LMFDB - Embedded newform 81.9.f.a.35.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [81,9,Mod(8,81)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(81, base_ring=CyclotomicField(18))

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

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("81.8");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	81.f (of order $18$, degree $6$, not 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:	$32.9976674150$
Analytic rank:	$0$
Dimension:	$138$
Relative dimension:	$23$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			35.17
Character	$\chi$	$=$	81.35
Dual form			81.9.f.a.44.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(9.88054 - 11.7752i) q^{2} +(3.42444 + 19.4209i) q^{4} +(-249.434 + 685.313i) q^{5} +(166.167 - 942.382i) q^{7} +(3670.39 + 2119.10i) q^{8} +O(q^{10})$	\(q+(9.88054 - 11.7752i) q^{2} +(3.42444 + 19.4209i) q^{4} +(-249.434 + 685.313i) q^{5} +(166.167 - 942.382i) q^{7} +(3670.39 + 2119.10i) q^{8} +(5605.14 + 9708.38i) q^{10} +(-5438.06 - 14941.0i) q^{11} +(355.199 - 298.048i) q^{13} +(-9454.88 - 11267.9i) q^{14} +(56474.3 - 20554.9i) q^{16} +(-63070.2 + 36413.6i) q^{17} +(-102742. + 177954. i) q^{19} +(-14163.6 - 2497.42i) q^{20} +(-229663. - 83590.6i) q^{22} +(-379204. + 66863.9i) q^{23} +(-108201. - 90791.5i) q^{25} -7127.40i q^{26} +18871.0 q^{28} +(-567519. + 676343. i) q^{29} +(-97669.2 - 553910. i) q^{31} +(-55127.3 + 151461. i) q^{32} +(-194391. + 1.10245e6i) q^{34} +(604379. + 348938. i) q^{35} +(148109. + 256532. i) q^{37} +(1.08029e6 + 2.96808e6i) q^{38} +(-2.36777e6 + 1.98679e6i) q^{40} +(-1.81172e6 - 2.15913e6i) q^{41} +(2.61681e6 - 952442. i) q^{43} +(271545. - 156777. i) q^{44} +(-2.95941e6 + 5.12584e6i) q^{46} +(-8.06828e6 - 1.42265e6i) q^{47} +(4.55667e6 + 1.65849e6i) q^{49} +(-2.13817e6 + 377017. i) q^{50} +(7004.72 + 5877.66i) q^{52} +7.35774e6i q^{53} +1.15957e7 q^{55} +(2.60690e6 - 3.10679e6i) q^{56} +(2.35666e6 + 1.33653e7i) q^{58} +(1.04822e6 - 2.87997e6i) q^{59} +(-651982. + 3.69757e6i) q^{61} +(-7.48740e6 - 4.32285e6i) q^{62} +(8.93142e6 + 1.54697e7i) q^{64} +(115657. + 317766. i) q^{65} +(-2.25228e7 + 1.88988e7i) q^{67} +(-923167. - 1.10019e6i) q^{68} +(1.00804e7 - 3.66896e6i) q^{70} +(-2.78508e6 + 1.60797e6i) q^{71} +(9.35105e6 - 1.61965e7i) q^{73} +(4.48410e6 + 790668. i) q^{74} +(-3.80786e6 - 1.38595e6i) q^{76} +(-1.49837e7 + 2.64203e6i) q^{77} +(-3.85677e7 - 3.23621e7i) q^{79} +4.38296e7i q^{80} -4.33248e7 q^{82} +(-5.07949e7 + 6.05350e7i) q^{83} +(-9.22290e6 - 5.23057e7i) q^{85} +(1.46403e7 - 4.02240e7i) q^{86} +(1.17016e7 - 6.63630e7i) q^{88} +(8.67510e7 + 5.00857e7i) q^{89} +(-221852. - 384259. i) q^{91} +(-2.59712e6 - 7.13553e6i) q^{92} +(-9.64709e7 + 8.09487e7i) q^{94} +(-9.63268e7 - 1.14798e8i) q^{95} +(1.05909e8 - 3.85479e7i) q^{97} +(6.45513e7 - 3.72687e7i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 138 q + 6 q^{2} - 6 q^{4} + 447 q^{5} - 6 q^{7} + 9 q^{8}+O(q^{10}) $ 138 * q + 6 * q^2 - 6 * q^4 + 447 * q^5 - 6 * q^7 + 9 * q^8	$ 138 q + 6 q^{2} - 6 q^{4} + 447 q^{5} - 6 q^{7} + 9 q^{8} - 3 q^{10} - 28668 q^{11} - 6 q^{13} + 120975 q^{14} - 774 q^{16} + 9 q^{17} - 3 q^{19} - 137913 q^{20} - 185478 q^{22} - 68376 q^{23} + 507585 q^{25} - 12 q^{28} + 943980 q^{29} + 920739 q^{31} + 3005136 q^{32} + 660474 q^{34} - 6225408 q^{35} - 3 q^{37} + 23716884 q^{38} - 975273 q^{40} - 16694382 q^{41} + 4412514 q^{43} - 17341119 q^{44} - 3 q^{46} + 11341869 q^{47} + 11347482 q^{49} + 40948977 q^{50} + 14465511 q^{52} - 12 q^{55} - 52215771 q^{56} - 19078611 q^{58} - 76116738 q^{59} + 34059450 q^{61} + 223709616 q^{62} + 100663293 q^{64} - 20396037 q^{65} - 103603884 q^{67} - 101921427 q^{68} + 135373629 q^{70} - 125718795 q^{71} - 7632642 q^{73} + 66643887 q^{74} - 203790342 q^{76} + 343269159 q^{77} - 68767890 q^{79} - 12 q^{82} - 383244663 q^{83} + 170435619 q^{85} - 71426730 q^{86} - 192774918 q^{88} - 135692730 q^{89} + 77546796 q^{91} + 1343159175 q^{92} - 44451609 q^{94} - 881099997 q^{95} + 31339344 q^{97} - 1293135102 q^{98}+O(q^{100}) $ 138 * q + 6 * q^2 - 6 * q^4 + 447 * q^5 - 6 * q^7 + 9 * q^8 - 3 * q^10 - 28668 * q^11 - 6 * q^13 + 120975 * q^14 - 774 * q^16 + 9 * q^17 - 3 * q^19 - 137913 * q^20 - 185478 * q^22 - 68376 * q^23 + 507585 * q^25 - 12 * q^28 + 943980 * q^29 + 920739 * q^31 + 3005136 * q^32 + 660474 * q^34 - 6225408 * q^35 - 3 * q^37 + 23716884 * q^38 - 975273 * q^40 - 16694382 * q^41 + 4412514 * q^43 - 17341119 * q^44 - 3 * q^46 + 11341869 * q^47 + 11347482 * q^49 + 40948977 * q^50 + 14465511 * q^52 - 12 * q^55 - 52215771 * q^56 - 19078611 * q^58 - 76116738 * q^59 + 34059450 * q^61 + 223709616 * q^62 + 100663293 * q^64 - 20396037 * q^65 - 103603884 * q^67 - 101921427 * q^68 + 135373629 * q^70 - 125718795 * q^71 - 7632642 * q^73 + 66643887 * q^74 - 203790342 * q^76 + 343269159 * q^77 - 68767890 * q^79 - 12 * q^82 - 383244663 * q^83 + 170435619 * q^85 - 71426730 * q^86 - 192774918 * q^88 - 135692730 * q^89 + 77546796 * q^91 + 1343159175 * q^92 - 44451609 * q^94 - 881099997 * q^95 + 31339344 * q^97 - 1293135102 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{13}{18}\right)$

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 $

$2$	9.88054	−	11.7752i	0.617533	−	0.735948i	−0.363111	−	0.931746i	$-0.618285\pi$
$2$	9.88054	−	11.7752i	0.617533	−	0.735948i	0.980644	+	0.195798i	$0.0627298\pi$
$3$		0			0
$3$		0			0
$4$	3.42444	+	19.4209i	0.0133767	+	0.0758631i
$5$	−249.434	+	685.313i	−0.399094	+	1.09650i	0.563633	+	0.826025i	$0.309403\pi$
$5$	−249.434	+	685.313i	−0.399094	+	1.09650i	−0.962727	+	0.270476i	$0.912819\pi$
$6$		0			0
$7$	166.167	−	942.382i	0.0692076	−	0.392496i	−0.930452	−	0.366413i	$-0.880586\pi$
$7$	166.167	−	942.382i	0.0692076	−	0.392496i	0.999660	−	0.0260824i	$-0.00830322\pi$
$8$	3670.39	+	2119.10i	0.896092	+	0.517359i
$9$		0			0
$10$	5605.14	+	9708.38i	0.560514	+	0.970838i
$11$	−5438.06	−	14941.0i	−0.371427	−	1.02049i	−0.974810	−	0.223036i	$-0.928403\pi$
$11$	−5438.06	−	14941.0i	−0.371427	−	1.02049i	0.603383	−	0.797451i	$-0.293819\pi$
$12$		0			0
$13$	355.199	−	298.048i	0.0124365	−	0.0104355i	−0.636548	−	0.771237i	$-0.719638\pi$
$13$	355.199	−	298.048i	0.0124365	−	0.0104355i	0.648985	+	0.760801i	$0.275194\pi$
$14$	−9454.88	−	11267.9i	−0.246118	−	0.293312i
$15$		0			0
$16$	56474.3	−	20554.9i	0.861729	−	0.313644i
$17$	−63070.2	+	36413.6i	−0.755142	+	0.435982i	−0.827549	−	0.561394i	$-0.810265\pi$
$17$	−63070.2	+	36413.6i	−0.755142	+	0.435982i	0.0724067	+	0.997375i	$0.476932\pi$
$18$		0			0
$19$	−102742.	+	177954.i	−0.788374	+	1.36550i	0.138589	+	0.990350i	$0.455743\pi$
$19$	−102742.	+	177954.i	−0.788374	+	1.36550i	−0.926963	+	0.375153i	$0.877590\pi$
$20$	−14163.6	−	2497.42i	−0.0885225	−	0.0156089i
$21$		0			0
$22$	−229663.	−	83590.6i	−0.980394	−	0.356834i
$23$	−379204.	+	66863.9i	−1.35507	+	0.238935i	−0.803555	−	0.595230i	$-0.797061\pi$
$23$	−379204.	+	66863.9i	−1.35507	+	0.238935i	−0.551515	+	0.834165i	$0.685950\pi$
$24$		0			0
$25$	−108201.	−	90791.5i	−0.276995	−	0.232426i
$26$		−	7127.40i		−	0.0155969i
$27$		0			0
$28$	18871.0			0.0307017
$29$	−567519.	+	676343.i	−0.802396	+	0.956258i	−0.999710	−	0.0240824i	$-0.992334\pi$
$29$	−567519.	+	676343.i	−0.802396	+	0.956258i	0.197314	+	0.980340i	$0.436778\pi$
$30$		0			0
$31$	−97669.2	−	553910.i	−0.105757	−	0.599780i	−0.990915	−	0.134489i	$-0.957061\pi$
$31$	−97669.2	−	553910.i	−0.105757	−	0.599780i	0.885158	−	0.465291i	$-0.154050\pi$
$32$	−55127.3	+	151461.i	−0.0525735	+	0.144445i
$33$		0			0
$34$	−194391.	+	1.10245e6i	−0.145466	+	0.824978i
$35$	604379.	+	348938.i	0.402752	+	0.232529i
$36$		0			0
$37$	148109.	+	256532.i	0.0790267	+	0.136878i	0.902830	−	0.429997i	$-0.141485\pi$
$37$	148109.	+	256532.i	0.0790267	+	0.136878i	−0.823804	+	0.566875i	$0.808152\pi$
$38$	1.08029e6	+	2.96808e6i	0.518092	+	1.42345i
$39$		0			0
$40$	−2.36777e6	+	1.98679e6i	−0.924910	+	0.776092i
$41$	−1.81172e6	−	2.15913e6i	−0.641145	−	0.764087i	0.343406	−	0.939187i	$-0.388419\pi$
$41$	−1.81172e6	−	2.15913e6i	−0.641145	−	0.764087i	−0.984551	+	0.175101i	$0.943975\pi$
$42$		0			0
$43$	2.61681e6	−	952442.i	0.765418	−	0.278589i	0.0703394	−	0.997523i	$-0.477592\pi$
$43$	2.61681e6	−	952442.i	0.765418	−	0.278589i	0.695079	+	0.718934i	$0.255370\pi$
$44$	271545.	−	156777.i	0.0724488	−	0.0418283i
$45$		0			0
$46$	−2.95941e6	+	5.12584e6i	−0.660957	+	1.14481i
$47$	−8.06828e6	−	1.42265e6i	−1.65344	−	0.291547i	−0.732362	−	0.680916i	$-0.761582\pi$
$47$	−8.06828e6	−	1.42265e6i	−1.65344	−	0.291547i	−0.921082	+	0.389369i	$0.872693\pi$
$48$		0			0
