0.390657	+	0.390657i	−0.484264	+	0.874922i	$0.660913\pi$
$30$	−1350.96	−	919.767i	−0.0500356	−	0.0340654i
$31$			13501.8i			0.453218i	0.973986	+	0.226609i	$0.0727639\pi$
$31$			13501.8i			0.453218i	−0.973986	+	0.226609i	$0.927236\pi$
$32$	−4990.43	−	32385.8i	−0.152296	−	0.988335i
$33$	33034.9			0.919244
$34$	32560.2	−	47824.6i	0.828419	−	1.21679i
$35$	2968.86	−	2968.86i	0.0692446	−	0.0692446i
$36$	−14469.5	+	5700.84i	−0.310131	+	0.122189i
$37$	−964.122	+	964.122i	−0.0190339	+	0.0190339i	−0.716560	−	0.697526i	$-0.754284\pi$
$37$	−964.122	+	964.122i	−0.0190339	+	0.0190339i	0.697526	+	0.716560i	$0.254284\pi$
$38$	−10270.1	−	54083.7i	−0.187164	−	0.985633i
$39$	56138.0			0.946375
$40$	−5674.41	+	3581.12i	−0.0886627	+	0.0559550i
$41$		−	94673.7i		−	1.37366i	−0.726820	−	0.686828i	$-0.759003\pi$
$41$		−	94673.7i		−	1.37366i	0.726820	−	0.686828i	$-0.240997\pi$
$42$	−7453.56	−	39251.6i	−0.100604	−	0.529797i
$43$	61457.6	+	61457.6i	0.772984	+	0.772984i	0.978627	−	0.205643i	$-0.0659286\pi$
$43$	61457.6	+	61457.6i	0.772984	+	0.772984i	−0.205643	+	0.978627i	$0.565929\pi$
$44$	54072.9	−	124383.i	0.634778	−	1.46017i
$45$	2251.85	+	2251.85i	0.0247117	+	0.0247117i
$46$	−54938.6	+	80694.2i	−0.564422	+	0.829027i
$47$			125325.i			1.20710i	0.797325	+	0.603550i	$0.206247\pi$
$47$			125325.i			1.20710i	−0.797325	+	0.603550i	$0.793753\pi$
$48$	−2219.44	+	63811.7i	−0.0200687	+	0.577001i
$49$	−15010.0			−0.127583
$50$	−102190.	−	69573.8i	−0.817523	−	0.556590i
$51$	−79716.7	+	79716.7i	−0.600950	+	0.600950i
$52$	91889.1	−	211371.i	0.653512	−	1.50326i
$53$	92717.8	−	92717.8i	0.622781	−	0.622781i	−0.323461	−	0.946242i	$-0.604846\pi$
$53$	92717.8	−	92717.8i	0.622781	−	0.622781i	0.946242	+	0.323461i	$0.104846\pi$
$54$	29771.9	−	5653.46i	0.189071	−	0.0359032i
$55$	−27772.7			−0.166929
$56$	−159990.	−	36184.5i	−0.911023	−	0.206043i
$57$			107268.i			0.579225i
$58$	−105902.	+	20109.9i	−0.542773	+	0.103068i
$59$	−78971.2	−	78971.2i	−0.384514	−	0.384514i	0.488211	−	0.872726i	$-0.337650\pi$
$59$	−78971.2	−	78971.2i	−0.384514	−	0.384514i	−0.872726	+	0.488211i	$0.837650\pi$
$60$	12164.6	−	4792.75i	0.0563176	−	0.0221886i
$61$	14025.8	+	14025.8i	0.0617927	+	0.0617927i	0.737328	−	0.675535i	$-0.236087\pi$
$61$	14025.8	+	14025.8i	0.0617927	+	0.0617927i	−0.675535	+	0.737328i	$0.736087\pi$
$62$	−89285.7	−	60787.9i	−0.374634	−	0.255060i
$63$			77850.7i			0.311344i
$64$	236631.	+	112806.i	0.902675	+	0.430322i
$65$	−47195.8			−0.171855
$66$	−148730.	+	218456.i	−0.517329	+	0.759856i
$67$	−169382.	+	169382.i	−0.563175	+	0.563175i	−0.930208	−	0.367033i	$-0.880374\pi$
$67$	−169382.	+	169382.i	−0.563175	+	0.563175i	0.367033	+	0.930208i	$0.380374\pi$
$68$	169665.	+	430633.i	0.539593	+	1.36956i
$69$	134506.	−	134506.i	0.409442	−	0.409442i
$70$	6266.28	+	32999.2i	0.0182690	+	0.0962075i
$71$	239400.			0.668882			0.334441	−	0.942417i	$-0.391452\pi$
$71$	239400.			0.668882			0.334441	+	0.942417i	$0.391452\pi$
$72$	27445.6	−	121351.i	0.0735318	−	0.325122i
$73$		−	668710.i		−	1.71897i	−0.511159	−	0.859486i	$-0.670784\pi$
$73$		−	668710.i		−	1.71897i	0.511159	−	0.859486i	$-0.329216\pi$
$74$	−2034.94	−	10716.3i	−0.00502177	−	0.0264454i
$75$	170337.	+	170337.i	0.403761	+	0.403761i
$76$	403887.	+	175581.i	0.920065	+	0.399979i
$77$	−480077.	−	480077.i	−1.05157	−	1.05157i
$78$	−252745.	+	371234.i	−0.532597	+	0.782282i
$79$			572255.i			1.16067i	0.814378	+	0.580335i	$0.197078\pi$
$79$			572255.i			1.16067i	−0.814378	+	0.580335i	$0.802922\pi$
$80$	1865.91	−	53647.1i	0.00364435	−	0.104780i
$81$	−59049.0			−0.111111
$82$	626065.	+	426241.i	1.13548	+	0.773060i
$83$	−360998.	+	360998.i	−0.631350	+	0.631350i	−0.948407	−	0.317057i	$-0.897305\pi$
$83$	−360998.	+	360998.i	−0.631350	+	0.631350i	0.317057	+	0.948407i	$0.397305\pi$
$84$	293123.	+	127429.i	0.494552	+	0.214997i
$85$	67018.6	−	67018.6i	0.109129	−	0.109129i
$86$	−683107.	+	129717.i	−1.07397	+	0.203939i
$87$	210043.			0.318970
$88$	579081.	+	917575.i	0.849750	+	1.34646i
$89$			101646.i			0.144185i	0.997398	+	0.0720925i	$0.0229677\pi$
$89$			101646.i			0.144185i	−0.997398	+	0.0720925i	$0.977032\pi$
$90$	−25029.6	+	4752.91i	−0.0343341	+	0.00651977i
$91$	−815821.	−	815821.i	−1.08261	−	1.08261i
$92$	−286276.	−	726604.i	−0.367638	−	0.933113i
$93$	148826.	+	148826.i	0.185025	+	0.185025i
$94$	−828756.	−	564238.i	−0.997800	−	0.679327i
$95$		−	90181.5i		−	0.105183i
$96$	−411987.	−	301971.i	−0.465661	−	0.341312i
$97$	−1.29911e6			−1.42341			−0.711705	−	0.702479i	$-0.752076\pi$
$97$	−1.29911e6			−1.42341			−0.711705	+	0.702479i	$0.752076\pi$
$98$	67578.2	−	99259.3i	0.0718006	−	0.105461i
$99$	364134.	−	364134.i	0.375280	−	0.375280i
$100$	920165.	−	362537.i	0.920165	−	0.362537i
$101$	1.18300e6	−	1.18300e6i	1.14821	−	1.14821i	0.161305	−	0.986905i	$-0.448430\pi$
$101$	1.18300e6	−	1.18300e6i	1.14821	−	1.14821i	0.986905	−	0.161305i	$-0.0515704\pi$
$102$	−168255.	−	886058.i	−0.158551	−	0.834952i
$103$	−640196.			−0.585870			−0.292935	−	0.956132i	$-0.594632\pi$
$103$	−640196.			−0.585870			−0.292935	+	0.956132i	$0.594632\pi$
$104$	984064.	+	1.55929e6i	0.874829	+	1.38620i
$105$		−	65449.8i		−	0.0565380i
$106$	195696.	+	1.03057e6i	0.164310	+	0.865283i
$107$	685436.	+	685436.i	0.559520	+	0.559520i	0.929171	−	0.369651i	$-0.120523\pi$
$107$	685436.	+	685436.i	0.559520	+	0.559520i	−0.369651	+	0.929171i	$0.620523\pi$
$108$	−96653.9	+	222331.i	−0.0767270	+	0.176494i
$109$	−1.30645e6	−	1.30645e6i	−1.00882	−	1.00882i	−0.999961	−	0.00885608i	$-0.997181\pi$
$109$	−1.30645e6	−	1.30645e6i	−1.00882	−	1.00882i	−0.00885608	−	0.999961i	$-0.502819\pi$
$110$	125039.	−	183658.i	0.0939434	−	0.137985i
$111$			21254.5i			0.0155411i
$112$	959593.	−	895085.i	0.683019	−	0.637104i
$113$	−99366.9			−0.0688662			−0.0344331	−	0.999407i	$-0.510963\pi$
$113$	−99366.9			−0.0688662			−0.0344331	+	0.999407i	$0.510963\pi$
$114$	−709352.	−	482945.i	−0.478793	−	0.325974i
$115$	−113080.	+	113080.i	−0.0743520	+	0.0743520i
$116$	343807.	−	790853.i	0.220263	−	0.506666i
$117$	618793.	−	618793.i	0.386356	−	0.386356i
$118$	877771.	−	166682.i	0.534239	−	0.101448i
$119$	2.31695e6			1.37492
$120$	−23073.8	+	102021.i	−0.0133529	+	0.0590399i
$121$			2.71940e6i			1.53503i
$122$	−155898.	+	29603.7i	−0.0858538	+	0.0163030i
$123$	−1.04356e6	−	1.04356e6i	−0.560792	−	0.560792i
$124$	803966.	−	316755.i	0.421670	−	0.166134i
$125$	−287999.	−	287999.i	−0.147455	−	0.147455i
$126$	−514817.	−	350500.i	−0.257360	−	0.175217i
$127$			205844.i			0.100491i	0.998737	+	0.0502455i	$0.0160004\pi$
$127$			205844.i			0.100491i	−0.998737	+	0.0502455i	$0.984000\pi$
$128$	−1.81134e6	+	1.05693e6i	−0.863712	+	0.503985i
$129$	1.35486e6			0.631139
$130$	212485.	−	312100.i	0.0967160	−	0.142057i
$131$	926626.	−	926626.i	0.412183	−	0.412183i	−0.470315	−	0.882499i	$-0.655860\pi$
$131$	926626.	−	926626.i	0.412183	−	0.412183i	0.882499	+	0.470315i	$0.155860\pi$
$132$	−775006.	−	1.96706e6i	−0.336964	−	0.855257i
$133$	1.55887e6	−	1.55887e6i	0.662605	−	0.662605i
$134$	−357509.	−	1.88270e6i	−0.148584	−	0.782466i
$135$	49643.1			0.0201770
$136$	−3.61159e6	−	816822.i	−1.43576	−	0.324721i
$137$			2.54950e6i			0.991501i	0.868465	+	0.495751i	$0.165107\pi$
$137$			2.54950e6i			0.991501i	−0.868465	+	0.495751i	$0.834893\pi$
$138$	283896.	+	1.49504e6i	0.108025	+	0.568873i
$139$	−2.36008e6	−	2.36008e6i	−0.878785	−	0.878785i	0.114624	−	0.993409i	$-0.463434\pi$
$139$	−2.36008e6	−	2.36008e6i	−0.878785	−	0.878785i	−0.993409	+	0.114624i	$0.963434\pi$
$140$	−246431.	−	107131.i	−0.0898074	−	0.0390419i
$141$	1.38142e6	+	1.38142e6i	0.492796	+	0.492796i
$142$	−1.07783e6	+	1.58312e6i	−0.376431	+	0.552904i
$143$			7.63174e6i			2.60985i
$144$	678914.	+	727842.i	0.227367	+	0.243753i
$145$	−176585.			−0.0579229
$146$	4.42209e6	+	3.01067e6i	1.42092	+	0.967397i
$147$	−165451.	+	165451.i	−0.0520855	+	0.0520855i
$148$	80027.3	+	34790.2i	0.0246861	+	0.0107318i
$149$	−322325.	+	322325.i	−0.0974397	+	0.0974397i	−0.754146	−	0.656707i	$-0.771949\pi$
$149$	−322325.	+	322325.i	−0.0974397	+	0.0974397i	0.656707	+	0.754146i	$0.271949\pi$
$150$	−1.89331e6	+	359524.i	−0.560979	+	0.106526i
$151$	461709.			0.134103			0.0670514	−	0.997750i	$-0.478641\pi$
$151$	461709.			0.134103			0.0670514	+	0.997750i	$0.478641\pi$
$152$	−2.97948e6	+	1.88035e6i	−0.848417	+	0.535436i
$153$			1.75739e6i			0.490674i
$154$	5.33609e6	−	1.01328e6i	1.46104	−	0.277439i
$155$	−125120.	−	125120.i	−0.0335993	−	0.0335993i
$156$	−1.31701e6	−	3.34274e6i	−0.346909	−	0.880499i
$157$	689923.	+	689923.i	0.178280	+	0.178280i	0.790605	−	0.612326i	$-0.209766\pi$
$157$	689923.	+	689923.i	0.178280	+	0.178280i	−0.612326	+	0.790605i	$0.709766\pi$
