LMFDB - Embedded newform 147.7.d.a.97.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,7,Mod(97,147)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(147, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("147.97");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	147.d (of order $2$, degree $1$, minimal)

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:	no
Analytic conductor:	$33.8179502921$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 212x^{6} - 787x^{5} + 38792x^{4} - 92833x^{3} + 1563109x^{2} + 3107772x + 38787984 $ x^8 - x^7 + 212x^6 - 787x^5 + 38792x^4 - 92833x^3 + 1563109x^2 + 3107772x + 38787984
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{4}\cdot 3\cdot 7^{2} $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			97.5
Root			$4.15432 - 7.19549i$ of defining polynomial
Character	$\chi$	$=$	147.97
Dual form			147.7.d.a.97.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+9.30863 q^{2} -15.5885i q^{3} +22.6506 q^{4} +174.756i q^{5} -145.107i q^{6} -384.906 q^{8} -243.000 q^{9} +O(q^{10})$	\(q+9.30863 q^{2} -15.5885i q^{3} +22.6506 q^{4} +174.756i q^{5} -145.107i q^{6} -384.906 q^{8} -243.000 q^{9} +1626.74i q^{10} -185.399 q^{11} -353.088i q^{12} -3981.73i q^{13} +2724.17 q^{15} -5032.59 q^{16} -7045.09i q^{17} -2262.00 q^{18} -4693.37i q^{19} +3958.32i q^{20} -1725.81 q^{22} -6643.99 q^{23} +6000.09i q^{24} -14914.5 q^{25} -37064.5i q^{26} +3788.00i q^{27} +19385.8 q^{29} +25358.3 q^{30} -23952.9i q^{31} -22212.5 q^{32} +2890.09i q^{33} -65580.2i q^{34} -5504.10 q^{36} -39569.6 q^{37} -43688.9i q^{38} -62069.0 q^{39} -67264.5i q^{40} +46285.6i q^{41} -93128.7 q^{43} -4199.41 q^{44} -42465.6i q^{45} -61846.5 q^{46} +149475. i q^{47} +78450.3i q^{48} -138834. q^{50} -109822. q^{51} -90188.7i q^{52} -101825. q^{53} +35261.1i q^{54} -32399.5i q^{55} -73162.4 q^{57} +180455. q^{58} -152343. i q^{59} +61704.2 q^{60} -168547. i q^{61} -222968. i q^{62} +115317. q^{64} +695830. q^{65} +26902.7i q^{66} +61104.0 q^{67} -159576. i q^{68} +103570. i q^{69} -485262. q^{71} +93532.2 q^{72} +8928.98i q^{73} -368339. q^{74} +232495. i q^{75} -106308. i q^{76} -577778. q^{78} +443877. q^{79} -879473. i q^{80} +59049.0 q^{81} +430855. i q^{82} +559383. i q^{83} +1.23117e6 q^{85} -866901. q^{86} -302194. i q^{87} +71361.2 q^{88} -206755. i q^{89} -395297. i q^{90} -150491. q^{92} -373388. q^{93} +1.39140e6i q^{94} +820193. q^{95} +346259. i q^{96} -1.23197e6i q^{97} +45052.0 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 10 q^{2} + 346 q^{4} - 454 q^{8} - 1944 q^{9}+O(q^{10}) $ 8 * q + 10 * q^2 + 346 * q^4 - 454 * q^8 - 1944 * q^9	$ 8 q + 10 q^{2} + 346 q^{4} - 454 q^{8} - 1944 q^{9} + 2140 q^{11} - 756 q^{15} - 7822 q^{16} - 2430 q^{18} - 78 q^{22} + 30448 q^{23} - 44548 q^{25} + 32524 q^{29} - 4698 q^{30} - 140406 q^{32} - 84078 q^{36} + 91340 q^{37} - 186732 q^{39} - 445660 q^{43} + 377658 q^{44} - 1051608 q^{46} - 1218884 q^{50} - 129816 q^{51} + 26068 q^{53} - 442908 q^{57} + 319002 q^{58} - 859410 q^{60} - 1410446 q^{64} + 778008 q^{65} - 768188 q^{67} + 225688 q^{71} + 110322 q^{72} - 2371060 q^{74} - 342792 q^{78} + 1119184 q^{79} + 472392 q^{81} + 1953576 q^{85} + 4604804 q^{86} - 609774 q^{88} - 113064 q^{92} - 723600 q^{93} - 2320224 q^{95} - 520020 q^{99}+O(q^{100}) $ 8 * q + 10 * q^2 + 346 * q^4 - 454 * q^8 - 1944 * q^9 + 2140 * q^11 - 756 * q^15 - 7822 * q^16 - 2430 * q^18 - 78 * q^22 + 30448 * q^23 - 44548 * q^25 + 32524 * q^29 - 4698 * q^30 - 140406 * q^32 - 84078 * q^36 + 91340 * q^37 - 186732 * q^39 - 445660 * q^43 + 377658 * q^44 - 1051608 * q^46 - 1218884 * q^50 - 129816 * q^51 + 26068 * q^53 - 442908 * q^57 + 319002 * q^58 - 859410 * q^60 - 1410446 * q^64 + 778008 * q^65 - 768188 * q^67 + 225688 * q^71 + 110322 * q^72 - 2371060 * q^74 - 342792 * q^78 + 1119184 * q^79 + 472392 * q^81 + 1953576 * q^85 + 4604804 * q^86 - 609774 * q^88 - 113064 * q^92 - 723600 * q^93 - 2320224 * q^95 - 520020 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$.

$n$	$50$	$52$
$\chi(n)$	$1$	$-1$

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 $

$2$	9.30863	1.16358	0.581789	−	0.813339i	$-0.302353\pi$
$2$	9.30863	1.16358	0.581789	+	0.813339i	$0.302353\pi$
$3$	− 15.5885i	− 0.577350i
$3$	− 15.5885i	− 0.577350i
$4$	22.6506	0.353916
$5$	174.756i	1.39805i	0.715100	+	0.699023i	$0.246381\pi$
$5$	174.756i	1.39805i	−0.715100	+	0.699023i	$0.753619\pi$
$6$	− 145.107i	− 0.671793i
$7$	0	0
$7$	0	0
$8$	−384.906	−0.751770
$9$	−243.000	−0.333333
$10$	1626.74i	1.62674i
$11$	−185.399	−0.139293	−0.0696466	−	0.997572i	$-0.522187\pi$
$11$	−185.399	−0.139293	−0.0696466	+	0.997572i	$0.522187\pi$
$12$	− 353.088i	− 0.204334i
$13$	− 3981.73i	− 1.81235i	−0.422904	−	0.906174i	$-0.638989\pi$
$13$	− 3981.73i	− 1.81235i	0.422904	−	0.906174i	$-0.361011\pi$
$14$	0	0
$15$	2724.17	0.807162
$16$	−5032.59	−1.22866
$17$	− 7045.09i	− 1.43397i	−0.697089	−	0.716985i	$-0.745522\pi$
$17$	− 7045.09i	− 1.43397i	0.697089	−	0.716985i	$-0.254478\pi$
$18$	−2262.00	−0.387860
$19$	− 4693.37i	− 0.684265i	−0.939652	−	0.342132i	$-0.888851\pi$
$19$	− 4693.37i	− 0.684265i	0.939652	−	0.342132i	$-0.111149\pi$
$20$	3958.32i	0.494791i
$21$	0	0
$22$	−1725.81	−0.162079
$23$	−6643.99	−0.546067	−0.273033	−	0.962005i	$-0.588027\pi$
$23$	−6643.99	−0.546067	−0.273033	+	0.962005i	$0.588027\pi$
$24$	6000.09i	0.434034i
$25$	−14914.5	−0.954530
$26$	− 37064.5i	− 2.10881i
$27$	3788.00i	0.192450i
$28$	0	0
$29$	19385.8	0.794857	0.397429	−	0.917633i	$-0.369903\pi$
$29$	19385.8	0.794857	0.397429	+	0.917633i	$0.369903\pi$
$30$	25358.3	0.939196
$31$	− 23952.9i	− 0.804030i	−0.915633	−	0.402015i	$-0.868310\pi$
$31$	− 23952.9i	− 0.804030i	0.915633	−	0.402015i	$-0.131690\pi$
$32$	−22212.5	−0.677873
$33$	2890.09i	0.0804209i
$34$	− 65580.2i	− 1.66854i
$35$	0	0
$36$	−5504.10	−0.117972
$37$	−39569.6	−0.781190	−0.390595	−	0.920563i	$-0.627731\pi$
$37$	−39569.6	−0.781190	−0.390595	+	0.920563i	$0.627731\pi$
$38$	− 43688.9i	− 0.796196i
$39$	−62069.0	−1.04636
$40$	− 67264.5i	− 1.05101i
$41$	46285.6i	0.671575i	0.941938	+	0.335787i	$0.109002\pi$
$41$	46285.6i	0.671575i	−0.941938	+	0.335787i	$0.890998\pi$
$42$	0	0
$43$	−93128.7	−1.17133	−0.585664	−	0.810554i	$-0.699166\pi$
