LMFDB - Embedded newform 177.10.a.d.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,10,Mod(1,177)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(177, 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("177.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	177.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:	$91.1613430010$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	177.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-38.0945 q^{2} +81.0000 q^{3} +939.188 q^{4} -310.159 q^{5} -3085.65 q^{6} -4492.16 q^{7} -16273.5 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q-38.0945 q^{2} +81.0000 q^{3} +939.188 q^{4} -310.159 q^{5} -3085.65 q^{6} -4492.16 q^{7} -16273.5 q^{8} +6561.00 q^{9} +11815.4 q^{10} -57757.0 q^{11} +76074.2 q^{12} -158171. q^{13} +171126. q^{14} -25122.9 q^{15} +139065. q^{16} -406420. q^{17} -249938. q^{18} -588628. q^{19} -291298. q^{20} -363865. q^{21} +2.20022e6 q^{22} -2.03523e6 q^{23} -1.31815e6 q^{24} -1.85693e6 q^{25} +6.02545e6 q^{26} +531441. q^{27} -4.21898e6 q^{28} +4.76982e6 q^{29} +957044. q^{30} +1.42127e6 q^{31} +3.03440e6 q^{32} -4.67832e6 q^{33} +1.54823e7 q^{34} +1.39329e6 q^{35} +6.16201e6 q^{36} -404459. q^{37} +2.24234e7 q^{38} -1.28119e7 q^{39} +5.04737e6 q^{40} -7.85636e6 q^{41} +1.38612e7 q^{42} +6.47482e6 q^{43} -5.42447e7 q^{44} -2.03496e6 q^{45} +7.75309e7 q^{46} +1.12002e7 q^{47} +1.12643e7 q^{48} -2.01741e7 q^{49} +7.07386e7 q^{50} -3.29200e7 q^{51} -1.48553e8 q^{52} +5.38315e7 q^{53} -2.02450e7 q^{54} +1.79139e7 q^{55} +7.31031e7 q^{56} -4.76788e7 q^{57} -1.81704e8 q^{58} -1.21174e7 q^{59} -2.35951e7 q^{60} -1.25526e8 q^{61} -5.41425e7 q^{62} -2.94731e7 q^{63} -1.86795e8 q^{64} +4.90583e7 q^{65} +1.78218e8 q^{66} -8.34881e7 q^{67} -3.81705e8 q^{68} -1.64853e8 q^{69} -5.30764e7 q^{70} -2.26370e8 q^{71} -1.06770e8 q^{72} +3.98191e7 q^{73} +1.54076e7 q^{74} -1.50411e8 q^{75} -5.52832e8 q^{76} +2.59454e8 q^{77} +4.88061e8 q^{78} -4.27187e8 q^{79} -4.31324e7 q^{80} +4.30467e7 q^{81} +2.99284e8 q^{82} +6.54358e8 q^{83} -3.41737e8 q^{84} +1.26055e8 q^{85} -2.46655e8 q^{86} +3.86356e8 q^{87} +9.39908e8 q^{88} -8.81746e8 q^{89} +7.75205e7 q^{90} +7.10531e8 q^{91} -1.91146e9 q^{92} +1.15123e8 q^{93} -4.26665e8 q^{94} +1.82568e8 q^{95} +2.45787e8 q^{96} -1.21147e8 q^{97} +7.68522e8 q^{98} -3.78944e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 46 q^{2} + 1782 q^{3} + 5974 q^{4} + 5786 q^{5} + 3726 q^{6} + 7641 q^{7} + 61395 q^{8} + 144342 q^{9}+O(q^{10}) $ 22 * q + 46 * q^2 + 1782 * q^3 + 5974 * q^4 + 5786 * q^5 + 3726 * q^6 + 7641 * q^7 + 61395 * q^8 + 144342 * q^9	\( 22 q + 46 q^{2} + 1782 q^{3} + 5974 q^{4} + 5786 q^{5} + 3726 q^{6} + 7641 q^{7} + 61395 q^{8} + 144342 q^{9} + 45337 q^{10} + 111769 q^{11} + 483894 q^{12} + 189121 q^{13} + 251053 q^{14} + 468666 q^{15} + 2311074 q^{16} + 1113841 q^{17} + 301806 q^{18} + 476068 q^{19} - 42495 q^{20} + 618921 q^{21} - 2252022 q^{22} + 7103062 q^{23} + 4972995 q^{24} + 10628442 q^{25} + 6871048 q^{26} + 11691702 q^{27} + 8112650 q^{28} + 15279316 q^{29} + 3672297 q^{30} + 17610338 q^{31} + 32378276 q^{32} + 9053289 q^{33} + 29339436 q^{34} + 7134904 q^{35} + 39195414 q^{36} + 21961411 q^{37} + 65195131 q^{38} + 15318801 q^{39} + 75185084 q^{40} + 52781575 q^{41} + 20335293 q^{42} + 76191313 q^{43} + 61127768 q^{44} + 37961946 q^{45} + 290208769 q^{46} + 160572396 q^{47} + 187196994 q^{48} + 156292703 q^{49} + 169504821 q^{50} + 90221121 q^{51} + 65465920 q^{52} - 8762038 q^{53} + 24446286 q^{54} + 147125140 q^{55} + 9671794 q^{56} + 38561508 q^{57} - 37665424 q^{58} - 266581942 q^{59} - 3442095 q^{60} + 120750754 q^{61} - 152465186 q^{62} + 50132601 q^{63} - 40658803 q^{64} + 331055798 q^{65} - 182413782 q^{66} + 41371828 q^{67} + 145606631 q^{68} + 575348022 q^{69} - 920887614 q^{70} + 261018751 q^{71} + 402812595 q^{72} + 178388 q^{73} - 303908734 q^{74} + 860903802 q^{75} - 94541144 q^{76} + 299640561 q^{77} + 556554888 q^{78} - 905381353 q^{79} + 939128289 q^{80} + 947027862 q^{81} - 551739753 q^{82} + 1173257869 q^{83} + 657124650 q^{84} - 1546633210 q^{85} + 1384869460 q^{86} + 1237624596 q^{87} + 189740713 q^{88} + 898004974 q^{89} + 297456057 q^{90} + 591272339 q^{91} + 4328210270 q^{92} + 1426437378 q^{93} + 122568068 q^{94} + 2487967134 q^{95} + 2622640356 q^{96} + 3175709684 q^{97} + 5095778404 q^{98} + 733316409 q^{99}+O(q^{100}) \) 22 * q + 46 * q^2 + 1782 * q^3 + 5974 * q^4 + 5786 * q^5 + 3726 * q^6 + 7641 * q^7 + 61395 * q^8 + 144342 * q^9 + 45337 * q^10 + 111769 * q^11 + 483894 * q^12 + 189121 * q^13 + 251053 * q^14 + 468666 * q^15 + 2311074 * q^16 + 1113841 * q^17 + 301806 * q^18 + 476068 * q^19 - 42495 * q^20 + 618921 * q^21 - 2252022 * q^22 + 7103062 * q^23 + 4972995 * q^24 + 10628442 * q^25 + 6871048 * q^26 + 11691702 * q^27 + 8112650 * q^28 + 15279316 * q^29 + 3672297 * q^30 + 17610338 * q^31 + 32378276 * q^32 + 9053289 * q^33 + 29339436 * q^34 + 7134904 * q^35 + 39195414 * q^36 + 21961411 * q^37 + 65195131 * q^38 + 15318801 * q^39 + 75185084 * q^40 + 52781575 * q^41 + 20335293 * q^42 + 76191313 * q^43 + 61127768 * q^44 + 37961946 * q^45 + 290208769 * q^46 + 160572396 * q^47 + 187196994 * q^48 + 156292703 * q^49 + 169504821 * q^50 + 90221121 * q^51 + 65465920 * q^52 - 8762038 * q^53 + 24446286 * q^54 + 147125140 * q^55 + 9671794 * q^56 + 38561508 * q^57 - 37665424 * q^58 - 266581942 * q^59 - 3442095 * q^60 + 120750754 * q^61 - 152465186 * q^62 + 50132601 * q^63 - 40658803 * q^64 + 331055798 * q^65 - 182413782 * q^66 + 41371828 * q^67 + 145606631 * q^68 + 575348022 * q^69 - 920887614 * q^70 + 261018751 * q^71 + 402812595 * q^72 + 178388 * q^73 - 303908734 * q^74 + 860903802 * q^75 - 94541144 * q^76 + 299640561 * q^77 + 556554888 * q^78 - 905381353 * q^79 + 939128289 * q^80 + 947027862 * q^81 - 551739753 * q^82 + 1173257869 * q^83 + 657124650 * q^84 - 1546633210 * q^85 + 1384869460 * q^86 + 1237624596 * q^87 + 189740713 * q^88 + 898004974 * q^89 + 297456057 * q^90 + 591272339 * q^91 + 4328210270 * q^92 + 1426437378 * q^93 + 122568068 * q^94 + 2487967134 * q^95 + 2622640356 * q^96 + 3175709684 * q^97 + 5095778404 * q^98 + 733316409 * 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 $

$2$	−38.0945	−1.68355	−0.841777	−	0.539826i	$-0.818490\pi$
$2$	−38.0945	−1.68355	−0.841777	+	0.539826i	$0.818490\pi$
$3$	81.0000	0.577350
$3$	81.0000	0.577350
$4$	939.188	1.83435
$5$	−310.159	−0.221932	−0.110966	−	0.993824i	$-0.535394\pi$
$5$	−310.159	−0.221932	−0.110966	+	0.993824i	$0.535394\pi$
$6$	−3085.65	−0.972000
$7$	−4492.16	−0.707154	−0.353577	−	0.935405i	$-0.615035\pi$
$7$	−4492.16	−0.707154	−0.353577	+	0.935405i	$0.615035\pi$
$8$	−16273.5	−1.40467
$9$	6561.00	0.333333
$10$	11815.4	0.373634
$11$	−57757.0	−1.18943	−0.594713	−	0.803938i	$-0.702735\pi$
$11$	−57757.0	−1.18943	−0.594713	+	0.803938i	$0.702735\pi$
$12$	76074.2	1.05906
$13$	−158171.	−1.53597	−0.767985	−	0.640468i	$-0.778740\pi$
