LMFDB - Embedded newform 177.8.a.a.1.16

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			1.16
Root			$-19.6562$ 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)

$f(q)$	$=$	$q+19.6562 q^{2} -27.0000 q^{3} +258.365 q^{4} -436.761 q^{5} -530.717 q^{6} +956.841 q^{7} +2562.48 q^{8} +729.000 q^{9} +O(q^{10})$	\(q+19.6562 q^{2} -27.0000 q^{3} +258.365 q^{4} -436.761 q^{5} -530.717 q^{6} +956.841 q^{7} +2562.48 q^{8} +729.000 q^{9} -8585.06 q^{10} +1972.61 q^{11} -6975.86 q^{12} -5308.65 q^{13} +18807.8 q^{14} +11792.6 q^{15} +17297.8 q^{16} -19184.9 q^{17} +14329.3 q^{18} -21442.5 q^{19} -112844. q^{20} -25834.7 q^{21} +38773.9 q^{22} -34320.3 q^{23} -69186.9 q^{24} +112635. q^{25} -104348. q^{26} -19683.0 q^{27} +247214. q^{28} +40010.4 q^{29} +231796. q^{30} -95465.0 q^{31} +12010.9 q^{32} -53260.4 q^{33} -377103. q^{34} -417911. q^{35} +188348. q^{36} -269178. q^{37} -421478. q^{38} +143334. q^{39} -1.11919e6 q^{40} -360504. q^{41} -507811. q^{42} -929097. q^{43} +509653. q^{44} -318399. q^{45} -674606. q^{46} +54052.8 q^{47} -467040. q^{48} +92001.6 q^{49} +2.21398e6 q^{50} +517994. q^{51} -1.37157e6 q^{52} +680499. q^{53} -386892. q^{54} -861559. q^{55} +2.45188e6 q^{56} +578948. q^{57} +786452. q^{58} +205379. q^{59} +3.04678e6 q^{60} -1.27358e6 q^{61} -1.87648e6 q^{62} +697537. q^{63} -1.97803e6 q^{64} +2.31861e6 q^{65} -1.04690e6 q^{66} +630075. q^{67} -4.95672e6 q^{68} +926648. q^{69} -8.21453e6 q^{70} +2.05155e6 q^{71} +1.86805e6 q^{72} -5.36743e6 q^{73} -5.29101e6 q^{74} -3.04116e6 q^{75} -5.54000e6 q^{76} +1.88747e6 q^{77} +2.81739e6 q^{78} +4.57098e6 q^{79} -7.55500e6 q^{80} +531441. q^{81} -7.08613e6 q^{82} +9.49376e6 q^{83} -6.67478e6 q^{84} +8.37924e6 q^{85} -1.82625e7 q^{86} -1.08028e6 q^{87} +5.05477e6 q^{88} -2.45830e6 q^{89} -6.25851e6 q^{90} -5.07953e6 q^{91} -8.86717e6 q^{92} +2.57756e6 q^{93} +1.06247e6 q^{94} +9.36526e6 q^{95} -324293. q^{96} -1.41914e7 q^{97} +1.80840e6 q^{98} +1.43803e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	19.6562	1.73738	0.868688	−	0.495359i	$-0.164964\pi$
$2$	19.6562	1.73738	0.868688	+	0.495359i	$0.164964\pi$
$3$	−27.0000	−0.577350
$3$	−27.0000	−0.577350
$4$	258.365	2.01848
$5$	−436.761	−1.56260	−0.781302	−	0.624153i	$-0.785444\pi$
$5$	−436.761	−1.56260	−0.781302	+	0.624153i	$0.785444\pi$
$6$	−530.717	−1.00307
$7$	956.841	1.05438	0.527189	−	0.849748i	$-0.323246\pi$
$7$	956.841	1.05438	0.527189	+	0.849748i	$0.323246\pi$
$8$	2562.48	1.76948
$9$	729.000	0.333333
$10$	−8585.06	−2.71483
$11$	1972.61	0.446855	0.223427	−	0.974721i	$-0.428275\pi$
$11$	1972.61	0.446855	0.223427	+	0.974721i	$0.428275\pi$
$12$	−6975.86	−1.16537
$13$	−5308.65	−0.670166	−0.335083	−	0.942189i	$-0.608764\pi$
$13$	−5308.65	−0.670166	−0.335083	+	0.942189i	$0.608764\pi$
$14$	18807.8	1.83185
$15$	11792.6	0.902170
$16$	17297.8	1.05577
$17$	−19184.9	−0.947086	−0.473543	−	0.880771i	$-0.657025\pi$
$17$	−19184.9	−0.947086	−0.473543	+	0.880771i	$0.657025\pi$
$18$	14329.3	0.579125
$19$	−21442.5	−0.717196	−0.358598	−	0.933492i	$-0.616745\pi$
$19$	−21442.5	−0.717196	−0.358598	+	0.933492i	$0.616745\pi$
$20$	−112844.	−3.15408
$21$	−25834.7	−0.608746
$22$	38773.9	0.776355
$23$	−34320.3	−0.588171	−0.294086	−	0.955779i	$-0.595015\pi$
$23$	−34320.3	−0.588171	−0.294086	+	0.955779i	$0.595015\pi$
$24$	−69186.9	−1.02161
$25$	112635.	1.44173
$26$	−104348.	−1.16433
$27$	−19683.0	−0.192450
$28$	247214.	2.12824
$29$	40010.4	0.304635	0.152318	−	0.988332i	$-0.451326\pi$
$29$	40010.4	0.304635	0.152318	+	0.988332i	$0.451326\pi$
$30$	231796.	1.56741
$31$	−95465.0	−0.575544	−0.287772	−	0.957699i	$-0.592915\pi$
$31$	−95465.0	−0.575544	−0.287772	+	0.957699i	$0.592915\pi$
$32$	12010.9	0.0647961
$33$	−53260.4	−0.257992
$34$	−377103.	−1.64544
$35$	−417911.	−1.64758
$36$	188348.	0.672826
$37$	−269178.	−0.873642	−0.436821	−	0.899549i	$-0.643896\pi$
$37$	−269178.	−0.873642	−0.436821	+	0.899549i	$0.643896\pi$
$38$	−421478.	−1.24604
$39$	143334.	0.386920
$40$	−1.11919e6	−2.76499
$41$	−360504.	−0.816896	−0.408448	−	0.912782i	$-0.633930\pi$
$41$	−360504.	−0.816896	−0.408448	+	0.912782i	$0.633930\pi$
$42$	−507811.	−1.05762
$43$	−929097.	−1.78206	−0.891028	−	0.453949i	$-0.850015\pi$
$43$	−929097.	−1.78206	−0.891028	+	0.453949i	$0.850015\pi$
$44$	509653.	0.901967
$45$	−318399.	−0.520868
$46$	−674606.	−1.02187
$47$	54052.8	0.0759408	0.0379704	−	0.999279i	$-0.487911\pi$
$47$	54052.8	0.0759408	0.0379704	+	0.999279i	$0.487911\pi$
$48$	−467040.	−0.609550
$49$	92001.6	0.111714
$50$	2.21398e6	2.50483
$51$	517994.	0.546800
$52$	−1.37157e6	−1.35271
$53$	680499.	0.627859	0.313929	−	0.949446i	$-0.398354\pi$
$53$	680499.	0.627859	0.313929	+	0.949446i	$0.398354\pi$
$54$	−386892.	−0.334358
$55$	−861559.	−0.698258
$56$	2.45188e6	1.86570
$57$	578948.	0.414073
$58$	786452.	0.529266
$59$	205379.	0.130189
$59$	205379.	0.130189
$60$	3.04678e6	1.82101
$61$	−1.27358e6	−0.718408	−0.359204	−	0.933259i	$-0.616952\pi$
$61$	−1.27358e6	−0.718408	−0.359204	+	0.933259i	$0.616952\pi$
$62$	−1.87648e6	−0.999936
$63$	697537.	0.351460
$64$	−1.97803e6	−0.943197
$65$	2.31861e6	1.04720
$66$	−1.04690e6	−0.448229
$67$	630075.	0.255936	0.127968	−	0.991778i	$-0.459155\pi$
$67$	630075.	0.255936	0.127968	+	0.991778i	$0.459155\pi$
$68$	−4.95672e6	−1.91167
$69$	926648.	0.339581
$70$	−8.21453e6	−2.86246
$71$	2.05155e6	0.680265	0.340133	−	0.940377i	$-0.389528\pi$
$71$	2.05155e6	0.680265	0.340133	+	0.940377i	$0.389528\pi$
$72$	1.86805e6	0.589826
$73$	−5.36743e6	−1.61487	−0.807433	−	0.589959i	$-0.799144\pi$
$73$	−5.36743e6	−1.61487	−0.807433	+	0.589959i	$0.799144\pi$
$74$	−5.29101e6	−1.51784
$75$	−3.04116e6	−0.832385
$76$	−5.54000e6	−1.44764
$77$	1.88747e6	0.471154
$78$	2.81739e6	0.672227
$79$	4.57098e6	1.04307	0.521536	−	0.853229i	$-0.325359\pi$
$79$	4.57098e6	1.04307	0.521536	+	0.853229i	$0.325359\pi$
$80$	−7.55500e6	−1.64975
