LMFDB - Embedded newform 81.10.e.a.10.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [81,10,Mod(10,81)]

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([8]))

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("81.10");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	81.e (of order $9$, 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:	$41.7179027293$
Analytic rank:	$0$
Dimension:	$156$
Relative dimension:	$26$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			10.4
Character	$\chi$	$=$	81.10
Dual form			81.10.e.a.73.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-6.40153 - 36.3049i) q^{2} +(-795.940 + 289.699i) q^{4} +(170.489 + 143.057i) q^{5} +(-5644.86 - 2054.56i) q^{7} +(6175.28 + 10695.9i) q^{8} +(4102.29 - 7105.37i) q^{10} +(-36452.8 + 30587.5i) q^{11} +(935.040 - 5302.88i) q^{13} +(-38454.8 + 218088. i) q^{14} +(16567.1 - 13901.5i) q^{16} +(-73376.8 + 127092. i) q^{17} +(157159. + 272207. i) q^{19} +(-177143. - 64474.7i) q^{20} +(1.34383e6 + 1.12761e6i) q^{22} +(397465. - 144666. i) q^{23} +(-330555. - 1.87467e6i) q^{25} -198506. q^{26} +5.08817e6 q^{28} +(675466. + 3.83076e6i) q^{29} +(8.85575e6 - 3.22323e6i) q^{31} +(4.23332e6 + 3.55218e6i) q^{32} +(5.08379e6 + 1.85035e6i) q^{34} +(-668467. - 1.15782e6i) q^{35} +(1.03140e7 - 1.78644e7i) q^{37} +(8.87638e6 - 7.44817e6i) q^{38} +(-477309. + 2.70695e6i) q^{40} +(-2.02245e6 + 1.14699e7i) q^{41} +(-2.70604e7 + 2.27064e7i) q^{43} +(2.01531e7 - 3.49061e7i) q^{44} +(-7.79645e6 - 1.35038e7i) q^{46} +(2.73737e7 + 9.96322e6i) q^{47} +(-3.26946e6 - 2.74340e6i) q^{49} +(-6.59437e7 + 2.40015e7i) q^{50} +(792000. + 4.49165e6i) q^{52} -2.44455e7 q^{53} -1.05906e7 q^{55} +(-1.28832e7 - 7.30643e7i) q^{56} +(1.34751e8 - 4.90454e7i) q^{58} +(-5.30049e6 - 4.44764e6i) q^{59} +(-1.03660e8 - 3.77293e7i) q^{61} +(-1.73709e8 - 3.00873e8i) q^{62} +(1.07398e8 - 1.86019e8i) q^{64} +(918030. - 770319. i) q^{65} +(2.77008e7 - 1.57099e8i) q^{67} +(2.15851e7 - 1.22415e8i) q^{68} +(-3.77552e7 + 3.16804e7i) q^{70} +(1.75857e8 - 3.04593e8i) q^{71} +(2.14081e8 + 3.70799e8i) q^{73} +(-7.14592e8 - 2.60090e8i) q^{74} +(-2.03947e8 - 1.71132e8i) q^{76} +(2.68615e8 - 9.77677e7i) q^{77} +(1.07628e7 + 6.10386e7i) q^{79} +4.81322e6 q^{80} +4.29359e8 q^{82} +(4.52437e7 + 2.56590e8i) q^{83} +(-3.06915e7 + 1.11708e7i) q^{85} +(9.97581e8 + 8.37070e8i) q^{86} +(-5.52267e8 - 2.01009e8i) q^{88} +(4.26988e8 + 7.39565e8i) q^{89} +(-1.61732e7 + 2.80129e7i) q^{91} +(-2.74449e8 + 2.30290e8i) q^{92} +(1.86480e8 - 1.05758e9i) q^{94} +(-1.21474e7 + 6.88911e7i) q^{95} +(1.48323e8 - 1.24458e8i) q^{97} +(-7.86692e7 + 1.36259e8i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 156 q + 6 q^{2} - 6 q^{4} - 2382 q^{5} - 6 q^{7} - 36861 q^{8} - 3 q^{10} + 121767 q^{11} - 6 q^{13} + 720417 q^{14} + 1530 q^{16} - 1002249 q^{17} - 3 q^{19} + 8448573 q^{20} - 1585014 q^{22} - 9316482 q^{23}+ \cdots - 6901039926 q^{98}+O(q^{100}) $ 156 * q + 6 * q^2 - 6 * q^4 - 2382 * q^5 - 6 * q^7 - 36861 * q^8 - 3 * q^10 + 121767 * q^11 - 6 * q^13 + 720417 * q^14 + 1530 * q^16 - 1002249 * q^17 - 3 * q^19 + 8448573 * q^20 - 1585014 * q^22 - 9316482 * q^23 + 2192178 * q^25 + 33129678 * q^26 - 12 * q^28 - 19657236 * q^29 - 4633692 * q^31 + 37550952 * q^32 + 14341770 * q^34 - 34449663 * q^35 - 3 * q^37 + 92022060 * q^38 + 6645801 * q^40 + 33127221 * q^41 + 2356203 * q^43 - 1001541 * q^44 - 3 * q^46 + 33488952 * q^47 - 93214644 * q^49 + 72027753 * q^50 + 160531713 * q^52 - 4841352 * q^53 - 12 * q^55 + 91770981 * q^56 - 320682489 * q^58 - 538090854 * q^59 + 36683436 * q^61 + 55862958 * q^62 - 956301315 * q^64 + 852347310 * q^65 - 109026897 * q^67 + 508886217 * q^68 - 815297649 * q^70 - 940878639 * q^71 - 221849931 * q^73 - 838884579 * q^74 + 908401146 * q^76 + 967811358 * q^77 - 1228059150 * q^79 + 2497115154 * q^80 - 12 * q^82 + 297703284 * q^83 + 1535949369 * q^85 - 2930201574 * q^86 + 2837227002 * q^88 - 1774997208 * q^89 + 551343507 * q^91 + 6896645517 * q^92 + 414852915 * q^94 + 9000269169 * q^95 + 3371772333 * q^97 - 6901039926 * q^98

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{9}\right)$

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 $

$2$	−6.40153	−	36.3049i	−0.282910	−	1.60446i	−0.712656	−	0.701513i	$-0.752508\pi$
$2$	−6.40153	−	36.3049i	−0.282910	−	1.60446i	0.429746	−	0.902950i	$-0.358603\pi$
$3$		0			0
$3$		0			0
$4$	−795.940	+	289.699i	−1.55457	+	0.565817i
$5$	170.489	+	143.057i	0.121992	+	0.102364i	0.701743	−	0.712430i	$-0.252406\pi$
$5$	170.489	+	143.057i	0.121992	+	0.102364i	−0.579751	+	0.814794i	$0.696850\pi$
$6$		0			0
$7$	−5644.86	−	2054.56i	−0.888611	−	0.323428i	−0.142932	−	0.989733i	$-0.545653\pi$
$7$	−5644.86	−	2054.56i	−0.888611	−	0.323428i	−0.745680	+	0.666305i	$0.767875\pi$
$8$	6175.28	+	10695.9i	0.533030	+	0.923235i
$9$		0			0
$10$	4102.29	−	7105.37i	0.129726	−	0.224692i
$11$	−36452.8	+	30587.5i	−0.750695	+	0.629908i	−0.935687	−	0.352832i	$-0.885219\pi$
$11$	−36452.8	+	30587.5i	−0.750695	+	0.629908i	0.184992	+	0.982740i	$0.440774\pi$
$12$		0			0
$13$	935.040	−	5302.88i	0.00907999	−	0.0514952i	−0.979931	−	0.199336i	$-0.936121\pi$
$13$	935.040	−	5302.88i	0.00907999	−	0.0514952i	0.989011	+	0.147841i	$0.0472325\pi$
$14$	−38454.8	+	218088.i	−0.267531	+	1.51724i
$15$		0			0
$16$	16567.1	−	13901.5i	0.0631985	−	0.0530298i
$17$	−73376.8	+	127092.i	−0.213078	+	0.369062i	−0.952676	−	0.303987i	$-0.901682\pi$
$17$	−73376.8	+	127092.i	−0.213078	+	0.369062i	0.739598	+	0.673049i	$0.235016\pi$
$18$		0			0
$19$	157159.	+	272207.i	0.276661	+	0.479191i	0.970553	−	0.240888i	$-0.0774388\pi$
$19$	157159.	+	272207.i	0.276661	+	0.479191i	−0.693892	+	0.720079i	$0.744105\pi$
$20$	−177143.	−	64474.7i	−0.247564	−	0.0901061i
$21$		0			0
$22$	1.34383e6	+	1.12761e6i	1.22304	+	1.02626i
$23$	397465.	−	144666.i	0.296158	−	0.107793i	−0.189668	−	0.981848i	$-0.560741\pi$
$23$	397465.	−	144666.i	0.296158	−	0.107793i	0.485826	+	0.874055i	$0.338519\pi$
$24$		0			0
$25$	−330555.	−	1.87467e6i	−0.169244	−	0.959833i
$26$	−198506.			−0.0851909
$27$		0			0
$28$	5.08817e6			1.56441
$29$	675466.	+	3.83076e6i	0.177342	+	1.00576i	0.935405	+	0.353577i	$0.115035\pi$
$29$	675466.	+	3.83076e6i	0.177342	+	1.00576i	−0.758063	+	0.652181i	$0.773854\pi$
$30$		0			0
$31$	8.85575e6	−	3.22323e6i	1.72226	−	0.626850i	0.724224	−	0.689565i	$-0.242198\pi$
$31$	8.85575e6	−	3.22323e6i	1.72226	−	0.626850i	0.998031	+	0.0627154i	$0.0199761\pi$
$32$	4.23332e6	+	3.55218e6i	0.713685	+	0.598853i
$33$		0			0
$34$	5.08379e6	+	1.85035e6i	0.652428	+	0.237465i
$35$	−668467.	−	1.15782e6i	−0.0752963	−	0.130417i
$36$		0			0
$37$	1.03140e7	−	1.78644e7i	0.904734	−	1.56705i	0.0834609	−	0.996511i	$-0.473403\pi$
$37$	1.03140e7	−	1.78644e7i	0.904734	−	1.56705i	0.821273	−	0.570535i	$-0.193264\pi$
$38$	8.87638e6	−	7.44817e6i	0.690574	−	0.579460i
$39$		0			0
$40$	−477309.	+	2.70695e6i	−0.0294801	+	0.167190i
$41$	−2.02245e6	+	1.14699e7i	−0.111776	+	0.633915i	0.876520	+	0.481366i	$0.159859\pi$
$41$	−2.02245e6	+	1.14699e7i	−0.111776	+	0.633915i	−0.988296	+	0.152549i	$0.951252\pi$
$42$		0			0
$43$	−2.70604e7	+	2.27064e7i	−1.20705	+	1.01284i	−0.207654	+	0.978202i	$0.566583\pi$
$43$	−2.70604e7	+	2.27064e7i	−1.20705	+	1.01284i	−0.999400	+	0.0346367i	$0.988973\pi$
$44$	2.01531e7	−	3.49061e7i	0.810596	−	1.40399i
$45$		0			0
$46$	−7.79645e6	−	1.35038e7i	−0.256736	−	0.444680i
$47$	2.73737e7	+	9.96322e6i	0.818264	+	0.297824i	0.717033	−	0.697039i	$-0.245500\pi$
$47$	2.73737e7	+	9.96322e6i	0.818264	+	0.297824i	0.101231	+	0.994863i	$0.467722\pi$
$48$		0			0
$49$	−3.26946e6	−	2.74340e6i	−0.0810202	−	0.0679840i
$50$	−6.59437e7	+	2.40015e7i	−1.49214	+	0.543093i
$51$		0			0
$52$	792000.	+	4.49165e6i	0.0150214	+	0.0851905i
$53$	−2.44455e7			−0.425557			−0.212779	−	0.977100i	$-0.568251\pi$
$53$	−2.44455e7			−0.425557			−0.212779	+	0.977100i	$0.568251\pi$
$54$		0			0
$55$	−1.05906e7			−0.156058
$56$	−1.28832e7	−	7.30643e7i	−0.175056	−	0.992793i
$57$		0			0
$58$	1.34751e8	−	4.90454e7i	1.56353	−	0.569078i
$59$	−5.30049e6	−	4.44764e6i	−0.0569485	−	0.0477855i	0.613869	−	0.789408i	$-0.289612\pi$
$59$	−5.30049e6	−	4.44764e6i	−0.0569485	−	0.0477855i	−0.670818	+	0.741622i	$0.734057\pi$
$60$		0			0
$61$	−1.03660e8	−	3.77293e7i	−0.958580	−	0.348895i	−0.185103	−	0.982719i	$-0.559262\pi$
$61$	−1.03660e8	−	3.77293e7i	−0.958580	−	0.348895i	−0.773477	+	0.633825i	$0.781484\pi$
