LMFDB - Embedded newform 338.10.a.e.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [338,10,Mod(1,338)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(338, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("338.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 338 = 2 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	338.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:	$174.082112623$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.2119705.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 376x + 1820 $ x^3 - x^2 - 376*x + 1820
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2\cdot 3^{3} $
Twist minimal:	no (minimal twist has level 26)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-21.0141$ of defining polynomial
Character	$\chi$	$=$	338.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-16.0000 q^{2} +85.7459 q^{3} +256.000 q^{4} -1787.19 q^{5} -1371.94 q^{6} +751.989 q^{7} -4096.00 q^{8} -12330.6 q^{9} +28595.0 q^{10} -58551.0 q^{11} +21951.0 q^{12} -12031.8 q^{14} -153244. q^{15} +65536.0 q^{16} +234846. q^{17} +197290. q^{18} +103190. q^{19} -457520. q^{20} +64480.0 q^{21} +936816. q^{22} +1.08806e6 q^{23} -351215. q^{24} +1.24092e6 q^{25} -2.74504e6 q^{27} +192509. q^{28} +3.17511e6 q^{29} +2.45191e6 q^{30} +6.17201e6 q^{31} -1.04858e6 q^{32} -5.02051e6 q^{33} -3.75753e6 q^{34} -1.34395e6 q^{35} -3.15664e6 q^{36} +1.56181e7 q^{37} -1.65103e6 q^{38} +7.32032e6 q^{40} +2.01455e7 q^{41} -1.03168e6 q^{42} -2.69024e7 q^{43} -1.49891e7 q^{44} +2.20372e7 q^{45} -1.74089e7 q^{46} +3.03118e7 q^{47} +5.61945e6 q^{48} -3.97881e7 q^{49} -1.98547e7 q^{50} +2.01371e7 q^{51} +6.56149e7 q^{53} +4.39206e7 q^{54} +1.04642e8 q^{55} -3.08015e6 q^{56} +8.84808e6 q^{57} -5.08018e7 q^{58} -1.12025e8 q^{59} -3.92305e7 q^{60} +2.44277e7 q^{61} -9.87522e7 q^{62} -9.27250e6 q^{63} +1.67772e7 q^{64} +8.03282e7 q^{66} -1.29055e8 q^{67} +6.01205e7 q^{68} +9.32967e7 q^{69} +2.15031e7 q^{70} +1.12546e8 q^{71} +5.05063e7 q^{72} +1.77758e8 q^{73} -2.49889e8 q^{74} +1.06404e8 q^{75} +2.64165e7 q^{76} -4.40297e7 q^{77} -6.05015e8 q^{79} -1.17125e8 q^{80} +7.32791e6 q^{81} -3.22328e8 q^{82} -2.01755e8 q^{83} +1.65069e7 q^{84} -4.19714e8 q^{85} +4.30439e8 q^{86} +2.72253e8 q^{87} +2.39825e8 q^{88} -8.62460e8 q^{89} -3.52595e8 q^{90} +2.78543e8 q^{92} +5.29225e8 q^{93} -4.84989e8 q^{94} -1.84419e8 q^{95} -8.99111e7 q^{96} +2.15081e8 q^{97} +6.36610e8 q^{98} +7.21971e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 48 q^{2} + 156 q^{3} + 768 q^{4} + 1272 q^{5} - 2496 q^{6} - 17058 q^{7} - 12288 q^{8} + 42273 q^{9} - 20352 q^{10} - 73974 q^{11} + 39936 q^{12} + 272928 q^{14} - 393756 q^{15} + 196608 q^{16} + 374976 q^{17}+ \cdots + 2480087466 q^{99}+O(q^{100}) $ 3 * q - 48 * q^2 + 156 * q^3 + 768 * q^4 + 1272 * q^5 - 2496 * q^6 - 17058 * q^7 - 12288 * q^8 + 42273 * q^9 - 20352 * q^10 - 73974 * q^11 + 39936 * q^12 + 272928 * q^14 - 393756 * q^15 + 196608 * q^16 + 374976 * q^17 - 676368 * q^18 - 418338 * q^19 + 325632 * q^20 + 284694 * q^21 + 1183584 * q^22 + 1026168 * q^23 - 638976 * q^24 + 3337287 * q^25 + 4218588 * q^27 - 4366848 * q^28 - 3075834 * q^29 + 6300096 * q^30 - 9286482 * q^31 - 3145728 * q^32 + 25456452 * q^33 - 5999616 * q^34 - 31802592 * q^35 + 10821888 * q^36 + 17647776 * q^37 + 6693408 * q^38 - 5210112 * q^40 + 47257110 * q^41 - 4555104 * q^42 - 60023760 * q^43 - 18937344 * q^44 + 81112122 * q^45 - 16418688 * q^46 + 40824726 * q^47 + 10223616 * q^48 + 45921177 * q^49 - 53396592 * q^50 - 27559188 * q^51 + 8072046 * q^53 - 67497408 * q^54 - 36910236 * q^55 + 69869568 * q^56 - 245224476 * q^57 + 49213344 * q^58 - 138035310 * q^59 - 100801536 * q^60 + 264203886 * q^61 + 148583712 * q^62 - 436094838 * q^63 + 50331648 * q^64 - 407303232 * q^66 - 203167074 * q^67 + 95993856 * q^68 - 397637544 * q^69 + 508841472 * q^70 - 123067110 * q^71 - 173150208 * q^72 + 433013250 * q^73 - 282364416 * q^74 - 884469216 * q^75 - 107094528 * q^76 + 380043264 * q^77 + 406418748 * q^79 + 83361792 * q^80 + 100121427 * q^81 - 756113760 * q^82 - 105365610 * q^83 + 72881664 * q^84 - 5268186 * q^85 + 960380160 * q^86 - 12753768 * q^87 + 302997504 * q^88 - 1365375798 * q^89 - 1297793952 * q^90 + 262699008 * q^92 + 95909856 * q^93 - 653195616 * q^94 - 85600692 * q^95 - 163577856 * q^96 - 669691662 * q^97 - 734738832 * q^98 + 2480087466 * q^99

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 $

$2$	−16.0000	−0.707107
$2$	−16.0000	−0.707107
$3$	85.7459	0.611178	0.305589	−	0.952163i	$-0.401147\pi$
$3$	85.7459	0.611178	0.305589	+	0.952163i	$0.401147\pi$
$4$	256.000	0.500000
$5$	−1787.19	−1.27881	−0.639404	−	0.768871i	$-0.720819\pi$
$5$	−1787.19	−1.27881	−0.639404	+	0.768871i	$0.720819\pi$
$6$	−1371.94	−0.432168
$7$	751.989	0.118378	0.0591889	−	0.998247i	$-0.481149\pi$
$7$	751.989	0.118378	0.0591889	+	0.998247i	$0.481149\pi$
$8$	−4096.00	−0.353553
$9$	−12330.6	−0.626461
$10$	28595.0	0.904254
$11$	−58551.0	−1.20578	−0.602889	−	0.797825i	$-0.705984\pi$
$11$	−58551.0	−1.20578	−0.602889	+	0.797825i	$0.705984\pi$
$12$	21951.0	0.305589
$13$	0	0
$13$	0	0
$14$	−12031.8	−0.0837057
$15$	−153244.	−0.781580
$16$	65536.0	0.250000
$17$	234846.	0.681966	0.340983	−	0.940069i	$-0.389240\pi$
$17$	234846.	0.681966	0.340983	+	0.940069i	$0.389240\pi$
$18$	197290.	0.442975
$19$	103190.	0.181654	0.0908269	−	0.995867i	$-0.471049\pi$
$19$	103190.	0.181654	0.0908269	+	0.995867i	$0.471049\pi$
$20$	−457520.	−0.639404
$21$	64480.0	0.0723499
$22$	936816.	0.852614
$23$	1.08806e6	0.810732	0.405366	−	0.914154i	$-0.367144\pi$
$23$	1.08806e6	0.810732	0.405366	+	0.914154i	$0.367144\pi$
$24$	−351215.	−0.216084
$25$	1.24092e6	0.635350
$26$	0	0
$27$	−2.74504e6	−0.994058
$28$	192509.	0.0591889
$29$	3.17511e6	0.833620	0.416810	−	0.908994i	$-0.363148\pi$
$29$	3.17511e6	0.833620	0.416810	+	0.908994i	$0.363148\pi$
$30$	2.45191e6	0.552660
$31$	6.17201e6	1.20033	0.600163	−	0.799878i	$-0.295102\pi$
$31$	6.17201e6	1.20033	0.600163	+	0.799878i	$0.295102\pi$
$32$	−1.04858e6	−0.176777
$33$	−5.02051e6	−0.736945
$34$	−3.75753e6	−0.482223
$35$	−1.34395e6	−0.151382
$36$	−3.15664e6	−0.313231
$37$	1.56181e7	1.37000	0.684998	−	0.728545i	$-0.259803\pi$
$37$	1.56181e7	1.37000	0.684998	+	0.728545i	$0.259803\pi$
$38$	−1.65103e6	−0.128449
$39$	0	0
$40$	7.32032e6	0.452127
