LMFDB - Embedded newform 35.8.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [35,8,Mod(1,35)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(35, 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("35.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 35 = 5 \cdot 7 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	35.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:	$10.9334758919$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 584x^{3} + 2550x^{2} + 46220x - 155664 $ x^5 - x^4 - 584x^3 + 2550x^2 + 46220*x - 155664
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-23.9723$ of defining polynomial
Character	$\chi$	$=$	35.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-21.9723 q^{2} +9.99965 q^{3} +354.783 q^{4} +125.000 q^{5} -219.716 q^{6} +343.000 q^{7} -4982.95 q^{8} -2087.01 q^{9} +O(q^{10})$	\(q-21.9723 q^{2} +9.99965 q^{3} +354.783 q^{4} +125.000 q^{5} -219.716 q^{6} +343.000 q^{7} -4982.95 q^{8} -2087.01 q^{9} -2746.54 q^{10} +4691.00 q^{11} +3547.71 q^{12} -1370.87 q^{13} -7536.51 q^{14} +1249.96 q^{15} +64074.8 q^{16} -20817.8 q^{17} +45856.4 q^{18} +52350.5 q^{19} +44347.9 q^{20} +3429.88 q^{21} -103072. q^{22} +22775.7 q^{23} -49827.8 q^{24} +15625.0 q^{25} +30121.2 q^{26} -42738.6 q^{27} +121691. q^{28} -46694.1 q^{29} -27464.4 q^{30} +248695. q^{31} -770055. q^{32} +46908.3 q^{33} +457415. q^{34} +42875.0 q^{35} -740435. q^{36} +316892. q^{37} -1.15026e6 q^{38} -13708.2 q^{39} -622869. q^{40} +477258. q^{41} -75362.4 q^{42} +741079. q^{43} +1.66429e6 q^{44} -260876. q^{45} -500436. q^{46} +114606. q^{47} +640726. q^{48} +117649. q^{49} -343318. q^{50} -208171. q^{51} -486361. q^{52} +1.19602e6 q^{53} +939066. q^{54} +586375. q^{55} -1.70915e6 q^{56} +523487. q^{57} +1.02598e6 q^{58} -657680. q^{59} +443463. q^{60} -2.35085e6 q^{61} -5.46441e6 q^{62} -715843. q^{63} +8.71832e6 q^{64} -171359. q^{65} -1.03069e6 q^{66} -2.54170e6 q^{67} -7.38580e6 q^{68} +227749. q^{69} -942064. q^{70} +2.16146e6 q^{71} +1.03995e7 q^{72} +2.68249e6 q^{73} -6.96285e6 q^{74} +156245. q^{75} +1.85731e7 q^{76} +1.60901e6 q^{77} +301201. q^{78} +199437. q^{79} +8.00935e6 q^{80} +4.13691e6 q^{81} -1.04865e7 q^{82} -6.23761e6 q^{83} +1.21686e6 q^{84} -2.60222e6 q^{85} -1.62832e7 q^{86} -466925. q^{87} -2.33750e7 q^{88} +1.69283e6 q^{89} +5.73205e6 q^{90} -470208. q^{91} +8.08045e6 q^{92} +2.48686e6 q^{93} -2.51817e6 q^{94} +6.54381e6 q^{95} -7.70028e6 q^{96} -4.22828e6 q^{97} -2.58502e6 q^{98} -9.79014e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 11 q^{2} + 65 q^{3} + 553 q^{4} + 625 q^{5} + 96 q^{6} + 1715 q^{7} - 1647 q^{8} - 12 q^{9}+O(q^{10}) $ 5 * q + 11 * q^2 + 65 * q^3 + 553 * q^4 + 625 * q^5 + 96 * q^6 + 1715 * q^7 - 1647 * q^8 - 12 * q^9	\( 5 q + 11 q^{2} + 65 q^{3} + 553 q^{4} + 625 q^{5} + 96 q^{6} + 1715 q^{7} - 1647 q^{8} - 12 q^{9} + 1375 q^{10} + 10027 q^{11} + 10024 q^{12} + 16141 q^{13} + 3773 q^{14} + 8125 q^{15} + 94169 q^{16} + 17427 q^{17} + 47547 q^{18} + 44394 q^{19} + 69125 q^{20} + 22295 q^{21} - 89168 q^{22} + 55698 q^{23} + 18324 q^{24} + 78125 q^{25} + 163750 q^{26} - 53389 q^{27} + 189679 q^{28} - 164219 q^{29} + 12000 q^{30} + 138440 q^{31} - 509615 q^{32} - 213271 q^{33} + 132338 q^{34} + 214375 q^{35} - 1408655 q^{36} + 181518 q^{37} - 1725140 q^{38} - 481621 q^{39} - 205875 q^{40} - 369676 q^{41} + 32928 q^{42} + 386 q^{43} - 37608 q^{44} - 1500 q^{45} - 2610592 q^{46} + 962985 q^{47} - 1271004 q^{48} + 588245 q^{49} + 171875 q^{50} - 1305827 q^{51} + 2349706 q^{52} + 396244 q^{53} + 2641788 q^{54} + 1253375 q^{55} - 564921 q^{56} + 4322278 q^{57} - 4408538 q^{58} + 6284948 q^{59} + 1253000 q^{60} + 1975828 q^{61} - 2246384 q^{62} - 4116 q^{63} + 13769617 q^{64} + 2017625 q^{65} + 798284 q^{66} - 554376 q^{67} - 11618770 q^{68} + 9051046 q^{69} + 471625 q^{70} + 6526040 q^{71} - 3026835 q^{72} + 7479766 q^{73} - 3948102 q^{74} + 1015625 q^{75} + 9203364 q^{76} + 3439261 q^{77} - 12300388 q^{78} + 4851305 q^{79} + 11771125 q^{80} - 4256091 q^{81} - 29262330 q^{82} - 11813196 q^{83} + 3438232 q^{84} + 2178375 q^{85} - 34717484 q^{86} - 263021 q^{87} - 54461828 q^{88} + 12879896 q^{89} + 5943375 q^{90} + 5536363 q^{91} - 18484672 q^{92} - 17648536 q^{93} + 23744524 q^{94} + 5549250 q^{95} - 39241860 q^{96} + 11704767 q^{97} + 1294139 q^{98} + 20972602 q^{99}+O(q^{100}) \) 5 * q + 11 * q^2 + 65 * q^3 + 553 * q^4 + 625 * q^5 + 96 * q^6 + 1715 * q^7 - 1647 * q^8 - 12 * q^9 + 1375 * q^10 + 10027 * q^11 + 10024 * q^12 + 16141 * q^13 + 3773 * q^14 + 8125 * q^15 + 94169 * q^16 + 17427 * q^17 + 47547 * q^18 + 44394 * q^19 + 69125 * q^20 + 22295 * q^21 - 89168 * q^22 + 55698 * q^23 + 18324 * q^24 + 78125 * q^25 + 163750 * q^26 - 53389 * q^27 + 189679 * q^28 - 164219 * q^29 + 12000 * q^30 + 138440 * q^31 - 509615 * q^32 - 213271 * q^33 + 132338 * q^34 + 214375 * q^35 - 1408655 * q^36 + 181518 * q^37 - 1725140 * q^38 - 481621 * q^39 - 205875 * q^40 - 369676 * q^41 + 32928 * q^42 + 386 * q^43 - 37608 * q^44 - 1500 * q^45 - 2610592 * q^46 + 962985 * q^47 - 1271004 * q^48 + 588245 * q^49 + 171875 * q^50 - 1305827 * q^51 + 2349706 * q^52 + 396244 * q^53 + 2641788 * q^54 + 1253375 * q^55 - 564921 * q^56 + 4322278 * q^57 - 4408538 * q^58 + 6284948 * q^59 + 1253000 * q^60 + 1975828 * q^61 - 2246384 * q^62 - 4116 * q^63 + 13769617 * q^64 + 2017625 * q^65 + 798284 * q^66 - 554376 * q^67 - 11618770 * q^68 + 9051046 * q^69 + 471625 * q^70 + 6526040 * q^71 - 3026835 * q^72 + 7479766 * q^73 - 3948102 * q^74 + 1015625 * q^75 + 9203364 * q^76 + 3439261 * q^77 - 12300388 * q^78 + 4851305 * q^79 + 11771125 * q^80 - 4256091 * q^81 - 29262330 * q^82 - 11813196 * q^83 + 3438232 * q^84 + 2178375 * q^85 - 34717484 * q^86 - 263021 * q^87 - 54461828 * q^88 + 12879896 * q^89 + 5943375 * q^90 + 5536363 * q^91 - 18484672 * q^92 - 17648536 * q^93 + 23744524 * q^94 + 5549250 * q^95 - 39241860 * q^96 + 11704767 * q^97 + 1294139 * q^98 + 20972602 * 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 $

$2$	−21.9723	−1.94210	−0.971049	−	0.238881i	$-0.923219\pi$
$2$	−21.9723	−1.94210	−0.971049	+	0.238881i	$0.923219\pi$
$3$	9.99965	0.213826	0.106913	−	0.994268i	$-0.465903\pi$
$3$	9.99965	0.213826	0.106913	+	0.994268i	$0.465903\pi$
$4$	354.783	2.77174
$5$	125.000	0.447214
$5$	125.000	0.447214
$6$	−219.716	−0.415271
$7$	343.000	0.377964
$7$	343.000	0.377964
$8$	−4982.95	−3.44090
$9$	−2087.01	−0.954278
$10$	−2746.54	−0.868532
$11$	4691.00	1.06265	0.531326	−	0.847168i	$-0.321694\pi$
$11$	4691.00	1.06265	0.531326	+	0.847168i	$0.321694\pi$
$12$	3547.71	0.592671
$13$	−1370.87	−0.173059	−0.0865296	−	0.996249i	$-0.527578\pi$
$13$	−1370.87	−0.173059	−0.0865296	+	0.996249i	$0.527578\pi$
$14$	−7536.51	−0.734044
$15$	1249.96	0.0956259
$16$	64074.8	3.91082
$17$	−20817.8	−1.02769	−0.513846	−	0.857882i	$-0.671780\pi$