$43$	−93128.7	−1.17133	−0.585664	+	0.810554i	$0.699166\pi$
$44$	−4199.41	−0.0492981
$45$	− 42465.6i	− 0.466015i
$46$	−61846.5	−0.635392
$47$	149475.i	1.43971i	0.694127	+	0.719853i	$0.255791\pi$
$47$	149475.i	1.43971i	−0.694127	+	0.719853i	$0.744209\pi$
$48$	78450.3i	0.709367i
$49$	0	0
$50$	−138834.	−1.11067
$51$	−109822.	−0.827903
$52$	− 90188.7i	− 0.641419i
$53$	−101825.	−0.683956	−0.341978	−	0.939708i	$-0.611097\pi$
$53$	−101825.	−0.683956	−0.341978	+	0.939708i	$0.611097\pi$
$54$	35261.1i	0.223931i
$55$	− 32399.5i	− 0.194738i
$56$	0	0
$57$	−73162.4	−0.395060
$58$	180455.	0.924879
$59$	− 152343.i	− 0.741766i	−0.928680	−	0.370883i	$-0.879055\pi$
$59$	− 152343.i	− 0.741766i	0.928680	−	0.370883i	$-0.120945\pi$
$60$	61704.2	0.285667
$61$	− 168547.i	− 0.742560i	−0.928521	−	0.371280i	$-0.878919\pi$
$61$	− 168547.i	− 0.742560i	0.928521	−	0.371280i	$-0.121081\pi$
$62$	− 222968.i	− 0.935553i
$63$	0	0
$64$	115317.	0.439901
$65$	695830.	2.53375
$66$	26902.7i	0.0935761i
$67$	61104.0	0.203163	0.101582	−	0.994827i	$-0.467610\pi$
$67$	61104.0	0.203163	0.101582	+	0.994827i	$0.467610\pi$
$68$	− 159576.i	− 0.507505i
$69$	103570.i	0.315272i
$70$	0	0
$71$	−485262.	−1.35582	−0.677909	−	0.735146i	$-0.737114\pi$
$71$	−485262.	−1.35582	−0.677909	+	0.735146i	$0.737114\pi$
$72$	93532.2	0.250590
$73$	8928.98i	0.0229527i	0.999934	+	0.0114763i	$0.00365311\pi$
$73$	8928.98i	0.0229527i	−0.999934	+	0.0114763i	$0.996347\pi$
$74$	−368339.	−0.908977
$75$	232495.i	0.551098i
$76$	− 106308.i	− 0.242172i
$77$	0	0
$78$	−577778.	−1.21752
$79$	443877.	0.900287	0.450144	−	0.892956i	$-0.351373\pi$
$79$	443877.	0.900287	0.450144	+	0.892956i	$0.351373\pi$
$80$	− 879473.i	− 1.71772i
$81$	59049.0	0.111111
$82$	430855.i	0.781430i
$83$	559383.i	0.978306i	0.872198	+	0.489153i	$0.162694\pi$
$83$	559383.i	0.978306i	−0.872198	+	0.489153i	$0.837306\pi$
$84$	0	0
$85$	1.23117e6	2.00475
$86$	−866901.	−1.36293
$87$	− 302194.i	− 0.458911i
$88$	71361.2	0.104716
$89$	− 206755.i	− 0.293283i	−0.989190	−	0.146641i	$-0.953154\pi$
$89$	− 206755.i	− 0.293283i	0.989190	−	0.146641i	$-0.0468463\pi$
$90$	− 395297.i	− 0.542245i
$91$	0	0
$92$	−150491.	−0.193262
$93$	−373388.	−0.464207
$94$	1.39140e6i	1.67521i
$95$	820193.	0.956633
$96$	346259.i	0.391370i
$97$	− 1.23197e6i	− 1.34984i	−0.737889	−	0.674922i	$-0.764177\pi$
$97$	− 1.23197e6i	− 1.34984i	0.737889	−	0.674922i	$-0.235823\pi$
$98$	0	0
$99$	45052.0	0.0464310
$100$	−337824.	−0.337824
$101$	896888.i	0.870511i	0.900307	+	0.435255i	$0.143342\pi$
$101$	896888.i	0.870511i	−0.900307	+	0.435255i	$0.856658\pi$
$102$	−1.02229e6	−0.963330
$103$	− 1.33355e6i	− 1.22039i	−0.792252	−	0.610194i	$-0.791092\pi$
$103$	− 1.33355e6i	− 1.22039i	0.792252	−	0.610194i	$-0.208908\pi$
$104$	1.53259e6i	1.36247i
$105$	0	0
$106$	−947855.	−0.795837
$107$	−101018.	−0.0824607	−0.0412304	−	0.999150i	$-0.513128\pi$
$107$	−101018.	−0.0824607	−0.0412304	+	0.999150i	$0.513128\pi$
$108$	85800.5i	0.0681112i
$109$	−1.95260e6	−1.50776	−0.753881	−	0.657010i	$-0.771821\pi$
$109$	−1.95260e6	−1.50776	−0.753881	+	0.657010i	$0.771821\pi$
$110$	− 301595.i	− 0.226593i
$111$	616829.i	0.451020i
$112$	0	0
$113$	1.13981e6	0.789945	0.394972	−	0.918693i	$-0.370754\pi$
$113$	1.13981e6	0.789945	0.394972	+	0.918693i	$0.370754\pi$
$114$	−681042.	−0.459684
$115$	− 1.16107e6i	− 0.763426i
$116$	439100.	0.281313
$117$	967561.i	0.604116i
$118$	− 1.41811e6i	− 0.863104i
$119$	0	0
$120$	−1.04855e6	−0.606800
$121$	−1.73719e6	−0.980597
$122$	− 1.56894e6i	− 0.864027i
$123$	721521.	0.387734
$124$	− 542547.i	− 0.284559i
$125$	124158.i	0.0635691i
$126$	0	0
$127$	3.37006e6	1.64523	0.822614	−	0.568600i	$-0.192515\pi$
$127$	3.37006e6	1.64523	0.822614	+	0.568600i	$0.192515\pi$
$128$	2.49505e6	1.18973
$129$	1.45173e6i	0.676266i
$130$	6.47722e6	2.94821
$131$	− 2.99233e6i	− 1.33105i	−0.746374	−	0.665527i	$-0.768207\pi$
$131$	− 2.99233e6i	− 1.33105i	0.746374	−	0.665527i	$-0.231793\pi$
$132$	65462.3i	0.0284623i
$133$	0	0
$134$	568794.	0.236396
$135$	−661973.	−0.269054
$136$	2.71170e6i	1.07801i
$137$	−2.54463e6	−0.989608	−0.494804	−	0.869004i	$-0.664760\pi$
$137$	−2.54463e6	−0.989608	−0.494804	+	0.869004i	$0.664760\pi$
$138$	964091.i	0.366844i
$139$	1.61651e6i	0.601913i	0.953638	+	0.300956i	$0.0973059\pi$
$139$	1.61651e6i	0.601913i	−0.953638	+	0.300956i	$0.902694\pi$
$140$	0	0
$141$	2.33008e6	0.831214
$142$	−4.51713e6	−1.57760
$143$	738209.i	0.252448i
$144$	1.22292e6	0.409553
$145$	3.38777e6i	1.11125i
$146$	83116.6i	0.0267072i
$147$	0	0
$148$	−896277.	−0.276476
$149$	1.14065e6	0.344821	0.172411	−	0.985025i	$-0.444844\pi$
$149$	1.14065e6	0.344821	0.172411	+	0.985025i	$0.444844\pi$
$150$	2.16421e6i	0.641246i
$151$	−436055.	−0.126652	−0.0633258	−	0.997993i	$-0.520171\pi$
$151$	−436055.	−0.126652	−0.0633258	+	0.997993i	$0.520171\pi$
$152$	1.80651e6i	0.514409i
$153$	1.71196e6i	0.477990i
$154$	0	0
$155$	4.18590e6	1.12407
$156$	−1.40590e6	−0.370324
$157$	5.34559e6i	1.38133i	0.723176	+	0.690664i	$0.242682\pi$
$157$	5.34559e6i	1.38133i	−0.723176	+	0.690664i	$0.757318\pi$
$158$	4.13189e6	1.04756
$159$	1.58730e6i	0.394882i
$160$	− 3.88177e6i	− 0.947697i
$161$	0	0
$162$	549665.	0.129287
$163$	1.67050e6	0.385731	0.192866	−	0.981225i	$-0.438222\pi$
$163$	1.67050e6	0.385731	0.192866	+	0.981225i	$0.438222\pi$
$164$	1.04840e6i	0.237681i
$165$	−505059.	−0.112432
$166$	5.20709e6i	1.13834i
$167$	144090.i	0.0309375i	0.999880	+	0.0154687i	$0.00492405\pi$
$167$	144090.i	0.0309375i	−0.999880	+	0.0154687i	$0.995076\pi$
$168$	0	0
$169$	−1.10274e7	−2.28461
$170$	1.14605e7	2.33269
$171$	1.14049e6i	0.228088i
$172$	−2.10942e6	−0.414552
$173$	− 1.75834e6i	− 0.339597i	−0.985479	−	0.169798i	$-0.945688\pi$
$173$	− 1.75834e6i	− 0.339597i	0.985479	−	0.169798i	$-0.0543117\pi$
$174$	− 2.81302e6i	− 0.533979i
$175$	0	0
$176$	933038.	0.171144
$177$	−2.37480e6	−0.428259
$178$	− 1.92461e6i	− 0.341258i
$179$	9.98465e6	1.74090	0.870450	−	0.492257i	$-0.163828\pi$
$179$	9.98465e6	1.74090	0.870450	+	0.492257i	$0.163828\pi$
$180$	− 961873.i	− 0.164930i
$181$	7.80413e6i	1.31610i	0.752974	+	0.658050i	$0.228618\pi$
$181$	7.80413e6i	1.31610i	−0.752974	+	0.658050i	$0.771382\pi$
$182$	0	0
$183$	−2.62739e6	−0.428717
$184$	2.55731e6	0.410516