$41$	2.01455e7	1.11340	0.556700	−	0.830714i	$-0.312067\pi$
$41$	2.01455e7	1.11340	0.556700	+	0.830714i	$0.312067\pi$
$42$	−1.03168e6	−0.0511591
$43$	−2.69024e7	−1.20001	−0.600003	−	0.799998i	$-0.704834\pi$
$43$	−2.69024e7	−1.20001	−0.600003	+	0.799998i	$0.704834\pi$
$44$	−1.49891e7	−0.602889
$45$	2.20372e7	0.801123
$46$	−1.74089e7	−0.573274
$47$	3.03118e7	0.906090	0.453045	−	0.891488i	$-0.350338\pi$
$47$	3.03118e7	0.906090	0.453045	+	0.891488i	$0.350338\pi$
$48$	5.61945e6	0.152795
$49$	−3.97881e7	−0.985987
$50$	−1.98547e7	−0.449260
$51$	2.01371e7	0.416803
$52$	0	0
$53$	6.56149e7	1.14225	0.571125	−	0.820863i	$-0.306507\pi$
$53$	6.56149e7	1.14225	0.571125	+	0.820863i	$0.306507\pi$
$54$	4.39206e7	0.702905
$55$	1.04642e8	1.54196
$56$	−3.08015e6	−0.0418529
$57$	8.84808e6	0.111023
$58$	−5.08018e7	−0.589459
$59$	−1.12025e8	−1.20359	−0.601796	−	0.798650i	$-0.705548\pi$
$59$	−1.12025e8	−1.20359	−0.601796	+	0.798650i	$0.705548\pi$
$60$	−3.92305e7	−0.390790
$61$	2.44277e7	0.225891	0.112945	−	0.993601i	$-0.463971\pi$
$61$	2.44277e7	0.225891	0.112945	+	0.993601i	$0.463971\pi$
$62$	−9.87522e7	−0.848759
$63$	−9.27250e6	−0.0741591
$64$	1.67772e7	0.125000
$65$	0	0
$66$	8.03282e7	0.521099
$67$	−1.29055e8	−0.782419	−0.391209	−	0.920302i	$-0.627943\pi$
$67$	−1.29055e8	−0.782419	−0.391209	+	0.920302i	$0.627943\pi$
$68$	6.01205e7	0.340983
$69$	9.32967e7	0.495502
$70$	2.15031e7	0.107044
$71$	1.12546e8	0.525616	0.262808	−	0.964848i	$-0.415351\pi$
$71$	1.12546e8	0.525616	0.262808	+	0.964848i	$0.415351\pi$
$72$	5.05063e7	0.221487
$73$	1.77758e8	0.732617	0.366308	−	0.930493i	$-0.380622\pi$
$73$	1.77758e8	0.732617	0.366308	+	0.930493i	$0.380622\pi$
$74$	−2.49889e8	−0.968733
$75$	1.06404e8	0.388312
$76$	2.64165e7	0.0908269
$77$	−4.40297e7	−0.142737
$78$	0	0
$79$	−6.05015e8	−1.74761	−0.873805	−	0.486277i	$-0.838355\pi$
$79$	−6.05015e8	−1.74761	−0.873805	+	0.486277i	$0.838355\pi$
$80$	−1.17125e8	−0.319702
$81$	7.32791e6	0.0189146
$82$	−3.22328e8	−0.787293
$83$	−2.01755e8	−0.466630	−0.233315	−	0.972401i	$-0.574957\pi$
$83$	−2.01755e8	−0.466630	−0.233315	+	0.972401i	$0.574957\pi$
$84$	1.65069e7	0.0361750
$85$	−4.19714e8	−0.872103
$86$	4.30439e8	0.848532
$87$	2.72253e8	0.509491
$88$	2.39825e8	0.426307
$89$	−8.62460e8	−1.45708	−0.728541	−	0.685002i	$-0.759801\pi$
$89$	−8.62460e8	−1.45708	−0.728541	+	0.685002i	$0.759801\pi$
$90$	−3.52595e8	−0.566480
$91$	0	0
$92$	2.78543e8	0.405366
$93$	5.29225e8	0.733613
$94$	−4.84989e8	−0.640702
$95$	−1.84419e8	−0.232300
$96$	−8.99111e7	−0.108042
$97$	2.15081e8	0.246677	0.123339	−	0.992365i	$-0.460640\pi$
$97$	2.15081e8	0.246677	0.123339	+	0.992365i	$0.460640\pi$
$98$	6.36610e8	0.697198
$99$	7.21971e8	0.755373
$100$	3.17675e8	0.317675
$101$	8.80961e8	0.842385	0.421192	−	0.906971i	$-0.361612\pi$
$101$	8.80961e8	0.842385	0.421192	+	0.906971i	$0.361612\pi$
$102$	−3.22193e8	−0.294724
$103$	−1.67438e9	−1.46584	−0.732918	−	0.680317i	$-0.761842\pi$
$103$	−1.67438e9	−1.46584	−0.732918	+	0.680317i	$0.761842\pi$
$104$	0	0
$105$	−1.15238e8	−0.0925217
$106$	−1.04984e9	−0.807692
$107$	−3.53576e8	−0.260769	−0.130385	−	0.991463i	$-0.541621\pi$
$107$	−3.53576e8	−0.260769	−0.130385	+	0.991463i	$0.541621\pi$
$108$	−7.02730e8	−0.497029
$109$	−1.69143e9	−1.14772	−0.573858	−	0.818955i	$-0.694554\pi$
$109$	−1.69143e9	−1.14772	−0.573858	+	0.818955i	$0.694554\pi$
$110$	−1.67427e9	−1.09033
$111$	1.33918e9	0.837312
$112$	4.92823e7	0.0295944
$113$	2.01468e9	1.16239	0.581196	−	0.813763i	$-0.302585\pi$
$113$	2.01468e9	1.16239	0.581196	+	0.813763i	$0.302585\pi$
$114$	−1.41569e8	−0.0785050
$115$	−1.94457e9	−1.03677
$116$	8.12829e8	0.416810
$117$	0	0
$118$	1.79239e9	0.851067
$119$	1.76601e8	0.0807296
$120$	6.27688e8	0.276330
$121$	1.07027e9	0.453901
$122$	−3.90843e8	−0.159729
$123$	1.72740e9	0.680486
$124$	1.58004e9	0.600163
$125$	1.27285e9	0.466317
$126$	1.48360e8	0.0524384
$127$	−3.44437e8	−0.117488	−0.0587439	−	0.998273i	$-0.518710\pi$
$127$	−3.44437e8	−0.117488	−0.0587439	+	0.998273i	$0.518710\pi$
$128$	−2.68435e8	−0.0883883
$129$	−2.30677e9	−0.733418
$130$	0	0
$131$	−1.13152e9	−0.335692	−0.167846	−	0.985813i	$-0.553681\pi$
$131$	−1.13152e9	−0.335692	−0.167846	+	0.985813i	$0.553681\pi$
$132$	−1.28525e9	−0.368473
$133$	7.75974e7	0.0215038
$134$	2.06488e9	0.553253
$135$	4.90590e9	1.27121
$136$	−9.61928e8	−0.241111
$137$	1.20622e8	0.0292540	0.0146270	−	0.999893i	$-0.495344\pi$
$137$	1.20622e8	0.0292540	0.0146270	+	0.999893i	$0.495344\pi$
$138$	−1.49275e9	−0.350373
$139$	5.00754e9	1.13778	0.568889	−	0.822414i	$-0.307373\pi$
$139$	5.00754e9	1.13778	0.568889	+	0.822414i	$0.307373\pi$
$140$	−3.44050e8	−0.0756912
$141$	2.59911e9	0.553782
$142$	−1.80074e9	−0.371667
$143$	0	0
$144$	−8.08100e8	−0.156615
$145$	−5.67453e9	−1.06604
$146$	−2.84413e9	−0.518038
$147$	−3.41167e9	−0.602614
$148$	3.99822e9	0.684998
$149$	8.79381e9	1.46164	0.730818	−	0.682573i	$-0.239139\pi$
$149$	8.79381e9	1.46164	0.730818	+	0.682573i	$0.239139\pi$
$150$	−1.70246e9	−0.274578
$151$	1.89322e9	0.296350	0.148175	−	0.988961i	$-0.452660\pi$
$151$	1.89322e9	0.296350	0.148175	+	0.988961i	$0.452660\pi$
$152$	−4.22664e8	−0.0642243
$153$	−2.89580e9	−0.427225
$154$	7.04475e8	0.100931
$155$	−1.10306e10	−1.53499
$156$	0	0
$157$	1.42967e10	1.87797	0.938984	−	0.343961i	$-0.111769\pi$
$157$	1.42967e10	1.87797	0.938984	+	0.343961i	$0.111769\pi$
$158$	9.68024e9	1.23575
$159$	5.62621e9	0.698118
$160$	1.87400e9	0.226063
$161$	8.18208e8	0.0959726
$162$	−1.17247e8	−0.0133747
$163$	−1.35312e10	−1.50139	−0.750694	−	0.660650i	$-0.770281\pi$
$163$	−1.35312e10	−1.50139	−0.750694	+	0.660650i	$0.770281\pi$
$164$	5.15725e9	0.556700
$165$	8.97260e9	0.942412
$166$	3.22808e9	0.329957
$167$	8.67633e9	0.863201	0.431600	−	0.902065i	$-0.357949\pi$
$167$	8.67633e9	0.863201	0.431600	+	0.902065i	$0.357949\pi$
$168$	−2.64110e8	−0.0255796
$169$	0	0
$170$	6.71542e9	0.616670
$171$	−1.27239e9	−0.113799
$172$	−6.88702e9	−0.600003
$173$	2.02999e10	1.72301	0.861504	−	0.507750i	$-0.169523\pi$
$173$	2.02999e10	1.72301	0.861504	+	0.507750i	$0.169523\pi$
$174$	−4.35605e9	−0.360264
$175$	9.33156e8	0.0752113
$176$	−3.83720e9	−0.301445
$177$	−9.60565e9	−0.735609
$178$	1.37994e10	1.03031
$179$	−1.08759e10	−0.791817	−0.395908	−	0.918290i	$-0.629570\pi$
$179$	−1.08759e10	−0.791817	−0.395908	+	0.918290i	$0.629570\pi$
$180$	5.64151e9	0.400562
$181$	1.52561e10	1.05655	0.528275	−	0.849073i	$-0.322839\pi$
