LMFDB - Embedded newform 354.8.a.c.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,8,Mod(1,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, 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("354.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	354.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:	$110.584299021$
Analytic rank:	$1$
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} - 2 x^{6} - 77333 x^{5} - 3585829 x^{4} + 1295511138 x^{3} + 69321224657 x^{2} + \cdots - 316178833801950 $ x^7 - 2x^6 - 77333x^5 - 3585829x^4 + 1295511138x^3 + 69321224657x^2 - 5554636281450x - 316178833801950
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{3}\cdot 3^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$265.867$ of defining polynomial
Character	$\chi$	$=$	354.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} +176.399 q^{5} -216.000 q^{6} -148.362 q^{7} -512.000 q^{8} +729.000 q^{9} +O(q^{10})$	\(q-8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} +176.399 q^{5} -216.000 q^{6} -148.362 q^{7} -512.000 q^{8} +729.000 q^{9} -1411.19 q^{10} +994.072 q^{11} +1728.00 q^{12} -10986.9 q^{13} +1186.89 q^{14} +4762.77 q^{15} +4096.00 q^{16} +9147.31 q^{17} -5832.00 q^{18} +33208.9 q^{19} +11289.5 q^{20} -4005.76 q^{21} -7952.58 q^{22} -22801.3 q^{23} -13824.0 q^{24} -47008.4 q^{25} +87895.0 q^{26} +19683.0 q^{27} -9495.14 q^{28} -205204. q^{29} -38102.2 q^{30} +234834. q^{31} -32768.0 q^{32} +26839.9 q^{33} -73178.5 q^{34} -26170.8 q^{35} +46656.0 q^{36} -170436. q^{37} -265671. q^{38} -296646. q^{39} -90316.2 q^{40} -754464. q^{41} +32046.1 q^{42} +481262. q^{43} +63620.6 q^{44} +128595. q^{45} +182410. q^{46} +461184. q^{47} +110592. q^{48} -801532. q^{49} +376067. q^{50} +246977. q^{51} -703160. q^{52} -828062. q^{53} -157464. q^{54} +175353. q^{55} +75961.1 q^{56} +896641. q^{57} +1.64164e6 q^{58} -205379. q^{59} +304817. q^{60} -468784. q^{61} -1.87867e6 q^{62} -108156. q^{63} +262144. q^{64} -1.93807e6 q^{65} -214720. q^{66} -4.04159e6 q^{67} +585428. q^{68} -615635. q^{69} +209367. q^{70} +1.34614e6 q^{71} -373248. q^{72} -2.27429e6 q^{73} +1.36349e6 q^{74} -1.26923e6 q^{75} +2.12537e6 q^{76} -147482. q^{77} +2.37317e6 q^{78} +4.13743e6 q^{79} +722530. q^{80} +531441. q^{81} +6.03571e6 q^{82} +2.97289e6 q^{83} -256369. q^{84} +1.61358e6 q^{85} -3.85010e6 q^{86} -5.54052e6 q^{87} -508965. q^{88} +2.24354e6 q^{89} -1.02876e6 q^{90} +1.63003e6 q^{91} -1.45928e6 q^{92} +6.34053e6 q^{93} -3.68947e6 q^{94} +5.85802e6 q^{95} -884736. q^{96} -5.71245e6 q^{97} +6.41225e6 q^{98} +724679. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 56 q^{2} + 189 q^{3} + 448 q^{4} - 158 q^{5} - 1512 q^{6} - 581 q^{7} - 3584 q^{8} + 5103 q^{9}+O(q^{10}) $ 7 * q - 56 * q^2 + 189 * q^3 + 448 * q^4 - 158 * q^5 - 1512 * q^6 - 581 * q^7 - 3584 * q^8 + 5103 * q^9	\( 7 q - 56 q^{2} + 189 q^{3} + 448 q^{4} - 158 q^{5} - 1512 q^{6} - 581 q^{7} - 3584 q^{8} + 5103 q^{9} + 1264 q^{10} - 2201 q^{11} + 12096 q^{12} - 8421 q^{13} + 4648 q^{14} - 4266 q^{15} + 28672 q^{16} - 2425 q^{17} - 40824 q^{18} - 37084 q^{19} - 10112 q^{20} - 15687 q^{21} + 17608 q^{22} + 99364 q^{23} - 96768 q^{24} + 101361 q^{25} + 67368 q^{26} + 137781 q^{27} - 37184 q^{28} + 2498 q^{29} + 34128 q^{30} - 57962 q^{31} - 229376 q^{32} - 59427 q^{33} + 19400 q^{34} + 190586 q^{35} + 326592 q^{36} - 6497 q^{37} + 296672 q^{38} - 227367 q^{39} + 80896 q^{40} - 319165 q^{41} + 125496 q^{42} - 633743 q^{43} - 140864 q^{44} - 115182 q^{45} - 794912 q^{46} - 1626560 q^{47} + 774144 q^{48} - 3846354 q^{49} - 810888 q^{50} - 65475 q^{51} - 538944 q^{52} - 1215602 q^{53} - 1102248 q^{54} - 3329556 q^{55} + 297472 q^{56} - 1001268 q^{57} - 19984 q^{58} - 1437653 q^{59} - 273024 q^{60} - 3180086 q^{61} + 463696 q^{62} - 423549 q^{63} + 1835008 q^{64} + 544086 q^{65} + 475416 q^{66} - 5349632 q^{67} - 155200 q^{68} + 2682828 q^{69} - 1524688 q^{70} + 1752423 q^{71} - 2612736 q^{72} - 1843424 q^{73} + 51976 q^{74} + 2736747 q^{75} - 2373376 q^{76} - 3885063 q^{77} + 1818936 q^{78} - 4769243 q^{79} - 647168 q^{80} + 3720087 q^{81} + 2553320 q^{82} + 5154441 q^{83} - 1003968 q^{84} - 4594902 q^{85} + 5069944 q^{86} + 67446 q^{87} + 1126912 q^{88} + 20086462 q^{89} + 921456 q^{90} + 6733847 q^{91} + 6359296 q^{92} - 1564974 q^{93} + 13012480 q^{94} + 12936212 q^{95} - 6193152 q^{96} + 6244248 q^{97} + 30770832 q^{98} - 1604529 q^{99}+O(q^{100}) \) 7 * q - 56 * q^2 + 189 * q^3 + 448 * q^4 - 158 * q^5 - 1512 * q^6 - 581 * q^7 - 3584 * q^8 + 5103 * q^9 + 1264 * q^10 - 2201 * q^11 + 12096 * q^12 - 8421 * q^13 + 4648 * q^14 - 4266 * q^15 + 28672 * q^16 - 2425 * q^17 - 40824 * q^18 - 37084 * q^19 - 10112 * q^20 - 15687 * q^21 + 17608 * q^22 + 99364 * q^23 - 96768 * q^24 + 101361 * q^25 + 67368 * q^26 + 137781 * q^27 - 37184 * q^28 + 2498 * q^29 + 34128 * q^30 - 57962 * q^31 - 229376 * q^32 - 59427 * q^33 + 19400 * q^34 + 190586 * q^35 + 326592 * q^36 - 6497 * q^37 + 296672 * q^38 - 227367 * q^39 + 80896 * q^40 - 319165 * q^41 + 125496 * q^42 - 633743 * q^43 - 140864 * q^44 - 115182 * q^45 - 794912 * q^46 - 1626560 * q^47 + 774144 * q^48 - 3846354 * q^49 - 810888 * q^50 - 65475 * q^51 - 538944 * q^52 - 1215602 * q^53 - 1102248 * q^54 - 3329556 * q^55 + 297472 * q^56 - 1001268 * q^57 - 19984 * q^58 - 1437653 * q^59 - 273024 * q^60 - 3180086 * q^61 + 463696 * q^62 - 423549 * q^63 + 1835008 * q^64 + 544086 * q^65 + 475416 * q^66 - 5349632 * q^67 - 155200 * q^68 + 2682828 * q^69 - 1524688 * q^70 + 1752423 * q^71 - 2612736 * q^72 - 1843424 * q^73 + 51976 * q^74 + 2736747 * q^75 - 2373376 * q^76 - 3885063 * q^77 + 1818936 * q^78 - 4769243 * q^79 - 647168 * q^80 + 3720087 * q^81 + 2553320 * q^82 + 5154441 * q^83 - 1003968 * q^84 - 4594902 * q^85 + 5069944 * q^86 + 67446 * q^87 + 1126912 * q^88 + 20086462 * q^89 + 921456 * q^90 + 6733847 * q^91 + 6359296 * q^92 - 1564974 * q^93 + 13012480 * q^94 + 12936212 * q^95 - 6193152 * q^96 + 6244248 * q^97 + 30770832 * q^98 - 1604529 * 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 $

$2$	−8.00000	−0.707107
$2$	−8.00000	−0.707107
$3$	27.0000	0.577350
$3$	27.0000	0.577350
$4$	64.0000	0.500000
$5$	176.399	0.631104	0.315552	−	0.948908i	$-0.397810\pi$
$5$	176.399	0.631104	0.315552	+	0.948908i	$0.397810\pi$
$6$	−216.000	−0.408248
$7$	−148.362	−0.163485	−0.0817426	−	0.996653i	$-0.526049\pi$
$7$	−148.362	−0.163485	−0.0817426	+	0.996653i	$0.526049\pi$
$8$	−512.000	−0.353553
$9$	729.000	0.333333
$10$	−1411.19	−0.446258
$11$	994.072	0.225187	0.112594	−	0.993641i	$-0.464084\pi$
$11$	994.072	0.225187	0.112594	+	0.993641i	$0.464084\pi$
$12$	1728.00	0.288675
$13$	−10986.9	−1.38699	−0.693494	−	0.720462i	$-0.743930\pi$
$13$	−10986.9	−1.38699	−0.693494	+	0.720462i	$0.743930\pi$
