LMFDB - Embedded newform 177.8.a.a.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,8,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, 8, names="a")

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

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 8 $
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:	$55.2921495107$
Analytic rank:	$1$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} - 1493 x^{14} + 8791 x^{13} + 890490 x^{12} - 5107725 x^{11} - 269092298 x^{10} + \cdots - 23\!\cdots\!32 $ x^16 - 6x^15 - 1493x^14 + 8791x^13 + 890490x^12 - 5107725x^11 - 269092298x^10 + 1488374176x^9 + 42885295136x^8 - 226132003872x^7 - 3353576629440x^6 + 16796366777600x^5 + 99470801612800x^4 - 494039551757568x^3 - 493048066650624x^2 + 3193975642099712*x - 2385018853548032
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{9}\cdot 3^{5} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$7.00808$ of defining polynomial
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)

$f(q)$	$=$	$q-7.00808 q^{2} -27.0000 q^{3} -78.8868 q^{4} +449.079 q^{5} +189.218 q^{6} -271.717 q^{7} +1449.88 q^{8} +729.000 q^{9} +O(q^{10})$	\(q-7.00808 q^{2} -27.0000 q^{3} -78.8868 q^{4} +449.079 q^{5} +189.218 q^{6} -271.717 q^{7} +1449.88 q^{8} +729.000 q^{9} -3147.18 q^{10} -3164.33 q^{11} +2129.94 q^{12} -9448.56 q^{13} +1904.22 q^{14} -12125.1 q^{15} -63.3641 q^{16} -6793.30 q^{17} -5108.89 q^{18} +34097.6 q^{19} -35426.4 q^{20} +7336.36 q^{21} +22175.9 q^{22} -31238.0 q^{23} -39146.7 q^{24} +123547. q^{25} +66216.3 q^{26} -19683.0 q^{27} +21434.9 q^{28} +82712.9 q^{29} +84974.0 q^{30} +283828. q^{31} -185141. q^{32} +85437.0 q^{33} +47608.0 q^{34} -122023. q^{35} -57508.5 q^{36} +26823.2 q^{37} -238959. q^{38} +255111. q^{39} +651111. q^{40} -19538.2 q^{41} -51413.8 q^{42} -417223. q^{43} +249624. q^{44} +327379. q^{45} +218919. q^{46} -27684.6 q^{47} +1710.83 q^{48} -749713. q^{49} -865829. q^{50} +183419. q^{51} +745366. q^{52} +29017.7 q^{53} +137940. q^{54} -1.42104e6 q^{55} -393957. q^{56} -920636. q^{57} -579659. q^{58} +205379. q^{59} +956514. q^{60} +1.53434e6 q^{61} -1.98909e6 q^{62} -198082. q^{63} +1.30559e6 q^{64} -4.24315e6 q^{65} -598749. q^{66} -2.52949e6 q^{67} +535901. q^{68} +843427. q^{69} +855144. q^{70} -3.35724e6 q^{71} +1.05696e6 q^{72} -1.90625e6 q^{73} -187979. q^{74} -3.33578e6 q^{75} -2.68985e6 q^{76} +859803. q^{77} -1.78784e6 q^{78} +2.26955e6 q^{79} -28455.5 q^{80} +531441. q^{81} +136925. q^{82} -5.96358e6 q^{83} -578742. q^{84} -3.05073e6 q^{85} +2.92393e6 q^{86} -2.23325e6 q^{87} -4.58790e6 q^{88} +5.11791e6 q^{89} -2.29430e6 q^{90} +2.56733e6 q^{91} +2.46427e6 q^{92} -7.66336e6 q^{93} +194016. q^{94} +1.53125e7 q^{95} +4.99879e6 q^{96} -145042. q^{97} +5.25405e6 q^{98} -2.30680e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{2} - 432 q^{3} + 974 q^{4} - 68 q^{5} + 162 q^{6} - 2343 q^{7} + 819 q^{8} + 11664 q^{9}+O(q^{10}) $ 16 * q - 6 * q^2 - 432 * q^3 + 974 * q^4 - 68 * q^5 + 162 * q^6 - 2343 * q^7 + 819 * q^8 + 11664 * q^9	\( 16 q - 6 q^{2} - 432 q^{3} + 974 q^{4} - 68 q^{5} + 162 q^{6} - 2343 q^{7} + 819 q^{8} + 11664 q^{9} - 3479 q^{10} + 898 q^{11} - 26298 q^{12} - 8172 q^{13} - 13315 q^{14} + 1836 q^{15} + 3138 q^{16} - 44985 q^{17} - 4374 q^{18} - 40137 q^{19} + 130657 q^{20} + 63261 q^{21} + 109394 q^{22} - 2833 q^{23} - 22113 q^{24} + 285746 q^{25} - 129420 q^{26} - 314928 q^{27} + 112890 q^{28} + 144375 q^{29} + 93933 q^{30} - 141759 q^{31} - 36224 q^{32} - 24246 q^{33} - 341332 q^{34} - 78859 q^{35} + 710046 q^{36} - 297971 q^{37} + 329075 q^{38} + 220644 q^{39} - 203048 q^{40} + 659077 q^{41} + 359505 q^{42} - 1431608 q^{43} + 254916 q^{44} - 49572 q^{45} + 873113 q^{46} - 1574073 q^{47} - 84726 q^{48} + 1893545 q^{49} + 302533 q^{50} + 1214595 q^{51} - 4972548 q^{52} + 587736 q^{53} + 118098 q^{54} - 4624036 q^{55} - 5798506 q^{56} + 1083699 q^{57} - 6991380 q^{58} + 3286064 q^{59} - 3527739 q^{60} - 6117131 q^{61} - 11570258 q^{62} - 1708047 q^{63} - 19063011 q^{64} - 5335514 q^{65} - 2953638 q^{66} - 16518710 q^{67} - 17284669 q^{68} + 76491 q^{69} - 39189486 q^{70} - 10882582 q^{71} + 597051 q^{72} - 21097441 q^{73} - 16717030 q^{74} - 7715142 q^{75} - 40864952 q^{76} - 3404601 q^{77} + 3494340 q^{78} - 3784458 q^{79} - 27466195 q^{80} + 8503056 q^{81} - 24990117 q^{82} - 1951425 q^{83} - 3048030 q^{84} - 23238675 q^{85} - 35910572 q^{86} - 3898125 q^{87} - 27843055 q^{88} + 10499443 q^{89} - 2536191 q^{90} + 699217 q^{91} - 20062766 q^{92} + 3827493 q^{93} - 59358988 q^{94} - 29236333 q^{95} + 978048 q^{96} - 25158976 q^{97} + 2120460 q^{98} + 654642 q^{99}+O(q^{100}) \) 16 * q - 6 * q^2 - 432 * q^3 + 974 * q^4 - 68 * q^5 + 162 * q^6 - 2343 * q^7 + 819 * q^8 + 11664 * q^9 - 3479 * q^10 + 898 * q^11 - 26298 * q^12 - 8172 * q^13 - 13315 * q^14 + 1836 * q^15 + 3138 * q^16 - 44985 * q^17 - 4374 * q^18 - 40137 * q^19 + 130657 * q^20 + 63261 * q^21 + 109394 * q^22 - 2833 * q^23 - 22113 * q^24 + 285746 * q^25 - 129420 * q^26 - 314928 * q^27 + 112890 * q^28 + 144375 * q^29 + 93933 * q^30 - 141759 * q^31 - 36224 * q^32 - 24246 * q^33 - 341332 * q^34 - 78859 * q^35 + 710046 * q^36 - 297971 * q^37 + 329075 * q^38 + 220644 * q^39 - 203048 * q^40 + 659077 * q^41 + 359505 * q^42 - 1431608 * q^43 + 254916 * q^44 - 49572 * q^45 + 873113 * q^46 - 1574073 * q^47 - 84726 * q^48 + 1893545 * q^49 + 302533 * q^50 + 1214595 * q^51 - 4972548 * q^52 + 587736 * q^53 + 118098 * q^54 - 4624036 * q^55 - 5798506 * q^56 + 1083699 * q^57 - 6991380 * q^58 + 3286064 * q^59 - 3527739 * q^60 - 6117131 * q^61 - 11570258 * q^62 - 1708047 * q^63 - 19063011 * q^64 - 5335514 * q^65 - 2953638 * q^66 - 16518710 * q^67 - 17284669 * q^68 + 76491 * q^69 - 39189486 * q^70 - 10882582 * q^71 + 597051 * q^72 - 21097441 * q^73 - 16717030 * q^74 - 7715142 * q^75 - 40864952 * q^76 - 3404601 * q^77 + 3494340 * q^78 - 3784458 * q^79 - 27466195 * q^80 + 8503056 * q^81 - 24990117 * q^82 - 1951425 * q^83 - 3048030 * q^84 - 23238675 * q^85 - 35910572 * q^86 - 3898125 * q^87 - 27843055 * q^88 + 10499443 * q^89 - 2536191 * q^90 + 699217 * q^91 - 20062766 * q^92 + 3827493 * q^93 - 59358988 * q^94 - 29236333 * q^95 + 978048 * q^96 - 25158976 * q^97 + 2120460 * q^98 + 654642 * 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 $

$2$	−7.00808	−0.619433	−0.309716	−	0.950829i	$-0.600234\pi$
$2$	−7.00808	−0.619433	−0.309716	+	0.950829i	$0.600234\pi$
$3$	−27.0000	−0.577350
$3$	−27.0000	−0.577350
$4$	−78.8868	−0.616303
$5$	449.079	1.60668	0.803338	−	0.595524i	$-0.203056\pi$
$5$	449.079	1.60668	0.803338	+	0.595524i	$0.203056\pi$
$6$	189.218	0.357630
$7$	−271.717	−0.299415	−0.149708	−	0.988730i	$-0.547833\pi$
$7$	−271.717	−0.299415	−0.149708	+	0.988730i	$0.547833\pi$
$8$	1449.88	1.00119
$9$	729.000	0.333333
$10$	−3147.18	−0.995227