$181$	1.52561e10	1.05655	0.528275	+	0.849073i	$0.322839\pi$
$182$	0	0
$183$	2.09458e9	0.138060
$184$	−4.45669e9	−0.286637
$185$	−2.79124e10	−1.75196
$186$	−8.46760e9	−0.518743
$187$	−1.37505e10	−0.822300
$188$	7.75982e9	0.453045
$189$	−2.06424e9	−0.117674
$190$	2.95071e9	0.164261
$191$	1.20771e9	0.0656616	0.0328308	−	0.999461i	$-0.489548\pi$
$191$	1.20771e9	0.0656616	0.0328308	+	0.999461i	$0.489548\pi$
$192$	1.43858e9	0.0763973
$193$	−1.46443e10	−0.759730	−0.379865	−	0.925042i	$-0.624030\pi$
$193$	−1.46443e10	−0.759730	−0.379865	+	0.925042i	$0.624030\pi$
$194$	−3.44129e9	−0.174427
$195$	0	0
$196$	−1.01858e10	−0.492993
$197$	−3.80476e10	−1.79982	−0.899911	−	0.436075i	$-0.856368\pi$
$197$	−3.80476e10	−1.79982	−0.899911	+	0.436075i	$0.856368\pi$
$198$	−1.15515e10	−0.534129
$199$	−2.69086e10	−1.21633	−0.608166	−	0.793810i	$-0.708095\pi$
$199$	−2.69086e10	−1.21633	−0.608166	+	0.793810i	$0.708095\pi$
$200$	−5.08280e9	−0.224630
$201$	−1.10660e10	−0.478197
$202$	−1.40954e10	−0.595656
$203$	2.38765e9	0.0986821
$204$	5.15509e9	0.208401
$205$	−3.60038e10	−1.42382
$206$	2.67900e10	1.03650
$207$	−1.34165e10	−0.507892
$208$	0	0
$209$	−6.04185e9	−0.219034
$210$	1.84381e9	0.0654227
$211$	−2.87876e10	−0.999849	−0.499925	−	0.866069i	$-0.666639\pi$
$211$	−2.87876e10	−0.999849	−0.499925	+	0.866069i	$0.666639\pi$
$212$	1.67974e10	0.571125
$213$	9.65038e9	0.321245
$214$	5.65722e9	0.184392
$215$	4.80797e10	1.53458
$216$	1.12437e10	0.351452
$217$	4.64129e9	0.142092
$218$	2.70628e10	0.811557
$219$	1.52420e10	0.447760
$220$	2.67883e10	0.770979
$221$	0	0
$222$	−2.14270e10	−0.592069
$223$	−5.58460e10	−1.51224	−0.756120	−	0.654433i	$-0.772907\pi$
$223$	−5.58460e10	−1.51224	−0.756120	+	0.654433i	$0.772907\pi$
$224$	−7.88517e8	−0.0209264
$225$	−1.53013e10	−0.398022
$226$	−3.22349e10	−0.821936
$227$	2.12255e10	0.530567	0.265284	−	0.964170i	$-0.414534\pi$
$227$	2.12255e10	0.530567	0.265284	+	0.964170i	$0.414534\pi$
$228$	2.26511e9	0.0555114
$229$	−5.16671e10	−1.24152	−0.620761	−	0.784000i	$-0.713176\pi$
$229$	−5.16671e10	−1.24152	−0.620761	+	0.784000i	$0.713176\pi$
$230$	3.11131e10	0.733107
$231$	−3.77537e9	−0.0872380
$232$	−1.30053e10	−0.294729
$233$	−6.99428e10	−1.55468	−0.777341	−	0.629080i	$-0.783432\pi$
$233$	−6.99428e10	−1.55468	−0.777341	+	0.629080i	$0.783432\pi$
$234$	0	0
$235$	−5.41729e10	−1.15871
$236$	−2.86783e10	−0.601796
$237$	−5.18776e10	−1.06810
$238$	−2.82562e9	−0.0570845
$239$	−9.50597e10	−1.88454	−0.942271	−	0.334850i	$-0.891314\pi$
$239$	−9.50597e10	−1.88454	−0.942271	+	0.334850i	$0.891314\pi$
$240$	−1.00430e10	−0.195395
$241$	−5.96117e10	−1.13829	−0.569147	−	0.822235i	$-0.692727\pi$
$241$	−5.96117e10	−1.13829	−0.569147	+	0.822235i	$0.692727\pi$
$242$	−1.71244e10	−0.320956
$243$	5.46589e10	1.00562
$244$	6.25349e9	0.112945
$245$	7.11089e10	1.26089
$246$	−2.76383e10	−0.481176
$247$	0	0
$248$	−2.52806e10	−0.424379
$249$	−1.72997e10	−0.285194
$250$	−2.03656e10	−0.329736
$251$	−6.63592e10	−1.05528	−0.527642	−	0.849467i	$-0.676924\pi$
$251$	−6.63592e10	−1.05528	−0.527642	+	0.849467i	$0.676924\pi$
$252$	−2.37376e9	−0.0370795
$253$	−6.37070e10	−0.977563
$254$	5.51098e9	0.0830764
$255$	−3.59887e10	−0.533011
$256$	4.29497e9	0.0625000
$257$	−3.60015e10	−0.514779	−0.257390	−	0.966308i	$-0.582862\pi$
$257$	−3.60015e10	−0.514779	−0.257390	+	0.966308i	$0.582862\pi$
$258$	3.69084e10	0.518605
$259$	1.17446e10	0.162177
$260$	0	0
$261$	−3.91512e10	−0.522231
$262$	1.81043e10	0.237370
$263$	5.53571e10	0.713465	0.356732	−	0.934207i	$-0.383891\pi$
$263$	5.53571e10	0.713465	0.356732	+	0.934207i	$0.383891\pi$
$264$	2.05640e10	0.260550
$265$	−1.17266e11	−1.46072
$266$	−1.24156e9	−0.0152055
$267$	−7.39525e10	−0.890537
$268$	−3.30381e10	−0.391209
$269$	9.87231e10	1.14956	0.574782	−	0.818306i	$-0.305087\pi$
$269$	9.87231e10	1.14956	0.574782	+	0.818306i	$0.305087\pi$
$270$	−7.84944e10	−0.898880
$271$	1.57825e11	1.77752	0.888760	−	0.458372i	$-0.151567\pi$
$271$	1.57825e11	1.77752	0.888760	+	0.458372i	$0.151567\pi$
$272$	1.53909e10	0.170491
$273$	0	0
$274$	−1.92996e9	−0.0206857
$275$	−7.26570e10	−0.766091
$276$	2.38839e10	0.247751
$277$	2.52506e10	0.257700	0.128850	−	0.991664i	$-0.458872\pi$
$277$	2.52506e10	0.257700	0.128850	+	0.991664i	$0.458872\pi$
$278$	−8.01206e10	−0.804530
$279$	−7.61049e10	−0.751958
$280$	5.50480e9	0.0535218
$281$	7.44249e10	0.712098	0.356049	−	0.934467i	$-0.384124\pi$
$281$	7.44249e10	0.712098	0.356049	+	0.934467i	$0.384124\pi$
$282$	−4.15858e10	−0.391583
$283$	−1.08399e11	−1.00458	−0.502291	−	0.864699i	$-0.667509\pi$
$283$	−1.08399e11	−1.00458	−0.502291	+	0.864699i	$0.667509\pi$
$284$	2.88118e10	0.262808
$285$	−1.58132e10	−0.141977
$286$	0	0
$287$	1.51492e10	0.131802
$288$	1.29296e10	0.110744
$289$	−6.34353e10	−0.534922
$290$	9.07924e10	0.753804
$291$	1.84423e10	0.150764
$292$	4.55061e10	0.366308
$293$	−4.84627e10	−0.384152	−0.192076	−	0.981380i	$-0.561522\pi$
$293$	−4.84627e10	−0.384152	−0.192076	+	0.981380i	$0.561522\pi$
$294$	5.45867e10	0.426112
$295$	2.00209e11	1.53916
$296$	−6.39716e10	−0.484367
$297$	1.60725e11	1.19861
$298$	−1.40701e11	−1.03353
$299$	0	0
$300$	2.72393e10	0.194156
$301$	−2.02303e10	−0.142054
$302$	−3.02915e10	−0.209551
$303$	7.55388e10	0.514847
$304$	6.76263e9	0.0454134
$305$	−4.36569e10	−0.288871
$306$	4.63328e10	0.302094
$307$	8.71117e10	0.559698	0.279849	−	0.960044i	$-0.409716\pi$
$307$	8.71117e10	0.559698	0.279849	+	0.960044i	$0.409716\pi$
$308$	−1.12716e10	−0.0713687
$309$	−1.43571e11	−0.895887
$310$	1.76489e11	1.08540
$311$	−1.81111e10	−0.109780	−0.0548900	−	0.998492i	$-0.517481\pi$
$311$	−1.81111e10	−0.109780	−0.0548900	+	0.998492i	$0.517481\pi$
$312$	0	0
$313$	−2.50444e11	−1.47490	−0.737449	−	0.675403i	$-0.763970\pi$
$313$	−2.50444e11	−1.47490	−0.737449	+	0.675403i	$0.763970\pi$
$314$	−2.28748e11	−1.32792
$315$	1.65717e10	0.0948352
$316$	−1.54884e11	−0.873805
$317$	1.62467e11	0.903644	0.451822	−	0.892108i	$-0.350774\pi$
$317$	1.62467e11	0.903644	0.451822	+	0.892108i	$0.350774\pi$
$318$	−9.00193e10	−0.493644
$319$	−1.85906e11	−1.00516
$320$	−2.99840e10	−0.159851
$321$	−3.03177e10	−0.159376
$322$	−1.30913e10	−0.0678629
$323$	2.42336e10	0.123882
$324$	1.87595e9	0.00945731
$325$	0	0
$326$	2.16500e11	1.06164
$327$	−1.45033e11	−0.701459
$328$	−8.25161e10	−0.393646
$329$	2.27941e10	0.107261
$330$	−1.43562e11	−0.666386