$17$	−20817.8	−1.02769	−0.513846	+	0.857882i	$0.671780\pi$
$18$	45856.4	1.85330
$19$	52350.5	1.75099	0.875494	−	0.483229i	$-0.160536\pi$
$19$	52350.5	1.75099	0.875494	+	0.483229i	$0.160536\pi$
$20$	44347.9	1.23956
$21$	3429.88	0.0808186
$22$	−103072.	−2.06377
$23$	22775.7	0.390324	0.195162	−	0.980771i	$-0.437477\pi$
$23$	22775.7	0.390324	0.195162	+	0.980771i	$0.437477\pi$
$24$	−49827.8	−0.735753
$25$	15625.0	0.200000
$26$	30121.2	0.336098
$27$	−42738.6	−0.417875
$28$	121691.	1.04762
$29$	−46694.1	−0.355524	−0.177762	−	0.984073i	$-0.556886\pi$
$29$	−46694.1	−0.355524	−0.177762	+	0.984073i	$0.556886\pi$
$30$	−27464.4	−0.185715
$31$	248695.	1.49934	0.749672	−	0.661809i	$-0.230211\pi$
$31$	248695.	1.49934	0.749672	+	0.661809i	$0.230211\pi$
$32$	−770055.	−4.15429
$33$	46908.3	0.227222
$34$	457415.	1.99588
$35$	42875.0	0.169031
$36$	−740435.	−2.64501
$37$	316892.	1.02850	0.514251	−	0.857640i	$-0.328070\pi$
$37$	316892.	1.02850	0.514251	+	0.857640i	$0.328070\pi$
$38$	−1.15026e6	−3.40059
$39$	−13708.2	−0.0370045
$40$	−622869.	−1.53882
$41$	477258.	1.08146	0.540729	−	0.841197i	$-0.318148\pi$
$41$	477258.	1.08146	0.540729	+	0.841197i	$0.318148\pi$
$42$	−75362.4	−0.156958
$43$	741079.	1.42143	0.710714	−	0.703481i	$-0.248372\pi$
$43$	741079.	1.42143	0.710714	+	0.703481i	$0.248372\pi$
$44$	1.66429e6	2.94540
$45$	−260876.	−0.426766
$46$	−500436.	−0.758047
$47$	114606.	0.161015	0.0805074	−	0.996754i	$-0.474346\pi$
$47$	114606.	0.161015	0.0805074	+	0.996754i	$0.474346\pi$
$48$	640726.	0.836234
$49$	117649.	0.142857
$50$	−343318.	−0.388420
$51$	−208171.	−0.219747
$52$	−486361.	−0.479675
$53$	1.19602e6	1.10350	0.551749	−	0.834010i	$-0.313961\pi$
$53$	1.19602e6	1.10350	0.551749	+	0.834010i	$0.313961\pi$
$54$	939066.	0.811555
$55$	586375.	0.475232
$56$	−1.70915e6	−1.30054
$57$	523487.	0.374407
$58$	1.02598e6	0.690463
$59$	−657680.	−0.416901	−0.208450	−	0.978033i	$-0.566842\pi$
$59$	−657680.	−0.416901	−0.208450	+	0.978033i	$0.566842\pi$
$60$	443463.	0.265050
$61$	−2.35085e6	−1.32608	−0.663041	−	0.748583i	$-0.730734\pi$
$61$	−2.35085e6	−1.32608	−0.663041	+	0.748583i	$0.730734\pi$
$62$	−5.46441e6	−2.91187
$63$	−715843.	−0.360683
$64$	8.71832e6	4.15722
$65$	−171359.	−0.0773944
$66$	−1.03069e6	−0.441288
$67$	−2.54170e6	−1.03243	−0.516217	−	0.856458i	$-0.672660\pi$
$67$	−2.54170e6	−1.03243	−0.516217	+	0.856458i	$0.672660\pi$
$68$	−7.38580e6	−2.84850
$69$	227749.	0.0834614
$70$	−942064.	−0.328274
$71$	2.16146e6	0.716710	0.358355	−	0.933585i	$-0.383338\pi$
$71$	2.16146e6	0.716710	0.358355	+	0.933585i	$0.383338\pi$
$72$	1.03995e7	3.28358
$73$	2.68249e6	0.807064	0.403532	−	0.914966i	$-0.367782\pi$
$73$	2.68249e6	0.807064	0.403532	+	0.914966i	$0.367782\pi$
$74$	−6.96285e6	−1.99745
$75$	156245.	0.0427652
$76$	1.85731e7	4.85329
$77$	1.60901e6	0.401644
$78$	301201.	0.0718664
$79$	199437.	0.0455104	0.0227552	−	0.999741i	$-0.492756\pi$
$79$	199437.	0.0455104	0.0227552	+	0.999741i	$0.492756\pi$
$80$	8.00935e6	1.74897
$81$	4.13691e6	0.864926
$82$	−1.04865e7	−2.10030
$83$	−6.23761e6	−1.19742	−0.598708	−	0.800967i	$-0.704319\pi$
$83$	−6.23761e6	−1.19742	−0.598708	+	0.800967i	$0.704319\pi$
$84$	1.21686e6	0.224008
$85$	−2.60222e6	−0.459598
$86$	−1.62832e7	−2.76055
$87$	−466925.	−0.0760203
$88$	−2.33750e7	−3.65648
$89$	1.69283e6	0.254535	0.127267	−	0.991868i	$-0.459379\pi$
$89$	1.69283e6	0.254535	0.127267	+	0.991868i	$0.459379\pi$
$90$	5.73205e6	0.828822
$91$	−470208.	−0.0654102
$92$	8.08045e6	1.08188
$93$	2.48686e6	0.320599
$94$	−2.51817e6	−0.312706
$95$	6.54381e6	0.783066
$96$	−7.70028e6	−0.888295
$97$	−4.22828e6	−0.470395	−0.235198	−	0.971948i	$-0.575574\pi$
$97$	−4.22828e6	−0.470395	−0.235198	+	0.971948i	$0.575574\pi$
$98$	−2.58502e6	−0.277443
$99$	−9.79014e6	−1.01407
$100$	5.54349e6	0.554349
$101$	−1.45736e7	−1.40748	−0.703739	−	0.710459i	$-0.748488\pi$
$101$	−1.45736e7	−1.40748	−0.703739	+	0.710459i	$0.748488\pi$
$102$	4.57399e6	0.426771
$103$	2.00327e7	1.80638	0.903190	−	0.429242i	$-0.141219\pi$
$103$	2.00327e7	1.80638	0.903190	+	0.429242i	$0.141219\pi$
$104$	6.83098e6	0.595479
$105$	428735.	0.0361432
$106$	−2.62793e7	−2.14310
$107$	2.12385e7	1.67602	0.838012	−	0.545651i	$-0.183718\pi$
$107$	2.12385e7	1.67602	0.838012	+	0.545651i	$0.183718\pi$
$108$	−1.51629e7	−1.15824
$109$	−1.47380e6	−0.109005	−0.0545023	−	0.998514i	$-0.517357\pi$
$109$	−1.47380e6	−0.109005	−0.0545023	+	0.998514i	$0.517357\pi$
$110$	−1.28840e7	−0.922947
$111$	3.16881e6	0.219920
$112$	2.19777e7	1.47815
$113$	4.52415e6	0.294959	0.147480	−	0.989065i	$-0.452884\pi$
$113$	4.52415e6	0.294959	0.147480	+	0.989065i	$0.452884\pi$
$114$	−1.15022e7	−0.727135
$115$	2.84697e6	0.174558
$116$	−1.65663e7	−0.985422
$117$	2.86101e6	0.165147
$118$	1.44508e7	0.809662
$119$	−7.14050e6	−0.388431
$120$	−6.22847e6	−0.329039
$121$	2.51829e6	0.129228
$122$	5.16536e7	2.57538
$123$	4.77242e6	0.231244
$124$	8.82329e7	4.15580
$125$	1.95312e6	0.0894427
$126$	1.57287e7	0.700482
$127$	−4.15006e7	−1.79780	−0.898901	−	0.438152i	$-0.855633\pi$
$127$	−4.15006e7	−1.79780	−0.898901	+	0.438152i	$0.855633\pi$
$128$	−9.29948e7	−3.91944
$129$	7.41053e6	0.303938
$130$	3.76515e6	0.150307
$131$	−3.93760e6	−0.153032	−0.0765159	−	0.997068i	$-0.524380\pi$
$131$	−3.93760e6	−0.153032	−0.0765159	+	0.997068i	$0.524380\pi$
$132$	1.66423e7	0.629802
$133$	1.79562e7	0.661811
$134$	5.58470e7	2.00509
$135$	−5.34232e6	−0.186880
$136$	1.03734e8	3.53619
$137$	4.33458e6	0.144021	0.0720104	−	0.997404i	$-0.477059\pi$
$137$	4.33458e6	0.144021	0.0720104	+	0.997404i	$0.477059\pi$
$138$	−5.00418e6	−0.162090
$139$	1.75512e7	0.554312	0.277156	−	0.960825i	$-0.410608\pi$
$139$	1.75512e7	0.554312	0.277156	+	0.960825i	$0.410608\pi$
$140$	1.52113e7	0.468510
$141$	1.14602e6	0.0344291
$142$	−4.74923e7	−1.39192
$143$	−6.43075e6	−0.183901
$144$	−1.33725e8	−3.73201
$145$	−5.83677e6	−0.158995
$146$	−5.89405e7	−1.56740
$147$	1.17645e6	0.0305466
$148$	1.12428e8	2.85074
$149$	−4.26530e7	−1.05633	−0.528163	−	0.849143i	$-0.677119\pi$
$149$	−4.26530e7	−1.05633	−0.528163	+	0.849143i	$0.677119\pi$
$150$	−3.43306e6	−0.0830542
$151$	−3.12813e7	−0.739375	−0.369688	−	0.929156i	$-0.620535\pi$
$151$	−3.12813e7	−0.739375	−0.369688	+	0.929156i	$0.620535\pi$
$152$	−2.60860e8	−6.02497
$153$	4.34469e7	0.980705
$154$	−3.53537e7	−0.780033
$155$	3.10869e7	0.670527
$156$	−4.86344e6	−0.102567
$157$	−1.24307e7	−0.256358	−0.128179	−	0.991751i	$-0.540913\pi$
$157$	−1.24307e7	−0.256358	−0.128179	+	0.991751i	$0.540913\pi$
$158$	−4.38209e6	−0.0883856
$159$	1.19597e7	0.235957
$160$	−9.62569e7	−1.85786
$161$	7.81208e6	0.147529
$162$	−9.08976e7	−1.67977
$163$	−2.25389e7	−0.407639	−0.203819	−	0.979009i	$-0.565335\pi$
$163$	−2.25389e7	−0.407639	−0.203819	+	0.979009i	$0.565335\pi$
$164$	1.69323e8	2.99753
$165$	5.86354e6	0.101617
$166$	1.37055e8	2.32550