$49$	4.55667e6	+	1.65849e6i	0.790430	+	0.287693i
$50$	−2.13817e6	+	377017.i	−0.342107	+	0.0603227i
$51$		0			0
$52$	7004.72	+	5877.66i	0.000958026	+	0.000803879i
$53$			7.35774e6i			0.932483i	0.884658	+	0.466241i	$0.154392\pi$
$53$			7.35774e6i			0.932483i	−0.884658	+	0.466241i	$0.845608\pi$
$54$		0			0
$55$	1.15957e7			1.26720
$56$	2.60690e6	−	3.10679e6i	0.265078	−	0.315907i
$57$		0			0
$58$	2.35666e6	+	1.33653e7i	0.208250	+	1.18104i
$59$	1.04822e6	−	2.87997e6i	0.0865060	−	0.237673i	−0.888895	−	0.458111i	$-0.848526\pi$
$59$	1.04822e6	−	2.87997e6i	0.0865060	−	0.237673i	0.975401	+	0.220438i	$0.0707485\pi$
$60$		0			0
$61$	−651982.	+	3.69757e6i	−0.0470887	+	0.267053i	−0.999258	−	0.0385181i	$-0.987736\pi$
$61$	−651982.	+	3.69757e6i	−0.0470887	+	0.267053i	0.952169	+	0.305571i	$0.0988474\pi$
$62$	−7.48740e6	−	4.32285e6i	−0.506716	−	0.292552i
$63$		0			0
$64$	8.93142e6	+	1.54697e7i	0.532354	+	0.922064i
$65$	115657.	+	317766.i	0.00647917	+	0.0178014i
$66$		0			0
$67$	−2.25228e7	+	1.88988e7i	−1.11769	+	0.937856i	−0.998486	−	0.0550138i	$-0.982480\pi$
$67$	−2.25228e7	+	1.88988e7i	−1.11769	+	0.937856i	−0.119207	+	0.992869i	$0.538035\pi$
$68$	−923167.	−	1.10019e6i	−0.0431762	−	0.0514554i
$69$		0			0
$70$	1.00804e7	−	3.66896e6i	0.419842	−	0.152810i
$71$	−2.78508e6	+	1.60797e6i	−0.109599	+	0.0632768i	−0.553797	−	0.832652i	$-0.686822\pi$
$71$	−2.78508e6	+	1.60797e6i	−0.109599	+	0.0632768i	0.444199	+	0.895928i	$0.353488\pi$
$72$		0			0
$73$	9.35105e6	−	1.61965e7i	0.329283	−	0.570334i	−0.653087	−	0.757283i	$-0.726526\pi$
$73$	9.35105e6	−	1.61965e7i	0.329283	−	0.570334i	0.982370	+	0.186948i	$0.0598597\pi$
$74$	4.48410e6	+	790668.i	0.149537	+	0.0263674i
$75$		0			0
$76$	−3.80786e6	−	1.38595e6i	−0.114137	−	0.0415425i
$77$	−1.49837e7	+	2.64203e6i	−0.426242	+	0.0751580i
$78$		0			0
$79$	−3.85677e7	−	3.23621e7i	−0.990183	−	0.830862i	−0.00458868	−	0.999989i	$-0.501461\pi$
$79$	−3.85677e7	−	3.23621e7i	−0.990183	−	0.830862i	−0.985594	+	0.169127i	$0.945905\pi$
$80$			4.38296e7i			1.07006i
$81$		0			0
$82$	−4.33248e7			−0.958256
$83$	−5.07949e7	+	6.05350e7i	−1.07030	+	1.27554i	−0.110801	+	0.993843i	$0.535342\pi$
$83$	−5.07949e7	+	6.05350e7i	−1.07030	+	1.27554i	−0.959503	+	0.281697i	$0.909103\pi$
$84$		0			0
$85$	−9.22290e6	−	5.23057e7i	−0.176682	−	1.00201i
$86$	1.46403e7	−	4.02240e7i	0.267644	−	0.735346i
$87$		0			0
$88$	1.17016e7	−	6.63630e7i	0.195126	−	1.10661i
$89$	8.67510e7	+	5.00857e7i	1.38266	+	0.798277i	0.992473	−	0.122460i	$-0.0390784\pi$
$89$	8.67510e7	+	5.00857e7i	1.38266	+	0.798277i	0.390183	+	0.920737i	$0.372412\pi$
$90$		0			0
$91$	−221852.	−	384259.i	−0.00323518	−	0.00560349i
$92$	−2.59712e6	−	7.13553e6i	−0.0362527	−	0.0996036i
$93$		0			0
$94$	−9.64709e7	+	8.09487e7i	−1.23562	+	1.03681i
$95$	−9.63268e7	−	1.14798e8i	−1.18264	−	1.40942i
$96$		0			0
$97$	1.05909e8	−	3.85479e7i	1.19632	−	0.435425i	0.334382	−	0.942438i	$-0.391473\pi$
$97$	1.05909e8	−	3.85479e7i	1.19632	−	0.435425i	0.861939	+	0.507013i	$0.169250\pi$
$98$	6.45513e7	−	3.72687e7i	0.699844	−	0.404055i
$99$		0			0
$100$	1.39273e6	−	2.41228e6i	0.0139273	−	0.0241228i
$101$	9.86284e7	+	1.73908e7i	0.947799	+	0.167123i	0.626120	−	0.779726i	$-0.284642\pi$
$101$	9.86284e7	+	1.73908e7i	0.947799	+	0.167123i	0.321679	+	0.946849i	$0.395753\pi$
$102$		0			0
$103$	9.90079e7	+	3.60359e7i	0.879672	+	0.320175i	0.742078	−	0.670314i	$-0.233841\pi$
$103$	9.90079e7	+	3.60359e7i	0.879672	+	0.320175i	0.137595	+	0.990489i	$0.456063\pi$
$104$	1.93531e6	−	341248.i	0.0165431	−	0.00291700i
$105$		0			0
$106$	8.66385e7	+	7.26984e7i	0.686258	+	0.575839i
$107$		−	7.74341e7i		−	0.590741i	−0.955383	−	0.295370i	$-0.904557\pi$
$107$		−	7.74341e7i		−	0.590741i	0.955383	−	0.295370i	$-0.0954431\pi$
$108$		0			0
$109$	−5.16388e7			−0.365822			−0.182911	−	0.983129i	$-0.558552\pi$
$109$	−5.16388e7			−0.365822			−0.182911	+	0.983129i	$0.558552\pi$
$110$	1.14571e8	−	1.36541e8i	0.782538	−	0.932593i
$111$		0			0
$112$	−9.98643e6	−	5.66359e7i	−0.0634656	−	0.359931i
$113$	5.81596e7	−	1.59792e8i	0.356704	−	0.980036i	−0.623461	−	0.781854i	$-0.714274\pi$
$113$	5.81596e7	−	1.59792e8i	0.356704	−	0.980036i	0.980165	−	0.198182i	$-0.0635036\pi$
$114$		0			0
$115$	4.87635e7	−	2.76552e8i	0.278807	−	1.58119i
$116$	−1.50787e7	−	8.70566e6i	−0.0832781	−	0.0480806i
$117$		0			0
$118$	−2.35551e7	−	4.07987e7i	−0.121495	−	0.210435i
$119$	2.38353e7	+	6.54870e7i	0.118859	+	0.326563i
$120$		0			0
$121$	−2.94512e7	+	2.47125e7i	−0.137392	+	0.115286i
$122$	3.70976e7	+	4.42112e7i	0.167458	+	0.199569i
$123$		0			0
$124$	1.04230e7	−	3.79366e6i	0.0440865	−	0.0160462i
$125$	−1.57505e8	+	9.09353e7i	−0.645139	+	0.372471i
$126$		0			0
$127$	1.06994e8	−	1.85319e8i	0.411286	−	0.712368i	−0.583745	−	0.811937i	$-0.698413\pi$
$127$	1.06994e8	−	1.85319e8i	0.411286	−	0.712368i	0.995031	+	0.0995689i	$0.0317464\pi$
$128$	2.29769e8	+	4.05146e7i	0.855958	+	0.150928i
$129$		0			0
$130$	4.88450e6	+	1.77781e6i	0.0171020	+	0.00622462i
$131$	−8.59778e6	+	1.51602e6i	−0.0291945	+	0.00514778i	−0.188226	−	0.982126i	$-0.560274\pi$
$131$	−8.59778e6	+	1.51602e6i	−0.0291945	+	0.00514778i	0.159032	+	0.987273i	$0.449163\pi$
$132$		0			0
$133$	1.50628e8	+	1.26392e8i	0.481393	+	0.403936i
$134$			4.51940e8i			1.40172i
$135$		0			0
$136$	−3.08657e8			−0.902236
$137$	3.14049e8	−	3.74269e8i	0.891488	−	1.06243i	−0.106192	−	0.994346i	$-0.533866\pi$
$137$	3.14049e8	−	3.74269e8i	0.891488	−	1.06243i	0.997679	−	0.0680880i	$-0.0216899\pi$
$138$		0			0
$139$	7.43508e7	+	4.21664e8i	0.199171	+	1.12956i	0.906352	+	0.422523i	$0.138856\pi$
$139$	7.43508e7	+	4.21664e8i	0.199171	+	1.12956i	−0.707181	+	0.707033i	$0.750033\pi$
$140$	−4.70706e6	+	1.29325e7i	−0.0122529	+	0.0336644i
$141$		0			0
$142$	−8.58402e6	+	4.86824e7i	−0.0211124	+	0.119734i
$143$	−6.38471e6	−	3.68621e6i	−0.0152685	−	0.00881529i
$144$		0			0
$145$	−3.21949e8	−	5.57631e8i	−0.728307	−	1.26146i
$146$	−9.83230e7	−	2.70140e8i	−0.216393	−	0.594536i
$147$		0			0
$148$	−4.47490e6	+	3.75489e6i	−0.00932689	+	0.00782619i
$149$	−1.16323e8	−	1.38628e8i	−0.236004	−	0.281259i	0.635023	−	0.772493i	$-0.280990\pi$
$149$	−1.16323e8	−	1.38628e8i	−0.236004	−	0.281259i	−0.871028	+	0.491234i	$0.836546\pi$
$150$		0			0
$151$	−1.24586e8	+	4.53455e7i	−0.239641	+	0.0872222i	−0.459049	−	0.888411i	$-0.651810\pi$
$151$	−1.24586e8	+	4.53455e7i	−0.239641	+	0.0872222i	0.219408	+	0.975633i	$0.429587\pi$
$152$	−7.54205e8	+	4.35440e8i	−1.41291	+	0.815745i
$153$		0			0
$154$	−1.16937e8	+	2.02540e8i	−0.207907	+	0.360105i
$155$	4.03964e8	+	7.12297e7i	0.699867	+	0.123405i
$156$		0			0
$157$	9.30730e8	+	3.38758e8i	1.53188	+	0.557559i	0.964081	−	0.265607i	$-0.0855724\pi$
$157$	9.30730e8	+	3.38758e8i	1.53188	+	0.557559i	0.567800	+	0.823166i	$0.307795\pi$
$158$	−7.62139e8	+	1.34386e8i	−1.22294	+	0.215638i
$159$		0			0
$160$	−9.00477e7	−	7.55590e7i	−0.137402	−	0.115294i
$161$			3.68466e8i			0.548395i
$162$		0			0
$163$	−1.23450e9			−1.74880			−0.874399	−	0.485207i	$-0.838744\pi$
$163$	−1.23450e9			−1.74880			−0.874399	+	0.485207i	$0.838744\pi$
$164$	3.57281e7	−	4.25791e7i	0.0493895	−	0.0588602i
$165$		0			0
$166$	2.10929e8	+	1.19624e9i	0.277781	+	1.57538i
$167$	−3.34660e8	+	9.19469e8i	−0.430266	+	1.18215i	0.515383	+	0.856960i	$0.327650\pi$
$167$	−3.34660e8	+	9.19469e8i	−0.430266	+	1.18215i	−0.945650	+	0.325187i	$0.894573\pi$
$168$		0			0
$169$	−1.41613e8	+	8.03126e8i	−0.173602	+	0.984548i
$170$	−7.07035e8	−	4.08207e8i	−0.846535	−	0.488747i
$171$		0			0
$172$	2.74584e7	+	4.75594e7i	0.0313734	+	0.0543403i
$173$	2.12893e8	+	5.84919e8i	0.237672	+	0.652997i	0.999983	+	0.00578720i	$0.00184213\pi$
$173$	2.12893e8	+	5.84919e8i	0.237672	+	0.652997i	−0.762312	+	0.647210i	$0.775936\pi$
$174$		0			0
$175$	−1.03540e8	+	8.68801e7i	−0.110396	+	0.0926336i
$176$	−6.14221e8	−	7.32000e8i	−0.640139	−	0.762888i
$177$		0			0
$178$	1.44691e9	−	5.26633e8i	1.44133	−	0.524600i
$179$	−1.05782e9	+	6.10734e8i	−1.03039	+	0.594894i	−0.917095	−	0.398668i	$-0.869473\pi$
$179$	−1.05782e9	+	6.10734e8i	−1.03039	+	0.594894i	−0.113291	+	0.993562i	$0.536139\pi$
$180$		0			0
$181$	5.91167e8	−	1.02393e9i	0.550803	−	0.954018i	−0.447414	−	0.894327i	$-0.647655\pi$
$181$	5.91167e8	−	1.02393e9i	0.550803	−	0.954018i	0.998217	−	0.0596915i	$-0.0190117\pi$
$182$	−6.71673e6	−	1.18434e6i	−0.00612170	−	0.00107942i
$183$		0			0
$184$	−1.53352e9	−	5.58156e8i	−1.33788	−	0.486950i
$185$	−2.12748e8	+	3.75132e7i	−0.181626	+	0.0320256i
$186$		0			0
$187$	8.87034e8	+	7.44310e8i	0.725394	+	0.608678i
$188$		−	1.61565e8i		−	0.129335i
$189$		0			0
$190$	−2.30352e9			−1.76758
$191$	4.26602e8	−	5.08405e8i	0.320545	−	0.382011i	−0.581577	−	0.813491i	$-0.697564\pi$