$14$	1186.89	0.115601
$15$	4762.77	0.364368
$16$	4096.00	0.250000
$17$	9147.31	0.451567	0.225783	−	0.974178i	$-0.427506\pi$
$17$	9147.31	0.451567	0.225783	+	0.974178i	$0.427506\pi$
$18$	−5832.00	−0.235702
$19$	33208.9	1.11075	0.555376	−	0.831599i	$-0.312574\pi$
$19$	33208.9	1.11075	0.555376	+	0.831599i	$0.312574\pi$
$20$	11289.5	0.315552
$21$	−4005.76	−0.0943882
$22$	−7952.58	−0.159231
$23$	−22801.3	−0.390762	−0.195381	−	0.980727i	$-0.562594\pi$
$23$	−22801.3	−0.390762	−0.195381	+	0.980727i	$0.562594\pi$
$24$	−13824.0	−0.204124
$25$	−47008.4	−0.601708
$26$	87895.0	0.980748
$27$	19683.0	0.192450
$28$	−9495.14	−0.0817426
$29$	−205204.	−1.56241	−0.781203	−	0.624277i	$-0.785394\pi$
$29$	−205204.	−1.56241	−0.781203	+	0.624277i	$0.785394\pi$
$30$	−38102.2	−0.257647
$31$	234834.	1.41578	0.707890	−	0.706323i	$-0.249647\pi$
$31$	234834.	1.41578	0.707890	+	0.706323i	$0.249647\pi$
$32$	−32768.0	−0.176777
$33$	26839.9	0.130012
$34$	−73178.5	−0.319306
$35$	−26170.8	−0.103176
$36$	46656.0	0.166667
$37$	−170436.	−0.553167	−0.276583	−	0.960990i	$-0.589202\pi$
$37$	−170436.	−0.553167	−0.276583	+	0.960990i	$0.589202\pi$
$38$	−265671.	−0.785421
$39$	−296646.	−0.800778
$40$	−90316.2	−0.223129
$41$	−754464.	−1.70960	−0.854801	−	0.518956i	$-0.826321\pi$
$41$	−754464.	−1.70960	−0.854801	+	0.518956i	$0.826321\pi$
$42$	32046.1	0.0667425
$43$	481262.	0.923086	0.461543	−	0.887118i	$-0.347296\pi$
$43$	481262.	0.923086	0.461543	+	0.887118i	$0.347296\pi$
$44$	63620.6	0.112594
$45$	128595.	0.210368
$46$	182410.	0.276310
$47$	461184.	0.647935	0.323968	−	0.946068i	$-0.394983\pi$
$47$	461184.	0.647935	0.323968	+	0.946068i	$0.394983\pi$
$48$	110592.	0.144338
$49$	−801532.	−0.973273
$50$	376067.	0.425472
$51$	246977.	0.260712
$52$	−703160.	−0.693494
$53$	−828062.	−0.764007	−0.382003	−	0.924161i	$-0.624766\pi$
$53$	−828062.	−0.764007	−0.382003	+	0.924161i	$0.624766\pi$
$54$	−157464.	−0.136083
$55$	175353.	0.142116
$56$	75961.1	0.0578007
$57$	896641.	0.641293
$58$	1.64164e6	1.10479
$59$	−205379.	−0.130189
$59$	−205379.	−0.130189
$60$	304817.	0.182184
$61$	−468784.	−0.264435	−0.132217	−	0.991221i	$-0.542210\pi$
$61$	−468784.	−0.264435	−0.132217	+	0.991221i	$0.542210\pi$
$62$	−1.87867e6	−1.00111
$63$	−108156.	−0.0544951
$64$	262144.	0.125000
$65$	−1.93807e6	−0.875333
$66$	−214720.	−0.0919322
$67$	−4.04159e6	−1.64169	−0.820843	−	0.571154i	$-0.806496\pi$
$67$	−4.04159e6	−1.64169	−0.820843	+	0.571154i	$0.806496\pi$
$68$	585428.	0.225783
$69$	−615635.	−0.225606
$70$	209367.	0.0729565
$71$	1.34614e6	0.446361	0.223180	−	0.974777i	$-0.428356\pi$
$71$	1.34614e6	0.446361	0.223180	+	0.974777i	$0.428356\pi$
$72$	−373248.	−0.117851
$73$	−2.27429e6	−0.684251	−0.342125	−	0.939654i	$-0.611147\pi$
$73$	−2.27429e6	−0.684251	−0.342125	+	0.939654i	$0.611147\pi$
$74$	1.36349e6	0.391148
$75$	−1.26923e6	−0.347396
$76$	2.12537e6	0.555376
$77$	−147482.	−0.0368148
$78$	2.37317e6	0.566235
$79$	4.13743e6	0.944139	0.472069	−	0.881561i	$-0.343507\pi$
$79$	4.13743e6	0.944139	0.472069	+	0.881561i	$0.343507\pi$
$80$	722530.	0.157776
$81$	531441.	0.111111
$82$	6.03571e6	1.20887
$83$	2.97289e6	0.570697	0.285349	−	0.958424i	$-0.407891\pi$
$83$	2.97289e6	0.570697	0.285349	+	0.958424i	$0.407891\pi$
$84$	−256369.	−0.0471941
$85$	1.61358e6	0.284986
$86$	−3.85010e6	−0.652720
$87$	−5.54052e6	−0.902055
$88$	−508965.	−0.0796157
$89$	2.24354e6	0.337341	0.168670	−	0.985673i	$-0.446053\pi$
$89$	2.24354e6	0.337341	0.168670	+	0.985673i	$0.446053\pi$
$90$	−1.02876e6	−0.148753
$91$	1.63003e6	0.226752
$92$	−1.45928e6	−0.195381
$93$	6.34053e6	0.817401
$94$	−3.68947e6	−0.458160
$95$	5.85802e6	0.701000
$96$	−884736.	−0.102062
$97$	−5.71245e6	−0.635508	−0.317754	−	0.948173i	$-0.602929\pi$
$97$	−5.71245e6	−0.635508	−0.317754	+	0.948173i	$0.602929\pi$
$98$	6.41225e6	0.688208
$99$	724679.	0.0750624
$100$	−3.00854e6	−0.300854
$101$	1.01553e7	0.980774	0.490387	−	0.871505i	$-0.336856\pi$
$101$	1.01553e7	0.980774	0.490387	+	0.871505i	$0.336856\pi$
$102$	−1.97582e6	−0.184351
$103$	5.57226e6	0.502459	0.251230	−	0.967928i	$-0.419165\pi$
$103$	5.57226e6	0.502459	0.251230	+	0.967928i	$0.419165\pi$
$104$	5.62528e6	0.490374
$105$	−706612.	−0.0595688
$106$	6.62449e6	0.540234
$107$	1.58715e7	1.25249	0.626246	−	0.779626i	$-0.284591\pi$
$107$	1.58715e7	1.25249	0.626246	+	0.779626i	$0.284591\pi$
$108$	1.25971e6	0.0962250
$109$	−6.91713e6	−0.511603	−0.255802	−	0.966729i	$-0.582339\pi$
$109$	−6.91713e6	−0.511603	−0.255802	+	0.966729i	$0.582339\pi$
$110$	−1.40283e6	−0.100492
$111$	−4.60178e6	−0.319371
$112$	−607689.	−0.0408713
$113$	2.65191e6	0.172896	0.0864479	−	0.996256i	$-0.472448\pi$
$113$	2.65191e6	0.172896	0.0864479	+	0.996256i	$0.472448\pi$
$114$	−7.17313e6	−0.453463
$115$	−4.02212e6	−0.246611
$116$	−1.31331e7	−0.781203
$117$	−8.00944e6	−0.462329
$118$	1.64303e6	0.0920575
$119$	−1.35711e6	−0.0738245
$120$	−2.43854e6	−0.128824
$121$	−1.84990e7	−0.949291
$122$	3.75027e6	0.186984
$123$	−2.03705e7	−0.987039
$124$	1.50294e7	0.707890
$125$	−2.20734e7	−1.01084
$126$	865245.	0.0385338
$127$	−8.34491e6	−0.361500	−0.180750	−	0.983529i	$-0.557853\pi$
$127$	−8.34491e6	−0.361500	−0.180750	+	0.983529i	$0.557853\pi$
$128$	−2.09715e6	−0.0883883
$129$	1.29941e7	0.532944
$130$	1.55046e7	0.618954
$131$	−3.74688e7	−1.45620	−0.728098	−	0.685473i	$-0.759596\pi$
$131$	−3.74688e7	−1.45620	−0.728098	+	0.685473i	$0.759596\pi$
$132$	1.71776e6	0.0650059
$133$	−4.92693e6	−0.181592
$134$	3.23327e7	1.16085
$135$	3.47206e6	0.121456
$136$	−4.68342e6	−0.159653
$137$	−1.90754e6	−0.0633799	−0.0316900	−	0.999498i	$-0.510089\pi$
$137$	−1.90754e6	−0.0633799	−0.0316900	+	0.999498i	$0.510089\pi$
$138$	4.92508e6	0.159528
$139$	3.22224e7	1.01767	0.508833	−	0.860865i	$-0.330077\pi$
$139$	3.22224e7	1.01767	0.508833	+	0.860865i	$0.330077\pi$
$140$	−1.67493e6	−0.0515881
$141$	1.24520e7	0.374086
$142$	−1.07691e7	−0.315625
$143$	−1.09218e7	−0.312332
$144$	2.98598e6	0.0833333
$145$	−3.61978e7	−0.986040
$146$	1.81943e7	0.483838
$147$	−2.16414e7	−0.561919
$148$	−1.09079e7	−0.276583
$149$	−3.64166e7	−0.901876	−0.450938	−	0.892555i	$-0.648911\pi$
$149$	−3.64166e7	−0.901876	−0.450938	+	0.892555i	$0.648911\pi$
$150$	1.01538e7	0.245646
$151$	−4.35952e7	−1.03043	−0.515217	−	0.857060i	$-0.672288\pi$
$151$	−4.35952e7	−1.03043	−0.515217	+	0.857060i	$0.672288\pi$
$152$	−1.70030e7	−0.392710
$153$	6.66839e6	0.150522
$154$	1.17986e6	0.0260320
$155$	4.14245e7	0.893504
$156$	−1.89853e7	−0.400389
$157$	−5.42531e7	−1.11886	−0.559430	−	0.828878i	$-0.688980\pi$
$157$	−5.42531e7	−1.11886	−0.559430	+	0.828878i	$0.688980\pi$
$158$	−3.30994e7	−0.667607
$159$	−2.23577e7	−0.441099
$160$	−5.78024e6	−0.111564
$161$	3.38284e6	0.0638838
$162$	−4.25153e6	−0.0785674
$163$	2.56078e7	0.463144	0.231572	−	0.972818i	$-0.425613\pi$
$163$	2.56078e7	0.463144	0.231572	+	0.972818i	$0.425613\pi$