$158$	−3.78425e6	−	2.57641e6i	−0.959420	−	0.653197i
$159$		−	2.04400e6i		−	0.508499i
$160$	346361.	+	253870.i	0.0845608	+	0.0619799i
$161$	−3.90938e6			−0.936765
$162$	265851.	−	390484.i	0.0625307	−	0.0918455i
$163$	−2.75709e6	+	2.75709e6i	−0.636633	+	0.636633i	−0.949723	−	0.313091i	$-0.898636\pi$
$163$	−2.75709e6	+	2.75709e6i	−0.636633	+	0.636633i	0.313091	+	0.949723i	$0.398636\pi$
$164$	−5.63735e6	+	2.22107e6i	−1.27804	+	0.503536i
$165$	−306131.	+	306131.i	−0.0681483	+	0.0681483i
$166$	−761945.	−	4.01252e6i	−0.166571	−	0.877188i
$167$	5.64426e6			1.21188			0.605938	−	0.795512i	$-0.292798\pi$
$167$	5.64426e6			1.21188			0.605938	+	0.795512i	$0.292798\pi$
$168$	−2.16238e6	+	1.36467e6i	−0.456040	+	0.287807i
$169$			8.14223e6i			1.68688i
$170$	141454.	+	744917.i	0.0287917	+	0.151622i
$171$	1.18239e6	+	1.18239e6i	0.236467	+	0.236467i
$172$	2.21769e6	−	5.10131e6i	0.435828	−	1.00253i
$173$	4.11406e6	+	4.11406e6i	0.794571	+	0.794571i	0.982234	−	0.187663i	$-0.0600912\pi$
$173$	4.11406e6	+	4.11406e6i	0.794571	+	0.794571i	−0.187663	+	0.982234i	$0.560091\pi$
$174$	−945657.	+	1.38899e6i	−0.179509	+	0.263664i
$175$		−	4.95081e6i		−	0.923766i
$176$	−8.67495e6	−	301724.i	−1.59122	−	0.0553442i
$177$	−1.74095e6			−0.313955
$178$	−672172.	−	457631.i	−0.119185	−	0.0811439i
$179$	570577.	−	570577.i	0.0994844	−	0.0994844i	−0.655613	−	0.755097i	$-0.727590\pi$
$179$	570577.	−	570577.i	0.0994844	−	0.0994844i	0.755097	+	0.655613i	$0.227590\pi$
$180$	81257.8	−	186916.i	0.0139331	−	0.0320501i
$181$	266807.	−	266807.i	0.0449947	−	0.0449947i	−0.684251	−	0.729246i	$-0.739871\pi$
$181$	266807.	−	266807.i	0.0449947	−	0.0449947i	0.729246	+	0.684251i	$0.239871\pi$
$182$	9.06792e6	−	1.72193e6i	1.50416	−	0.285628i
$183$	309204.			0.0504535
$184$	6.09381e6	+	1.37822e6i	0.978218	+	0.221241i
$185$		−	17868.8i		−	0.00282216i
$186$	−1.65422e6	+	314123.i	−0.257071	+	0.0488158i
$187$	−1.08372e7	−	1.08372e7i	−1.65726	−	1.65726i
$188$	7.46247e6	−	2.94015e6i	1.12308	−	0.442482i
$189$	858125.	+	858125.i	0.127106	+	0.127106i
$190$	596359.	+	406016.i	0.0869455	+	0.0591946i
$191$		−	1.04021e7i		−	1.49287i	−0.665458	−	0.746436i	$-0.731764\pi$
$191$		−	1.04021e7i		−	1.49287i	0.665458	−	0.746436i	$-0.268236\pi$
$192$	3.85174e6	−	1.36488e6i	0.544194	−	0.192837i
$193$	2.18186e6			0.303498			0.151749	−	0.988419i	$-0.451509\pi$
$193$	2.18186e6			0.303498			0.151749	+	0.988419i	$0.451509\pi$
$194$	5.84885e6	−	8.59083e6i	0.801061	−	1.17660i
$195$	−520225.	+	520225.i	−0.0701596	+	0.0701596i
$196$	352138.	+	893772.i	0.0467676	+	0.118702i
$197$	5.20197e6	−	5.20197e6i	0.680407	−	0.680407i	−0.279685	−	0.960092i	$-0.590230\pi$
$197$	5.20197e6	−	5.20197e6i	0.680407	−	0.680407i	0.960092	+	0.279685i	$0.0902299\pi$
$198$	768565.	+	4.04738e6i	0.0990113	+	0.521408i
$199$	1.41709e7			1.79821			0.899103	−	0.437737i	$-0.144220\pi$
$199$	1.41709e7			1.79821			0.899103	+	0.437737i	$0.144220\pi$
$200$	−1.74536e6	+	7.71715e6i	−0.218171	+	0.964644i
$201$			3.73410e6i			0.459830i
$202$	2.49692e6	+	1.31492e7i	0.302936	+	1.59531i
$203$	−3.05243e6	−	3.05243e6i	−0.364887	−	0.364887i
$204$	6.61691e6	+	2.87656e6i	0.779408	+	0.338831i
$205$	877331.	+	877331.i	0.101836	+	0.101836i
$206$	2.88230e6	−	4.23353e6i	0.329714	−	0.484285i
$207$		−	2.96523e6i		−	0.334308i
$208$	−1.47418e7	−	512737.i	−1.63818	−	0.0569776i
$209$	−1.45827e7			−1.59735
$210$	432811.	+	294669.i	0.0467348	+	0.0318182i
$211$	8.87390e6	−	8.87390e6i	0.944642	−	0.944642i	−0.0539044	−	0.998546i	$-0.517167\pi$
$211$	8.87390e6	−	8.87390e6i	0.944642	−	0.944642i	0.998546	+	0.0539044i	$0.0171666\pi$
$212$	−7.69607e6	−	3.34571e6i	−0.807721	−	0.351140i
$213$	2.63884e6	−	2.63884e6i	0.273070	−	0.273070i
$214$	−7.61868e6	+	1.44673e6i	−0.777389	+	0.147620i
$215$	−1.13904e6			−0.114611
$216$	−1.03509e6	−	1.64014e6i	−0.102711	−	0.162750i
$217$		−	4.32562e6i		−	0.423320i
$218$	1.45213e7	−	2.75747e6i	1.40164	−	0.266159i
$219$	−7.37099e6	−	7.37099e6i	−0.701768	−	0.701768i
$220$	651555.	+	1.65373e6i	0.0611903	+	0.155309i
$221$	−1.84162e7	−	1.84162e7i	−1.70617	−	1.70617i
$222$	−140553.	−	95692.0i	−0.0128464	−	0.00874615i
$223$			1.84583e7i			1.66447i	0.554422	+	0.832236i	$0.312939\pi$
$223$			1.84583e7i			1.66447i	−0.554422	+	0.832236i	$0.687061\pi$
$224$	1.59880e6	+	1.03755e7i	0.142249	+	0.923137i
$225$	3.75514e6			0.329669
$226$	447370.	−	657101.i	0.0387563	−	0.0569255i
$227$	−2.33494e6	+	2.33494e6i	−0.199617	+	0.199617i	−0.799836	−	0.600219i	$-0.795080\pi$
$227$	−2.33494e6	+	2.33494e6i	−0.199617	+	0.199617i	0.600219	+	0.799836i	$0.295080\pi$
$228$	6.38730e6	−	2.51654e6i	0.538906	−	0.212324i
$229$	−1.10078e7	+	1.10078e7i	−0.916627	+	0.916627i	−0.996782	−	0.0801554i	$-0.974458\pi$
$229$	−1.10078e7	+	1.10078e7i	−0.916627	+	0.916627i	0.0801554	+	0.996782i	$0.474458\pi$
$230$	−238674.	−	1.25689e6i	−0.0196165	−	0.103304i
$231$	−1.05835e7			−0.858604
$232$	3.68192e6	+	5.83414e6i	0.294856	+	0.467211i
$233$		−	8.59203e6i		−	0.679247i	−0.940561	−	0.339624i	$-0.889700\pi$
$233$		−	8.59203e6i		−	0.679247i	0.940561	−	0.339624i	$-0.110300\pi$
$234$	1.30606e6	+	6.87793e6i	0.101934	+	0.536797i
$235$	−1.16137e6	−	1.16137e6i	−0.0894885	−	0.0894885i
$236$	−2.84966e6	+	6.55503e6i	−0.216799	+	0.498699i
$237$	6.30780e6	+	6.30780e6i	0.473841	+	0.473841i
$238$	−1.04314e7	+	1.53217e7i	−0.773770	+	1.13652i
$239$			1.57460e6i			0.115339i	0.998336	+	0.0576696i	$0.0183670\pi$
$239$			1.57460e6i			0.115339i	−0.998336	+	0.0576696i	$0.981633\pi$
$240$	−570769.	−	611904.i	−0.0412883	−	0.0442639i
$241$	1.53998e7			1.10018			0.550089	−	0.835106i	$-0.314594\pi$
$241$	1.53998e7			1.10018			0.550089	+	0.835106i	$0.314594\pi$
$242$	−1.79830e7	−	1.22433e7i	−1.26887	−	0.863878i
$243$	−650880.	+	650880.i	−0.0453609	+	0.0453609i
$244$	506118.	−	1.16421e6i	0.0348403	−	0.0801425i
$245$	139096.	−	139096.i	0.00945838	−	0.00945838i
$246$	1.15993e7	−	2.20261e6i	0.779157	−	0.147956i
$247$	−2.47812e7			−1.64449
$248$	−1.52496e6	+	6.74263e6i	−0.0999777	+	0.442053i
$249$			7.95834e6i			0.515495i
$250$	3.20113e6	−	607869.i	0.204872	−	0.0389036i
$251$	1.04108e7	+	1.04108e7i	0.658356	+	0.658356i	0.954991	−	0.296635i	$-0.0958644\pi$
$251$	1.04108e7	+	1.04108e7i	0.658356	+	0.658356i	−0.296635	+	0.954991i	$0.595864\pi$
$252$	4.63563e6	−	1.82640e6i	0.289672	−	0.114128i
$253$	1.82855e7	+	1.82855e7i	1.12913	+	1.12913i
$254$	−1.36122e6	−	926752.i	−0.0830667	−	0.0565539i
$255$		−	1.47745e6i		−	0.0891031i
$256$	1.16565e6	−	1.67367e7i	0.0694781	−	0.997583i
$257$	−6.82403e6			−0.402014			−0.201007	−	0.979590i	$-0.564421\pi$
$257$	−6.82403e6			−0.402014			−0.201007	+	0.979590i	$0.564421\pi$
$258$	−6.09986e6	+	8.95951e6i	−0.355190	+	0.521705i
$259$	308879.	−	308879.i	0.0177782	−	0.0177782i
$260$	1.10722e6	+	2.81028e6i	0.0629963	+	0.159893i
$261$	2.31524e6	−	2.31524e6i	0.130219	−	0.130219i
$262$	1.95580e6	+	1.02995e7i	0.108748	+	0.572682i
$263$	2.62642e7			1.44377			0.721883	−	0.692015i	$-0.243277\pi$
$263$	2.62642e7			1.44377			0.721883	+	0.692015i	$0.243277\pi$
$264$	1.64972e7	+	3.73112e6i	0.896599	+	0.202781i
$265$			1.71841e6i			0.0923399i
$266$	3.29025e6	+	1.73270e7i	0.174817	+	0.920614i
$267$	1.12041e6	+	1.12041e6i	0.0588633	+	0.0588633i
$268$	1.40596e7	+	6.11213e6i	0.730414	+	0.317532i
$269$	−1.87243e7	−	1.87243e7i	−0.961941	−	0.961941i	0.0373605	−	0.999302i	$-0.488105\pi$
$269$	−1.87243e7	−	1.87243e7i	−0.961941	−	0.961941i	−0.999302	+	0.0373605i	$0.988105\pi$
$270$	−223503.	+	328283.i	−0.0113551	+	0.0166785i
$271$		−	6.11650e6i		−	0.307323i	−0.988124	−	0.153661i	$-0.950893\pi$
$271$		−	6.11650e6i		−	0.307323i	0.988124	−	0.153661i	$-0.0491065\pi$
$272$	2.16617e7	−	2.02055e7i	1.07643	−	1.00407i
$273$	−1.79851e7			−0.883945
$274$	−1.68595e7	−	1.14784e7i	−0.819584	−	0.557993i
$275$	−2.31566e7	+	2.31566e7i	−1.11346	+	1.11346i
$276$	−1.11647e7	−	4.85361e6i	−0.531030	−	0.230854i
$277$	2.42422e7	−	2.42422e7i	1.14060	−	1.14060i	0.152258	−	0.988341i	$-0.451345\pi$
$277$	2.42422e7	−	2.42422e7i	1.14060	−	1.14060i	0.988341	−	0.152258i	$-0.0486546\pi$
$278$	2.62325e7	−	4.98134e6i	1.22097	−	0.231853i
$279$	3.28094e6			0.151073
$280$	1.81793e6	−	1.14729e6i	0.0828139	−	0.0522638i
$281$		−	1.13379e7i		−	0.510993i	−0.966810	−	0.255496i	$-0.917761\pi$
$281$		−	1.13379e7i		−	0.510993i	0.966810	−	0.255496i	$-0.0822389\pi$
$282$	−1.53546e7	+	2.91571e6i	−0.684684	+	0.130016i
$283$	2.38467e7	+	2.38467e7i	1.05213	+	1.05213i	0.998564	+	0.0535657i	$0.0170587\pi$
$283$	2.38467e7	+	2.38467e7i	1.05213	+	1.05213i	0.0535657	+	0.998564i	$0.482941\pi$
$284$	−5.61639e6	−	1.42551e7i	−0.245190	−	0.622323i
$285$	−994044.	−	994044.i	−0.0429409	−	0.0429409i
$286$	−5.04677e7	−	3.43597e7i	−2.15733	−	1.46876i
