LMFDB - Embedded newform 177.8.a.b.1.1

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:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 2 x^{16} - 1639 x^{15} + 1625 x^{14} + 1070274 x^{13} - 274939 x^{12} - 357079564 x^{11} + \cdots - 58\!\cdots\!76 $ x^17 - 2x^16 - 1639x^15 + 1625x^14 + 1070274x^13 - 274939x^12 - 357079564x^11 - 89298188x^10 + 64650816672x^9 + 33122051904x^8 - 6210397064704x^7 - 2735256748800x^6 + 288860762071040x^5 - 34502173230080x^4 - 5633463408885760x^3 + 4719471961341952x^2 + 37636623107620864x - 58321181718347776
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	multiple of $ 2^{10}\cdot 3^{5} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-20.3182$ 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)

$f(q)$	$=$	$q-22.3182 q^{2} +27.0000 q^{3} +370.104 q^{4} -84.4166 q^{5} -602.593 q^{6} +1532.13 q^{7} -5403.34 q^{8} +729.000 q^{9} +O(q^{10})$	\(q-22.3182 q^{2} +27.0000 q^{3} +370.104 q^{4} -84.4166 q^{5} -602.593 q^{6} +1532.13 q^{7} -5403.34 q^{8} +729.000 q^{9} +1884.03 q^{10} +4639.41 q^{11} +9992.81 q^{12} -1710.47 q^{13} -34194.5 q^{14} -2279.25 q^{15} +73219.7 q^{16} -14226.6 q^{17} -16270.0 q^{18} -21902.8 q^{19} -31242.9 q^{20} +41367.5 q^{21} -103543. q^{22} -107697. q^{23} -145890. q^{24} -70998.8 q^{25} +38174.6 q^{26} +19683.0 q^{27} +567048. q^{28} -195131. q^{29} +50868.8 q^{30} -68117.7 q^{31} -942507. q^{32} +125264. q^{33} +317512. q^{34} -129337. q^{35} +269806. q^{36} -309640. q^{37} +488831. q^{38} -46182.6 q^{39} +456131. q^{40} +873409. q^{41} -923251. q^{42} +159630. q^{43} +1.71706e6 q^{44} -61539.7 q^{45} +2.40360e6 q^{46} -615386. q^{47} +1.97693e6 q^{48} +1.52388e6 q^{49} +1.58457e6 q^{50} -384117. q^{51} -633051. q^{52} -745946. q^{53} -439290. q^{54} -391643. q^{55} -8.27862e6 q^{56} -591374. q^{57} +4.35498e6 q^{58} -205379. q^{59} -843558. q^{60} -2.69167e6 q^{61} +1.52027e6 q^{62} +1.11692e6 q^{63} +1.16630e7 q^{64} +144392. q^{65} -2.79567e6 q^{66} +2.11862e6 q^{67} -5.26531e6 q^{68} -2.90781e6 q^{69} +2.88658e6 q^{70} -1.64750e6 q^{71} -3.93903e6 q^{72} -2.91422e6 q^{73} +6.91062e6 q^{74} -1.91697e6 q^{75} -8.10630e6 q^{76} +7.10818e6 q^{77} +1.03071e6 q^{78} +171784. q^{79} -6.18095e6 q^{80} +531441. q^{81} -1.94930e7 q^{82} +4.94728e6 q^{83} +1.53103e7 q^{84} +1.20096e6 q^{85} -3.56266e6 q^{86} -5.26854e6 q^{87} -2.50683e7 q^{88} -1.83391e6 q^{89} +1.37346e6 q^{90} -2.62066e6 q^{91} -3.98589e7 q^{92} -1.83918e6 q^{93} +1.37343e7 q^{94} +1.84896e6 q^{95} -2.54477e7 q^{96} -1.09662e7 q^{97} -3.40104e7 q^{98} +3.38213e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q - 32 q^{2} + 459 q^{3} + 1166 q^{4} - 1072 q^{5} - 864 q^{6} - 2407 q^{7} - 6645 q^{8} + 12393 q^{9}+O(q^{10}) $ 17 * q - 32 * q^2 + 459 * q^3 + 1166 * q^4 - 1072 * q^5 - 864 * q^6 - 2407 * q^7 - 6645 * q^8 + 12393 * q^9	\( 17 q - 32 q^{2} + 459 q^{3} + 1166 q^{4} - 1072 q^{5} - 864 q^{6} - 2407 q^{7} - 6645 q^{8} + 12393 q^{9} - 6391 q^{10} - 8888 q^{11} + 31482 q^{12} - 12702 q^{13} - 17555 q^{14} - 28944 q^{15} + 139226 q^{16} - 36167 q^{17} - 23328 q^{18} - 71037 q^{19} - 274883 q^{20} - 64989 q^{21} - 325182 q^{22} - 269995 q^{23} - 179415 q^{24} + 97329 q^{25} - 336906 q^{26} + 334611 q^{27} - 901362 q^{28} - 543825 q^{29} - 172557 q^{30} - 633109 q^{31} - 837062 q^{32} - 239976 q^{33} - 529288 q^{34} - 287621 q^{35} + 850014 q^{36} - 867607 q^{37} - 1727169 q^{38} - 342954 q^{39} - 815662 q^{40} - 1428939 q^{41} - 473985 q^{42} - 477060 q^{43} - 1667926 q^{44} - 781488 q^{45} + 5305549 q^{46} - 1217849 q^{47} + 3759102 q^{48} + 4350738 q^{49} + 4561369 q^{50} - 976509 q^{51} + 4175994 q^{52} - 3487068 q^{53} - 629856 q^{54} - 960484 q^{55} - 5363196 q^{56} - 1917999 q^{57} - 3082906 q^{58} - 3491443 q^{59} - 7421841 q^{60} + 998917 q^{61} - 5742614 q^{62} - 1754703 q^{63} + 17531621 q^{64} - 6075816 q^{65} - 8779914 q^{66} - 356026 q^{67} - 16149231 q^{68} - 7289865 q^{69} - 548798 q^{70} - 12879428 q^{71} - 4844205 q^{72} - 6176157 q^{73} - 5971906 q^{74} + 2627883 q^{75} - 17624580 q^{76} + 239687 q^{77} - 9096462 q^{78} - 18886490 q^{79} - 70463349 q^{80} + 9034497 q^{81} - 19351611 q^{82} - 22824893 q^{83} - 24336774 q^{84} - 7973079 q^{85} - 27502196 q^{86} - 14683275 q^{87} - 62527651 q^{88} - 30609647 q^{89} - 4659039 q^{90} - 36301521 q^{91} - 41388548 q^{92} - 17093943 q^{93} + 1010176 q^{94} - 29303629 q^{95} - 22600674 q^{96} - 26249806 q^{97} - 93110852 q^{98} - 6479352 q^{99}+O(q^{100}) \) 17 * q - 32 * q^2 + 459 * q^3 + 1166 * q^4 - 1072 * q^5 - 864 * q^6 - 2407 * q^7 - 6645 * q^8 + 12393 * q^9 - 6391 * q^10 - 8888 * q^11 + 31482 * q^12 - 12702 * q^13 - 17555 * q^14 - 28944 * q^15 + 139226 * q^16 - 36167 * q^17 - 23328 * q^18 - 71037 * q^19 - 274883 * q^20 - 64989 * q^21 - 325182 * q^22 - 269995 * q^23 - 179415 * q^24 + 97329 * q^25 - 336906 * q^26 + 334611 * q^27 - 901362 * q^28 - 543825 * q^29 - 172557 * q^30 - 633109 * q^31 - 837062 * q^32 - 239976 * q^33 - 529288 * q^34 - 287621 * q^35 + 850014 * q^36 - 867607 * q^37 - 1727169 * q^38 - 342954 * q^39 - 815662 * q^40 - 1428939 * q^41 - 473985 * q^42 - 477060 * q^43 - 1667926 * q^44 - 781488 * q^45 + 5305549 * q^46 - 1217849 * q^47 + 3759102 * q^48 + 4350738 * q^49 + 4561369 * q^50 - 976509 * q^51 + 4175994 * q^52 - 3487068 * q^53 - 629856 * q^54 - 960484 * q^55 - 5363196 * q^56 - 1917999 * q^57 - 3082906 * q^58 - 3491443 * q^59 - 7421841 * q^60 + 998917 * q^61 - 5742614 * q^62 - 1754703 * q^63 + 17531621 * q^64 - 6075816 * q^65 - 8779914 * q^66 - 356026 * q^67 - 16149231 * q^68 - 7289865 * q^69 - 548798 * q^70 - 12879428 * q^71 - 4844205 * q^72 - 6176157 * q^73 - 5971906 * q^74 + 2627883 * q^75 - 17624580 * q^76 + 239687 * q^77 - 9096462 * q^78 - 18886490 * q^79 - 70463349 * q^80 + 9034497 * q^81 - 19351611 * q^82 - 22824893 * q^83 - 24336774 * q^84 - 7973079 * q^85 - 27502196 * q^86 - 14683275 * q^87 - 62527651 * q^88 - 30609647 * q^89 - 4659039 * q^90 - 36301521 * q^91 - 41388548 * q^92 - 17093943 * q^93 + 1010176 * q^94 - 29303629 * q^95 - 22600674 * q^96 - 26249806 * q^97 - 93110852 * q^98 - 6479352 * 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 $

$2$	−22.3182	−1.97267	−0.986336	−	0.164744i	$-0.947320\pi$
$2$	−22.3182	−1.97267	−0.986336	+	0.164744i	$0.947320\pi$
$3$	27.0000	0.577350
$3$	27.0000	0.577350
$4$	370.104	2.89144
$5$	−84.4166	−0.302018	−0.151009	−	0.988532i	$-0.548252\pi$
$5$	−84.4166	−0.302018	−0.151009	+	0.988532i	$0.548252\pi$
$6$	−602.593	−1.13892
$7$	1532.13	1.68831	0.844156	−	0.536097i	$-0.180102\pi$
$7$	1532.13	1.68831	0.844156	+	0.536097i	$0.180102\pi$
$8$	−5403.34	−3.73119
$9$	729.000	0.333333
$10$	1884.03	0.595782
$11$	4639.41	1.05097	0.525483	−	0.850804i	$-0.323885\pi$
$11$	4639.41	1.05097	0.525483	+	0.850804i	$0.323885\pi$