$81$	531441.	0.111111
$82$	−7.08613e6	−1.41926
$83$	9.49376e6	1.82249	0.911245	−	0.411865i	$-0.135122\pi$
$83$	9.49376e6	1.82249	0.911245	+	0.411865i	$0.135122\pi$
$84$	−6.67478e6	−1.22874
$85$	8.37924e6	1.47992
$86$	−1.82625e7	−3.09610
$87$	−1.08028e6	−0.175881
$88$	5.05477e6	0.790700
$89$	−2.45830e6	−0.369633	−0.184816	−	0.982773i	$-0.559169\pi$
$89$	−2.45830e6	−0.369633	−0.184816	+	0.982773i	$0.559169\pi$
$90$	−6.25851e6	−0.904944
$91$	−5.07953e6	−0.706609
$92$	−8.86717e6	−1.18721
$93$	2.57756e6	0.332290
$94$	1.06247e6	0.131938
$95$	9.36526e6	1.12069
$96$	−324293.	−0.0374101
$97$	−1.41914e7	−1.57879	−0.789397	−	0.613883i	$-0.789607\pi$
$97$	−1.41914e7	−1.57879	−0.789397	+	0.613883i	$0.789607\pi$
$98$	1.80840e6	0.194090
$99$	1.43803e6	0.148952
$100$	2.91011e7	2.91011
$101$	3.81799e6	0.368731	0.184366	−	0.982858i	$-0.440977\pi$
$101$	3.81799e6	0.368731	0.184366	+	0.982858i	$0.440977\pi$
$102$	1.01818e7	0.949998
$103$	1.77672e7	1.60210	0.801049	−	0.598599i	$-0.204276\pi$
$103$	1.77672e7	1.60210	0.801049	+	0.598599i	$0.204276\pi$
$104$	−1.36033e7	−1.18584
$105$	1.12836e7	0.951229
$106$	1.33760e7	1.09083
$107$	2.35965e7	1.86210	0.931051	−	0.364888i	$-0.118893\pi$
$107$	2.35965e7	1.86210	0.931051	+	0.364888i	$0.118893\pi$
$108$	−5.08540e6	−0.388456
$109$	3.99327e6	0.295349	0.147675	−	0.989036i	$-0.452821\pi$
$109$	3.99327e6	0.295349	0.147675	+	0.989036i	$0.452821\pi$
$110$	−1.69350e7	−1.21314
$111$	7.26780e6	0.504397
$112$	1.65512e7	1.11318
$113$	−2.69156e6	−0.175481	−0.0877405	−	0.996143i	$-0.527965\pi$
$113$	−2.69156e6	−0.175481	−0.0877405	+	0.996143i	$0.527965\pi$
$114$	1.13799e7	0.719401
$115$	1.49898e7	0.919079
$116$	1.03373e7	0.614900
$117$	−3.87001e6	−0.223389
$118$	4.03696e6	0.226187
$119$	−1.83569e7	−0.998587
$120$	3.02182e7	1.59637
$121$	−1.55960e7	−0.800321
$122$	−2.50337e7	−1.24815
$123$	9.73362e6	0.471635
$124$	−2.46648e7	−1.16172
$125$	−1.50728e7	−0.690255
$126$	1.37109e7	0.610618
$127$	1.72960e6	0.0749261	0.0374631	−	0.999298i	$-0.488072\pi$
$127$	1.72960e6	0.0749261	0.0374631	+	0.999298i	$0.488072\pi$
$128$	−4.04178e7	−1.70348
$129$	2.50856e7	1.02887
$130$	4.55750e7	1.81939
$131$	1.21153e7	0.470854	0.235427	−	0.971892i	$-0.424351\pi$
$131$	1.21153e7	0.470854	0.235427	+	0.971892i	$0.424351\pi$
$132$	−1.37606e7	−0.520751
$133$	−2.05171e7	−0.756196
$134$	1.23849e7	0.444657
$135$	8.59677e6	0.300723
$136$	−4.91610e7	−1.67585
$137$	−3.48264e7	−1.15714	−0.578571	−	0.815632i	$-0.696389\pi$
$137$	−3.48264e7	−1.15714	−0.578571	+	0.815632i	$0.696389\pi$
$138$	1.82144e7	0.589980
$139$	3.29388e7	1.04029	0.520147	−	0.854077i	$-0.325877\pi$
$139$	3.29388e7	1.04029	0.520147	+	0.854077i	$0.325877\pi$
$140$	−1.07974e8	−3.32560
$141$	−1.45942e6	−0.0438445
$142$	4.03257e7	1.18188
$143$	−1.04719e7	−0.299467
$144$	1.26101e7	0.351924
$145$	−1.74750e7	−0.476025
$146$	−1.05503e8	−2.80563
$147$	−2.48404e6	−0.0644983
$148$	−6.95461e7	−1.76343
$149$	3.14675e7	0.779311	0.389656	−	0.920961i	$-0.372594\pi$
$149$	3.14675e7	0.779311	0.389656	+	0.920961i	$0.372594\pi$
$150$	−5.97775e7	−1.44617
$151$	−2.53600e6	−0.0599419	−0.0299710	−	0.999551i	$-0.509541\pi$
$151$	−2.53600e6	−0.0599419	−0.0299710	+	0.999551i	$0.509541\pi$
$152$	−5.49460e7	−1.26906
$153$	−1.39858e7	−0.315695
$154$	3.71005e7	0.818572
$155$	4.16954e7	0.899348
$156$	3.70324e7	0.780990
$157$	−5.81479e7	−1.19918	−0.599591	−	0.800306i	$-0.704670\pi$
$157$	−5.81479e7	−1.19918	−0.599591	+	0.800306i	$0.704670\pi$
$158$	8.98479e7	1.81221
$159$	−1.83735e7	−0.362494
$160$	−5.24588e6	−0.101251
$161$	−3.28391e7	−0.620155
$162$	1.04461e7	0.193042
$163$	−4.39268e7	−0.794461	−0.397230	−	0.917719i	$-0.630029\pi$
$163$	−4.39268e7	−0.794461	−0.397230	+	0.917719i	$0.630029\pi$
$164$	−9.31417e7	−1.64889
$165$	2.32621e7	0.403139
$166$	1.86611e8	3.16635
$167$	−9.02250e7	−1.49906	−0.749530	−	0.661970i	$-0.769720\pi$
$167$	−9.02250e7	−1.49906	−0.749530	+	0.661970i	$0.769720\pi$
$168$	−6.62009e7	−1.07716
$169$	−3.45668e7	−0.550878
$170$	1.64704e8	2.57118
$171$	−1.56316e7	−0.239065
$172$	−2.40046e8	−3.59704
$173$	2.25125e7	0.330569	0.165285	−	0.986246i	$-0.447146\pi$
$173$	2.25125e7	0.330569	0.165285	+	0.986246i	$0.447146\pi$
$174$	−2.12342e7	−0.305572
$175$	1.07774e8	1.52013
$176$	3.41217e7	0.471777
$177$	−5.54523e6	−0.0751646
$178$	−4.83208e7	−0.642191
$179$	1.26881e8	1.65353	0.826766	−	0.562546i	$-0.190178\pi$
$179$	1.26881e8	1.65353	0.826766	+	0.562546i	$0.190178\pi$
$180$	−8.22632e7	−1.05136
$181$	9.29702e7	1.16538	0.582691	−	0.812694i	$-0.302000\pi$
$181$	9.29702e7	1.16538	0.582691	+	0.812694i	$0.302000\pi$
$182$	−9.98442e7	−1.22765
$183$	3.43866e7	0.414773
$184$	−8.79450e7	−1.04076
$185$	1.17566e8	1.36516
$186$	5.06649e7	0.577314
$187$	−3.78444e7	−0.423210
$188$	1.39653e7	0.153285
$189$	−1.88335e7	−0.202915
$190$	1.84085e8	1.94707
$191$	−1.55664e8	−1.61649	−0.808243	−	0.588850i	$-0.799581\pi$
$191$	−1.55664e8	−1.61649	−0.808243	+	0.588850i	$0.799581\pi$
$192$	5.34067e7	0.544555
$193$	1.85473e7	0.185708	0.0928539	−	0.995680i	$-0.470401\pi$
$193$	1.85473e7	0.185708	0.0928539	+	0.995680i	$0.470401\pi$
$194$	−2.78949e8	−2.74296
$195$	−6.26025e7	−0.604604
$196$	2.37700e7	0.225493
$197$	3.60337e7	0.335798	0.167899	−	0.985804i	$-0.446302\pi$
$197$	3.60337e7	0.335798	0.167899	+	0.985804i	$0.446302\pi$
$198$	2.82662e7	0.258785
$199$	3.41912e7	0.307559	0.153780	−	0.988105i	$-0.450855\pi$
$199$	3.41912e7	0.307559	0.153780	+	0.988105i	$0.450855\pi$
$200$	2.88626e8	2.55112
$201$	−1.70120e7	−0.147765
$202$	7.50471e7	0.640625
$203$	3.82836e7	0.321201
$204$	1.33831e8	1.10370
$205$	1.57454e8	1.27649
$206$	3.49235e8	2.78345
$207$	−2.50195e7	−0.196057
$208$	−9.18278e7	−0.707543
$209$	−4.22977e7	−0.320483
$210$	2.21792e8	1.65264
$211$	1.66203e8	1.21801	0.609005	−	0.793166i	$-0.291569\pi$
$211$	1.66203e8	1.21801	0.609005	+	0.793166i	$0.291569\pi$
$212$	1.75817e8	1.26732