$164$	−4.82857e7	−0.854801
$165$	4.73454e6	0.0820510
$166$	−2.37831e7	−0.403544
$167$	−8.96820e7	−1.49004	−0.745020	−	0.667042i	$-0.767560\pi$
$167$	−8.96820e7	−1.49004	−0.745020	+	0.667042i	$0.767560\pi$
$168$	2.05095e6	0.0333713
$169$	5.79630e7	0.923735
$170$	−1.29086e7	−0.201515
$171$	2.42093e7	0.370251
$172$	3.08008e7	0.461543
$173$	5.55889e7	0.816256	0.408128	−	0.912925i	$-0.366182\pi$
$173$	5.55889e7	0.816256	0.408128	+	0.912925i	$0.366182\pi$
$174$	4.43242e7	0.637850
$175$	6.97425e6	0.0983703
$176$	4.07172e6	0.0562968
$177$	−5.54523e6	−0.0751646
$178$	−1.79483e7	−0.238536
$179$	−1.44873e8	−1.88800	−0.944002	−	0.329939i	$-0.892972\pi$
$179$	−1.44873e8	−1.88800	−0.944002	+	0.329939i	$0.892972\pi$
$180$	8.23007e6	0.105184
$181$	−1.51992e8	−1.90523	−0.952613	−	0.304186i	$-0.901616\pi$
$181$	−1.51992e8	−1.90523	−0.952613	+	0.304186i	$0.901616\pi$
$182$	−1.30402e7	−0.160338
$183$	−1.26572e7	−0.152671
$184$	1.16743e7	0.138155
$185$	−3.00648e7	−0.349106
$186$	−5.07242e7	−0.577990
$187$	9.09308e6	0.101687
$188$	2.95158e7	0.323968
$189$	−2.92020e6	−0.0314627
$190$	−4.68642e7	−0.495682
$191$	4.75059e7	0.493323	0.246661	−	0.969102i	$-0.420666\pi$
$191$	4.75059e7	0.493323	0.246661	+	0.969102i	$0.420666\pi$
$192$	7.07789e6	0.0721688
$193$	−2.34785e7	−0.235082	−0.117541	−	0.993068i	$-0.537501\pi$
$193$	−2.34785e7	−0.235082	−0.117541	+	0.993068i	$0.537501\pi$
$194$	4.56996e7	0.449372
$195$	−5.23280e7	−0.505374
$196$	−5.12980e7	−0.486636
$197$	1.46531e8	1.36552	0.682758	−	0.730645i	$-0.260781\pi$
$197$	1.46531e8	1.36552	0.682758	+	0.730645i	$0.260781\pi$
$198$	−5.79743e6	−0.0530771
$199$	−9.12927e7	−0.821203	−0.410601	−	0.911815i	$-0.634681\pi$
$199$	−9.12927e7	−0.821203	−0.410601	+	0.911815i	$0.634681\pi$
$200$	2.40683e7	0.212736
$201$	−1.09123e8	−0.947828
$202$	−8.12425e7	−0.693512
$203$	3.04445e7	0.255430
$204$	1.58065e7	0.130356
$205$	−1.33087e8	−1.07894
$206$	−4.45780e7	−0.355292
$207$	−1.66221e7	−0.130254
$208$	−4.50023e7	−0.346747
$209$	3.30121e7	0.250127
$210$	5.65290e6	0.0421215
$211$	−2.24551e8	−1.64561	−0.822804	−	0.568325i	$-0.807592\pi$
$211$	−2.24551e8	−1.64561	−0.822804	+	0.568325i	$0.807592\pi$
$212$	−5.29960e7	−0.382003
$213$	3.63458e7	0.257706
$214$	−1.26972e8	−0.885645
$215$	8.48941e7	0.582563
$216$	−1.00777e7	−0.0680414
$217$	−3.48404e7	−0.231459
$218$	5.53371e7	0.361758
$219$	−6.14058e7	−0.395052
$220$	1.12226e7	0.0710582
$221$	−1.00500e8	−0.626318
$222$	3.68142e7	0.225829
$223$	−4.64788e7	−0.280665	−0.140332	−	0.990104i	$-0.544817\pi$
$223$	−4.64788e7	−0.280665	−0.140332	+	0.990104i	$0.544817\pi$
$224$	4.86151e6	0.0289004
$225$	−3.42691e7	−0.200569
$226$	−2.12153e7	−0.122256
$227$	1.50771e8	0.855514	0.427757	−	0.903894i	$-0.359304\pi$
$227$	1.50771e8	0.855514	0.427757	+	0.903894i	$0.359304\pi$
$228$	5.73850e7	0.320647
$229$	−1.46464e8	−0.805946	−0.402973	−	0.915212i	$-0.632023\pi$
$229$	−1.46464e8	−0.805946	−0.402973	+	0.915212i	$0.632023\pi$
$230$	3.21770e7	0.174381
$231$	−3.98202e6	−0.0212550
$232$	1.05065e8	0.552394
$233$	5.08251e6	0.0263228	0.0131614	−	0.999913i	$-0.495810\pi$
$233$	5.08251e6	0.0263228	0.0131614	+	0.999913i	$0.495810\pi$
$234$	6.40755e7	0.326916
$235$	8.13524e7	0.408915
$236$	−1.31443e7	−0.0650945
$237$	1.11711e8	0.545099
$238$	1.08569e7	0.0522018
$239$	−3.80281e8	−1.80182	−0.900911	−	0.434003i	$-0.857101\pi$
$239$	−3.80281e8	−1.80182	−0.900911	+	0.434003i	$0.857101\pi$
$240$	1.95083e7	0.0910920
$241$	3.27252e7	0.150599	0.0752996	−	0.997161i	$-0.476009\pi$
$241$	3.27252e7	0.150599	0.0752996	+	0.997161i	$0.476009\pi$
$242$	1.47992e8	0.671250
$243$	1.43489e7	0.0641500
$244$	−3.00022e7	−0.132217
$245$	−1.41389e8	−0.614236
$246$	1.62964e8	0.697942
$247$	−3.64863e8	−1.54060
$248$	−1.20235e8	−0.500554
$249$	8.02681e7	0.329492
$250$	1.76587e8	0.714775
$251$	−3.40128e8	−1.35764	−0.678820	−	0.734305i	$-0.737508\pi$
$251$	−3.40128e8	−1.35764	−0.678820	+	0.734305i	$0.737508\pi$
$252$	−6.92196e6	−0.0272475
$253$	−2.26661e7	−0.0879945
$254$	6.67592e7	0.255619
$255$	4.35665e7	0.164537
$256$	1.67772e7	0.0625000
$257$	4.28106e8	1.57321	0.786603	−	0.617459i	$-0.211838\pi$
$257$	4.28106e8	1.57321	0.786603	+	0.617459i	$0.211838\pi$
$258$	−1.03953e8	−0.376848
$259$	2.52862e7	0.0904346
$260$	−1.24037e8	−0.437667
$261$	−1.49594e8	−0.520802
$262$	2.99750e8	1.02969
$263$	−4.12104e8	−1.39689	−0.698444	−	0.715665i	$-0.746124\pi$
$263$	−4.12104e8	−1.39689	−0.698444	+	0.715665i	$0.746124\pi$
$264$	−1.37421e7	−0.0459661
$265$	−1.46069e8	−0.482168
$266$	3.94154e7	0.128405
$267$	6.05756e7	0.194764
$268$	−2.58662e8	−0.820843
$269$	1.19256e8	0.373549	0.186775	−	0.982403i	$-0.440197\pi$
$269$	1.19256e8	0.373549	0.186775	+	0.982403i	$0.440197\pi$
$270$	−2.77765e7	−0.0858824
$271$	−5.77685e8	−1.76319	−0.881594	−	0.472008i	$-0.843529\pi$
$271$	−5.77685e8	−1.76319	−0.881594	+	0.472008i	$0.843529\pi$
$272$	3.74674e7	0.112892
$273$	4.40108e7	0.130915
$274$	1.52603e7	0.0448164
$275$	−4.67298e7	−0.135497
$276$	−3.94006e7	−0.112803
$277$	−1.18353e8	−0.334581	−0.167290	−	0.985908i	$-0.553502\pi$
$277$	−1.18353e8	−0.334581	−0.167290	+	0.985908i	$0.553502\pi$
$278$	−2.57779e8	−0.719599
$279$	1.71194e8	0.471927
$280$	1.33995e7	0.0364783
$281$	2.03512e8	0.547164	0.273582	−	0.961849i	$-0.411792\pi$
$281$	2.03512e8	0.547164	0.273582	+	0.961849i	$0.411792\pi$
$282$	−9.96157e7	−0.264519
$283$	7.59702e7	0.199246	0.0996232	−	0.995025i	$-0.468236\pi$
$283$	7.59702e7	0.199246	0.0996232	+	0.995025i	$0.468236\pi$
$284$	8.61529e7	0.223180
$285$	1.58167e8	0.404723
$286$	8.73740e7	0.220852
$287$	1.11933e8	0.279495
$288$	−2.38879e7	−0.0589256
$289$	−3.26665e8	−0.796087
$290$	2.89583e8	0.697236
$291$	−1.54236e8	−0.366911
$292$	−1.45554e8	−0.342125
$293$	6.11987e8	1.42136	0.710682	−	0.703513i	$-0.248386\pi$
$293$	6.11987e8	1.42136	0.710682	+	0.703513i	$0.248386\pi$
$294$	1.73131e8	0.397337
$295$	−3.62286e7	−0.0821627
$296$	8.72634e7	0.195574
$297$	1.95663e7	0.0433373
$298$	2.91333e8	0.637723
$299$	2.50515e8	0.541982
$300$	−8.12306e7	−0.173698
$301$	−7.14008e7	−0.150911
$302$	3.48762e8	0.728626
$303$	2.74194e8	0.566250
$304$	1.36024e8	0.277688
$305$	−8.26930e7	−0.166886
$306$	−5.33471e7	−0.106435
$307$	8.42823e8	1.66246	0.831231	−	0.555927i	$-0.187637\pi$
$307$	8.42823e8	1.66246	0.831231	+	0.555927i	$0.187637\pi$
$308$	−9.43886e6	−0.0184074
$309$	1.50451e8	0.290095
$310$	−3.31396e8	−0.631803
$311$	7.99015e8	1.50624	0.753119	−	0.657884i	$-0.228548\pi$
$311$	7.99015e8	1.50624	0.753119	+	0.657884i	$0.228548\pi$
$312$	1.51883e8	0.283118
$313$	−4.09410e8	−0.754663	−0.377332	−	0.926078i	$-0.623158\pi$
$313$	−4.09410e8	−0.754663	−0.377332	+	0.926078i	$0.623158\pi$
$314$	4.34025e8	0.791153
$315$	−1.90785e7	−0.0343920
$316$	2.64796e8	0.472069
$317$	−2.57727e7	−0.0454415	−0.0227208	−	0.999742i	$-0.507233\pi$
