LMFDB - Embedded newform 17.10.a.b.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [17,10,Mod(1,17)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(17, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("17.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 17 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	17.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:	$8.75560921479$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 2986x^{5} + 8252x^{4} + 2252056x^{3} - 10388768x^{2} - 243559296x - 675998208 $ x^7 - x^6 - 2986x^5 + 8252x^4 + 2252056x^3 - 10388768x^2 - 243559296*x - 675998208
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{4} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$28.6400$ of defining polynomial
Character	$\chi$	$=$	17.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-28.6400 q^{2} +243.971 q^{3} +308.250 q^{4} +1776.79 q^{5} -6987.32 q^{6} -9598.61 q^{7} +5835.40 q^{8} +39838.7 q^{9} +O(q^{10})$	\(q-28.6400 q^{2} +243.971 q^{3} +308.250 q^{4} +1776.79 q^{5} -6987.32 q^{6} -9598.61 q^{7} +5835.40 q^{8} +39838.7 q^{9} -50887.2 q^{10} +18658.0 q^{11} +75204.0 q^{12} +118081. q^{13} +274904. q^{14} +433484. q^{15} -324950. q^{16} +83521.0 q^{17} -1.14098e6 q^{18} +365652. q^{19} +547695. q^{20} -2.34178e6 q^{21} -534365. q^{22} +1.22678e6 q^{23} +1.42367e6 q^{24} +1.20385e6 q^{25} -3.38183e6 q^{26} +4.91741e6 q^{27} -2.95877e6 q^{28} -2.55483e6 q^{29} -1.24150e7 q^{30} +8.56431e6 q^{31} +6.31884e6 q^{32} +4.55201e6 q^{33} -2.39204e6 q^{34} -1.70547e7 q^{35} +1.22803e7 q^{36} -7.97315e6 q^{37} -1.04723e7 q^{38} +2.88083e7 q^{39} +1.03683e7 q^{40} -3.21617e7 q^{41} +6.70686e7 q^{42} -2.38617e7 q^{43} +5.75133e6 q^{44} +7.07850e7 q^{45} -3.51351e7 q^{46} -1.94506e7 q^{47} -7.92783e7 q^{48} +5.17797e7 q^{49} -3.44784e7 q^{50} +2.03767e7 q^{51} +3.63984e7 q^{52} -1.96101e7 q^{53} -1.40835e8 q^{54} +3.31513e7 q^{55} -5.60118e7 q^{56} +8.92083e7 q^{57} +7.31702e7 q^{58} +1.58423e7 q^{59} +1.33622e8 q^{60} -1.09913e8 q^{61} -2.45282e8 q^{62} -3.82396e8 q^{63} -1.45973e7 q^{64} +2.09805e8 q^{65} -1.30370e8 q^{66} -8.19198e7 q^{67} +2.57453e7 q^{68} +2.99299e8 q^{69} +4.88447e8 q^{70} +1.93682e8 q^{71} +2.32475e8 q^{72} -1.53405e7 q^{73} +2.28351e8 q^{74} +2.93705e8 q^{75} +1.12712e8 q^{76} -1.79091e8 q^{77} -8.25069e8 q^{78} +1.36544e8 q^{79} -5.77367e8 q^{80} +4.15558e8 q^{81} +9.21111e8 q^{82} -6.51497e8 q^{83} -7.21854e8 q^{84} +1.48399e8 q^{85} +6.83399e8 q^{86} -6.23303e8 q^{87} +1.08877e8 q^{88} -6.97006e8 q^{89} -2.02728e9 q^{90} -1.13341e9 q^{91} +3.78156e8 q^{92} +2.08944e9 q^{93} +5.57064e8 q^{94} +6.49686e8 q^{95} +1.54161e9 q^{96} -4.50260e8 q^{97} -1.48297e9 q^{98} +7.43311e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - q^{2} + 88 q^{3} + 2389 q^{4} + 1362 q^{5} - 11720 q^{6} + 9388 q^{7} + 16821 q^{8} + 81419 q^{9}+O(q^{10}) $ 7 * q - q^2 + 88 * q^3 + 2389 * q^4 + 1362 * q^5 - 11720 * q^6 + 9388 * q^7 + 16821 * q^8 + 81419 * q^9	\( 7 q - q^{2} + 88 q^{3} + 2389 q^{4} + 1362 q^{5} - 11720 q^{6} + 9388 q^{7} + 16821 q^{8} + 81419 q^{9} + 154226 q^{10} + 135536 q^{11} + 198160 q^{12} + 166122 q^{13} + 447252 q^{14} + 159048 q^{15} + 1463585 q^{16} + 584647 q^{17} + 149027 q^{18} + 777172 q^{19} - 917162 q^{20} - 3412104 q^{21} - 1222520 q^{22} + 1357764 q^{23} - 8487360 q^{24} + 1065785 q^{25} - 14379966 q^{26} - 4519064 q^{27} - 3328892 q^{28} + 967002 q^{29} - 12558992 q^{30} + 3546740 q^{31} + 4825461 q^{32} + 11928016 q^{33} - 83521 q^{34} - 530736 q^{35} + 4535009 q^{36} + 18296498 q^{37} - 49363020 q^{38} + 86306872 q^{39} + 127155062 q^{40} + 10285686 q^{41} + 14620416 q^{42} + 21913204 q^{43} + 96696624 q^{44} + 108916410 q^{45} - 151509484 q^{46} + 56639800 q^{47} - 201398496 q^{48} + 27010351 q^{49} - 261150303 q^{50} + 7349848 q^{51} - 156226378 q^{52} + 121813562 q^{53} - 93375344 q^{54} + 40793128 q^{55} - 196175436 q^{56} + 153612960 q^{57} - 236833910 q^{58} + 29222388 q^{59} - 628643488 q^{60} - 49915846 q^{61} - 73506556 q^{62} - 2185356 q^{63} + 317922057 q^{64} - 122633668 q^{65} - 624886144 q^{66} + 301863420 q^{67} + 199531669 q^{68} + 379683432 q^{69} + 966315960 q^{70} + 652473940 q^{71} + 655760385 q^{72} + 306656342 q^{73} + 249173874 q^{74} + 919071912 q^{75} + 128694700 q^{76} - 102442536 q^{77} + 323434416 q^{78} + 959147884 q^{79} - 692173602 q^{80} - 374486977 q^{81} + 1046441254 q^{82} - 1512945268 q^{83} - 481790592 q^{84} + 113755602 q^{85} - 164953236 q^{86} - 1612550856 q^{87} + 1132038848 q^{88} - 1971327114 q^{89} - 2284664662 q^{90} - 1061062864 q^{91} + 901186756 q^{92} - 798598936 q^{93} + 2534831232 q^{94} - 3249631512 q^{95} - 4442036640 q^{96} + 2006526254 q^{97} - 2170640009 q^{98} - 2579159272 q^{99}+O(q^{100}) \) 7 * q - q^2 + 88 * q^3 + 2389 * q^4 + 1362 * q^5 - 11720 * q^6 + 9388 * q^7 + 16821 * q^8 + 81419 * q^9 + 154226 * q^10 + 135536 * q^11 + 198160 * q^12 + 166122 * q^13 + 447252 * q^14 + 159048 * q^15 + 1463585 * q^16 + 584647 * q^17 + 149027 * q^18 + 777172 * q^19 - 917162 * q^20 - 3412104 * q^21 - 1222520 * q^22 + 1357764 * q^23 - 8487360 * q^24 + 1065785 * q^25 - 14379966 * q^26 - 4519064 * q^27 - 3328892 * q^28 + 967002 * q^29 - 12558992 * q^30 + 3546740 * q^31 + 4825461 * q^32 + 11928016 * q^33 - 83521 * q^34 - 530736 * q^35 + 4535009 * q^36 + 18296498 * q^37 - 49363020 * q^38 + 86306872 * q^39 + 127155062 * q^40 + 10285686 * q^41 + 14620416 * q^42 + 21913204 * q^43 + 96696624 * q^44 + 108916410 * q^45 - 151509484 * q^46 + 56639800 * q^47 - 201398496 * q^48 + 27010351 * q^49 - 261150303 * q^50 + 7349848 * q^51 - 156226378 * q^52 + 121813562 * q^53 - 93375344 * q^54 + 40793128 * q^55 - 196175436 * q^56 + 153612960 * q^57 - 236833910 * q^58 + 29222388 * q^59 - 628643488 * q^60 - 49915846 * q^61 - 73506556 * q^62 - 2185356 * q^63 + 317922057 * q^64 - 122633668 * q^65 - 624886144 * q^66 + 301863420 * q^67 + 199531669 * q^68 + 379683432 * q^69 + 966315960 * q^70 + 652473940 * q^71 + 655760385 * q^72 + 306656342 * q^73 + 249173874 * q^74 + 919071912 * q^75 + 128694700 * q^76 - 102442536 * q^77 + 323434416 * q^78 + 959147884 * q^79 - 692173602 * q^80 - 374486977 * q^81 + 1046441254 * q^82 - 1512945268 * q^83 - 481790592 * q^84 + 113755602 * q^85 - 164953236 * q^86 - 1612550856 * q^87 + 1132038848 * q^88 - 1971327114 * q^89 - 2284664662 * q^90 - 1061062864 * q^91 + 901186756 * q^92 - 798598936 * q^93 + 2534831232 * q^94 - 3249631512 * q^95 - 4442036640 * q^96 + 2006526254 * q^97 - 2170640009 * q^98 - 2579159272 * 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 $

$2$	−28.6400	−1.26572	−0.632861	−	0.774266i	$-0.718119\pi$
$2$	−28.6400	−1.26572	−0.632861	+	0.774266i	$0.718119\pi$
$3$	243.971	1.73897	0.869485	−	0.493959i	$-0.164451\pi$
$3$	243.971	1.73897	0.869485	+	0.493959i	$0.164451\pi$
$4$	308.250	0.602051
$5$	1776.79	1.27137	0.635683	−	0.771950i	$-0.280718\pi$
$5$	1776.79	1.27137	0.635683	+	0.771950i	$0.280718\pi$
$6$	−6987.32	−2.20105
$7$	−9598.61	−1.51101	−0.755505	−	0.655143i	$-0.772608\pi$