$167$	−4.00165e7	−0.664862	−0.332431	−	0.943128i	$-0.607869\pi$
$167$	−4.00165e7	−0.664862	−0.332431	+	0.943128i	$0.607869\pi$
$168$	−1.70909e7	−0.278089
$169$	−6.08692e7	−0.970051
$170$	5.71769e7	0.892585
$171$	−1.09256e8	−1.67093
$172$	2.62922e8	3.93983
$173$	1.05309e8	1.54633	0.773167	−	0.634203i	$-0.218672\pi$
$173$	1.05309e8	1.54633	0.773167	+	0.634203i	$0.218672\pi$
$174$	1.02594e7	0.147639
$175$	5.35938e6	0.0755929
$176$	3.00575e8	4.15584
$177$	−6.57657e6	−0.0891442
$178$	−3.71953e7	−0.494332
$179$	2.10469e7	0.274286	0.137143	−	0.990551i	$-0.456208\pi$
$179$	2.10469e7	0.274286	0.137143	+	0.990551i	$0.456208\pi$
$180$	−9.25544e7	−1.18289
$181$	−1.09144e8	−1.36813	−0.684064	−	0.729422i	$-0.739789\pi$
$181$	−1.09144e8	−1.36813	−0.684064	+	0.729422i	$0.739789\pi$
$182$	1.03316e7	0.127033
$183$	−2.35077e7	−0.283551
$184$	−1.13490e8	−1.34306
$185$	3.96115e7	0.459960
$186$	−5.46422e7	−0.622634
$187$	−9.76562e7	−1.09208
$188$	4.06604e7	0.446292
$189$	−1.46593e7	−0.157942
$190$	−1.43783e8	−1.52079
$191$	2.91019e7	0.302207	0.151104	−	0.988518i	$-0.451717\pi$
$191$	2.91019e7	0.302207	0.151104	+	0.988518i	$0.451717\pi$
$192$	8.71802e7	0.888922
$193$	−3.63242e7	−0.363702	−0.181851	−	0.983326i	$-0.558209\pi$
$193$	−3.63242e7	−0.363702	−0.181851	+	0.983326i	$0.558209\pi$
$194$	9.29052e7	0.913553
$195$	−1.71353e6	−0.0165489
$196$	4.17399e7	0.395963
$197$	−8.08278e7	−0.753232	−0.376616	−	0.926369i	$-0.622912\pi$
$197$	−8.08278e7	−0.753232	−0.376616	+	0.926369i	$0.622912\pi$
$198$	2.15112e8	1.96941
$199$	−1.33619e8	−1.20194	−0.600969	−	0.799272i	$-0.705219\pi$
$199$	−1.33619e8	−1.20194	−0.600969	+	0.799272i	$0.705219\pi$
$200$	−7.78586e7	−0.688180
$201$	−2.54161e7	−0.220761
$202$	3.20216e8	2.73346
$203$	−1.60161e7	−0.134376
$204$	−7.38554e7	−0.609083
$205$	5.96573e7	0.483643
$206$	−4.40165e8	−3.50817
$207$	−4.75331e7	−0.372478
$208$	−8.78382e7	−0.676803
$209$	2.45576e8	1.86069
$210$	−9.42031e6	−0.0701936
$211$	−1.16058e8	−0.850521	−0.425261	−	0.905071i	$-0.639818\pi$
$211$	−1.16058e8	−0.850521	−0.425261	+	0.905071i	$0.639818\pi$
$212$	4.24327e8	3.05861
$213$	2.16139e7	0.153251
$214$	−4.66659e8	−3.25500
$215$	9.26348e7	0.635682
$216$	2.12964e8	1.43787
$217$	8.53025e7	0.566699
$218$	3.23827e7	0.211697
$219$	2.68240e7	0.172571
$220$	2.08036e8	1.31722
$221$	2.85385e7	0.177852
$222$	−6.96260e7	−0.427107
$223$	1.25642e8	0.758694	0.379347	−	0.925254i	$-0.376149\pi$
$223$	1.25642e8	0.758694	0.379347	+	0.925254i	$0.376149\pi$
$224$	−2.64129e8	−1.57017
$225$	−3.26095e7	−0.190856
$226$	−9.94061e7	−0.572840
$227$	−1.54062e8	−0.874190	−0.437095	−	0.899415i	$-0.643993\pi$
$227$	−1.54062e8	−0.874190	−0.437095	+	0.899415i	$0.643993\pi$
$228$	1.85724e8	1.03776
$229$	2.05398e8	1.13024	0.565122	−	0.825007i	$-0.308829\pi$
$229$	2.05398e8	1.13024	0.565122	+	0.825007i	$0.308829\pi$
$230$	−6.25545e7	−0.339009
$231$	1.60896e7	0.0858820
$232$	2.32675e8	1.22332
$233$	6.18314e7	0.320231	0.160115	−	0.987098i	$-0.448813\pi$
$233$	6.18314e7	0.320231	0.160115	+	0.987098i	$0.448813\pi$
$234$	−6.28631e7	−0.320731
$235$	1.43258e7	0.0720080
$236$	−2.33334e8	−1.15554
$237$	1.99430e6	0.00973130
$238$	1.56893e8	0.754372
$239$	−3.17420e8	−1.50398	−0.751990	−	0.659175i	$-0.770906\pi$
$239$	−3.17420e8	−1.50398	−0.751990	+	0.659175i	$0.770906\pi$
$240$	8.00907e7	0.373975
$241$	4.25764e8	1.95934	0.979668	−	0.200623i	$-0.0642967\pi$
$241$	4.25764e8	1.95934	0.979668	+	0.200623i	$0.0642967\pi$
$242$	−5.53326e7	−0.250973
$243$	1.34837e8	0.602819
$244$	−8.34041e8	−3.67556
$245$	1.47061e7	0.0638877
$246$	−1.04861e8	−0.449098
$247$	−7.17657e7	−0.303024
$248$	−1.23924e9	−5.15909
$249$	−6.23739e7	−0.256039
$250$	−4.29147e7	−0.173706
$251$	3.92351e8	1.56609	0.783045	−	0.621965i	$-0.213666\pi$
$251$	3.92351e8	1.56609	0.783045	+	0.621965i	$0.213666\pi$
$252$	−2.53969e8	−0.999722
$253$	1.06841e8	0.414778
$254$	9.11866e8	3.49151
$255$	−2.60213e7	−0.0982740
$256$	9.27367e8	3.45471
$257$	3.00664e8	1.10488	0.552440	−	0.833553i	$-0.313697\pi$
$257$	3.00664e8	1.10488	0.552440	+	0.833553i	$0.313697\pi$
$258$	−1.62827e8	−0.590277
$259$	1.08694e8	0.388737
$260$	−6.07952e7	−0.214517
$261$	9.74510e7	0.339269
$262$	8.65182e7	0.297203
$263$	2.82557e8	0.957768	0.478884	−	0.877878i	$-0.341041\pi$
$263$	2.82557e8	0.957768	0.478884	+	0.877878i	$0.341041\pi$
$264$	−2.33742e8	−0.781849
$265$	1.49502e8	0.493499
$266$	−3.94540e8	−1.28530
$267$	1.69277e7	0.0544262
$268$	−9.01752e8	−2.86164
$269$	2.00244e8	0.627229	0.313614	−	0.949550i	$-0.398460\pi$
$269$	2.00244e8	0.627229	0.313614	+	0.949550i	$0.398460\pi$
$270$	1.17383e8	0.362938
$271$	7.99119e6	0.0243904	0.0121952	−	0.999926i	$-0.496118\pi$
$271$	7.99119e6	0.0243904	0.0121952	+	0.999926i	$0.496118\pi$
$272$	−1.33390e9	−4.01912
$273$	−4.70192e6	−0.0139864
$274$	−9.52409e7	−0.279703
$275$	7.32968e7	0.212530
$276$	8.08017e7	0.231333
$277$	−2.66186e8	−0.752498	−0.376249	−	0.926519i	$-0.622786\pi$
$277$	−2.66186e8	−0.752498	−0.376249	+	0.926519i	$0.622786\pi$
$278$	−3.85640e8	−1.07653
$279$	−5.19029e8	−1.43079
$280$	−2.13644e8	−0.581618
$281$	−4.97735e8	−1.33822	−0.669108	−	0.743165i	$-0.733324\pi$
$281$	−4.97735e8	−1.33822	−0.669108	+	0.743165i	$0.733324\pi$
$282$	−2.51808e7	−0.0668648
$283$	−3.27235e8	−0.858237	−0.429118	−	0.903248i	$-0.641176\pi$
$283$	−3.27235e8	−0.858237	−0.429118	+	0.903248i	$0.641176\pi$
$284$	7.66850e8	1.98654
$285$	6.54358e7	0.167440
$286$	1.41298e8	0.357155
$287$	1.63700e8	0.408753
$288$	1.60711e9	3.96435
$289$	2.30416e7	0.0561526
$290$	1.28247e8	0.308784
$291$	−4.22813e7	−0.100583
$292$	9.51702e8	2.23697
$293$	5.65933e8	1.31440	0.657201	−	0.753715i	$-0.271740\pi$
$293$	5.65933e8	1.31440	0.657201	+	0.753715i	$0.271740\pi$
$294$	−2.58493e7	−0.0593244
$295$	−8.22100e7	−0.186444
$296$	−1.57906e9	−3.53897
$297$	−2.00487e8	−0.444056
$298$	9.37186e8	2.05149
$299$	−3.12226e7	−0.0675491
$300$	5.54329e7	0.118534
$301$	2.54190e8	0.537249
$302$	6.87322e8	1.43594
$303$	−1.45731e8	−0.300955
$304$	3.35435e9	6.84780
$305$	−2.93856e8	−0.593042
$306$	−9.54629e8	−1.90463
$307$	−2.61887e8	−0.516570	−0.258285	−	0.966069i	$-0.583157\pi$
$307$	−2.61887e8	−0.516570	−0.258285	+	0.966069i	$0.583157\pi$
$308$	5.70850e8	1.11326
$309$	2.00320e8	0.386251
$310$	−6.83051e8	−1.30223
$311$	8.26410e6	0.0155788	0.00778941	−	0.999970i	$-0.497521\pi$
$311$	8.26410e6	0.0155788	0.00778941	+	0.999970i	$0.497521\pi$
$312$	6.83074e7	0.127329
$313$	−1.82393e8	−0.336205	−0.168102	−	0.985770i	$-0.553764\pi$
$313$	−1.82393e8	−0.336205	−0.168102	+	0.985770i	$0.553764\pi$
$314$	2.73131e8	0.497872
$315$	−8.94804e7	−0.161303
$316$	7.07568e7	0.126143
$317$	−4.32315e7	−0.0762241	−0.0381121	−	0.999273i	$-0.512134\pi$
$317$	−4.32315e7	−0.0762241	−0.0381121	+	0.999273i	$0.512134\pi$
$318$	−2.62784e8	−0.458251
$319$	−2.19042e8	−0.377798
$320$	1.08979e9	1.85917
$321$	2.12377e8	0.358378