$13$	−158171.	−1.53597	−0.767985	+	0.640468i	$0.778740\pi$
$14$	171126.	1.19053
$15$	−25122.9	−0.128132
$16$	139065.	0.530492
$17$	−406420.	−1.18020	−0.590099	−	0.807331i	$-0.700911\pi$
$17$	−406420.	−1.18020	−0.590099	+	0.807331i	$0.700911\pi$
$18$	−249938.	−0.561184
$19$	−588628.	−1.03621	−0.518107	−	0.855316i	$-0.673363\pi$
$19$	−588628.	−1.03621	−0.518107	+	0.855316i	$0.673363\pi$
$20$	−291298.	−0.407101
$21$	−363865.	−0.408275
$22$	2.20022e6	2.00246
$23$	−2.03523e6	−1.51648	−0.758242	−	0.651973i	$-0.773941\pi$
$23$	−2.03523e6	−1.51648	−0.758242	+	0.651973i	$0.773941\pi$
$24$	−1.31815e6	−0.810989
$25$	−1.85693e6	−0.950746
$26$	6.02545e6	2.58589
$27$	531441.	0.192450
$28$	−4.21898e6	−1.29717
$29$	4.76982e6	1.25231	0.626154	−	0.779699i	$-0.284628\pi$
$29$	4.76982e6	1.25231	0.626154	+	0.779699i	$0.284628\pi$
$30$	957044.	0.215718
$31$	1.42127e6	0.276407	0.138203	−	0.990404i	$-0.455867\pi$
$31$	1.42127e6	0.276407	0.138203	+	0.990404i	$0.455867\pi$
$32$	3.03440e6	0.511562
$33$	−4.67832e6	−0.686716
$34$	1.54823e7	1.98693
$35$	1.39329e6	0.156940
$36$	6.16201e6	0.611450
$37$	−404459.	−0.0354786	−0.0177393	−	0.999843i	$-0.505647\pi$
$37$	−404459.	−0.0354786	−0.0177393	+	0.999843i	$0.505647\pi$
$38$	2.24234e7	1.74452
$39$	−1.28119e7	−0.886792
$40$	5.04737e6	0.311742
$41$	−7.85636e6	−0.434204	−0.217102	−	0.976149i	$-0.569660\pi$
$41$	−7.85636e6	−0.434204	−0.217102	+	0.976149i	$0.569660\pi$
$42$	1.38612e7	0.687353
$43$	6.47482e6	0.288815	0.144407	−	0.989518i	$-0.453872\pi$
$43$	6.47482e6	0.288815	0.144407	+	0.989518i	$0.453872\pi$
$44$	−5.42447e7	−2.18183
$45$	−2.03496e6	−0.0739773
$46$	7.75309e7	2.55308
$47$	1.12002e7	0.334800	0.167400	−	0.985889i	$-0.446463\pi$
$47$	1.12002e7	0.334800	0.167400	+	0.985889i	$0.446463\pi$
$48$	1.12643e7	0.306280
$49$	−2.01741e7	−0.499933
$50$	7.07386e7	1.60063
$51$	−3.29200e7	−0.681388
$52$	−1.48553e8	−2.81751
$53$	5.38315e7	0.937120	0.468560	−	0.883432i	$-0.344773\pi$
$53$	5.38315e7	0.937120	0.468560	+	0.883432i	$0.344773\pi$
$54$	−2.02450e7	−0.324000
$55$	1.79139e7	0.263972
$56$	7.31031e7	0.993321
$57$	−4.76788e7	−0.598258
$58$	−1.81704e8	−2.10833
$59$	−1.21174e7	−0.130189
$59$	−1.21174e7	−0.130189
$60$	−2.35951e7	−0.235040
$61$	−1.25526e8	−1.16078	−0.580388	−	0.814340i	$-0.697099\pi$
$61$	−1.25526e8	−1.16078	−0.580388	+	0.814340i	$0.697099\pi$
$62$	−5.41425e7	−0.465346
$63$	−2.94731e7	−0.235718
$64$	−1.86795e8	−1.39173
$65$	4.90583e7	0.340881
$66$	1.78218e8	1.15612
$67$	−8.34881e7	−0.506160	−0.253080	−	0.967445i	$-0.581444\pi$
$67$	−8.34881e7	−0.506160	−0.253080	+	0.967445i	$0.581444\pi$
$68$	−3.81705e8	−2.16490
$69$	−1.64853e8	−0.875542
$70$	−5.30764e7	−0.264217
$71$	−2.26370e8	−1.05720	−0.528598	−	0.848872i	$-0.677282\pi$
$71$	−2.26370e8	−1.05720	−0.528598	+	0.848872i	$0.677282\pi$
$72$	−1.06770e8	−0.468225
$73$	3.98191e7	0.164111	0.0820557	−	0.996628i	$-0.473851\pi$
$73$	3.98191e7	0.164111	0.0820557	+	0.996628i	$0.473851\pi$
$74$	1.54076e7	0.0597301
$75$	−1.50411e8	−0.548914
$76$	−5.52832e8	−1.90078
$77$	2.59454e8	0.841108
$78$	4.88061e8	1.49296
$79$	−4.27187e8	−1.23395	−0.616973	−	0.786984i	$-0.711641\pi$
$79$	−4.27187e8	−1.23395	−0.616973	+	0.786984i	$0.711641\pi$
$80$	−4.31324e7	−0.117733
$81$	4.30467e7	0.111111
$82$	2.99284e8	0.731006
$83$	6.54358e8	1.51343	0.756717	−	0.653742i	$-0.226802\pi$
$83$	6.54358e8	1.51343	0.756717	+	0.653742i	$0.226802\pi$
$84$	−3.41737e8	−0.748920
$85$	1.26055e8	0.261924
$86$	−2.46655e8	−0.486235
$87$	3.86356e8	0.723020
$88$	9.39908e8	1.67076
$89$	−8.81746e8	−1.48966	−0.744832	−	0.667252i	$-0.767470\pi$
$89$	−8.81746e8	−1.48966	−0.744832	+	0.667252i	$0.767470\pi$
$90$	7.75205e7	0.124545
$91$	7.10531e8	1.08617
$92$	−1.91146e9	−2.78176
$93$	1.15123e8	0.159584
$94$	−4.26665e8	−0.563653
$95$	1.82568e8	0.229969
$96$	2.45787e8	0.295351
$97$	−1.21147e8	−0.138944	−0.0694719	−	0.997584i	$-0.522131\pi$
$97$	−1.21147e8	−0.138944	−0.0694719	+	0.997584i	$0.522131\pi$
$98$	7.68522e8	0.841665
$99$	−3.78944e8	−0.396476
$100$	−1.74400e9	−1.74400
$101$	7.20450e8	0.688902	0.344451	−	0.938804i	$-0.388065\pi$
$101$	7.20450e8	0.688902	0.344451	+	0.938804i	$0.388065\pi$
$102$	1.25407e9	1.14715
$103$	8.16532e7	0.0714835	0.0357418	−	0.999361i	$-0.488621\pi$
$103$	8.16532e7	0.0714835	0.0357418	+	0.999361i	$0.488621\pi$
$104$	2.57400e9	2.15754
$105$	1.12856e8	0.0906094
$106$	−2.05068e9	−1.57769
$107$	2.38390e9	1.75817	0.879084	−	0.476666i	$-0.158155\pi$
$107$	2.38390e9	1.75817	0.879084	+	0.476666i	$0.158155\pi$
$108$	4.99123e8	0.353021
$109$	1.05053e9	0.712838	0.356419	−	0.934326i	$-0.383997\pi$
$109$	1.05053e9	0.712838	0.356419	+	0.934326i	$0.383997\pi$
$110$	−6.82420e8	−0.444411
$111$	−3.27612e7	−0.0204836
$112$	−6.24704e8	−0.375140
$113$	1.25128e9	0.721943	0.360971	−	0.932577i	$-0.382445\pi$
$113$	1.25128e9	0.721943	0.360971	+	0.932577i	$0.382445\pi$
$114$	1.81630e9	1.00720
$115$	6.31245e8	0.336556
$116$	4.47976e9	2.29717
$117$	−1.03776e9	−0.511990
$118$	4.61604e8	0.219180
$119$	1.82570e9	0.834581
$120$	4.08837e8	0.179984
$121$	9.77927e8	0.414737
$122$	4.78183e9	1.95423
$123$	−6.36365e8	−0.250688
$124$	1.33484e9	0.507027
$125$	1.18172e9	0.432933
$126$	1.12276e9	0.396844
$127$	−5.45028e9	−1.85910	−0.929549	−	0.368699i	$-0.879803\pi$
$127$	−5.45028e9	−1.85910	−0.929549	+	0.368699i	$0.879803\pi$
$128$	5.56226e9	1.83150
$129$	5.24460e8	0.166747
$130$	−1.86885e9	−0.573891
$131$	−4.37579e9	−1.29818	−0.649092	−	0.760710i	$-0.724851\pi$
$131$	−4.37579e9	−1.29818	−0.649092	+	0.760710i	$0.724851\pi$
$132$	−4.39382e9	−1.25968
$133$	2.64421e9	0.732763
$134$	3.18044e9	0.852148
$135$	−1.64831e8	−0.0427108
$136$	6.61387e9	1.65779
$137$	−6.28431e9	−1.52410	−0.762052	−	0.647515i	$-0.775808\pi$
$137$	−6.28431e9	−1.52410	−0.762052	+	0.647515i	$0.775808\pi$
$138$	6.28000e9	1.47402
$139$	9.44036e8	0.214497	0.107249	−	0.994232i	$-0.465796\pi$
$139$	9.44036e8	0.214497	0.107249	+	0.994232i	$0.465796\pi$
$140$	1.30856e9	0.287883
$141$	9.07216e8	0.193297
$142$	8.62342e9	1.77985
$143$	9.13550e9	1.82692
$144$	9.12408e8	0.176831
$145$	−1.47941e9	−0.277927
$146$	−1.51689e9	−0.276290
$147$	−1.63410e9	−0.288637
$148$	−3.79863e8	−0.0650802
$149$	6.46830e9	1.07511	0.537553	−	0.843230i	$-0.319349\pi$
$149$	6.46830e9	1.07511	0.537553	+	0.843230i	$0.319349\pi$
$150$	5.72983e9	0.924125
$151$	−9.85249e9	−1.54223	−0.771116	−	0.636695i	$-0.780301\pi$
$151$	−9.85249e9	−1.54223	−0.771116	+	0.636695i	$0.780301\pi$
$152$	9.57902e9	1.45554
$153$	−2.66652e9	−0.393399
$154$	−9.88375e9	−1.41605
$155$	−4.40820e8	−0.0613435
$156$	−1.20328e10	−1.62669
$157$	−8.11415e9	−1.06585	−0.532923	−	0.846164i	$-0.678906\pi$
$157$	−8.11415e9	−1.06585	−0.532923	+	0.846164i	$0.678906\pi$
$158$	1.62735e10	2.07741
$159$	4.36035e9	0.541047
$160$	−9.41149e8	−0.113532
$161$	9.14257e9	1.07239
$162$	−1.63984e9	−0.187061
$163$	9.11000e9	1.01082	0.505410	−	0.862879i	$-0.331341\pi$
$163$	9.11000e9	1.01082	0.505410	+	0.862879i	$0.331341\pi$
$164$	−7.37859e9	−0.796483