$7$	−9598.61	−1.51101	−0.755505	+	0.655143i	$0.772608\pi$
$8$	5835.40	0.503693
$9$	39838.7	2.02402
$10$	−50887.2	−1.60920
$11$	18658.0	0.384236	0.192118	−	0.981372i	$-0.438464\pi$
$11$	18658.0	0.384236	0.192118	+	0.981372i	$0.438464\pi$
$12$	75204.0	1.04695
$13$	118081.	1.14666	0.573329	−	0.819325i	$-0.305652\pi$
$13$	118081.	1.14666	0.573329	+	0.819325i	$0.305652\pi$
$14$	274904.	1.91252
$15$	433484.	2.21087
$16$	−324950.	−1.23959
$17$	83521.0	0.242536
$17$	83521.0	0.242536
$18$	−1.14098e6	−2.56184
$19$	365652.	0.643690	0.321845	−	0.946792i	$-0.395697\pi$
$19$	365652.	0.643690	0.321845	+	0.946792i	$0.395697\pi$
$20$	547695.	0.765427
$21$	−2.34178e6	−2.62760
$22$	−534365.	−0.486336
$23$	1.22678e6	0.914098	0.457049	−	0.889441i	$-0.348906\pi$
$23$	1.22678e6	0.914098	0.457049	+	0.889441i	$0.348906\pi$
$24$	1.42367e6	0.875907
$25$	1.20385e6	0.616373
$26$	−3.38183e6	−1.45135
$27$	4.91741e6	1.78073
$28$	−2.95877e6	−0.909704
$29$	−2.55483e6	−0.670765	−0.335382	−	0.942082i	$-0.608866\pi$
$29$	−2.55483e6	−0.670765	−0.335382	+	0.942082i	$0.608866\pi$
$30$	−1.24150e7	−2.79834
$31$	8.56431e6	1.66558	0.832789	−	0.553591i	$-0.186743\pi$
$31$	8.56431e6	1.66558	0.832789	+	0.553591i	$0.186743\pi$
$32$	6.31884e6	1.06528
$33$	4.55201e6	0.668175
$34$	−2.39204e6	−0.306983
$35$	−1.70547e7	−1.92105
$36$	1.22803e7	1.21856
$37$	−7.97315e6	−0.699394	−0.349697	−	0.936863i	$-0.613715\pi$
$37$	−7.97315e6	−0.699394	−0.349697	+	0.936863i	$0.613715\pi$
$38$	−1.04723e7	−0.814732
$39$	2.88083e7	1.99400
$40$	1.03683e7	0.640378
$41$	−3.21617e7	−1.77751	−0.888754	−	0.458384i	$-0.848428\pi$
$41$	−3.21617e7	−1.77751	−0.888754	+	0.458384i	$0.848428\pi$
$42$	6.70686e7	3.32581
$43$	−2.38617e7	−1.06437	−0.532186	−	0.846628i	$-0.678629\pi$
$43$	−2.38617e7	−1.06437	−0.532186	+	0.846628i	$0.678629\pi$
$44$	5.75133e6	0.231330
$45$	7.07850e7	2.57327
$46$	−3.51351e7	−1.15699
$47$	−1.94506e7	−0.581423	−0.290711	−	0.956811i	$-0.593892\pi$
$47$	−1.94506e7	−0.581423	−0.290711	+	0.956811i	$0.593892\pi$
$48$	−7.92783e7	−2.15560
$49$	5.17797e7	1.28315
$50$	−3.44784e7	−0.780156
$51$	2.03767e7	0.421762
$52$	3.63984e7	0.690347
$53$	−1.96101e7	−0.341380	−0.170690	−	0.985325i	$-0.554600\pi$
$53$	−1.96101e7	−0.341380	−0.170690	+	0.985325i	$0.554600\pi$
$54$	−1.40835e8	−2.25391
$55$	3.31513e7	0.488505
$56$	−5.60118e7	−0.761085
$57$	8.92083e7	1.11936
$58$	7.31702e7	0.849002
$59$	1.58423e7	0.170210	0.0851051	−	0.996372i	$-0.472877\pi$
$59$	1.58423e7	0.170210	0.0851051	+	0.996372i	$0.472877\pi$
$60$	1.33622e8	1.33105
$61$	−1.09913e8	−1.01640	−0.508201	−	0.861238i	$-0.669689\pi$
$61$	−1.09913e8	−1.01640	−0.508201	+	0.861238i	$0.669689\pi$
$62$	−2.45282e8	−2.10816
$63$	−3.82396e8	−3.05831
$64$	−1.45973e7	−0.108759
$65$	2.09805e8	1.45782
$66$	−1.30370e8	−0.845723
$67$	−8.19198e7	−0.496652	−0.248326	−	0.968677i	$-0.579880\pi$
$67$	−8.19198e7	−0.496652	−0.248326	+	0.968677i	$0.579880\pi$
$68$	2.57453e7	0.146019
$69$	2.99299e8	1.58959
$70$	4.88447e8	2.43151
$71$	1.93682e8	0.904537	0.452268	−	0.891882i	$-0.350615\pi$
$71$	1.93682e8	0.904537	0.452268	+	0.891882i	$0.350615\pi$
$72$	2.32475e8	1.01948
$73$	−1.53405e7	−0.0632245	−0.0316123	−	0.999500i	$-0.510064\pi$
$73$	−1.53405e7	−0.0632245	−0.0316123	+	0.999500i	$0.510064\pi$
$74$	2.28351e8	0.885238
$75$	2.93705e8	1.07185
$76$	1.12712e8	0.387534
$77$	−1.79091e8	−0.580584
$78$	−8.25069e8	−2.52385
$79$	1.36544e8	0.394413	0.197206	−	0.980362i	$-0.436813\pi$
$79$	1.36544e8	0.394413	0.197206	+	0.980362i	$0.436813\pi$
$80$	−5.77367e8	−1.57597
$81$	4.15558e8	1.07263
$82$	9.21111e8	2.24983
$83$	−6.51497e8	−1.50682	−0.753409	−	0.657552i	$-0.771592\pi$
$83$	−6.51497e8	−1.50682	−0.753409	+	0.657552i	$0.771592\pi$
$84$	−7.21854e8	−1.58195
$85$	1.48399e8	0.308352
$86$	6.83399e8	1.34720
$87$	−6.23303e8	−1.16644
$88$	1.08877e8	0.193537
$89$	−6.97006e8	−1.17756	−0.588778	−	0.808295i	$-0.700391\pi$
$89$	−6.97006e8	−1.17756	−0.588778	+	0.808295i	$0.700391\pi$
$90$	−2.02728e9	−3.25704
$91$	−1.13341e9	−1.73261
$92$	3.78156e8	0.550334
$93$	2.08944e9	2.89639
$94$	5.57064e8	0.735919
$95$	6.49686e8	0.818365
$96$	1.54161e9	1.85249
$97$	−4.50260e8	−0.516405	−0.258203	−	0.966091i	$-0.583130\pi$
$97$	−4.50260e8	−0.516405	−0.258203	+	0.966091i	$0.583130\pi$
$98$	−1.48297e9	−1.62411
$99$	7.43311e8	0.777700
$100$	3.71088e8	0.371088
$101$	5.43766e8	0.519955	0.259978	−	0.965615i	$-0.416285\pi$
$101$	5.43766e8	0.519955	0.259978	+	0.965615i	$0.416285\pi$
$102$	−5.83588e8	−0.533833
$103$	9.99479e8	0.874996	0.437498	−	0.899219i	$-0.355865\pi$
$103$	9.99479e8	0.874996	0.437498	+	0.899219i	$0.355865\pi$
$104$	6.89049e8	0.577564
$105$	−4.16085e9	−3.34064
$106$	5.61633e8	0.432092
$107$	2.11598e7	0.0156058	0.00780289	−	0.999970i	$-0.497516\pi$
$107$	2.11598e7	0.0156058	0.00780289	+	0.999970i	$0.497516\pi$
$108$	1.51579e9	1.07209
$109$	−2.38161e9	−1.61604	−0.808019	−	0.589156i	$-0.799460\pi$
$109$	−2.38161e9	−1.61604	−0.808019	+	0.589156i	$0.799460\pi$
$110$	−9.49454e8	−0.618311
$111$	−1.94521e9	−1.21623
$112$	3.11907e9	1.87303
$113$	1.14225e9	0.659035	0.329517	−	0.944150i	$-0.393114\pi$
$113$	1.14225e9	0.659035	0.329517	+	0.944150i	$0.393114\pi$
$114$	−2.55493e9	−1.41679
$115$	2.17974e9	1.16215
$116$	−7.87525e8	−0.403835
$117$	4.70419e9	2.32086
$118$	−4.53725e8	−0.215439
$119$	−8.01686e8	−0.366474
$120$	2.52956e9	1.11360
$121$	−2.00983e9	−0.852363
$122$	3.14792e9	1.28648
$123$	−7.84651e9	−3.09103
$124$	2.63995e9	1.00276
$125$	−1.33130e9	−0.487731
$126$	1.09518e10	3.87097
$127$	5.42933e9	1.85195	0.925975	−	0.377584i	$-0.123245\pi$
$127$	5.42933e9	1.85195	0.925975	+	0.377584i	$0.123245\pi$
$128$	−2.81718e9	−0.927619
$129$	−5.82156e9	−1.85091
$130$	−6.00881e9	−1.84520
$131$	2.35819e9	0.699613	0.349806	−	0.936822i	$-0.386247\pi$
$131$	2.35819e9	0.699613	0.349806	+	0.936822i	$0.386247\pi$
$132$	1.40316e9	0.402275
$133$	−3.50975e9	−0.972621
$134$	2.34618e9	0.628623
$135$	8.73719e9	2.26397
$136$	4.87379e8	0.122163
$137$	−9.19603e8	−0.223027	−0.111514	−	0.993763i	$-0.535570\pi$
$137$	−9.19603e8	−0.223027	−0.111514	+	0.993763i	$0.535570\pi$
$138$	−8.57194e9	−2.01198
$139$	1.27752e9	0.290269	0.145135	−	0.989412i	$-0.453638\pi$
$139$	1.27752e9	0.290269	0.145135	+	0.989412i	$0.453638\pi$
$140$	−5.25711e9	−1.15657
$141$	−4.74537e9	−1.01108
$142$	−5.54705e9	−1.14489
$143$	2.20315e9	0.440588
$144$	−1.29456e10	−2.50894
$145$	−4.53939e9	−0.852788
$146$	4.39351e8	0.0800246
$147$	1.26327e10	2.23136
$148$	−2.45772e9	−0.421071
$149$	−1.13853e9	−0.189237	−0.0946183	−	0.995514i	$-0.530163\pi$
$149$	−1.13853e9	−0.189237	−0.0946183	+	0.995514i	$0.530163\pi$
$150$	−8.41171e9	−1.35667
$151$	1.89477e9	0.296593	0.148296	−	0.988943i	$-0.452621\pi$
$151$	1.89477e9	0.296593	0.148296	+	0.988943i	$0.452621\pi$
$152$	2.13373e9	0.324222
$153$	3.32737e9	0.490896
$154$	5.12917e9	0.734858
$155$	1.52170e10	2.11756
$156$	8.88014e9	1.20049
$157$	6.87991e9	0.903721	0.451860	−	0.892089i	$-0.350760\pi$
$157$	6.87991e9	0.903721	0.451860	+	0.892089i	$0.350760\pi$
