LMFDB - Embedded newform 78.10.a.f.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [78,10,Mod(1,78)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(78, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("78.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 78 = 2 \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	78.a (trivial)

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:	yes
Analytic conductor:	$40.1727952208$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{22}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 22 $ x^2 - 22
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2\cdot 3 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-4.69042$ of defining polynomial
Character	$\chi$	$=$	78.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+16.0000 q^{2} +81.0000 q^{3} +256.000 q^{4} -1390.41 q^{5} +1296.00 q^{6} -2081.63 q^{7} +4096.00 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q+16.0000 q^{2} +81.0000 q^{3} +256.000 q^{4} -1390.41 q^{5} +1296.00 q^{6} -2081.63 q^{7} +4096.00 q^{8} +6561.00 q^{9} -22246.6 q^{10} +7285.37 q^{11} +20736.0 q^{12} -28561.0 q^{13} -33306.1 q^{14} -112623. q^{15} +65536.0 q^{16} +208839. q^{17} +104976. q^{18} -1.02821e6 q^{19} -355946. q^{20} -168612. q^{21} +116566. q^{22} -2.21341e6 q^{23} +331776. q^{24} -19878.8 q^{25} -456976. q^{26} +531441. q^{27} -532897. q^{28} -1.76883e6 q^{29} -1.80197e6 q^{30} -6.35674e6 q^{31} +1.04858e6 q^{32} +590115. q^{33} +3.34143e6 q^{34} +2.89432e6 q^{35} +1.67962e6 q^{36} +1.28722e7 q^{37} -1.64514e7 q^{38} -2.31344e6 q^{39} -5.69513e6 q^{40} -1.94012e7 q^{41} -2.69779e6 q^{42} +4.02691e7 q^{43} +1.86505e6 q^{44} -9.12249e6 q^{45} -3.54146e7 q^{46} -5.70042e7 q^{47} +5.30842e6 q^{48} -3.60204e7 q^{49} -318060. q^{50} +1.69160e7 q^{51} -7.31162e6 q^{52} +5.79377e7 q^{53} +8.50306e6 q^{54} -1.01297e7 q^{55} -8.52635e6 q^{56} -8.32852e7 q^{57} -2.83012e7 q^{58} +1.51144e7 q^{59} -2.88316e7 q^{60} -1.04705e8 q^{61} -1.01708e8 q^{62} -1.36576e7 q^{63} +1.67772e7 q^{64} +3.97116e7 q^{65} +9.44184e6 q^{66} -1.87063e7 q^{67} +5.34629e7 q^{68} -1.79286e8 q^{69} +4.63091e7 q^{70} +7.63287e7 q^{71} +2.68739e7 q^{72} +3.09632e8 q^{73} +2.05956e8 q^{74} -1.61018e6 q^{75} -2.63222e8 q^{76} -1.51654e7 q^{77} -3.70151e7 q^{78} -4.82610e8 q^{79} -9.11221e7 q^{80} +4.30467e7 q^{81} -3.10419e8 q^{82} -2.85755e8 q^{83} -4.31646e7 q^{84} -2.90373e8 q^{85} +6.44306e8 q^{86} -1.43275e8 q^{87} +2.98409e7 q^{88} -2.17501e8 q^{89} -1.45960e8 q^{90} +5.94534e7 q^{91} -5.66633e8 q^{92} -5.14896e8 q^{93} -9.12067e8 q^{94} +1.42964e9 q^{95} +8.49347e7 q^{96} +4.21388e8 q^{97} -5.76327e8 q^{98} +4.77993e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 32 q^{2} + 162 q^{3} + 512 q^{4} - 248 q^{5} + 2592 q^{6} - 13000 q^{7} + 8192 q^{8} + 13122 q^{9}+O(q^{10}) $ 2 * q + 32 * q^2 + 162 * q^3 + 512 * q^4 - 248 * q^5 + 2592 * q^6 - 13000 * q^7 + 8192 * q^8 + 13122 * q^9	\( 2 q + 32 q^{2} + 162 q^{3} + 512 q^{4} - 248 q^{5} + 2592 q^{6} - 13000 q^{7} + 8192 q^{8} + 13122 q^{9} - 3968 q^{10} - 83140 q^{11} + 41472 q^{12} - 57122 q^{13} - 208000 q^{14} - 20088 q^{15} + 131072 q^{16} - 387084 q^{17} + 209952 q^{18} - 1520760 q^{19} - 63488 q^{20} - 1053000 q^{21} - 1330240 q^{22} - 318920 q^{23} + 663552 q^{24} - 667898 q^{25} - 913952 q^{26} + 1062882 q^{27} - 3328000 q^{28} + 4171588 q^{29} - 321408 q^{30} - 6668752 q^{31} + 2097152 q^{32} - 6734340 q^{33} - 6193344 q^{34} - 9578960 q^{35} + 3359232 q^{36} + 7653708 q^{37} - 24332160 q^{38} - 4626882 q^{39} - 1015808 q^{40} - 5349864 q^{41} - 16848000 q^{42} + 9645848 q^{43} - 21283840 q^{44} - 1627128 q^{45} - 5102720 q^{46} - 45295036 q^{47} + 10616832 q^{48} + 42836802 q^{49} - 10686368 q^{50} - 31353804 q^{51} - 14623232 q^{52} + 80817084 q^{53} + 17006112 q^{54} - 113432720 q^{55} - 53248000 q^{56} - 123181560 q^{57} + 66745408 q^{58} - 169730636 q^{59} - 5142528 q^{60} - 133384348 q^{61} - 106700032 q^{62} - 85293000 q^{63} + 33554432 q^{64} + 7083128 q^{65} - 107749440 q^{66} - 27500800 q^{67} - 99093504 q^{68} - 25832520 q^{69} - 153263360 q^{70} + 401208260 q^{71} + 53747712 q^{72} + 21876508 q^{73} + 122459328 q^{74} - 54099738 q^{75} - 389314560 q^{76} + 972132368 q^{77} - 74030112 q^{78} - 642214304 q^{79} - 16252928 q^{80} + 86093442 q^{81} - 85597824 q^{82} - 935734356 q^{83} - 269568000 q^{84} - 971163024 q^{85} + 154333568 q^{86} + 337898628 q^{87} - 340541440 q^{88} - 868756080 q^{89} - 26034048 q^{90} + 371293000 q^{91} - 81643520 q^{92} - 540168912 q^{93} - 724720576 q^{94} + 866946000 q^{95} + 169869312 q^{96} + 1084497388 q^{97} + 685388832 q^{98} - 545481540 q^{99}+O(q^{100}) \) 2 * q + 32 * q^2 + 162 * q^3 + 512 * q^4 - 248 * q^5 + 2592 * q^6 - 13000 * q^7 + 8192 * q^8 + 13122 * q^9 - 3968 * q^10 - 83140 * q^11 + 41472 * q^12 - 57122 * q^13 - 208000 * q^14 - 20088 * q^15 + 131072 * q^16 - 387084 * q^17 + 209952 * q^18 - 1520760 * q^19 - 63488 * q^20 - 1053000 * q^21 - 1330240 * q^22 - 318920 * q^23 + 663552 * q^24 - 667898 * q^25 - 913952 * q^26 + 1062882 * q^27 - 3328000 * q^28 + 4171588 * q^29 - 321408 * q^30 - 6668752 * q^31 + 2097152 * q^32 - 6734340 * q^33 - 6193344 * q^34 - 9578960 * q^35 + 3359232 * q^36 + 7653708 * q^37 - 24332160 * q^38 - 4626882 * q^39 - 1015808 * q^40 - 5349864 * q^41 - 16848000 * q^42 + 9645848 * q^43 - 21283840 * q^44 - 1627128 * q^45 - 5102720 * q^46 - 45295036 * q^47 + 10616832 * q^48 + 42836802 * q^49 - 10686368 * q^50 - 31353804 * q^51 - 14623232 * q^52 + 80817084 * q^53 + 17006112 * q^54 - 113432720 * q^55 - 53248000 * q^56 - 123181560 * q^57 + 66745408 * q^58 - 169730636 * q^59 - 5142528 * q^60 - 133384348 * q^61 - 106700032 * q^62 - 85293000 * q^63 + 33554432 * q^64 + 7083128 * q^65 - 107749440 * q^66 - 27500800 * q^67 - 99093504 * q^68 - 25832520 * q^69 - 153263360 * q^70 + 401208260 * q^71 + 53747712 * q^72 + 21876508 * q^73 + 122459328 * q^74 - 54099738 * q^75 - 389314560 * q^76 + 972132368 * q^77 - 74030112 * q^78 - 642214304 * q^79 - 16252928 * q^80 + 86093442 * q^81 - 85597824 * q^82 - 935734356 * q^83 - 269568000 * q^84 - 971163024 * q^85 + 154333568 * q^86 + 337898628 * q^87 - 340541440 * q^88 - 868756080 * q^89 - 26034048 * q^90 + 371293000 * q^91 - 81643520 * q^92 - 540168912 * q^93 - 724720576 * q^94 + 866946000 * q^95 + 169869312 * q^96 + 1084497388 * q^97 + 685388832 * q^98 - 545481540 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	16.0000	0.707107
$2$	16.0000	0.707107
$3$	81.0000	0.577350
$3$	81.0000	0.577350
$4$	256.000	0.500000
$5$	−1390.41	−0.994898	−0.497449	−	0.867493i	$-0.665730\pi$
$5$	−1390.41	−0.994898	−0.497449	+	0.867493i	$0.665730\pi$
$6$	1296.00	0.408248
$7$	−2081.63	−0.327689	−0.163845	−	0.986486i	$-0.552390\pi$
$7$	−2081.63	−0.327689	−0.163845	+	0.986486i	$0.552390\pi$
$8$	4096.00	0.353553
$9$	6561.00	0.333333
$10$	−22246.6	−0.703499
$11$	7285.37	0.150032	0.0750161	−	0.997182i	$-0.476099\pi$
$11$	7285.37	0.150032	0.0750161	+	0.997182i	$0.476099\pi$
