LMFDB - Embedded newform 354.8.a.c.1.2

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			1.2
Root			$-61.8652$ 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)

$f(q)$	$=$	$q-8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} -290.695 q^{5} -216.000 q^{6} +419.510 q^{7} -512.000 q^{8} +729.000 q^{9} +O(q^{10})$	\(q-8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} -290.695 q^{5} -216.000 q^{6} +419.510 q^{7} -512.000 q^{8} +729.000 q^{9} +2325.56 q^{10} +119.089 q^{11} +1728.00 q^{12} -4145.40 q^{13} -3356.08 q^{14} -7848.76 q^{15} +4096.00 q^{16} +26162.8 q^{17} -5832.00 q^{18} -15385.0 q^{19} -18604.5 q^{20} +11326.8 q^{21} -952.713 q^{22} -72543.0 q^{23} -13824.0 q^{24} +6378.52 q^{25} +33163.2 q^{26} +19683.0 q^{27} +26848.7 q^{28} +163981. q^{29} +62790.1 q^{30} +47951.4 q^{31} -32768.0 q^{32} +3215.41 q^{33} -209302. q^{34} -121950. q^{35} +46656.0 q^{36} +295103. q^{37} +123080. q^{38} -111926. q^{39} +148836. q^{40} +248846. q^{41} -90614.3 q^{42} -440629. q^{43} +7621.70 q^{44} -211917. q^{45} +580344. q^{46} -462236. q^{47} +110592. q^{48} -647554. q^{49} -51028.1 q^{50} +706395. q^{51} -265306. q^{52} +1.98497e6 q^{53} -157464. q^{54} -34618.6 q^{55} -214789. q^{56} -415396. q^{57} -1.31185e6 q^{58} -205379. q^{59} -502321. q^{60} +698018. q^{61} -383611. q^{62} +305823. q^{63} +262144. q^{64} +1.20505e6 q^{65} -25723.2 q^{66} -4.87466e6 q^{67} +1.67442e6 q^{68} -1.95866e6 q^{69} +975596. q^{70} -4.63534e6 q^{71} -373248. q^{72} -1.13266e6 q^{73} -2.36082e6 q^{74} +172220. q^{75} -984642. q^{76} +49959.1 q^{77} +895407. q^{78} -3.99257e6 q^{79} -1.19069e6 q^{80} +531441. q^{81} -1.99077e6 q^{82} +8.95050e6 q^{83} +724914. q^{84} -7.60539e6 q^{85} +3.52503e6 q^{86} +4.42748e6 q^{87} -60973.6 q^{88} +1.26724e7 q^{89} +1.69533e6 q^{90} -1.73904e6 q^{91} -4.64275e6 q^{92} +1.29469e6 q^{93} +3.69789e6 q^{94} +4.47235e6 q^{95} -884736. q^{96} +1.26303e7 q^{97} +5.18043e6 q^{98} +86816.0 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−290.695	−1.04002	−0.520011	−	0.854160i	$-0.674072\pi$
$5$	−290.695	−1.04002	−0.520011	+	0.854160i	$0.674072\pi$
$6$	−216.000	−0.408248
$7$	419.510	0.462274	0.231137	−	0.972921i	$-0.425755\pi$
$7$	419.510	0.462274	0.231137	+	0.972921i	$0.425755\pi$
$8$	−512.000	−0.353553
$9$	729.000	0.333333
$10$	2325.56	0.735406
$11$	119.089	0.0269772	0.0134886	−	0.999909i	$-0.495706\pi$
$11$	119.089	0.0269772	0.0134886	+	0.999909i	$0.495706\pi$
$12$	1728.00	0.288675
$13$	−4145.40	−0.523317	−0.261659	−	0.965160i	$-0.584269\pi$
$13$	−4145.40	−0.523317	−0.261659	+	0.965160i	$0.584269\pi$
$14$	−3356.08	−0.326877
$15$	−7848.76	−0.600457
$16$	4096.00	0.250000
$17$	26162.8	1.29155	0.645777	−	0.763526i	$-0.276534\pi$
$17$	26162.8	1.29155	0.645777	+	0.763526i	$0.276534\pi$
$18$	−5832.00	−0.235702
$19$	−15385.0	−0.514589	−0.257295	−	0.966333i	$-0.582831\pi$
$19$	−15385.0	−0.514589	−0.257295	+	0.966333i	$0.582831\pi$
$20$	−18604.5	−0.520011
$21$	11326.8	0.266894
$22$	−952.713	−0.0190758
$23$	−72543.0	−1.24322	−0.621610	−	0.783327i	$-0.713521\pi$
$23$	−72543.0	−1.24322	−0.621610	+	0.783327i	$0.713521\pi$
$24$	−13824.0	−0.204124
$25$	6378.52	0.0816450
$26$	33163.2	0.370041
$27$	19683.0	0.192450
$28$	26848.7	0.231137
$29$	163981.	1.24853	0.624267	−	0.781211i	$-0.285398\pi$
$29$	163981.	1.24853	0.624267	+	0.781211i	$0.285398\pi$
$30$	62790.1	0.424587
$31$	47951.4	0.289091	0.144546	−	0.989498i	$-0.453828\pi$
$31$	47951.4	0.289091	0.144546	+	0.989498i	$0.453828\pi$
$32$	−32768.0	−0.176777
$33$	3215.41	0.0155753
$34$	−209302.	−0.913267
$35$	−121950.	−0.480775
$36$	46656.0	0.166667
$37$	295103.	0.957783	0.478891	−	0.877874i	$-0.341039\pi$
$37$	295103.	0.957783	0.478891	+	0.877874i	$0.341039\pi$
$38$	123080.	0.363870
$39$	−111926.	−0.302137
$40$	148836.	0.367703
$41$	248846.	0.563881	0.281941	−	0.959432i	$-0.409022\pi$
$41$	248846.	0.563881	0.281941	+	0.959432i	$0.409022\pi$
$42$	−90614.3	−0.188723
$43$	−440629.	−0.845149	−0.422575	−	0.906328i	$-0.638874\pi$
$43$	−440629.	−0.845149	−0.422575	+	0.906328i	$0.638874\pi$
$44$	7621.70	0.0134886
$45$	−211917.	−0.346674
$46$	580344.	0.879089
$47$	−462236.	−0.649413	−0.324707	−	0.945815i	$-0.605266\pi$
$47$	−462236.	−0.649413	−0.324707	+	0.945815i	$0.605266\pi$
$48$	110592.	0.144338
$49$	−647554.	−0.786303
$50$	−51028.1	−0.0577317
$51$	706395.	0.745679
$52$	−265306.	−0.261659
$53$	1.98497e6	1.83142	0.915710	−	0.401840i	$-0.131629\pi$
$53$	1.98497e6	1.83142	0.915710	+	0.401840i	$0.131629\pi$
$54$	−157464.	−0.136083
$55$	−34618.6	−0.0280569
$56$	−214789.	−0.163439
$57$	−415396.	−0.297098
$58$	−1.31185e6	−0.882847
$59$	−205379.	−0.130189
$59$	−205379.	−0.130189
$60$	−502321.	−0.300228
$61$	698018.	0.393742	0.196871	−	0.980429i	$-0.436922\pi$
$61$	698018.	0.393742	0.196871	+	0.980429i	$0.436922\pi$
$62$	−383611.	−0.204419
$63$	305823.	0.154091
$64$	262144.	0.125000
$65$	1.20505e6	0.544261
$66$	−25723.2	−0.0110134
$67$	−4.87466e6	−1.98008	−0.990040	−	0.140787i	$-0.955037\pi$
$67$	−4.87466e6	−1.98008	−0.990040	+	0.140787i	$0.955037\pi$
$68$	1.67442e6	0.645777
$69$	−1.95866e6	−0.717773
$70$	975596.	0.339959
$71$	−4.63534e6	−1.53701	−0.768506	−	0.639843i	$-0.778999\pi$
$71$	−4.63534e6	−1.53701	−0.768506	+	0.639843i	$0.778999\pi$
$72$	−373248.	−0.117851
$73$	−1.13266e6	−0.340775	−0.170388	−	0.985377i	$-0.554502\pi$
$73$	−1.13266e6	−0.340775	−0.170388	+	0.985377i	$0.554502\pi$
$74$	−2.36082e6	−0.677255
$75$	172220.	0.0471378
$76$	−984642.	−0.257295
$77$	49959.1	0.0124709
$78$	895407.	0.213643
$79$	−3.99257e6	−0.911083	−0.455542	−	0.890214i	$-0.650554\pi$
$79$	−3.99257e6	−0.911083	−0.455542	+	0.890214i	$0.650554\pi$
$80$	−1.19069e6	−0.260005
$81$	531441.	0.111111
$82$	−1.99077e6	−0.398724
$83$	8.95050e6	1.71820	0.859100	−	0.511807i	$-0.171024\pi$
$83$	8.95050e6	1.71820	0.859100	+	0.511807i	$0.171024\pi$
$84$	724914.	0.133447