$185$	− 6.91502e6i	− 1.09214i
$186$	−3.47573e6	−0.540142
$187$	1.30615e6i	0.199742i
$188$	3.38569e6i	0.509535i
$189$	0	0
$190$	7.63488e6	1.11312
$191$	−511623.	−0.0734260	−0.0367130	−	0.999326i	$-0.511689\pi$
$191$	−511623.	−0.0734260	−0.0367130	+	0.999326i	$0.511689\pi$
$192$	− 1.79762e6i	− 0.253977i
$193$	−8.70658e6	−1.21109	−0.605544	−	0.795812i	$-0.707044\pi$
$193$	−8.70658e6	−1.21109	−0.605544	+	0.795812i	$0.707044\pi$
$194$	− 1.14679e7i	− 1.57065i
$195$	− 1.08469e7i	− 1.46286i
$196$	0	0
$197$	4.44972e6	0.582015	0.291007	−	0.956721i	$-0.406010\pi$
$197$	4.44972e6	0.582015	0.291007	+	0.956721i	$0.406010\pi$
$198$	419372.	0.0540262
$199$	− 7.11790e6i	− 0.903218i	−0.892216	−	0.451609i	$-0.850850\pi$
$199$	− 7.11790e6i	− 0.903218i	0.892216	−	0.451609i	$-0.149150\pi$
$200$	5.74069e6	0.717587
$201$	− 952516.i	− 0.117296i
$202$	8.34880e6i	1.01291i
$203$	0	0
$204$	−2.48754e6	−0.293008
$205$	−8.08867e6	−0.938891
$206$	− 1.24135e7i	− 1.42002i
$207$	1.61449e6	0.182022
$208$	2.00384e7i	2.22676i
$209$	870147.i	0.0953134i
$210$	0	0
$211$	−1.12917e7	−1.20203	−0.601013	−	0.799239i	$-0.705236\pi$
$211$	−1.12917e7	−1.20203	−0.601013	+	0.799239i	$0.705236\pi$
$212$	−2.30641e6	−0.242063
$213$	7.56449e6i	0.782782i
$214$	−940339.	−0.0959496
$215$	− 1.62748e7i	− 1.63757i
$216$	− 1.45802e6i	− 0.144678i
$217$	0	0
$218$	−1.81760e7	−1.75440
$219$	139189.	0.0132517
$220$	− 733870.i	− 0.0689209i
$221$	−2.80517e7	−2.59885
$222$	5.74184e6i	0.524798i
$223$	1.12380e6i	0.101338i	0.998715	+	0.0506692i	$0.0161354\pi$
$223$	1.12380e6i	0.101338i	−0.998715	+	0.0506692i	$0.983865\pi$
$224$	0	0
$225$	3.62423e6	0.318177
$226$	1.06101e7	0.919163
$227$	− 9.97156e6i	− 0.852483i	−0.904609	−	0.426241i	$-0.859837\pi$
$227$	− 9.97156e6i	− 0.852483i	0.904609	−	0.426241i	$-0.140163\pi$
$228$	−1.65717e6	−0.139818
$229$	− 1.95432e7i	− 1.62738i	−0.581297	−	0.813692i	$-0.697454\pi$
$229$	− 1.95432e7i	− 1.62738i	0.581297	−	0.813692i	$-0.302546\pi$
$230$	− 1.08080e7i	− 0.888306i
$231$	0	0
$232$	−7.46170e6	−0.597550
$233$	−3.20239e6	−0.253167	−0.126583	−	0.991956i	$-0.540401\pi$
$233$	−3.20239e6	−0.253167	−0.126583	+	0.991956i	$0.540401\pi$
$234$	9.00667e6i	0.702937i
$235$	−2.61215e7	−2.01277
$236$	− 3.45067e6i	− 0.262523i
$237$	− 6.91935e6i	− 0.519781i
$238$	0	0
$239$	1.42350e7	1.04271	0.521355	−	0.853340i	$-0.325427\pi$
$239$	1.42350e7	1.04271	0.521355	+	0.853340i	$0.325427\pi$
$240$	−1.37096e7	−0.991727
$241$	5.05832e6i	0.361373i	0.983541	+	0.180686i	$0.0578319\pi$
$241$	5.05832e6i	0.361373i	−0.983541	+	0.180686i	$0.942168\pi$
$242$	−1.61708e7	−1.14100
$243$	− 920483.i	− 0.0641500i
$244$	− 3.81770e6i	− 0.262804i
$245$	0	0
$246$	6.71637e6	0.451159
$247$	−1.86877e7	−1.24013
$248$	9.21960e6i	0.604446i
$249$	8.71992e6	0.564825
$250$	1.15575e6i	0.0739677i
$251$	− 1.09278e7i	− 0.691050i	−0.938409	−	0.345525i	$-0.887701\pi$
$251$	− 1.09278e7i	− 0.691050i	0.938409	−	0.345525i	$-0.112299\pi$
$252$	0	0
$253$	1.23179e6	0.0760633
$254$	3.13706e7	1.91435
$255$	− 1.91920e7i	− 1.15745i
$256$	1.58452e7	0.944446
$257$	− 9.67373e6i	− 0.569895i	−0.958543	−	0.284947i	$-0.908024\pi$
$257$	− 9.67373e6i	− 0.569895i	0.958543	−	0.284947i	$-0.0919761\pi$
$258$	1.35136e7i	0.786889i
$259$	0	0
$260$	1.57610e7	0.896733
$261$	−4.71074e6	−0.264952
$262$	− 2.78545e7i	− 1.54879i
$263$	2.35873e7	1.29661	0.648307	−	0.761379i	$-0.275477\pi$
$263$	2.35873e7	1.29661	0.648307	+	0.761379i	$0.275477\pi$
$264$	− 1.11241e6i	− 0.0604580i
$265$	− 1.77946e7i	− 0.956202i
$266$	0	0
$267$	−3.22300e6	−0.169327
$268$	1.38404e6	0.0719027
$269$	− 1.20014e7i	− 0.616559i	−0.951296	−	0.308280i	$-0.900247\pi$
$269$	− 1.20014e7i	− 0.616559i	0.951296	−	0.308280i	$-0.0997532\pi$
$270$	−6.16207e6	−0.313065
$271$	− 3.90139e6i	− 0.196025i	−0.995185	−	0.0980125i	$-0.968751\pi$
$271$	− 3.90139e6i	− 0.196025i	0.995185	−	0.0980125i	$-0.0312485\pi$
$272$	3.54551e7i	1.76186i
$273$	0	0
$274$	−2.36870e7	−1.15149
$275$	2.76514e6	0.132959
$276$	2.34592e6i	0.111580i
$277$	2.12536e7	0.999984	0.499992	−	0.866030i	$-0.333336\pi$
$277$	2.12536e7	0.999984	0.499992	+	0.866030i	$0.333336\pi$
$278$	1.50475e7i	0.700373i
$279$	5.82055e6i	0.268010i
$280$	0	0
$281$	−1.01968e7	−0.459561	−0.229781	−	0.973242i	$-0.573801\pi$
$281$	−1.01968e7	−0.459561	−0.229781	+	0.973242i	$0.573801\pi$
$282$	2.16898e7	0.967183
$283$	3.85694e6i	0.170170i	0.996374	+	0.0850851i	$0.0271162\pi$
$283$	3.85694e6i	0.170170i	−0.996374	+	0.0850851i	$0.972884\pi$
$284$	−1.09915e7	−0.479846
$285$	− 1.27855e7i	− 0.552312i
$286$	6.87172e6i	0.293743i
$287$	0	0
$288$	5.39765e6	0.225958
$289$	−2.54958e7	−1.05627
$290$	3.15355e7i	1.29302i
$291$	−1.92044e7	−0.779333
$292$	202247.i	0.00812332i
$293$	− 2.88091e7i	− 1.14532i	−0.819793	−	0.572660i	$-0.805911\pi$
$293$	− 2.88091e7i	− 1.14532i	0.819793	−	0.572660i	$-0.194089\pi$
$294$	0	0
$295$	2.66228e7	1.03702
$296$	1.52306e7	0.587275
$297$	− 702291.i	− 0.0268070i
$298$	1.06179e7	0.401227
$299$	2.64546e7i	0.989663i
$300$	5.26615e6i	0.195042i
$301$	0	0
$302$	−4.05907e6	−0.147369
$303$	1.39811e7	0.502590
$304$	2.36198e7i	0.840728i
$305$	2.94545e7	1.03813
$306$	1.59360e7i	0.556179i
$307$	− 2.70175e7i	− 0.933747i	−0.884324	−	0.466874i	$-0.845380\pi$
$307$	− 2.70175e7i	− 0.933747i	0.884324	−	0.466874i	$-0.154620\pi$
$308$	0	0
$309$	−2.07880e7	−0.704591
$310$	3.89650e7	1.30794
$311$	5.60572e6i	0.186359i	0.995649	+	0.0931795i	$0.0297030\pi$
$311$	5.60572e6i	0.186359i	−0.995649	+	0.0931795i	$0.970297\pi$
$312$	2.38908e7	0.786622
$313$	2.87959e7i	0.939069i	0.882914	+	0.469534i	$0.155578\pi$
$313$	2.87959e7i	0.939069i	−0.882914	+	0.469534i	$0.844422\pi$
$314$	4.97602e7i	1.60728i
$315$	0	0
$316$	1.00541e7	0.318626
$317$	−3.65491e7	−1.14736	−0.573679	−	0.819080i	$-0.694484\pi$
$317$	−3.65491e7	−1.14736	−0.573679	+	0.819080i	$0.694484\pi$
$318$	1.47756e7i	0.459477i
$319$	−3.59411e6	−0.110718
$320$	2.01524e7i	0.615002i
$321$	1.57471e6i	0.0476087i
$322$	0	0
$323$	−3.30652e7	−0.981215
$324$	1.33750e6	0.0393240
$325$	5.93856e7i	1.72994i
$326$	1.55501e7	0.448829
$327$	3.04380e7i	0.870507i
$328$	− 1.78156e7i	− 0.504869i
$329$	0	0
$330$	−4.70141e6	−0.130824
$331$	2.32085e7	0.639974	0.319987	−	0.947422i	$-0.396321\pi$
$331$	2.32085e7	0.639974	0.319987	+	0.947422i	$0.396321\pi$