$331$	6.54231e10	0.299575	0.149787	−	0.988718i	$-0.452141\pi$
$331$	6.54231e10	0.299575	0.149787	+	0.988718i	$0.452141\pi$
$332$	−5.16492e10	−0.233315
$333$	−1.92581e11	−0.858249
$334$	−1.38821e11	−0.610375
$335$	2.30646e11	1.00056
$336$	4.22576e9	0.0180875
$337$	−8.37766e10	−0.353825	−0.176912	−	0.984227i	$-0.556611\pi$
$337$	−8.37766e10	−0.353825	−0.176912	+	0.984227i	$0.556611\pi$
$338$	0	0
$339$	1.72751e11	0.710429
$340$	−1.07447e11	−0.436052
$341$	−3.61378e11	−1.44733
$342$	2.03583e10	0.0804681
$343$	−6.02657e10	−0.235097
$344$	1.10192e11	0.424266
$345$	−1.66739e11	−0.633652
$346$	−3.24799e11	−1.21835
$347$	5.18275e11	1.91901	0.959506	−	0.281689i	$-0.0908946\pi$
$347$	5.18275e11	1.91901	0.959506	+	0.281689i	$0.0908946\pi$
$348$	6.96968e10	0.254745
$349$	−2.77982e11	−1.00300	−0.501502	−	0.865157i	$-0.667219\pi$
$349$	−2.77982e11	−1.00300	−0.501502	+	0.865157i	$0.667219\pi$
$350$	−1.49305e10	−0.0531824
$351$	0	0
$352$	6.13952e10	0.213153
$353$	1.60940e11	0.551669	0.275835	−	0.961205i	$-0.411046\pi$
$353$	1.60940e11	0.551669	0.275835	+	0.961205i	$0.411046\pi$
$354$	1.53690e11	0.520154
$355$	−2.01141e11	−0.672162
$356$	−2.20790e11	−0.728541
$357$	1.51429e10	0.0493402
$358$	1.74014e11	0.559899
$359$	1.45229e11	0.461455	0.230728	−	0.973018i	$-0.425889\pi$
$359$	1.45229e11	0.461455	0.230728	+	0.973018i	$0.425889\pi$
$360$	−9.02642e10	−0.283240
$361$	−3.12040e11	−0.967002
$362$	−2.44098e11	−0.747094
$363$	9.17717e10	0.277414
$364$	0	0
$365$	−3.17688e11	−0.936876
$366$	−3.35132e10	−0.0976228
$367$	−5.88415e11	−1.69311	−0.846557	−	0.532298i	$-0.821329\pi$
$367$	−5.88415e11	−1.69311	−0.846557	+	0.532298i	$0.821329\pi$
$368$	7.13071e10	0.202683
$369$	−2.48407e11	−0.697502
$370$	4.46599e11	1.23882
$371$	4.93416e10	0.135217
$372$	1.35482e11	0.366807
$373$	2.92744e11	0.783065	0.391533	−	0.920164i	$-0.371945\pi$
$373$	2.92744e11	0.783065	0.391533	+	0.920164i	$0.371945\pi$
$374$	2.20007e11	0.581454
$375$	1.09142e11	0.285003
$376$	−1.24157e11	−0.320351
$377$	0	0
$378$	3.30278e10	0.0832083
$379$	−1.16451e11	−0.289912	−0.144956	−	0.989438i	$-0.546304\pi$
$379$	−1.16451e11	−0.289912	−0.144956	+	0.989438i	$0.546304\pi$
$380$	−4.72113e10	−0.116150
$381$	−2.95340e10	−0.0718059
$382$	−1.93233e10	−0.0464298
$383$	3.18071e11	0.755318	0.377659	−	0.925945i	$-0.376729\pi$
$383$	3.18071e11	0.755318	0.377659	+	0.925945i	$0.376729\pi$
$384$	−2.30173e10	−0.0540210
$385$	7.86894e10	0.182534
$386$	2.34308e11	0.537210
$387$	3.31724e11	0.751757
$388$	5.50607e10	0.123339
$389$	−1.88045e11	−0.416379	−0.208190	−	0.978088i	$-0.566757\pi$
$389$	−1.88045e11	−0.416379	−0.208190	+	0.978088i	$0.566757\pi$
$390$	0	0
$391$	2.55526e11	0.552892
$392$	1.62972e11	0.348599
$393$	−9.70231e10	−0.205168
$394$	6.08762e11	1.27267
$395$	1.08128e12	2.23486
$396$	1.84825e11	0.377687
$397$	8.16657e11	1.64999	0.824997	−	0.565137i	$-0.191177\pi$
$397$	8.16657e11	1.64999	0.824997	+	0.565137i	$0.191177\pi$
$398$	4.30538e11	0.860077
$399$	6.65366e9	0.0131426
$400$	8.13248e10	0.158837
$401$	−9.64580e11	−1.86290	−0.931448	−	0.363875i	$-0.881454\pi$
$401$	−9.64580e11	−1.86290	−0.931448	+	0.363875i	$0.881454\pi$
$402$	1.77055e11	0.338136
$403$	0	0
$404$	2.25526e11	0.421192
$405$	−1.30964e10	−0.0241882
$406$	−3.82024e10	−0.0697788
$407$	−9.14453e11	−1.65191
$408$	−8.24815e10	−0.147362
$409$	−4.92782e11	−0.870763	−0.435381	−	0.900246i	$-0.643386\pi$
$409$	−4.92782e11	−0.870763	−0.435381	+	0.900246i	$0.643386\pi$
$410$	5.76061e11	1.00680
$411$	1.03429e10	0.0178794
$412$	−4.28640e11	−0.732918
$413$	−8.42412e10	−0.142478
$414$	2.14663e11	0.359134
$415$	3.60574e11	0.596730
$416$	0	0
$417$	4.29376e11	0.695385
$418$	9.66696e10	0.154881
$419$	1.06792e11	0.169268	0.0846338	−	0.996412i	$-0.473028\pi$
$419$	1.06792e11	0.169268	0.0846338	+	0.996412i	$0.473028\pi$
$420$	−2.95009e10	−0.0462608
$421$	9.06902e10	0.140699	0.0703495	−	0.997522i	$-0.477589\pi$
$421$	9.06902e10	0.140699	0.0703495	+	0.997522i	$0.477589\pi$
$422$	4.60602e11	0.707000
$423$	−3.73764e11	−0.567630
$424$	−2.68758e11	−0.403846
$425$	2.91424e11	0.433287
$426$	−1.54406e11	−0.227155
$427$	1.83694e10	0.0267404
$428$	−9.05155e10	−0.130385
$429$	0	0
$430$	−7.69275e11	−1.08511
$431$	−5.39153e11	−0.752600	−0.376300	−	0.926498i	$-0.622804\pi$
$431$	−5.39153e11	−0.752600	−0.376300	+	0.926498i	$0.622804\pi$
$432$	−1.79899e11	−0.248514
$433$	4.68512e11	0.640509	0.320254	−	0.947332i	$-0.396232\pi$
$433$	4.68512e11	0.640509	0.320254	+	0.947332i	$0.396232\pi$
$434$	−7.42606e10	−0.100474
$435$	−4.86568e11	−0.651541
$436$	−4.33005e11	−0.573858
$437$	1.12276e11	0.147273
$438$	−2.43873e11	−0.316614
$439$	3.60014e11	0.462624	0.231312	−	0.972880i	$-0.425698\pi$
$439$	3.60014e11	0.462624	0.231312	+	0.972880i	$0.425698\pi$
$440$	−4.28612e11	−0.545165
$441$	4.90613e11	0.617682
$442$	0	0
$443$	1.35127e12	1.66697	0.833483	−	0.552546i	$-0.186344\pi$
$443$	1.35127e12	1.66697	0.833483	+	0.552546i	$0.186344\pi$
$444$	3.42831e11	0.418656
$445$	1.54138e12	1.86333
$446$	8.93537e11	1.06931
$447$	7.54034e11	0.893320
$448$	1.26163e10	0.0147972
$449$	−1.10673e12	−1.28509	−0.642547	−	0.766246i	$-0.722122\pi$
$449$	−1.10673e12	−1.28509	−0.642547	+	0.766246i	$0.722122\pi$
$450$	2.44821e11	0.281444
$451$	−1.17954e12	−1.34251
$452$	5.15758e11	0.581196
$453$	1.62336e11	0.181123
$454$	−3.39607e11	−0.375168
$455$	0	0
$456$	−3.62417e10	−0.0392525
$457$	1.50037e12	1.60908	0.804538	−	0.593901i	$-0.202413\pi$
$457$	1.50037e12	1.60908	0.804538	+	0.593901i	$0.202413\pi$
$458$	8.26673e11	0.877888
$459$	−6.44661e11	−0.677913
$460$	−4.97809e11	−0.518385
$461$	−1.25558e12	−1.29476	−0.647382	−	0.762166i	$-0.724136\pi$
$461$	−1.25558e12	−1.29476	−0.647382	+	0.762166i	$0.724136\pi$
$462$	6.04059e10	0.0616866
$463$	4.59412e11	0.464610	0.232305	−	0.972643i	$-0.425373\pi$
$463$	4.59412e11	0.464610	0.232305	+	0.972643i	$0.425373\pi$
$464$	2.08084e11	0.208405
$465$	−9.45825e11	−0.938151
$466$	1.11909e12	1.09933
$467$	−1.97470e12	−1.92121	−0.960605	−	0.277917i	$-0.910356\pi$
$467$	−1.97470e12	−1.92121	−0.960605	+	0.277917i	$0.910356\pi$
$468$	0	0
$469$	−9.70481e10	−0.0926210
$470$	8.66766e11	0.819335
$471$	1.22589e12	1.14777
$472$	4.58852e11	0.425534
$473$	1.57516e12	1.44694
$474$	8.30042e11	0.755261
$475$	1.28050e11	0.115414
$476$	4.52100e10	0.0403648
$477$	−8.09073e11	−0.715575
$478$	1.52096e12	1.33257