$85$	−7.60539e6	−1.34324
$86$	3.52503e6	0.597611
$87$	4.42748e6	0.720841
$88$	−60973.6	−0.00953790
$89$	1.26724e7	1.90543	0.952714	−	0.303868i	$-0.0982782\pi$
$89$	1.26724e7	1.90543	0.952714	+	0.303868i	$0.0982782\pi$
$90$	1.69533e6	0.245135
$91$	−1.73904e6	−0.241916
$92$	−4.64275e6	−0.621610
$93$	1.29469e6	0.166907
$94$	3.69789e6	0.459204
$95$	4.47235e6	0.535184
$96$	−884736.	−0.102062
$97$	1.26303e7	1.40512	0.702561	−	0.711623i	$-0.252040\pi$
$97$	1.26303e7	1.40512	0.702561	+	0.711623i	$0.252040\pi$
$98$	5.18043e6	0.556000
$99$	86816.0	0.00899242
$100$	408225.	0.0408225
$101$	4.78646e6	0.462264	0.231132	−	0.972922i	$-0.425757\pi$
$101$	4.78646e6	0.462264	0.231132	+	0.972922i	$0.425757\pi$
$102$	−5.65116e6	−0.527275
$103$	−1.78013e6	−0.160517	−0.0802586	−	0.996774i	$-0.525575\pi$
$103$	−1.78013e6	−0.160517	−0.0802586	+	0.996774i	$0.525575\pi$
$104$	2.12245e6	0.185021
$105$	−3.29264e6	−0.277576
$106$	−1.58797e7	−1.29501
$107$	−2.21910e7	−1.75119	−0.875595	−	0.483046i	$-0.839530\pi$
$107$	−2.21910e7	−1.75119	−0.875595	+	0.483046i	$0.839530\pi$
$108$	1.25971e6	0.0962250
$109$	−6.54416e6	−0.484018	−0.242009	−	0.970274i	$-0.577806\pi$
$109$	−6.54416e6	−0.484018	−0.242009	+	0.970274i	$0.577806\pi$
$110$	276949.	0.0198392
$111$	7.96777e6	0.552976
$112$	1.71831e6	0.115569
$113$	−5.09147e6	−0.331947	−0.165973	−	0.986130i	$-0.553077\pi$
$113$	−5.09147e6	−0.331947	−0.165973	+	0.986130i	$0.553077\pi$
$114$	3.32317e6	0.210080
$115$	2.10879e7	1.29298
$116$	1.04948e7	0.624267
$117$	−3.02200e6	−0.174439
$118$	1.64303e6	0.0920575
$119$	1.09756e7	0.597052
$120$	4.01857e6	0.212294
$121$	−1.94730e7	−0.999272
$122$	−5.58414e6	−0.278418
$123$	6.71885e6	0.325557
$124$	3.06889e6	0.144546
$125$	2.08563e7	0.955109
$126$	−2.44658e6	−0.108959
$127$	2.09881e7	0.909200	0.454600	−	0.890696i	$-0.349782\pi$
$127$	2.09881e7	0.909200	0.454600	+	0.890696i	$0.349782\pi$
$128$	−2.09715e6	−0.0883883
$129$	−1.18970e7	−0.487947
$130$	−9.64038e6	−0.384851
$131$	−3.99129e7	−1.55118	−0.775592	−	0.631235i	$-0.782548\pi$
$131$	−3.99129e7	−1.55118	−0.775592	+	0.631235i	$0.782548\pi$
$132$	205786.	0.00778766
$133$	−6.45418e6	−0.237881
$134$	3.89973e7	1.40013
$135$	−5.72175e6	−0.200152
$136$	−1.33953e7	−0.456633
$137$	−2.94778e6	−0.0979429	−0.0489715	−	0.998800i	$-0.515594\pi$
$137$	−2.94778e6	−0.0979429	−0.0489715	+	0.998800i	$0.515594\pi$
$138$	1.56693e7	0.507542
$139$	−1.72640e7	−0.545243	−0.272621	−	0.962121i	$-0.587891\pi$
$139$	−1.72640e7	−0.545243	−0.272621	+	0.962121i	$0.587891\pi$
$140$	−7.80477e6	−0.240388
$141$	−1.24804e7	−0.374939
$142$	3.70827e7	1.08683
$143$	−493672.	−0.0141177
$144$	2.98598e6	0.0833333
$145$	−4.76684e7	−1.29850
$146$	9.06125e6	0.240965
$147$	−1.74840e7	−0.453972
$148$	1.88866e7	0.478891
$149$	−2.44254e7	−0.604908	−0.302454	−	0.953164i	$-0.597806\pi$
$149$	−2.44254e7	−0.604908	−0.302454	+	0.953164i	$0.597806\pi$
$150$	−1.37776e6	−0.0333314
$151$	−3.86728e6	−0.0914084	−0.0457042	−	0.998955i	$-0.514553\pi$
$151$	−3.86728e6	−0.0914084	−0.0457042	+	0.998955i	$0.514553\pi$
$152$	7.87713e6	0.181935
$153$	1.90727e7	0.430518
$154$	−399673.	−0.00881825
$155$	−1.39392e7	−0.300661
$156$	−7.16326e6	−0.151069
$157$	−1.43454e7	−0.295845	−0.147923	−	0.988999i	$-0.547259\pi$
$157$	−1.43454e7	−0.295845	−0.147923	+	0.988999i	$0.547259\pi$
$158$	3.19406e7	0.644233
$159$	5.35941e7	1.05737
$160$	9.52549e6	0.183852
$161$	−3.04325e7	−0.574708
$162$	−4.25153e6	−0.0785674
$163$	−1.06607e8	−1.92809	−0.964046	−	0.265735i	$-0.914385\pi$
$163$	−1.06607e8	−1.92809	−0.964046	+	0.265735i	$0.914385\pi$
$164$	1.59262e7	0.281941
$165$	−934702.	−0.0161987
$166$	−7.16040e7	−1.21495
$167$	−1.51947e7	−0.252456	−0.126228	−	0.992001i	$-0.540287\pi$
$167$	−1.51947e7	−0.252456	−0.126228	+	0.992001i	$0.540287\pi$
$168$	−5.79931e6	−0.0943613
$169$	−4.55641e7	−0.726139
$170$	6.08431e7	0.949817
$171$	−1.12157e7	−0.171530
$172$	−2.82002e7	−0.422575
$173$	−8.14102e7	−1.19541	−0.597706	−	0.801715i	$-0.703921\pi$
$173$	−8.14102e7	−1.19541	−0.597706	+	0.801715i	$0.703921\pi$
$174$	−3.54199e7	−0.509712
$175$	2.67585e6	0.0377424
$176$	487789.	0.00674431
$177$	−5.54523e6	−0.0751646
$178$	−1.01379e8	−1.34734
$179$	−3.55776e7	−0.463651	−0.231826	−	0.972757i	$-0.574470\pi$
$179$	−3.55776e7	−0.463651	−0.231826	+	0.972757i	$0.574470\pi$
$180$	−1.35627e7	−0.173337
$181$	−9.62410e7	−1.20638	−0.603191	−	0.797596i	$-0.706104\pi$
$181$	−9.62410e7	−1.20638	−0.603191	+	0.797596i	$0.706104\pi$
$182$	1.39123e7	0.171061
$183$	1.88465e7	0.227327
$184$	3.71420e7	0.439545
$185$	−8.57848e7	−0.996115
$186$	−1.03575e7	−0.118021
$187$	3.11570e6	0.0348426
$188$	−2.95831e7	−0.324707
$189$	8.25722e6	0.0889647
$190$	−3.57788e7	−0.378432
$191$	−1.34033e8	−1.39185	−0.695927	−	0.718112i	$-0.745006\pi$
$191$	−1.34033e8	−1.39185	−0.695927	+	0.718112i	$0.745006\pi$
$192$	7.07789e6	0.0721688
$193$	−1.18627e8	−1.18777	−0.593885	−	0.804550i	$-0.702406\pi$
$193$	−1.18627e8	−1.18777	−0.593885	+	0.804550i	$0.702406\pi$
$194$	−1.01043e8	−0.993571
$195$	3.25363e7	0.314229
$196$	−4.14435e7	−0.393151
$197$	−1.06120e8	−0.988934	−0.494467	−	0.869196i	$-0.664637\pi$
$197$	−1.06120e8	−0.988934	−0.494467	+	0.869196i	$0.664637\pi$
$198$	−694528.	−0.00635860
$199$	−2.85527e6	−0.0256839	−0.0128420	−	0.999918i	$-0.504088\pi$
$199$	−2.85527e6	−0.0256839	−0.0128420	+	0.999918i	$0.504088\pi$
$200$	−3.26580e6	−0.0288659
$201$	−1.31616e8	−1.14320
$202$	−3.82917e7	−0.326870
$203$	6.87917e7	0.577165
$204$	4.52093e7	0.372840
$205$	−7.23383e7	−0.586449
$206$	1.42411e7	0.113503
$207$	−5.28838e7	−0.414407
$208$	−1.69796e7	−0.130829
$209$	−1.83219e6	−0.0138822
$210$	2.63411e7	0.196276
$211$	1.96620e8	1.44092	0.720460	−	0.693496i	$-0.243931\pi$
$211$	1.96620e8	1.44092	0.720460	+	0.693496i	$0.243931\pi$
$212$	1.27038e8	0.915710
$213$	−1.25154e8	−0.887394
$214$	1.77528e8	1.23828
$215$	1.28089e8	0.878973