$11$	−3164.33	−0.716816	−0.358408	−	0.933565i	$-0.616680\pi$
$11$	−3164.33	−0.716816	−0.358408	+	0.933565i	$0.616680\pi$
$12$	2129.94	0.355823
$13$	−9448.56	−1.19279	−0.596395	−	0.802691i	$-0.703401\pi$
$13$	−9448.56	−1.19279	−0.596395	+	0.802691i	$0.703401\pi$
$14$	1904.22	0.185468
$15$	−12125.1	−0.927614
$16$	−63.3641	−0.00386744
$17$	−6793.30	−0.335358	−0.167679	−	0.985842i	$-0.553627\pi$
$17$	−6793.30	−0.335358	−0.167679	+	0.985842i	$0.553627\pi$
$18$	−5108.89	−0.206478
$19$	34097.6	1.14048	0.570239	−	0.821479i	$-0.306851\pi$
$19$	34097.6	1.14048	0.570239	+	0.821479i	$0.306851\pi$
$20$	−35426.4	−0.990199
$21$	7336.36	0.172867
$22$	22175.9	0.444019
$23$	−31238.0	−0.535348	−0.267674	−	0.963510i	$-0.586255\pi$
$23$	−31238.0	−0.535348	−0.267674	+	0.963510i	$0.586255\pi$
$24$	−39146.7	−0.578038
$25$	123547.	1.58141
$26$	66216.3	0.738853
$27$	−19683.0	−0.192450
$28$	21434.9	0.184531
$29$	82712.9	0.629767	0.314884	−	0.949130i	$-0.398034\pi$
$29$	82712.9	0.629767	0.314884	+	0.949130i	$0.398034\pi$
$30$	84974.0	0.574595
$31$	283828.	1.71116	0.855578	−	0.517673i	$-0.173202\pi$
$31$	283828.	1.71116	0.855578	+	0.517673i	$0.173202\pi$
$32$	−185141.	−0.998795
$33$	85437.0	0.413854
$34$	47608.0	0.207732
$35$	−122023.	−0.481063
$36$	−57508.5	−0.205434
$37$	26823.2	0.0870571	0.0435286	−	0.999052i	$-0.486140\pi$
$37$	26823.2	0.0870571	0.0435286	+	0.999052i	$0.486140\pi$
$38$	−238959.	−0.706449
$39$	255111.	0.688657
$40$	651111.	1.60859
$41$	−19538.2	−0.0442732	−0.0221366	−	0.999755i	$-0.507047\pi$
$41$	−19538.2	−0.0442732	−0.0221366	+	0.999755i	$0.507047\pi$
$42$	−51413.8	−0.107080
$43$	−417223.	−0.800255	−0.400128	−	0.916459i	$-0.631034\pi$
$43$	−417223.	−0.800255	−0.400128	+	0.916459i	$0.631034\pi$
$44$	249624.	0.441776
$45$	327379.	0.535558
$46$	218919.	0.331612
$47$	−27684.6	−0.0388952	−0.0194476	−	0.999811i	$-0.506191\pi$
$47$	−27684.6	−0.0388952	−0.0194476	+	0.999811i	$0.506191\pi$
$48$	1710.83	0.00223287
$49$	−749713.	−0.910351
$50$	−865829.	−0.979574
$51$	183419.	0.193619
$52$	745366.	0.735120
$53$	29017.7	0.0267730	0.0133865	−	0.999910i	$-0.495739\pi$
$53$	29017.7	0.0267730	0.0133865	+	0.999910i	$0.495739\pi$
$54$	137940.	0.119210
$55$	−1.42104e6	−1.15169
$56$	−393957.	−0.299772
$57$	−920636.	−0.658455
$58$	−579659.	−0.390099
$59$	205379.	0.130189
$59$	205379.	0.130189
$60$	956514.	0.571692
$61$	1.53434e6	0.865499	0.432749	−	0.901514i	$-0.357543\pi$
$61$	1.53434e6	0.865499	0.432749	+	0.901514i	$0.357543\pi$
$62$	−1.98909e6	−1.05995
$63$	−198082.	−0.0998051
$64$	1.30559e6	0.622554
$65$	−4.24315e6	−1.91642
$66$	−598749.	−0.256355
$67$	−2.52949e6	−1.02748	−0.513738	−	0.857947i	$-0.671740\pi$
$67$	−2.52949e6	−1.02748	−0.513738	+	0.857947i	$0.671740\pi$
$68$	535901.	0.206682
$69$	843427.	0.309083
$70$	855144.	0.297986
$71$	−3.35724e6	−1.11321	−0.556606	−	0.830776i	$-0.687897\pi$
$71$	−3.35724e6	−1.11321	−0.556606	+	0.830776i	$0.687897\pi$
$72$	1.05696e6	0.333730
$73$	−1.90625e6	−0.573521	−0.286761	−	0.958002i	$-0.592578\pi$
$73$	−1.90625e6	−0.573521	−0.286761	+	0.958002i	$0.592578\pi$
$74$	−187979.	−0.0539260
$75$	−3.33578e6	−0.913025
$76$	−2.68985e6	−0.702880
$77$	859803.	0.214626
$78$	−1.78784e6	−0.426577
$79$	2.26955e6	0.517899	0.258950	−	0.965891i	$-0.416624\pi$
$79$	2.26955e6	0.517899	0.258950	+	0.965891i	$0.416624\pi$
$80$	−28455.5	−0.00621372
$81$	531441.	0.111111
$82$	136925.	0.0274243
$83$	−5.96358e6	−1.14481	−0.572405	−	0.819971i	$-0.693989\pi$
$83$	−5.96358e6	−1.14481	−0.572405	+	0.819971i	$0.693989\pi$
$84$	−578742.	−0.106539
$85$	−3.05073e6	−0.538812
$86$	2.92393e6	0.495704
$87$	−2.23325e6	−0.363596
$88$	−4.58790e6	−0.717670
$89$	5.11791e6	0.769533	0.384767	−	0.923014i	$-0.374282\pi$
$89$	5.11791e6	0.769533	0.384767	+	0.923014i	$0.374282\pi$
$90$	−2.29430e6	−0.331742
$91$	2.56733e6	0.357139
$92$	2.46427e6	0.329937
$93$	−7.66336e6	−0.987937
$94$	194016.	0.0240930
$95$	1.53125e7	1.83238
$96$	4.99879e6	0.576655
$97$	−145042.	−0.0161359	−0.00806793	−	0.999967i	$-0.502568\pi$
$97$	−145042.	−0.0161359	−0.00806793	+	0.999967i	$0.502568\pi$
$98$	5.25405e6	0.563901
$99$	−2.30680e6	−0.238939
$100$	−9.74625e6	−0.974625
$101$	7.21193e6	0.696509	0.348254	−	0.937400i	$-0.386775\pi$
$101$	7.21193e6	0.696509	0.348254	+	0.937400i	$0.386775\pi$
$102$	−1.28542e6	−0.119934
$103$	1.50882e6	0.136052	0.0680262	−	0.997684i	$-0.478330\pi$
$103$	1.50882e6	0.136052	0.0680262	+	0.997684i	$0.478330\pi$
$104$	−1.36993e7	−1.19421
$105$	3.29461e6	0.277742
$106$	−203359.	−0.0165841
$107$	−1.20706e7	−0.952545	−0.476272	−	0.879298i	$-0.658012\pi$
$107$	−1.20706e7	−0.952545	−0.476272	+	0.879298i	$0.658012\pi$
$108$	1.55273e6	0.118608
$109$	−1.99398e7	−1.47479	−0.737393	−	0.675464i	$-0.763943\pi$
$109$	−1.99398e7	−1.47479	−0.737393	+	0.675464i	$0.763943\pi$
$110$	9.95874e6	0.713395
$111$	−724226.	−0.0502625
$112$	17217.1	0.00115797
$113$	−2.25861e7	−1.47254	−0.736269	−	0.676688i	$-0.763414\pi$
$113$	−2.25861e7	−1.47254	−0.736269	+	0.676688i	$0.763414\pi$
$114$	6.45189e6	0.407869
$115$	−1.40284e7	−0.860130
$116$	−6.52495e6	−0.388128
$117$	−6.88800e6	−0.397596
$118$	−1.43931e6	−0.0806433
$119$	1.84585e6	0.100411
$120$	−1.75800e7	−0.928719
$121$	−9.47417e6	−0.486175
$122$	−1.07528e7	−0.536118
$123$	527531.	0.0255611
$124$	−2.23903e7	−1.05459
$125$	2.03982e7	0.934129
$126$	1.38817e6	0.0618225
$127$	−3.83609e7	−1.66179	−0.830895	−	0.556429i	$-0.812171\pi$
$127$	−3.83609e7	−1.66179	−0.830895	+	0.556429i	$0.812171\pi$
$128$	1.45483e7	0.613165
$129$	1.12650e7	0.462027
$130$	2.97364e7	1.18710
$131$	−2.06635e7	−0.803070	−0.401535	−	0.915844i	$-0.631523\pi$
$131$	−2.06635e7	−0.803070	−0.401535	+	0.915844i	$0.631523\pi$
$132$	−6.73985e6	−0.255059
$133$	−9.26491e6	−0.341476
$134$	1.77269e7	0.636452
$135$	−8.83923e6	−0.309205
$136$	−9.84946e6	−0.335758
$137$	−2.08600e7	−0.693095	−0.346547	−	0.938033i	$-0.612646\pi$
$137$	−2.08600e7	−0.693095	−0.346547	+	0.938033i	$0.612646\pi$
$138$	−5.91080e6	−0.191456
$139$	−4.87015e7	−1.53812	−0.769061	−	0.639176i	$-0.779276\pi$
$139$	−4.87015e7	−1.53812	−0.769061	+	0.639176i	$0.779276\pi$
$140$	9.62597e6	0.296481
$141$	747485.	0.0224562
$142$	2.35278e7	0.689560
$143$	2.98984e7	0.855011
$144$	−46192.4	−0.00128915
$145$	3.71447e7	1.01183
$146$	1.33591e7	0.355258
$147$	2.02422e7	0.525591
$148$	−2.11600e6	−0.0536536
$149$	1.01955e7	0.252497	0.126249	−	0.991999i	$-0.459706\pi$
$149$	1.01955e7	0.252497	0.126249	+	0.991999i	$0.459706\pi$
$150$	2.33774e7	0.565557
$151$	3.94880e7	0.933354	0.466677	−	0.884428i	$-0.345451\pi$
$151$	3.94880e7	0.933354	0.466677	+	0.884428i	$0.345451\pi$
$152$	4.94375e7	1.14184
$153$	−4.95231e6	−0.111786
$154$	−6.02557e6	−0.132946
$155$	1.27461e8	2.74927
$156$	−2.01249e7	−0.424422
$157$	4.95090e7	1.02102	0.510511	−	0.859871i	$-0.329456\pi$
$157$	4.95090e7	1.02102	0.510511	+	0.859871i	$0.329456\pi$
$158$	−1.59052e7	−0.320804