$158$	−3.91062e9	−0.499217
$159$	−4.78429e9	−0.593650
$160$	1.12272e10	1.35436
$161$	−1.17754e10	−1.38121
$162$	−1.19016e10	−1.35765
$163$	1.18995e10	1.32034	0.660171	−	0.751116i	$-0.270484\pi$
$163$	1.18995e10	1.32034	0.660171	+	0.751116i	$0.270484\pi$
$164$	−9.91384e9	−1.07015
$165$	8.08795e9	0.849495
$166$	1.86589e10	1.90721
$167$	−1.62243e10	−1.61415	−0.807073	−	0.590451i	$-0.798950\pi$
$167$	−1.62243e10	−1.61415	−0.807073	+	0.590451i	$0.798950\pi$
$168$	−1.36652e10	−1.32350
$169$	3.33857e9	0.314826
$170$	−4.25015e9	−0.390287
$171$	1.45671e10	1.30284
$172$	−7.35537e9	−0.640806
$173$	9.77316e9	0.829521	0.414761	−	0.909931i	$-0.363865\pi$
$173$	9.77316e9	0.829521	0.414761	+	0.909931i	$0.363865\pi$
$174$	1.78514e10	1.47639
$175$	−1.15553e10	−0.931345
$176$	−6.06292e9	−0.476293
$177$	3.86507e9	0.295990
$178$	1.99623e10	1.49046
$179$	−1.22507e10	−0.891915	−0.445958	−	0.895054i	$-0.647137\pi$
$179$	−1.22507e10	−0.891915	−0.445958	+	0.895054i	$0.647137\pi$
$180$	2.18195e10	1.54924
$181$	1.21812e10	0.843597	0.421798	−	0.906690i	$-0.361399\pi$
$181$	1.21812e10	0.843597	0.421798	+	0.906690i	$0.361399\pi$
$182$	3.24609e10	2.19300
$183$	−2.68156e10	−1.76749
$184$	7.15878e9	0.460425
$185$	−1.41666e10	−0.889186
$186$	−5.98416e10	−3.66602
$187$	1.55834e9	0.0931909
$188$	−5.99564e9	−0.350046
$189$	−4.72003e10	−2.69071
$190$	−1.86070e10	−1.03582
$191$	−1.62713e10	−0.884651	−0.442325	−	0.896855i	$-0.645846\pi$
$191$	−1.62713e10	−0.884651	−0.442325	+	0.896855i	$0.645846\pi$
$192$	−3.56132e9	−0.189128
$193$	1.78626e10	0.926696	0.463348	−	0.886176i	$-0.346648\pi$
$193$	1.78626e10	0.926696	0.463348	+	0.886176i	$0.346648\pi$
$194$	1.28954e10	0.653625
$195$	5.11862e10	2.53511
$196$	1.59611e10	0.772522
$197$	1.24709e10	0.589927	0.294963	−	0.955509i	$-0.404693\pi$
$197$	1.24709e10	0.589927	0.294963	+	0.955509i	$0.404693\pi$
$198$	−2.12884e10	−0.984352
$199$	−1.76972e10	−0.799957	−0.399978	−	0.916525i	$-0.630982\pi$
$199$	−1.76972e10	−0.799957	−0.399978	+	0.916525i	$0.630982\pi$
$200$	7.02497e9	0.310463
$201$	−1.99860e10	−0.863663
$202$	−1.55735e10	−0.658119
$203$	2.45228e10	1.01353
$204$	6.28111e9	0.253922
$205$	−5.71445e10	−2.25986
$206$	−2.86251e10	−1.10750
$207$	4.88735e10	1.85015
$208$	−3.83703e10	−1.42138
$209$	6.82233e9	0.247329
$210$	1.19167e11	4.22832
$211$	−3.49985e10	−1.21556	−0.607782	−	0.794104i	$-0.707941\pi$
$211$	−3.49985e10	−1.21556	−0.607782	+	0.794104i	$0.707941\pi$
$212$	−6.04481e9	−0.205528
$213$	4.72527e10	1.57296
$214$	−6.06018e8	−0.0197526
$215$	−4.23972e10	−1.35321
$216$	2.86950e10	0.896943
$217$	−8.22055e10	−2.51670
$218$	6.82094e10	2.04545
$219$	−3.74262e9	−0.109946
$220$	1.02189e10	0.294105
$221$	9.86223e9	0.278106
$222$	5.57110e10	1.53940
$223$	4.75965e10	1.28885	0.644426	−	0.764667i	$-0.277096\pi$
$223$	4.75965e10	1.28885	0.644426	+	0.764667i	$0.277096\pi$
$224$	−6.06521e10	−1.60964
$225$	4.79600e10	1.24755
$226$	−3.27141e10	−0.834154
$227$	1.17164e10	0.292873	0.146436	−	0.989220i	$-0.453220\pi$
$227$	1.17164e10	0.292873	0.146436	+	0.989220i	$0.453220\pi$
$228$	2.74985e10	0.673910
$229$	2.48997e10	0.598321	0.299161	−	0.954203i	$-0.403293\pi$
$229$	2.48997e10	0.598321	0.299161	+	0.954203i	$0.403293\pi$
$230$	−6.24277e10	−1.47096
$231$	−4.36929e10	−1.00962
$232$	−1.49084e10	−0.337860
$233$	6.50866e10	1.44674	0.723369	−	0.690462i	$-0.242593\pi$
$233$	6.50866e10	1.44674	0.723369	+	0.690462i	$0.242593\pi$
$234$	−1.34728e11	−2.93756
$235$	−3.45596e10	−0.739201
$236$	4.88340e9	0.102475
$237$	3.33128e10	0.685872
$238$	2.29603e10	0.463854
$239$	4.29823e10	0.852117	0.426058	−	0.904696i	$-0.359902\pi$
$239$	4.29823e10	0.852117	0.426058	+	0.904696i	$0.359902\pi$
$240$	−1.40861e11	−2.74056
$241$	−7.83992e10	−1.49705	−0.748523	−	0.663109i	$-0.769236\pi$
$241$	−7.83992e10	−1.49705	−0.748523	+	0.663109i	$0.769236\pi$
$242$	5.75614e10	1.07885
$243$	4.59462e9	0.0845320
$244$	−3.38807e10	−0.611926
$245$	9.20017e10	1.63135
$246$	2.24724e11	3.91239
$247$	4.31764e10	0.738092
$248$	4.99762e10	0.838940
$249$	−1.58946e11	−2.62031
$250$	3.81284e10	0.617331
$251$	2.92884e10	0.465762	0.232881	−	0.972505i	$-0.425185\pi$
$251$	2.92884e10	0.465762	0.232881	+	0.972505i	$0.425185\pi$
$252$	−1.17874e11	−1.84126
$253$	2.28893e10	0.351230
$254$	−1.55496e11	−2.34405
$255$	3.62051e10	0.536214
$256$	8.81579e10	1.28287
$257$	3.01696e10	0.431390	0.215695	−	0.976461i	$-0.430798\pi$
$257$	3.01696e10	0.431390	0.215695	+	0.976461i	$0.430798\pi$
$258$	1.66729e11	2.34274
$259$	7.65311e10	1.05679
$260$	6.46723e10	0.877684
$261$	−1.01781e11	−1.35764
$262$	−6.75385e10	−0.885515
$263$	−9.10348e10	−1.17329	−0.586647	−	0.809843i	$-0.699552\pi$
$263$	−9.10348e10	−1.17329	−0.586647	+	0.809843i	$0.699552\pi$
$264$	2.65628e10	0.336555
$265$	−3.48430e10	−0.434019
$266$	1.00519e11	1.23107
$267$	−1.70049e11	−2.04774
$268$	−2.52518e10	−0.299010
$269$	−6.95622e10	−0.810005	−0.405003	−	0.914316i	$-0.632729\pi$
$269$	−6.95622e10	−0.810005	−0.405003	+	0.914316i	$0.632729\pi$
$270$	−2.50233e11	−2.86555
$271$	−9.57591e10	−1.07849	−0.539247	−	0.842147i	$-0.681291\pi$
$271$	−9.57591e10	−1.07849	−0.539247	+	0.842147i	$0.681291\pi$
$272$	−2.71401e10	−0.300644
$273$	−2.76519e11	−3.01296
$274$	2.63374e10	0.282290
$275$	2.24615e10	0.236833
$276$	9.22591e10	0.957014
$277$	−8.55452e10	−0.873045	−0.436523	−	0.899693i	$-0.643790\pi$
$277$	−8.55452e10	−0.873045	−0.436523	+	0.899693i	$0.643790\pi$
$278$	−3.65882e10	−0.367400
$279$	3.41191e11	3.37116
$280$	−9.95211e10	−0.967618
$281$	−4.39159e10	−0.420188	−0.210094	−	0.977681i	$-0.567377\pi$
$281$	−4.39159e10	−0.420188	−0.210094	+	0.977681i	$0.567377\pi$
$282$	1.35907e11	1.27974
$283$	8.04249e10	0.745335	0.372668	−	0.927965i	$-0.378443\pi$
$283$	8.04249e10	0.745335	0.372668	+	0.927965i	$0.378443\pi$
$284$	5.97024e10	0.544577
$285$	1.58504e11	1.42311
$286$	−6.30983e10	−0.557661
$287$	3.08708e11	2.68583
$288$	2.51735e11	2.15614
$289$	6.97576e9	0.0588235
$290$	1.30008e11	1.07939
$291$	−1.09850e11	−0.898013
$292$	−4.72870e9	−0.0380644
$293$	−2.21747e10	−0.175774	−0.0878869	−	0.996130i	$-0.528011\pi$
$293$	−2.21747e10	−0.175774	−0.0878869	+	0.996130i	$0.528011\pi$
$294$	−3.61802e11	−2.82428
$295$	2.81485e10	0.216399
$296$	−4.65265e10	−0.352280
$297$	9.17490e10	0.684222
$298$	3.26074e10	0.239521
$299$	1.44860e11	1.04816
$300$	9.05345e10	0.645310
$301$	2.29039e11	1.60828
$302$	−5.42663e10	−0.375404
$303$	1.32663e11	0.904187
$304$	−1.18819e11	−0.797908
$305$	−1.95293e11	−1.29222
$306$	−9.52959e10	−0.621338
$307$	1.36198e11	0.875081	0.437540	−	0.899199i	$-0.355850\pi$
$307$	1.36198e11	0.875081	0.437540	+	0.899199i	$0.355850\pi$
$308$	−5.52048e10	−0.349541
$309$	2.43844e11	1.52159
$310$	−4.35814e11	−2.68024
$311$	2.63133e11	1.59497	0.797486	−	0.603337i	$-0.206163\pi$
$311$	2.63133e11	1.59497	0.797486	+	0.603337i	$0.206163\pi$
$312$	1.68108e11	1.00437
$313$	1.85944e11	1.09504	0.547522	−	0.836791i	$-0.315571\pi$
$313$	1.85944e11	1.09504	0.547522	+	0.836791i	$0.315571\pi$
$314$	−1.97041e11	−1.14386
$315$	−6.79438e11	−3.88823