$12$	9992.81	1.66937
$13$	−1710.47	−0.215930	−0.107965	−	0.994155i	$-0.534433\pi$
$13$	−1710.47	−0.215930	−0.107965	+	0.994155i	$0.534433\pi$
$14$	−34194.5	−3.33049
$15$	−2279.25	−0.174370
$16$	73219.7	4.46897
$17$	−14226.6	−0.702310	−0.351155	−	0.936317i	$-0.614211\pi$
$17$	−14226.6	−0.702310	−0.351155	+	0.936317i	$0.614211\pi$
$18$	−16270.0	−0.657558
$19$	−21902.8	−0.732590	−0.366295	−	0.930499i	$-0.619374\pi$
$19$	−21902.8	−0.732590	−0.366295	+	0.930499i	$0.619374\pi$
$20$	−31242.9	−0.873266
$21$	41367.5	0.974748
$22$	−103543.	−2.07321
$23$	−107697.	−1.84567	−0.922836	−	0.385194i	$-0.874135\pi$
$23$	−107697.	−1.84567	−0.922836	+	0.385194i	$0.874135\pi$
$24$	−145890.	−2.15420
$25$	−70998.8	−0.908785
$26$	38174.6	0.425959
$27$	19683.0	0.192450
$28$	567048.	4.88165
$29$	−195131.	−1.48571	−0.742853	−	0.669454i	$-0.766528\pi$
$29$	−195131.	−1.48571	−0.742853	+	0.669454i	$0.766528\pi$
$30$	50868.8	0.343975
$31$	−68117.7	−0.410671	−0.205336	−	0.978692i	$-0.565829\pi$
$31$	−68117.7	−0.410671	−0.205336	+	0.978692i	$0.565829\pi$
$32$	−942507.	−5.08463
$33$	125264.	0.606775
$34$	317512.	1.38543
$35$	−129337.	−0.509901
$36$	269806.	0.963812
$37$	−309640.	−1.00496	−0.502482	−	0.864588i	$-0.667580\pi$
$37$	−309640.	−1.00496	−0.502482	+	0.864588i	$0.667580\pi$
$38$	488831.	1.44516
$39$	−46182.6	−0.124667
$40$	456131.	1.12689
$41$	873409.	1.97913	0.989565	−	0.144086i	$-0.0460242\pi$
$41$	873409.	1.97913	0.989565	+	0.144086i	$0.0460242\pi$
$42$	−923251.	−1.92286
$43$	159630.	0.306179	0.153089	−	0.988212i	$-0.451078\pi$
$43$	159630.	0.306179	0.153089	+	0.988212i	$0.451078\pi$
$44$	1.71706e6	3.03880
$45$	−61539.7	−0.100673
$46$	2.40360e6	3.64091
$47$	−615386.	−0.864580	−0.432290	−	0.901735i	$-0.642294\pi$
$47$	−615386.	−0.864580	−0.432290	+	0.901735i	$0.642294\pi$
$48$	1.97693e6	2.58016
$49$	1.52388e6	1.85040
$50$	1.58457e6	1.79274
$51$	−384117.	−0.405479
$52$	−633051.	−0.624348
$53$	−745946.	−0.688243	−0.344121	−	0.938925i	$-0.611823\pi$
$53$	−745946.	−0.688243	−0.344121	+	0.938925i	$0.611823\pi$
$54$	−439290.	−0.379641
$55$	−391643.	−0.317410
$56$	−8.27862e6	−6.29941
$57$	−591374.	−0.422961
$58$	4.35498e6	2.93081
$59$	−205379.	−0.130189
$59$	−205379.	−0.130189
$60$	−843558.	−0.504180
$61$	−2.69167e6	−1.51833	−0.759167	−	0.650896i	$-0.774393\pi$
$61$	−2.69167e6	−1.51833	−0.759167	+	0.650896i	$0.774393\pi$
$62$	1.52027e6	0.810119
$63$	1.11692e6	0.562771
$64$	1.16630e7	5.56135
$65$	144392.	0.0652147
$66$	−2.79567e6	−1.19697
$67$	2.11862e6	0.860581	0.430290	−	0.902691i	$-0.358411\pi$
$67$	2.11862e6	0.860581	0.430290	+	0.902691i	$0.358411\pi$
$68$	−5.26531e6	−2.03068
$69$	−2.90781e6	−1.06560
$70$	2.88658e6	1.00587
$71$	−1.64750e6	−0.546289	−0.273144	−	0.961973i	$-0.588064\pi$
$71$	−1.64750e6	−0.546289	−0.273144	+	0.961973i	$0.588064\pi$
$72$	−3.93903e6	−1.24373
$73$	−2.91422e6	−0.876783	−0.438391	−	0.898784i	$-0.644452\pi$
$73$	−2.91422e6	−0.876783	−0.438391	+	0.898784i	$0.644452\pi$
$74$	6.91062e6	1.98247
$75$	−1.91697e6	−0.524687
$76$	−8.10630e6	−2.11824
$77$	7.10818e6	1.77436
$78$	1.03071e6	0.245928
$79$	171784.	0.0392002	0.0196001	−	0.999808i	$-0.493761\pi$
$79$	171784.	0.0392002	0.0196001	+	0.999808i	$0.493761\pi$
$80$	−6.18095e6	−1.34971
$81$	531441.	0.111111
$82$	−1.94930e7	−3.90418
$83$	4.94728e6	0.949714	0.474857	−	0.880063i	$-0.342500\pi$
$83$	4.94728e6	0.949714	0.474857	+	0.880063i	$0.342500\pi$
$84$	1.53103e7	2.81842
$85$	1.20096e6	0.212110
$86$	−3.56266e6	−0.603990
$87$	−5.26854e6	−0.857773
$88$	−2.50683e7	−3.92135
$89$	−1.83391e6	−0.275748	−0.137874	−	0.990450i	$-0.544027\pi$
$89$	−1.83391e6	−0.275748	−0.137874	+	0.990450i	$0.544027\pi$
$90$	1.37346e6	0.198594
$91$	−2.62066e6	−0.364557
$92$	−3.98589e7	−5.33664
$93$	−1.83918e6	−0.237101
$94$	1.37343e7	1.70553
$95$	1.84896e6	0.221255
$96$	−2.54477e7	−2.93561
$97$	−1.09662e7	−1.21998	−0.609992	−	0.792408i	$-0.708827\pi$
$97$	−1.09662e7	−1.21998	−0.609992	+	0.792408i	$0.708827\pi$
$98$	−3.40104e7	−3.65023
$99$	3.38213e6	0.350322
$100$	−2.62770e7	−2.62770
$101$	−7.80317e6	−0.753610	−0.376805	−	0.926293i	$-0.622977\pi$
$101$	−7.80317e6	−0.753610	−0.376805	+	0.926293i	$0.622977\pi$
$102$	8.57282e6	0.799877
$103$	−150244.	−0.0135477	−0.00677386	−	0.999977i	$-0.502156\pi$
$103$	−150244.	−0.0135477	−0.00677386	+	0.999977i	$0.502156\pi$
$104$	9.24223e6	0.805675
$105$	−3.49211e6	−0.294391
$106$	1.66482e7	1.35768
$107$	8.15970e6	0.643918	0.321959	−	0.946754i	$-0.395659\pi$
$107$	8.15970e6	0.643918	0.321959	+	0.946754i	$0.395659\pi$
$108$	7.28476e6	0.556457
$109$	6.65386e6	0.492131	0.246066	−	0.969253i	$-0.420862\pi$
$109$	6.65386e6	0.492131	0.246066	+	0.969253i	$0.420862\pi$
$110$	8.74078e6	0.626147
$111$	−8.36027e6	−0.580217
$112$	1.12182e8	7.54502
$113$	1.76235e7	1.14899	0.574496	−	0.818507i	$-0.305198\pi$
$113$	1.76235e7	1.14899	0.574496	+	0.818507i	$0.305198\pi$
$114$	1.31984e7	0.834364
$115$	9.09137e6	0.557426
$116$	−7.22187e7	−4.29583
$117$	−1.24693e6	−0.0719767
$118$	4.58370e6	0.256820
$119$	−2.17970e7	−1.18572
$120$	1.23155e7	0.650607
$121$	2.03695e6	0.104528
$122$	6.00733e7	2.99517
$123$	2.35821e7	1.14265
$124$	−2.52106e7	−1.18743
$125$	1.25885e7	0.576487
$126$	−2.49278e7	−1.11016
$127$	−2.94003e7	−1.27362	−0.636808	−	0.771023i	$-0.719745\pi$
$127$	−2.94003e7	−1.27362	−0.636808	+	0.771023i	$0.719745\pi$
$128$	−1.39656e8	−5.88608
$129$	4.31001e6	0.176772
$130$	−3.22257e6	−0.128647
$131$	4.56665e6	0.177480	0.0887398	−	0.996055i	$-0.471716\pi$
$131$	4.56665e6	0.177480	0.0887398	+	0.996055i	$0.471716\pi$
$132$	4.63607e7	1.75445
$133$	−3.35579e7	−1.23684
$134$	−4.72839e7	−1.69764
$135$	−1.66157e6	−0.0581234
$136$	7.68709e7	2.62045
$137$	3.33611e6	0.110846	0.0554228	−	0.998463i	$-0.482349\pi$
$137$	3.33611e6	0.110846	0.0554228	+	0.998463i	$0.482349\pi$
$138$	6.48971e7	2.10208
$139$	2.57204e7	0.812317	0.406158	−	0.913803i	$-0.366868\pi$
$139$	2.57204e7	0.812317	0.406158	+	0.913803i	$0.366868\pi$
$140$	−4.78682e7	−1.47435
$141$	−1.66154e7	−0.499166
$142$	3.67694e7	1.07765
$143$	−7.93556e6	−0.226935
$144$	5.33771e7	1.48966
$145$	1.64723e7	0.448710
$146$	6.50402e7	1.72961
$147$	4.11448e7	1.06833
$148$	−1.14599e8	−2.90579
$149$	−7.15213e7	−1.77127	−0.885633	−	0.464387i	$-0.846275\pi$
$149$	−7.15213e7	−1.77127	−0.885633	+	0.464387i	$0.846275\pi$
$150$	4.27834e7	1.03504
$151$	3.70730e7	0.876271	0.438135	−	0.898909i	$-0.355639\pi$
$151$	3.70730e7	0.876271	0.438135	+	0.898909i	$0.355639\pi$
$152$	1.18348e8	2.73343
$153$	−1.03712e7	−0.234103
$154$	−1.58642e8	−3.50023
$155$	5.75026e6	0.124030
$156$	−1.70924e7	−0.360467
$157$	−5.84600e7	−1.20562	−0.602810	−	0.797885i	$-0.705952\pi$
$157$	−5.84600e7	−1.20562	−0.602810	+	0.797885i	$0.705952\pi$
$158$	−3.83392e6	−0.0773291
$159$	−2.01405e7	−0.397357
$160$	7.95632e7	1.53565
$161$	−1.65005e8	−3.11607