$12$	20736.0	0.288675
$13$	−28561.0	−0.277350
$13$	−28561.0	−0.277350
$14$	−33306.1	−0.231711
$15$	−112623.	−0.574405
$16$	65536.0	0.250000
$17$	208839.	0.606446	0.303223	−	0.952920i	$-0.401937\pi$
$17$	208839.	0.606446	0.303223	+	0.952920i	$0.401937\pi$
$18$	104976.	0.235702
$19$	−1.02821e6	−1.81005	−0.905027	−	0.425354i	$-0.860150\pi$
$19$	−1.02821e6	−1.81005	−0.905027	+	0.425354i	$0.860150\pi$
$20$	−355946.	−0.497449
$21$	−168612.	−0.189191
$22$	116566.	0.106089
$23$	−2.21341e6	−1.64925	−0.824626	−	0.565678i	$-0.808614\pi$
$23$	−2.21341e6	−1.64925	−0.824626	+	0.565678i	$0.808614\pi$
$24$	331776.	0.204124
$25$	−19878.8	−0.0101779
$26$	−456976.	−0.196116
$27$	531441.	0.192450
$28$	−532897.	−0.163845
$29$	−1.76883e6	−0.464402	−0.232201	−	0.972668i	$-0.574593\pi$
$29$	−1.76883e6	−0.464402	−0.232201	+	0.972668i	$0.574593\pi$
$30$	−1.80197e6	−0.406165
$31$	−6.35674e6	−1.23625	−0.618126	−	0.786079i	$-0.712108\pi$
$31$	−6.35674e6	−1.23625	−0.618126	+	0.786079i	$0.712108\pi$
$32$	1.04858e6	0.176777
$33$	590115.	0.0866211
$34$	3.34143e6	0.428822
$35$	2.89432e6	0.326017
$36$	1.67962e6	0.166667
$37$	1.28722e7	1.12914	0.564568	−	0.825386i	$-0.309043\pi$
$37$	1.28722e7	1.12914	0.564568	+	0.825386i	$0.309043\pi$
$38$	−1.64514e7	−1.27990
$39$	−2.31344e6	−0.160128
$40$	−5.69513e6	−0.351750
$41$	−1.94012e7	−1.07226	−0.536131	−	0.844135i	$-0.680115\pi$
$41$	−1.94012e7	−1.07226	−0.536131	+	0.844135i	$0.680115\pi$
$42$	−2.69779e6	−0.133779
$43$	4.02691e7	1.79624	0.898120	−	0.439751i	$-0.144933\pi$
$43$	4.02691e7	1.79624	0.898120	+	0.439751i	$0.144933\pi$
$44$	1.86505e6	0.0750161
$45$	−9.12249e6	−0.331633
$46$	−3.54146e7	−1.16620
$47$	−5.70042e7	−1.70399	−0.851993	−	0.523553i	$-0.824606\pi$
$47$	−5.70042e7	−1.70399	−0.851993	+	0.523553i	$0.824606\pi$
$48$	5.30842e6	0.144338
$49$	−3.60204e7	−0.892620
$50$	−318060.	−0.00719688
$51$	1.69160e7	0.350132
$52$	−7.31162e6	−0.138675
$53$	5.79377e7	1.00860	0.504301	−	0.863528i	$-0.331750\pi$
$53$	5.79377e7	1.00860	0.504301	+	0.863528i	$0.331750\pi$
$54$	8.50306e6	0.136083
$55$	−1.01297e7	−0.149267
$56$	−8.52635e6	−0.115856
$57$	−8.32852e7	−1.04504
$58$	−2.83012e7	−0.328382
$59$	1.51144e7	0.162390	0.0811948	−	0.996698i	$-0.474126\pi$
$59$	1.51144e7	0.162390	0.0811948	+	0.996698i	$0.474126\pi$
$60$	−2.88316e7	−0.287202
$61$	−1.04705e8	−0.968244	−0.484122	−	0.875001i	$-0.660861\pi$
$61$	−1.04705e8	−0.968244	−0.484122	+	0.875001i	$0.660861\pi$
$62$	−1.01708e8	−0.874162
$63$	−1.36576e7	−0.109230
$64$	1.67772e7	0.125000
$65$	3.97116e7	0.275935
$66$	9.44184e6	0.0612504
$67$	−1.87063e7	−0.113410	−0.0567049	−	0.998391i	$-0.518059\pi$
$67$	−1.87063e7	−0.113410	−0.0567049	+	0.998391i	$0.518059\pi$
$68$	5.34629e7	0.303223
$69$	−1.79286e8	−0.952196
$70$	4.63091e7	0.230529
$71$	7.63287e7	0.356472	0.178236	−	0.983988i	$-0.442961\pi$
$71$	7.63287e7	0.356472	0.178236	+	0.983988i	$0.442961\pi$
$72$	2.68739e7	0.117851
$73$	3.09632e8	1.27612	0.638061	−	0.769986i	$-0.279737\pi$
$73$	3.09632e8	1.27612	0.638061	+	0.769986i	$0.279737\pi$
$74$	2.05956e8	0.798420
$75$	−1.61018e6	−0.00587623
$76$	−2.63222e8	−0.905027
$77$	−1.51654e7	−0.0491639
$78$	−3.70151e7	−0.113228
$79$	−4.82610e8	−1.39404	−0.697019	−	0.717053i	$-0.745491\pi$
$79$	−4.82610e8	−1.39404	−0.697019	+	0.717053i	$0.745491\pi$
$80$	−9.11221e7	−0.248725
$81$	4.30467e7	0.111111
$82$	−3.10419e8	−0.758203
$83$	−2.85755e8	−0.660910	−0.330455	−	0.943822i	$-0.607202\pi$
$83$	−2.85755e8	−0.660910	−0.330455	+	0.943822i	$0.607202\pi$
$84$	−4.31646e7	−0.0945957
$85$	−2.90373e8	−0.603352
$86$	6.44306e8	1.27013
$87$	−1.43275e8	−0.268123
$88$	2.98409e7	0.0530444
$89$	−2.17501e8	−0.367457	−0.183728	−	0.982977i	$-0.558817\pi$
$89$	−2.17501e8	−0.367457	−0.183728	+	0.982977i	$0.558817\pi$
$90$	−1.45960e8	−0.234500
$91$	5.94534e7	0.0908846
$92$	−5.66633e8	−0.824626
$93$	−5.14896e8	−0.713750
$94$	−9.12067e8	−1.20490
$95$	1.42964e9	1.80082
$96$	8.49347e7	0.102062
$97$	4.21388e8	0.483292	0.241646	−	0.970364i	$-0.422313\pi$
$97$	4.21388e8	0.483292	0.241646	+	0.970364i	$0.422313\pi$
$98$	−5.76327e8	−0.631178
$99$	4.77993e7	0.0500107
$100$	−5.08896e6	−0.00508896
$101$	−7.04017e8	−0.673189	−0.336594	−	0.941650i	$-0.609275\pi$
$101$	−7.04017e8	−0.673189	−0.336594	+	0.941650i	$0.609275\pi$
$102$	2.70656e8	0.247581
$103$	1.66827e9	1.46049	0.730244	−	0.683187i	$-0.239406\pi$
$103$	1.66827e9	1.46049	0.730244	+	0.683187i	$0.239406\pi$
$104$	−1.16986e8	−0.0980581
$105$	2.34440e8	0.188226
$106$	9.27003e8	0.713190
$107$	1.36947e9	1.01001	0.505004	−	0.863117i	$-0.331491\pi$
$107$	1.36947e9	1.01001	0.505004	+	0.863117i	$0.331491\pi$
$108$	1.36049e8	0.0962250
$109$	8.66277e8	0.587811	0.293905	−	0.955835i	$-0.405045\pi$
$109$	8.66277e8	0.587811	0.293905	+	0.955835i	$0.405045\pi$
$110$	−1.62075e8	−0.105548
$111$	1.04265e9	0.651907
$112$	−1.36422e8	−0.0819223
$113$	1.52682e9	0.880918	0.440459	−	0.897773i	$-0.354816\pi$
$113$	1.52682e9	0.880918	0.440459	+	0.897773i	$0.354816\pi$
$114$	−1.33256e9	−0.738951
$115$	3.07755e9	1.64084
$116$	−4.52820e8	−0.232201
$117$	−1.87389e8	−0.0924500
$118$	2.41831e8	0.114827
$119$	−4.34726e8	−0.198726
$120$	−4.61305e8	−0.203083
$121$	−2.30487e9	−0.977490
$122$	−1.67529e9	−0.684652
$123$	−1.57149e9	−0.619070
$124$	−1.62733e9	−0.618126
$125$	2.74329e9	1.00502
$126$	−2.18521e8	−0.0772371
$127$	4.04311e9	1.37911	0.689554	−	0.724234i	$-0.257806\pi$
$127$	4.04311e9	1.37911	0.689554	+	0.724234i	$0.257806\pi$
$128$	2.68435e8	0.0883883
$129$	3.26180e9	1.03706
$130$	6.35385e8	0.195116
$131$	7.84570e8	0.232761	0.116381	−	0.993205i	$-0.462871\pi$
$131$	7.84570e8	0.232761	0.116381	+	0.993205i	$0.462871\pi$
$132$	1.51069e8	0.0433106
$133$	2.14036e9	0.593135
$134$	−2.99300e8	−0.0801928
$135$	−7.38922e8	−0.191468
$136$	8.55406e8	0.214411
$137$	−2.19324e9	−0.531917	−0.265959	−	0.963984i	$-0.585688\pi$
$137$	−2.19324e9	−0.531917	−0.265959	+	0.963984i	$0.585688\pi$
$138$	−2.86858e9	−0.673304
$139$	7.85736e9	1.78529	0.892647	−	0.450756i	$-0.148846\pi$
$139$	7.85736e9	1.78529	0.892647	+	0.450756i	$0.148846\pi$
$140$	7.40946e8	0.163009
$141$	−4.61734e9	−0.983797
$142$	1.22126e9	0.252064
$143$	−2.08077e8	−0.0416115
$144$	4.29982e8	0.0833333
$145$	2.45940e9	0.462033
$146$	4.95411e9	0.902355
$147$	−2.91765e9	−0.515354
$148$	3.29529e9	0.564568
$149$	−1.44655e9	−0.240433	−0.120217	−	0.992748i	$-0.538359\pi$
$149$	−1.44655e9	−0.240433	−0.120217	+	0.992748i	$0.538359\pi$
$150$	−2.57629e7	−0.00415512
$151$	2.42893e9	0.380206	0.190103	−	0.981764i	$-0.439118\pi$
$151$	2.42893e9	0.380206	0.190103	+	0.981764i	$0.439118\pi$
$152$	−4.21156e9	−0.639951
$153$	1.37020e9	0.202149
$154$	−2.42647e8	−0.0347641
$155$	8.83849e9	1.22994
$156$	−5.92241e8	−0.0800641
$157$	3.65911e9	0.480648	0.240324	−	0.970693i	$-0.422746\pi$
$157$	3.65911e9	0.480648	0.240324	+	0.970693i	$0.422746\pi$
$158$	−7.72176e9	−0.985733
$159$	4.69295e9	0.582317
$160$	−1.45795e9	−0.175875
$161$	4.60750e9	0.540442
$162$	6.88748e8	0.0785674
$163$	−1.23469e10	−1.36998	−0.684991	−	0.728552i	$-0.740194\pi$