$332$	1.26704e7i	0.346238i
$333$	9.61542e6	0.260397
$334$	1.34128e6i	0.0359982i
$335$	1.06783e7i	0.284031i
$336$	0	0
$337$	2.11044e7	0.551421	0.275710	−	0.961241i	$-0.411087\pi$
$337$	2.11044e7	0.551421	0.275710	+	0.961241i	$0.411087\pi$
$338$	−1.02650e8	−2.65832
$339$	− 1.77679e7i	− 0.456075i
$340$	2.78868e7	0.709515
$341$	4.44084e6i	0.111996i
$342$	1.06164e7i	0.265399i
$343$	0	0
$344$	3.58458e7	0.880568
$345$	−1.80994e7	−0.440764
$346$	− 1.63677e7i	− 0.395148i
$347$	−806791.	−0.0193096	−0.00965479	−	0.999953i	$-0.503073\pi$
$347$	−806791.	−0.0193096	−0.00965479	+	0.999953i	$0.503073\pi$
$348$	− 6.84489e6i	− 0.162416i
$349$	6.98266e7i	1.64265i	0.570462	+	0.821324i	$0.306764\pi$
$349$	6.98266e7i	1.64265i	−0.570462	+	0.821324i	$0.693236\pi$
$350$	0	0
$351$	1.50828e7	0.348787
$352$	4.11818e6	0.0944230
$353$	− 2.67944e7i	− 0.609145i	−0.952489	−	0.304572i	$-0.901486\pi$
$353$	− 2.67944e7i	− 0.609145i	0.952489	−	0.304572i	$-0.0985135\pi$
$354$	−2.21061e7	−0.498313
$355$	− 8.48023e7i	− 1.89550i
$356$	− 4.68314e6i	− 0.103797i
$357$	0	0
$358$	9.29435e7	2.02567
$359$	2.56130e7	0.553575	0.276787	−	0.960931i	$-0.410730\pi$
$359$	2.56130e7	0.553575	0.276787	+	0.960931i	$0.410730\pi$
$360$	1.63453e7i	0.350336i
$361$	2.50181e7	0.531782
$362$	7.26458e7i	1.53139i
$363$	2.70801e7i	0.566148i
$364$	0	0
$365$	−1.56039e6	−0.0320889
$366$	−2.44574e7	−0.498846
$367$	2.78978e7i	0.564380i	0.959359	+	0.282190i	$0.0910608\pi$
$367$	2.78978e7i	0.564380i	−0.959359	+	0.282190i	$0.908939\pi$
$368$	3.34365e7	0.670930
$369$	− 1.12474e7i	− 0.223858i
$370$	− 6.43693e7i	− 1.27079i
$371$	0	0
$372$	−8.45748e6	−0.164290
$373$	2.23581e7	0.430833	0.215416	−	0.976522i	$-0.430889\pi$
$373$	2.23581e7	0.430833	0.215416	+	0.976522i	$0.430889\pi$
$374$	1.21585e7i	0.232416i
$375$	1.93544e6	0.0367017
$376$	− 5.75337e7i	− 1.08233i
$377$	− 7.71889e7i	− 1.44056i
$378$	0	0
$379$	5.91089e7	1.08576	0.542882	−	0.839809i	$-0.317333\pi$
$379$	5.91089e7	1.08576	0.542882	+	0.839809i	$0.317333\pi$
$380$	1.85779e7	0.338568
$381$	− 5.25340e7i	− 0.949873i
$382$	−4.76251e6	−0.0854370
$383$	− 4.60460e7i	− 0.819589i	−0.912178	−	0.409794i	$-0.865600\pi$
$383$	− 4.60460e7i	− 0.819589i	0.912178	−	0.409794i	$-0.134400\pi$
$384$	− 3.88940e7i	− 0.686892i
$385$	0	0
$386$	−8.10464e7	−1.40920
$387$	2.26303e7	0.390442
$388$	− 2.79048e7i	− 0.477731i
$389$	−4.33961e7	−0.737228	−0.368614	−	0.929583i	$-0.620168\pi$
$389$	−4.33961e7	−0.737228	−0.368614	+	0.929583i	$0.620168\pi$
$390$	− 1.00970e8i	− 1.70215i
$391$	4.68075e7i	0.783043i
$392$	0	0
$393$	−4.66458e7	−0.768484
$394$	4.14208e7	0.677220
$395$	7.75700e7i	1.25864i
$396$	1.02046e6	0.0164327
$397$	− 3.92013e7i	− 0.626512i	−0.949669	−	0.313256i	$-0.898580\pi$
$397$	− 3.92013e7i	− 0.626512i	0.949669	−	0.313256i	$-0.101420\pi$
$398$	− 6.62579e7i	− 1.05097i
$399$	0	0
$400$	7.50587e7	1.17279
$401$	−9.55248e7	−1.48144	−0.740718	−	0.671816i	$-0.765514\pi$
$401$	−9.55248e7	−1.48144	−0.740718	+	0.671816i	$0.765514\pi$
$402$	− 8.86663e6i	− 0.136484i
$403$	−9.53739e7	−1.45718
$404$	2.03151e7i	0.308088i
$405$	1.03191e7i	0.155338i
$406$	0	0
$407$	7.33617e6	0.108814
$408$	4.22712e7	0.622392
$409$	− 1.90221e7i	− 0.278028i	−0.990290	−	0.139014i	$-0.955607\pi$
$409$	− 1.90221e7i	− 0.278028i	0.990290	−	0.139014i	$-0.0443933\pi$
$410$	−7.52944e7	−1.09247
$411$	3.96669e7i	0.571351i
$412$	− 3.02057e7i	− 0.431915i
$413$	0	0
$414$	1.50287e7	0.211797
$415$	−9.77553e7	−1.36772
$416$	8.84443e7i	1.22854i
$417$	2.51989e7	0.347515
$418$	8.09988e6i	0.110905i
$419$	3.79635e7i	0.516089i	0.966133	+	0.258044i	$0.0830781\pi$
$419$	3.79635e7i	0.516089i	−0.966133	+	0.258044i	$0.916922\pi$
$420$	0	0
$421$	−1.18733e8	−1.59120	−0.795600	−	0.605823i	$-0.792844\pi$
$421$	−1.18733e8	−1.59120	−0.795600	+	0.605823i	$0.792844\pi$
$422$	−1.05111e8	−1.39865
$423$	− 3.63223e7i	− 0.479902i
$424$	3.91932e7	0.514178
$425$	1.05074e8i	1.36877i
$426$	7.04151e7i	0.910829i
$427$	0	0
$428$	−2.28812e6	−0.0291842
$429$	1.15075e7	0.145751
$430$	− 1.51496e8i	− 1.90544i
$431$	−5.88573e7	−0.735138	−0.367569	−	0.929996i	$-0.619810\pi$
$431$	−5.88573e7	−0.735138	−0.367569	+	0.929996i	$0.619810\pi$
$432$	− 1.90634e7i	− 0.236456i
$433$	5.48589e7i	0.675746i	0.941192	+	0.337873i	$0.109707\pi$
$433$	5.48589e7i	0.675746i	−0.941192	+	0.337873i	$0.890293\pi$
$434$	0	0
$435$	5.28102e7	0.641578
$436$	−4.42275e7	−0.533622
$437$	3.11827e7i	0.373654i
$438$	1.29566e6	0.0154194
$439$	7.20111e7i	0.851150i	0.904923	+	0.425575i	$0.139928\pi$
$439$	7.20111e7i	0.851150i	−0.904923	+	0.425575i	$0.860072\pi$
$440$	1.24708e7i	0.146398i
$441$	0	0
$442$	−2.61123e8	−3.02397
$443$	1.34716e8	1.54956	0.774779	−	0.632232i	$-0.217861\pi$
$443$	1.34716e8	1.54956	0.774779	+	0.632232i	$0.217861\pi$
$444$	1.39716e7i	0.159623i
$445$	3.61316e7	0.410023
$446$	1.04610e7i	0.117915i
$447$	− 1.77810e7i	− 0.199083i
$448$	0	0
$449$	1.73542e8	1.91719	0.958594	−	0.284777i	$-0.0919196\pi$
$449$	1.73542e8	1.91719	0.958594	+	0.284777i	$0.0919196\pi$
$450$	3.37366e7	0.370224
$451$	− 8.58131e6i	− 0.0935457i
$452$	2.58174e7	0.279574
$453$	6.79742e6i	0.0731223i
$454$	− 9.28216e7i	− 0.991931i
$455$	0	0
$456$	2.81607e7	0.296994
$457$	1.46345e8	1.53330	0.766652	−	0.642063i	$-0.221921\pi$
$457$	1.46345e8	1.53330	0.766652	+	0.642063i	$0.221921\pi$
$458$	− 1.81921e8i	− 1.89359i
$459$	2.66868e7	0.275968
$460$	− 2.62991e7i	− 0.270189i
$461$	− 6.84094e7i	− 0.698254i	−0.937075	−	0.349127i	$-0.886478\pi$
$461$	− 6.84094e7i	− 0.698254i	0.937075	−	0.349127i	$-0.113522\pi$
$462$	0	0
$463$	2.01813e7	0.203332	0.101666	−	0.994819i	$-0.467583\pi$
$463$	2.01813e7	0.203332	0.101666	+	0.994819i	$0.467583\pi$
$464$	−9.75606e7	−0.976609
$465$	− 6.52517e7i	− 0.648982i
$466$	−2.98099e7	−0.294580
$467$	− 7.90972e7i	− 0.776623i	−0.921528	−	0.388311i	$-0.873058\pi$
$467$	− 7.90972e7i	− 0.776623i	0.921528	−	0.388311i	$-0.126942\pi$
$468$	2.19159e7i	0.213806i
$469$	0	0
$470$	−2.43156e8	−2.34202
$471$	8.33296e7	0.797510
$472$	5.86378e7i	0.557637i
$473$	1.72660e7	0.163158
$474$	− 6.44097e7i	− 0.604806i
$475$	6.99994e7i	0.653151i
$476$	0	0
$477$	2.47436e7	0.227985
$478$	1.32508e8	1.21328
$479$	3.04774e6i	0.0277314i	0.999904	+	0.0138657i	$0.00441373\pi$
$479$	3.04774e6i	0.0277314i	−0.999904	+	0.0138657i	$0.995586\pi$