$216$	−1.00777e7	−0.0680414
$217$	2.01161e7	0.133639
$218$	5.23533e7	0.342252
$219$	−3.05817e7	−0.196747
$220$	−2.21559e6	−0.0140285
$221$	−1.08455e8	−0.675893
$222$	−6.37422e7	−0.391013
$223$	−2.83993e8	−1.71491	−0.857454	−	0.514560i	$-0.827955\pi$
$223$	−2.83993e8	−1.71491	−0.857454	+	0.514560i	$0.827955\pi$
$224$	−1.37465e7	−0.0817193
$225$	4.64994e6	0.0272150
$226$	4.07318e7	0.234722
$227$	−1.22833e8	−0.696988	−0.348494	−	0.937311i	$-0.613307\pi$
$227$	−1.22833e8	−0.696988	−0.348494	+	0.937311i	$0.613307\pi$
$228$	−2.65853e7	−0.148549
$229$	4.28696e7	0.235899	0.117949	−	0.993020i	$-0.462368\pi$
$229$	4.28696e7	0.235899	0.117949	+	0.993020i	$0.462368\pi$
$230$	−1.68703e8	−0.914272
$231$	1.34890e6	0.00720007
$232$	−8.39582e7	−0.441423
$233$	2.12450e8	1.10030	0.550149	−	0.835066i	$-0.314571\pi$
$233$	2.12450e8	1.10030	0.550149	+	0.835066i	$0.314571\pi$
$234$	2.41760e7	0.123347
$235$	1.34370e8	0.675404
$236$	−1.31443e7	−0.0650945
$237$	−1.07799e8	−0.526014
$238$	−8.78045e7	−0.422180
$239$	−2.26672e8	−1.07400	−0.537001	−	0.843582i	$-0.680443\pi$
$239$	−2.26672e8	−1.07400	−0.537001	+	0.843582i	$0.680443\pi$
$240$	−3.21485e7	−0.150114
$241$	7.63930e7	0.351556	0.175778	−	0.984430i	$-0.443756\pi$
$241$	7.63930e7	0.351556	0.175778	+	0.984430i	$0.443756\pi$
$242$	1.55784e8	0.706592
$243$	1.43489e7	0.0641500
$244$	4.46731e7	0.196871
$245$	1.88241e8	0.817772
$246$	−5.37508e7	−0.230204
$247$	6.37772e7	0.269293
$248$	−2.45511e7	−0.102209
$249$	2.41663e8	0.992004
$250$	−1.66851e8	−0.675364
$251$	−1.46844e8	−0.586137	−0.293068	−	0.956092i	$-0.594676\pi$
$251$	−1.46844e8	−0.586137	−0.293068	+	0.956092i	$0.594676\pi$
$252$	1.95727e7	0.0770457
$253$	−8.63908e6	−0.0335386
$254$	−1.67904e8	−0.642901
$255$	−2.05345e8	−0.775522
$256$	1.67772e7	0.0625000
$257$	5.40734e7	0.198709	0.0993545	−	0.995052i	$-0.468322\pi$
$257$	5.40734e7	0.198709	0.0993545	+	0.995052i	$0.468322\pi$
$258$	9.51758e7	0.345031
$259$	1.23799e8	0.442758
$260$	7.71231e7	0.272131
$261$	1.19542e8	0.416178
$262$	3.19303e8	1.09685
$263$	2.59643e8	0.880101	0.440050	−	0.897973i	$-0.354961\pi$
$263$	2.59643e8	0.880101	0.440050	+	0.897973i	$0.354961\pi$
$264$	−1.64629e6	−0.00550671
$265$	−5.77020e8	−1.90472
$266$	5.16334e7	0.168207
$267$	3.42154e8	1.10010
$268$	−3.11978e8	−0.990040
$269$	3.35075e8	1.04956	0.524782	−	0.851237i	$-0.324147\pi$
$269$	3.35075e8	1.04956	0.524782	+	0.851237i	$0.324147\pi$
$270$	4.57740e7	0.141529
$271$	−2.54988e8	−0.778265	−0.389132	−	0.921182i	$-0.627225\pi$
$271$	−2.54988e8	−0.778265	−0.389132	+	0.921182i	$0.627225\pi$
$272$	1.07163e8	0.322889
$273$	−4.69541e7	−0.139670
$274$	2.35822e7	0.0692561
$275$	759612.	0.00220256
$276$	−1.25354e8	−0.358887
$277$	−6.62398e8	−1.87258	−0.936288	−	0.351233i	$-0.885763\pi$
$277$	−6.62398e8	−1.87258	−0.936288	+	0.351233i	$0.885763\pi$
$278$	1.38112e8	0.385545
$279$	3.49566e7	0.0963638
$280$	6.24382e7	0.169980
$281$	2.71773e7	0.0730691	0.0365345	−	0.999332i	$-0.488368\pi$
$281$	2.71773e7	0.0730691	0.0365345	+	0.999332i	$0.488368\pi$
$282$	9.98429e7	0.265122
$283$	1.01502e8	0.266210	0.133105	−	0.991102i	$-0.457505\pi$
$283$	1.01502e8	0.266210	0.133105	+	0.991102i	$0.457505\pi$
$284$	−2.96662e8	−0.768506
$285$	1.20753e8	0.308989
$286$	3.94938e6	0.00998269
$287$	1.04394e8	0.260668
$288$	−2.38879e7	−0.0589256
$289$	2.74152e8	0.668112
$290$	3.81347e8	0.918180
$291$	3.41019e8	0.811248
$292$	−7.24900e7	−0.170388
$293$	−5.73758e7	−0.133258	−0.0666288	−	0.997778i	$-0.521224\pi$
$293$	−5.73758e7	−0.133258	−0.0666288	+	0.997778i	$0.521224\pi$
$294$	1.39872e8	0.321007
$295$	5.97026e7	0.135399
$296$	−1.51093e8	−0.338627
$297$	2.34403e6	0.00519177
$298$	1.95403e8	0.427735
$299$	3.00720e8	0.650598
$300$	1.10221e7	0.0235689
$301$	−1.84848e8	−0.390691
$302$	3.09382e7	0.0646355
$303$	1.29234e8	0.266888
$304$	−6.30171e7	−0.128647
$305$	−2.02910e8	−0.409501
$306$	−1.52581e8	−0.304422
$307$	6.30142e8	1.24295	0.621475	−	0.783434i	$-0.286534\pi$
$307$	6.30142e8	1.24295	0.621475	+	0.783434i	$0.286534\pi$
$308$	3.19738e6	0.00623544
$309$	−4.80635e7	−0.0926747
$310$	1.11514e8	0.212600
$311$	−3.79131e8	−0.714706	−0.357353	−	0.933969i	$-0.616321\pi$
$311$	−3.79131e8	−0.714706	−0.357353	+	0.933969i	$0.616321\pi$
$312$	5.73061e7	0.106822
$313$	8.31629e8	1.53294	0.766468	−	0.642282i	$-0.222012\pi$
$313$	8.31629e8	1.53294	0.766468	+	0.642282i	$0.222012\pi$
$314$	1.14763e8	0.209194
$315$	−8.89012e7	−0.160258
$316$	−2.55525e8	−0.455542
$317$	−9.33091e8	−1.64519	−0.822596	−	0.568626i	$-0.807475\pi$
$317$	−9.33091e8	−1.64519	−0.822596	+	0.568626i	$0.807475\pi$
$318$	−4.28753e8	−0.747674
$319$	1.95283e7	0.0336820
$320$	−7.62039e7	−0.130003
$321$	−5.99156e8	−1.01105
$322$	2.43460e8	0.406380
$323$	−4.02515e8	−0.664620
$324$	3.40122e7	0.0555556
$325$	−2.64415e7	−0.0427263
$326$	8.52853e8	1.36337
$327$	−1.76692e8	−0.279448
$328$	−1.27409e8	−0.199362
$329$	−1.93913e8	−0.300207
$330$	7.47762e6	0.0114542
$331$	−9.93373e8	−1.50562	−0.752808	−	0.658240i	$-0.771301\pi$
$331$	−9.93373e8	−1.50562	−0.752808	+	0.658240i	$0.771301\pi$
$332$	5.72832e8	0.859100
$333$	2.15130e8	0.319261
$334$	1.21558e8	0.178513
$335$	1.41704e9	2.05933
$336$	4.63945e7	0.0667235
$337$	−4.25441e8	−0.605529	−0.302764	−	0.953065i	$-0.597909\pi$
$337$	−4.25441e8	−0.605529	−0.302764	+	0.953065i	$0.597909\pi$
$338$	3.64513e8	0.513458
$339$	−1.37470e8	−0.191650
$340$	−4.86745e8	−0.671622
$341$	5.71049e6	0.00779889
$342$	8.97255e7	0.121290
$343$	−6.17141e8	−0.825762
$344$	2.25602e8	0.298805
$345$	5.69372e8	0.746500
$346$	6.51282e8	0.845284
$347$	−8.72635e8	−1.12119	−0.560595	−	0.828090i	$-0.689428\pi$
$347$	−8.72635e8	−1.12119	−0.560595	+	0.828090i	$0.689428\pi$
$348$	2.83359e8	0.360421
$349$	−2.30586e8	−0.290365	−0.145182	−	0.989405i	$-0.546377\pi$
$349$	−2.30586e8	−0.290365	−0.145182	+	0.989405i	$0.546377\pi$
$350$	−2.14068e7	−0.0266879
$351$	−8.15940e7	−0.100712