$159$	−783479.	−0.0154574
$160$	−8.31428e7	−1.60474
$161$	8.48791e6	0.160291
$162$	−3.72438e6	−0.0688259
$163$	−7.43101e7	−1.34397	−0.671987	−	0.740563i	$-0.734559\pi$
$163$	−7.43101e7	−1.34397	−0.671987	+	0.740563i	$0.734559\pi$
$164$	1.54131e6	0.0272857
$165$	3.83680e7	0.664929
$166$	4.17932e7	0.709133
$167$	2.90320e7	0.482358	0.241179	−	0.970481i	$-0.422466\pi$
$167$	2.90320e7	0.482358	0.241179	+	0.970481i	$0.422466\pi$
$168$	1.06368e7	0.173073
$169$	2.65267e7	0.422746
$170$	2.13798e7	0.333758
$171$	2.48572e7	0.380159
$172$	3.29134e7	0.493200
$173$	5.40154e7	0.793152	0.396576	−	0.918002i	$-0.370198\pi$
$173$	5.40154e7	0.793152	0.396576	+	0.918002i	$0.370198\pi$
$174$	1.56508e7	0.225224
$175$	−3.35699e7	−0.473497
$176$	200505.	0.00277224
$177$	−5.54523e6	−0.0751646
$178$	−3.58667e7	−0.476674
$179$	−5.61319e7	−0.731516	−0.365758	−	0.930710i	$-0.619190\pi$
$179$	−5.61319e7	−0.731516	−0.365758	+	0.930710i	$0.619190\pi$
$180$	−2.58259e7	−0.330066
$181$	4.15020e7	0.520228	0.260114	−	0.965578i	$-0.416240\pi$
$181$	4.15020e7	0.520228	0.260114	+	0.965578i	$0.416240\pi$
$182$	−1.79921e7	−0.221224
$183$	−4.14271e7	−0.499696
$184$	−4.52914e7	−0.535986
$185$	1.20457e7	0.139873
$186$	5.37055e7	0.611960
$187$	2.14962e7	0.240390
$188$	2.18395e6	0.0239712
$189$	5.34821e6	0.0576225
$190$	−1.07312e8	−1.13503
$191$	−5.65111e7	−0.586837	−0.293418	−	0.955984i	$-0.594793\pi$
$191$	−5.65111e7	−0.586837	−0.293418	+	0.955984i	$0.594793\pi$
$192$	−3.52509e7	−0.359432
$193$	1.59119e8	1.59321	0.796604	−	0.604502i	$-0.206628\pi$
$193$	1.59119e8	1.59321	0.796604	+	0.604502i	$0.206628\pi$
$194$	1.01646e6	0.00999508
$195$	1.14565e8	1.10645
$196$	5.91424e7	0.561052
$197$	6.46721e7	0.602678	0.301339	−	0.953517i	$-0.402566\pi$
$197$	6.46721e7	0.602678	0.301339	+	0.953517i	$0.402566\pi$
$198$	1.61662e7	0.148006
$199$	−1.88894e8	−1.69915	−0.849576	−	0.527467i	$-0.823142\pi$
$199$	−1.88894e8	−1.69915	−0.849576	+	0.527467i	$0.823142\pi$
$200$	1.79129e8	1.58329
$201$	6.82963e7	0.593214
$202$	−5.05418e7	−0.431440
$203$	−2.24745e7	−0.188562
$204$	−1.44693e7	−0.119328
$205$	−8.77420e6	−0.0711326
$206$	−1.05739e7	−0.0842754
$207$	−2.27725e7	−0.178449
$208$	598700.	0.00461304
$209$	−1.07896e8	−0.817513
$210$	−2.30889e7	−0.172042
$211$	8.23127e7	0.603224	0.301612	−	0.953431i	$-0.402475\pi$
$211$	8.23127e7	0.603224	0.301612	+	0.953431i	$0.402475\pi$
$212$	−2.28912e6	−0.0165003
$213$	9.06455e7	0.642714
$214$	8.45917e7	0.590037
$215$	−1.87366e8	−1.28575
$216$	−2.85380e7	−0.192679
$217$	−7.71210e7	−0.512346
$218$	1.39740e8	0.913531
$219$	5.14687e7	0.331123
$220$	1.12101e8	0.709790
$221$	6.41868e7	0.400012
$222$	5.07544e6	0.0311342
$223$	−1.37252e8	−0.828801	−0.414400	−	0.910095i	$-0.636009\pi$
$223$	−1.37252e8	−0.828801	−0.414400	+	0.910095i	$0.636009\pi$
$224$	5.03058e7	0.299055
$225$	9.00660e7	0.527135
$226$	1.58285e8	0.912139
$227$	−1.70002e8	−0.964635	−0.482317	−	0.875997i	$-0.660205\pi$
$227$	−1.70002e8	−0.964635	−0.482317	+	0.875997i	$0.660205\pi$
$228$	7.26260e7	0.405808
$229$	2.30825e8	1.27016	0.635082	−	0.772445i	$-0.280966\pi$
$229$	2.30825e8	1.27016	0.635082	+	0.772445i	$0.280966\pi$
$230$	9.83119e7	0.532793
$231$	−2.32147e7	−0.123914
$232$	1.19924e8	0.630518
$233$	−1.24871e8	−0.646719	−0.323359	−	0.946276i	$-0.604812\pi$
$233$	−1.24871e8	−0.646719	−0.323359	+	0.946276i	$0.604812\pi$
$234$	4.82717e7	0.246284
$235$	−1.24326e7	−0.0624920
$236$	−1.62017e7	−0.0802358
$237$	−6.12779e7	−0.299009
$238$	−1.29359e7	−0.0621981
$239$	−2.73260e8	−1.29474	−0.647371	−	0.762175i	$-0.724132\pi$
$239$	−2.73260e8	−1.29474	−0.647371	+	0.762175i	$0.724132\pi$
$240$	768299.	0.00358749
$241$	−2.70017e8	−1.24260	−0.621301	−	0.783572i	$-0.713396\pi$
$241$	−2.70017e8	−1.24260	−0.621301	+	0.783572i	$0.713396\pi$
$242$	6.63957e7	0.301152
$243$	−1.43489e7	−0.0641500
$244$	−1.21039e8	−0.533410
$245$	−3.36681e8	−1.46264
$246$	−3.69698e6	−0.0158334
$247$	−3.22173e8	−1.36035
$248$	4.11517e8	1.71319
$249$	1.61017e8	0.660956
$250$	−1.42952e8	−0.578630
$251$	1.21031e7	0.0483103	0.0241551	−	0.999708i	$-0.492310\pi$
$251$	1.21031e7	0.0483103	0.0241551	+	0.999708i	$0.492310\pi$
$252$	1.56260e7	0.0615102
$253$	9.88475e7	0.383746
$254$	2.68836e8	1.02937
$255$	8.23697e7	0.311083
$256$	−2.69071e8	−1.00237
$257$	2.89004e8	1.06203	0.531017	−	0.847361i	$-0.321810\pi$
$257$	2.89004e8	1.06203	0.531017	+	0.847361i	$0.321810\pi$
$258$	−7.89461e7	−0.286195
$259$	−7.28832e6	−0.0260662
$260$	3.34729e8	1.18110
$261$	6.02977e7	0.209922
$262$	1.44811e8	0.497448
$263$	−7.64989e6	−0.0259304	−0.0129652	−	0.999916i	$-0.504127\pi$
$263$	−7.64989e6	−0.0259304	−0.0129652	+	0.999916i	$0.504127\pi$
$264$	1.23873e8	0.414347
$265$	1.30313e7	0.0430156
$266$	6.49293e7	0.211522
$267$	−1.38183e8	−0.444290
$268$	1.99544e8	0.633237
$269$	2.10692e8	0.659956	0.329978	−	0.943989i	$-0.392959\pi$
$269$	2.10692e8	0.659956	0.329978	+	0.943989i	$0.392959\pi$
$270$	6.19460e7	0.191532
$271$	−3.98910e8	−1.21754	−0.608769	−	0.793348i	$-0.708336\pi$
$271$	−3.98910e8	−1.21754	−0.608769	+	0.793348i	$0.708336\pi$
$272$	430451.	0.00129698
$273$	−6.93180e7	−0.206194
$274$	1.46189e8	0.429325
$275$	−3.90945e8	−1.13358
$276$	−6.65352e7	−0.190489
$277$	−5.06287e8	−1.43126	−0.715628	−	0.698481i	$-0.753859\pi$
$277$	−5.06287e8	−1.43126	−0.715628	+	0.698481i	$0.753859\pi$
$278$	3.41304e8	0.952763
$279$	2.06911e8	0.570386
$280$	−1.76918e8	−0.481636
$281$	−4.35455e8	−1.17077	−0.585384	−	0.810756i	$-0.699056\pi$
$281$	−4.35455e8	−1.17077	−0.585384	+	0.810756i	$0.699056\pi$
$282$	−5.23843e6	−0.0139101
$283$	−1.36270e7	−0.0357394	−0.0178697	−	0.999840i	$-0.505688\pi$
$283$	−1.36270e7	−0.0357394	−0.0178697	+	0.999840i	$0.505688\pi$
$284$	2.64842e8	0.686076
$285$	−4.13439e8	−1.05792
$286$	−2.09530e8	−0.529622
$287$	5.30886e6	0.0132561
$288$	−1.34967e8	−0.332932
$289$	−3.64190e8	−0.887535
$290$	−2.60313e8	−0.626762
$291$	3.91613e6	0.00931604
$292$	1.50378e8	0.353463
$293$	−5.24778e8	−1.21882	−0.609409	−	0.792856i	$-0.708593\pi$
$293$	−5.24778e8	−1.21882	−0.609409	+	0.792856i	$0.708593\pi$
$294$	−1.41859e8	−0.325568
$295$	9.22315e7	0.209171
$296$	3.88904e7	0.0871608
$297$	6.22836e7	0.137951
$298$	−7.14510e7	−0.156405
$299$	2.95154e8	0.638558
$300$	2.63149e8	0.562700
$301$	1.13367e8	0.239609
$302$	−2.76735e8	−0.578150
$303$	−1.94722e8	−0.402129
$304$	−2.16057e6	−0.00441073
$305$	6.89039e8	1.39058
$306$	3.47062e7	0.0692440
$307$	−5.40106e8	−1.06536	−0.532678	−	0.846318i	$-0.678814\pi$
$307$	−5.40106e8	−1.06536	−0.532678	+	0.846318i	$0.678814\pi$
$308$	−6.78271e7	−0.132274
$309$	−4.07381e7	−0.0785499
$310$	−8.93260e8	−1.70299
$311$	−1.89139e8	−0.356549	−0.178275	−	0.983981i	$-0.557052\pi$
$311$	−1.89139e8	−0.356549	−0.178275	+	0.983981i	$0.557052\pi$
$312$	3.69880e8	0.689477
$313$	5.77137e8	1.06383	0.531917	−	0.846797i	$-0.321472\pi$
