LMFDB - Embedded newform 42.10.e.d.37.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [42,10,Mod(25,42)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("42.25"); S:= CuspForms(chi, 10); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(42, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 10, names="a")

Level:	$ N $	$=$	$ 42 = 2 \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	42.e (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [6,48] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$21.6315051189$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 373x^{4} - 756x^{3} + 139129x^{2} - 140994x + 142884 $ x^6 + 373x^4 - 756x^3 + 139129x^2 - 140994x + 142884
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{8}\cdot 3\cdot 5^{2}\cdot 7^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			37.3
Root			$9.39252 - 16.2683i$ of defining polynomial
Character	$\chi$	$=$	42.37
Dual form			42.10.e.d.25.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(8.00000 - 13.8564i) q^{2} +(40.5000 + 70.1481i) q^{3} +(-128.000 - 221.703i) q^{4} +(1070.48 - 1854.13i) q^{5} +1296.00 q^{6} +(1163.76 - 6244.94i) q^{7} -4096.00 q^{8} +(-3280.50 + 5681.99i) q^{9} +(-17127.7 - 29666.1i) q^{10} +(38719.2 + 67063.6i) q^{11} +(10368.0 - 17957.9i) q^{12} -92014.0 q^{13} +(-77222.3 - 66085.1i) q^{14} +173418. q^{15} +(-32768.0 + 56755.8i) q^{16} +(-328781. - 569465. i) q^{17} +(52488.0 + 90911.9i) q^{18} +(371263. - 643047. i) q^{19} -548087. q^{20} +(485203. - 171285. i) q^{21} +1.23901e6 q^{22} +(3231.59 - 5597.28i) q^{23} +(-165888. - 287326. i) q^{24} +(-1.31530e6 - 2.27817e6i) q^{25} +(-736112. + 1.27498e6i) q^{26} -531441. q^{27} +(-1.53348e6 + 541344. i) q^{28} -2.55350e6 q^{29} +(1.38734e6 - 2.40295e6i) q^{30} +(-431646. - 747632. i) q^{31} +(524288. + 908093. i) q^{32} +(-3.13625e6 + 5.43215e6i) q^{33} -1.05210e7 q^{34} +(-1.03331e7 - 8.84286e6i) q^{35} +1.67962e6 q^{36} +(3.87152e6 - 6.70567e6i) q^{37} +(-5.94021e6 - 1.02888e7i) q^{38} +(-3.72657e6 - 6.45460e6i) q^{39} +(-4.38470e6 + 7.59451e6i) q^{40} +2.13515e7 q^{41} +(1.50823e6 - 8.09344e6i) q^{42} +1.01098e7 q^{43} +(9.91211e6 - 1.71683e7i) q^{44} +(7.02343e6 + 1.21649e7i) q^{45} +(-51705.5 - 89556.5i) q^{46} +(-1.31759e7 + 2.28213e7i) q^{47} -5.30842e6 q^{48} +(-3.76449e7 - 1.45352e7i) q^{49} -4.20897e7 q^{50} +(2.66312e7 - 4.61266e7i) q^{51} +(1.17778e7 + 2.03997e7i) q^{52} +(1.19254e7 + 2.06555e7i) q^{53} +(-4.25153e6 + 7.36386e6i) q^{54} +1.65793e8 q^{55} +(-4.76676e6 + 2.55793e7i) q^{56} +6.01447e7 q^{57} +(-2.04280e7 + 3.53823e7i) q^{58} +(-7.76530e7 - 1.34499e8i) q^{59} +(-2.21975e7 - 3.84472e7i) q^{60} +(-4.28559e7 + 7.42286e7i) q^{61} -1.38127e7 q^{62} +(3.16660e7 + 2.70990e7i) q^{63} +1.67772e7 q^{64} +(-9.84994e7 + 1.70606e8i) q^{65} +(5.01800e7 + 8.69144e7i) q^{66} +(1.11224e8 + 1.92646e8i) q^{67} +(-8.41678e7 + 1.45783e8i) q^{68} +523518. q^{69} +(-2.05195e8 + 7.24373e7i) q^{70} +2.65826e8 q^{71} +(1.34369e7 - 2.32734e7i) q^{72} +(1.87429e8 + 3.24637e8i) q^{73} +(-6.19443e7 - 1.07291e8i) q^{74} +(1.06539e8 - 1.84532e8i) q^{75} -1.90087e8 q^{76} +(4.63868e8 - 1.63753e8i) q^{77} -1.19250e8 q^{78} +(-4.81092e6 + 8.33275e6i) q^{79} +(7.01551e7 + 1.21512e8i) q^{80} +(-2.15234e7 - 3.72796e7i) q^{81} +(1.70812e8 - 2.95855e8i) q^{82} +5.90221e8 q^{83} +(-1.00080e8 - 8.56462e7i) q^{84} -1.40782e9 q^{85} +(8.08785e7 - 1.40086e8i) q^{86} +(-1.03417e8 - 1.79123e8i) q^{87} +(-1.58594e8 - 2.74692e8i) q^{88} +(2.74589e8 - 4.75603e8i) q^{89} +2.24750e8 q^{90} +(-1.07082e8 + 5.74622e8i) q^{91} -1.65458e6 q^{92} +(3.49633e7 - 6.05582e7i) q^{93} +(2.10814e8 + 3.65140e8i) q^{94} +(-7.94862e8 - 1.37674e9i) q^{95} +(-4.24673e7 + 7.35556e7i) q^{96} +6.67265e8 q^{97} +(-5.02565e8 + 4.05342e8i) q^{98} -5.08073e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 48 q^{2} + 243 q^{3} - 768 q^{4} + 361 q^{5} + 7776 q^{6} + 12509 q^{7} - 24576 q^{8} - 19683 q^{9} - 5776 q^{10} + 37799 q^{11} + 62208 q^{12} - 441172 q^{13} + 38752 q^{14} + 58482 q^{15} - 196608 q^{16}+ \cdots - 495998478 q^{99}+O(q^{100}) $ 6 * q + 48 * q^2 + 243 * q^3 - 768 * q^4 + 361 * q^5 + 7776 * q^6 + 12509 * q^7 - 24576 * q^8 - 19683 * q^9 - 5776 * q^10 + 37799 * q^11 + 62208 * q^12 - 441172 * q^13 + 38752 * q^14 + 58482 * q^15 - 196608 * q^16 - 781816 * q^17 + 314928 * q^18 - 620154 * q^19 - 184832 * q^20 + 817047 * q^21 + 1209568 * q^22 + 1204784 * q^23 - 995328 * q^24 - 4020946 * q^25 - 3529376 * q^26 - 3188646 * q^27 - 2582272 * q^28 - 10561070 * q^29 + 467856 * q^30 + 12838457 * q^31 + 3145728 * q^32 - 3061719 * q^33 - 25018112 * q^34 - 20450416 * q^35 + 10077696 * q^36 + 8014770 * q^37 + 9922464 * q^38 - 17867466 * q^39 - 1478656 * q^40 + 13006056 * q^41 + 16211664 * q^42 - 45086976 * q^43 + 9676544 * q^44 + 2368521 * q^45 - 19276544 * q^46 - 21473082 * q^47 - 31850496 * q^48 - 92935311 * q^49 - 128670272 * q^50 + 63327096 * q^51 + 56470016 * q^52 + 13685715 * q^53 - 25509168 * q^54 + 610214782 * q^55 - 51236864 * q^56 - 100464948 * q^57 - 84488560 * q^58 - 92528141 * q^59 - 7485696 * q^60 - 7516114 * q^61 + 410830624 * q^62 - 15890742 * q^63 + 100663296 * q^64 + 79637616 * q^65 + 48987504 * q^66 - 137325404 * q^67 - 200144896 * q^68 + 195175008 * q^69 + 33639760 * q^70 + 16380692 * q^71 + 80621568 * q^72 + 394016164 * q^73 - 128236320 * q^74 + 325696626 * q^75 + 317518848 * q^76 + 140332213 * q^77 - 571758912 * q^78 + 35090117 * q^79 + 23658496 * q^80 - 129140163 * q^81 + 104048448 * q^82 + 1913896010 * q^83 + 50222592 * q^84 - 823798640 * q^85 - 360695808 * q^86 - 427723335 * q^87 - 154824704 * q^88 - 855499686 * q^89 + 75792672 * q^90 - 1675912546 * q^91 - 616849408 * q^92 - 1039915017 * q^93 + 343569312 * q^94 - 2705508088 * q^95 - 254803968 * q^96 + 4021139590 * q^97 - 2185772400 * q^98 - 495998478 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/42\mathbb{Z}\right)^\times$.

$n$	$29$	$31$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	8.00000	−	13.8564i	0.353553	−	0.612372i
$2$	8.00000	−	13.8564i	0.353553	−	0.612372i
$3$	40.5000	+	70.1481i	0.288675	+	0.500000i
$3$	40.5000	+	70.1481i	0.288675	+	0.500000i
$4$	−128.000	−	221.703i	−0.250000	−	0.433013i
$5$	1070.48	−	1854.13i	0.765975	−	1.32671i	−0.173755	−	0.984789i	$-0.555590\pi$
$5$	1070.48	−	1854.13i	0.765975	−	1.32671i	0.939730	−	0.341918i	$-0.111077\pi$
$6$	1296.00			0.408248
$7$	1163.76	−	6244.94i	0.183199	−	0.983076i
$7$	1163.76	−	6244.94i	0.183199	−	0.983076i
$8$	−4096.00			−0.353553
$9$	−3280.50	+	5681.99i	−0.166667	+	0.288675i
$10$	−17127.7	−	29666.1i	−0.541626	−	0.938124i
$11$	38719.2	+	67063.6i	0.797368	+	1.38108i	0.921324	+	0.388795i	$0.127108\pi$
$11$	38719.2	+	67063.6i	0.797368	+	1.38108i	−0.123956	+	0.992288i	$0.539558\pi$
$12$	10368.0	−	17957.9i	0.144338	−	0.250000i
$13$	−92014.0			−0.893530			−0.446765	−	0.894651i	$-0.647424\pi$
$13$	−92014.0			−0.893530			−0.446765	+	0.894651i	$0.647424\pi$
$14$	−77222.3	−	66085.1i	−0.537238	−	0.459756i
$15$	173418.			0.884471
$16$	−32768.0	+	56755.8i	−0.125000	+	0.216506i
$17$	−328781.	−	569465.i	−0.954742	−	1.65366i	−0.734957	−	0.678113i	$-0.762798\pi$
$17$	−328781.	−	569465.i	−0.954742	−	1.65366i	−0.219785	−	0.975548i	$-0.570536\pi$
$18$	52488.0	+	90911.9i	0.117851	+	0.204124i
$19$	371263.	−	643047.i	0.653568	−	1.13201i	−0.328682	−	0.944441i	$-0.606605\pi$
$19$	371263.	−	643047.i	0.653568	−	1.13201i	0.982251	−	0.187573i	$-0.0600621\pi$
$20$	−548087.			−0.765975
$21$	485203.	−	171285.i	0.544423	−	0.192190i
$22$	1.23901e6			1.12765
$23$	3231.59	−	5597.28i	0.00240792	−	0.00417063i	−0.864819	−	0.502084i	$-0.832567\pi$
$23$	3231.59	−	5597.28i	0.00240792	−	0.00417063i	0.867227	+	0.497913i	$0.165900\pi$
$24$	−165888.	−	287326.i	−0.102062	−	0.176777i
$25$	−1.31530e6	−	2.27817e6i	−0.673435	−	1.16642i
$26$	−736112.	+	1.27498e6i	−0.315910	+	0.547173i
$27$	−531441.			−0.192450
$28$	−1.53348e6	+	541344.i	−0.471484	+	0.166442i
$29$	−2.55350e6			−0.670416			−0.335208	−	0.942144i	$-0.608807\pi$
$29$	−2.55350e6			−0.670416			−0.335208	+	0.942144i	$0.608807\pi$
$30$	1.38734e6	−	2.40295e6i	0.312708	−	0.541626i
$31$	−431646.	−	747632.i	−0.0839460	−	0.145399i	0.820996	−	0.570934i	$-0.193419\pi$
$31$	−431646.	−	747632.i	−0.0839460	−	0.145399i	−0.904942	+	0.425536i	$0.860086\pi$
$32$	524288.	+	908093.i	0.0883883	+	0.153093i
$33$	−3.13625e6	+	5.43215e6i	−0.460361	+	0.797368i
$34$	−1.05210e7			−1.35021
$35$	−1.03331e7	−	8.84286e6i	−1.16393	−	0.996062i
$36$	1.67962e6			0.166667
$37$	3.87152e6	−	6.70567e6i	0.339605	−	0.588213i	−0.644754	−	0.764390i	$-0.723040\pi$
$37$	3.87152e6	−	6.70567e6i	0.339605	−	0.588213i	0.984358	+	0.176178i	$0.0563733\pi$
$38$	−5.94021e6	−	1.02888e7i	−0.462143	−	0.800454i
$39$	−3.72657e6	−	6.45460e6i	−0.257940	−	0.446765i
$40$	−4.38470e6	+	7.59451e6i	−0.270813	+	0.469062i
$41$	2.13515e7			1.18005			0.590025	−	0.807385i	$-0.299118\pi$
$41$	2.13515e7			1.18005			0.590025	+	0.807385i	$0.299118\pi$
$42$	1.50823e6	−	8.09344e6i	0.0747905	−	0.401339i
$43$	1.01098e7			0.450957			0.225478	−	0.974248i	$-0.427606\pi$
$43$	1.01098e7			0.450957			0.225478	+	0.974248i	$0.427606\pi$
$44$	9.91211e6	−	1.71683e7i	0.398684	−	0.690541i
$45$	7.02343e6	+	1.21649e7i	0.255325	+	0.442236i
$46$	−51705.5	−	89556.5i	−0.00170265	−	0.00294908i
$47$	−1.31759e7	+	2.28213e7i	−0.393857	+	0.682180i	−0.992955	−	0.118496i	$-0.962193\pi$
$47$	−1.31759e7	+	2.28213e7i	−0.393857	+	0.682180i	0.599098	+	0.800676i	$0.295526\pi$
$48$	−5.30842e6			−0.144338
$49$	−3.76449e7	−	1.45352e7i	−0.932876	−	0.360196i
$50$	−4.20897e7			−0.952380
$51$	2.66312e7	−	4.61266e7i	0.551221	−	0.954742i
$52$	1.17778e7	+	2.03997e7i	0.223382	+	0.386910i
$53$	1.19254e7	+	2.06555e7i	0.207603	+	0.359578i	0.950959	−	0.309317i	$-0.100101\pi$