$479$	−1.97850e12	−1.71723	−0.858613	−	0.512625i	$-0.828673\pi$
$479$	−1.97850e12	−1.71723	−0.858613	+	0.512625i	$0.828673\pi$
$480$	1.60688e11	0.138165
$481$	0	0
$482$	9.53787e11	0.804896
$483$	7.01580e10	0.0586564
$484$	2.73990e11	0.226950
$485$	−3.84390e11	−0.315453
$486$	−8.74543e11	−0.711079
$487$	−8.70430e11	−0.701219	−0.350609	−	0.936522i	$-0.614026\pi$
$487$	−8.70430e11	−0.701219	−0.350609	+	0.936522i	$0.614026\pi$
$488$	−1.00056e11	−0.0798644
$489$	−1.16025e12	−0.917616
$490$	−1.13774e12	−0.891582
$491$	−9.15629e11	−0.710973	−0.355486	−	0.934681i	$-0.615685\pi$
$491$	−9.15629e11	−0.710973	−0.355486	+	0.934681i	$0.615685\pi$
$492$	4.42214e11	0.340243
$493$	7.45662e11	0.568501
$494$	0	0
$495$	−1.29030e12	−0.965977
$496$	4.04489e11	0.300082
$497$	8.46335e10	0.0622212
$498$	2.76795e11	0.201663
$499$	1.04001e12	0.750906	0.375453	−	0.926841i	$-0.377487\pi$
$499$	1.04001e12	0.750906	0.375453	+	0.926841i	$0.377487\pi$
$500$	3.25849e11	0.233159
$501$	7.43960e11	0.527570
$502$	1.06175e12	0.746198
$503$	1.96238e11	0.136687	0.0683435	−	0.997662i	$-0.478229\pi$
$503$	1.96238e11	0.136687	0.0683435	+	0.997662i	$0.478229\pi$
$504$	3.79802e10	0.0262192
$505$	−1.57444e12	−1.07725
$506$	1.01931e12	0.691241
$507$	0	0
$508$	−8.81758e10	−0.0587439
$509$	9.33446e11	0.616395	0.308197	−	0.951322i	$-0.400274\pi$
$509$	9.33446e11	0.616395	0.308197	+	0.951322i	$0.400274\pi$
$510$	5.75820e11	0.376895
$511$	1.33672e11	0.0867256
$512$	−6.87195e10	−0.0441942
$513$	−2.83259e11	−0.180574
$514$	5.76023e11	0.364004
$515$	2.99243e12	1.87452
$516$	−5.90534e11	−0.366709
$517$	−1.77479e12	−1.09254
$518$	−1.87914e11	−0.114676
$519$	1.74064e12	1.05307
$520$	0	0
$521$	−2.60930e12	−1.55151	−0.775754	−	0.631036i	$-0.782630\pi$
$521$	−2.60930e12	−1.55151	−0.775754	+	0.631036i	$0.782630\pi$
$522$	6.26419e11	0.369273
$523$	1.76867e12	1.03368	0.516842	−	0.856081i	$-0.327107\pi$
$523$	1.76867e12	1.03368	0.516842	+	0.856081i	$0.327107\pi$
$524$	−2.89669e11	−0.167846
$525$	8.00144e10	0.0459675
$526$	−8.85714e11	−0.504496
$527$	1.44947e12	0.818582
$528$	−3.29024e11	−0.184236
$529$	−6.17280e11	−0.342714
$530$	1.87626e12	1.03288
$531$	1.38133e12	0.754003
$532$	1.98649e10	0.0107519
$533$	0	0
$534$	1.18324e12	0.629705
$535$	6.31908e11	0.333474
$536$	5.28610e11	0.276627
$537$	−9.32560e11	−0.483941
$538$	−1.57957e12	−0.812865
$539$	2.32964e12	1.18888
$540$	1.25591e12	0.635604
$541$	−3.95324e12	−1.98411	−0.992056	−	0.125800i	$-0.959850\pi$
$541$	−3.95324e12	−1.98411	−0.992056	+	0.125800i	$0.959850\pi$
$542$	−2.52520e12	−1.25690
$543$	1.30815e12	0.645740
$544$	−2.46254e11	−0.120556
$545$	3.02290e12	1.46771
$546$	0	0
$547$	−2.49418e12	−1.19120	−0.595601	−	0.803281i	$-0.703086\pi$
$547$	−2.49418e12	−1.19120	−0.595601	+	0.803281i	$0.703086\pi$
$548$	3.08793e10	0.0146270
$549$	−3.01209e11	−0.141512
$550$	1.16251e12	0.541708
$551$	3.27639e11	0.151430
$552$	−3.82143e11	−0.175186
$553$	−4.54965e11	−0.206878
$554$	−4.04010e11	−0.182221
$555$	−2.39338e12	−1.07076
$556$	1.28193e12	0.568889
$557$	−2.22532e12	−0.979588	−0.489794	−	0.871838i	$-0.662928\pi$
$557$	−2.22532e12	−0.979588	−0.489794	+	0.871838i	$0.662928\pi$
$558$	1.21768e12	0.531714
$559$	0	0
$560$	−8.80768e10	−0.0378456
$561$	−1.17905e12	−0.502572
$562$	−1.19080e12	−0.503529
$563$	−3.00484e12	−1.26047	−0.630237	−	0.776403i	$-0.717042\pi$
$563$	−3.00484e12	−1.26047	−0.630237	+	0.776403i	$0.717042\pi$
$564$	6.65373e11	0.276891
$565$	−3.60061e12	−1.48648
$566$	1.73438e12	0.710347
$567$	5.51051e9	0.00223907
$568$	−4.60989e11	−0.185833
$569$	3.35545e12	1.34198	0.670989	−	0.741467i	$-0.265870\pi$
$569$	3.35545e12	1.34198	0.670989	+	0.741467i	$0.265870\pi$
$570$	2.53011e11	0.100393
$571$	2.15636e12	0.848903	0.424451	−	0.905451i	$-0.360467\pi$
$571$	2.15636e12	0.848903	0.424451	+	0.905451i	$0.360467\pi$
$572$	0	0
$573$	1.03556e11	0.0401310
$574$	−2.42387e11	−0.0931979
$575$	1.35019e12	0.515098
$576$	−2.06874e11	−0.0783076
$577$	2.02642e12	0.761095	0.380547	−	0.924761i	$-0.375736\pi$
$577$	2.02642e12	0.761095	0.380547	+	0.924761i	$0.375736\pi$
$578$	1.01497e12	0.378247
$579$	−1.25569e12	−0.464331
$580$	−1.45268e12	−0.533020
$581$	−1.51717e11	−0.0552386
$582$	−2.95077e11	−0.106606
$583$	−3.84182e12	−1.37730
$584$	−7.28098e11	−0.259019
$585$	0	0
$586$	7.75403e11	0.271636
$587$	1.74926e12	0.608112	0.304056	−	0.952654i	$-0.401659\pi$
$587$	1.74926e12	0.608112	0.304056	+	0.952654i	$0.401659\pi$
$588$	−8.73387e11	−0.301307
$589$	6.36887e11	0.218044
$590$	−3.20334e12	−1.08835
$591$	−3.26243e12	−1.10001
$592$	1.02354e12	0.342499
$593$	−2.36850e12	−0.786551	−0.393275	−	0.919421i	$-0.628658\pi$
$593$	−2.36850e12	−0.786551	−0.393275	+	0.919421i	$0.628658\pi$
$594$	−2.57160e12	−0.847547
$595$	−3.15620e11	−0.103238
$596$	2.25122e12	0.730818
$597$	−2.30730e12	−0.743396
$598$	0	0
$599$	3.95956e12	1.25668	0.628342	−	0.777937i	$-0.283734\pi$
$599$	3.95956e12	1.25668	0.628342	+	0.777937i	$0.283734\pi$
$600$	−4.35829e11	−0.137289
$601$	−1.46479e12	−0.457974	−0.228987	−	0.973429i	$-0.573541\pi$
$601$	−1.46479e12	−0.457974	−0.228987	+	0.973429i	$0.573541\pi$
$602$	3.23685e11	0.100447
$603$	1.59133e12	0.490155
$604$	4.84665e11	0.148175
$605$	−1.91278e12	−0.580452
$606$	−1.20862e12	−0.364052
$607$	2.37878e12	0.711221	0.355610	−	0.934634i	$-0.384273\pi$
$607$	2.37878e12	0.711221	0.355610	+	0.934634i	$0.384273\pi$
$608$	−1.08202e11	−0.0321122
$609$	2.04731e11	0.0603124
$610$	6.98511e11	0.204263
$611$	0	0
$612$	−7.41324e11	−0.213613
$613$	3.04291e12	0.870397	0.435198	−	0.900335i	$-0.356678\pi$
$613$	3.04291e12	0.870397	0.435198	+	0.900335i	$0.356678\pi$
$614$	−1.39379e12	−0.395766
$615$	−3.08718e12	−0.870211
$616$	1.80346e11	0.0504653
$617$	6.91186e12	1.92005	0.960024	−	0.279918i	$-0.0903074\pi$
$617$	6.91186e12	1.92005	0.960024	+	0.279918i	$0.0903074\pi$
$618$	2.29714e12	0.633488
$619$	9.28522e10	0.0254205	0.0127103	−	0.999919i	$-0.495954\pi$
$619$	9.28522e10	0.0254205	0.0127103	+	0.999919i	$0.495954\pi$
$620$	−2.82382e12	−0.767493
$621$	−2.98677e12	−0.805914
$622$	2.89778e11	0.0776262
$623$	−6.48561e11	−0.172486
$624$	0	0
$625$	−4.69849e12	−1.23168
$626$	4.00711e12	1.04291
$627$	−5.18064e11	−0.133869
$628$	3.65996e12	0.938984
$629$	3.66784e12	0.934290
$630$	−2.65147e11	−0.0670586
$631$	−3.44921e12	−0.866139	−0.433070	−	0.901360i	$-0.642570\pi$
$631$	−3.44921e12	−0.866139	−0.433070	+	0.901360i	$0.642570\pi$