$165$	1.45102e9	0.152404
$166$	−2.49274e10	−2.54795
$167$	1.33957e10	1.33272	0.666362	−	0.745629i	$-0.267851\pi$
$167$	1.33957e10	1.33272	0.666362	+	0.745629i	$0.267851\pi$
$168$	5.92135e9	0.573494
$169$	1.44137e10	1.35920
$170$	−4.80200e9	−0.440962
$171$	−3.86199e9	−0.345405
$172$	6.08107e9	0.529788
$173$	1.43423e9	0.121733	0.0608667	−	0.998146i	$-0.480614\pi$
$173$	1.43423e9	0.121733	0.0608667	+	0.998146i	$0.480614\pi$
$174$	−1.47180e10	−1.21724
$175$	8.34161e9	0.672324
$176$	−8.03200e9	−0.630982
$177$	−9.81506e8	−0.0751646
$178$	3.35896e10	2.50793
$179$	5.05798e9	0.368246	0.184123	−	0.982903i	$-0.441055\pi$
$179$	5.05798e9	0.368246	0.184123	+	0.982903i	$0.441055\pi$
$180$	−1.91121e9	−0.135700
$181$	7.33273e9	0.507823	0.253911	−	0.967228i	$-0.418283\pi$
$181$	7.33273e9	0.507823	0.253911	+	0.967228i	$0.418283\pi$
$182$	−2.70673e10	−1.82862
$183$	−1.01676e10	−0.670174
$184$	3.31202e10	2.13017
$185$	1.25447e8	0.00787384
$186$	−4.38554e9	−0.268667
$187$	2.34736e10	1.40376
$188$	1.05191e10	0.614140
$189$	−2.38732e9	−0.136092
$190$	−6.95484e9	−0.387165
$191$	6.28320e9	0.341610	0.170805	−	0.985305i	$-0.445363\pi$
$191$	6.28320e9	0.341610	0.170805	+	0.985305i	$0.445363\pi$
$192$	−1.51304e10	−0.803518
$193$	2.89695e10	1.50291	0.751454	−	0.659785i	$-0.229353\pi$
$193$	2.89695e10	1.50291	0.751454	+	0.659785i	$0.229353\pi$
$194$	4.61502e9	0.233919
$195$	3.97372e9	0.196808
$196$	−1.89473e10	−0.917053
$197$	−3.19275e10	−1.51031	−0.755156	−	0.655545i	$-0.772439\pi$
$197$	−3.19275e10	−1.51031	−0.755156	+	0.655545i	$0.772439\pi$
$198$	1.44357e10	0.667488
$199$	−4.30163e10	−1.94444	−0.972220	−	0.234070i	$-0.924795\pi$
$199$	−4.30163e10	−1.94444	−0.972220	+	0.234070i	$0.924795\pi$
$200$	3.02187e10	1.33549
$201$	−6.76254e9	−0.292232
$202$	−2.74451e10	−1.15980
$203$	−2.14268e10	−0.885574
$204$	−3.09181e10	−1.24990
$205$	2.43672e9	0.0963638
$206$	−3.11054e9	−0.120346
$207$	−1.33531e10	−0.505495
$208$	−2.19961e10	−0.814820
$209$	3.39974e10	1.23250
$210$	−4.29919e9	−0.152546
$211$	4.42161e10	1.53571	0.767855	−	0.640623i	$-0.221324\pi$
$211$	4.42161e10	1.53571	0.767855	+	0.640623i	$0.221324\pi$
$212$	5.05579e10	1.71901
$213$	−1.83359e10	−0.610372
$214$	−9.08133e10	−2.95997
$215$	−2.00823e9	−0.0640973
$216$	−8.64840e9	−0.270330
$217$	−6.38457e9	−0.195462
$218$	−4.00195e10	−1.20010
$219$	3.22535e9	0.0947497
$220$	1.68245e10	0.484217
$221$	6.42840e10	1.81275
$222$	1.24802e9	0.0344852
$223$	−3.54715e10	−0.960523	−0.480262	−	0.877125i	$-0.659458\pi$
$223$	−3.54715e10	−0.960523	−0.480262	+	0.877125i	$0.659458\pi$
$224$	−1.36310e10	−0.361753
$225$	−1.21833e10	−0.316915
$226$	−4.76670e10	−1.21543
$227$	3.93316e10	0.983163	0.491581	−	0.870832i	$-0.336419\pi$
$227$	3.93316e10	0.983163	0.491581	+	0.870832i	$0.336419\pi$
$228$	−4.47794e10	−1.09742
$229$	−4.92726e9	−0.118398	−0.0591992	−	0.998246i	$-0.518855\pi$
$229$	−4.92726e9	−0.118398	−0.0591992	+	0.998246i	$0.518855\pi$
$230$	−2.40469e10	−0.566610
$231$	2.10158e10	0.485614
$232$	−7.76216e10	−1.75908
$233$	−5.84819e10	−1.29993	−0.649964	−	0.759965i	$-0.725216\pi$
$233$	−5.84819e10	−1.29993	−0.649964	+	0.759965i	$0.725216\pi$
$234$	3.95330e10	0.861962
$235$	−3.47384e9	−0.0743028
$236$	−1.13805e10	−0.238812
$237$	−3.46021e10	−0.712419
$238$	−6.95492e10	−1.40506
$239$	−2.25238e10	−0.446530	−0.223265	−	0.974758i	$-0.571672\pi$
$239$	−2.25238e10	−0.446530	−0.223265	+	0.974758i	$0.571672\pi$
$240$	−3.49373e9	−0.0679733
$241$	−3.91475e10	−0.747527	−0.373764	−	0.927524i	$-0.621933\pi$
$241$	−3.91475e10	−0.747527	−0.373764	+	0.927524i	$0.621933\pi$
$242$	−3.72536e10	−0.698231
$243$	3.48678e9	0.0641500
$244$	−1.17892e11	−2.12927
$245$	6.25719e9	0.110951
$246$	2.42420e10	0.422046
$247$	9.31040e10	1.59159
$248$	−2.31290e10	−0.388262
$249$	5.30030e10	0.873782
$250$	−4.50171e10	−0.728866
$251$	9.22468e10	1.46696	0.733482	−	0.679709i	$-0.237894\pi$
$251$	9.22468e10	1.46696	0.733482	+	0.679709i	$0.237894\pi$
$252$	−2.76807e10	−0.432389
$253$	1.17549e11	1.80375
$254$	2.07625e11	3.12989
$255$	1.02105e10	0.151222
$256$	−1.16252e11	−1.69169
$257$	−1.22545e11	−1.75226	−0.876129	−	0.482076i	$-0.839883\pi$
$257$	−1.22545e11	−1.75226	−0.876129	+	0.482076i	$0.839883\pi$
$258$	−1.99790e10	−0.280728
$259$	1.81689e9	0.0250888
$260$	4.60750e10	0.625295
$261$	3.12948e10	0.417436
$262$	1.66694e11	2.18556
$263$	3.47682e10	0.448106	0.224053	−	0.974577i	$-0.428071\pi$
$263$	3.47682e10	0.448106	0.224053	+	0.974577i	$0.428071\pi$
$264$	7.61325e10	0.964612
$265$	−1.66964e10	−0.207977
$266$	−1.00730e11	−1.23364
$267$	−7.14214e10	−0.860058
$268$	−7.84110e10	−0.928476
$269$	3.58870e10	0.417881	0.208940	−	0.977928i	$-0.432999\pi$
$269$	3.58870e10	0.417881	0.208940	+	0.977928i	$0.432999\pi$
$270$	6.27916e9	0.0719060
$271$	5.73561e10	0.645978	0.322989	−	0.946403i	$-0.395312\pi$
$271$	5.73561e10	0.645978	0.322989	+	0.946403i	$0.395312\pi$
$272$	−5.65189e10	−0.626086
$273$	5.75530e10	0.627099
$274$	2.39397e11	2.56591
$275$	1.07251e11	1.13084
$276$	−1.54828e11	−1.60605
$277$	−1.63860e11	−1.67230	−0.836152	−	0.548498i	$-0.815200\pi$
$277$	−1.63860e11	−1.67230	−0.836152	+	0.548498i	$0.815200\pi$
$278$	−3.59625e10	−0.361118
$279$	9.32495e9	0.0921356
$280$	−2.26736e10	−0.220450
$281$	−4.45125e10	−0.425896	−0.212948	−	0.977064i	$-0.568306\pi$
$281$	−4.45125e10	−0.425896	−0.212948	+	0.977064i	$0.568306\pi$
$282$	−3.45599e10	−0.325425
$283$	8.38421e10	0.777004	0.388502	−	0.921448i	$-0.372993\pi$
$283$	8.38421e10	0.777004	0.388502	+	0.921448i	$0.372993\pi$
$284$	−2.12603e11	−1.93927
$285$	1.47880e10	0.132773
$286$	−3.48012e11	−3.07572
$287$	3.52920e10	0.307049
$288$	1.99087e10	0.170521
$289$	4.65893e10	0.392867
$290$	5.63571e10	0.467905
$291$	−9.81288e9	−0.0802192
$292$	3.73976e10	0.301038
$293$	1.10535e10	0.0876186	0.0438093	−	0.999040i	$-0.486051\pi$
$293$	1.10535e10	0.0876186	0.0438093	+	0.999040i	$0.486051\pi$
$294$	6.22503e10	0.485935
$295$	3.75831e9	0.0288931
$296$	6.58195e9	0.0498359
$297$	−3.06945e10	−0.228905
$298$	−2.46406e11	−1.81000
$299$	3.21915e11	2.32927
$300$	−1.41264e11	−1.00690
$301$	−2.90859e10	−0.204237
$302$	3.75325e11	2.59643
$303$	5.83564e10	0.397738
$304$	−8.18577e10	−0.549703
$305$	3.89330e10	0.257613
$306$	1.01580e11	0.662309
$307$	1.66454e11	1.06948	0.534740	−	0.845017i	$-0.320409\pi$
$307$	1.66454e11	1.06948	0.534740	+	0.845017i	$0.320409\pi$
$308$	2.43676e11	1.54289
$309$	6.61391e9	0.0412710
$310$	1.67928e10	0.103275
$311$	−1.85159e11	−1.12233	−0.561167	−	0.827702i	$-0.689648\pi$
$311$	−1.85159e11	−1.12233	−0.561167	+	0.827702i	$0.689648\pi$
$312$	2.08494e11	1.24565
$313$	1.58942e11	0.936030	0.468015	−	0.883720i	$-0.344969\pi$
$313$	1.58942e11	0.936030	0.468015	+	0.883720i	$0.344969\pi$
$314$	3.09104e11	1.79441
$315$	9.14134e9	0.0523134
$316$	−4.01209e11	−2.26349
$317$	1.97998e11	1.10127	0.550635	−	0.834746i	$-0.314386\pi$
$317$	1.97998e11	1.10127	0.550635	+	0.834746i	$0.314386\pi$
$318$	−1.66105e11	−0.910881
$319$	−2.75491e11	−1.48953