$53$	1.19254e7	+	2.06555e7i	0.207603	+	0.359578i	−0.743356	+	0.668896i	$0.766767\pi$
$54$	−4.25153e6	+	7.36386e6i	−0.0680414	+	0.117851i
$55$	1.65793e8			2.44306
$56$	−4.76676e6	+	2.55793e7i	−0.0647705	+	0.347570i
$57$	6.01447e7			0.754676
$58$	−2.04280e7	+	3.53823e7i	−0.237028	+	0.410544i
$59$	−7.76530e7	−	1.34499e8i	−0.834303	−	1.44506i	−0.894596	−	0.446875i	$-0.852537\pi$
$59$	−7.76530e7	−	1.34499e8i	−0.834303	−	1.44506i	0.0602929	−	0.998181i	$-0.480797\pi$
$60$	−2.21975e7	−	3.84472e7i	−0.221118	−	0.382987i
$61$	−4.28559e7	+	7.42286e7i	−0.396302	+	0.686415i	−0.993266	−	0.115853i	$-0.963040\pi$
$61$	−4.28559e7	+	7.42286e7i	−0.396302	+	0.686415i	0.596964	+	0.802268i	$0.296373\pi$
$62$	−1.38127e7			−0.118718
$63$	3.16660e7	+	2.70990e7i	0.253256	+	0.216731i
$64$	1.67772e7			0.125000
$65$	−9.84994e7	+	1.70606e8i	−0.684421	+	1.18545i
$66$	5.01800e7	+	8.69144e7i	0.325524	+	0.563825i
$67$	1.11224e8	+	1.92646e8i	0.674317	+	1.16795i	0.976668	+	0.214754i	$0.0688950\pi$
$67$	1.11224e8	+	1.92646e8i	0.674317	+	1.16795i	−0.302352	+	0.953196i	$0.597772\pi$
$68$	−8.41678e7	+	1.45783e8i	−0.477371	+	0.826831i
$69$	523518.			0.00278042
$70$	−2.05195e8	+	7.24373e7i	−1.02147	+	0.360596i
$71$	2.65826e8			1.24147			0.620734	−	0.784022i	$-0.286835\pi$
$71$	2.65826e8			1.24147			0.620734	+	0.784022i	$0.286835\pi$
$72$	1.34369e7	−	2.32734e7i	0.0589256	−	0.102062i
$73$	1.87429e8	+	3.24637e8i	0.772475	+	1.33797i	0.936203	+	0.351460i	$0.114315\pi$
$73$	1.87429e8	+	3.24637e8i	0.772475	+	1.33797i	−0.163728	+	0.986505i	$0.552352\pi$
$74$	−6.19443e7	−	1.07291e8i	−0.240137	−	0.415929i
$75$	1.06539e8	−	1.84532e8i	0.388808	−	0.673435i
$76$	−1.90087e8			−0.653568
$77$	4.63868e8	−	1.63753e8i	1.50379	−	0.530861i
$78$	−1.19250e8			−0.364782
$79$	−4.81092e6	+	8.33275e6i	−0.0138965	+	0.0240695i	−0.872890	−	0.487917i	$-0.837757\pi$
$79$	−4.81092e6	+	8.33275e6i	−0.0138965	+	0.0240695i	0.858994	+	0.511986i	$0.171090\pi$
$80$	7.01551e7	+	1.21512e8i	0.191494	+	0.331677i
$81$	−2.15234e7	−	3.72796e7i	−0.0555556	−	0.0962250i
$82$	1.70812e8	−	2.95855e8i	0.417211	−	0.722630i
$83$	5.90221e8			1.36510			0.682548	−	0.730841i	$-0.260872\pi$
$83$	5.90221e8			1.36510			0.682548	+	0.730841i	$0.260872\pi$
$84$	−1.00080e8	−	8.56462e7i	−0.219327	−	0.187694i
$85$	−1.40782e9			−2.92523
$86$	8.08785e7	−	1.40086e8i	0.159437	−	0.276153i
$87$	−1.03417e8	−	1.79123e8i	−0.193532	−	0.335208i
$88$	−1.58594e8	−	2.74692e8i	−0.281912	−	0.488286i
$89$	2.74589e8	−	4.75603e8i	0.463904	−	0.803506i	−0.535247	−	0.844696i	$-0.679781\pi$
$89$	2.74589e8	−	4.75603e8i	0.463904	−	0.803506i	0.999151	+	0.0411896i	$0.0131148\pi$
$90$	2.24750e8			0.361084
$91$	−1.07082e8	+	5.74622e8i	−0.163693	+	0.878407i
$92$	−1.65458e6			−0.00240792
$93$	3.49633e7	−	6.05582e7i	0.0484662	−	0.0839460i
$94$	2.10814e8	+	3.65140e8i	0.278499	+	0.482374i
$95$	−7.94862e8	−	1.37674e9i	−1.00123	−	1.73419i
$96$	−4.24673e7	+	7.35556e7i	−0.0510310	+	0.0883883i
$97$	6.67265e8			0.765289			0.382644	−	0.923896i	$-0.375013\pi$
$97$	6.67265e8			0.765289			0.382644	+	0.923896i	$0.375013\pi$
$98$	−5.02565e8	+	4.05342e8i	−0.550396	+	0.443919i
$99$	−5.08073e8			−0.531579
$100$	−3.36717e8	+	5.83211e8i	−0.336717	+	0.583211i
$101$	−7.45596e8	−	1.29141e9i	−0.712947	−	1.23486i	−0.963746	−	0.266821i	$-0.914027\pi$
$101$	−7.45596e8	−	1.29141e9i	−0.712947	−	1.23486i	0.250799	−	0.968039i	$-0.419307\pi$
$102$	−4.26100e8	−	7.38026e8i	−0.389772	−	0.675105i
$103$	−5.17697e8	+	8.96677e8i	−0.453219	+	0.784998i	−0.998584	−	0.0532006i	$-0.983058\pi$
$103$	−5.17697e8	+	8.96677e8i	−0.453219	+	0.784998i	0.545365	+	0.838199i	$0.316391\pi$
$104$	3.76889e8			0.315910
$105$	2.01817e8	−	1.08299e9i	0.162034	−	0.869503i
$106$	3.81614e8			0.293595
$107$	−6.40566e8	+	1.10949e9i	−0.472429	+	0.818272i	−0.999502	−	0.0315484i	$-0.989956\pi$
$107$	−6.40566e8	+	1.10949e9i	−0.472429	+	0.818272i	0.527073	+	0.849820i	$0.323290\pi$
$108$	6.80244e7	+	1.17822e8i	0.0481125	+	0.0833333i
$109$	−9.66590e7	−	1.67418e8i	−0.0655878	−	0.113601i	0.831367	−	0.555724i	$-0.187559\pi$
$109$	−9.66590e7	−	1.67418e8i	−0.0655878	−	0.113601i	−0.896955	+	0.442123i	$0.854226\pi$
$110$	1.32634e9	−	2.29729e9i	0.863751	−	1.49606i
$111$	6.27186e8			0.392142
$112$	3.16303e8	+	2.70684e8i	0.189942	+	0.162548i
$113$	2.50261e9			1.44391			0.721955	−	0.691940i	$-0.243244\pi$
$113$	2.50261e9			1.44391			0.721955	+	0.691940i	$0.243244\pi$
$114$	4.81157e8	−	8.33389e8i	0.266818	−	0.462143i
$115$	−6.91872e6	−	1.19836e7i	−0.00368880	−	0.00638920i
$116$	3.26848e8	+	5.66117e8i	0.167604	+	0.290299i
$117$	3.01852e8	−	5.22823e8i	0.148922	−	0.257940i
$118$	−2.48490e9			−1.17988
$119$	−3.93889e9	+	1.39049e9i	−1.80058	+	0.635635i
$120$	−7.10321e8			−0.312708
$121$	−1.81937e9	+	3.15125e9i	−0.771593	+	1.33644i
$122$	6.85694e8	+	1.18766e9i	0.280228	+	0.485369i
$123$	8.64734e8	+	1.49776e9i	0.340651	+	0.590025i
$124$	−1.10501e8	+	1.91394e8i	−0.0419730	+	0.0726993i
$125$	−1.45046e9			−0.531386
$126$	6.28823e8	−	2.21985e8i	0.222260	−	0.0784613i
$127$	1.61401e9			0.550540			0.275270	−	0.961367i	$-0.411233\pi$
$127$	1.61401e9			0.550540			0.275270	+	0.961367i	$0.411233\pi$
$128$	1.34218e8	−	2.32472e8i	0.0441942	−	0.0765466i
$129$	4.09447e8	+	7.09183e8i	0.130180	+	0.225478i
$130$	1.57599e9	+	2.72969e9i	0.483959	+	0.838241i
$131$	1.67488e9	−	2.90098e9i	0.496893	−	0.860644i	−0.503101	−	0.864228i	$-0.667808\pi$
$131$	1.67488e9	−	2.90098e9i	0.496893	−	0.860644i	0.999994	+	0.00358415i	$0.00114087\pi$
$132$	1.60576e9			0.460361
$133$	−3.58373e9	−	3.06687e9i	−0.993122	−	0.849891i
$134$	3.55918e9			0.953628
$135$	−5.68898e8	+	9.85360e8i	−0.147412	+	0.255325i
$136$	1.34669e9	+	2.33253e9i	0.337552	+	0.584658i
$137$	2.61593e9	+	4.53093e9i	0.634430	+	1.09887i	0.986636	+	0.162943i	$0.0520986\pi$
$137$	2.61593e9	+	4.53093e9i	0.634430	+	1.09887i	−0.352205	+	0.935923i	$0.614568\pi$
$138$	4.18814e6	−	7.25408e6i	0.000983027	−	0.00170265i
$139$	4.86927e9			1.10636			0.553181	−	0.833061i	$-0.313414\pi$
$139$	4.86927e9			1.10636			0.553181	+	0.833061i	$0.313414\pi$
$140$	−6.37842e8	+	3.42277e9i	−0.140326	+	0.753011i
$141$	−2.13449e9			−0.454787
$142$	2.12661e9	−	3.68340e9i	0.438925	−	0.760240i
$143$	−3.56271e9	−	6.17079e9i	−0.712472	−	1.23404i
$144$	−2.14991e8	−	3.72375e8i	−0.0416667	−	0.0721688i
$145$	−2.73347e9	+	4.73451e9i	−0.513522	+	0.889446i
$146$	5.99773e9			1.09244
$147$	−5.05002e8	−	3.22940e9i	−0.0892000	−	0.570418i
$148$	−1.98222e9			−0.339605
$149$	−4.28903e8	+	7.42882e8i	−0.0712888	+	0.123476i	−0.899466	−	0.436990i	$-0.856045\pi$
$149$	−4.28903e8	+	7.42882e8i	−0.0712888	+	0.123476i	0.828178	+	0.560466i	$0.189378\pi$
$150$	−1.70463e9	−	2.95251e9i	−0.274929	−	0.476190i
$151$	7.13023e8	+	1.23499e9i	0.111611	+	0.193316i	0.916420	−	0.400218i	$-0.131066\pi$
$151$	7.13023e8	+	1.23499e9i	0.111611	+	0.193316i	−0.804809	+	0.593534i	$0.797732\pi$
$152$	−1.52069e9	+	2.63392e9i	−0.231071	+	0.400227i
$153$	4.31426e9			0.636495
$154$	1.44191e9	−	7.73756e9i	0.206584	−	1.10856i
$155$	−1.84828e9			−0.257202
$156$	−9.54001e8	+	1.65238e9i	−0.128970	+	0.223382i
$157$	5.43197e9	+	9.40846e9i	0.713525	+	1.23586i	0.963526	+	0.267616i	$0.0862359\pi$
$157$	5.43197e9	+	9.40846e9i	0.713525	+	1.23586i	−0.250001	+	0.968246i	$0.580431\pi$
$158$	7.69746e7	+	1.33324e8i	0.00982632	+	0.0170197i
$159$	−9.65961e8	+	1.67309e9i	−0.119859	+	0.207603i
$160$	2.24496e9			0.270813
$161$	−3.11939e7	−	2.66950e7i	−0.00365892	−	0.00313122i
$162$	−6.88748e8			−0.0785674
$163$	4.46717e9	−	7.73737e9i	0.495665	−	0.858518i	−0.504322	−	0.863516i	$-0.668258\pi$
$163$	4.46717e9	−	7.73737e9i	0.495665	−	0.858518i	0.999988	+	0.00499805i	$0.00159094\pi$
$164$	−2.73299e9	−	4.73367e9i	−0.295012	−	0.510976i
$165$	6.71461e9	+	1.16300e10i	0.705250	+	1.22153i
$166$	4.72177e9	−	8.17834e9i	0.482634	−	0.835947i
$167$	−1.45791e10			−1.45046			−0.725231	−	0.688505i	$-0.758267\pi$
$167$	−1.45791e10			−1.45046			−0.725231	+	0.688505i	$0.758267\pi$
$168$	−1.98739e9	+	7.01581e8i	−0.192483	+	0.0679495i
$169$	−2.13792e9			−0.201605
$170$	−1.12625e10	+	1.95073e10i	−1.03423	+	1.79133i
$171$	2.43586e9	+	4.21903e9i	0.217856	+	0.377338i
$172$	−1.29406e9	−	2.24137e9i	−0.112739	−	0.195270i
$173$	1.95829e9	−	3.39186e9i	0.166215	−	0.287892i	−0.770871	−	0.636991i	$-0.780179\pi$
$173$	1.95829e9	−	3.39186e9i	0.166215	−	0.287892i	0.937086	+	0.349099i	$0.113512\pi$
$174$	−3.30933e9			−0.273696
$175$	−1.57577e10	+	5.56274e9i	−1.27005	+	0.448350i
$176$	−5.07500e9			−0.398684
$177$	6.28989e9	−	1.08944e10i	0.481685	−	0.834303i
$178$	−4.39343e9	−	7.60964e9i	−0.328030	−	0.568165i
$179$	−2.25086e9	−	3.89861e9i	−0.163874	−	0.283838i	0.772381	−	0.635160i	$-0.219066\pi$
$179$	−2.25086e9	−	3.89861e9i	−0.163874	−	0.283838i	−0.936255	+	0.351322i	$0.885732\pi$
$180$	1.79800e9	−	3.11423e9i	0.127662	−	0.221118i
$181$	6.07935e9			0.421021			0.210510	−	0.977592i	$-0.432487\pi$
$181$	6.07935e9			0.421021			0.210510	+	0.977592i	$0.432487\pi$
$182$	7.10554e9	+	6.08075e9i	0.480038	+	0.410805i
$183$	−6.94265e9			−0.457610
$184$	−1.32366e7	+	2.29265e7i	−0.000851327	+	0.00147454i
$185$	−8.28879e9	−	1.43566e10i	−0.520257	−	0.901112i
$186$	−5.59413e8	−	9.68931e8i	−0.0342708	−	0.0593588i
$187$	2.54602e10	−	4.40984e10i	1.52256	−	2.63716i
$188$	6.74604e9			0.393857
$189$	−6.18470e8	+	3.31882e9i	−0.0352566	+	0.189193i
$190$	−2.54356e10			−1.41596
$191$	4.49180e9	−	7.78003e9i	0.244214	−	0.422991i	−0.717696	−	0.696356i	$-0.754803\pi$
$191$	4.49180e9	−	7.78003e9i	0.244214	−	0.422991i	0.961910	+	0.273365i	$0.0881367\pi$
$192$	6.79477e8	+	1.17689e9i	0.0360844	+	0.0625000i
$193$	6.07803e9	+	1.05275e10i	0.315322	+	0.546154i	0.979506	−	0.201415i	$-0.0645540\pi$
$193$	6.07803e9	+	1.05275e10i	0.315322	+	0.546154i	−0.664184	+	0.747569i	$0.731221\pi$