$287$			3.03309e7i			1.28304i
$288$	−7.86974e6	+	1.21267e6i	−0.329445	+	0.0507652i
$289$	2.81649e7			1.16685
$290$	795023.	−	1.16773e6i	0.0325976	−	0.0478796i
$291$	−1.43197e7	+	1.43197e7i	−0.581104	+	0.581104i
$292$	−3.98184e7	+	1.56881e7i	−1.59932	+	0.630117i
$293$	445531.	−	445531.i	0.0177123	−	0.0177123i	−0.698195	−	0.715907i	$-0.746013\pi$
$293$	445531.	−	445531.i	0.0177123	−	0.0177123i	0.715907	+	0.698195i	$0.246013\pi$
$294$	−349212.	−	1.83900e6i	−0.0137419	−	0.0723669i
$295$	1.46363e6			0.0570120
$296$	−590363.	+	372578.i	−0.0227638	+	0.0143662i
$297$		−	8.02748e6i		−	0.306415i
$298$	−680321.	−	3.58267e6i	−0.0257078	−	0.135381i
$299$	3.10735e7	+	3.10735e7i	1.16246	+	1.16246i
$300$	6.14657e6	−	1.41388e7i	0.227651	−	0.523661i
$301$	−1.96894e7	−	1.96894e7i	−0.721992	−	0.721992i
$302$	−2.07871e6	+	3.05322e6i	−0.0754698	+	0.110851i
$303$		−	2.60798e7i		−	0.937509i
$304$	979736.	−	2.81686e7i	0.0348729	−	1.00264i
$305$	−259950.			−0.00916201
$306$	−1.16214e7	−	7.91212e6i	−0.405596	−	0.276140i
$307$	2.00977e7	−	2.00977e7i	0.694593	−	0.694593i	−0.268646	−	0.963239i	$-0.586576\pi$
$307$	2.00977e7	−	2.00977e7i	0.694593	−	0.694593i	0.963239	+	0.268646i	$0.0865762\pi$
$308$	−1.73235e7	+	3.98489e7i	−0.592903	+	1.36384i
$309$	−7.05669e6	+	7.05669e6i	−0.239180	+	0.239180i
$310$	1.39072e6	−	264086.i	0.0466824	−	0.00886463i
$311$	−4.83931e7			−1.60880			−0.804401	−	0.594087i	$-0.797514\pi$
$311$	−4.83931e7			−1.60880			−0.804401	+	0.594087i	$0.797514\pi$
$312$	2.80346e7	+	6.34050e6i	0.923061	+	0.208766i
$313$		−	2.89787e7i		−	0.945029i	−0.881323	−	0.472515i	$-0.843346\pi$
$313$		−	2.89787e7i		−	0.945029i	0.881323	−	0.472515i	$-0.156654\pi$
$314$	−7.66855e6	+	1.45620e6i	−0.247699	+	0.0470361i
$315$	−721434.	−	721434.i	−0.0230815	−	0.0230815i
$316$	3.40750e7	−	1.34252e7i	1.07988	−	0.425462i
$317$	3.32948e7	+	3.32948e7i	1.04520	+	1.04520i	0.998929	+	0.0462701i	$0.0147335\pi$
$317$	3.32948e7	+	3.32948e7i	1.04520	+	1.04520i	0.0462701	+	0.998929i	$0.485267\pi$
$318$	1.35167e7	+	9.20252e6i	0.420330	+	0.286171i
$319$			2.85545e7i			0.879635i
$320$	−3.23820e6	+	1.14747e6i	−0.0988219	+	0.0350180i
$321$	1.51107e7			0.456846
$322$	1.76009e7	−	2.58523e7i	0.527189	−	0.774338i
$323$	3.51896e7	−	3.51896e7i	1.04426	−	1.04426i
$324$	1.38530e6	+	3.51608e6i	0.0407296	+	0.103377i
$325$	−3.93513e7	+	3.93513e7i	−1.14633	+	1.14633i
$326$	−5.81931e6	−	3.06453e7i	−0.167965	−	0.884528i
$327$	−2.88012e7			−0.823696
$328$	1.06929e7	−	4.72788e7i	0.303022	−	1.33982i
$329$		−	4.01507e7i		−	1.12747i
$330$	−646140.	−	3.40267e6i	−0.0179798	−	0.0946842i
$331$	−9.41834e6	−	9.41834e6i	−0.259711	−	0.259711i	0.565225	−	0.824937i	$-0.308789\pi$
$331$	−9.41834e6	−	9.41834e6i	−0.259711	−	0.259711i	−0.824937	+	0.565225i	$0.808789\pi$
$332$	2.99647e7	+	1.30265e7i	0.818834	+	0.355971i
$333$	234282.	+	234282.i	0.00634462	+	0.00634462i
$334$	−2.54117e7	+	3.73248e7i	−0.682015	+	1.00175i
$335$		−	3.13929e6i		−	0.0835020i
$336$	711050.	−	2.04436e7i	0.0187449	−	0.538938i
$337$	6.32702e7			1.65314			0.826570	−	0.562834i	$-0.190289\pi$
$337$	6.32702e7			1.65314			0.826570	+	0.562834i	$0.190289\pi$
$338$	−5.38435e7	−	3.66580e7i	−1.39439	−	0.949333i
$339$	−1.09529e6	+	1.09529e6i	−0.0281145	+	0.0281145i
$340$	−5.56290e6	−	2.41836e6i	−0.141535	−	0.0615295i
$341$	−2.02324e7	+	2.02324e7i	−0.510250	+	0.510250i
$342$	−1.31423e7	+	2.49562e6i	−0.328544	+	0.0623880i
$343$	4.25004e7			1.05320
$344$	2.37498e7	+	3.76325e7i	0.583425	+	0.924458i
$345$			2.49290e6i			0.0607081i
$346$	−4.57281e7	+	8.68341e6i	−1.10397	+	0.209634i
$347$	4.92780e7	+	4.92780e7i	1.17941	+	1.17941i	0.979895	+	0.199516i	$0.0639369\pi$
$347$	4.92780e7	+	4.92780e7i	1.17941	+	1.17941i	0.199516	+	0.979895i	$0.436063\pi$
$348$	−4.92766e6	−	1.25070e7i	−0.116924	−	0.296767i
$349$	−2.27583e7	−	2.27583e7i	−0.535382	−	0.535382i	0.386787	−	0.922169i	$-0.373585\pi$
$349$	−2.27583e7	−	2.27583e7i	−0.535382	−	0.535382i	−0.922169	+	0.386787i	$0.873585\pi$
$350$	3.27391e7	+	2.22896e7i	0.763593	+	0.519873i
$351$		−	1.36415e7i		−	0.315458i
$352$	4.10517e7	−	5.60079e7i	0.941246	−	1.28417i
$353$	−3.62510e7			−0.824130			−0.412065	−	0.911154i	$-0.635192\pi$
$353$	−3.62510e7			−0.824130			−0.412065	+	0.911154i	$0.635192\pi$
$354$	7.83813e6	−	1.15127e7i	0.176686	−	0.259518i
$355$	−2.21850e6	+	2.21850e6i	−0.0495877	+	0.0495877i
$356$	6.05252e6	−	2.38464e6i	0.134149	−	0.0528533i
$357$	2.55391e7	−	2.55391e7i	0.561307	−	0.561307i
$358$	1.20430e6	+	6.34201e6i	0.0262473	+	0.138222i
$359$	−2.29503e7			−0.496026			−0.248013	−	0.968757i	$-0.579778\pi$
$359$	−2.29503e7			−0.496026			−0.248013	+	0.968757i	$0.579778\pi$
$360$	870212.	+	1.37888e6i	0.0186517	+	0.0295542i
$361$		−	305966.i		−	0.00650357i
$362$	563141.	+	2.96558e6i	0.0118711	+	0.0625150i
$363$	2.99751e7	+	2.99751e7i	0.626673	+	0.626673i
$364$	−2.94388e7	+	6.77175e7i	−0.610402	+	1.40410i
$365$	6.19686e6	+	6.19686e6i	0.127436	+	0.127436i
$366$	−1.39210e6	+	2.04472e6i	−0.0283940	+	0.0417053i
$367$			1.41526e7i			0.286311i	0.989700	+	0.143155i	$0.0457249\pi$
$367$			1.41526e7i			0.286311i	−0.989700	+	0.143155i	$0.954275\pi$
$368$	−3.65496e7	+	3.40926e7i	−0.733397	+	0.684095i
$369$	−2.30057e7			−0.457885
$370$	118164.	+	80449.2i	0.00233282	+	0.00158824i
$371$	−2.97043e7	+	2.97043e7i	−0.581698	+	0.581698i
$372$	5.37038e6	−	1.23534e7i	0.104322	−	0.239970i
$373$	−7.14687e7	+	7.14687e7i	−1.37718	+	1.37718i	−0.527820	+	0.849356i	$0.676990\pi$
$373$	−7.14687e7	+	7.14687e7i	−1.37718	+	1.37718i	−0.849356	+	0.527820i	$0.823010\pi$
$374$	1.20456e8	−	2.28736e7i	2.30257	−	0.437240i
$375$	−6.34905e6			−0.120397
$376$	−1.41548e7	+	6.25855e7i	−0.266281	+	1.17736i
$377$			4.85242e7i			0.905596i
$378$	−9.53813e6	+	1.81122e6i	−0.176599	+	0.0335347i
$379$	−6.85276e7	−	6.85276e7i	−1.25878	−	1.25878i	−0.951678	−	0.307097i	$-0.900642\pi$
$379$	−6.85276e7	−	6.85276e7i	−1.25878	−	1.25878i	−0.307097	−	0.951678i	$-0.599358\pi$
$380$	−5.36987e6	+	2.11568e6i	−0.0978617	+	0.0385566i
$381$	2.26896e6	+	2.26896e6i	0.0410253	+	0.0410253i
$382$	6.87880e7	+	4.68326e7i	1.23402	+	0.840152i
$383$		−	8.56510e7i		−	1.52453i	−0.647264	−	0.762266i	$-0.724087\pi$
$383$		−	8.56510e7i		−	1.52453i	0.647264	−	0.762266i	$-0.275913\pi$
$384$	−8.31557e6	+	3.16161e7i	−0.146858	+	0.558360i
$385$	8.89764e6			0.155917
$386$	−9.82321e6	+	1.44284e7i	−0.170801	+	0.250874i
$387$	1.49342e7	−	1.49342e7i	0.257661	−	0.257661i
$388$	3.04774e7	+	7.73554e7i	0.521774	+	1.32433i
$389$	3.62694e7	−	3.62694e7i	0.616157	−	0.616157i	−0.328387	−	0.944543i	$-0.606505\pi$
$389$	3.62694e7	−	3.62694e7i	0.616157	−	0.616157i	0.944543	+	0.328387i	$0.106505\pi$
$390$	−1.09802e6	−	5.78234e6i	−0.0185104	−	0.0974788i
$391$	−8.82496e7			−1.47633
$392$	−7.49580e6	−	1.69530e6i	−0.124440	−	0.0281442i
$393$		−	2.04278e7i		−	0.336546i
$394$	1.09796e7	+	5.78203e7i	0.179514	+	0.945348i
$395$	−5.30303e6	−	5.30303e6i	−0.0860464	−	0.0860464i
$396$	−3.02250e7	−	1.31397e7i	−0.486722	−	0.211593i
$397$	−1.44442e7	−	1.44442e7i	−0.230846	−	0.230846i	0.582200	−	0.813046i	$-0.302192\pi$
$397$	−1.44442e7	−	1.44442e7i	−0.230846	−	0.230846i	−0.813046	+	0.582200i	$0.802192\pi$
$398$	−6.38005e7	+	9.37106e7i	−1.01199	+	1.48641i
$399$		−	3.43659e7i		−	0.541015i
$400$	−4.31746e7	−	4.62861e7i	−0.674603	−	0.723221i
$401$	2.71458e7			0.420988			0.210494	−	0.977595i	$-0.432493\pi$
$401$	2.71458e7			0.420988			0.210494	+	0.977595i	$0.432493\pi$
$402$	−2.46931e7	−	1.68117e7i	−0.380100	−	0.258781i
$403$	−3.43820e7	+	3.43820e7i	−0.525310	+	0.525310i
$404$	−9.81954e7	−	4.26884e7i	−1.48918	−	0.647390i
$405$	547201.	−	547201.i	0.00823724	−	0.00823724i
$406$	3.39280e7	−	6.44267e6i	0.506968	−	0.0962692i
$407$	−2.88946e6			−0.0428581
$408$	−4.88131e7	+	3.08059e7i	−0.718713	+	0.453579i
$409$		−	9.99364e7i		−	1.46068i	−0.683086	−	0.730338i	$-0.739363\pi$
$409$		−	9.99364e7i		−	1.46068i	0.683086	−	0.730338i	$-0.260637\pi$
$410$	−9.75161e6	+	1.85175e6i	−0.141490	+	0.0268678i
$411$	2.81024e7	+	2.81024e7i	0.404779	+	0.404779i
$412$	1.50191e7	+	3.81205e7i	0.214760	+	0.545089i
$413$	2.53003e7	+	2.53003e7i	0.359149	+	0.359149i
$414$	1.96087e7	+	1.33501e7i	0.276342	+	0.188141i
$415$		−	6.69065e6i		−	0.0936104i
$416$	6.97614e7	−	9.51774e7i	0.969026	−	1.32207i
$417$	−5.20290e7			−0.717525
$418$	6.56544e7	−	9.64336e7i	0.898949	−	1.32038i
$419$	1.68960e7	−	1.68960e7i	0.229690	−	0.229690i	−0.582873	−	0.812563i	$-0.698072\pi$
$419$	1.68960e7	−	1.68960e7i	0.229690	−	0.229690i	0.812563	+	0.582873i	$0.198072\pi$
$420$	−3.89721e6	+	1.53547e6i	−0.0526025	+	0.0207249i
$421$	−6.18271e7	+	6.18271e7i	−0.828576	+	0.828576i	−0.987320	−	0.158744i	$-0.949256\pi$