$352$	−3.90231e6	−0.00476895
$353$	8.97923e8	1.08649	0.543247	−	0.839573i	$-0.317195\pi$
$353$	8.97923e8	1.08649	0.543247	+	0.839573i	$0.317195\pi$
$354$	4.43619e7	0.0531494
$355$	1.34747e9	1.59852
$356$	8.11031e8	0.952714
$357$	2.96340e8	0.344708
$358$	2.84621e8	0.327851
$359$	1.06992e9	1.22046	0.610228	−	0.792226i	$-0.291078\pi$
$359$	1.06992e9	1.22046	0.610228	+	0.792226i	$0.291078\pi$
$360$	1.08501e8	0.122568
$361$	−6.57173e8	−0.735198
$362$	7.69928e8	0.853041
$363$	−5.25771e8	−0.576930
$364$	−1.11299e8	−0.120958
$365$	3.29258e8	0.354414
$366$	−1.50772e8	−0.160745
$367$	2.33035e8	0.246088	0.123044	−	0.992401i	$-0.460734\pi$
$367$	2.33035e8	0.246088	0.123044	+	0.992401i	$0.460734\pi$
$368$	−2.97136e8	−0.310805
$369$	1.81409e8	0.187960
$370$	6.86279e8	0.704359
$371$	8.32715e8	0.846618
$372$	8.28600e7	0.0834535
$373$	−1.26701e9	−1.26416	−0.632078	−	0.774905i	$-0.717798\pi$
$373$	−1.26701e9	−1.26416	−0.632078	+	0.774905i	$0.717798\pi$
$374$	−2.49256e7	−0.0246374
$375$	5.63121e8	0.551432
$376$	2.36665e8	0.229602
$377$	−6.79767e8	−0.653379
$378$	−6.60578e7	−0.0629075
$379$	1.95439e9	1.84405	0.922027	−	0.387125i	$-0.126532\pi$
$379$	1.95439e9	1.84405	0.922027	+	0.387125i	$0.126532\pi$
$380$	2.86230e8	0.267592
$381$	5.66678e8	0.524927
$382$	1.07226e9	0.984190
$383$	4.57342e8	0.415954	0.207977	−	0.978134i	$-0.433312\pi$
$383$	4.57342e8	0.415954	0.207977	+	0.978134i	$0.433312\pi$
$384$	−5.66231e7	−0.0510310
$385$	−1.45229e7	−0.0129700
$386$	9.49014e8	0.839880
$387$	−3.21218e8	−0.281716
$388$	8.08342e8	0.702561
$389$	1.07011e9	0.921734	0.460867	−	0.887469i	$-0.347539\pi$
$389$	1.07011e9	0.921734	0.460867	+	0.887469i	$0.347539\pi$
$390$	−2.60290e8	−0.222194
$391$	−1.89793e9	−1.60569
$392$	3.31548e8	0.278000
$393$	−1.07765e9	−0.895576
$394$	8.48963e8	0.699282
$395$	1.16062e9	0.947546
$396$	5.55622e6	0.00449621
$397$	−1.24269e9	−0.996769	−0.498384	−	0.866956i	$-0.666073\pi$
$397$	−1.24269e9	−0.996769	−0.498384	+	0.866956i	$0.666073\pi$
$398$	2.28422e7	0.0181613
$399$	−1.74263e8	−0.137341
$400$	2.61264e7	0.0204113
$401$	−7.35190e8	−0.569370	−0.284685	−	0.958621i	$-0.591889\pi$
$401$	−7.35190e8	−0.569370	−0.284685	+	0.958621i	$0.591889\pi$
$402$	1.05293e9	0.808364
$403$	−1.98778e8	−0.151287
$404$	3.06334e8	0.231132
$405$	−1.54487e8	−0.115558
$406$	−5.50334e8	−0.408117
$407$	3.51435e7	0.0258383
$408$	−3.61674e8	−0.263637
$409$	−1.45364e9	−1.05057	−0.525287	−	0.850925i	$-0.676042\pi$
$409$	−1.45364e9	−1.05057	−0.525287	+	0.850925i	$0.676042\pi$
$410$	5.78707e8	0.414682
$411$	−7.95901e7	−0.0565474
$412$	−1.13928e8	−0.0802586
$413$	−8.61586e7	−0.0601830
$414$	4.23071e8	0.293030
$415$	−2.60186e9	−1.78697
$416$	1.35837e8	0.0925103
$417$	−4.66128e8	−0.314796
$418$	1.46575e7	0.00981620
$419$	1.80447e9	1.19840	0.599199	−	0.800600i	$-0.295486\pi$
$419$	1.80447e9	1.19840	0.599199	+	0.800600i	$0.295486\pi$
$420$	−2.10729e8	−0.138788
$421$	1.91877e9	1.25324	0.626622	−	0.779323i	$-0.284437\pi$
$421$	1.91877e9	1.25324	0.626622	+	0.779323i	$0.284437\pi$
$422$	−1.57296e9	−1.01888
$423$	−3.36970e8	−0.216471
$424$	−1.01630e9	−0.647505
$425$	1.66880e8	0.105449
$426$	1.00123e9	0.627482
$427$	2.92826e8	0.182017
$428$	−1.42022e9	−0.875595
$429$	−1.33292e7	−0.00815084
$430$	−1.02471e9	−0.621528
$431$	9.27622e8	0.558086	0.279043	−	0.960279i	$-0.409983\pi$
$431$	9.27622e8	0.558086	0.279043	+	0.960279i	$0.409983\pi$
$432$	8.06216e7	0.0481125
$433$	4.10556e8	0.243033	0.121516	−	0.992589i	$-0.461224\pi$
$433$	4.10556e8	0.243033	0.121516	+	0.992589i	$0.461224\pi$
$434$	−1.60929e8	−0.0944974
$435$	−1.28705e9	−0.749691
$436$	−4.18826e8	−0.242009
$437$	1.11608e9	0.639747
$438$	2.44654e8	0.139121
$439$	−1.85064e9	−1.04399	−0.521996	−	0.852948i	$-0.674812\pi$
$439$	−1.85064e9	−1.04399	−0.521996	+	0.852948i	$0.674812\pi$
$440$	1.77247e7	0.00991962
$441$	−4.72067e8	−0.262101
$442$	8.67642e8	0.477928
$443$	1.82745e9	0.998691	0.499346	−	0.866403i	$-0.333574\pi$
$443$	1.82745e9	0.998691	0.499346	+	0.866403i	$0.333574\pi$
$444$	5.09937e8	0.276488
$445$	−3.68379e9	−1.98169
$446$	2.27195e9	1.21262
$447$	−6.59486e8	−0.349244
$448$	1.09972e8	0.0577843
$449$	3.39569e9	1.77038	0.885190	−	0.465230i	$-0.154028\pi$
$449$	3.39569e9	1.77038	0.885190	+	0.465230i	$0.154028\pi$
$450$	−3.71995e7	−0.0192439
$451$	2.96349e7	0.0152120
$452$	−3.25854e8	−0.165973
$453$	−1.04417e8	−0.0527747
$454$	9.82666e8	0.492845
$455$	5.05530e8	0.251598
$456$	2.12683e8	0.105040
$457$	3.25985e9	1.59768	0.798841	−	0.601542i	$-0.205447\pi$
$457$	3.25985e9	1.59768	0.798841	+	0.601542i	$0.205447\pi$
$458$	−3.42957e8	−0.166806
$459$	5.14962e8	0.248560
$460$	1.34962e9	0.646488
$461$	−2.92073e9	−1.38848	−0.694239	−	0.719745i	$-0.744259\pi$
$461$	−2.92073e9	−1.38848	−0.694239	+	0.719745i	$0.744259\pi$
$462$	−1.07912e7	−0.00509122
$463$	−1.52497e8	−0.0714050	−0.0357025	−	0.999362i	$-0.511367\pi$
$463$	−1.52497e8	−0.0714050	−0.0357025	+	0.999362i	$0.511367\pi$
$464$	6.71666e8	0.312133
$465$	−3.76359e8	−0.173587
$466$	−1.69960e9	−0.778029
$467$	1.83190e8	0.0832324	0.0416162	−	0.999134i	$-0.486749\pi$
$467$	1.83190e8	0.0832324	0.0416162	+	0.999134i	$0.486749\pi$
$468$	−1.93408e8	−0.0872196
$469$	−2.04497e9	−0.915340
$470$	−1.07496e9	−0.477583
$471$	−3.87327e8	−0.170806
$472$	1.05154e8	0.0460287
$473$	−5.24741e7	−0.0227998
$474$	8.62396e8	0.371948
$475$	−9.81337e7	−0.0420136
$476$	7.02436e8	0.298526
$477$	1.44704e9	0.610473
$478$	1.81338e9	0.759434
$479$	−3.39912e9	−1.41316	−0.706582	−	0.707631i	$-0.749764\pi$
$479$	−3.39912e9	−1.41316	−0.706582	+	0.707631i	$0.749764\pi$
$480$	2.57188e8	0.106147
$481$	−1.22332e9	−0.501224
$482$	−6.11144e8	−0.248587
$483$	−8.21678e8	−0.331808
$484$	−1.24627e9	−0.499636
$485$	−3.67158e9	−1.46136
$486$	−1.14791e8	−0.0453609
$487$	1.44701e9	0.567700	0.283850	−	0.958869i	$-0.408388\pi$
$487$	1.44701e9	0.567700	0.283850	+	0.958869i	$0.408388\pi$