$194$	5.33812e9	−	9.24589e9i	0.270570	−	0.468642i
$195$	−1.59569e10			−0.790301
$196$	1.59606e9	+	1.02065e10i	0.0772495	+	0.493996i
$197$	−2.25902e10			−1.06862			−0.534308	−	0.845290i	$-0.679428\pi$
$197$	−2.25902e10			−1.06862			−0.534308	+	0.845290i	$0.679428\pi$
$198$	−4.06458e9	+	7.04007e9i	−0.187942	+	0.325524i
$199$	−1.40098e9	−	2.42658e9i	−0.0633278	−	0.109687i	0.832623	−	0.553840i	$-0.186838\pi$
$199$	−1.40098e9	−	2.42658e9i	−0.0633278	−	0.109687i	−0.895951	+	0.444153i	$0.853505\pi$
$200$	5.38748e9	+	9.33138e9i	0.238095	+	0.412393i
$201$	−9.00918e9	+	1.56044e10i	−0.389317	+	0.674317i
$202$	−2.38591e10			−1.00826
$203$	−2.97166e9	+	1.59464e10i	−0.122819	+	0.659070i
$204$	−1.36352e10			−0.551221
$205$	2.28564e10	−	3.95884e10i	0.903888	−	1.56558i
$206$	8.28315e9	+	1.43468e10i	0.320474	+	0.555077i
$207$	2.12025e7	+	3.67238e7i	0.000802639	+	0.00139021i
$208$	3.01512e9	−	5.22233e9i	0.111691	−	0.193455i
$209$	5.75001e10			2.08454
$210$	−1.33918e10	−	1.14603e10i	−0.475172	−	0.406641i
$211$	1.43493e9			0.0498380			0.0249190	−	0.999689i	$-0.492067\pi$
$211$	1.43493e9			0.0498380			0.0249190	+	0.999689i	$0.492067\pi$
$212$	3.05291e9	−	5.28780e9i	0.103801	−	0.179789i
$213$	1.07660e10	+	1.86472e10i	0.358381	+	0.620734i
$214$	1.02491e10	+	1.77519e10i	0.334058	+	0.578605i
$215$	1.08224e10	−	1.87449e10i	0.345421	−	0.598287i
$216$	2.17678e9			0.0680414
$217$	−5.17125e9	+	1.82554e9i	−0.158317	+	0.0558884i
$218$	−3.09309e9			−0.0927552
$219$	−1.51818e10	+	2.62956e10i	−0.445988	+	0.772475i
$220$	−2.12215e10	−	3.67567e10i	−0.610764	−	1.05787i
$221$	3.02524e10	+	5.23987e10i	0.853090	+	1.47760i
$222$	5.01749e9	−	8.69055e9i	0.138643	−	0.240137i
$223$	−2.50519e9			−0.0678372			−0.0339186	−	0.999425i	$-0.510799\pi$
$223$	−2.50519e9			−0.0678372			−0.0339186	+	0.999425i	$0.510799\pi$
$224$	6.28113e9	−	2.21734e9i	0.166695	−	0.0588460i
$225$	1.72594e10			0.448956
$226$	2.00209e10	−	3.46772e10i	0.510499	−	0.884210i
$227$	−3.25982e9	−	5.64618e9i	−0.0814850	−	0.141136i	0.822403	−	0.568905i	$-0.192633\pi$
$227$	−3.25982e9	−	5.64618e9i	−0.0814850	−	0.141136i	−0.903888	+	0.427769i	$0.859300\pi$
$228$	−7.69852e9	−	1.33342e10i	−0.188669	−	0.326784i
$229$	2.69070e9	−	4.66043e9i	0.0646556	−	0.111987i	−0.831886	−	0.554947i	$-0.812738\pi$
$229$	2.69070e9	−	4.66043e9i	0.0646556	−	0.111987i	0.896541	+	0.442960i	$0.146072\pi$
$230$	−2.21399e8			−0.00521676
$231$	3.02736e10	+	2.59074e10i	0.699536	+	0.598646i
$232$	1.04591e10			0.237028
$233$	2.78378e10	−	4.82164e10i	0.618775	−	1.07175i	−0.370935	−	0.928659i	$-0.620963\pi$
$233$	2.78378e10	−	4.82164e10i	0.618775	−	1.07175i	0.989710	−	0.143091i	$-0.0457040\pi$
$234$	−4.82963e9	−	8.36517e9i	−0.105303	−	0.182391i
$235$	2.82090e10	+	4.88595e10i	0.603369	+	1.04507i
$236$	−1.98792e10	+	3.44317e10i	−0.417152	+	0.722528i
$237$	−7.79368e8			−0.0160463
$238$	−1.22439e10	+	6.57029e10i	−0.247357	+	1.32736i
$239$	−9.46283e10			−1.87599			−0.937995	−	0.346648i	$-0.887320\pi$
$239$	−9.46283e10			−1.87599			−0.937995	+	0.346648i	$0.887320\pi$
$240$	−5.68256e9	+	9.84249e9i	−0.110559	+	0.191494i
$241$	1.39422e10	+	2.41485e10i	0.266228	+	0.461120i	0.967885	−	0.251395i	$-0.0808893\pi$
$241$	1.39422e10	+	2.41485e10i	0.266228	+	0.461120i	−0.701657	+	0.712515i	$0.747556\pi$
$242$	2.91100e10	+	5.04200e10i	0.545598	+	0.945004i
$243$	1.74339e9	−	3.01964e9i	0.0320750	−	0.0555556i
$244$	2.19422e10			0.396302
$245$	−6.72484e10	+	5.42389e10i	−1.19243	+	0.961753i
$246$	2.76715e10			0.481753
$247$	−3.41614e10	+	5.91694e10i	−0.583983	+	1.01149i
$248$	1.76802e9	+	3.06230e9i	0.0296794	+	0.0514062i
$249$	2.39039e10	+	4.14028e10i	0.394069	+	0.682548i
$250$	−1.16037e10	+	2.00981e10i	−0.187873	+	0.325406i
$251$	3.03736e10			0.483019			0.241509	−	0.970398i	$-0.422358\pi$
$251$	3.03736e10			0.483019			0.241509	+	0.970398i	$0.422358\pi$
$252$	1.95467e9	−	1.04891e10i	0.0305331	−	0.163846i
$253$	5.00498e8			0.00767998
$254$	1.29121e10	−	2.23643e10i	0.194645	−	0.337135i
$255$	−5.70165e10	−	9.87555e10i	−0.844442	−	1.46262i
$256$	−2.14748e9	−	3.71955e9i	−0.0312500	−	0.0541266i
$257$	−4.50692e10	+	7.80621e10i	−0.644437	+	1.11620i	0.339994	+	0.940428i	$0.389575\pi$
$257$	−4.50692e10	+	7.80621e10i	−0.644437	+	1.11620i	−0.984431	+	0.175771i	$0.943758\pi$
$258$	1.31023e10			0.184102
$259$	−3.73710e10	−	3.19812e10i	−0.516043	−	0.441617i
$260$	5.04317e10			0.684421
$261$	8.37675e9	−	1.45090e10i	0.111736	−	0.193532i
$262$	−2.67981e10	−	4.64156e10i	−0.351356	−	0.608567i
$263$	−4.06474e10	−	7.04033e10i	−0.523880	−	0.907386i	−0.999614	−	0.0277971i	$-0.991151\pi$
$263$	−4.06474e10	−	7.04033e10i	−0.523880	−	0.907386i	0.475734	−	0.879589i	$-0.342183\pi$
$264$	1.28461e10	−	2.22501e10i	0.162762	−	0.281912i
$265$	5.10639e10			0.636074
$266$	−7.11656e10	+	2.51226e10i	−0.871571	+	0.307679i
$267$	4.44835e10			0.535671
$268$	2.84735e10	−	4.93175e10i	0.337158	−	0.583975i
$269$	−5.35167e10	−	9.26936e10i	−0.623166	−	1.07935i	−0.988892	−	0.148633i	$-0.952513\pi$
$269$	−5.35167e10	−	9.26936e10i	−0.623166	−	1.07935i	0.365727	−	0.930722i	$-0.380821\pi$
$270$	9.10237e9	+	1.57658e10i	0.104236	+	0.180542i
$271$	3.35168e10	−	5.80527e10i	0.377485	−	0.653824i	−0.613210	−	0.789920i	$-0.710122\pi$
$271$	3.35168e10	−	5.80527e10i	0.377485	−	0.653824i	0.990696	+	0.136096i	$0.0434555\pi$
$272$	4.30939e10			0.477371
$273$	−4.46454e10	+	1.57606e10i	−0.486458	+	0.171728i
$274$	8.37098e10			0.897220
$275$	1.01855e11	−	1.76418e11i	1.07395	−	1.86014i
$276$	−6.70103e7	−	1.16065e8i	−0.000695105	−	0.00120396i
$277$	7.05918e10	+	1.22269e11i	0.720436	+	1.24783i	0.960825	+	0.277155i	$0.0893916\pi$
$277$	7.05918e10	+	1.22269e11i	0.720436	+	1.24783i	−0.240389	+	0.970677i	$0.577275\pi$
$278$	3.89542e10	−	6.74706e10i	0.391158	−	0.677506i
$279$	5.66405e9			0.0559640
$280$	4.23246e10	+	3.62204e10i	0.411511	+	0.352161i
$281$	−7.98623e10			−0.764123			−0.382061	−	0.924137i	$-0.624786\pi$
$281$	−7.98623e10			−0.764123			−0.382061	+	0.924137i	$0.624786\pi$
$282$	−1.70759e10	+	2.95763e10i	−0.160791	+	0.278499i
$283$	−4.40429e10	−	7.62846e10i	−0.408166	−	0.706965i	0.586518	−	0.809936i	$-0.300498\pi$
$283$	−4.40429e10	−	7.62846e10i	−0.408166	−	0.706965i	−0.994684	+	0.102971i	$0.967165\pi$
$284$	−3.40258e10	−	5.89343e10i	−0.310367	−	0.537571i
$285$	6.43838e10	−	1.11516e11i	0.578062	−	1.00123i
$286$	−1.14007e11			−1.00759
$287$	2.48480e10	−	1.33339e11i	0.216184	−	1.16008i
$288$	−6.87971e9			−0.0589256
$289$	−1.56899e11	+	2.71758e11i	−1.32306	+	2.29162i
$290$	4.37356e10	+	7.57522e10i	0.363115	+	0.628933i
$291$	2.70242e10	+	4.68073e10i	0.220920	+	0.382644i
$292$	4.79819e10	−	8.31070e10i	0.386237	−	0.668983i
$293$	−7.12696e10			−0.564937			−0.282469	−	0.959277i	$-0.591153\pi$
$293$	−7.12696e10			−0.564937			−0.282469	+	0.959277i	$0.591153\pi$
$294$	−4.87878e10	−	1.88377e10i	−0.380845	−	0.147050i
$295$	−3.32505e11			−2.55622
$296$	−1.58577e10	+	2.74664e10i	−0.120068	+	0.207965i
$297$	−2.05770e10	−	3.56403e10i	−0.153454	−	0.265789i
$298$	6.86245e9	+	1.18861e10i	0.0504088	+	0.0873105i
$299$	−2.97352e8	+	5.15028e8i	−0.00215154	+	0.00372658i
$300$	−5.45482e10			−0.388808
$301$	1.17654e10	−	6.31351e10i	0.0826147	−	0.443325i
$302$	2.28167e10			0.157842
$303$	6.03933e10	−	1.04604e11i	0.411620	−	0.712947i
$304$	2.43311e10	+	4.21427e10i	0.163392	+	0.283003i
$305$	9.17529e10	+	1.58921e11i	0.607115	+	1.05155i
$306$	3.45141e10	−	5.97801e10i	0.225035	−	0.389772i
$307$	−1.31777e10			−0.0846677			−0.0423338	−	0.999104i	$-0.513479\pi$
$307$	−1.31777e10			−0.0846677			−0.0423338	+	0.999104i	$0.513479\pi$
$308$	−9.56795e10	−	8.18803e10i	−0.605816	−	0.518443i
$309$	−8.38669e10			−0.523332
$310$	−1.47862e10	+	2.56105e10i	−0.0909346	+	0.157503i
$311$	1.10435e11	+	1.91279e11i	0.669400	+	1.15943i	0.978072	+	0.208266i	$0.0667819\pi$
$311$	1.10435e11	+	1.91279e11i	0.669400	+	1.15943i	−0.308673	+	0.951168i	$0.599885\pi$
$312$	1.52640e10	+	2.64381e10i	0.0911955	+	0.157955i
$313$	1.50518e10	−	2.60704e10i	0.0886417	−	0.153532i	−0.818296	−	0.574798i	$-0.805081\pi$
$313$	1.50518e10	−	2.60704e10i	0.0886417	−	0.153532i	0.906937	+	0.421266i	$0.138414\pi$
$314$	1.73823e11			1.00908
$315$	8.41429e10	−	2.97038e10i	0.481526	−	0.169987i
$316$	2.46319e9			0.0138965
$317$	4.56593e10	−	7.90843e10i	0.253959	−	0.439869i	−0.710654	−	0.703542i	$-0.751601\pi$
$317$	4.56593e10	−	7.90843e10i	0.253959	−	0.439869i	0.964612	+	0.263673i	$0.0849340\pi$
$318$	1.54554e10	+	2.67695e10i	0.0847535	+	0.146797i
$319$	−9.88693e10	−	1.71247e11i	−0.534568	−	0.925900i
$320$	1.79597e10	−	3.11071e10i	0.0957468	−	0.165838i
$321$	−1.03772e11			−0.545514
$322$	−6.19448e8	+	2.18675e8i	−0.00321110	+	0.00113357i
$323$	−4.88257e11			−2.49596
$324$	−5.50998e9	+	9.54357e9i	−0.0277778	+	0.0481125i
$325$	1.21026e11	+	2.09624e11i	0.601734	+	1.04223i
$326$	−7.14748e10	−	1.23798e11i	−0.350488	−	0.607064i
$327$	7.82938e9	−	1.35609e10i	0.0378671	−	0.0655878i
$328$	−8.74556e10			−0.417211
$329$	1.27184e11	+	1.08841e11i	0.598481	+	0.512166i
$330$	2.14867e11			0.997373
$331$	−7.24179e10	+	1.25432e11i	−0.331604	+	0.574356i	−0.982827	−	0.184531i	$-0.940923\pi$
$331$	−7.24179e10	+	1.25432e11i	−0.331604	+	0.574356i	0.651222	+	0.758887i	$0.274257\pi$
$332$	−7.55483e10	−	1.30853e11i	−0.341274	−	0.591104i
$333$	2.54010e10	+	4.39959e10i	0.113202	+	0.196071i
$334$	−1.16633e11	+	2.02014e11i	−0.512816	+	0.888223i
$335$	4.76255e11			2.06604
$336$	−6.17772e9	+	3.31507e10i	−0.0264425	+	0.141895i
$337$	4.40381e11			1.85992			0.929959	−	0.367664i	$-0.119842\pi$
$337$	4.40381e11			1.85992			0.929959	+	0.367664i	$0.119842\pi$
$338$	−1.71034e10	+	2.96239e10i	−0.0712781	+	0.123457i
$339$	1.01356e11	+	1.75553e11i	0.416821	+	0.721955i
$340$	1.80200e11	+	3.12116e11i	0.731308	+	1.26666i
