LMFDB - Embedded newform 338.10.a.f.1.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [338,10,Mod(1,338)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage: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")

magma://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:traces = [3,48,0,768,-248] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$174.082112623$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	$\mathbb{Q}[x]/(x^{3} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 6144x - 66096 $ x^3 - x^2 - 6144*x - 66096
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 26)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-10.9937$ 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)

$f(q)$	$=$	\(q+16.0000 q^{2} +159.509 q^{3} +256.000 q^{4} -1767.44 q^{5} +2552.15 q^{6} -6243.46 q^{7} +4096.00 q^{8} +5760.16 q^{9} -28279.1 q^{10} +41072.0 q^{11} +40834.3 q^{12} -99895.4 q^{14} -281924. q^{15} +65536.0 q^{16} +98274.9 q^{17} +92162.5 q^{18} -507054. q^{19} -452466. q^{20} -995890. q^{21} +657152. q^{22} +1.89860e6 q^{23} +653349. q^{24} +1.17074e6 q^{25} -2.22082e6 q^{27} -1.59833e6 q^{28} -321475. q^{29} -4.51078e6 q^{30} +6.09551e6 q^{31} +1.04858e6 q^{32} +6.55136e6 q^{33} +1.57240e6 q^{34} +1.10350e7 q^{35} +1.47460e6 q^{36} -1.77236e7 q^{37} -8.11287e6 q^{38} -7.23945e6 q^{40} +1.79328e7 q^{41} -1.59342e7 q^{42} -1.22817e7 q^{43} +1.05144e7 q^{44} -1.01808e7 q^{45} +3.03776e7 q^{46} -4.23821e7 q^{47} +1.04536e7 q^{48} -1.37275e6 q^{49} +1.87318e7 q^{50} +1.56757e7 q^{51} +3.92537e6 q^{53} -3.55331e7 q^{54} -7.25925e7 q^{55} -2.55732e7 q^{56} -8.08798e7 q^{57} -5.14360e6 q^{58} +1.72026e8 q^{59} -7.21724e7 q^{60} +1.36776e8 q^{61} +9.75281e7 q^{62} -3.59633e7 q^{63} +1.67772e7 q^{64} +1.04822e8 q^{66} -1.21248e8 q^{67} +2.51584e7 q^{68} +3.02844e8 q^{69} +1.76560e8 q^{70} +3.66817e8 q^{71} +2.35936e7 q^{72} +1.13266e8 q^{73} -2.83577e8 q^{74} +1.86743e8 q^{75} -1.29806e8 q^{76} -2.56432e8 q^{77} +2.79788e8 q^{79} -1.15831e8 q^{80} -4.67618e8 q^{81} +2.86926e8 q^{82} +7.50041e8 q^{83} -2.54948e8 q^{84} -1.73695e8 q^{85} -1.96507e8 q^{86} -5.12782e7 q^{87} +1.68231e8 q^{88} +7.04433e8 q^{89} -1.62892e8 q^{90} +4.86041e8 q^{92} +9.72289e8 q^{93} -6.78113e8 q^{94} +8.96190e8 q^{95} +1.67257e8 q^{96} +1.21751e9 q^{97} -2.19641e7 q^{98} +2.36581e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 48 q^{2} + 768 q^{4} - 248 q^{5} + 2956 q^{7} + 12288 q^{8} - 20863 q^{9} - 3968 q^{10} + 31324 q^{11} + 47296 q^{14} - 392140 q^{15} + 196608 q^{16} + 905228 q^{17} - 333808 q^{18} - 1726316 q^{19}+ \cdots + 304026580 q^{99}+O(q^{100}) $ 3 * q + 48 * q^2 + 768 * q^4 - 248 * q^5 + 2956 * q^7 + 12288 * q^8 - 20863 * q^9 - 3968 * q^10 + 31324 * q^11 + 47296 * q^14 - 392140 * q^15 + 196608 * q^16 + 905228 * q^17 - 333808 * q^18 - 1726316 * q^19 - 63488 * q^20 - 1771246 * q^21 + 501184 * q^22 + 2135256 * q^23 + 4074295 * q^25 + 3038724 * q^27 + 756736 * q^28 + 372426 * q^29 - 6274240 * q^30 + 1444776 * q^31 + 3145728 * q^32 + 7719476 * q^33 + 14483648 * q^34 - 3459436 * q^35 - 5340928 * q^36 + 2809672 * q^37 - 27621056 * q^38 - 1015808 * q^40 + 7424806 * q^41 - 28339936 * q^42 + 36070040 * q^43 + 8018944 * q^44 - 32156162 * q^45 + 34164096 * q^46 - 7032884 * q^47 + 