$163$	−1.23469e10	−1.36998	−0.684991	+	0.728552i	$0.740194\pi$
$164$	−4.96670e9	−0.536131
$165$	−8.20503e8	−0.0861792
$166$	−4.57208e9	−0.467334
$167$	−1.23014e10	−1.22386	−0.611928	−	0.790913i	$-0.709606\pi$
$167$	−1.23014e10	−1.22386	−0.611928	+	0.790913i	$0.709606\pi$
$168$	−6.90634e8	−0.0668893
$169$	8.15731e8	0.0769231
$170$	−4.64597e9	−0.426634
$171$	−6.74610e9	−0.603351
$172$	1.03089e10	0.898120
$173$	−1.76524e10	−1.49829	−0.749145	−	0.662406i	$-0.769535\pi$
$173$	−1.76524e10	−1.49829	−0.749145	+	0.662406i	$0.769535\pi$
$174$	−2.29240e9	−0.189591
$175$	4.13802e7	0.00333520
$176$	4.77454e8	0.0375081
$177$	1.22427e9	0.0937556
$178$	−3.48002e9	−0.259831
$179$	−1.86970e10	−1.36123	−0.680617	−	0.732640i	$-0.738288\pi$
$179$	−1.86970e10	−1.36123	−0.680617	+	0.732640i	$0.738288\pi$
$180$	−2.33536e9	−0.165816
$181$	−9.44069e8	−0.0653808	−0.0326904	−	0.999466i	$-0.510408\pi$
$181$	−9.44069e8	−0.0653808	−0.0326904	+	0.999466i	$0.510408\pi$
$182$	9.51254e8	0.0642651
$183$	−8.48113e9	−0.559016
$184$	−9.06613e9	−0.583099
$185$	−1.78977e10	−1.12338
$186$	−8.23833e9	−0.504697
$187$	1.52147e9	0.0909865
$188$	−1.45931e10	−0.851993
$189$	−1.10626e9	−0.0630638
$190$	2.28742e10	1.27337
$191$	−1.61425e10	−0.877646	−0.438823	−	0.898574i	$-0.644604\pi$
$191$	−1.61425e10	−0.877646	−0.438823	+	0.898574i	$0.644604\pi$
$192$	1.35895e9	0.0721688
$193$	5.75447e9	0.298536	0.149268	−	0.988797i	$-0.452308\pi$
$193$	5.75447e9	0.298536	0.149268	+	0.988797i	$0.452308\pi$
$194$	6.74222e9	0.341739
$195$	3.21664e9	0.159311
$196$	−9.22123e9	−0.446310
$197$	−1.01896e10	−0.482014	−0.241007	−	0.970523i	$-0.577478\pi$
$197$	−1.01896e10	−0.482014	−0.241007	+	0.970523i	$0.577478\pi$
$198$	7.64789e8	0.0353629
$199$	2.26278e10	1.02283	0.511416	−	0.859333i	$-0.329121\pi$
$199$	2.26278e10	1.02283	0.511416	+	0.859333i	$0.329121\pi$
$200$	−8.14234e7	−0.00359844
$201$	−1.51521e9	−0.0654772
$202$	−1.12643e10	−0.476016
$203$	3.68204e9	0.152180
$204$	4.33049e9	0.175066
$205$	2.69756e10	1.06679
$206$	2.66923e10	1.03272
$207$	−1.45222e10	−0.549751
$208$	−1.87177e9	−0.0693375
$209$	−7.49091e9	−0.271566
$210$	3.75104e9	0.133096
$211$	2.90958e10	1.01055	0.505276	−	0.862958i	$-0.331391\pi$
$211$	2.90958e10	1.01055	0.505276	+	0.862958i	$0.331391\pi$
$212$	1.48321e10	0.504301
$213$	6.18262e9	0.205809
$214$	2.19115e10	0.714183
$215$	−5.59907e10	−1.78707
$216$	2.17678e9	0.0680414
$217$	1.32324e10	0.405106
$218$	1.38604e10	0.415645
$219$	2.50802e10	0.736770
$220$	−2.59320e9	−0.0746334
$221$	−5.96466e9	−0.168198
$222$	1.66824e10	0.460968
$223$	−2.03823e10	−0.551926	−0.275963	−	0.961168i	$-0.588997\pi$
$223$	−2.03823e10	−0.551926	−0.275963	+	0.961168i	$0.588997\pi$
$224$	−2.18275e9	−0.0579278
$225$	−1.30425e8	−0.00339264
$226$	2.44292e10	0.622903
$227$	−2.77678e10	−0.694105	−0.347052	−	0.937846i	$-0.612817\pi$
$227$	−2.77678e10	−0.694105	−0.347052	+	0.937846i	$0.612817\pi$
$228$	−2.13210e10	−0.522518
$229$	−3.12929e10	−0.751945	−0.375972	−	0.926631i	$-0.622691\pi$
$229$	−3.12929e10	−0.751945	−0.375972	+	0.926631i	$0.622691\pi$
$230$	4.92409e10	1.16025
$231$	−1.22840e9	−0.0283848
$232$	−7.24512e9	−0.164191
$233$	5.05824e10	1.12434	0.562170	−	0.827022i	$-0.309967\pi$
$233$	5.05824e10	1.12434	0.562170	+	0.827022i	$0.309967\pi$
$234$	−2.99822e9	−0.0653720
$235$	7.92593e10	1.69529
$236$	3.86930e9	0.0811948
$237$	−3.90914e10	−0.804848
$238$	−6.95562e9	−0.140520
$239$	−1.12663e10	−0.223352	−0.111676	−	0.993745i	$-0.535622\pi$
$239$	−1.12663e10	−0.223352	−0.111676	+	0.993745i	$0.535622\pi$
$240$	−7.38089e9	−0.143601
$241$	1.71972e10	0.328384	0.164192	−	0.986428i	$-0.447498\pi$
$241$	1.71972e10	0.328384	0.164192	+	0.986428i	$0.447498\pi$
$242$	−3.68779e10	−0.691190
$243$	3.48678e9	0.0641500
$244$	−2.68046e10	−0.484122
$245$	5.00832e10	0.888066
$246$	−2.51439e10	−0.437749
$247$	2.93668e10	0.502019
$248$	−2.60372e10	−0.437081
$249$	−2.31462e10	−0.381577
$250$	4.38926e10	0.710659
$251$	−3.98401e10	−0.633562	−0.316781	−	0.948499i	$-0.602602\pi$
$251$	−3.98401e10	−0.633562	−0.316781	+	0.948499i	$0.602602\pi$
$252$	−3.49634e9	−0.0546149
$253$	−1.61255e10	−0.247441
$254$	6.46897e10	0.975177
$255$	−2.35202e10	−0.348345
$256$	4.29497e9	0.0625000
$257$	9.96848e10	1.42538	0.712689	−	0.701480i	$-0.247477\pi$
$257$	9.96848e10	1.42538	0.712689	+	0.701480i	$0.247477\pi$
$258$	5.21888e10	0.733312
$259$	−2.67952e10	−0.370006
$260$	1.01662e10	0.137968
$261$	−1.16053e10	−0.154801
$262$	1.25531e10	0.164587
$263$	−2.62586e10	−0.338432	−0.169216	−	0.985579i	$-0.554124\pi$
$263$	−2.62586e10	−0.338432	−0.169216	+	0.985579i	$0.554124\pi$
$264$	2.41711e9	0.0306252
$265$	−8.05573e10	−1.00346
$266$	3.42457e10	0.419410
$267$	−1.76176e10	−0.212151
$268$	−4.78880e9	−0.0567049
$269$	−1.25587e11	−1.46238	−0.731191	−	0.682173i	$-0.761035\pi$
$269$	−1.25587e11	−1.46238	−0.731191	+	0.682173i	$0.761035\pi$
$270$	−1.18228e10	−0.135388
$271$	7.63990e10	0.860451	0.430225	−	0.902721i	$-0.358434\pi$
$271$	7.63990e10	0.860451	0.430225	+	0.902721i	$0.358434\pi$
$272$	1.36865e10	0.151612
$273$	4.81572e9	0.0524723
$274$	−3.50919e10	−0.376122
$275$	−1.44824e8	−0.00152702
$276$	−4.58973e10	−0.476098
$277$	1.50652e11	1.53751	0.768753	−	0.639546i	$-0.220878\pi$
$277$	1.50652e11	1.53751	0.768753	+	0.639546i	$0.220878\pi$
$278$	1.25718e11	1.26239
$279$	−4.17066e10	−0.412084
$280$	1.18551e10	0.115265
$281$	3.87314e10	0.370582	0.185291	−	0.982684i	$-0.440677\pi$
$281$	3.87314e10	0.370582	0.185291	+	0.982684i	$0.440677\pi$
$282$	−7.38774e10	−0.695650
$283$	−1.17471e11	−1.08866	−0.544331	−	0.838871i	$-0.683216\pi$
$283$	−1.17471e11	−1.08866	−0.544331	+	0.838871i	$0.683216\pi$
$284$	1.95401e10	0.178236
$285$	1.15801e11	1.03970
$286$	−3.32924e9	−0.0294237
$287$	4.03860e10	0.351368
$288$	6.87971e9	0.0589256
$289$	−7.49740e10	−0.632223
$290$	3.93504e10	0.326707
$291$	3.41325e10	0.279029
$292$	7.92657e10	0.638061
$293$	−7.67257e10	−0.608186	−0.304093	−	0.952642i	$-0.598353\pi$
$293$	−7.67257e10	−0.608186	−0.304093	+	0.952642i	$0.598353\pi$
$294$	−4.66825e10	−0.364411
$295$	−2.10153e10	−0.161561
$296$	5.27247e10	0.399210
$297$	3.87174e9	0.0288737
$298$	−2.31448e10	−0.170012
$299$	6.32173e10	0.457420
$300$	−4.12206e8	−0.00293811
$301$	−8.38254e10	−0.588608
$302$	3.88629e10	0.268846
$303$	−5.70254e10	−0.388666
$304$	−6.73849e10	−0.452513
$305$	1.45584e11	0.963304
$306$	2.19231e10	0.142941
$307$	7.17244e9	0.0460834	0.0230417	−	0.999735i	$-0.492665\pi$
$307$	7.17244e9	0.0460834	0.0230417	+	0.999735i	$0.492665\pi$
$308$	−3.88235e9	−0.0245820
$309$	1.35130e11	0.843213
$310$	1.41416e11	0.869702
$311$	6.90631e10	0.418624	0.209312	−	0.977849i	$-0.432878\pi$
$311$	6.90631e10	0.418624	0.209312	+	0.977849i	$0.432878\pi$
$312$	−9.47585e9	−0.0566139
$313$	−1.62651e11	−0.957869	−0.478934	−	0.877851i	$-0.658977\pi$
$313$	−1.62651e11	−0.957869	−0.478934	+	0.877851i	$0.658977\pi$
$314$	5.85458e10	0.339869
$315$	1.89896e10	0.108672
$316$	−1.23548e11	−0.697019
$317$	−2.21812e11	−1.23373	−0.616863	−	0.787070i	$-0.711597\pi$