$341$	3.34259e10	−	5.78954e10i	0.133872	−	0.231873i
$342$	7.79475e10			0.308095
$343$	−1.34581e11	+	2.18175e11i	−0.525002	+	0.851101i
$344$	−4.14098e10			−0.159437
$345$	5.60417e8	−	9.70670e8i	0.00212973	−	0.00368880i
$346$	−3.13326e10	−	5.42697e10i	−0.117531	−	0.203571i
$347$	−6.60794e10	−	1.14453e11i	−0.244672	−	0.423784i	0.717368	−	0.696695i	$-0.245347\pi$
$347$	−6.60794e10	−	1.14453e11i	−0.244672	−	0.423784i	−0.962039	+	0.272911i	$0.912014\pi$
$348$	−2.64747e10	+	4.58555e10i	−0.0967662	+	0.167604i
$349$	1.26079e11			0.454911			0.227456	−	0.973788i	$-0.426959\pi$
$349$	1.26079e11			0.454911			0.227456	+	0.973788i	$0.426959\pi$
$350$	−4.89823e10	+	2.62847e11i	−0.174475	+	0.936262i
$351$	4.89000e10			0.171960
$352$	−4.06000e10	+	7.03213e10i	−0.140956	+	0.244143i
$353$	1.44777e11	+	2.50762e11i	0.496266	+	0.859557i	0.999991	−	0.00430667i	$-0.00137086\pi$
$353$	1.44777e11	+	2.50762e11i	0.496266	+	0.859557i	−0.503725	+	0.863864i	$0.668038\pi$
$354$	−1.00638e11	−	1.74311e11i	−0.340603	−	0.589942i
$355$	2.84562e11	−	4.92876e11i	0.950933	−	1.64706i
$356$	−1.40590e11			−0.463904
$357$	−2.57066e11	−	2.19991e11i	−0.837601	−	0.716799i
$358$	−7.20276e10			−0.231753
$359$	−1.05817e11	+	1.83280e11i	−0.336225	+	0.582359i	−0.983719	−	0.179711i	$-0.942484\pi$
$359$	−1.05817e11	+	1.83280e11i	−0.336225	+	0.582359i	0.647494	+	0.762070i	$0.275817\pi$
$360$	−2.87680e10	−	4.98276e10i	−0.0902710	−	0.156354i
$361$	−1.14329e11	−	1.98024e11i	−0.354303	−	0.613671i
$362$	4.86348e10	−	8.42379e10i	0.148853	−	0.257821i
$363$	−2.94739e11			−0.890958
$364$	1.41102e11	−	4.98112e10i	0.421285	−	0.148721i
$365$	8.02558e11			2.36678
$366$	−5.55412e10	+	9.62002e10i	−0.161790	+	0.280228i
$367$	3.00433e11	+	5.20365e11i	0.864471	+	1.49731i	0.867572	+	0.497312i	$0.165680\pi$
$367$	3.00433e11	+	5.20365e11i	0.864471	+	1.49731i	−0.00310083	+	0.999995i	$0.500987\pi$
$368$	2.11786e8	+	3.66823e8i	0.000601979	+	0.00104266i
$369$	−7.00435e10	+	1.21319e11i	−0.196675	+	0.340651i
$370$	−2.65241e11			−0.735755
$371$	1.42871e11	−	5.04356e10i	0.391525	−	0.138215i
$372$	−1.79012e10			−0.0484662
$373$	7.00479e10	−	1.21326e11i	0.187372	−	0.324538i	−0.757001	−	0.653414i	$-0.773336\pi$
$373$	7.00479e10	−	1.21326e11i	0.187372	−	0.324538i	0.944373	+	0.328875i	$0.106670\pi$
$374$	−4.07364e11	−	7.05575e11i	−1.07661	−	1.86475i
$375$	−5.87435e10	−	1.01747e11i	−0.153398	−	0.265693i
$376$	5.39683e10	−	9.34759e10i	0.139249	−	0.241187i
$377$	2.34958e11			0.599037
$378$	4.10391e10	+	3.51203e10i	0.103392	+	0.0884800i
$379$	−5.87185e11			−1.46183			−0.730917	−	0.682466i	$-0.760907\pi$
$379$	−5.87185e11			−1.46183			−0.730917	+	0.682466i	$0.760907\pi$
$380$	−2.03485e11	+	3.52446e11i	−0.500617	+	0.867094i
$381$	6.53673e10	+	1.13219e11i	0.158927	+	0.275270i
$382$	−7.18689e10	−	1.24481e11i	−0.172685	−	0.299100i
$383$	−1.94963e11	+	3.37685e11i	−0.462975	+	0.801895i	−0.999108	−	0.0422381i	$-0.986551\pi$
$383$	−1.94963e11	+	3.37685e11i	−0.462975	+	0.801895i	0.536133	+	0.844134i	$0.319885\pi$
$384$	2.17433e10			0.0510310
$385$	1.92943e11	−	1.03537e12i	0.447565	−	2.40171i
$386$	1.94497e11			0.445933
$387$	−3.31652e10	+	5.74438e10i	−0.0751594	+	0.130180i
$388$	−8.54099e10	−	1.47934e11i	−0.191322	−	0.331380i
$389$	−6.76642e10	−	1.17198e11i	−0.149826	−	0.259506i	0.781337	−	0.624109i	$-0.214538\pi$
$389$	−6.76642e10	−	1.17198e11i	−0.149826	−	0.259506i	−0.931163	+	0.364603i	$0.881205\pi$
$390$	−1.27655e11	+	2.21105e11i	−0.279414	+	0.483959i
$391$	−4.24994e9			−0.00919575
$392$	1.54194e11	+	5.95363e10i	0.329822	+	0.127349i
$393$	2.71330e11			0.573762
$394$	−1.80721e11	+	3.13019e11i	−0.377813	+	0.654391i
$395$	1.03000e10	+	1.78401e10i	0.0212888	+	0.0368732i
$396$	6.50333e10	+	1.12641e11i	0.132895	+	0.230180i
$397$	−3.85624e11	+	6.67920e11i	−0.779124	+	1.34948i	0.153324	+	0.988176i	$0.451002\pi$
$397$	−3.85624e11	+	6.67920e11i	−0.779124	+	1.34948i	−0.932447	+	0.361306i	$0.882331\pi$
$398$	−4.48315e10			−0.0895590
$399$	6.99940e10	−	3.75600e11i	0.138256	−	0.741903i
$400$	1.72399e11			0.336717
$401$	5.59446e10	−	9.68988e10i	0.108046	−	0.187141i	−0.806933	−	0.590643i	$-0.798874\pi$
$401$	5.59446e10	−	9.68988e10i	0.108046	−	0.187141i	0.914979	+	0.403502i	$0.132207\pi$
$402$	1.44147e11	+	2.49670e11i	0.275289	+	0.476814i
$403$	3.97175e10	+	6.87926e10i	0.0750082	+	0.129918i
$404$	−1.90873e11	+	3.30601e11i	−0.356474	+	0.617430i
$405$	−9.21615e10			−0.170217
$406$	1.97187e11	+	1.68748e11i	0.360173	+	0.308228i
$407$	5.99608e11			1.08316
$408$	−1.09082e11	+	1.88935e11i	−0.194886	+	0.337552i
$409$	−5.18709e11	−	8.98430e11i	−0.916576	−	1.58756i	−0.804577	−	0.593848i	$-0.797608\pi$
$409$	−5.18709e11	−	8.98430e11i	−0.916576	−	1.58756i	−0.111999	−	0.993708i	$-0.535725\pi$
$410$	−3.65702e11	−	6.33414e11i	−0.639145	−	1.10703i
$411$	−2.11890e11	+	3.67005e11i	−0.366288	+	0.634430i
$412$	2.65061e11			0.453219
$413$	−9.30307e11	+	3.28414e11i	−1.57344	+	0.555451i
$414$	6.78479e8			0.00113510
$415$	6.31821e11	−	1.09435e12i	1.04563	−	1.81108i
$416$	−4.82418e10	−	8.35573e10i	−0.0789776	−	0.136793i
$417$	1.97206e11	+	3.41570e11i	0.319379	+	0.553181i
$418$	4.60000e11	−	7.96744e11i	0.736996	−	1.27651i
$419$	−3.17331e11			−0.502978			−0.251489	−	0.967860i	$-0.580920\pi$
$419$	−3.17331e11			−0.502978			−0.251489	+	0.967860i	$0.580920\pi$
$420$	−2.65933e11	+	9.38788e10i	−0.417014	+	0.147213i
$421$	−7.33305e11			−1.13767			−0.568833	−	0.822453i	$-0.692605\pi$
$421$	−7.33305e11			−1.13767			−0.568833	+	0.822453i	$0.692605\pi$
$422$	1.14795e10	−	1.98830e10i	0.0176204	−	0.0305194i
$423$	−8.64468e10	−	1.49730e11i	−0.131286	−	0.227393i
$424$	−4.88466e10	−	8.46048e10i	−0.0733986	−	0.127130i
$425$	−8.64892e11	+	1.49804e12i	−1.28591	+	2.22727i
$426$	3.44511e11			0.506827
$427$	4.13679e11	+	3.54017e11i	0.602196	+	0.515345i
$428$	3.27970e11			0.472429
$429$	2.88579e11	−	4.99834e11i	0.411346	−	0.712472i
$430$	−1.73158e11	−	2.99918e11i	−0.244250	−	0.423053i
$431$	−6.55600e11	−	1.13553e12i	−0.915148	−	1.58508i	−0.806685	−	0.590982i	$-0.798740\pi$
$431$	−6.55600e11	−	1.13553e12i	−0.915148	−	1.58508i	−0.108463	−	0.994100i	$-0.534593\pi$
$432$	1.74143e10	−	3.01624e10i	0.0240563	−	0.0416667i
$433$	5.23536e11			0.715734			0.357867	−	0.933773i	$-0.383504\pi$
$433$	5.23536e11			0.715734			0.357867	+	0.933773i	$0.383504\pi$
$434$	−1.60746e10	+	8.62592e10i	−0.0217489	+	0.116708i
$435$	−4.42823e11			−0.592964
$436$	−2.47447e10	+	4.28591e10i	−0.0327939	+	0.0568007i
$437$	−2.39954e9	−	4.15613e9i	−0.00314747	−	0.00545159i
$438$	2.42908e11	+	4.20729e11i	0.315361	+	0.546222i
$439$	2.15186e11	−	3.72714e11i	0.276519	−	0.478945i	−0.693998	−	0.719977i	$-0.744153\pi$
$439$	2.15186e11	−	3.72714e11i	0.276519	−	0.478945i	0.970517	+	0.241032i	$0.0774859\pi$
$440$	−6.79087e11			−0.863751
$441$	2.06083e11	−	1.66215e11i	0.259459	−	0.209266i
$442$	9.68078e11			1.20645
$443$	−9.97795e10	+	1.72823e11i	−0.123091	+	0.213199i	−0.920985	−	0.389598i	$-0.872614\pi$
$443$	−9.97795e10	+	1.72823e11i	−0.123091	+	0.213199i	0.797894	+	0.602797i	$0.205947\pi$
$444$	−8.02799e10	−	1.39049e11i	−0.0980355	−	0.169802i
$445$	−5.87886e11	−	1.01825e12i	−0.710678	−	1.23093i
$446$	−2.00415e10	+	3.47129e10i	−0.0239841	+	0.0415417i
$447$	−6.94823e10			−0.0823172
$448$	1.95247e10	−	1.04773e11i	0.0228998	−	0.122884i
$449$	−1.34444e11			−0.156111			−0.0780555	−	0.996949i	$-0.524871\pi$
$449$	−1.34444e11			−0.156111			−0.0780555	+	0.996949i	$0.524871\pi$
$450$	1.38075e11	−	2.39153e11i	0.158730	−	0.274929i
$451$	8.26711e11	+	1.43191e12i	0.940934	+	1.62975i
$452$	−3.20334e11	−	5.54835e11i	−0.360977	−	0.625231i
$453$	−5.77549e10	+	1.00034e11i	−0.0644387	+	0.111611i
$454$	−1.04314e11			−0.115237
$455$	9.50794e11	+	8.13667e11i	1.04000	+	0.890011i
$456$	−2.46353e11			−0.266818
$457$	−1.05963e11	+	1.83534e11i	−0.113640	+	0.196831i	−0.917235	−	0.398346i	$-0.869584\pi$
$457$	−1.05963e11	+	1.83534e11i	−0.113640	+	0.196831i	0.803595	+	0.595176i	$0.202918\pi$
$458$	−4.30513e10	−	7.45670e10i	−0.0457184	−	0.0791866i
$459$	1.74728e11	+	3.02637e11i	0.183740	+	0.318247i
$460$	−1.77119e9	+	3.06780e9i	−0.00184440	+	0.00319460i
$461$	−1.04842e12			−1.08114			−0.540570	−	0.841299i	$-0.681791\pi$
$461$	−1.04842e12			−1.08114			−0.540570	+	0.841299i	$0.681791\pi$
$462$	6.01173e11	−	2.12224e11i	0.613918	−	0.216723i
$463$	4.22312e11			0.427089			0.213545	−	0.976933i	$-0.431499\pi$
$463$	4.22312e11			0.427089			0.213545	+	0.976933i	$0.431499\pi$
$464$	8.36730e10	−	1.44926e11i	0.0838020	−	0.145149i
$465$	−7.48552e10	−	1.29653e11i	−0.0742478	−	0.128601i
$466$	−4.45404e11	−	7.71463e11i	−0.437540	−	0.757841i
$467$	−2.43784e10	+	4.22246e10i	−0.0237180	+	0.0410808i	−0.877641	−	0.479319i	$-0.840884\pi$
$467$	−2.43784e10	+	4.22246e10i	−0.0237180	+	0.0410808i	0.853923	+	0.520400i	$0.174217\pi$
$468$	−1.54548e11			−0.148922
$469$	1.33250e12	−	4.70396e11i	1.27172	−	0.448937i
$470$	9.02689e11			0.853292
$471$	−4.39990e11	+	7.62085e11i	−0.411954	+	0.713525i
$472$	3.18067e11	+	5.50907e11i	0.294971	+	0.510904i
$473$	3.91443e11	+	6.78000e11i	0.359579	+	0.622808i
$474$	−6.23495e9	+	1.07992e10i	−0.00567323	+	0.00982632i
$475$	−1.95329e12			−1.76054
$476$	8.12455e11	+	6.95279e11i	0.725384	+	0.620766i
$477$	−1.56486e11			−0.138402
$478$	−7.57027e11	+	1.31121e12i	−0.663263	+	1.14881i
$479$	2.01070e11	+	3.48263e11i	0.174517	+	0.302272i	0.939994	−	0.341191i	$-0.110830\pi$
$479$	2.01070e11	+	3.48263e11i	0.174517	+	0.302272i	−0.765477	+	0.643463i	$0.777497\pi$
$480$	9.09210e10	+	1.57480e11i	0.0781770	+	0.135406i
$481$	−3.56234e11	+	6.17016e11i	−0.303447	+	0.525586i
$482$	4.46149e11			0.376503
$483$	6.09249e8	−	3.26934e9i	0.000509370	−	0.00273337i
$484$	9.31520e11			0.771593
$485$	7.14295e11	−	1.23720e12i	0.586192	−	1.01531i