$316$	4.20897e10	0.237456
$317$	−3.15409e11	−1.75431	−0.877157	−	0.480203i	$-0.840563\pi$
$317$	−3.15409e11	−1.75431	−0.877157	+	0.480203i	$0.840563\pi$
$318$	1.37022e11	0.751395
$319$	−4.76680e10	−0.257732
$320$	−2.59364e10	−0.138272
$321$	5.16238e9	0.0271380
$322$	3.37248e11	1.74823
$323$	3.05396e10	0.156118
$324$	1.28096e11	0.645776
$325$	1.42152e11	0.706769
$326$	−3.40803e11	−1.67118
$327$	−5.81043e11	−2.81024
$328$	−1.87676e11	−0.895318
$329$	1.86698e11	0.878535
$330$	−2.31639e11	−1.07522
$331$	−1.33188e10	−0.0609871	−0.0304936	−	0.999535i	$-0.509708\pi$
$331$	−1.33188e10	−0.0609871	−0.0304936	+	0.999535i	$0.509708\pi$
$332$	−2.00824e11	−0.907181
$333$	−3.17640e11	−1.41559
$334$	4.64665e11	2.04306
$335$	−1.45554e11	−0.631426
$336$	7.60961e11	3.25714
$337$	−8.96864e10	−0.378785	−0.189392	−	0.981902i	$-0.560652\pi$
$337$	−8.96864e10	−0.378785	−0.189392	+	0.981902i	$0.560652\pi$
$338$	−9.56167e10	−0.398482
$339$	2.78676e11	1.14604
$340$	4.57440e10	0.185643
$341$	1.59793e11	0.639975
$342$	−4.17202e11	−1.64903
$343$	−1.09675e11	−0.427843
$344$	−1.39243e11	−0.536117
$345$	5.31792e11	2.02095
$346$	−2.79903e11	−1.04994
$347$	−3.71901e11	−1.37703	−0.688516	−	0.725221i	$-0.741738\pi$
$347$	−3.71901e11	−1.37703	−0.688516	+	0.725221i	$0.741738\pi$
$348$	−1.92133e11	−0.702256
$349$	2.40556e11	0.867963	0.433982	−	0.900922i	$-0.357108\pi$
$349$	2.40556e11	0.867963	0.433982	+	0.900922i	$0.357108\pi$
$350$	3.30944e11	1.17882
$351$	5.80651e11	2.04189
$352$	1.17897e11	0.409318
$353$	−2.31047e11	−0.791980	−0.395990	−	0.918255i	$-0.629599\pi$
$353$	−2.31047e11	−0.791980	−0.395990	+	0.918255i	$0.629599\pi$
$354$	−1.10696e11	−0.374641
$355$	3.44132e11	1.15000
$356$	−2.14852e11	−0.708949
$357$	−1.95588e11	−0.637287
$358$	3.50861e11	1.12892
$359$	2.17507e11	0.691110	0.345555	−	0.938398i	$-0.387691\pi$
$359$	2.17507e11	0.691110	0.345555	+	0.938398i	$0.387691\pi$
$360$	4.13059e11	1.29614
$361$	−1.88986e11	−0.585664
$362$	−3.48868e11	−1.06776
$363$	−4.90339e11	−1.48223
$364$	−3.49374e11	−1.04312
$365$	−2.72568e10	−0.0803815
$366$	7.67999e11	2.23715
$367$	1.24703e11	0.358823	0.179412	−	0.983774i	$-0.442581\pi$
$367$	1.24703e11	0.358823	0.179412	+	0.983774i	$0.442581\pi$
$368$	−3.98644e11	−1.13310
$369$	−1.28128e12	−3.59771
$370$	4.05731e11	1.12546
$371$	1.88230e11	0.515829
$372$	6.44070e11	1.74377
$373$	6.71444e11	1.79606	0.898028	−	0.439938i	$-0.144999\pi$
$373$	6.71444e11	1.79606	0.898028	+	0.439938i	$0.144999\pi$
$374$	−4.46307e10	−0.117954
$375$	−3.24798e11	−0.848149
$376$	−1.13502e11	−0.292858
$377$	−3.01676e11	−0.769138
$378$	1.35182e12	3.40569
$379$	−2.57132e11	−0.640147	−0.320073	−	0.947393i	$-0.603708\pi$
$379$	−2.57132e11	−0.640147	−0.320073	+	0.947393i	$0.603708\pi$
$380$	2.00266e11	0.492697
$381$	1.32460e12	3.22049
$382$	4.66010e11	1.11972
$383$	−1.54303e11	−0.366420	−0.183210	−	0.983074i	$-0.558649\pi$
$383$	−1.54303e11	−0.366420	−0.183210	+	0.983074i	$0.558649\pi$
$384$	−6.87309e11	−1.61310
$385$	−3.18207e11	−0.738135
$386$	−5.11586e11	−1.17294
$387$	−9.50620e11	−2.15431
$388$	−1.38793e11	−0.310902
$389$	1.53781e11	0.340510	0.170255	−	0.985400i	$-0.445541\pi$
$389$	1.53781e11	0.340510	0.170255	+	0.985400i	$0.445541\pi$
$390$	−1.46597e12	−3.20874
$391$	1.02462e11	0.221701
$392$	3.02156e11	0.646314
$393$	5.75329e11	1.21661
$394$	−3.57165e11	−0.746683
$395$	2.42610e11	0.501443
$396$	2.29126e11	0.468215
$397$	−5.53284e10	−0.111787	−0.0558934	−	0.998437i	$-0.517801\pi$
$397$	−5.53284e10	−0.111787	−0.0558934	+	0.998437i	$0.517801\pi$
$398$	5.06849e11	1.01252
$399$	−8.56276e11	−1.69136
$400$	−3.91192e11	−0.764047
$401$	−5.98775e11	−1.15642	−0.578208	−	0.815890i	$-0.696248\pi$
$401$	−5.98775e11	−1.15642	−0.578208	+	0.815890i	$0.696248\pi$
$402$	5.72400e11	1.09316
$403$	1.01128e12	1.90985
$404$	1.67616e11	0.313039
$405$	7.38358e11	1.36370
$406$	−7.02333e11	−1.28285
$407$	−1.48763e11	−0.268732
$408$	1.18906e11	0.212439
$409$	−8.67423e11	−1.53277	−0.766384	−	0.642383i	$-0.777946\pi$
$409$	−8.67423e11	−1.53277	−0.766384	+	0.642383i	$0.777946\pi$
$410$	1.63662e12	2.86036
$411$	−2.24356e11	−0.387838
$412$	3.08089e11	0.526792
$413$	−1.52065e11	−0.257189
$414$	−1.39974e12	−2.34178
$415$	−1.15757e12	−1.91572
$416$	7.46134e11	1.22151
$417$	3.11678e11	0.504770
$418$	−1.95392e11	−0.313049
$419$	−6.41732e11	−1.01716	−0.508581	−	0.861014i	$-0.669830\pi$
$419$	−6.41732e11	−1.01716	−0.508581	+	0.861014i	$0.669830\pi$
$420$	−1.28258e12	−2.01124
$421$	4.57623e11	0.709967	0.354983	−	0.934873i	$-0.384487\pi$
$421$	4.57623e11	0.709967	0.354983	+	0.934873i	$0.384487\pi$
$422$	1.00236e12	1.53857
$423$	−7.74886e11	−1.17681
$424$	−1.14433e11	−0.171951
$425$	1.00547e11	0.149492
$426$	−1.35332e12	−1.99093
$427$	1.05501e12	1.53579
$428$	6.52252e9	0.00939547
$429$	5.37505e11	0.766169
$430$	1.21426e12	1.71278
$431$	7.38734e10	0.103119	0.0515597	−	0.998670i	$-0.483581\pi$
$431$	7.38734e10	0.103119	0.0515597	+	0.998670i	$0.483581\pi$
$432$	−1.59791e12	−2.20737
$433$	1.03868e12	1.41999	0.709995	−	0.704206i	$-0.248697\pi$
$433$	1.03868e12	1.41999	0.709995	+	0.704206i	$0.248697\pi$
$434$	2.35437e12	3.18545
$435$	−1.10748e12	−1.48297
$436$	−7.34132e11	−0.972937
$437$	4.48576e11	0.588396
$438$	1.07189e11	0.139160
$439$	9.61297e11	1.23529	0.617643	−	0.786459i	$-0.288088\pi$
$439$	9.61297e11	1.23529	0.617643	+	0.786459i	$0.288088\pi$
$440$	1.93451e11	0.246056
$441$	2.06284e12	2.59712
$442$	−2.82454e11	−0.352004
$443$	2.39240e11	0.295132	0.147566	−	0.989052i	$-0.452856\pi$
$443$	2.39240e11	0.295132	0.147566	+	0.989052i	$0.452856\pi$
$444$	−5.99612e11	−0.732229
$445$	−1.23843e12	−1.49711
$446$	−1.36316e12	−1.63133
$447$	−2.77767e11	−0.329077
$448$	1.40114e11	0.164335
$449$	−5.56831e11	−0.646569	−0.323285	−	0.946302i	$-0.604787\pi$
$449$	−5.56831e11	−0.646569	−0.323285	+	0.946302i	$0.604787\pi$
$450$	−1.37357e12	−1.57905
$451$	−6.00073e11	−0.682983
$452$	3.52099e11	0.396772
$453$	4.62269e11	0.515766
$454$	−3.35558e11	−0.370695
$455$	−2.01383e12	−2.20279
$456$	5.20566e11	0.563812
$457$	6.83226e11	0.732726	0.366363	−	0.930472i	$-0.380603\pi$
$457$	6.83226e11	0.732726	0.366363	+	0.930472i	$0.380603\pi$
$458$	−7.13128e11	−0.757308
$459$	4.10707e11	0.431892
$460$	6.71904e11	0.699676
$461$	−9.09123e11	−0.937494	−0.468747	−	0.883333i	$-0.655294\pi$
$461$	−9.09123e11	−0.937494	−0.468747	+	0.883333i	$0.655294\pi$
$462$	1.25137e12	1.27790
$463$	3.46507e11	0.350427	0.175213	−	0.984530i	$-0.443938\pi$
$463$	3.46507e11	0.350427	0.175213	+	0.984530i	$0.443938\pi$
$464$	8.30191e11	0.831471
$465$	3.71250e12	3.68237
$466$	−1.86408e12	−1.83117
$467$	3.54586e11	0.344982	0.172491	−	0.985011i	$-0.444818\pi$
$467$	3.54586e11	0.344982	0.172491	+	0.985011i	$0.444818\pi$
$468$	1.45007e12	1.39727
$469$	7.86316e11	0.750446
$470$	9.89786e11	0.935623
$471$	1.67850e12	1.57154
$472$	9.24465e10	0.0857336
$473$	−4.45212e11	−0.408970
$474$	−9.54078e11	−0.868123
$475$	4.40191e11	0.396753
$476$	−2.47120e11	−0.220636
$477$	−7.81241e11	−0.690959
$478$	−1.23101e12	−1.07854