$317$	−2.21812e11	−1.23373	−0.616863	+	0.787070i	$0.711597\pi$
$318$	7.50873e10	0.411760
$319$	−1.28866e10	−0.0696753
$320$	−2.33272e10	−0.124362
$321$	1.10927e11	0.583128
$322$	7.37200e10	0.382150
$323$	−2.14731e11	−1.09770
$324$	1.10200e10	0.0555556
$325$	5.67757e8	0.00282285
$326$	−1.97551e11	−0.968723
$327$	7.01684e10	0.339373
$328$	−7.94672e10	−0.379102
$329$	1.18661e11	0.558378
$330$	−1.31281e10	−0.0609379
$331$	−2.94269e11	−1.34747	−0.673735	−	0.738973i	$-0.735311\pi$
$331$	−2.94269e11	−1.34747	−0.673735	+	0.738973i	$0.735311\pi$
$332$	−7.31533e10	−0.330455
$333$	8.44548e10	0.376379
$334$	−1.96822e11	−0.865397
$335$	2.60094e10	0.112831
$336$	−1.10501e10	−0.0472978
$337$	−2.61572e11	−1.10473	−0.552365	−	0.833602i	$-0.686275\pi$
$337$	−2.61572e11	−1.10473	−0.552365	+	0.833602i	$0.686275\pi$
$338$	1.30517e10	0.0543928
$339$	1.23673e11	0.508598
$340$	−7.43354e10	−0.301676
$341$	−4.63112e10	−0.185478
$342$	−1.07938e11	−0.426634
$343$	1.58982e11	0.620191
$344$	1.64942e11	0.635066
$345$	2.49282e11	0.947338
$346$	−2.82438e11	−1.05945
$347$	−1.88506e11	−0.697978	−0.348989	−	0.937127i	$-0.613475\pi$
$347$	−1.88506e11	−0.697978	−0.348989	+	0.937127i	$0.613475\pi$
$348$	−3.66784e10	−0.134061
$349$	2.13718e11	0.771130	0.385565	−	0.922681i	$-0.374007\pi$
$349$	2.13718e11	0.771130	0.385565	+	0.922681i	$0.374007\pi$
$350$	6.62083e8	0.00235834
$351$	−1.51785e10	−0.0533761
$352$	7.63926e9	0.0265222
$353$	4.88330e11	1.67389	0.836946	−	0.547285i	$-0.184339\pi$
$353$	4.88330e11	1.67389	0.836946	+	0.547285i	$0.184339\pi$
$354$	1.95883e10	0.0662952
$355$	−1.06128e11	−0.354653
$356$	−5.56803e10	−0.183728
$357$	−3.52128e10	−0.114734
$358$	−2.99152e11	−0.962537
$359$	−3.32354e11	−1.05603	−0.528014	−	0.849236i	$-0.677063\pi$
$359$	−3.32354e11	−1.05603	−0.528014	+	0.849236i	$0.677063\pi$
$360$	−3.73657e10	−0.117250
$361$	7.34532e11	2.27630
$362$	−1.51051e10	−0.0462312
$363$	−1.86695e11	−0.564354
$364$	1.52201e10	0.0454423
$365$	−4.30516e11	−1.26961
$366$	−1.35698e11	−0.395284
$367$	−6.15022e11	−1.76967	−0.884837	−	0.465900i	$-0.845730\pi$
$367$	−6.15022e11	−1.76967	−0.884837	+	0.465900i	$0.845730\pi$
$368$	−1.45058e11	−0.412313
$369$	−1.27291e11	−0.357420
$370$	−2.86364e11	−0.794347
$371$	−1.20605e11	−0.330508
$372$	−1.31813e11	−0.356875
$373$	−6.08808e10	−0.162851	−0.0814256	−	0.996679i	$-0.525947\pi$
$373$	−6.08808e10	−0.162851	−0.0814256	+	0.996679i	$0.525947\pi$
$374$	2.43436e10	0.0643372
$375$	2.22206e11	0.580251
$376$	−2.33489e11	−0.602450
$377$	5.05195e10	0.128802
$378$	−1.77002e10	−0.0445928
$379$	4.83380e11	1.20341	0.601703	−	0.798720i	$-0.294489\pi$
$379$	4.83380e11	1.20341	0.601703	+	0.798720i	$0.294489\pi$
$380$	3.65988e11	0.900410
$381$	3.27492e11	0.796229
$382$	−2.58279e11	−0.620589
$383$	−2.77341e11	−0.658597	−0.329299	−	0.944226i	$-0.606812\pi$
$383$	−2.77341e11	−0.658597	−0.329299	+	0.944226i	$0.606812\pi$
$384$	2.17433e10	0.0510310
$385$	2.10862e10	0.0489131
$386$	9.20715e10	0.211097
$387$	2.64206e11	0.598746
$388$	1.07875e11	0.241646
$389$	1.05471e11	0.233538	0.116769	−	0.993159i	$-0.462746\pi$
$389$	1.05471e11	0.233538	0.116769	+	0.993159i	$0.462746\pi$
$390$	5.14662e10	0.112650
$391$	−4.62248e11	−1.00018
$392$	−1.47540e11	−0.315589
$393$	6.35502e10	0.134385
$394$	−1.63034e11	−0.340836
$395$	6.71027e11	1.38693
$396$	1.22366e10	0.0250054
$397$	−4.84996e11	−0.979897	−0.489949	−	0.871751i	$-0.662985\pi$
$397$	−4.84996e11	−0.979897	−0.489949	+	0.871751i	$0.662985\pi$
$398$	3.62045e11	0.723251
$399$	1.73369e11	0.342447
$400$	−1.30277e9	−0.00254448
$401$	1.42959e11	0.276097	0.138048	−	0.990425i	$-0.455917\pi$
$401$	1.42959e11	0.276097	0.138048	+	0.990425i	$0.455917\pi$
$402$	−2.42433e10	−0.0462993
$403$	1.81555e11	0.342874
$404$	−1.80228e11	−0.336594
$405$	−5.98527e10	−0.110544
$406$	5.89127e10	0.107607
$407$	9.37791e10	0.169407
$408$	6.92879e10	0.123790
$409$	3.59333e11	0.634954	0.317477	−	0.948266i	$-0.397164\pi$
$409$	3.59333e11	0.634954	0.317477	+	0.948266i	$0.397164\pi$
$410$	4.31610e11	0.754335
$411$	−1.77653e11	−0.307103
$412$	4.27076e11	0.730244
$413$	−3.14626e10	−0.0532133
$414$	−2.32355e11	−0.388732
$415$	3.97317e11	0.657538
$416$	−2.99484e10	−0.0490290
$417$	6.36446e11	1.03074
$418$	−1.19855e11	−0.192026
$419$	−5.45284e11	−0.864290	−0.432145	−	0.901804i	$-0.642243\pi$
$419$	−5.45284e11	−0.864290	−0.432145	+	0.901804i	$0.642243\pi$
$420$	6.00167e10	0.0941131
$421$	6.86545e11	1.06512	0.532561	−	0.846392i	$-0.321230\pi$
$421$	6.86545e11	1.06512	0.532561	+	0.846392i	$0.321230\pi$
$422$	4.65532e11	0.714568
$423$	−3.74004e11	−0.567996
$424$	2.37313e11	0.356595
$425$	−4.15147e9	−0.00617236
$426$	9.89220e10	0.145529
$427$	2.17958e11	0.317283
$428$	3.50583e11	0.505004
$429$	−1.68543e10	−0.0240244
$430$	−8.95851e11	−1.26365
$431$	−1.38123e12	−1.92804	−0.964022	−	0.265822i	$-0.914357\pi$
$431$	−1.38123e12	−1.92804	−0.964022	+	0.265822i	$0.914357\pi$
$432$	3.48285e10	0.0481125
$433$	5.30447e11	0.725181	0.362590	−	0.931949i	$-0.381892\pi$
$433$	5.30447e11	0.725181	0.362590	+	0.931949i	$0.381892\pi$
$434$	2.11718e11	0.286453
$435$	1.99211e11	0.266755
$436$	2.21767e11	0.293905
$437$	2.27586e12	2.98523
$438$	4.01283e11	0.520975
$439$	−3.83376e11	−0.492645	−0.246323	−	0.969188i	$-0.579222\pi$
$439$	−3.83376e11	−0.492645	−0.246323	+	0.969188i	$0.579222\pi$
$440$	−4.14911e10	−0.0527738
$441$	−2.36330e11	−0.297540
$442$	−9.54346e10	−0.118934
$443$	−1.34793e12	−1.66284	−0.831418	−	0.555647i	$-0.812471\pi$
$443$	−1.34793e12	−1.66284	−0.831418	+	0.555647i	$0.812471\pi$
$444$	2.66919e11	0.325954
$445$	3.02416e11	0.365582
$446$	−3.26117e11	−0.390271
$447$	−1.17170e11	−0.138814
$448$	−3.49239e10	−0.0409611
$449$	3.47211e11	0.403167	0.201584	−	0.979471i	$-0.435391\pi$
$449$	3.47211e11	0.403167	0.201584	+	0.979471i	$0.435391\pi$
$450$	−2.08679e9	−0.00239896
$451$	−1.41345e11	−0.160874
$452$	3.90867e11	0.440459
$453$	1.96743e11	0.219512
$454$	−4.44285e11	−0.490806
$455$	−8.26647e10	−0.0904209
$456$	−3.41136e11	−0.369476
$457$	−1.91293e11	−0.205152	−0.102576	−	0.994725i	$-0.532708\pi$
$457$	−1.91293e11	−0.205152	−0.102576	+	0.994725i	$0.532708\pi$
$458$	−5.00686e11	−0.531705
$459$	1.10986e11	0.116711
$460$	7.87854e11	0.820419
$461$	−1.17441e12	−1.21106	−0.605530	−	0.795823i	$-0.707039\pi$
$461$	−1.17441e12	−1.21106	−0.605530	+	0.795823i	$0.707039\pi$
$462$	−1.96544e10	−0.0200711
$463$	1.60358e12	1.62172	0.810858	−	0.585243i	$-0.199001\pi$
$463$	1.60358e12	1.62172	0.810858	+	0.585243i	$0.199001\pi$
$464$	−1.15922e11	−0.116101
$465$	7.15918e11	0.710109
$466$	8.09318e11	0.795028
$467$	9.57140e11	0.931214	0.465607	−	0.884992i	$-0.345836\pi$
$467$	9.57140e11	0.931214	0.465607	+	0.884992i	$0.345836\pi$
$468$	−4.79715e10	−0.0462250
$469$	3.89395e10	0.0371631
$470$	1.26815e12	1.19875
$471$	2.96388e11	0.277502
$472$	6.19087e10	0.0574134
$473$	2.93376e11	0.269494
$474$	−6.25463e11	−0.569113
$475$	2.04396e10	0.0184226
$476$	−1.11290e11	−0.0993629
$477$	3.80129e11	0.336201
$478$	−1.80261e11	−0.157934
$479$	−1.57491e12	−1.36693	−0.683464	−	0.729984i	$-0.739528\pi$