$213$	−5.53919e7	−0.392751
$214$	4.63816e8	3.23517
$215$	4.05793e8	2.78465
$216$	−5.04373e7	−0.340536
$217$	−9.13449e7	−0.606841
$218$	7.84923e7	0.513133
$219$	1.44921e8	0.932343
$220$	−2.22597e8	−1.40942
$221$	1.01846e8	0.634705
$222$	1.42857e8	0.876328
$223$	−2.57838e8	−1.55697	−0.778485	−	0.627663i	$-0.784012\pi$
$223$	−2.57838e8	−1.55697	−0.778485	+	0.627663i	$0.784012\pi$
$224$	1.14925e7	0.0683197
$225$	8.21112e7	0.480578
$226$	−5.29058e7	−0.304877
$227$	−2.27009e8	−1.28811	−0.644055	−	0.764979i	$-0.722749\pi$
$227$	−2.27009e8	−1.28811	−0.644055	+	0.764979i	$0.722749\pi$
$228$	1.49580e8	0.835798
$229$	−7.40017e7	−0.407209	−0.203605	−	0.979053i	$-0.565266\pi$
$229$	−7.40017e7	−0.407209	−0.203605	+	0.979053i	$0.565266\pi$
$230$	2.94642e8	1.59679
$231$	−5.09618e7	−0.272021
$232$	1.02526e8	0.539046
$233$	6.77414e7	0.350839	0.175420	−	0.984494i	$-0.443872\pi$
$233$	6.77414e7	0.350839	0.175420	+	0.984494i	$0.443872\pi$
$234$	−7.60695e7	−0.388110
$235$	−2.36082e7	−0.118665
$236$	5.30628e7	0.262783
$237$	−1.23416e8	−0.602218
$238$	−3.60827e8	−1.73492
$239$	1.28770e8	0.610128	0.305064	−	0.952332i	$-0.401322\pi$
$239$	1.28770e8	0.610128	0.305064	+	0.952332i	$0.401322\pi$
$240$	2.03985e8	0.952486
$241$	−2.97076e8	−1.36712	−0.683561	−	0.729893i	$-0.739570\pi$
$241$	−2.97076e8	−1.36712	−0.683561	+	0.729893i	$0.739570\pi$
$242$	−3.06557e8	−1.39046
$243$	−1.43489e7	−0.0641500
$244$	−3.29048e8	−1.45009
$245$	−4.01827e7	−0.174565
$246$	1.91326e8	0.819408
$247$	1.13831e8	0.480640
$248$	−2.44627e8	−1.01841
$249$	−2.56332e8	−1.05221
$250$	−2.96274e8	−1.19923
$251$	−6.81145e7	−0.271883	−0.135941	−	0.990717i	$-0.543406\pi$
$251$	−6.81145e7	−0.271883	−0.135941	+	0.990717i	$0.543406\pi$
$252$	1.80219e8	0.709413
$253$	−6.77005e7	−0.262827
$254$	3.39974e7	0.130175
$255$	−2.26240e8	−0.854433
$256$	−5.41272e8	−2.01640
$257$	−1.12934e8	−0.415010	−0.207505	−	0.978234i	$-0.566534\pi$
$257$	−1.12934e8	−0.415010	−0.207505	+	0.978234i	$0.566534\pi$
$258$	4.93087e8	1.78754
$259$	−2.57560e8	−0.921149
$260$	5.99049e8	2.11376
$261$	2.91676e7	0.101545
$262$	2.38141e8	0.818050
$263$	5.13397e8	1.74024	0.870119	−	0.492842i	$-0.164042\pi$
$263$	5.13397e8	1.74024	0.870119	+	0.492842i	$0.164042\pi$
$264$	−1.36479e8	−0.456511
$265$	−2.97216e8	−0.981095
$266$	−4.03287e8	−1.31380
$267$	6.63742e7	0.213408
$268$	1.62789e8	0.516600
$269$	−7.41447e7	−0.232245	−0.116123	−	0.993235i	$-0.537047\pi$
$269$	−7.41447e7	−0.232245	−0.116123	+	0.993235i	$0.537047\pi$
$270$	1.68980e8	0.522470
$271$	1.72102e8	0.525285	0.262642	−	0.964893i	$-0.415406\pi$
$271$	1.72102e8	0.525285	0.262642	+	0.964893i	$0.415406\pi$
$272$	−3.31857e8	−0.999907
$273$	1.37147e8	0.407961
$274$	−6.84554e8	−2.01039
$275$	2.22186e8	0.644246
$276$	2.39414e8	0.685436
$277$	4.25097e8	1.20174	0.600868	−	0.799348i	$-0.294822\pi$
$277$	4.25097e8	1.20174	0.600868	+	0.799348i	$0.294822\pi$
$278$	6.47451e8	1.80738
$279$	−6.95940e7	−0.191848
$280$	−1.07089e9	−2.91535
$281$	3.70445e7	0.0995983	0.0497991	−	0.998759i	$-0.484142\pi$
$281$	3.70445e7	0.0995983	0.0497991	+	0.998759i	$0.484142\pi$
$282$	−2.86867e7	−0.0761743
$283$	−2.60297e7	−0.0682679	−0.0341339	−	0.999417i	$-0.510867\pi$
$283$	−2.60297e7	−0.0682679	−0.0341339	+	0.999417i	$0.510867\pi$
$284$	5.30049e8	1.37310
$285$	−2.52862e8	−0.647033
$286$	−2.05837e8	−0.520287
$287$	−3.44945e8	−0.861318
$288$	8.75591e6	0.0215987
$289$	−4.22765e7	−0.103028
$290$	−3.43492e8	−0.827034
$291$	3.83169e8	0.911517
$292$	−1.38676e9	−3.25957
$293$	6.51952e8	1.51418	0.757092	−	0.653308i	$-0.226619\pi$
$293$	6.51952e8	1.51418	0.757092	+	0.653308i	$0.226619\pi$
$294$	−4.88268e7	−0.112058
$295$	−8.97016e7	−0.203434
$296$	−6.89762e8	−1.54589
$297$	−3.88269e7	−0.0859973
$298$	6.18532e8	1.35396
$299$	1.82194e8	0.394172
$300$	−7.85729e8	−1.68015
$301$	−8.88998e8	−1.87896
$302$	−4.98481e7	−0.104142
$303$	−1.03086e8	−0.212887
$304$	−3.70908e8	−0.757196
$305$	5.56250e8	1.12259
$306$	−2.74908e8	−0.548482
$307$	8.07706e8	1.59320	0.796598	−	0.604510i	$-0.206631\pi$
$307$	8.07706e8	1.59320	0.796598	+	0.604510i	$0.206631\pi$
$308$	4.87657e8	0.951014
$309$	−4.79715e8	−0.924972
$310$	8.19573e8	1.56251
$311$	−1.60231e8	−0.302055	−0.151027	−	0.988530i	$-0.548258\pi$
$311$	−1.60231e8	−0.302055	−0.151027	+	0.988530i	$0.548258\pi$
$312$	3.67289e8	0.684647
$313$	2.15368e8	0.396987	0.198494	−	0.980102i	$-0.436395\pi$
$313$	2.15368e8	0.396987	0.198494	+	0.980102i	$0.436395\pi$
$314$	−1.14296e9	−2.08343
$315$	−3.04657e8	−0.549192
$316$	1.18098e9	2.10542
$317$	−8.64021e8	−1.52341	−0.761705	−	0.647924i	$-0.775638\pi$
$317$	−8.64021e8	−1.52341	−0.761705	+	0.647924i	$0.775638\pi$
$318$	−3.61152e8	−0.629789
$319$	7.89250e7	0.136128
$320$	8.63926e8	1.47384
$321$	−6.37104e8	−1.07509
$322$	−6.45490e8	−1.07744
$323$	4.11373e8	0.679246
$324$	1.37306e8	0.224275
$325$	−5.97942e8	−0.966201
$326$	−8.63432e8	−1.38028
$327$	−1.07818e8	−0.170520
$328$	−9.23784e8	−1.44548
$329$	5.17199e7	0.0800704
$330$	4.57244e8	0.700405
$331$	9.12406e8	1.38290	0.691449	−	0.722425i	$-0.256973\pi$
$331$	9.12406e8	1.38290	0.691449	+	0.722425i	$0.256973\pi$
$332$	2.45286e9	3.67865
$333$	−1.96231e8	−0.291214
$334$	−1.77348e9	−2.60443
$335$	−2.75193e8	−0.399926
$336$	−4.46883e8	−0.642697
$337$	5.45796e8	0.776829	0.388414	−	0.921485i	$-0.373023\pi$
$337$	5.45796e8	0.776829	0.388414	+	0.921485i	$0.373023\pi$
$338$	−6.79450e8	−0.957082
$339$	7.26722e7	0.101314
$340$	2.16490e9	2.98719
$341$	−1.88315e8	−0.257185
$342$	−3.07257e8	−0.415347
$343$	−6.99969e8	−0.936589
$344$	−2.38079e9	−3.15331
$345$	−4.04724e8	−0.530631
$346$	4.42510e8	0.574323
$347$	−5.84036e8	−0.750389	−0.375194	−	0.926946i	$-0.622424\pi$
$347$	−5.84036e8	−0.750389	−0.375194	+	0.926946i	$0.622424\pi$
$348$	−2.79107e8	−0.355012
$349$	−7.64386e8	−0.962551	−0.481276	−	0.876569i	$-0.659826\pi$