$62$	−1.73709e8	−	3.00873e8i	−1.49300	−	2.58595i
$63$		0			0
$64$	1.07398e8	−	1.86019e8i	0.800178	−	1.38595i
$65$	918030.	−	770319.i	0.00637891	−	0.00535254i
$66$		0			0
$67$	2.77008e7	−	1.57099e8i	0.167941	−	0.952439i	−0.778040	−	0.628215i	$-0.783786\pi$
$67$	2.77008e7	−	1.57099e8i	0.167941	−	0.952439i	0.945980	−	0.324224i	$-0.105103\pi$
$68$	2.15851e7	−	1.22415e8i	0.122423	−	0.694296i
$69$		0			0
$70$	−3.77552e7	+	3.16804e7i	−0.187947	+	0.157706i
$71$	1.75857e8	−	3.04593e8i	0.821292	−	1.42252i	−0.0834291	−	0.996514i	$-0.526587\pi$
$71$	1.75857e8	−	3.04593e8i	0.821292	−	1.42252i	0.904721	−	0.426005i	$-0.140079\pi$
$72$		0			0
$73$	2.14081e8	+	3.70799e8i	0.882318	+	1.52822i	0.848757	+	0.528782i	$0.177351\pi$
$73$	2.14081e8	+	3.70799e8i	0.882318	+	1.52822i	0.0335604	+	0.999437i	$0.489315\pi$
$74$	−7.14592e8	−	2.60090e8i	−2.77023	−	1.00828i
$75$		0			0
$76$	−2.03947e8	−	1.71132e8i	−0.701223	−	0.588396i
$77$	2.68615e8	−	9.77677e7i	0.870806	−	0.316947i
$78$		0			0
$79$	1.07628e7	+	6.10386e7i	0.0310886	+	0.176312i	0.996398	−	0.0847949i	$-0.0270235\pi$
$79$	1.07628e7	+	6.10386e7i	0.0310886	+	0.176312i	−0.965310	+	0.261107i	$0.915912\pi$
$80$	4.81322e6			0.0131380
$81$		0			0
$82$	4.29359e8			1.04872
$83$	4.52437e7	+	2.56590e8i	0.104642	+	0.593455i	0.991363	+	0.131149i	$0.0418667\pi$
$83$	4.52437e7	+	2.56590e8i	0.104642	+	0.593455i	−0.886721	+	0.462306i	$0.847022\pi$
$84$		0			0
$85$	−3.06915e7	+	1.11708e7i	−0.0637724	+	0.0232112i
$86$	9.97581e8	+	8.37070e8i	1.96655	+	1.65013i
$87$		0			0
$88$	−5.52267e8	−	2.01009e8i	−0.981696	−	0.357308i
$89$	4.26988e8	+	7.39565e8i	0.721375	+	1.24946i	0.960449	+	0.278456i	$0.0898227\pi$
$89$	4.26988e8	+	7.39565e8i	0.721375	+	1.24946i	−0.239074	+	0.971001i	$0.576844\pi$
$90$		0			0
$91$	−1.61732e7	+	2.80129e7i	−0.0247236	+	0.0428225i
$92$	−2.74449e8	+	2.30290e8i	−0.399408	+	0.335143i
$93$		0			0
$94$	1.86480e8	−	1.05758e9i	0.246352	−	1.39713i
$95$	−1.21474e7	+	6.88911e7i	−0.0153012	+	0.0867775i
$96$		0			0
$97$	1.48323e8	−	1.24458e8i	0.170112	−	0.142741i	−0.553757	−	0.832678i	$-0.686806\pi$
$97$	1.48323e8	−	1.24458e8i	0.170112	−	0.142741i	0.723869	+	0.689937i	$0.242362\pi$
$98$	−7.86692e7	+	1.36259e8i	−0.0861564	+	0.149227i
$99$		0			0
$100$	8.06192e8	+	1.39637e9i	0.806192	+	1.39637i
$101$	−1.04282e9	−	3.79556e8i	−0.997159	−	0.362936i	−0.208670	−	0.977986i	$-0.566914\pi$
$101$	−1.04282e9	−	3.79556e8i	−0.997159	−	0.362936i	−0.788488	+	0.615050i	$0.789136\pi$
$102$		0			0
$103$	−4.27114e8	−	3.58391e8i	−0.373918	−	0.313754i	0.436391	−	0.899757i	$-0.356256\pi$
$103$	−4.27114e8	−	3.58391e8i	−0.373918	−	0.313754i	−0.810309	+	0.586003i	$0.800701\pi$
$104$	6.24931e7	−	2.27456e7i	0.0523820	−	0.0190655i
$105$		0			0
$106$	1.56489e8	+	8.87492e8i	0.120394	+	0.682791i
$107$	1.39325e9			1.02755			0.513775	−	0.857925i	$-0.328246\pi$
$107$	1.39325e9			1.02755			0.513775	+	0.857925i	$0.328246\pi$
$108$		0			0
$109$	2.09480e9			1.42142			0.710711	−	0.703484i	$-0.248373\pi$
$109$	2.09480e9			1.42142			0.710711	+	0.703484i	$0.248373\pi$
$110$	6.77958e7	+	3.84489e8i	0.0441505	+	0.250390i
$111$		0			0
$112$	−1.22080e8	+	4.44336e7i	−0.0733102	+	0.0266827i
$113$	1.80963e9	+	1.51846e9i	1.04408	+	0.876091i	0.992459	−	0.122575i	$-0.0391153\pi$
$113$	1.80963e9	+	1.51846e9i	1.04408	+	0.876091i	0.0516257	+	0.998667i	$0.483560\pi$
$114$		0			0
$115$	8.84590e7	+	3.21965e7i	0.0471630	+	0.0171659i
$116$	−1.64740e9	−	2.85337e9i	−0.844767	−	1.46318i
$117$		0			0
$118$	−1.27540e8	+	2.20905e8i	−0.0605587	+	0.104891i
$119$	6.75321e8	−	5.66661e8i	0.308709	−	0.259037i
$120$		0			0
$121$	−1.62442e7	+	9.21254e7i	−0.00688913	+	0.0390702i
$122$	−7.06172e8	+	4.00490e9i	−0.288596	+	1.63671i
$123$		0			0
$124$	−6.11488e9	+	5.13099e9i	−2.32268	+	1.94896i
$125$	4.29171e8	−	7.43347e8i	0.157230	−	0.272330i
$126$		0			0
$127$	−1.05275e9	−	1.82342e9i	−0.359095	−	0.621970i	0.628715	−	0.777636i	$-0.283581\pi$
$127$	−1.05275e9	−	1.82342e9i	−0.359095	−	0.621970i	−0.987810	+	0.155665i	$0.950248\pi$
$128$	−4.78212e9	−	1.74055e9i	−1.57462	−	0.573114i
$129$		0			0
$130$	−3.38431e7	−	2.83977e7i	−0.0103926	−	0.00872044i
$131$	5.60440e8	−	2.03983e8i	0.166268	−	0.0605166i	−0.257545	−	0.966266i	$-0.582914\pi$
$131$	5.60440e8	−	2.03983e8i	0.166268	−	0.0605166i	0.423813	+	0.905750i	$0.360691\pi$
$132$		0			0
$133$	−3.27874e8	−	1.85946e9i	−0.0908603	−	0.515294i
$134$	−5.88079e9			−1.57566
$135$		0			0
$136$	−1.81249e9			−0.454308
$137$	1.38950e9	+	7.88023e9i	0.336989	+	1.91116i	0.406646	+	0.913586i	$0.366698\pi$
$137$	1.38950e9	+	7.88023e9i	0.336989	+	1.91116i	−0.0696575	+	0.997571i	$0.522191\pi$
$138$		0			0
$139$	1.55806e9	−	5.67087e8i	0.354011	−	0.128850i	−0.158892	−	0.987296i	$-0.550792\pi$
$139$	1.55806e9	−	5.67087e8i	0.354011	−	0.128850i	0.512903	+	0.858446i	$0.328570\pi$
$140$	8.67478e8	+	7.27901e8i	0.190846	+	0.160139i
$141$		0			0
$142$	−1.21840e10	−	4.43460e9i	−2.51473	−	0.915287i
$143$	1.28117e8	+	2.21905e8i	0.0256209	+	0.0443767i
$144$		0			0
$145$	−4.32859e8	+	7.49733e8i	−0.0813186	+	0.140848i
$146$	1.20914e10	−	1.01459e10i	2.20235	−	1.84799i
$147$		0			0
$148$	−3.03406e9	+	1.72070e10i	−0.519812	+	2.94800i
$149$	−7.95091e8	+	4.50918e9i	−0.132153	+	0.749479i	0.844646	+	0.535325i	$0.179811\pi$
$149$	−7.95091e8	+	4.50918e9i	−0.132153	+	0.749479i	−0.976800	+	0.214155i	$0.931300\pi$
$150$		0			0
$151$	−8.41399e8	+	7.06017e8i	−0.131706	+	0.110514i	−0.706261	−	0.707951i	$-0.749620\pi$
$151$	−8.41399e8	+	7.06017e8i	−0.131706	+	0.110514i	0.574555	+	0.818466i	$0.305175\pi$
$152$	−1.94100e9	+	3.36191e9i	−0.294937	+	0.510846i
$153$		0			0
$154$	−5.26899e9	−	9.12615e9i	−0.754890	−	1.30751i
$155$	1.97092e9	+	7.17354e8i	0.274268	+	0.0998254i
$156$		0			0
$157$	4.71688e9	+	3.95793e9i	0.619592	+	0.519900i	0.897675	−	0.440657i	$-0.145255\pi$
$157$	4.71688e9	+	3.95793e9i	0.619592	+	0.519900i	−0.278083	+	0.960557i	$0.589699\pi$
$158$	2.14710e9	−	7.81480e8i	0.274091	−	0.0997611i
$159$		0			0
$160$	2.13570e8	+	1.21122e9i	0.0257632	+	0.146111i
$161$	−2.54086e9			−0.298033
$162$		0			0
$163$	9.36113e9			1.03869			0.519343	−	0.854566i	$-0.326177\pi$
$163$	9.36113e9			1.03869			0.519343	+	0.854566i	$0.326177\pi$
$164$	−1.71306e9	−	9.71523e9i	−0.184916	−	1.04871i
$165$		0			0
$166$	9.02582e9	−	3.28513e9i	0.922572	−	0.335789i
$167$	−2.62106e9	−	2.19933e9i	−0.260767	−	0.218810i	0.503025	−	0.864272i	$-0.332220\pi$
$167$	−2.62106e9	−	2.19933e9i	−0.260767	−	0.218810i	−0.763792	+	0.645462i	$0.776665\pi$
$168$		0			0
$169$	9.93772e9	+	3.61704e9i	0.937123	+	0.341085i
$170$	6.02026e8	+	1.04274e9i	0.0552834	+	0.0957537i
$171$		0			0
$172$	1.49605e10	−	2.59123e10i	1.30337	−	2.25750i
$173$	1.41514e10	−	1.18745e10i	1.20114	−	1.00787i	0.201540	−	0.979480i	$-0.435405\pi$
$173$	1.41514e10	−	1.18745e10i	1.20114	−	1.00787i	0.999597	−	0.0283934i	$-0.00903911\pi$
$174$		0			0
$175$	−1.98569e9	+	1.12614e10i	−0.160044	+	0.907656i
$176$	−1.78706e8	+	1.01349e9i	−0.0140389	+	0.0796185i
$177$		0			0
$178$	2.41164e10	−	2.02361e10i	1.80062	−	1.51090i
$179$	−1.14380e10	+	1.98111e10i	−0.832740	+	1.44235i	0.0631167	+	0.998006i	$0.479896\pi$
$179$	−1.14380e10	+	1.98111e10i	−0.832740	+	1.44235i	−0.895857	+	0.444342i	$0.853437\pi$
$180$		0			0
$181$	−2.75553e9	−	4.77271e9i	−0.190832	−	0.330530i	0.754694	−	0.656077i	$-0.227785\pi$
$181$	−2.75553e9	−	4.77271e9i	−0.190832	−	0.330530i	−0.945526	+	0.325546i	$0.894452\pi$
$182$	1.12054e9	+	4.07842e8i	0.0757016	+	0.0275531i
$183$		0			0
$184$	4.00179e9	+	3.35790e9i	0.257379	+	0.215967i
$185$	4.31407e9	−	1.57019e9i	0.270779	−	0.0985554i
$186$		0			0
$187$	−1.21265e9	−	6.87729e9i	−0.0725185	−	0.411273i
$188$	−2.46742e10			−1.44056
$189$		0			0
$190$	2.57884e9			0.143560
$191$	1.57468e9	+	8.93044e9i	0.0856133	+	0.485537i	0.997223	+	0.0744794i	$0.0237295\pi$
$191$	1.57468e9	+	8.93044e9i	0.0856133	+	0.485537i	−0.911609	+	0.411058i	$0.865159\pi$
$192$		0			0
$193$	1.35158e10	−	4.91936e9i	0.701189	−	0.255212i	0.0332703	−	0.999446i	$-0.489408\pi$
$193$	1.35158e10	−	4.91936e9i	0.701189	−	0.255212i	0.667918	+	0.744235i	$0.267186\pi$
$194$	−5.46791e9	−	4.58812e9i	−0.277149	−	0.232556i
$195$		0			0
$196$	3.39705e9	+	1.23643e9i	0.164418	+	0.0598433i
$197$	6.16599e9	+	1.06798e10i	0.291679	+	0.505202i	0.974207	−	0.225657i	$-0.0724529\pi$
$197$	6.16599e9	+	1.06798e10i	0.291679	+	0.505202i	−0.682528	+	0.730859i	$0.739120\pi$
$198$		0			0