$479$	−1.57491e12	−1.36693	−0.683464	+	0.729984i	$0.739528\pi$
$480$	−1.18094e11	−0.101541
$481$	−3.67644e11	−0.313166
$482$	2.75156e11	0.232203
$483$	3.73208e11	0.312024
$484$	−5.90047e11	−0.488745
$485$	−5.85904e11	−0.480826
$486$	5.57886e10	0.0453609
$487$	−1.71112e12	−1.37848	−0.689240	−	0.724533i	$-0.742056\pi$
$487$	−1.71112e12	−1.37848	−0.689240	+	0.724533i	$0.742056\pi$
$488$	−4.28873e11	−0.342326
$489$	−1.00010e12	−0.790959
$490$	8.01332e11	0.627957
$491$	2.07673e12	1.61255	0.806274	−	0.591542i	$-0.201481\pi$
$491$	2.07673e12	1.61255	0.806274	+	0.591542i	$0.201481\pi$
$492$	−4.02303e11	−0.309535
$493$	−3.69401e11	−0.281635
$494$	4.69868e11	0.354981
$495$	−6.64608e10	−0.0497556
$496$	−4.16595e11	−0.309063
$497$	−1.58888e11	−0.116812
$498$	−3.70338e11	−0.269815
$499$	−1.02931e12	−0.743177	−0.371588	−	0.928398i	$-0.621187\pi$
$499$	−1.02931e12	−0.743177	−0.371588	+	0.928398i	$0.621187\pi$
$500$	7.02282e11	0.502512
$501$	−9.96414e11	−0.706594
$502$	−6.37442e11	−0.447996
$503$	1.89575e12	1.32046	0.660230	−	0.751063i	$-0.270459\pi$
$503$	1.89575e12	1.32046	0.660230	+	0.751063i	$0.270459\pi$
$504$	−5.59414e10	−0.0386185
$505$	9.78874e11	0.669754
$506$	−2.58008e11	−0.174967
$507$	6.60742e10	0.0444116
$508$	1.03504e12	0.689554
$509$	−4.00031e10	−0.0264158	−0.0132079	−	0.999913i	$-0.504204\pi$
$509$	−4.00031e10	−0.0264158	−0.0132079	+	0.999913i	$0.504204\pi$
$510$	−3.76323e11	−0.246317
$511$	−6.44538e11	−0.418171
$512$	6.87195e10	0.0441942
$513$	−5.46434e11	−0.348345
$514$	1.59496e12	1.00789
$515$	−2.31958e12	−1.45304
$516$	8.35021e11	0.518530
$517$	−4.15296e11	−0.255653
$518$	−4.28724e11	−0.261634
$519$	−1.42984e12	−0.865038
$520$	1.62659e11	0.0975578
$521$	−2.37756e12	−1.41371	−0.706857	−	0.707356i	$-0.749888\pi$
$521$	−2.37756e12	−1.41371	−0.706857	+	0.707356i	$0.749888\pi$
$522$	−1.85684e11	−0.109461
$523$	−1.03565e12	−0.605277	−0.302638	−	0.953105i	$-0.597867\pi$
$523$	−1.03565e12	−0.605277	−0.302638	+	0.953105i	$0.597867\pi$
$524$	2.00850e11	0.116381
$525$	3.35180e9	0.00192558
$526$	−4.20138e11	−0.239308
$527$	−1.32754e12	−0.749720
$528$	3.86738e10	0.0216553
$529$	3.09804e12	1.72003
$530$	−1.28892e12	−0.709551
$531$	9.91658e10	0.0541298
$532$	5.47931e11	0.296567
$533$	5.54117e11	0.297392
$534$	−2.81881e11	−0.150014
$535$	−1.90412e12	−1.00485
$536$	−7.66209e10	−0.0400964
$537$	−1.51445e12	−0.785908
$538$	−2.00940e12	−1.03406
$539$	−2.62422e11	−0.133922
$540$	−1.89164e11	−0.0957341
$541$	−2.66226e12	−1.33617	−0.668087	−	0.744083i	$-0.732887\pi$
$541$	−2.66226e12	−1.33617	−0.668087	+	0.744083i	$0.732887\pi$
$542$	1.22238e12	0.608431
$543$	−7.64696e10	−0.0377476
$544$	2.18984e11	0.107206
$545$	−1.20448e12	−0.584812
$546$	7.70516e10	0.0371035
$547$	4.52407e10	0.0216066	0.0108033	−	0.999942i	$-0.496561\pi$
$547$	4.52407e10	0.0216066	0.0108033	+	0.999942i	$0.496561\pi$
$548$	−5.61470e11	−0.265959
$549$	−6.86972e11	−0.322748
$550$	−2.31719e9	−0.00107976
$551$	1.81873e12	0.840593
$552$	−7.34357e11	−0.336652
$553$	1.00461e12	0.456811
$554$	2.41044e12	1.08718
$555$	−1.44972e12	−0.648581
$556$	2.01148e12	0.892647
$557$	−1.74312e12	−0.767323	−0.383662	−	0.923474i	$-0.625337\pi$
$557$	−1.74312e12	−0.767323	−0.383662	+	0.923474i	$0.625337\pi$
$558$	−6.67305e11	−0.291387
$559$	−1.15013e12	−0.498187
$560$	1.89682e11	0.0815043
$561$	1.23239e11	0.0525311
$562$	6.19702e11	0.262041
$563$	−1.40686e12	−0.590152	−0.295076	−	0.955474i	$-0.595345\pi$
$563$	−1.40686e12	−0.590152	−0.295076	+	0.955474i	$0.595345\pi$
$564$	−1.18204e12	−0.491899
$565$	−2.12291e12	−0.876424
$566$	−1.87954e12	−0.769800
$567$	−8.96073e10	−0.0364099
$568$	3.12642e11	0.126032
$569$	−4.85272e11	−0.194080	−0.0970398	−	0.995281i	$-0.530937\pi$
$569$	−4.85272e11	−0.194080	−0.0970398	+	0.995281i	$0.530937\pi$
$570$	1.85281e12	0.735181
$571$	−8.75728e11	−0.344752	−0.172376	−	0.985031i	$-0.555144\pi$
$571$	−8.75728e11	−0.344752	−0.172376	+	0.985031i	$0.555144\pi$
$572$	−5.32678e10	−0.0208057
$573$	−1.30754e12	−0.506709
$574$	6.46176e11	0.248455
$575$	4.39999e10	0.0167860
$576$	1.10075e11	0.0416667
$577$	5.11159e12	1.91984	0.959920	−	0.280275i	$-0.0904256\pi$
$577$	5.11159e12	1.91984	0.959920	+	0.280275i	$0.0904256\pi$
$578$	−1.19958e12	−0.447049
$579$	4.66112e11	0.172360
$580$	6.29606e11	0.231016
$581$	5.94836e11	0.216573
$582$	5.46119e11	0.197303
$583$	4.22098e11	0.151323
$584$	1.26825e12	0.451177
$585$	2.60548e11	0.0919784
$586$	−1.22761e12	−0.430052
$587$	2.58758e11	0.0899545	0.0449773	−	0.998988i	$-0.485678\pi$
$587$	2.58758e11	0.0899545	0.0449773	+	0.998988i	$0.485678\pi$
$588$	−7.46920e11	−0.257677
$589$	6.53608e12	2.23768
$590$	−3.36245e11	−0.114241
$591$	−8.25359e11	−0.278291
$592$	8.43595e11	0.282284
$593$	−3.74818e11	−0.124473	−0.0622364	−	0.998061i	$-0.519823\pi$
$593$	−3.74818e11	−0.124473	−0.0622364	+	0.998061i	$0.519823\pi$
$594$	6.19479e10	0.0204168
$595$	6.04448e11	0.197712
$596$	−3.70317e11	−0.120217
$597$	1.83285e12	0.590532
$598$	1.01148e12	0.323445
$599$	−3.41166e12	−1.08279	−0.541395	−	0.840768i	$-0.682104\pi$
$599$	−3.41166e12	−1.08279	−0.541395	+	0.840768i	$0.682104\pi$
$600$	−6.59530e9	−0.00207756
$601$	1.37995e12	0.431447	0.215723	−	0.976455i	$-0.430789\pi$
$601$	1.37995e12	0.431447	0.215723	+	0.976455i	$0.430789\pi$
$602$	−1.34121e12	−0.416209
$603$	−1.22732e11	−0.0378033
$604$	6.21806e11	0.190103
$605$	3.20472e12	0.972503
$606$	−9.12406e11	−0.274828
$607$	4.87996e12	1.45904	0.729520	−	0.683960i	$-0.239744\pi$
$607$	4.87996e12	1.45904	0.729520	+	0.683960i	$0.239744\pi$
$608$	−1.07816e12	−0.319975
$609$	2.98245e11	0.0878609
$610$	2.32934e12	0.681159
$611$	1.62810e12	0.472601
$612$	3.50770e11	0.101074
$613$	1.37745e12	0.394008	0.197004	−	0.980403i	$-0.436879\pi$
$613$	1.37745e12	0.394008	0.197004	+	0.980403i	$0.436879\pi$
$614$	1.14759e11	0.0325859
$615$	2.18503e12	0.615912
$616$	−6.21176e10	−0.0173821
$617$	−4.66059e11	−0.129467	−0.0647333	−	0.997903i	$-0.520620\pi$
$617$	−4.66059e11	−0.129467	−0.0647333	+	0.997903i	$0.520620\pi$
$618$	2.16207e12	0.596242
$619$	−4.23249e12	−1.15875	−0.579373	−	0.815063i	$-0.696702\pi$
$619$	−4.23249e12	−1.15875	−0.579373	+	0.815063i	$0.696702\pi$
$620$	2.26265e12	0.614972
$621$	−1.17630e12	−0.317399
$622$	1.10501e12	0.296012
$623$	4.52756e11	0.120412
$624$	−1.51614e11	−0.0400320
$625$	−3.77548e12	−0.989718
$626$	−2.60241e12	−0.677315
$627$	−6.06763e11	−0.156789
$628$	9.36732e11	0.240324
$629$	2.68823e12	0.684761
$630$	3.03834e11	0.0768430
$631$	4.63519e12	1.16395	0.581977	−	0.813205i	$-0.302279\pi$
$631$	4.63519e12	1.16395	0.581977	+	0.813205i	$0.302279\pi$
$632$	−1.97677e12	−0.492867
$633$	2.35676e12	0.583443
$634$	−3.54900e12	−0.872376
$635$	−5.62158e12	−1.37207
$636$	1.20140e12	0.291158
$637$	1.02878e12	0.247568
$638$	−2.06185e11	−0.0492679
$639$	5.00792e11	0.118824
$640$	−3.73236e11	−0.0879374
$641$	4.86720e12	1.13872	0.569362	−	0.822087i	$-0.307190\pi$
$641$	4.86720e12	1.13872	0.569362	+	0.822087i	$0.307190\pi$
$642$	1.77483e12	0.412334