$349$	−7.64386e8	−0.962551	−0.481276	+	0.876569i	$0.659826\pi$
$350$	2.11843e9	2.64104
$351$	1.04490e8	0.128973
$352$	2.36927e7	0.0289545
$353$	−1.06373e9	−1.28712	−0.643559	−	0.765396i	$-0.722543\pi$
$353$	−1.06373e9	−1.28712	−0.643559	+	0.765396i	$0.722543\pi$
$354$	−1.08998e8	−0.130589
$355$	−8.96039e8	−1.06299
$356$	−6.35140e8	−0.746095
$357$	4.95637e8	0.576535
$358$	2.49400e9	2.87281
$359$	−1.09179e9	−1.24540	−0.622700	−	0.782461i	$-0.713964\pi$
$359$	−1.09179e9	−1.24540	−0.622700	+	0.782461i	$0.713964\pi$
$360$	−8.15890e8	−0.921665
$361$	−4.34091e8	−0.485630
$362$	1.82744e9	2.02471
$363$	4.21092e8	0.462065
$364$	−1.31237e9	−1.42627
$365$	2.34429e9	2.52340
$366$	6.75909e8	0.720617
$367$	−1.92123e8	−0.202884	−0.101442	−	0.994841i	$-0.532346\pi$
$367$	−1.92123e8	−0.202884	−0.101442	+	0.994841i	$0.532346\pi$
$368$	−5.93665e8	−0.620975
$369$	−2.62808e8	−0.272299
$370$	2.31091e9	2.37179
$371$	6.51129e8	0.662001
$372$	6.65950e8	0.670721
$373$	−1.24365e9	−1.24085	−0.620423	−	0.784267i	$-0.713039\pi$
$373$	−1.24365e9	−1.24085	−0.620423	+	0.784267i	$0.713039\pi$
$374$	−7.43876e8	−0.735275
$375$	4.06966e8	0.398519
$376$	1.38509e8	0.134376
$377$	−2.12401e8	−0.204156
$378$	−3.70194e8	−0.352540
$379$	−2.03376e9	−1.91894	−0.959472	−	0.281805i	$-0.909067\pi$
$379$	−2.03376e9	−1.91894	−0.959472	+	0.281805i	$0.909067\pi$
$380$	2.41966e9	2.26210
$381$	−4.66993e7	−0.0432586
$382$	−3.05976e9	−2.80844
$383$	−8.58688e8	−0.780979	−0.390490	−	0.920607i	$-0.627694\pi$
$383$	−8.58688e8	−0.780979	−0.390490	+	0.920607i	$0.627694\pi$
$384$	1.09128e9	0.983507
$385$	−8.24375e8	−0.736228
$386$	3.64569e8	0.322645
$387$	−6.77311e8	−0.594019
$388$	−3.66657e9	−3.18676
$389$	−1.79662e9	−1.54751	−0.773755	−	0.633485i	$-0.781624\pi$
$389$	−1.79662e9	−1.54751	−0.773755	+	0.633485i	$0.781624\pi$
$390$	−1.23053e9	−1.05042
$391$	6.58433e8	0.557049
$392$	2.35752e8	0.197676
$393$	−3.27114e8	−0.271848
$394$	7.08285e8	0.583407
$395$	−1.99643e9	−1.62991
$396$	3.71537e8	0.300656
$397$	−1.32366e9	−1.06172	−0.530860	−	0.847460i	$-0.678131\pi$
$397$	−1.32366e9	−1.06172	−0.530860	+	0.847460i	$0.678131\pi$
$398$	6.72069e8	0.534347
$399$	5.53961e8	0.436590
$400$	1.94834e9	1.52214
$401$	−1.25074e9	−0.968635	−0.484317	−	0.874892i	$-0.660932\pi$
$401$	−1.25074e9	−0.968635	−0.484317	+	0.874892i	$0.660932\pi$
$402$	−3.34392e8	−0.256723
$403$	5.06790e8	0.385710
$404$	9.86435e8	0.744276
$405$	−2.32113e8	−0.173623
$406$	7.52510e8	0.558047
$407$	−5.30983e8	−0.390391
$408$	1.32735e9	0.967551
$409$	1.84026e9	1.32999	0.664993	−	0.746850i	$-0.268435\pi$
$409$	1.84026e9	1.32999	0.664993	+	0.746850i	$0.268435\pi$
$410$	3.09495e9	2.21774
$411$	9.40313e8	0.668076
$412$	4.59043e9	3.23380
$413$	1.96515e8	0.137268
$414$	−4.91788e8	−0.340625
$415$	−4.14651e9	−2.84783
$416$	−6.37614e7	−0.0434242
$417$	−8.89348e8	−0.600614
$418$	−8.31411e8	−0.556799
$419$	1.97514e9	1.31174	0.655871	−	0.754873i	$-0.272301\pi$
$419$	1.97514e9	1.31174	0.655871	+	0.754873i	$0.272301\pi$
$420$	2.91529e9	1.92003
$421$	1.04914e9	0.685247	0.342624	−	0.939473i	$-0.388684\pi$
$421$	1.04914e9	0.685247	0.342624	+	0.939473i	$0.388684\pi$
$422$	3.26692e9	2.11614
$423$	3.94045e7	0.0253136
$424$	1.74376e9	1.11098
$425$	−2.16091e9	−1.36545
$426$	−1.08879e9	−0.682357
$427$	−1.21861e9	−0.757474
$428$	6.09650e9	3.75861
$429$	2.82741e8	0.172897
$430$	7.97635e9	4.83798
$431$	1.15205e9	0.693109	0.346554	−	0.938030i	$-0.387352\pi$
$431$	1.15205e9	0.693109	0.346554	+	0.938030i	$0.387352\pi$
$432$	−3.40472e8	−0.203183
$433$	2.37623e9	1.40663	0.703317	−	0.710877i	$-0.251702\pi$
$433$	2.37623e9	1.40663	0.703317	+	0.710877i	$0.251702\pi$
$434$	−1.79549e9	−1.05431
$435$	4.71825e8	0.274833
$436$	1.03172e9	0.596155
$437$	7.35913e8	0.421834
$438$	2.84858e9	1.61983
$439$	−6.70393e8	−0.378185	−0.189092	−	0.981959i	$-0.560555\pi$
$439$	−6.70393e8	−0.378185	−0.189092	+	0.981959i	$0.560555\pi$
$440$	−2.20773e9	−1.23555
$441$	6.70691e7	0.0372381
$442$	2.00191e9	1.10272
$443$	−2.24468e9	−1.22671	−0.613354	−	0.789808i	$-0.710180\pi$
$443$	−2.24468e9	−1.22671	−0.613354	+	0.789808i	$0.710180\pi$
$444$	1.87775e9	1.01811
$445$	1.07369e9	0.577590
$446$	−5.06811e9	−2.70504
$447$	−8.49624e8	−0.449936
$448$	−1.89266e9	−0.994487
$449$	−5.76894e8	−0.300769	−0.150385	−	0.988628i	$-0.548051\pi$
$449$	−5.76894e8	−0.300769	−0.150385	+	0.988628i	$0.548051\pi$
$450$	1.61399e9	0.834945
$451$	−7.11134e8	−0.365034
$452$	−6.95406e8	−0.354204
$453$	6.84721e7	0.0346075
$454$	−4.46213e9	−2.23793
$455$	2.21854e9	1.10415
$456$	1.48354e9	0.732694
$457$	9.02311e8	0.442231	0.221116	−	0.975248i	$-0.429030\pi$
$457$	9.02311e8	0.442231	0.221116	+	0.975248i	$0.429030\pi$
$458$	−1.45459e9	−0.707476
$459$	3.77617e8	0.182267
$460$	3.87284e9	1.85514
$461$	1.56907e9	0.745913	0.372956	−	0.927849i	$-0.378344\pi$
$461$	1.56907e9	0.745913	0.372956	+	0.927849i	$0.378344\pi$
$462$	−1.00171e9	−0.472603
$463$	6.01283e8	0.281543	0.140772	−	0.990042i	$-0.455042\pi$
$463$	6.01283e8	0.281543	0.140772	+	0.990042i	$0.455042\pi$
$464$	6.92092e8	0.321626
$465$	−1.12578e9	−0.519239
$466$	1.33154e9	0.609540
$467$	−2.18611e9	−0.993260	−0.496630	−	0.867962i	$-0.665429\pi$
$467$	−2.18611e9	−0.993260	−0.496630	+	0.867962i	$0.665429\pi$
$468$	−9.99874e8	−0.450905
$469$	6.02882e8	0.269853
$470$	−4.64046e8	−0.206167
$471$	1.56999e9	0.692348
$472$	5.26279e8	0.230366
$473$	−1.83274e9	−0.796320
$474$	−2.42589e9	−1.04628
$475$	−2.41519e9	−1.03401
$476$	−4.74279e9	−2.01563
$477$	4.96084e8	0.209286
$478$	2.53112e9	1.06002
$479$	1.17364e9	0.487936	0.243968	−	0.969783i	$-0.421551\pi$
$479$	1.17364e9	0.487936	0.243968	+	0.969783i	$0.421551\pi$
$480$	1.41639e8	0.0584571
$481$	1.42897e9	0.585485
$482$	−5.83937e9	−2.37521
$483$	8.86655e8	0.358047
$484$	−4.02946e9	−1.61543
$485$	6.19827e9	2.46703
$486$	−2.82045e8	−0.111453
$487$	1.37532e9	0.539574	0.269787	−	0.962920i	$-0.413047\pi$