$479$	1.13858e12	0.988222	0.494111	−	0.869399i	$-0.335494\pi$
$479$	1.13858e12	0.988222	0.494111	+	0.869399i	$0.335494\pi$
$480$	2.73912e12	2.35519
$481$	−9.41475e11	−0.801966
$482$	2.24535e12	1.89484
$483$	−2.87286e12	−2.40189
$484$	−6.19529e11	−0.513166
$485$	−8.00017e11	−0.656540
$486$	−1.31590e11	−0.106994
$487$	1.19842e10	0.00965450	0.00482725	−	0.999988i	$-0.498463\pi$
$487$	1.19842e10	0.00965450	0.00482725	+	0.999988i	$0.498463\pi$
$488$	−6.41388e11	−0.511955
$489$	2.90314e12	2.29603
$490$	−2.63493e12	−2.06484
$491$	−1.60620e11	−0.124719	−0.0623597	−	0.998054i	$-0.519863\pi$
$491$	−1.60620e11	−0.124719	−0.0623597	+	0.998054i	$0.519863\pi$
$492$	−2.41869e12	−1.86096
$493$	−2.13382e11	−0.162684
$494$	−1.23657e12	−0.934219
$495$	1.32071e12	0.988742
$496$	−2.78297e12	−2.06463
$497$	−1.85908e12	−1.36676
$498$	4.55222e12	3.31658
$499$	−1.44413e12	−1.04269	−0.521345	−	0.853346i	$-0.674569\pi$
$499$	−1.44413e12	−1.04269	−0.521345	+	0.853346i	$0.674569\pi$
$500$	−4.10373e11	−0.293639
$501$	−3.95826e12	−2.80695
$502$	−8.38820e11	−0.589525
$503$	1.19095e12	0.829539	0.414769	−	0.909927i	$-0.363862\pi$
$503$	1.19095e12	0.829539	0.414769	+	0.909927i	$0.363862\pi$
$504$	−2.23144e12	−1.54045
$505$	9.66158e11	0.661054
$506$	−6.55551e11	−0.444559
$507$	8.14514e11	0.547473
$508$	1.67359e12	1.11497
$509$	−2.34412e12	−1.54793	−0.773963	−	0.633231i	$-0.781728\pi$
$509$	−2.34412e12	−1.54793	−0.773963	+	0.633231i	$0.781728\pi$
$510$	−1.03691e12	−0.678698
$511$	1.47247e11	0.0955328
$512$	−1.08245e12	−0.696132
$513$	1.79806e12	1.14624
$514$	−8.64056e11	−0.546019
$515$	1.77586e12	1.11244
$516$	−1.79449e12	−1.11434
$517$	−3.62909e11	−0.223404
$518$	−2.19185e12	−1.33760
$519$	2.38437e12	1.44251
$520$	1.22429e12	0.734295
$521$	1.55789e12	0.926333	0.463166	−	0.886271i	$-0.346713\pi$
$521$	1.55789e12	0.926333	0.463166	+	0.886271i	$0.346713\pi$
$522$	2.91501e12	1.71839
$523$	5.98253e10	0.0349645	0.0174823	−	0.999847i	$-0.494435\pi$
$523$	5.98253e10	0.0349645	0.0174823	+	0.999847i	$0.494435\pi$
$524$	7.26912e11	0.421202
$525$	−2.81916e12	−1.61958
$526$	2.60724e12	1.48506
$527$	7.15300e11	0.403962
$528$	−1.47917e12	−0.828260
$529$	−2.96153e11	−0.164424
$530$	9.97904e11	0.549348
$531$	6.31139e11	0.344508
$532$	−1.08188e12	−0.585567
$533$	−3.79768e12	−2.03820
$534$	4.87021e12	2.59186
$535$	3.75966e10	0.0198407
$536$	−4.78035e11	−0.250160
$537$	−2.98882e12	−1.55101
$538$	1.99226e12	1.02524
$539$	9.66107e11	0.493033
$540$	2.69324e12	1.36302
$541$	2.35116e12	1.18004	0.590018	−	0.807390i	$-0.299121\pi$
$541$	2.35116e12	1.18004	0.590018	+	0.807390i	$0.299121\pi$
$542$	2.74254e12	1.36507
$543$	2.97185e12	1.46699
$544$	5.27756e11	0.258368
$545$	−4.23162e12	−2.05458
$546$	7.91951e12	3.81357
$547$	3.16333e12	1.51078	0.755391	−	0.655274i	$-0.227447\pi$
$547$	3.16333e12	1.51078	0.755391	+	0.655274i	$0.227447\pi$
$548$	−2.83468e11	−0.134274
$549$	−4.37880e12	−2.05722
$550$	−6.43297e11	−0.299764
$551$	−9.34177e11	−0.431764
$552$	1.74653e12	0.800665
$553$	−1.31063e12	−0.595961
$554$	2.45002e12	1.10503
$555$	−3.45624e12	−1.54627
$556$	3.93796e11	0.174757
$557$	3.53542e12	1.55630	0.778148	−	0.628081i	$-0.216159\pi$
$557$	3.53542e12	1.55630	0.778148	+	0.628081i	$0.216159\pi$
$558$	−9.77172e12	−4.26695
$559$	−2.81761e12	−1.22047
$560$	5.54193e12	2.38130
$561$	3.80188e11	0.162056
$562$	1.25775e12	0.531841
$563$	−1.75567e12	−0.736472	−0.368236	−	0.929732i	$-0.620038\pi$
$563$	−1.75567e12	−0.736472	−0.368236	+	0.929732i	$0.620038\pi$
$564$	−1.46276e12	−0.608719
$565$	2.02954e12	0.837875
$566$	−2.30337e12	−0.943387
$567$	−3.98878e12	−1.62075
$568$	1.13021e12	0.455609
$569$	−2.32211e9	−0.000928706 0	−0.000464353	−	1.00000i	$-0.500148\pi$
$569$	−2.32211e9	−0.000928706 0	−0.000464353		1.00000i	$0.500148\pi$
$570$	−4.53957e12	−1.80126
$571$	−2.57323e12	−1.01302	−0.506509	−	0.862235i	$-0.669064\pi$
$571$	−2.57323e12	−1.01302	−0.506509	+	0.862235i	$0.669064\pi$
$572$	6.79121e11	0.265256
$573$	−3.96972e12	−1.53838
$574$	−8.84139e12	−3.39952
$575$	1.47687e12	0.563425
$576$	−5.81539e11	−0.220129
$577$	−1.59532e12	−0.599178	−0.299589	−	0.954068i	$-0.596850\pi$
$577$	−1.59532e12	−0.599178	−0.299589	+	0.954068i	$0.596850\pi$
$578$	−1.99786e11	−0.0744542
$579$	4.35796e12	1.61150
$580$	−1.39927e12	−0.513422
$581$	6.25346e12	2.27682
$582$	3.14611e12	1.13663
$583$	−3.65885e11	−0.131171
$584$	−8.95177e10	−0.0318457
$585$	8.35835e12	2.95066
$586$	6.35085e11	0.222481
$587$	−2.68434e12	−0.933182	−0.466591	−	0.884473i	$-0.654518\pi$
$587$	−2.68434e12	−0.933182	−0.466591	+	0.884473i	$0.654518\pi$
$588$	3.89404e12	1.34339
$589$	3.13156e12	1.07212
$590$	−8.06173e11	−0.273901
$591$	3.04252e12	1.02586
$592$	2.59087e12	0.866959
$593$	4.50719e12	1.49679	0.748393	−	0.663256i	$-0.230826\pi$
$593$	4.50719e12	1.49679	0.748393	+	0.663256i	$0.230826\pi$
$594$	−2.62769e12	−0.866035
$595$	−1.42443e12	−0.465922
$596$	−3.50951e11	−0.113930
$597$	−4.31761e12	−1.39110
$598$	−4.14878e12	−1.32668
$599$	−4.19976e12	−1.33292	−0.666459	−	0.745542i	$-0.732191\pi$
$599$	−4.19976e12	−1.33292	−0.666459	+	0.745542i	$0.732191\pi$
$600$	1.71389e12	0.539885
$601$	4.96222e12	1.55146	0.775730	−	0.631065i	$-0.217382\pi$
$601$	4.96222e12	1.55146	0.775730	+	0.631065i	$0.217382\pi$
$602$	−6.55968e12	−2.03563
$603$	−3.26358e12	−1.00523
$604$	5.84063e11	0.178564
$605$	−3.57104e12	−1.08367
$606$	−3.79947e12	−1.14445
$607$	4.06493e12	1.21536	0.607679	−	0.794183i	$-0.292101\pi$
$607$	4.06493e12	1.21536	0.607679	+	0.794183i	$0.292101\pi$
$608$	2.31050e12	0.685708
$609$	5.98284e12	1.76250
$610$	5.59318e12	1.63559
$611$	−2.29674e12	−0.666693
$612$	1.02566e12	0.295544
$613$	−3.12747e12	−0.894583	−0.447291	−	0.894388i	$-0.647611\pi$
$613$	−3.12747e12	−0.894583	−0.447291	+	0.894388i	$0.647611\pi$
$614$	−3.90071e12	−1.10761
$615$	−1.39416e13	−3.92984
$616$	−1.04507e12	−0.292436
$617$	1.99199e12	0.553354	0.276677	−	0.960963i	$-0.410767\pi$
$617$	1.99199e12	0.553354	0.276677	+	0.960963i	$0.410767\pi$
$618$	−6.98368e12	−1.92591
$619$	5.76812e12	1.57916	0.789581	−	0.613647i	$-0.210298\pi$
$619$	5.76812e12	1.57916	0.789581	+	0.613647i	$0.210298\pi$
$620$	4.69063e12	1.27488
$621$	6.03260e12	1.62777
$622$	−7.53613e12	−2.01879
$623$	6.69029e12	1.77930
$624$	−9.36124e12	−2.47174
$625$	−4.71671e12	−1.23646
$626$	−5.32543e12	−1.38602
$627$	1.66445e12	0.430097
$628$	2.12073e12	0.544086
$629$	−6.65925e11	−0.169628
$630$	1.94591e13	4.92142
$631$	−2.73184e12	−0.685999	−0.342999	−	0.939336i	$-0.611443\pi$
$631$	−2.73184e12	−0.685999	−0.342999	+	0.939336i	$0.611443\pi$
$632$	7.96789e11	0.198663
$633$	−8.53860e12	−2.11383
$634$	9.03332e12	2.22047
$635$	9.64677e12	2.35451
$636$	−1.47476e12	−0.357407
$637$	6.11419e12	1.47134
$638$	1.36521e12	0.326217
$639$	7.71604e12	1.83080
$640$	−5.00553e12	−1.17934
$641$	−3.77475e12	−0.883135	−0.441567	−	0.897228i	$-0.645577\pi$
$641$	−3.77475e12	−0.883135	−0.441567	+	0.897228i	$0.645577\pi$
$642$	−1.47851e11	−0.0343491
$643$	1.26222e12	0.291197	0.145598	−	0.989344i	$-0.453489\pi$
$643$	1.26222e12	0.291197	0.145598	+	0.989344i	$0.453489\pi$