$480$	−6.05107e7	−0.547153
$481$	1.57556e8i	1.41579i
$482$	4.70861e7i	0.420486i
$483$	0	0
$484$	−3.93484e7	−0.347049
$485$	2.15293e8	1.88714
$486$	− 8.56844e6i	− 0.0746436i
$487$	−7.37522e7	−0.638540	−0.319270	−	0.947664i	$-0.603438\pi$
$487$	−7.37522e7	−0.638540	−0.319270	+	0.947664i	$0.603438\pi$
$488$	6.48748e7i	0.558234i
$489$	− 2.60406e7i	− 0.222702i
$490$	0	0
$491$	−8.29108e7	−0.700433	−0.350216	−	0.936669i	$-0.613892\pi$
$491$	−8.29108e7	−0.700433	−0.350216	+	0.936669i	$0.613892\pi$
$492$	1.63429e7	0.137225
$493$	− 1.36575e8i	− 1.13980i
$494$	−1.73957e8	−1.44298
$495$	7.87309e6i	0.0649127i
$496$	1.20545e8i	0.987879i
$497$	0	0
$498$	8.11705e7	0.657219
$499$	4.91078e7	0.395229	0.197615	−	0.980280i	$-0.436681\pi$
$499$	4.91078e7	0.395229	0.197615	+	0.980280i	$0.436681\pi$
$500$	2.81227e6i	0.0224981i
$501$	2.24614e6	0.0178618
$502$	− 1.01722e8i	− 0.804092i
$503$	1.66557e8i	1.30875i	0.756169	+	0.654377i	$0.227069\pi$
$503$	1.66557e8i	1.30875i	−0.756169	+	0.654377i	$0.772931\pi$
$504$	0	0
$505$	−1.56736e8	−1.21701
$506$	1.14663e7	0.0885057
$507$	1.71900e8i	1.31902i
$508$	7.63339e7	0.582273
$509$	9.32153e7i	0.706861i	0.935461	+	0.353430i	$0.114985\pi$
$509$	9.32153e7i	0.706861i	−0.935461	+	0.353430i	$0.885015\pi$
$510$	− 1.78652e8i	− 1.34678i
$511$	0	0
$512$	−1.21862e7	−0.0907942
$513$	1.77785e7	0.131687
$514$	− 9.00492e7i	− 0.663117i
$515$	2.33045e8	1.70616
$516$	3.28827e7i	0.239341i
$517$	− 2.77124e7i	− 0.200541i
$518$	0	0
$519$	−2.74098e7	−0.196066
$520$	−2.67829e8	−1.90479
$521$	1.24414e8i	0.879746i	0.898060	+	0.439873i	$0.144977\pi$
$521$	1.24414e8i	0.879746i	−0.898060	+	0.439873i	$0.855023\pi$
$522$	−4.38506e7	−0.308293
$523$	− 6.40833e7i	− 0.447961i	−0.974594	−	0.223980i	$-0.928095\pi$
$523$	− 6.40833e7i	− 0.447961i	0.974594	−	0.223980i	$-0.0719051\pi$
$524$	− 6.77781e7i	− 0.471081i
$525$	0	0
$526$	2.19565e8	1.50871
$527$	−1.68750e8	−1.15295
$528$	− 1.45446e7i	− 0.0988099i
$529$	−1.03893e8	−0.701811
$530$	− 1.65643e8i	− 1.11262i
$531$	3.70194e7i	0.247255i
$532$	0	0
$533$	1.84297e8	1.21713
$534$	−3.00017e7	−0.197025
$535$	− 1.76535e7i	− 0.115284i
$536$	−2.35193e7	−0.152732
$537$	− 1.55645e8i	− 1.00511i
$538$	− 1.11717e8i	− 0.717415i
$539$	0	0
$540$	−1.49941e7	−0.0952225
$541$	1.17205e8	0.740210	0.370105	−	0.928990i	$-0.379322\pi$
$541$	1.17205e8	0.740210	0.370105	+	0.928990i	$0.379322\pi$
$542$	− 3.63166e7i	− 0.228091i
$543$	1.21654e8	0.759851
$544$	1.56489e8i	0.972049i
$545$	− 3.41227e8i	− 2.10792i
$546$	0	0
$547$	−1.64328e8	−1.00403	−0.502017	−	0.864858i	$-0.667409\pi$
$547$	−1.64328e8	−1.00403	−0.502017	+	0.864858i	$0.667409\pi$
$548$	−5.76375e7	−0.350238
$549$	4.09569e7i	0.247520i
$550$	2.57397e7	0.154709
$551$	− 9.09846e7i	− 0.543893i
$552$	− 3.98646e7i	− 0.237012i
$553$	0	0
$554$	1.97842e8	1.16356
$555$	−1.07794e8	−0.630547
$556$	3.66149e7i	0.213027i
$557$	2.02204e8	1.17010	0.585052	−	0.810996i	$-0.301074\pi$
$557$	2.02204e8	1.17010	0.585052	+	0.810996i	$0.301074\pi$
$558$	5.41813e7i	0.311851i
$559$	3.70813e8i	2.12285i
$560$	0	0
$561$	2.03609e7	0.115321
$562$	−9.49179e7	−0.534736
$563$	1.41747e8i	0.794310i	0.917752	+	0.397155i	$0.130002\pi$
$563$	1.41747e8i	0.794310i	−0.917752	+	0.397155i	$0.869998\pi$
$564$	5.27777e7	0.294180
$565$	1.99188e8i	1.10438i
$566$	3.59028e7i	0.198006i
$567$	0	0
$568$	1.86780e8	1.01926
$569$	−3.41601e8	−1.85431	−0.927156	−	0.374676i	$-0.877754\pi$
$569$	−3.41601e8	−1.85431	−0.927156	+	0.374676i	$0.877754\pi$
$570$	− 1.19016e8i	− 0.642659i
$571$	−2.62828e8	−1.41177	−0.705883	−	0.708328i	$-0.749450\pi$
$571$	−2.62828e8	−1.41177	−0.705883	+	0.708328i	$0.749450\pi$
$572$	1.67209e7i	0.0893453i
$573$	7.97541e6i	0.0423925i
$574$	0	0
$575$	9.90920e7	0.521237
$576$	−2.80221e7	−0.146634
$577$	2.07708e8i	1.08125i	0.841264	+	0.540625i	$0.181812\pi$
$577$	2.07708e8i	1.08125i	−0.841264	+	0.540625i	$0.818188\pi$
$578$	−2.37331e8	−1.22905
$579$	1.35722e8i	0.699222i
$580$	7.67352e7i	0.393288i
$581$	0	0
$582$	−1.78767e8	−0.906815
$583$	1.88783e7	0.0952704
$584$	− 3.43682e6i	− 0.0172551i
$585$	−1.69087e8	−0.844582
$586$	− 2.68174e8i	− 1.33267i
$587$	− 2.00752e8i	− 0.992537i	−0.868169	−	0.496268i	$-0.834703\pi$
$587$	− 2.00752e8i	− 0.992537i	0.868169	−	0.496268i	$-0.165297\pi$
$588$	0	0
$589$	−1.12420e8	−0.550169
$590$	2.47822e8	1.20666
$591$	− 6.93643e7i	− 0.336026i
$592$	1.99138e8	0.959817
$593$	− 1.59419e8i	− 0.764498i	−0.924059	−	0.382249i	$-0.875150\pi$
$593$	− 1.59419e8i	− 0.764498i	0.924059	−	0.382249i	$-0.124850\pi$
$594$	− 6.53737e6i	− 0.0311920i
$595$	0	0
$596$	2.58365e7	0.122038
$597$	−1.10957e8	−0.521473
$598$	2.46256e8i	1.15155i
$599$	8.54057e7	0.397381	0.198690	−	0.980062i	$-0.436331\pi$
$599$	8.54057e7	0.397381	0.198690	+	0.980062i	$0.436331\pi$
$600$	− 8.94886e7i	− 0.414299i
$601$	− 1.61501e8i	− 0.743962i	−0.928240	−	0.371981i	$-0.878679\pi$
$601$	− 1.61501e8i	− 0.743962i	0.928240	−	0.371981i	$-0.121321\pi$
$602$	0	0
$603$	−1.48483e7	−0.0677211
$604$	−9.87692e6	−0.0448240
$605$	− 3.03583e8i	− 1.37092i
$606$	1.30145e8	0.584803
$607$	− 2.33726e7i	− 0.104506i	−0.998634	−	0.0522530i	$-0.983360\pi$
$607$	− 2.33726e7i	− 0.104506i	0.998634	−	0.0522530i	$-0.0166402\pi$
$608$	1.04252e8i	0.463844i
$609$	0	0
$610$	2.74181e8	1.20795
$611$	5.95167e8	2.60925
$612$	3.87769e7i	0.169168i
$613$	3.33485e8	1.44776	0.723878	−	0.689928i	$-0.242358\pi$
$613$	3.33485e8	1.44776	0.723878	+	0.689928i	$0.242358\pi$
$614$	− 2.51496e8i	− 1.08649i
$615$	1.26090e8i	0.542069i
$616$	0	0
$617$	−1.74626e8	−0.743451	−0.371726	−	0.928343i	$-0.621234\pi$
$617$	−1.74626e8	−0.743451	−0.371726	+	0.928343i	$0.621234\pi$
$618$	−1.93508e8	−0.819847
$619$	5.20287e7i	0.219367i	0.993967	+	0.109683i	$0.0349837\pi$
$619$	5.20287e7i	0.219367i	−0.993967	+	0.109683i	$0.965016\pi$
$620$	9.48132e7	0.397827
$621$	− 2.51674e7i	− 0.105091i
$622$	5.21816e7i	0.216843i
$623$	0	0
$624$	3.12368e8	1.28562
$625$	−2.54737e8	−1.04340
$626$	2.68050e8i	1.09268i
$627$	1.35642e7	0.0550292
$628$	1.21081e8i	0.488874i
$629$	2.78772e8i	1.12020i
$630$	0	0
$631$	3.39999e8	1.35329	0.676643	−	0.736311i	$-0.263434\pi$
$631$	3.39999e8	1.35329	0.676643	+	0.736311i	$0.263434\pi$
$632$	−1.70851e8	−0.676809
$633$	1.76021e8i	0.693990i