$162$	−1.18608e7	−0.219186
$163$	1.08299e8	1.95869	0.979346	−	0.202190i	$-0.0648057\pi$
$163$	1.08299e8	1.95869	0.979346	+	0.202190i	$0.0648057\pi$
$164$	3.23252e8	5.72253
$165$	−1.05744e7	−0.183257
$166$	−1.10415e8	−1.87347
$167$	−6.99062e6	−0.116147	−0.0580735	−	0.998312i	$-0.518496\pi$
$167$	−6.99062e6	−0.116147	−0.0580735	+	0.998312i	$0.518496\pi$
$168$	−2.23523e8	−3.63697
$169$	−5.98228e7	−0.953374
$170$	−2.68033e7	−0.418424
$171$	−1.59671e7	−0.244197
$172$	5.90797e7	0.885296
$173$	−9.78233e7	−1.43642	−0.718209	−	0.695827i	$-0.755038\pi$
$173$	−9.78233e7	−1.43642	−0.718209	+	0.695827i	$0.755038\pi$
$174$	1.17584e8	1.69211
$175$	−1.08780e8	−1.53431
$176$	3.39696e8	4.69674
$177$	−5.54523e6	−0.0751646
$178$	4.09296e7	0.543961
$179$	7.71690e7	1.00567	0.502837	−	0.864381i	$-0.332290\pi$
$179$	7.71690e7	1.00567	0.502837	+	0.864381i	$0.332290\pi$
$180$	−2.27761e7	−0.291089
$181$	−6.26316e7	−0.785088	−0.392544	−	0.919733i	$-0.628405\pi$
$181$	−6.26316e7	−0.785088	−0.392544	+	0.919733i	$0.628405\pi$
$182$	5.84885e7	0.719152
$183$	−7.26750e7	−0.876610
$184$	5.81921e8	6.88655
$185$	2.61387e7	0.303517
$186$	4.10472e7	0.467723
$187$	−6.60028e7	−0.738103
$188$	−2.27757e8	−2.49988
$189$	3.01569e7	0.324916
$190$	−4.12654e7	−0.436464
$191$	−2.82767e7	−0.293638	−0.146819	−	0.989163i	$-0.546903\pi$
$191$	−2.82767e7	−0.293638	−0.146819	+	0.989163i	$0.546903\pi$
$192$	3.14901e8	3.21084
$193$	−3.31268e7	−0.331688	−0.165844	−	0.986152i	$-0.553035\pi$
$193$	−3.31268e7	−0.331688	−0.165844	+	0.986152i	$0.553035\pi$
$194$	2.44746e8	2.40663
$195$	3.89858e6	0.0376517
$196$	5.63995e8	5.35031
$197$	−1.09797e8	−1.02320	−0.511598	−	0.859225i	$-0.670946\pi$
$197$	−1.09797e8	−1.02320	−0.511598	+	0.859225i	$0.670946\pi$
$198$	−7.54832e7	−0.691070
$199$	1.14654e8	1.03134	0.515671	−	0.856787i	$-0.327543\pi$
$199$	1.14654e8	1.03134	0.515671	+	0.856787i	$0.327543\pi$
$200$	3.83631e8	3.39085
$201$	5.72028e7	0.496856
$202$	1.74153e8	1.48663
$203$	−2.98966e8	−2.50834
$204$	−1.42163e8	−1.17242
$205$	−7.37302e7	−0.597733
$206$	3.35318e6	0.0267252
$207$	−7.85108e7	−0.615224
$208$	−1.25240e8	−0.964985
$209$	−1.01616e8	−0.769927
$210$	7.79377e7	0.580737
$211$	−1.35295e8	−0.991502	−0.495751	−	0.868465i	$-0.665107\pi$
$211$	−1.35295e8	−0.991502	−0.495751	+	0.868465i	$0.665107\pi$
$212$	−2.76077e8	−1.99001
$213$	−4.44826e7	−0.315400
$214$	−1.82110e8	−1.27024
$215$	−1.34754e7	−0.0924714
$216$	−1.06354e8	−0.718067
$217$	−1.04365e8	−0.693341
$218$	−1.48502e8	−0.970814
$219$	−7.86839e7	−0.506211
$220$	−1.44949e8	−0.917772
$221$	2.43341e7	0.151650
$222$	1.86587e8	1.14458
$223$	9.14456e7	0.552199	0.276100	−	0.961129i	$-0.410958\pi$
$223$	9.14456e7	0.552199	0.276100	+	0.961129i	$0.410958\pi$
$224$	−1.44404e9	−8.58445
$225$	−5.17582e7	−0.302928
$226$	−3.93325e8	−2.26659
$227$	−8.92462e7	−0.506406	−0.253203	−	0.967413i	$-0.581484\pi$
$227$	−8.92462e7	−0.506406	−0.253203	+	0.967413i	$0.581484\pi$
$228$	−2.18870e8	−1.22297
$229$	2.51758e8	1.38535	0.692673	−	0.721251i	$-0.256433\pi$
$229$	2.51758e8	1.38535	0.692673	+	0.721251i	$0.256433\pi$
$230$	−2.02903e8	−1.09962
$231$	1.91921e8	1.02443
$232$	1.05436e9	5.54345
$233$	3.50359e8	1.81455	0.907273	−	0.420542i	$-0.138160\pi$
$233$	3.50359e8	1.81455	0.907273	+	0.420542i	$0.138160\pi$
$234$	2.78293e7	0.141986
$235$	5.19488e7	0.261119
$236$	−7.60116e7	−0.376433
$237$	4.63817e6	0.0226322
$238$	4.86470e8	2.33903
$239$	1.94400e8	0.921092	0.460546	−	0.887636i	$-0.347654\pi$
$239$	1.94400e8	0.921092	0.460546	+	0.887636i	$0.347654\pi$
$240$	−1.66886e8	−0.779255
$241$	6.19386e7	0.285038	0.142519	−	0.989792i	$-0.454480\pi$
$241$	6.19386e7	0.285038	0.142519	+	0.989792i	$0.454480\pi$
$242$	−4.54612e7	−0.206199
$243$	1.43489e7	0.0641500
$244$	−9.96197e8	−4.39017
$245$	−1.28641e8	−0.558853
$246$	−5.26310e8	−2.25408
$247$	3.74639e7	0.158188
$248$	3.68063e8	1.53229
$249$	1.33576e8	0.548318
$250$	−2.80954e8	−1.13722
$251$	2.42156e8	0.966577	0.483289	−	0.875461i	$-0.339442\pi$
$251$	2.42156e8	0.966577	0.483289	+	0.875461i	$0.339442\pi$
$252$	4.13378e8	1.62722
$253$	−4.99648e8	−1.93974
$254$	6.56162e8	2.51243
$255$	3.24259e7	0.122462
$256$	1.62403e9	6.04996
$257$	−3.80530e8	−1.39837	−0.699187	−	0.714939i	$-0.746454\pi$
$257$	−3.80530e8	−1.39837	−0.699187	+	0.714939i	$0.746454\pi$
$258$	−9.61918e7	−0.348714
$259$	−4.74409e8	−1.69669
$260$	5.34400e7	0.188564
$261$	−1.42250e8	−0.495236
$262$	−1.01920e8	−0.350109
$263$	−1.88914e8	−0.640353	−0.320176	−	0.947358i	$-0.603742\pi$
$263$	−1.88914e8	−0.640353	−0.320176	+	0.947358i	$0.603742\pi$
$264$	−6.76844e8	−2.26399
$265$	6.29702e7	0.207862
$266$	7.48953e8	2.43988
$267$	−4.95155e7	−0.159203
$268$	7.84110e8	2.48832
$269$	2.07575e8	0.650194	0.325097	−	0.945681i	$-0.394603\pi$
$269$	2.07575e8	0.650194	0.325097	+	0.945681i	$0.394603\pi$
$270$	3.70834e7	0.114658
$271$	−7.81832e7	−0.238628	−0.119314	−	0.992857i	$-0.538069\pi$
$271$	−7.81832e7	−0.238628	−0.119314	+	0.992857i	$0.538069\pi$
$272$	−1.04166e9	−3.13860
$273$	−7.07578e7	−0.210477
$274$	−7.44562e7	−0.218662
$275$	−3.29393e8	−0.955102
$276$	−1.07619e9	−3.08111
$277$	−1.30983e8	−0.370284	−0.185142	−	0.982712i	$-0.559274\pi$
$277$	−1.30983e8	−0.370284	−0.185142	+	0.982712i	$0.559274\pi$
$278$	−5.74033e8	−1.60243
$279$	−4.96578e7	−0.136890
$280$	6.98853e8	1.90253
$281$	1.69682e8	0.456209	0.228105	−	0.973637i	$-0.426747\pi$
$281$	1.69682e8	0.456209	0.228105	+	0.973637i	$0.426747\pi$
$282$	3.70827e8	0.984691
$283$	2.01304e8	0.527958	0.263979	−	0.964528i	$-0.414965\pi$
$283$	2.01304e8	0.527958	0.263979	+	0.964528i	$0.414965\pi$
$284$	−6.09748e8	−1.57956
$285$	4.99218e7	0.127742
$286$	1.77108e8	0.447668
$287$	1.33818e9	3.34139
$288$	−6.87088e8	−1.69488
$289$	−2.07944e8	−0.506761
$290$	−3.67632e8	−0.885158
$291$	−2.96087e8	−0.704358
$292$	−1.07856e9	−2.53516
$293$	−4.63019e7	−0.107538	−0.0537691	−	0.998553i	$-0.517123\pi$
$293$	−4.63019e7	−0.107538	−0.0537691	+	0.998553i	$0.517123\pi$
$294$	−9.18280e8	−2.10746
$295$	1.73374e7	0.0393194
$296$	1.67309e9	3.74971
$297$	9.13175e7	0.202258
$298$	1.59623e9	3.49413
$299$	1.84211e8	0.398536
$300$	−7.09478e8	−1.51710
$301$	2.44574e8	0.516925
$302$	−8.27404e8	−1.72859
$303$	−2.10686e8	−0.435097
$304$	−1.60371e9	−3.27393
$305$	2.27221e8	0.458564
$306$	2.31466e8	0.461809
$307$	−8.24546e8	−1.62641	−0.813206	−	0.581975i	$-0.802280\pi$
$307$	−8.24546e8	−1.62641	−0.813206	+	0.581975i	$0.802280\pi$
$308$	2.63077e9	5.13044
$309$	−4.05658e6	−0.00782178
$310$	−1.28336e8	−0.244671
$311$	8.21297e8	1.54824	0.774121	−	0.633038i	$-0.218192\pi$
$311$	8.21297e8	1.54824	0.774121	+	0.633038i	$0.218192\pi$
$312$	2.49540e8	0.465157
$313$	4.00974e8	0.739113	0.369557	−	0.929208i	$-0.379510\pi$
$313$	4.00974e8	0.739113	0.369557	+	0.929208i	$0.379510\pi$
$314$	1.30472e9	2.37829
$315$	−9.42868e7	−0.169967
$316$	6.35779e7	0.113345