$486$	−2.78943e10	−	4.83143e10i	−0.0226805	−	0.0392837i
$487$	−4.97415e11	−	8.61548e11i	−0.400718	−	0.694063i	0.593095	−	0.805132i	$-0.297906\pi$
$487$	−4.97415e11	−	8.61548e11i	−0.400718	−	0.694063i	−0.993813	+	0.111069i	$0.964572\pi$
$488$	1.75538e11	−	3.04040e11i	0.140114	−	0.242684i
$489$	7.23682e11			0.572345
$490$	2.13569e11	+	1.36573e12i	0.167361	+	1.07025i
$491$	1.77339e11			0.137702			0.0688508	−	0.997627i	$-0.478067\pi$
$491$	1.77339e11			0.137702			0.0688508	+	0.997627i	$0.478067\pi$
$492$	2.21372e11	−	3.83427e11i	0.170325	−	0.295012i
$493$	8.39540e11	+	1.45413e12i	0.640074	+	1.10864i
$494$	5.46583e11	+	9.46710e11i	0.412938	+	0.715230i
$495$	−5.43883e11	+	9.42033e11i	−0.407176	+	0.705250i
$496$	5.65767e10			0.0419730
$497$	3.09358e11	−	1.66007e12i	0.227435	−	1.22046i
$498$	7.64926e11			0.557298
$499$	5.12949e10	−	8.88454e10i	0.0370358	−	0.0641479i	−0.846913	−	0.531731i	$-0.821542\pi$
$499$	5.12949e10	−	8.88454e10i	0.0370358	−	0.0641479i	0.883949	+	0.467583i	$0.154875\pi$
$500$	1.85659e11	+	3.21570e11i	0.132846	+	0.230097i
$501$	−5.90454e11	−	1.02270e12i	−0.418713	−	0.725231i
$502$	2.42988e11	−	4.20868e11i	0.170773	−	0.295787i
$503$	2.35796e12			1.64241			0.821203	−	0.570637i	$-0.193304\pi$
$503$	2.35796e12			1.64241			0.821203	+	0.570637i	$0.193304\pi$
$504$	−1.29704e11	−	1.10998e11i	−0.0895397	−	0.0766259i
$505$	−3.19259e12			−2.18440
$506$	4.00399e9	−	6.93511e9i	0.00271528	−	0.00470301i
$507$	−8.65857e10	−	1.49971e11i	−0.0581983	−	0.100802i
$508$	−2.06593e11	−	3.57829e11i	−0.137635	−	0.238391i
$509$	−3.05373e11	+	5.28922e11i	−0.201651	+	0.349270i	−0.949061	−	0.315094i	$-0.897964\pi$
$509$	−3.05373e11	+	5.28922e11i	−0.201651	+	0.349270i	0.747409	+	0.664364i	$0.231297\pi$
$510$	−1.82453e12			−1.19422
$511$	2.24546e12	−	7.92684e11i	1.45684	−	0.514288i
$512$	−6.87195e10			−0.0441942
$513$	−1.97305e11	+	3.41742e11i	−0.125779	+	0.217856i
$514$	7.21107e11	+	1.24899e12i	0.455686	+	0.789271i
$515$	1.10837e12	+	1.91975e12i	0.694308	+	1.20258i
$516$	1.04818e11	−	1.81551e11i	0.0650900	−	0.112739i
$517$	−2.04063e12			−1.25620
$518$	−7.42112e11	+	2.61978e11i	−0.452883	+	0.159875i
$519$	3.17243e11			0.191928
$520$	4.03453e11	−	6.98802e11i	0.241979	−	0.419121i
$521$	−3.24713e11	−	5.62419e11i	−0.193077	−	0.334418i	0.753192	−	0.657801i	$-0.228513\pi$
$521$	−3.24713e11	−	5.62419e11i	−0.193077	−	0.334418i	−0.946268	+	0.323383i	$0.895180\pi$
$522$	−1.34028e11	−	2.32143e11i	−0.0790093	−	0.136848i
$523$	−8.23475e11	+	1.42630e12i	−0.481274	+	0.833591i	−0.999769	−	0.0214893i	$-0.993159\pi$
$523$	−8.23475e11	+	1.42630e12i	−0.481274	+	0.833591i	0.518495	+	0.855081i	$0.326493\pi$
$524$	−8.57538e11			−0.496893
$525$	−1.02840e12	−	8.80083e11i	−0.590808	−	0.505600i
$526$	−1.30072e12			−0.740878
$527$	−2.83833e11	+	4.91614e11i	−0.160293	+	0.277636i
$528$	−2.05537e11	−	3.56001e11i	−0.115090	−	0.199342i
$529$	9.00555e11	+	1.55981e12i	0.499988	+	0.866005i
$530$	4.08511e11	−	7.07562e11i	0.224886	−	0.389514i
$531$	1.01896e12			0.556202
$532$	−2.21216e11	+	1.18708e12i	−0.119733	+	0.642507i
$533$	−1.96463e12			−1.05441
$534$	3.55868e11	−	6.16381e11i	0.189388	−	0.328030i
$535$	1.37143e12	+	2.37538e12i	0.723738	+	1.25355i
$536$	−4.55576e11	−	7.89080e11i	−0.238407	−	0.412933i
$537$	1.82320e11	−	3.15787e11i	0.0946127	−	0.163874i
$538$	−1.71253e12			−0.881290
$539$	−4.82796e11	−	3.08740e12i	−0.246385	−	1.57559i
$540$	2.91276e11			0.147412
$541$	−2.50530e11	+	4.33931e11i	−0.125740	+	0.217788i	−0.922022	−	0.387138i	$-0.873464\pi$
$541$	−2.50530e11	+	4.33931e11i	−0.125740	+	0.217788i	0.796282	+	0.604925i	$0.206797\pi$
$542$	−5.36268e11	−	9.28844e11i	−0.266923	−	0.462323i
$543$	2.46214e11	+	4.26454e11i	0.121538	+	0.210510i
$544$	3.44751e11	−	5.97127e11i	0.168776	−	0.292329i
$545$	−4.13887e11			−0.200954
$546$	−1.38779e11	+	7.44710e11i	−0.0668276	+	0.358608i
$547$	1.31820e12			0.629560			0.314780	−	0.949165i	$-0.398069\pi$
$547$	1.31820e12			0.629560			0.314780	+	0.949165i	$0.398069\pi$
$548$	6.69679e11	−	1.15992e12i	0.317215	−	0.549433i
$549$	−2.81177e11	−	4.87014e11i	−0.132101	−	0.228805i
$550$	−1.62968e12	−	2.82268e12i	−0.759398	−	1.31532i
$551$	−9.48020e11	+	1.64202e12i	−0.438163	+	0.758920i
$552$	−2.14433e9			−0.000983027
$553$	4.64388e10	+	3.97412e10i	0.0211163	+	0.0180708i
$554$	2.25894e12			1.01885
$555$	6.71392e11	−	1.16288e12i	0.300371	−	0.520257i
$556$	−6.23267e11	−	1.07953e12i	−0.276591	−	0.479069i
$557$	−1.04867e12	−	1.81635e12i	−0.461625	−	0.799558i	0.537417	−	0.843317i	$-0.319400\pi$
$557$	−1.04867e12	−	1.81635e12i	−0.461625	−	0.799558i	−0.999042	+	0.0437586i	$0.986067\pi$
$558$	4.53124e10	−	7.84834e10i	0.0197863	−	0.0342708i
$559$	−9.30244e11			−0.402943
$560$	8.40480e11	−	2.96703e11i	0.361145	−	0.127490i
$561$	4.12456e12			1.75810
$562$	−6.38898e11	+	1.10660e12i	−0.270158	+	0.467928i
$563$	−1.77041e12	−	3.06644e12i	−0.742654	−	1.28631i	−0.951283	−	0.308319i	$-0.900233\pi$
$563$	−1.77041e12	−	3.06644e12i	−0.742654	−	1.28631i	0.208629	−	0.977995i	$-0.433100\pi$
$564$	2.73215e11	+	4.73221e11i	0.113697	+	0.196928i
$565$	2.67900e12	−	4.64016e12i	1.10600	−	1.91565i
$566$	−1.40937e12			−0.577234
$567$	−2.57857e11	+	9.10276e10i	−0.104774	+	0.0369870i
$568$	−1.08882e12			−0.438925
$569$	1.16613e12	−	2.01979e12i	0.466381	−	0.807795i	−0.532882	−	0.846190i	$-0.678891\pi$
$569$	1.16613e12	−	2.01979e12i	0.466381	−	0.807795i	0.999263	+	0.0383943i	$0.0122243\pi$
$570$	−1.03014e12	−	1.78426e12i	−0.408752	−	0.707979i
$571$	5.78780e11	+	1.00248e12i	0.227851	+	0.394649i	0.957171	−	0.289523i	$-0.0934968\pi$
$571$	5.78780e11	+	1.00248e12i	0.227851	+	0.394649i	−0.729320	+	0.684173i	$0.760163\pi$
$572$	−9.12053e11	+	1.57972e12i	−0.356236	+	0.617019i
$573$	7.27672e11			0.281994
$574$	−1.64881e12	−	1.41101e12i	−0.633968	−	0.542534i
$575$	−1.70021e10			−0.00648629
$576$	−5.50377e10	+	9.53280e10i	−0.0208333	+	0.0360844i
$577$	−1.85995e12	−	3.22152e12i	−0.698570	−	1.20996i	−0.968962	−	0.247208i	$-0.920487\pi$
$577$	−1.85995e12	−	3.22152e12i	−0.698570	−	1.20996i	0.270393	−	0.962750i	$-0.412846\pi$
$578$	2.51039e12	+	4.34813e12i	0.935548	+	1.62042i
$579$	−4.92320e11	+	8.52724e11i	−0.182051	+	0.315322i
$580$	1.39954e12			0.513522
$581$	6.86875e11	−	3.68589e12i	0.250084	−	1.34199i
$582$	8.64775e11			0.312428
$583$	−9.23486e11	+	1.59953e12i	−0.331072	+	0.573433i
$584$	−7.67710e11	−	1.32971e12i	−0.273111	−	0.473042i
$585$	−6.46254e11	−	1.11935e12i	−0.228140	−	0.395151i
$586$	−5.70157e11	+	9.87541e11i	−0.199735	+	0.345952i
$587$	4.35998e12			1.51570			0.757849	−	0.652429i	$-0.226250\pi$
$587$	4.35998e12			1.51570			0.757849	+	0.652429i	$0.226250\pi$
$588$	−6.51325e11	+	5.25323e11i	−0.224698	+	0.181229i
$589$	−6.41017e11			−0.219458
$590$	−2.66004e12	+	4.60732e12i	−0.903761	+	1.56536i
$591$	−9.14902e11	−	1.58466e12i	−0.308483	−	0.534308i
$592$	2.53724e11	+	4.39463e11i	0.0849012	+	0.147053i
$593$	−6.15758e11	+	1.06652e12i	−0.204486	+	0.354180i	−0.949969	−	0.312345i	$-0.898886\pi$
$593$	−6.15758e11	+	1.06652e12i	−0.204486	+	0.354180i	0.745483	+	0.666525i	$0.232219\pi$
$594$	−6.58463e11			−0.217016
$595$	−1.63836e12	+	8.79172e12i	−0.535899	+	2.87573i
$596$	2.19598e11			0.0712888
$597$	1.13480e11	−	1.96553e11i	0.0365623	−	0.0633278i
$598$	4.75763e9	+	8.24045e9i	0.00152137	+	0.00263509i
$599$	−2.54603e12	−	4.40985e12i	−0.808058	−	1.39960i	−0.914207	−	0.405247i	$-0.867186\pi$
$599$	−2.54603e12	−	4.40985e12i	−0.808058	−	1.39960i	0.106150	−	0.994350i	$-0.466148\pi$
$600$	−4.36386e11	+	7.55842e11i	−0.137464	+	0.238095i
$601$	−1.32105e12			−0.413033			−0.206516	−	0.978443i	$-0.566213\pi$
$601$	−1.32105e12			−0.413033			−0.206516	+	0.978443i	$0.566213\pi$
$602$	−7.80703e11	−	6.68107e11i	−0.242271	−	0.207330i
$603$	−1.45949e12			−0.449544
$604$	1.82534e11	−	3.16158e11i	0.0558055	−	0.0966580i
$605$	3.89522e12	+	6.74671e12i	1.18204	+	2.04735i
$606$	−9.66292e11	−	1.67367e12i	−0.291059	−	0.504130i
$607$	−5.11679e11	+	8.86255e11i	−0.152985	+	0.264978i	−0.932324	−	0.361625i	$-0.882222\pi$
$607$	−5.11679e11	+	8.86255e11i	−0.152985	+	0.264978i	0.779338	+	0.626603i	$0.215555\pi$
$608$	7.78596e11			0.231071
$609$	−1.23896e12	+	4.37375e11i	−0.364990	+	0.128847i
$610$	2.93609e12			0.858590
$611$	1.21236e12	−	2.09988e12i	0.351923	−	0.609548i
$612$	−5.52225e11	−	9.56482e11i	−0.159124	−	0.275610i
$613$	2.65817e12	+	4.60408e12i	0.760344	+	1.31695i	0.942674	+	0.333716i	$0.108303\pi$
$613$	2.65817e12	+	4.60408e12i	0.760344	+	1.31695i	−0.182330	+	0.983237i	$0.558364\pi$
$614$	−1.05422e11	+	1.82596e11i	−0.0299345	+	0.0518482i
$615$	3.70273e12			1.04372
$616$	−1.90000e12	+	6.70732e11i	−0.531669	+	0.187688i
$617$	−1.84099e10			−0.00511409			−0.00255705	−	0.999997i	$-0.500814\pi$
$617$	−1.84099e10			−0.00511409			−0.00255705	+	0.999997i	$0.500814\pi$
$618$	−6.70935e11	+	1.16209e12i	−0.185026	+	0.320474i
$619$	1.01330e12	+	1.75509e12i	0.277415	+	0.480498i	0.970742	−	0.240126i	$-0.0771888\pi$
$619$	1.01330e12	+	1.75509e12i	0.277415	+	0.480498i	−0.693326	+	0.720624i	$0.743856\pi$
$620$	2.36579e11	+	4.09767e11i	0.0643005	+	0.111372i
$621$	−1.71740e9	+	2.97462e9i	−0.000463404	+	0.000802639i
$622$	3.53392e12			0.946674
$623$	−2.65055e12	−	2.26828e12i	−0.704921	−	0.603254i
$624$	4.88449e11			0.128970
$625$	1.01626e12	−	1.76021e12i	0.266406	−	0.461429i
$626$	−2.40828e11	−	4.17127e11i	−0.0626791	−	0.108563i
$627$	2.32875e12	+	4.03352e12i	0.601754	+	1.04227i
$628$	1.39059e12	−	2.40856e12i	0.356763	−	0.617931i
$629$	−5.09152e12			−1.29694
$630$	2.61555e11	−	1.40355e12i	0.0661501	−	0.354973i
$631$	−2.70186e12			−0.678471			−0.339235	−	0.940702i	$-0.610168\pi$
$631$	−2.70186e12			−0.678471			−0.339235	+	0.940702i	$0.610168\pi$
$632$	1.97055e10	−	3.41309e10i	0.00491316	−	0.00850984i