$322$	−1.71650e8	−0.286515
$323$	−1.08982e9	−1.79948
$324$	1.46771e9	2.39735
$325$	−2.14198e7	−0.0346118
$326$	4.95231e8	0.791674
$327$	−1.47374e7	−0.0233080
$328$	−2.37816e9	−3.72119
$329$	3.93099e7	0.0608579
$330$	−1.28836e8	−0.197350
$331$	−2.29704e8	−0.348153	−0.174077	−	0.984732i	$-0.555694\pi$
$331$	−2.29704e8	−0.348153	−0.174077	+	0.984732i	$0.555694\pi$
$332$	−2.21300e9	−3.31893
$333$	−6.61355e8	−0.981477
$334$	8.79256e8	1.29123
$335$	−3.17712e8	−0.461719
$336$	2.19769e8	0.316067
$337$	−6.71914e8	−0.956333	−0.478166	−	0.878269i	$-0.658698\pi$
$337$	−6.71914e8	−0.956333	−0.478166	+	0.878269i	$0.658698\pi$
$338$	1.33744e9	1.88393
$339$	4.52399e7	0.0630700
$340$	−9.23225e8	−1.27389
$341$	1.16663e9	1.59328
$342$	2.40061e9	3.24511
$343$	4.03536e7	0.0539949
$344$	−3.69276e9	−4.89099
$345$	2.84687e7	0.0373251
$346$	−2.31388e9	−3.00313
$347$	−5.09833e8	−0.655050	−0.327525	−	0.944843i	$-0.606215\pi$
$347$	−5.09833e8	−0.655050	−0.327525	+	0.944843i	$0.606215\pi$
$348$	−1.65657e8	−0.210709
$349$	−4.83053e8	−0.608283	−0.304141	−	0.952627i	$-0.598370\pi$
$349$	−4.83053e8	−0.608283	−0.304141	+	0.952627i	$0.598370\pi$
$350$	−1.17758e8	−0.146809
$351$	5.85890e7	0.0723171
$352$	−3.61233e9	−4.41456
$353$	−2.36640e7	−0.0286337	−0.0143168	−	0.999898i	$-0.504557\pi$
$353$	−2.36640e7	−0.0286337	−0.0143168	+	0.999898i	$0.504557\pi$
$354$	1.44502e8	0.173127
$355$	2.70183e8	0.320522
$356$	6.00586e8	0.705506
$357$	−7.14025e7	−0.0830567
$358$	−4.62450e8	−0.532690
$359$	−1.13273e8	−0.129210	−0.0646050	−	0.997911i	$-0.520579\pi$
$359$	−1.13273e8	−0.129210	−0.0646050	+	0.997911i	$0.520579\pi$
$360$	1.29993e9	1.46846
$361$	1.84670e9	2.06596
$362$	2.39816e9	2.65704
$363$	2.51820e7	0.0276323
$364$	−1.66822e8	−0.181300
$365$	3.35311e8	0.360930
$366$	5.16518e8	0.550683
$367$	5.36621e8	0.566678	0.283339	−	0.959020i	$-0.408558\pi$
$367$	5.36621e8	0.566678	0.283339	+	0.959020i	$0.408558\pi$
$368$	1.45935e9	1.52649
$369$	−9.96041e8	−1.03201
$370$	−8.70356e8	−0.893287
$371$	4.10234e8	0.417083
$372$	8.82298e8	0.888618
$373$	−1.21095e9	−1.20822	−0.604108	−	0.796902i	$-0.706471\pi$
$373$	−1.21095e9	−1.20822	−0.604108	+	0.796902i	$0.706471\pi$
$374$	2.14573e9	2.12092
$375$	1.95306e7	0.0191252
$376$	−5.71078e8	−0.554036
$377$	6.40116e7	0.0615267
$378$	3.22100e8	0.306739
$379$	−1.03649e9	−0.977975	−0.488987	−	0.872291i	$-0.662634\pi$
$379$	−1.03649e9	−0.977975	−0.488987	+	0.872291i	$0.662634\pi$
$380$	2.32163e9	2.17046
$381$	−4.14992e8	−0.384417
$382$	−6.39437e8	−0.586916
$383$	2.92527e8	0.266055	0.133027	−	0.991112i	$-0.457530\pi$
$383$	2.92527e8	0.266055	0.133027	+	0.991112i	$0.457530\pi$
$384$	−9.29916e8	−0.838078
$385$	2.01127e8	0.179621
$386$	7.98128e8	0.706345
$387$	−1.54664e9	−1.35644
$388$	−1.50012e9	−1.30381
$389$	6.19809e8	0.533868	0.266934	−	0.963715i	$-0.413989\pi$
$389$	6.19809e8	0.533868	0.266934	+	0.963715i	$0.413989\pi$
$390$	3.76502e7	0.0321396
$391$	−4.74141e8	−0.401133
$392$	−5.86239e8	−0.491557
$393$	−3.93746e7	−0.0327222
$394$	1.77597e9	1.46285
$395$	2.49296e7	0.0203529
$396$	−3.47338e9	−2.81073
$397$	5.61597e8	0.450462	0.225231	−	0.974305i	$-0.427686\pi$
$397$	5.61597e8	0.450462	0.225231	+	0.974305i	$0.427686\pi$
$398$	2.93592e9	2.33428
$399$	1.79556e8	0.141512
$400$	1.00117e9	0.782163
$401$	2.04560e9	1.58422	0.792111	−	0.610377i	$-0.208982\pi$
$401$	2.04560e9	1.58422	0.792111	+	0.610377i	$0.208982\pi$
$402$	5.58451e8	0.428740
$403$	−3.40929e8	−0.259475
$404$	−5.17046e9	−3.90117
$405$	5.17114e8	0.386807
$406$	3.51911e8	0.260971
$407$	1.48654e9	1.09294
$408$	1.03730e9	0.756128
$409$	5.84907e8	0.422722	0.211361	−	0.977408i	$-0.432210\pi$
$409$	5.84907e8	0.422722	0.211361	+	0.977408i	$0.432210\pi$
$410$	−1.31081e9	−0.939282
$411$	4.33443e7	0.0307954
$412$	7.10726e9	5.00682
$413$	−2.25584e8	−0.157574
$414$	1.04441e9	0.723388
$415$	−7.79701e8	−0.535501
$416$	1.05565e9	0.718938
$417$	1.75506e8	0.118526
$418$	−5.39588e9	−3.61364
$419$	−8.59314e7	−0.0570694	−0.0285347	−	0.999593i	$-0.509084\pi$
$419$	−8.59314e7	−0.0570694	−0.0285347	+	0.999593i	$0.509084\pi$
$420$	1.52108e8	0.100180
$421$	2.35308e9	1.53692	0.768458	−	0.639900i	$-0.221024\pi$
$421$	2.35308e9	1.53692	0.768458	+	0.639900i	$0.221024\pi$
$422$	2.55006e9	1.65180
$423$	−2.39184e8	−0.153653
$424$	−5.95970e9	−3.79703
$425$	−3.25278e8	−0.205539
$426$	−4.74907e8	−0.297629
$427$	−8.06341e8	−0.501212
$428$	7.53506e9	4.64551
$429$	−6.43052e7	−0.0393229
$430$	−2.03540e9	−1.23456
$431$	−2.89357e7	−0.0174086	−0.00870430	−	0.999962i	$-0.502771\pi$
$431$	−2.89357e7	−0.0174086	−0.00870430	+	0.999962i	$0.502771\pi$
$432$	−2.73847e9	−1.63423
$433$	−3.07779e9	−1.82193	−0.910964	−	0.412487i	$-0.864660\pi$
$433$	−3.07779e9	−1.82193	−0.910964	+	0.412487i	$0.864660\pi$
$434$	−1.87429e9	−1.10058
$435$	−5.83656e7	−0.0339973
$436$	−5.22878e8	−0.302133
$437$	1.19232e9	0.683453
$438$	−5.89385e8	−0.335150
$439$	3.11034e9	1.75461	0.877307	−	0.479929i	$-0.159338\pi$
$439$	3.11034e9	1.75461	0.877307	+	0.479929i	$0.159338\pi$
$440$	−2.92188e9	−1.63523
$441$	−2.45534e8	−0.136325
$442$	−6.27057e8	−0.345405
$443$	−2.08895e9	−1.14160	−0.570800	−	0.821089i	$-0.693367\pi$
$443$	−2.08895e9	−1.14160	−0.570800	+	0.821089i	$0.693367\pi$
$444$	1.12424e9	0.609563
$445$	2.11603e8	0.113831
$446$	−2.76064e9	−1.47346
$447$	−4.26515e8	−0.225870
$448$	2.99039e9	1.57128
$449$	−9.78929e8	−0.510374	−0.255187	−	0.966892i	$-0.582137\pi$
$449$	−9.78929e8	−0.510374	−0.255187	+	0.966892i	$0.582137\pi$
$450$	7.16506e8	0.370660
$451$	2.23882e9	1.14921
$452$	1.60509e9	0.817552
$453$	−3.12802e8	−0.158098
$454$	3.38511e9	1.69776
$455$	−5.87760e7	−0.0292523
$456$	−2.60851e9	−1.28830
$457$	1.19064e9	0.583542	0.291771	−	0.956488i	$-0.405755\pi$
$457$	1.19064e9	0.583542	0.291771	+	0.956488i	$0.405755\pi$
$458$	−4.51308e9	−2.19505
$459$	8.89723e8	0.429448
$460$	1.01006e9	0.483830
$461$	−1.80350e9	−0.857361	−0.428680	−	0.903456i	$-0.641021\pi$
$461$	−1.80350e9	−0.857361	−0.428680	+	0.903456i	$0.641021\pi$
$462$	−3.53525e8	−0.166791
$463$	8.72594e8	0.408582	0.204291	−	0.978910i	$-0.434511\pi$
$463$	8.72594e8	0.408582	0.204291	+	0.978910i	$0.434511\pi$
$464$	−2.99192e9	−1.39039
$465$	3.10858e8	0.143376
$466$	−1.35858e9	−0.621920
$467$	−7.83209e8	−0.355851	−0.177926	−	0.984044i	$-0.556939\pi$
$467$	−7.83209e8	−0.355851	−0.177926	+	0.984044i	$0.556939\pi$
$468$	1.01504e9	0.457744
$469$	−8.71803e8	−0.390223
$470$	−3.14771e8	−0.139847
$471$	−1.24303e8	−0.0548160
$472$	3.27719e9	1.43451
$473$	3.47640e9	1.51048
$474$	−4.38194e7	−0.0188991
$475$	8.17977e8	0.350198
$476$	−2.53333e9	−1.07663
$477$	−2.49610e9	−1.05304
$478$	6.97446e9	2.92088
$479$	−1.36730e9	−0.568447	−0.284223	−	0.958758i	$-0.591736\pi$
$479$	−1.36730e9	−0.568447	−0.284223	+	0.958758i	$0.591736\pi$
$480$	−9.62535e8	−0.397258
$481$	−4.34417e8	−0.177992
$482$	−9.35502e9	−3.80522