$634$	−3.40222e8	−1.33504
$635$	5.88936e8i	2.30010i
$636$	3.59534e7i	0.139755i
$637$	0	0
$638$	−3.34562e7	−0.128829
$639$	1.17919e8	0.451940
$640$	4.36024e8i	1.66330i
$641$	−1.54570e7	−0.0586883	−0.0293441	−	0.999569i	$-0.509342\pi$
$641$	−1.54570e7	−0.0586883	−0.0293441	+	0.999569i	$0.509342\pi$
$642$	1.46584e7i	0.0553965i
$643$	− 1.06911e8i	− 0.402152i	−0.979576	−	0.201076i	$-0.935556\pi$
$643$	− 1.06911e8i	− 0.402152i	0.979576	−	0.201076i	$-0.0644438\pi$
$644$	0	0
$645$	−2.53699e8	−0.945451
$646$	−3.07792e8	−1.14172
$647$	− 5.00171e8i	− 1.84674i	−0.383914	−	0.923369i	$-0.625424\pi$
$647$	− 5.00171e8i	− 1.84674i	0.383914	−	0.923369i	$-0.374576\pi$
$648$	−2.27283e7	−0.0835300
$649$	2.82443e7i	0.103323i
$650$	5.52799e8i	2.01292i
$651$	0	0
$652$	3.78380e7	0.136516
$653$	1.96667e8	0.706304	0.353152	−	0.935566i	$-0.385110\pi$
$653$	1.96667e8	0.706304	0.353152	+	0.935566i	$0.385110\pi$
$654$	2.83336e8i	1.01290i
$655$	5.22926e8	1.86087
$656$	− 2.32936e8i	− 0.825136i
$657$	− 2.16974e6i	− 0.00765089i
$658$	0	0
$659$	2.58438e8	0.903026	0.451513	−	0.892264i	$-0.350884\pi$
$659$	2.58438e8	0.903026	0.451513	+	0.892264i	$0.350884\pi$
$660$	−1.14399e7	−0.0397915
$661$	− 4.63307e8i	− 1.60422i	−0.597174	−	0.802111i	$-0.703710\pi$
$661$	− 4.63307e8i	− 1.60422i	0.597174	−	0.802111i	$-0.296290\pi$
$662$	2.16039e8	0.744660
$663$	4.37282e8i	1.50045i
$664$	− 2.15310e8i	− 0.735461i
$665$	0	0
$666$	8.95064e7	0.302992
$667$	−1.28799e8	−0.434045
$668$	3.26373e6i	0.0109493i
$669$	1.75183e7	0.0585078
$670$	9.94000e7i	0.330493i
$671$	3.12485e7i	0.103433i
$672$	0	0
$673$	−3.81262e8	−1.25077	−0.625385	−	0.780316i	$-0.715058\pi$
$673$	−3.81262e8	−1.25077	−0.625385	+	0.780316i	$0.715058\pi$
$674$	1.96453e8	0.641621
$675$	− 5.64962e7i	− 0.183699i
$676$	−2.49777e8	−0.808560
$677$	− 4.29992e8i	− 1.38578i	−0.721044	−	0.692890i	$-0.756337\pi$
$677$	− 4.29992e8i	− 1.38578i	0.721044	−	0.692890i	$-0.243663\pi$
$678$	− 1.65394e8i	− 0.530679i
$679$	0	0
$680$	−4.73885e8	−1.50711
$681$	−1.55441e8	−0.492181
$682$	4.13381e7i	0.130316i
$683$	1.52930e8	0.479989	0.239995	−	0.970774i	$-0.422854\pi$
$683$	1.52930e8	0.479989	0.239995	+	0.970774i	$0.422854\pi$
$684$	2.58328e7i	0.0807241i
$685$	− 4.44689e8i	− 1.38352i
$686$	0	0
$687$	−3.04649e8	−0.939570
$688$	4.68679e8	1.43916
$689$	4.05441e8i	1.23957i
$690$	−1.68480e8	−0.512864
$691$	2.30188e8i	0.697667i	0.937185	+	0.348834i	$0.113422\pi$
$691$	2.30188e8i	0.697667i	−0.937185	+	0.348834i	$0.886578\pi$
$692$	− 3.98274e7i	− 0.120189i
$693$	0	0
$694$	−7.51012e6	−0.0224682
$695$	−2.82494e8	−0.841501
$696$	1.16316e8i	0.344995i
$697$	3.26086e8	0.963017
$698$	6.49990e8i	1.91135i
$699$	4.99204e7i	0.146166i
$700$	0	0
$701$	8.76414e7	0.254422	0.127211	−	0.991876i	$-0.459397\pi$
$701$	8.76414e7	0.254422	0.127211	+	0.991876i	$0.459397\pi$
$702$	1.40400e8	0.405841
$703$	1.85715e8i	0.534541i
$704$	−2.13797e7	−0.0612752
$705$	4.07194e8i	1.16207i
$706$	− 2.49419e8i	− 0.708788i
$707$	0	0
$708$	−5.37906e7	−0.151568
$709$	3.13312e8	0.879101	0.439550	−	0.898218i	$-0.355138\pi$
$709$	3.13312e8	0.879101	0.439550	+	0.898218i	$0.355138\pi$
$710$	− 7.89394e8i	− 2.20556i
$711$	−1.07862e8	−0.300096
$712$	7.95814e7i	0.220481i
$713$	1.59143e8i	0.439054i
$714$	0	0
$715$	−1.29006e8	−0.352933
$716$	2.26159e8	0.616133
$717$	− 2.21902e8i	− 0.602009i
$718$	2.38422e8	0.644128
$719$	− 7.15454e8i	− 1.92484i	−0.271561	−	0.962421i	$-0.587540\pi$
$719$	− 7.15454e8i	− 1.92484i	0.271561	−	0.962421i	$-0.412460\pi$
$720$	2.13712e8i	0.572574i
$721$	0	0
$722$	2.32885e8	0.618770
$723$	7.88515e7	0.208639
$724$	1.76768e8i	0.465789i
$725$	−2.89130e8	−0.758715
$726$	2.52079e8i	0.658758i
$727$	− 7.42437e8i	− 1.93222i	−0.258132	−	0.966110i	$-0.583107\pi$
$727$	− 7.42437e8i	− 1.93222i	0.258132	−	0.966110i	$-0.416893\pi$
$728$	0	0
$729$	−1.43489e7	−0.0370370
$730$	−1.45251e7	−0.0373379
$731$	6.56100e8i	1.67965i
$732$	−5.95120e7	−0.151730
$733$	− 4.44621e8i	− 1.12896i	−0.825447	−	0.564479i	$-0.809077\pi$
$733$	− 4.44621e8i	− 1.12896i	0.825447	−	0.564479i	$-0.190923\pi$
$734$	2.59690e8i	0.656700i
$735$	0	0
$736$	1.47580e8	0.370164
$737$	−1.13286e7	−0.0282992
$738$	− 1.04698e8i	− 0.260477i
$739$	−4.77974e8	−1.18432	−0.592162	−	0.805819i	$-0.701726\pi$
$739$	−4.77974e8	−1.18432	−0.592162	+	0.805819i	$0.701726\pi$
$740$	− 1.56629e8i	− 0.386526i
$741$	2.91313e8i	0.715987i
$742$	0	0
$743$	4.11550e8	1.00336	0.501679	−	0.865054i	$-0.332716\pi$
$743$	4.11550e8	1.00336	0.501679	+	0.865054i	$0.332716\pi$
$744$	1.43719e8	0.348977
$745$	1.99335e8i	0.482076i
$746$	2.08124e8	0.501308
$747$	− 1.35930e8i	− 0.326102i
$748$	2.95852e7i	0.0706919i
$749$	0	0
$750$	1.80163e7	0.0427053
$751$	8.05590e6	0.0190193	0.00950965	−	0.999955i	$-0.496973\pi$
$751$	8.05590e6	0.0190193	0.00950965	+	0.999955i	$0.496973\pi$
$752$	− 7.52244e8i	− 1.76891i
$753$	−1.70347e8	−0.398978
$754$	− 7.18523e8i	− 1.67620i
$755$	− 7.62031e7i	− 0.177065i
$756$	0	0
$757$	−6.97539e7	−0.160798	−0.0803990	−	0.996763i	$-0.525619\pi$
$757$	−6.97539e7	−0.160798	−0.0803990	+	0.996763i	$0.525619\pi$
$758$	5.50223e8	1.26337
$759$	− 1.92017e7i	− 0.0439152i
$760$	−3.15697e8	−0.719168
$761$	− 3.85007e8i	− 0.873604i	−0.899558	−	0.436802i	$-0.856111\pi$
$761$	− 3.85007e8i	− 0.873604i	0.899558	−	0.436802i	$-0.143889\pi$
$762$	− 4.89020e8i	− 1.10525i
$763$	0	0
$764$	−1.15886e7	−0.0259867
$765$	−2.99174e8	−0.668251
$766$	− 4.28626e8i	− 0.953656i
$767$	−6.06590e8	−1.34434
$768$	− 2.47002e8i	− 0.545276i
$769$	5.19869e8i	1.14318i	0.820539	+	0.571590i	$0.193673\pi$
$769$	5.19869e8i	1.14318i	−0.820539	+	0.571590i	$0.806327\pi$
$770$	0	0
$771$	−1.50799e8	−0.329029
$772$	−1.97210e8	−0.428624
$773$	− 3.79848e8i	− 0.822377i	−0.911550	−	0.411188i	$-0.865114\pi$
$773$	− 3.79848e8i	− 0.822377i	0.911550	−	0.411188i	$-0.134886\pi$
$774$	2.10657e8	0.454311
$775$	3.57246e8i	0.767471i
$776$	4.74191e8i	1.01477i
$777$	0	0
$778$	−4.03958e8	−0.857823
$779$	2.17235e8	0.459535
$780$	− 2.45689e8i	− 0.517729i
$781$	8.99672e7	0.188856
$782$	4.35714e8i	0.911132i
$783$	7.34332e7i	0.152970i
$784$	0	0
$785$	−9.34173e8	−1.93116
$786$	−4.34208e8	−0.894192
$787$	− 5.89540e8i	− 1.20945i	−0.796433	−	0.604727i	$-0.793282\pi$
$787$	− 5.89540e8i	− 1.20945i	0.796433	−	0.604727i	$-0.206718\pi$