$320$	5.79363e10	0.308870
$321$	1.93096e11	1.01508
$322$	−3.48281e11	−1.80542
$323$	2.39230e11	1.22294
$324$	4.04289e10	0.203817
$325$	2.93712e11	1.46032
$326$	−3.47040e11	−1.70177
$327$	8.50933e10	0.411557
$328$	1.27850e11	0.609915
$329$	−5.03130e10	−0.236755
$330$	−5.52760e10	−0.256581
$331$	−1.52643e11	−0.698960	−0.349480	−	0.936944i	$-0.613642\pi$
$331$	−1.52643e11	−0.698960	−0.349480	+	0.936944i	$0.613642\pi$
$332$	6.14565e11	2.77617
$333$	−2.65365e9	−0.0118262
$334$	−5.10300e11	−2.24371
$335$	2.58946e10	0.112333
$336$	−5.06010e10	−0.216587
$337$	−2.98538e11	−1.26085	−0.630426	−	0.776249i	$-0.717120\pi$
$337$	−2.98538e11	−1.26085	−0.630426	+	0.776249i	$0.717120\pi$
$338$	−5.49081e11	−2.28829
$339$	1.01354e11	0.416814
$340$	1.18389e11	0.480460
$341$	−8.20883e10	−0.328766
$342$	1.47120e11	0.581507
$343$	2.71900e11	1.06068
$344$	−1.05368e11	−0.405691
$345$	5.11308e10	0.194311
$346$	−5.46360e10	−0.204945
$347$	3.17389e11	1.17519	0.587597	−	0.809154i	$-0.300074\pi$
$347$	3.17389e11	1.17519	0.587597	+	0.809154i	$0.300074\pi$
$348$	3.62860e11	1.32627
$349$	4.57145e10	0.164945	0.0824725	−	0.996593i	$-0.473718\pi$
$349$	4.57145e10	0.164945	0.0824725	+	0.996593i	$0.473718\pi$
$350$	−3.17769e11	−1.13189
$351$	−8.40587e10	−0.295597
$352$	−1.75258e11	−0.608466
$353$	−2.23119e11	−0.764803	−0.382401	−	0.923996i	$-0.624903\pi$
$353$	−2.23119e11	−0.764803	−0.382401	+	0.923996i	$0.624903\pi$
$354$	3.73899e10	0.126544
$355$	7.02106e10	0.234626
$356$	−8.28125e11	−2.73257
$357$	1.47882e11	0.481846
$358$	−1.92681e11	−0.619962
$359$	−2.18766e10	−0.0695112	−0.0347556	−	0.999396i	$-0.511065\pi$
$359$	−2.18766e10	−0.0695112	−0.0347556	+	0.999396i	$0.511065\pi$
$360$	3.31158e10	0.103914
$361$	2.37947e10	0.0737390
$362$	−2.79336e11	−0.854946
$363$	7.92121e10	0.239448
$364$	6.67322e11	1.99241
$365$	−1.23503e10	−0.0364216
$366$	3.87328e11	1.12827
$367$	−3.93075e11	−1.13104	−0.565520	−	0.824734i	$-0.691325\pi$
$367$	−3.93075e11	−1.13104	−0.565520	+	0.824734i	$0.691325\pi$
$368$	−2.83030e11	−0.804483
$369$	−5.15456e10	−0.144735
$370$	−4.77882e9	−0.0132560
$371$	−2.41820e11	−0.662688
$372$	1.08122e11	0.292732
$373$	−1.13683e11	−0.304094	−0.152047	−	0.988373i	$-0.548586\pi$
$373$	−1.13683e11	−0.304094	−0.152047	+	0.988373i	$0.548586\pi$
$374$	−8.94214e11	−2.36330
$375$	9.57196e10	0.249954
$376$	−1.82266e11	−0.470284
$377$	−7.54449e11	−1.92351
$378$	9.09436e10	0.229118
$379$	−6.69019e11	−1.66557	−0.832783	−	0.553599i	$-0.813254\pi$
$379$	−6.69019e11	−1.66557	−0.832783	+	0.553599i	$0.813254\pi$
$380$	1.71466e11	0.421844
$381$	−4.41473e11	−1.07335
$382$	−2.39355e11	−0.575118
$383$	−1.08110e11	−0.256728	−0.128364	−	0.991727i	$-0.540973\pi$
$383$	−1.08110e11	−0.256728	−0.128364	+	0.991727i	$0.540973\pi$
$384$	4.50543e11	1.05741
$385$	−8.04720e10	−0.186669
$386$	−1.10358e12	−2.53023
$387$	4.24813e10	0.0962716
$388$	−1.13780e11	−0.254872
$389$	−7.24664e10	−0.160459	−0.0802294	−	0.996776i	$-0.525565\pi$
$389$	−7.24664e10	−0.160459	−0.0802294	+	0.996776i	$0.525565\pi$
$390$	−1.51377e11	−0.331336
$391$	8.27157e11	1.78975
$392$	3.28303e11	0.702244
$393$	−3.54439e11	−0.749507
$394$	1.21626e12	2.54269
$395$	1.32496e11	0.273852
$396$	−3.55899e11	−0.727275
$397$	2.66907e11	0.539265	0.269632	−	0.962963i	$-0.413098\pi$
$397$	2.66907e11	0.539265	0.269632	+	0.962963i	$0.413098\pi$
$398$	1.63868e12	3.27357
$399$	2.14181e11	0.423061
$400$	−2.58234e11	−0.504364
$401$	5.84873e11	1.12957	0.564783	−	0.825239i	$-0.308960\pi$
$401$	5.84873e11	1.12957	0.564783	+	0.825239i	$0.308960\pi$
$402$	2.57615e11	0.491988
$403$	−2.24804e11	−0.424552
$404$	6.76638e11	1.26369
$405$	−1.33513e10	−0.0246591
$406$	8.16242e11	1.49091
$407$	2.33603e10	0.0421992
$408$	5.35723e11	0.957127
$409$	6.63222e11	1.17194	0.585968	−	0.810334i	$-0.300714\pi$
$409$	6.63222e11	1.17194	0.585968	+	0.810334i	$0.300714\pi$
$410$	−9.28256e10	−0.162234
$411$	−5.09029e11	−0.879942
$412$	7.66877e10	0.131126
$413$	5.44331e10	0.0920636
$414$	5.08680e11	0.851027
$415$	−2.02955e11	−0.335880
$416$	−4.79955e11	−0.785744
$417$	7.64669e10	0.123840
$418$	−1.29511e12	−2.07498
$419$	−5.68468e11	−0.901038	−0.450519	−	0.892767i	$-0.648761\pi$
$419$	−5.68468e11	−0.901038	−0.450519	+	0.892767i	$0.648761\pi$
$420$	1.05993e11	0.166209
$421$	−1.97121e11	−0.305819	−0.152910	−	0.988240i	$-0.548864\pi$
$421$	−1.97121e11	−0.305819	−0.152910	+	0.988240i	$0.548864\pi$
$422$	−1.68439e12	−2.58545
$423$	7.34845e10	0.111600
$424$	−8.76027e11	−1.31635
$425$	7.54692e11	1.12207
$426$	6.98497e11	1.02759
$427$	5.63881e11	0.820847
$428$	2.23893e12	3.22510
$429$	7.39976e11	1.05477
$430$	7.65023e10	0.107911
$431$	−1.11083e12	−1.55060	−0.775301	−	0.631592i	$-0.782402\pi$
$431$	−1.11083e12	−1.55060	−0.775301	+	0.631592i	$0.782402\pi$
$432$	7.39050e10	0.102093
$433$	1.29398e12	1.76901	0.884506	−	0.466528i	$-0.154495\pi$
$433$	1.29398e12	1.76901	0.884506	+	0.466528i	$0.154495\pi$
$434$	2.43217e11	0.329071
$435$	−1.19832e11	−0.160461
$436$	9.86649e11	1.30760
$437$	1.19799e12	1.57140
$438$	−1.22868e11	−0.159516
$439$	−4.93869e10	−0.0634631	−0.0317316	−	0.999496i	$-0.510102\pi$
$439$	−4.93869e10	−0.0634631	−0.0317316	+	0.999496i	$0.510102\pi$
$440$	−2.91521e11	−0.370794
$441$	−1.32362e11	−0.166644
$442$	−2.44886e12	−3.05186
$443$	−1.04957e12	−1.29477	−0.647386	−	0.762162i	$-0.724138\pi$
$443$	−1.04957e12	−1.29477	−0.647386	+	0.762162i	$0.724138\pi$
$444$	−3.07689e10	−0.0375741
$445$	2.73482e11	0.330604
$446$	1.35127e12	1.61709
$447$	5.23932e11	0.620713
$448$	8.39115e11	0.984170
$449$	5.61708e11	0.652232	0.326116	−	0.945330i	$-0.394260\pi$
$449$	5.61708e11	0.652232	0.326116	+	0.945330i	$0.394260\pi$
$450$	4.64116e11	0.533544
$451$	4.53760e11	0.516454
$452$	1.17519e12	1.32430
$453$	−7.98051e11	−0.890408
$454$	−1.49832e12	−1.65521
$455$	−2.20378e11	−0.241055
$456$	7.75901e11	0.840358
$457$	2.07985e11	0.223054	0.111527	−	0.993761i	$-0.464426\pi$
$457$	2.07985e11	0.223054	0.111527	+	0.993761i	$0.464426\pi$
$458$	1.87701e11	0.199330
$459$	−2.15988e11	−0.227129
$460$	5.92857e11	0.617362
$461$	−9.15854e11	−0.944435	−0.472217	−	0.881482i	$-0.656546\pi$
$461$	−9.15854e11	−0.944435	−0.472217	+	0.881482i	$0.656546\pi$
$462$	−8.00584e11	−0.817557
$463$	1.29254e12	1.30716	0.653580	−	0.756857i	$-0.273266\pi$
$463$	1.29254e12	1.30716	0.653580	+	0.756857i	$0.273266\pi$
$464$	6.63317e11	0.664340
$465$	−3.57064e10	−0.0354167
$466$	2.22784e12	2.18850
$467$	−1.89579e12	−1.84444	−0.922218	−	0.386669i	$-0.873626\pi$
$467$	−1.89579e12	−1.84444	−0.922218	+	0.386669i	$0.873626\pi$
$468$	−9.74653e11	−0.939169
$469$	3.75042e11	0.357933
$470$	1.32334e11	0.125093
$471$	−6.57246e11	−0.615367
$472$	1.97192e11	0.182873
$473$	−3.73966e11	−0.343524
$474$	1.31815e12	1.19940
$475$	1.09304e12	0.985176
$476$	1.71468e12	1.53092
$477$	3.53189e11	0.312373
$478$	8.58031e11	0.751757
$479$	−8.05471e11	−0.699101	−0.349551	−	0.936917i	$-0.613666\pi$
$479$	−8.05471e11	−0.699101	−0.349551	+	0.936917i	$0.613666\pi$