$317$	−2.57727e7	−0.0454415	−0.0227208	+	0.999742i	$0.507233\pi$
$318$	1.78861e8	0.311904
$319$	−2.03988e8	−0.351834
$320$	4.62419e7	0.0788880
$321$	4.28530e8	0.723126
$322$	−2.70627e7	−0.0451727
$323$	3.03772e8	0.501579
$324$	3.40122e7	0.0555556
$325$	5.16476e8	0.834562
$326$	−2.04863e8	−0.327492
$327$	−1.86763e8	−0.295374
$328$	3.86285e8	0.604435
$329$	−6.84220e7	−0.105928
$330$	−3.78763e7	−0.0580188
$331$	1.95154e8	0.295787	0.147893	−	0.989003i	$-0.452751\pi$
$331$	1.95154e8	0.295787	0.147893	+	0.989003i	$0.452751\pi$
$332$	1.90265e8	0.285349
$333$	−1.24248e8	−0.184389
$334$	7.17456e8	1.05362
$335$	−7.12931e8	−1.03607
$336$	−1.64076e7	−0.0235971
$337$	−6.88279e8	−0.979625	−0.489812	−	0.871828i	$-0.662935\pi$
$337$	−6.88279e8	−0.979625	−0.489812	+	0.871828i	$0.662935\pi$
$338$	−4.63704e8	−0.653179
$339$	7.16016e7	0.0998214
$340$	1.03269e8	0.142493
$341$	2.33442e8	0.318815
$342$	−1.93675e8	−0.261807
$343$	2.41099e8	0.322601
$344$	−2.46406e8	−0.326360
$345$	−1.08597e8	−0.142381
$346$	−4.44711e8	−0.577180
$347$	1.09612e9	1.40833	0.704163	−	0.710039i	$-0.251323\pi$
$347$	1.09612e9	1.40833	0.704163	+	0.710039i	$0.251323\pi$
$348$	−3.54593e8	−0.451028
$349$	2.81438e8	0.354401	0.177200	−	0.984175i	$-0.443296\pi$
$349$	2.81438e8	0.354401	0.177200	+	0.984175i	$0.443296\pi$
$350$	−5.57940e7	−0.0695583
$351$	−2.16255e8	−0.266926
$352$	−3.25738e7	−0.0398078
$353$	−3.83158e8	−0.463625	−0.231812	−	0.972761i	$-0.574466\pi$
$353$	−3.83158e8	−0.463625	−0.231812	+	0.972761i	$0.574466\pi$
$354$	4.43619e7	0.0531494
$355$	2.37458e8	0.281700
$356$	1.43587e8	0.168670
$357$	−3.66420e7	−0.0426226
$358$	1.15899e9	1.33502
$359$	4.19892e8	0.478969	0.239485	−	0.970900i	$-0.423022\pi$
$359$	4.19892e8	0.478969	0.239485	+	0.970900i	$0.423022\pi$
$360$	−6.58405e7	−0.0743763
$361$	2.08962e8	0.233771
$362$	1.21594e9	1.34720
$363$	−4.99473e8	−0.548073
$364$	1.04322e8	0.113376
$365$	−4.01182e8	−0.431833
$366$	1.01257e8	0.107955
$367$	1.05726e9	1.11648	0.558238	−	0.829681i	$-0.311478\pi$
$367$	1.05726e9	1.11648	0.558238	+	0.829681i	$0.311478\pi$
$368$	−9.33941e7	−0.0976905
$369$	−5.50004e8	−0.569867
$370$	2.40518e8	0.246855
$371$	1.22853e8	0.124904
$372$	4.05794e8	0.408700
$373$	−1.07865e9	−1.07621	−0.538107	−	0.842876i	$-0.680861\pi$
$373$	−1.07865e9	−1.07621	−0.538107	+	0.842876i	$0.680861\pi$
$374$	−7.27447e7	−0.0719036
$375$	−5.95982e8	−0.583611
$376$	−2.36126e8	−0.229080
$377$	2.25456e9	2.16704
$378$	2.33616e7	0.0222475
$379$	1.44931e9	1.36749	0.683745	−	0.729721i	$-0.260350\pi$
$379$	1.44931e9	1.36749	0.683745	+	0.729721i	$0.260350\pi$
$380$	3.74913e8	0.350500
$381$	−2.25312e8	−0.208712
$382$	−3.80047e8	−0.348832
$383$	−8.21059e8	−0.746756	−0.373378	−	0.927679i	$-0.621800\pi$
$383$	−8.21059e8	−0.746756	−0.373378	+	0.927679i	$0.621800\pi$
$384$	−5.66231e7	−0.0510310
$385$	−2.60157e7	−0.0232339
$386$	1.87828e8	0.166228
$387$	3.50840e8	0.307695
$388$	−3.65597e8	−0.317754
$389$	−1.47112e9	−1.26714	−0.633568	−	0.773687i	$-0.718410\pi$
$389$	−1.47112e9	−1.26714	−0.633568	+	0.773687i	$0.718410\pi$
$390$	4.18624e8	0.357353
$391$	−2.08571e8	−0.176455
$392$	4.10384e8	0.344104
$393$	−1.01166e9	−0.840735
$394$	−1.17224e9	−0.965565
$395$	7.29838e8	0.595850
$396$	4.63794e7	0.0375312
$397$	−1.09710e9	−0.879997	−0.439998	−	0.897999i	$-0.645021\pi$
$397$	−1.09710e9	−0.879997	−0.439998	+	0.897999i	$0.645021\pi$
$398$	7.30342e8	0.580678
$399$	−1.33027e8	−0.104842
$400$	−1.92547e8	−0.150427
$401$	1.15894e9	0.897547	0.448774	−	0.893645i	$-0.351861\pi$
$401$	1.15894e9	0.897547	0.448774	+	0.893645i	$0.351861\pi$
$402$	8.72983e8	0.670215
$403$	−2.58010e9	−1.96367
$404$	6.49940e8	0.490387
$405$	9.37456e7	0.0701227
$406$	−2.43556e8	−0.180616
$407$	−1.69426e8	−0.124566
$408$	−1.26452e8	−0.0921757
$409$	2.00514e9	1.44915	0.724576	−	0.689195i	$-0.242036\pi$
$409$	2.00514e9	1.44915	0.724576	+	0.689195i	$0.242036\pi$
$410$	1.06469e9	0.762923
$411$	−5.15036e7	−0.0365924
$412$	3.56624e8	0.251230
$413$	3.04704e7	0.0212840
$414$	1.32977e8	0.0921035
$415$	5.24415e8	0.360169
$416$	3.60018e8	0.245187
$417$	8.70004e8	0.587550
$418$	−2.64097e8	−0.176867
$419$	5.27772e8	0.350507	0.175254	−	0.984523i	$-0.443925\pi$
$419$	5.27772e8	0.350507	0.175254	+	0.984523i	$0.443925\pi$
$420$	−4.52232e7	−0.0297844
$421$	−1.55101e9	−1.01304	−0.506521	−	0.862228i	$-0.669069\pi$
$421$	−1.55101e9	−1.01304	−0.506521	+	0.862228i	$0.669069\pi$
$422$	1.79641e9	1.16362
$423$	3.36203e8	0.215978
$424$	4.23968e8	0.270117
$425$	−4.30001e8	−0.271711
$426$	−2.90766e8	−0.182226
$427$	6.95496e7	0.0432312
$428$	1.01578e9	0.626246
$429$	−2.94887e8	−0.180325
$430$	−6.79153e8	−0.411934
$431$	−4.67340e8	−0.281166	−0.140583	−	0.990069i	$-0.544898\pi$
$431$	−4.67340e8	−0.281166	−0.140583	+	0.990069i	$0.544898\pi$
$432$	8.06216e7	0.0481125
$433$	1.81114e9	1.07212	0.536061	−	0.844179i	$-0.319912\pi$
$433$	1.81114e9	1.07212	0.536061	+	0.844179i	$0.319912\pi$
$434$	2.78723e8	0.163666
$435$	−9.77342e8	−0.569291
$436$	−4.42696e8	−0.255802
$437$	−7.57207e8	−0.434040
$438$	4.91246e8	0.279344
$439$	1.34891e9	0.760952	0.380476	−	0.924791i	$-0.375760\pi$
$439$	1.34891e9	0.760952	0.380476	+	0.924791i	$0.375760\pi$
$440$	−8.97809e7	−0.0502458
$441$	−5.84317e8	−0.324424
$442$	8.04003e8	0.442874
$443$	9.27112e8	0.506663	0.253332	−	0.967379i	$-0.418474\pi$
$443$	9.27112e8	0.506663	0.253332	+	0.967379i	$0.418474\pi$
$444$	−2.94514e8	−0.159685
$445$	3.95758e8	0.212897
$446$	3.71831e8	0.198460
$447$	−9.83247e8	−0.520699
$448$	−3.88921e7	−0.0204356
$449$	−2.84394e9	−1.48272	−0.741359	−	0.671108i	$-0.765818\pi$
$449$	−2.84394e9	−1.48272	−0.741359	+	0.671108i	$0.765818\pi$
$450$	2.74153e8	0.141824
$451$	−7.49991e8	−0.384980
$452$	1.69722e8	0.0864479
$453$	−1.17707e9	−0.594921
$454$	−1.20617e9	−0.604940
$455$	2.87536e8	0.143104
$456$	−4.59080e8	−0.226731
$457$	−3.45147e9	−1.69160	−0.845800	−	0.533500i	$-0.820876\pi$
$457$	−3.45147e9	−1.69160	−0.845800	+	0.533500i	$0.820876\pi$
$458$	1.17171e9	0.569890
$459$	1.80046e8	0.0869041
$460$	−2.57416e8	−0.123306
$461$	7.31210e8	0.347607	0.173804	−	0.984780i	$-0.444394\pi$
$461$	7.31210e8	0.347607	0.173804	+	0.984780i	$0.444394\pi$
$462$	3.18561e7	0.0150296
$463$	−4.08236e8	−0.191152	−0.0955758	−	0.995422i	$-0.530469\pi$
$463$	−4.08236e8	−0.191152	−0.0955758	+	0.995422i	$0.530469\pi$
$464$	−8.40518e8	−0.390601
$465$	1.11846e9	0.515865
$466$	−4.06601e7	−0.0186131
$467$	−1.89754e9	−0.862149	−0.431074	−	0.902316i	$-0.641865\pi$
$467$	−1.89754e9	−0.862149	−0.431074	+	0.902316i	$0.641865\pi$
$468$	−5.12604e8	−0.231165
$469$	5.99616e8	0.268391
$470$	−6.50819e8	−0.289146
$471$	−1.46483e9	−0.645974
$472$	1.05154e8	0.0460287
$473$	4.78409e8	0.207867
$474$	−8.93685e8	−0.385443
$475$	−1.56110e9	−0.668349
$476$	−8.68550e7	−0.0369122