$488$	−3.57385e8	−0.139209
$489$	−2.87838e9	−1.11318
$490$	−1.50593e9	−0.578252
$491$	5.05033e9	1.92546	0.962730	−	0.270463i	$-0.0871768\pi$
$491$	5.05033e9	1.92546	0.962730	+	0.270463i	$0.0871768\pi$
$492$	4.30006e8	0.162778
$493$	4.29020e9	1.61255
$494$	−5.10217e8	−0.190419
$495$	−2.52370e7	−0.00935231
$496$	1.96409e8	0.0722729
$497$	−1.94457e9	−0.710521
$498$	−1.93331e9	−0.701453
$499$	−8.23477e8	−0.296688	−0.148344	−	0.988936i	$-0.547394\pi$
$499$	−8.23477e8	−0.296688	−0.148344	+	0.988936i	$0.547394\pi$
$500$	1.33481e9	0.477555
$501$	−4.10258e8	−0.145755
$502$	1.17475e9	0.414461
$503$	−3.30072e9	−1.15643	−0.578216	−	0.815884i	$-0.696251\pi$
$503$	−3.30072e9	−1.15643	−0.578216	+	0.815884i	$0.696251\pi$
$504$	−1.56581e8	−0.0544795
$505$	−1.39140e9	−0.480764
$506$	6.91126e7	0.0237154
$507$	−1.23023e9	−0.419236
$508$	1.34324e9	0.454600
$509$	2.68105e9	0.901140	0.450570	−	0.892741i	$-0.351221\pi$
$509$	2.68105e9	0.901140	0.450570	+	0.892741i	$0.351221\pi$
$510$	1.64276e9	0.548377
$511$	−4.75161e8	−0.157532
$512$	−1.34218e8	−0.0441942
$513$	−3.02823e8	−0.0990327
$514$	−4.32587e8	−0.140509
$515$	5.17475e8	0.166941
$516$	−7.61407e8	−0.243974
$517$	−5.50472e7	−0.0175194
$518$	−9.90389e8	−0.313077
$519$	−2.19808e9	−0.690171
$520$	−6.16985e8	−0.192425
$521$	3.02288e9	0.936459	0.468230	−	0.883607i	$-0.344892\pi$
$521$	3.02288e9	0.936459	0.468230	+	0.883607i	$0.344892\pi$
$522$	−9.56337e8	−0.294282
$523$	−5.44377e8	−0.166396	−0.0831981	−	0.996533i	$-0.526513\pi$
$523$	−5.44377e8	−0.166396	−0.0831981	+	0.996533i	$0.526513\pi$
$524$	−2.55442e9	−0.775592
$525$	7.22481e7	0.0217906
$526$	−2.07715e9	−0.622325
$527$	1.25454e9	0.373377
$528$	1.31703e7	0.00389383
$529$	1.85766e9	0.545595
$530$	4.61616e9	1.34684
$531$	−1.49721e8	−0.0433963
$532$	−4.13067e8	−0.118941
$533$	−1.03157e9	−0.295089
$534$	−2.73723e9	−0.777888
$535$	6.45080e9	1.82128
$536$	2.49583e9	0.700064
$537$	−9.60596e8	−0.267689
$538$	−2.68060e9	−0.742153
$539$	−7.71166e7	−0.0212123
$540$	−3.66192e8	−0.100076
$541$	−1.06836e9	−0.290086	−0.145043	−	0.989425i	$-0.546332\pi$
$541$	−1.06836e9	−0.290086	−0.145043	+	0.989425i	$0.546332\pi$
$542$	2.03990e9	0.550316
$543$	−2.59851e9	−0.696505
$544$	−8.57302e8	−0.228317
$545$	1.90235e9	0.503389
$546$	3.75633e8	0.0987618
$547$	−1.85998e9	−0.485906	−0.242953	−	0.970038i	$-0.578116\pi$
$547$	−1.85998e9	−0.485906	−0.242953	+	0.970038i	$0.578116\pi$
$548$	−1.88658e8	−0.0489715
$549$	5.08855e8	0.131247
$550$	−6.07690e6	−0.00155744
$551$	−2.52285e9	−0.642482
$552$	1.00283e9	0.253771
$553$	−1.67493e9	−0.421170
$554$	5.29918e9	1.32411
$555$	−2.31619e9	−0.575107
$556$	−1.10490e9	−0.272621
$557$	4.52218e9	1.10880	0.554402	−	0.832249i	$-0.312947\pi$
$557$	4.52218e9	1.10880	0.554402	+	0.832249i	$0.312947\pi$
$558$	−2.79652e8	−0.0681395
$559$	1.82658e9	0.442281
$560$	−4.99505e8	−0.120194
$561$	8.41239e7	0.0201164
$562$	−2.17418e8	−0.0516677
$563$	−2.73686e9	−0.646359	−0.323180	−	0.946338i	$-0.604752\pi$
$563$	−2.73686e9	−0.646359	−0.323180	+	0.946338i	$0.604752\pi$
$564$	−7.98744e8	−0.187469
$565$	1.48006e9	0.345232
$566$	−8.12019e8	−0.188239
$567$	2.22945e8	0.0513638
$568$	2.37329e9	0.543416
$569$	−3.87764e9	−0.882418	−0.441209	−	0.897404i	$-0.645450\pi$
$569$	−3.87764e9	−0.882418	−0.441209	+	0.897404i	$0.645450\pi$
$570$	−9.66027e8	−0.218488
$571$	7.21591e9	1.62205	0.811026	−	0.585010i	$-0.198910\pi$
$571$	7.21591e9	1.62205	0.811026	+	0.585010i	$0.198910\pi$
$572$	−3.15950e7	−0.00705883
$573$	−3.61888e9	−0.803587
$574$	−8.35149e8	−0.184320
$575$	−4.62717e8	−0.101503
$576$	1.91103e8	0.0416667
$577$	4.24639e9	0.920247	0.460124	−	0.887855i	$-0.347805\pi$
$577$	4.24639e9	0.920247	0.460124	+	0.887855i	$0.347805\pi$
$578$	−2.19322e9	−0.472427
$579$	−3.20292e9	−0.685759
$580$	−3.05078e9	−0.649251
$581$	3.75483e9	0.794280
$582$	−2.72815e9	−0.573639
$583$	2.36388e8	0.0494067
$584$	5.79920e8	0.120482
$585$	8.78480e8	0.181420
$586$	4.59006e8	0.0942273
$587$	9.36908e9	1.91189	0.955946	−	0.293541i	$-0.0948337\pi$
$587$	9.36908e9	1.91189	0.955946	+	0.293541i	$0.0948337\pi$
$588$	−1.11897e9	−0.226986
$589$	−7.37733e8	−0.148763
$590$	−4.77621e8	−0.0957418
$591$	−2.86525e9	−0.570961
$592$	1.20874e9	0.239446
$593$	2.86726e9	0.564644	0.282322	−	0.959320i	$-0.408895\pi$
$593$	2.86726e9	0.564644	0.282322	+	0.959320i	$0.408895\pi$
$594$	−1.87522e7	−0.00367114
$595$	−3.19054e9	−0.620947
$596$	−1.56322e9	−0.302454
$597$	−7.70923e7	−0.0148286
$598$	−2.40576e9	−0.460043
$599$	−7.94027e9	−1.50953	−0.754765	−	0.655996i	$-0.772249\pi$
$599$	−7.94027e9	−1.50953	−0.754765	+	0.655996i	$0.772249\pi$
$600$	−8.81766e7	−0.0166657
$601$	−4.21662e9	−0.792325	−0.396163	−	0.918180i	$-0.629658\pi$
$601$	−4.21662e9	−0.792325	−0.396163	+	0.918180i	$0.629658\pi$
$602$	1.47879e9	0.276260
$603$	−3.55363e9	−0.660027
$604$	−2.47506e8	−0.0457042
$605$	5.66070e9	1.03926
$606$	−1.03388e9	−0.188718
$607$	−7.33736e9	−1.33162	−0.665809	−	0.746122i	$-0.731913\pi$
$607$	−7.33736e9	−1.33162	−0.665809	+	0.746122i	$0.731913\pi$
$608$	5.04137e8	0.0909674
$609$	1.85738e9	0.333226
$610$	1.62328e9	0.289561
$611$	1.91615e9	0.339849
$612$	1.22065e9	0.215259
$613$	9.14326e9	1.60321	0.801603	−	0.597856i	$-0.203981\pi$
$613$	9.14326e9	1.60321	0.801603	+	0.597856i	$0.203981\pi$
$614$	−5.04113e9	−0.878899
$615$	−1.95314e9	−0.338586
$616$	−2.55791e7	−0.00440912
$617$	−9.43998e9	−1.61798	−0.808990	−	0.587823i	$-0.799985\pi$
$617$	−9.43998e9	−1.61798	−0.808990	+	0.587823i	$0.799985\pi$
$618$	3.84508e8	0.0655309
$619$	−1.55927e9	−0.264244	−0.132122	−	0.991233i	$-0.542179\pi$
$619$	−1.55927e9	−0.264244	−0.132122	+	0.991233i	$0.542179\pi$
$620$	−8.92110e8	−0.150331
$621$	−1.42786e9	−0.239258
$622$	3.03304e9	0.505373
$623$	5.31619e9	0.880830
$624$	−4.58449e8	−0.0755344
$625$	−6.56115e9	−1.07498
$626$	−6.65303e9	−1.08395
$627$	−4.94691e7	−0.00801489
$628$	−9.18108e8	−0.147923