$199$	−1.25465e10	+	2.17311e10i	−0.567131	+	0.982299i	0.429717	+	0.902963i	$0.358613\pi$
$199$	−1.25465e10	+	2.17311e10i	−0.567131	+	0.982299i	−0.996848	+	0.0793356i	$0.974720\pi$
$200$	1.80100e10	−	1.51122e10i	0.795938	−	0.667872i
$201$		0			0
$202$	−7.10408e9	+	4.02893e10i	−0.300211	+	1.70258i
$203$	4.05761e9	−	2.30119e10i	0.167702	−	0.951086i
$204$		0			0
$205$	−1.98566e9	+	1.66616e9i	−0.0785256	+	0.0658908i
$206$	−1.02772e10	+	1.78005e10i	−0.397622	+	0.688701i
$207$		0			0
$208$	−5.82268e7	−	1.00852e8i	−0.00215694	−	0.00373593i
$209$	−1.40550e10	−	5.11561e9i	−0.509534	−	0.185455i
$210$		0			0
$211$	−1.30381e10	−	1.09402e10i	−0.452837	−	0.379976i	0.387650	−	0.921807i	$-0.373287\pi$
$211$	−1.30381e10	−	1.09402e10i	−0.452837	−	0.379976i	−0.840487	+	0.541831i	$0.817731\pi$
$212$	1.94572e10	−	7.08184e9i	0.661559	−	0.240788i
$213$		0			0
$214$	−8.91895e9	−	5.05819e10i	−0.290704	−	1.64867i
$215$	−7.86183e9			−0.250929
$216$		0			0
$217$	−5.66117e10			−1.73316
$218$	−1.34099e10	−	7.60514e10i	−0.402135	−	2.28062i
$219$		0			0
$220$	8.42946e9	−	3.06807e9i	0.242604	−	0.0883006i
$221$	6.05345e8	+	5.07945e8i	0.0170702	+	0.0143236i
$222$		0			0
$223$	−2.06463e10	−	7.51465e9i	−0.559076	−	0.203487i	0.0469983	−	0.998895i	$-0.485034\pi$
$223$	−2.06463e10	−	7.51465e9i	−0.559076	−	0.203487i	−0.606075	+	0.795408i	$0.707257\pi$
$224$	−1.65983e10	−	2.87492e10i	−0.440503	−	0.762973i
$225$		0			0
$226$	4.35430e10	−	7.54186e10i	1.11027	−	1.92305i
$227$	1.89209e10	−	1.58766e10i	0.472962	−	0.396862i	−0.374912	−	0.927061i	$-0.622327\pi$
$227$	1.89209e10	−	1.58766e10i	0.472962	−	0.396862i	0.847874	+	0.530198i	$0.177882\pi$
$228$		0			0
$229$	−9.82004e9	+	5.56922e10i	−0.235968	+	1.33824i	0.604597	+	0.796532i	$0.293334\pi$
$229$	−9.82004e9	+	5.56922e10i	−0.235968	+	1.33824i	−0.840565	+	0.541710i	$0.817777\pi$
$230$	6.02615e8	−	3.41760e9i	0.0141992	−	0.0805278i
$231$		0			0
$232$	−3.68022e10	+	3.08807e10i	−0.834022	+	0.699828i
$233$	−9.95140e9	+	1.72363e10i	−0.221199	+	0.383127i	−0.955172	−	0.296051i	$-0.904330\pi$
$233$	−9.95140e9	+	1.72363e10i	−0.221199	+	0.383127i	0.733974	+	0.679178i	$0.237664\pi$
$234$		0			0
$235$	3.24161e9	+	5.61464e9i	0.0693355	+	0.120093i
$236$	5.50735e9	+	2.00451e9i	0.115568	+	0.0420634i
$237$		0			0
$238$	−2.48956e10	−	2.08899e10i	−0.502953	−	0.422027i
$239$	−3.44982e10	+	1.25563e10i	−0.683922	+	0.248927i	−0.660530	−	0.750799i	$-0.729669\pi$
$239$	−3.44982e10	+	1.25563e10i	−0.683922	+	0.248927i	−0.0233912	+	0.999726i	$0.507446\pi$
$240$		0			0
$241$	1.92542e8	+	1.09196e9i	0.00367663	+	0.0208512i	0.986591	−	0.163213i	$-0.0521857\pi$
$241$	1.92542e8	+	1.09196e9i	0.00367663	+	0.0208512i	−0.982914	+	0.184064i	$0.941075\pi$
$242$	3.44859e9			0.0646356
$243$		0			0
$244$	9.34375e10			1.68759
$245$	−1.64943e8	−	9.35440e8i	−0.00292474	−	0.0165870i
$246$		0			0
$247$	1.59043e9	−	5.78870e8i	0.0271881	−	0.00989565i
$248$	8.91620e10	+	7.48158e10i	1.49674	+	1.25592i
$249$		0			0
$250$	−2.97344e10	−	1.08224e10i	−0.481426	−	0.175225i
$251$	−1.01467e10	−	1.75746e10i	−0.161359	−	0.279482i	0.773997	−	0.633189i	$-0.218254\pi$
$251$	−1.01467e10	−	1.75746e10i	−0.161359	−	0.279482i	−0.935356	+	0.353707i	$0.884921\pi$
$252$		0			0
$253$	−1.00638e10	+	1.74309e10i	−0.154425	+	0.267472i
$254$	−5.94597e10	+	4.98926e10i	−0.896337	+	0.752116i
$255$		0			0
$256$	−1.34804e10	+	7.64514e10i	−0.196166	+	1.11251i
$257$	−6.29806e9	+	3.57181e10i	−0.0900550	+	0.510727i	0.906096	+	0.423072i	$0.139048\pi$
$257$	−6.29806e9	+	3.57181e10i	−0.0900550	+	0.510727i	−0.996151	+	0.0876550i	$0.972063\pi$
$258$		0			0
$259$	−9.49249e10	+	7.96514e10i	−1.31078	+	1.09988i
$260$	−5.07537e8	+	8.79079e8i	−0.00688791	+	0.0119302i
$261$		0			0
$262$	−1.09933e10	−	1.90409e10i	−0.144135	−	0.249650i
$263$	1.41128e11	+	5.13665e10i	1.81892	+	0.662033i	0.995518	+	0.0945732i	$0.0301486\pi$
$263$	1.41128e11	+	5.13665e10i	1.81892	+	0.662033i	0.823401	+	0.567459i	$0.192074\pi$
$264$		0			0
$265$	−4.16770e9	−	3.49711e9i	−0.0519146	−	0.0435616i
$266$	−6.54086e10	+	2.38068e10i	−0.801065	+	0.291564i
$267$		0			0
$268$	2.34632e10	+	1.33066e11i	0.277831	+	1.57566i
$269$	−3.65710e10			−0.425845			−0.212922	−	0.977069i	$-0.568298\pi$
$269$	−3.65710e10			−0.425845			−0.212922	+	0.977069i	$0.568298\pi$
$270$		0			0
$271$	−1.03536e10			−0.116608			−0.0583039	−	0.998299i	$-0.518569\pi$
$271$	−1.03536e10			−0.116608			−0.0583039	+	0.998299i	$0.518569\pi$
$272$	5.51127e8	+	3.12560e9i	0.00610509	+	0.0346237i
$273$		0			0
$274$	2.77196e11	−	1.00891e11i	2.97104	−	1.08137i
$275$	6.93913e10	+	5.82262e10i	0.731657	+	0.613933i
$276$		0			0
$277$	−9.83901e10	−	3.58111e10i	−1.00414	−	0.365475i	−0.212958	−	0.977061i	$-0.568310\pi$
$277$	−9.83901e10	−	3.58111e10i	−1.00414	−	0.365475i	−0.791178	+	0.611586i	$0.790532\pi$
$278$	−3.05619e10	−	5.29348e10i	−0.306888	−	0.531545i
$279$		0			0
$280$	8.25594e9	−	1.42997e10i	0.0802704	−	0.139032i
$281$	−1.24873e11	+	1.04781e11i	−1.19478	+	1.00254i	−0.195021	+	0.980799i	$0.562478\pi$
$281$	−1.24873e11	+	1.04781e11i	−1.19478	+	1.00254i	−0.999764	+	0.0217445i	$0.993078\pi$
$282$		0			0
$283$	−2.04952e10	+	1.16234e11i	−0.189939	+	1.07720i	0.729506	+	0.683975i	$0.239750\pi$
$283$	−2.04952e10	+	1.16234e11i	−0.189939	+	1.07720i	−0.919444	+	0.393221i	$0.871361\pi$
$284$	−5.17315e10	+	2.93384e11i	−0.471870	+	2.67611i
$285$		0			0
$286$	7.23609e9	−	6.07180e9i	0.0639524	−	0.0536624i
$287$	3.49820e10	−	6.05906e10i	0.304352	−	0.527153i
$288$		0			0
$289$	4.85256e10	+	8.40488e10i	0.409195	+	0.708747i
$290$	2.99899e10	+	1.09154e10i	0.248991	+	0.0906254i
$291$		0			0
$292$	−2.77815e11	−	2.33115e11i	−2.23632	−	1.87649i
$293$	1.18073e11	−	4.29750e10i	0.935935	−	0.340653i	0.171376	−	0.985206i	$-0.445179\pi$
$293$	1.18073e11	−	4.29750e10i	0.935935	−	0.340653i	0.764560	+	0.644553i	$0.222957\pi$
$294$		0			0
$295$	−2.67409e8	−	1.51655e9i	−0.00205578	−	0.0116589i
$296$	2.54768e11			1.92900
$297$		0			0
$298$	1.68795e11			1.23990
$299$	−3.95498e8	−	2.24298e9i	−0.00286170	−	0.0162295i
$300$		0			0
$301$	1.99404e11	−	7.25771e10i	1.40018	−	0.509625i
$302$	3.10181e10	+	2.60273e10i	0.214577	+	0.180052i
$303$		0			0
$304$	6.38774e9	+	2.32495e9i	0.0428960	+	0.0156129i
$305$	−1.22755e10	−	2.12618e10i	−0.0812251	−	0.140686i
$306$		0			0
$307$	−1.29425e11	+	2.24170e11i	−0.831563	+	1.44031i	0.0652363	+	0.997870i	$0.479220\pi$
$307$	−1.29425e11	+	2.24170e11i	−0.831563	+	1.44031i	−0.896799	+	0.442439i	$0.854113\pi$
$308$	−1.85478e11	+	1.55635e11i	−1.17440	+	0.985434i
$309$		0			0
$310$	1.34266e10	−	7.61459e10i	0.0825730	−	0.468295i
$311$	4.07695e10	−	2.31215e11i	0.247123	−	1.40151i	−0.568386	−	0.822762i	$-0.692432\pi$
$311$	4.07695e10	−	2.31215e11i	0.247123	−	1.40151i	0.815509	−	0.578744i	$-0.196457\pi$
$312$		0			0
$313$	3.67264e10	−	3.08171e10i	0.216286	−	0.181486i	−0.528207	−	0.849116i	$-0.677136\pi$
$313$	3.67264e10	−	3.08171e10i	0.216286	−	0.181486i	0.744493	+	0.667630i	$0.232691\pi$
$314$	1.13497e11	−	1.96582e11i	0.658871	−	1.14120i
$315$		0			0
$316$	−2.62493e10	−	4.54651e10i	−0.148090	−	0.256499i
$317$	−7.27839e10	−	2.64912e10i	−0.404826	−	0.147345i	0.131578	−	0.991306i	$-0.457996\pi$
$317$	−7.27839e10	−	2.64912e10i	−0.404826	−	0.147345i	−0.536404	+	0.843961i	$0.680218\pi$
$318$		0			0
$319$	−1.41796e11	−	1.18981e11i	−0.766665	−	0.643309i
$320$	4.49216e10	−	1.63501e10i	0.239486	−	0.0871658i
$321$		0			0
$322$	1.62654e10	+	9.22455e10i	0.0843165	+	0.478183i
$323$	−4.61273e10			−0.235801
$324$		0			0
$325$	−1.02502e10			−0.0509635
$326$	−5.99255e10	−	3.39854e11i	−0.293854	−	1.66653i
$327$		0			0
$328$	−1.35170e11	+	4.91977e10i	−0.644833	+	0.234700i
$329$	−1.34051e11	−	1.12482e11i	−0.630794	−	0.529299i
$330$		0			0
$331$	−2.64223e10	−	9.61694e9i	−0.120989	−	0.0440363i	0.280816	−	0.959762i	$-0.409395\pi$
$331$	−2.64223e10	−	9.61694e9i	−0.120989	−	0.0440363i	−0.401805	+	0.915725i	$0.631617\pi$
$332$	−1.10345e11	−	1.91123e11i	−0.498461	−	0.863359i
$333$		0			0
$334$	−6.30677e10	+	1.09236e11i	−0.277299	+	0.480295i
$335$	2.71969e10	−	2.28209e10i	0.117982	−	0.0989990i
$336$		0			0
$337$	−1.38244e10	+	7.84022e10i	−0.0583865	+	0.331127i	−0.999984	−	0.00561338i	$-0.998213\pi$
$337$	−1.38244e10	+	7.84022e10i	−0.0583865	+	0.331127i	0.941598	+	0.336740i	$0.109324\pi$
$338$	6.76994e10	−	3.83942e11i	0.282137	−	1.60008i
$339$		0			0
$340$	2.11924e10	−	1.77825e10i	0.0860053	−	0.0721670i