$633$	5.81148e10	+	1.00658e11i	0.0143870	+	0.0249190i
$634$	−7.30549e11	−	1.26535e12i	−0.179576	−	0.311034i
$635$	1.72777e12	−	2.99258e12i	0.421699	−	0.730405i
$636$	4.94572e11			0.119859
$637$	3.46386e12	+	1.33744e12i	0.833553	+	0.321846i
$638$	−3.16382e12			−0.755994
$639$	−8.72043e11	+	1.51042e12i	−0.206911	+	0.358381i
$640$	−2.87355e11	−	4.97714e11i	−0.0677032	−	0.117265i
$641$	3.23955e12	+	5.61107e12i	0.757920	+	1.31276i	0.943909	+	0.330205i	$0.107118\pi$
$641$	3.23955e12	+	5.61107e12i	0.757920	+	1.31276i	−0.185989	+	0.982552i	$0.559549\pi$
$642$	−8.30174e11	+	1.43790e12i	−0.192868	+	0.334058i
$643$	6.59134e12			1.52063			0.760317	−	0.649553i	$-0.225044\pi$
$643$	6.59134e12			1.52063			0.760317	+	0.649553i	$0.225044\pi$
$644$	−1.92553e9	+	1.03327e10i	−0.000441127	+	0.00236716i
$645$	1.75322e12			0.398858
$646$	−3.90606e12	+	6.76549e12i	−0.882454	+	1.52845i
$647$	1.44155e12	+	2.49683e12i	0.323414	+	0.560170i	0.981190	−	0.193044i	$-0.0618360\pi$
$647$	1.44155e12	+	2.49683e12i	0.323414	+	0.560170i	−0.657776	+	0.753214i	$0.728503\pi$
$648$	8.81597e10	+	1.52697e11i	0.0196419	+	0.0340207i
$649$	6.01332e12	−	1.04154e13i	1.33049	−	2.30448i
$650$	3.87284e12			0.850980
$651$	−3.37493e11	−	2.88819e11i	−0.0736463	−	0.0630248i
$652$	−2.28719e12			−0.495665
$653$	−2.99660e12	+	5.19027e12i	−0.644941	+	1.11707i	0.339374	+	0.940651i	$0.389785\pi$
$653$	−2.99660e12	+	5.19027e12i	−0.644941	+	1.11707i	−0.984315	+	0.176419i	$0.943549\pi$
$654$	−1.25270e11	−	2.16974e11i	−0.0267761	−	0.0463776i
$655$	−3.58586e12	−	6.21089e12i	−0.761215	−	1.31846i
$656$	−6.99645e11	+	1.21182e12i	−0.147506	+	0.255488i
$657$	−2.45944e12			−0.514983
$658$	2.52561e12	−	8.91583e11i	0.525231	−	0.185415i
$659$	−7.08700e11			−0.146379			−0.0731894	−	0.997318i	$-0.523318\pi$
$659$	−7.08700e11			−0.146379			−0.0731894	+	0.997318i	$0.523318\pi$
$660$	1.71894e12	−	2.97729e12i	0.352625	−	0.610764i
$661$	4.19907e12	+	7.27301e12i	0.855553	+	1.48186i	0.876131	+	0.482072i	$0.160116\pi$
$661$	4.19907e12	+	7.27301e12i	0.855553	+	1.48186i	−0.0205788	+	0.999788i	$0.506551\pi$
$662$	1.15869e12	+	2.00691e12i	0.234480	+	0.406131i
$663$	−2.45045e12	+	4.24430e12i	−0.492532	+	0.853090i
$664$	−2.41754e12			−0.482634
$665$	−9.52269e12	+	3.36167e12i	−1.88826	+	0.666588i
$666$	8.12834e11			0.160091
$667$	−8.25186e9	+	1.42926e10i	−0.00161431	+	0.00279606i
$668$	1.86612e12	+	3.23222e12i	0.362616	+	0.628069i
$669$	−1.01460e11	−	1.75734e11i	−0.0195829	−	0.0339186i
$670$	3.81004e12	−	6.59919e12i	0.730455	−	1.26518i
$671$	−6.63738e12			−1.26399
$672$	4.09928e11	+	3.50807e11i	0.0775436	+	0.0663600i
$673$	−1.06217e13			−1.99584			−0.997920	−	0.0644576i	$-0.979468\pi$
$673$	−1.06217e13			−1.99584			−0.997920	+	0.0644576i	$0.979468\pi$
$674$	3.52305e12	−	6.10209e12i	0.657580	−	1.13896i
$675$	6.99005e11	+	1.21071e12i	0.129603	+	0.224478i
$676$	2.73654e11	+	4.73982e11i	0.0504012	+	0.0872975i
$677$	1.12868e12	−	1.95492e12i	0.206500	−	0.357669i	−0.744110	−	0.668058i	$-0.767126\pi$
$677$	1.12868e12	−	1.95492e12i	0.206500	−	0.357669i	0.950610	+	0.310389i	$0.100459\pi$
$678$	3.24338e12			0.589474
$679$	7.76536e11	−	4.16703e12i	0.140200	−	0.752337i
$680$	5.76641e12			1.03423
$681$	2.64046e11	−	4.57341e11i	0.0470454	−	0.0814850i
$682$	−5.34815e11	−	9.26326e11i	−0.0946616	−	0.163959i
$683$	3.16248e12	+	5.47758e12i	0.556077	+	0.963153i	0.997819	+	0.0660110i	$0.0210272\pi$
$683$	3.16248e12	+	5.47758e12i	0.556077	+	0.963153i	−0.441742	+	0.897142i	$0.645639\pi$
$684$	6.23580e11	−	1.08007e12i	0.108928	−	0.188669i
$685$	1.12012e13			1.94383
$686$	1.94647e12	+	3.61021e12i	0.335574	+	0.622406i
$687$	4.35894e11			0.0746579
$688$	−3.31278e11	+	5.73791e11i	−0.0563696	+	0.0976350i
$689$	−1.09731e12	−	1.90059e12i	−0.185499	−	0.321294i
$690$	−8.96667e9	−	1.55307e10i	−0.00150595	−	0.00260838i
$691$	1.78903e12	−	3.09869e12i	0.298515	−	0.517043i	−0.677282	−	0.735724i	$-0.736842\pi$
$691$	1.78903e12	−	3.09869e12i	0.298515	−	0.517043i	0.975796	+	0.218681i	$0.0701754\pi$
$692$	−1.00264e12			−0.166215
$693$	−5.91275e11	+	3.17289e12i	−0.0973846	+	0.522582i
$694$	−2.11454e12			−0.346018
$695$	5.21247e12	−	9.02826e12i	0.847446	−	1.46782i
$696$	4.23595e11	+	7.33687e11i	0.0684240	+	0.118514i
$697$	−7.01995e12	−	1.21589e13i	−1.12664	−	1.95140i
$698$	1.00863e12	−	1.74700e12i	0.160835	−	0.278575i
$699$	4.50972e12			0.714500
$700$	3.25026e12	+	2.78150e12i	0.511655	+	0.437862i
$701$	−1.11407e12			−0.174253			−0.0871264	−	0.996197i	$-0.527768\pi$
$701$	−1.11407e12			−0.174253			−0.0871264	+	0.996197i	$0.527768\pi$
$702$	3.91200e11	−	6.77579e11i	0.0607970	−	0.105303i
$703$	−2.87471e12	−	4.97914e12i	−0.443910	−	0.768874i
$704$	6.49600e11	+	1.12514e12i	0.0996710	+	0.172635i
$705$	−2.28493e12	+	3.95762e12i	−0.348355	+	0.603369i
$706$	4.63287e12			0.701826
$707$	−8.93247e12	+	3.15331e12i	−1.34457	+	0.474656i
$708$	−3.22042e12			−0.481685
$709$	−1.06699e12	+	1.84808e12i	−0.158582	+	0.274672i	−0.934357	−	0.356337i	$-0.884025\pi$
$709$	−1.06699e12	+	1.84808e12i	−0.158582	+	0.274672i	0.775776	+	0.631009i	$0.217359\pi$
$710$	−4.55300e12	−	7.88602e12i	−0.672411	−	1.16465i
$711$	−3.15644e10	−	5.46712e10i	−0.00463217	−	0.00802315i
$712$	−1.12472e12	+	1.94807e12i	−0.164015	+	0.284082i
$713$	−5.57961e9			−0.000808539
$714$	−5.10481e12	+	1.80208e12i	−0.735085	+	0.259497i
$715$	−1.52553e13			−2.18294
$716$	−5.76221e11	+	9.98043e11i	−0.0819370	+	0.141919i
$717$	−3.83245e12	−	6.63799e12i	−0.541552	−	0.937995i
$718$	1.69307e12	+	2.93248e12i	0.237747	+	0.411790i
$719$	5.08025e12	−	8.79926e12i	0.708933	−	1.22791i	−0.256320	−	0.966592i	$-0.582510\pi$
$719$	5.08025e12	−	8.79926e12i	0.708933	−	1.22791i	0.965253	−	0.261317i	$-0.0841567\pi$
$720$	−9.20576e11			−0.127662
$721$	4.99722e12	+	4.27650e12i	0.688684	+	0.589359i
$722$	−3.65853e12			−0.501060
$723$	−1.12932e12	+	1.95603e12i	−0.153707	+	0.266228i
$724$	−7.78156e11	−	1.34781e12i	−0.105255	−	0.182307i
$725$	3.35862e12	+	5.81730e12i	0.451481	+	0.781989i
$726$	−2.35791e12	+	4.08402e12i	−0.315001	+	0.545598i
$727$	−4.40678e12			−0.585082			−0.292541	−	0.956253i	$-0.594501\pi$
$727$	−4.40678e12			−0.585082			−0.292541	+	0.956253i	$0.594501\pi$
$728$	4.38609e11	−	2.35365e12i	0.0578744	−	0.310564i
$729$	2.82430e11			0.0370370
$730$	6.42047e12	−	1.11206e13i	0.836784	−	1.44935i
$731$	−3.32391e12	−	5.75718e12i	−0.430547	−	0.745730i
$732$	8.88660e11	+	1.53920e12i	0.114403	+	0.198151i
$733$	2.66792e12	−	4.62096e12i	0.341353	−	0.591241i	−0.643331	−	0.765588i	$-0.722448\pi$
$733$	2.66792e12	−	4.62096e12i	0.341353	−	0.591241i	0.984684	+	0.174347i	$0.0557814\pi$
$734$	9.61386e12			1.22255
$735$	−6.52831e12	−	2.52067e12i	−0.825103	−	0.318583i
$736$	6.77714e9			0.000851327
$737$	−8.61304e12	+	1.49182e13i	−1.07536	+	1.86257i
$738$	1.12070e12	+	1.94110e12i	0.139070	+	0.240877i
$739$	−2.08742e12	−	3.61551e12i	−0.257460	−	0.445933i	0.708101	−	0.706111i	$-0.249552\pi$
$739$	−2.08742e12	−	3.61551e12i	−0.257460	−	0.445933i	−0.965561	+	0.260178i	$0.916219\pi$
$740$	−2.12193e12	+	3.67529e12i	−0.260129	+	0.450556i
$741$	−5.53415e12			−0.674325
$742$	4.44107e11	−	2.38316e12i	0.0537861	−	0.288626i
$743$	8.87391e12			1.06823			0.534116	−	0.845411i	$-0.320645\pi$
$743$	8.87391e12			1.06823			0.534116	+	0.845411i	$0.320645\pi$
$744$	−1.43210e11	+	2.48046e11i	−0.0171354	+	0.0296794i
$745$	9.18266e11	+	1.59048e12i	0.109211	+	0.189159i
$746$	−1.12077e12	−	1.94122e12i	−0.132492	−	0.229483i
$747$	−1.93622e12	+	3.35363e12i	−0.227516	+	0.394069i
$748$	−1.30356e13			−1.52256
$749$	6.18325e12	+	5.29148e12i	0.717875	+	0.614340i
$750$	−1.87979e12			−0.216937
$751$	−1.31241e12	+	2.27317e12i	−0.150554	+	0.260766i	−0.931431	−	0.363918i	$-0.881439\pi$
$751$	−1.31241e12	+	2.27317e12i	−0.150554	+	0.260766i	0.780878	+	0.624684i	$0.214772\pi$
$752$	−8.63493e11	−	1.49561e12i	−0.0984642	−	0.170545i
$753$	1.23013e12	+	2.13065e12i	0.139435	+	0.241509i
$754$	1.87966e12	−	3.25567e12i	0.211791	−	0.366833i
$755$	3.05311e12			0.341965
$756$	8.14954e11	−	2.87692e11i	0.0907371	−	0.0320317i
$757$	−8.31291e12			−0.920071			−0.460036	−	0.887900i	$-0.652163\pi$
$757$	−8.31291e12			−0.920071			−0.460036	+	0.887900i	$0.652163\pi$
$758$	−4.69748e12	+	8.13627e12i	−0.516837	+	0.895187i
$759$	2.02702e10	+	3.51090e10i	0.00221702	+	0.00383999i
$760$	3.25575e12	+	5.63913e12i	0.353990	+	0.613128i
$761$	1.69837e12	−	2.94166e12i	0.183570	−	0.317952i	−0.759524	−	0.650480i	$-0.774568\pi$
$761$	1.69837e12	−	2.94166e12i	0.183570	−	0.317952i	0.943094	+	0.332527i	$0.107901\pi$
$762$	2.09175e12			0.224757
$763$	−1.15801e12	+	4.08795e11i	−0.123694	+	0.0436662i
$764$	−2.29980e12			−0.244214
$765$	4.61834e12	−	7.99920e12i	0.487539	−	0.844442i
$766$	3.11940e12	+	5.40297e12i	0.327372	+	0.567026i
$767$	7.14516e12	+	1.23758e13i	0.745475	+	1.29120i
$768$	1.73946e11	−	3.01284e11i	0.0180422	−	0.0312500i
$769$	4.79457e12			0.494403			0.247201	−	0.968964i	$-0.420489\pi$
$769$	4.79457e12			0.494403			0.247201	+	0.968964i	$0.420489\pi$
$770$	−1.28029e13	−	1.09564e13i	−1.31250	−	1.12321i
$771$	−7.30121e12			−0.744132
$772$	1.55598e12	−	2.69503e12i	0.157661	−	0.273077i
$773$	−7.38674e12	−	1.27942e13i	−0.744124	−	1.28886i	−0.950603	−	0.310409i	$-0.899534\pi$
$773$	−7.38674e12	−	1.27942e13i	−0.744124	−	1.28886i	0.206479	−	0.978451i	$-0.433799\pi$
$774$	5.30644e11	+	9.19102e11i	0.0531458	+	0.0920511i
$775$	−1.13549e12	+	1.96672e12i	−0.113064	+	0.195833i
$776$	−2.73312e12			−0.270570
$777$	7.29895e11	−	3.91674e12i	0.0718399	−	0.385505i
$778$	−2.16526e12			−0.211885
$779$	7.92702e12	−	1.37300e13i	0.771243	−	1.33583i
$780$	2.04248e12	+	3.53768e12i	0.197575	+	0.342211i
$781$	1.02926e13	+	1.78273e13i	0.989907	+	1.71457i
$782$	−3.39995e10	+	5.88889e10i	−0.00325119	+	0.00563123i