$629$	7.72070e9	1.23703
$630$	7.11210e8	0.113320
$631$	−9.58130e9	−1.51817	−0.759087	−	0.650989i	$-0.774355\pi$
$631$	−9.58130e9	−1.51817	−0.759087	+	0.650989i	$0.774355\pi$
$632$	2.04420e9	0.322117
$633$	5.30875e9	0.831916
$634$	7.46473e9	1.16333
$635$	−6.10112e9	−0.945587
$636$	3.43002e9	0.528685
$637$	2.68437e9	0.411486
$638$	−1.56227e8	−0.0238168
$639$	−3.37916e9	−0.512337
$640$	6.09631e8	0.0919258
$641$	6.29194e9	0.943586	0.471793	−	0.881709i	$-0.343607\pi$
$641$	6.29194e9	0.943586	0.471793	+	0.881709i	$0.343607\pi$
$642$	4.79325e9	0.714920
$643$	6.40885e9	0.950696	0.475348	−	0.879798i	$-0.342322\pi$
$643$	6.40885e9	0.950696	0.475348	+	0.879798i	$0.342322\pi$
$644$	−1.94768e9	−0.287354
$645$	3.45839e9	0.507475
$646$	3.22012e9	0.469957
$647$	1.06588e10	1.54719	0.773597	−	0.633678i	$-0.218456\pi$
$647$	1.06588e10	1.54719	0.773597	+	0.633678i	$0.218456\pi$
$648$	−2.72098e8	−0.0392837
$649$	−2.44584e7	−0.00351214
$650$	2.11532e8	0.0302120
$651$	5.43135e8	0.0771568
$652$	−6.82283e9	−0.964046
$653$	−4.27069e9	−0.600208	−0.300104	−	0.953906i	$-0.597021\pi$
$653$	−4.27069e9	−0.600208	−0.300104	+	0.953906i	$0.597021\pi$
$654$	1.41354e9	0.197599
$655$	1.16025e10	1.61326
$656$	1.01927e9	0.140970
$657$	−8.25707e8	−0.113592
$658$	1.55130e9	0.212278
$659$	−1.11050e10	−1.51155	−0.755773	−	0.654833i	$-0.772739\pi$
$659$	−1.11050e10	−1.51155	−0.755773	+	0.654833i	$0.772739\pi$
$660$	−5.98209e7	−0.00809934
$661$	6.83369e9	0.920343	0.460172	−	0.887830i	$-0.347788\pi$
$661$	6.83369e9	0.920343	0.460172	+	0.887830i	$0.347788\pi$
$662$	7.94699e9	1.06463
$663$	−2.92829e9	−0.390227
$664$	−4.58266e9	−0.607476
$665$	1.87620e9	0.247402
$666$	−1.72104e9	−0.225752
$667$	−1.18957e10	−1.55220
$668$	−9.72463e8	−0.126228
$669$	−7.66782e9	−0.990103
$670$	−1.13363e10	−1.45616
$671$	8.31263e7	0.0106221
$672$	−3.71156e8	−0.0471807
$673$	−8.41655e9	−1.06434	−0.532171	−	0.846637i	$-0.678624\pi$
$673$	−8.41655e9	−1.06434	−0.532171	+	0.846637i	$0.678624\pi$
$674$	3.40353e9	0.428173
$675$	1.25548e8	0.0157126
$676$	−2.91610e9	−0.363069
$677$	−8.34890e9	−1.03412	−0.517058	−	0.855951i	$-0.672973\pi$
$677$	−8.34890e9	−1.03412	−0.517058	+	0.855951i	$0.672973\pi$
$678$	1.09976e9	0.135517
$679$	5.29856e9	0.649552
$680$	3.89396e9	0.474909
$681$	−3.31650e9	−0.402406
$682$	−4.56839e7	−0.00551465
$683$	−3.12693e9	−0.375530	−0.187765	−	0.982214i	$-0.560124\pi$
$683$	−3.12693e9	−0.375530	−0.187765	+	0.982214i	$0.560124\pi$
$684$	−7.17804e8	−0.0857649
$685$	8.56905e8	0.101863
$686$	4.93712e9	0.583902
$687$	1.15748e9	0.136196
$688$	−1.80482e9	−0.211287
$689$	−8.22849e9	−0.958414
$690$	−4.55498e9	−0.527855
$691$	1.05547e9	0.121695	0.0608475	−	0.998147i	$-0.480620\pi$
$691$	1.05547e9	0.121695	0.0608475	+	0.998147i	$0.480620\pi$
$692$	−5.21025e9	−0.597706
$693$	3.64202e7	0.00415696
$694$	6.98108e9	0.792802
$695$	5.01856e9	0.567064
$696$	−2.26687e9	−0.254856
$697$	6.51051e9	0.728283
$698$	1.84469e9	0.205319
$699$	5.73614e9	0.635258
$700$	1.71255e8	0.0188712
$701$	2.84634e9	0.312086	0.156043	−	0.987750i	$-0.450126\pi$
$701$	2.84634e9	0.312086	0.156043	+	0.987750i	$0.450126\pi$
$702$	6.52752e8	0.0712145
$703$	−4.54016e9	−0.492865
$704$	3.12185e7	0.00337216
$705$	3.62798e9	0.389945
$706$	−7.18338e9	−0.768268
$707$	2.00797e9	0.213693
$708$	−3.54895e8	−0.0375823
$709$	−2.76722e9	−0.291596	−0.145798	−	0.989314i	$-0.546575\pi$
$709$	−2.76722e9	−0.291596	−0.145798	+	0.989314i	$0.546575\pi$
$710$	−1.07797e10	−1.13033
$711$	−2.91059e9	−0.303694
$712$	−6.48825e9	−0.673671
$713$	−3.47854e9	−0.359404
$714$	−2.37072e9	−0.243745
$715$	1.43508e8	0.0146827
$716$	−2.27697e9	−0.231826
$717$	−6.12014e9	−0.620075
$718$	−8.55939e9	−0.862993
$719$	−9.05447e9	−0.908473	−0.454237	−	0.890881i	$-0.650088\pi$
$719$	−9.05447e9	−0.908473	−0.454237	+	0.890881i	$0.650088\pi$
$720$	−8.68010e8	−0.0866685
$721$	−7.46784e8	−0.0742030
$722$	5.25738e9	0.519863
$723$	2.06261e9	0.202971
$724$	−6.15942e9	−0.603191
$725$	1.04596e9	0.101937
$726$	4.20617e9	0.407951
$727$	−1.09329e10	−1.05527	−0.527637	−	0.849470i	$-0.676922\pi$
$727$	−1.09329e10	−1.05527	−0.527637	+	0.849470i	$0.676922\pi$
$728$	8.90389e8	0.0855303
$729$	3.87420e8	0.0370370
$730$	−2.63406e9	−0.250608
$731$	−1.15281e10	−1.09156
$732$	1.20617e9	0.113664
$733$	1.53395e10	1.43862	0.719311	−	0.694688i	$-0.244458\pi$
$733$	1.53395e10	1.43862	0.719311	+	0.694688i	$0.244458\pi$
$734$	−1.86428e9	−0.174011
$735$	5.08250e9	0.472141
$736$	2.37709e9	0.219772
$737$	−5.80519e8	−0.0534171
$738$	−1.45127e9	−0.132908
$739$	1.05178e10	0.958673	0.479337	−	0.877631i	$-0.340877\pi$
$739$	1.05178e10	0.958673	0.479337	+	0.877631i	$0.340877\pi$
$740$	−5.49023e9	−0.498057
$741$	1.72198e9	0.155477
$742$	−6.66172e9	−0.598649
$743$	2.09385e10	1.87277	0.936386	−	0.350971i	$-0.114149\pi$
$743$	2.09385e10	1.87277	0.936386	+	0.350971i	$0.114149\pi$
$744$	−6.62880e8	−0.0590105
$745$	7.10034e9	0.629118
$746$	1.01361e10	0.893894
$747$	6.52491e9	0.572734
$748$	1.99405e8	0.0174213
$749$	−9.30935e9	−0.809530
$750$	−4.50497e9	−0.389922
$751$	−1.58632e10	−1.36663	−0.683315	−	0.730124i	$-0.739462\pi$
$751$	−1.58632e10	−1.36663	−0.683315	+	0.730124i	$0.739462\pi$
$752$	−1.89332e9	−0.162353
$753$	−3.96479e9	−0.338406
$754$	5.43814e9	0.462009
$755$	1.12420e9	0.0950668
$756$	5.28462e8	0.0444824
$757$	−7.89351e9	−0.661355	−0.330677	−	0.943744i	$-0.607277\pi$
$757$	−7.89351e9	−0.661355	−0.330677	+	0.943744i	$0.607277\pi$
$758$	−1.56351e10	−1.30394
$759$	−2.33255e8	−0.0193635
$760$	−2.28984e9	−0.189216
$761$	−9.55592e9	−0.786007	−0.393003	−	0.919537i	$-0.628564\pi$
$761$	−9.55592e9	−0.786007	−0.393003	+	0.919537i	$0.628564\pi$
$762$	−4.53342e9	−0.371179
$763$	−2.74534e9	−0.223749
$764$	−8.57809e9	−0.695927
$765$	−5.54433e9	−0.447748
$766$	−3.65873e9	−0.294124
$767$	8.51379e8	0.0681301
$768$	4.52985e8	0.0360844
$769$	1.72329e10	1.36652	0.683262	−	0.730174i	$-0.260561\pi$