$317$	2.03257e8	0.358375	0.179187	−	0.983815i	$-0.442653\pi$
$317$	2.03257e8	0.358375	0.179187	+	0.983815i	$0.442653\pi$
$318$	4.49501e8	0.783855
$319$	−9.05292e8	−1.56143
$320$	−9.84549e8	−1.67963
$321$	2.20312e8	0.371766
$322$	3.68263e9	6.14699
$323$	3.11601e8	0.514505
$324$	1.96688e8	0.321271
$325$	1.21441e8	0.196234
$326$	−2.41704e9	−3.86386
$327$	1.79654e8	0.284132
$328$	−4.71932e9	−7.38451
$329$	−9.42853e8	−1.45968
$330$	2.36001e8	0.361506
$331$	4.59053e8	0.695769	0.347884	−	0.937537i	$-0.386900\pi$
$331$	4.59053e8	0.695769	0.347884	+	0.937537i	$0.386900\pi$
$332$	1.83101e9	2.74604
$333$	−2.25727e8	−0.334988
$334$	1.56018e8	0.229120
$335$	−1.78847e8	−0.259911
$336$	3.02892e9	4.35612
$337$	−1.03100e9	−1.46741	−0.733706	−	0.679467i	$-0.762211\pi$
$337$	−1.03100e9	−1.46741	−0.733706	+	0.679467i	$0.762211\pi$
$338$	1.33514e9	1.88070
$339$	4.75834e8	0.663371
$340$	4.44479e8	0.613303
$341$	−3.16026e8	−0.431601
$342$	3.56358e8	0.481720
$343$	1.07301e9	1.43574
$344$	−8.62534e8	−1.14241
$345$	2.45467e8	0.321830
$346$	2.18324e9	2.83358
$347$	8.50881e8	1.09324	0.546620	−	0.837381i	$-0.315914\pi$
$347$	8.50881e8	1.09324	0.546620	+	0.837381i	$0.315914\pi$
$348$	−1.94991e9	−2.48020
$349$	−7.28476e8	−0.917331	−0.458666	−	0.888609i	$-0.651672\pi$
$349$	−7.28476e8	−0.917331	−0.458666	+	0.888609i	$0.651672\pi$
$350$	2.42777e9	3.02670
$351$	−3.36671e7	−0.0415557
$352$	−4.37268e9	−5.34377
$353$	1.14502e9	1.38548	0.692741	−	0.721186i	$-0.256403\pi$
$353$	1.14502e9	1.38548	0.692741	+	0.721186i	$0.256403\pi$
$354$	1.23760e8	0.148275
$355$	1.39077e8	0.164989
$356$	−6.78737e8	−0.797309
$357$	−5.88518e8	−0.684575
$358$	−1.72228e9	−1.98387
$359$	4.66157e8	0.531743	0.265871	−	0.964008i	$-0.414340\pi$
$359$	4.66157e8	0.531743	0.265871	+	0.964008i	$0.414340\pi$
$360$	3.32520e8	0.375628
$361$	−4.14141e8	−0.463312
$362$	1.39783e9	1.54872
$363$	5.49977e7	0.0603491
$364$	−9.69917e8	−1.05409
$365$	2.46008e8	0.264804
$366$	1.62198e9	1.72926
$367$	1.98730e8	0.209861	0.104930	−	0.994480i	$-0.466538\pi$
$367$	1.98730e8	0.209861	0.104930	+	0.994480i	$0.466538\pi$
$368$	−7.88551e9	−8.24826
$369$	6.36716e8	0.659710
$370$	−5.83370e8	−0.598740
$371$	−1.14289e9	−1.16197
$372$	−6.80687e8	−0.685563
$373$	9.45866e8	0.943732	0.471866	−	0.881670i	$-0.343581\pi$
$373$	9.45866e8	0.943732	0.471866	+	0.881670i	$0.343581\pi$
$374$	1.47307e9	1.45604
$375$	3.39890e8	0.332835
$376$	3.32514e9	3.22591
$377$	3.33765e8	0.320809
$378$	−6.73050e8	−0.640953
$379$	−1.07925e9	−1.01832	−0.509162	−	0.860671i	$-0.670044\pi$
$379$	−1.07925e9	−1.01832	−0.509162	+	0.860671i	$0.670044\pi$
$380$	6.84306e8	0.639746
$381$	−7.93807e8	−0.735322
$382$	6.31086e8	0.579251
$383$	−5.46503e8	−0.497046	−0.248523	−	0.968626i	$-0.579945\pi$
$383$	−5.46503e8	−0.497046	−0.248523	+	0.968626i	$0.579945\pi$
$384$	−3.77073e9	−3.39833
$385$	−6.00048e8	−0.535888
$386$	7.39333e8	0.654311
$387$	1.16370e8	0.102060
$388$	−4.05863e9	−3.52751
$389$	−6.83446e8	−0.588682	−0.294341	−	0.955700i	$-0.595100\pi$
$389$	−6.83446e8	−0.588682	−0.294341	+	0.955700i	$0.595100\pi$
$390$	−8.70094e7	−0.0742745
$391$	1.53215e9	1.29623
$392$	−8.23405e9	−6.90418
$393$	1.23300e8	0.102468
$394$	2.45048e9	2.01843
$395$	−1.45014e7	−0.0118391
$396$	1.25174e9	1.01293
$397$	−1.21932e9	−0.978030	−0.489015	−	0.872275i	$-0.662644\pi$
$397$	−1.21932e9	−0.978030	−0.489015	+	0.872275i	$0.662644\pi$
$398$	−2.55887e9	−2.03450
$399$	−9.06063e8	−0.714091
$400$	−5.19851e9	−4.06134
$401$	−1.27738e9	−0.989268	−0.494634	−	0.869101i	$-0.664698\pi$
$401$	−1.27738e9	−0.989268	−0.494634	+	0.869101i	$0.664698\pi$
$402$	−1.27667e9	−0.980135
$403$	1.16513e8	0.0886762
$404$	−2.88799e9	−2.17902
$405$	−4.48624e7	−0.0335575
$406$	6.67240e9	4.94813
$407$	−1.43655e9	−1.05618
$408$	2.07551e9	1.51292
$409$	−1.52758e9	−1.10401	−0.552004	−	0.833842i	$-0.686137\pi$
$409$	−1.52758e9	−1.10401	−0.552004	+	0.833842i	$0.686137\pi$
$410$	1.64553e9	1.17913
$411$	9.00750e7	0.0639968
$412$	−5.56058e7	−0.0391724
$413$	−3.14668e8	−0.219800
$414$	1.75222e9	1.21364
$415$	−4.17632e8	−0.286831
$416$	1.61213e9	1.09792
$417$	6.94450e8	0.468991
$418$	2.26789e9	1.51881
$419$	2.15816e9	1.43329	0.716645	−	0.697438i	$-0.245677\pi$
$419$	2.15816e9	1.43329	0.716645	+	0.697438i	$0.245677\pi$
$420$	−1.29244e9	−0.851214
$421$	−4.86121e8	−0.317509	−0.158755	−	0.987318i	$-0.550748\pi$
$421$	−4.86121e8	−0.317509	−0.158755	+	0.987318i	$0.550748\pi$
$422$	3.01955e9	1.95591
$423$	−4.48617e8	−0.288193
$424$	4.03059e9	2.56796
$425$	1.01007e9	0.638249
$426$	9.92773e8	0.622181
$427$	−4.12399e9	−2.56342
$428$	3.01994e9	1.86185
$429$	−2.14260e8	−0.131021
$430$	3.00747e8	0.182416
$431$	8.97584e8	0.540013	0.270007	−	0.962858i	$-0.412974\pi$
$431$	8.97584e8	0.540013	0.270007	+	0.962858i	$0.412974\pi$
$432$	1.44118e9	0.860054
$433$	−1.07413e8	−0.0635843	−0.0317921	−	0.999495i	$-0.510121\pi$
$433$	−1.07413e8	−0.0635843	−0.0317921	+	0.999495i	$0.510121\pi$
$434$	2.32925e9	1.36773
$435$	4.44752e8	0.259063
$436$	2.46262e9	1.42297
$437$	2.35885e9	1.35212
$438$	1.75609e9	0.998588
$439$	−4.23839e8	−0.239097	−0.119549	−	0.992828i	$-0.538145\pi$
$439$	−4.23839e8	−0.239097	−0.119549	+	0.992828i	$0.538145\pi$
$440$	2.11618e9	1.18432
$441$	1.11091e9	0.616799
$442$	−5.43094e8	−0.299155
$443$	−1.56918e9	−0.857552	−0.428776	−	0.903411i	$-0.641055\pi$
$443$	−1.56918e9	−0.857552	−0.428776	+	0.903411i	$0.641055\pi$
$444$	−3.09417e9	−1.67766
$445$	1.54812e8	0.0832809
$446$	−2.04091e9	−1.08931
$447$	−1.93108e9	−1.02264
$448$	1.78692e10	9.38929
$449$	−6.52660e8	−0.340271	−0.170135	−	0.985421i	$-0.554420\pi$
$449$	−6.52660e8	−0.340271	−0.170135	+	0.985421i	$0.554420\pi$
$450$	1.15515e9	0.597579
$451$	4.05210e9	2.08000
$452$	6.52252e9	3.32224
$453$	1.00097e9	0.505915
$454$	1.99182e9	0.998974
$455$	2.21227e8	0.110103
$456$	3.19539e9	1.57815
$457$	−3.14784e9	−1.54278	−0.771392	−	0.636360i	$-0.780439\pi$
$457$	−3.14784e9	−1.54278	−0.771392	+	0.636360i	$0.780439\pi$
$458$	−5.61879e9	−2.73284
$459$	−2.80021e8	−0.135160
$460$	3.36475e9	1.61176
$461$	3.81603e9	1.81409	0.907044	−	0.421037i	$-0.138334\pi$
$461$	3.81603e9	1.81409	0.907044	+	0.421037i	$0.138334\pi$
$462$	−4.28334e9	−2.02086
$463$	7.32034e8	0.342766	0.171383	−	0.985204i	$-0.445176\pi$
$463$	7.32034e8	0.342766	0.171383	+	0.985204i	$0.445176\pi$
$464$	−1.42874e10	−6.63958
$465$	1.55257e8	0.0716087
$466$	−7.81941e9	−3.57951
$467$	−9.56937e8	−0.434785	−0.217392	−	0.976084i	$-0.569755\pi$
$467$	−9.56937e8	−0.434785	−0.217392	+	0.976084i	$0.569755\pi$
$468$	−4.61494e8	−0.208116
$469$	3.24601e9	1.45293
$470$	−1.15941e9	−0.515102
$471$	−1.57842e9	−0.696065
$472$	1.10973e9	0.485759
$473$	7.40589e8	0.321783
$474$	−1.03516e8	−0.0446460
$475$	1.55507e9	0.665767
$476$	−8.06714e9	−3.42843
$477$	−5.43794e8	−0.229414
$478$	−4.33866e9	−1.81701