$783$	1.35703e12			0.129022
$784$	2.05851e12	−	1.66028e12i	0.194594	−	0.156949i
$785$	2.32593e13			2.18617
$786$	2.17064e12	−	3.75967e12i	0.202856	−	0.351356i
$787$	1.02538e12	+	1.77602e12i	0.0952798	+	0.165029i	0.909725	−	0.415211i	$-0.136292\pi$
$787$	1.02538e12	+	1.77602e12i	0.0952798	+	0.165029i	−0.814446	+	0.580240i	$0.802959\pi$
$788$	2.89154e12	+	5.00830e12i	0.267154	+	0.462724i
$789$	3.29244e12	−	5.70267e12i	0.302462	−	0.523880i
$790$	3.29600e11			0.0301068
$791$	2.91244e12	−	1.56286e13i	0.264522	−	1.41947i
$792$	2.08107e12			0.187942
$793$	3.94334e12	−	6.83007e12i	0.354107	−	0.613332i
$794$	6.16998e12	+	1.06867e13i	0.550924	+	0.954228i
$795$	2.06809e12	+	3.58203e12i	0.183619	+	0.318037i
$796$	−3.58652e11	+	6.21203e11i	−0.0316639	+	0.0548435i
$797$	−1.19235e13			−1.04675			−0.523373	−	0.852104i	$-0.675327\pi$
$797$	−1.19235e13			−1.04675			−0.523373	+	0.852104i	$0.675327\pi$
$798$	−4.64451e12	−	3.97466e12i	−0.405440	−	0.346966i
$799$	1.73279e13			1.50413
$800$	1.37919e12	−	2.38883e12i	0.119048	−	0.206196i
$801$	1.80158e12	+	3.12043e12i	0.154635	+	0.267835i
$802$	−8.95113e11	−	1.55038e12i	−0.0764000	−	0.132329i
$803$	−1.45142e13	+	2.51393e13i	−1.23189	+	2.13370i
$804$	4.61270e12			0.389317
$805$	−8.28885e10	+	2.92610e10i	−0.00695685	+	0.00245588i
$806$	1.27096e12			0.106078
$807$	4.33485e12	−	7.50818e12i	0.359785	−	0.623166i
$808$	3.05396e12	+	5.28962e12i	0.252065	+	0.436589i
$809$	1.92036e12	+	3.32616e12i	0.157621	+	0.273007i	0.934010	−	0.357246i	$-0.116284\pi$
$809$	1.92036e12	+	3.32616e12i	0.157621	+	0.273007i	−0.776389	+	0.630254i	$0.782951\pi$
$810$	−7.37292e11	+	1.27703e12i	−0.0601807	+	0.104236i
$811$	−7.57838e12			−0.615152			−0.307576	−	0.951524i	$-0.599518\pi$
$811$	−7.57838e12			−0.615152			−0.307576	+	0.951524i	$0.599518\pi$
$812$	3.91574e12	−	1.38232e12i	0.316090	−	0.111585i
$813$	5.42971e12			0.435883
$814$	4.79687e12	−	8.30842e12i	0.382955	−	0.663298i
$815$	−9.56406e12	−	1.65654e13i	−0.759334	−	1.31521i
$816$	1.74530e12	+	3.02296e12i	0.137805	+	0.238686i
$817$	3.75340e12	−	6.50108e12i	0.294731	−	0.510489i
$818$	−1.65987e13			−1.29623
$819$	−2.91371e12	−	2.49349e12i	−0.226292	−	0.193655i
$820$	−1.17025e13			−0.903888
$821$	−6.60158e12	+	1.14343e13i	−0.507112	+	0.878343i	0.492854	+	0.870112i	$0.335954\pi$
$821$	−6.60158e12	+	1.14343e13i	−0.507112	+	0.878343i	−0.999966	+	0.00823152i	$0.997380\pi$
$822$	3.39025e12	+	5.87208e12i	0.259005	+	0.448610i
$823$	6.89186e11	+	1.19370e12i	0.0523645	+	0.0906980i	0.891020	−	0.453965i	$-0.149991\pi$
$823$	6.89186e11	+	1.19370e12i	0.0523645	+	0.0906980i	−0.838655	+	0.544663i	$0.816658\pi$
$824$	2.12049e12	−	3.67279e12i	0.160237	−	0.277539i
$825$	1.65005e13			1.24009
$826$	−2.89182e12	+	1.55180e13i	−0.216153	+	1.15991i
$827$	1.26509e13			0.940474			0.470237	−	0.882540i	$-0.344168\pi$
$827$	1.26509e13			0.940474			0.470237	+	0.882540i	$0.344168\pi$
$828$	5.42783e9	−	9.40128e9i	0.000401319	−	0.000695105i
$829$	−1.39141e12	−	2.40999e12i	−0.102320	−	0.177223i	0.810320	−	0.585987i	$-0.199293\pi$
$829$	−1.39141e12	−	2.40999e12i	−0.102320	−	0.177223i	−0.912640	+	0.408764i	$0.865960\pi$
$830$	−1.01091e13	−	1.75095e13i	−0.739371	−	1.28063i
$831$	−5.71794e12	+	9.90376e12i	−0.415944	+	0.720436i
$832$	−1.54374e12			−0.111691
$833$	4.09963e12	+	2.62164e13i	0.295013	+	1.88656i
$834$	6.31058e12			0.451671
$835$	−1.56067e13	+	2.70315e13i	−1.11102	+	1.92434i
$836$	−7.36001e12	−	1.27479e13i	−0.521135	−	0.902632i
$837$	2.29394e11	+	3.97322e11i	0.0161554	+	0.0279820i
$838$	−2.53865e12	+	4.39707e12i	−0.177830	+	0.308010i
$839$	2.84268e12			0.198061			0.0990304	−	0.995084i	$-0.468426\pi$
$839$	2.84268e12			0.198061			0.0990304	+	0.995084i	$0.468426\pi$
$840$	−8.26643e11	+	4.43591e12i	−0.0572877	+	0.307416i
$841$	−7.98680e12			−0.550542
$842$	−5.86644e12	+	1.01610e13i	−0.402226	+	0.696676i
$843$	−3.23442e12	−	5.60218e12i	−0.220583	−	0.382061i
$844$	−1.83672e11	−	3.18128e11i	−0.0124595	−	0.0215805i
$845$	−2.28860e12	+	3.96398e12i	−0.154424	+	0.267471i
$846$	−2.76630e12			−0.185666
$847$	1.75620e13	+	1.50292e13i	1.17246	+	1.00337i
$848$	−1.56309e12			−0.103801
$849$	3.56748e12	−	6.17905e12i	0.235655	−	0.408166i
$850$	1.38383e13	+	2.39686e13i	0.909278	+	1.57491i
$851$	−2.50224e10	−	4.33400e10i	−0.00163548	−	0.00283273i
$852$	2.75609e12	−	4.77368e12i	0.179190	−	0.310367i
$853$	2.28579e12			0.147831			0.0739156	−	0.997265i	$-0.476450\pi$
$853$	2.28579e12			0.147831			0.0739156	+	0.997265i	$0.476450\pi$
$854$	8.21483e12	−	2.89997e12i	0.528492	−	0.186566i
$855$	1.04302e13			0.667489
$856$	2.62376e12	−	4.54448e12i	0.167029	−	0.289303i
$857$	9.74082e12	+	1.68716e13i	0.616853	+	1.06842i	0.990056	+	0.140671i	$0.0449260\pi$
$857$	9.74082e12	+	1.68716e13i	0.616853	+	1.06842i	−0.373203	+	0.927750i	$0.621741\pi$
$858$	−4.61727e12	−	7.99734e12i	−0.290866	−	0.503794i
$859$	1.10241e13	−	1.90943e13i	0.690835	−	1.19656i	−0.280729	−	0.959787i	$-0.590576\pi$
$859$	1.10241e13	−	1.90943e13i	0.690835	−	1.19656i	0.971565	−	0.236775i	$-0.0760904\pi$
$860$	−5.54105e12			−0.345421
$861$	1.03598e13	−	3.65717e12i	0.642446	−	0.226794i
$862$	−2.09792e13			−1.29421
$863$	1.12778e13	−	1.95337e13i	0.692110	−	1.19877i	−0.279035	−	0.960281i	$-0.590015\pi$
$863$	1.12778e13	−	1.95337e13i	0.692110	−	1.19877i	0.971145	−	0.238489i	$-0.0766521\pi$
$864$	−2.78628e11	−	4.82598e11i	−0.0170103	−	0.0294628i
$865$	−4.19263e12	−	7.26184e12i	−0.254632	−	0.441036i
$866$	4.18829e12	−	7.25433e12i	0.253050	−	0.438296i
$867$	−2.54177e13			−1.52774
$868$	1.06665e12	+	9.12810e11i	0.0637796	+	0.0545810i
$869$	−7.45099e11			−0.0443226
$870$	−3.54258e12	+	6.13593e12i	−0.209644	+	0.363115i
$871$	−1.02342e13	−	1.77262e13i	−0.602522	−	1.04360i
$872$	3.95915e11	+	6.85745e11i	0.0231888	+	0.0401642i
$873$	−2.18896e12	+	3.79139e12i	−0.127548	+	0.220920i
$874$	−7.67854e10			−0.00445120
$875$	−1.68799e12	+	9.05802e12i	−0.0973492	+	0.522393i
$876$	7.77306e12			0.445988
$877$	−1.54052e13	+	2.66826e13i	−0.879367	+	1.52311i	−0.0273297	+	0.999626i	$0.508700\pi$
$877$	−1.54052e13	+	2.66826e13i	−0.879367	+	1.52311i	−0.852037	+	0.523481i	$0.824633\pi$
$878$	−3.44298e12	−	5.96342e12i	−0.195528	−	0.338665i
$879$	−2.88642e12	−	4.99942e12i	−0.163083	−	0.282469i
$880$	−5.43270e12	+	9.40971e12i	−0.305382	+	0.528937i
$881$	−1.72758e11			−0.00966157			−0.00483078	−	0.999988i	$-0.501538\pi$
$881$	−1.72758e11			−0.00966157			−0.00483078	+	0.999988i	$0.501538\pi$
$882$	−6.54482e11	−	4.18530e12i	−0.0364158	−	0.232872i
$883$	1.07928e13			0.597460			0.298730	−	0.954338i	$-0.403437\pi$
$883$	1.07928e13			0.597460			0.298730	+	0.954338i	$0.403437\pi$
$884$	7.74462e12	−	1.34141e13i	0.426545	−	0.738798i
$885$	−1.34664e13	−	2.33245e13i	−0.737918	−	1.27811i
$886$	1.59647e12	+	2.76517e12i	0.0870382	+	0.150755i
$887$	1.17452e13	−	2.03432e13i	0.637093	−	1.10348i	−0.348974	−	0.937132i	$-0.613470\pi$
$887$	1.17452e13	−	2.03432e13i	0.637093	−	1.10348i	0.986067	−	0.166346i	$-0.0531968\pi$
$888$	−2.56896e12			−0.138643
$889$	1.87832e12	−	1.00794e13i	0.100858	−	0.541222i
$890$	−1.88123e13			−1.00505
$891$	1.66673e12	−	2.88687e12i	0.0885965	−	0.153454i
$892$	3.20664e11	+	5.55406e11i	0.0169593	+	0.0293744i
$893$	9.78343e12	+	1.69454e13i	0.514825	+	0.891703i
$894$	−5.55859e11	+	9.62775e11i	−0.0291035	+	0.0504088i
$895$	−9.63803e12			−0.502093
$896$	−1.29558e12	−	1.10872e12i	−0.0671548	−	0.0574695i
$897$	−4.81710e10			−0.00248439
$898$	−1.07555e12	+	1.86291e12i	−0.0551936	+	0.0955981i
$899$	1.10221e12	+	1.90908e12i	0.0562787	+	0.0974776i
$900$	−2.20920e12	−	3.82645e12i	−0.112239	−	0.194404i
$901$	7.84171e12	−	1.35822e13i	0.396414	−	0.686609i
$902$	2.64547e13			1.33068
$903$	4.90531e12	−	1.73165e12i	0.245511	−	0.0866695i
$904$	−1.02507e13			−0.510499
$905$	6.50783e12	−	1.12719e13i	0.322491	−	0.558571i
$906$	9.24078e11	+	1.60055e12i	0.0455650	+	0.0789210i
$907$	−1.19812e13	−	2.07521e13i	−0.587852	−	1.01819i	−0.994513	−	0.104610i	$-0.966641\pi$
$907$	−1.19812e13	−	2.07521e13i	−0.587852	−	1.01819i	0.406662	−	0.913579i	$-0.366693\pi$
$908$	−8.34515e11	+	1.44542e12i	−0.0407425	+	0.0705681i
$909$	9.78371e12			0.475298
$910$	1.88809e13	−	6.66525e12i	0.912715	−	0.322204i
$911$	7.80479e12			0.375429			0.187715	−	0.982224i	$-0.439892\pi$
$911$	7.80479e12			0.375429			0.187715	+	0.982224i	$0.439892\pi$
$912$	−1.97082e12	+	3.41356e12i	−0.0943345	+	0.163392i
$913$	2.28529e13	+	3.95823e13i	1.08848	+	1.88531i
$914$	1.69541e12	+	2.93654e12i	0.0803559	+	0.139180i
$915$	−7.43199e12	+	1.28726e13i	−0.350518	+	0.607115i
$916$	−1.37764e12			−0.0646556
$917$	−1.61673e13	−	1.38356e13i	−0.755048	−	0.646152i
$918$	5.59128e12			0.259848
$919$	−4.00028e12	+	6.92868e12i	−0.184999	+	0.320428i	−0.943576	−	0.331155i	$-0.892562\pi$
$919$	−4.00028e12	+	6.92868e12i	−0.184999	+	0.320428i	0.758577	+	0.651583i	$0.225895\pi$
$920$	2.83391e10	+	4.90847e10i	0.00130419	+	0.00225892i
$921$	−5.33698e11	−	9.24392e11i	−0.0244415	−	0.0423338i
$922$	−8.38738e12	+	1.45274e13i	−0.382241	+	0.662061i
$923$	−2.44597e13			−1.10929
$924$	1.86872e12	−	1.00279e13i	0.0843375	−	0.452570i
$925$	−2.03689e13			−0.914806
$926$	3.37849e12	−	5.85172e12i	0.150999	−	0.261538i
$927$	−3.39661e12	−	5.88310e12i	−0.151073	−	0.261666i
$928$	−1.33877e12	−	2.31881e12i	−0.0592570	−	0.102636i
$929$	−1.83611e12	+	3.18024e12i	−0.0808778	+	0.140084i	−0.903627	−	0.428320i	$-0.859106\pi$
$929$	−1.83611e12	+	3.18024e12i	−0.0808778	+	0.140084i	0.822749	+	0.568404i	$0.192439\pi$
$930$	−2.39537e12			−0.105002
$931$	−2.33230e13	+	1.88111e13i	−1.01745	+	0.820616i
$932$	−1.42529e13			−0.618775
$933$	−8.94524e12	+	1.54936e13i	−0.386478	+	0.669400i
$934$	3.90054e11	+	6.75593e11i	0.0167712	+	0.0290485i
$935$	−5.45094e13	−	9.44131e13i	−2.33249	−	4.03999i