$313$	5.77137e8	1.06383	0.531917	+	0.846797i	$0.321472\pi$
$314$	−3.46963e8	−0.632454
$315$	−8.89544e7	−0.160354
$316$	−1.79038e8	−0.319183
$317$	1.18644e6	0.00209189	0.00104595	−	0.999999i	$-0.499667\pi$
$317$	1.18644e6	0.00209189	0.00104595	+	0.999999i	$0.499667\pi$
$318$	5.49068e6	0.00957484
$319$	−2.61731e8	−0.451427
$320$	5.86314e8	1.00024
$321$	3.25906e8	0.549952
$322$	−5.94840e7	−0.0992897
$323$	−2.31635e8	−0.382469
$324$	−4.19237e7	−0.0684781
$325$	−1.16734e9	−1.88628
$326$	5.20771e8	0.832502
$327$	5.38376e8	0.851468
$328$	−2.83280e7	−0.0443259
$329$	7.52238e6	0.0116458
$330$	−2.68886e8	−0.411879
$331$	−8.08372e8	−1.22522	−0.612609	−	0.790386i	$-0.709880\pi$
$331$	−8.08372e8	−1.22522	−0.612609	+	0.790386i	$0.709880\pi$
$332$	4.70447e8	0.705550
$333$	1.95541e7	0.0290190
$334$	−2.03459e8	−0.298788
$335$	−1.13594e9	−1.65082
$336$	−464862.	−0.000668554 0
$337$	8.85349e8	1.26011	0.630057	−	0.776549i	$-0.283032\pi$
$337$	8.85349e8	1.26011	0.630057	+	0.776549i	$0.283032\pi$
$338$	−1.85901e8	−0.261863
$339$	6.09825e8	0.850171
$340$	2.40662e8	0.332072
$341$	−8.98127e8	−1.22658
$342$	−1.74201e8	−0.235483
$343$	4.27481e8	0.571988
$344$	−6.04923e8	−0.801208
$345$	3.78766e8	0.496597
$346$	−3.78544e8	−0.491304
$347$	7.51351e8	0.965361	0.482680	−	0.875797i	$-0.339663\pi$
$347$	7.51351e8	0.965361	0.482680	+	0.875797i	$0.339663\pi$
$348$	1.76174e8	0.224086
$349$	5.06457e8	0.637755	0.318877	−	0.947796i	$-0.396694\pi$
$349$	5.06457e8	0.637755	0.318877	+	0.947796i	$0.396694\pi$
$350$	2.35261e8	0.293299
$351$	1.85976e8	0.229552
$352$	5.85846e8	0.715953
$353$	7.31006e8	0.884523	0.442262	−	0.896886i	$-0.354176\pi$
$353$	7.31006e8	0.884523	0.442262	+	0.896886i	$0.354176\pi$
$354$	3.88614e7	0.0465594
$355$	−1.50767e9	−1.78857
$356$	−4.03735e8	−0.474266
$357$	−4.98381e7	−0.0579726
$358$	3.93377e8	0.453125
$359$	1.09721e9	1.25158	0.625790	−	0.779992i	$-0.284777\pi$
$359$	1.09721e9	1.25158	0.625790	+	0.779992i	$0.284777\pi$
$360$	4.74660e8	0.536196
$361$	2.68777e8	0.300688
$362$	−2.90849e8	−0.322246
$363$	2.55803e8	0.280693
$364$	−2.02529e8	−0.220106
$365$	−8.56057e8	−0.921462
$366$	2.90325e8	0.309528
$367$	2.58816e8	0.273313	0.136657	−	0.990618i	$-0.456364\pi$
$367$	2.58816e8	0.273313	0.136657	+	0.990618i	$0.456364\pi$
$368$	1.97937e6	0.00207043
$369$	−1.42433e7	−0.0147577
$370$	−8.44175e7	−0.0866416
$371$	−7.88461e6	−0.00801626
$372$	6.04538e8	0.608868
$373$	1.37810e9	1.37499	0.687497	−	0.726187i	$-0.258709\pi$
$373$	1.37810e9	1.37499	0.687497	+	0.726187i	$0.258709\pi$
$374$	−1.50647e8	−0.148906
$375$	−5.50751e8	−0.539320
$376$	−4.01394e7	−0.0389415
$377$	−7.81517e8	−0.751180
$378$	−3.74807e7	−0.0356933
$379$	−1.56880e8	−0.148024	−0.0740119	−	0.997257i	$-0.523580\pi$
$379$	−1.56880e8	−0.148024	−0.0740119	+	0.997257i	$0.523580\pi$
$380$	−1.20796e9	−1.12930
$381$	1.03575e9	0.959435
$382$	3.96035e8	0.363506
$383$	−8.83458e8	−0.803508	−0.401754	−	0.915748i	$-0.631599\pi$
$383$	−8.83458e8	−0.803508	−0.401754	+	0.915748i	$0.631599\pi$
$384$	−3.92804e8	−0.354011
$385$	3.86120e8	0.344834
$386$	−1.11512e9	−0.986885
$387$	−3.04155e8	−0.266752
$388$	1.14419e7	0.00994458
$389$	9.53014e8	0.820873	0.410436	−	0.911889i	$-0.365376\pi$
$389$	9.53014e8	0.820873	0.410436	+	0.911889i	$0.365376\pi$
$390$	−8.02882e8	−0.685370
$391$	2.12209e8	0.179534
$392$	−1.08699e9	−0.911435
$393$	5.57913e8	0.463653
$394$	−4.53227e8	−0.373318
$395$	1.01921e9	0.832095
$396$	1.81976e8	0.147259
$397$	−2.30889e9	−1.85198	−0.925992	−	0.377544i	$-0.876769\pi$
$397$	−2.30889e9	−1.85198	−0.925992	+	0.377544i	$0.876769\pi$
$398$	1.32378e9	1.05251
$399$	2.50153e8	0.197151
$400$	−7.82846e6	−0.00611599
$401$	1.15700e9	0.896039	0.448019	−	0.894024i	$-0.352130\pi$
$401$	1.15700e9	0.896039	0.448019	+	0.894024i	$0.352130\pi$
$402$	−4.78626e8	−0.367456
$403$	−2.68177e9	−2.04105
$404$	−5.68926e8	−0.429260
$405$	2.38659e8	0.178519
$406$	1.57503e8	0.116801
$407$	−8.48775e7	−0.0624040
$408$	2.65935e8	0.193850
$409$	1.94341e9	1.40454	0.702269	−	0.711911i	$-0.252170\pi$
$409$	1.94341e9	1.40454	0.702269	+	0.711911i	$0.252170\pi$
$410$	6.14903e7	0.0440619
$411$	5.63220e8	0.400158
$412$	−1.19026e8	−0.0838496
$413$	−5.58050e7	−0.0389805
$414$	1.59592e8	0.110537
$415$	−2.67812e9	−1.83934
$416$	1.74931e9	1.19135
$417$	1.31494e9	0.888035
$418$	7.56146e8	0.506394
$419$	2.16975e9	1.44099	0.720495	−	0.693460i	$-0.243915\pi$
$419$	2.16975e9	1.44099	0.720495	+	0.693460i	$0.243915\pi$
$420$	−2.59901e8	−0.171173
$421$	−6.64386e8	−0.433943	−0.216972	−	0.976178i	$-0.569618\pi$
$421$	−6.64386e8	−0.433943	−0.216972	+	0.976178i	$0.569618\pi$
$422$	−5.76854e8	−0.373657
$423$	−2.01821e7	−0.0129651
$424$	4.20722e7	0.0268049
$425$	−8.39293e8	−0.530338
$426$	−6.35251e8	−0.398118
$427$	−4.16906e8	−0.259144
$428$	9.52210e8	0.587056
$429$	−8.07256e8	−0.493641
$430$	1.31308e9	0.796436
$431$	−2.35268e9	−1.41545	−0.707723	−	0.706490i	$-0.750277\pi$
$431$	−2.35268e9	−1.41545	−0.707723	+	0.706490i	$0.750277\pi$
$432$	1.24720e6	0.000744289 0
$433$	1.41032e8	0.0834852	0.0417426	−	0.999128i	$-0.486709\pi$
$433$	1.41032e8	0.0834852	0.0417426	+	0.999128i	$0.486709\pi$
$434$	5.40470e8	0.317364
$435$	−1.00291e9	−0.584181
$436$	1.57299e9	0.908915
$437$	−1.06514e9	−0.610552
$438$	−3.60697e8	−0.205108
$439$	−2.83909e9	−1.60159	−0.800797	−	0.598935i	$-0.795591\pi$
$439$	−2.83909e9	−1.60159	−0.800797	+	0.598935i	$0.795591\pi$
$440$	−2.06033e9	−1.15306
$441$	−5.46541e8	−0.303450
$442$	−4.49827e8	−0.247781
$443$	−3.44158e9	−1.88081	−0.940405	−	0.340058i	$-0.889553\pi$
$443$	−3.44158e9	−1.88081	−0.940405	+	0.340058i	$0.889553\pi$
$444$	5.71319e7	0.0309769
$445$	2.29835e9	1.23639
$446$	9.61870e8	0.513386
$447$	−2.75279e8	−0.145779
$448$	−3.54751e8	−0.186402
$449$	8.59881e8	0.448308	0.224154	−	0.974554i	$-0.428038\pi$
$449$	8.59881e8	0.448308	0.224154	+	0.974554i	$0.428038\pi$
$450$	−6.31190e8	−0.326525
$451$	6.18253e7	0.0317357
$452$	1.78175e9	0.907530
$453$	−1.06618e9	−0.538872
$454$	1.19139e9	0.597526
$455$	1.15294e9	0.573807
$456$	−1.33481e9	−0.659239
$457$	−1.71007e9	−0.838124	−0.419062	−	0.907958i	$-0.637641\pi$
$457$	−1.71007e9	−0.838124	−0.419062	+	0.907958i	$0.637641\pi$
$458$	−1.61764e9	−0.786781
$459$	1.33712e8	0.0645398
$460$	1.10665e9	0.530101
$461$	2.48943e9	1.18344	0.591720	−	0.806143i	$-0.298449\pi$
$461$	2.48943e9	1.18344	0.591720	+	0.806143i	$0.298449\pi$
$462$	1.62690e8	0.0767565
$463$	2.91198e9	1.36350	0.681749	−	0.731587i	$-0.261220\pi$
$463$	2.91198e9	1.36350	0.681749	+	0.731587i	$0.261220\pi$
$464$	−5.24103e6	−0.00243559
$465$	−3.44146e9	−1.58729
$466$	8.75105e8	0.400599
$467$	3.22506e9	1.46531	0.732654	−	0.680601i	$-0.238281\pi$
$467$	3.22506e9	1.46531	0.732654	+	0.680601i	$0.238281\pi$
$468$	5.43372e8	0.245040
$469$	6.87307e8	0.307642
$470$	8.71286e7	0.0387096
$471$	−1.33674e9	−0.589487
$472$	2.97775e8	0.130344
$473$	1.32023e9	0.573636
$474$	4.29440e8	0.185216