$191$	4.26602e8	−	5.08405e8i	0.320545	−	0.382011i	0.902122	+	0.431480i	$0.142009\pi$
$192$		0			0
$193$	1.59425e8	+	9.04142e8i	0.114902	+	0.651640i	0.986799	+	0.161951i	$0.0517785\pi$
$193$	1.59425e8	+	9.04142e8i	0.114902	+	0.651640i	−0.871897	+	0.489689i	$0.837110\pi$
$194$	5.92534e8	−	1.62797e9i	0.418318	−	1.14932i
$195$		0			0
$196$	−1.66055e7	+	9.41742e7i	−0.0112519	+	0.0638128i
$197$	1.08459e9	+	6.26188e8i	0.720113	+	0.415757i	0.814794	−	0.579750i	$-0.196850\pi$
$197$	1.08459e9	+	6.26188e8i	0.720113	+	0.415757i	−0.0946815	+	0.995508i	$0.530183\pi$
$198$		0			0
$199$	1.49015e9	+	2.58101e9i	0.950204	+	1.64580i	0.744979	+	0.667087i	$0.232459\pi$
$199$	1.49015e9	+	2.58101e9i	0.950204	+	1.64580i	0.205225	+	0.978715i	$0.434207\pi$
$200$	−2.04744e8	−	5.62530e8i	−0.127965	−	0.351581i
$201$		0			0
$202$	1.17928e9	−	9.89534e8i	0.708291	−	0.594327i
$203$	5.43070e8	+	6.47206e8i	0.319795	+	0.381117i
$204$		0			0
$205$	1.93158e9	−	7.03038e8i	1.09370	−	0.398074i
$206$	1.40258e9	−	8.09780e8i	0.778859	−	0.449674i
$207$		0			0
$208$	1.39333e7	−	2.41331e7i	0.00744388	−	0.0128932i
$209$	3.21751e9	+	5.67335e8i	1.68630	+	0.297341i
$210$		0			0
$211$	−6.41995e7	−	2.33667e7i	−0.0323893	−	0.0117887i	0.325775	−	0.945447i	$-0.394375\pi$
$211$	−6.41995e7	−	2.33667e7i	−0.0323893	−	0.0117887i	−0.358164	+	0.933659i	$0.616597\pi$
$212$	−1.42894e8	+	2.51961e7i	−0.0707410	+	0.0124735i
$213$		0			0
$214$	−9.11799e8	−	7.65090e8i	−0.434754	−	0.364802i
$215$			2.03091e9i			0.950465i
$216$		0			0
$217$	−5.38224e8			−0.242730
$218$	−5.10219e8	+	6.08055e8i	−0.225907	+	0.269226i
$219$		0			0
$220$	3.97086e7	+	2.25199e8i	0.0169510	+	0.0961337i
$221$	−1.15495e7	+	3.17320e7i	−0.00484166	+	0.0133024i
$222$		0			0
$223$	7.32804e8	−	4.15594e9i	0.296325	−	1.68054i	−0.365443	−	0.930834i	$-0.619082\pi$
$223$	7.32804e8	−	4.15594e9i	0.296325	−	1.68054i	0.661768	−	0.749709i	$-0.269806\pi$
$224$	1.33574e8	+	7.71189e7i	0.0530554	+	0.0306315i
$225$		0			0
$226$	−1.30693e9	−	2.26367e9i	−0.500979	−	0.867720i
$227$	−6.51293e8	−	1.78941e9i	−0.245286	−	0.673918i	−0.999844	−	0.0176840i	$-0.994371\pi$
$227$	−6.51293e8	−	1.78941e9i	−0.245286	−	0.673918i	0.754558	−	0.656234i	$-0.227852\pi$
$228$		0			0
$229$	−9.93160e8	+	8.33360e8i	−0.361141	+	0.303034i	−0.805246	−	0.592942i	$-0.797967\pi$
$229$	−9.93160e8	+	8.33360e8i	−0.361141	+	0.303034i	0.444104	+	0.895975i	$0.353522\pi$
$230$	−2.77463e9	−	3.30668e9i	−0.991503	−	1.18163i
$231$		0			0
$232$	−3.51626e9	+	1.27981e9i	−1.21375	+	0.441769i
$233$	1.99798e9	−	1.15353e9i	0.677902	−	0.391387i	−0.121162	−	0.992633i	$-0.538662\pi$
$233$	1.99798e9	−	1.15353e9i	0.677902	−	0.391387i	0.799064	+	0.601246i	$0.205329\pi$
$234$		0			0
$235$	2.98746e9	−	5.17444e9i	0.979560	−	1.69665i
$236$	5.95214e7	+	1.04952e7i	0.0191878	+	0.00338332i
$237$		0			0
$238$	1.00663e9	+	3.66382e8i	0.313733	+	0.114189i
$239$	1.48333e9	−	2.61550e8i	0.454616	−	0.0801612i	0.0583490	−	0.998296i	$-0.481416\pi$
$239$	1.48333e9	−	2.61550e8i	0.454616	−	0.0801612i	0.396268	+	0.918135i	$0.370305\pi$
$240$		0			0
$241$	−1.49049e9	−	1.25067e9i	−0.441835	−	0.370744i	0.394561	−	0.918870i	$-0.370897\pi$
$241$	−1.49049e9	−	1.25067e9i	−0.441835	−	0.370744i	−0.836396	+	0.548126i	$0.815341\pi$
$242$			5.90966e8i			0.172306i
$243$		0			0
$244$	−7.40430e7			−0.0208894
$245$	−2.27317e9	+	2.70906e9i	−0.630911	+	0.751891i
$246$		0			0
$247$	1.65449e7	+	9.38309e7i	0.00444505	+	0.0252091i
$248$	8.15307e8	−	2.24004e9i	0.215533	−	0.592173i
$249$		0			0
$250$	−4.85451e8	+	2.75313e9i	−0.124276	+	0.704802i
$251$	−1.17911e9	−	6.80760e8i	−0.297071	−	0.171514i	0.344055	−	0.938949i	$-0.388199\pi$
$251$	−1.17911e9	−	6.80760e8i	−0.297071	−	0.171514i	−0.641126	+	0.767435i	$0.721533\pi$
$252$		0			0
$253$	3.06115e9	+	5.30206e9i	0.747140	+	1.29408i
$254$	−1.12500e9	−	3.09092e9i	−0.270283	−	0.742596i
$255$		0			0
$256$	−7.55723e8	+	6.34127e8i	−0.175955	+	0.147644i
$257$	3.23578e9	+	3.85626e9i	0.741732	+	0.883962i	0.996547	−	0.0830279i	$-0.0264591\pi$
$257$	3.23578e9	+	3.85626e9i	0.741732	+	0.883962i	−0.254815	+	0.966990i	$0.582015\pi$
$258$		0			0
$259$	2.66362e8	−	9.69478e7i	0.0591934	−	0.0215446i
$260$	−5.77525e6	+	3.33434e6i	−0.00126380	+	0.000729654i
$261$		0			0
$262$	−6.70993e7	+	1.16219e8i	−0.0142401	+	0.0246646i
$263$	−1.25261e8	−	2.20869e7i	−0.0261814	−	0.00461649i	0.160542	−	0.987029i	$-0.448676\pi$
$263$	−1.25261e8	−	2.20869e7i	−0.0261814	−	0.00461649i	−0.186724	+	0.982413i	$0.559787\pi$
$264$		0			0
$265$	−5.04235e9	−	1.83527e9i	−1.02247	−	0.372148i
$266$	2.97657e9	−	5.24850e8i	0.594552	−	0.104836i
$267$		0			0
$268$	−4.44161e8	−	3.72695e8i	−0.0860996	−	0.0722462i
$269$		−	6.25434e9i		−	1.19446i	−0.802069	−	0.597231i	$-0.796268\pi$
$269$		−	6.25434e9i		−	1.19446i	0.802069	−	0.597231i	$-0.203732\pi$
$270$		0			0
$271$	2.99105e9			0.554557			0.277278	−	0.960790i	$-0.410568\pi$
$271$	2.99105e9			0.554557			0.277278	+	0.960790i	$0.410568\pi$
$272$	−2.81336e9	+	3.35284e9i	−0.513985	+	0.612543i
$273$		0			0
$274$	−1.30411e9	−	7.39596e9i	−0.231372	−	1.31218i
$275$	−7.68107e8	+	2.11036e9i	−0.134305	+	0.368999i
$276$		0			0
$277$	1.59017e9	−	9.01832e9i	0.270100	−	1.53182i	−0.484007	−	0.875064i	$-0.660819\pi$
$277$	1.59017e9	−	9.01832e9i	0.270100	−	1.53182i	0.754107	−	0.656751i	$-0.228070\pi$
$278$	5.69979e9	+	3.29078e9i	0.954289	+	0.550959i
$279$		0			0
$280$	1.47887e9	+	2.56148e9i	0.240602	+	0.416734i
$281$	1.71612e9	+	4.71501e9i	0.275247	+	0.756235i	0.997885	+	0.0650082i	$0.0207074\pi$
$281$	1.71612e9	+	4.71501e9i	0.275247	+	0.756235i	−0.722638	+	0.691227i	$0.757070\pi$
$282$		0			0
$283$	−3.49142e9	+	2.92965e9i	−0.544322	+	0.456741i	−0.873013	−	0.487697i	$-0.837837\pi$
$283$	−3.49142e9	+	2.92965e9i	−0.544322	+	0.456741i	0.328691	+	0.944438i	$0.393393\pi$
$284$	−4.07656e7	−	4.85826e7i	−0.00626644	−	0.00746805i
$285$		0			0
$286$	−1.06490e8	+	3.87592e7i	−0.0159164	+	0.00579310i
$287$	−2.33577e9	+	1.34856e9i	−0.344273	+	0.198766i
$288$		0			0
$289$	−8.35975e8	+	1.44795e9i	−0.119840	+	0.207569i
$290$	−9.74722e9	−	1.71870e9i	−1.37813	−	0.243001i
$291$		0			0
$292$	3.46573e8	+	1.26142e8i	0.0476720	+	0.0173512i
$293$	1.04157e9	−	1.83657e8i	0.141325	−	0.0249193i	−0.102538	−	0.994729i	$-0.532696\pi$
$293$	1.04157e9	−	1.83657e8i	0.141325	−	0.0249193i	0.243863	+	0.969810i	$0.421585\pi$
$294$		0			0
$295$	1.71222e9	+	1.43672e9i	0.226085	+	0.189708i
$296$			1.25543e9i			0.163541i
$297$		0			0
$298$	−2.78170e9			−0.352732
$299$	−1.14764e8	+	1.36771e8i	−0.0143589	+	0.0171123i
$300$		0			0
$301$	−4.62735e8	−	2.62430e9i	−0.0563724	−	0.319704i
$302$	−6.97024e8	+	1.91506e9i	−0.0837953	+	0.230226i
$303$		0			0
$304$	−2.14443e9	+	1.21617e10i	−0.251083	+	1.42396i
$305$	−2.37137e9	−	1.36911e9i	−0.274031	−	0.158212i
$306$		0			0
$307$	6.93825e9	+	1.20174e10i	0.781082	+	1.35287i	0.931312	+	0.364223i	$0.118665\pi$
$307$	6.93825e9	+	1.20174e10i	0.781082	+	1.35287i	−0.150230	+	0.988651i	$0.548001\pi$
$308$	−1.02622e8	−	2.81950e8i	−0.0114034	−	0.0313307i
$309$		0			0
$310$	4.83012e9	−	4.05295e9i	0.523011	−	0.438859i
$311$	1.18032e9	+	1.40665e9i	0.126171	+	0.150364i	0.825432	−	0.564502i	$-0.190932\pi$
$311$	1.18032e9	+	1.40665e9i	0.126171	+	0.150364i	−0.699261	+	0.714867i	$0.746487\pi$
$312$		0			0
$313$	−1.18395e10	+	4.30924e9i	−1.23355	+	0.448976i	−0.874812	−	0.484462i	$-0.839015\pi$
$313$	−1.18395e10	+	4.30924e9i	−1.23355	+	0.448976i	−0.358739	+	0.933438i	$0.616793\pi$
$314$	1.31850e10	−	7.61239e9i	1.35632	−	0.783073i
$315$		0			0
$316$	4.96431e8	−	8.59843e8i	0.0497864	−	0.0862325i
$317$	4.64613e9	+	8.19239e8i	0.460102	+	0.0811285i	0.398895	−	0.916997i	$-0.369394\pi$
$317$	4.64613e9	+	8.19239e8i	0.460102	+	0.0811285i	0.0612074	+	0.998125i	$0.480505\pi$
$318$		0			0
$319$	1.31914e10	+	4.80128e9i	1.27388	+	0.463655i
$320$	−1.28294e10	+	2.26216e9i	−1.22350	+	0.215737i
$321$		0			0
$322$	4.33874e9	+	3.64064e9i	0.403590	+	0.338652i
$323$		−	1.49648e10i		−	1.37487i
$324$		0			0
$325$	−6.54931e7			−0.00587032
$326$	−1.21975e10	+	1.45364e10i	−1.07994	+	1.28702i
$327$		0			0
$328$	−2.07432e9	−	1.17641e10i	−0.179218	−	1.01639i
$329$	−2.68137e9	+	7.36700e9i	−0.228862	+	0.628792i
$330$		0			0
$331$	−2.48123e9	+	1.40717e10i	−0.206707	+	1.17229i	0.688024	+	0.725688i	$0.258478\pi$
$331$	−2.48123e9	+	1.40717e10i	−0.206707	+	1.17229i	−0.894731	+	0.446605i	$0.852633\pi$
$332$	−1.34959e9	−	7.79186e8i	−0.111083	−	0.0641341i
$333$		0			0
$334$	7.52029e9	+	1.30255e10i	0.604294	+	1.04667i
$335$	−7.33369e9	−	2.01492e10i	−0.582296	−	1.59984i
$336$		0			0
$337$	−9.59268e8	+	8.04922e8i	−0.0743739	+	0.0624071i	−0.679217	−	0.733938i	$-0.737680\pi$