$644$	−3.62978e12	−0.831559
$645$	−1.03437e13	−2.35319
$646$	−8.74654e11	−0.197601
$647$	5.94830e12	1.33451	0.667257	−	0.744827i	$-0.267468\pi$
$647$	5.94830e12	1.33451	0.667257	+	0.744827i	$0.267468\pi$
$648$	2.42495e12	0.540275
$649$	2.95587e11	0.0654009
$650$	−4.07123e12	−0.894573
$651$	−2.00557e13	−4.37647
$652$	3.66804e12	0.794913
$653$	−1.12364e12	−0.241835	−0.120918	−	0.992663i	$-0.538584\pi$
$653$	−1.12364e12	−0.241835	−0.120918	+	0.992663i	$0.538584\pi$
$654$	1.66411e13	3.55698
$655$	4.19000e12	0.889464
$656$	1.04509e13	2.20337
$657$	−6.11144e11	−0.127967
$658$	−5.34705e12	−1.11198
$659$	−8.58385e11	−0.177296	−0.0886478	−	0.996063i	$-0.528255\pi$
$659$	−8.58385e11	−0.177296	−0.0886478	+	0.996063i	$0.528255\pi$
$660$	2.49311e12	0.511439
$661$	−2.45857e12	−0.500929	−0.250465	−	0.968126i	$-0.580583\pi$
$661$	−2.45857e12	−0.500929	−0.250465	+	0.968126i	$0.580583\pi$
$662$	3.81450e11	0.0771927
$663$	2.40609e12	0.483617
$664$	−3.80174e12	−0.758973
$665$	−6.23608e12	−1.23656
$666$	9.09721e12	1.79174
$667$	−3.13422e12	−0.613145
$668$	−5.00115e12	−0.971798
$669$	1.16121e13	2.24127
$670$	4.16867e12	0.799210
$671$	−2.05076e12	−0.390538
$672$	−1.47973e13	−2.79912
$673$	2.80053e12	0.526225	0.263113	−	0.964765i	$-0.415251\pi$
$673$	2.80053e12	0.526225	0.263113	+	0.964765i	$0.415251\pi$
$674$	2.56862e12	0.479436
$675$	5.91984e12	1.09760
$676$	1.02911e12	0.189541
$677$	−3.74996e12	−0.686085	−0.343042	−	0.939320i	$-0.611457\pi$
$677$	−3.74996e12	−0.686085	−0.343042	+	0.939320i	$0.611457\pi$
$678$	−7.98127e12	−1.45057
$679$	4.32187e12	0.780293
$680$	8.65969e11	0.155315
$681$	2.85846e12	0.509297
$682$	−4.57647e12	−0.810030
$683$	−4.38021e12	−0.770197	−0.385099	−	0.922875i	$-0.625833\pi$
$683$	−4.38021e12	−0.770197	−0.385099	+	0.922875i	$0.625833\pi$
$684$	4.49031e12	0.784375
$685$	−1.63394e12	−0.283549
$686$	3.14109e12	0.541530
$687$	6.07480e12	1.04046
$688$	7.75386e12	1.31938
$689$	−2.31558e12	−0.391447
$690$	−1.52305e13	−2.55796
$691$	1.91905e11	0.0320211	0.0160105	−	0.999872i	$-0.494903\pi$
$691$	1.91905e11	0.0320211	0.0160105	+	0.999872i	$0.494903\pi$
$692$	3.01258e12	0.499414
$693$	−7.13475e12	−1.17511
$694$	1.06512e13	1.74294
$695$	2.26988e12	0.369039
$696$	−3.63722e12	−0.587528
$697$	−2.68618e12	−0.431109
$698$	−6.88952e12	−1.09860
$699$	1.58792e13	2.51583
$700$	−3.56193e12	−0.560717
$701$	4.79909e12	0.750633	0.375316	−	0.926897i	$-0.377534\pi$
$701$	4.79909e12	0.750633	0.375316	+	0.926897i	$0.377534\pi$
$702$	−1.66299e13	−2.58447
$703$	−2.91540e12	−0.450193
$704$	−2.72357e11	−0.0417890
$705$	−8.43152e12	−1.28545
$706$	6.61719e12	1.00243
$707$	−5.21940e12	−0.785658
$708$	1.19141e12	0.178201
$709$	−7.09288e12	−1.05418	−0.527090	−	0.849810i	$-0.676717\pi$
$709$	−7.09288e12	−1.05418	−0.527090	+	0.849810i	$0.676717\pi$
$710$	−9.85593e12	−1.45558
$711$	5.43974e12	0.798298
$712$	−4.06731e12	−0.593127
$713$	1.05066e13	1.52250
$714$	5.60164e12	0.806627
$715$	3.91454e12	0.560148
$716$	−3.77629e12	−0.536978
$717$	1.04864e13	1.48181
$718$	−6.22939e12	−0.874753
$719$	8.16373e12	1.13922	0.569611	−	0.821914i	$-0.307094\pi$
$719$	8.16373e12	1.13922	0.569611	+	0.821914i	$0.307094\pi$
$720$	−2.30016e13	−3.18979
$721$	−9.59361e12	−1.32213
$722$	5.41257e12	0.741287
$723$	−1.91271e13	−2.60332
$724$	3.75484e12	0.507888
$725$	−3.07564e12	−0.413441
$726$	1.40433e13	1.87609
$727$	1.27003e13	1.68619	0.843097	−	0.537762i	$-0.180730\pi$
$727$	1.27003e13	1.68619	0.843097	+	0.537762i	$0.180730\pi$
$728$	−6.61391e12	−0.872705
$729$	−7.05847e12	−0.925629
$730$	7.80634e11	0.101741
$731$	−1.99295e12	−0.258148
$732$	−8.26591e12	−1.06412
$733$	−9.65924e12	−1.23588	−0.617938	−	0.786227i	$-0.712032\pi$
$733$	−9.65924e12	−1.23588	−0.617938	+	0.786227i	$0.712032\pi$
$734$	−3.57150e12	−0.454170
$735$	2.24457e13	2.83688
$736$	7.75186e12	0.973768
$737$	−1.52846e12	−0.190832
$738$	3.66959e13	4.55369
$739$	5.87320e11	0.0724394	0.0362197	−	0.999344i	$-0.488468\pi$
$739$	5.87320e11	0.0724394	0.0362197	+	0.999344i	$0.488468\pi$
$740$	−4.36685e12	−0.535335
$741$	1.05338e13	1.28352
$742$	−5.39090e12	−0.652895
$743$	−6.32905e12	−0.761884	−0.380942	−	0.924599i	$-0.624400\pi$
$743$	−6.32905e12	−0.761884	−0.380942	+	0.924599i	$0.624400\pi$
$744$	1.21927e13	1.45889
$745$	−2.02292e12	−0.240589
$746$	−1.92302e13	−2.27331
$747$	−2.59548e13	−3.04982
$748$	4.80357e11	0.0561057
$749$	−2.03105e11	−0.0235805
$750$	9.30221e12	1.07352
$751$	−5.48219e12	−0.628889	−0.314445	−	0.949276i	$-0.601818\pi$
$751$	−5.48219e12	−0.628889	−0.314445	+	0.949276i	$0.601818\pi$
$752$	6.32046e12	0.720723
$753$	7.14551e12	0.809946
$754$	8.64000e12	0.973515
$755$	3.36661e12	0.377078
$756$	−1.45495e13	−1.61994
$757$	6.94071e12	0.768197	0.384099	−	0.923292i	$-0.374512\pi$
$757$	6.94071e12	0.768197	0.384099	+	0.923292i	$0.374512\pi$
$758$	7.36426e12	0.810247
$759$	5.58433e12	0.610778
$760$	3.79118e12	0.412205
$761$	−1.18446e13	−1.28023	−0.640117	−	0.768277i	$-0.721114\pi$
$761$	−1.18446e13	−1.28023	−0.640117	+	0.768277i	$0.721114\pi$
$762$	−3.79365e13	−4.07624
$763$	2.28602e13	2.44185
$764$	−5.01562e12	−0.532605
$765$	5.91203e12	0.624109
$766$	4.41923e12	0.463786
$767$	1.87068e12	0.195173
$768$	2.15079e13	2.23087
$769$	−1.22311e12	−0.126123	−0.0630617	−	0.998010i	$-0.520086\pi$
$769$	−1.22311e12	−0.126123	−0.0630617	+	0.998010i	$0.520086\pi$
$770$	9.11344e12	0.934274
$771$	7.36049e12	0.750174
$772$	5.50615e12	0.557918
$773$	2.56478e12	0.258370	0.129185	−	0.991621i	$-0.458764\pi$
$773$	2.56478e12	0.258370	0.129185	+	0.991621i	$0.458764\pi$
$774$	2.72258e13	2.72675
$775$	1.03102e13	1.02662
$776$	−2.62745e12	−0.260110
$777$	1.86714e13	1.83773
$778$	−4.40429e12	−0.430991
$779$	−1.17600e13	−1.14416
$780$	1.57781e13	1.52627
$781$	3.61372e12	0.347556
$782$	−2.93452e12	−0.280612
$783$	−1.25631e13	−1.19445
$784$	−1.68258e13	−1.59057
$785$	1.22241e13	1.14896
$786$	−1.64774e13	−1.53988
$787$	−7.44338e12	−0.691646	−0.345823	−	0.938300i	$-0.612400\pi$
$787$	−7.44338e12	−0.691646	−0.345823	+	0.938300i	$0.612400\pi$
$788$	3.84414e12	0.355166
$789$	−2.22098e13	−2.04032
$790$	−6.94835e12	−0.634687
$791$	−1.09640e13	−0.995808
$792$	4.33752e12	0.391722
$793$	−1.29786e13	−1.16547
$794$	1.58460e12	0.141491
$795$	−8.50067e12	−0.754747
$796$	−5.45517e12	−0.481615
$797$	1.00963e13	0.886337	0.443168	−	0.896438i	$-0.353854\pi$
$797$	1.00963e13	0.886337	0.443168	+	0.896438i	$0.353854\pi$
$798$	2.45238e13	2.14079
$799$	−1.62453e12	−0.141016
$800$	7.60696e12	0.656608
$801$	−2.77678e13	−2.38339
$802$	1.71489e13	1.46370
$803$	−2.86222e11	−0.0242931
$804$	−6.16069e12	−0.519969
$805$	−2.09224e13	−1.75603
$806$	−2.89631e13	−2.41734
$807$	−1.69711e13	−1.40857
$808$	3.17309e12	0.261898
$809$	−8.02349e12	−0.658560	−0.329280	−	0.944232i	$-0.606806\pi$
$809$	−8.02349e12	−0.658560	−0.329280	+	0.944232i	$0.606806\pi$
$810$	−2.11466e13	−1.72607
$811$	2.03065e13	1.64832	0.824160	−	0.566357i	$-0.191648\pi$
$811$	2.03065e13	1.64832	0.824160	+	0.566357i	$0.191648\pi$
$812$	7.55915e12	0.610198