$475$	4.21267e9	1.80356
$476$	−1.45614e8	−0.0618839
$477$	2.11539e7	0.00892435
$478$	1.91503e9	0.802006
$479$	3.79747e9	1.57877	0.789386	−	0.613897i	$-0.210399\pi$
$479$	3.79747e9	1.57877	0.789386	+	0.613897i	$0.210399\pi$
$480$	2.24486e9	0.926497
$481$	−2.53440e8	−0.103841
$482$	1.89230e9	0.769709
$483$	−2.29174e8	−0.0925443
$484$	7.47387e8	0.299631
$485$	−6.51353e7	−0.0259251
$486$	1.00558e8	0.0397366
$487$	2.70012e9	1.05933	0.529665	−	0.848207i	$-0.322318\pi$
$487$	2.70012e9	1.05933	0.529665	+	0.848207i	$0.322318\pi$
$488$	2.22460e9	0.866530
$489$	2.00637e9	0.775944
$490$	2.35948e9	0.906006
$491$	1.96974e9	0.750971	0.375485	−	0.926828i	$-0.377476\pi$
$491$	1.96974e9	0.750971	0.375485	+	0.926828i	$0.377476\pi$
$492$	−4.16152e7	−0.0157534
$493$	−5.61893e8	−0.211198
$494$	2.25782e9	0.842645
$495$	−1.03594e9	−0.383897
$496$	−1.79845e7	−0.00661779
$497$	9.12219e8	0.333313
$498$	−1.12842e9	−0.409418
$499$	6.68650e8	0.240906	0.120453	−	0.992719i	$-0.461565\pi$
$499$	6.68650e8	0.240906	0.120453	+	0.992719i	$0.461565\pi$
$500$	−1.60915e9	−0.575707
$501$	−7.83864e8	−0.278489
$502$	−8.48197e7	−0.0299250
$503$	8.13925e8	0.285165	0.142583	−	0.989783i	$-0.454459\pi$
$503$	8.13925e8	0.285165	0.142583	+	0.989783i	$0.454459\pi$
$504$	−2.87195e8	−0.0999239
$505$	3.23873e9	1.11906
$506$	−6.92732e8	−0.237705
$507$	−7.16221e8	−0.244073
$508$	3.02617e9	1.02417
$509$	3.90482e9	1.31247	0.656235	−	0.754557i	$-0.272148\pi$
$509$	3.90482e9	1.31247	0.656235	+	0.754557i	$0.272148\pi$
$510$	−5.77253e8	−0.192695
$511$	5.17960e8	0.171721
$512$	2.34907e7	0.00773483
$513$	−6.71144e8	−0.219485
$514$	−2.02537e9	−0.657859
$515$	6.77579e8	0.218592
$516$	−8.88661e8	−0.284749
$517$	8.76033e7	0.0278807
$518$	5.10771e7	0.0161463
$519$	−1.45842e9	−0.457926
$520$	−6.15206e9	−1.91871
$521$	−1.40413e9	−0.434984	−0.217492	−	0.976062i	$-0.569788\pi$
$521$	−1.40413e9	−0.434984	−0.217492	+	0.976062i	$0.569788\pi$
$522$	−4.22571e8	−0.130033
$523$	5.53390e8	0.169151	0.0845756	−	0.996417i	$-0.473047\pi$
$523$	5.53390e8	0.169151	0.0845756	+	0.996417i	$0.473047\pi$
$524$	1.63007e9	0.494935
$525$	9.06387e8	0.273373
$526$	5.36110e7	0.0160622
$527$	−1.92813e9	−0.573851
$528$	−5.41364e6	−0.00160056
$529$	−2.42901e9	−0.713402
$530$	−9.13241e7	−0.0266453
$531$	1.49721e8	0.0433963
$532$	7.30879e8	0.210453
$533$	1.84608e8	0.0528086
$534$	9.68401e8	0.275208
$535$	−5.42065e9	−1.53043
$536$	−3.66746e9	−1.02870
$537$	1.51556e9	0.422341
$538$	−1.47655e9	−0.408798
$539$	2.37234e9	0.652554
$540$	6.97298e8	0.190564
$541$	2.74177e8	0.0744459	0.0372229	−	0.999307i	$-0.488149\pi$
$541$	2.74177e8	0.0744459	0.0372229	+	0.999307i	$0.488149\pi$
$542$	2.79559e9	0.754183
$543$	−1.12055e9	−0.300354
$544$	1.25771e9	0.334954
$545$	−8.95457e9	−2.36950
$546$	4.85786e8	0.127724
$547$	3.89224e8	0.101682	0.0508410	−	0.998707i	$-0.483810\pi$
$547$	3.89224e8	0.101682	0.0508410	+	0.998707i	$0.483810\pi$
$548$	1.64558e9	0.427156
$549$	1.11853e9	0.288500
$550$	2.73977e9	0.702174
$551$	2.82031e9	0.718236
$552$	1.22287e9	0.309452
$553$	−6.16676e8	−0.155067
$554$	3.54810e9	0.886567
$555$	−3.25235e8	−0.0807554
$556$	3.84191e9	0.947949
$557$	−1.89599e9	−0.464883	−0.232441	−	0.972610i	$-0.574671\pi$
$557$	−1.89599e9	−0.464883	−0.232441	+	0.972610i	$0.574671\pi$
$558$	−1.45005e9	−0.353316
$559$	3.94215e9	0.954536
$560$	7.73185e6	0.00186048
$561$	−5.80399e8	−0.138789
$562$	3.05170e9	0.725212
$563$	−5.24086e9	−1.23772	−0.618861	−	0.785501i	$-0.712406\pi$
$563$	−5.24086e9	−1.23772	−0.618861	+	0.785501i	$0.712406\pi$
$564$	−5.89667e7	−0.0138398
$565$	−1.01430e10	−2.36589
$566$	9.54991e7	0.0221382
$567$	−1.44402e8	−0.0332684
$568$	−4.86759e9	−1.11454
$569$	−6.24592e9	−1.42136	−0.710678	−	0.703517i	$-0.751612\pi$
$569$	−6.24592e9	−1.42136	−0.710678	+	0.703517i	$0.751612\pi$
$570$	2.89741e9	0.655312
$571$	−4.35962e9	−0.979991	−0.489996	−	0.871725i	$-0.663002\pi$
$571$	−4.35962e9	−0.979991	−0.489996	+	0.871725i	$0.663002\pi$
$572$	−2.35859e9	−0.526946
$573$	1.52580e9	0.338810
$574$	−3.72049e7	−0.00821124
$575$	−3.85937e9	−0.846602
$576$	9.51775e8	0.207518
$577$	1.25822e9	0.272672	0.136336	−	0.990663i	$-0.456467\pi$
$577$	1.25822e9	0.272672	0.136336	+	0.990663i	$0.456467\pi$
$578$	2.55227e9	0.549768
$579$	−4.29622e9	−0.919839
$580$	−2.93022e9	−0.623595
$581$	1.62041e9	0.342773
$582$	−2.74446e7	−0.00577066
$583$	−9.18217e7	−0.0191914
$584$	−2.76383e9	−0.574204
$585$	−3.09326e9	−0.638808
$586$	3.67768e9	0.754975
$587$	−7.19197e9	−1.46762	−0.733812	−	0.679353i	$-0.762261\pi$
$587$	−7.19197e9	−1.46762	−0.733812	+	0.679353i	$0.762261\pi$
$588$	−1.59685e9	−0.323923
$589$	9.67787e9	1.95154
$590$	−6.46366e8	−0.129568
$591$	−1.74615e9	−0.347956
$592$	−1.69963e6	−0.000336688 0
$593$	−8.65682e9	−1.70477	−0.852387	−	0.522911i	$-0.824846\pi$
$593$	−8.65682e9	−1.70477	−0.852387	+	0.522911i	$0.824846\pi$
$594$	−4.36488e8	−0.0854516
$595$	8.28935e8	0.161329
$596$	−8.04291e8	−0.155615
$597$	5.10013e9	0.981005
$598$	−2.06847e9	−0.395543
$599$	5.85691e9	1.11346	0.556730	−	0.830693i	$-0.312056\pi$
$599$	5.85691e9	1.11346	0.556730	+	0.830693i	$0.312056\pi$
$600$	−4.83647e9	−0.914112
$601$	5.94489e9	1.11708	0.558539	−	0.829478i	$-0.311362\pi$
$601$	5.94489e9	1.11708	0.558539	+	0.829478i	$0.311362\pi$
$602$	−7.94482e8	−0.148421
$603$	−1.84400e9	−0.342492
$604$	−3.11509e9	−0.575229
$605$	−4.25465e9	−0.781125
$606$	1.36463e9	0.249092
$607$	7.31720e9	1.32796	0.663979	−	0.747751i	$-0.268866\pi$
$607$	7.31720e9	1.32796	0.663979	+	0.747751i	$0.268866\pi$
$608$	−6.31285e9	−1.13910
$609$	6.06812e8	0.108866
$610$	−4.82884e9	−0.861368
$611$	2.61580e8	0.0463938
$612$	3.90672e8	0.0688942
$613$	8.17131e8	0.143278	0.0716391	−	0.997431i	$-0.477177\pi$
$613$	8.17131e8	0.143278	0.0716391	+	0.997431i	$0.477177\pi$
$614$	3.78511e9	0.659917
$615$	2.36903e8	0.0410685
$616$	1.24661e9	0.214881
$617$	−4.81332e9	−0.824985	−0.412493	−	0.910961i	$-0.635342\pi$
$617$	−4.81332e9	−0.824985	−0.412493	+	0.910961i	$0.635342\pi$
$618$	2.85496e8	0.0486564
$619$	−4.14223e8	−0.0701968	−0.0350984	−	0.999384i	$-0.511174\pi$
$619$	−4.14223e8	−0.0701968	−0.0350984	+	0.999384i	$0.511174\pi$
$620$	−1.00550e10	−1.69439
$621$	6.14858e8	0.103028
$622$	1.32550e9	0.220858
$623$	−1.39062e9	−0.230410
$624$	−1.61649e7	−0.00266334
$625$	−4.91719e8	−0.0805632
$626$	−4.04462e9	−0.658973
$627$	2.91320e9	0.471991
$628$	−3.90560e9	−0.629259
$629$	−1.82218e8	−0.0291953
$630$	6.23400e8	0.0993287
$631$	−2.20305e9	−0.349078	−0.174539	−	0.984650i	$-0.555843\pi$
$631$	−2.20305e9	−0.349078	−0.174539	+	0.984650i	$0.555843\pi$
$632$	3.29058e9	0.518516
$633$	−2.22244e9	−0.348271
$634$	−8.31469e6	−0.00129579
$635$	−1.72271e10	−2.66996
$636$	6.18061e7	0.00952646
$637$	7.08370e9	1.08586
$638$	1.83423e9	0.279629
$639$	−2.44743e9	−0.371071
$640$	6.53334e9	0.985157
$641$	4.40972e9	0.661315	0.330657	−	0.943751i	$-0.392730\pi$