$487$	1.37532e9	0.539574	0.269787	+	0.962920i	$0.413047\pi$
$488$	−3.26352e9	−1.27121
$489$	1.18602e9	0.458682
$490$	−7.89838e8	−0.303286
$491$	4.93551e9	1.88168	0.940842	−	0.338845i	$-0.110036\pi$
$491$	4.93551e9	1.88168	0.940842	+	0.338845i	$0.110036\pi$
$492$	2.51483e9	0.951985
$493$	−7.67598e8	−0.288516
$494$	2.23748e9	0.835053
$495$	−6.28077e8	−0.232753
$496$	−1.65133e9	−0.607643
$497$	1.96301e9	0.717257
$498$	−5.03850e9	−1.82809
$499$	−4.54580e9	−1.63779	−0.818895	−	0.573943i	$-0.805413\pi$
$499$	−4.54580e9	−1.63779	−0.818895	+	0.573943i	$0.805413\pi$
$500$	−3.89429e9	−1.39326
$501$	2.43607e9	0.865483
$502$	−1.33887e9	−0.472362
$503$	1.13170e9	0.396500	0.198250	−	0.980151i	$-0.436474\pi$
$503$	1.13170e9	0.396500	0.198250	+	0.980151i	$0.436474\pi$
$504$	1.78742e9	0.621900
$505$	−1.66755e9	−0.576181
$506$	−1.33073e9	−0.456630
$507$	9.33302e8	0.318049
$508$	4.46869e8	0.151237
$509$	3.02720e9	1.01749	0.508743	−	0.860918i	$-0.330110\pi$
$509$	3.02720e9	1.01749	0.508743	+	0.860918i	$0.330110\pi$
$510$	−4.44700e9	−1.48447
$511$	−5.13578e9	−1.70268
$512$	−5.46586e9	−1.79976
$513$	4.22053e8	0.138024
$514$	−2.21985e9	−0.721028
$515$	−7.76003e9	−2.50345
$516$	6.48124e9	2.07675
$517$	1.06625e8	0.0339345
$518$	−5.06265e9	−1.60038
$519$	−6.07838e8	−0.190854
$520$	5.94139e9	1.85301
$521$	9.37018e8	0.290279	0.145140	−	0.989411i	$-0.453637\pi$
$521$	9.37018e8	0.290279	0.145140	+	0.989411i	$0.453637\pi$
$522$	5.73324e8	0.176422
$523$	2.52142e9	0.770708	0.385354	−	0.922769i	$-0.374079\pi$
$523$	2.52142e9	0.770708	0.385354	+	0.922769i	$0.374079\pi$
$524$	3.13018e9	0.950407
$525$	−2.90990e9	−0.877649
$526$	1.00914e10	3.02345
$527$	1.83149e9	0.545089
$528$	−9.21287e8	−0.272381
$529$	−2.22694e9	−0.654055
$530$	−5.84212e9	−1.70453
$531$	1.49721e8	0.0433963
$532$	−5.30089e9	−1.52637
$533$	1.91379e9	0.547456
$534$	1.30466e9	0.370769
$535$	−1.03060e10	−2.90973
$536$	1.61455e9	0.452872
$537$	−3.42580e9	−0.954667
$538$	−1.45740e9	−0.403497
$539$	1.81483e8	0.0499201
$540$	2.22111e9	0.607003
$541$	5.53185e8	0.150204	0.0751018	−	0.997176i	$-0.476072\pi$
$541$	5.53185e8	0.150204	0.0751018	+	0.997176i	$0.476072\pi$
$542$	3.38288e9	0.912617
$543$	−2.51019e9	−0.672834
$544$	−2.30428e8	−0.0613675
$545$	−1.74410e9	−0.461514
$546$	2.69579e9	0.708781
$547$	4.50977e8	0.117814	0.0589072	−	0.998263i	$-0.481238\pi$
$547$	4.50977e8	0.117814	0.0589072	+	0.998263i	$0.481238\pi$
$548$	−8.99792e9	−2.33566
$549$	−9.28439e8	−0.239469
$550$	4.36732e9	1.11930
$551$	−8.57924e8	−0.218483
$552$	2.37452e9	0.600881
$553$	4.37370e9	1.09979
$554$	8.35578e9	2.08787
$555$	−3.17429e9	−0.788173
$556$	8.51024e9	2.09981
$557$	−3.86605e9	−0.947926	−0.473963	−	0.880545i	$-0.657177\pi$
$557$	−3.86605e9	−0.947926	−0.473963	+	0.880545i	$0.657177\pi$
$558$	−1.36795e9	−0.333312
$559$	4.93225e9	1.19427
$560$	−7.22893e9	−1.73947
$561$	1.02180e9	0.244340
$562$	7.28153e8	0.173040
$563$	2.10838e9	0.497930	0.248965	−	0.968512i	$-0.419910\pi$
$563$	2.10838e9	0.497930	0.248965	+	0.968512i	$0.419910\pi$
$564$	−3.77064e8	−0.0884990
$565$	1.17557e9	0.274207
$566$	−5.11644e8	−0.118607
$567$	5.08504e8	0.117153
$568$	5.25706e9	1.20371
$569$	−5.98974e9	−1.36306	−0.681530	−	0.731790i	$-0.738685\pi$
$569$	−5.98974e9	−1.36306	−0.681530	+	0.731790i	$0.738685\pi$
$570$	−4.97030e9	−1.12414
$571$	5.77991e9	1.29925	0.649627	−	0.760253i	$-0.274925\pi$
$571$	5.77991e9	1.29925	0.649627	+	0.760253i	$0.274925\pi$
$572$	−2.70557e9	−0.604467
$573$	4.20293e9	0.933278
$574$	−6.78030e9	−1.49643
$575$	−3.86568e9	−0.847986
$576$	−1.44198e9	−0.314399
$577$	8.69442e8	0.188419	0.0942096	−	0.995552i	$-0.469968\pi$
$577$	8.69442e8	0.188419	0.0942096	+	0.995552i	$0.469968\pi$
$578$	−8.30994e8	−0.178999
$579$	−5.00777e8	−0.107219
$580$	−4.51493e9	−0.960845
$581$	9.08402e9	1.92159
$582$	7.53163e9	1.58365
$583$	1.34236e9	0.280562
$584$	−1.37539e10	−2.85747
$585$	1.69027e9	0.349068
$586$	1.28149e10	2.63071
$587$	−1.19117e9	−0.243074	−0.121537	−	0.992587i	$-0.538782\pi$
$587$	−1.19117e9	−0.243074	−0.121537	+	0.992587i	$0.538782\pi$
$588$	−6.41790e8	−0.130188
$589$	2.04701e9	0.412778
$590$	−1.76319e9	−0.353441
$591$	−9.72911e8	−0.193873
$592$	−4.65618e9	−0.922367
$593$	5.37577e9	1.05864	0.529321	−	0.848421i	$-0.322447\pi$
$593$	5.37577e9	1.05864	0.529321	+	0.848421i	$0.322447\pi$
$594$	−7.63187e8	−0.149410
$595$	8.01760e9	1.56040
$596$	8.13012e9	1.57302
$597$	−9.23164e8	−0.177570
$598$	3.58125e9	0.684826
$599$	−7.00918e9	−1.33252	−0.666260	−	0.745720i	$-0.732106\pi$
$599$	−7.00918e9	−1.33252	−0.666260	+	0.745720i	$0.732106\pi$
$600$	−7.79290e9	−1.47289
$601$	5.18595e9	0.974469	0.487235	−	0.873271i	$-0.338006\pi$
$601$	5.18595e9	0.974469	0.487235	+	0.873271i	$0.338006\pi$
$602$	−1.74743e10	−3.26446
$603$	4.59325e8	0.0853119
$604$	−6.55215e8	−0.120991
$605$	6.81172e9	1.25058
$606$	−2.02627e9	−0.369865
$607$	5.60023e9	1.01636	0.508178	−	0.861252i	$-0.330319\pi$
$607$	5.60023e9	1.01636	0.508178	+	0.861252i	$0.330319\pi$
$608$	−2.57543e8	−0.0464715
$609$	−1.03366e9	−0.185446
$610$	1.09337e10	1.95036
$611$	−2.86947e8	−0.0508929
$612$	−3.61345e9	−0.637224
$613$	3.23965e9	0.568051	0.284025	−	0.958817i	$-0.408330\pi$
$613$	3.23965e9	0.568051	0.284025	+	0.958817i	$0.408330\pi$
$614$	1.58764e10	2.76798
$615$	−4.25127e9	−0.736980
$616$	4.83661e9	0.833697
$617$	1.21036e9	0.207451	0.103726	−	0.994606i	$-0.466924\pi$
$617$	1.21036e9	0.207451	0.103726	+	0.994606i	$0.466924\pi$
$618$	−9.42936e9	−1.60702
$619$	−9.96098e9	−1.68805	−0.844024	−	0.536305i	$-0.819820\pi$
$619$	−9.96098e9	−1.68805	−0.844024	+	0.536305i	$0.819820\pi$
$620$	1.07726e10	1.81531
$621$	6.75527e8	0.113194
$622$	−3.14953e9	−0.524783
$623$	−2.35221e9	−0.389733
$624$	2.47935e9	0.408500
$625$	−2.21642e9	−0.363138
$626$	4.23332e9	0.689717
$627$	1.14204e9	0.185031
$628$	−1.50234e10	−2.42052
$629$	5.16416e9	0.827414
$630$	−5.98839e9	−0.954154