$341$	−2.24226e11	+	3.88371e11i	−0.898031	+	1.55544i
$342$		0			0
$343$	1.34024e11	+	2.32136e11i	0.522828	+	0.905564i
$344$	−4.09971e11	−	1.49217e11i	−1.57848	−	0.574521i
$345$		0			0
$346$	−5.21691e11	−	4.37751e11i	−1.95691	−	1.64204i
$347$	1.24542e11	−	4.53295e10i	0.461140	−	0.167841i	−0.100995	−	0.994887i	$-0.532203\pi$
$347$	1.24542e11	−	4.53295e10i	0.461140	−	0.167841i	0.562135	+	0.827046i	$0.309980\pi$
$348$		0			0
$349$	−7.68067e10	−	4.35592e11i	−0.277131	−	1.57169i	−0.732112	−	0.681185i	$-0.761465\pi$
$349$	−7.68067e10	−	4.35592e11i	−0.277131	−	1.57169i	0.454981	−	0.890501i	$-0.349646\pi$
$350$	4.21555e11			1.50158
$351$		0			0
$352$	−2.62969e11			−0.912982
$353$	6.93131e10	+	3.93094e11i	0.237591	+	1.34744i	0.837089	+	0.547067i	$0.184256\pi$
$353$	6.93131e10	+	3.93094e11i	0.237591	+	1.34744i	−0.599498	+	0.800376i	$0.704633\pi$
$354$		0			0
$355$	7.35561e10	−	2.67722e10i	0.245805	−	0.0894658i
$356$	−5.54108e11	−	4.64952e11i	−1.82839	−	1.53420i
$357$		0			0
$358$	7.92460e11	+	2.88432e11i	2.54979	+	0.928046i
$359$	2.10653e11	+	3.64862e11i	0.669333	+	1.15932i	0.978091	+	0.208179i	$0.0667535\pi$
$359$	2.10653e11	+	3.64862e11i	0.669333	+	1.15932i	−0.308757	+	0.951141i	$0.599913\pi$
$360$		0			0
$361$	1.11946e11	−	1.93896e11i	0.346918	−	0.600879i
$362$	−1.55633e11	+	1.30592e11i	−0.476336	+	0.399693i
$363$		0			0
$364$	4.75765e9	−	2.69819e10i	0.0142048	−	0.0805596i
$365$	−1.65471e10	+	9.38431e10i	−0.0487981	+	0.276748i
$366$		0			0
$367$	4.38435e11	−	3.67891e11i	1.26156	−	1.05858i	0.266047	−	0.963960i	$-0.414282\pi$
$367$	4.38435e11	−	3.67891e11i	1.26156	−	1.05858i	0.995514	−	0.0946156i	$-0.0301622\pi$
$368$	4.57379e9	−	7.92204e9i	0.0130005	−	0.0225176i
$369$		0			0
$370$	−8.46223e10	−	1.46570e11i	−0.234735	−	0.406572i
$371$	1.37992e11	+	5.02248e10i	0.378155	+	0.137637i
$372$		0			0
$373$	3.71902e11	+	3.12063e11i	0.994806	+	0.834742i	0.986256	−	0.165222i	$-0.0528340\pi$
$373$	3.71902e11	+	3.12063e11i	0.994806	+	0.834742i	0.00854993	+	0.999963i	$0.497278\pi$
$374$	−2.41916e11	+	8.80502e10i	−0.639356	+	0.232706i
$375$		0			0
$376$	6.24748e10	+	3.54312e11i	0.161198	+	0.914199i
$377$	2.09456e10			0.0534020
$378$		0			0
$379$	−1.76515e11			−0.439446			−0.219723	−	0.975562i	$-0.570515\pi$
$379$	−1.76515e11			−0.439446			−0.219723	+	0.975562i	$0.570515\pi$
$380$	−1.02891e10	−	5.83523e10i	−0.0253134	−	0.143559i
$381$		0			0
$382$	3.14138e11	−	1.14337e11i	0.754806	−	0.274727i
$383$	−2.95459e11	−	2.47919e11i	−0.701620	−	0.588729i	0.220614	−	0.975361i	$-0.429194\pi$
$383$	−2.95459e11	−	2.47919e11i	−0.701620	−	0.588729i	−0.922234	+	0.386632i	$0.873638\pi$
$384$		0			0
$385$	5.97823e10	+	2.17590e10i	0.138675	+	0.0504737i
$386$	−2.65119e11	−	4.59199e11i	−0.607851	−	1.05283i
$387$		0			0
$388$	−8.20009e10	+	1.42030e11i	−0.183686	+	0.318153i
$389$	5.74522e11	−	4.82081e11i	1.27214	−	1.06745i	0.277857	−	0.960622i	$-0.410376\pi$
$389$	5.74522e11	−	4.82081e11i	1.27214	−	1.06745i	0.994278	−	0.106826i	$-0.0340687\pi$
$390$		0			0
$391$	−1.07789e10	+	6.11299e10i	−0.0233226	+	0.132269i
$392$	9.15331e9	−	5.19110e10i	0.0195790	−	0.111038i
$393$		0			0
$394$	3.48257e11	−	2.92222e11i	0.728060	−	0.610915i
$395$	−6.89709e9	+	1.19461e10i	−0.0142554	+	0.0246910i
$396$		0			0
$397$	−5.80196e10	−	1.00493e11i	−0.117224	−	0.203038i	0.801442	−	0.598072i	$-0.204066\pi$
$397$	−5.80196e10	−	1.00493e11i	−0.117224	−	0.203038i	−0.918667	+	0.395034i	$0.870733\pi$
$398$	8.69263e11	+	3.16386e11i	1.73651	+	0.632038i
$399$		0			0
$400$	−3.15370e10	−	2.64627e10i	−0.0615958	−	0.0516850i
$401$	1.45692e10	−	5.30277e9i	0.0281376	−	0.0102412i	−0.327913	−	0.944708i	$-0.606345\pi$
$401$	1.45692e10	−	5.30277e9i	0.0281376	−	0.0102412i	0.356051	+	0.934467i	$0.384123\pi$
$402$		0			0
$403$	−8.81190e9	−	4.99748e10i	−0.0166417	−	0.0943796i
$404$	9.39981e11			1.75551
$405$		0			0
$406$	−8.61417e11			−1.57343
$407$	1.70453e11	+	9.66689e11i	0.307915	+	1.74627i
$408$		0			0
$409$	8.25039e11	−	3.00289e11i	1.45787	−	0.530622i	0.513094	−	0.858333i	$-0.328499\pi$
$409$	8.25039e11	−	3.00289e11i	1.45787	−	0.530622i	0.944778	+	0.327711i	$0.106277\pi$
$410$	7.32010e10	+	6.14229e10i	0.127935	+	0.107350i
$411$		0			0
$412$	4.43782e11	+	1.61524e11i	0.758809	+	0.276184i
$413$	2.07826e10	+	3.59965e10i	0.0351499	+	0.0608814i
$414$		0			0
$415$	−2.89935e10	+	5.02182e10i	−0.0479826	+	0.0831084i
$416$	2.27951e10	−	1.91274e10i	0.0373183	−	0.0313137i
$417$		0			0
$418$	−9.57479e10	+	5.43013e11i	−0.153404	+	0.869996i
$419$	1.02324e11	−	5.80310e11i	0.162187	−	0.919807i	−0.789731	−	0.613453i	$-0.789780\pi$
$419$	1.02324e11	−	5.80310e11i	0.162187	−	0.919807i	0.951918	−	0.306354i	$-0.0991090\pi$
$420$		0			0
$421$	2.34819e11	−	1.97037e11i	0.364305	−	0.305688i	−0.442199	−	0.896917i	$-0.645802\pi$
$421$	2.34819e11	−	1.97037e11i	0.364305	−	0.305688i	0.806504	+	0.591229i	$0.201357\pi$
$422$	−3.13720e11	+	5.43379e11i	−0.481545	+	0.834060i
$423$		0			0
$424$	−1.50958e11	−	2.61467e11i	−0.226835	−	0.392889i
$425$	2.62512e11	+	9.55465e10i	0.390300	+	0.142058i
$426$		0			0
$427$	5.07631e11	+	4.25953e11i	0.738963	+	0.620063i
$428$	−1.10895e12	+	4.03624e11i	−1.59740	+	0.581406i
$429$		0			0
$430$	5.03277e10	+	2.85423e11i	0.0709903	+	0.402606i
$431$	−6.35532e11			−0.887135			−0.443568	−	0.896241i	$-0.646287\pi$
$431$	−6.35532e11			−0.887135			−0.443568	+	0.896241i	$0.646287\pi$
$432$		0			0
$433$	−4.34254e11			−0.593675			−0.296837	−	0.954928i	$-0.595932\pi$
$433$	−4.34254e11			−0.593675			−0.296837	+	0.954928i	$0.595932\pi$
$434$	3.62401e11	+	2.05528e12i	0.490327	+	2.78078i
$435$		0			0
$436$	−1.66733e12	+	6.06860e11i	−2.20970	+	0.804265i
$437$	1.01844e11	+	8.54575e10i	0.133589	+	0.112094i
$438$		0			0
$439$	−1.07757e12	−	3.92204e11i	−1.38470	−	0.503990i	−0.461101	−	0.887348i	$-0.652545\pi$
$439$	−1.07757e12	−	3.92204e11i	−1.38470	−	0.503990i	−0.923600	+	0.383358i	$0.874768\pi$
$440$	−6.53997e10	−	1.13276e11i	−0.0831838	−	0.144079i
$441$		0			0
$442$	1.45657e10	−	2.52286e10i	0.0181523	−	0.0314407i
$443$	9.54438e11	−	8.00869e11i	1.17742	−	0.987972i	0.177426	−	0.984134i	$-0.443223\pi$
$443$	9.54438e11	−	8.00869e11i	1.17742	−	0.987972i	0.999993	−	0.00383775i	$-0.00122160\pi$
$444$		0			0
$445$	−3.30034e10	+	1.87172e11i	−0.0398969	+	0.226266i
$446$	−1.40650e11	+	7.97667e11i	−0.168319	+	0.954586i
$447$		0			0
$448$	−9.88434e11	+	8.29395e11i	−1.15930	+	0.972770i
$449$	−6.88438e11	+	1.19241e12i	−0.799386	+	1.38458i	0.120631	+	0.992697i	$0.461508\pi$
$449$	−6.88438e11	+	1.19241e12i	−0.799386	+	1.38458i	−0.920017	+	0.391879i	$0.871825\pi$
$450$		0			0
$451$	−2.77111e11	−	4.79970e11i	−0.315398	−	0.546286i
$452$	−1.88025e12	−	6.84355e11i	−2.11881	−	0.771184i
$453$		0			0
$454$	−6.97519e11	−	5.85288e11i	−0.770557	−	0.646574i
$455$	−6.76481e9	+	2.46219e9i	−0.00739954	+	0.00269321i
$456$		0			0
$457$	8.01533e10	+	4.54572e11i	0.0859604	+	0.487506i	0.997145	+	0.0755079i	$0.0240578\pi$
$457$	8.01533e10	+	4.54572e11i	0.0859604	+	0.487506i	−0.911185	+	0.411998i	$0.864831\pi$
$458$	2.08476e12			2.21392
$459$		0			0
$460$	−7.97354e10			−0.0830311
$461$	−1.78683e11	−	1.01336e12i	−0.184259	−	1.04499i	−0.926903	−	0.375301i	$-0.877540\pi$
$461$	−1.78683e11	−	1.01336e12i	−0.184259	−	1.04499i	0.742644	−	0.669687i	$-0.233572\pi$
$462$		0			0
$463$	−4.99548e11	+	1.81821e11i	−0.505200	+	0.183878i	−0.582031	−	0.813166i	$-0.697742\pi$
$463$	−4.99548e11	+	1.81821e11i	−0.505200	+	0.183878i	0.0768316	+	0.997044i	$0.475520\pi$
$464$	6.44436e10	+	5.40746e10i	0.0645430	+	0.0541580i
$465$		0			0
$466$	6.89466e11	+	2.50945e11i	0.677293	+	0.246514i
$467$	−6.15190e11	−	1.06554e12i	−0.598526	−	1.03668i	−0.993039	−	0.117787i	$-0.962420\pi$
$467$	−6.15190e11	−	1.06554e12i	−0.598526	−	1.03668i	0.394512	−	0.918891i	$-0.370913\pi$
$468$		0			0
$469$	−4.79137e11	+	8.29889e11i	−0.457279	+	0.792031i
$470$	1.83087e11	−	1.53628e11i	0.173068	−	0.145222i
$471$		0			0
$472$	1.48395e10	−	8.41589e10i	0.0137619	−	0.0780479i
$473$	2.91896e11	−	1.65542e12i	0.268135	−	1.52067i
$474$		0			0
$475$	4.58350e11	−	3.84601e11i	0.413120	−	0.346648i
$476$	−3.73354e11	+	6.46668e11i	−0.333342	+	0.577365i
$477$		0			0
$478$	6.76697e11	+	1.17207e12i	0.592883	+	1.02690i
$479$	−1.22723e12	−	4.46674e11i	−1.06516	−	0.387687i	−0.250796	−	0.968040i	$-0.580692\pi$
$479$	−1.22723e12	−	4.46674e11i	−1.06516	−	0.387687i	−0.814365	+	0.580353i	$0.802914\pi$
$480$		0			0