$483$	7.81181e7	0.0315454
$484$	8.93446e8	0.358187
$485$	−5.28535e8	−0.210367
$486$	−2.96268e9	−1.17073
$487$	−6.06862e6	−0.00238089	−0.00119044	−	0.999999i	$-0.500379\pi$
$487$	−6.06862e6	−0.00238089	−0.00119044	+	0.999999i	$0.500379\pi$
$488$	1.17142e10	4.56291
$489$	−2.25381e8	−0.0871637
$490$	−3.23128e8	−0.124076
$491$	2.21255e9	0.843543	0.421771	−	0.906702i	$-0.361408\pi$
$491$	2.21255e9	0.843543	0.421771	+	0.906702i	$0.361408\pi$
$492$	1.69317e9	0.640949
$493$	9.72069e8	0.365370
$494$	1.57686e9	0.588503
$495$	−1.22377e9	−0.453504
$496$	1.59351e10	5.86366
$497$	7.41381e8	0.270891
$498$	1.37050e9	0.497252
$499$	−1.16657e9	−0.420300	−0.210150	−	0.977669i	$-0.567395\pi$
$499$	−1.16657e9	−0.420300	−0.210150	+	0.977669i	$0.567395\pi$
$500$	6.92936e8	0.247912
$501$	−4.00151e8	−0.142165
$502$	−8.62086e9	−3.04150
$503$	−7.26410e8	−0.254504	−0.127252	−	0.991870i	$-0.540616\pi$
$503$	−7.26410e8	−0.254504	−0.127252	+	0.991870i	$0.540616\pi$
$504$	3.56701e9	1.24107
$505$	−1.82170e9	−0.629443
$506$	−2.34754e9	−0.805540
$507$	−6.08671e8	−0.207422
$508$	−1.47237e10	−4.98305
$509$	2.55979e8	0.0860385	0.0430192	−	0.999074i	$-0.486302\pi$
$509$	2.55979e8	0.0860385	0.0430192	+	0.999074i	$0.486302\pi$
$510$	5.71749e8	0.190858
$511$	9.20094e8	0.305042
$512$	−8.47307e9	−2.78995
$513$	−2.23739e9	−0.731695
$514$	−6.60628e9	−2.14579
$515$	2.50409e9	0.807837
$516$	2.62913e9	0.842438
$517$	5.37618e8	0.171103
$518$	−2.38826e9	−0.754965
$519$	1.05305e9	0.330646
$520$	8.53872e8	0.266306
$521$	1.93196e9	0.598504	0.299252	−	0.954174i	$-0.403263\pi$
$521$	1.93196e9	0.598504	0.299252	+	0.954174i	$0.403263\pi$
$522$	−2.14123e9	−0.658894
$523$	6.33523e7	0.0193645	0.00968225	−	0.999953i	$-0.496918\pi$
$523$	6.33523e7	0.0193645	0.00968225	+	0.999953i	$0.496918\pi$
$524$	−1.39699e9	−0.424165
$525$	5.35919e7	0.0161637
$526$	−6.20842e9	−1.86008
$527$	−5.17728e9	−1.54087
$528$	3.00564e9	0.888625
$529$	−2.88609e9	−0.847647
$530$	−3.28491e9	−0.958424
$531$	1.37258e9	0.397839
$532$	6.37057e9	1.83437
$533$	−6.54259e8	−0.187156
$534$	−3.71940e8	−0.105701
$535$	2.65481e9	0.749541
$536$	1.26652e10	3.55250
$537$	2.10462e8	0.0586494
$538$	−4.39982e9	−1.21814
$539$	5.51891e8	0.151807
$540$	−1.89537e9	−0.517982
$541$	−4.62338e9	−1.25536	−0.627681	−	0.778471i	$-0.715996\pi$
$541$	−4.62338e9	−1.25536	−0.627681	+	0.778471i	$0.715996\pi$
$542$	−1.75585e8	−0.0473685
$543$	−1.09141e9	−0.292541
$544$	1.60308e10	4.26934
$545$	−1.84225e8	−0.0487483
$546$	1.03312e8	0.0271629
$547$	5.16805e9	1.35012	0.675058	−	0.737764i	$-0.264118\pi$
$547$	5.16805e9	1.35012	0.675058	+	0.737764i	$0.264118\pi$
$548$	1.53784e9	0.399189
$549$	4.90624e9	1.26545
$550$	−1.61050e9	−0.412755
$551$	−2.44446e9	−0.622519
$552$	−1.13486e9	−0.287182
$553$	6.84068e7	0.0172013
$554$	5.84872e9	1.46142
$555$	3.96101e8	0.0983513
$556$	6.22686e9	1.53641
$557$	1.13435e8	0.0278133	0.0139066	−	0.999903i	$-0.495573\pi$
$557$	1.13435e8	0.0278133	0.0139066	+	0.999903i	$0.495573\pi$
$558$	1.14043e10	2.77874
$559$	−1.01592e9	−0.245991
$560$	2.74721e9	0.661049
$561$	−9.76528e8	−0.233515
$562$	1.09364e10	2.59895
$563$	5.73636e9	1.35474	0.677372	−	0.735641i	$-0.263119\pi$
$563$	5.73636e9	1.35474	0.677372	+	0.735641i	$0.263119\pi$
$564$	4.06589e8	0.0954287
$565$	5.65519e8	0.131910
$566$	7.19011e9	1.66678
$567$	1.41896e9	0.326911
$568$	−1.07705e10	−2.46613
$569$	−5.12961e9	−1.16732	−0.583661	−	0.811997i	$-0.698380\pi$
$569$	−5.12961e9	−1.16732	−0.583661	+	0.811997i	$0.698380\pi$
$570$	−1.43778e9	−0.325184
$571$	3.30945e9	0.743925	0.371963	−	0.928248i	$-0.378685\pi$
$571$	3.30945e9	0.743925	0.371963	+	0.928248i	$0.378685\pi$
$572$	−2.28152e9	−0.509728
$573$	2.91009e8	0.0646197
$574$	−3.59686e9	−0.793838
$575$	3.55871e8	0.0780648
$576$	−1.81952e10	−3.96715
$577$	−2.42137e9	−0.524743	−0.262371	−	0.964967i	$-0.584505\pi$
$577$	−2.42137e9	−0.524743	−0.262371	+	0.964967i	$0.584505\pi$
$578$	−5.06277e8	−0.109054
$579$	−3.63229e8	−0.0777689
$580$	−2.07079e9	−0.440694
$581$	−2.13950e9	−0.452581
$582$	9.29019e8	0.195341
$583$	5.61051e9	1.17263
$584$	−1.33667e10	−2.77703
$585$	3.57627e8	0.0738558
$586$	−1.24349e10	−2.55270
$587$	−2.06077e9	−0.420529	−0.210264	−	0.977645i	$-0.567432\pi$
$587$	−2.06077e9	−0.420529	−0.210264	+	0.977645i	$0.567432\pi$
$588$	4.17384e8	0.0846672
$589$	1.30193e10	2.62534
$590$	1.80634e9	0.362092
$591$	−8.08250e8	−0.161061
$592$	2.03048e10	4.02228
$593$	−4.94845e8	−0.0974491	−0.0487245	−	0.998812i	$-0.515516\pi$
$593$	−4.94845e8	−0.0974491	−0.0487245	+	0.998812i	$0.515516\pi$
$594$	4.40516e9	0.862400
$595$	−8.92563e8	−0.173712
$596$	−1.51326e10	−2.92786
$597$	−1.33614e9	−0.257006
$598$	6.86033e8	0.131187
$599$	3.63748e9	0.691523	0.345762	−	0.938322i	$-0.387621\pi$
$599$	3.63748e9	0.691523	0.345762	+	0.938322i	$0.387621\pi$
$600$	−7.78559e8	−0.147151
$601$	−9.82926e9	−1.84697	−0.923485	−	0.383634i	$-0.874673\pi$
$601$	−9.82926e9	−1.84697	−0.923485	+	0.383634i	$0.874673\pi$
$602$	−5.58515e9	−1.04339
$603$	5.30454e9	0.985230
$604$	−1.10981e10	−2.04936
$605$	3.14786e8	0.0577925
$606$	3.20204e9	0.584485
$607$	−4.70643e8	−0.0854144	−0.0427072	−	0.999088i	$-0.513598\pi$
$607$	−4.70643e8	−0.0854144	−0.0427072	+	0.999088i	$0.513598\pi$
$608$	−4.03128e10	−7.27412
$609$	−1.60155e8	−0.0287330
$610$	6.45670e9	1.15174
$611$	−1.57110e8	−0.0278651
$612$	1.54142e10	2.71826
$613$	8.42314e9	1.47694	0.738469	−	0.674287i	$-0.235549\pi$
$613$	8.42314e9	1.47694	0.738469	+	0.674287i	$0.235549\pi$
$614$	5.75427e9	1.00323
$615$	5.96552e8	0.103415
$616$	−8.01763e9	−1.38202
$617$	−5.10463e8	−0.0874916	−0.0437458	−	0.999043i	$-0.513929\pi$
$617$	−5.10463e8	−0.0874916	−0.0437458	+	0.999043i	$0.513929\pi$
$618$	−4.40149e9	−0.750137
$619$	−6.16774e9	−1.04522	−0.522611	−	0.852571i	$-0.675042\pi$
$619$	−6.16774e9	−1.04522	−0.522611	+	0.852571i	$0.675042\pi$
$620$	1.10291e10	1.85853
$621$	−9.73403e8	−0.163107
$622$	−1.81582e8	−0.0302556
$623$	5.80639e8	0.0962052
$624$	−8.78352e8	−0.144718
$625$	2.44141e8	0.0400000
$626$	4.00761e9	0.652943
$627$	2.45568e9	0.397864
$628$	−4.41020e9	−0.710559
$629$	−6.59698e9	−1.05698
$630$	1.96609e9	0.313265
$631$	−5.45650e8	−0.0864593	−0.0432296	−	0.999065i	$-0.513765\pi$
$631$	−5.45650e8	−0.0864593	−0.0432296	+	0.999065i	$0.513765\pi$
$632$	−9.93784e8	−0.156597
$633$	−1.16054e9	−0.181863
$634$	9.49896e8	0.148035
$635$	−5.18758e9	−0.804001
$636$	4.24312e9	0.654011
$637$	−1.61281e8	−0.0247227
$638$	4.81286e9	0.733722
$639$	−4.51099e9	−0.683941
$640$	−1.16244e10	−1.75283
$641$	−8.18964e9	−1.22818	−0.614090	−	0.789236i	$-0.710477\pi$
$641$	−8.18964e9	−1.22818	−0.614090	+	0.789236i	$0.710477\pi$
$642$	−4.66643e9	−0.696004
$643$	9.47956e9	1.40621	0.703105	−	0.711086i	$-0.251797\pi$
$643$	9.47956e9	1.40621	0.703105	+	0.711086i	$0.251797\pi$
$644$	2.77159e9	0.408911
$645$	9.26316e8	0.135925