$643$	3.61752e12	0.834569	0.417284	−	0.908776i	$-0.362982\pi$
$643$	3.61752e12	0.834569	0.417284	+	0.908776i	$0.362982\pi$
$644$	1.17952e12	0.270221
$645$	−4.53525e12	−1.03177
$646$	−3.43570e12	−0.776191
$647$	2.23865e12	0.502246	0.251123	−	0.967955i	$-0.419200\pi$
$647$	2.23865e12	0.502246	0.251123	+	0.967955i	$0.419200\pi$
$648$	1.76319e11	0.0392837
$649$	1.10114e11	0.0243637
$650$	9.08412e9	0.00199606
$651$	1.07182e12	0.233888
$652$	−3.16081e12	−0.684991
$653$	7.26294e12	1.56316	0.781580	−	0.623806i	$-0.214414\pi$
$653$	7.26294e12	1.56316	0.781580	+	0.623806i	$0.214414\pi$
$654$	1.12269e12	0.239973
$655$	−1.09088e12	−0.231574
$656$	−1.27148e12	−0.268065
$657$	2.03149e12	0.425374
$658$	1.89858e12	0.394833
$659$	−4.49084e12	−0.927563	−0.463781	−	0.885950i	$-0.653508\pi$
$659$	−4.49084e12	−0.927563	−0.463781	+	0.885950i	$0.653508\pi$
$660$	−2.10049e11	−0.0430896
$661$	1.37947e12	0.281064	0.140532	−	0.990076i	$-0.455119\pi$
$661$	1.37947e12	0.281064	0.140532	+	0.990076i	$0.455119\pi$
$662$	−4.70831e12	−0.952804
$663$	−4.83138e11	−0.0971091
$664$	−1.17045e12	−0.233667
$665$	−2.97598e12	−0.590109
$666$	1.35128e12	0.266140
$667$	3.91514e12	0.765916
$668$	−3.14916e12	−0.611928
$669$	−1.65097e12	−0.318655
$670$	4.16151e11	0.0797837
$671$	−7.62817e11	−0.145268
$672$	−1.76802e11	−0.0334446
$673$	4.10144e12	0.770670	0.385335	−	0.922777i	$-0.374086\pi$
$673$	4.10144e12	0.770670	0.385335	+	0.922777i	$0.374086\pi$
$674$	−4.18515e12	−0.781163
$675$	−1.05644e10	−0.00195874
$676$	2.08827e11	0.0384615
$677$	2.97625e12	0.544528	0.272264	−	0.962223i	$-0.412228\pi$
$677$	2.97625e12	0.544528	0.272264	+	0.962223i	$0.412228\pi$
$678$	1.97876e12	0.359633
$679$	−8.77174e11	−0.158370
$680$	−1.18937e12	−0.213317
$681$	−2.24919e12	−0.400742
$682$	−7.40979e11	−0.131152
$683$	9.53362e12	1.67635	0.838175	−	0.545401i	$-0.183623\pi$
$683$	9.53362e12	1.67635	0.838175	+	0.545401i	$0.183623\pi$
$684$	−1.72700e12	−0.301676
$685$	3.04951e12	0.529204
$686$	2.54372e12	0.438541
$687$	−2.53472e12	−0.434136
$688$	2.63908e12	0.449060
$689$	−1.65476e12	−0.279736
$690$	3.98851e12	0.669869
$691$	−2.82334e12	−0.471099	−0.235550	−	0.971862i	$-0.575689\pi$
$691$	−2.82334e12	−0.471099	−0.235550	+	0.971862i	$0.575689\pi$
$692$	−4.51901e12	−0.749145
$693$	−9.95004e10	−0.0163880
$694$	−3.01609e12	−0.493545
$695$	−1.09250e13	−1.77619
$696$	−5.86854e11	−0.0947957
$697$	−4.05173e12	−0.650269
$698$	3.41949e12	0.545271
$699$	4.09717e12	0.649138
$700$	1.05933e10	0.00166760
$701$	8.98549e12	1.40544	0.702718	−	0.711469i	$-0.251970\pi$
$701$	8.98549e12	1.40544	0.702718	+	0.711469i	$0.251970\pi$
$702$	−2.42856e11	−0.0377426
$703$	−1.32354e13	−2.04380
$704$	1.22228e11	0.0187540
$705$	6.42000e12	0.978778
$706$	7.81329e12	1.18362
$707$	1.46550e12	0.220597
$708$	3.13413e11	0.0468778
$709$	−3.15675e12	−0.469171	−0.234586	−	0.972095i	$-0.575373\pi$
$709$	−3.15675e12	−0.469171	−0.234586	+	0.972095i	$0.575373\pi$
$710$	−1.69805e12	−0.250778
$711$	−3.16640e12	−0.464679
$712$	−8.90884e11	−0.129916
$713$	1.40701e13	2.03889
$714$	−5.63405e11	−0.0811295
$715$	2.89313e11	0.0413992
$716$	−4.78642e12	−0.680617
$717$	−9.12570e11	−0.128953
$718$	−5.31766e12	−0.746724
$719$	2.23010e12	0.311203	0.155601	−	0.987820i	$-0.450268\pi$
$719$	2.23010e12	0.311203	0.155601	+	0.987820i	$0.450268\pi$
$720$	−5.97852e11	−0.0829082
$721$	−3.47271e12	−0.478586
$722$	1.17525e13	1.60958
$723$	1.39298e12	0.189593
$724$	−2.41682e11	−0.0326904
$725$	3.51621e10	0.00472665
$726$	−2.98711e12	−0.399059
$727$	−9.55503e12	−1.26861	−0.634304	−	0.773084i	$-0.718713\pi$
$727$	−9.55503e12	−1.26861	−0.634304	+	0.773084i	$0.718713\pi$
$728$	2.43521e11	0.0321326
$729$	2.82430e11	0.0370370
$730$	−6.88825e12	−0.897751
$731$	8.40978e12	1.08932
$732$	−2.17117e12	−0.279508
$733$	7.03811e11	0.0900509	0.0450255	−	0.998986i	$-0.485663\pi$
$733$	7.03811e11	0.0900509	0.0450255	+	0.998986i	$0.485663\pi$
$734$	−9.84035e12	−1.25135
$735$	4.05674e12	0.512725
$736$	−2.32093e12	−0.291549
$737$	−1.36282e11	−0.0170151
$738$	−2.03666e12	−0.252734
$739$	−1.81149e12	−0.223427	−0.111714	−	0.993740i	$-0.535634\pi$
$739$	−1.81149e12	−0.223427	−0.111714	+	0.993740i	$0.535634\pi$
$740$	−4.58182e12	−0.561688
$741$	2.37871e12	0.289841
$742$	−1.92968e12	−0.233704
$743$	−3.29997e12	−0.397247	−0.198624	−	0.980076i	$-0.563647\pi$
$743$	−3.29997e12	−0.397247	−0.198624	+	0.980076i	$0.563647\pi$
$744$	−2.10901e12	−0.252349
$745$	2.01130e12	0.239207
$746$	−9.74093e11	−0.115153
$747$	−1.87484e12	−0.220303
$748$	3.89497e11	0.0454932
$749$	−2.85072e12	−0.330968
$750$	3.55530e12	0.410299
$751$	−2.53583e12	−0.290898	−0.145449	−	0.989366i	$-0.546463\pi$
$751$	−2.53583e12	−0.290898	−0.145449	+	0.989366i	$0.546463\pi$
$752$	−3.73582e12	−0.425997
$753$	−3.22705e12	−0.365787
$754$	8.08312e11	0.0910768
$755$	−3.37721e12	−0.378266
$756$	−2.83203e11	−0.0315319
$757$	−5.24647e12	−0.580678	−0.290339	−	0.956924i	$-0.593768\pi$
$757$	−5.24647e12	−0.580678	−0.290339	+	0.956924i	$0.593768\pi$
$758$	7.73408e12	0.850937
$759$	−1.30617e12	−0.142860
$760$	5.85580e12	0.636686
$761$	5.27151e11	0.0569776	0.0284888	−	0.999594i	$-0.490931\pi$
$761$	5.27151e11	0.0569776	0.0284888	+	0.999594i	$0.490931\pi$
$762$	5.23987e12	0.563019
$763$	−1.80327e12	−0.192619
$764$	−4.13247e12	−0.438823
$765$	−1.90514e12	−0.201117
$766$	−4.43746e12	−0.465699
$767$	−4.31684e11	−0.0450388
$768$	3.47892e11	0.0360844
$769$	−1.69040e13	−1.74310	−0.871548	−	0.490311i	$-0.836883\pi$
$769$	−1.69040e13	−1.74310	−0.871548	+	0.490311i	$0.836883\pi$
$770$	3.37379e11	0.0345868
$771$	8.07447e12	0.822942
$772$	1.47314e12	0.149268
$773$	4.73738e12	0.477233	0.238617	−	0.971114i	$-0.423306\pi$
$773$	4.73738e12	0.477233	0.238617	+	0.971114i	$0.423306\pi$
$774$	4.22729e12	0.423378
$775$	1.26364e11	0.0125825
$776$	1.72601e12	0.170870
$777$	−2.17041e12	−0.213623
$778$	1.68753e12	0.165136
$779$	1.99485e13	1.94085
$780$	8.23459e11	0.0796556
$781$	5.56083e11	0.0534823
$782$	−7.39596e12	−0.707236
$783$	−9.40027e11	−0.0893743
$784$	−2.36063e12	−0.223155
$785$	−5.08767e12	−0.478196
$786$	1.01680e12	0.0950245
$787$	1.35336e13	1.25756	0.628779	−	0.777584i	$-0.283555\pi$
$787$	1.35336e13	1.25756	0.628779	+	0.777584i	$0.283555\pi$
$788$	−2.60854e12	−0.241007
$789$	−2.12695e12	−0.195394
$790$	1.07364e13	0.980704
$791$	−3.17828e12	−0.288667
$792$	1.95786e11	0.0176815
$793$	2.99049e12	0.268542
$794$	−7.75993e12	−0.692892
$795$	−6.52514e12	−0.579346
$796$	5.79273e12	0.511416
$797$	−4.23447e12	−0.371738	−0.185869	−	0.982575i	$-0.559510\pi$
$797$	−4.23447e12	−0.371738	−0.185869	+	0.982575i	$0.559510\pi$
$798$	2.77390e12	0.242146
$799$	−1.19047e13	−1.03338
$800$	−2.08444e10	−0.00179922
$801$	−1.42702e12	−0.122486
$802$	2.28734e12	0.195230
$803$	2.25578e12	0.191460
$804$	−3.87893e11	−0.0327386
$805$	−6.40633e12	−0.537685
$806$	2.90488e12	0.242449
$807$	−1.01726e13	−0.844307
$808$	−2.88365e12	−0.238008
$809$	1.02662e13	0.842635	0.421317	−	0.906913i	$-0.361568\pi$
$809$	1.02662e13	0.842635	0.421317	+	0.906913i	$0.361568\pi$
$810$	−9.57643e11	−0.0781666