$337$	−9.59268e8	+	8.04922e8i	−0.0743739	+	0.0624071i	0.604843	+	0.796345i	$0.293236\pi$
$338$	8.05773e9	+	9.60283e9i	0.617371	+	0.735754i
$339$		0			0
$340$	9.84242e8	−	3.58235e8i	0.0736523	−	0.0268072i
$341$	−7.74481e9	+	4.47147e9i	−0.572787	+	0.330699i
$342$		0			0
$343$	5.07833e9	−	8.79592e9i	0.366897	−	0.635484i
$344$	1.16231e10	+	2.04946e9i	0.830016	+	0.146354i
$345$		0			0
$346$	8.99102e9	+	3.27246e9i	0.627342	+	0.228334i
$347$	1.50803e10	−	2.65906e9i	1.04014	−	0.183405i	0.372611	−	0.927988i	$-0.378463\pi$
$347$	1.50803e10	−	2.65906e9i	1.04014	−	0.183405i	0.667530	+	0.744583i	$0.267352\pi$
$348$		0			0
$349$	1.53306e9	+	1.28639e9i	0.103338	+	0.0867106i	0.692993	−	0.720945i	$-0.256292\pi$
$349$	1.53306e9	+	1.28639e9i	0.103338	+	0.0867106i	−0.589655	+	0.807655i	$0.700736\pi$
$350$			2.07762e9i			0.138450i
$351$		0			0
$352$	2.56276e9			0.166931
$353$	−1.41892e10	+	1.69101e10i	−0.913819	+	1.08905i	0.0819028	+	0.996640i	$0.473900\pi$
$353$	−1.41892e10	+	1.69101e10i	−0.913819	+	1.08905i	−0.995721	+	0.0924062i	$0.970544\pi$
$354$		0			0
$355$	−4.07269e8	−	2.30974e9i	−0.0256429	−	0.145428i
$356$	−6.75638e8	+	1.85630e9i	−0.0420643	+	0.115571i
$357$		0			0
$358$	−3.26036e9	+	1.84904e10i	−0.198487	+	1.12568i
$359$	−2.73306e10	−	1.57793e10i	−1.64540	−	0.949970i	−0.978869	−	0.204490i	$-0.934446\pi$
$359$	−2.73306e10	−	1.57793e10i	−1.64540	−	0.949970i	−0.666528	−	0.745480i	$-0.732220\pi$
$360$		0			0
$361$	−1.26199e10	−	2.18583e10i	−0.743066	−	1.28703i
$362$	−6.21592e9	−	1.70781e10i	−0.361969	−	0.994500i
$363$		0			0
$364$	6.70295e6	−	5.62445e6i	0.000381822	−	0.000320387i
$365$	8.76721e9	+	1.04484e10i	0.493958	+	0.588676i
$366$		0			0
$367$	−1.65994e10	+	6.04170e9i	−0.915017	+	0.333039i	−0.756254	−	0.654278i	$-0.772973\pi$
$367$	−1.65994e10	+	6.04170e9i	−0.915017	+	0.333039i	−0.158763	+	0.987317i	$0.550751\pi$
$368$	−2.00409e10	+	1.15706e10i	−1.09276	+	0.630907i
$369$		0			0
$370$	−1.66034e9	+	2.87579e9i	−0.0885911	+	0.153444i
$371$	6.93380e9	+	1.22262e9i	0.365995	+	0.0645348i
$372$		0			0
$373$	−2.34037e10	−	8.51825e9i	−1.20906	−	0.440063i	−0.342685	−	0.939451i	$-0.611336\pi$
$373$	−2.34037e10	−	8.51825e9i	−1.20906	−	0.440063i	−0.866379	+	0.499387i	$0.833558\pi$
$374$	1.75287e10	−	3.09079e9i	0.895910	−	0.157973i
$375$		0			0
$376$	−2.65990e10	−	2.23192e10i	−1.33080	−	1.11668i
$377$			4.09384e8i			0.0202659i
$378$		0			0
$379$	−6.26061e9			−0.303431			−0.151716	−	0.988424i	$-0.548480\pi$
$379$	−6.26061e9			−0.303431			−0.151716	+	0.988424i	$0.548480\pi$
$380$	1.89962e9	−	2.26388e9i	0.0911028	−	0.108572i
$381$		0			0
$382$	−1.77149e9	−	1.00466e10i	−0.0831927	−	0.471809i
$383$	−1.13421e10	+	3.11622e10i	−0.527107	+	1.44822i	0.335354	+	0.942092i	$0.391144\pi$
$383$	−1.13421e10	+	3.11622e10i	−0.527107	+	1.44822i	−0.862461	+	0.506123i	$0.831078\pi$
$384$		0			0
$385$	1.92682e9	−	1.09276e10i	0.0876998	−	0.497370i
$386$	1.22216e10	+	7.05616e9i	0.550528	+	0.317848i
$387$		0			0
$388$	1.11132e9	+	1.92486e9i	0.0490355	+	0.0849320i
$389$	−1.07959e10	−	2.96615e10i	−0.471477	−	1.29537i	−0.916565	−	0.399886i	$-0.869050\pi$
$389$	−1.07959e10	−	2.96615e10i	−0.471477	−	1.29537i	0.445087	−	0.895487i	$-0.353173\pi$
$390$		0			0
$391$	2.14817e10	−	1.80253e10i	0.919099	−	0.771216i
$392$	1.32103e10	+	1.57434e10i	0.559457	+	0.666735i
$393$		0			0
$394$	1.80898e10	−	6.58414e9i	0.750669	−	0.273221i
$395$	3.17983e10	−	1.83588e10i	1.30622	−	0.754145i
$396$		0			0
$397$	1.75421e9	−	3.03838e9i	0.0706187	−	0.122315i	−0.828554	−	0.559909i	$-0.810836\pi$
$397$	1.75421e9	−	3.03838e9i	0.0706187	−	0.122315i	0.899173	+	0.437594i	$0.144169\pi$
$398$	4.51153e10	+	7.95504e9i	1.79801	+	0.317037i
$399$		0			0
$400$	−7.97679e9	−	2.90331e9i	−0.311593	−	0.113411i
$401$	−1.74810e10	+	3.08237e9i	−0.676065	+	0.119208i	−0.501131	−	0.865372i	$-0.667082\pi$
$401$	−1.74810e10	+	3.08237e9i	−0.676065	+	0.119208i	−0.174934	+	0.984580i	$0.555971\pi$
$402$		0			0
$403$	−1.99783e8	−	1.67638e8i	−0.00757424	−	0.00635555i
$404$			1.97501e9i			0.0741385i
$405$		0			0
$406$	1.29868e10			0.477966
$407$	3.02741e9	−	3.60792e9i	0.110330	−	0.131486i
$408$		0			0
$409$	6.34096e9	+	3.59614e10i	0.226601	+	1.28512i	0.859601	+	0.510966i	$0.170712\pi$
$409$	6.34096e9	+	3.59614e10i	0.226601	+	1.28512i	−0.633000	+	0.774152i	$0.718177\pi$
$410$	1.08067e10	−	2.96911e10i	0.382434	−	1.05073i
$411$		0			0
$412$	−3.60805e8	+	2.04623e9i	−0.0125223	+	0.0710175i
$413$	−2.53985e9	−	1.46639e9i	−0.0872988	−	0.0504020i
$414$		0			0
$415$	−2.88155e10	−	4.99098e10i	−0.971479	−	1.68265i
$416$	2.55614e7	+	7.02294e7i	0.000853516	+	0.00234502i
$417$		0			0
$418$	3.84712e10	−	3.22812e10i	1.26018	−	1.05741i
$419$	−9.00844e9	−	1.07358e10i	−0.292276	−	0.348321i	0.599846	−	0.800115i	$-0.295229\pi$
$419$	−9.00844e9	−	1.07358e10i	−0.292276	−	0.348321i	−0.892122	+	0.451794i	$0.850784\pi$
$420$		0			0
$421$	−8.00459e8	+	2.91343e8i	−0.0254807	+	0.00927420i	−0.354729	−	0.934969i	$-0.615427\pi$
$421$	−8.00459e8	+	2.91343e8i	−0.0254807	+	0.00927420i	0.329248	+	0.944243i	$0.393205\pi$
$422$	−9.09472e8	+	5.25084e8i	−0.0286774	+	0.0165569i
$423$		0			0
$424$	−1.55918e10	+	2.70058e10i	−0.482428	+	0.835591i
$425$	1.01303e10	+	1.78625e9i	0.310504	+	0.0547502i
$426$		0			0
$427$	3.37619e9	+	1.22883e9i	0.101558	+	0.0369642i
$428$	1.50384e9	−	2.65168e8i	0.0448154	−	0.00790216i
$429$		0			0
$430$	2.39143e10	+	2.00664e10i	0.699493	+	0.586944i
$431$		−	2.04180e10i		−	0.591703i	−0.955234	−	0.295852i	$-0.904397\pi$
$431$		−	2.04180e10i		−	0.591703i	0.955234	−	0.295852i	$-0.0956034\pi$
$432$		0			0
$433$	5.67296e10			1.61383			0.806915	−	0.590667i	$-0.201135\pi$
$433$	5.67296e10			1.61383			0.806915	+	0.590667i	$0.201135\pi$
$434$	−5.31794e9	+	6.33768e9i	−0.149894	+	0.178637i
$435$		0			0
$436$	−1.76834e8	−	1.00287e9i	−0.00489350	−	0.0277524i
$437$	2.70614e10	−	7.43505e10i	0.742034	−	2.03872i
$438$		0			0
$439$	7.25861e9	−	4.11656e10i	0.195432	−	1.10835i	−0.716370	−	0.697720i	$-0.754198\pi$
$439$	7.25861e9	−	4.11656e10i	0.195432	−	1.10835i	0.911802	−	0.410630i	$-0.134691\pi$
$440$	4.25607e10	+	2.45724e10i	1.13553	+	0.655598i
$441$		0			0
$442$	2.59534e8	+	4.49527e8i	0.00679995	+	0.0117779i
$443$	1.10129e10	+	3.02578e10i	0.285949	+	0.785639i	0.996623	+	0.0821168i	$0.0261681\pi$
$443$	1.10129e10	+	3.02578e10i	0.285949	+	0.785639i	−0.710674	+	0.703522i	$0.751610\pi$
$444$		0			0
$445$	−5.59630e10	+	4.69585e10i	−1.42712	+	1.19750i
$446$	−4.16963e10	−	4.96918e10i	−1.05380	−	1.25587i
$447$		0			0
$448$	1.60624e10	−	5.84625e9i	0.398749	−	0.145133i
$449$	1.66372e10	−	9.60550e9i	0.409350	−	0.236339i	−0.281160	−	0.959661i	$-0.590719\pi$
$449$	1.66372e10	−	9.60550e9i	0.409350	−	0.236339i	0.690511	+	0.723322i	$0.257386\pi$
$450$		0			0
$451$	−2.24072e10	+	3.88103e10i	−0.541602	+	0.938083i
$452$	3.30248e9	+	5.82316e8i	0.0791200	+	0.0139510i
$453$		0			0
$454$	−2.75057e10	−	1.00113e10i	−0.647441	−	0.235649i
$455$	3.18675e8	−	5.61910e7i	0.00743537	−	0.00131106i
$456$		0			0
$457$	2.64971e10	+	2.22337e10i	0.607482	+	0.509738i	0.893841	−	0.448385i	$-0.148000\pi$
$457$	2.64971e10	+	2.22337e10i	0.607482	+	0.509738i	−0.286359	+	0.958122i	$0.592445\pi$
$458$			1.99287e10i			0.452915i
$459$		0			0
$460$	5.53788e9			0.123684
$461$	−4.71120e10	+	5.61459e10i	−1.04310	+	1.24312i	−0.0737963	+	0.997273i	$0.523511\pi$
$461$	−4.71120e10	+	5.61459e10i	−1.04310	+	1.24312i	−0.969308	+	0.245850i	$0.920933\pi$
$462$		0			0
$463$	3.70460e8	+	2.10098e9i	0.00806153	+	0.0457192i	0.988573	−	0.150742i	$-0.0481662\pi$
$463$	3.70460e8	+	2.10098e9i	0.00806153	+	0.0457192i	−0.980512	+	0.196461i	$0.937055\pi$
$464$	−1.81480e10	+	4.98613e10i	−0.391523	+	1.07570i
$465$		0			0
$466$	6.15805e9	−	3.49240e10i	0.130587	−	0.740595i
$467$	−4.58784e9	−	2.64879e9i	−0.0964585	−	0.0556904i	0.450995	−	0.892527i	$-0.351069\pi$
$467$	−4.58784e9	−	2.64879e9i	−0.0964585	−	0.0556904i	−0.547453	+	0.836836i	$0.684403\pi$
$468$		0			0
$469$	1.40674e10	+	2.43654e10i	0.290751	+	0.503596i
$470$	−3.14121e10	−	8.63041e10i	−0.643733	−	1.76864i
$471$		0			0
$472$	9.95036e9	−	8.34934e9i	0.200480	−	0.168223i
$473$	−2.84608e10	−	3.39182e10i	−0.568594	−	0.677624i
$474$		0			0
$475$	2.72734e10	−	9.92672e9i	0.535754	−	0.194998i
$476$	−1.19020e9	+	6.87160e8i	−0.0231841	+	0.0133854i
$477$		0			0
$478$	1.15763e10	−	2.00507e10i	0.221746	−	0.384076i
$479$	5.44311e10	+	9.59767e9i	1.03396	+	0.182316i	0.664779	−	0.747040i	$-0.268526\pi$
$479$	5.44311e10	+	9.59767e9i	1.03396	+	0.182316i	0.369185	+	0.929356i	$0.379637\pi$
$480$		0			0
$481$	1.29067e8	+	4.69765e7i	0.00241121	+	0.000877607i
$482$	−2.94536e10	+	5.19347e9i	−0.545696	+	0.0962209i