$646$	2.39459e10	3.49476
$647$	5.74956e9	0.834584	0.417292	−	0.908773i	$-0.362979\pi$
$647$	5.74956e9	0.834584	0.417292	+	0.908773i	$0.362979\pi$
$648$	−2.06140e10	−2.97612
$649$	−3.08517e9	−0.443020
$650$	4.70644e8	0.0672195
$651$	8.52995e8	0.121175
$652$	−7.99641e9	−1.12987
$653$	−8.96673e9	−1.26020	−0.630098	−	0.776516i	$-0.716985\pi$
$653$	−8.96673e9	−1.26020	−0.630098	+	0.776516i	$0.716985\pi$
$654$	3.23816e8	0.0452664
$655$	−4.92200e8	−0.0684379
$656$	3.05802e10	4.22939
$657$	−5.59837e9	−0.770164
$658$	−8.63731e8	−0.118192
$659$	−7.80821e9	−1.06280	−0.531401	−	0.847120i	$-0.678334\pi$
$659$	−7.80821e9	−1.06280	−0.531401	+	0.847120i	$0.678334\pi$
$660$	2.08029e9	0.281656
$661$	8.38991e9	1.12993	0.564966	−	0.825114i	$-0.308889\pi$
$661$	8.38991e9	1.12993	0.564966	+	0.825114i	$0.308889\pi$
$662$	5.04713e9	0.676148
$663$	2.85375e8	0.0380293
$664$	3.10817e10	4.12019
$665$	2.24453e9	0.295971
$666$	1.45315e10	1.90612
$667$	−1.06349e9	−0.138770
$668$	−1.41972e10	−1.84283
$669$	1.25637e9	0.162228
$670$	6.98088e9	0.896703
$671$	−1.10278e10	−1.40916
$672$	−2.64120e9	−0.335744
$673$	−4.79306e8	−0.0606122	−0.0303061	−	0.999541i	$-0.509648\pi$
$673$	−4.79306e8	−0.0606122	−0.0303061	+	0.999541i	$0.509648\pi$
$674$	1.47635e10	1.85729
$675$	−6.67790e8	−0.0835751
$676$	−2.15954e10	−2.68873
$677$	2.19066e9	0.271340	0.135670	−	0.990754i	$-0.456681\pi$
$677$	2.19066e9	0.271340	0.135670	+	0.990754i	$0.456681\pi$
$678$	−9.94026e8	−0.122488
$679$	−1.45030e9	−0.177793
$680$	1.29668e10	1.58143
$681$	−1.54057e9	−0.186925
$682$	−2.56335e10	−3.09431
$683$	−6.09109e9	−0.731514	−0.365757	−	0.930710i	$-0.619190\pi$
$683$	−6.09109e9	−0.731514	−0.365757	+	0.930710i	$0.619190\pi$
$684$	−3.87621e10	−4.63139
$685$	5.41823e8	0.0644081
$686$	−8.86663e8	−0.104863
$687$	2.05391e9	0.241676
$688$	4.74845e10	5.55894
$689$	−1.63958e9	−0.190970
$690$	−6.25523e8	−0.0724889
$691$	1.88926e9	0.217830	0.108915	−	0.994051i	$-0.465262\pi$
$691$	1.88926e9	0.217830	0.108915	+	0.994051i	$0.465262\pi$
$692$	3.73618e10	4.28604
$693$	−3.35802e9	−0.383281
$694$	1.12022e10	1.27217
$695$	2.19390e9	0.247896
$696$	2.32667e9	0.261578
$697$	−9.93546e9	−1.11141
$698$	1.06138e10	1.18134
$699$	6.18292e8	0.0684737
$700$	1.90142e9	0.209524
$701$	−1.00875e10	−1.10604	−0.553020	−	0.833168i	$-0.686525\pi$
$701$	−1.00875e10	−1.10604	−0.553020	+	0.833168i	$0.686525\pi$
$702$	−1.28734e9	−0.140447
$703$	1.65894e10	1.80089
$704$	4.08976e10	4.41768
$705$	1.43253e8	0.0153972
$706$	5.19953e8	0.0556094
$707$	−4.99874e9	−0.531977
$708$	−2.33326e9	−0.247085
$709$	−1.10711e9	−0.116662	−0.0583312	−	0.998297i	$-0.518578\pi$
$709$	−1.10711e9	−0.116662	−0.0583312	+	0.998297i	$0.518578\pi$
$710$	−5.93654e9	−0.622486
$711$	−4.16226e8	−0.0434296
$712$	−8.43527e9	−0.875829
$713$	5.66422e9	0.585230
$714$	1.56888e9	0.161304
$715$	−8.03843e8	−0.0822432
$716$	7.46710e9	0.760250
$717$	−3.17409e9	−0.321590
$718$	2.48887e9	0.250939
$719$	1.71901e10	1.72476	0.862379	−	0.506263i	$-0.168973\pi$
$719$	1.71901e10	1.72476	0.862379	+	0.506263i	$0.168973\pi$
$720$	−1.67156e10	−1.66901
$721$	6.87121e9	0.682747
$722$	−4.05764e10	−4.01230
$723$	4.25749e9	0.418957
$724$	−3.87226e10	−3.79210
$725$	−7.29596e8	−0.0711049
$726$	−5.53307e8	−0.0536646
$727$	7.92241e9	0.764693	0.382346	−	0.924019i	$-0.375116\pi$
$727$	7.92241e9	0.764693	0.382346	+	0.924019i	$0.375116\pi$
$728$	2.34303e9	0.225070
$729$	−7.69911e9	−0.736027
$730$	−7.36757e9	−0.700961
$731$	−1.54276e10	−1.46079
$732$	−8.34012e9	−0.785930
$733$	−1.46598e10	−1.37488	−0.687440	−	0.726242i	$-0.741265\pi$
$733$	−1.46598e10	−1.37488	−0.687440	+	0.726242i	$0.741265\pi$
$734$	−1.17908e10	−1.10054
$735$	1.47056e8	0.0136608
$736$	−1.75386e10	−1.62152
$737$	−1.19231e10	−1.09712
$738$	2.18853e10	2.00427
$739$	−1.13020e10	−1.03015	−0.515073	−	0.857146i	$-0.672235\pi$
$739$	−1.13020e10	−1.03015	−0.515073	+	0.857146i	$0.672235\pi$
$740$	1.40535e10	1.27489
$741$	−7.17632e8	−0.0647945
$742$	−9.01379e9	−0.810016
$743$	−8.49325e9	−0.759649	−0.379825	−	0.925059i	$-0.624016\pi$
$743$	−8.49325e9	−0.759649	−0.379825	+	0.925059i	$0.624016\pi$
$744$	−1.23919e10	−1.10315
$745$	−5.33163e9	−0.472403
$746$	2.66074e10	2.34647
$747$	1.30179e10	1.14267
$748$	−3.46468e10	−3.02696
$749$	7.28480e9	0.633478
$750$	−4.29132e8	−0.0371430
$751$	−1.28152e9	−0.110404	−0.0552020	−	0.998475i	$-0.517580\pi$
$751$	−1.28152e9	−0.110404	−0.0552020	+	0.998475i	$0.517580\pi$
$752$	7.34338e9	0.629699
$753$	3.92337e9	0.334871
$754$	−1.40648e9	−0.119491
$755$	−3.91016e9	−0.330659
$756$	−5.20088e9	−0.437775
$757$	1.47937e10	1.23949	0.619744	−	0.784804i	$-0.287237\pi$
$757$	1.47937e10	1.23949	0.619744	+	0.784804i	$0.287237\pi$
$758$	2.27741e10	1.89932
$759$	1.06837e9	0.0886903
$760$	−3.26075e10	−2.69445
$761$	−1.75172e10	−1.44085	−0.720423	−	0.693535i	$-0.756052\pi$
$761$	−1.75172e10	−1.44085	−0.720423	+	0.693535i	$0.756052\pi$
$762$	9.11834e9	0.746575
$763$	−5.05512e8	−0.0411998
$764$	1.03249e10	0.837641
$765$	5.43086e9	0.438585
$766$	−6.42751e9	−0.516704
$767$	9.01593e8	0.0721484
$768$	9.27334e9	0.738707
$769$	2.02325e10	1.60438	0.802189	−	0.597070i	$-0.203668\pi$
$769$	2.02325e10	1.60438	0.802189	+	0.597070i	$0.203668\pi$
$770$	−4.41922e9	−0.348841
$771$	3.00653e9	0.236252
$772$	−1.28872e10	−1.00809
$773$	−8.78895e9	−0.684398	−0.342199	−	0.939628i	$-0.611172\pi$
$773$	−8.78895e9	−0.684398	−0.342199	+	0.939628i	$0.611172\pi$
$774$	3.39832e10	2.63433
$775$	3.88586e9	0.299869
$776$	2.10693e10	1.61858
$777$	1.08690e9	0.0831220
$778$	−1.36186e10	−1.03682
$779$	2.49847e10	1.89362
$780$	−6.07931e8	−0.0458694
$781$	1.01394e10	0.761613
$782$	1.04180e10	0.779040
$783$	1.99564e9	0.148565
$784$	7.53834e9	0.558688
$785$	−1.55384e9	−0.114647
$786$	8.65152e8	0.0635497
$787$	7.63870e8	0.0558609	0.0279304	−	0.999610i	$-0.491108\pi$
$787$	7.63870e8	0.0558609	0.0279304	+	0.999610i	$0.491108\pi$
$788$	−2.86763e10	−2.08777
$789$	2.82547e9	0.204796
$790$	−5.47761e8	−0.0395272
$791$	1.55178e9	0.111484
$792$	4.87838e10	3.48930
$793$	3.22271e9	0.229490
$794$	−1.23396e10	−0.874841
$795$	1.49497e9	0.105523
$796$	−4.74058e10	−3.33147
$797$	3.11252e8	0.0217775	0.0108887	−	0.999941i	$-0.496534\pi$
$797$	3.11252e8	0.0217775	0.0108887	+	0.999941i	$0.496534\pi$
$798$	−3.94526e9	−0.274831
$799$	−2.38585e9	−0.165474
$800$	−1.20321e10	−0.830858
$801$	−3.53294e9	−0.242897
$802$	−4.49467e10	−3.07671
$803$	1.25836e10	0.857628
$804$	−9.01720e9	−0.611893
$805$	9.76510e8	0.0659768
$806$	7.49100e9	0.503926
$807$	2.00237e9	0.134118
$808$	7.26195e10	4.84299
$809$	4.00490e9	0.265933	0.132967	−	0.991121i	$-0.457550\pi$
$809$	4.00490e9	0.265933	0.132967	+	0.991121i	$0.457550\pi$
$810$	−1.13622e10	−0.751216
$811$	9.38420e9	0.617766	0.308883	−	0.951100i	$-0.400045\pi$
$811$	9.38420e9	0.617766	0.308883	+	0.951100i	$0.400045\pi$
$812$	−5.68224e9	−0.372455