$421$	−6.18271e7	+	6.18271e7i	−0.828576	+	0.828576i	0.158744	+	0.987320i	$0.449256\pi$
$422$	1.87298e7	+	9.86341e7i	0.249228	+	1.31247i
$423$	3.04539e7			0.402366
$424$	5.67741e7	−	3.58301e7i	0.744822	−	0.470057i
$425$		−	1.11759e8i		−	1.45584i
$426$	5.56971e6	+	2.93309e7i	0.0720450	+	0.379400i
$427$	−4.49348e6	−	4.49348e6i	−0.0577164	−	0.0577164i
$428$	2.47339e7	−	5.68948e7i	0.315472	−	0.725674i
$429$	8.41224e7	+	8.41224e7i	1.06547	+	1.06547i
$430$	5.12821e6	−	7.53234e6i	0.0645001	−	0.0947381i
$431$		−	1.26217e8i		−	1.57647i	−0.615377	−	0.788233i	$-0.710996\pi$
$431$		−	1.26217e8i		−	1.57647i	0.615377	−	0.788233i	$-0.289004\pi$
$432$	1.55063e7	+	539324.i	0.192334	+	0.00668958i
$433$	1.94684e7			0.239809			0.119905	−	0.992785i	$-0.461741\pi$
$433$	1.94684e7			0.239809			0.119905	+	0.992785i	$0.461741\pi$
$434$	2.86048e7	+	1.94748e7i	0.349920	+	0.238234i
$435$	−1.94644e6	+	1.94644e6i	−0.0236469	+	0.0236469i
$436$	−4.71430e7	+	1.08442e8i	−0.568797	+	1.30839i
$437$	−5.93752e7	+	5.93752e7i	−0.711477	+	0.711477i
$438$	8.19292e7	−	1.55577e7i	0.975026	−	0.185150i
$439$	1.02252e7			0.120858			0.0604292	−	0.998172i	$-0.480753\pi$
$439$	1.02252e7			0.120858			0.0604292	+	0.998172i	$0.480753\pi$
$440$	−1.38693e7	−	3.13679e6i	−0.162816	−	0.0368237i
$441$			3.64743e6i			0.0425277i
$442$	2.04698e8	−	3.88704e7i	2.37053	−	0.450145i
$443$	−5.79230e7	−	5.79230e7i	−0.666255	−	0.666255i	0.290592	−	0.956847i	$-0.406148\pi$
$443$	−5.79230e7	−	5.79230e7i	−0.666255	−	0.666255i	−0.956847	+	0.290592i	$0.906148\pi$
$444$	1.26560e6	−	498635.i	0.0144593	−	0.00569683i
$445$	−941942.	−	941942.i	−0.0106892	−	0.0106892i
$446$	−1.22062e8	−	8.31030e7i	−1.37587	−	0.936725i
$447$			7.10580e6i			0.0795592i
$448$	−7.58102e7	−	3.61401e7i	−0.843128	−	0.401935i
$449$	6.91954e7			0.764431			0.382215	−	0.924073i	$-0.375161\pi$
$449$	6.91954e7			0.764431			0.382215	+	0.924073i	$0.375161\pi$
$450$	−1.69064e7	+	2.48323e7i	−0.185530	+	0.272508i
$451$	1.41868e8	−	1.41868e8i	1.54652	−	1.54652i
$452$	2.33117e6	+	5.91681e6i	0.0252440	+	0.0640726i
$453$	5.08928e6	−	5.08928e6i	0.0547472	−	0.0547472i
$454$	−4.92828e6	−	2.59530e7i	−0.0526657	−	0.277345i
$455$	1.51203e7			0.160518
$456$	−1.21154e7	+	5.35684e7i	−0.127774	+	0.564956i
$457$			1.14975e8i			1.20463i	0.798258	+	0.602316i	$0.205755\pi$
$457$			1.14975e8i			1.20463i	−0.798258	+	0.602316i	$0.794245\pi$
$458$	−2.32337e7	−	1.22352e8i	−0.241837	−	1.27355i
$459$	1.93712e7	+	1.93712e7i	0.200317	+	0.200317i
$460$	9.38625e6	+	4.08048e6i	0.0964314	+	0.0419216i
$461$	1.10716e7	+	1.10716e7i	0.113008	+	0.113008i	0.761350	−	0.648342i	$-0.224537\pi$
$461$	1.10716e7	+	1.10716e7i	0.113008	+	0.113008i	−0.648342	+	0.761350i	$0.724537\pi$
$462$	4.76491e7	−	6.99873e7i	0.483202	−	0.709730i
$463$			4.60447e7i			0.463913i	0.972726	+	0.231956i	$0.0745127\pi$
$463$			4.60447e7i			0.463913i	−0.972726	+	0.231956i	$0.925487\pi$
$464$	−5.51572e7	−	1.91843e6i	−0.552139	−	0.0192040i
$465$	−2.75832e6			−0.0274337
$466$	5.68180e7	+	3.86831e7i	0.561472	+	0.382264i
$467$	−1.78764e7	+	1.78764e7i	−0.175521	+	0.175521i	−0.789400	−	0.613879i	$-0.789608\pi$
$467$	−1.78764e7	+	1.78764e7i	−0.175521	+	0.175521i	0.613879	+	0.789400i	$0.289608\pi$
$468$	−5.13631e7	−	2.23290e7i	−0.501087	−	0.217837i
$469$	5.42655e7	−	5.42655e7i	0.526023	−	0.526023i
$470$	1.29087e7	−	2.45126e6i	0.124334	−	0.0236100i
$471$	1.52096e7			0.145565
$472$	−3.05178e7	−	4.83566e7i	−0.290220	−	0.459864i
$473$			1.84188e8i			1.74051i
$474$	−7.01117e7	+	1.33137e7i	−0.658348	+	0.125015i
$475$	−7.51923e7	−	7.51923e7i	−0.701605	−	0.701605i
$476$	−5.43563e7	−	1.37963e8i	−0.503998	−	1.27921i
$477$	−2.25304e7	−	2.25304e7i	−0.207594	−	0.207594i
$478$	−1.04126e7	−	7.08919e6i	−0.0953405	−	0.0649102i
$479$		−	2.69923e7i		−	0.245603i	−0.992431	−	0.122802i	$-0.960812\pi$
$479$		−	2.69923e7i		−	0.245603i	0.992431	−	0.122802i	$-0.0391879\pi$
$480$	6.61616e6	−	1.01951e6i	0.0598250	−	0.00921863i
$481$	−4.91022e6			−0.0441231
$482$	−6.93330e7	+	1.01837e8i	−0.619154	+	0.909418i
$483$	−4.30920e7	+	4.30920e7i	−0.382433	+	0.382433i
$484$	1.61927e8	−	6.37977e7i	1.42818	−	0.562690i
$485$	1.20387e7	−	1.20387e7i	0.105525	−	0.105525i
$486$	−1.37379e6	−	7.23458e6i	−0.0119677	−	0.0630238i
$487$	4.16825e7			0.360883			0.180442	−	0.983586i	$-0.442247\pi$
$487$	4.16825e7			0.360883			0.180442	+	0.983586i	$0.442247\pi$
$488$	5.42015e6	+	8.58842e6i	0.0466393	+	0.0739016i
$489$			6.07813e7i			0.519808i
$490$	293585.	+	1.54607e6i	0.00249544	+	0.0131413i
$491$	7.03027e6	+	7.03027e6i	0.0593920	+	0.0593920i	0.736179	−	0.676787i	$-0.236628\pi$
$491$	7.03027e6	+	7.03027e6i	0.0593920	+	0.0593920i	−0.676787	+	0.736179i	$0.736628\pi$
$492$	−3.76567e7	+	8.66211e7i	−0.316189	+	0.727324i
$493$	−6.89050e7	−	6.89050e7i	−0.575056	−	0.575056i
$494$	1.11570e8	−	1.63875e8i	0.925480	−	1.35935i
$495$			6.74877e6i			0.0556428i
$496$	−3.77225e7	−	4.04411e7i	−0.309140	−	0.331419i
$497$	−7.66975e7			−0.624758
$498$	−5.26275e7	−	3.58301e7i	−0.426113	−	0.290108i
$499$	−3.49256e7	+	3.49256e7i	−0.281088	+	0.281088i	−0.833543	−	0.552455i	$-0.813691\pi$
$499$	−3.49256e7	+	3.49256e7i	−0.281088	+	0.281088i	0.552455	+	0.833543i	$0.313691\pi$
$500$	−1.03924e7	+	2.39054e7i	−0.0831392	+	0.191243i
$501$	6.22151e7	−	6.22151e7i	0.494746	−	0.494746i
$502$	−1.15716e8	+	2.19736e7i	−0.914711	+	0.173696i
$503$	−2.71399e7			−0.213257			−0.106629	−	0.994299i	$-0.534006\pi$
$503$	−2.71399e7			−0.213257			−0.106629	+	0.994299i	$0.534006\pi$
$504$	−8.79283e6	+	3.88776e7i	−0.0686811	+	0.303674i
$505$			2.19255e7i			0.170245i
$506$	−2.03245e8	+	3.85946e7i	−1.56880	+	0.297903i
$507$	8.97493e7	+	8.97493e7i	0.688664	+	0.688664i
$508$	1.22570e7	−	4.82915e6i	0.0934960	−	0.0368366i
$509$	1.51625e8	+	1.51625e8i	1.14979	+	1.14979i	0.986594	+	0.163196i	$0.0521805\pi$
$509$	1.51625e8	+	1.51625e8i	1.14979	+	1.14979i	0.163196	+	0.986594i	$0.447820\pi$
$510$	9.77020e6	+	6.65180e6i	0.0736534	+	0.0501451i
$511$			2.14237e8i			1.60558i
$512$	1.05430e8	+	8.30603e7i	0.785511	+	0.618847i
$513$	2.60662e7			0.193075
$514$	3.07232e7	−	4.51264e7i	0.226244	−	0.332309i
$515$	5.93262e6	−	5.93262e6i	0.0434335	−	0.0434335i
$516$	−3.17853e7	−	8.06752e7i	−0.231354	−	0.587206i
$517$	−1.87798e8	+	1.87798e8i	−1.35900	+	1.35900i
$518$	651940.	+	3.43321e6i	0.00469049	+	0.0247008i
$519$	9.06962e7			0.648764
$520$	−2.35689e7	−	5.33052e6i	−0.167622	−	0.0379105i
$521$			2.02048e8i			1.42870i	0.699788	+	0.714351i	$0.253278\pi$
$521$			2.02048e8i			1.42870i	−0.699788	+	0.714351i	$0.746722\pi$
$522$	4.88670e6	+	2.57341e7i	0.0343561	+	0.180924i
$523$	7.38808e7	+	7.38808e7i	0.516448	+	0.516448i	0.916495	−	0.400047i	$-0.131006\pi$
$523$	7.38808e7	+	7.38808e7i	0.516448	+	0.516448i	−0.400047	+	0.916495i	$0.631006\pi$
$524$	−7.69149e7	−	3.34372e7i	−0.534584	−	0.232400i
$525$	−5.45713e7	−	5.45713e7i	−0.377126	−	0.377126i
$526$	−1.18247e8	+	1.73682e8i	−0.812517	+	1.19343i
$527$		−	9.76456e7i		−	0.667146i
$528$	−9.89472e7	+	9.22956e7i	−0.672205	+	0.627017i
$529$	867245.			0.00585834
$530$	−1.13636e7	−	7.73665e6i	−0.0763290	−	0.0519667i
$531$	−1.91900e7	+	1.91900e7i	−0.128171	+	0.128171i
$532$	−1.29394e8	−	5.62516e7i	−0.859371	−	0.373594i
$533$	2.41084e8	−	2.41084e8i	1.59216	−	1.59216i
$534$	−1.24535e7	+	2.36482e6i	−0.0817838	+	0.0155301i
$535$	−1.27037e7			−0.0829602
$536$	−1.03718e8	+	6.54564e7i	−0.673535	+	0.425067i
$537$		−	1.25786e7i		−	0.0812287i
$538$	2.08122e8	−	3.95207e7i	1.33651	−	0.253792i
$539$	−2.24924e7	−	2.24924e7i	−0.143638	−	0.143638i
$540$	−1.16464e6	−	2.95600e6i	−0.00739621	−	0.0187725i
$541$	−1.36253e8	−	1.36253e8i	−0.860506	−	0.860506i	0.130891	−	0.991397i	$-0.458216\pi$
$541$	−1.36253e8	−	1.36253e8i	−0.860506	−	0.860506i	−0.991397	+	0.130891i	$0.958216\pi$
$542$	4.04476e7	+	2.75377e7i	0.254036	+	0.172954i
$543$		−	5.88187e6i		−	0.0367381i
$544$	3.60910e7	+	2.34215e8i	0.224183	+	1.45485i
$545$	2.42134e7			0.149578
$546$	8.09727e7	−	1.18933e8i	0.497463	−	0.730677i
$547$	5.77218e7	−	5.77218e7i	0.352678	−	0.352678i	−0.508427	−	0.861105i	$-0.669773\pi$
$547$	5.77218e7	−	5.77218e7i	0.352678	−	0.352678i	0.861105	+	0.508427i	$0.169773\pi$
$548$	1.51810e8	−	5.98119e7i	0.922485	−	0.363451i
$549$	3.40826e6	−	3.40826e6i	0.0205976	−	0.0205976i
$550$	−4.88758e7	−	2.57387e8i	−0.293769	−	1.54703i
$551$	−9.27200e7			−0.554266
$552$	8.23620e7	−	5.19786e7i	0.489677	−	0.309035i
$553$		−	1.83335e8i		−	1.08410i
$554$	5.11672e7	+	2.69454e8i	0.300928	+	1.58473i
$555$	−196963.	−	196963.i	−0.00115214	−	0.00115214i
$556$	−8.51632e7	+	1.95899e8i	−0.495482	+	1.13975i
$557$	7.21755e7	+	7.21755e7i	0.417661	+	0.417661i	0.884397	−	0.466736i	$-0.154570\pi$