$641$	4.40972e9	0.661315	0.330657	+	0.943751i	$0.392730\pi$
$642$	−2.28398e9	−0.340658
$643$	8.75195e9	1.29827	0.649137	−	0.760671i	$-0.275130\pi$
$643$	8.75195e9	1.29827	0.649137	+	0.760671i	$0.275130\pi$
$644$	−6.69584e8	−0.0987881
$645$	5.05889e9	0.742328
$646$	1.62332e9	0.236914
$647$	4.86345e9	0.705959	0.352979	−	0.935631i	$-0.385169\pi$
$647$	4.86345e9	0.705959	0.352979	+	0.935631i	$0.385169\pi$
$648$	7.70525e8	0.111243
$649$	−6.49888e8	−0.0933215
$650$	8.18084e9	1.16843
$651$	2.08227e9	0.295803
$652$	5.86208e9	0.828296
$653$	−9.35709e9	−1.31506	−0.657529	−	0.753429i	$-0.728398\pi$
$653$	−9.35709e9	−1.31506	−0.657529	+	0.753429i	$0.728398\pi$
$654$	−3.77298e9	−0.527427
$655$	−9.27953e9	−1.29027
$656$	1.23802e6	0.000171224 0
$657$	−1.38966e9	−0.191174
$658$	−5.27175e7	−0.00721380
$659$	5.87424e9	0.799562	0.399781	−	0.916611i	$-0.369086\pi$
$659$	5.87424e9	0.799562	0.399781	+	0.916611i	$0.369086\pi$
$660$	−3.02673e9	−0.409798
$661$	4.45812e8	0.0600408	0.0300204	−	0.999549i	$-0.490443\pi$
$661$	4.45812e8	0.0600408	0.0300204	+	0.999549i	$0.490443\pi$
$662$	5.66514e9	0.758940
$663$	−1.73304e9	−0.230947
$664$	−8.64647e9	−1.14617
$665$	−4.16068e9	−0.548641
$666$	−1.37037e8	−0.0179753
$667$	−2.58379e9	−0.337145
$668$	−2.29024e9	−0.297279
$669$	3.70579e9	0.478508
$670$	7.96078e9	1.02257
$671$	−4.85515e9	−0.620404
$672$	−1.35826e9	−0.172659
$673$	2.90168e9	0.366942	0.183471	−	0.983025i	$-0.441267\pi$
$673$	2.90168e9	0.366942	0.183471	+	0.983025i	$0.441267\pi$
$674$	−6.20460e9	−0.780556
$675$	−2.43178e9	−0.304342
$676$	−2.09261e9	−0.260540
$677$	8.77680e9	1.08712	0.543558	−	0.839372i	$-0.317077\pi$
$677$	8.77680e9	1.08712	0.543558	+	0.839372i	$0.317077\pi$
$678$	−4.27370e9	−0.526624
$679$	3.94103e7	0.00483132
$680$	−4.42319e9	−0.539454
$681$	4.59005e9	0.556932
$682$	6.29415e9	0.759787
$683$	6.96062e9	0.835940	0.417970	−	0.908461i	$-0.362742\pi$
$683$	6.96062e9	0.835940	0.417970	+	0.908461i	$0.362742\pi$
$684$	−1.96090e9	−0.234293
$685$	−9.36780e9	−1.11358
$686$	−2.99582e9	−0.354308
$687$	−6.23229e9	−0.733329
$688$	2.64370e7	0.00309494
$689$	−2.74176e8	−0.0319346
$690$	−2.65442e9	−0.307608
$691$	−5.57378e8	−0.0642653	−0.0321326	−	0.999484i	$-0.510230\pi$
$691$	−5.57378e8	−0.0642653	−0.0321326	+	0.999484i	$0.510230\pi$
$692$	−4.26110e9	−0.488822
$693$	6.26797e8	0.0715419
$694$	−5.26553e9	−0.597976
$695$	−2.18708e10	−2.47126
$696$	−3.23794e9	−0.364029
$697$	1.32729e8	0.0148474
$698$	−3.54929e9	−0.395046
$699$	3.37151e9	0.373383
$700$	2.64822e9	0.291817
$701$	1.27904e10	1.40240	0.701201	−	0.712963i	$-0.252647\pi$
$701$	1.27904e10	1.40240	0.701201	+	0.712963i	$0.252647\pi$
$702$	−1.30333e9	−0.142192
$703$	9.14607e8	0.0992867
$704$	−4.13132e9	−0.446257
$705$	3.35680e8	0.0360797
$706$	−5.12295e9	−0.547903
$707$	−1.95960e9	−0.208545
$708$	4.37446e8	0.0463242
$709$	−1.68769e10	−1.77841	−0.889205	−	0.457508i	$-0.848742\pi$
$709$	−1.68769e10	−1.77841	−0.889205	+	0.457508i	$0.848742\pi$
$710$	1.05659e10	1.10790
$711$	1.65450e9	0.172633
$712$	7.42035e9	0.770450
$713$	−8.86624e9	−0.916065
$714$	3.49269e8	0.0359101
$715$	1.34267e10	1.37372
$716$	4.42806e9	0.450836
$717$	7.37802e9	0.747520
$718$	−7.68933e9	−0.775270
$719$	1.65145e10	1.65697	0.828484	−	0.560013i	$-0.189204\pi$
$719$	1.65145e10	1.65697	0.828484	+	0.560013i	$0.189204\pi$
$720$	−2.07441e7	−0.00207124
$721$	−4.09972e8	−0.0407362
$722$	−1.88361e9	−0.186256
$723$	7.29047e9	0.717417
$724$	−3.27396e9	−0.320618
$725$	1.02190e10	0.995917
$726$	−1.79269e9	−0.173870
$727$	1.21987e10	1.17745	0.588727	−	0.808332i	$-0.299629\pi$
$727$	1.21987e10	1.17745	0.588727	+	0.808332i	$0.299629\pi$
$728$	3.72233e9	0.357565
$729$	3.87420e8	0.0370370
$730$	5.99932e9	0.570784
$731$	2.83432e9	0.268372
$732$	3.26805e9	0.307964
$733$	−9.19756e9	−0.862598	−0.431299	−	0.902209i	$-0.641945\pi$
$733$	−9.19756e9	−0.862598	−0.431299	+	0.902209i	$0.641945\pi$
$734$	−1.81381e9	−0.169299
$735$	9.09037e9	0.844454
$736$	5.78343e9	0.534703
$737$	8.00416e9	0.736511
$738$	9.98185e7	0.00914142
$739$	−1.94615e10	−1.77386	−0.886932	−	0.461900i	$-0.847168\pi$
$739$	−1.94615e10	−1.77386	−0.886932	+	0.461900i	$0.847168\pi$
$740$	−9.50250e8	−0.0862039
$741$	8.69868e9	0.785398
$742$	5.52560e7	0.00496553
$743$	1.39586e10	1.24848	0.624238	−	0.781235i	$-0.285410\pi$
$743$	1.39586e10	1.24848	0.624238	+	0.781235i	$0.285410\pi$
$744$	−1.11110e10	−0.989113
$745$	4.57859e9	0.405681
$746$	−9.65786e9	−0.851717
$747$	−4.34745e9	−0.381603
$748$	−1.69577e9	−0.148153
$749$	3.27979e9	0.285206
$750$	3.85971e9	0.334072
$751$	−9.03865e9	−0.778688	−0.389344	−	0.921092i	$-0.627298\pi$
$751$	−9.03865e9	−0.778688	−0.389344	+	0.921092i	$0.627298\pi$
$752$	1.75421e6	0.000150425 0
$753$	−3.26784e8	−0.0278919
$754$	5.47694e9	0.465305
$755$	1.77333e10	1.49960
$756$	−4.21903e8	−0.0355129
$757$	4.80250e9	0.402376	0.201188	−	0.979553i	$-0.435520\pi$
$757$	4.80250e9	0.402376	0.201188	+	0.979553i	$0.435520\pi$
$758$	1.09943e9	0.0916908
$759$	−2.66888e9	−0.221556
$760$	2.22013e10	1.83456
$761$	−1.41275e10	−1.16203	−0.581015	−	0.813893i	$-0.697344\pi$
$761$	−1.41275e10	−1.16203	−0.581015	+	0.813893i	$0.697344\pi$
$762$	−7.25859e9	−0.594305
$763$	5.41800e9	0.441573
$764$	4.45798e9	0.361669
$765$	−2.22398e9	−0.179604
$766$	6.19135e9	0.497719
$767$	−1.94054e9	−0.155288
$768$	7.26492e9	0.578718
$769$	1.40261e10	1.11223	0.556113	−	0.831106i	$-0.312292\pi$
$769$	1.40261e10	1.11223	0.556113	+	0.831106i	$0.312292\pi$
$770$	−2.70596e9	−0.213601
$771$	−7.80312e9	−0.613166
$772$	−1.25524e10	−0.981899
$773$	2.02962e8	0.0158047	0.00790236	−	0.999969i	$-0.497485\pi$
$773$	2.02962e8	0.0158047	0.00790236	+	0.999969i	$0.497485\pi$
$774$	2.13155e9	0.165235
$775$	3.50662e10	2.70603
$776$	−2.10293e8	−0.0161551
$777$	1.96785e8	0.0150493
$778$	−6.67880e9	−0.508475
$779$	−6.66206e8	−0.0504926
$780$	−9.03767e9	−0.681908
$781$	1.06234e10	0.797969
$782$	−1.48718e9	−0.111209
$783$	−1.62804e9	−0.121199
$784$	4.75049e7	0.00352073
$785$	2.22335e10	1.64045
$786$	−3.90990e9	−0.287202
$787$	8.88769e9	0.649946	0.324973	−	0.945723i	$-0.394645\pi$
$787$	8.88769e9	0.649946	0.324973	+	0.945723i	$0.394645\pi$
$788$	−5.10178e9	−0.371432
$789$	2.06547e8	0.0149709
$790$	−7.14270e9	−0.515427
$791$	6.13703e9	0.440901
$792$	−3.34458e9	−0.239223
$793$	−1.44973e10	−1.03236
$794$	1.61809e10	1.14718
$795$	−3.51844e8	−0.0248351
$796$	1.49012e10	1.04719
$797$	−9.59859e9	−0.671589	−0.335794	−	0.941935i	$-0.609005\pi$
$797$	−9.59859e9	−0.671589	−0.335794	+	0.941935i	$0.609005\pi$
$798$	−1.75309e9	−0.122122
$799$	1.88070e8	0.0130438
$800$	−2.28736e10	−1.57950
$801$	3.73095e9	0.256511
$802$	−8.10833e9	−0.555036
$803$	6.03200e9	0.411109
$804$	−5.38768e9	−0.365599
$805$	3.81174e9	0.257536
$806$	1.87940e10	1.26429
$807$	−5.68868e9	−0.381026
$808$	1.04564e10	0.697338
$809$	1.06933e10	0.710054	0.355027	−	0.934856i	$-0.384472\pi$