$479$	3.19983e9	1.33031	0.665154	−	0.746706i	$-0.268366\pi$
$479$	3.19983e9	1.33031	0.665154	+	0.746706i	$0.268366\pi$
$480$	2.14821e9	0.886608
$481$	5.29629e8	0.217002
$482$	−1.38236e9	−0.562286
$483$	−4.45514e9	−1.79906
$484$	7.53884e8	0.302236
$485$	9.25727e8	0.368457
$486$	−3.20242e8	−0.126547
$487$	−3.55741e8	−0.139567	−0.0697834	−	0.997562i	$-0.522231\pi$
$487$	−3.55741e8	−0.139567	−0.0697834	+	0.997562i	$0.522231\pi$
$488$	1.45440e10	5.66518
$489$	2.92406e9	1.13085
$490$	2.87104e9	1.10243
$491$	−1.77516e7	−0.00676788	−0.00338394	−	0.999994i	$-0.501077\pi$
$491$	−1.77516e7	−0.00676788	−0.00338394	+	0.999994i	$0.501077\pi$
$492$	8.72781e9	3.30391
$493$	2.77604e9	1.04343
$494$	−8.36129e8	−0.312054
$495$	−2.85508e8	−0.105803
$496$	−4.98755e9	−1.83528
$497$	−2.52419e9	−0.922306
$498$	−2.98119e9	−1.08165
$499$	1.97045e9	0.709927	0.354963	−	0.934880i	$-0.384493\pi$
$499$	1.97045e9	0.709927	0.354963	+	0.934880i	$0.384493\pi$
$500$	4.65906e9	1.66688
$501$	−1.88747e8	−0.0670575
$502$	−5.40449e9	−1.90674
$503$	−4.77882e9	−1.67430	−0.837148	−	0.546976i	$-0.815779\pi$
$503$	−4.77882e9	−1.67430	−0.837148	+	0.546976i	$0.815779\pi$
$504$	−6.03511e9	−2.09980
$505$	6.58717e8	0.227604
$506$	1.11513e10	3.82647
$507$	−1.61522e9	−0.550431
$508$	−1.08812e10	−3.68258
$509$	−2.21746e9	−0.745321	−0.372660	−	0.927968i	$-0.621554\pi$
$509$	−2.21746e9	−0.745321	−0.372660	+	0.927968i	$0.621554\pi$
$510$	−7.23688e8	−0.241577
$511$	−4.46496e9	−1.48028
$512$	−1.83694e10	−6.04852
$513$	−4.31112e8	−0.140987
$514$	8.49277e9	2.75853
$515$	1.26831e7	0.00409165
$516$	1.59515e9	0.511126
$517$	−2.85503e9	−0.908644
$518$	1.05880e10	3.34702
$519$	−2.64123e9	−0.829317
$520$	−7.80197e8	−0.243328
$521$	−2.05916e9	−0.637908	−0.318954	−	0.947770i	$-0.603332\pi$
$521$	−2.05916e9	−0.637908	−0.318954	+	0.947770i	$0.603332\pi$
$522$	3.17478e9	0.976938
$523$	4.60384e9	1.40723	0.703614	−	0.710582i	$-0.251568\pi$
$523$	4.60384e9	1.40723	0.703614	+	0.710582i	$0.251568\pi$
$524$	1.69014e9	0.513171
$525$	−2.93705e9	−0.885836
$526$	4.21623e9	1.26321
$527$	9.69081e8	0.288418
$528$	9.17179e9	2.71166
$529$	8.19372e9	2.40650
$530$	−1.40538e9	−0.410043
$531$	−1.49721e8	−0.0433963
$532$	−1.24199e10	−3.57625
$533$	−1.49394e9	−0.427354
$534$	1.10510e9	0.314056
$535$	−6.88814e8	−0.194475
$536$	−1.14476e10	−3.21099
$537$	2.08356e9	0.580626
$538$	−4.63272e9	−1.28262
$539$	7.06992e9	1.94470
$540$	−6.14954e8	−0.168060
$541$	−5.44524e9	−1.47852	−0.739258	−	0.673422i	$-0.764824\pi$
$541$	−5.44524e9	−1.47852	−0.739258	+	0.673422i	$0.764824\pi$
$542$	1.74491e9	0.470735
$543$	−1.69105e9	−0.453271
$544$	1.34086e10	3.57099
$545$	−5.61696e8	−0.148632
$546$	1.57919e9	0.415203
$547$	−2.09397e9	−0.547035	−0.273518	−	0.961867i	$-0.588187\pi$
$547$	−2.09397e9	−0.547035	−0.273518	+	0.961867i	$0.588187\pi$
$548$	1.23471e9	0.320503
$549$	−1.96223e9	−0.506111
$550$	7.35147e9	1.88410
$551$	4.27390e9	1.08841
$552$	1.57119e10	3.97595
$553$	2.63196e8	0.0661821
$554$	2.92330e9	0.730449
$555$	7.05746e8	0.175236
$556$	9.51921e9	2.34876
$557$	4.55263e9	1.11627	0.558135	−	0.829750i	$-0.311517\pi$
$557$	4.55263e9	1.11627	0.558135	+	0.829750i	$0.311517\pi$
$558$	1.10827e9	0.270040
$559$	−2.73042e8	−0.0661131
$560$	−9.47003e9	−2.27873
$561$	−1.78208e9	−0.426144
$562$	−3.78701e9	−0.899952
$563$	−2.34649e9	−0.554166	−0.277083	−	0.960846i	$-0.589368\pi$
$563$	−2.34649e9	−0.554166	−0.277083	+	0.960846i	$0.589368\pi$
$564$	−6.14944e9	−1.44331
$565$	−1.48771e9	−0.347016
$566$	−4.49274e9	−1.04149
$567$	8.14237e8	0.187590
$568$	8.90202e9	2.03831
$569$	−2.75800e9	−0.627626	−0.313813	−	0.949485i	$-0.601606\pi$
$569$	−2.75800e9	−0.627626	−0.313813	+	0.949485i	$0.601606\pi$
$570$	−1.11417e9	−0.251993
$571$	−1.49430e9	−0.335901	−0.167950	−	0.985795i	$-0.553715\pi$
$571$	−1.49430e9	−0.335901	−0.167950	+	0.985795i	$0.553715\pi$
$572$	−2.93698e9	−0.656168
$573$	−7.63470e8	−0.169532
$574$	−2.98658e10	−6.59147
$575$	7.64633e9	1.67732
$576$	8.50232e9	1.85378
$577$	−5.27606e8	−0.114339	−0.0571695	−	0.998364i	$-0.518208\pi$
$577$	−5.27606e8	−0.114339	−0.0571695	+	0.998364i	$0.518208\pi$
$578$	4.64094e9	0.999673
$579$	−8.94425e8	−0.191500
$580$	6.09646e9	1.29742
$581$	7.57987e9	1.60341
$582$	6.60814e9	1.38947
$583$	−3.46075e9	−0.723319
$584$	1.57465e10	3.27144
$585$	1.05262e8	0.0217382
$586$	1.03338e9	0.212138
$587$	−3.02681e9	−0.617664	−0.308832	−	0.951117i	$-0.599938\pi$
$587$	−3.02681e9	−0.617664	−0.308832	+	0.951117i	$0.599938\pi$
$588$	1.52279e10	3.08900
$589$	1.49197e9	0.300854
$590$	−3.86940e8	−0.0775643
$591$	−2.96452e9	−0.590743
$592$	−2.26717e10	−4.49116
$593$	−7.55687e9	−1.48816	−0.744081	−	0.668089i	$-0.767113\pi$
$593$	−7.55687e9	−1.48816	−0.744081	+	0.668089i	$0.767113\pi$
$594$	−2.03805e9	−0.398990
$595$	1.84002e9	0.358108
$596$	−2.64703e10	−5.12150
$597$	3.09565e9	0.595445
$598$	−4.11127e9	−0.786181
$599$	−7.21826e9	−1.37227	−0.686133	−	0.727476i	$-0.740693\pi$
$599$	−7.21826e9	−1.37227	−0.686133	+	0.727476i	$0.740693\pi$
$600$	1.03580e10	1.95771
$601$	−4.11700e9	−0.773607	−0.386803	−	0.922162i	$-0.626421\pi$
$601$	−4.11700e9	−0.773607	−0.386803	+	0.922162i	$0.626421\pi$
$602$	−5.45846e9	−1.01972
$603$	1.54448e9	0.286860
$604$	1.37209e10	2.53368
$605$	−1.71952e8	−0.0315693
$606$	4.70213e9	0.858303
$607$	3.42535e9	0.621649	0.310824	−	0.950467i	$-0.399395\pi$
$607$	3.42535e9	0.621649	0.310824	+	0.950467i	$0.399395\pi$
$608$	2.06435e10	3.72495
$609$	−8.07209e9	−1.44819
$610$	−5.07118e9	−0.904596
$611$	1.05260e9	0.186689
$612$	−3.83841e9	−0.676895
$613$	−8.07359e9	−1.41565	−0.707823	−	0.706390i	$-0.750323\pi$
$613$	−8.07359e9	−1.41565	−0.707823	+	0.706390i	$0.750323\pi$
$614$	1.84024e10	3.20838
$615$	−1.99072e9	−0.345101
$616$	−3.84079e10	−6.62046
$617$	−7.36421e9	−1.26220	−0.631100	−	0.775702i	$-0.717396\pi$
$617$	−7.36421e9	−1.26220	−0.631100	+	0.775702i	$0.717396\pi$
$618$	9.05358e7	0.0154298
$619$	9.33576e9	1.58210	0.791048	−	0.611755i	$-0.209536\pi$
$619$	9.33576e9	1.58210	0.791048	+	0.611755i	$0.209536\pi$
$620$	2.12820e9	0.358625
$621$	−2.11979e9	−0.355200
$622$	−1.83299e10	−3.05417
$623$	−2.80979e9	−0.465549
$624$	−3.38147e9	−0.557134
$625$	4.48410e9	0.734676
$626$	−8.94903e9	−1.45803
$627$	−2.74363e9	−0.444517
$628$	−2.16363e10	−3.48597
$629$	4.40511e9	0.705796
$630$	2.10432e9	0.335289
$631$	1.58549e9	0.251225	0.125612	−	0.992079i	$-0.459910\pi$
$631$	1.58549e9	0.251225	0.125612	+	0.992079i	$0.459910\pi$
$632$	−9.28206e8	−0.146263
$633$	−3.65297e9	−0.572444
$634$	−4.53633e9	−0.706956
$635$	2.48187e9	0.384655
$636$	−7.45409e9	−1.14893
$637$	−2.60655e9	−0.399556
$638$	2.02045e10	3.08018
$639$	−1.20103e9	−0.182096
$640$	1.17893e10	1.77770
$641$	7.99377e9	1.19880	0.599402	−	0.800448i	$-0.295405\pi$
$641$	7.99377e9	1.19880	0.599402	+	0.800448i	$0.295405\pi$
$642$	−4.91697e9	−0.733373