$788$	1.00789e8	0.205984
$789$	− 3.67689e8i	− 0.748600i
$790$	7.22070e8i	1.46453i
$791$	0	0
$792$	−1.73408e7	−0.0349054
$793$	−6.71109e8	−1.34578
$794$	− 3.64911e8i	− 0.728996i
$795$	−2.77390e8	−0.552063
$796$	− 1.61225e8i	− 0.319663i
$797$	− 6.68330e8i	− 1.32013i	−0.751210	−	0.660063i	$-0.770529\pi$
$797$	− 6.68330e8i	− 1.32013i	0.751210	−	0.660063i	$-0.229471\pi$
$798$	0	0
$799$	1.05306e9	2.06449
$800$	3.31289e8	0.647050
$801$	5.02415e7i	0.0977609i
$802$	−8.89205e8	−1.72377
$803$	− 1.65542e6i	− 0.00319715i
$804$	− 2.15751e7i	− 0.0415130i
$805$	0	0
$806$	−8.87800e8	−1.69555
$807$	−1.87083e8	−0.355971
$808$	− 3.45218e8i	− 0.654423i
$809$	−5.03726e8	−0.951369	−0.475685	−	0.879616i	$-0.657800\pi$
$809$	−5.03726e8	−0.951369	−0.475685	+	0.879616i	$0.657800\pi$
$810$	9.60571e7i	0.180748i
$811$	7.44534e7i	0.139580i	0.997562	+	0.0697898i	$0.0222329\pi$
$811$	7.44534e7i	0.139580i	−0.997562	+	0.0697898i	$0.977767\pi$
$812$	0	0
$813$	−6.08167e7	−0.113175
$814$	6.82898e7	0.126614
$815$	2.91930e8i	0.539269i
$816$	5.52690e8	1.01721
$817$	4.37088e8i	0.801498i
$818$	− 1.77070e8i	− 0.323508i
$819$	0	0
$820$	−1.83213e8	−0.332289
$821$	−1.85383e8	−0.334997	−0.167499	−	0.985872i	$-0.553569\pi$
$821$	−1.85383e8	−0.334997	−0.167499	+	0.985872i	$0.553569\pi$
$822$	3.69245e8i	0.664812i
$823$	−257264.	−0.000461509 0	−0.000230755	−	1.00000i	$-0.500073\pi$
$823$	−257264.	−0.000461509 0	−0.000230755		1.00000i	$0.500073\pi$
$824$	5.13292e8i	0.917450i
$825$	− 4.31043e7i	− 0.0767642i
$826$	0	0
$827$	4.71800e8	0.834144	0.417072	−	0.908873i	$-0.363056\pi$
$827$	4.71800e8	0.834144	0.417072	+	0.908873i	$0.363056\pi$
$828$	3.65692e7	0.0644206
$829$	1.28235e8i	0.225083i	0.993647	+	0.112542i	$0.0358991\pi$
$829$	1.28235e8i	0.225083i	−0.993647	+	0.112542i	$0.964101\pi$
$830$	−9.09968e8	−1.59145
$831$	− 3.31311e8i	− 0.577341i
$832$	− 4.59163e8i	− 0.797254i
$833$	0	0
$834$	2.34567e8	0.404361
$835$	−2.51806e7	−0.0432520
$836$	1.97094e7i	0.0337329i
$837$	9.07333e7	0.154736
$838$	3.53389e8i	0.600510i
$839$	− 1.11310e9i	− 1.88473i	−0.334590	−	0.942364i	$-0.608598\pi$
$839$	− 1.11310e9i	− 1.88473i	0.334590	−	0.942364i	$-0.391402\pi$
$840$	0	0
$841$	−2.19015e8	−0.368202
$842$	−1.10524e9	−1.85149
$843$	1.58952e8i	0.265328i
$844$	−2.55765e8	−0.425416
$845$	− 1.92710e9i	− 3.19399i
$846$	− 3.38111e8i	− 0.558404i
$847$	0	0
$848$	5.12445e8	0.840350
$849$	6.01237e7	0.0982478
$850$	9.78098e8i	1.59267i
$851$	2.62900e8	0.426582
$852$	1.71341e8i	0.277039i
$853$	2.87514e8i	0.463247i	0.972806	+	0.231623i	$0.0744037\pi$
$853$	2.87514e8i	0.463247i	−0.972806	+	0.231623i	$0.925596\pi$
$854$	0	0
$855$	−1.99307e8	−0.318878
$856$	3.88824e7	0.0619915
$857$	− 1.16000e8i	− 0.184296i	−0.995745	−	0.0921478i	$-0.970627\pi$
$857$	− 1.16000e8i	− 0.184296i	0.995745	−	0.0921478i	$-0.0293732\pi$
$858$	1.07120e8	0.169593
$859$	− 1.66551e8i	− 0.262765i	−0.991332	−	0.131382i	$-0.958058\pi$
$859$	− 1.66551e8i	− 0.262765i	0.991332	−	0.131382i	$-0.0419416\pi$
$860$	− 3.68634e8i	− 0.579562i
$861$	0	0
$862$	−5.47881e8	−0.855391
$863$	8.54169e8	1.32896	0.664479	−	0.747307i	$-0.268653\pi$
$863$	8.54169e8	1.32896	0.664479	+	0.747307i	$0.268653\pi$
$864$	− 8.41410e7i	− 0.130457i
$865$	3.07279e8	0.474772
$866$	5.10661e8i	0.786284i
$867$	3.97440e8i	0.609837i
$868$	0	0
$869$	−8.22944e7	−0.125404
$870$	4.91590e8	0.746527
$871$	− 2.43300e8i	− 0.368203i
$872$	7.51566e8	1.13349
$873$	2.99368e8i	0.449948i
$874$	2.90268e8i	0.434776i
$875$	0	0
$876$	3.15272e6	0.00469000
$877$	−1.69895e8	−0.251873	−0.125936	−	0.992038i	$-0.540194\pi$
$877$	−1.69895e8	−0.251873	−0.125936	+	0.992038i	$0.540194\pi$
$878$	6.70325e8i	0.990380i
$879$	−4.49090e8	−0.661251
$880$	1.63054e8i	0.239267i
$881$	8.77883e7i	0.128383i	0.997938	+	0.0641917i	$0.0204469\pi$
$881$	8.77883e7i	0.128383i	−0.997938	+	0.0641917i	$0.979553\pi$
$882$	0	0
$883$	−1.75158e8	−0.254417	−0.127209	−	0.991876i	$-0.540602\pi$
$883$	−1.75158e8	−0.254417	−0.127209	+	0.991876i	$0.540602\pi$
$884$	−6.35388e8	−0.919776
$885$	− 4.15009e8i	− 0.598725i
$886$	1.25402e9	1.80303
$887$	1.11026e9i	1.59095i	0.605990	+	0.795473i	$0.292777\pi$
$887$	1.11026e9i	1.59095i	−0.605990	+	0.795473i	$0.707223\pi$
$888$	− 2.37421e8i	− 0.339063i
$889$	0	0
$890$	3.36336e8	0.477094
$891$	−1.09476e7	−0.0154770
$892$	2.54548e7i	0.0358653i
$893$	7.01539e8	0.985139
$894$	− 1.65517e8i	− 0.231648i
$895$	1.74487e9i	2.43386i
$896$	0	0
$897$	4.12386e8	0.571382
$898$	1.61543e9	2.23080
$899$	− 4.64345e8i	− 0.639089i
$900$	8.20911e7	0.112608
$901$	7.17369e8i	0.980773i
$902$	− 7.98802e7i	− 0.108848i
$903$	0	0
$904$	−4.38719e8	−0.593856
$905$	−1.36382e9	−1.83997
$906$	6.32747e7i	0.0850835i
$907$	−7.08926e8	−0.950121	−0.475060	−	0.879953i	$-0.657574\pi$
$907$	−7.08926e8	−0.950121	−0.475060	+	0.879953i	$0.657574\pi$
$908$	− 2.25862e8i	− 0.301707i
$909$	− 2.17944e8i	− 0.290170i
$910$	0	0
$911$	9.81055e8	1.29759	0.648796	−	0.760962i	$-0.275273\pi$
$911$	9.81055e8	1.29759	0.648796	+	0.760962i	$0.275273\pi$
$912$	3.68196e8	0.485395
$913$	− 1.03709e8i	− 0.136271i
$914$	1.36227e9	1.78412
$915$	− 4.59151e8i	− 0.599366i
$916$	− 4.42666e8i	− 0.575957i
$917$	0	0
$918$	2.48417e8	0.321110
$919$	5.13524e8	0.661628	0.330814	−	0.943696i	$-0.392677\pi$
$919$	5.13524e8	0.661628	0.330814	+	0.943696i	$0.392677\pi$
$920$	4.46905e8i	0.573920i
$921$	−4.21160e8	−0.539099
$922$	− 6.36798e8i	− 0.812473i
$923$	1.93218e9i	2.45722i
$924$	0	0
$925$	5.90162e8	0.745670
$926$	1.87860e8	0.236593
$927$	3.24053e8i	0.406796i
$928$	−4.30607e8	−0.538812
$929$	1.87591e8i	0.233973i	0.993133	+	0.116987i	$0.0373234\pi$
$929$	1.87591e8i	0.233973i	−0.993133	+	0.116987i	$0.962677\pi$
$930$	− 6.07404e8i	− 0.755142i
$931$	0	0
$932$	−7.25362e7	−0.0895998
$933$	8.73845e7	0.107594
$934$	− 7.36286e8i	− 0.903662i
$935$	−2.28258e8	−0.279248
$936$	− 3.72420e8i	− 0.454156i
$937$	− 7.38833e8i	− 0.898106i	−0.893505	−	0.449053i	$-0.851761\pi$
$937$	− 7.38833e8i	− 0.898106i	0.893505	−	0.449053i	$-0.148239\pi$
$938$	0	0
$939$	4.48883e8	0.542172
$940$	−5.91669e8	−0.712353
$941$	1.33442e9i	1.60149i	0.599007	+	0.800744i	$0.295562\pi$
$941$	1.33442e9i	1.60149i	−0.599007	+	0.800744i	$0.704438\pi$
$942$	7.75684e8	0.927966
$943$	− 3.07521e8i	− 0.366724i