$557$	7.21755e7	+	7.21755e7i	0.417661	+	0.417661i	−0.466736	+	0.884397i	$0.654570\pi$
$558$	−1.47715e7	+	2.16964e7i	−0.0850200	+	0.124878i
$559$			3.13000e8i			1.79188i
$560$	−597786.	+	1.71871e7i	−0.00340394	+	0.0978675i
$561$	−2.38910e8			−1.35315
$562$	7.49763e7	+	5.10457e7i	0.422391	+	0.287575i
$563$	2.63528e6	−	2.63528e6i	0.0147673	−	0.0147673i	−0.699685	−	0.714452i	$-0.746676\pi$
$563$	2.63528e6	−	2.63528e6i	0.0147673	−	0.0147673i	0.714452	+	0.699685i	$0.246676\pi$
$564$	4.98482e7	−	1.14665e8i	0.277851	−	0.639136i
$565$	920822.	−	920822.i	0.00510541	−	0.00510541i
$566$	−2.65058e8	+	5.03325e7i	−1.46181	+	0.277587i
$567$	1.89177e7			0.103781
$568$	1.19553e8	+	2.70390e7i	0.652405	+	0.147552i
$569$			1.21428e8i			0.659147i	0.944130	+	0.329574i	$0.106905\pi$
$569$			1.21428e8i			0.659147i	−0.944130	+	0.329574i	$0.893095\pi$
$570$	1.10489e7	−	2.09810e6i	0.0596615	−	0.0113292i
$571$	−1.54218e8	−	1.54218e8i	−0.828372	−	0.828372i	0.158919	−	0.987292i	$-0.449199\pi$
$571$	−1.54218e8	−	1.54218e8i	−0.828372	−	0.828372i	−0.987292	+	0.158919i	$0.949199\pi$
$572$	4.54432e8	−	1.79042e8i	2.42818	−	0.956682i
$573$	−1.14660e8	−	1.14660e8i	−0.609462	−	0.609462i
$574$	−2.00575e8	−	1.36556e8i	−1.06057	−	0.722064i
$575$			1.88570e8i			0.991901i
$576$	2.74120e7	−	5.75013e7i	0.143441	−	0.300892i
$577$	3.35652e8			1.74728			0.873638	−	0.486576i	$-0.161754\pi$
$577$	3.35652e8			1.74728			0.873638	+	0.486576i	$0.161754\pi$
$578$	−1.26804e8	+	1.86251e8i	−0.656674	+	0.964528i
$579$	2.40500e7	−	2.40500e7i	0.123903	−	0.123903i
$580$	4.14273e6	+	1.05148e7i	0.0212326	+	0.0538910i
$581$	1.15654e8	−	1.15654e8i	0.589701	−	0.589701i
$582$	−3.02240e7	−	1.59164e8i	−0.153315	−	0.807378i
$583$	2.77874e8			1.40230
$584$	7.55273e7	−	3.33945e8i	0.379197	−	1.67663i
$585$			1.14686e7i			0.0572851i
$586$	940368.	+	4.95212e6i	0.00467310	+	0.0246092i
$587$	−1.46642e8	−	1.46642e8i	−0.725012	−	0.725012i	0.244610	−	0.969622i	$-0.421340\pi$
$587$	−1.46642e8	−	1.46642e8i	−0.725012	−	0.725012i	−0.969622	+	0.244610i	$0.921340\pi$
$588$	1.37333e7	+	5.97027e6i	0.0675527	+	0.0293672i
$589$	−6.56970e7	−	6.56970e7i	−0.321514	−	0.321514i
$590$	−6.58959e6	+	9.67883e6i	−0.0320850	+	0.0471267i
$591$		−	1.14679e8i		−	0.555550i
$592$	194128.	−	5.58142e6i	0.000935670	−	0.0269017i
$593$	−2.09211e8			−1.00328			−0.501639	−	0.865077i	$-0.667269\pi$
$593$	−2.09211e8			−1.00328			−0.501639	+	0.865077i	$0.667269\pi$
$594$	5.30847e7	+	3.61414e7i	0.253285	+	0.172443i
$595$	−2.14710e7	+	2.14710e7i	−0.101930	+	0.101930i
$596$	2.67547e7	+	1.16311e7i	0.126375	+	0.0549390i
$597$	1.56202e8	−	1.56202e8i	0.734114	−	0.734114i
$598$	−3.45385e8	+	6.55859e7i	−1.61510	+	0.306695i
$599$	3.54843e7			0.165103			0.0825516	−	0.996587i	$-0.473693\pi$
$599$	3.54843e7			0.165103			0.0825516	+	0.996587i	$0.473693\pi$
$600$	6.58253e7	+	1.04303e8i	0.304747	+	0.482882i
$601$			1.17448e7i			0.0541033i	0.999634	+	0.0270516i	$0.00861186\pi$
$601$			1.17448e7i			0.0541033i	−0.999634	+	0.0270516i	$0.991388\pi$
$602$	2.18849e8	−	4.15577e7i	1.00313	−	0.190486i
$603$	4.11598e7	+	4.11598e7i	0.187725	+	0.187725i
$604$	−1.08318e7	−	2.74925e7i	−0.0491575	−	0.124768i
$605$	−2.52004e7	−	2.52004e7i	−0.113800	−	0.113800i
$606$	1.72462e8	+	1.17417e8i	0.774954	+	0.527608i
$607$			6.66131e7i			0.297847i	0.988849	+	0.148924i	$0.0475809\pi$
$607$			6.66131e7i			0.297847i	−0.988849	+	0.148924i	$0.952419\pi$
$608$	1.81865e8	+	1.33300e8i	0.809166	+	0.593088i
$609$	−6.72921e7			−0.297929
$610$	1.17035e6	−	1.71902e6i	0.00515616	−	0.00757341i
$611$	−3.19136e8	+	3.19136e8i	−1.39911	+	1.39911i
$612$	1.04644e8	−	4.12287e7i	0.456519	−	0.179864i
$613$	2.90977e8	−	2.90977e8i	1.26321	−	1.26321i	0.313687	−	0.949527i	$-0.398436\pi$
$613$	2.90977e8	−	2.90977e8i	1.26321	−	1.26321i	0.949527	−	0.313687i	$-0.101564\pi$
$614$	4.24194e7	+	2.23387e8i	0.183257	+	0.965057i
$615$	1.93411e7			0.0831489
$616$	−1.85522e8	−	2.93966e8i	−0.793694	−	1.25764i
$617$		−	2.26992e8i		−	0.966398i	−0.875511	−	0.483199i	$-0.839475\pi$
$617$		−	2.26992e8i		−	0.966398i	0.875511	−	0.483199i	$-0.160525\pi$
$618$	−1.48943e7	−	7.84357e7i	−0.0631037	−	0.332314i
$619$	−1.74883e8	−	1.74883e8i	−0.737351	−	0.737351i	0.234713	−	0.972065i	$-0.424585\pi$
$619$	−1.74883e8	−	1.74883e8i	−0.737351	−	0.737351i	−0.972065	+	0.234713i	$0.924585\pi$
$620$	−4.51493e6	+	1.03856e7i	−0.0189442	+	0.0435769i
$621$	−3.26848e7	−	3.26848e7i	−0.136481	−	0.136481i
$622$	2.17876e8	−	3.20018e8i	0.905395	−	1.32985i
$623$		−	3.25646e7i		−	0.134673i
$624$	−1.68147e8	+	1.56843e8i	−0.692045	+	0.645523i
$625$	−2.36119e8			−0.967145
$626$	1.91632e8	+	1.30468e8i	0.781170	+	0.531840i
$627$	−1.60741e8	+	1.60741e8i	−0.652114	+	0.652114i
$628$	2.48958e7	−	5.72673e7i	0.100519	−	0.231221i
$629$	6.97257e6	−	6.97257e6i	0.0280183	−	0.0280183i
$630$	8.01880e6	−	1.52271e6i	0.0320692	−	0.00608968i
$631$	1.45037e8			0.577284			0.288642	−	0.957437i	$-0.406796\pi$
$631$	1.45037e8			0.577284			0.288642	+	0.957437i	$0.406796\pi$
$632$	−6.46333e7	+	2.85777e8i	−0.256038	+	1.13208i
$633$		−	1.95629e8i		−	0.771297i
$634$	−3.70075e8	+	7.02743e7i	−1.45218	+	0.275758i
$635$	−1.90753e6	−	1.90753e6i	−0.00744991	−	0.00744991i
$636$	−1.21710e8	+	4.79527e7i	−0.473103	+	0.186398i
$637$	−3.82226e7	−	3.82226e7i	−0.147877	−	0.147877i
$638$	−1.88827e8	−	1.28558e8i	−0.727114	−	0.495037i
$639$		−	5.81743e7i		−	0.222961i
$640$	6.99098e6	−	2.65799e7i	0.0266685	−	0.101394i
$641$	−1.67425e8			−0.635693			−0.317847	−	0.948142i	$-0.602960\pi$
$641$	−1.67425e8			−0.635693			−0.317847	+	0.948142i	$0.602960\pi$
$642$	−6.80316e7	+	9.99253e7i	−0.257102	+	0.377633i
$643$	−1.26691e8	+	1.26691e8i	−0.476553	+	0.476553i	−0.904027	−	0.427474i	$-0.859403\pi$
$643$	−1.26691e8	+	1.26691e8i	−0.476553	+	0.476553i	0.427474	+	0.904027i	$0.359403\pi$
$644$	9.17150e7	+	2.32784e8i	0.343386	+	0.871558i
$645$	−1.25553e7	+	1.25553e7i	−0.0467895	+	0.0467895i
$646$	7.42735e7	+	3.91136e8i	0.275509	+	1.45087i
$647$	7.73707e7			0.285669			0.142835	−	0.989747i	$-0.454378\pi$
$647$	7.73707e7			0.285669			0.142835	+	0.989747i	$0.454378\pi$
$648$	−2.94883e7	−	6.66928e6i	−0.108374	−	0.0245106i
$649$		−	2.36675e8i		−	0.865803i
$650$	−8.30574e7	−	4.37393e8i	−0.302439	−	1.59269i
$651$	−4.76800e7	−	4.76800e7i	−0.172820	−	0.172820i
$652$	2.28854e8	+	9.94894e7i	0.825686	+	0.358950i
$653$	−2.47347e8	−	2.47347e8i	−0.888317	−	0.888317i	0.106044	−	0.994361i	$-0.466181\pi$
$653$	−2.47347e8	−	2.47347e8i	−0.888317	−	0.888317i	−0.994361	+	0.106044i	$0.966181\pi$
$654$	1.29669e8	−	1.90458e8i	0.463556	−	0.680874i
$655$			1.71739e7i			0.0611145i
$656$	2.64507e8	+	2.83570e8i	0.936971	+	1.00450i
$657$	−1.62496e8			−0.572991
$658$	2.65511e8	+	1.80767e8i	0.931977	+	0.634513i
$659$	2.75597e8	−	2.75597e8i	0.962982	−	0.962982i	−0.0363568	−	0.999339i	$-0.511575\pi$
$659$	2.75597e8	−	2.75597e8i	0.962982	−	0.962982i	0.999339	+	0.0363568i	$0.0115753\pi$
$660$	2.54105e7	+	1.10467e7i	0.0883855	+	0.0384238i
$661$	1.54371e8	−	1.54371e8i	0.534517	−	0.534517i	−0.387396	−	0.921913i	$-0.626625\pi$
$661$	1.54371e8	−	1.54371e8i	0.534517	−	0.534517i	0.921913	+	0.387396i	$0.126625\pi$
$662$	1.04686e8	−	1.98790e7i	0.360839	−	0.0685204i
$663$	−4.05992e8			−1.39308
$664$	−2.21050e8	+	1.39505e8i	−0.755069	+	0.476524i
$665$			2.88917e7i			0.0982446i
$666$	−2.60406e6	+	494490.i	−0.00881512	+	0.00167392i
$667$	1.16263e8	+	1.16263e8i	0.391800	+	0.391800i
$668$	−1.32416e8	−	3.36088e8i	−0.444232	−	1.12752i
$669$	2.03460e8	+	2.03460e8i	0.679518	+	0.679518i
$670$	2.07597e7	+	1.41337e7i	0.0690236	+	0.0469929i
$671$			4.20350e7i			0.139137i
$672$	1.31989e8	+	9.67433e7i	0.434942	+	0.318796i
$673$	−1.40609e7			−0.0461284			−0.0230642	−	0.999734i	$-0.507342\pi$
$673$	−1.40609e7			−0.0461284			−0.0230642	+	0.999734i	$0.507342\pi$
$674$	−2.84856e8	+	4.18398e8i	−0.930348	+	1.36650i
$675$	4.13918e7	−	4.13918e7i	0.134587	−	0.134587i
$676$	4.84830e8	−	1.91019e8i	1.56946	−	0.618351i
$677$	−1.11330e8	+	1.11330e8i	−0.358795	+	0.358795i	−0.863369	−	0.504573i	$-0.831650\pi$
$677$	−1.11330e8	+	1.11330e8i	−0.358795	+	0.358795i	0.504573	+	0.863369i	$0.331650\pi$
$678$	−2.31179e6	−	1.21743e7i	−0.00741755	−	0.0390619i
$679$	4.16199e8			1.32951
$680$	4.10376e7	−	2.58988e7i	0.130513	−	0.0823669i
$681$			5.14747e7i			0.162987i
$682$	−4.27037e7	−	2.24884e8i	−0.134621	−	0.708934i
$683$	1.14911e8	+	1.14911e8i	0.360660	+	0.360660i	0.864056	−	0.503396i	$-0.167916\pi$
$683$	1.14911e8	+	1.14911e8i	0.360660	+	0.360660i	−0.503396	+	0.864056i	$0.667916\pi$
$684$	4.26663e7	−	9.81444e7i	0.133326	−	0.306688i
$685$	−2.36259e7	−	2.36259e7i	−0.0735051	−	0.0735051i