$483$		0			0
$484$	−5.80794e8	−	4.87344e8i	−0.0105838	−	0.00888085i
$485$			8.21962e10i			1.48554i
$486$		0			0
$487$	−9.18684e10			−1.63324			−0.816620	−	0.577175i	$-0.804155\pi$
$487$	−9.18684e10			−1.63324			−0.816620	+	0.577175i	$0.804155\pi$
$488$	−1.02286e10	+	1.21899e10i	−0.180358	+	0.214942i
$489$		0			0
$490$	9.43948e9	+	5.35340e10i	0.163743	+	0.928635i
$491$	−8.34815e8	+	2.29364e9i	−0.0143636	+	0.0394638i	−0.946667	−	0.322213i	$-0.895573\pi$
$491$	−8.34815e8	+	2.29364e9i	−0.0143636	+	0.0394638i	0.932304	+	0.361677i	$0.117796\pi$
$492$		0			0
$493$	1.11655e10	−	6.33225e10i	0.189012	−	1.07194i
$494$	1.26835e9	+	7.32280e8i	0.0212976	+	0.0122962i
$495$		0			0
$496$	−1.69014e10	−	2.92741e10i	−0.279252	−	0.483678i
$497$	1.05253e9	+	2.89181e9i	0.0172508	+	0.0473962i
$498$		0			0
$499$	−8.20362e10	+	6.88366e10i	−1.32313	+	1.11024i	−0.337502	+	0.941325i	$0.609582\pi$
$499$	−8.20362e10	+	6.88366e10i	−1.32313	+	1.11024i	−0.985631	+	0.168915i	$0.945974\pi$
$500$	−2.30541e9	−	2.74748e9i	−0.0368866	−	0.0439597i
$501$		0			0
$502$	−1.96663e10	+	7.15796e9i	−0.309676	+	0.112713i
$503$	−7.90715e10	+	4.56519e10i	−1.23523	+	0.713160i	−0.968115	−	0.250504i	$-0.919404\pi$
$503$	−7.90715e10	+	4.56519e10i	−1.23523	+	0.713160i	−0.267114	+	0.963665i	$0.586070\pi$
$504$		0			0
$505$	−3.65194e10	+	6.32535e10i	−0.561511	+	0.972565i
$506$	9.26784e10	+	1.63417e10i	1.41376	+	0.249285i
$507$		0			0
$508$	3.96546e9	+	1.44331e9i	0.0595441	+	0.0216723i
$509$	−4.83841e9	+	8.53142e8i	−0.0720828	+	0.0127101i	−0.209573	−	0.977793i	$-0.567207\pi$
$509$	−4.83841e9	+	8.53142e8i	−0.0720828	+	0.0127101i	0.137490	+	0.990503i	$0.456096\pi$
$510$		0			0
$511$	−1.37094e10	−	1.15036e10i	−0.201065	−	0.168713i
$512$			7.48927e10i			1.08983i
$513$		0			0
$514$	7.73793e10			1.10859
$515$	−4.93918e10	+	5.88629e10i	−0.702144	+	0.836782i
$516$		0			0
$517$	2.26200e10	+	1.28284e11i	0.316614	+	1.79561i
$518$	1.49022e9	−	4.09435e9i	0.0206982	−	0.0568678i
$519$		0			0
$520$	−2.48871e8	+	1.41142e9i	−0.00340377	+	0.0193037i
$521$	−1.00292e10	−	5.79034e9i	−0.136117	−	0.0785874i	0.430395	−	0.902641i	$-0.358374\pi$
$521$	−1.00292e10	−	5.79034e9i	−0.136117	−	0.0785874i	−0.566512	+	0.824053i	$0.691708\pi$
$522$		0			0
$523$	−5.64658e10	−	9.78017e10i	−0.754708	−	1.30719i	−0.945519	−	0.325566i	$-0.894445\pi$
$523$	−5.64658e10	−	9.78017e10i	−0.754708	−	1.30719i	0.190812	−	0.981627i	$-0.438888\pi$
$524$	−5.88851e7	−	1.61786e8i	−0.000781053	−	0.00214593i
$525$		0			0
$526$	−1.49772e9	+	1.25674e9i	−0.0195654	+	0.0164173i
$527$	2.63299e10	+	3.13787e10i	0.341355	+	0.406811i
$528$		0			0
$529$	6.57367e10	−	2.39262e10i	0.839432	−	0.305528i
$530$	−7.14317e10	+	4.12411e10i	−0.905290	+	0.522669i
$531$		0			0
$532$	−1.93883e9	+	3.35816e9i	−0.0242044	+	0.0419232i
$533$	−1.28704e9	−	2.26941e8i	−0.0159472	−	0.00281192i
$534$		0			0
$535$	5.30666e10	+	1.93147e10i	0.647748	+	0.235761i
$536$	−1.22716e11	+	2.16381e10i	−1.48676	+	0.262157i
$537$		0			0
$538$	−7.36458e10	−	6.17962e10i	−0.879061	−	0.737620i
$539$		−	7.71000e10i		−	0.913480i
$540$		0			0
$541$	1.28398e10			0.149889			0.0749445	−	0.997188i	$-0.476122\pi$
$541$	1.28398e10			0.149889			0.0749445	+	0.997188i	$0.476122\pi$
$542$	2.95531e10	−	3.52201e10i	0.342457	−	0.408125i
$543$		0			0
$544$	−2.03835e9	−	1.15601e10i	−0.0232747	−	0.131997i
$545$	1.28805e10	−	3.53888e10i	0.145997	−	0.401125i
$546$		0			0
$547$	−2.42472e10	+	1.37513e11i	−0.270840	+	1.53601i	0.481035	+	0.876701i	$0.340261\pi$
$547$	−2.42472e10	+	1.37513e11i	−0.270840	+	1.53601i	−0.751875	+	0.659306i	$0.770850\pi$
$548$	8.34410e9	+	4.81747e9i	0.0925246	+	0.0534191i
$549$		0			0
$550$	1.72605e10	+	2.98960e10i	0.188626	+	0.326710i
$551$	−6.20499e10	−	1.70481e11i	−0.673186	−	1.84956i
$552$		0			0
$553$	−3.69062e10	+	3.09680e10i	−0.394638	+	0.331140i
$554$	−9.04804e10	−	1.07830e11i	−0.960540	−	1.14473i
$555$		0			0
$556$	−7.93451e9	+	2.88793e9i	−0.0830273	+	0.0302195i
$557$	−1.02153e10	+	5.89783e9i	−0.106128	+	0.0612733i	−0.552125	−	0.833762i	$-0.686183\pi$
$557$	−1.02153e10	+	5.89783e9i	−0.106128	+	0.0612733i	0.445996	+	0.895035i	$0.352849\pi$
$558$		0			0
$559$	6.45617e8	−	1.11824e9i	0.00661192	−	0.0114522i
$560$	4.13043e10	+	7.28306e9i	0.419994	+	0.0740562i
$561$		0			0
$562$	7.24762e10	+	2.63792e10i	0.726524	+	0.264433i
$563$	1.04092e11	−	1.83542e10i	1.03606	−	0.182685i	0.370346	−	0.928894i	$-0.379239\pi$
$563$	1.04092e11	−	1.83542e10i	1.03606	−	0.182685i	0.665712	+	0.746209i	$0.268128\pi$
$564$		0			0
$565$	9.50008e10	+	7.97151e10i	0.932252	+	0.782253i
$566$			7.00585e10i			0.682645i
$567$		0			0
$568$	−1.36298e10			−0.130947
$569$	−5.46161e10	+	6.50889e10i	−0.521040	+	0.620952i	−0.960826	−	0.277151i	$-0.910610\pi$
$569$	−5.46161e10	+	6.50889e10i	−0.521040	+	0.620952i	0.439786	+	0.898103i	$0.355054\pi$
$570$		0			0
$571$	−3.08111e10	−	1.74739e11i	−0.289843	−	1.64378i	−0.687454	−	0.726228i	$-0.741272\pi$
$571$	−3.08111e10	−	1.74739e11i	−0.289843	−	1.64378i	0.397611	−	0.917554i	$-0.369839\pi$
$572$	4.97257e7	−	1.36620e8i	0.000464512	−	0.00127624i
$573$		0			0
$574$	−7.19917e9	+	4.08285e10i	−0.0663186	+	0.376111i
$575$	4.71010e10	+	2.71938e10i	0.430882	+	0.248770i
$576$		0			0
$577$	−2.65967e10	−	4.60669e10i	−0.239952	−	0.415610i	0.720748	−	0.693197i	$-0.243798\pi$
$577$	−2.65967e10	−	4.60669e10i	−0.239952	−	0.415610i	−0.960700	+	0.277588i	$0.910465\pi$
$578$	8.78999e9	+	2.41503e10i	0.0787548	+	0.216377i
$579$		0			0
$580$	9.72723e9	−	8.16212e9i	0.0859562	−	0.0721258i
$581$	4.86066e10	+	5.79271e10i	0.426570	+	0.508367i
$582$		0			0
$583$	1.09932e11	−	4.00118e10i	0.951587	−	0.346349i
$584$	6.86441e10	−	3.96317e10i	0.590136	−	0.340715i
$585$		0			0
$586$	8.12867e9	−	1.40793e10i	0.0689333	−	0.119396i
$587$	2.14074e11	+	3.77471e10i	1.80307	+	0.317930i	0.971419	−	0.237371i	$-0.0762857\pi$
$587$	2.14074e11	+	3.77471e10i	1.80307	+	0.317930i	0.831650	+	0.555301i	$0.187397\pi$
$588$		0			0
$589$	1.08605e11	+	3.95290e10i	0.902378	+	0.328439i
$590$	3.38353e10	−	5.96608e9i	0.279230	−	0.0492358i
$591$		0			0
$592$	1.36373e10	+	1.14431e10i	0.111031	+	0.0931657i
$593$		−	1.52309e11i		−	1.23171i	−0.787861	−	0.615853i	$-0.788812\pi$
$593$		−	1.52309e11i		−	1.23171i	0.787861	−	0.615853i	$-0.211188\pi$
$594$		0			0
$595$	−5.08244e10			−0.405513
$596$	2.29395e9	−	2.73382e9i	0.0181802	−	0.0216663i
$597$		0			0
$598$	4.76566e8	+	2.70274e9i	0.00372665	+	0.0211349i
$599$	2.58964e10	−	7.11497e10i	0.201155	−	0.552670i	−0.797565	−	0.603232i	$-0.793879\pi$
$599$	2.58964e10	−	7.11497e10i	0.201155	−	0.552670i	0.998721	+	0.0505624i	$0.0161014\pi$
$600$		0			0
$601$	2.12195e10	−	1.20342e11i	0.162643	−	0.922397i	−0.788818	−	0.614627i	$-0.789306\pi$
$601$	2.12195e10	−	1.20342e11i	0.162643	−	0.922397i	0.951461	−	0.307769i	$-0.0995825\pi$
$602$	−3.54736e10	−	2.04807e10i	−0.270097	−	0.155941i
$603$		0			0
$604$	−1.30729e9	−	2.26429e9i	−0.00982254	−	0.0170131i
$605$	−9.58969e9	−	2.63475e10i	−0.0715786	−	0.196661i
$606$		0			0
$607$	5.11102e10	−	4.28865e10i	0.376489	−	0.315912i	−0.434833	−	0.900511i	$-0.643193\pi$
$607$	5.11102e10	−	4.28865e10i	0.376489	−	0.315912i	0.811322	+	0.584599i	$0.198748\pi$
$608$	−2.12892e10	−	2.53715e10i	−0.155792	−	0.185666i
$609$		0			0
$610$	−3.95519e10	+	1.43957e10i	−0.285659	+	0.103971i
$611$	−3.28986e9	+	1.89940e9i	−0.0236055	+	0.0136286i
$612$		0			0
$613$	−9.84468e9	+	1.70515e10i	−0.0697204	+	0.120759i	−0.898778	−	0.438404i	$-0.855544\pi$
$613$	−9.84468e9	+	1.70515e10i	−0.0697204	+	0.120759i	0.829058	+	0.559163i	$0.188877\pi$
$614$	2.10061e11	+	3.70394e10i	1.47799	+	0.260609i
$615$		0			0
$616$	−6.05949e10	−	2.20547e10i	−0.420836	−	0.153172i
$617$	3.18097e10	−	5.60891e9i	0.219492	−	0.0387024i	−0.0628206	−	0.998025i	$-0.520010\pi$
$617$	3.18097e10	−	5.60891e9i	0.219492	−	0.0387024i	0.282313	+	0.959322i	$0.408898\pi$
$618$		0			0
$619$	−9.24892e8	−	7.76076e8i	−0.00629982	−	0.00528618i	0.639632	−	0.768681i	$-0.279087\pi$
$619$	−9.24892e8	−	7.76076e8i	−0.00629982	−	0.00528618i	−0.645932	+	0.763395i	$0.723531\pi$
$620$			8.08928e9i			0.0547448i
$621$		0			0
$622$	2.82257e10			0.188575
$623$	6.16150e10	−	7.34299e10i	0.409010	−	0.487440i
$624$		0			0
$625$	−3.26132e10	−	1.84958e11i	−0.213734	−	1.21214i
$626$	−6.62390e10	+	1.81990e11i	−0.431337	+	1.18509i
$627$		0			0
$628$	−3.39177e9	+	1.92357e10i	−0.0218066	+	0.123672i
$629$	−1.86825e10	−	1.07864e10i	−0.119353	−	0.0689084i
$630$		0			0
$631$	−1.35713e11	−	2.35062e11i	−0.856061	−	1.48274i	−0.875657	−	0.482933i	$-0.839571\pi$
$631$	−1.35713e11	−	2.35062e11i	−0.856061	−	1.48274i	0.0195964	−	0.999808i	$-0.493762\pi$