$811$	−1.52846e13	−1.24068	−0.620341	−	0.784332i	$-0.713006\pi$
$811$	−1.52846e13	−1.24068	−0.620341	+	0.784332i	$0.713006\pi$
$812$	9.42602e11	0.0760898
$813$	6.18832e12	0.496782
$814$	1.50047e12	0.119789
$815$	1.71673e13	1.36299
$816$	1.10861e12	0.0875330
$817$	−4.14052e13	−3.25129
$818$	5.74933e12	0.448980
$819$	3.90074e11	0.0302949
$820$	6.90576e12	0.533395
$821$	−1.95952e13	−1.50524	−0.752620	−	0.658455i	$-0.771210\pi$
$821$	−1.95952e13	−1.50524	−0.752620	+	0.658455i	$0.771210\pi$
$822$	−2.84244e12	−0.217154
$823$	1.16825e13	0.887639	0.443820	−	0.896116i	$-0.353623\pi$
$823$	1.16825e13	0.887639	0.443820	+	0.896116i	$0.353623\pi$
$824$	6.83322e12	0.516360
$825$	−1.17308e10	−0.000881624 0
$826$	−5.03402e11	−0.0376275
$827$	1.49938e13	1.11465	0.557324	−	0.830295i	$-0.311828\pi$
$827$	1.49938e13	1.11465	0.557324	+	0.830295i	$0.311828\pi$
$828$	−3.71768e12	−0.274875
$829$	6.37372e12	0.468703	0.234351	−	0.972152i	$-0.424703\pi$
$829$	6.37372e12	0.468703	0.234351	+	0.972152i	$0.424703\pi$
$830$	6.35708e12	0.464950
$831$	1.22028e13	0.887680
$832$	−4.79174e11	−0.0346688
$833$	−7.52248e12	−0.541326
$834$	1.01831e13	0.728843
$835$	1.71040e13	1.21761
$836$	−1.91767e12	−0.135783
$837$	−3.37823e12	−0.237917
$838$	−8.72454e12	−0.611145
$839$	2.35433e12	0.164035	0.0820177	−	0.996631i	$-0.473864\pi$
$839$	2.35433e12	0.164035	0.0820177	+	0.996631i	$0.473864\pi$
$840$	9.60266e11	0.0665480
$841$	−1.13784e13	−0.784330
$842$	1.09847e13	0.753155
$843$	3.13724e12	0.213956
$844$	7.44852e12	0.505276
$845$	−1.13420e12	−0.0765306
$846$	−5.98407e12	−0.401633
$847$	4.79788e12	0.320313
$848$	3.79701e12	0.252151
$849$	−9.51518e12	−0.628539
$850$	−6.64235e10	−0.00436452
$851$	−2.84916e13	−1.86223
$852$	1.58275e12	0.102905
$853$	−1.89147e13	−1.22329	−0.611644	−	0.791133i	$-0.709492\pi$
$853$	−1.89147e13	−1.22329	−0.611644	+	0.791133i	$0.709492\pi$
$854$	3.48732e12	0.224353
$855$	9.37986e12	0.600273
$856$	5.60933e12	0.357091
$857$	−2.71973e13	−1.72232	−0.861158	−	0.508338i	$-0.830260\pi$
$857$	−2.71973e13	−1.72232	−0.861158	+	0.508338i	$0.830260\pi$
$858$	−2.69668e11	−0.0169878
$859$	−2.62634e13	−1.64582	−0.822908	−	0.568175i	$-0.807650\pi$
$859$	−2.62634e13	−1.64582	−0.822908	+	0.568175i	$0.807650\pi$
$860$	−1.43336e13	−0.893537
$861$	3.27127e12	0.202863
$862$	−2.20996e13	−1.36333
$863$	−2.09329e13	−1.28464	−0.642320	−	0.766437i	$-0.722028\pi$
$863$	−2.09329e13	−1.28464	−0.642320	+	0.766437i	$0.722028\pi$
$864$	5.57256e11	0.0340207
$865$	2.45441e13	1.49065
$866$	8.48715e12	0.512780
$867$	−6.07289e12	−0.365014
$868$	3.38749e12	0.202553
$869$	−3.51599e12	−0.209151
$870$	3.18738e12	0.188624
$871$	5.34270e11	0.0314542
$872$	3.54827e12	0.207822
$873$	2.76473e12	0.161097
$874$	3.64137e13	2.11088
$875$	−5.71051e12	−0.329335
$876$	6.42052e12	0.368385
$877$	−1.60239e13	−0.914683	−0.457341	−	0.889291i	$-0.651198\pi$
$877$	−1.60239e13	−0.914683	−0.457341	+	0.889291i	$0.651198\pi$
$878$	−6.13401e12	−0.348353
$879$	−6.21478e12	−0.351136
$880$	−6.63858e11	−0.0373167
$881$	3.24707e13	1.81594	0.907968	−	0.419039i	$-0.137633\pi$
$881$	3.24707e13	1.81594	0.907968	+	0.419039i	$0.137633\pi$
$882$	−3.78128e12	−0.210393
$883$	2.24655e13	1.24363	0.621817	−	0.783162i	$-0.286395\pi$
$883$	2.24655e13	1.24363	0.621817	+	0.783162i	$0.286395\pi$
$884$	−1.52695e12	−0.0840990
$885$	−1.70224e12	−0.0932773
$886$	−2.15668e13	−1.17580
$887$	8.95463e12	0.485726	0.242863	−	0.970061i	$-0.421913\pi$
$887$	8.95463e12	0.485726	0.242863	+	0.970061i	$0.421913\pi$
$888$	4.27070e12	0.230484
$889$	−8.41625e12	−0.451919
$890$	4.83866e12	0.258506
$891$	3.13611e11	0.0166702
$892$	−5.21787e12	−0.275963
$893$	5.86124e13	3.08431
$894$	−1.87473e12	−0.0981566
$895$	2.59965e13	1.35429
$896$	−5.58783e11	−0.0289639
$897$	5.12060e12	0.264092
$898$	5.55538e12	0.285082
$899$	1.12440e13	0.574118
$900$	−3.33887e10	−0.00169632
$901$	1.20997e13	0.611663
$902$	−2.26152e12	−0.113755
$903$	−6.78985e12	−0.339833
$904$	6.25386e12	0.311452
$905$	1.31264e12	0.0650472
$906$	3.14789e12	0.155218
$907$	−3.51601e13	−1.72511	−0.862555	−	0.505963i	$-0.831137\pi$
$907$	−3.51601e13	−1.72511	−0.862555	+	0.505963i	$0.831137\pi$
$908$	−7.10856e12	−0.347052
$909$	−4.61906e12	−0.224396
$910$	−1.32264e12	−0.0639372
$911$	2.85789e13	1.37472	0.687359	−	0.726318i	$-0.258770\pi$
$911$	2.85789e13	1.37472	0.687359	+	0.726318i	$0.258770\pi$
$912$	−5.45818e12	−0.261259
$913$	−2.08183e12	−0.0991578
$914$	−3.06069e12	−0.145064
$915$	1.17923e13	0.556164
$916$	−8.01098e12	−0.375972
$917$	−1.63318e12	−0.0762734
$918$	1.77577e12	0.0825269
$919$	3.91754e13	1.81173	0.905866	−	0.423564i	$-0.139221\pi$
$919$	3.91754e13	1.81173	0.905866	+	0.423564i	$0.139221\pi$
$920$	1.26057e13	0.580124
$921$	5.80968e11	0.0266062
$922$	−1.87906e13	−0.856348
$923$	−2.18002e12	−0.0988675
$924$	−3.14470e11	−0.0141924
$925$	−2.55884e11	−0.0114923
$926$	2.56572e13	1.14673
$927$	1.09455e13	0.486829
$928$	−1.85475e12	−0.0820955
$929$	−1.29260e13	−0.569367	−0.284684	−	0.958621i	$-0.591889\pi$
$929$	−1.29260e13	−0.569367	−0.284684	+	0.958621i	$0.591889\pi$
$930$	1.14547e13	0.502123
$931$	3.70366e13	1.61569
$932$	1.29491e13	0.562170
$933$	5.59411e12	0.241693
$934$	1.53142e13	0.658467
$935$	−2.11547e12	−0.0905223
$936$	−7.67544e11	−0.0326860
$937$	−2.22429e13	−0.942678	−0.471339	−	0.881952i	$-0.656229\pi$
$937$	−2.22429e13	−0.942678	−0.471339	+	0.881952i	$0.656229\pi$
$938$	6.23032e11	0.0262783
$939$	−1.31747e13	−0.553026
$940$	2.02904e13	0.847646
$941$	−4.52304e13	−1.88052	−0.940258	−	0.340463i	$-0.889416\pi$
$941$	−4.52304e13	−1.88052	−0.940258	+	0.340463i	$0.889416\pi$
$942$	4.74221e12	0.196224
$943$	4.29428e13	1.76843
$944$	9.90540e11	0.0405974
$945$	1.53816e12	0.0627420
$946$	4.69401e12	0.190561
$947$	2.86559e13	1.15781	0.578907	−	0.815394i	$-0.303480\pi$
$947$	2.86559e13	1.15781	0.578907	+	0.815394i	$0.303480\pi$
$948$	−1.00074e13	−0.402424
$949$	−8.84339e12	−0.353933
$950$	3.27033e11	0.0130267
$951$	−1.79668e13	−0.712292
$952$	−1.78064e12	−0.0702602
$953$	3.67653e13	1.44384	0.721921	−	0.691976i	$-0.243259\pi$
$953$	3.67653e13	1.44384	0.721921	+	0.691976i	$0.243259\pi$
$954$	6.08207e12	0.237730
$955$	2.24447e13	0.873168
$956$	−2.88417e12	−0.111676
$957$	−1.04381e12	−0.0402271
$958$	−2.51986e13	−0.966565
$959$	4.56552e12	0.174304
$960$	−1.88951e12	−0.0718006
$961$	1.39685e13	0.528317
$962$	−5.88231e12	−0.221442
$963$	8.98507e12	0.336669
$964$	4.40249e12	0.164192
$965$	−8.00108e12	−0.297013
$966$	5.97132e12	0.220634
$967$	4.44465e13	1.63462	0.817312	−	0.576195i	$-0.195463\pi$
$967$	4.44465e13	1.63462	0.817312	+	0.576195i	$0.195463\pi$
$968$	−9.44075e12	−0.345595
$969$	−1.73932e13	−0.633758
$970$	−9.37446e12	−0.339996
$971$	−1.62531e13	−0.586744	−0.293372	−	0.955998i	$-0.594777\pi$
$971$	−1.62531e13	−0.586744	−0.293372	+	0.955998i	$0.594777\pi$
$972$	8.92617e11	0.0320750
$973$	−1.63561e13	−0.585022
$974$	−2.73779e13	−0.974733
$975$	4.59883e10	0.00162977
$976$	−6.86197e12	−0.242061
$977$	−3.36694e13	−1.18225	−0.591125	−	0.806580i	$-0.701316\pi$