$686$	−1.91346e8	+	2.81050e8i	−0.592715	+	0.870584i
$687$			2.42671e8i			0.748423i
$688$	−3.55785e8	−	1.23746e7i	−1.09250	−	0.0379985i
$689$	4.72206e8			1.44369
$690$	−1.64852e7	−	1.12235e7i	−0.0501819	−	0.0341651i
$691$	3.16526e8	−	3.16526e8i	0.959345	−	0.959345i	−0.0398604	−	0.999205i	$-0.512691\pi$
$691$	3.16526e8	−	3.16526e8i	0.959345	−	0.959345i	0.999205	+	0.0398604i	$0.0126913\pi$
$692$	1.48455e8	−	3.41489e8i	0.448000	−	1.03052i
$693$	−1.16659e8	+	1.16659e8i	−0.350524	+	0.350524i
$694$	−5.47729e8	+	1.04009e8i	−1.63866	+	0.311168i
$695$	4.37412e7			0.130298
$696$	1.04893e8	+	2.37233e7i	0.311113	+	0.0703634i
$697$			6.84684e8i			2.02205i
$698$	2.52961e8	−	4.80352e7i	0.743852	−	0.141252i
$699$	−9.47074e7	−	9.47074e7i	−0.277302	−	0.277302i
$700$	−2.94796e8	+	1.16147e8i	−0.859464	+	0.338621i
$701$	2.13815e8	+	2.13815e8i	0.620704	+	0.620704i	0.945711	−	0.325008i	$-0.105367\pi$
$701$	2.13815e8	+	2.13815e8i	0.620704	+	0.620704i	−0.325008	+	0.945711i	$0.605367\pi$
$702$	9.02098e7	+	6.14170e7i	0.260761	+	0.177532i
$703$		−	9.38243e6i		−	0.0270053i
$704$	1.85550e8	+	5.23629e8i	0.531794	+	1.50074i
$705$	−2.56029e7			−0.0730670
$706$	1.63210e8	−	2.39723e8i	0.463801	−	0.681234i
$707$	−3.79002e8	+	3.79002e8i	−1.07247	+	1.07247i
$708$	4.08431e7	+	1.03665e8i	0.115085	+	0.292101i
$709$	−1.45979e8	+	1.45979e8i	−0.409593	+	0.409593i	−0.881597	−	0.472003i	$-0.843531\pi$
$709$	−1.45979e8	+	1.45979e8i	−0.409593	+	0.409593i	0.472003	+	0.881597i	$0.343531\pi$
$710$	−4.68251e6	−	2.46588e7i	−0.0130829	−	0.0688964i
$711$	1.39058e8			0.386890
$712$	−1.14804e7	+	5.07607e7i	−0.0318065	+	0.140633i
$713$			1.64757e8i			0.454543i
$714$	5.39045e7	+	2.83869e8i	0.148092	+	0.779872i
$715$	−7.07225e7	−	7.07225e7i	−0.193481	−	0.193481i
$716$	−4.73609e7	−	2.05892e7i	−0.129027	−	0.0560919i
$717$	1.73564e7	+	1.73564e7i	0.0470870	+	0.0470870i
$718$	1.03327e8	−	1.51767e8i	0.279152	−	0.410020i
$719$		−	1.30421e8i		−	0.350882i	−0.984490	−	0.175441i	$-0.943865\pi$
$719$		−	1.30421e8i		−	0.350882i	0.984490	−	0.175441i	$-0.0561351\pi$
$720$	−1.30363e7	−	453415.i	−0.0349265	−	0.00121478i
$721$	2.05102e8			0.547222
$722$	2.02331e6	+	1.37752e6i	0.00537591	+	0.00366005i
$723$	1.69747e8	−	1.69747e8i	0.449146	−	0.449146i
$724$	−2.21464e7	−	9.62770e6i	−0.0583563	−	0.0253692i
$725$	−1.47235e8	+	1.47235e8i	−0.386363	+	0.386363i
$726$	−3.33176e8	+	6.32675e7i	−0.870691	+	0.165337i
$727$	−1.55032e8			−0.403475			−0.201738	−	0.979440i	$-0.564659\pi$
$727$	−1.55032e8			−0.403475			−0.201738	+	0.979440i	$0.564659\pi$
$728$	−3.15268e8	−	4.99553e8i	−0.817119	−	1.29476i
$729$			1.43489e7i			0.0370370i
$730$	−6.88786e7	+	1.30795e7i	−0.177058	+	0.0336219i
$731$	−4.44464e8	−	4.44464e8i	−1.13785	−	1.13785i
$732$	−7.25399e6	−	1.84116e7i	−0.0184945	−	0.0469415i
$733$	1.89149e8	+	1.89149e8i	0.480278	+	0.480278i	0.905220	−	0.424942i	$-0.139706\pi$
$733$	1.89149e8	+	1.89149e8i	0.480278	+	0.480278i	−0.424942	+	0.905220i	$0.639706\pi$
$734$	−9.35893e7	−	6.37179e7i	−0.236667	−	0.161129i
$735$		−	3.06643e6i		−	0.00772273i
$736$	−6.08961e7	−	3.95190e8i	−0.152741	−	0.991226i
$737$	−5.07635e8			−1.26809
$738$	1.03577e8	−	1.52134e8i	0.257687	−	0.378492i
$739$	−4.72512e7	+	4.72512e7i	−0.117079	+	0.117079i	−0.763219	−	0.646140i	$-0.776382\pi$
$739$	−4.72512e7	+	4.72512e7i	−0.117079	+	0.117079i	0.646140	+	0.763219i	$0.276382\pi$
$740$	−1.06400e6	+	419207.i	−0.00262571	+	0.00103451i
$741$	−2.73156e8	+	2.73156e8i	−0.671361	+	0.671361i
$742$	−6.26958e7	−	3.30166e8i	−0.153471	−	0.808203i
$743$	−1.17829e8			−0.287267			−0.143633	−	0.989631i	$-0.545879\pi$
$743$	−1.17829e8			−0.287267			−0.143633	+	0.989631i	$0.545879\pi$
$744$	5.75128e7	+	9.11312e7i	0.139652	+	0.221283i
$745$		−	5.97391e6i		−	0.0144474i
$746$	−1.50847e8	−	7.94381e8i	−0.363345	−	1.91343i
$747$	8.77224e7	+	8.77224e7i	0.210450	+	0.210450i
$748$	−3.91057e8	+	8.99542e8i	−0.934406	+	2.14940i
$749$	−2.19595e8	−	2.19595e8i	−0.522610	−	0.522610i
$750$	2.85847e7	−	4.19855e7i	0.0677564	−	0.0995211i
$751$			3.83595e8i			0.905635i	0.891603	+	0.452818i	$0.149581\pi$
$751$			3.83595e8i			0.905635i	−0.891603	+	0.452818i	$0.850419\pi$
$752$	−3.50142e8	−	3.75377e8i	−0.823363	−	0.882702i
$753$	2.29509e8			0.537546
$754$	−3.20885e8	−	2.18466e8i	−0.748574	−	0.509648i
$755$	−4.27861e6	+	4.27861e6i	−0.00994172	+	0.00994172i
$756$	3.09653e7	−	7.12289e7i	0.0716655	−	0.164851i
$757$	−2.38231e8	+	2.38231e8i	−0.549175	+	0.549175i	−0.926202	−	0.377027i	$-0.876946\pi$
$757$	−2.38231e8	+	2.38231e8i	−0.549175	+	0.549175i	0.377027	+	0.926202i	$0.376946\pi$
$758$	7.61690e8	−	1.44639e8i	1.74892	−	0.332107i
$759$	4.03111e8			0.921933
$760$	1.01855e7	−	4.50355e7i	0.0232029	−	0.102592i
$761$			5.51987e7i			0.125249i	0.998037	+	0.0626246i	$0.0199471\pi$
$761$			5.51987e7i			0.125249i	−0.998037	+	0.0626246i	$0.980053\pi$
$762$	−2.52196e7	+	4.78901e6i	−0.0569999	+	0.0108238i
$763$	4.18551e8	+	4.18551e8i	0.942268	+	0.942268i
$764$	−6.19396e8	+	2.44037e8i	−1.38896	+	0.547236i
$765$	−1.62855e7	−	1.62855e7i	−0.0363762	−	0.0363762i
$766$	5.66400e8	+	3.85619e8i	1.26019	+	0.857970i
$767$		−	4.02196e8i		−	0.891356i
$768$	−1.71635e8	−	1.97332e8i	−0.378897	−	0.435626i
$769$	6.75649e8			1.48574			0.742869	−	0.669437i	$-0.233465\pi$
$769$	6.75649e8			1.48574			0.742869	+	0.669437i	$0.233465\pi$
$770$	−4.00590e7	+	5.88390e7i	−0.0877462	+	0.128882i
$771$	−7.52192e7	+	7.52192e7i	−0.164122	+	0.164122i
$772$	−5.11870e7	−	1.29919e8i	−0.111252	−	0.282372i
$773$	4.62396e7	−	4.62396e7i	0.100110	−	0.100110i	−0.655278	−	0.755388i	$-0.727449\pi$
$773$	4.62396e7	−	4.62396e7i	0.100110	−	0.100110i	0.755388	+	0.655278i	$0.227449\pi$
$774$	3.15211e7	+	1.65995e8i	0.0679796	+	0.357991i
$775$	−2.08647e8			−0.448236
$776$	−6.48757e8	−	1.46727e8i	−1.38834	−	0.313997i
$777$		−	6.80936e6i		−	0.0145159i
$778$	7.65525e7	+	4.03137e8i	0.162563	+	0.856079i
$779$	4.60662e8	+	4.60662e8i	0.974474	+	0.974474i
$780$	4.31814e7	+	1.87722e7i	0.0909941	+	0.0395578i
$781$	3.58740e8	+	3.58740e8i	0.753054	+	0.753054i
$782$	3.97318e8	−	5.83584e8i	0.830842	−	1.22035i
$783$		−	5.10404e7i		−	0.106323i
$784$	4.49585e7	−	4.19362e7i	0.0932961	−	0.0870244i
$785$	−1.27869e7			−0.0264336
$786$	1.35087e8	+	9.19704e7i	0.278192	+	0.189400i
$787$	−1.72365e8	+	1.72365e8i	−0.353610	+	0.353610i	−0.861451	−	0.507841i	$-0.830444\pi$
$787$	−1.72365e8	+	1.72365e8i	−0.353610	+	0.353610i	0.507841	+	0.861451i	$0.330444\pi$
$788$	−4.31791e8	−	1.87712e8i	−0.882460	−	0.383631i
$789$	2.89503e8	−	2.89503e8i	0.589415	−	0.589415i
$790$	5.89436e7	−	1.11929e7i	0.119552	−	0.0227019i
$791$	3.18345e7			0.0643233
$792$	2.22971e8	−	1.40717e8i	0.448820	−	0.283250i
$793$			7.14324e7i			0.143244i
$794$	1.60549e8	−	3.04870e7i	0.320735	−	0.0609050i
$795$	1.89415e7	+	1.89415e7i	0.0376976	+	0.0376976i
$796$	−3.32454e8	−	8.43810e8i	−0.659161	−	1.67304i
$797$	2.67781e8	+	2.67781e8i	0.528939	+	0.528939i	0.920256	−	0.391317i	$-0.127980\pi$
$797$	2.67781e8	+	2.67781e8i	0.528939	+	0.528939i	−0.391317	+	0.920256i	$0.627980\pi$
$798$	2.27257e8	+	1.54722e8i	0.447208	+	0.304470i
$799$		−	9.06354e8i		−	1.77688i
$800$	5.00465e8	−	7.71183e7i	0.977471	−	0.150622i
$801$	2.47000e7			0.0480617
$802$	−1.22216e8	+	1.79512e8i	−0.236922	+	0.347992i
$803$	1.00206e9	−	1.00206e9i	1.93529	−	1.93529i
$804$	2.22347e8	−	8.76028e7i	0.427822	−	0.168558i
$805$	3.62278e7	−	3.62278e7i	0.0694472	−	0.0694472i
$806$	−7.25688e7	−	3.82158e8i	−0.138594	−	0.729858i
$807$	−4.12785e8			−0.785422
$808$	7.24390e8	−	4.57162e8i	1.37321	−	0.866634i
$809$		−	5.16479e8i		−	0.975454i	−0.872996	−	0.487727i	$-0.837826\pi$
$809$		−	5.16479e8i		−	0.975454i	0.872996	−	0.487727i	$-0.162174\pi$
$810$	1.15496e6	+	6.08218e6i	0.00217326	+	0.0114447i
$811$	−2.03401e8	−	2.03401e8i	−0.381321	−	0.381321i	0.490257	−	0.871578i	$-0.336903\pi$
$811$	−2.03401e8	−	2.03401e8i	−0.381321	−	0.381321i	−0.871578	+	0.490257i	$0.836903\pi$
$812$	−1.10147e8	+	2.53368e8i	−0.205733	+	0.473243i
$813$	−6.74203e7	−	6.74203e7i	−0.125464	−	0.125464i
$814$	1.30090e7	−	1.91076e7i	0.0241195	−	0.0354269i
$815$		−	5.10994e7i		−	0.0943937i
$816$	1.60511e7	−	4.61489e8i	0.0295416	−	0.849359i
$817$	−5.98080e8			−1.09671
$818$	6.60867e8	+	4.49934e8i	1.20741	+	0.822033i
$819$	−1.98245e8	+	1.98245e8i	−0.360869	+	0.360869i
$820$	3.16584e7	−	7.28231e7i	0.0574178	−	0.132077i
$821$	2.23660e8	−	2.23660e8i	0.404165	−	0.404165i	−0.475533	−	0.879698i	$-0.657745\pi$
$821$	2.23660e8	−	2.23660e8i	0.404165	−	0.404165i	0.879698	+	0.475533i	$0.157745\pi$
$822$	−3.12360e8	+	5.93148e7i	−0.562394	+	0.106794i
$823$	−5.55024e8			−0.995663			−0.497831	−	0.867274i	$-0.665870\pi$
$823$	−5.55024e8			−0.995663			−0.497831	+	0.867274i	$0.665870\pi$