$480$	−7.62330e10	−0.0655477
$481$	6.39738e10	0.0544941
$482$	1.49130e12	1.25850
$483$	7.40548e11	0.619143
$484$	9.18457e11	0.760772
$485$	3.75748e10	0.0308361
$486$	−1.32827e11	−0.108000
$487$	−8.81732e11	−0.710324	−0.355162	−	0.934805i	$-0.615574\pi$
$487$	−8.81732e11	−0.710324	−0.355162	+	0.934805i	$0.615574\pi$
$488$	2.04274e12	1.63051
$489$	7.37910e11	0.583597
$490$	−2.38364e11	−0.186792
$491$	1.27407e12	0.989299	0.494649	−	0.869093i	$-0.335296\pi$
$491$	1.27407e12	0.989299	0.494649	+	0.869093i	$0.335296\pi$
$492$	−5.97666e11	−0.459849
$493$	−1.93855e12	−1.47797
$494$	−3.54675e12	−2.67953
$495$	1.17533e11	0.0879906
$496$	1.97649e11	0.146632
$497$	1.01689e12	0.747600
$498$	−2.01912e12	−1.47106
$499$	−1.28674e12	−0.929050	−0.464525	−	0.885560i	$-0.653775\pi$
$499$	−1.28674e12	−0.929050	−0.464525	+	0.885560i	$0.653775\pi$
$500$	1.10986e12	0.794151
$501$	1.08505e12	0.769448
$502$	−3.51409e12	−2.46971
$503$	2.49635e12	1.73880	0.869401	−	0.494107i	$-0.164505\pi$
$503$	2.49635e12	1.73880	0.869401	+	0.494107i	$0.164505\pi$
$504$	4.79629e11	0.331107
$505$	−2.23454e11	−0.152889
$506$	−4.47795e12	−3.03670
$507$	1.16751e12	0.784736
$508$	−5.11884e12	−3.41024
$509$	−7.37598e11	−0.487068	−0.243534	−	0.969892i	$-0.578307\pi$
$509$	−7.37598e11	−0.487068	−0.243534	+	0.969892i	$0.578307\pi$
$510$	−3.88962e11	−0.254590
$511$	−1.78874e11	−0.116052
$512$	1.58068e12	1.01655
$513$	−3.12821e11	−0.199419
$514$	4.66830e12	2.95002
$515$	−2.53255e10	−0.0158645
$516$	4.92567e11	0.305873
$517$	−6.46890e11	−0.398220
$518$	−6.92136e10	−0.0422384
$519$	1.16172e11	0.0702828
$520$	−7.98350e11	−0.478826
$521$	−9.55838e11	−0.568348	−0.284174	−	0.958773i	$-0.591719\pi$
$521$	−9.55838e11	−0.568348	−0.284174	+	0.958773i	$0.591719\pi$
$522$	−1.19216e12	−0.702776
$523$	−2.33681e12	−1.36573	−0.682867	−	0.730542i	$-0.739267\pi$
$523$	−2.33681e12	−1.36573	−0.682867	+	0.730542i	$0.739267\pi$
$524$	−4.10969e12	−2.38132
$525$	6.75670e11	0.388166
$526$	−1.32447e12	−0.754411
$527$	−5.77632e11	−0.326215
$528$	−6.50592e11	−0.364298
$529$	2.34100e12	1.29972
$530$	6.36039e11	0.350140
$531$	−7.95020e10	−0.0433963
$532$	2.48341e12	1.34414
$533$	1.24265e12	0.666924
$534$	2.72076e12	1.44795
$535$	−7.39388e11	−0.390194
$536$	1.35864e12	0.710990
$537$	4.09696e11	0.212607
$538$	−1.36710e12	−0.703525
$539$	1.16520e12	0.594634
$540$	−1.54808e11	−0.0783467
$541$	−5.47294e10	−0.0274684	−0.0137342	−	0.999906i	$-0.504372\pi$
$541$	−5.47294e10	−0.0274684	−0.0137342	+	0.999906i	$0.504372\pi$
$542$	−2.18495e12	−1.08754
$543$	5.93951e11	0.293191
$544$	−1.23324e12	−0.603745
$545$	−3.25833e11	−0.158202
$546$	−2.19245e12	−1.05575
$547$	4.41803e11	0.211002	0.105501	−	0.994419i	$-0.466355\pi$
$547$	4.41803e11	0.211002	0.105501	+	0.994419i	$0.466355\pi$
$548$	−5.90214e12	−2.79574
$549$	−8.23574e11	−0.386925
$550$	−4.08565e12	−1.90383
$551$	−2.80765e12	−1.29766
$552$	2.68274e12	1.22985
$553$	1.91899e12	0.872589
$554$	6.24217e12	2.81541
$555$	1.01612e10	0.00454596
$556$	8.86627e11	0.393463
$557$	3.93748e12	1.73329	0.866643	−	0.498929i	$-0.166273\pi$
$557$	3.93748e12	1.73329	0.866643	+	0.498929i	$0.166273\pi$
$558$	−3.55229e11	−0.155115
$559$	−1.02413e12	−0.443611
$560$	1.93758e11	0.0832555
$561$	1.90136e12	0.810461
$562$	1.69568e12	0.717018
$563$	−2.31827e11	−0.0972472	−0.0486236	−	0.998817i	$-0.515483\pi$
$563$	−2.31827e11	−0.0972472	−0.0486236	+	0.998817i	$0.515483\pi$
$564$	8.52046e11	0.354574
$565$	−3.88097e11	−0.160222
$566$	−3.19392e12	−1.30813
$567$	−1.93373e11	−0.0785726
$568$	3.68382e12	1.48502
$569$	1.34218e12	0.536792	0.268396	−	0.963309i	$-0.413506\pi$
$569$	1.34218e12	0.536792	0.268396	+	0.963309i	$0.413506\pi$
$570$	−5.63342e11	−0.223530
$571$	8.66924e11	0.341286	0.170643	−	0.985333i	$-0.445416\pi$
$571$	8.66924e11	0.341286	0.170643	+	0.985333i	$0.445416\pi$
$572$	8.57995e12	3.35122
$573$	5.08939e11	0.197229
$574$	−1.34443e12	−0.516933
$575$	3.77927e12	1.44179
$576$	−1.22556e12	−0.463911
$577$	3.24740e11	0.121968	0.0609839	−	0.998139i	$-0.480576\pi$
$577$	3.24740e11	0.121968	0.0609839	+	0.998139i	$0.480576\pi$
$578$	−1.77479e12	−0.661413
$579$	2.34653e12	0.867704
$580$	−1.38944e12	−0.509816
$581$	−2.93948e12	−1.07023
$582$	3.73817e11	0.135053
$583$	−3.10915e12	−1.11464
$584$	−6.47995e11	−0.230523
$585$	3.21872e11	0.113627
$586$	−4.21078e11	−0.147511
$587$	−8.84855e11	−0.307610	−0.153805	−	0.988101i	$-0.549153\pi$
$587$	−8.84855e11	−0.307610	−0.153805	+	0.988101i	$0.549153\pi$
$588$	−1.53473e12	−0.529461
$589$	−8.36598e11	−0.286417
$590$	−1.43171e11	−0.0486430
$591$	−2.58613e12	−0.871979
$592$	−5.62462e10	−0.0188211
$593$	−1.35974e12	−0.451553	−0.225777	−	0.974179i	$-0.572492\pi$
$593$	−1.35974e12	−0.451553	−0.225777	+	0.974179i	$0.572492\pi$
$594$	1.16929e12	0.385374
$595$	−5.66259e11	−0.185220
$596$	6.07494e12	1.97212
$597$	−3.48432e12	−1.12262
$598$	−1.22632e13	−3.92145
$599$	1.06411e11	0.0337728	0.0168864	−	0.999857i	$-0.494625\pi$
$599$	1.06411e11	0.0337728	0.0168864	+	0.999857i	$0.494625\pi$
$600$	2.44771e12	0.771045
$601$	−3.77150e12	−1.17918	−0.589589	−	0.807704i	$-0.700710\pi$
$601$	−3.77150e12	−1.17918	−0.589589	+	0.807704i	$0.700710\pi$
$602$	1.10801e12	0.343843
$603$	−5.47766e11	−0.168720
$604$	−9.25333e12	−2.82899
$605$	−3.03313e11	−0.0920433
$606$	−2.22306e12	−0.669613
$607$	4.83527e12	1.44568	0.722839	−	0.691017i	$-0.242837\pi$
$607$	4.83527e12	1.44568	0.722839	+	0.691017i	$0.242837\pi$
$608$	−1.78613e12	−0.530088
$609$	−1.73557e12	−0.511287
$610$	−1.48313e12	−0.433706
$611$	−1.77155e12	−0.514242
$612$	−2.50436e12	−0.721632
$613$	9.11706e11	0.260785	0.130393	−	0.991462i	$-0.458376\pi$
$613$	9.11706e11	0.260785	0.130393	+	0.991462i	$0.458376\pi$
$614$	−6.34099e12	−1.80053
$615$	1.97375e11	0.0556356
$616$	−4.22222e12	−1.18148
$617$	3.14494e12	0.873633	0.436816	−	0.899551i	$-0.356106\pi$
$617$	3.14494e12	0.873633	0.436816	+	0.899551i	$0.356106\pi$
$618$	−2.51953e11	−0.0694820
$619$	−5.36136e12	−1.46780	−0.733900	−	0.679257i	$-0.762302\pi$
$619$	−5.36136e12	−1.46780	−0.733900	+	0.679257i	$0.762302\pi$
$620$	−4.14013e11	−0.112526
$621$	−1.08160e12	−0.291847
$622$	7.05352e12	1.88951
$623$	3.96094e12	1.05342
$624$	−1.78169e12	−0.470437
$625$	3.26029e12	0.854665
$626$	−6.05482e12	−1.57586
$627$	2.75379e12	0.711585
$628$	−7.62071e12	−1.95514
$629$	1.64380e11	0.0418718
$630$	−3.48235e11	−0.0880723
$631$	4.20961e11	0.105708	0.0528542	−	0.998602i	$-0.483168\pi$
$631$	4.20961e11	0.105708	0.0528542	+	0.998602i	$0.483168\pi$
$632$	6.95182e12	1.73329
$633$	3.58150e12	0.886643
$634$	−7.54262e12	−1.85405
$635$	1.69046e12	0.412593
$636$	4.09519e12	0.992469
$637$	3.19097e12	0.767883
$638$	1.04947e13	2.50770
$639$	−1.48521e12	−0.352399
$640$	−1.72519e12	−0.406468
$641$	−7.18622e12	−1.68128	−0.840639	−	0.541596i	$-0.817820\pi$
$641$	−7.18622e12	−1.68128	−0.840639	+	0.541596i	$0.817820\pi$
$642$	−7.35588e12	−1.70894
$643$	8.02563e11	0.185153	0.0925763	−	0.995706i	$-0.470490\pi$