$944$	7.66681e8i	0.911378i
$945$	0	0
$946$	1.60723e8	0.189847
$947$	6.38139e7	0.0751390	0.0375695	−	0.999294i	$-0.488038\pi$
$947$	6.38139e7	0.0751390	0.0375695	+	0.999294i	$0.488038\pi$
$948$	− 1.56728e8i	− 0.183959i
$949$	3.55528e7	0.0415982
$950$	6.51599e8i	0.759993i
$951$	5.69744e8i	0.662428i
$952$	0	0
$953$	5.83137e8	0.673740	0.336870	−	0.941551i	$-0.390632\pi$
$953$	5.83137e8	0.673740	0.336870	+	0.941551i	$0.390632\pi$
$954$	2.30329e8	0.265279
$955$	− 8.94090e7i	− 0.102653i
$956$	3.22432e8	0.369032
$957$	5.60266e7i	0.0639232i
$958$	2.83703e7i	0.0322677i
$959$	0	0
$960$	3.14144e8	0.355071
$961$	3.13764e8	0.353535
$962$	1.46663e9i	1.64738i
$963$	2.45474e7	0.0274869
$964$	1.14574e8i	0.127896i
$965$	− 1.52152e9i	− 1.69316i
$966$	0	0
$967$	−1.30054e9	−1.43828	−0.719140	−	0.694865i	$-0.755464\pi$
$967$	−1.30054e9	−1.43828	−0.719140	+	0.694865i	$0.755464\pi$
$968$	6.68654e8	0.737183
$969$	5.15436e8i	0.566505i
$970$	2.00408e9	2.19584
$971$	1.53209e9i	1.67350i	0.547583	+	0.836752i	$0.315548\pi$
$971$	1.53209e9i	1.67350i	−0.547583	+	0.836752i	$0.684452\pi$
$972$	− 2.08495e7i	− 0.0227037i
$973$	0	0
$974$	−6.86532e8	−0.742992
$975$	9.25731e8	0.998782
$976$	8.48228e8i	0.912353i
$977$	6.06025e8	0.649841	0.324920	−	0.945741i	$-0.394663\pi$
$977$	6.06025e8	0.649841	0.324920	+	0.945741i	$0.394663\pi$
$978$	− 2.42402e8i	− 0.259131i
$979$	3.83322e7i	0.0408523i
$980$	0	0
$981$	4.74481e8	0.502588
$982$	−7.71786e8	−0.815009
$983$	1.38350e9i	1.45653i	0.685296	+	0.728265i	$0.259673\pi$
$983$	1.38350e9i	1.45653i	−0.685296	+	0.728265i	$0.740327\pi$
$984$	−2.77718e8	−0.291486
$985$	7.77613e8i	0.813683i
$986$	− 1.27132e9i	− 1.32625i
$987$	0	0
$988$	−4.23289e8	−0.438901
$989$	6.18746e8	0.639623
$990$	7.32877e7i	0.0755310i
$991$	2.04405e8	0.210025	0.105013	−	0.994471i	$-0.466512\pi$
$991$	2.04405e8	0.210025	0.105013	+	0.994471i	$0.466512\pi$
$992$	5.32054e8i	0.545030i
$993$	− 3.61784e8i	− 0.369489i
$994$	0	0
$995$	1.24389e9	1.26274
$996$	1.97512e8	0.199901
$997$	− 1.52872e9i	− 1.54257i	−0.636493	−	0.771283i	$-0.719616\pi$
$997$	− 1.52872e9i	− 1.54257i	0.636493	−	0.771283i	$-0.280384\pi$
$998$	4.57127e8	0.459881
$999$	− 1.49890e8i	− 0.150340i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.7.d.a.97.5		8
3.2	odd	2		441.7.d.d.244.3		8
7.2	even	3		21.7.f.b.10.2	✓	8
7.3	odd	6		21.7.f.b.19.2	yes	8
7.4	even	3		147.7.f.a.19.2		8
7.5	odd	6		147.7.f.a.31.2		8
7.6	odd	2	inner	147.7.d.a.97.6		8
21.2	odd	6		63.7.m.c.10.3		8
21.17	even	6		63.7.m.c.19.3		8
21.20	even	2		441.7.d.d.244.4		8
28.3	even	6		336.7.bh.b.145.4		8
28.23	odd	6		336.7.bh.b.241.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.7.f.b.10.2	✓	8	7.2	even	3
21.7.f.b.19.2	yes	8	7.3	odd	6
63.7.m.c.10.3		8	21.2	odd	6
63.7.m.c.19.3		8	21.17	even	6
147.7.d.a.97.5		8	1.1	even	1	trivial
147.7.d.a.97.6		8	7.6	odd	2	inner
147.7.f.a.19.2		8	7.4	even	3
147.7.f.a.31.2		8	7.5	odd	6
336.7.bh.b.145.4		8	28.3	even	6
336.7.bh.b.241.4		8	28.23	odd	6
441.7.d.d.244.3		8	3.2	odd	2
441.7.d.d.244.4		8	21.20	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	147.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+9.30863 q^{2} -15.5885i q^{3} +22.6506 q^{4} +174.756i q^{5} -145.107i q^{6} -384.906 q^{8} -243.000 q^{9} +O(q^{10})\)	\(q+9.30863 q^{2} -15.5885i q^{3} +22.6506 q^{4} +174.756i q^{5} -145.107i q^{6} -384.906 q^{8} -243.000 q^{9} +1626.74i q^{10} -185.399 q^{11} -353.088i q^{12} -3981.73i q^{13} +2724.17 q^{15} -5032.59 q^{16} -7045.09i q^{17} -2262.00 q^{18} -4693.37i q^{19} +3958.32i q^{20} -1725.81 q^{22} -6643.99 q^{23} +6000.09i q^{24} -14914.5 q^{25} -37064.5i q^{26} +3788.00i q^{27} +19385.8 q^{29} +25358.3 q^{30} -23952.9i q^{31} -22212.5 q^{32} +2890.09i q^{33} -65580.2i q^{34} -5504.10 q^{36} -39569.6 q^{37} -43688.9i q^{38} -62069.0 q^{39} -67264.5i q^{40} +46285.6i q^{41} -93128.7 q^{43} -4199.41 q^{44} -42465.6i q^{45} -61846.5 q^{46} +149475. i q^{47} +78450.3i q^{48} -138834. q^{50} -109822. q^{51} -90188.7i q^{52} -101825. q^{53} +35261.1i q^{54} -32399.5i q^{55} -73162.4 q^{57} +180455. q^{58} -152343. i q^{59} +61704.2 q^{60} -168547. i q^{61} -222968. i q^{62} +115317. q^{64} +695830. q^{65} +26902.7i q^{66} +61104.0 q^{67} -159576. i q^{68} +103570. i q^{69} -485262. q^{71} +93532.2 q^{72} +8928.98i q^{73} -368339. q^{74} +232495. i q^{75} -106308. i q^{76} -577778. q^{78} +443877. q^{79} -879473. i q^{80} +59049.0 q^{81} +430855. i q^{82} +559383. i q^{83} +1.23117e6 q^{85} -866901. q^{86} -302194. i q^{87} +71361.2 q^{88} -206755. i q^{89} -395297. i q^{90} -150491. q^{92} -373388. q^{93} +1.39140e6i q^{94} +820193. q^{95} +346259. i q^{96} -1.23197e6i q^{97} +45052.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 10 q^{2} + 346 q^{4} - 454 q^{8} - 1944 q^{9}+O(q^{10}) \) 8 * q + 10 * q^2 + 346 * q^4 - 454 * q^8 - 1944 * q^9	\( 8 q + 10 q^{2} + 346 q^{4} - 454 q^{8} - 1944 q^{9} + 2140 q^{11} - 756 q^{15} - 7822 q^{16} - 2430 q^{18} - 78 q^{22} + 30448 q^{23} - 44548 q^{25} + 32524 q^{29} - 4698 q^{30} - 140406 q^{32} - 84078 q^{36} + 91340 q^{37} - 186732 q^{39} - 445660 q^{43} + 377658 q^{44} - 1051608 q^{46} - 1218884 q^{50} - 129816 q^{51} + 26068 q^{53} - 442908 q^{57} + 319002 q^{58} - 859410 q^{60} - 1410446 q^{64} + 778008 q^{65} - 768188 q^{67} + 225688 q^{71} + 110322 q^{72} - 2371060 q^{74} - 342792 q^{78} + 1119184 q^{79} + 472392 q^{81} + 1953576 q^{85} + 4604804 q^{86} - 609774 q^{88} - 113064 q^{92} - 723600 q^{93} - 2320224 q^{95} - 520020 q^{99}+O(q^{100}) \) 8 * q + 10 * q^2 + 346 * q^4 - 454 * q^8 - 1944 * q^9 + 2140 * q^11 - 756 * q^15 - 7822 * q^16 - 2430 * q^18 - 78 * q^22 + 30448 * q^23 - 44548 * q^25 + 32524 * q^29 - 4698 * q^30 - 140406 * q^32 - 84078 * q^36 + 91340 * q^37 - 186732 * q^39 - 445660 * q^43 + 377658 * q^44 - 1051608 * q^46 - 1218884 * q^50 - 129816 * q^51 + 26068 * q^53 - 442908 * q^57 + 319002 * q^58 - 859410 * q^60 - 1410446 * q^64 + 778008 * q^65 - 768188 * q^67 + 225688 * q^71 + 110322 * q^72 - 2371060 * q^74 - 342792 * q^78 + 1119184 * q^79 + 472392 * q^81 + 1953576 * q^85 + 4604804 * q^86 - 609774 * q^88 - 113064 * q^92 - 723600 * q^93 - 2320224 * q^95 - 520020 * q^99

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