$977$	−3.36694e13	−1.18225	−0.591125	+	0.806580i	$0.701316\pi$
$978$	−1.60016e13	−0.559293
$979$	−1.58458e12	−0.0551304
$980$	1.28213e13	0.444033
$981$	5.68364e12	0.195937
$982$	3.32276e13	1.14024
$983$	−5.46040e13	−1.86524	−0.932618	−	0.360865i	$-0.882482\pi$
$983$	−5.46040e13	−1.86524	−0.932618	+	0.360865i	$0.882482\pi$
$984$	−6.43684e12	−0.218874
$985$	1.41678e13	0.479555
$986$	−5.91041e12	−0.199146
$987$	9.61158e12	0.322380
$988$	7.51789e12	0.251009
$989$	−8.91322e13	−2.96245
$990$	−1.06337e12	−0.0351825
$991$	−2.24624e13	−0.739818	−0.369909	−	0.929068i	$-0.620611\pi$
$991$	−2.24624e13	−0.739818	−0.369909	+	0.929068i	$0.620611\pi$
$992$	−6.66552e12	−0.218540
$993$	−2.38358e13	−0.777962
$994$	−2.54221e12	−0.0825985
$995$	−3.14620e13	−1.01761
$996$	−5.92542e12	−0.190788
$997$	1.93731e13	0.620971	0.310486	−	0.950578i	$-0.399508\pi$
$997$	1.93731e13	0.620971	0.310486	+	0.950578i	$0.399508\pi$
$998$	−1.64689e13	−0.525505
$999$	6.84084e12	0.217302

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	78.10.a.f.1.1	✓	2
3.2	odd	2		234.10.a.e.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.10.a.f.1.1	✓	2	1.1	even	1	trivial
234.10.a.e.1.2		2	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 78 = 2 \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	78.a (trivial)

\(f(q)\)	\(=\)	\(q+16.0000 q^{2} +81.0000 q^{3} +256.000 q^{4} -1390.41 q^{5} +1296.00 q^{6} -2081.63 q^{7} +4096.00 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q+16.0000 q^{2} +81.0000 q^{3} +256.000 q^{4} -1390.41 q^{5} +1296.00 q^{6} -2081.63 q^{7} +4096.00 q^{8} +6561.00 q^{9} -22246.6 q^{10} +7285.37 q^{11} +20736.0 q^{12} -28561.0 q^{13} -33306.1 q^{14} -112623. q^{15} +65536.0 q^{16} +208839. q^{17} +104976. q^{18} -1.02821e6 q^{19} -355946. q^{20} -168612. q^{21} +116566. q^{22} -2.21341e6 q^{23} +331776. q^{24} -19878.8 q^{25} -456976. q^{26} +531441. q^{27} -532897. q^{28} -1.76883e6 q^{29} -1.80197e6 q^{30} -6.35674e6 q^{31} +1.04858e6 q^{32} +590115. q^{33} +3.34143e6 q^{34} +2.89432e6 q^{35} +1.67962e6 q^{36} +1.28722e7 q^{37} -1.64514e7 q^{38} -2.31344e6 q^{39} -5.69513e6 q^{40} -1.94012e7 q^{41} -2.69779e6 q^{42} +4.02691e7 q^{43} +1.86505e6 q^{44} -9.12249e6 q^{45} -3.54146e7 q^{46} -5.70042e7 q^{47} +5.30842e6 q^{48} -3.60204e7 q^{49} -318060. q^{50} +1.69160e7 q^{51} -7.31162e6 q^{52} +5.79377e7 q^{53} +8.50306e6 q^{54} -1.01297e7 q^{55} -8.52635e6 q^{56} -8.32852e7 q^{57} -2.83012e7 q^{58} +1.51144e7 q^{59} -2.88316e7 q^{60} -1.04705e8 q^{61} -1.01708e8 q^{62} -1.36576e7 q^{63} +1.67772e7 q^{64} +3.97116e7 q^{65} +9.44184e6 q^{66} -1.87063e7 q^{67} +5.34629e7 q^{68} -1.79286e8 q^{69} +4.63091e7 q^{70} +7.63287e7 q^{71} +2.68739e7 q^{72} +3.09632e8 q^{73} +2.05956e8 q^{74} -1.61018e6 q^{75} -2.63222e8 q^{76} -1.51654e7 q^{77} -3.70151e7 q^{78} -4.82610e8 q^{79} -9.11221e7 q^{80} +4.30467e7 q^{81} -3.10419e8 q^{82} -2.85755e8 q^{83} -4.31646e7 q^{84} -2.90373e8 q^{85} +6.44306e8 q^{86} -1.43275e8 q^{87} +2.98409e7 q^{88} -2.17501e8 q^{89} -1.45960e8 q^{90} +5.94534e7 q^{91} -5.66633e8 q^{92} -5.14896e8 q^{93} -9.12067e8 q^{94} +1.42964e9 q^{95} +8.49347e7 q^{96} +4.21388e8 q^{97} -5.76327e8 q^{98} +4.77993e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 32 q^{2} + 162 q^{3} + 512 q^{4} - 248 q^{5} + 2592 q^{6} - 13000 q^{7} + 8192 q^{8} + 13122 q^{9}+O(q^{10}) \) 2 * q + 32 * q^2 + 162 * q^3 + 512 * q^4 - 248 * q^5 + 2592 * q^6 - 13000 * q^7 + 8192 * q^8 + 13122 * q^9	\( 2 q + 32 q^{2} + 162 q^{3} + 512 q^{4} - 248 q^{5} + 2592 q^{6} - 13000 q^{7} + 8192 q^{8} + 13122 q^{9} - 3968 q^{10} - 83140 q^{11} + 41472 q^{12} - 57122 q^{13} - 208000 q^{14} - 20088 q^{15} + 131072 q^{16} - 387084 q^{17} + 209952 q^{18} - 1520760 q^{19} - 63488 q^{20} - 1053000 q^{21} - 1330240 q^{22} - 318920 q^{23} + 663552 q^{24} - 667898 q^{25} - 913952 q^{26} + 1062882 q^{27} - 3328000 q^{28} + 4171588 q^{29} - 321408 q^{30} - 6668752 q^{31} + 2097152 q^{32} - 6734340 q^{33} - 6193344 q^{34} - 9578960 q^{35} + 3359232 q^{36} + 7653708 q^{37} - 24332160 q^{38} - 4626882 q^{39} - 1015808 q^{40} - 5349864 q^{41} - 16848000 q^{42} + 9645848 q^{43} - 21283840 q^{44} - 1627128 q^{45} - 5102720 q^{46} - 45295036 q^{47} + 10616832 q^{48} + 42836802 q^{49} - 10686368 q^{50} - 31353804 q^{51} - 14623232 q^{52} + 80817084 q^{53} + 17006112 q^{54} - 113432720 q^{55} - 53248000 q^{56} - 123181560 q^{57} + 66745408 q^{58} - 169730636 q^{59} - 5142528 q^{60} - 133384348 q^{61} - 106700032 q^{62} - 85293000 q^{63} + 33554432 q^{64} + 7083128 q^{65} - 107749440 q^{66} - 27500800 q^{67} - 99093504 q^{68} - 25832520 q^{69} - 153263360 q^{70} + 401208260 q^{71} + 53747712 q^{72} + 21876508 q^{73} + 122459328 q^{74} - 54099738 q^{75} - 389314560 q^{76} + 972132368 q^{77} - 74030112 q^{78} - 642214304 q^{79} - 16252928 q^{80} + 86093442 q^{81} - 85597824 q^{82} - 935734356 q^{83} - 269568000 q^{84} - 971163024 q^{85} + 154333568 q^{86} + 337898628 q^{87} - 340541440 q^{88} - 868756080 q^{89} - 26034048 q^{90} + 371293000 q^{91} - 81643520 q^{92} - 540168912 q^{93} - 724720576 q^{94} + 866946000 q^{95} + 169869312 q^{96} + 1084497388 q^{97} + 685388832 q^{98} - 545481540 q^{99}+O(q^{100}) \) 2 * q + 32 * q^2 + 162 * q^3 + 512 * q^4 - 248 * q^5 + 2592 * q^6 - 13000 * q^7 + 8192 * q^8 + 13122 * q^9 - 3968 * q^10 - 83140 * q^11 + 41472 * q^12 - 57122 * q^13 - 208000 * q^14 - 20088 * q^15 + 131072 * q^16 - 387084 * q^17 + 209952 * q^18 - 1520760 * q^19 - 63488 * q^20 - 1053000 * q^21 - 1330240 * q^22 - 318920 * q^23 + 663552 * q^24 - 667898 * q^25 - 913952 * q^26 + 1062882 * q^27 - 3328000 * q^28 + 4171588 * q^29 - 321408 * q^30 - 6668752 * q^31 + 2097152 * q^32 - 6734340 * q^33 - 6193344 * q^34 - 9578960 * q^35 + 3359232 * q^36 + 7653708 * q^37 - 24332160 * q^38 - 4626882 * q^39 - 1015808 * q^40 - 5349864 * q^41 - 16848000 * q^42 + 9645848 * q^43 - 21283840 * q^44 - 1627128 * q^45 - 5102720 * q^46 - 45295036 * q^47 + 10616832 * q^48 + 42836802 * q^49 - 10686368 * q^50 - 31353804 * q^51 - 14623232 * q^52 + 80817084 * q^53 + 17006112 * q^54 - 113432720 * q^55 - 53248000 * q^56 - 123181560 * q^57 + 66745408 * q^58 - 169730636 * q^59 - 5142528 * q^60 - 133384348 * q^61 - 106700032 * q^62 - 85293000 * q^63 + 33554432 * q^64 + 7083128 * q^65 - 107749440 * q^66 - 27500800 * q^67 - 99093504 * q^68 - 25832520 * q^69 - 153263360 * q^70 + 401208260 * q^71 + 53747712 * q^72 + 21876508 * q^73 + 122459328 * q^74 - 54099738 * q^75 - 389314560 * q^76 + 972132368 * q^77 - 74030112 * q^78 - 642214304 * q^79 - 16252928 * q^80 + 86093442 * q^81 - 85597824 * q^82 - 935734356 * q^83 - 269568000 * q^84 - 971163024 * q^85 + 154333568 * q^86 + 337898628 * q^87 - 340541440 * q^88 - 868756080 * q^89 - 26034048 * q^90 + 371293000 * q^91 - 81643520 * q^92 - 540168912 * q^93 - 724720576 * q^94 + 866946000 * q^95 + 169869312 * q^96 + 1084497388 * q^97 + 685388832 * q^98 - 545481540 * q^99

Introduction

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