$477$	−6.03657e8	−0.254669
$478$	3.04225e9	1.27408
$479$	4.42753e8	0.184072	0.0920359	−	0.995756i	$-0.470663\pi$
$479$	4.42753e8	0.184072	0.0920359	+	0.995756i	$0.470663\pi$
$480$	−1.56066e8	−0.0644118
$481$	1.87256e9	0.767235
$482$	−2.61801e8	−0.106490
$483$	9.13366e7	0.0368833
$484$	−1.18394e9	−0.474645
$485$	−1.00767e9	−0.401072
$486$	−1.14791e8	−0.0453609
$487$	−3.21102e9	−1.25977	−0.629885	−	0.776688i	$-0.716898\pi$
$487$	−3.21102e9	−1.25977	−0.629885	+	0.776688i	$0.716898\pi$
$488$	2.40018e8	0.0934918
$489$	6.91412e8	0.267396
$490$	1.13111e9	0.434331
$491$	1.48242e9	0.565178	0.282589	−	0.959241i	$-0.408807\pi$
$491$	1.48242e9	0.565178	0.282589	+	0.959241i	$0.408807\pi$
$492$	−1.30371e9	−0.493519
$493$	−1.87707e9	−0.705531
$494$	2.91890e9	1.08937
$495$	1.27833e8	0.0473721
$496$	9.61881e8	0.353945
$497$	−1.99715e8	−0.0729734
$498$	−6.42145e8	−0.232986
$499$	−2.29476e9	−0.826770	−0.413385	−	0.910556i	$-0.635654\pi$
$499$	−2.29476e9	−0.826770	−0.413385	+	0.910556i	$0.635654\pi$
$500$	−1.41270e9	−0.505422
$501$	−2.42142e9	−0.860275
$502$	2.72102e9	0.959996
$503$	4.64457e9	1.62726	0.813631	−	0.581382i	$-0.197488\pi$
$503$	4.64457e9	1.62726	0.813631	+	0.581382i	$0.197488\pi$
$504$	5.53757e7	0.0192669
$505$	1.79139e9	0.618970
$506$	1.81329e8	0.0622215
$507$	1.56500e9	0.533319
$508$	−5.34074e8	−0.180750
$509$	5.16874e9	1.73729	0.868645	−	0.495436i	$-0.164992\pi$
$509$	5.16874e9	1.73729	0.868645	+	0.495436i	$0.164992\pi$
$510$	−3.48532e8	−0.116345
$511$	3.37417e8	0.111865
$512$	−1.34218e8	−0.0441942
$513$	6.53651e8	0.213764
$514$	−3.42485e9	−1.11242
$515$	9.82940e8	0.317104
$516$	8.31621e8	0.266472
$517$	4.58450e8	0.145907
$518$	−2.02290e8	−0.0639469
$519$	1.50090e9	0.471266
$520$	9.92294e8	0.309477
$521$	−4.08118e9	−1.26431	−0.632155	−	0.774842i	$-0.717829\pi$
$521$	−4.08118e9	−1.26431	−0.632155	+	0.774842i	$0.717829\pi$
$522$	1.19675e9	0.368263
$523$	1.99439e9	0.609613	0.304806	−	0.952414i	$-0.401408\pi$
$523$	1.99439e9	0.609613	0.304806	+	0.952414i	$0.401408\pi$
$524$	−2.39800e9	−0.728098
$525$	1.88305e8	0.0567941
$526$	3.29683e9	0.987749
$527$	2.14810e9	0.639319
$528$	1.09936e8	0.0325030
$529$	−2.88493e9	−0.847305
$530$	1.16855e9	0.340944
$531$	−1.49721e8	−0.0433963
$532$	−3.15324e8	−0.0907958
$533$	8.28920e9	2.37120
$534$	−4.84604e8	−0.137719
$535$	2.79972e9	0.790452
$536$	2.06929e9	0.580424
$537$	−3.91158e9	−1.09004
$538$	−9.54049e8	−0.264139
$539$	−7.96780e8	−0.219168
$540$	2.22212e8	0.0607280
$541$	−5.89460e9	−1.60053	−0.800265	−	0.599646i	$-0.795308\pi$
$541$	−5.89460e9	−1.60053	−0.800265	+	0.599646i	$0.795308\pi$
$542$	4.62148e9	1.24676
$543$	−4.10379e9	−1.09998
$544$	−2.99739e8	−0.0798265
$545$	−1.22017e9	−0.322875
$546$	−3.52087e8	−0.0925711
$547$	9.99732e8	0.261173	0.130586	−	0.991437i	$-0.458314\pi$
$547$	9.99732e8	0.261173	0.130586	+	0.991437i	$0.458314\pi$
$548$	−1.22083e8	−0.0316900
$549$	−3.41744e8	−0.0881449
$550$	3.73838e8	0.0958107
$551$	−6.81462e9	−1.73545
$552$	3.15205e8	0.0797639
$553$	−6.13836e8	−0.154353
$554$	9.46826e8	0.236584
$555$	−8.11749e8	−0.201556
$556$	2.06223e9	0.508833
$557$	−7.42429e9	−1.82038	−0.910189	−	0.414194i	$-0.864064\pi$
$557$	−7.42429e9	−1.82038	−0.910189	+	0.414194i	$0.864064\pi$
$558$	−1.36955e9	−0.333702
$559$	−5.28757e9	−1.28031
$560$	−1.07196e8	−0.0257940
$561$	2.45513e8	0.0587090
$562$	−1.62809e9	−0.386903
$563$	4.11353e9	0.971483	0.485741	−	0.874103i	$-0.338550\pi$
$563$	4.11353e9	0.971483	0.485741	+	0.874103i	$0.338550\pi$
$564$	7.96926e8	0.187043
$565$	4.67794e8	0.109115
$566$	−6.07761e8	−0.140888
$567$	−7.88454e7	−0.0181650
$568$	−6.89224e8	−0.157812
$569$	8.30701e9	1.89039	0.945196	−	0.326504i	$-0.105871\pi$
$569$	8.30701e9	1.89039	0.945196	+	0.326504i	$0.105871\pi$
$570$	−1.26533e9	−0.286182
$571$	5.96440e9	1.34073	0.670364	−	0.742033i	$-0.266138\pi$
$571$	5.96440e9	1.34073	0.670364	+	0.742033i	$0.266138\pi$
$572$	−6.98992e8	−0.156166
$573$	1.28266e9	0.284820
$574$	−8.95468e8	−0.197632
$575$	1.07185e9	0.235125
$576$	1.91103e8	0.0416667
$577$	−8.46542e9	−1.83457	−0.917283	−	0.398237i	$-0.869622\pi$
$577$	−8.46542e9	−1.83457	−0.917283	+	0.398237i	$0.869622\pi$
$578$	2.61332e9	0.562919
$579$	−6.33919e8	−0.135725
$580$	−2.31666e9	−0.493020
$581$	−4.41063e8	−0.0933005
$582$	1.23389e9	0.259445
$583$	−8.23153e8	−0.172044
$584$	1.16444e9	0.241919
$585$	−1.41286e9	−0.291778
$586$	−4.89590e9	−1.00506
$587$	4.89388e9	0.998665	0.499333	−	0.866410i	$-0.333579\pi$
$587$	4.89388e9	0.998665	0.499333	+	0.866410i	$0.333579\pi$
$588$	−1.38505e9	−0.280960
$589$	7.79860e9	1.57258
$590$	2.89829e8	0.0580978
$591$	3.95633e9	0.788381
$592$	−6.98107e8	−0.138292
$593$	−4.75515e9	−0.936424	−0.468212	−	0.883616i	$-0.655102\pi$
$593$	−4.75515e9	−0.936424	−0.468212	+	0.883616i	$0.655102\pi$
$594$	−1.56531e8	−0.0306441
$595$	−2.39393e8	−0.0465909
$596$	−2.33066e9	−0.450938
$597$	−2.46490e9	−0.474122
$598$	−2.00412e9	−0.383239
$599$	−3.73421e8	−0.0709912	−0.0354956	−	0.999370i	$-0.511301\pi$
$599$	−3.73421e8	−0.0709912	−0.0354956	+	0.999370i	$0.511301\pi$
$600$	6.49845e8	0.122823
$601$	8.64006e9	1.62351	0.811757	−	0.583995i	$-0.198511\pi$
$601$	8.64006e9	1.62351	0.811757	+	0.583995i	$0.198511\pi$
$602$	5.71206e8	0.106710
$603$	−2.94632e9	−0.547229
$604$	−2.79010e9	−0.515217
$605$	−3.26320e9	−0.599101
$606$	−2.19355e9	−0.400399
$607$	−7.80951e8	−0.141730	−0.0708652	−	0.997486i	$-0.522576\pi$
$607$	−7.80951e8	−0.141730	−0.0708652	+	0.997486i	$0.522576\pi$
$608$	−1.08819e9	−0.196355
$609$	8.22001e8	0.147473
$610$	6.61544e8	0.118006
$611$	−5.06697e9	−0.898679
$612$	4.26777e8	0.0752611
$613$	1.90752e9	0.334470	0.167235	−	0.985917i	$-0.446516\pi$
$613$	1.90752e9	0.334470	0.167235	+	0.985917i	$0.446516\pi$
$614$	−6.74258e9	−1.17554
$615$	−3.59334e9	−0.622924
$616$	7.55109e7	0.0130160
$617$	2.11043e9	0.361720	0.180860	−	0.983509i	$-0.442112\pi$
$617$	2.11043e9	0.361720	0.180860	+	0.983509i	$0.442112\pi$
$618$	−1.20361e9	−0.205128
$619$	−3.63085e9	−0.615306	−0.307653	−	0.951499i	$-0.599544\pi$
$619$	−3.63085e9	−0.615306	−0.307653	+	0.951499i	$0.599544\pi$
$620$	2.65117e9	0.446752
$621$	−4.48798e8	−0.0752022
$622$	−6.39212e9	−1.06507
$623$	−3.32855e8	−0.0551502
$624$	−1.21506e9	−0.200194
$625$	−2.21190e8	−0.0362397
$626$	3.27528e9	0.533628
$627$	8.91326e8	0.144411
$628$	−3.47220e9	−0.559430
$629$	−1.55903e9	−0.249792
$630$	1.52628e8	0.0243188
$631$	4.29045e9	0.679829	0.339915	−	0.940456i	$-0.389602\pi$
$631$	4.29045e9	0.679829	0.339915	+	0.940456i	$0.389602\pi$
$632$	−2.11836e9	−0.333804
$633$	−6.06288e9	−0.950093
$634$	2.06182e8	0.0321320
$635$	−1.47203e9	−0.228144
$636$	−1.43089e9	−0.220550
$637$	8.80633e9	1.34992
$638$	1.63190e9	0.248784
$639$	9.81336e8	0.148787
$640$	−3.69935e8	−0.0557822
$641$	−1.71528e9	−0.257236	−0.128618	−	0.991694i	$-0.541054\pi$