$813$	7.99091e7	0.00521530
$814$	−3.26627e10	−2.12259
$815$	−2.81736e9	−0.182301
$816$	−1.33385e10	−0.859392
$817$	3.87958e10	2.48890
$818$	−1.28518e10	−0.820968
$819$	9.81328e8	0.0624195
$820$	2.11654e10	1.34053
$821$	1.47974e10	0.933221	0.466611	−	0.884463i	$-0.345475\pi$
$821$	1.47974e10	0.933221	0.466611	+	0.884463i	$0.345475\pi$
$822$	−9.52375e8	−0.0598077
$823$	3.05249e9	0.190877	0.0954386	−	0.995435i	$-0.469575\pi$
$823$	3.05249e9	0.190877	0.0954386	+	0.995435i	$0.469575\pi$
$824$	−9.98220e10	−6.21557
$825$	7.32943e8	0.0454445
$826$	4.95661e9	0.306023
$827$	6.10667e9	0.375435	0.187718	−	0.982223i	$-0.439891\pi$
$827$	6.10667e9	0.375435	0.187718	+	0.982223i	$0.439891\pi$
$828$	−1.68640e10	−1.03241
$829$	1.71271e10	1.04410	0.522051	−	0.852914i	$-0.325167\pi$
$829$	1.71271e10	1.04410	0.522051	+	0.852914i	$0.325167\pi$
$830$	1.71319e10	1.03999
$831$	−2.66176e9	−0.160904
$832$	−1.19517e10	−0.719445
$833$	−2.44919e9	−0.146813
$834$	−3.85627e9	−0.230190
$835$	−5.00206e9	−0.297335
$836$	8.71263e10	5.15736
$837$	−1.06289e10	−0.626539
$838$	1.88811e9	0.110834
$839$	−1.48682e10	−0.869142	−0.434571	−	0.900638i	$-0.643100\pi$
$839$	−1.48682e10	−0.869142	−0.434571	+	0.900638i	$0.643100\pi$
$840$	−2.13637e9	−0.124365
$841$	−1.50695e10	−0.873602
$842$	−5.17027e10	−2.98484
$843$	−4.97718e9	−0.286145
$844$	−4.11753e10	−2.35743
$845$	−7.60865e9	−0.433820
$846$	5.25543e9	0.298409
$847$	8.63773e8	0.0488436
$848$	7.66346e10	4.31558
$849$	−3.27223e9	−0.183513
$850$	7.14711e9	0.399176
$851$	7.21744e9	0.401449
$852$	7.66823e9	0.424773
$853$	−2.28348e9	−0.125972	−0.0629862	−	0.998014i	$-0.520062\pi$
$853$	−2.28348e9	−0.125972	−0.0629862	+	0.998014i	$0.520062\pi$
$854$	1.77172e10	0.973402
$855$	−1.36570e10	−0.747263
$856$	−1.05830e11	−5.76703
$857$	−3.24400e9	−0.176055	−0.0880274	−	0.996118i	$-0.528056\pi$
$857$	−3.24400e9	−0.176055	−0.0880274	+	0.996118i	$0.528056\pi$
$858$	1.41294e9	0.0763689
$859$	−3.36500e9	−0.181138	−0.0905688	−	0.995890i	$-0.528869\pi$
$859$	−3.36500e9	−0.181138	−0.0905688	+	0.995890i	$0.528869\pi$
$860$	3.28653e10	1.76195
$861$	1.63694e9	0.0874020
$862$	6.35785e8	0.0338092
$863$	−2.16750e10	−1.14795	−0.573974	−	0.818874i	$-0.694599\pi$
$863$	−2.16750e10	−1.14795	−0.573974	+	0.818874i	$0.694599\pi$
$864$	3.29111e10	1.73598
$865$	1.31636e10	0.691541
$866$	6.76262e10	3.53836
$867$	2.30408e8	0.0120069
$868$	3.02639e10	1.57074
$869$	9.35558e8	0.0483617
$870$	1.28243e9	0.0660261
$871$	3.48434e9	0.178672
$872$	7.34386e9	0.375074
$873$	8.82445e9	0.448888
$874$	−2.61981e10	−1.32733
$875$	6.69922e8	0.0338062
$876$	9.51669e9	0.478323
$877$	3.77629e10	1.89046	0.945229	−	0.326408i	$-0.105838\pi$
$877$	3.77629e10	1.89046	0.945229	+	0.326408i	$0.105838\pi$
$878$	−6.83413e10	−3.40763
$879$	5.65913e9	0.281053
$880$	3.75719e10	1.85855
$881$	1.04212e10	0.513454	0.256727	−	0.966484i	$-0.417356\pi$
$881$	1.04212e10	0.513454	0.256727	+	0.966484i	$0.417356\pi$
$882$	5.39496e9	0.264757
$883$	−3.01599e10	−1.47424	−0.737119	−	0.675763i	$-0.763814\pi$
$883$	−3.01599e10	−1.47424	−0.737119	+	0.675763i	$0.763814\pi$
$884$	1.01250e10	0.492959
$885$	−8.22071e8	−0.0398665
$886$	4.58990e10	2.21710
$887$	2.13345e10	1.02648	0.513240	−	0.858245i	$-0.328445\pi$
$887$	2.13345e10	1.02648	0.513240	+	0.858245i	$0.328445\pi$
$888$	−1.57900e10	−0.756723
$889$	−1.42347e10	−0.679505
$890$	−4.64942e9	−0.221072
$891$	1.94063e10	0.919115
$892$	4.45755e10	2.10290
$893$	5.99970e9	0.281935
$894$	9.37153e9	0.438661
$895$	2.63087e9	0.122664
$896$	−3.18972e10	−1.48141
$897$	−3.12215e8	−0.0144437
$898$	2.15093e10	0.991197
$899$	−1.16126e10	−0.533054
$900$	−1.15693e10	−0.529003
$901$	−2.48984e10	−1.13406
$902$	−4.91920e10	−2.23188
$903$	2.54181e9	0.114878
$904$	−2.25436e10	−1.01493
$905$	−1.36431e10	−0.611846
$906$	6.87298e9	0.307041
$907$	1.23720e10	0.550571	0.275286	−	0.961362i	$-0.411228\pi$
$907$	1.23720e10	0.550571	0.275286	+	0.961362i	$0.411228\pi$
$908$	−5.46587e10	−2.42303
$909$	3.04152e10	1.34313
$910$	1.29145e9	0.0568109
$911$	−3.06858e10	−1.34469	−0.672346	−	0.740237i	$-0.734713\pi$
$911$	−3.06858e10	−1.34469	−0.672346	+	0.740237i	$0.734713\pi$
$912$	3.35423e10	1.46424
$913$	−2.92606e10	−1.27244
$914$	−2.61610e10	−1.13330
$915$	−2.93846e9	−0.126808
$916$	7.28718e10	3.13275
$917$	−1.35060e9	−0.0578406
$918$	−1.95493e10	−0.834029
$919$	−2.69057e10	−1.14351	−0.571756	−	0.820424i	$-0.693737\pi$
$919$	−2.69057e10	−1.14351	−0.571756	+	0.820424i	$0.693737\pi$
$920$	−1.41863e10	−0.600637
$921$	−2.61878e9	−0.110456
$922$	3.96271e10	1.66508
$923$	−2.96308e9	−0.124033
$924$	5.70830e9	0.238043
$925$	4.95143e9	0.205700
$926$	−1.91729e10	−0.793505
$927$	−4.18084e10	−1.72379
$928$	3.59571e10	1.47695
$929$	3.61733e9	0.148024	0.0740122	−	0.997257i	$-0.476420\pi$
$929$	3.61733e9	0.148024	0.0740122	+	0.997257i	$0.476420\pi$
$930$	−6.83028e9	−0.278450
$931$	6.15898e9	0.250141
$932$	2.19367e10	0.887598
$933$	8.26382e7	0.00333116
$934$	1.72089e10	0.691098
$935$	−1.22070e10	−0.488393
$936$	−1.42563e10	−0.568253
$937$	−9.49935e9	−0.377229	−0.188615	−	0.982051i	$-0.560400\pi$
$937$	−9.49935e9	−0.377229	−0.188615	+	0.982051i	$0.560400\pi$
$938$	1.91555e10	0.757852
$939$	−1.82387e9	−0.0718893
$940$	5.08255e9	0.199588
$941$	2.74445e10	1.07372	0.536861	−	0.843671i	$-0.319610\pi$
$941$	2.74445e10	1.07372	0.536861	+	0.843671i	$0.319610\pi$
$942$	2.73122e9	0.106458
$943$	1.08699e10	0.422119
$944$	−4.21407e10	−1.63042
$945$	−1.83242e9	−0.0706338
$946$	−7.63846e10	−2.93350
$947$	5.46414e9	0.209072	0.104536	−	0.994521i	$-0.466664\pi$
$947$	5.46414e9	0.209072	0.104536	+	0.994521i	$0.466664\pi$
$948$	7.07543e8	0.0269727
$949$	−3.67734e9	−0.139670
$950$	−1.79729e10	−0.680118
$951$	−4.32299e8	−0.0162987
$952$	3.55808e10	1.33655
$953$	−2.46022e9	−0.0920764	−0.0460382	−	0.998940i	$-0.514660\pi$
$953$	−2.46022e9	−0.0920764	−0.0460382	+	0.998940i	$0.514660\pi$
$954$	5.48450e10	2.04512
$955$	3.63774e9	0.135151
$956$	−1.12615e11	−4.16865
$957$	−2.19034e9	−0.0807831
$958$	3.00428e10	1.10398
$959$	1.48676e9	0.0544348
$960$	1.08975e10	0.397538
$961$	3.43367e10	1.24803
$962$	9.54516e9	0.345677
$963$	−4.43249e10	−1.59939
$964$	1.51054e11	5.43078
$965$	−4.54053e9	−0.162652
$966$	−1.71644e9	−0.0612643
$967$	−3.08046e10	−1.09552	−0.547762	−	0.836634i	$-0.684520\pi$
$967$	−3.08046e10	−1.09552	−0.547762	+	0.836634i	$0.684520\pi$
$968$	−1.25485e10	−0.444660
$969$	−1.08978e10	−0.384775
$970$	1.16131e10	0.408553
$971$	−3.39805e10	−1.19114	−0.595569	−	0.803304i	$-0.703073\pi$
$971$	−3.39805e10	−1.19114	−0.595569	+	0.803304i	$0.703073\pi$
$972$	4.78379e10	1.67086
$973$	6.02005e9	0.209510
$974$	1.33342e8	0.00462392
$975$	−2.14191e8	−0.00740091
$976$	−1.50630e11	−5.18606
$977$	−2.64735e10	−0.908197	−0.454098	−	0.890952i	$-0.650039\pi$
$977$	−2.64735e10	−0.908197	−0.454098	+	0.890952i	$0.650039\pi$