$643$	8.02563e11	0.185153	0.0925763	+	0.995706i	$0.470490\pi$
$644$	8.58658e12	1.96713
$645$	−1.62666e11	−0.0370066
$646$	−9.11334e12	−2.05888
$647$	−3.90264e12	−0.875568	−0.437784	−	0.899080i	$-0.644236\pi$
$647$	−3.90264e12	−0.875568	−0.437784	+	0.899080i	$0.644236\pi$
$648$	−7.00520e11	−0.156075
$649$	6.99863e11	0.154850
$650$	−1.11888e13	−2.45852
$651$	−5.17150e11	−0.112850
$652$	8.55600e12	1.85420
$653$	2.14699e12	0.462084	0.231042	−	0.972944i	$-0.425787\pi$
$653$	2.14699e12	0.462084	0.231042	+	0.972944i	$0.425787\pi$
$654$	−3.24158e12	−0.692879
$655$	1.35719e12	0.288108
$656$	−1.09255e12	−0.230342
$657$	2.61253e11	0.0547038
$658$	1.91665e12	0.398589
$659$	−2.75092e11	−0.0568191	−0.0284096	−	0.999596i	$-0.509044\pi$
$659$	−2.75092e11	−0.0568191	−0.0284096	+	0.999596i	$0.509044\pi$
$660$	1.36278e12	0.279563
$661$	3.39394e12	0.691509	0.345755	−	0.938325i	$-0.387623\pi$
$661$	3.39394e12	0.691509	0.345755	+	0.938325i	$0.387623\pi$
$662$	5.81487e12	1.17674
$663$	5.20700e12	1.04659
$664$	−1.06487e13	−2.12588
$665$	−8.20126e11	−0.162623
$666$	1.01090e11	0.0199100
$667$	−9.70767e12	−1.89910
$668$	1.25810e13	2.44468
$669$	−2.87319e12	−0.554558
$670$	−9.86442e11	−0.189119
$671$	7.24999e12	1.38066
$672$	−1.10411e12	−0.208858
$673$	−1.26928e12	−0.238501	−0.119251	−	0.992864i	$-0.538049\pi$
$673$	−1.26928e12	−0.238501	−0.119251	+	0.992864i	$0.538049\pi$
$674$	1.13726e13	2.12271
$675$	−9.86847e11	−0.182971
$676$	1.35371e13	2.49325
$677$	−9.30849e12	−1.70306	−0.851530	−	0.524306i	$-0.824325\pi$
$677$	−9.30849e12	−1.70306	−0.851530	+	0.524306i	$0.824325\pi$
$678$	−3.86102e12	−0.701728
$679$	5.44210e11	0.0982546
$680$	−2.05135e12	−0.367917
$681$	3.18586e12	0.567629
$682$	3.12711e12	0.553495
$683$	−7.85825e12	−1.38176	−0.690880	−	0.722969i	$-0.742777\pi$
$683$	−7.85825e12	−1.38176	−0.690880	+	0.722969i	$0.742777\pi$
$684$	−3.62713e12	−0.633593
$685$	1.94914e12	0.338248
$686$	−1.03579e13	−1.78572
$687$	−3.99108e11	−0.0683573
$688$	9.00423e11	0.153214
$689$	−8.51460e12	−1.43939
$690$	−1.94780e12	−0.327133
$691$	−1.07981e12	−0.180176	−0.0900880	−	0.995934i	$-0.528715\pi$
$691$	−1.07981e12	−0.180176	−0.0900880	+	0.995934i	$0.528715\pi$
$692$	1.34701e12	0.223302
$693$	1.70228e12	0.280369
$694$	−1.20908e13	−1.97850
$695$	−2.92802e11	−0.0476038
$696$	−6.28735e12	−1.01561
$697$	3.19298e12	0.512447
$698$	−1.74147e12	−0.277694
$699$	−4.73703e12	−0.750514
$700$	7.83433e12	1.23328
$701$	−6.14310e11	−0.0960853	−0.0480426	−	0.998845i	$-0.515298\pi$
$701$	−6.14310e11	−0.0960853	−0.0480426	+	0.998845i	$0.515298\pi$
$702$	3.20217e12	0.497654
$703$	2.38076e11	0.0367634
$704$	1.07887e13	1.65537
$705$	−2.81381e11	−0.0428987
$706$	8.49958e12	1.28759
$707$	−3.23637e12	−0.487160
$708$	−9.21819e11	−0.137878
$709$	8.40205e11	0.124875	0.0624377	−	0.998049i	$-0.480113\pi$
$709$	8.40205e11	0.124875	0.0624377	+	0.998049i	$0.480113\pi$
$710$	−2.67464e12	−0.395005
$711$	−2.80277e12	−0.411315
$712$	1.43491e13	2.09249
$713$	−2.89261e12	−0.419166
$714$	−5.63348e12	−0.811213
$715$	−2.83346e12	−0.405453
$716$	4.75039e12	0.675493
$717$	−1.82443e12	−0.257804
$718$	8.33377e11	0.117026
$719$	1.19567e13	1.66852	0.834259	−	0.551373i	$-0.185896\pi$
$719$	1.19567e13	1.66852	0.834259	+	0.551373i	$0.185896\pi$
$720$	−2.82992e11	−0.0392444
$721$	−3.66799e11	−0.0505498
$722$	−9.06445e11	−0.124144
$723$	−3.17094e12	−0.431585
$724$	6.88681e12	0.931525
$725$	−8.85721e12	−1.19063
$726$	−3.01754e12	−0.403124
$727$	1.29650e13	1.72135	0.860674	−	0.509157i	$-0.170043\pi$
$727$	1.29650e13	1.72135	0.860674	+	0.509157i	$0.170043\pi$
$728$	−1.15628e13	−1.52571
$729$	2.82430e11	0.0370370
$730$	4.70477e11	0.0613176
$731$	−2.63150e12	−0.340859
$732$	−9.54926e12	−1.22933
$733$	4.24918e12	0.543673	0.271836	−	0.962344i	$-0.412369\pi$
$733$	4.24918e12	0.543673	0.271836	+	0.962344i	$0.412369\pi$
$734$	1.49740e13	1.90417
$735$	5.06833e11	0.0640577
$736$	−6.17570e12	−0.775776
$737$	4.82203e12	0.602041
$738$	1.96360e12	0.243669
$739$	1.58146e13	1.95056	0.975279	−	0.220979i	$-0.0709252\pi$
$739$	1.58146e13	1.95056	0.975279	+	0.220979i	$0.0709252\pi$
$740$	1.17818e11	0.0144434
$741$	7.54142e12	0.918907
$742$	9.21199e12	1.11567
$743$	−4.05714e11	−0.0488394	−0.0244197	−	0.999702i	$-0.507774\pi$
$743$	−4.05714e11	−0.0488394	−0.0244197	+	0.999702i	$0.507774\pi$
$744$	−1.87345e12	−0.224163
$745$	−2.00620e12	−0.238601
$746$	4.33071e12	0.511958
$747$	4.29324e12	0.504478
$748$	2.20461e13	2.57499
$749$	−1.07088e13	−1.24330
$750$	−3.64639e12	−0.420811
$751$	6.14962e12	0.705453	0.352727	−	0.935726i	$-0.385255\pi$
$751$	6.14962e12	0.705453	0.352727	+	0.935726i	$0.385255\pi$
$752$	1.55756e12	0.177609
$753$	7.47199e12	0.846952
$754$	2.87403e13	3.23833
$755$	3.05584e12	0.342271
$756$	−2.24214e12	−0.249640
$757$	8.16991e12	0.904245	0.452122	−	0.891956i	$-0.350667\pi$
$757$	8.16991e12	0.904245	0.452122	+	0.891956i	$0.350667\pi$
$758$	2.54859e13	2.80407
$759$	9.52145e12	1.04139
$760$	−2.97102e12	−0.323031
$761$	1.02310e13	1.10583	0.552916	−	0.833237i	$-0.313515\pi$
$761$	1.02310e13	1.10583	0.552916	+	0.833237i	$0.313515\pi$
$762$	1.68177e13	1.80704
$763$	−4.71917e12	−0.504086
$764$	5.90110e12	0.626632
$765$	8.27047e11	0.0873079
$766$	4.11841e12	0.432215
$767$	1.91662e12	0.199966
$768$	−9.41640e12	−0.976696
$769$	1.60525e13	1.65529	0.827647	−	0.561249i	$-0.189679\pi$
$769$	1.60525e13	1.65529	0.827647	+	0.561249i	$0.189679\pi$
$770$	3.06554e12	0.314267
$771$	−9.92618e12	−1.01167
$772$	2.72078e13	2.75686
$773$	1.14431e13	1.15276	0.576378	−	0.817183i	$-0.304465\pi$
$773$	1.14431e13	1.15276	0.576378	+	0.817183i	$0.304465\pi$
$774$	−1.61830e12	−0.162078
$775$	−2.63919e12	−0.262793
$776$	1.97148e12	0.195171
$777$	1.47168e11	0.0144850
$778$	2.76057e12	0.270141
$779$	4.62447e12	0.449928
$780$	3.73207e12	0.361014
$781$	1.30744e13	1.25746
$782$	−3.15101e13	−3.01314
$783$	2.53488e12	0.241007
$784$	−2.80552e12	−0.265211
$785$	2.51668e12	0.236545
$786$	1.35022e13	1.26183
$787$	7.94547e12	0.738301	0.369150	−	0.929370i	$-0.379649\pi$
$787$	7.94547e12	0.738301	0.369150	+	0.929370i	$0.379649\pi$
$788$	−2.99859e13	−2.77044
$789$	2.81622e12	0.258714
$790$	−5.04736e12	−0.461044
$791$	−5.62096e12	−0.510525
$792$	6.16674e12	0.556919
$793$	1.98546e13	1.78292
$794$	−1.01677e13	−0.907881
$795$	−1.35240e12	−0.120076
$796$	−4.04004e13	−3.56678
$797$	3.65709e12	0.321050	0.160525	−	0.987032i	$-0.448681\pi$
$797$	3.65709e12	0.321050	0.160525	+	0.987032i	$0.448681\pi$
$798$	−8.15910e12	−0.712245
$799$	−4.55198e12	−0.395130
$800$	−5.63466e12	−0.486366
$801$	−5.78514e12	−0.496555
$802$	−2.22804e13	−1.90169
$803$	−2.29983e12	−0.195198
$804$	−6.35129e12	−0.536056
$805$	−2.83565e12	−0.237997
$806$	8.56379e12	0.714757
$807$	2.90685e12	0.241264
$808$	−1.17242e13	−0.967683
$809$	−8.52827e12	−0.699991	−0.349995	−	0.936751i	$-0.613817\pi$
$809$	−8.52827e12	−0.699991	−0.349995	+	0.936751i	$0.613817\pi$
$810$	5.08612e11	0.0415149
$811$	−9.42454e11	−0.0765009	−0.0382504	−	0.999268i	$-0.512178\pi$