$641$	−1.71528e9	−0.257236	−0.128618	+	0.991694i	$0.541054\pi$
$642$	−3.42824e9	−0.511327
$643$	5.63520e8	0.0835931	0.0417966	−	0.999126i	$-0.486692\pi$
$643$	5.63520e8	0.0835931	0.0417966	+	0.999126i	$0.486692\pi$
$644$	2.16502e8	0.0319419
$645$	2.29214e9	0.336343
$646$	−2.43018e9	−0.354670
$647$	4.39751e8	0.0638325	0.0319163	−	0.999491i	$-0.489839\pi$
$647$	4.39751e8	0.0638325	0.0319163	+	0.999491i	$0.489839\pi$
$648$	−2.72098e8	−0.0392837
$649$	−2.04162e8	−0.0293169
$650$	−4.13181e9	−0.590124
$651$	−9.40691e8	−0.133633
$652$	1.63890e9	0.231572
$653$	6.05835e9	0.851449	0.425724	−	0.904853i	$-0.360019\pi$
$653$	6.05835e9	0.851449	0.425724	+	0.904853i	$0.360019\pi$
$654$	1.49410e9	0.208861
$655$	−6.60945e9	−0.919011
$656$	−3.09028e9	−0.427400
$657$	−1.65796e9	−0.228084
$658$	5.47376e8	0.0749023
$659$	−4.47780e6	−0.000609489 0	−0.000304744	−	1.00000i	$-0.500097\pi$
$659$	−4.47780e6	−0.000609489 0	−0.000304744		1.00000i	$0.500097\pi$
$660$	3.03010e8	0.0410255
$661$	−2.41977e9	−0.325888	−0.162944	−	0.986635i	$-0.552099\pi$
$661$	−2.41977e9	−0.325888	−0.162944	+	0.986635i	$0.552099\pi$
$662$	−1.56123e9	−0.209153
$663$	−2.71351e9	−0.361605
$664$	−1.52212e9	−0.201772
$665$	−8.69105e8	−0.114603
$666$	9.93984e8	0.130383
$667$	4.67893e9	0.610529
$668$	−5.73965e9	−0.745020
$669$	−1.25493e9	−0.162042
$670$	5.70345e9	0.732615
$671$	−4.66005e8	−0.0595473
$672$	1.31261e8	0.0166856
$673$	5.22908e9	0.661261	0.330630	−	0.943760i	$-0.392739\pi$
$673$	5.22908e9	0.661261	0.330630	+	0.943760i	$0.392739\pi$
$674$	5.50623e9	0.692699
$675$	−9.25267e8	−0.115799
$676$	3.70963e9	0.461868
$677$	1.04801e10	1.29809	0.649045	−	0.760750i	$-0.275169\pi$
$677$	1.04801e10	1.29809	0.649045	+	0.760750i	$0.275169\pi$
$678$	−5.72813e8	−0.0705844
$679$	8.47508e8	0.103896
$680$	−8.26150e8	−0.100758
$681$	4.07082e9	0.493931
$682$	−1.86754e9	−0.225436
$683$	7.04794e9	0.846428	0.423214	−	0.906030i	$-0.360902\pi$
$683$	7.04794e9	0.846428	0.423214	+	0.906030i	$0.360902\pi$
$684$	1.54940e9	0.185125
$685$	−3.36488e8	−0.0399993
$686$	−1.92879e9	−0.228113
$687$	−3.95452e9	−0.465313
$688$	1.97125e9	0.230771
$689$	9.09782e9	1.05967
$690$	8.68779e8	0.100679
$691$	4.95727e9	0.571570	0.285785	−	0.958294i	$-0.407746\pi$
$691$	4.95727e9	0.571570	0.285785	+	0.958294i	$0.407746\pi$
$692$	3.55769e9	0.408128
$693$	−1.07514e8	−0.0122716
$694$	−8.76892e9	−0.995837
$695$	5.68399e9	0.642253
$696$	2.83675e9	0.318925
$697$	−6.90131e9	−0.771999
$698$	−2.25151e9	−0.250599
$699$	1.37228e8	0.0151975
$700$	4.46352e8	0.0491852
$701$	−7.36087e9	−0.807079	−0.403539	−	0.914962i	$-0.632220\pi$
$701$	−7.36087e9	−0.807079	−0.403539	+	0.914962i	$0.632220\pi$
$702$	1.73004e9	0.188745
$703$	−5.66001e9	−0.614431
$704$	2.60590e8	0.0281484
$705$	2.19651e9	0.236087
$706$	3.06527e9	0.327832
$707$	−1.50666e9	−0.160342
$708$	−3.54895e8	−0.0375823
$709$	1.50447e10	1.58533	0.792667	−	0.609655i	$-0.208692\pi$
$709$	1.50447e10	1.58533	0.792667	+	0.609655i	$0.208692\pi$
$710$	−1.89966e9	−0.199192
$711$	3.01619e9	0.314713
$712$	−1.14869e9	−0.119268
$713$	−5.35453e9	−0.553233
$714$	2.93136e8	0.0301387
$715$	−1.92658e9	−0.197114
$716$	−9.27190e9	−0.944002
$717$	−1.02676e10	−1.04028
$718$	−3.35914e9	−0.338682
$719$	−8.77958e9	−0.880892	−0.440446	−	0.897779i	$-0.645180\pi$
$719$	−8.77958e9	−0.880892	−0.440446	+	0.897779i	$0.645180\pi$
$720$	5.26724e8	0.0525920
$721$	−8.26709e8	−0.0821446
$722$	−1.67169e9	−0.165301
$723$	8.83580e8	0.0869485
$724$	−9.72750e9	−0.952613
$725$	9.64634e9	0.940112
$726$	3.99578e9	0.387546
$727$	−2.88415e9	−0.278386	−0.139193	−	0.990265i	$-0.544451\pi$
$727$	−2.88415e9	−0.278386	−0.139193	+	0.990265i	$0.544451\pi$
$728$	−8.34576e8	−0.0801689
$729$	3.87420e8	0.0370370
$730$	3.20945e9	0.305352
$731$	4.40225e9	0.416835
$732$	−8.10059e8	−0.0763357
$733$	−2.06470e10	−1.93639	−0.968193	−	0.250203i	$-0.919503\pi$
$733$	−2.06470e10	−1.93639	−0.968193	+	0.250203i	$0.919503\pi$
$734$	−8.45805e9	−0.789467
$735$	−3.81751e9	−0.354629
$736$	7.47153e8	0.0690776
$737$	−4.01763e9	−0.369686
$738$	4.40003e9	0.402957
$739$	−9.32640e9	−0.850078	−0.425039	−	0.905175i	$-0.639740\pi$
$739$	−9.32640e9	−0.850078	−0.425039	+	0.905175i	$0.639740\pi$
$740$	−1.92415e9	−0.174553
$741$	−9.85129e9	−0.889466
$742$	−9.82821e8	−0.0883203
$743$	2.10353e9	0.188143	0.0940716	−	0.995565i	$-0.470012\pi$
$743$	2.10353e9	0.188143	0.0940716	+	0.995565i	$0.470012\pi$
$744$	−3.24635e9	−0.288995
$745$	−6.42384e9	−0.569178
$746$	8.62919e9	0.760999
$747$	2.16724e9	0.190232
$748$	5.81957e8	0.0508435
$749$	−2.35472e9	−0.204764
$750$	4.76785e9	0.412675
$751$	1.07679e10	0.927662	0.463831	−	0.885924i	$-0.346474\pi$
$751$	1.07679e10	0.927662	0.463831	+	0.885924i	$0.346474\pi$
$752$	1.88901e9	0.161984
$753$	−9.18346e9	−0.783833
$754$	−1.80365e10	−1.53233
$755$	−7.69015e9	−0.650310
$756$	−1.86893e8	−0.0157314
$757$	2.00654e10	1.68117	0.840584	−	0.541681i	$-0.182212\pi$
$757$	2.00654e10	1.68117	0.840584	+	0.541681i	$0.182212\pi$
$758$	−1.15945e10	−0.966962
$759$	−6.11986e8	−0.0508037
$760$	−2.99931e9	−0.247841
$761$	−3.91593e9	−0.322098	−0.161049	−	0.986946i	$-0.551488\pi$
$761$	−3.91593e9	−0.322098	−0.161049	+	0.986946i	$0.551488\pi$
$762$	1.80250e9	0.147582
$763$	1.02624e9	0.0836396
$764$	3.04038e9	0.246661
$765$	1.17630e9	0.0949952
$766$	6.56847e9	0.528036
$767$	2.25647e9	0.180570
$768$	4.52985e8	0.0360844
$769$	−1.15095e9	−0.0912670	−0.0456335	−	0.998958i	$-0.514531\pi$
$769$	−1.15095e9	−0.0912670	−0.0456335	+	0.998958i	$0.514531\pi$
$770$	2.08125e8	0.0164289
$771$	1.15589e10	0.908291
$772$	−1.50262e9	−0.117541
$773$	7.73925e9	0.602658	0.301329	−	0.953520i	$-0.402570\pi$
$773$	7.73925e9	0.602658	0.301329	+	0.953520i	$0.402570\pi$
$774$	−2.80672e9	−0.217573
$775$	−1.10392e10	−0.851886
$776$	2.92477e9	0.224686
$777$	6.82727e8	0.0522124
$778$	1.17689e10	0.896001
$779$	−2.50549e10	−1.89894
$780$	−3.34899e9	−0.252687
$781$	1.33816e9	0.100515
$782$	1.66856e9	0.124773
$783$	−4.03904e9	−0.300685
$784$	−3.28307e9	−0.243318
$785$	−9.57019e9	−0.706117
$786$	8.09325e9	0.594490
$787$	1.69996e10	1.24316	0.621579	−	0.783352i	$-0.286492\pi$
$787$	1.69996e10	1.24316	0.621579	+	0.783352i	$0.286492\pi$
$788$	9.37796e9	0.682758
$789$	−1.11268e10	−0.806494
$790$	−5.83871e9	−0.421329
$791$	−3.93442e8	−0.0282659
$792$	−3.71035e8	−0.0265386
$793$	5.15048e9	0.366768
$794$	8.77683e9	0.622252
$795$	−3.94387e9	−0.278380
$796$	−5.84273e9	−0.410601
$797$	−7.00414e9	−0.490062	−0.245031	−	0.969515i	$-0.578798\pi$
$797$	−7.00414e9	−0.490062	−0.245031	+	0.969515i	$0.578798\pi$
$798$	1.06422e9	0.0741345
$799$	4.21859e9	0.292586
$800$	1.54037e9	0.106368
$801$	1.63554e9	0.112447
$802$	−9.27156e9	−0.634662
$803$	−2.26081e9	−0.154084
$804$	−6.98386e9	−0.473914
$805$	5.96729e8	0.0403173
$806$	2.06408e10	1.38852
$807$	3.21992e9	0.215669