$643$	−2.26242e9	−0.335610	−0.167805	−	0.985820i	$-0.553668\pi$
$643$	−2.26242e9	−0.335610	−0.167805	+	0.985820i	$0.553668\pi$
$644$	−6.10691e10	−9.00992
$645$	−3.63836e8	−0.0533884
$646$	−6.95438e9	−1.01495
$647$	4.58044e8	0.0664879	0.0332439	−	0.999447i	$-0.489416\pi$
$647$	4.58044e8	0.0664879	0.0332439	+	0.999447i	$0.489416\pi$
$648$	−2.87155e9	−0.414576
$649$	−9.52837e8	−0.136824
$650$	−2.71035e9	−0.387105
$651$	−2.81786e9	−0.400301
$652$	4.00818e10	5.66344
$653$	8.67155e9	1.21871	0.609355	−	0.792897i	$-0.291428\pi$
$653$	8.67155e9	1.21871	0.609355	+	0.792897i	$0.291428\pi$
$654$	−4.00957e9	−0.560500
$655$	−3.85501e8	−0.0536020
$656$	6.39507e10	8.84468
$657$	−2.12446e9	−0.292261
$658$	2.10428e10	2.87947
$659$	8.76494e9	1.19303	0.596513	−	0.802603i	$-0.296552\pi$
$659$	8.76494e9	1.19303	0.596513	+	0.802603i	$0.296552\pi$
$660$	−3.91361e9	−0.529876
$661$	1.58045e9	0.212850	0.106425	−	0.994321i	$-0.466060\pi$
$661$	1.58045e9	0.212850	0.106425	+	0.994321i	$0.466060\pi$
$662$	−1.02453e10	−1.37252
$663$	6.57020e8	0.0875550
$664$	−2.67318e10	−3.54356
$665$	2.83284e9	0.373548
$666$	5.03784e9	0.660822
$667$	2.10149e10	2.74213
$668$	−2.58726e9	−0.335832
$669$	2.46903e9	0.318812
$670$	3.99155e9	0.512719
$671$	−1.24877e10	−1.59572
$672$	−3.89892e10	−4.95623
$673$	−2.26086e9	−0.285905	−0.142952	−	0.989730i	$-0.545660\pi$
$673$	−2.26086e9	−0.285905	−0.142952	+	0.989730i	$0.545660\pi$
$674$	2.30100e10	2.89472
$675$	−1.39747e9	−0.174896
$676$	−2.21407e10	−2.75662
$677$	6.78561e9	0.840483	0.420241	−	0.907412i	$-0.361945\pi$
$677$	6.78561e9	0.840483	0.420241	+	0.907412i	$0.361945\pi$
$678$	−1.06198e10	−1.30861
$679$	−1.68016e10	−2.05971
$680$	−6.48918e9	−0.791423
$681$	−2.40965e9	−0.292374
$682$	7.05314e9	0.851407
$683$	−7.74627e9	−0.930294	−0.465147	−	0.885234i	$-0.653998\pi$
$683$	−7.74627e9	−0.930294	−0.465147	+	0.885234i	$0.653998\pi$
$684$	−5.90949e9	−0.706080
$685$	−2.81623e8	−0.0334774
$686$	−2.39477e10	−2.83224
$687$	6.79746e9	0.799830
$688$	1.16880e10	1.36830
$689$	1.27592e9	0.148612
$690$	−5.47839e9	−0.634865
$691$	−5.90227e9	−0.680528	−0.340264	−	0.940330i	$-0.610516\pi$
$691$	−5.90227e9	−0.680528	−0.340264	+	0.940330i	$0.610516\pi$
$692$	−3.62048e10	−4.15331
$693$	5.18187e9	0.591452
$694$	−1.89902e10	−2.15660
$695$	−2.17122e9	−0.245334
$696$	2.84677e10	3.20051
$697$	−1.24256e10	−1.38996
$698$	1.62583e10	1.80959
$699$	9.45970e9	1.04763
$700$	−4.02597e10	−4.43637
$701$	−1.01648e10	−1.11452	−0.557259	−	0.830339i	$-0.688147\pi$
$701$	−1.01648e10	−1.11452	−0.557259	+	0.830339i	$0.688147\pi$
$702$	7.51391e8	0.0819759
$703$	6.78196e9	0.736227
$704$	5.41094e10	5.84478
$705$	1.40262e9	0.150757
$706$	−2.55548e10	−2.73310
$707$	−1.19555e10	−1.27233
$708$	−2.05231e9	−0.217334
$709$	−7.24332e9	−0.763266	−0.381633	−	0.924314i	$-0.624638\pi$
$709$	−7.24332e9	−0.763266	−0.381633	+	0.924314i	$0.624638\pi$
$710$	−3.10395e9	−0.325469
$711$	1.25231e8	0.0130667
$712$	9.90922e9	1.02887
$713$	7.33604e9	0.757964
$714$	1.31347e10	1.35044
$715$	6.69892e8	0.0685384
$716$	2.85606e10	2.90784
$717$	5.24879e9	0.531792
$718$	−1.04038e10	−1.04895
$719$	1.37810e10	1.38270	0.691350	−	0.722520i	$-0.257016\pi$
$719$	1.37810e10	1.38270	0.691350	+	0.722520i	$0.257016\pi$
$720$	−4.50591e9	−0.449903
$721$	−2.30193e8	−0.0228728
$722$	9.24290e9	0.913962
$723$	1.67234e9	0.164567
$724$	−2.31802e10	−2.27003
$725$	1.38541e10	1.35019
$726$	−1.22745e9	−0.119049
$727$	−1.04638e10	−1.00999	−0.504996	−	0.863122i	$-0.668506\pi$
$727$	−1.04638e10	−1.00999	−0.504996	+	0.863122i	$0.668506\pi$
$728$	1.41603e10	1.36023
$729$	3.87420e8	0.0370370
$730$	−5.49047e9	−0.522372
$731$	−2.27099e9	−0.215032
$732$	−2.68973e10	−2.53466
$733$	−6.09625e9	−0.571740	−0.285870	−	0.958268i	$-0.592283\pi$
$733$	−6.09625e9	−0.571740	−0.285870	+	0.958268i	$0.592283\pi$
$734$	−4.43530e9	−0.413987
$735$	−3.47331e9	−0.322654
$736$	1.01505e11	9.38456
$737$	9.82915e9	0.904440
$738$	−1.42104e10	−1.30139
$739$	1.62223e10	1.47862	0.739308	−	0.673367i	$-0.235153\pi$
$739$	1.62223e10	1.47862	0.739308	+	0.673367i	$0.235153\pi$
$740$	9.67405e9	0.877601
$741$	1.01153e9	0.0913300
$742$	2.55072e10	2.29218
$743$	−2.03461e10	−1.81978	−0.909891	−	0.414847i	$-0.863835\pi$
$743$	−2.03461e10	−1.81978	−0.909891	+	0.414847i	$0.863835\pi$
$744$	9.93770e9	0.884668
$745$	6.03758e9	0.534954
$746$	−2.11101e10	−1.86167
$747$	3.60656e9	0.316571
$748$	−2.44279e10	−2.13418
$749$	1.25017e10	1.08714
$750$	−7.58575e9	−0.656575
$751$	6.71015e9	0.578086	0.289043	−	0.957316i	$-0.406663\pi$
$751$	6.71015e9	0.578086	0.289043	+	0.957316i	$0.406663\pi$
$752$	−4.50584e10	−3.86379
$753$	6.53820e9	0.558054
$754$	−7.44905e9	−0.632850
$755$	−3.12957e9	−0.264649
$756$	1.11612e10	0.939474
$757$	7.51213e9	0.629401	0.314700	−	0.949191i	$-0.398096\pi$
$757$	7.51213e9	0.629401	0.314700	+	0.949191i	$0.398096\pi$
$758$	2.40870e10	2.00882
$759$	−1.34905e10	−1.11991
$760$	−9.99053e9	−0.825545
$761$	1.17043e10	0.962721	0.481361	−	0.876523i	$-0.340143\pi$
$761$	1.17043e10	0.962721	0.481361	+	0.876523i	$0.340143\pi$
$762$	1.77164e10	1.45055
$763$	1.01946e10	0.830871
$764$	−1.04653e10	−0.849035
$765$	8.75498e8	0.0707034
$766$	1.21970e10	0.980509
$767$	3.51294e8	0.0281117
$768$	4.38487e10	3.49295
$769$	−2.01241e9	−0.159579	−0.0797894	−	0.996812i	$-0.525425\pi$
$769$	−2.01241e9	−0.159579	−0.0797894	+	0.996812i	$0.525425\pi$
$770$	1.33920e10	1.05713
$771$	−1.02743e10	−0.807351
$772$	−1.22604e10	−0.959055
$773$	−5.06105e9	−0.394105	−0.197053	−	0.980393i	$-0.563137\pi$
$773$	−5.06105e9	−0.394105	−0.197053	+	0.980393i	$0.563137\pi$
$774$	−2.59718e9	−0.201330
$775$	4.83628e9	0.373212
$776$	5.92539e10	4.55199
$777$	−1.28090e10	−0.979587
$778$	1.52533e10	1.16128
$779$	−1.91301e10	−1.44989
$780$	1.44288e9	0.108868
$781$	−7.64344e9	−0.574130
$782$	−3.41949e10	−2.55704
$783$	−3.84076e9	−0.285924
$784$	1.11578e11	8.26938
$785$	4.93499e9	0.364119
$786$	−2.75183e9	−0.202136
$787$	−1.29130e10	−0.944311	−0.472155	−	0.881515i	$-0.656524\pi$
$787$	−1.29130e10	−0.944311	−0.472155	+	0.881515i	$0.656524\pi$
$788$	−4.06364e10	−2.95851
$789$	−5.10068e9	−0.369708
$790$	3.23646e8	0.0233548
$791$	2.70015e10	1.93986
$792$	−1.82748e10	−1.30712
$793$	4.60401e9	0.327854
$794$	2.72132e10	1.92933
$795$	1.70019e9	0.120009
$796$	4.24338e10	2.98206
$797$	−1.75345e10	−1.22684	−0.613422	−	0.789755i	$-0.710208\pi$
$797$	−1.75345e10	−1.22684	−0.613422	+	0.789755i	$0.710208\pi$
$798$	2.02217e10	1.40867
$799$	8.75483e9	0.607203
$800$	6.69169e10	4.62084
$801$	−1.33692e9	−0.0919161
$802$	2.85088e10	1.95150
$803$	−1.35203e10	−0.921468
$804$	2.11710e10	1.43663
$805$	1.39292e10	0.941109
$806$	−2.60037e9	−0.174929
$807$	5.60454e9	0.375390
$808$	4.21632e10	2.81186
$809$	3.03994e9	0.201858	0.100929	−	0.994894i	$-0.467819\pi$
$809$	3.03994e9	0.201858	0.100929	+	0.994894i	$0.467819\pi$