$809$	1.06933e10	0.710054	0.355027	+	0.934856i	$0.384472\pi$
$810$	−1.67254e9	−0.110581
$811$	−1.87262e10	−1.23275	−0.616376	−	0.787452i	$-0.711400\pi$
$811$	−1.87262e10	−1.23275	−0.616376	+	0.787452i	$0.711400\pi$
$812$	1.77294e9	0.116211
$813$	1.07706e10	0.702946
$814$	5.94828e8	0.0386551
$815$	−3.33711e10	−2.15933
$816$	−1.16222e7	−0.000748811 0
$817$	−1.42263e10	−0.912673
$818$	−1.36196e10	−0.870017
$819$	1.87159e9	0.119046
$820$	6.92168e8	0.0438393
$821$	−1.83953e10	−1.16013	−0.580065	−	0.814570i	$-0.696973\pi$
$821$	−1.83953e10	−1.16013	−0.580065	+	0.814570i	$0.696973\pi$
$822$	−3.94709e9	−0.247871
$823$	−6.29971e9	−0.393932	−0.196966	−	0.980410i	$-0.563109\pi$
$823$	−6.29971e9	−0.393932	−0.196966	+	0.980410i	$0.563109\pi$
$824$	2.18760e9	0.136215
$825$	1.05555e10	0.654471
$826$	3.91086e8	0.0241458
$827$	−1.00387e10	−0.617175	−0.308587	−	0.951196i	$-0.599856\pi$
$827$	−1.00387e10	−0.617175	−0.308587	+	0.951196i	$0.599856\pi$
$828$	1.79645e9	0.109979
$829$	2.76027e8	0.0168271	0.00841357	−	0.999965i	$-0.497322\pi$
$829$	2.76027e8	0.0168271	0.00841357	+	0.999965i	$0.497322\pi$
$830$	1.87685e10	1.13935
$831$	1.36697e10	0.826336
$832$	−1.23359e10	−0.742576
$833$	5.09302e9	0.305294
$834$	−9.21521e9	−0.550078
$835$	1.30377e10	0.774992
$836$	8.51159e9	0.503835
$837$	−5.58659e9	−0.329312
$838$	−1.52058e10	−0.892597
$839$	2.00764e10	1.17360	0.586799	−	0.809733i	$-0.300388\pi$
$839$	2.00764e10	1.17360	0.586799	+	0.809733i	$0.300388\pi$
$840$	4.77679e9	0.278073
$841$	−1.04085e10	−0.603393
$842$	4.65607e9	0.268799
$843$	1.17573e10	0.675944
$844$	−6.49339e9	−0.371769
$845$	1.19126e10	0.679216
$846$	1.41438e8	0.00803099
$847$	2.57429e9	0.145568
$848$	−1.83868e6	−0.000103543 0
$849$	3.67929e8	0.0206342
$850$	5.88183e9	0.328508
$851$	−8.37904e8	−0.0466059
$852$	−7.15073e9	−0.396106
$853$	7.43953e9	0.410415	0.205208	−	0.978718i	$-0.434213\pi$
$853$	7.43953e9	0.410415	0.205208	+	0.978718i	$0.434213\pi$
$854$	2.92171e9	0.160522
$855$	1.11628e10	0.610792
$856$	−1.75009e10	−0.953679
$857$	−2.02954e10	−1.10145	−0.550726	−	0.834686i	$-0.685649\pi$
$857$	−2.02954e10	−1.10145	−0.550726	+	0.834686i	$0.685649\pi$
$858$	5.65732e9	0.305777
$859$	1.59155e10	0.856728	0.428364	−	0.903606i	$-0.359090\pi$
$859$	1.59155e10	0.856728	0.428364	+	0.903606i	$0.359090\pi$
$860$	1.47807e10	0.792412
$861$	−1.43339e8	−0.00765339
$862$	1.64878e10	0.876774
$863$	8.64458e9	0.457832	0.228916	−	0.973446i	$-0.426482\pi$
$863$	8.64458e9	0.457832	0.228916	+	0.973446i	$0.426482\pi$
$864$	3.64412e9	0.192218
$865$	2.42572e10	1.27434
$866$	−9.88363e8	−0.0517135
$867$	9.83312e9	0.512418
$868$	6.08383e9	0.315761
$869$	−7.18161e9	−0.371238
$870$	7.02844e9	0.361861
$871$	2.39001e10	1.22556
$872$	−2.89104e10	−1.47654
$873$	−1.05735e8	−0.00537862
$874$	7.46461e9	0.378196
$875$	−5.54254e9	−0.279692
$876$	−4.06020e9	−0.204072
$877$	−3.61467e10	−1.80955	−0.904775	−	0.425890i	$-0.859961\pi$
$877$	−3.61467e10	−1.80955	−0.904775	+	0.425890i	$0.859961\pi$
$878$	1.98965e10	0.992080
$879$	1.41690e10	0.703684
$880$	9.00427e7	0.00445409
$881$	−2.55814e10	−1.26040	−0.630199	−	0.776433i	$-0.717027\pi$
$881$	−2.55814e10	−1.26040	−0.630199	+	0.776433i	$0.717027\pi$
$882$	3.83020e9	0.187967
$883$	−3.64985e10	−1.78407	−0.892036	−	0.451964i	$-0.850724\pi$
$883$	−3.64985e10	−1.78407	−0.892036	+	0.451964i	$0.850724\pi$
$884$	−5.06349e9	−0.246529
$885$	−2.49025e9	−0.120765
$886$	2.41189e10	1.16503
$887$	1.11780e10	0.537812	0.268906	−	0.963166i	$-0.413338\pi$
$887$	1.11780e10	0.537812	0.268906	+	0.963166i	$0.413338\pi$
$888$	−1.05004e9	−0.0503223
$889$	1.04233e10	0.497565
$890$	−1.61070e10	−0.765860
$891$	−1.68166e9	−0.0796462
$892$	1.08273e10	0.510792
$893$	−9.43980e8	−0.0443591
$894$	1.92918e9	0.0903006
$895$	−2.52077e10	−1.17531
$896$	−3.95302e9	−0.183591
$897$	−7.96917e9	−0.368671
$898$	−6.02612e9	−0.277697
$899$	2.34763e10	1.07763
$900$	−7.10501e9	−0.324875
$901$	−1.97126e8	−0.00897857
$902$	−4.33277e8	−0.0196582
$903$	−3.06090e9	−0.138338
$904$	−3.27471e10	−1.47429
$905$	1.86377e10	0.835837
$906$	7.47186e9	0.333795
$907$	−3.45269e10	−1.53650	−0.768250	−	0.640150i	$-0.778872\pi$
$907$	−3.45269e10	−1.53650	−0.768250	+	0.640150i	$0.778872\pi$
$908$	1.34109e10	0.594507
$909$	5.25749e9	0.232170
$910$	−8.07988e9	−0.355435
$911$	1.85678e10	0.813665	0.406832	−	0.913503i	$-0.366633\pi$
$911$	1.85678e10	0.813665	0.406832	+	0.913503i	$0.366633\pi$
$912$	5.83353e7	0.00254653
$913$	1.88707e10	0.820618
$914$	1.19843e10	0.519161
$915$	−1.86041e10	−0.802849
$916$	−1.82091e10	−0.782806
$917$	5.61462e9	0.240451
$918$	−9.37068e8	−0.0399780
$919$	−3.89221e10	−1.65422	−0.827108	−	0.562044i	$-0.810015\pi$
$919$	−3.89221e10	−1.65422	−0.827108	+	0.562044i	$0.810015\pi$
$920$	−2.03394e10	−0.861155
$921$	1.45829e10	0.615084
$922$	−1.74461e10	−0.733062
$923$	3.17211e10	1.32783
$924$	1.83133e9	0.0763687
$925$	3.31393e9	0.137673
$926$	−2.04074e10	−0.844595
$927$	1.09993e9	0.0453508
$928$	−1.53135e10	−0.629009
$929$	−7.85450e9	−0.321413	−0.160707	−	0.987002i	$-0.551377\pi$
$929$	−7.85450e9	−0.321413	−0.160707	+	0.987002i	$0.551377\pi$
$930$	2.41180e10	0.983222
$931$	−2.55634e10	−1.03823
$932$	9.85066e9	0.398575
$933$	5.10675e9	0.205854
$934$	−2.26015e10	−0.907660
$935$	9.65352e9	0.386229
$936$	−9.98677e9	−0.398070
$937$	1.64761e10	0.654283	0.327142	−	0.944975i	$-0.393915\pi$
$937$	1.64761e10	0.654283	0.327142	+	0.944975i	$0.393915\pi$
$938$	−4.81670e9	−0.190563
$939$	−1.55827e10	−0.614205
$940$	9.80767e8	0.0385140
$941$	3.54317e10	1.38621	0.693105	−	0.720837i	$-0.256242\pi$
$941$	3.54317e10	1.38621	0.693105	+	0.720837i	$0.256242\pi$
$942$	9.36800e9	0.365148
$943$	6.10335e8	0.0237016
$944$	−1.30137e7	−0.000503498 0
$945$	2.40177e9	0.0925806
$946$	−9.25229e9	−0.355329
$947$	−1.07477e10	−0.411237	−0.205618	−	0.978632i	$-0.565921\pi$
$947$	−1.07477e10	−0.411237	−0.205618	+	0.978632i	$0.565921\pi$
$948$	4.83401e9	0.184280
$949$	1.80113e10	0.684090
$950$	−2.95227e10	−1.11718
$951$	−3.20339e7	−0.00120775
$952$	2.67627e9	0.100531
$953$	−4.52936e10	−1.69516	−0.847581	−	0.530666i	$-0.821942\pi$
$953$	−4.52936e10	−1.69516	−0.847581	+	0.530666i	$0.821942\pi$
$954$	−1.48248e8	−0.00552803
$955$	−2.53780e10	−0.942856
$956$	2.15566e10	0.797953
$957$	7.06674e9	0.260632
$958$	−2.66129e10	−0.977943
$959$	5.66802e9	0.207523
$960$	−1.58305e10	−0.577490
$961$	5.30459e10	1.92806
$962$	1.77613e9	0.0643224
$963$	−8.79946e9	−0.317515
$964$	2.13008e10	0.765820
$965$	7.14572e10	2.55977
$966$	1.60607e9	0.0573249
$967$	−4.08323e10	−1.45215	−0.726074	−	0.687617i	$-0.758657\pi$
$967$	−4.08323e10	−1.45215	−0.726074	+	0.687617i	$0.758657\pi$
$968$	−1.37364e10	−0.486754
$969$	6.25415e9	0.220818
$970$	4.56473e8	0.0160588
$971$	3.91677e10	1.37297	0.686484	−	0.727145i	$-0.259153\pi$
$971$	3.91677e10	1.37297	0.686484	+	0.727145i	$0.259153\pi$