41844597 * q^49 + 65188720 * q^50 - 47158124 * q^51 - 15011674 * q^53 + 48619584 * q^54 + 121479136 * q^55 + 12107776 * q^56 + 14804300 * q^57 + 5958816 * q^58 + 40286396 * q^59 - 100387840 * q^60 + 230710478 * q^61 + 23116416 * q^62 - 151778040 * q^63 + 50331648 * q^64 + 123511616 * q^66 - 201453084 * q^67 + 231738368 * q^68 + 268135008 * q^69 - 55350976 * q^70 + 99165572 * q^71 - 85454848 * q^72 + 350942946 * q^73 + 44954752 * q^74 - 28166788 * q^75 - 441936896 * q^76 - 1066624588 * q^77 + 138794592 * q^79 - 16252928 * q^80 - 363498349 * q^81 + 118796896 * q^82 + 1364469516 * q^83 - 453438976 * q^84 + 1225485962 * q^85 + 577120640 * q^86 - 93372576 * q^87 + 128303104 * q^88 + 709437058 * q^89 - 514498592 * q^90 + 546625536 * q^92 + 1382471232 * q^93 - 112526144 * q^94 - 833387824 * q^95 + 362189698 * q^97 + 669513552 * q^98 + 304026580 * 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
$3$	159.509	1.13695	0.568473	−	0.822702i	$-0.307534\pi$
$3$	159.509	1.13695	0.568473	+	0.822702i	$0.307534\pi$
$4$	256.000	0.500000
$5$	−1767.44	−1.26468	−0.632340	−	0.774691i	$-0.717905\pi$
$5$	−1767.44	−1.26468	−0.632340	+	0.774691i	$0.717905\pi$
$6$	2552.15	0.803942
$7$	−6243.46	−0.982844	−0.491422	−	0.870922i	$-0.663523\pi$
$7$	−6243.46	−0.982844	−0.491422	+	0.870922i	$0.663523\pi$
$8$	4096.00	0.353553
$9$	5760.16	0.292646
$10$	−28279.1	−0.894264
$11$	41072.0	0.845821	0.422911	−	0.906171i	$-0.361008\pi$
$11$	41072.0	0.845821	0.422911	+	0.906171i	$0.361008\pi$
$12$	40834.3	0.568473
$13$	0	0
$13$	0	0
$14$	−99895.4	−0.694976
$15$	−281924.	−1.43787
$16$	65536.0	0.250000
$17$	98274.9	0.285379	0.142690	−	0.989767i	$-0.454425\pi$
$17$	98274.9	0.285379	0.142690	+	0.989767i	$0.454425\pi$
$18$	92162.5	0.206932
$19$	−507054.	−0.892613	−0.446307	−	0.894880i	$-0.647261\pi$
$19$	−507054.	−0.892613	−0.446307	+	0.894880i	$0.647261\pi$
$20$	−452466.	−0.632340
$21$	−995890.	−1.11744
$22$	657152.	0.598086
$23$	1.89860e6	1.41468	0.707340	−	0.706874i	$-0.249895\pi$
$23$	1.89860e6	1.41468	0.707340	+	0.706874i	$0.249895\pi$
$24$	653349.	0.401971
$25$	1.17074e6	0.599416
$26$	0	0
$27$	−2.22082e6	−0.804223
$28$	−1.59833e6	−0.491422
$29$	−321475.	−0.0844027	−0.0422013	−	0.999109i	$-0.513437\pi$
$29$	−321475.	−0.0844027	−0.0422013	+	0.999109i	$0.513437\pi$
$30$	−4.51078e6	−1.01673
$31$	6.09551e6	1.18545	0.592724	−	0.805406i	$-0.298053\pi$
$31$	6.09551e6	1.18545	0.592724	+	0.805406i	$0.298053\pi$
$32$	1.04858e6	0.176777
$33$	6.55136e6	0.961653
$34$	1.57240e6	0.201794
$35$	1.10350e7	1.24298
$36$	1.47460e6	0.146323
$37$	−1.77236e7	−1.55469	−0.777344	−	0.629076i	$-0.783434\pi$
$37$	−1.77236e7	−1.55469	−0.777344	+	0.629076i	$0.783434\pi$
$38$	−8.11287e6	−0.631173
$39$	0	0
$40$	−7.23945e6	−0.447132
$41$	1.79328e7	0.991110	0.495555	−	0.868577i	$-0.334965\pi$
$41$	1.79328e7	0.991110	0.495555	+	0.868577i	$0.334965\pi$
$42$	−1.59342e7	−0.790150
$43$	−1.22817e7	−0.547834	−0.273917	−	0.961753i	$-0.588319\pi$
$43$	−1.22817e7	−0.547834	−0.273917	+	0.961753i	$0.588319\pi$
$44$	1.05144e7	0.422911
$45$	−1.01808e7	−0.370104
$46$	3.03776e7	1.00033
$47$	−4.23821e7	−1.26690	−0.633449	−	0.773784i	$-0.718361\pi$
$47$	−4.23821e7	−1.26690	−0.633449	+	0.773784i	$0.718361\pi$
$48$	1.04536e7	0.284237
$49$	−1.37275e6	−0.0340181
$50$	1.87318e7	0.423851