$769$	1.72329e10	1.36652	0.683262	+	0.730174i	$0.260561\pi$
$770$	1.16183e8	0.00917117
$771$	1.45998e9	0.114725
$772$	−7.59211e9	−0.593885
$773$	−2.46458e10	−1.91917	−0.959587	−	0.281412i	$-0.909197\pi$
$773$	−2.46458e10	−1.91917	−0.959587	+	0.281412i	$0.909197\pi$
$774$	2.56975e9	0.199204
$775$	3.05859e8	0.0236029
$776$	−6.46674e9	−0.496786
$777$	3.34256e9	0.255627
$778$	−8.56089e9	−0.651764
$779$	−3.82851e9	−0.290167
$780$	2.08232e9	0.157115
$781$	−5.52018e8	−0.0414643
$782$	1.51834e10	1.13539
$783$	3.22764e9	0.240280
$784$	−2.65238e9	−0.196576
$785$	4.17014e9	0.307686
$786$	8.62118e9	0.633268
$787$	2.77315e9	0.202797	0.101399	−	0.994846i	$-0.467668\pi$
$787$	2.77315e9	0.202797	0.101399	+	0.994846i	$0.467668\pi$
$788$	−6.79171e9	−0.494467
$789$	7.01037e9	0.508126
$790$	−9.28497e9	−0.670016
$791$	−2.13592e9	−0.153450
$792$	−4.44498e7	−0.00317930
$793$	−2.89357e9	−0.206052
$794$	9.94148e9	0.704822
$795$	−1.55795e10	−1.09969
$796$	−1.82737e8	−0.0128420
$797$	2.59643e10	1.81665	0.908327	−	0.418261i	$-0.137360\pi$
$797$	2.59643e10	1.81665	0.908327	+	0.418261i	$0.137360\pi$
$798$	1.39410e9	0.0971146
$799$	−1.20934e10	−0.838752
$800$	−2.09011e8	−0.0144329
$801$	9.23815e9	0.635143
$802$	5.88152e9	0.402605
$803$	−1.34887e8	−0.00919318
$804$	−8.42342e9	−0.571600
$805$	8.84658e9	0.597709
$806$	1.59022e9	0.106976
$807$	9.04702e9	0.605966
$808$	−2.45067e9	−0.163435
$809$	1.56545e10	1.03949	0.519744	−	0.854322i	$-0.326027\pi$
$809$	1.56545e10	1.03949	0.519744	+	0.854322i	$0.326027\pi$
$810$	1.23590e9	0.0817118
$811$	−9.62692e9	−0.633745	−0.316872	−	0.948468i	$-0.602633\pi$
$811$	−9.62692e9	−0.633745	−0.316872	+	0.948468i	$0.602633\pi$
$812$	4.40267e9	0.288582
$813$	−6.88468e9	−0.449331
$814$	−2.81148e8	−0.0182705
$815$	3.09900e10	2.00526
$816$	2.89339e9	0.186420
$817$	6.77909e9	0.434905
$818$	1.16292e10	0.742868
$819$	−1.26776e9	−0.0806387
$820$	−4.62965e9	−0.293224
$821$	4.15363e9	0.261955	0.130978	−	0.991385i	$-0.458188\pi$
$821$	4.15363e9	0.261955	0.130978	+	0.991385i	$0.458188\pi$
$822$	6.36721e8	0.0399850
$823$	1.46715e10	0.917433	0.458716	−	0.888583i	$-0.348309\pi$
$823$	1.46715e10	0.917433	0.458716	+	0.888583i	$0.348309\pi$
$824$	9.11427e8	0.0567514
$825$	2.05095e7	0.00127165
$826$	6.89269e8	0.0425558
$827$	2.11569e10	1.30072	0.650360	−	0.759626i	$-0.274618\pi$
$827$	2.11569e10	1.30072	0.650360	+	0.759626i	$0.274618\pi$
$828$	−3.38456e9	−0.207203
$829$	−2.04989e10	−1.24965	−0.624826	−	0.780764i	$-0.714830\pi$
$829$	−2.04989e10	−1.24965	−0.624826	+	0.780764i	$0.714830\pi$
$830$	2.08149e10	1.26358
$831$	−1.78847e10	−1.08113
$832$	−1.08669e9	−0.0654147
$833$	−1.69418e10	−1.01555
$834$	3.72903e9	0.222594
$835$	4.41703e9	0.262559
$836$	−1.17260e8	−0.00694110
$837$	9.43827e8	0.0556357
$838$	−1.44358e10	−0.847395
$839$	2.85293e10	1.66773	0.833863	−	0.551971i	$-0.186124\pi$
$839$	2.85293e10	1.66773	0.833863	+	0.551971i	$0.186124\pi$
$840$	1.68583e9	0.0981378
$841$	9.63986e9	0.558836
$842$	−1.53502e10	−0.886177
$843$	7.33786e8	0.0421865
$844$	1.25837e10	0.720460
$845$	1.32453e10	0.755200
$846$	2.69576e9	0.153068
$847$	−8.16912e9	−0.461938
$848$	8.13043e9	0.457855
$849$	2.74056e9	0.153696
$850$	−1.33504e9	−0.0745637
$851$	−2.14076e10	−1.19073
$852$	−8.00986e9	−0.443697
$853$	−1.22546e10	−0.676047	−0.338023	−	0.941138i	$-0.609758\pi$
$853$	−1.22546e10	−0.676047	−0.338023	+	0.941138i	$0.609758\pi$
$854$	−2.34261e9	−0.128705
$855$	3.26034e9	0.178395
$856$	1.13618e10	0.619139
$857$	4.17939e9	0.226819	0.113410	−	0.993548i	$-0.463823\pi$
$857$	4.17939e9	0.226819	0.113410	+	0.993548i	$0.463823\pi$
$858$	1.06633e8	0.00576351
$859$	−7.48329e8	−0.0402825	−0.0201413	−	0.999797i	$-0.506412\pi$
$859$	−7.48329e8	−0.0402825	−0.0201413	+	0.999797i	$0.506412\pi$
$860$	8.19767e9	0.439487
$861$	2.81863e9	0.150497
$862$	−7.42098e9	−0.394626
$863$	−1.45627e10	−0.771267	−0.385634	−	0.922652i	$-0.626017\pi$
$863$	−1.45627e10	−0.771267	−0.385634	+	0.922652i	$0.626017\pi$
$864$	−6.44973e8	−0.0340207
$865$	2.36655e10	1.24325
$866$	−3.28445e9	−0.171850
$867$	7.40211e9	0.385735
$868$	1.28743e9	0.0668197
$869$	−4.75472e8	−0.0245785
$870$	1.02964e10	0.530111
$871$	2.02074e10	1.03621
$872$	3.35061e9	0.171126
$873$	9.20752e9	0.468374
$874$	−8.92860e9	−0.452370
$875$	8.74945e9	0.441522
$876$	−1.95723e9	−0.0983734
$877$	−1.58880e10	−0.795374	−0.397687	−	0.917521i	$-0.630187\pi$
$877$	−1.58880e10	−0.795374	−0.397687	+	0.917521i	$0.630187\pi$
$878$	1.48051e10	0.738213
$879$	−1.54915e9	−0.0769363
$880$	−1.41798e8	−0.00701423
$881$	−1.34925e10	−0.664779	−0.332389	−	0.943142i	$-0.607855\pi$
$881$	−1.34925e10	−0.664779	−0.332389	+	0.943142i	$0.607855\pi$
$882$	3.77653e9	0.185333
$883$	3.01082e10	1.47171	0.735856	−	0.677138i	$-0.236780\pi$
$883$	3.01082e10	1.47171	0.735856	+	0.677138i	$0.236780\pi$
$884$	−6.94114e9	−0.337946
$885$	1.61197e9	0.0781728
$886$	−1.46196e10	−0.706181
$887$	−3.65851e10	−1.76024	−0.880120	−	0.474751i	$-0.842538\pi$
$887$	−3.65851e10	−1.76024	−0.880120	+	0.474751i	$0.842538\pi$
$888$	−4.07950e9	−0.195507
$889$	8.80471e9	0.420300
$890$	2.94703e10	1.40126
$891$	6.32888e7	0.00299747
$892$	−1.81756e10	−0.857454
$893$	7.11151e9	0.334181
$894$	5.27588e9	0.246953
$895$	1.03422e10	0.482207
$896$	−8.79777e8	−0.0408596
$897$	8.11944e9	0.375623
$898$	−2.71656e10	−1.25185
$899$	7.86311e9	0.360940
$900$	2.97596e8	0.0136075
$901$	5.19323e10	2.36538
$902$	−2.37079e8	−0.0107565
$903$	−4.99091e9	−0.225565
$904$	2.60683e9	0.117361
$905$	2.79768e10	1.25466
$906$	8.35332e8	0.0373173
$907$	−1.39384e9	−0.0620278	−0.0310139	−	0.999519i	$-0.509874\pi$
$907$	−1.39384e9	−0.0620278	−0.0310139	+	0.999519i	$0.509874\pi$
$908$	−7.86133e9	−0.348494
$909$	3.48933e9	0.154088
$910$	−4.04424e9	−0.177907
$911$	3.48446e10	1.52694	0.763468	−	0.645846i	$-0.223495\pi$
$911$	3.48446e10	1.52694	0.763468	+	0.645846i	$0.223495\pi$