$481$	−8.50889e10	−	7.13981e10i	−0.0724803	−	0.0608182i
$482$	3.84110e10	−	1.39804e10i	0.0324148	−	0.0117980i
$483$		0			0
$484$	−1.37592e10	−	7.80322e10i	−0.0113970	−	0.0646353i
$485$	4.30920e10			0.0353638
$486$		0			0
$487$	1.46641e12			1.18134			0.590669	−	0.806914i	$-0.298864\pi$
$487$	1.46641e12			1.18134			0.590669	+	0.806914i	$0.298864\pi$
$488$	−2.36583e11	−	1.34173e12i	−0.188840	−	1.07097i
$489$		0			0
$490$	−3.29051e10	+	1.19765e10i	−0.0257858	+	0.00938527i
$491$	−4.16887e11	−	3.49810e11i	−0.323707	−	0.271622i	0.466423	−	0.884562i	$-0.345543\pi$
$491$	−4.16887e11	−	3.49810e11i	−0.323707	−	0.271622i	−0.790130	+	0.612939i	$0.789987\pi$
$492$		0			0
$493$	−5.36424e11	−	1.95242e11i	−0.408975	−	0.148855i
$494$	−3.11970e10	−	5.40347e10i	−0.0235690	−	0.0408227i
$495$		0			0
$496$	1.01907e11	−	1.76507e11i	0.0756022	−	0.130947i
$497$	−1.61849e12	+	1.35808e12i	−1.18989	+	0.998438i
$498$		0			0
$499$	2.64439e11	−	1.49971e12i	0.190929	−	1.08281i	−0.727169	−	0.686459i	$-0.759164\pi$
$499$	2.64439e11	−	1.49971e12i	0.190929	−	1.08281i	0.918098	−	0.396354i	$-0.129725\pi$
$500$	−1.26248e11	+	7.15990e11i	−0.0903359	+	0.512321i
$501$		0			0
$502$	−5.73089e11	+	4.80879e11i	−0.402769	+	0.337963i
$503$	3.18848e11	−	5.52260e11i	0.222089	−	0.384670i	−0.733353	−	0.679848i	$-0.762046\pi$
$503$	3.18848e11	−	5.52260e11i	0.222089	−	0.384670i	0.955442	+	0.295178i	$0.0953791\pi$
$504$		0			0
$505$	−1.23492e11	−	2.13894e11i	−0.0844941	−	0.146348i
$506$	6.97251e11	+	2.53779e11i	0.472838	+	0.172099i
$507$		0			0
$508$	1.36617e12	+	1.14635e12i	0.910160	+	0.763715i
$509$	1.83169e12	−	6.66681e11i	1.20955	−	0.440239i	0.343000	−	0.939336i	$-0.388557\pi$
$509$	1.83169e12	−	6.66681e11i	1.20955	−	0.440239i	0.866546	+	0.499097i	$0.166335\pi$
$510$		0			0
$511$	−4.46627e11	−	2.53295e12i	−0.289769	−	1.64336i
$512$	2.56271e11			0.164811
$513$		0			0
$514$	1.33706e12			0.844921
$515$	−2.15478e10	−	1.22204e11i	−0.0134980	−	0.0765511i
$516$		0			0
$517$	−1.30260e12	+	4.74107e11i	−0.801869	+	0.291856i
$518$	3.49940e12	+	2.93634e12i	2.13555	+	1.79194i
$519$		0			0
$520$	1.39083e10	+	5.06222e9i	0.00834180	+	0.00303617i
$521$	4.55095e9	+	7.88248e9i	0.00270603	+	0.00468698i	0.867375	−	0.497655i	$-0.165805\pi$
$521$	4.55095e9	+	7.88248e9i	0.00270603	+	0.00468698i	−0.864669	+	0.502342i	$0.832472\pi$
$522$		0			0
$523$	−7.13405e11	+	1.23565e12i	−0.416945	+	0.722169i	−0.995630	−	0.0933813i	$-0.970232\pi$
$523$	−7.13405e11	+	1.23565e12i	−0.416945	+	0.722169i	0.578686	+	0.815551i	$0.303566\pi$
$524$	−3.86983e11	+	3.24717e11i	−0.224234	+	0.188155i
$525$		0			0
$526$	9.61417e11	−	5.45247e12i	0.547616	−	3.10568i
$527$	−2.40159e11	+	1.36201e12i	−0.135628	+	0.769187i
$528$		0			0
$529$	−1.24271e12	+	1.04276e12i	−0.689954	+	0.578940i
$530$	−1.00283e11	+	1.73695e11i	−0.0552057	+	0.0956191i
$531$		0			0
$532$	7.99651e11	+	1.38504e12i	0.432811	+	0.749651i
$533$	5.89322e10	+	2.14496e10i	0.0316286	+	0.0115119i
$534$		0			0
$535$	2.37535e11	+	1.99315e11i	0.125353	+	0.105184i
$536$	1.85137e12	−	6.73845e11i	0.968842	−	0.352630i
$537$		0			0
$538$	2.34110e11	+	1.32770e12i	0.120476	+	0.683252i
$539$	2.03095e11			0.103645
$540$		0			0
$541$	1.43983e12			0.722641			0.361320	−	0.932442i	$-0.382326\pi$
$541$	1.43983e12			0.722641			0.361320	+	0.932442i	$0.382326\pi$
$542$	6.62786e10	+	3.75884e11i	0.0329895	+	0.187093i
$543$		0			0
$544$	−7.62083e11	+	2.77376e11i	−0.373085	+	0.135792i
$545$	3.57140e11	+	2.99676e11i	0.173402	+	0.145502i
$546$		0			0
$547$	−3.45780e11	−	1.25854e11i	−0.165142	−	0.0601067i	0.258126	−	0.966111i	$-0.416895\pi$
$547$	−3.45780e11	−	1.25854e11i	−0.165142	−	0.0601067i	−0.423268	+	0.906004i	$0.639117\pi$
$548$	−3.38885e12	−	5.86966e12i	−1.60524	−	2.78035i
$549$		0			0
$550$	1.66968e12	−	2.89198e12i	0.778040	−	1.34760i
$551$	−9.36604e11	+	7.85904e11i	−0.432886	+	0.363235i
$552$		0			0
$553$	6.46533e10	−	3.66667e11i	0.0293986	−	0.166728i
$554$	−6.70269e11	+	3.80128e12i	−0.302312	+	1.71450i
$555$		0			0
$556$	−1.07584e12	+	9.02734e11i	−0.477430	+	0.400611i
$557$	−4.28201e11	+	7.41665e11i	−0.188495	+	0.326482i	−0.944749	−	0.327796i	$-0.893694\pi$
$557$	−4.28201e11	+	7.41665e11i	−0.188495	+	0.326482i	0.756254	+	0.654278i	$0.227027\pi$
$558$		0			0
$559$	9.51067e10	+	1.64730e11i	0.0411963	+	0.0713540i
$560$	−2.71699e10	−	9.88905e9i	−0.0116746	−	0.00424921i
$561$		0			0
$562$	4.60343e12	+	3.86273e12i	1.94656	+	1.63336i
$563$	−6.58635e11	+	2.39724e11i	−0.276285	+	0.100559i	−0.476447	−	0.879203i	$-0.658075\pi$
$563$	−6.58635e11	+	2.39724e11i	−0.276285	+	0.100559i	0.200162	+	0.979763i	$0.435853\pi$
$564$		0			0
$565$	9.12952e10	+	5.17761e11i	0.0376903	+	0.213752i
$566$	4.35106e12			1.78206
$567$		0			0
$568$	4.34387e12			1.75109
$569$	−6.69270e11	−	3.79562e12i	−0.267668	−	1.51802i	−0.761329	−	0.648366i	$-0.775453\pi$
$569$	−6.69270e11	−	3.79562e12i	−0.267668	−	1.51802i	0.493661	−	0.869654i	$-0.335658\pi$
$570$		0			0
$571$	−7.21760e11	+	2.62699e11i	−0.284139	+	0.103418i	−0.480158	−	0.877182i	$-0.659421\pi$
$571$	−7.21760e11	+	2.62699e11i	−0.284139	+	0.103418i	0.196019	+	0.980600i	$0.437198\pi$
$572$	−1.66259e11	−	1.39508e11i	−0.0649386	−	0.0544900i
$573$		0			0
$574$	−2.42367e12	−	8.82143e11i	−0.931901	−	0.339184i
$575$	−4.02585e11	−	6.97298e11i	−0.153586	−	0.266019i
$576$		0			0
$577$	2.13129e12	−	3.69150e12i	0.800481	−	1.38647i	−0.118819	−	0.992916i	$-0.537911\pi$
$577$	2.13129e12	−	3.69150e12i	0.800481	−	1.38647i	0.919300	−	0.393557i	$-0.128756\pi$
$578$	2.74074e12	−	2.29976e12i	1.02139	−	0.857051i
$579$		0			0
$580$	1.27333e11	−	7.22141e11i	0.0467213	−	0.264970i
$581$	2.71785e11	−	1.54137e12i	0.0989538	−	0.561195i
$582$		0			0
$583$	8.91108e11	−	7.47728e11i	0.319464	−	0.268062i
$584$	−2.64402e12	+	4.57957e12i	−0.940603	+	1.62917i
$585$		0			0
$586$	−2.31605e12	−	4.01151e12i	−0.811350	−	1.40530i
$587$	−2.14624e12	−	7.81167e11i	−0.746116	−	0.271564i	−0.0591456	−	0.998249i	$-0.518838\pi$
$587$	−2.14624e12	−	7.81167e11i	−0.746116	−	0.271564i	−0.686970	+	0.726685i	$0.741060\pi$
$588$		0			0
$589$	2.26914e12	+	1.90404e12i	0.776861	+	0.651864i
$590$	−5.33463e10	+	1.94165e10i	−0.0181247	+	0.00659684i
$591$		0			0
$592$	−7.74679e10	−	4.39342e11i	−0.0259223	−	0.147013i
$593$	−2.44394e12			−0.811604			−0.405802	−	0.913961i	$-0.633008\pi$
$593$	−2.44394e12			−0.811604			−0.405802	+	0.913961i	$0.633008\pi$
$594$		0			0
$595$	1.96200e11			0.0641760
$596$	−6.73459e11	−	3.81938e12i	−0.218627	−	1.23989i
$597$		0			0
$598$	−7.88992e10	+	2.87170e10i	−0.0252300	+	0.00918297i
$599$	−1.38527e12	−	1.16238e12i	−0.439657	−	0.368916i	0.395924	−	0.918283i	$-0.370424\pi$
$599$	−1.38527e12	−	1.16238e12i	−0.439657	−	0.368916i	−0.835581	+	0.549367i	$0.814869\pi$
$600$		0			0
$601$	−3.03595e12	−	1.10500e12i	−0.949204	−	0.345482i	−0.179410	−	0.983774i	$-0.557419\pi$
$601$	−3.03595e12	−	1.10500e12i	−0.949204	−	0.345482i	−0.769794	+	0.638293i	$0.779641\pi$
$602$	−3.91139e12	−	6.77473e12i	−1.21380	−	2.10236i
$603$		0			0
$604$	4.65171e11	−	8.05699e11i	0.142215	−	0.246324i
$605$	−1.59487e10	+	1.33825e10i	−0.00483978	+	0.00406106i
$606$		0			0
$607$	−2.53816e11	+	1.43946e12i	−0.0758874	+	0.430379i	0.923066	+	0.384641i	$0.125675\pi$
$607$	−2.53816e11	+	1.43946e12i	−0.0758874	+	0.430379i	−0.998953	+	0.0457375i	$0.985436\pi$
$608$	−3.01625e11	+	1.71060e12i	−0.0895160	+	0.507670i
$609$		0			0
$610$	−6.93325e11	+	5.81769e11i	−0.202746	+	0.170124i
$611$	7.84293e10	−	1.35844e11i	0.0227663	−	0.0394324i
$612$		0			0
$613$	8.53243e11	+	1.47786e12i	0.244062	+	0.422728i	0.961868	−	0.273516i	$-0.0881865\pi$
$613$	8.53243e11	+	1.47786e12i	0.244062	+	0.422728i	−0.717805	+	0.696244i	$0.754853\pi$
$614$	8.96699e12	+	3.26372e12i	2.54618	+	0.926733i
$615$		0			0
$616$	2.70448e12	+	2.26933e12i	0.756782	+	0.635016i
$617$	−2.27334e12	+	8.27426e11i	−0.631510	+	0.229851i	−0.637888	−	0.770129i	$-0.720192\pi$
$617$	−2.27334e12	+	8.27426e11i	−0.631510	+	0.229851i	0.00637834	+	0.999980i	$0.497970\pi$
$618$		0			0
$619$	8.56840e10	+	4.85938e11i	0.0234581	+	0.133037i	0.994288	−	0.106733i	$-0.0340390\pi$
$619$	8.56840e10	+	4.85938e11i	0.0234581	+	0.133037i	−0.970830	+	0.239770i	$0.922928\pi$
$620$	−1.77655e12			−0.482852
$621$		0			0
$622$	−8.65523e12			−2.31858
$623$	−8.90806e11	−	5.05201e12i	−0.236912	−	1.34359i
$624$		0			0
$625$	−3.31422e12	+	1.20628e12i	−0.868804	+	0.316219i
$626$	−1.35392e12	−	1.13607e12i	−0.352377	−	0.295679i