$813$	−2.33624e13	−1.87547
$814$	4.26057e12	0.340140
$815$	2.11430e13	1.67864
$816$	−6.62140e12	−0.522810
$817$	−8.72507e12	−0.685125
$818$	2.48430e13	1.94006
$819$	−4.51537e13	−3.50684
$820$	−1.76148e13	−1.36055
$821$	2.20512e13	1.69390	0.846951	−	0.531671i	$-0.178436\pi$
$821$	2.20512e13	1.69390	0.846951	+	0.531671i	$0.178436\pi$
$822$	6.42557e12	0.490894
$823$	8.31984e12	0.632143	0.316072	−	0.948735i	$-0.397636\pi$
$823$	8.31984e12	0.632143	0.316072	+	0.948735i	$0.397636\pi$
$824$	5.83236e12	0.440729
$825$	5.47995e12	0.411845
$826$	4.35513e12	0.325530
$827$	6.70382e12	0.498365	0.249182	−	0.968457i	$-0.419838\pi$
$827$	6.70382e12	0.498365	0.249182	+	0.968457i	$0.419838\pi$
$828$	1.50653e13	1.11388
$829$	−1.86852e13	−1.37405	−0.687025	−	0.726634i	$-0.741084\pi$
$829$	−1.86852e13	−1.37405	−0.687025	+	0.726634i	$0.741084\pi$
$830$	3.31529e13	2.42476
$831$	−2.08705e13	−1.51820
$832$	−1.72366e12	−0.124709
$833$	4.32470e12	0.311210
$834$	−8.92645e12	−0.638898
$835$	−2.88272e13	−2.05217
$836$	2.10298e12	0.148904
$837$	4.21142e13	2.96595
$838$	1.83792e13	1.28744
$839$	2.31979e13	1.61629	0.808147	−	0.588980i	$-0.200470\pi$
$839$	2.31979e13	1.61629	0.808147	+	0.588980i	$0.200470\pi$
$840$	−2.42802e13	−1.68266
$841$	−7.98001e12	−0.550074
$842$	−1.31063e13	−0.898620
$843$	−1.07142e13	−0.730694
$844$	−1.07883e13	−0.731831
$845$	5.93194e12	0.400259
$846$	2.21927e13	1.48951
$847$	1.92915e13	1.28793
$848$	6.37230e12	0.423170
$849$	1.96213e13	1.29612
$850$	−2.87967e12	−0.189216
$851$	−9.78133e12	−0.639315
$852$	1.45656e13	0.947003
$853$	−6.15810e12	−0.398269	−0.199134	−	0.979972i	$-0.563813\pi$
$853$	−6.15810e12	−0.398269	−0.199134	+	0.979972i	$0.563813\pi$
$854$	−3.02156e13	−1.94389
$855$	2.58827e13	1.65639
$856$	1.23476e11	0.00786052
$857$	8.90805e12	0.564117	0.282058	−	0.959397i	$-0.408983\pi$
$857$	8.90805e12	0.564117	0.282058	+	0.959397i	$0.408983\pi$
$858$	−1.53941e13	−0.969756
$859$	−1.06938e13	−0.670135	−0.335068	−	0.942194i	$-0.608759\pi$
$859$	−1.06938e13	−0.670135	−0.335068	+	0.942194i	$0.608759\pi$
$860$	−1.30689e13	−0.814699
$861$	7.53156e13	4.67058
$862$	−2.11574e12	−0.130520
$863$	−6.21448e12	−0.381379	−0.190689	−	0.981650i	$-0.561072\pi$
$863$	−6.21448e12	−0.381379	−0.190689	+	0.981650i	$0.561072\pi$
$864$	3.10723e13	1.89698
$865$	1.73648e13	1.05463
$866$	−2.97478e13	−1.79731
$867$	1.70188e12	0.102292
$868$	−2.53399e13	−1.51518
$869$	2.54764e12	0.151548
$870$	3.17182e13	1.87703
$871$	−9.67315e12	−0.569490
$872$	−1.38977e13	−0.813987
$873$	−1.79378e13	−1.04521
$874$	−1.28472e13	−0.744745
$875$	1.27786e13	0.736966
$876$	−1.15366e12	−0.0661928
$877$	1.74120e13	0.993916	0.496958	−	0.867775i	$-0.334450\pi$
$877$	1.74120e13	0.993916	0.496958	+	0.867775i	$0.334450\pi$
$878$	−2.75316e13	−1.56353
$879$	−5.40999e12	−0.305665
$880$	−1.07725e13	−0.605544
$881$	1.85361e13	1.03664	0.518318	−	0.855188i	$-0.326558\pi$
$881$	1.85361e13	1.03664	0.518318	+	0.855188i	$0.326558\pi$
$882$	−5.90797e13	−3.28723
$883$	−5.46626e12	−0.302599	−0.151299	−	0.988488i	$-0.548346\pi$
$883$	−5.46626e12	−0.302599	−0.151299	+	0.988488i	$0.548346\pi$
$884$	3.04003e12	0.167434
$885$	6.86741e12	0.376312
$886$	−6.85183e12	−0.373555
$887$	−3.61417e13	−1.96043	−0.980216	−	0.197930i	$-0.936578\pi$
$887$	−3.61417e13	−1.96043	−0.980216	+	0.197930i	$0.936578\pi$
$888$	−1.13511e13	−0.612604
$889$	−5.21140e13	−2.79832
$890$	3.54687e13	1.89492
$891$	7.75348e12	0.412142
$892$	1.46716e13	0.775954
$893$	−7.11214e12	−0.374256
$894$	7.95525e12	0.416519
$895$	−2.17670e13	−1.13395
$896$	2.70410e13	1.40164
$897$	3.53415e13	1.82272
$898$	1.59476e13	0.818376
$899$	−2.18803e13	−1.11721
$900$	1.47837e13	0.751088
$901$	−1.63785e12	−0.0827968
$902$	1.71861e13	0.864466
$903$	5.58789e13	2.79674
$904$	6.66549e12	0.331951
$905$	2.16433e13	1.07252
$906$	−1.32394e13	−0.652816
$907$	−3.39738e13	−1.66691	−0.833454	−	0.552589i	$-0.813640\pi$
$907$	−3.39738e13	−1.66691	−0.833454	+	0.552589i	$0.813640\pi$
$908$	3.61159e12	0.176324
$909$	2.16630e13	1.05240
$910$	5.76762e13	2.78811
$911$	2.01195e12	0.0967797	0.0483898	−	0.998829i	$-0.484591\pi$
$911$	2.01195e12	0.0967797	0.0483898	+	0.998829i	$0.484591\pi$
$912$	−2.89882e13	−1.38754
$913$	−1.21556e13	−0.578974
$914$	−1.95676e13	−0.927427
$915$	−4.76457e13	−2.24713
$916$	7.67533e12	0.360220
$917$	−2.26353e13	−1.05712
$918$	−1.17626e13	−0.546654
$919$	1.59408e11	0.00737207	0.00368604	−	0.999993i	$-0.498827\pi$
$919$	1.59408e11	0.00737207	0.00368604	+	0.999993i	$0.498827\pi$
$920$	1.27196e13	0.585369
$921$	3.32283e13	1.52174
$922$	2.60373e13	1.18661
$923$	2.28701e13	1.03720
$924$	−1.34683e13	−0.607842
$925$	−9.59850e12	−0.431088
$926$	−9.92396e12	−0.443543
$927$	3.98180e13	1.77101
$928$	−1.61435e13	−0.714551
$929$	4.18504e13	1.84344	0.921721	−	0.387854i	$-0.126784\pi$
$929$	4.18504e13	1.84344	0.921721	+	0.387854i	$0.126784\pi$
$930$	−1.06326e14	−4.66086
$931$	1.89334e13	0.825950
$932$	2.00629e13	0.871009
$933$	6.41967e13	2.77361
$934$	−1.01554e13	−0.436651
$935$	2.76883e12	0.118480
$936$	2.74508e13	1.16900
$937$	1.52091e13	0.644576	0.322288	−	0.946642i	$-0.395548\pi$
$937$	1.52091e13	0.644576	0.322288	+	0.946642i	$0.395548\pi$
$938$	−2.25201e13	−0.949855
$939$	4.53648e13	1.90425
$940$	−1.06530e13	−0.445037
$941$	−1.93636e13	−0.805067	−0.402534	−	0.915405i	$-0.631870\pi$
$941$	−1.93636e13	−0.805067	−0.402534	+	0.915405i	$0.631870\pi$
$942$	−4.80722e13	−1.98914
$943$	−3.94555e13	−1.62482
$944$	−5.14797e12	−0.210990
$945$	−8.38649e13	−3.42087
$946$	1.27509e13	0.517642
$947$	−3.99237e13	−1.61308	−0.806540	−	0.591179i	$-0.798663\pi$
$947$	−3.99237e13	−1.61308	−0.806540	+	0.591179i	$0.798663\pi$
$948$	1.02687e13	0.412930
$949$	−1.81141e12	−0.0724969
$950$	−1.26071e13	−0.502178
$951$	−7.69506e13	−3.05070
$952$	−4.67816e12	−0.184590
$953$	−3.60339e13	−1.41512	−0.707559	−	0.706654i	$-0.750204\pi$
$953$	−3.60339e13	−1.41512	−0.707559	+	0.706654i	$0.750204\pi$
$954$	2.23748e13	0.874562
$955$	−2.89106e13	−1.12472
$956$	1.32493e13	0.513018
$957$	−1.16296e13	−0.448188
$958$	−3.26090e13	−1.25081
$959$	8.82691e12	0.336996
$960$	−6.32771e12	−0.240451
$961$	4.69079e13	1.77415
$962$	2.69639e13	1.01507
$963$	8.42981e11	0.0315864
$964$	−2.41666e13	−0.901297
$965$	3.17381e13	1.17817
$966$	8.22787e13	3.04012
$967$	2.93298e13	1.07867	0.539337	−	0.842090i	$-0.318675\pi$
$967$	2.93298e13	1.07867	0.539337	+	0.842090i	$0.318675\pi$
$968$	−1.17281e13	−0.429329
$969$	7.45077e12	0.271484
$970$	2.29125e13	0.830997
$971$	4.26932e13	1.54125	0.770623	−	0.637291i	$-0.219945\pi$
$971$	4.26932e13	1.54125	0.770623	+	0.637291i	$0.219945\pi$
$972$	1.41629e12	0.0508925
$973$	−1.22624e13	−0.438600
$974$	−3.43228e11	−0.0122199
$975$	3.46809e13	1.22905
$976$	3.57163e13	1.25992
$977$	−3.65451e12	−0.128323	−0.0641613	−	0.997940i	$-0.520437\pi$
$977$	−3.65451e12	−0.128323	−0.0641613	+	0.997940i	$0.520437\pi$
$978$	−8.31460e13	−2.90614
$979$	−1.30047e13	−0.452460
$980$	2.83595e13	0.982158
$981$	−9.48803e13	−3.27089
$982$	4.60017e12	0.157860