$972$	1.13194e9	0.0395359
$973$	1.32330e10	0.460537
$974$	−1.89226e10	−0.656183
$975$	3.15183e10	1.08905
$976$	−9.72220e7	−0.00334726
$977$	4.38079e10	1.50287	0.751435	−	0.659808i	$-0.229362\pi$
$977$	4.38079e10	1.50287	0.751435	+	0.659808i	$0.229362\pi$
$978$	−1.40608e10	−0.480645
$979$	−1.61948e10	−0.551614
$980$	2.65596e10	0.901428
$981$	−1.45361e10	−0.491595
$982$	−1.38041e10	−0.465176
$983$	3.95635e10	1.32849	0.664244	−	0.747516i	$-0.268754\pi$
$983$	3.95635e10	1.32849	0.664244	+	0.747516i	$0.268754\pi$
$984$	7.64857e8	0.0255916
$985$	2.90429e10	0.968308
$986$	3.93779e9	0.130823
$987$	−2.03104e8	−0.00672371
$988$	2.54152e10	0.838387
$989$	1.30332e10	0.428415
$990$	7.25992e9	0.237798
$991$	−6.12206e10	−1.99820	−0.999102	−	0.0423753i	$-0.986507\pi$
$991$	−6.12206e10	−1.99820	−0.999102	+	0.0423753i	$0.986507\pi$
$992$	−5.25481e10	−1.70910
$993$	2.18261e10	0.707380
$994$	−6.39291e9	−0.206465
$995$	−8.48283e10	−2.72998
$996$	−1.27021e10	−0.407349
$997$	−2.27542e10	−0.727156	−0.363578	−	0.931564i	$-0.618445\pi$
$997$	−2.27542e10	−0.727156	−0.363578	+	0.931564i	$0.618445\pi$
$998$	−4.68595e9	−0.149225
$999$	−5.27961e8	−0.0167542

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.8.a.a.1.6	✓	16
3.2	odd	2		531.8.a.b.1.11		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.8.a.a.1.6	✓	16	1.1	even	1	trivial
531.8.a.b.1.11		16	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:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q-7.00808 q^{2} -27.0000 q^{3} -78.8868 q^{4} +449.079 q^{5} +189.218 q^{6} -271.717 q^{7} +1449.88 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q-7.00808 q^{2} -27.0000 q^{3} -78.8868 q^{4} +449.079 q^{5} +189.218 q^{6} -271.717 q^{7} +1449.88 q^{8} +729.000 q^{9} -3147.18 q^{10} -3164.33 q^{11} +2129.94 q^{12} -9448.56 q^{13} +1904.22 q^{14} -12125.1 q^{15} -63.3641 q^{16} -6793.30 q^{17} -5108.89 q^{18} +34097.6 q^{19} -35426.4 q^{20} +7336.36 q^{21} +22175.9 q^{22} -31238.0 q^{23} -39146.7 q^{24} +123547. q^{25} +66216.3 q^{26} -19683.0 q^{27} +21434.9 q^{28} +82712.9 q^{29} +84974.0 q^{30} +283828. q^{31} -185141. q^{32} +85437.0 q^{33} +47608.0 q^{34} -122023. q^{35} -57508.5 q^{36} +26823.2 q^{37} -238959. q^{38} +255111. q^{39} +651111. q^{40} -19538.2 q^{41} -51413.8 q^{42} -417223. q^{43} +249624. q^{44} +327379. q^{45} +218919. q^{46} -27684.6 q^{47} +1710.83 q^{48} -749713. q^{49} -865829. q^{50} +183419. q^{51} +745366. q^{52} +29017.7 q^{53} +137940. q^{54} -1.42104e6 q^{55} -393957. q^{56} -920636. q^{57} -579659. q^{58} +205379. q^{59} +956514. q^{60} +1.53434e6 q^{61} -1.98909e6 q^{62} -198082. q^{63} +1.30559e6 q^{64} -4.24315e6 q^{65} -598749. q^{66} -2.52949e6 q^{67} +535901. q^{68} +843427. q^{69} +855144. q^{70} -3.35724e6 q^{71} +1.05696e6 q^{72} -1.90625e6 q^{73} -187979. q^{74} -3.33578e6 q^{75} -2.68985e6 q^{76} +859803. q^{77} -1.78784e6 q^{78} +2.26955e6 q^{79} -28455.5 q^{80} +531441. q^{81} +136925. q^{82} -5.96358e6 q^{83} -578742. q^{84} -3.05073e6 q^{85} +2.92393e6 q^{86} -2.23325e6 q^{87} -4.58790e6 q^{88} +5.11791e6 q^{89} -2.29430e6 q^{90} +2.56733e6 q^{91} +2.46427e6 q^{92} -7.66336e6 q^{93} +194016. q^{94} +1.53125e7 q^{95} +4.99879e6 q^{96} -145042. q^{97} +5.25405e6 q^{98} -2.30680e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{2} - 432 q^{3} + 974 q^{4} - 68 q^{5} + 162 q^{6} - 2343 q^{7} + 819 q^{8} + 11664 q^{9}+O(q^{10}) \) 16 * q - 6 * q^2 - 432 * q^3 + 974 * q^4 - 68 * q^5 + 162 * q^6 - 2343 * q^7 + 819 * q^8 + 11664 * q^9	\( 16 q - 6 q^{2} - 432 q^{3} + 974 q^{4} - 68 q^{5} + 162 q^{6} - 2343 q^{7} + 819 q^{8} + 11664 q^{9} - 3479 q^{10} + 898 q^{11} - 26298 q^{12} - 8172 q^{13} - 13315 q^{14} + 1836 q^{15} + 3138 q^{16} - 44985 q^{17} - 4374 q^{18} - 40137 q^{19} + 130657 q^{20} + 63261 q^{21} + 109394 q^{22} - 2833 q^{23} - 22113 q^{24} + 285746 q^{25} - 129420 q^{26} - 314928 q^{27} + 112890 q^{28} + 144375 q^{29} + 93933 q^{30} - 141759 q^{31} - 36224 q^{32} - 24246 q^{33} - 341332 q^{34} - 78859 q^{35} + 710046 q^{36} - 297971 q^{37} + 329075 q^{38} + 220644 q^{39} - 203048 q^{40} + 659077 q^{41} + 359505 q^{42} - 1431608 q^{43} + 254916 q^{44} - 49572 q^{45} + 873113 q^{46} - 1574073 q^{47} - 84726 q^{48} + 1893545 q^{49} + 302533 q^{50} + 1214595 q^{51} - 4972548 q^{52} + 587736 q^{53} + 118098 q^{54} - 4624036 q^{55} - 5798506 q^{56} + 1083699 q^{57} - 6991380 q^{58} + 3286064 q^{59} - 3527739 q^{60} - 6117131 q^{61} - 11570258 q^{62} - 1708047 q^{63} - 19063011 q^{64} - 5335514 q^{65} - 2953638 q^{66} - 16518710 q^{67} - 17284669 q^{68} + 76491 q^{69} - 39189486 q^{70} - 10882582 q^{71} + 597051 q^{72} - 21097441 q^{73} - 16717030 q^{74} - 7715142 q^{75} - 40864952 q^{76} - 3404601 q^{77} + 3494340 q^{78} - 3784458 q^{79} - 27466195 q^{80} + 8503056 q^{81} - 24990117 q^{82} - 1951425 q^{83} - 3048030 q^{84} - 23238675 q^{85} - 35910572 q^{86} - 3898125 q^{87} - 27843055 q^{88} + 10499443 q^{89} - 2536191 q^{90} + 699217 q^{91} - 20062766 q^{92} + 3827493 q^{93} - 59358988 q^{94} - 29236333 q^{95} + 978048 q^{96} - 25158976 q^{97} + 2120460 q^{98} + 654642 q^{99}+O(q^{100}) \) 16 * q - 6 * q^2 - 432 * q^3 + 974 * q^4 - 68 * q^5 + 162 * q^6 - 2343 * q^7 + 819 * q^8 + 11664 * q^9 - 3479 * q^10 + 898 * q^11 - 26298 * q^12 - 8172 * q^13 - 13315 * q^14 + 1836 * q^15 + 3138 * q^16 - 44985 * q^17 - 4374 * q^18 - 40137 * q^19 + 130657 * q^20 + 63261 * q^21 + 109394 * q^22 - 2833 * q^23 - 22113 * q^24 + 285746 * q^25 - 129420 * q^26 - 314928 * q^27 + 112890 * q^28 + 144375 * q^29 + 93933 * q^30 - 141759 * q^31 - 36224 * q^32 - 24246 * q^33 - 341332 * q^34 - 78859 * q^35 + 710046 * q^36 - 297971 * q^37 + 329075 * q^38 + 220644 * q^39 - 203048 * q^40 + 659077 * q^41 + 359505 * q^42 - 1431608 * q^43 + 254916 * q^44 - 49572 * q^45 + 873113 * q^46 - 1574073 * q^47 - 84726 * q^48 + 1893545 * q^49 + 302533 * q^50 + 1214595 * q^51 - 4972548 * q^52 + 587736 * q^53 + 118098 * q^54 - 4624036 * q^55 - 5798506 * q^56 + 1083699 * q^57 - 6991380 * q^58 + 3286064 * q^59 - 3527739 * q^60 - 6117131 * q^61 - 11570258 * q^62 - 1708047 * q^63 - 19063011 * q^64 - 5335514 * q^65 - 2953638 * q^66 - 16518710 * q^67 - 17284669 * q^68 + 76491 * q^69 - 39189486 * q^70 - 10882582 * q^71 + 597051 * q^72 - 21097441 * q^73 - 16717030 * q^74 - 7715142 * q^75 - 40864952 * q^76 - 3404601 * q^77 + 3494340 * q^78 - 3784458 * q^79 - 27466195 * q^80 + 8503056 * q^81 - 24990117 * q^82 - 1951425 * q^83 - 3048030 * q^84 - 23238675 * q^85 - 35910572 * q^86 - 3898125 * q^87 - 27843055 * q^88 + 10499443 * q^89 - 2536191 * q^90 + 699217 * q^91 - 20062766 * q^92 + 3827493 * q^93 - 59358988 * q^94 - 29236333 * q^95 + 978048 * q^96 - 25158976 * q^97 + 2120460 * q^98 + 654642 * q^99

Introduction

L-functions

Modular forms

Varieties

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