$632$	−7.29800e10	−	2.00511e11i	−0.457441	−	1.25681i
$633$		0			0
$634$	5.55529e10	−	4.66145e10i	0.343835	−	0.288512i
$635$	1.00314e11	+	1.19549e11i	0.616971	+	0.735278i
$636$		0			0
$637$	2.11283e9	−	7.69009e8i	0.0128324	−	0.00467061i
$638$	1.86874e11	−	1.07892e11i	1.12789	−	0.651187i
$639$		0			0
$640$	−8.50774e10	+	1.47358e11i	−0.507101	+	0.878324i
$641$	−2.17823e11	−	3.84081e10i	−1.29024	−	0.227505i	−0.513919	−	0.857838i	$-0.671807\pi$
$641$	−2.17823e11	−	3.84081e10i	−1.29024	−	0.227505i	−0.776324	+	0.630334i	$0.782918\pi$
$642$		0			0
$643$	1.70218e10	+	6.19544e9i	0.0995778	+	0.0362434i	0.391329	−	0.920251i	$-0.372016\pi$
$643$	1.70218e10	+	6.19544e9i	0.0995778	+	0.0362434i	−0.291751	+	0.956494i	$0.594238\pi$
$644$	−7.15595e9	+	1.26179e9i	−0.0416029	+	0.00733572i
$645$		0			0
$646$	−1.76213e11	−	1.47860e11i	−1.01183	−	0.849025i
$647$		−	5.37827e9i		−	0.0306920i	−0.999882	−	0.0153460i	$-0.995115\pi$
$647$		−	5.37827e9i		−	0.0306920i	0.999882	−	0.0153460i	$-0.00488498\pi$
$648$		0			0
$649$	−4.87299e10			−0.274673
$650$	−6.47107e8	+	7.71192e8i	−0.00362512	+	0.00432025i
$651$		0			0
$652$	−4.22746e9	−	2.39751e10i	−0.0233932	−	0.132669i
$653$	−5.55830e10	+	1.52713e11i	−0.305696	+	0.839892i	0.687787	+	0.725912i	$0.258582\pi$
$653$	−5.55830e10	+	1.52713e11i	−0.305696	+	0.839892i	−0.993483	+	0.113980i	$0.963640\pi$
$654$		0			0
$655$	1.10563e9	−	6.27032e9i	0.00600680	−	0.0340663i
$656$	−1.46696e11	−	8.46952e10i	−0.792144	−	0.457344i
$657$		0			0
$658$	6.02543e10	+	1.04363e11i	0.321428	+	0.556730i
$659$	7.22542e10	+	1.98517e11i	0.383108	+	1.05258i	0.970040	+	0.242945i	$0.0781135\pi$
$659$	7.22542e10	+	1.98517e11i	0.383108	+	1.05258i	−0.586932	+	0.809636i	$0.699664\pi$
$660$		0			0
$661$	1.19450e10	−	1.00230e10i	0.0625720	−	0.0525041i	−0.610965	−	0.791657i	$-0.709219\pi$
$661$	1.19450e10	−	1.00230e10i	0.0625720	−	0.0525041i	0.673537	+	0.739153i	$0.264774\pi$
$662$	1.41181e11	+	1.68253e11i	0.735098	+	0.876055i
$663$		0			0
$664$	−3.14717e11	+	1.14548e11i	−1.61900	+	0.589269i
$665$	−1.24190e11	+	7.17010e10i	−0.635037	+	0.366639i
$666$		0			0
$667$	1.69983e11	−	2.94419e11i	0.858818	−	1.48752i
$668$	−1.90030e10	−	3.35074e9i	−0.0954368	−	0.0168281i
$669$		0			0
$670$	−3.09720e11	−	1.12729e11i	−1.53699	−	0.559418i
$671$	5.87908e10	−	1.03664e10i	0.290014	−	0.0511374i
$672$		0			0
$673$	2.04051e11	+	1.71219e11i	0.994667	+	0.834624i	0.986237	−	0.165340i	$-0.0528722\pi$
$673$	2.04051e11	+	1.71219e11i	0.994667	+	0.834624i	0.00842997	+	0.999964i	$0.497317\pi$
$674$			1.92486e10i			0.0932738i
$675$		0			0
$676$	−1.60824e10			−0.0770131
$677$	−2.25462e11	+	2.68695e11i	−1.07329	+	1.27910i	−0.114983	+	0.993367i	$0.536681\pi$
$677$	−2.25462e11	+	2.68695e11i	−1.07329	+	1.27910i	−0.958309	+	0.285733i	$0.907763\pi$
$678$		0			0
$679$	−1.87281e10	−	1.06212e11i	−0.0881080	−	0.499685i
$680$	7.69894e10	−	2.11527e11i	0.360077	−	0.989303i
$681$		0			0
$682$	−2.38706e10	+	1.35377e11i	−0.110338	+	0.625759i
$683$	−1.04565e11	−	6.03707e10i	−0.480511	−	0.277423i	0.240118	−	0.970744i	$-0.422814\pi$
$683$	−1.04565e11	−	6.03707e10i	−0.480511	−	0.277423i	−0.720630	+	0.693320i	$0.756147\pi$
$684$		0			0
$685$	1.78157e11	+	3.08577e11i	0.809173	+	1.40153i
$686$	−5.33968e10	−	1.46707e11i	−0.241112	−	0.662450i
$687$		0			0
$688$	1.28205e11	−	1.07577e11i	0.572205	−	0.480137i
$689$	2.19295e9	+	2.61346e9i	0.00973090	+	0.0115968i
$690$		0			0
$691$	5.28931e10	−	1.92515e10i	0.231999	−	0.0844409i	−0.223404	−	0.974726i	$-0.571717\pi$
$691$	5.28931e10	−	1.92515e10i	0.231999	−	0.0844409i	0.455404	+	0.890285i	$0.349495\pi$
$692$	−1.06306e10	+	6.13760e9i	−0.0463591	+	0.0267654i
$693$		0			0
$694$	1.17691e11	−	2.03846e11i	0.507345	−	0.878748i
$695$	−3.07518e11	−	5.42237e10i	−1.31805	−	0.232407i
$696$		0			0
$697$	1.92887e11	+	7.02052e10i	0.817283	+	0.297467i
$698$	3.02950e10	−	5.34182e9i	0.127629	−	0.0225044i
$699$		0			0
$700$	−2.04186e9	−	1.71332e9i	−0.00850420	−	0.00713587i
$701$		−	1.43093e11i		−	0.592578i	−0.955098	−	0.296289i	$-0.904251\pi$
$701$		−	1.43093e11i		−	0.592578i	0.955098	−	0.296289i	$-0.0957491\pi$
$702$		0			0
$703$	−6.08678e10			−0.249210
$704$	1.82562e11	−	2.17569e11i	0.743224	−	0.885740i
$705$		0			0
$706$	5.89216e10	+	3.34161e11i	0.237168	+	1.34505i
$707$	3.27776e10	−	9.00558e10i	0.131190	−	0.360441i
$708$		0			0
$709$	−2.79876e10	+	1.58726e11i	−0.110760	+	0.628149i	0.878003	+	0.478655i	$0.158875\pi$
$709$	−2.79876e10	+	1.58726e11i	−0.110760	+	0.628149i	−0.988763	+	0.149494i	$0.952236\pi$
$710$	−3.12216e10	−	1.80258e10i	−0.122863	−	0.0709350i
$711$		0			0
$712$	2.12273e11	+	3.67668e11i	0.825992	+	1.43066i
$713$	7.40732e10	+	2.03514e11i	0.286618	+	0.787475i
$714$		0			0
$715$	4.11877e9	−	3.45606e9i	0.0157595	−	0.0132238i
$716$	−1.54835e10	−	1.84525e10i	−0.0589137	−	0.0702106i
$717$		0			0
$718$	−4.55844e11	+	1.65914e11i	−1.71522	+	0.624288i
$719$	3.14548e11	−	1.81604e11i	1.17698	−	0.679533i	0.221670	−	0.975122i	$-0.428849\pi$
$719$	3.14548e11	−	1.81604e11i	1.17698	−	0.679533i	0.955315	+	0.295589i	$0.0955160\pi$
$720$		0			0
$721$	5.04115e10	−	8.73153e10i	0.186547	−	0.323109i
$722$	−3.82077e11	−	6.73704e10i	−1.40605	−	0.247925i
$723$		0			0
$724$	2.19101e10	+	7.97464e9i	0.0797427	+	0.0290240i
$725$	1.22812e11	−	2.16551e10i	0.444519	−	0.0783806i
$726$		0			0
$727$	−1.63570e11	−	1.37252e11i	−0.585554	−	0.491338i	0.301212	−	0.953557i	$-0.402609\pi$
$727$	−1.63570e11	−	1.37252e11i	−0.585554	−	0.491338i	−0.886766	+	0.462219i	$0.847053\pi$
$728$		−	1.88051e9i		−	0.00669499i
$729$		0			0
$730$	2.09656e11			0.738270
$731$	−1.30361e11	+	1.55358e11i	−0.456540	+	0.544083i
$732$		0			0
$733$	4.77230e10	+	2.70650e11i	0.165315	+	0.937547i	0.948739	+	0.316060i	$0.102360\pi$
$733$	4.77230e10	+	2.70650e11i	0.165315	+	0.937547i	−0.783425	+	0.621487i	$0.786529\pi$
$734$	−9.28694e10	+	2.55156e11i	−0.319955	+	0.879068i
$735$		0			0
$736$	1.07772e10	−	6.11207e10i	0.0367279	−	0.208294i
$737$	4.04847e11	+	2.33739e11i	1.37221	+	0.792247i
$738$		0			0
$739$	1.34162e11	+	2.32376e11i	0.449835	+	0.779137i	0.998375	−	0.0569872i	$-0.0181494\pi$
$739$	1.34162e11	+	2.32376e11i	0.449835	+	0.779137i	−0.548540	+	0.836124i	$0.684816\pi$
$740$	−1.45708e9	−	4.00331e9i	−0.00485912	−	0.0133503i
$741$		0			0
$742$	8.29061e10	−	6.95665e10i	0.273509	−	0.229501i
$743$	1.19369e11	+	1.42258e11i	0.391684	+	0.466790i	0.925465	−	0.378832i	$-0.123674\pi$
$743$	1.19369e11	+	1.42258e11i	0.391684	+	0.466790i	−0.533782	+	0.845622i	$0.679230\pi$
$744$		0			0
$745$	1.24019e11	−	4.51391e10i	0.402589	−	0.146530i
$746$	−3.31545e11	+	1.91417e11i	−1.07050	+	0.618054i
$747$		0			0
$748$	−1.14176e10	+	1.97759e10i	−0.0364728	+	0.0631727i
$749$	−7.29725e10	−	1.28670e10i	−0.231863	−	0.0408837i
$750$		0			0
$751$	−2.48381e11	−	9.04032e10i	−0.780833	−	0.284200i	−0.0793131	−	0.996850i	$-0.525273\pi$
$751$	−2.48381e11	−	9.04032e10i	−0.780833	−	0.284200i	−0.701520	+	0.712650i	$0.747495\pi$
$752$	−4.84892e11	+	8.54996e10i	−1.51626	+	0.267358i
$753$		0			0
$754$	4.82057e9	+	4.04493e9i	0.0149146	+	0.0125149i
$755$		−	9.66910e10i		−	0.297576i
$756$		0			0
$757$	−1.85325e11			−0.564352			−0.282176	−	0.959363i	$-0.591056\pi$
$757$	−1.85325e11			−0.564352			−0.282176	+	0.959363i	$0.591056\pi$
$758$	−6.18582e10	+	7.37197e10i	−0.187379	+	0.223309i
$759$		0			0
$760$	−1.10289e11	−	6.25480e11i	−0.330581	−	1.87482i
$761$	−6.71533e10	+	1.84502e11i	−0.200230	+	0.550127i	−0.998648	−	0.0519760i	$-0.983448\pi$
$761$	−6.71533e10	+	1.84502e11i	−0.200230	+	0.550127i	0.798419	+	0.602103i	$0.205670\pi$
$762$		0			0
$763$	−8.58068e9	+	4.86635e10i	−0.0253177	+	0.143584i
$764$	1.13346e10	+	6.54401e9i	0.0332684	+	0.0192075i
$765$		0			0
$766$	2.54874e11	+	4.41455e11i	0.740304	+	1.28224i
$767$	−4.86040e8	−	1.33538e9i	−0.00140440	−	0.00385856i
$768$		0			0
$769$	−3.81976e10	+	3.20516e10i	−0.109227	+	0.0916524i	−0.695766	−	0.718269i	$-0.744935\pi$
$769$	−3.81976e10	+	3.20516e10i	−0.109227	+	0.0916524i	0.586538	+	0.809921i	$0.300490\pi$
$770$	−1.09636e11	−	1.30659e11i	−0.311881	−	0.371685i
$771$		0			0
$772$	−1.70133e10	+	6.19235e9i	−0.0478984	+	0.0174336i
$773$	2.62075e11	−	1.51309e11i	0.734018	−	0.423786i	−0.0858722	−	0.996306i	$-0.527368\pi$
$773$	2.62075e11	−	1.51309e11i	0.734018	−	0.423786i	0.819890	+	0.572521i	$0.194034\pi$
$774$		0			0
$775$	−3.97224e10	+	6.88012e10i	−0.110110	+	0.190717i
$776$	4.70416e11	+	8.29470e10i	1.29728	+	0.228746i
$777$		0			0
$778$	−4.55939e11	−	1.65948e11i	−1.24448	−	0.452954i
$779$	5.70364e11	−	1.00571e11i	1.54882	−	0.273099i
$780$		0			0
$781$	3.91701e10	+	3.28676e10i	0.105281	+	0.0883413i
$782$		−	4.31051e11i		−	1.15266i
$783$		0			0