$808$	−5.19952e9	−0.346756
$809$	6.36135e9	0.422406	0.211203	−	0.977442i	$-0.432262\pi$
$809$	6.36135e9	0.422406	0.211203	+	0.977442i	$0.432262\pi$
$810$	−7.49965e8	−0.0495842
$811$	1.23349e10	0.812015	0.406008	−	0.913870i	$-0.366921\pi$
$811$	1.23349e10	0.812015	0.406008	+	0.913870i	$0.366921\pi$
$812$	1.94845e9	0.127715
$813$	−1.55975e10	−1.01798
$814$	1.35541e9	0.0880815
$815$	4.51719e9	0.292292
$816$	1.01162e9	0.0651781
$817$	1.59822e10	1.02532
$818$	−1.60412e10	−1.02471
$819$	1.18829e9	0.0755840
$820$	−8.51754e9	−0.539468
$821$	9.11844e9	0.575068	0.287534	−	0.957770i	$-0.407165\pi$
$821$	9.11844e9	0.575068	0.287534	+	0.957770i	$0.407165\pi$
$822$	4.12029e8	0.0258747
$823$	3.05772e9	0.191205	0.0956023	−	0.995420i	$-0.469522\pi$
$823$	3.05772e9	0.191205	0.0956023	+	0.995420i	$0.469522\pi$
$824$	−2.85299e9	−0.177646
$825$	−1.26170e9	−0.0782291
$826$	−2.43763e8	−0.0150500
$827$	2.33210e10	1.43377	0.716884	−	0.697193i	$-0.245568\pi$
$827$	2.33210e10	1.43377	0.716884	+	0.697193i	$0.245568\pi$
$828$	−1.06382e9	−0.0651270
$829$	−2.12050e10	−1.29270	−0.646350	−	0.763041i	$-0.723705\pi$
$829$	−2.12050e10	−1.29270	−0.646350	+	0.763041i	$0.723705\pi$
$830$	−4.19532e9	−0.254678
$831$	−3.19554e9	−0.193170
$832$	−2.88014e9	−0.173373
$833$	−7.33186e9	−0.439498
$834$	−6.96003e9	−0.415461
$835$	−1.58198e10	−0.940370
$836$	2.11277e9	0.125064
$837$	4.62224e9	0.272467
$838$	−4.22217e9	−0.247846
$839$	1.93177e10	1.12925	0.564623	−	0.825349i	$-0.309022\pi$
$839$	1.93177e10	1.12925	0.564623	+	0.825349i	$0.309022\pi$
$840$	3.61785e8	0.0210607
$841$	2.48590e10	1.44111
$842$	1.24081e10	0.716329
$843$	5.49482e9	0.315905
$844$	−1.43713e10	−0.822804
$845$	1.02246e10	0.582973
$846$	−2.68963e9	−0.152720
$847$	2.74454e9	0.155195
$848$	−3.39174e9	−0.191002
$849$	2.05119e9	0.115035
$850$	3.44000e9	0.192129
$851$	3.88617e9	0.216156
$852$	2.32613e9	0.128853
$853$	6.40981e8	0.0353609	0.0176805	−	0.999844i	$-0.494372\pi$
$853$	6.40981e8	0.0353609	0.0176805	+	0.999844i	$0.494372\pi$
$854$	−5.56397e8	−0.0305690
$855$	4.27050e9	0.233667
$856$	−8.12621e9	−0.442823
$857$	1.34538e10	0.730151	0.365075	−	0.930978i	$-0.381043\pi$
$857$	1.34538e10	0.730151	0.365075	+	0.930978i	$0.381043\pi$
$858$	2.35910e9	0.127509
$859$	1.49173e9	0.0803000	0.0401500	−	0.999194i	$-0.487216\pi$
$859$	1.49173e9	0.0803000	0.0401500	+	0.999194i	$0.487216\pi$
$860$	5.43322e9	0.291281
$861$	3.02220e9	0.161366
$862$	3.73872e9	0.198814
$863$	−8.76887e9	−0.464415	−0.232207	−	0.972666i	$-0.574595\pi$
$863$	−8.76887e9	−0.464415	−0.232207	+	0.972666i	$0.574595\pi$
$864$	−6.44973e8	−0.0340207
$865$	9.80582e9	0.515143
$866$	−1.44891e10	−0.758104
$867$	−8.81997e9	−0.459621
$868$	−2.22979e9	−0.115729
$869$	4.11290e9	0.212608
$870$	7.81873e9	0.402549
$871$	4.44044e10	2.27700
$872$	3.54157e9	0.180879
$873$	−4.16437e9	−0.211836
$874$	6.05766e9	0.306912
$875$	3.27484e9	0.165258
$876$	−3.92997e9	−0.197526
$877$	−2.84727e10	−1.42538	−0.712689	−	0.701480i	$-0.752523\pi$
$877$	−2.84727e10	−1.42538	−0.712689	+	0.701480i	$0.752523\pi$
$878$	−1.07913e10	−0.538074
$879$	1.65237e10	0.820625
$880$	7.18247e8	0.0355291
$881$	3.05231e10	1.50388	0.751938	−	0.659233i	$-0.229119\pi$
$881$	3.05231e10	1.50388	0.751938	+	0.659233i	$0.229119\pi$
$882$	4.67453e9	0.229403
$883$	−4.59850e8	−0.0224778	−0.0112389	−	0.999937i	$-0.503578\pi$
$883$	−4.59850e8	−0.0224778	−0.0112389	+	0.999937i	$0.503578\pi$
$884$	−6.43202e9	−0.313159
$885$	−9.78173e8	−0.0474367
$886$	−7.41690e9	−0.358265
$887$	3.04061e10	1.46294	0.731472	−	0.681871i	$-0.238834\pi$
$887$	3.04061e10	1.46294	0.731472	+	0.681871i	$0.238834\pi$
$888$	2.35611e9	0.112915
$889$	1.23806e9	0.0590999
$890$	−3.16606e9	−0.150541
$891$	5.28291e8	0.0250208
$892$	−2.97464e9	−0.140332
$893$	1.53154e10	0.719696
$894$	7.86598e9	0.368190
$895$	−2.55555e10	−1.19153
$896$	3.11137e8	0.0144502
$897$	6.76391e9	0.312913
$898$	2.27515e10	1.04844
$899$	−4.81891e10	−2.21202
$900$	−2.19323e9	−0.100285
$901$	−7.57454e9	−0.345000
$902$	5.99993e9	0.272222
$903$	−1.92782e9	−0.0871284
$904$	−1.35778e9	−0.0611279
$905$	−2.68113e10	−1.20240
$906$	9.41657e9	0.420673
$907$	−2.12004e10	−0.943450	−0.471725	−	0.881746i	$-0.656368\pi$
$907$	−2.12004e10	−0.943450	−0.471725	+	0.881746i	$0.656368\pi$
$908$	9.64934e9	0.427757
$909$	7.40323e9	0.326925
$910$	−2.30029e9	−0.101190
$911$	−4.33867e9	−0.190126	−0.0950632	−	0.995471i	$-0.530305\pi$
$911$	−4.33867e9	−0.190126	−0.0950632	+	0.995471i	$0.530305\pi$
$912$	3.67264e9	0.160323
$913$	2.95527e9	0.128514
$914$	2.76118e10	1.19614
$915$	−2.23271e9	−0.0963516
$916$	−9.37368e9	−0.402973
$917$	5.55893e9	0.238067
$918$	−1.44037e9	−0.0614505
$919$	1.36807e10	0.581441	0.290720	−	0.956808i	$-0.406105\pi$
$919$	1.36807e10	0.581441	0.290720	+	0.956808i	$0.406105\pi$
$920$	2.05933e9	0.0871903
$921$	2.27562e10	0.959823
$922$	−5.84968e9	−0.245795
$923$	−1.47899e10	−0.619097
$924$	−2.54849e8	−0.0106275
$925$	8.01194e9	0.332845
$926$	3.26589e9	0.135165
$927$	4.06217e9	0.167486
$928$	6.72414e9	0.276197
$929$	3.12214e10	1.27761	0.638804	−	0.769370i	$-0.279430\pi$
$929$	3.12214e10	1.27761	0.638804	+	0.769370i	$0.279430\pi$
$930$	−8.94770e9	−0.364771
$931$	−2.66180e10	−1.08107
$932$	3.25281e8	0.0131614
$933$	2.15734e10	0.869627
$934$	1.51803e10	0.609631
$935$	1.60401e9	0.0641751
$936$	4.10083e9	0.163458
$937$	7.76826e9	0.308486	0.154243	−	0.988033i	$-0.450706\pi$
$937$	7.76826e9	0.308486	0.154243	+	0.988033i	$0.450706\pi$
$938$	−4.79693e9	−0.189781
$939$	−1.10541e10	−0.435705
$940$	5.20655e9	0.204457
$941$	3.63624e10	1.42262	0.711310	−	0.702879i	$-0.248102\pi$
$941$	3.63624e10	1.42262	0.711310	+	0.702879i	$0.248102\pi$
$942$	1.17187e10	0.456773
$943$	1.72028e10	0.668047
$944$	−8.41232e8	−0.0325472
$945$	−5.15120e8	−0.0198563
$946$	−3.82727e9	−0.146984
$947$	−3.17601e10	−1.21523	−0.607614	−	0.794233i	$-0.707873\pi$
$947$	−3.17601e10	−1.21523	−0.607614	+	0.794233i	$0.707873\pi$
$948$	7.14948e9	0.272549
$949$	2.49873e10	0.949048
$950$	1.24888e10	0.472594
$951$	−6.95864e8	−0.0262357
$952$	6.94840e8	0.0261009
$953$	2.00489e10	0.750353	0.375176	−	0.926953i	$-0.377582\pi$
$953$	2.00489e10	0.750353	0.375176	+	0.926953i	$0.377582\pi$
$954$	4.82926e9	0.180078
$955$	8.37999e9	0.311338
$956$	−2.43380e10	−0.900911
$957$	−5.50768e9	−0.203131
$958$	−3.54202e9	−0.130158
$959$	2.83006e8	0.0103617
$960$	1.24853e9	0.0455460
$961$	2.76345e10	1.00443
$962$	−1.49805e10	−0.542517
$963$	1.15703e10	0.417497
$964$	2.09441e9	0.0752996
$965$	−4.14158e9	−0.148361
$966$	−7.30693e8	−0.0260804
$967$	4.55706e10	1.62066	0.810330	−	0.585973i	$-0.199288\pi$
$967$	4.55706e10	1.62066	0.810330	+	0.585973i	$0.199288\pi$
$968$	9.47148e9	0.335625
$969$	8.20185e9	0.289587
$970$	8.06135e9	0.283600
$971$	−4.47185e10	−1.56754	−0.783772	−	0.621049i	$-0.786707\pi$