$983$	−5.51397e13	−1.88353	−0.941767	−	0.336265i	$-0.890836\pi$
$983$	−5.51397e13	−1.88353	−0.941767	+	0.336265i	$0.890836\pi$
$984$	−4.57876e13	−1.55693
$985$	2.21581e13	0.750013
$986$	6.11125e12	0.205913
$987$	4.55490e13	1.52775
$988$	1.33091e13	0.444369
$989$	−2.92732e13	−0.972941
$990$	−3.78250e13	−1.25147
$991$	4.65397e13	1.53282	0.766412	−	0.642350i	$-0.222040\pi$
$991$	4.65397e13	1.53282	0.766412	+	0.642350i	$0.222040\pi$
$992$	5.41166e13	1.77430
$993$	−3.24939e12	−0.106055
$994$	5.32440e13	1.72994
$995$	−3.14442e13	−1.01704
$996$	−4.89951e13	−1.57756
$997$	4.29398e13	1.37636	0.688179	−	0.725541i	$-0.258410\pi$
$997$	4.29398e13	1.37636	0.688179	+	0.725541i	$0.258410\pi$
$998$	4.13600e13	1.31975
$999$	−3.92072e13	−1.24544

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.10.a.b.1.2	✓	7
3.2	odd	2		153.10.a.f.1.6		7
4.3	odd	2		272.10.a.g.1.1		7
17.16	even	2		289.10.a.b.1.2		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.10.a.b.1.2	✓	7	1.1	even	1	trivial
153.10.a.f.1.6		7	3.2	odd	2
272.10.a.g.1.1		7	4.3	odd	2
289.10.a.b.1.2		7	17.16	even	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:	\( N \)	\(=\)	\( 17 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	17.a (trivial)

\(f(q)\)	\(=\)	\(q-28.6400 q^{2} +243.971 q^{3} +308.250 q^{4} +1776.79 q^{5} -6987.32 q^{6} -9598.61 q^{7} +5835.40 q^{8} +39838.7 q^{9} +O(q^{10})\)	\(q-28.6400 q^{2} +243.971 q^{3} +308.250 q^{4} +1776.79 q^{5} -6987.32 q^{6} -9598.61 q^{7} +5835.40 q^{8} +39838.7 q^{9} -50887.2 q^{10} +18658.0 q^{11} +75204.0 q^{12} +118081. q^{13} +274904. q^{14} +433484. q^{15} -324950. q^{16} +83521.0 q^{17} -1.14098e6 q^{18} +365652. q^{19} +547695. q^{20} -2.34178e6 q^{21} -534365. q^{22} +1.22678e6 q^{23} +1.42367e6 q^{24} +1.20385e6 q^{25} -3.38183e6 q^{26} +4.91741e6 q^{27} -2.95877e6 q^{28} -2.55483e6 q^{29} -1.24150e7 q^{30} +8.56431e6 q^{31} +6.31884e6 q^{32} +4.55201e6 q^{33} -2.39204e6 q^{34} -1.70547e7 q^{35} +1.22803e7 q^{36} -7.97315e6 q^{37} -1.04723e7 q^{38} +2.88083e7 q^{39} +1.03683e7 q^{40} -3.21617e7 q^{41} +6.70686e7 q^{42} -2.38617e7 q^{43} +5.75133e6 q^{44} +7.07850e7 q^{45} -3.51351e7 q^{46} -1.94506e7 q^{47} -7.92783e7 q^{48} +5.17797e7 q^{49} -3.44784e7 q^{50} +2.03767e7 q^{51} +3.63984e7 q^{52} -1.96101e7 q^{53} -1.40835e8 q^{54} +3.31513e7 q^{55} -5.60118e7 q^{56} +8.92083e7 q^{57} +7.31702e7 q^{58} +1.58423e7 q^{59} +1.33622e8 q^{60} -1.09913e8 q^{61} -2.45282e8 q^{62} -3.82396e8 q^{63} -1.45973e7 q^{64} +2.09805e8 q^{65} -1.30370e8 q^{66} -8.19198e7 q^{67} +2.57453e7 q^{68} +2.99299e8 q^{69} +4.88447e8 q^{70} +1.93682e8 q^{71} +2.32475e8 q^{72} -1.53405e7 q^{73} +2.28351e8 q^{74} +2.93705e8 q^{75} +1.12712e8 q^{76} -1.79091e8 q^{77} -8.25069e8 q^{78} +1.36544e8 q^{79} -5.77367e8 q^{80} +4.15558e8 q^{81} +9.21111e8 q^{82} -6.51497e8 q^{83} -7.21854e8 q^{84} +1.48399e8 q^{85} +6.83399e8 q^{86} -6.23303e8 q^{87} +1.08877e8 q^{88} -6.97006e8 q^{89} -2.02728e9 q^{90} -1.13341e9 q^{91} +3.78156e8 q^{92} +2.08944e9 q^{93} +5.57064e8 q^{94} +6.49686e8 q^{95} +1.54161e9 q^{96} -4.50260e8 q^{97} -1.48297e9 q^{98} +7.43311e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - q^{2} + 88 q^{3} + 2389 q^{4} + 1362 q^{5} - 11720 q^{6} + 9388 q^{7} + 16821 q^{8} + 81419 q^{9}+O(q^{10}) \) 7 * q - q^2 + 88 * q^3 + 2389 * q^4 + 1362 * q^5 - 11720 * q^6 + 9388 * q^7 + 16821 * q^8 + 81419 * q^9	\( 7 q - q^{2} + 88 q^{3} + 2389 q^{4} + 1362 q^{5} - 11720 q^{6} + 9388 q^{7} + 16821 q^{8} + 81419 q^{9} + 154226 q^{10} + 135536 q^{11} + 198160 q^{12} + 166122 q^{13} + 447252 q^{14} + 159048 q^{15} + 1463585 q^{16} + 584647 q^{17} + 149027 q^{18} + 777172 q^{19} - 917162 q^{20} - 3412104 q^{21} - 1222520 q^{22} + 1357764 q^{23} - 8487360 q^{24} + 1065785 q^{25} - 14379966 q^{26} - 4519064 q^{27} - 3328892 q^{28} + 967002 q^{29} - 12558992 q^{30} + 3546740 q^{31} + 4825461 q^{32} + 11928016 q^{33} - 83521 q^{34} - 530736 q^{35} + 4535009 q^{36} + 18296498 q^{37} - 49363020 q^{38} + 86306872 q^{39} + 127155062 q^{40} + 10285686 q^{41} + 14620416 q^{42} + 21913204 q^{43} + 96696624 q^{44} + 108916410 q^{45} - 151509484 q^{46} + 56639800 q^{47} - 201398496 q^{48} + 27010351 q^{49} - 261150303 q^{50} + 7349848 q^{51} - 156226378 q^{52} + 121813562 q^{53} - 93375344 q^{54} + 40793128 q^{55} - 196175436 q^{56} + 153612960 q^{57} - 236833910 q^{58} + 29222388 q^{59} - 628643488 q^{60} - 49915846 q^{61} - 73506556 q^{62} - 2185356 q^{63} + 317922057 q^{64} - 122633668 q^{65} - 624886144 q^{66} + 301863420 q^{67} + 199531669 q^{68} + 379683432 q^{69} + 966315960 q^{70} + 652473940 q^{71} + 655760385 q^{72} + 306656342 q^{73} + 249173874 q^{74} + 919071912 q^{75} + 128694700 q^{76} - 102442536 q^{77} + 323434416 q^{78} + 959147884 q^{79} - 692173602 q^{80} - 374486977 q^{81} + 1046441254 q^{82} - 1512945268 q^{83} - 481790592 q^{84} + 113755602 q^{85} - 164953236 q^{86} - 1612550856 q^{87} + 1132038848 q^{88} - 1971327114 q^{89} - 2284664662 q^{90} - 1061062864 q^{91} + 901186756 q^{92} - 798598936 q^{93} + 2534831232 q^{94} - 3249631512 q^{95} - 4442036640 q^{96} + 2006526254 q^{97} - 2170640009 q^{98} - 2579159272 q^{99}+O(q^{100}) \) 7 * q - q^2 + 88 * q^3 + 2389 * q^4 + 1362 * q^5 - 11720 * q^6 + 9388 * q^7 + 16821 * q^8 + 81419 * q^9 + 154226 * q^10 + 135536 * q^11 + 198160 * q^12 + 166122 * q^13 + 447252 * q^14 + 159048 * q^15 + 1463585 * q^16 + 584647 * q^17 + 149027 * q^18 + 777172 * q^19 - 917162 * q^20 - 3412104 * q^21 - 1222520 * q^22 + 1357764 * q^23 - 8487360 * q^24 + 1065785 * q^25 - 14379966 * q^26 - 4519064 * q^27 - 3328892 * q^28 + 967002 * q^29 - 12558992 * q^30 + 3546740 * q^31 + 4825461 * q^32 + 11928016 * q^33 - 83521 * q^34 - 530736 * q^35 + 4535009 * q^36 + 18296498 * q^37 - 49363020 * q^38 + 86306872 * q^39 + 127155062 * q^40 + 10285686 * q^41 + 14620416 * q^42 + 21913204 * q^43 + 96696624 * q^44 + 108916410 * q^45 - 151509484 * q^46 + 56639800 * q^47 - 201398496 * q^48 + 27010351 * q^49 - 261150303 * q^50 + 7349848 * q^51 - 156226378 * q^52 + 121813562 * q^53 - 93375344 * q^54 + 40793128 * q^55 - 196175436 * q^56 + 153612960 * q^57 - 236833910 * q^58 + 29222388 * q^59 - 628643488 * q^60 - 49915846 * q^61 - 73506556 * q^62 - 2185356 * q^63 + 317922057 * q^64 - 122633668 * q^65 - 624886144 * q^66 + 301863420 * q^67 + 199531669 * q^68 + 379683432 * q^69 + 966315960 * q^70 + 652473940 * q^71 + 655760385 * q^72 + 306656342 * q^73 + 249173874 * q^74 + 919071912 * q^75 + 128694700 * q^76 - 102442536 * q^77 + 323434416 * q^78 + 959147884 * q^79 - 692173602 * q^80 - 374486977 * q^81 + 1046441254 * q^82 - 1512945268 * q^83 - 481790592 * q^84 + 113755602 * q^85 - 164953236 * q^86 - 1612550856 * q^87 + 1132038848 * q^88 - 1971327114 * q^89 - 2284664662 * q^90 - 1061062864 * q^91 + 901186756 * q^92 - 798598936 * q^93 + 2534831232 * q^94 - 3249631512 * q^95 - 4442036640 * q^96 + 2006526254 * q^97 - 2170640009 * q^98 - 2579159272 * q^99

Introduction

L-functions

Modular forms

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