$631$	8.86210e9	1.40422	0.702108	−	0.712071i	$-0.252243\pi$
$631$	8.86210e9	1.40422	0.702108	+	0.712071i	$0.252243\pi$
$632$	1.17130e10	1.84569
$633$	−4.48749e9	−0.703219
$634$	−1.69833e10	−2.64674
$635$	−7.55424e8	−0.117080
$636$	−4.74706e9	−0.731687
$637$	−4.88404e8	−0.0748671
$638$	1.55136e9	0.236505
$639$	1.49558e9	0.226755
$640$	1.76529e10	2.66187
$641$	1.08624e10	1.62901	0.814507	−	0.580154i	$-0.197008\pi$
$641$	1.08624e10	1.62901	0.814507	+	0.580154i	$0.197008\pi$
$642$	−1.25230e10	−1.86783
$643$	−5.64420e9	−0.837267	−0.418634	−	0.908155i	$-0.637491\pi$
$643$	−5.64420e9	−0.837267	−0.418634	+	0.908155i	$0.637491\pi$
$644$	−8.48447e9	−1.25177
$645$	−1.09564e10	−1.60772
$646$	8.08603e9	1.18011
$647$	1.50140e7	0.00217937	0.00108968	−	0.999999i	$-0.499653\pi$
$647$	1.50140e7	0.00217937	0.00108968	+	0.999999i	$0.499653\pi$
$648$	1.36181e9	0.196609
$649$	4.05132e8	0.0581756
$650$	−1.17533e10	−1.67865
$651$	2.46631e9	0.350360
$652$	−1.13491e10	−1.60360
$653$	−3.25704e9	−0.457748	−0.228874	−	0.973456i	$-0.573504\pi$
$653$	−3.25704e9	−0.457748	−0.228874	+	0.973456i	$0.573504\pi$
$654$	−2.11929e9	−0.296257
$655$	−5.29151e9	−0.735758
$656$	−6.23592e9	−0.862457
$657$	−3.91286e9	−0.538289
$658$	1.01661e9	0.139112
$659$	9.09574e9	1.23805	0.619026	−	0.785370i	$-0.287527\pi$
$659$	9.09574e9	1.23805	0.619026	+	0.785370i	$0.287527\pi$
$660$	6.01011e9	0.813727
$661$	−8.48609e9	−1.14289	−0.571443	−	0.820642i	$-0.693616\pi$
$661$	−8.48609e9	−1.14289	−0.571443	+	0.820642i	$0.693616\pi$
$662$	1.79344e10	2.40261
$663$	−2.74985e9	−0.366447
$664$	2.43276e10	3.22486
$665$	8.96106e9	1.18164
$666$	−3.85714e9	−0.505948
$667$	−1.37317e9	−0.179178
$668$	−2.33110e10	−3.02582
$669$	6.96164e9	0.898918
$670$	−5.40923e9	−0.694822
$671$	−2.51227e9	−0.321024
$672$	−3.10297e8	−0.0394444
$673$	−1.43232e10	−1.81129	−0.905646	−	0.424035i	$-0.860613\pi$
$673$	−1.43232e10	−1.81129	−0.905646	+	0.424035i	$0.860613\pi$
$674$	1.07283e10	1.34964
$675$	−2.21700e9	−0.277462
$676$	−8.93084e9	−1.11193
$677$	−2.38817e9	−0.295805	−0.147902	−	0.989002i	$-0.547252\pi$
$677$	−2.38817e9	−0.295805	−0.147902	+	0.989002i	$0.547252\pi$
$678$	1.42846e9	0.176021
$679$	−1.35789e10	−1.66465
$680$	2.14716e10	2.61869
$681$	6.12925e9	0.743690
$682$	−3.70156e9	−0.446827
$683$	1.52714e10	1.83403	0.917013	−	0.398857i	$-0.130593\pi$
$683$	1.52714e10	1.83403	0.917013	+	0.398857i	$0.130593\pi$
$684$	−4.03866e9	−0.482548
$685$	1.52108e10	1.80816
$686$	−1.37587e10	−1.62721
$687$	1.99805e9	0.235102
$688$	−1.60713e10	−1.88145
$689$	−3.61253e9	−0.420770
$690$	−7.95533e9	−0.921905
$691$	−1.01080e10	−1.16544	−0.582721	−	0.812672i	$-0.698012\pi$
$691$	−1.01080e10	−1.16544	−0.582721	+	0.812672i	$0.698012\pi$
$692$	5.81645e9	0.667247
$693$	1.37597e9	0.157051
$694$	−1.14799e10	−1.30371
$695$	−1.43864e10	−1.62557
$696$	−2.76820e9	−0.311218
$697$	6.91626e9	0.773671
$698$	−1.50249e10	−1.67231
$699$	−1.82902e9	−0.202557
$700$	2.78451e10	3.06835
$701$	1.18838e10	1.30299	0.651494	−	0.758654i	$-0.274143\pi$
$701$	1.18838e10	1.30299	0.651494	+	0.758654i	$0.274143\pi$
$702$	2.05388e9	0.224076
$703$	5.77185e9	0.626572
$704$	−3.90188e9	−0.421472
$705$	6.37420e8	0.0685116
$706$	−2.09088e10	−2.23621
$707$	3.65321e9	0.388782
$708$	−1.43269e9	−0.151718
$709$	−1.60939e10	−1.69589	−0.847946	−	0.530082i	$-0.822161\pi$
$709$	−1.60939e10	−1.69589	−0.847946	+	0.530082i	$0.822161\pi$
$710$	−1.76127e10	−1.84681
$711$	3.33224e9	0.347691
$712$	−6.29935e9	−0.654057
$713$	3.27639e9	0.338518
$714$	9.74233e9	1.00166
$715$	4.57372e9	0.467949
$716$	3.27817e10	3.33762
$717$	−3.47678e9	−0.352257
$718$	−2.14604e10	−2.16373
$719$	6.07025e9	0.609053	0.304527	−	0.952504i	$-0.401502\pi$
$719$	6.07025e9	0.609053	0.304527	+	0.952504i	$0.401502\pi$
$720$	−5.50759e9	−0.549918
$721$	1.70004e10	1.68922
$722$	−8.53256e9	−0.843721
$723$	8.02104e9	0.789308
$724$	2.40202e10	2.35230
$725$	4.50659e9	0.439203
$726$	8.27705e9	0.802781
$727$	−1.05256e10	−1.01596	−0.507979	−	0.861369i	$-0.669607\pi$
$727$	−1.05256e10	−1.01596	−0.507979	+	0.861369i	$0.669607\pi$
$728$	−1.30162e10	−1.25033
$729$	3.87420e8	0.0370370
$730$	4.60797e10	4.38409
$731$	1.78247e10	1.68776
$732$	8.88430e9	0.837210
$733$	−8.12696e9	−0.762192	−0.381096	−	0.924536i	$-0.624453\pi$
$733$	−8.12696e9	−0.762192	−0.381096	+	0.924536i	$0.624453\pi$
$734$	−3.77639e9	−0.352485
$735$	1.08493e9	0.100785
$736$	−4.12216e8	−0.0381112
$737$	1.24289e9	0.114366
$738$	−5.16579e9	−0.473086
$739$	−5.50602e9	−0.501860	−0.250930	−	0.968005i	$-0.580736\pi$
$739$	−5.50602e9	−0.501860	−0.250930	+	0.968005i	$0.580736\pi$
$740$	3.03751e10	2.75554
$741$	−3.07343e9	−0.277498
$742$	1.27987e10	1.15014
$743$	−4.28129e9	−0.382925	−0.191462	−	0.981500i	$-0.561323\pi$
$743$	−4.28129e9	−0.382925	−0.191462	+	0.981500i	$0.561323\pi$
$744$	6.60493e9	0.587981
$745$	−1.37438e10	−1.21776
$746$	−2.44455e10	−2.15582
$747$	6.92095e9	0.607497
$748$	−9.77767e9	−0.854240
$749$	2.25781e10	1.96336
$750$	7.99940e9	0.692378
$751$	7.38153e9	0.635926	0.317963	−	0.948103i	$-0.397001\pi$
$751$	7.38153e9	0.635926	0.317963	+	0.948103i	$0.397001\pi$
$752$	9.34992e8	0.0801762
$753$	1.83909e9	0.156971
$754$	−4.17500e9	−0.354696
$755$	1.10763e9	0.0936655
$756$	−4.86592e9	−0.409580
$757$	−2.14892e10	−1.80046	−0.900232	−	0.435410i	$-0.856604\pi$
$757$	−2.14892e10	−1.80046	−0.900232	+	0.435410i	$0.856604\pi$
$758$	−3.99759e10	−3.33393
$759$	1.82791e9	0.151743
$760$	2.39983e10	1.98304
$761$	9.48902e9	0.780504	0.390252	−	0.920708i	$-0.372388\pi$
$761$	9.48902e9	0.780504	0.390252	+	0.920708i	$0.372388\pi$
$762$	−9.17929e8	−0.0751565
$763$	3.82092e9	0.311410
$764$	−4.02182e10	−3.26284
$765$	6.10847e9	0.493307
$766$	−1.68785e10	−1.35685
$767$	−1.09029e9	−0.0872482
$768$	1.46144e10	1.16417
$769$	−2.02433e9	−0.160524	−0.0802620	−	0.996774i	$-0.525576\pi$
$769$	−2.02433e9	−0.160524	−0.0802620	+	0.996774i	$0.525576\pi$