$784$	2.91425e11			0.771369
$785$	−4.64311e11	+	5.53344e11i	−1.22273	+	1.45719i
$786$		0			0
$787$	7.96352e10	+	4.51634e11i	0.207590	+	1.17730i	0.893312	+	0.449437i	$0.148375\pi$
$787$	7.96352e10	+	4.51634e11i	0.207590	+	1.17730i	−0.685722	+	0.727863i	$0.740513\pi$
$788$	−8.44705e9	+	2.32081e10i	−0.0219079	+	0.0601914i
$789$		0			0
$790$	9.80068e10	−	5.55824e11i	0.251622	−	1.42702i
$791$	−1.40921e11	−	8.13608e10i	−0.359973	−	0.207831i
$792$		0			0
$793$	8.70469e8	+	1.50770e9i	0.00220121	+	0.00381260i
$794$	−1.84449e10	−	5.06770e10i	−0.0464082	−	0.127505i
$795$		0			0
$796$	−4.50228e10	+	3.77786e10i	−0.112145	+	0.0941008i
$797$	−2.33453e11	−	2.78219e11i	−0.578584	−	0.689530i	0.394785	−	0.918774i	$-0.370819\pi$
$797$	−2.33453e11	−	2.78219e11i	−0.578584	−	0.689530i	−0.973369	+	0.229244i	$0.926375\pi$
$798$		0			0
$799$	5.60672e11	−	2.04068e11i	1.37569	−	0.500712i
$800$	1.97162e10	−	1.13832e10i	0.0481353	−	0.0277909i
$801$		0			0
$802$	−1.36426e11	+	2.36297e11i	−0.329761	+	0.571164i
$803$	−2.92843e11	−	5.16361e10i	−0.704324	−	0.124191i
$804$		0			0
$805$	−2.52514e11	−	9.19077e10i	−0.601316	−	0.218861i
$806$	−3.94794e9	+	6.96127e8i	−0.00935470	+	0.00164949i
$807$		0			0
$808$	3.25152e11	+	2.72835e11i	0.762853	+	0.640110i
$809$			4.29994e11i			1.00385i	0.864912	+	0.501924i	$0.167374\pi$
$809$			4.29994e11i			1.00385i	−0.864912	+	0.501924i	$0.832626\pi$
$810$		0			0
$811$	−1.23577e11			−0.285664			−0.142832	−	0.989747i	$-0.545621\pi$
$811$	−1.23577e11			−0.285664			−0.142832	+	0.989747i	$0.545621\pi$
$812$	−1.07096e10	+	1.27633e10i	−0.0246349	+	0.0293587i
$813$		0			0
$814$	−1.25715e10	−	7.12964e10i	−0.0286345	−	0.162394i
$815$	3.07925e11	−	8.46018e11i	0.697935	−	1.91756i
$816$		0			0
$817$	−9.93650e10	+	5.63527e11i	−0.223021	+	1.26481i
$818$	4.86103e11	+	2.80652e11i	1.08571	+	0.626837i
$819$		0			0
$820$	2.02682e10	+	3.51056e10i	0.0448292	+	0.0776464i
$821$	8.74448e10	+	2.40253e11i	0.192469	+	0.528805i	0.997963	−	0.0637997i	$-0.0203219\pi$
$821$	8.74448e10	+	2.40253e11i	0.192469	+	0.528805i	−0.805493	+	0.592605i	$0.798100\pi$
$822$		0			0
$823$	5.10970e10	−	4.28755e10i	0.111377	−	0.0934566i	−0.585398	−	0.810746i	$-0.699062\pi$
$823$	5.10970e10	−	4.28755e10i	0.111377	−	0.0934566i	0.696775	+	0.717289i	$0.254617\pi$
$824$	2.87034e11	+	3.42074e11i	0.622622	+	0.742013i
$825$		0			0
$826$	−4.23620e10	+	1.54185e10i	−0.0910032	+	0.0331225i
$827$	2.31795e11	−	1.33827e11i	0.495544	−	0.286103i	−0.231327	−	0.972876i	$-0.574307\pi$
$827$	2.31795e11	−	1.33827e11i	0.495544	−	0.286103i	0.726872	+	0.686773i	$0.240973\pi$
$828$		0			0
$829$	1.38352e11	−	2.39632e11i	0.292932	−	0.507372i	−0.681570	−	0.731753i	$-0.738702\pi$
$829$	1.38352e11	−	2.39632e11i	0.292932	−	0.507372i	0.974502	+	0.224380i	$0.0720358\pi$
$830$	−8.72409e11	−	1.53829e11i	−1.83826	−	0.324135i
$831$		0			0
$832$	7.78313e9	+	2.83283e9i	0.0162428	+	0.00591190i
$833$	−3.47782e11	+	6.13233e10i	−0.722316	+	0.127364i
$834$		0			0
$835$	−5.46649e11	−	4.58693e11i	−1.12451	−	0.943575i
$836$			6.44300e10i			0.131905i
$837$		0			0
$838$	−2.15424e11			−0.436836
$839$	2.84474e11	−	3.39023e11i	0.574110	−	0.684197i	−0.398359	−	0.917229i	$-0.630420\pi$
$839$	2.84474e11	−	3.39023e11i	0.574110	−	0.684197i	0.972469	+	0.233032i	$0.0748647\pi$
$840$		0			0
$841$	−4.84950e10	−	2.75029e11i	−0.0969422	−	0.549787i
$842$	−4.47835e9	+	1.23042e10i	−0.00890983	+	0.0244796i
$843$		0			0
$844$	2.33956e8	−	1.32683e9i	0.000461068	−	0.00261485i
$845$	−5.15070e11	−	2.97376e11i	−1.01027	−	0.583282i
$846$		0			0
$847$	1.83948e10	+	3.18607e10i	0.0357406	+	0.0619045i
$848$	1.51238e11	+	4.15523e11i	0.292467	+	0.803547i
$849$		0			0
$850$	1.21126e11	−	1.01637e11i	0.232040	−	0.194705i
$851$	−7.33162e10	−	8.73748e10i	−0.139792	−	0.166597i
$852$		0			0
$853$	−4.48182e11	+	1.63125e11i	−0.846561	+	0.308123i	−0.728638	−	0.684899i	$-0.759846\pi$
$853$	−4.48182e11	+	1.63125e11i	−0.846561	+	0.308123i	−0.117924	+	0.993023i	$0.537624\pi$
$854$	4.78283e10	−	2.76137e10i	0.0899193	−	0.0519150i
$855$		0			0
$856$	1.64091e11	−	2.84214e11i	0.305625	−	0.529358i
$857$	4.07054e11	+	7.17746e10i	0.754621	+	0.133060i	0.537708	−	0.843131i	$-0.319290\pi$
$857$	4.07054e11	+	7.17746e10i	0.754621	+	0.133060i	0.216913	+	0.976191i	$0.430401\pi$
$858$		0			0
$859$	6.16001e11	+	2.24206e11i	1.13138	+	0.411789i	0.838793	−	0.544450i	$-0.183262\pi$
$859$	6.16001e11	+	2.24206e11i	1.13138	+	0.411789i	0.292587	+	0.956239i	$0.405484\pi$
$860$	−3.94421e10	+	6.95471e9i	−0.0721052	+	0.0127141i
$861$		0			0
$862$	−2.40425e11	−	2.01741e11i	−0.435463	−	0.365397i
$863$		−	5.72425e11i		−	1.03199i	−0.856591	−	0.515995i	$-0.827422\pi$
$863$		−	5.72425e11i		−	1.03199i	0.856591	−	0.515995i	$-0.172578\pi$
$864$		0			0
$865$	−4.53956e11			−0.810866
$866$	5.60519e11	−	6.68000e11i	0.996594	−	1.18769i
$867$		0			0
$868$	−1.84311e9	−	1.04528e10i	−0.00324693	−	0.0184143i
$869$	−2.73788e11	+	7.52226e11i	−0.480104	+	1.31907i
$870$		0			0
$871$	−2.36731e9	+	1.34257e10i	−0.00411323	+	0.0233273i
$872$	−1.89535e11	−	1.09428e11i	−0.327811	−	0.189262i
$873$		0			0
$874$	−6.08108e11	−	1.05327e12i	−1.04216	−	1.80508i
$875$	5.95237e10	+	1.63540e11i	0.101545	+	0.278992i
$876$		0			0
$877$	−6.98294e11	+	5.85939e11i	−1.18043	+	0.990498i	−0.180454	+	0.983583i	$0.557757\pi$
$877$	−6.98294e11	+	5.85939e11i	−1.18043	+	0.990498i	−0.999976	+	0.00691481i	$0.997799\pi$
$878$	−4.13013e11	−	4.92210e11i	−0.695002	−	0.828271i
$879$		0			0
$880$	6.54857e11	−	2.38348e11i	1.09198	−	0.397449i
$881$	−4.59564e11	+	2.65330e11i	−0.762856	+	0.440435i	−0.830320	−	0.557287i	$-0.811842\pi$
$881$	−4.59564e11	+	2.65330e11i	−0.762856	+	0.440435i	0.0674642	+	0.997722i	$0.478509\pi$
$882$		0			0
$883$	2.84872e11	−	4.93412e11i	0.468605	−	0.811647i	−0.530751	−	0.847528i	$-0.678090\pi$
$883$	2.84872e11	−	4.93412e11i	0.468605	−	0.811647i	0.999356	+	0.0358805i	$0.0114236\pi$
$884$	−6.55816e8	−	1.15638e8i	−0.00107392	−	0.000189362i
$885$		0			0
$886$	4.65105e11	+	1.69284e11i	0.754772	+	0.274715i
$887$	−6.61130e10	+	1.16575e10i	−0.106805	+	0.0188326i	−0.226795	−	0.973942i	$-0.572825\pi$
$887$	−6.61130e10	+	1.16575e10i	−0.106805	+	0.0188326i	0.119990	+	0.992775i	$0.461714\pi$
$888$		0			0
$889$	−1.56862e11	−	1.31623e11i	−0.251137	−	0.210729i
$890$			1.12295e12i			1.78978i
$891$		0			0
$892$	8.32217e10			0.131455
$893$	1.08211e12	−	1.28961e12i	1.70164	−	2.02793i
$894$		0			0
$895$	−1.54688e11	−	8.77277e11i	−0.241081	−	1.36724i
$896$	7.63604e10	−	2.09798e11i	0.118478	−	0.325514i
$897$		0			0
$898$	5.12782e10	−	2.90813e11i	0.0788547	−	0.447207i
$899$	4.30062e11	+	2.48297e11i	0.658404	+	0.380130i
$900$		0			0
$901$	−2.67922e11	−	4.64054e11i	−0.406545	−	0.704157i
$902$	2.35603e11	+	6.47315e11i	0.355922	+	0.977888i
$903$		0			0
$904$	5.52085e11	−	4.63254e11i	0.826670	−	0.693659i
$905$	5.54257e11	+	6.60538e11i	0.826260	+	0.984699i
$906$		0			0
$907$	4.25149e10	−	1.54741e10i	0.0628220	−	0.0228653i	−0.310418	−	0.950600i	$-0.600469\pi$
$907$	4.25149e10	−	1.54741e10i	0.0628220	−	0.0228653i	0.373240	+	0.927735i	$0.378247\pi$
$908$	3.25218e10	−	1.87764e10i	0.0478443	−	0.0276229i
$909$		0			0
$910$	2.48702e9	−	4.30765e9i	0.00362672	−	0.00628167i
$911$	−2.62080e11	−	4.62117e10i	−0.380504	−	0.0670932i	−0.0198752	−	0.999802i	$-0.506327\pi$
$911$	−2.62080e11	−	4.62117e10i	−0.380504	−	0.0670932i	−0.360629	+	0.932709i	$0.617438\pi$
$912$		0			0
$913$	1.18068e12	+	4.29731e11i	1.69921	+	0.618463i
$914$	5.23611e11	−	9.23267e10i	0.750281	−	0.132295i
$915$		0			0
$916$	−1.95857e10	−	1.64343e10i	−0.0278199	−	0.0233437i
$917$			8.35431e9i			0.0118150i
$918$		0			0
$919$	−3.44198e11			−0.482554			−0.241277	−	0.970456i	$-0.577566\pi$
$919$	−3.44198e11			−0.482554			−0.241277	+	0.970456i	$0.577566\pi$
$920$	7.65023e11	−	9.11719e11i	1.06788	−	1.27265i
$921$		0			0
$922$	1.95635e11	+	1.10950e12i	0.270722	+	1.53534i
$923$	−5.10008e8	+	1.40124e9i	−0.000702701	+	0.00193066i
$924$		0			0
$925$	7.26538e9	−	4.12040e10i	0.00992411	−	0.0562824i
$926$	2.83998e10	+	1.63966e10i	0.0386252	+	0.0223003i
$927$		0			0
$928$	−7.11538e10	−	1.23242e11i	−0.0959415	−	0.166176i
$929$	−1.21285e9	−	3.33227e9i	−0.00162833	−	0.00447380i	0.938876	−	0.344256i	$-0.111869\pi$
$929$	−1.21285e9	−	3.33227e9i	−0.00162833	−	0.00447380i	−0.940504	+	0.339782i	$0.889647\pi$
$930$		0			0
$931$	−7.63294e11	+	6.40480e11i	−1.01600	+	0.852525i
$932$	2.92446e10	+	3.48524e10i	0.0387599	+	0.0461922i
$933$		0			0
$934$	−7.65202e10	+	2.78511e10i	−0.100552	+	0.0365978i
$935$	−7.31342e11	+	4.22240e11i	−0.956916	+	0.552476i
$936$		0			0
$937$	−3.29613e11	+	5.70907e11i	−0.427609	+	0.740640i	−0.996660	−	0.0816619i	$-0.973977\pi$