$936$	−1.23639e12	+	2.14148e12i	−0.0526517	+	0.0911955i
$937$	−4.58091e13			−1.94144			−0.970719	−	0.240218i	$-0.922781\pi$
$937$	−4.58091e13			−1.94144			−0.970719	+	0.240218i	$0.922781\pi$
$938$	4.14204e12	−	2.22269e13i	0.174703	−	0.937488i
$939$	2.43839e12			0.102355
$940$	7.22151e12	−	1.25080e13i	0.301684	−	0.522533i
$941$	1.69377e13	+	2.93370e13i	0.704210	+	1.21973i	0.966976	+	0.254868i	$0.0820320\pi$
$941$	1.69377e13	+	2.93370e13i	0.704210	+	1.21973i	−0.262766	+	0.964860i	$0.584635\pi$
$942$	7.03984e12	+	1.21934e13i	0.291295	+	0.504538i
$943$	6.89992e10	−	1.19510e11i	0.00284146	−	0.00492155i
$944$	1.01781e13			0.417152
$945$	5.49146e12	+	4.69946e12i	0.223998	+	0.191692i
$946$	1.25262e13			0.508521
$947$	−3.39394e12	+	5.87847e12i	−0.137129	+	0.237514i	−0.926409	−	0.376519i	$-0.877121\pi$
$947$	−3.39394e12	+	5.87847e12i	−0.137129	+	0.237514i	0.789280	+	0.614034i	$0.210454\pi$
$948$	9.97591e10	+	1.72788e11i	0.00401158	+	0.00694826i
$949$	−1.72461e13	−	2.98711e13i	−0.690229	−	1.19551i
$950$	−1.56264e13	+	2.70656e13i	−0.622446	+	1.07811i
$951$	7.39681e12			0.293246
$952$	1.61337e13	−	5.69547e12i	0.636602	−	0.224731i
$953$	5.28058e12			0.207378			0.103689	−	0.994610i	$-0.466935\pi$
$953$	5.28058e12			0.207378			0.103689	+	0.994610i	$0.466935\pi$
$954$	−1.25189e12	+	2.16833e12i	−0.0489324	+	0.0847535i
$955$	−9.61679e12	−	1.66568e13i	−0.374124	−	0.648001i
$956$	1.21124e13	+	2.09793e13i	0.468998	+	0.812328i
$957$	8.00841e12	−	1.38710e13i	0.308633	−	0.534568i
$958$	6.43424e12			0.246804
$959$	3.13397e13	−	1.10634e13i	1.19649	−	0.422382i
$960$	2.90947e12			0.110559
$961$	1.28472e13	−	2.22520e13i	0.485906	−	0.841614i
$962$	5.69975e12	+	9.87225e12i	0.214569	+	0.371645i
$963$	−4.20275e12	−	7.27938e12i	−0.157476	−	0.272757i
$964$	3.56920e12	−	6.18203e12i	0.133114	−	0.230560i
$965$	2.60257e13			0.966116
$966$	−4.04273e10	−	3.45967e10i	−0.00149375	−	0.00127831i
$967$	4.33872e13			1.59567			0.797834	−	0.602878i	$-0.205979\pi$
$967$	4.33872e13			1.59567			0.797834	+	0.602878i	$0.205979\pi$
$968$	7.45216e12	−	1.29075e13i	0.272799	−	0.472502i
$969$	−1.97744e13	−	3.42503e13i	−0.720521	−	1.24798i
$970$	−1.14287e13	−	1.97951e13i	−0.414500	−	0.717935i
$971$	−2.68045e13	+	4.64268e13i	−0.967658	+	1.67603i	−0.265361	+	0.964149i	$0.585491\pi$
$971$	−2.68045e13	+	4.64268e13i	−0.967658	+	1.67603i	−0.702297	+	0.711884i	$0.747842\pi$
$972$	−8.92617e11			−0.0320750
$973$	5.66667e12	−	3.04083e13i	0.202684	−	1.08764i
$974$	−1.59173e13			−0.566700
$975$	−9.80312e12	+	1.69795e13i	−0.347411	+	0.601734i
$976$	−2.80860e12	−	4.86464e12i	−0.0990755	−	0.171604i
$977$	−5.27189e12	−	9.13119e12i	−0.185115	−	0.320628i	0.758500	−	0.651673i	$-0.225932\pi$
$977$	−5.27189e12	−	9.13119e12i	−0.185115	−	0.320628i	−0.943615	+	0.331044i	$0.892599\pi$
$978$	5.78946e12	−	1.00276e13i	0.202355	−	0.350488i
$979$	4.25275e13			1.47961
$980$	2.06327e13	+	7.96657e12i	0.714560	+	0.275901i
$981$	1.26836e12			0.0437252
$982$	1.41872e12	−	2.45729e12i	0.0486848	−	0.0843246i
$983$	2.28178e13	+	3.95217e13i	0.779442	+	1.35003i	0.932264	+	0.361779i	$0.117831\pi$
$983$	2.28178e13	+	3.95217e13i	0.779442	+	1.35003i	−0.152822	+	0.988254i	$0.548836\pi$
$984$	−3.54195e12	−	6.13484e12i	−0.120438	−	0.208605i
$985$	−2.41824e13	+	4.18851e13i	−0.818533	+	1.41774i
$986$	2.68653e13			0.905202
$987$	−2.48403e12	+	1.33298e13i	−0.0833163	+	0.447090i
$988$	1.74907e13			0.583983
$989$	3.26708e10	−	5.65874e10i	0.00108587	−	0.00188077i
$990$	8.70213e12	+	1.50725e13i	0.287917	+	0.498687i
$991$	1.24239e13	+	2.15188e13i	0.409191	+	0.708739i	0.994799	−	0.101855i	$-0.0324778\pi$
$991$	1.24239e13	+	2.15188e13i	0.409191	+	0.708739i	−0.585609	+	0.810594i	$0.699144\pi$
$992$	4.52613e11	−	7.83949e11i	0.0148397	−	0.0257031i
$993$	−1.17317e13			−0.382904
$994$	−2.05277e13	−	1.75671e13i	−0.666963	−	0.570772i
$995$	−5.99891e12			−0.194030
$996$	6.11941e12	−	1.05991e13i	0.197035	−	0.341274i
$997$	7.52003e12	+	1.30251e13i	0.241041	+	0.417496i	0.961011	−	0.276510i	$-0.0891778\pi$
$997$	7.52003e12	+	1.30251e13i	0.241041	+	0.417496i	−0.719970	+	0.694005i	$0.755844\pi$
$998$	−8.20719e11	−	1.42153e12i	−0.0261883	−	0.0453594i
$999$	−2.05748e12	+	3.56367e12i	−0.0653570	+	0.113202i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	42.10.e.d.37.3	yes	6
3.2	odd	2		126.10.g.d.37.1		6
7.2	even	3		294.10.a.r.1.1		3
7.4	even	3	inner	42.10.e.d.25.3	✓	6
7.5	odd	6		294.10.a.u.1.3		3
21.11	odd	6		126.10.g.d.109.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.10.e.d.25.3	✓	6	7.4	even	3	inner
42.10.e.d.37.3	yes	6	1.1	even	1	trivial
126.10.g.d.37.1		6	3.2	odd	2
126.10.g.d.109.1		6	21.11	odd	6
294.10.a.r.1.1		3	7.2	even	3
294.10.a.u.1.3		3	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 42 = 2 \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	42.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(8.00000 - 13.8564i) q^{2} +(40.5000 + 70.1481i) q^{3} +(-128.000 - 221.703i) q^{4} +(1070.48 - 1854.13i) q^{5} +1296.00 q^{6} +(1163.76 - 6244.94i) q^{7} -4096.00 q^{8} +(-3280.50 + 5681.99i) q^{9} +(-17127.7 - 29666.1i) q^{10} +(38719.2 + 67063.6i) q^{11} +(10368.0 - 17957.9i) q^{12} -92014.0 q^{13} +(-77222.3 - 66085.1i) q^{14} +173418. q^{15} +(-32768.0 + 56755.8i) q^{16} +(-328781. - 569465. i) q^{17} +(52488.0 + 90911.9i) q^{18} +(371263. - 643047. i) q^{19} -548087. q^{20} +(485203. - 171285. i) q^{21} +1.23901e6 q^{22} +(3231.59 - 5597.28i) q^{23} +(-165888. - 287326. i) q^{24} +(-1.31530e6 - 2.27817e6i) q^{25} +(-736112. + 1.27498e6i) q^{26} -531441. q^{27} +(-1.53348e6 + 541344. i) q^{28} -2.55350e6 q^{29} +(1.38734e6 - 2.40295e6i) q^{30} +(-431646. - 747632. i) q^{31} +(524288. + 908093. i) q^{32} +(-3.13625e6 + 5.43215e6i) q^{33} -1.05210e7 q^{34} +(-1.03331e7 - 8.84286e6i) q^{35} +1.67962e6 q^{36} +(3.87152e6 - 6.70567e6i) q^{37} +(-5.94021e6 - 1.02888e7i) q^{38} +(-3.72657e6 - 6.45460e6i) q^{39} +(-4.38470e6 + 7.59451e6i) q^{40} +2.13515e7 q^{41} +(1.50823e6 - 8.09344e6i) q^{42} +1.01098e7 q^{43} +(9.91211e6 - 1.71683e7i) q^{44} +(7.02343e6 + 1.21649e7i) q^{45} +(-51705.5 - 89556.5i) q^{46} +(-1.31759e7 + 2.28213e7i) q^{47} -5.30842e6 q^{48} +(-3.76449e7 - 1.45352e7i) q^{49} -4.20897e7 q^{50} +(2.66312e7 - 4.61266e7i) q^{51} +(1.17778e7 + 2.03997e7i) q^{52} +(1.19254e7 + 2.06555e7i) q^{53} +(-4.25153e6 + 7.36386e6i) q^{54} +1.65793e8 q^{55} +(-4.76676e6 + 2.55793e7i) q^{56} +6.01447e7 q^{57} +(-2.04280e7 + 3.53823e7i) q^{58} +(-7.76530e7 - 1.34499e8i) q^{59} +(-2.21975e7 - 3.84472e7i) q^{60} +(-4.28559e7 + 7.42286e7i) q^{61} -1.38127e7 q^{62} +(3.16660e7 + 2.70990e7i) q^{63} +1.67772e7 q^{64} +(-9.84994e7 + 1.70606e8i) q^{65} +(5.01800e7 + 8.69144e7i) q^{66} +(1.11224e8 + 1.92646e8i) q^{67} +(-8.41678e7 + 1.45783e8i) q^{68} +523518. q^{69} +(-2.05195e8 + 7.24373e7i) q^{70} +2.65826e8 q^{71} +(1.34369e7 - 2.32734e7i) q^{72} +(1.87429e8 + 3.24637e8i) q^{73} +(-6.19443e7 - 1.07291e8i) q^{74} +(1.06539e8 - 1.84532e8i) q^{75} -1.90087e8 q^{76} +(4.63868e8 - 1.63753e8i) q^{77} -1.19250e8 q^{78} +(-4.81092e6 + 8.33275e6i) q^{79} +(7.01551e7 + 1.21512e8i) q^{80} +(-2.15234e7 - 3.72796e7i) q^{81} +(1.70812e8 - 2.95855e8i) q^{82} +5.90221e8 q^{83} +(-1.00080e8 - 8.56462e7i) q^{84} -1.40782e9 q^{85} +(8.08785e7 - 1.40086e8i) q^{86} +(-1.03417e8 - 1.79123e8i) q^{87} +(-1.58594e8 - 2.74692e8i) q^{88} +(2.74589e8 - 4.75603e8i) q^{89} +2.24750e8 q^{90} +(-1.07082e8 + 5.74622e8i) q^{91} -1.65458e6 q^{92} +(3.49633e7 - 6.05582e7i) q^{93} +(2.10814e8 + 3.65140e8i) q^{94} +(-7.94862e8 - 1.37674e9i) q^{95} +(-4.24673e7 + 7.35556e7i) q^{96} +6.67265e8 q^{97} +(-5.02565e8 + 4.05342e8i) q^{98} -5.08073e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 48 q^{2} + 243 q^{3} - 768 q^{4} + 361 q^{5} + 7776 q^{6} + 12509 q^{7} - 24576 q^{8} - 19683 q^{9} - 5776 q^{10} + 37799 q^{11} + 62208 q^{12} - 441172 q^{13} + 38752 q^{14} + 58482 q^{15} - 196608 q^{16}+ \cdots - 495998478 q^{99}+O(q^{100}) \) 6 * q + 48 * q^2 + 243 * q^3 - 768 * q^4 + 361 * q^5 + 7776 * q^6 + 12509 * q^7 - 24576 * q^8 - 19683 * q^9 - 5776 * q^10 + 37799 * q^11 + 62208 * q^12 - 441172 * q^13 + 38752 * q^14 + 58482 * q^15 - 196608 * q^16 - 781816 * q^17 + 314928 * q^18 - 620154 * q^19 - 184832 * q^20 + 817047 * q^21 + 1209568 * q^22 + 1204784 * q^23 - 995328 * q^24 - 4020946 * q^25 - 3529376 * q^26 - 3188646 * q^27 - 2582272 * q^28 - 10561070 * q^29 + 467856 * q^30 + 12838457 * q^31 + 3145728 * q^32 - 3061719 * q^33 - 25018112 * q^34 - 20450416 * q^35 + 10077696 * q^36 + 8014770 * q^37 + 9922464 * q^38 - 17867466 * q^39 - 1478656 * q^40 + 13006056 * q^41 + 16211664 * q^42 - 45086976 * q^43 + 9676544 * q^44 + 2368521 * q^45 - 19276544 * q^46 - 21473082 * q^47 - 31850496 * q^48 - 92935311 * q^49 - 128670272 * q^50 + 63327096 * q^51 + 56470016 * q^52 + 13685715 * q^53 - 25509168 * q^54 + 610214782 * q^55 - 51236864 * q^56 - 100464948 * q^57 - 84488560 * q^58 - 92528141 * q^59 - 7485696 * q^60 - 7516114 * q^61 + 410830624 * q^62 - 15890742 * q^63 + 100663296 * q^64 + 79637616 * q^65 + 48987504 * q^66 - 137325404 * q^67 - 200144896 * q^68 + 195175008 * q^69 + 33639760 * q^70 + 16380692 * q^71 + 80621568 * q^72 + 394016164 * q^73 - 128236320 * q^74 + 325696626 * q^75 + 317518848 * q^76 + 140332213 * q^77 - 571758912 * q^78 + 35090117 * q^79 + 23658496 * q^80 - 129140163 * q^81 + 104048448 * q^82 + 1913896010 * q^83 + 50222592 * q^84 - 823798640 * q^85 - 360695808 * q^86 - 427723335 * q^87 - 154824704 * q^88 - 855499686 * q^89 + 75792672 * q^90 - 1675912546 * q^91 - 616849408 * q^92 - 1039915017 * q^93 + 343569312 * q^94 - 2705508088 * q^95 - 254803968 * q^96 + 4021139590 * q^97 - 2185772400 * q^98 - 495998478 * q^99

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