$770$	−1.62041e10	−1.27911
$771$	3.04921e9	0.239606
$772$	4.79198e9	0.374847
$773$	−5.39051e9	−0.419761	−0.209880	−	0.977727i	$-0.567307\pi$
$773$	−5.39051e9	−0.419761	−0.209880	+	0.977727i	$0.567307\pi$
$774$	−1.33133e10	−1.03203
$775$	−1.07527e10	−0.829781
$776$	−3.63652e10	−2.79364
$777$	6.95413e9	0.531826
$778$	−3.53147e10	−2.68861
$779$	7.73012e9	0.585875
$780$	−1.61743e10	−1.22038
$781$	4.04691e9	0.303980
$782$	1.29423e10	0.967803
$783$	−7.87526e8	−0.0586271
$784$	1.59142e9	0.117945
$785$	2.53968e10	1.87385
$786$	−6.42981e9	−0.472301
$787$	−3.44573e8	−0.0251982	−0.0125991	−	0.999921i	$-0.504011\pi$
$787$	−3.44573e8	−0.0251982	−0.0125991	+	0.999921i	$0.504011\pi$
$788$	9.30986e9	0.677800
$789$	−1.38617e10	−1.00473
$790$	−3.92421e10	−2.83177
$791$	−2.57540e9	−0.185023
$792$	3.68492e9	0.263567
$793$	6.76098e9	0.481453
$794$	−2.60181e10	−1.84461
$795$	8.02482e9	0.566436
$796$	8.83382e9	0.620802
$797$	7.94031e9	0.555563	0.277781	−	0.960644i	$-0.410401\pi$
$797$	7.94031e9	0.555563	0.277781	+	0.960644i	$0.410401\pi$
$798$	1.08888e10	0.758522
$799$	−1.03700e9	−0.0719225
$800$	1.35285e9	0.0934188
$801$	−1.79210e9	−0.123211
$802$	−2.45847e10	−1.68288
$803$	−1.05878e10	−0.721611
$804$	−4.39532e9	−0.298259
$805$	1.43428e10	0.969057
$806$	9.96156e9	0.670123
$807$	2.00191e9	0.134087
$808$	9.78352e9	0.652462
$809$	1.83573e10	1.21896	0.609478	−	0.792803i	$-0.291379\pi$
$809$	1.83573e10	1.21896	0.609478	+	0.792803i	$0.291379\pi$
$810$	−4.56245e9	−0.301648
$811$	−2.86473e10	−1.88587	−0.942934	−	0.332979i	$-0.891946\pi$
$811$	−2.86473e10	−1.88587	−0.942934	+	0.332979i	$0.891946\pi$
$812$	9.89115e9	0.648337
$813$	−4.64677e9	−0.303273
$814$	−1.04371e10	−0.678256
$815$	1.91855e10	1.24143
$816$	8.96014e9	0.577297
$817$	1.99222e10	1.27808
$818$	3.61724e10	2.31069
$819$	−3.70298e9	−0.235536
$820$	4.06807e10	2.57656
$821$	−1.87449e10	−1.18218	−0.591088	−	0.806607i	$-0.701302\pi$
$821$	−1.87449e10	−1.18218	−0.591088	+	0.806607i	$0.701302\pi$
$822$	1.84829e10	1.16070
$823$	2.20970e10	1.38176	0.690881	−	0.722969i	$-0.257223\pi$
$823$	2.20970e10	1.38176	0.690881	+	0.722969i	$0.257223\pi$
$824$	4.55281e10	2.83488
$825$	−5.99901e9	−0.371956
$826$	3.86273e9	0.238487
$827$	7.00279e9	0.430529	0.215264	−	0.976556i	$-0.430939\pi$
$827$	7.00279e9	0.430529	0.215264	+	0.976556i	$0.430939\pi$
$828$	−6.46417e9	−0.395737
$829$	−1.55766e10	−0.949581	−0.474791	−	0.880099i	$-0.657476\pi$
$829$	−1.55766e10	−0.949581	−0.474791	+	0.880099i	$0.657476\pi$
$830$	−8.15045e10	−4.94776
$831$	−1.14776e10	−0.693823
$832$	1.05007e10	0.632099
$833$	−1.76505e9	−0.105803
$834$	−1.74812e10	−1.04349
$835$	3.94068e10	2.34244
$836$	−1.09282e10	−0.646887
$837$	1.87904e9	0.110763
$838$	3.88237e10	2.27899
$839$	−2.48824e10	−1.45454	−0.727268	−	0.686353i	$-0.759210\pi$
$839$	−2.48824e10	−1.45454	−0.727268	+	0.686353i	$0.759210\pi$
$840$	2.89140e10	1.68318
$841$	−1.56490e10	−0.907197
$842$	2.06221e10	1.19053
$843$	−1.00020e9	−0.0575031
$844$	4.29411e10	2.45853
$845$	1.50974e10	0.860804
$846$	7.74541e8	0.0439793
$847$	−1.49229e10	−0.843841
$848$	1.17711e10	0.662876
$849$	7.02802e8	0.0394145
$850$	−4.24751e10	−2.37229
$851$	9.23827e9	0.513851
$852$	−1.43113e10	−0.792760
$853$	−1.67988e10	−0.926736	−0.463368	−	0.886166i	$-0.653359\pi$
$853$	−1.67988e10	−0.926736	−0.463368	+	0.886166i	$0.653359\pi$
$854$	−2.39533e10	−1.31602
$855$	6.82727e9	0.373565
$856$	6.04654e10	3.29495
$857$	−2.93017e10	−1.59023	−0.795115	−	0.606458i	$-0.792590\pi$
$857$	−2.93017e10	−1.59023	−0.795115	+	0.606458i	$0.792590\pi$
$858$	5.55761e9	0.300388
$859$	2.65222e10	1.42769	0.713844	−	0.700305i	$-0.246952\pi$
$859$	2.65222e10	1.42769	0.713844	+	0.700305i	$0.246952\pi$
$860$	1.04843e11	5.62075
$861$	9.31352e9	0.497282
$862$	2.26449e10	1.20419
$863$	2.67744e10	1.41802	0.709009	−	0.705199i	$-0.249142\pi$
$863$	2.67744e10	1.41802	0.709009	+	0.705199i	$0.249142\pi$
$864$	−2.36410e8	−0.0124700
$865$	−9.83259e9	−0.516549
$866$	4.67076e10	2.44385
$867$	1.14147e9	0.0594834
$868$	−2.36003e10	−1.22489
$869$	9.01675e9	0.466102
$870$	9.27428e9	0.477488
$871$	−3.34485e9	−0.171519
$872$	1.02327e10	0.522614
$873$	−1.03456e10	−0.526265
$874$	1.44652e10	0.732885
$875$	−1.44223e10	−0.727790
$876$	3.74424e10	1.88191
$877$	2.17802e10	1.09034	0.545171	−	0.838325i	$-0.316465\pi$
$877$	2.17802e10	1.09034	0.545171	+	0.838325i	$0.316465\pi$
$878$	−1.31774e10	−0.657049
$879$	−1.76027e10	−0.874215
$880$	−1.49031e10	−0.737201
$881$	−2.03738e10	−1.00382	−0.501910	−	0.864920i	$-0.667369\pi$
$881$	−2.03738e10	−1.00382	−0.501910	+	0.864920i	$0.667369\pi$
$882$	1.31832e9	0.0646966
$883$	2.67217e10	1.30618	0.653088	−	0.757282i	$-0.273473\pi$
$883$	2.67217e10	1.30618	0.653088	+	0.757282i	$0.273473\pi$
$884$	2.63135e10	1.28114
$885$	2.42194e9	0.117453
$886$	−4.41218e10	−2.13125
$887$	6.91217e9	0.332569	0.166285	−	0.986078i	$-0.446823\pi$
$887$	6.91217e9	0.332569	0.166285	+	0.986078i	$0.446823\pi$
$888$	1.86236e10	0.892520
$889$	1.65495e9	0.0790005
$890$	2.11047e10	1.00349
$891$	1.04833e9	0.0496506
$892$	−6.66164e10	−3.14271
$893$	−1.15903e9	−0.0544645
$894$	−1.67004e10	−0.781708
$895$	−5.54169e10	−2.58382
$896$	−3.86734e10	−1.79612
$897$	−4.91925e9	−0.227575
$898$	−1.13395e10	−0.522550
$899$	−3.81960e9	−0.175331
$900$	2.12147e10	0.970035
$901$	−1.30553e10	−0.594636
$902$	−1.39782e10	−0.634202
$903$	2.40029e10	1.08482
$904$	−6.89707e9	−0.310510
$905$	−4.06058e10	−1.82103
$906$	1.34590e9	0.0601262
$907$	−1.77215e10	−0.788632	−0.394316	−	0.918975i	$-0.629018\pi$
$907$	−1.77215e10	−0.788632	−0.394316	+	0.918975i	$0.629018\pi$
$908$	−5.86512e10	−2.60002
$909$	2.78332e9	0.122910
$910$	4.36081e10	1.91832
$911$	−2.97591e10	−1.30408	−0.652042	−	0.758183i	$-0.726087\pi$
$911$	−2.97591e10	−1.30408	−0.652042	+	0.758183i	$0.726087\pi$
$912$	1.00145e10	0.437167
$913$	1.87275e10	0.814389