$937$	−3.29613e11	+	5.70907e11i	−0.427609	+	0.740640i	0.569051	+	0.822302i	$0.307311\pi$
$938$	4.25900e11	+	7.50977e10i	0.550169	+	0.0970097i
$939$		0			0
$940$	1.10723e11	+	4.02998e10i	0.141816	+	0.0516169i
$941$	5.03620e11	−	8.88018e10i	0.642310	−	0.113257i	0.157000	−	0.987599i	$-0.449818\pi$
$941$	5.03620e11	−	8.88018e10i	0.642310	−	0.113257i	0.485310	+	0.874342i	$0.338707\pi$
$942$		0			0
$943$	8.31380e11	+	6.97611e11i	1.05136	+	0.882199i
$944$		−	1.84191e11i		−	0.231942i
$945$		0			0
$946$	−6.80600e11			−0.849821
$947$	8.59544e11	−	1.02436e12i	1.06873	−	1.27366i	0.108608	−	0.994085i	$-0.465361\pi$
$947$	8.59544e11	−	1.02436e12i	1.06873	−	1.27366i	0.960123	−	0.279579i	$-0.0901948\pi$
$948$		0			0
$949$	−1.50584e9	−	8.54004e9i	−0.00185658	−	0.0105292i
$950$	1.52587e11	−	4.19230e11i	0.187337	−	0.514705i
$951$		0			0
$952$	−5.12887e10	+	2.90873e11i	−0.0624416	+	0.354124i
$953$	−5.40015e11	−	3.11778e11i	−0.654688	−	0.377984i	0.135562	−	0.990769i	$-0.456716\pi$
$953$	−5.40015e11	−	3.11778e11i	−0.654688	−	0.377984i	−0.790250	+	0.612785i	$0.790049\pi$
$954$		0			0
$955$	2.42007e11	+	4.19169e11i	0.290948	+	0.503937i
$956$	1.01591e10	+	2.79119e10i	0.0121625	+	0.0334163i
$957$		0			0
$958$	6.50823e11	−	5.46105e11i	0.772682	−	0.648357i
$959$	−3.00520e11	−	3.58146e11i	−0.355303	−	0.423433i
$960$		0			0
$961$	5.04179e11	−	1.83506e11i	0.591141	−	0.215158i
$962$	1.82841e9	−	1.05563e9i	0.00213487	−	0.00123257i
$963$		0			0
$964$	1.91851e10	−	3.32295e10i	0.0222154	−	0.0384783i
$965$	−6.59386e11	−	1.16268e11i	−0.760380	−	0.134076i
$966$		0			0
$967$	−9.49667e11	−	3.45651e11i	−1.08609	−	0.395304i	−0.263919	−	0.964545i	$-0.585015\pi$
$967$	−9.49667e11	−	3.45651e11i	−1.08609	−	0.395304i	−0.822171	+	0.569241i	$0.807237\pi$
$968$	−1.60466e11	+	2.82945e10i	−0.182760	+	0.0322256i
$969$		0			0
$970$	9.67874e11	+	8.12143e11i	1.09328	+	0.917372i
$971$		−	4.71279e11i		−	0.530153i	−0.964227	−	0.265077i	$-0.914603\pi$
$971$		−	4.71279e11i		−	0.530153i	0.964227	−	0.265077i	$-0.0853972\pi$
$972$		0			0
$973$	4.09724e11			0.457130
$974$	−9.07709e11	+	1.08177e12i	−1.00858	+	1.20198i
$975$		0			0
$976$	3.91832e10	+	2.22219e11i	0.0431818	+	0.244896i
$977$	−1.45484e11	+	3.99715e11i	−0.159675	+	0.438704i	−0.993570	−	0.113219i	$-0.963884\pi$
$977$	−1.45484e11	+	3.99715e11i	−0.159675	+	0.438704i	0.833895	+	0.551923i	$0.186106\pi$
$978$		0			0
$979$	2.76571e11	−	1.56851e12i	0.301076	−	1.70749i
$980$	−6.03969e10	−	3.48702e10i	−0.0654802	−	0.0378050i
$981$		0			0
$982$	1.87595e10	+	3.24924e10i	0.0201732	+	0.0349411i
$983$	2.29223e11	+	6.29785e11i	0.245496	+	0.674494i	0.999838	+	0.0180123i	$0.00573382\pi$
$983$	2.29223e11	+	6.29785e11i	0.245496	+	0.674494i	−0.754342	+	0.656482i	$0.772044\pi$
$984$		0			0
$985$	−6.99668e11	+	5.87091e11i	−0.743271	+	0.623678i
$986$	−6.35312e11	−	7.57136e11i	−0.672171	−	0.801062i
$987$		0			0
$988$	−1.76563e9	+	6.42636e8i	−0.00185298	+	0.000674430i
$989$	−9.28622e11	+	5.36140e11i	−0.970630	+	0.560394i
$990$		0			0
$991$	−1.12227e11	+	1.94382e11i	−0.116359	+	0.201540i	−0.918322	−	0.395833i	$-0.870456\pi$
$991$	−1.12227e11	+	1.94382e11i	−0.116359	+	0.201540i	0.801963	+	0.597374i	$0.203789\pi$
$992$	8.92800e10	+	1.57425e10i	0.0921950	+	0.0162565i
$993$		0			0
$994$	4.44510e10	+	1.61789e10i	0.0455341	+	0.0165730i
$995$	−2.14049e12	+	3.77427e11i	−2.18385	+	0.385071i
$996$		0			0
$997$	3.52268e11	+	2.95588e11i	0.356527	+	0.299162i	0.803405	−	0.595433i	$-0.203020\pi$
$997$	3.52268e11	+	2.95588e11i	0.356527	+	0.299162i	−0.446878	+	0.894595i	$0.647464\pi$
$998$			1.64613e12i			1.65937i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.9.f.a.35.17		138
3.2	odd	2		27.9.f.a.11.7	yes	138
27.5	odd	18	inner	81.9.f.a.44.17		138
27.22	even	9		27.9.f.a.5.7	✓	138

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.9.f.a.5.7	✓	138	27.22	even	9
27.9.f.a.11.7	yes	138	3.2	odd	2
81.9.f.a.35.17		138	1.1	even	1	trivial
81.9.f.a.44.17		138	27.5	odd	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	81.f (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(9.88054 - 11.7752i) q^{2} +(3.42444 + 19.4209i) q^{4} +(-249.434 + 685.313i) q^{5} +(166.167 - 942.382i) q^{7} +(3670.39 + 2119.10i) q^{8} +O(q^{10})\)	\(q+(9.88054 - 11.7752i) q^{2} +(3.42444 + 19.4209i) q^{4} +(-249.434 + 685.313i) q^{5} +(166.167 - 942.382i) q^{7} +(3670.39 + 2119.10i) q^{8} +(5605.14 + 9708.38i) q^{10} +(-5438.06 - 14941.0i) q^{11} +(355.199 - 298.048i) q^{13} +(-9454.88 - 11267.9i) q^{14} +(56474.3 - 20554.9i) q^{16} +(-63070.2 + 36413.6i) q^{17} +(-102742. + 177954. i) q^{19} +(-14163.6 - 2497.42i) q^{20} +(-229663. - 83590.6i) q^{22} +(-379204. + 66863.9i) q^{23} +(-108201. - 90791.5i) q^{25} -7127.40i q^{26} +18871.0 q^{28} +(-567519. + 676343. i) q^{29} +(-97669.2 - 553910. i) q^{31} +(-55127.3 + 151461. i) q^{32} +(-194391. + 1.10245e6i) q^{34} +(604379. + 348938. i) q^{35} +(148109. + 256532. i) q^{37} +(1.08029e6 + 2.96808e6i) q^{38} +(-2.36777e6 + 1.98679e6i) q^{40} +(-1.81172e6 - 2.15913e6i) q^{41} +(2.61681e6 - 952442. i) q^{43} +(271545. - 156777. i) q^{44} +(-2.95941e6 + 5.12584e6i) q^{46} +(-8.06828e6 - 1.42265e6i) q^{47} +(4.55667e6 + 1.65849e6i) q^{49} +(-2.13817e6 + 377017. i) q^{50} +(7004.72 + 5877.66i) q^{52} +7.35774e6i q^{53} +1.15957e7 q^{55} +(2.60690e6 - 3.10679e6i) q^{56} +(2.35666e6 + 1.33653e7i) q^{58} +(1.04822e6 - 2.87997e6i) q^{59} +(-651982. + 3.69757e6i) q^{61} +(-7.48740e6 - 4.32285e6i) q^{62} +(8.93142e6 + 1.54697e7i) q^{64} +(115657. + 317766. i) q^{65} +(-2.25228e7 + 1.88988e7i) q^{67} +(-923167. - 1.10019e6i) q^{68} +(1.00804e7 - 3.66896e6i) q^{70} +(-2.78508e6 + 1.60797e6i) q^{71} +(9.35105e6 - 1.61965e7i) q^{73} +(4.48410e6 + 790668. i) q^{74} +(-3.80786e6 - 1.38595e6i) q^{76} +(-1.49837e7 + 2.64203e6i) q^{77} +(-3.85677e7 - 3.23621e7i) q^{79} +4.38296e7i q^{80} -4.33248e7 q^{82} +(-5.07949e7 + 6.05350e7i) q^{83} +(-9.22290e6 - 5.23057e7i) q^{85} +(1.46403e7 - 4.02240e7i) q^{86} +(1.17016e7 - 6.63630e7i) q^{88} +(8.67510e7 + 5.00857e7i) q^{89} +(-221852. - 384259. i) q^{91} +(-2.59712e6 - 7.13553e6i) q^{92} +(-9.64709e7 + 8.09487e7i) q^{94} +(-9.63268e7 - 1.14798e8i) q^{95} +(1.05909e8 - 3.85479e7i) q^{97} +(6.45513e7 - 3.72687e7i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 138 q + 6 q^{2} - 6 q^{4} + 447 q^{5} - 6 q^{7} + 9 q^{8}+O(q^{10}) \) 138 * q + 6 * q^2 - 6 * q^4 + 447 * q^5 - 6 * q^7 + 9 * q^8	\( 138 q + 6 q^{2} - 6 q^{4} + 447 q^{5} - 6 q^{7} + 9 q^{8} - 3 q^{10} - 28668 q^{11} - 6 q^{13} + 120975 q^{14} - 774 q^{16} + 9 q^{17} - 3 q^{19} - 137913 q^{20} - 185478 q^{22} - 68376 q^{23} + 507585 q^{25} - 12 q^{28} + 943980 q^{29} + 920739 q^{31} + 3005136 q^{32} + 660474 q^{34} - 6225408 q^{35} - 3 q^{37} + 23716884 q^{38} - 975273 q^{40} - 16694382 q^{41} + 4412514 q^{43} - 17341119 q^{44} - 3 q^{46} + 11341869 q^{47} + 11347482 q^{49} + 40948977 q^{50} + 14465511 q^{52} - 12 q^{55} - 52215771 q^{56} - 19078611 q^{58} - 76116738 q^{59} + 34059450 q^{61} + 223709616 q^{62} + 100663293 q^{64} - 20396037 q^{65} - 103603884 q^{67} - 101921427 q^{68} + 135373629 q^{70} - 125718795 q^{71} - 7632642 q^{73} + 66643887 q^{74} - 203790342 q^{76} + 343269159 q^{77} - 68767890 q^{79} - 12 q^{82} - 383244663 q^{83} + 170435619 q^{85} - 71426730 q^{86} - 192774918 q^{88} - 135692730 q^{89} + 77546796 q^{91} + 1343159175 q^{92} - 44451609 q^{94} - 881099997 q^{95} + 31339344 q^{97} - 1293135102 q^{98}+O(q^{100}) \) 138 * q + 6 * q^2 - 6 * q^4 + 447 * q^5 - 6 * q^7 + 9 * q^8 - 3 * q^10 - 28668 * q^11 - 6 * q^13 + 120975 * q^14 - 774 * q^16 + 9 * q^17 - 3 * q^19 - 137913 * q^20 - 185478 * q^22 - 68376 * q^23 + 507585 * q^25 - 12 * q^28 + 943980 * q^29 + 920739 * q^31 + 3005136 * q^32 + 660474 * q^34 - 6225408 * q^35 - 3 * q^37 + 23716884 * q^38 - 975273 * q^40 - 16694382 * q^41 + 4412514 * q^43 - 17341119 * q^44 - 3 * q^46 + 11341869 * q^47 + 11347482 * q^49 + 40948977 * q^50 + 14465511 * q^52 - 12 * q^55 - 52215771 * q^56 - 19078611 * q^58 - 76116738 * q^59 + 34059450 * q^61 + 223709616 * q^62 + 100663293 * q^64 - 20396037 * q^65 - 103603884 * q^67 - 101921427 * q^68 + 135373629 * q^70 - 125718795 * q^71 - 7632642 * q^73 + 66643887 * q^74 - 203790342 * q^76 + 343269159 * q^77 - 68767890 * q^79 - 12 * q^82 - 383244663 * q^83 + 170435619 * q^85 - 71426730 * q^86 - 192774918 * q^88 - 135692730 * q^89 + 77546796 * q^91 + 1343159175 * q^92 - 44451609 * q^94 - 881099997 * q^95 + 31339344 * q^97 - 1293135102 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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