$632$	2.47814e12	0.617873
$633$	−2.46842e12	−0.611086
$634$	−2.59946e12	−0.638973
$635$	6.15573e11	0.150244
$636$	1.44031e12	0.349059
$637$	0	0
$638$	2.97450e12	0.710756
$639$	−1.38777e12	−0.329278
$640$	4.79745e11	0.113032
$641$	1.38534e12	0.324111	0.162056	−	0.986782i	$-0.448188\pi$
$641$	1.38534e12	0.324111	0.162056	+	0.986782i	$0.448188\pi$
$642$	4.85084e11	0.112696
$643$	1.95260e12	0.450468	0.225234	−	0.974305i	$-0.427685\pi$
$643$	1.95260e12	0.450468	0.225234	+	0.974305i	$0.427685\pi$
$644$	2.09461e11	0.0479863
$645$	4.12264e12	0.937900
$646$	−3.87738e11	−0.0875976
$647$	7.01375e11	0.157355	0.0786775	−	0.996900i	$-0.474930\pi$
$647$	7.01375e11	0.157355	0.0786775	+	0.996900i	$0.474930\pi$
$648$	−3.00151e10	−0.00668733
$649$	6.55915e12	1.45126
$650$	0	0
$651$	3.97971e11	0.0868435
$652$	−3.46399e12	−0.750694
$653$	2.16551e12	0.466070	0.233035	−	0.972468i	$-0.425134\pi$
$653$	2.16551e12	0.466070	0.233035	+	0.972468i	$0.425134\pi$
$654$	2.32053e12	0.496006
$655$	2.02224e12	0.429285
$656$	1.32026e12	0.278350
$657$	−2.19187e12	−0.458956
$658$	−3.64706e11	−0.0758449
$659$	6.99434e12	1.44465	0.722325	−	0.691554i	$-0.243074\pi$
$659$	6.99434e12	1.44465	0.722325	+	0.691554i	$0.243074\pi$
$660$	2.29699e12	0.471206
$661$	7.13364e12	1.45347	0.726733	−	0.686920i	$-0.241038\pi$
$661$	7.13364e12	1.45347	0.726733	+	0.686920i	$0.241038\pi$
$662$	−1.04677e12	−0.211831
$663$	0	0
$664$	8.26388e11	0.164979
$665$	−1.38681e11	−0.0274992
$666$	3.08129e12	0.606874
$667$	3.45471e12	0.675843
$668$	2.22114e12	0.431600
$669$	−4.78857e12	−0.924248
$670$	−3.69034e12	−0.707505
$671$	−1.43027e12	−0.272374
$672$	−6.76122e10	−0.0127898
$673$	−5.90336e12	−1.10925	−0.554627	−	0.832099i	$-0.687139\pi$
$673$	−5.90336e12	−1.10925	−0.554627	+	0.832099i	$0.687139\pi$
$674$	1.34043e12	0.250192
$675$	−3.40637e12	−0.631574
$676$	0	0
$677$	4.09197e12	0.748657	0.374329	−	0.927296i	$-0.377873\pi$
$677$	4.09197e12	0.748657	0.374329	+	0.927296i	$0.377873\pi$
$678$	−2.76401e12	−0.502349
$679$	1.61738e11	0.0292011
$680$	1.71915e12	0.308335
$681$	1.82000e12	0.324271
$682$	5.78204e12	1.02341
$683$	1.90878e12	0.335631	0.167816	−	0.985818i	$-0.446329\pi$
$683$	1.90878e12	0.335631	0.167816	+	0.985818i	$0.446329\pi$
$684$	−3.25732e11	−0.0568995
$685$	−2.15575e11	−0.0374102
$686$	9.64251e11	0.166238
$687$	−4.43024e12	−0.758791
$688$	−1.76308e12	−0.300002
$689$	0	0
$690$	2.66782e12	0.448059
$691$	1.26665e12	0.211352	0.105676	−	0.994401i	$-0.466299\pi$
$691$	1.26665e12	0.211352	0.105676	+	0.994401i	$0.466299\pi$
$692$	5.19679e12	0.861504
$693$	5.42914e11	0.0894194
$694$	−8.29240e12	−1.35695
$695$	−8.94941e12	−1.45500
$696$	−1.11515e12	−0.180132
$697$	4.73109e12	0.759301
$698$	4.44771e12	0.709230
$699$	−5.99731e12	−0.950188
$700$	2.38888e11	0.0376057
$701$	−5.95358e12	−0.931208	−0.465604	−	0.884993i	$-0.654163\pi$
$701$	−5.95358e12	−0.931208	−0.465604	+	0.884993i	$0.654163\pi$
$702$	0	0
$703$	1.61162e12	0.248865
$704$	−9.82323e11	−0.150722
$705$	−4.64510e12	−0.708181
$706$	−2.57505e12	−0.390089
$707$	6.62473e11	0.0997196
$708$	−2.45905e12	−0.367804
$709$	−8.83324e11	−0.131284	−0.0656420	−	0.997843i	$-0.520910\pi$
$709$	−8.83324e11	−0.131284	−0.0656420	+	0.997843i	$0.520910\pi$
$710$	3.21826e12	0.475290
$711$	7.46022e12	1.09481
$712$	3.53264e12	0.515156
$713$	6.71552e12	0.973143
$714$	−2.42286e11	−0.0348888
$715$	0	0
$716$	−2.78422e12	−0.395908
$717$	−8.15099e12	−1.15179
$718$	−2.32367e12	−0.326298
$719$	2.53369e12	0.353568	0.176784	−	0.984250i	$-0.443431\pi$
$719$	2.53369e12	0.353568	0.176784	+	0.984250i	$0.443431\pi$
$720$	1.44423e12	0.200281
$721$	−1.25911e12	−0.173522
$722$	4.99263e12	0.683774
$723$	−5.11146e12	−0.695701
$724$	3.90556e12	0.528275
$725$	3.94006e12	0.529641
$726$	−1.46835e12	−0.196162
$727$	−8.73905e12	−1.16027	−0.580135	−	0.814520i	$-0.697000\pi$
$727$	−8.73905e12	−1.16027	−0.580135	+	0.814520i	$0.697000\pi$
$728$	0	0
$729$	4.54255e12	0.595697
$730$	5.08300e12	0.662472
$731$	−6.31792e12	−0.818363
$732$	5.36212e11	0.0690298
$733$	2.45358e12	0.313930	0.156965	−	0.987604i	$-0.449829\pi$
$733$	2.45358e12	0.313930	0.156965	+	0.987604i	$0.449829\pi$
$734$	9.41463e12	1.19721
$735$	6.09730e12	0.770627
$736$	−1.14091e12	−0.143319
$737$	7.55632e12	0.943423
$738$	3.97451e12	0.493208
$739$	−1.44149e13	−1.77792	−0.888960	−	0.457985i	$-0.848571\pi$
$739$	−1.44149e13	−1.77792	−0.888960	+	0.457985i	$0.848571\pi$
$740$	−7.14558e12	−0.875981
$741$	0	0
$742$	−7.89466e11	−0.0956128
$743$	−2.25852e12	−0.271878	−0.135939	−	0.990717i	$-0.543405\pi$
$743$	−2.25852e12	−0.271878	−0.135939	+	0.990717i	$0.543405\pi$
$744$	−2.16771e12	−0.259371
$745$	−1.57162e13	−1.86915
$746$	−4.68390e12	−0.553711
$747$	2.48777e12	0.292325
$748$	−3.52012e12	−0.411150
$749$	−2.65885e11	−0.0308693
$750$	−1.74627e12	−0.201528
$751$	5.94360e12	0.681821	0.340910	−	0.940096i	$-0.389265\pi$
$751$	5.94360e12	0.681821	0.340910	+	0.940096i	$0.389265\pi$
$752$	1.98651e12	0.226522
$753$	−5.69003e12	−0.644967
$754$	0	0
$755$	−3.38354e12	−0.378975
$756$	−5.28445e11	−0.0588372
$757$	−5.15480e12	−0.570533	−0.285266	−	0.958448i	$-0.592082\pi$
$757$	−5.15480e12	−0.570533	−0.285266	+	0.958448i	$0.592082\pi$
$758$	1.86321e12	0.204999
$759$	−5.46261e12	−0.597465
$760$	7.55381e11	0.0821306
$761$	−6.04018e11	−0.0652858	−0.0326429	−	0.999467i	$-0.510392\pi$
$761$	−6.04018e11	−0.0652858	−0.0326429	+	0.999467i	$0.510392\pi$
$762$	4.72545e11	0.0507745
$763$	−1.27193e12	−0.135864
$764$	3.09173e11	0.0328308
$765$	5.17534e12	0.546339
$766$	−5.08914e12	−0.534090
$767$	0	0
$768$	3.68276e11	0.0381986
$769$	−1.50501e12	−0.155193	−0.0775963	−	0.996985i	$-0.524725\pi$
$769$	−1.50501e12	−0.155193	−0.0775963	+	0.996985i	$0.524725\pi$
$770$	−1.25903e12	−0.129071
$771$	−3.08698e12	−0.314622
$772$	−3.74893e12	−0.379865
$773$	−7.53437e12	−0.758996	−0.379498	−	0.925193i	$-0.623903\pi$
$773$	−7.53437e12	−0.758996	−0.379498	+	0.925193i	$0.623903\pi$
$774$	−5.30758e12	−0.531573
$775$	7.65896e12	0.762627
$776$	−8.80971e11	−0.0872135
$777$	1.00705e12	0.0991191
$778$	3.00872e12	0.294424
$779$	2.07881e12	0.202253
$780$	0	0
$781$	−6.58970e12	−0.633776
$782$	−4.08842e12	−0.390953
$783$	−8.71581e12	−0.828667
$784$	−2.60755e12	−0.246497
$785$	−2.55509e13	−2.40156
$786$	1.55237e12	0.145075
$787$	4.10896e12	0.381809	0.190904	−	0.981609i	$-0.438858\pi$