$810$	1.00125e9	0.0661980
$811$	1.35418e10	0.891465	0.445733	−	0.895166i	$-0.352943\pi$
$811$	1.35418e10	0.891465	0.445733	+	0.895166i	$0.352943\pi$
$812$	−1.10649e11	−7.25270
$813$	−2.11095e9	−0.137772
$814$	3.20612e10	2.08350
$815$	−9.14220e9	−0.591560
$816$	−2.81249e10	−1.81207
$817$	−3.49634e9	−0.224303
$818$	3.40929e10	2.17785
$819$	−1.91046e9	−0.121519
$820$	−2.72879e10	−1.72831
$821$	−1.44424e10	−0.910834	−0.455417	−	0.890278i	$-0.650510\pi$
$821$	−1.44424e10	−0.910834	−0.455417	+	0.890278i	$0.650510\pi$
$822$	−2.01032e9	−0.126245
$823$	1.58161e10	0.989009	0.494504	−	0.869175i	$-0.335350\pi$
$823$	1.58161e10	0.989009	0.494504	+	0.869175i	$0.335350\pi$
$824$	8.11818e8	0.0505491
$825$	−8.89360e9	−0.551428
$826$	7.02283e9	0.433593
$827$	−2.91022e10	−1.78919	−0.894594	−	0.446879i	$-0.852535\pi$
$827$	−2.91022e10	−1.78919	−0.894594	+	0.446879i	$0.852535\pi$
$828$	−2.90572e10	−1.77888
$829$	−1.38090e10	−0.841825	−0.420913	−	0.907101i	$-0.638290\pi$
$829$	−1.38090e10	−0.841825	−0.420913	+	0.907101i	$0.638290\pi$
$830$	9.32081e9	0.565823
$831$	−3.53653e9	−0.213784
$832$	−1.99492e10	−1.20086
$833$	−2.16796e10	−1.29955
$834$	−1.54989e10	−0.925166
$835$	5.90124e8	0.0350785
$836$	−3.76084e10	−2.22620
$837$	−1.34076e9	−0.0790337
$838$	−4.81663e10	−2.82741
$839$	2.26960e10	1.32673	0.663366	−	0.748295i	$-0.269127\pi$
$839$	2.26960e10	1.32673	0.663366	+	0.748295i	$0.269127\pi$
$840$	1.88690e10	1.09843
$841$	2.08262e10	1.20732
$842$	1.08494e10	0.626342
$843$	4.58142e9	0.263393
$844$	−5.00733e10	−2.86687
$845$	5.05004e9	0.287936
$846$	1.00123e10	0.568511
$847$	3.12088e9	0.176476
$848$	−5.46179e10	−3.07574
$849$	5.43520e9	0.304817
$850$	−2.25430e10	−1.25906
$851$	3.33471e10	1.85483
$852$	−1.64632e10	−0.911959
$853$	−2.76986e9	−0.152804	−0.0764022	−	0.997077i	$-0.524343\pi$
$853$	−2.76986e9	−0.152804	−0.0764022	+	0.997077i	$0.524343\pi$
$854$	9.20402e10	5.05679
$855$	1.34789e9	0.0737518
$856$	−4.40896e10	−2.40258
$857$	8.53606e9	0.463260	0.231630	−	0.972804i	$-0.425594\pi$
$857$	8.53606e9	0.463260	0.231630	+	0.972804i	$0.425594\pi$
$858$	4.78191e9	0.258461
$859$	−7.27081e9	−0.391387	−0.195694	−	0.980665i	$-0.562696\pi$
$859$	−7.27081e9	−0.391387	−0.195694	+	0.980665i	$0.562696\pi$
$860$	−4.98730e9	−0.267375
$861$	3.61308e10	1.92915
$862$	−2.00325e10	−1.06527
$863$	2.06289e10	1.09254	0.546270	−	0.837609i	$-0.316047\pi$
$863$	2.06289e10	1.09254	0.546270	+	0.837609i	$0.316047\pi$
$864$	−1.85514e10	−0.978538
$865$	8.25791e9	0.433824
$866$	2.39727e9	0.125431
$867$	−5.61448e9	−0.292579
$868$	−3.86260e10	−2.00475
$869$	7.96976e8	0.0411980
$870$	−9.92607e9	−0.511046
$871$	−3.62383e9	−0.185825
$872$	−3.59530e10	−1.83623
$873$	−7.99434e9	−0.406661
$874$	−5.26454e10	−2.66729
$875$	1.92873e10	0.973291
$876$	−2.91212e10	−1.46368
$877$	1.04224e10	0.521760	0.260880	−	0.965371i	$-0.415987\pi$
$877$	1.04224e10	0.521760	0.260880	+	0.965371i	$0.415987\pi$
$878$	9.45934e9	0.471661
$879$	−1.25015e9	−0.0620872
$880$	−2.86760e10	−1.41850
$881$	3.28267e10	1.61738	0.808690	−	0.588235i	$-0.200177\pi$
$881$	3.28267e10	1.61738	0.808690	+	0.588235i	$0.200177\pi$
$882$	−2.47936e10	−1.21674
$883$	2.09738e10	1.02522	0.512608	−	0.858623i	$-0.328680\pi$
$883$	2.09738e10	1.02522	0.512608	+	0.858623i	$0.328680\pi$
$884$	9.00613e9	0.438486
$885$	4.68110e8	0.0227011
$886$	3.50214e10	1.69167
$887$	4.36272e9	0.209906	0.104953	−	0.994477i	$-0.466531\pi$
$887$	4.36272e9	0.209906	0.104953	+	0.994477i	$0.466531\pi$
$888$	4.51734e10	2.16490
$889$	−4.50451e10	−2.15026
$890$	−3.45514e9	−0.164286
$891$	2.46557e9	0.116774
$892$	3.38444e10	1.59665
$893$	1.34787e10	0.633383
$894$	4.30982e10	2.01733
$895$	−6.51434e9	−0.303732
$896$	−2.13972e11	−9.93754
$897$	4.97371e9	0.230095
$898$	1.45662e10	0.671243
$899$	1.32919e10	0.610137
$900$	−1.91559e10	−0.875899
$901$	1.06122e10	0.483360
$902$	−9.04359e10	−4.10315
$903$	6.60350e9	0.298447
$904$	−9.52256e10	−4.28711
$905$	5.28714e9	0.237111
$906$	−2.23399e10	−0.998005
$907$	9.67343e9	0.430482	0.215241	−	0.976561i	$-0.430946\pi$
$907$	9.67343e9	0.430482	0.215241	+	0.976561i	$0.430946\pi$
$908$	−3.30304e10	−1.46424
$909$	−5.68851e9	−0.251203
$910$	−4.93740e9	−0.217197
$911$	1.13862e10	0.498959	0.249480	−	0.968380i	$-0.419740\pi$
$911$	1.13862e10	0.498959	0.249480	+	0.968380i	$0.419740\pi$
$912$	−4.33002e10	−1.89020
$913$	2.29524e10	0.998116
$914$	7.02542e10	3.04341
$915$	6.13498e9	0.264752
$916$	9.31765e10	4.00564
$917$	6.99671e9	0.299641
$918$	6.24959e9	0.266626
$919$	−1.74980e9	−0.0743676	−0.0371838	−	0.999308i	$-0.511839\pi$
$919$	−1.74980e9	−0.0743676	−0.0371838	+	0.999308i	$0.511839\pi$
$920$	−4.91237e10	−2.07986
$921$	−2.22628e10	−0.939010
$922$	−8.51670e10	−3.57860
$923$	2.81800e9	0.117960
$924$	7.10307e10	2.96206
$925$	2.19841e10	0.913297
$926$	−1.63377e10	−0.676165
$927$	−1.09528e8	−0.00451591
$928$	1.83912e11	7.55428
$929$	−5.01633e9	−0.205273	−0.102636	−	0.994719i	$-0.532728\pi$
$929$	−5.01633e9	−0.205273	−0.102636	+	0.994719i	$0.532728\pi$
$930$	−3.46507e9	−0.141261
$931$	−3.33772e10	−1.35558
$932$	1.29669e11	5.24665
$933$	2.21750e10	0.893878
$934$	2.13572e10	0.857688
$935$	5.57173e9	0.222920
$936$	6.73758e9	0.268558
$937$	2.41581e10	0.959343	0.479672	−	0.877448i	$-0.340756\pi$
$937$	2.41581e10	0.959343	0.479672	+	0.877448i	$0.340756\pi$
$938$	−7.24452e10	−2.86615
$939$	1.08263e10	0.426727
$940$	1.92265e10	0.755009
$941$	−2.00603e10	−0.784826	−0.392413	−	0.919789i	$-0.628360\pi$
$941$	−2.00603e10	−0.784826	−0.392413	+	0.919789i	$0.628360\pi$
$942$	3.52276e10	1.37311
$943$	−9.40632e10	−3.65282
$944$	−1.50378e10	−0.581811
$945$	−2.54574e9	−0.0981304
$946$	−1.65286e10	−0.634772
$947$	−1.33454e10	−0.510632	−0.255316	−	0.966858i	$-0.582180\pi$
$947$	−1.33454e10	−0.510632	−0.255316	+	0.966858i	$0.582180\pi$
$948$	1.71660e9	0.0654396
$949$	4.98467e9	0.189324
$950$	−3.47064e10	−1.31334
$951$	5.48793e9	0.206908
$952$	1.17776e11	4.42414
$953$	−4.58477e10	−1.71590	−0.857950	−	0.513733i	$-0.828262\pi$
$953$	−4.58477e10	−1.71590	−0.857950	+	0.513733i	$0.828262\pi$
$954$	1.21365e10	0.452559
$955$	2.38702e9	0.0886838
$956$	7.19481e10	2.66328
$957$	−2.44429e10	−0.901490
$958$	−7.14146e10	−2.62426
$959$	5.11136e9	0.187142
$960$	−2.65828e10	−0.969732
$961$	−2.28726e10	−0.831349
$962$	−1.18204e10	−0.428074
$963$	5.94842e9	0.214639
$964$	2.29237e10	0.824168
$965$	2.79645e9	0.100176
$966$	9.94309e10	3.54896
$967$	2.81641e10	1.00162	0.500810	−	0.865557i	$-0.333036\pi$
$967$	2.81641e10	1.00162	0.500810	+	0.865557i	$0.333036\pi$
$968$	−1.10063e10	−0.390013
$969$	8.41322e9	0.297050
$970$	−2.06606e10	−0.726845
$971$	2.91527e10	1.02191	0.510954	−	0.859608i	$-0.329292\pi$
$971$	2.91527e10	1.02191	0.510954	+	0.859608i	$0.329292\pi$
$972$	5.31059e9	0.185486
$973$	3.94070e10	1.37144
$974$	7.93951e9	0.275320