$627$		0			0
$628$	−4.90096e12	−	1.78380e12i	−1.25737	−	0.457645i
$629$	1.51362e12	+	2.62167e12i	0.385558	+	0.667806i
$630$		0			0
$631$	2.11783e12	−	3.66819e12i	0.531814	−	0.921128i	−0.467497	−	0.883995i	$-0.654844\pi$
$631$	2.11783e12	−	3.66819e12i	0.531814	−	0.921128i	0.999310	−	0.0371334i	$-0.0118227\pi$
$632$	−5.86399e11	+	4.92047e11i	−0.146206	+	0.122682i
$633$		0			0
$634$	−4.95830e11	+	2.81199e12i	−0.121880	+	0.691214i
$635$	8.13708e10	−	4.61477e11i	0.0198604	−	0.112634i
$636$		0			0
$637$	−1.76050e10	+	1.47723e10i	−0.00423651	+	0.00355485i
$638$	−3.41188e12	+	5.90954e12i	−0.815267	+	1.41208i
$639$		0			0
$640$	−5.66301e11	−	9.80862e11i	−0.133425	−	0.231099i
$641$	3.31662e12	+	1.20715e12i	0.775952	+	0.282423i	0.699484	−	0.714649i	$-0.253413\pi$
$641$	3.31662e12	+	1.20715e12i	0.775952	+	0.282423i	0.0764684	+	0.997072i	$0.475636\pi$
$642$		0			0
$643$	6.96875e11	+	5.84747e11i	0.160770	+	0.134902i	0.719624	−	0.694364i	$-0.244314\pi$
$643$	6.96875e11	+	5.84747e11i	0.160770	+	0.134902i	−0.558854	+	0.829266i	$0.688759\pi$
$644$	2.02237e12	−	7.36083e11i	0.463313	−	0.168632i
$645$		0			0
$646$	2.95285e11	+	1.67464e12i	0.0667106	+	0.378335i
$647$	1.74424e12			0.391324			0.195662	−	0.980671i	$-0.437314\pi$
$647$	1.74424e12			0.391324			0.195662	+	0.980671i	$0.437314\pi$
$648$		0			0
$649$	3.29260e11			0.0728514
$650$	6.56172e10	+	3.72134e11i	0.0144181	+	0.0817690i
$651$		0			0
$652$	−7.45090e12	+	2.71190e12i	−1.61471	+	0.587706i
$653$	2.12427e12	+	1.78247e12i	0.457193	+	0.383631i	0.842097	−	0.539326i	$-0.181321\pi$
$653$	2.12427e12	+	1.78247e12i	0.457193	+	0.383631i	−0.384904	+	0.922957i	$0.625765\pi$
$654$		0			0
$655$	1.24730e11	+	4.53981e10i	0.0264781	+	0.00963722i
$656$	1.25942e11	+	2.18138e11i	0.0265523	+	0.0459900i
$657$		0			0
$658$	−3.22551e12	+	5.58675e12i	−0.670783	+	1.16183i
$659$	−5.88085e12	+	4.93462e12i	−1.21466	+	1.01922i	−0.215577	+	0.976487i	$0.569163\pi$
$659$	−5.88085e12	+	4.93462e12i	−1.21466	+	1.01922i	−0.999086	+	0.0427364i	$0.986392\pi$
$660$		0			0
$661$	−4.99155e11	+	2.83085e12i	−0.101702	+	0.576779i	0.890785	+	0.454425i	$0.150155\pi$
$661$	−4.99155e11	+	2.83085e12i	−0.101702	+	0.576779i	−0.992487	+	0.122354i	$0.960956\pi$
$662$	−1.79998e11	+	1.02082e12i	−0.0364257	+	0.206580i
$663$		0			0
$664$	−2.46506e12	+	2.06843e12i	−0.492121	+	0.412938i
$665$	2.10111e11	−	3.63923e11i	0.0416631	−	0.0721626i
$666$		0			0
$667$	8.22653e11	+	1.42488e12i	0.160935	+	0.278748i
$668$	2.72335e12	+	9.91219e11i	0.529188	+	0.192609i
$669$		0			0
$670$	−1.00261e12	−	8.41290e11i	−0.192219	−	0.161291i
$671$	4.93275e12	−	1.79537e12i	0.939373	−	0.341904i
$672$		0			0
$673$	−4.30691e11	−	2.44257e12i	−0.0809279	−	0.458965i	−0.998161	−	0.0606145i	$-0.980694\pi$
$673$	−4.30691e11	−	2.44257e12i	−0.0809279	−	0.458965i	0.917233	−	0.398350i	$-0.130417\pi$
$674$	2.93488e12			0.547798
$675$		0			0
$676$	−8.95768e12			−1.64982
$677$	8.46807e11	+	4.80248e12i	0.154930	+	0.878652i	0.958850	+	0.283914i	$0.0916330\pi$
$677$	8.46807e11	+	4.80248e12i	0.154930	+	0.878652i	−0.803920	+	0.594738i	$0.797256\pi$
$678$		0			0
$679$	−1.09297e12	+	3.97807e11i	−0.197330	+	0.0718222i
$680$	−3.09010e11	−	2.59290e11i	−0.0554220	−	0.0465046i
$681$		0			0
$682$	1.55351e13	+	5.65433e12i	2.74970	+	1.00081i
$683$	2.95284e12	+	5.11447e12i	0.519215	+	0.899307i	0.999751	+	0.0223315i	$0.00710893\pi$
$683$	2.95284e12	+	5.11447e12i	0.519215	+	0.899307i	−0.480536	+	0.876975i	$0.659558\pi$
$684$		0			0
$685$	−8.90431e11	+	1.54227e12i	−0.154523	+	0.267641i
$686$	7.56971e12	−	6.35174e12i	1.30503	−	1.09505i
$687$		0			0
$688$	−1.32661e11	+	7.52359e11i	−0.0225733	+	0.128020i
$689$	−2.28576e10	+	1.29632e11i	−0.00386406	+	0.0219141i
$690$		0			0
$691$	4.65251e12	−	3.90392e12i	0.776312	−	0.651403i	−0.166005	−	0.986125i	$-0.553087\pi$
$691$	4.65251e12	−	3.90392e12i	0.776312	−	0.651403i	0.942317	+	0.334722i	$0.108642\pi$
$692$	−7.82367e12	+	1.35510e13i	−1.29698	+	2.24644i
$693$		0			0
$694$	−2.44294e12	−	4.23129e12i	−0.399756	−	0.692398i
$695$	3.46758e11	+	1.26210e11i	0.0563761	+	0.0205192i
$696$		0			0
$697$	−1.30933e12	−	1.09866e12i	−0.210137	−	0.176326i
$698$	−1.53224e13	+	5.57691e12i	−2.44331	+	0.889292i
$699$		0			0
$700$	−1.68192e12	−	9.53866e12i	−0.264768	−	1.50157i
$701$	1.19134e13			1.86340			0.931700	−	0.363230i	$-0.118326\pi$
$701$	1.19134e13			1.86340			0.931700	+	0.363230i	$0.118326\pi$
$702$		0			0
$703$	6.48377e12			1.00122
$704$	1.77490e12	+	1.00660e13i	0.272331	+	1.54446i
$705$		0			0
$706$	1.38275e13	−	5.03280e12i	2.09471	−	0.762410i
$707$	5.10676e12	+	4.28508e12i	0.768703	+	0.645018i
$708$		0			0
$709$	5.62894e12	+	2.04877e12i	0.836601	+	0.304498i	0.724565	−	0.689206i	$-0.242041\pi$
$709$	5.62894e12	+	2.04877e12i	0.836601	+	0.304498i	0.112036	+	0.993704i	$0.464263\pi$
$710$	−1.44283e12	−	2.49906e12i	−0.213085	−	0.369075i
$711$		0			0
$712$	−5.27354e12	+	9.13404e12i	−0.769028	+	1.33200i
$713$	3.05356e12	−	2.56224e12i	0.442490	−	0.371294i
$714$		0			0
$715$	−9.90261e9	+	5.61605e10i	−0.00141701	+	0.00803626i
$716$	3.36467e12	−	1.90820e13i	0.478448	−	2.71341i
$717$		0			0
$718$	1.18977e13	−	9.98339e12i	1.67072	−	1.40190i
$719$	−6.57047e12	+	1.13804e13i	−0.916888	+	1.58810i	−0.112775	+	0.993621i	$0.535974\pi$
$719$	−6.57047e12	+	1.13804e13i	−0.916888	+	1.58810i	−0.804113	+	0.594476i	$0.797359\pi$
$720$		0			0
$721$	1.67466e12	+	2.90060e12i	0.230791	+	0.399741i
$722$	−7.75600e12	−	2.82295e12i	−1.06223	−	0.386622i
$723$		0			0
$724$	3.57588e12	+	3.00052e12i	0.483682	+	0.405857i
$725$	6.95814e12	−	2.53256e12i	0.935346	−	0.340438i
$726$		0			0
$727$	1.31808e12	+	7.47519e12i	0.174999	+	0.992470i	0.938145	+	0.346243i	$0.112543\pi$
$727$	1.31808e12	+	7.47519e12i	0.174999	+	0.992470i	−0.763145	+	0.646227i	$0.776346\pi$
$728$	−3.99497e11			−0.0527136
$729$		0			0
$730$	3.51288e12			0.457837
$731$	−9.00202e11	−	5.10530e12i	−0.116604	−	0.661292i
$732$		0			0
$733$	−1.07102e13	+	3.89819e12i	−1.37034	+	0.498764i	−0.919237	−	0.393706i	$-0.871193\pi$
$733$	−1.07102e13	+	3.89819e12i	−1.37034	+	0.498764i	−0.451107	+	0.892470i	$0.648971\pi$
$734$	−1.61629e13	−	1.35623e13i	−2.05535	−	1.72465i
$735$		0			0
$736$	2.19648e12	+	7.99453e11i	0.275916	+	0.100425i
$737$	3.79550e12	+	6.57400e12i	0.473876	+	0.820778i
$738$		0			0
$739$	5.66629e12	−	9.81430e12i	0.698874	−	1.21048i	−0.269984	−	0.962865i	$-0.587018\pi$
$739$	5.66629e12	−	9.81430e12i	0.698874	−	1.21048i	0.968857	−	0.247620i	$-0.0796484\pi$
$740$	−2.97886e12	+	2.49956e12i	−0.365180	+	0.306423i
$741$		0			0
$742$	9.40048e11	−	5.33128e12i	0.113850	−	0.645675i
$743$	−5.38829e11	+	3.05585e12i	−0.0648637	+	0.367860i	0.935047	+	0.354523i	$0.115357\pi$
$743$	−5.38829e11	+	3.05585e12i	−0.0648637	+	0.367860i	−0.999911	+	0.0133374i	$0.995754\pi$
$744$		0			0
$745$	−7.80626e11	+	6.55023e11i	−0.0928410	+	0.0779029i
$746$	8.94865e12	−	1.54995e13i	1.05787	−	1.83229i
$747$		0			0
$748$	2.95754e12	+	5.12261e12i	0.345440	+	0.598320i
$749$	−7.86472e12	−	2.86252e12i	−0.913093	−	0.332339i
$750$		0			0
$751$	−4.08838e12	−	3.43056e12i	−0.468998	−	0.393536i	0.377431	−	0.926038i	$-0.376808\pi$
$751$	−4.08838e12	−	3.43056e12i	−0.468998	−	0.393536i	−0.846429	+	0.532501i	$0.821252\pi$
$752$	5.92007e11	−	2.15473e11i	0.0675067	−	0.0245704i
$753$		0			0
$754$	−1.34084e11	−	7.60428e11i	−0.0151080	−	0.0856815i
$755$	−2.44450e11			−0.0273797
$756$		0			0
$757$	−2.46692e12			−0.273039			−0.136519	−	0.990637i	$-0.543592\pi$
$757$	−2.46692e12			−0.273039			−0.136519	+	0.990637i	$0.543592\pi$
$758$	1.12997e12	+	6.40836e12i	0.124324	+	0.705075i
$759$		0			0
$760$	−8.11865e11	+	2.95495e11i	−0.0882720	+	0.0321284i
$761$	9.96894e12	+	8.36493e12i	1.07750	+	0.904131i	0.995711	−	0.0925181i	$-0.0294916\pi$
$761$	9.96894e12	+	8.36493e12i	1.07750	+	0.904131i	0.0817909	+	0.996650i	$0.473936\pi$
$762$		0			0
$763$	−1.18248e13	−	4.30389e12i	−1.26309	−	0.459728i
$764$	−3.84048e12	−	6.65191e12i	−0.407817	−	0.706360i
$765$		0			0
$766$	−7.10928e12	+	1.23136e13i	−0.746099	+	1.29228i
$767$	−2.85415e10	+	2.39491e10i	−0.00297781	+	0.00249868i
$768$		0			0
$769$	−2.20732e12	+	1.25183e13i	−0.227613	+	1.29086i	0.630015	+	0.776583i	$0.283049\pi$
$769$	−2.20732e12	+	1.25183e13i	−0.227613	+	1.29086i	−0.857627	+	0.514272i	$0.828062\pi$
$770$	4.07258e11	−	2.30968e12i	0.0417505	−	0.236779i
$771$		0			0
$772$	−9.33266e12	+	7.83103e12i	−0.945644	+	0.793490i