$787$	4.10896e12	0.381809	0.190904	+	0.981609i	$0.438858\pi$
$788$	−9.74019e12	−0.899911
$789$	4.74665e12	0.436054
$790$	−1.73004e13	−1.58028
$791$	1.51502e12	0.137601
$792$	−2.95719e12	−0.267065
$793$	0	0
$794$	−1.30665e13	−1.16672
$795$	−1.00551e13	−0.892759
$796$	−6.88860e12	−0.608166
$797$	−3.53460e12	−0.310297	−0.155149	−	0.987891i	$-0.549586\pi$
$797$	−3.53460e12	−0.310297	−0.155149	+	0.987891i	$0.549586\pi$
$798$	−1.06459e11	−0.00929325
$799$	7.11860e12	0.617922
$800$	−1.30120e12	−0.112315
$801$	1.06347e13	0.912806
$802$	1.54333e13	1.31727
$803$	−1.04079e13	−0.883373
$804$	−2.83289e12	−0.239099
$805$	−1.46229e12	−0.122731
$806$	0	0
$807$	8.46510e12	0.702589
$808$	−3.60842e12	−0.297828
$809$	8.96434e12	0.735783	0.367892	−	0.929869i	$-0.380080\pi$
$809$	8.96434e12	0.735783	0.367892	+	0.929869i	$0.380080\pi$
$810$	2.09542e11	0.0171036
$811$	8.61534e12	0.699324	0.349662	−	0.936876i	$-0.386296\pi$
$811$	8.61534e12	0.699324	0.349662	+	0.936876i	$0.386296\pi$
$812$	6.11238e11	0.0493411
$813$	1.35329e13	1.08638
$814$	1.46313e13	1.16808
$815$	2.41829e13	1.91999
$816$	1.31970e12	0.104201
$817$	−2.77605e12	−0.217986
$818$	7.88451e12	0.615722
$819$	0	0
$820$	−9.21698e12	−0.711912
$821$	−2.09873e13	−1.61218	−0.806088	−	0.591796i	$-0.798419\pi$
$821$	−2.09873e13	−1.61218	−0.806088	+	0.591796i	$0.798419\pi$
$822$	−1.65486e11	−0.0126426
$823$	1.47480e13	1.12056	0.560280	−	0.828304i	$-0.310694\pi$
$823$	1.47480e13	1.12056	0.560280	+	0.828304i	$0.310694\pi$
$824$	6.85824e12	0.518251
$825$	−6.23004e12	−0.468218
$826$	1.34786e12	0.100747
$827$	−1.00085e13	−0.744037	−0.372018	−	0.928225i	$-0.621334\pi$
$827$	−1.00085e13	−0.744037	−0.372018	+	0.928225i	$0.621334\pi$
$828$	−3.43461e12	−0.253946
$829$	8.15300e12	0.599546	0.299773	−	0.954011i	$-0.403089\pi$
$829$	8.15300e12	0.599546	0.299773	+	0.954011i	$0.403089\pi$
$830$	−5.76918e12	−0.421952
$831$	2.16514e12	0.157500
$832$	0	0
$833$	−9.34407e12	−0.672409
$834$	−6.87001e12	−0.491712
$835$	−1.55062e13	−1.10387
$836$	−1.54671e12	−0.109517
$837$	−1.69424e13	−1.19319
$838$	−1.70867e12	−0.119690
$839$	−1.94338e13	−1.35403	−0.677017	−	0.735968i	$-0.736728\pi$
$839$	−1.94338e13	−1.35403	−0.677017	+	0.735968i	$0.736728\pi$
$840$	4.72014e11	0.0327113
$841$	−4.42580e12	−0.305077
$842$	−1.45104e12	−0.0994892
$843$	6.38163e12	0.435219
$844$	−7.36963e12	−0.499925
$845$	0	0
$846$	5.98022e12	0.401375
$847$	8.04834e11	0.0537318
$848$	4.30014e12	0.285562
$849$	−9.29475e12	−0.613979
$850$	−4.66279e12	−0.306380
$851$	1.69934e13	1.11070
$852$	2.47050e12	0.160623
$853$	8.40777e12	0.543764	0.271882	−	0.962331i	$-0.412354\pi$
$853$	8.40777e12	0.543764	0.271882	+	0.962331i	$0.412354\pi$
$854$	−2.93910e11	−0.0189083
$855$	2.27400e12	0.145527
$856$	1.44825e12	0.0921958
$857$	1.57510e13	0.997458	0.498729	−	0.866758i	$-0.333800\pi$
$857$	1.57510e13	0.997458	0.498729	+	0.866758i	$0.333800\pi$
$858$	0	0
$859$	3.45790e12	0.216692	0.108346	−	0.994113i	$-0.465445\pi$
$859$	3.45790e12	0.216692	0.108346	+	0.994113i	$0.465445\pi$
$860$	1.23084e13	0.767289
$861$	1.29898e12	0.0805544
$862$	8.62645e12	0.532169
$863$	−5.82263e12	−0.357331	−0.178665	−	0.983910i	$-0.557178\pi$
$863$	−5.82263e12	−0.357331	−0.178665	+	0.983910i	$0.557178\pi$
$864$	2.87838e12	0.175726
$865$	−3.62798e13	−2.20340
$866$	−7.49619e12	−0.452908
$867$	−5.43932e12	−0.326933
$868$	1.18817e12	0.0710460
$869$	3.54243e13	2.10723
$870$	7.78508e12	0.460709
$871$	0	0
$872$	6.92809e12	0.405779
$873$	−2.65208e12	−0.154534
$874$	−1.79642e12	−0.104137
$875$	9.57168e11	0.0552016
$876$	3.90196e12	0.223880
$877$	5.98999e12	0.341923	0.170961	−	0.985278i	$-0.445313\pi$
$877$	5.98999e12	0.341923	0.170961	+	0.985278i	$0.445313\pi$
$878$	−5.76022e12	−0.327125
$879$	−4.15548e12	−0.234785
$880$	6.85780e12	0.385490
$881$	−2.57327e13	−1.43911	−0.719554	−	0.694437i	$-0.755654\pi$
$881$	−2.57327e13	−1.43911	−0.719554	+	0.694437i	$0.755654\pi$
$882$	−7.84980e12	−0.436767
$883$	−3.22167e13	−1.78344	−0.891719	−	0.452590i	$-0.850500\pi$
$883$	−3.22167e13	−1.78344	−0.891719	+	0.452590i	$0.850500\pi$
$884$	0	0
$885$	1.71671e13	0.940702
$886$	−2.16204e13	−1.17872
$887$	−1.54777e13	−0.839557	−0.419779	−	0.907627i	$-0.637892\pi$
$887$	−1.54777e13	−0.839557	−0.419779	+	0.907627i	$0.637892\pi$
$888$	−5.48530e12	−0.296034
$889$	−2.59012e11	−0.0139079
$890$	−2.46621e13	−1.31757
$891$	−4.29057e11	−0.0228068
$892$	−1.42966e13	−0.756120
$893$	3.12786e12	0.164595
$894$	−1.20645e13	−0.631672
$895$	1.94372e13	1.01258
$896$	−2.01860e11	−0.0104632
$897$	0	0
$898$	1.77077e13	0.908699
$899$	1.95968e13	1.00062
$900$	−3.91713e12	−0.199011
$901$	1.54094e13	0.778975
$902$	1.88727e13	0.949300
$903$	−1.73467e12	−0.0868203
$904$	−8.25212e12	−0.410968
$905$	−2.72655e13	−1.35112
$906$	−2.59738e12	−0.128073
$907$	−4.09617e12	−0.200977	−0.100488	−	0.994938i	$-0.532040\pi$
$907$	−4.09617e12	−0.200977	−0.100488	+	0.994938i	$0.532040\pi$
$908$	5.43372e12	0.265284
$909$	−1.08628e13	−0.527721
$910$	0	0
$911$	−3.19819e13	−1.53841	−0.769204	−	0.639003i	$-0.779347\pi$
$911$	−3.19819e13	−1.53841	−0.769204	+	0.639003i	$0.779347\pi$
$912$	5.79868e11	0.0277557
$913$	1.18130e13	0.562652
$914$	−2.40060e13	−1.13779
$915$	−3.74340e12	−0.176552
$916$	−1.32268e13	−0.620761
$917$	−8.50889e11	−0.0397384
$918$	1.03146e13	0.479357
$919$	−3.05636e13	−1.41347	−0.706733	−	0.707481i	$-0.749832\pi$
$919$	−3.05636e13	−1.41347	−0.706733	+	0.707481i	$0.749832\pi$
$920$	7.96495e12	0.366554
$921$	7.46947e12	0.342075
$922$	2.00893e13	0.915536
$923$	0	0
$924$	−9.66494e11	−0.0436190
$925$	1.93807e13	0.870427
$926$	−7.35060e12	−0.328529
$927$	2.06461e13	0.918289
$928$	−3.32935e12	−0.147365
$929$	1.96670e13	0.866300	0.433150	−	0.901322i	$-0.357402\pi$
$929$	1.96670e13	0.866300	0.433150	+	0.901322i	$0.357402\pi$
$930$	1.51332e13	0.663373
$931$	−4.10572e12	−0.179108
$932$	−1.79054e13	−0.777341
$933$	−1.55295e12	−0.0670952
$934$	3.15952e13	1.35850
$935$	2.45747e13	1.05156
$936$	0	0
$937$	5.88474e12	0.249401	0.124701	−	0.992194i	$-0.460203\pi$
$937$	5.88474e12	0.249401	0.124701	+	0.992194i	$0.460203\pi$
$938$	1.55277e12	0.0654929
$939$	−2.14746e13	−0.901425
$940$	−1.38683e13	−0.579357
$941$	1.79868e13	0.747827	0.373914	−	0.927464i	$-0.378016\pi$
$941$	1.79868e13	0.747827	0.373914	+	0.927464i	$0.378016\pi$
$942$	−1.96142e13	−0.811598
$943$	2.19195e13	0.902669