$824$	−3.19706e8	−	7.23068e7i	−0.571437	−	0.129240i
$825$			5.10496e8i			0.909140i
$826$	−2.81214e8	+	5.34004e7i	−0.498996	+	0.0947555i
$827$	3.43167e8	+	3.43167e8i	0.606722	+	0.606722i	0.942088	−	0.335366i	$-0.108860\pi$
$827$	3.43167e8	+	3.43167e8i	0.606722	+	0.606722i	−0.335366	+	0.942088i	$0.608860\pi$
$828$	−1.76565e8	+	6.95650e7i	−0.311038	+	0.122546i
$829$	3.19773e8	+	3.19773e8i	0.561278	+	0.561278i	0.929670	−	0.368393i	$-0.120092\pi$
$829$	3.19773e8	+	3.19773e8i	0.561278	+	0.561278i	−0.368393	+	0.929670i	$0.620092\pi$
$830$	4.42444e7	+	3.01227e7i	0.0773792	+	0.0526817i
$831$		−	5.34430e8i		−	0.931295i
$832$	3.15316e8	+	8.89832e8i	0.547489	+	1.54503i
$833$	1.08553e8			0.187805
$834$	2.34245e8	−	3.44061e8i	0.403806	−	0.593113i
$835$	−5.23048e7	+	5.23048e7i	−0.0898425	+	0.0898425i
$836$	3.42114e8	+	8.68328e8i	0.585533	+	1.48616i
$837$	3.61648e7	−	3.61648e7i	0.0616751	−	0.0616751i
$838$	3.56619e7	+	1.87801e8i	0.0605999	+	0.319128i
$839$	−3.67753e8			−0.622687			−0.311344	−	0.950297i	$-0.600779\pi$
$839$	−3.67753e8			−0.622687			−0.311344	+	0.950297i	$0.600779\pi$
$840$	7.39222e6	−	3.26848e7i	0.0124720	−	0.0551452i
$841$		−	4.13268e8i		−	0.694774i
$842$	−1.30496e8	−	6.87213e8i	−0.218606	−	1.15121i
$843$	−1.24975e8	−	1.24975e8i	−0.208612	−	0.208612i
$844$	−7.36581e8	−	3.20213e8i	−1.22516	−	0.532613i
$845$	−7.54531e7	−	7.54531e7i	−0.125057	−	0.125057i
$846$	−1.37110e8	+	2.01388e8i	−0.226442	+	0.332600i
$847$		−	8.71223e8i		−	1.43377i
$848$	−1.86689e7	+	5.36754e8i	−0.0306148	+	0.880213i
$849$	5.25711e8			0.859061
$850$	7.39045e8	+	5.03160e8i	1.20341	+	0.819313i
$851$	−1.17648e7	+	1.17648e7i	−0.0190895	+	0.0190895i
$852$	−2.19038e8	−	9.52221e7i	−0.354160	−	0.153964i
$853$	−4.71292e8	+	4.71292e8i	−0.759351	+	0.759351i	−0.976204	−	0.216853i	$-0.930421\pi$
$853$	−4.71292e8	+	4.71292e8i	−0.759351	+	0.759351i	0.216853	+	0.976204i	$0.430421\pi$
$854$	4.99454e7	−	9.48423e6i	0.0801903	−	0.0152275i
$855$	−2.19141e7			−0.0350611
$856$	2.64881e8	+	4.19714e8i	0.422309	+	0.669164i
$857$		−	4.41918e8i		−	0.702101i	−0.936357	−	0.351050i	$-0.885825\pi$
$857$		−	4.41918e8i		−	0.702101i	0.936357	−	0.351050i	$-0.114175\pi$
$858$	−9.35027e8	+	1.77554e8i	−1.48034	+	0.281105i
$859$	−2.13804e8	−	2.13804e8i	−0.337316	−	0.337316i	0.518040	−	0.855356i	$-0.326662\pi$
$859$	−2.13804e8	−	2.13804e8i	−0.337316	−	0.337316i	−0.855356	+	0.518040i	$0.826662\pi$
$860$	2.67222e7	+	6.78244e7i	0.0420123	+	0.106633i
$861$	3.34329e8	+	3.34329e8i	0.523799	+	0.523799i
$862$	8.34654e8	+	5.68253e8i	1.30312	+	0.887197i
$863$			8.85672e8i			1.37797i	0.724774	+	0.688987i	$0.241944\pi$
$863$			8.85672e8i			1.37797i	−0.724774	+	0.688987i	$0.758056\pi$
$864$	−7.33789e7	+	1.00113e8i	−0.113771	+	0.155220i
$865$	−7.62491e7			−0.117811
$866$	−8.76506e7	+	1.28742e8i	−0.134959	+	0.198228i
$867$	3.10453e8	−	3.10453e8i	0.476364	−	0.476364i
$868$	−2.57569e8	+	1.01480e8i	−0.393854	+	0.155175i
$869$	−8.57520e8	+	8.57520e8i	−1.30673	+	1.30673i
$870$	−4.10830e6	−	2.16349e7i	−0.00623884	−	0.0328547i
$871$	−8.62653e8			−1.30551
$872$	−5.04866e8	−	7.99979e8i	−0.761425	−	1.20651i
$873$			3.15683e8i			0.474470i
$874$	−1.25321e8	−	6.59961e8i	−0.187711	−	0.988516i
$875$	9.22671e7	+	9.22671e7i	0.137728	+	0.137728i
$876$	−2.65981e8	+	6.11831e8i	−0.395675	+	0.910163i
$877$	−5.18981e8	−	5.18981e8i	−0.769401	−	0.769401i	0.208600	−	0.978001i	$-0.433109\pi$
$877$	−5.18981e8	−	5.18981e8i	−0.769401	−	0.769401i	−0.978001	+	0.208600i	$0.933109\pi$
$878$	−4.60358e7	+	6.76178e7i	−0.0680162	+	0.0999027i
$879$		−	9.82192e6i		−	0.0144620i
$880$	8.31859e7	−	7.75938e7i	0.122068	−	0.113862i
$881$	1.55711e7			0.0227715			0.0113858	−	0.999935i	$-0.496376\pi$
$881$	1.55711e7			0.0227715			0.0113858	+	0.999935i	$0.496376\pi$
$882$	−2.41200e7	−	1.64215e7i	−0.0351538	−	0.0239335i
$883$	1.82187e8	−	1.82187e8i	0.264628	−	0.264628i	−0.562303	−	0.826931i	$-0.690085\pi$
$883$	1.82187e8	−	1.82187e8i	0.264628	−	0.264628i	0.826931	+	0.562303i	$0.190085\pi$
$884$	−6.64546e8	+	1.52864e9i	−0.961984	+	2.21283i
$885$	1.61332e7	−	1.61332e7i	0.0232751	−	0.0232751i
$886$	6.43819e8	−	1.22256e8i	0.925684	−	0.175780i
$887$	3.07661e8			0.440860			0.220430	−	0.975403i	$-0.429254\pi$
$887$	3.07661e8			0.440860			0.220430	+	0.975403i	$0.429254\pi$
$888$	−2.40058e6	+	1.06142e7i	−0.00342829	+	0.0151582i
$889$		−	6.59469e7i		−	0.0938618i
$890$	1.04698e7	−	1.98812e6i	0.0148514	−	0.00282016i
$891$	−8.84845e7	−	8.84845e7i	−0.125093	−	0.125093i
$892$	1.09910e9	−	4.33035e8i	1.54861	−	0.610139i
$893$	−6.09804e8	−	6.09804e8i	−0.856319	−	0.856319i
$894$	−4.69897e7	−	3.19918e7i	−0.0657643	−	0.0447740i
$895$			1.05749e7i			0.0147506i
$896$	5.80304e8	−	3.38613e8i	0.806736	−	0.470738i
$897$	6.85029e8			0.949143
$898$	−3.11532e8	+	4.57581e8i	−0.430203	+	0.631886i
$899$	−1.28642e8	+	1.28642e8i	−0.177053	+	0.177053i
$900$	−8.80964e7	−	2.23600e8i	−0.120846	−	0.306722i
$901$	−6.70539e8	+	6.70539e8i	−0.916747	+	0.916747i
$902$	2.99436e8	+	1.57687e9i	0.408022	+	2.14871i
$903$	−4.34060e8			−0.589504
$904$	−4.96225e7	−	1.12230e7i	−0.0671697	−	0.0151916i
$905$			4.94495e6i			0.00667138i
$906$	1.07418e7	+	5.65678e7i	0.0144441	+	0.0760650i
$907$	3.83442e8	+	3.83442e8i	0.513900	+	0.513900i	0.915719	−	0.401819i	$-0.131622\pi$
$907$	3.83442e8	+	3.83442e8i	0.513900	+	0.513900i	−0.401819	+	0.915719i	$0.631622\pi$
$908$	1.93812e8	+	8.42560e7i	0.258895	+	0.112549i
$909$	−2.87469e8	−	2.87469e8i	−0.382737	−	0.382737i
$910$	−6.80745e7	+	9.99883e7i	−0.0903359	+	0.132686i
$911$			8.08876e8i			1.06986i	0.844896	+	0.534930i	$0.179662\pi$
$911$			8.08876e8i			1.06986i	−0.844896	+	0.534930i	$0.820338\pi$
$912$	−2.99695e8	−	3.21294e8i	−0.395089	−	0.423563i
$913$	−1.08190e9			−1.42160
$914$	−7.60314e8	−	5.17641e8i	−0.995760	−	0.677938i
$915$	−2.86536e6	+	2.86536e6i	−0.00374038	+	0.00374038i
$916$	9.13703e8	+	3.97214e8i	1.18883	+	0.516818i
$917$	−2.96866e8	+	2.96866e8i	−0.384993	+	0.384993i
$918$	−2.15312e8	+	4.08860e7i	−0.278317	+	0.0528502i
$919$	−3.67372e8			−0.473326			−0.236663	−	0.971592i	$-0.576054\pi$
$919$	−3.67372e8			−0.473326			−0.236663	+	0.971592i	$0.576054\pi$
$920$	−6.92425e7	+	4.36989e7i	−0.0889220	+	0.0561186i
$921$		−	4.43061e8i		−	0.567133i
$922$	−1.23062e8	+	2.33685e7i	−0.157011	+	0.0298152i
$923$	6.09626e8	+	6.09626e8i	0.775280	+	0.775280i
$924$	2.48291e8	+	6.30195e8i	0.314735	+	0.798838i
$925$	−1.48988e7	−	1.48988e7i	−0.0188246	−	0.0188246i
$926$	−3.04488e8	−	2.07303e8i	−0.383475	−	0.261079i
$927$			1.55568e8i			0.195290i
$928$	2.61016e8	−	3.56111e8i	0.326605	−	0.445596i
$929$	1.50587e9			1.87819			0.939097	−	0.343653i	$-0.111664\pi$
$929$	1.50587e9			1.87819			0.939097	+	0.343653i	$0.111664\pi$
$930$	1.24185e7	−	1.82404e7i	0.0154391	−	0.0226770i
$931$	7.30356e7	−	7.30356e7i	0.0905077	−	0.0905077i
$932$	−5.11613e8	+	2.01571e8i	−0.631966	+	0.248989i
$933$	−5.33423e8	+	5.33423e8i	−0.656791	+	0.656791i
$934$	−3.77311e7	−	1.98698e8i	−0.0463083	−	0.243866i
$935$	2.00854e8			0.245722
$936$	3.78906e8	−	2.39128e8i	0.462066	−	0.291610i
$937$		−	5.87413e8i		−	0.714044i	−0.934096	−	0.357022i	$-0.883792\pi$
$937$		−	5.87413e8i		−	0.714044i	0.934096	−	0.357022i	$-0.116208\pi$
$938$	1.14536e8	+	6.03165e8i	0.138782	+	0.730849i
$939$	−3.19423e8	−	3.19423e8i	−0.385807	−	0.385807i
$940$	−4.19079e7	+	9.63999e7i	−0.0504559	+	0.116063i
$941$	−8.18451e8	−	8.18451e8i	−0.982253	−	0.982253i	0.0175918	−	0.999845i	$-0.494400\pi$
$941$	−8.18451e8	−	8.18451e8i	−0.982253	−	0.982253i	−0.999845	+	0.0175918i	$0.994400\pi$
$942$	−6.84769e7	+	1.00579e8i	−0.0819203	+	0.120325i
$943$		−	1.15526e9i		−	1.37767i
$944$	4.57174e8	+	1.59010e7i	0.543457	+	0.0189020i
$945$	−1.59043e7			−0.0188460
$946$	−1.21801e9	−	8.29251e8i	−1.43872	−	0.979518i
$947$	−5.49457e8	+	5.49457e8i	−0.646970	+	0.646970i	−0.952259	−	0.305290i	$-0.901247\pi$
$947$	−5.49457e8	+	5.49457e8i	−0.646970	+	0.646970i	0.305290	+	0.952259i	$0.401247\pi$
$948$	2.27616e8	−	5.23581e8i	0.267164	−	0.614552i
$949$	1.70285e9	−	1.70285e9i	1.99241	−	1.99241i
$950$	8.35769e8	−	1.58706e8i	0.974799	−	0.185107i
$951$	7.33998e8			0.853401
$952$	1.15706e9	+	2.61688e8i	1.34105	+	0.303300i
$953$			2.49315e8i			0.288051i	0.989574	+	0.144026i	$0.0460048\pi$
$953$			2.49315e8i			0.288051i	−0.989574	+	0.144026i	$0.953995\pi$
$954$	2.50428e8	−	4.75542e7i	0.288428	−	0.0547701i
$955$	9.63955e7	+	9.63955e7i	0.110674	+	0.110674i
$956$	9.37598e7	−	3.69405e7i	0.107311	−	0.0422795i
$957$	3.14748e8	+	3.14748e8i	0.359109	+	0.359109i
$958$	1.78497e8	+	1.21525e8i	0.203018	+	0.138220i
$959$		−	8.16792e8i		−	0.926095i
$960$	−2.30455e7	+	4.83419e7i	−0.0260479	+	0.0546399i