$773$	4.42976e12	−	7.67257e12i	0.446244	−	0.772918i	−0.551894	−	0.833914i	$-0.686095\pi$
$773$	4.42976e12	−	7.67257e12i	0.446244	−	0.772918i	0.998138	+	0.0609967i	$0.0194279\pi$
$774$		0			0
$775$	−8.96981e12	−	1.55362e13i	−0.893153	−	1.54699i
$776$	2.24712e12	+	8.17885e11i	0.222458	+	0.0809682i
$777$		0			0
$778$	−2.11797e13	−	1.77719e13i	−2.07258	−	1.73910i
$779$	−3.44003e12	+	1.25207e12i	−0.334690	+	0.121817i
$780$		0			0
$781$	2.90628e12	+	1.64823e13i	0.279516	+	1.58522i
$782$	2.28831e12			0.218819
$783$		0			0
$784$	−9.23027e10			−0.00872554
$785$	2.37965e11	+	1.34957e12i	0.0223666	+	0.126847i
$786$		0			0
$787$	5.01926e12	−	1.82686e12i	0.466395	−	0.169754i	−0.0981238	−	0.995174i	$-0.531284\pi$
$787$	5.01926e12	−	1.82686e12i	0.466395	−	0.169754i	0.564518	+	0.825420i	$0.309062\pi$
$788$	−8.00168e12	−	6.71421e12i	−0.739287	−	0.620336i
$789$		0			0
$790$	4.77854e11	+	1.73924e11i	0.0436489	+	0.0158869i
$791$	−7.09532e12	−	1.22895e13i	−0.644433	−	1.11619i
$792$		0			0
$793$	−2.97000e11	+	5.14420e11i	−0.0266703	+	0.0461943i
$794$	−3.27697e12	+	2.74970e12i	−0.292604	+	0.245524i
$795$		0			0
$796$	3.69077e12	−	2.09314e13i	0.325843	−	1.84795i
$797$	−2.45807e12	+	1.39404e13i	−0.215790	+	1.22381i	0.663741	+	0.747963i	$0.268968\pi$
$797$	−2.45807e12	+	1.39404e13i	−0.215790	+	1.22381i	−0.879530	+	0.475843i	$0.842143\pi$
$798$		0			0
$799$	−3.27485e12	+	2.74792e12i	−0.284270	+	0.238531i
$800$	5.25983e12	−	9.11029e12i	0.454011	−	0.786371i
$801$		0			0
$802$	−2.85781e11	−	4.94988e11i	−0.0243921	−	0.0422484i
$803$	−1.91457e13	−	6.96845e12i	−1.62499	−	0.591448i
$804$		0			0
$805$	−4.33189e11	−	3.63489e11i	−0.0363577	−	0.0305077i
$806$	−1.75792e12	+	6.39830e11i	−0.146720	+	0.0534019i
$807$		0			0
$808$	−2.38002e12	−	1.34978e13i	−0.196440	−	1.11407i
$809$	1.37409e13			1.12784			0.563918	−	0.825831i	$-0.309293\pi$
$809$	1.37409e13			1.12784			0.563918	+	0.825831i	$0.309293\pi$
$810$		0			0
$811$	1.57716e13			1.28021			0.640106	−	0.768287i	$-0.278891\pi$
$811$	1.57716e13			1.28021			0.640106	+	0.768287i	$0.278891\pi$
$812$	3.43689e12	+	1.94916e13i	0.277436	+	1.57342i
$813$		0			0
$814$	3.40044e13	−	1.23766e13i	2.71472	−	0.988077i
$815$	1.59597e12	+	1.33918e12i	0.126711	+	0.106323i
$816$		0			0
$817$	−1.04336e13	−	3.79753e12i	−0.819288	−	0.298196i
$818$	−1.61835e13	−	2.80306e13i	−1.26381	−	2.18898i
$819$		0			0
$820$	1.09778e12	−	1.90141e12i	0.0847915	−	0.146863i
$821$	4.98670e12	−	4.18434e12i	0.383062	−	0.321427i	−0.430841	−	0.902428i	$-0.641783\pi$
$821$	4.98670e12	−	4.18434e12i	0.383062	−	0.321427i	0.813903	+	0.581000i	$0.197339\pi$
$822$		0			0
$823$	6.20738e10	−	3.52038e11i	0.00471639	−	0.0267480i	−0.982359	−	0.187006i	$-0.940122\pi$
$823$	6.20738e10	−	3.52038e11i	0.00471639	−	0.0267480i	0.987075	+	0.160258i	$0.0512327\pi$
$824$	1.19577e12	−	6.78152e12i	0.0903595	−	0.512454i
$825$		0			0
$826$	1.17381e12	−	9.84941e11i	0.0877377	−	0.0736207i
$827$	5.49928e12	−	9.52504e12i	0.408819	−	0.708096i	−0.585939	−	0.810355i	$-0.699274\pi$
$827$	5.49928e12	−	9.52504e12i	0.408819	−	0.708096i	0.994758	+	0.102260i	$0.0326073\pi$
$828$		0			0
$829$	1.10939e13	+	1.92152e13i	0.815811	+	1.41303i	0.908744	+	0.417353i	$0.137042\pi$
$829$	1.10939e13	+	1.92152e13i	0.815811	+	1.41303i	−0.0929337	+	0.995672i	$0.529624\pi$
$830$	2.00877e12	+	7.31131e11i	0.146919	+	0.0534742i
$831$		0			0
$832$	−8.86014e11	−	7.43454e11i	−0.0641041	−	0.0537897i
$833$	5.88568e11	−	2.14221e11i	0.0423539	−	0.0154156i
$834$		0			0
$835$	−1.32232e11	−	7.49925e11i	−0.00941342	−	0.0533861i
$836$	1.26689e13			0.897040
$837$		0			0
$838$	−2.17231e13			−1.52168
$839$	−6.77461e11	−	3.84207e12i	−0.0472015	−	0.267693i	0.952069	−	0.305883i	$-0.0989518\pi$
$839$	−6.77461e11	−	3.84207e12i	−0.0472015	−	0.267693i	−0.999270	+	0.0381904i	$0.987841\pi$
$840$		0			0
$841$	−5.86193e11	+	2.13357e11i	−0.0404072	+	0.0147070i
$842$	−8.65660e12	−	7.26375e12i	−0.593530	−	0.498031i
$843$		0			0
$844$	1.35469e13	+	4.93067e12i	0.918964	+	0.334476i
$845$	1.17683e12	+	2.03833e12i	0.0794070	+	0.137537i
$846$		0			0
$847$	2.80973e11	−	4.86660e11i	0.0187581	−	0.0324901i
$848$	−4.04992e11	+	3.39829e11i	−0.0268946	+	0.0225672i
$849$		0			0
$850$	1.78833e12	−	1.01421e13i	0.117506	−	0.666412i
$851$	1.51510e12	−	8.59258e12i	0.0990284	−	0.561618i
$852$		0			0
$853$	−1.69523e12	+	1.42247e12i	−0.109637	+	0.0919965i	−0.695958	−	0.718082i	$-0.745020\pi$
$853$	−1.69523e12	+	1.42247e12i	−0.109637	+	0.0919965i	0.586321	+	0.810079i	$0.300576\pi$
$854$	1.22145e13	−	2.11562e13i	0.785808	−	1.36106i
$855$		0			0
$856$	8.60373e12	+	1.49021e13i	0.547715	+	0.948670i
$857$	−1.02276e13	−	3.72253e12i	−0.647677	−	0.235735i	−0.00276999	−	0.999996i	$-0.500882\pi$
$857$	−1.02276e13	−	3.72253e12i	−0.647677	−	0.235735i	−0.644907	+	0.764261i	$0.723104\pi$
$858$		0			0
$859$	−1.49802e13	−	1.25699e13i	−0.938749	−	0.787704i	0.0386185	−	0.999254i	$-0.487704\pi$
$859$	−1.49802e13	−	1.25699e13i	−0.938749	−	0.787704i	−0.977367	+	0.211550i	$0.932149\pi$
$860$	6.25755e12	−	2.27756e12i	0.390087	−	0.141980i
$861$		0			0
$862$	4.06838e12	+	2.30729e13i	0.250980	+	1.42338i
$863$	−9.05491e12			−0.555694			−0.277847	−	0.960625i	$-0.589621\pi$
$863$	−9.05491e12			−0.555694			−0.277847	+	0.960625i	$0.589621\pi$
$864$		0			0
$865$	4.11139e12			0.249699
$866$	2.77989e12	+	1.57655e13i	0.167957	+	0.952529i
$867$		0			0
$868$	4.50596e13	−	1.64003e13i	2.69431	−	0.980650i
$869$	−2.25935e12	−	1.89582e12i	−0.134399	−	0.112774i
$870$		0			0
$871$	−8.07176e11	−	2.93788e11i	−0.0475211	−	0.0172963i
$872$	1.29360e13	+	2.24057e13i	0.757660	+	1.31231i
$873$		0			0
$874$	2.45056e12	−	4.24450e12i	0.142058	−	0.246051i
$875$	−3.94986e12	+	3.31433e12i	−0.227796	+	0.191143i
$876$		0			0
$877$	−4.61716e12	+	2.61852e13i	−0.263559	+	1.49471i	0.509550	+	0.860441i	$0.329812\pi$
$877$	−4.61716e12	+	2.61852e13i	−0.263559	+	1.49471i	−0.773109	+	0.634274i	$0.781299\pi$
$878$	−7.34081e12	+	4.16318e13i	−0.416887	+	2.36428i
$879$		0			0
$880$	−1.75455e11	+	1.47224e11i	−0.00986266	+	0.00827576i
$881$	−7.60735e12	+	1.31763e13i	−0.425443	+	0.736889i	−0.996462	−	0.0840479i	$-0.973215\pi$
$881$	−7.60735e12	+	1.31763e13i	−0.425443	+	0.736889i	0.571018	+	0.820937i	$0.306548\pi$
$882$		0			0
$883$	2.36850e12	+	4.10237e12i	0.131115	+	0.227097i	0.924106	−	0.382135i	$-0.124811\pi$
$883$	2.36850e12	+	4.10237e12i	0.131115	+	0.227097i	−0.792992	+	0.609232i	$0.791478\pi$
$884$	−6.28969e11	−	2.28926e11i	−0.0346413	−	0.0126084i
$885$		0			0
$886$	−3.51853e13	−	2.95240e13i	−1.91827	−	1.60962i
$887$	−7.59273e12	+	2.76353e12i	−0.411853	+	0.149902i	−0.539633	−	0.841900i	$-0.681437\pi$
$887$	−7.59273e12	+	2.76353e12i	−0.411853	+	0.149902i	0.127780	+	0.991802i	$0.459215\pi$
$888$		0			0
$889$	2.19631e12	+	1.24559e13i	0.117933	+	0.668831i
$890$	7.00651e12			0.374323
$891$		0			0
$892$	1.86102e13			0.984260
$893$	1.58996e12	+	9.01714e12i	0.0836673	+	0.474501i
$894$		0			0
$895$	−4.78417e12	+	1.74130e12i	−0.249232	+	0.0907129i
$896$	2.34183e13	+	1.96503e13i	1.21386	+	1.01855i
$897$		0			0
$898$	4.76973e13	+	1.73604e13i	2.44766	+	0.890874i
$899$	1.83292e13	+	3.17470e13i	0.935888	+	1.62101i
$900$		0			0
$901$	1.79374e12	−	3.10684e12i	0.0906770	−	0.157057i
$902$	−1.56513e13	+	1.31330e13i	−0.787266	+	0.660595i
$903$		0			0
$904$	−5.06631e12	+	2.87325e13i	−0.252309	+	1.43092i
$905$	2.12984e11	−	1.20789e12i	0.0105543	−	0.0598563i
$906$		0			0
$907$	6.71396e12	−	5.63368e12i	0.329417	−	0.276413i	−0.463045	−	0.886335i	$-0.653243\pi$
$907$	6.71396e12	−	5.63368e12i	0.329417	−	0.276413i	0.792462	+	0.609921i	$0.208799\pi$
$908$	−1.04605e13	+	1.81182e13i	−0.510701	+	0.884561i
$909$		0			0
$910$	1.32695e11	+	2.29834e11i	0.00641456	+	0.0111103i
$911$	−1.20635e13	−	4.39074e12i	−0.580283	−	0.211206i	0.0351675	−	0.999381i	$-0.488804\pi$
$911$	−1.20635e13	−	4.39074e12i	−0.580283	−	0.211206i	−0.615450	+	0.788176i	$0.711026\pi$
$912$		0			0
$913$	−9.49770e12	−	7.96952e12i	−0.452376	−	0.379589i
$914$	1.59901e13	−	5.81991e12i	0.757866	−	0.275841i
$915$		0			0
$916$	−8.31779e12	−	4.71725e13i	−0.390371	−	2.21391i
$917$	−3.58270e12			−0.167320
$918$		0			0
$919$	8.09918e12			0.374560			0.187280	−	0.982307i	$-0.440033\pi$
$919$	8.09918e12			0.374560			0.187280	+	0.982307i	$0.440033\pi$
$920$	2.01889e11	+	1.14497e12i	0.00929111	+	0.0526925i
$921$		0			0
$922$	−3.56462e13	+	1.29741e13i	−1.62451	+	0.591275i
$923$	−1.45079e12	−	1.21736e12i	−0.0657955	−	0.0552090i