$912$	−1.70146e9	−0.0742746
$913$	1.06591e9	0.0463523
$914$	−2.60788e10	−1.12973
$915$	−5.47858e9	−0.236425
$916$	2.74366e9	0.117949
$917$	−1.67439e10	−0.717072
$918$	−4.11970e9	−0.175758
$919$	−1.37453e10	−0.584185	−0.292093	−	0.956390i	$-0.594352\pi$
$919$	−1.37453e10	−0.584185	−0.292093	+	0.956390i	$0.594352\pi$
$920$	−1.07970e10	−0.457136
$921$	1.70138e10	0.717618
$922$	2.33659e10	0.981802
$923$	1.92153e10	0.804345
$924$	8.63294e7	0.00360003
$925$	1.88232e9	0.0781982
$926$	1.21998e9	0.0504910
$927$	−1.29772e9	−0.0535058
$928$	−5.37333e9	−0.220712
$929$	1.56344e10	0.639775	0.319887	−	0.947456i	$-0.396355\pi$
$929$	1.56344e10	0.639775	0.319887	+	0.947456i	$0.396355\pi$
$930$	3.01087e9	0.122744
$931$	9.96264e9	0.404623
$932$	1.35968e10	0.550149
$933$	−1.02365e10	−0.412636
$934$	−1.46552e9	−0.0588542
$935$	−9.05718e8	−0.0362370
$936$	1.54726e9	0.0616735
$937$	−9.53897e9	−0.378802	−0.189401	−	0.981900i	$-0.560655\pi$
$937$	−9.53897e9	−0.378802	−0.189401	+	0.981900i	$0.560655\pi$
$938$	1.63598e10	0.647243
$939$	2.24540e10	0.885041
$940$	8.59965e9	0.337702
$941$	2.04232e9	0.0799023	0.0399512	−	0.999202i	$-0.487280\pi$
$941$	2.04232e9	0.0799023	0.0399512	+	0.999202i	$0.487280\pi$
$942$	3.09861e9	0.120778
$943$	−1.80520e10	−0.701028
$944$	−8.41232e8	−0.0325472
$945$	−2.40033e9	−0.0925252
$946$	4.19793e8	0.0161219
$947$	−4.26499e10	−1.63190	−0.815949	−	0.578125i	$-0.803785\pi$
$947$	−4.26499e10	−1.63190	−0.815949	+	0.578125i	$0.803785\pi$
$948$	−6.89917e9	−0.263007
$949$	4.69532e9	0.178334
$950$	7.85069e8	0.0297081
$951$	−2.51935e10	−0.949852
$952$	−5.61949e9	−0.211090
$953$	9.92563e9	0.371478	0.185739	−	0.982599i	$-0.440532\pi$
$953$	9.92563e9	0.371478	0.185739	+	0.982599i	$0.440532\pi$
$954$	−1.15763e10	−0.431670
$955$	3.89626e10	1.44756
$956$	−1.45070e10	−0.537001
$957$	5.27265e8	0.0194463
$958$	2.71930e10	0.999258
$959$	−1.23662e9	−0.0452765
$960$	−2.05751e9	−0.0750571
$961$	−2.52133e10	−0.916426
$962$	9.78656e9	0.354419
$963$	−1.61772e10	−0.583730
$964$	4.88915e9	0.175778
$965$	3.44842e10	1.23531
$966$	6.57343e9	0.234624
$967$	−9.06369e9	−0.322339	−0.161169	−	0.986927i	$-0.551527\pi$
$967$	−9.06369e9	−0.322339	−0.161169	+	0.986927i	$0.551527\pi$
$968$	9.97017e9	0.353296
$969$	−1.08679e10	−0.383718
$970$	2.93726e10	1.03334
$971$	3.23769e10	1.13493	0.567463	−	0.823399i	$-0.307925\pi$
$971$	3.23769e10	1.13493	0.567463	+	0.823399i	$0.307925\pi$
$972$	9.18330e8	0.0320750
$973$	−7.24243e9	−0.252052
$974$	−1.15761e10	−0.401425
$975$	−7.13921e8	−0.0246680
$976$	2.85908e9	0.0984356
$977$	−4.75019e10	−1.62960	−0.814799	−	0.579744i	$-0.803153\pi$
$977$	−4.75019e10	−1.62960	−0.814799	+	0.579744i	$0.803153\pi$
$978$	2.30270e10	0.787140
$979$	1.50914e9	0.0514032
$980$	1.20474e10	0.408886
$981$	−4.77069e9	−0.161339
$982$	−4.04027e10	−1.36151
$983$	−2.36220e10	−0.793194	−0.396597	−	0.917993i	$-0.629809\pi$
$983$	−2.36220e10	−0.793194	−0.396597	+	0.917993i	$0.629809\pi$
$984$	−3.44005e9	−0.115102
$985$	3.08487e10	1.02851
$986$	−3.43216e10	−1.14024
$987$	−5.23564e9	−0.173325
$988$	4.08174e9	0.134647
$989$	3.19645e10	1.05071
$990$	2.01896e8	0.00661308
$991$	−2.83985e9	−0.0926911	−0.0463455	−	0.998925i	$-0.514758\pi$
$991$	−2.83985e9	−0.0926911	−0.0463455	+	0.998925i	$0.514758\pi$
$992$	−1.57127e9	−0.0511046
$993$	−2.68211e10	−0.869268
$994$	1.55566e10	0.502414
$995$	8.30013e8	0.0267119
$996$	1.54665e10	0.496002
$997$	4.27013e10	1.36461	0.682304	−	0.731068i	$-0.260978\pi$
$997$	4.27013e10	1.36461	0.682304	+	0.731068i	$0.260978\pi$
$998$	6.58781e9	0.209790
$999$	5.80850e9	0.184325

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.8.a.c.1.2	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.8.a.c.1.2	✓	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)

\(f(q)\)	\(=\)	\(q-8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} -290.695 q^{5} -216.000 q^{6} +419.510 q^{7} -512.000 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q-8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} -290.695 q^{5} -216.000 q^{6} +419.510 q^{7} -512.000 q^{8} +729.000 q^{9} +2325.56 q^{10} +119.089 q^{11} +1728.00 q^{12} -4145.40 q^{13} -3356.08 q^{14} -7848.76 q^{15} +4096.00 q^{16} +26162.8 q^{17} -5832.00 q^{18} -15385.0 q^{19} -18604.5 q^{20} +11326.8 q^{21} -952.713 q^{22} -72543.0 q^{23} -13824.0 q^{24} +6378.52 q^{25} +33163.2 q^{26} +19683.0 q^{27} +26848.7 q^{28} +163981. q^{29} +62790.1 q^{30} +47951.4 q^{31} -32768.0 q^{32} +3215.41 q^{33} -209302. q^{34} -121950. q^{35} +46656.0 q^{36} +295103. q^{37} +123080. q^{38} -111926. q^{39} +148836. q^{40} +248846. q^{41} -90614.3 q^{42} -440629. q^{43} +7621.70 q^{44} -211917. q^{45} +580344. q^{46} -462236. q^{47} +110592. q^{48} -647554. q^{49} -51028.1 q^{50} +706395. q^{51} -265306. q^{52} +1.98497e6 q^{53} -157464. q^{54} -34618.6 q^{55} -214789. q^{56} -415396. q^{57} -1.31185e6 q^{58} -205379. q^{59} -502321. q^{60} +698018. q^{61} -383611. q^{62} +305823. q^{63} +262144. q^{64} +1.20505e6 q^{65} -25723.2 q^{66} -4.87466e6 q^{67} +1.67442e6 q^{68} -1.95866e6 q^{69} +975596. q^{70} -4.63534e6 q^{71} -373248. q^{72} -1.13266e6 q^{73} -2.36082e6 q^{74} +172220. q^{75} -984642. q^{76} +49959.1 q^{77} +895407. q^{78} -3.99257e6 q^{79} -1.19069e6 q^{80} +531441. q^{81} -1.99077e6 q^{82} +8.95050e6 q^{83} +724914. q^{84} -7.60539e6 q^{85} +3.52503e6 q^{86} +4.42748e6 q^{87} -60973.6 q^{88} +1.26724e7 q^{89} +1.69533e6 q^{90} -1.73904e6 q^{91} -4.64275e6 q^{92} +1.29469e6 q^{93} +3.69789e6 q^{94} +4.47235e6 q^{95} -884736. q^{96} +1.26303e7 q^{97} +5.18043e6 q^{98} +86816.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 56 q^{2} + 189 q^{3} + 448 q^{4} - 158 q^{5} - 1512 q^{6} - 581 q^{7} - 3584 q^{8} + 5103 q^{9}+O(q^{10}) \) 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

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more