$971$	−4.47185e10	−1.56754	−0.783772	+	0.621049i	$0.786707\pi$
$972$	9.18330e8	0.0320750
$973$	−4.78056e9	−0.166373
$974$	2.56881e10	0.890792
$975$	1.39449e10	0.481834
$976$	−1.92014e9	−0.0661087
$977$	2.22767e10	0.764224	0.382112	−	0.924116i	$-0.375197\pi$
$977$	2.22767e10	0.764224	0.382112	+	0.924116i	$0.375197\pi$
$978$	−5.53129e9	−0.189078
$979$	2.23024e9	0.0759648
$980$	−9.04892e9	−0.307118
$981$	−5.04259e9	−0.170534
$982$	−1.18593e10	−0.399641
$983$	−4.19806e9	−0.140965	−0.0704825	−	0.997513i	$-0.522454\pi$
$983$	−4.19806e9	−0.140965	−0.0704825	+	0.997513i	$0.522454\pi$
$984$	1.04297e10	0.348971
$985$	2.58478e10	0.861782
$986$	1.50165e10	0.498886
$987$	−1.84739e9	−0.0611575
$988$	−2.33512e10	−0.770300
$989$	−1.09734e10	−0.360707
$990$	−1.02266e9	−0.0334972
$991$	−2.53112e10	−0.826141	−0.413071	−	0.910699i	$-0.635544\pi$
$991$	−2.53112e10	−0.826141	−0.413071	+	0.910699i	$0.635544\pi$
$992$	−7.69505e9	−0.250277
$993$	5.26915e9	0.170773
$994$	1.59772e9	0.0516000
$995$	−1.61039e10	−0.518264
$996$	5.13716e9	0.164746
$997$	3.74471e10	1.19670	0.598349	−	0.801235i	$-0.295824\pi$
$997$	3.74471e10	1.19670	0.598349	+	0.801235i	$0.295824\pi$
$998$	1.83580e10	0.584614
$999$	−3.35470e9	−0.106457

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.8.a.c.1.5	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.8.a.c.1.5	✓	7	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	354.a (trivial)

\(f(q)\)	\(=\)	\(q-8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} +176.399 q^{5} -216.000 q^{6} -148.362 q^{7} -512.000 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q-8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} +176.399 q^{5} -216.000 q^{6} -148.362 q^{7} -512.000 q^{8} +729.000 q^{9} -1411.19 q^{10} +994.072 q^{11} +1728.00 q^{12} -10986.9 q^{13} +1186.89 q^{14} +4762.77 q^{15} +4096.00 q^{16} +9147.31 q^{17} -5832.00 q^{18} +33208.9 q^{19} +11289.5 q^{20} -4005.76 q^{21} -7952.58 q^{22} -22801.3 q^{23} -13824.0 q^{24} -47008.4 q^{25} +87895.0 q^{26} +19683.0 q^{27} -9495.14 q^{28} -205204. q^{29} -38102.2 q^{30} +234834. q^{31} -32768.0 q^{32} +26839.9 q^{33} -73178.5 q^{34} -26170.8 q^{35} +46656.0 q^{36} -170436. q^{37} -265671. q^{38} -296646. q^{39} -90316.2 q^{40} -754464. q^{41} +32046.1 q^{42} +481262. q^{43} +63620.6 q^{44} +128595. q^{45} +182410. q^{46} +461184. q^{47} +110592. q^{48} -801532. q^{49} +376067. q^{50} +246977. q^{51} -703160. q^{52} -828062. q^{53} -157464. q^{54} +175353. q^{55} +75961.1 q^{56} +896641. q^{57} +1.64164e6 q^{58} -205379. q^{59} +304817. q^{60} -468784. q^{61} -1.87867e6 q^{62} -108156. q^{63} +262144. q^{64} -1.93807e6 q^{65} -214720. q^{66} -4.04159e6 q^{67} +585428. q^{68} -615635. q^{69} +209367. q^{70} +1.34614e6 q^{71} -373248. q^{72} -2.27429e6 q^{73} +1.36349e6 q^{74} -1.26923e6 q^{75} +2.12537e6 q^{76} -147482. q^{77} +2.37317e6 q^{78} +4.13743e6 q^{79} +722530. q^{80} +531441. q^{81} +6.03571e6 q^{82} +2.97289e6 q^{83} -256369. q^{84} +1.61358e6 q^{85} -3.85010e6 q^{86} -5.54052e6 q^{87} -508965. q^{88} +2.24354e6 q^{89} -1.02876e6 q^{90} +1.63003e6 q^{91} -1.45928e6 q^{92} +6.34053e6 q^{93} -3.68947e6 q^{94} +5.85802e6 q^{95} -884736. q^{96} -5.71245e6 q^{97} +6.41225e6 q^{98} +724679. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 56 q^{2} + 189 q^{3} + 448 q^{4} - 158 q^{5} - 1512 q^{6} - 581 q^{7} - 3584 q^{8} + 5103 q^{9}+O(q^{10}) \) 7 * q - 56 * q^2 + 189 * q^3 + 448 * q^4 - 158 * q^5 - 1512 * q^6 - 581 * q^7 - 3584 * q^8 + 5103 * q^9	\( 7 q - 56 q^{2} + 189 q^{3} + 448 q^{4} - 158 q^{5} - 1512 q^{6} - 581 q^{7} - 3584 q^{8} + 5103 q^{9} + 1264 q^{10} - 2201 q^{11} + 12096 q^{12} - 8421 q^{13} + 4648 q^{14} - 4266 q^{15} + 28672 q^{16} - 2425 q^{17} - 40824 q^{18} - 37084 q^{19} - 10112 q^{20} - 15687 q^{21} + 17608 q^{22} + 99364 q^{23} - 96768 q^{24} + 101361 q^{25} + 67368 q^{26} + 137781 q^{27} - 37184 q^{28} + 2498 q^{29} + 34128 q^{30} - 57962 q^{31} - 229376 q^{32} - 59427 q^{33} + 19400 q^{34} + 190586 q^{35} + 326592 q^{36} - 6497 q^{37} + 296672 q^{38} - 227367 q^{39} + 80896 q^{40} - 319165 q^{41} + 125496 q^{42} - 633743 q^{43} - 140864 q^{44} - 115182 q^{45} - 794912 q^{46} - 1626560 q^{47} + 774144 q^{48} - 3846354 q^{49} - 810888 q^{50} - 65475 q^{51} - 538944 q^{52} - 1215602 q^{53} - 1102248 q^{54} - 3329556 q^{55} + 297472 q^{56} - 1001268 q^{57} - 19984 q^{58} - 1437653 q^{59} - 273024 q^{60} - 3180086 q^{61} + 463696 q^{62} - 423549 q^{63} + 1835008 q^{64} + 544086 q^{65} + 475416 q^{66} - 5349632 q^{67} - 155200 q^{68} + 2682828 q^{69} - 1524688 q^{70} + 1752423 q^{71} - 2612736 q^{72} - 1843424 q^{73} + 51976 q^{74} + 2736747 q^{75} - 2373376 q^{76} - 3885063 q^{77} + 1818936 q^{78} - 4769243 q^{79} - 647168 q^{80} + 3720087 q^{81} + 2553320 q^{82} + 5154441 q^{83} - 1003968 q^{84} - 4594902 q^{85} + 5069944 q^{86} + 67446 q^{87} + 1126912 q^{88} + 20086462 q^{89} + 921456 q^{90} + 6733847 q^{91} + 6359296 q^{92} - 1564974 q^{93} + 13012480 q^{94} + 12936212 q^{95} - 6193152 q^{96} + 6244248 q^{97} + 30770832 q^{98} - 1604529 q^{99}+O(q^{100}) \) 7 * q - 56 * q^2 + 189 * q^3 + 448 * q^4 - 158 * q^5 - 1512 * q^6 - 581 * q^7 - 3584 * q^8 + 5103 * q^9 + 1264 * q^10 - 2201 * q^11 + 12096 * q^12 - 8421 * q^13 + 4648 * q^14 - 4266 * q^15 + 28672 * q^16 - 2425 * q^17 - 40824 * q^18 - 37084 * q^19 - 10112 * q^20 - 15687 * q^21 + 17608 * q^22 + 99364 * q^23 - 96768 * q^24 + 101361 * q^25 + 67368 * q^26 + 137781 * q^27 - 37184 * q^28 + 2498 * q^29 + 34128 * q^30 - 57962 * q^31 - 229376 * q^32 - 59427 * q^33 + 19400 * q^34 + 190586 * q^35 + 326592 * q^36 - 6497 * q^37 + 296672 * q^38 - 227367 * q^39 + 80896 * q^40 - 319165 * q^41 + 125496 * q^42 - 633743 * q^43 - 140864 * q^44 - 115182 * q^45 - 794912 * q^46 - 1626560 * q^47 + 774144 * q^48 - 3846354 * q^49 - 810888 * q^50 - 65475 * q^51 - 538944 * q^52 - 1215602 * q^53 - 1102248 * q^54 - 3329556 * q^55 + 297472 * q^56 - 1001268 * q^57 - 19984 * q^58 - 1437653 * q^59 - 273024 * q^60 - 3180086 * q^61 + 463696 * q^62 - 423549 * q^63 + 1835008 * q^64 + 544086 * q^65 + 475416 * q^66 - 5349632 * q^67 - 155200 * q^68 + 2682828 * q^69 - 1524688 * q^70 + 1752423 * q^71 - 2612736 * q^72 - 1843424 * q^73 + 51976 * q^74 + 2736747 * q^75 - 2373376 * q^76 - 3885063 * q^77 + 1818936 * q^78 - 4769243 * q^79 - 647168 * q^80 + 3720087 * q^81 + 2553320 * q^82 + 5154441 * q^83 - 1003968 * q^84 - 4594902 * q^85 + 5069944 * q^86 + 67446 * q^87 + 1126912 * q^88 + 20086462 * q^89 + 921456 * q^90 + 6733847 * q^91 + 6359296 * q^92 - 1564974 * q^93 + 13012480 * q^94 + 12936212 * q^95 - 6193152 * q^96 + 6244248 * q^97 + 30770832 * q^98 - 1604529 * q^99

Introduction

L-functions

Modular forms

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