$924$		0			0
$925$	−3.68994e13	−	1.34303e13i	−1.65722	−	0.603180i
$926$	9.79884e12	+	1.69721e13i	0.437951	+	0.758553i
$927$		0			0
$928$	−1.07481e13	+	1.86162e13i	−0.475735	+	0.823997i
$929$	−2.26865e13	+	1.90363e13i	−0.999303	+	0.838515i	−0.986888	−	0.161408i	$-0.948396\pi$
$929$	−2.26865e13	+	1.90363e13i	−0.999303	+	0.838515i	−0.0124153	+	0.999923i	$0.503952\pi$
$930$		0			0
$931$	2.32949e11	−	1.32112e12i	0.0101622	−	0.0576326i
$932$	2.92738e12	−	1.66020e13i	0.127089	−	0.720756i
$933$		0			0
$934$	−3.47461e13	+	2.91555e13i	−1.49398	+	1.25360i
$935$	7.77103e11	−	1.34598e12i	0.0332526	−	0.0575953i
$936$		0			0
$937$	4.88007e12	+	8.45252e12i	0.206822	+	0.358227i	0.950712	−	0.310076i	$-0.100354\pi$
$937$	4.88007e12	+	8.45252e12i	0.206822	+	0.358227i	−0.743889	+	0.668303i	$0.767021\pi$
$938$	3.31962e13	+	1.20824e13i	1.40015	+	0.509614i
$939$		0			0
$940$	−4.20668e12	−	3.52982e12i	−0.175737	−	0.147461i
$941$	2.22728e13	−	8.10664e12i	0.926023	−	0.337045i	0.165391	−	0.986228i	$-0.447111\pi$
$941$	2.22728e13	−	8.10664e12i	0.926023	−	0.337045i	0.760632	+	0.649183i	$0.224889\pi$
$942$		0			0
$943$	8.55443e11	+	4.85146e12i	0.0352280	+	0.199788i
$944$	−1.49643e11			−0.00613312
$945$		0			0
$946$	−6.19685e13			−2.51571
$947$	−4.39432e12	−	2.49214e13i	−0.177548	−	1.00693i	−0.935161	−	0.354222i	$-0.884746\pi$
$947$	−4.39432e12	−	2.49214e13i	−0.177548	−	1.00693i	0.757613	−	0.652704i	$-0.226366\pi$
$948$		0			0
$949$	2.16648e12	−	7.88533e11i	0.0867073	−	0.0315589i
$950$	−1.68970e13	−	1.41783e13i	−0.673060	−	0.564765i
$951$		0			0
$952$	1.02312e13	+	3.72387e12i	0.403703	+	0.146936i
$953$	−6.87999e11	−	1.19165e12i	−0.0270190	−	0.0467983i	0.852200	−	0.523217i	$-0.175268\pi$
$953$	−6.87999e11	−	1.19165e12i	−0.0270190	−	0.0467983i	−0.879219	+	0.476418i	$0.841935\pi$
$954$		0			0
$955$	−1.00910e12	+	1.74781e12i	−0.0392572	+	0.0679954i
$956$	2.38210e13	−	1.99882e13i	0.922357	−	0.773950i
$957$		0			0
$958$	−8.36031e12	+	4.74137e13i	−0.320684	+	1.81869i
$959$	8.34689e12	−	4.73376e13i	0.318670	−	1.80727i
$960$		0			0
$961$	4.77811e13	−	4.00931e13i	1.80718	−	1.51640i
$962$	−2.04740e12	+	3.54620e12i	−0.0770751	+	0.133498i
$963$		0			0
$964$	−4.69592e11	−	8.13357e11i	−0.0175135	−	0.0303344i
$965$	3.00805e12	+	1.09484e12i	0.111664	+	0.0406423i
$966$		0			0
$967$	6.21910e12	+	5.21845e12i	0.228722	+	0.191921i	0.749946	−	0.661500i	$-0.230080\pi$
$967$	6.21910e12	+	5.21845e12i	0.228722	+	0.191921i	−0.521223	+	0.853420i	$0.674524\pi$
$968$	−1.08568e12	+	3.95154e11i	−0.0397430	+	0.0144653i
$969$		0			0
$970$	−2.75855e11	−	1.56445e12i	−0.0100048	−	0.0567399i
$971$	−4.23908e13			−1.53033			−0.765165	−	0.643834i	$-0.777343\pi$
$971$	−4.23908e13			−1.53033			−0.765165	+	0.643834i	$0.777343\pi$
$972$		0			0
$973$	−9.96013e12			−0.356252
$974$	−9.38725e12	−	5.32377e13i	−0.334213	−	1.89541i
$975$		0			0
$976$	−2.24184e12	+	8.15964e11i	−0.0790826	+	0.0287837i
$977$	−4.45418e12	−	3.73750e12i	−0.156402	−	0.131237i	0.561228	−	0.827661i	$-0.310329\pi$
$977$	−4.45418e12	−	3.73750e12i	−0.156402	−	0.131237i	−0.717631	+	0.696424i	$0.754773\pi$
$978$		0			0
$979$	−3.81864e13	−	1.38987e13i	−1.32858	−	0.483562i
$980$	4.02281e11	+	6.96770e11i	0.0139319	+	0.0241308i
$981$		0			0
$982$	−1.00311e13	+	1.73744e13i	−0.344228	+	0.596221i
$983$	1.00550e13	−	8.43718e12i	0.343473	−	0.288208i	−0.454690	−	0.890650i	$-0.650250\pi$
$983$	1.00550e13	−	8.43718e12i	0.343473	−	0.288208i	0.798163	+	0.602442i	$0.205805\pi$
$984$		0			0
$985$	−4.76591e11	+	2.70288e12i	−0.0161318	+	0.0914880i
$986$	−3.65431e12	+	2.07246e13i	−0.123129	+	0.698298i
$987$		0			0
$988$	−1.09819e12	+	9.21491e11i	−0.0366667	+	0.0307670i
$989$	−7.47075e12	+	1.29397e13i	−0.248303	+	0.430073i
$990$		0			0
$991$	−1.94361e13	−	3.36644e13i	−0.640145	−	1.10876i	−0.985400	−	0.170255i	$-0.945541\pi$
$991$	−1.94361e13	−	3.36644e13i	−0.640145	−	1.10876i	0.345255	−	0.938509i	$-0.387793\pi$
$992$	4.89387e13	+	1.78122e13i	1.60454	+	0.584004i
$993$		0			0
$994$	5.96656e13	+	5.00654e13i	1.93859	+	1.62667i
$995$	−5.24784e12	+	1.91006e12i	−0.169737	+	0.0617792i
$996$		0			0
$997$	1.00583e10	+	5.70434e10i	0.000322401	+	0.00182842i	0.984969	−	0.172734i	$-0.0552601\pi$
$997$	1.00583e10	+	5.70434e10i	0.000322401	+	0.00182842i	−0.984646	+	0.174562i	$0.944149\pi$
$998$	−5.61394e13			−1.79135
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.10.e.a.10.4		156
3.2	odd	2		27.10.e.a.13.23	✓	156
27.2	odd	18		27.10.e.a.25.23	yes	156
27.25	even	9	inner	81.10.e.a.73.4		156

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.10.e.a.13.23	✓	156	3.2	odd	2
27.10.e.a.25.23	yes	156	27.2	odd	18
81.10.e.a.10.4		156	1.1	even	1	trivial
81.10.e.a.73.4		156	27.25	even	9	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	81.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-6.40153 - 36.3049i) q^{2} +(-795.940 + 289.699i) q^{4} +(170.489 + 143.057i) q^{5} +(-5644.86 - 2054.56i) q^{7} +(6175.28 + 10695.9i) q^{8} +(4102.29 - 7105.37i) q^{10} +(-36452.8 + 30587.5i) q^{11} +(935.040 - 5302.88i) q^{13} +(-38454.8 + 218088. i) q^{14} +(16567.1 - 13901.5i) q^{16} +(-73376.8 + 127092. i) q^{17} +(157159. + 272207. i) q^{19} +(-177143. - 64474.7i) q^{20} +(1.34383e6 + 1.12761e6i) q^{22} +(397465. - 144666. i) q^{23} +(-330555. - 1.87467e6i) q^{25} -198506. q^{26} +5.08817e6 q^{28} +(675466. + 3.83076e6i) q^{29} +(8.85575e6 - 3.22323e6i) q^{31} +(4.23332e6 + 3.55218e6i) q^{32} +(5.08379e6 + 1.85035e6i) q^{34} +(-668467. - 1.15782e6i) q^{35} +(1.03140e7 - 1.78644e7i) q^{37} +(8.87638e6 - 7.44817e6i) q^{38} +(-477309. + 2.70695e6i) q^{40} +(-2.02245e6 + 1.14699e7i) q^{41} +(-2.70604e7 + 2.27064e7i) q^{43} +(2.01531e7 - 3.49061e7i) q^{44} +(-7.79645e6 - 1.35038e7i) q^{46} +(2.73737e7 + 9.96322e6i) q^{47} +(-3.26946e6 - 2.74340e6i) q^{49} +(-6.59437e7 + 2.40015e7i) q^{50} +(792000. + 4.49165e6i) q^{52} -2.44455e7 q^{53} -1.05906e7 q^{55} +(-1.28832e7 - 7.30643e7i) q^{56} +(1.34751e8 - 4.90454e7i) q^{58} +(-5.30049e6 - 4.44764e6i) q^{59} +(-1.03660e8 - 3.77293e7i) q^{61} +(-1.73709e8 - 3.00873e8i) q^{62} +(1.07398e8 - 1.86019e8i) q^{64} +(918030. - 770319. i) q^{65} +(2.77008e7 - 1.57099e8i) q^{67} +(2.15851e7 - 1.22415e8i) q^{68} +(-3.77552e7 + 3.16804e7i) q^{70} +(1.75857e8 - 3.04593e8i) q^{71} +(2.14081e8 + 3.70799e8i) q^{73} +(-7.14592e8 - 2.60090e8i) q^{74} +(-2.03947e8 - 1.71132e8i) q^{76} +(2.68615e8 - 9.77677e7i) q^{77} +(1.07628e7 + 6.10386e7i) q^{79} +4.81322e6 q^{80} +4.29359e8 q^{82} +(4.52437e7 + 2.56590e8i) q^{83} +(-3.06915e7 + 1.11708e7i) q^{85} +(9.97581e8 + 8.37070e8i) q^{86} +(-5.52267e8 - 2.01009e8i) q^{88} +(4.26988e8 + 7.39565e8i) q^{89} +(-1.61732e7 + 2.80129e7i) q^{91} +(-2.74449e8 + 2.30290e8i) q^{92} +(1.86480e8 - 1.05758e9i) q^{94} +(-1.21474e7 + 6.88911e7i) q^{95} +(1.48323e8 - 1.24458e8i) q^{97} +(-7.86692e7 + 1.36259e8i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 156 q + 6 q^{2} - 6 q^{4} - 2382 q^{5} - 6 q^{7} - 36861 q^{8} - 3 q^{10} + 121767 q^{11} - 6 q^{13} + 720417 q^{14} + 1530 q^{16} - 1002249 q^{17} - 3 q^{19} + 8448573 q^{20} - 1585014 q^{22} - 9316482 q^{23}+ \cdots - 6901039926 q^{98}+O(q^{100}) \) 156 * q + 6 * q^2 - 6 * q^4 - 2382 * q^5 - 6 * q^7 - 36861 * q^8 - 3 * q^10 + 121767 * q^11 - 6 * q^13 + 720417 * q^14 + 1530 * q^16 - 1002249 * q^17 - 3 * q^19 + 8448573 * q^20 - 1585014 * q^22 - 9316482 * q^23 + 2192178 * q^25 + 33129678 * q^26 - 12 * q^28 - 19657236 * q^29 - 4633692 * q^31 + 37550952 * q^32 + 14341770 * q^34 - 34449663 * q^35 - 3 * q^37 + 92022060 * q^38 + 6645801 * q^40 + 33127221 * q^41 + 2356203 * q^43 - 1001541 * q^44 - 3 * q^46 + 33488952 * q^47 - 93214644 * q^49 + 72027753 * q^50 + 160531713 * q^52 - 4841352 * q^53 - 12 * q^55 + 91770981 * q^56 - 320682489 * q^58 - 538090854 * q^59 + 36683436 * q^61 + 55862958 * q^62 - 956301315 * q^64 + 852347310 * q^65 - 109026897 * q^67 + 508886217 * q^68 - 815297649 * q^70 - 940878639 * q^71 - 221849931 * q^73 - 838884579 * q^74 + 908401146 * q^76 + 967811358 * q^77 - 1228059150 * q^79 + 2497115154 * q^80 - 12 * q^82 + 297703284 * q^83 + 1535949369 * q^85 - 2930201574 * q^86 + 2837227002 * q^88 - 1774997208 * q^89 + 551343507 * q^91 + 6896645517 * q^92 + 414852915 * q^94 + 9000269169 * q^95 + 3371772333 * q^97 - 6901039926 * q^98

Introduction

L-functions

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