$811$	−9.42454e11	−0.0765009	−0.0382504	+	0.999268i	$0.512178\pi$
$812$	−2.01238e13	−1.62445
$813$	4.64584e12	0.372956
$814$	−8.89899e11	−0.0710446
$815$	−2.82555e12	−0.224333
$816$	−4.57803e12	−0.361471
$817$	−3.81126e12	−0.299274
$818$	−2.52651e13	−1.97302
$819$	4.66179e12	0.362056
$820$	2.28854e12	0.176765
$821$	−1.99364e13	−1.53145	−0.765725	−	0.643168i	$-0.777620\pi$
$821$	−1.99364e13	−1.53145	−0.765725	+	0.643168i	$0.777620\pi$
$822$	1.93912e13	1.48143
$823$	6.25923e12	0.475578	0.237789	−	0.971317i	$-0.423577\pi$
$823$	6.25923e12	0.475578	0.237789	+	0.971317i	$0.423577\pi$
$824$	−1.32878e12	−0.100411
$825$	8.68729e12	0.652893
$826$	−2.07360e12	−0.154994
$827$	1.22495e13	0.910633	0.455317	−	0.890330i	$-0.349526\pi$
$827$	1.22495e13	0.910633	0.455317	+	0.890330i	$0.349526\pi$
$828$	−1.25411e13	−0.927254
$829$	−8.99661e12	−0.661582	−0.330791	−	0.943704i	$-0.607315\pi$
$829$	−8.99661e12	−0.661582	−0.330791	+	0.943704i	$0.607315\pi$
$830$	7.73147e12	0.565471
$831$	−1.32727e13	−0.965505
$832$	2.95457e13	2.13766
$833$	8.19916e12	0.590020
$834$	−2.91296e12	−0.208491
$835$	−4.15479e12	−0.295774
$836$	3.19299e13	2.26084
$837$	7.55321e11	0.0531945
$838$	2.16555e13	1.51695
$839$	−8.68437e12	−0.605076	−0.302538	−	0.953137i	$-0.597834\pi$
$839$	−8.68437e12	−0.605076	−0.302538	+	0.953137i	$0.597834\pi$
$840$	−1.83656e12	−0.127277
$841$	8.24405e12	0.568275
$842$	7.50924e12	0.514863
$843$	−3.60551e12	−0.245891
$844$	4.15272e13	2.81703
$845$	−4.47053e12	−0.301650
$846$	−2.79935e12	−0.187884
$847$	−4.39300e12	−0.293283
$848$	7.48610e12	0.497135
$849$	6.79121e12	0.448603
$850$	−2.87496e13	−1.88906
$851$	8.23166e11	0.0538027
$852$	−1.72209e13	−1.11964
$853$	−6.24777e12	−0.404068	−0.202034	−	0.979379i	$-0.564755\pi$
$853$	−6.24777e12	−0.404068	−0.202034	+	0.979379i	$0.564755\pi$
$854$	−2.14807e13	−1.38194
$855$	1.19783e12	0.0766563
$856$	−3.87943e13	−2.46965
$857$	−1.55002e13	−0.981578	−0.490789	−	0.871278i	$-0.663291\pi$
$857$	−1.55002e13	−0.981578	−0.490789	+	0.871278i	$0.663291\pi$
$858$	−2.81890e13	−1.77577
$859$	−1.19277e13	−0.747459	−0.373730	−	0.927538i	$-0.621921\pi$
$859$	−1.19277e13	−0.747459	−0.373730	+	0.927538i	$0.621921\pi$
$860$	−1.88610e12	−0.117577
$861$	2.85865e12	0.177275
$862$	4.23165e13	2.61052
$863$	−1.61967e13	−0.993982	−0.496991	−	0.867756i	$-0.665562\pi$
$863$	−1.61967e13	−0.993982	−0.496991	+	0.867756i	$0.665562\pi$
$864$	1.61261e12	0.0984502
$865$	−4.44838e11	−0.0270165
$866$	−4.92933e13	−2.97823
$867$	3.77373e12	0.226822
$868$	−5.99631e12	−0.358546
$869$	2.46731e13	1.46769
$870$	4.56493e12	0.270145
$871$	1.32054e13	0.777447
$872$	−1.70959e13	−1.00131
$873$	−7.94844e11	−0.0463146
$874$	−4.56368e13	−2.64554
$875$	−5.30849e12	−0.306150
$876$	3.02921e12	0.173804
$877$	−1.35706e13	−0.774643	−0.387322	−	0.921945i	$-0.626600\pi$
$877$	−1.35706e13	−0.774643	−0.387322	+	0.921945i	$0.626600\pi$
$878$	1.88137e12	0.106844
$879$	8.95335e11	0.0505866
$880$	2.49120e12	0.140035
$881$	−1.21126e13	−0.677401	−0.338700	−	0.940894i	$-0.609987\pi$
$881$	−1.21126e13	−0.677401	−0.338700	+	0.940894i	$0.609987\pi$
$882$	5.04227e12	0.280555
$883$	−2.64760e13	−1.46564	−0.732822	−	0.680420i	$-0.761797\pi$
$883$	−2.64760e13	−1.46564	−0.732822	+	0.680420i	$0.761797\pi$
$884$	6.03747e13	3.32522
$885$	3.04423e11	0.0166814
$886$	3.99827e13	2.17982
$887$	2.95615e12	0.160350	0.0801752	−	0.996781i	$-0.474452\pi$
$887$	2.95615e12	0.160350	0.0801752	+	0.996781i	$0.474452\pi$
$888$	5.33138e11	0.0287728
$889$	2.44835e13	1.31467
$890$	−1.04181e13	−0.556590
$891$	−2.48625e12	−0.132159
$892$	−3.33144e13	−1.76194
$893$	−6.59274e12	−0.346924
$894$	−1.99589e13	−1.04500
$895$	−1.56878e12	−0.0817256
$896$	−2.49865e13	−1.29515
$897$	2.60751e13	1.34481
$898$	−2.13980e13	−1.09807
$899$	6.77920e12	0.346147
$900$	−1.14424e13	−0.581334
$901$	−2.18782e13	−1.10599
$902$	−1.72857e13	−0.869478
$903$	−2.35596e12	−0.117916
$904$	−2.03627e13	−1.01409
$905$	−2.27431e12	−0.112702
$906$	3.04013e13	1.49905
$907$	−2.48130e13	−1.21744	−0.608718	−	0.793386i	$-0.708316\pi$
$907$	−2.48130e13	−1.21744	−0.608718	+	0.793386i	$0.708316\pi$
$908$	3.69398e13	1.80347
$909$	4.72687e12	0.229634
$910$	8.39517e12	0.405829
$911$	−2.19699e13	−1.05681	−0.528404	−	0.848993i	$-0.677209\pi$
$911$	−2.19699e13	−1.05681	−0.528404	+	0.848993i	$0.677209\pi$
$912$	−6.63047e12	−0.317371
$913$	−3.77938e13	−1.80012
$914$	−7.92309e12	−0.375523
$915$	3.15357e12	0.148733
$916$	−4.62762e12	−0.217184
$917$	1.96568e13	0.918015
$918$	8.22795e12	0.382384
$919$	6.05423e12	0.279988	0.139994	−	0.990152i	$-0.455292\pi$
$919$	6.05423e12	0.279988	0.139994	+	0.990152i	$0.455292\pi$
$920$	−1.02726e13	−0.472752
$921$	1.34828e13	0.617465
$922$	3.48890e13	1.59001
$923$	3.58052e13	1.62382
$924$	1.97377e13	0.890786
$925$	7.51050e11	0.0337311
$926$	−4.92385e13	−2.20067
$927$	5.35727e11	0.0238278
$928$	1.44736e13	0.640633
$929$	2.20766e13	0.972437	0.486219	−	0.873837i	$-0.338376\pi$
$929$	2.20766e13	0.972437	0.486219	+	0.873837i	$0.338376\pi$
$930$	1.36022e12	0.0596259
$931$	1.18750e13	0.518038
$932$	−5.49255e13	−2.38453
$933$	−1.49979e13	−0.647980
$934$	7.22190e13	3.10521
$935$	−7.28056e12	−0.311539
$936$	1.68880e13	0.719179
$937$	−2.81671e13	−1.19375	−0.596875	−	0.802334i	$-0.703591\pi$
$937$	−2.81671e13	−1.19375	−0.596875	+	0.802334i	$0.703591\pi$
$938$	−1.42870e13	−0.602600
$939$	1.28743e13	0.540417
$940$	−3.26259e12	−0.136297
$941$	−3.07024e12	−0.127650	−0.0638248	−	0.997961i	$-0.520330\pi$
$941$	−3.07024e12	−0.127650	−0.0638248	+	0.997961i	$0.520330\pi$
$942$	2.50374e13	1.03600
$943$	1.59895e13	0.658463
$944$	−1.68511e12	−0.0690642
$945$	7.40449e11	0.0302031
$946$	1.42460e13	0.578341
$947$	−1.07551e13	−0.434550	−0.217275	−	0.976110i	$-0.569717\pi$
$947$	−1.07551e13	−0.434550	−0.217275	+	0.976110i	$0.569717\pi$
$948$	−3.24979e13	−1.30683
$949$	−6.29824e12	−0.252070
$950$	−4.16387e13	−1.65860
$951$	1.60378e13	0.635818
$952$	−2.97105e13	−1.17231
$953$	−3.95867e13	−1.55465	−0.777323	−	0.629102i	$-0.783423\pi$
$953$	−3.95867e13	−1.55465	−0.777323	+	0.629102i	$0.783423\pi$
$954$	−1.34545e13	−0.525897
$955$	−1.94879e12	−0.0758142
$956$	−2.11540e13	−0.819093
$957$	−2.23148e13	−0.859980
$958$	3.06840e13	1.17697
$959$	2.82301e13	1.07778
$960$	4.69284e12	0.178326
$961$	−2.44196e13	−0.923599
$962$	−2.43705e12	−0.0917436
$963$	1.56408e13	0.586056
$964$	−3.67668e13	−1.37123
$965$	−8.98515e12	−0.333543
$966$	−2.82108e13	−1.04236
$967$	1.84320e13	0.677881	0.338941	−	0.940808i	$-0.389931\pi$
$967$	1.84320e13	0.677881	0.338941	+	0.940808i	$0.389931\pi$
$968$	−1.59143e13	−0.582570
$969$	1.93776e13	0.706063
$970$	−1.43139e12	−0.0519141
$971$	−3.67568e13	−1.32694	−0.663470	−	0.748203i	$-0.730917\pi$
$971$	−3.67568e13	−1.32694	−0.663470	+	0.748203i	$0.730917\pi$
$972$	3.27474e12	0.117674
$973$	−4.24076e12	−0.151683
$974$	3.35891e13	1.19587
$975$	2.37907e13	0.843115
$976$	−1.74563e13	−0.615782
$977$	2.58039e13	0.906066	0.453033	−	0.891494i	$-0.350342\pi$