$944$	−7.34164e12	−0.300898
$945$	3.68918e12	0.150483
$946$	−2.52026e13	−1.02314
$947$	1.42787e13	0.576917	0.288459	−	0.957492i	$-0.406857\pi$
$947$	1.42787e13	0.576917	0.288459	+	0.957492i	$0.406857\pi$
$948$	−1.32807e13	−0.534050
$949$	0	0
$950$	−2.04880e12	−0.0816098
$951$	1.39308e13	0.552287
$952$	−7.23359e11	−0.0285422
$953$	−4.85651e11	−0.0190724	−0.00953622	−	0.999955i	$-0.503036\pi$
$953$	−4.85651e11	−0.0190724	−0.00953622	+	0.999955i	$0.503036\pi$
$954$	1.29452e13	0.505988
$955$	−2.15840e12	−0.0839686
$956$	−2.43353e13	−0.942271
$957$	−1.59407e13	−0.614333
$958$	3.16561e13	1.21426
$959$	9.07066e10	0.00346302
$960$	−2.57101e12	−0.0976975
$961$	1.16541e13	0.440783
$962$	0	0
$963$	4.35982e12	0.163362
$964$	−1.52606e13	−0.569147
$965$	2.61720e13	0.971549
$966$	−1.12253e12	−0.0414763
$967$	−3.93014e13	−1.44540	−0.722702	−	0.691160i	$-0.757100\pi$
$967$	−3.93014e13	−1.44540	−0.722702	+	0.691160i	$0.757100\pi$
$968$	−4.38384e12	−0.160478
$969$	2.07794e12	0.0757138
$970$	6.15024e12	0.223059
$971$	7.17694e12	0.259091	0.129546	−	0.991573i	$-0.458648\pi$
$971$	7.17694e12	0.259091	0.129546	+	0.991573i	$0.458648\pi$
$972$	1.39927e13	0.502809
$973$	3.76561e12	0.134688
$974$	1.39269e13	0.495837
$975$	0	0
$976$	1.60089e12	0.0564727
$977$	−2.36882e13	−0.831775	−0.415888	−	0.909416i	$-0.636529\pi$
$977$	−2.36882e13	−0.831775	−0.415888	+	0.909416i	$0.636529\pi$
$978$	1.85640e13	0.648853
$979$	5.04979e13	1.75692
$980$	1.82039e13	0.630444
$981$	2.08564e13	0.718999
$982$	1.46501e13	0.502734
$983$	−2.27685e12	−0.0777755	−0.0388877	−	0.999244i	$-0.512381\pi$
$983$	−2.27685e12	−0.0777755	−0.0388877	+	0.999244i	$0.512381\pi$
$984$	−7.07542e12	−0.240588
$985$	6.79982e13	2.30163
$986$	−1.19306e13	−0.401991
$987$	1.95450e12	0.0655555
$988$	0	0
$989$	−2.92714e13	−0.972883
$990$	2.06448e13	0.683049
$991$	5.41684e13	1.78408	0.892041	−	0.451955i	$-0.149273\pi$
$991$	5.41684e13	1.78408	0.892041	+	0.451955i	$0.149273\pi$
$992$	−6.47183e12	−0.212190
$993$	5.60976e12	0.183094
$994$	−1.35414e12	−0.0439971
$995$	4.80908e13	1.55546
$996$	−4.42871e12	−0.142597
$997$	2.39920e12	0.0769020	0.0384510	−	0.999260i	$-0.487758\pi$
$997$	2.39920e12	0.0769020	0.0384510	+	0.999260i	$0.487758\pi$
$998$	−1.66402e13	−0.530971
$999$	−4.28722e13	−1.36185

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	338.10.a.e.1.2		3
13.12	even	2		26.10.a.e.1.2	✓	3
39.38	odd	2		234.10.a.k.1.1		3
52.51	odd	2		208.10.a.d.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.10.a.e.1.2	✓	3	13.12	even	2
208.10.a.d.1.2		3	52.51	odd	2
234.10.a.k.1.1		3	39.38	odd	2
338.10.a.e.1.2		3	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:	\( N \)	\(=\)	\( 338 = 2 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	338.a (trivial)

\(f(q)\)	\(=\)	\(q-16.0000 q^{2} +85.7459 q^{3} +256.000 q^{4} -1787.19 q^{5} -1371.94 q^{6} +751.989 q^{7} -4096.00 q^{8} -12330.6 q^{9} +28595.0 q^{10} -58551.0 q^{11} +21951.0 q^{12} -12031.8 q^{14} -153244. q^{15} +65536.0 q^{16} +234846. q^{17} +197290. q^{18} +103190. q^{19} -457520. q^{20} +64480.0 q^{21} +936816. q^{22} +1.08806e6 q^{23} -351215. q^{24} +1.24092e6 q^{25} -2.74504e6 q^{27} +192509. q^{28} +3.17511e6 q^{29} +2.45191e6 q^{30} +6.17201e6 q^{31} -1.04858e6 q^{32} -5.02051e6 q^{33} -3.75753e6 q^{34} -1.34395e6 q^{35} -3.15664e6 q^{36} +1.56181e7 q^{37} -1.65103e6 q^{38} +7.32032e6 q^{40} +2.01455e7 q^{41} -1.03168e6 q^{42} -2.69024e7 q^{43} -1.49891e7 q^{44} +2.20372e7 q^{45} -1.74089e7 q^{46} +3.03118e7 q^{47} +5.61945e6 q^{48} -3.97881e7 q^{49} -1.98547e7 q^{50} +2.01371e7 q^{51} +6.56149e7 q^{53} +4.39206e7 q^{54} +1.04642e8 q^{55} -3.08015e6 q^{56} +8.84808e6 q^{57} -5.08018e7 q^{58} -1.12025e8 q^{59} -3.92305e7 q^{60} +2.44277e7 q^{61} -9.87522e7 q^{62} -9.27250e6 q^{63} +1.67772e7 q^{64} +8.03282e7 q^{66} -1.29055e8 q^{67} +6.01205e7 q^{68} +9.32967e7 q^{69} +2.15031e7 q^{70} +1.12546e8 q^{71} +5.05063e7 q^{72} +1.77758e8 q^{73} -2.49889e8 q^{74} +1.06404e8 q^{75} +2.64165e7 q^{76} -4.40297e7 q^{77} -6.05015e8 q^{79} -1.17125e8 q^{80} +7.32791e6 q^{81} -3.22328e8 q^{82} -2.01755e8 q^{83} +1.65069e7 q^{84} -4.19714e8 q^{85} +4.30439e8 q^{86} +2.72253e8 q^{87} +2.39825e8 q^{88} -8.62460e8 q^{89} -3.52595e8 q^{90} +2.78543e8 q^{92} +5.29225e8 q^{93} -4.84989e8 q^{94} -1.84419e8 q^{95} -8.99111e7 q^{96} +2.15081e8 q^{97} +6.36610e8 q^{98} +7.21971e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 48 q^{2} + 156 q^{3} + 768 q^{4} + 1272 q^{5} - 2496 q^{6} - 17058 q^{7} - 12288 q^{8} + 42273 q^{9} - 20352 q^{10} - 73974 q^{11} + 39936 q^{12} + 272928 q^{14} - 393756 q^{15} + 196608 q^{16} + 374976 q^{17}+ \cdots + 2480087466 q^{99}+O(q^{100}) \) 3 * q - 48 * q^2 + 156 * q^3 + 768 * q^4 + 1272 * q^5 - 2496 * q^6 - 17058 * q^7 - 12288 * q^8 + 42273 * q^9 - 20352 * q^10 - 73974 * q^11 + 39936 * q^12 + 272928 * q^14 - 393756 * q^15 + 196608 * q^16 + 374976 * q^17 - 676368 * q^18 - 418338 * q^19 + 325632 * q^20 + 284694 * q^21 + 1183584 * q^22 + 1026168 * q^23 - 638976 * q^24 + 3337287 * q^25 + 4218588 * q^27 - 4366848 * q^28 - 3075834 * q^29 + 6300096 * q^30 - 9286482 * q^31 - 3145728 * q^32 + 25456452 * q^33 - 5999616 * q^34 - 31802592 * q^35 + 10821888 * q^36 + 17647776 * q^37 + 6693408 * q^38 - 5210112 * q^40 + 47257110 * q^41 - 4555104 * q^42 - 60023760 * q^43 - 18937344 * q^44 + 81112122 * q^45 - 16418688 * q^46 + 40824726 * q^47 + 10223616 * q^48 + 45921177 * q^49 - 53396592 * q^50 - 27559188 * q^51 + 8072046 * q^53 - 67497408 * q^54 - 36910236 * q^55 + 69869568 * q^56 - 245224476 * q^57 + 49213344 * q^58 - 138035310 * q^59 - 100801536 * q^60 + 264203886 * q^61 + 148583712 * q^62 - 436094838 * q^63 + 50331648 * q^64 - 407303232 * q^66 - 203167074 * q^67 + 95993856 * q^68 - 397637544 * q^69 + 508841472 * q^70 - 123067110 * q^71 - 173150208 * q^72 + 433013250 * q^73 - 282364416 * q^74 - 884469216 * q^75 - 107094528 * q^76 + 380043264 * q^77 + 406418748 * q^79 + 83361792 * q^80 + 100121427 * q^81 - 756113760 * q^82 - 105365610 * q^83 + 72881664 * q^84 - 5268186 * q^85 + 960380160 * q^86 - 12753768 * q^87 + 302997504 * q^88 - 1365375798 * q^89 - 1297793952 * q^90 + 262699008 * q^92 + 95909856 * q^93 - 653195616 * q^94 - 85600692 * q^95 - 163577856 * q^96 - 669691662 * q^97 - 734738832 * q^98 + 2480087466 * q^99

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