$978$	4.95214e9	0.169280
$979$	7.94104e9	0.270482
$980$	5.21749e9	0.177080
$981$	3.07582e9	0.104021
$982$	−4.86148e10	−1.63824
$983$	1.34414e10	0.451343	0.225671	−	0.974204i	$-0.427542\pi$
$983$	1.34414e10	0.451343	0.225671	+	0.974204i	$0.427542\pi$
$984$	−2.37807e10	−0.795687
$985$	−1.01035e10	−0.336856
$986$	−2.13586e10	−0.709584
$987$	3.93086e8	0.0130130
$988$	−2.54613e10	−0.839906
$989$	1.68786e10	0.554817
$990$	2.68890e10	0.880749
$991$	1.77580e10	0.579610	0.289805	−	0.957086i	$-0.406409\pi$
$991$	1.77580e10	0.579610	0.289805	+	0.957086i	$0.406409\pi$
$992$	−1.91509e11	−6.22871
$993$	−2.29696e9	−0.0744442
$994$	−1.62899e10	−0.526096
$995$	−1.67024e10	−0.537523
$996$	−2.21292e10	−0.709673
$997$	−1.21203e10	−0.387330	−0.193665	−	0.981068i	$-0.562037\pi$
$997$	−1.21203e10	−0.387330	−0.193665	+	0.981068i	$0.562037\pi$
$998$	2.56323e10	0.816263
$999$	−1.35435e10	−0.429785

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	35.8.a.d.1.1	✓	5
3.2	odd	2		315.8.a.m.1.5		5
4.3	odd	2		560.8.a.s.1.3		5
5.2	odd	4		175.8.b.f.99.1		10
5.3	odd	4		175.8.b.f.99.10		10
5.4	even	2		175.8.a.f.1.5		5
7.6	odd	2		245.8.a.f.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.8.a.d.1.1	✓	5	1.1	even	1	trivial
175.8.a.f.1.5		5	5.4	even	2
175.8.b.f.99.1		10	5.2	odd	4
175.8.b.f.99.10		10	5.3	odd	4
245.8.a.f.1.1		5	7.6	odd	2
315.8.a.m.1.5		5	3.2	odd	2
560.8.a.s.1.3		5	4.3	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:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	35.a (trivial)

\(f(q)\)	\(=\)	\(q-21.9723 q^{2} +9.99965 q^{3} +354.783 q^{4} +125.000 q^{5} -219.716 q^{6} +343.000 q^{7} -4982.95 q^{8} -2087.01 q^{9} +O(q^{10})\)	\(q-21.9723 q^{2} +9.99965 q^{3} +354.783 q^{4} +125.000 q^{5} -219.716 q^{6} +343.000 q^{7} -4982.95 q^{8} -2087.01 q^{9} -2746.54 q^{10} +4691.00 q^{11} +3547.71 q^{12} -1370.87 q^{13} -7536.51 q^{14} +1249.96 q^{15} +64074.8 q^{16} -20817.8 q^{17} +45856.4 q^{18} +52350.5 q^{19} +44347.9 q^{20} +3429.88 q^{21} -103072. q^{22} +22775.7 q^{23} -49827.8 q^{24} +15625.0 q^{25} +30121.2 q^{26} -42738.6 q^{27} +121691. q^{28} -46694.1 q^{29} -27464.4 q^{30} +248695. q^{31} -770055. q^{32} +46908.3 q^{33} +457415. q^{34} +42875.0 q^{35} -740435. q^{36} +316892. q^{37} -1.15026e6 q^{38} -13708.2 q^{39} -622869. q^{40} +477258. q^{41} -75362.4 q^{42} +741079. q^{43} +1.66429e6 q^{44} -260876. q^{45} -500436. q^{46} +114606. q^{47} +640726. q^{48} +117649. q^{49} -343318. q^{50} -208171. q^{51} -486361. q^{52} +1.19602e6 q^{53} +939066. q^{54} +586375. q^{55} -1.70915e6 q^{56} +523487. q^{57} +1.02598e6 q^{58} -657680. q^{59} +443463. q^{60} -2.35085e6 q^{61} -5.46441e6 q^{62} -715843. q^{63} +8.71832e6 q^{64} -171359. q^{65} -1.03069e6 q^{66} -2.54170e6 q^{67} -7.38580e6 q^{68} +227749. q^{69} -942064. q^{70} +2.16146e6 q^{71} +1.03995e7 q^{72} +2.68249e6 q^{73} -6.96285e6 q^{74} +156245. q^{75} +1.85731e7 q^{76} +1.60901e6 q^{77} +301201. q^{78} +199437. q^{79} +8.00935e6 q^{80} +4.13691e6 q^{81} -1.04865e7 q^{82} -6.23761e6 q^{83} +1.21686e6 q^{84} -2.60222e6 q^{85} -1.62832e7 q^{86} -466925. q^{87} -2.33750e7 q^{88} +1.69283e6 q^{89} +5.73205e6 q^{90} -470208. q^{91} +8.08045e6 q^{92} +2.48686e6 q^{93} -2.51817e6 q^{94} +6.54381e6 q^{95} -7.70028e6 q^{96} -4.22828e6 q^{97} -2.58502e6 q^{98} -9.79014e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 11 q^{2} + 65 q^{3} + 553 q^{4} + 625 q^{5} + 96 q^{6} + 1715 q^{7} - 1647 q^{8} - 12 q^{9}+O(q^{10}) \) 5 * q + 11 * q^2 + 65 * q^3 + 553 * q^4 + 625 * q^5 + 96 * q^6 + 1715 * q^7 - 1647 * q^8 - 12 * q^9	\( 5 q + 11 q^{2} + 65 q^{3} + 553 q^{4} + 625 q^{5} + 96 q^{6} + 1715 q^{7} - 1647 q^{8} - 12 q^{9} + 1375 q^{10} + 10027 q^{11} + 10024 q^{12} + 16141 q^{13} + 3773 q^{14} + 8125 q^{15} + 94169 q^{16} + 17427 q^{17} + 47547 q^{18} + 44394 q^{19} + 69125 q^{20} + 22295 q^{21} - 89168 q^{22} + 55698 q^{23} + 18324 q^{24} + 78125 q^{25} + 163750 q^{26} - 53389 q^{27} + 189679 q^{28} - 164219 q^{29} + 12000 q^{30} + 138440 q^{31} - 509615 q^{32} - 213271 q^{33} + 132338 q^{34} + 214375 q^{35} - 1408655 q^{36} + 181518 q^{37} - 1725140 q^{38} - 481621 q^{39} - 205875 q^{40} - 369676 q^{41} + 32928 q^{42} + 386 q^{43} - 37608 q^{44} - 1500 q^{45} - 2610592 q^{46} + 962985 q^{47} - 1271004 q^{48} + 588245 q^{49} + 171875 q^{50} - 1305827 q^{51} + 2349706 q^{52} + 396244 q^{53} + 2641788 q^{54} + 1253375 q^{55} - 564921 q^{56} + 4322278 q^{57} - 4408538 q^{58} + 6284948 q^{59} + 1253000 q^{60} + 1975828 q^{61} - 2246384 q^{62} - 4116 q^{63} + 13769617 q^{64} + 2017625 q^{65} + 798284 q^{66} - 554376 q^{67} - 11618770 q^{68} + 9051046 q^{69} + 471625 q^{70} + 6526040 q^{71} - 3026835 q^{72} + 7479766 q^{73} - 3948102 q^{74} + 1015625 q^{75} + 9203364 q^{76} + 3439261 q^{77} - 12300388 q^{78} + 4851305 q^{79} + 11771125 q^{80} - 4256091 q^{81} - 29262330 q^{82} - 11813196 q^{83} + 3438232 q^{84} + 2178375 q^{85} - 34717484 q^{86} - 263021 q^{87} - 54461828 q^{88} + 12879896 q^{89} + 5943375 q^{90} + 5536363 q^{91} - 18484672 q^{92} - 17648536 q^{93} + 23744524 q^{94} + 5549250 q^{95} - 39241860 q^{96} + 11704767 q^{97} + 1294139 q^{98} + 20972602 q^{99}+O(q^{100}) \) 5 * q + 11 * q^2 + 65 * q^3 + 553 * q^4 + 625 * q^5 + 96 * q^6 + 1715 * q^7 - 1647 * q^8 - 12 * q^9 + 1375 * q^10 + 10027 * q^11 + 10024 * q^12 + 16141 * q^13 + 3773 * q^14 + 8125 * q^15 + 94169 * q^16 + 17427 * q^17 + 47547 * q^18 + 44394 * q^19 + 69125 * q^20 + 22295 * q^21 - 89168 * q^22 + 55698 * q^23 + 18324 * q^24 + 78125 * q^25 + 163750 * q^26 - 53389 * q^27 + 189679 * q^28 - 164219 * q^29 + 12000 * q^30 + 138440 * q^31 - 509615 * q^32 - 213271 * q^33 + 132338 * q^34 + 214375 * q^35 - 1408655 * q^36 + 181518 * q^37 - 1725140 * q^38 - 481621 * q^39 - 205875 * q^40 - 369676 * q^41 + 32928 * q^42 + 386 * q^43 - 37608 * q^44 - 1500 * q^45 - 2610592 * q^46 + 962985 * q^47 - 1271004 * q^48 + 588245 * q^49 + 171875 * q^50 - 1305827 * q^51 + 2349706 * q^52 + 396244 * q^53 + 2641788 * q^54 + 1253375 * q^55 - 564921 * q^56 + 4322278 * q^57 - 4408538 * q^58 + 6284948 * q^59 + 1253000 * q^60 + 1975828 * q^61 - 2246384 * q^62 - 4116 * q^63 + 13769617 * q^64 + 2017625 * q^65 + 798284 * q^66 - 554376 * q^67 - 11618770 * q^68 + 9051046 * q^69 + 471625 * q^70 + 6526040 * q^71 - 3026835 * q^72 + 7479766 * q^73 - 3948102 * q^74 + 1015625 * q^75 + 9203364 * q^76 + 3439261 * q^77 - 12300388 * q^78 + 4851305 * q^79 + 11771125 * q^80 - 4256091 * q^81 - 29262330 * q^82 - 11813196 * q^83 + 3438232 * q^84 + 2178375 * q^85 - 34717484 * q^86 - 263021 * q^87 - 54461828 * q^88 + 12879896 * q^89 + 5943375 * q^90 + 5536363 * q^91 - 18484672 * q^92 - 17648536 * q^93 + 23744524 * q^94 + 5549250 * q^95 - 39241860 * q^96 + 11704767 * q^97 + 1294139 * q^98 + 20972602 * q^99

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