$975$	3.27891e9	0.113296
$976$	−1.97083e11	−6.78539
$977$	2.18798e10	0.750607	0.375303	−	0.926902i	$-0.377539\pi$
$977$	2.18798e10	0.750607	0.375303	+	0.926902i	$0.377539\pi$
$978$	−6.52599e10	−2.23080
$979$	−8.50825e9	−0.289802
$980$	−4.76105e10	−1.61589
$981$	4.85066e9	0.164044
$982$	3.96185e8	0.0133508
$983$	7.16781e9	0.240685	0.120342	−	0.992732i	$-0.461601\pi$
$983$	7.16781e9	0.240685	0.120342	+	0.992732i	$0.461601\pi$
$984$	−1.27422e11	−4.26345
$985$	9.26870e9	0.309024
$986$	−6.19564e10	−2.05834
$987$	−2.54570e10	−0.842748
$988$	1.38656e10	0.457391
$989$	−1.71916e10	−0.565105
$990$	6.37203e9	0.208716
$991$	−3.83800e9	−0.125270	−0.0626350	−	0.998037i	$-0.519950\pi$
$991$	−3.83800e9	−0.125270	−0.0626350	+	0.998037i	$0.519950\pi$
$992$	6.42014e10	2.08811
$993$	1.23944e10	0.401702
$994$	5.63355e10	1.81941
$995$	−9.67868e9	−0.311484
$996$	4.94372e10	1.58543
$997$	5.63360e10	1.80033	0.900166	−	0.435547i	$-0.143445\pi$
$997$	5.63360e10	1.80033	0.900166	+	0.435547i	$0.143445\pi$
$998$	−4.39770e10	−1.40045
$999$	−6.09464e9	−0.193406

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.8.a.b.1.1	✓	17
3.2	odd	2		531.8.a.d.1.17		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.8.a.b.1.1	✓	17	1.1	even	1	trivial
531.8.a.d.1.17		17	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)

\(f(q)\)	\(=\)	\(q-22.3182 q^{2} +27.0000 q^{3} +370.104 q^{4} -84.4166 q^{5} -602.593 q^{6} +1532.13 q^{7} -5403.34 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q-22.3182 q^{2} +27.0000 q^{3} +370.104 q^{4} -84.4166 q^{5} -602.593 q^{6} +1532.13 q^{7} -5403.34 q^{8} +729.000 q^{9} +1884.03 q^{10} +4639.41 q^{11} +9992.81 q^{12} -1710.47 q^{13} -34194.5 q^{14} -2279.25 q^{15} +73219.7 q^{16} -14226.6 q^{17} -16270.0 q^{18} -21902.8 q^{19} -31242.9 q^{20} +41367.5 q^{21} -103543. q^{22} -107697. q^{23} -145890. q^{24} -70998.8 q^{25} +38174.6 q^{26} +19683.0 q^{27} +567048. q^{28} -195131. q^{29} +50868.8 q^{30} -68117.7 q^{31} -942507. q^{32} +125264. q^{33} +317512. q^{34} -129337. q^{35} +269806. q^{36} -309640. q^{37} +488831. q^{38} -46182.6 q^{39} +456131. q^{40} +873409. q^{41} -923251. q^{42} +159630. q^{43} +1.71706e6 q^{44} -61539.7 q^{45} +2.40360e6 q^{46} -615386. q^{47} +1.97693e6 q^{48} +1.52388e6 q^{49} +1.58457e6 q^{50} -384117. q^{51} -633051. q^{52} -745946. q^{53} -439290. q^{54} -391643. q^{55} -8.27862e6 q^{56} -591374. q^{57} +4.35498e6 q^{58} -205379. q^{59} -843558. q^{60} -2.69167e6 q^{61} +1.52027e6 q^{62} +1.11692e6 q^{63} +1.16630e7 q^{64} +144392. q^{65} -2.79567e6 q^{66} +2.11862e6 q^{67} -5.26531e6 q^{68} -2.90781e6 q^{69} +2.88658e6 q^{70} -1.64750e6 q^{71} -3.93903e6 q^{72} -2.91422e6 q^{73} +6.91062e6 q^{74} -1.91697e6 q^{75} -8.10630e6 q^{76} +7.10818e6 q^{77} +1.03071e6 q^{78} +171784. q^{79} -6.18095e6 q^{80} +531441. q^{81} -1.94930e7 q^{82} +4.94728e6 q^{83} +1.53103e7 q^{84} +1.20096e6 q^{85} -3.56266e6 q^{86} -5.26854e6 q^{87} -2.50683e7 q^{88} -1.83391e6 q^{89} +1.37346e6 q^{90} -2.62066e6 q^{91} -3.98589e7 q^{92} -1.83918e6 q^{93} +1.37343e7 q^{94} +1.84896e6 q^{95} -2.54477e7 q^{96} -1.09662e7 q^{97} -3.40104e7 q^{98} +3.38213e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 32 q^{2} + 459 q^{3} + 1166 q^{4} - 1072 q^{5} - 864 q^{6} - 2407 q^{7} - 6645 q^{8} + 12393 q^{9}+O(q^{10}) \) 17 * q - 32 * q^2 + 459 * q^3 + 1166 * q^4 - 1072 * q^5 - 864 * q^6 - 2407 * q^7 - 6645 * q^8 + 12393 * q^9	\( 17 q - 32 q^{2} + 459 q^{3} + 1166 q^{4} - 1072 q^{5} - 864 q^{6} - 2407 q^{7} - 6645 q^{8} + 12393 q^{9} - 6391 q^{10} - 8888 q^{11} + 31482 q^{12} - 12702 q^{13} - 17555 q^{14} - 28944 q^{15} + 139226 q^{16} - 36167 q^{17} - 23328 q^{18} - 71037 q^{19} - 274883 q^{20} - 64989 q^{21} - 325182 q^{22} - 269995 q^{23} - 179415 q^{24} + 97329 q^{25} - 336906 q^{26} + 334611 q^{27} - 901362 q^{28} - 543825 q^{29} - 172557 q^{30} - 633109 q^{31} - 837062 q^{32} - 239976 q^{33} - 529288 q^{34} - 287621 q^{35} + 850014 q^{36} - 867607 q^{37} - 1727169 q^{38} - 342954 q^{39} - 815662 q^{40} - 1428939 q^{41} - 473985 q^{42} - 477060 q^{43} - 1667926 q^{44} - 781488 q^{45} + 5305549 q^{46} - 1217849 q^{47} + 3759102 q^{48} + 4350738 q^{49} + 4561369 q^{50} - 976509 q^{51} + 4175994 q^{52} - 3487068 q^{53} - 629856 q^{54} - 960484 q^{55} - 5363196 q^{56} - 1917999 q^{57} - 3082906 q^{58} - 3491443 q^{59} - 7421841 q^{60} + 998917 q^{61} - 5742614 q^{62} - 1754703 q^{63} + 17531621 q^{64} - 6075816 q^{65} - 8779914 q^{66} - 356026 q^{67} - 16149231 q^{68} - 7289865 q^{69} - 548798 q^{70} - 12879428 q^{71} - 4844205 q^{72} - 6176157 q^{73} - 5971906 q^{74} + 2627883 q^{75} - 17624580 q^{76} + 239687 q^{77} - 9096462 q^{78} - 18886490 q^{79} - 70463349 q^{80} + 9034497 q^{81} - 19351611 q^{82} - 22824893 q^{83} - 24336774 q^{84} - 7973079 q^{85} - 27502196 q^{86} - 14683275 q^{87} - 62527651 q^{88} - 30609647 q^{89} - 4659039 q^{90} - 36301521 q^{91} - 41388548 q^{92} - 17093943 q^{93} + 1010176 q^{94} - 29303629 q^{95} - 22600674 q^{96} - 26249806 q^{97} - 93110852 q^{98} - 6479352 q^{99}+O(q^{100}) \) 17 * q - 32 * q^2 + 459 * q^3 + 1166 * q^4 - 1072 * q^5 - 864 * q^6 - 2407 * q^7 - 6645 * q^8 + 12393 * q^9 - 6391 * q^10 - 8888 * q^11 + 31482 * q^12 - 12702 * q^13 - 17555 * q^14 - 28944 * q^15 + 139226 * q^16 - 36167 * q^17 - 23328 * q^18 - 71037 * q^19 - 274883 * q^20 - 64989 * q^21 - 325182 * q^22 - 269995 * q^23 - 179415 * q^24 + 97329 * q^25 - 336906 * q^26 + 334611 * q^27 - 901362 * q^28 - 543825 * q^29 - 172557 * q^30 - 633109 * q^31 - 837062 * q^32 - 239976 * q^33 - 529288 * q^34 - 287621 * q^35 + 850014 * q^36 - 867607 * q^37 - 1727169 * q^38 - 342954 * q^39 - 815662 * q^40 - 1428939 * q^41 - 473985 * q^42 - 477060 * q^43 - 1667926 * q^44 - 781488 * q^45 + 5305549 * q^46 - 1217849 * q^47 + 3759102 * q^48 + 4350738 * q^49 + 4561369 * q^50 - 976509 * q^51 + 4175994 * q^52 - 3487068 * q^53 - 629856 * q^54 - 960484 * q^55 - 5363196 * q^56 - 1917999 * q^57 - 3082906 * q^58 - 3491443 * q^59 - 7421841 * q^60 + 998917 * q^61 - 5742614 * q^62 - 1754703 * q^63 + 17531621 * q^64 - 6075816 * q^65 - 8779914 * q^66 - 356026 * q^67 - 16149231 * q^68 - 7289865 * q^69 - 548798 * q^70 - 12879428 * q^71 - 4844205 * q^72 - 6176157 * q^73 - 5971906 * q^74 + 2627883 * q^75 - 17624580 * q^76 + 239687 * q^77 - 9096462 * q^78 - 18886490 * q^79 - 70463349 * q^80 + 9034497 * q^81 - 19351611 * q^82 - 22824893 * q^83 - 24336774 * q^84 - 7973079 * q^85 - 27502196 * q^86 - 14683275 * q^87 - 62527651 * q^88 - 30609647 * q^89 - 4659039 * q^90 - 36301521 * q^91 - 41388548 * q^92 - 17093943 * q^93 + 1010176 * q^94 - 29303629 * q^95 - 22600674 * q^96 - 26249806 * q^97 - 93110852 * q^98 - 6479352 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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