$977$	2.58039e13	0.906066	0.453033	+	0.891494i	$0.350342\pi$
$978$	−2.81103e13	−0.982517
$979$	5.09270e13	1.77185
$980$	5.87668e12	0.203523
$981$	6.89256e12	0.237613
$982$	−4.85351e13	−1.66554
$983$	−3.96549e13	−1.35459	−0.677293	−	0.735713i	$-0.736847\pi$
$983$	−3.96549e13	−1.35459	−0.677293	+	0.735713i	$0.736847\pi$
$984$	1.03559e13	0.352135
$985$	9.90261e12	0.335186
$986$	7.38480e13	2.48824
$987$	−4.07536e12	−0.136691
$988$	8.74421e13	2.91954
$989$	−1.31777e13	−0.437983
$990$	−4.47736e12	−0.148137
$991$	3.92245e13	1.29189	0.645946	−	0.763383i	$-0.276463\pi$
$991$	3.92245e13	1.29189	0.645946	+	0.763383i	$0.276463\pi$
$992$	4.31270e12	0.141399
$993$	−1.23641e13	−0.403545
$994$	−3.87378e13	−1.25862
$995$	1.33419e13	0.431533
$996$	4.97797e13	1.60282
$997$	4.61994e12	0.148084	0.0740420	−	0.997255i	$-0.476410\pi$
$997$	4.61994e12	0.148084	0.0740420	+	0.997255i	$0.476410\pi$
$998$	4.90178e13	1.56411
$999$	−2.14946e11	−0.00682786

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.10.a.d.1.3	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.10.a.d.1.3	✓	22	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q-38.0945 q^{2} +81.0000 q^{3} +939.188 q^{4} -310.159 q^{5} -3085.65 q^{6} -4492.16 q^{7} -16273.5 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q-38.0945 q^{2} +81.0000 q^{3} +939.188 q^{4} -310.159 q^{5} -3085.65 q^{6} -4492.16 q^{7} -16273.5 q^{8} +6561.00 q^{9} +11815.4 q^{10} -57757.0 q^{11} +76074.2 q^{12} -158171. q^{13} +171126. q^{14} -25122.9 q^{15} +139065. q^{16} -406420. q^{17} -249938. q^{18} -588628. q^{19} -291298. q^{20} -363865. q^{21} +2.20022e6 q^{22} -2.03523e6 q^{23} -1.31815e6 q^{24} -1.85693e6 q^{25} +6.02545e6 q^{26} +531441. q^{27} -4.21898e6 q^{28} +4.76982e6 q^{29} +957044. q^{30} +1.42127e6 q^{31} +3.03440e6 q^{32} -4.67832e6 q^{33} +1.54823e7 q^{34} +1.39329e6 q^{35} +6.16201e6 q^{36} -404459. q^{37} +2.24234e7 q^{38} -1.28119e7 q^{39} +5.04737e6 q^{40} -7.85636e6 q^{41} +1.38612e7 q^{42} +6.47482e6 q^{43} -5.42447e7 q^{44} -2.03496e6 q^{45} +7.75309e7 q^{46} +1.12002e7 q^{47} +1.12643e7 q^{48} -2.01741e7 q^{49} +7.07386e7 q^{50} -3.29200e7 q^{51} -1.48553e8 q^{52} +5.38315e7 q^{53} -2.02450e7 q^{54} +1.79139e7 q^{55} +7.31031e7 q^{56} -4.76788e7 q^{57} -1.81704e8 q^{58} -1.21174e7 q^{59} -2.35951e7 q^{60} -1.25526e8 q^{61} -5.41425e7 q^{62} -2.94731e7 q^{63} -1.86795e8 q^{64} +4.90583e7 q^{65} +1.78218e8 q^{66} -8.34881e7 q^{67} -3.81705e8 q^{68} -1.64853e8 q^{69} -5.30764e7 q^{70} -2.26370e8 q^{71} -1.06770e8 q^{72} +3.98191e7 q^{73} +1.54076e7 q^{74} -1.50411e8 q^{75} -5.52832e8 q^{76} +2.59454e8 q^{77} +4.88061e8 q^{78} -4.27187e8 q^{79} -4.31324e7 q^{80} +4.30467e7 q^{81} +2.99284e8 q^{82} +6.54358e8 q^{83} -3.41737e8 q^{84} +1.26055e8 q^{85} -2.46655e8 q^{86} +3.86356e8 q^{87} +9.39908e8 q^{88} -8.81746e8 q^{89} +7.75205e7 q^{90} +7.10531e8 q^{91} -1.91146e9 q^{92} +1.15123e8 q^{93} -4.26665e8 q^{94} +1.82568e8 q^{95} +2.45787e8 q^{96} -1.21147e8 q^{97} +7.68522e8 q^{98} -3.78944e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 46 q^{2} + 1782 q^{3} + 5974 q^{4} + 5786 q^{5} + 3726 q^{6} + 7641 q^{7} + 61395 q^{8} + 144342 q^{9}+O(q^{10}) \) 22 * q + 46 * q^2 + 1782 * q^3 + 5974 * q^4 + 5786 * q^5 + 3726 * q^6 + 7641 * q^7 + 61395 * q^8 + 144342 * q^9	\( 22 q + 46 q^{2} + 1782 q^{3} + 5974 q^{4} + 5786 q^{5} + 3726 q^{6} + 7641 q^{7} + 61395 q^{8} + 144342 q^{9} + 45337 q^{10} + 111769 q^{11} + 483894 q^{12} + 189121 q^{13} + 251053 q^{14} + 468666 q^{15} + 2311074 q^{16} + 1113841 q^{17} + 301806 q^{18} + 476068 q^{19} - 42495 q^{20} + 618921 q^{21} - 2252022 q^{22} + 7103062 q^{23} + 4972995 q^{24} + 10628442 q^{25} + 6871048 q^{26} + 11691702 q^{27} + 8112650 q^{28} + 15279316 q^{29} + 3672297 q^{30} + 17610338 q^{31} + 32378276 q^{32} + 9053289 q^{33} + 29339436 q^{34} + 7134904 q^{35} + 39195414 q^{36} + 21961411 q^{37} + 65195131 q^{38} + 15318801 q^{39} + 75185084 q^{40} + 52781575 q^{41} + 20335293 q^{42} + 76191313 q^{43} + 61127768 q^{44} + 37961946 q^{45} + 290208769 q^{46} + 160572396 q^{47} + 187196994 q^{48} + 156292703 q^{49} + 169504821 q^{50} + 90221121 q^{51} + 65465920 q^{52} - 8762038 q^{53} + 24446286 q^{54} + 147125140 q^{55} + 9671794 q^{56} + 38561508 q^{57} - 37665424 q^{58} - 266581942 q^{59} - 3442095 q^{60} + 120750754 q^{61} - 152465186 q^{62} + 50132601 q^{63} - 40658803 q^{64} + 331055798 q^{65} - 182413782 q^{66} + 41371828 q^{67} + 145606631 q^{68} + 575348022 q^{69} - 920887614 q^{70} + 261018751 q^{71} + 402812595 q^{72} + 178388 q^{73} - 303908734 q^{74} + 860903802 q^{75} - 94541144 q^{76} + 299640561 q^{77} + 556554888 q^{78} - 905381353 q^{79} + 939128289 q^{80} + 947027862 q^{81} - 551739753 q^{82} + 1173257869 q^{83} + 657124650 q^{84} - 1546633210 q^{85} + 1384869460 q^{86} + 1237624596 q^{87} + 189740713 q^{88} + 898004974 q^{89} + 297456057 q^{90} + 591272339 q^{91} + 4328210270 q^{92} + 1426437378 q^{93} + 122568068 q^{94} + 2487967134 q^{95} + 2622640356 q^{96} + 3175709684 q^{97} + 5095778404 q^{98} + 733316409 q^{99}+O(q^{100}) \) 22 * q + 46 * q^2 + 1782 * q^3 + 5974 * q^4 + 5786 * q^5 + 3726 * q^6 + 7641 * q^7 + 61395 * q^8 + 144342 * q^9 + 45337 * q^10 + 111769 * q^11 + 483894 * q^12 + 189121 * q^13 + 251053 * q^14 + 468666 * q^15 + 2311074 * q^16 + 1113841 * q^17 + 301806 * q^18 + 476068 * q^19 - 42495 * q^20 + 618921 * q^21 - 2252022 * q^22 + 7103062 * q^23 + 4972995 * q^24 + 10628442 * q^25 + 6871048 * q^26 + 11691702 * q^27 + 8112650 * q^28 + 15279316 * q^29 + 3672297 * q^30 + 17610338 * q^31 + 32378276 * q^32 + 9053289 * q^33 + 29339436 * q^34 + 7134904 * q^35 + 39195414 * q^36 + 21961411 * q^37 + 65195131 * q^38 + 15318801 * q^39 + 75185084 * q^40 + 52781575 * q^41 + 20335293 * q^42 + 76191313 * q^43 + 61127768 * q^44 + 37961946 * q^45 + 290208769 * q^46 + 160572396 * q^47 + 187196994 * q^48 + 156292703 * q^49 + 169504821 * q^50 + 90221121 * q^51 + 65465920 * q^52 - 8762038 * q^53 + 24446286 * q^54 + 147125140 * q^55 + 9671794 * q^56 + 38561508 * q^57 - 37665424 * q^58 - 266581942 * q^59 - 3442095 * q^60 + 120750754 * q^61 - 152465186 * q^62 + 50132601 * q^63 - 40658803 * q^64 + 331055798 * q^65 - 182413782 * q^66 + 41371828 * q^67 + 145606631 * q^68 + 575348022 * q^69 - 920887614 * q^70 + 261018751 * q^71 + 402812595 * q^72 + 178388 * q^73 - 303908734 * q^74 + 860903802 * q^75 - 94541144 * q^76 + 299640561 * q^77 + 556554888 * q^78 - 905381353 * q^79 + 939128289 * q^80 + 947027862 * q^81 - 551739753 * q^82 + 1173257869 * q^83 + 657124650 * q^84 - 1546633210 * q^85 + 1384869460 * q^86 + 1237624596 * q^87 + 189740713 * q^88 + 898004974 * q^89 + 297456057 * q^90 + 591272339 * q^91 + 4328210270 * q^92 + 1426437378 * q^93 + 122568068 * q^94 + 2487967134 * q^95 + 2622640356 * q^96 + 3175709684 * q^97 + 5095778404 * q^98 + 733316409 * q^99

Introduction

L-functions

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