$914$	1.77360e10	0.768323
$915$	−1.50187e10	−0.648127
$916$	−1.91195e10	−0.821942
$917$	1.15925e10	0.496458
$918$	7.42251e9	0.316666
$919$	−7.49318e8	−0.0318465	−0.0159233	−	0.999873i	$-0.505069\pi$
$919$	−7.49318e8	−0.0318465	−0.0159233	+	0.999873i	$0.505069\pi$
$920$	3.84110e10	1.62629
$921$	−2.18081e10	−0.919832
$922$	3.08418e10	1.29593
$923$	−1.08910e10	−0.455891
$924$	−1.31667e10	−0.549068
$925$	−3.03190e10	−1.25956
$926$	1.18189e10	0.489147
$927$	1.29523e10	0.534033
$928$	4.80560e8	0.0197392
$929$	3.70776e10	1.51725	0.758623	−	0.651529i	$-0.225872\pi$
$929$	3.70776e10	1.51725	0.758623	+	0.651529i	$0.225872\pi$
$930$	−2.21285e10	−0.902113
$931$	−1.97274e9	−0.0801211
$932$	1.75020e10	0.708161
$933$	4.32624e9	0.174391
$934$	−4.29706e10	−1.72567
$935$	1.65290e10	0.661310
$936$	−9.91680e9	−0.395281
$937$	2.52127e10	1.00122	0.500611	−	0.865672i	$-0.333109\pi$
$937$	2.52127e10	1.00122	0.500611	+	0.865672i	$0.333109\pi$
$938$	1.18504e10	0.468836
$939$	−5.81495e9	−0.229201
$940$	−6.09952e9	−0.239524
$941$	2.49972e10	0.977975	0.488988	−	0.872291i	$-0.337366\pi$
$941$	2.49972e10	0.977975	0.488988	+	0.872291i	$0.337366\pi$
$942$	3.08601e10	1.20287
$943$	1.23726e10	0.480475
$944$	3.55260e9	0.137450
$945$	8.22574e9	0.317076
$946$	−3.60247e10	−1.38351
$947$	−1.83651e10	−0.702696	−0.351348	−	0.936245i	$-0.614277\pi$
$947$	−1.83651e10	−0.702696	−0.351348	+	0.936245i	$0.614277\pi$
$948$	−3.18865e10	−1.21556
$949$	2.84938e10	1.08223
$950$	−4.74733e10	−1.79646
$951$	2.33286e10	0.879541
$952$	−4.70393e10	−1.76698
$953$	−1.85113e10	−0.692805	−0.346403	−	0.938086i	$-0.612597\pi$
$953$	−1.85113e10	−0.692805	−0.346403	+	0.938086i	$0.612597\pi$
$954$	9.75111e9	0.363609
$955$	6.79881e10	2.52593
$956$	3.32696e10	1.23153
$957$	−2.13097e9	−0.0785935
$958$	2.30694e10	0.847728
$959$	−3.33233e10	−1.22007
$960$	−2.33260e10	−0.850924
$961$	−1.83990e10	−0.668749
$962$	2.80881e10	1.01721
$963$	1.72018e10	0.620701
$964$	−7.67540e10	−2.75950
$965$	−8.10075e9	−0.290188
$966$	1.74282e10	0.622062
$967$	−4.59158e10	−1.63294	−0.816469	−	0.577389i	$-0.804072\pi$
$967$	−4.59158e10	−1.63294	−0.816469	+	0.577389i	$0.804072\pi$
$968$	−3.99644e10	−1.41615
$969$	−1.11071e10	−0.392163
$970$	1.21834e11	4.28616
$971$	9.02722e9	0.316437	0.158218	−	0.987404i	$-0.449425\pi$
$971$	9.02722e9	0.316437	0.158218	+	0.987404i	$0.449425\pi$
$972$	−3.70726e9	−0.129485
$973$	3.15172e10	1.09686
$974$	2.70335e10	0.937444
$975$	1.61444e10	0.557836
$976$	−2.20301e10	−0.758476
$977$	2.33504e10	0.801058	0.400529	−	0.916284i	$-0.368826\pi$
$977$	2.33504e10	0.801058	0.400529	+	0.916284i	$0.368826\pi$
$978$	2.33127e10	0.796904
$979$	−4.84927e9	−0.165172
$980$	−1.03818e10	−0.352356
$981$	2.91109e9	0.0984497
$982$	9.70132e10	3.26919
$983$	−4.78814e10	−1.60779	−0.803895	−	0.594771i	$-0.797243\pi$
$983$	−4.78814e10	−1.60779	−0.803895	+	0.594771i	$0.797243\pi$
$984$	2.49422e10	0.834548
$985$	−1.57381e10	−0.524719
$986$	−1.50880e10	−0.501261
$987$	−1.39644e9	−0.0462287
$988$	2.94099e10	0.970162
$989$	3.18869e10	1.04815
$990$	−1.23456e10	−0.404379
$991$	−1.35826e10	−0.443329	−0.221664	−	0.975123i	$-0.571149\pi$
$991$	−1.35826e10	−0.443329	−0.221664	+	0.975123i	$0.571149\pi$
$992$	−1.14662e9	−0.0372930
$993$	−2.46350e10	−0.798417
$994$	3.85852e10	1.24615
$995$	−1.49334e10	−0.480594
$996$	−6.62271e10	−2.12387
$997$	4.46503e10	1.42689	0.713446	−	0.700710i	$-0.247133\pi$
$997$	4.46503e10	1.42689	0.713446	+	0.700710i	$0.247133\pi$
$998$	−8.93530e10	−2.84546
$999$	5.29823e9	0.168132

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.8.a.a.1.16	✓	16
3.2	odd	2		531.8.a.b.1.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.8.a.a.1.16	✓	16	1.1	even	1	trivial
531.8.a.b.1.1		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)

\(f(q)\)	\(=\)	\(q+19.6562 q^{2} -27.0000 q^{3} +258.365 q^{4} -436.761 q^{5} -530.717 q^{6} +956.841 q^{7} +2562.48 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q+19.6562 q^{2} -27.0000 q^{3} +258.365 q^{4} -436.761 q^{5} -530.717 q^{6} +956.841 q^{7} +2562.48 q^{8} +729.000 q^{9} -8585.06 q^{10} +1972.61 q^{11} -6975.86 q^{12} -5308.65 q^{13} +18807.8 q^{14} +11792.6 q^{15} +17297.8 q^{16} -19184.9 q^{17} +14329.3 q^{18} -21442.5 q^{19} -112844. q^{20} -25834.7 q^{21} +38773.9 q^{22} -34320.3 q^{23} -69186.9 q^{24} +112635. q^{25} -104348. q^{26} -19683.0 q^{27} +247214. q^{28} +40010.4 q^{29} +231796. q^{30} -95465.0 q^{31} +12010.9 q^{32} -53260.4 q^{33} -377103. q^{34} -417911. q^{35} +188348. q^{36} -269178. q^{37} -421478. q^{38} +143334. q^{39} -1.11919e6 q^{40} -360504. q^{41} -507811. q^{42} -929097. q^{43} +509653. q^{44} -318399. q^{45} -674606. q^{46} +54052.8 q^{47} -467040. q^{48} +92001.6 q^{49} +2.21398e6 q^{50} +517994. q^{51} -1.37157e6 q^{52} +680499. q^{53} -386892. q^{54} -861559. q^{55} +2.45188e6 q^{56} +578948. q^{57} +786452. q^{58} +205379. q^{59} +3.04678e6 q^{60} -1.27358e6 q^{61} -1.87648e6 q^{62} +697537. q^{63} -1.97803e6 q^{64} +2.31861e6 q^{65} -1.04690e6 q^{66} +630075. q^{67} -4.95672e6 q^{68} +926648. q^{69} -8.21453e6 q^{70} +2.05155e6 q^{71} +1.86805e6 q^{72} -5.36743e6 q^{73} -5.29101e6 q^{74} -3.04116e6 q^{75} -5.54000e6 q^{76} +1.88747e6 q^{77} +2.81739e6 q^{78} +4.57098e6 q^{79} -7.55500e6 q^{80} +531441. q^{81} -7.08613e6 q^{82} +9.49376e6 q^{83} -6.67478e6 q^{84} +8.37924e6 q^{85} -1.82625e7 q^{86} -1.08028e6 q^{87} +5.05477e6 q^{88} -2.45830e6 q^{89} -6.25851e6 q^{90} -5.07953e6 q^{91} -8.86717e6 q^{92} +2.57756e6 q^{93} +1.06247e6 q^{94} +9.36526e6 q^{95} -324293. q^{96} -1.41914e7 q^{97} +1.80840e6 q^{98} +1.43803e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{2} - 432 q^{3} + 974 q^{4} - 68 q^{5} + 162 q^{6} - 2343 q^{7} + 819 q^{8} + 11664 q^{9}+O(q^{10}) \) 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

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