$961$	7.05205e8			0.794594
$962$	2.21068e7	−	3.24707e7i	0.0248314	−	0.0364725i
$963$	1.66561e8	−	1.66561e8i	0.186507	−	0.186507i
$964$	−3.61282e8	−	9.16981e8i	−0.403288	−	1.02360i
$965$	−2.02191e7	+	2.02191e7i	−0.0224999	+	0.0224999i
$966$	−9.09527e7	−	4.78971e8i	−0.100898	−	0.531346i
$967$	−1.57264e9			−1.73920			−0.869600	−	0.493756i	$-0.835623\pi$
$967$	−1.57264e9			−1.73920			−0.869600	+	0.493756i	$0.835623\pi$
$968$	−3.07142e8	+	1.35803e9i	−0.338620	+	1.49721i
$969$		−	7.75769e8i		−	0.852631i
$970$	2.54096e7	+	1.33811e8i	0.0278409	+	0.146614i
$971$	2.68210e8	+	2.68210e8i	0.292966	+	0.292966i	0.838251	−	0.545285i	$-0.183579\pi$
$971$	2.68210e8	+	2.68210e8i	0.292966	+	0.292966i	−0.545285	+	0.838251i	$0.683579\pi$
$972$	5.40265e7	+	2.34869e7i	0.0588312	+	0.0255757i
$973$	7.56107e8	+	7.56107e8i	0.820814	+	0.820814i
$974$	−1.87663e8	+	2.75641e8i	−0.203096	+	0.298309i
$975$			8.67515e8i			0.935972i
$976$	−8.11968e7	−	2.82411e6i	−0.0873352	−	0.00303761i
$977$	−1.62967e9			−1.74750			−0.873749	−	0.486376i	$-0.838318\pi$
$977$	−1.62967e9			−1.74750			−0.873749	+	0.486376i	$0.838318\pi$
$978$	−4.01939e8	−	2.73650e8i	−0.429678	−	0.292536i
$979$	−1.52316e8	+	1.52316e8i	−0.162329	+	0.162329i
$980$	−1.15457e7	−	5.01926e6i	−0.0122671	−	0.00533288i
$981$	−3.17467e8	+	3.17467e8i	−0.336272	+	0.336272i
$982$	−7.81421e7	+	1.48386e7i	−0.0825183	+	0.0156696i
$983$	1.52921e9			1.60993			0.804967	−	0.593320i	$-0.202183\pi$
$983$	1.52921e9			1.60993			0.804967	+	0.593320i	$0.202183\pi$
$984$	−4.03276e8	−	6.39005e8i	−0.423269	−	0.670686i
$985$			9.64121e7i			0.100884i
$986$	7.65885e8	−	1.45436e8i	0.798974	−	0.151719i
$987$	−4.42569e8	−	4.42569e8i	−0.460288	−	0.460288i
$988$	5.81373e8	+	1.47560e9i	0.602815	+	1.53002i
$989$	7.49942e8	+	7.49942e8i	0.775245	+	0.775245i
$990$	−4.46288e7	−	3.03844e7i	−0.0459949	−	0.0313145i
$991$		−	5.68031e8i		−	0.583648i	−0.956472	−	0.291824i	$-0.905738\pi$
$991$		−	5.68031e8i		−	0.583648i	0.956472	−	0.291824i	$-0.0942622\pi$
$992$	4.37266e8	−	6.73798e7i	0.447931	−	0.0690231i
$993$	−2.07631e8			−0.212053
$994$	3.45308e8	−	5.07191e8i	0.351599	−	0.516431i
$995$	−1.31321e8	+	1.31321e8i	−0.133310	+	0.133310i
$996$	4.73880e8	−	1.86704e8i	0.479612	−	0.188963i
$997$	−2.71452e7	+	2.71452e7i	−0.0273910	+	0.0273910i	−0.720670	−	0.693279i	$-0.756166\pi$
$997$	−2.71452e7	+	2.71452e7i	−0.0273910	+	0.0273910i	0.693279	+	0.720670i	$0.256166\pi$
$998$	−7.37162e7	−	3.88201e8i	−0.0741603	−	0.390539i
$999$	5.16484e6			0.00518036

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.7.l.a.19.7	✓	48
4.3	odd	2		192.7.l.a.175.7		48
8.3	odd	2		384.7.l.a.223.18		48
8.5	even	2		384.7.l.b.223.7		48
16.3	odd	4		384.7.l.b.31.7		48
16.5	even	4		192.7.l.a.79.7		48
16.11	odd	4	inner	48.7.l.a.43.7	yes	48
16.13	even	4		384.7.l.a.31.18		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.7.l.a.19.7	✓	48	1.1	even	1	trivial
48.7.l.a.43.7	yes	48	16.11	odd	4	inner
192.7.l.a.79.7		48	16.5	even	4
192.7.l.a.175.7		48	4.3	odd	2
384.7.l.a.31.18		48	16.13	even	4
384.7.l.a.223.18		48	8.3	odd	2
384.7.l.b.31.7		48	16.3	odd	4
384.7.l.b.223.7		48	8.5	even	2

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:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	48.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.50221 + 6.61288i) q^{2} +(11.0227 - 11.0227i) q^{3} +(-23.4602 - 59.5451i) q^{4} +(-9.26689 + 9.26689i) q^{5} +(23.2652 + 122.518i) q^{6} -320.373 q^{7} +(499.387 + 112.945i) q^{8} -243.000i q^{9} +O(q^{10})\)	\(q+(-4.50221 + 6.61288i) q^{2} +(11.0227 - 11.0227i) q^{3} +(-23.4602 - 59.5451i) q^{4} +(-9.26689 + 9.26689i) q^{5} +(23.2652 + 122.518i) q^{6} -320.373 q^{7} +(499.387 + 112.945i) q^{8} -243.000i q^{9} +(-19.5593 - 103.002i) q^{10} +(1498.49 + 1498.49i) q^{11} +(-914.943 - 397.753i) q^{12} +(2546.47 + 2546.47i) q^{13} +(1442.39 - 2118.59i) q^{14} +204.292i q^{15} +(-2995.24 + 2793.88i) q^{16} -7232.04 q^{17} +(1606.93 + 1094.04i) q^{18} +(-4865.79 + 4865.79i) q^{19} +(769.201 + 334.394i) q^{20} +(-3531.38 + 3531.38i) q^{21} +(-16655.9 + 3162.82i) q^{22} +12202.6 q^{23} +(6749.55 - 4259.64i) q^{24} +15453.2i q^{25} +(-28304.2 + 5374.75i) q^{26} +(-2678.52 - 2678.52i) q^{27} +(7516.03 + 19076.7i) q^{28} +(9527.74 + 9527.74i) q^{29} +(-1350.96 - 919.767i) q^{30} +13501.8i q^{31} +(-4990.43 - 32385.8i) q^{32} +33034.9 q^{33} +(32560.2 - 47824.6i) q^{34} +(2968.86 - 2968.86i) q^{35} +(-14469.5 + 5700.84i) q^{36} +(-964.122 + 964.122i) q^{37} +(-10270.1 - 54083.7i) q^{38} +56138.0 q^{39} +(-5674.41 + 3581.12i) q^{40} -94673.7i q^{41} +(-7453.56 - 39251.6i) q^{42} +(61457.6 + 61457.6i) q^{43} +(54072.9 - 124383. i) q^{44} +(2251.85 + 2251.85i) q^{45} +(-54938.6 + 80694.2i) q^{46} +125325. i q^{47} +(-2219.44 + 63811.7i) q^{48} -15010.0 q^{49} +(-102190. - 69573.8i) q^{50} +(-79716.7 + 79716.7i) q^{51} +(91889.1 - 211371. i) q^{52} +(92717.8 - 92717.8i) q^{53} +(29771.9 - 5653.46i) q^{54} -27772.7 q^{55} +(-159990. - 36184.5i) q^{56} +107268. i q^{57} +(-105902. + 20109.9i) q^{58} +(-78971.2 - 78971.2i) q^{59} +(12164.6 - 4792.75i) q^{60} +(14025.8 + 14025.8i) q^{61} +(-89285.7 - 60787.9i) q^{62} +77850.7i q^{63} +(236631. + 112806. i) q^{64} -47195.8 q^{65} +(-148730. + 218456. i) q^{66} +(-169382. + 169382. i) q^{67} +(169665. + 430633. i) q^{68} +(134506. - 134506. i) q^{69} +(6266.28 + 32999.2i) q^{70} +239400. q^{71} +(27445.6 - 121351. i) q^{72} -668710. i q^{73} +(-2034.94 - 10716.3i) q^{74} +(170337. + 170337. i) q^{75} +(403887. + 175581. i) q^{76} +(-480077. - 480077. i) q^{77} +(-252745. + 371234. i) q^{78} +572255. i q^{79} +(1865.91 - 53647.1i) q^{80} -59049.0 q^{81} +(626065. + 426241. i) q^{82} +(-360998. + 360998. i) q^{83} +(293123. + 127429. i) q^{84} +(67018.6 - 67018.6i) q^{85} +(-683107. + 129717. i) q^{86} +210043. q^{87} +(579081. + 917575. i) q^{88} +101646. i q^{89} +(-25029.6 + 4752.91i) q^{90} +(-815821. - 815821. i) q^{91} +(-286276. - 726604. i) q^{92} +(148826. + 148826. i) q^{93} +(-828756. - 564238. i) q^{94} -90181.5i q^{95} +(-411987. - 301971. i) q^{96} -1.29911e6 q^{97} +(67578.2 - 99259.3i) q^{98} +(364134. - 364134. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 180 q^{4} - 1932 q^{8}+O(q^{10}) \) 48 * q - 180 * q^4 - 1932 * q^8	\( 48 q - 180 q^{4} - 1932 q^{8} + 744 q^{10} - 2720 q^{11} - 1944 q^{12} - 15388 q^{14} + 3744 q^{16} + 4860 q^{18} - 3936 q^{19} - 14000 q^{20} - 41184 q^{22} + 26240 q^{23} + 18468 q^{24} - 5300 q^{26} - 96120 q^{28} + 66400 q^{29} - 33048 q^{30} - 52960 q^{32} + 122208 q^{34} + 162336 q^{35} + 32076 q^{36} - 7200 q^{37} + 16968 q^{38} - 309072 q^{40} - 231660 q^{42} + 340704 q^{43} - 193192 q^{44} - 450264 q^{46} + 299376 q^{48} + 806736 q^{49} + 537764 q^{50} + 80352 q^{51} + 1126224 q^{52} + 443680 q^{53} + 78732 q^{54} + 232704 q^{55} - 420448 q^{56} - 1295664 q^{58} - 886144 q^{59} - 627912 q^{60} - 326496 q^{61} - 719652 q^{62} - 192024 q^{64} - 372832 q^{65} + 775656 q^{66} - 962112 q^{67} + 3197632 q^{68} + 541728 q^{69} + 642816 q^{70} + 534016 q^{71} + 82620 q^{72} - 4894836 q^{74} - 1073088 q^{75} - 3162552 q^{76} - 932960 q^{77} - 337284 q^{78} + 4668072 q^{80} - 2834352 q^{81} + 5077560 q^{82} - 2497760 q^{83} + 1312200 q^{84} - 372000 q^{85} + 4142928 q^{86} - 2794272 q^{88} - 507384 q^{90} + 775008 q^{91} - 9470992 q^{92} - 5050728 q^{94} + 1879200 q^{96} + 12708584 q^{98} - 660960 q^{99}+O(q^{100}) \) 48 * q - 180 * q^4 - 1932 * q^8 + 744 * q^10 - 2720 * q^11 - 1944 * q^12 - 15388 * q^14 + 3744 * q^16 + 4860 * q^18 - 3936 * q^19 - 14000 * q^20 - 41184 * q^22 + 26240 * q^23 + 18468 * q^24 - 5300 * q^26 - 96120 * q^28 + 66400 * q^29 - 33048 * q^30 - 52960 * q^32 + 122208 * q^34 + 162336 * q^35 + 32076 * q^36 - 7200 * q^37 + 16968 * q^38 - 309072 * q^40 - 231660 * q^42 + 340704 * q^43 - 193192 * q^44 - 450264 * q^46 + 299376 * q^48 + 806736 * q^49 + 537764 * q^50 + 80352 * q^51 + 1126224 * q^52 + 443680 * q^53 + 78732 * q^54 + 232704 * q^55 - 420448 * q^56 - 1295664 * q^58 - 886144 * q^59 - 627912 * q^60 - 326496 * q^61 - 719652 * q^62 - 192024 * q^64 - 372832 * q^65 + 775656 * q^66 - 962112 * q^67 + 3197632 * q^68 + 541728 * q^69 + 642816 * q^70 + 534016 * q^71 + 82620 * q^72 - 4894836 * q^74 - 1073088 * q^75 - 3162552 * q^76 - 932960 * q^77 - 337284 * q^78 + 4668072 * q^80 - 2834352 * q^81 + 5077560 * q^82 - 2497760 * q^83 + 1312200 * q^84 - 372000 * q^85 + 4142928 * q^86 - 2794272 * q^88 - 507384 * q^90 + 775008 * q^91 - 9470992 * q^92 - 5050728 * q^94 + 1879200 * q^96 + 12708584 * q^98 - 660960 * q^99

Introduction

L-functions

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