$51$	1.56757e7	0.324461
$52$	0	0
$53$	3.92537e6	0.0683344	0.0341672	−	0.999416i	$-0.489122\pi$
$53$	3.92537e6	0.0683344	0.0341672	+	0.999416i	$0.489122\pi$
$54$	−3.55331e7	−0.568672
$55$	−7.25925e7	−1.06969
$56$	−2.55732e7	−0.347488
$57$	−8.08798e7	−1.01485
$58$	−5.14360e6	−0.0596817
$59$	1.72026e8	1.84824	0.924122	−	0.382098i	$-0.124798\pi$
$59$	1.72026e8	1.84824	0.924122	+	0.382098i	$0.124798\pi$
$60$	−7.21724e7	−0.718937
$61$	1.36776e8	1.26481	0.632407	−	0.774636i	$-0.282067\pi$
$61$	1.36776e8	1.26481	0.632407	+	0.774636i	$0.282067\pi$
$62$	9.75281e7	0.838238
$63$	−3.59633e7	−0.287626
$64$	1.67772e7	0.125000
$65$	0	0
$66$	1.04822e8	0.679992
$67$	−1.21248e8	−0.735086	−0.367543	−	0.930006i	$-0.619801\pi$
$67$	−1.21248e8	−0.735086	−0.367543	+	0.930006i	$0.619801\pi$
$68$	2.51584e7	0.142690
$69$	3.02844e8	1.60841
$70$	1.76560e8	0.878922
$71$	3.66817e8	1.71311	0.856557	−	0.516052i	$-0.172599\pi$
$71$	3.66817e8	1.71311	0.856557	+	0.516052i	$0.172599\pi$
$72$	2.35936e7	0.103466
$73$	1.13266e8	0.466816	0.233408	−	0.972379i	$-0.425012\pi$
$73$	1.13266e8	0.466816	0.233408	+	0.972379i	$0.425012\pi$
$74$	−2.83577e8	−1.09933
$75$	1.86743e8	0.681504
$76$	−1.29806e8	−0.446307
$77$	−2.56432e8	−0.831310
$78$	0	0
$79$	2.79788e8	0.808179	0.404089	−	0.914720i	$-0.367588\pi$
$79$	2.79788e8	0.808179	0.404089	+	0.914720i	$0.367588\pi$
$80$	−1.15831e8	−0.316170
$81$	−4.67618e8	−1.20700
$82$	2.86926e8	0.700821
$83$	7.50041e8	1.73474	0.867368	−	0.497667i	$-0.165810\pi$
$83$	7.50041e8	1.73474	0.867368	+	0.497667i	$0.165810\pi$
$84$	−2.54948e8	−0.558720
$85$	−1.73695e8	−0.360914
$86$	−1.96507e8	−0.387377
$87$	−5.12782e7	−0.0959613
$88$	1.68231e8	0.299043
$89$	7.04433e8	1.19010	0.595052	−	0.803688i	$-0.297132\pi$
$89$	7.04433e8	1.19010	0.595052	+	0.803688i	$0.297132\pi$
$90$	−1.62892e8	−0.261703
$91$	0	0
$92$	4.86041e8	0.707340
$93$	9.72289e8	1.34779
$94$	−6.78113e8	−0.895832
$95$	8.96190e8	1.12887
$96$	1.67257e8	0.200986
$97$	1.21751e9	1.39637	0.698183	−	0.715920i	$-0.253992\pi$
$97$	1.21751e9	1.39637	0.698183	+	0.715920i	$0.253992\pi$
$98$	−2.19641e7	−0.0240544
$99$	2.36581e8	0.247527
$100$	2.99708e8	0.299708
$101$	−9.52618e8	−0.910904	−0.455452	−	0.890260i	$-0.650522\pi$
$101$	−9.52618e8	−0.910904	−0.455452	+	0.890260i	$0.650522\pi$
$102$	2.50812e8	0.229429
$103$	1.27341e9	1.11481	0.557405	−	0.830240i	$-0.311797\pi$
$103$	1.27341e9	1.11481	0.557405	+	0.830240i	$0.311797\pi$
$104$	0	0
$105$	1.76018e9	1.41320
$106$	6.28059e7	0.0483197
$107$	9.71126e8	0.716223	0.358112	−	0.933679i	$-0.383421\pi$
$107$	9.71126e8	0.716223	0.358112	+	0.933679i	$0.383421\pi$
$108$	−5.68530e8	−0.402111
$109$	1.35575e9	0.919940	0.459970	−	0.887935i	$-0.347860\pi$
$109$	1.35575e9	0.919940	0.459970	+	0.887935i	$0.347860\pi$
$110$	−1.16148e9	−0.756388
$111$	−2.82707e9	−1.76760
$112$	−4.09172e8	−0.245711
$113$	2.19491e9	1.26638	0.633189	−	0.773997i	$-0.281746\pi$
$113$	2.19491e9	1.26638	0.633189	+	0.773997i	$0.281746\pi$
$114$	−1.29408e9	−0.717609
$115$	−3.35567e9	−1.78912
$116$	−8.22976e7	−0.0422013
$117$	0	0
$118$	2.75241e9	1.30691
$119$	−6.13576e8	−0.280483
$120$	−1.15476e9	−0.508365
$121$	−6.71039e8	−0.284586
$122$	2.18842e9	0.894359
$123$	2.86045e9	1.12684
$124$	1.56045e9	0.592724
$125$	1.38283e9	0.506610
$126$	−5.75413e8	−0.203382
$127$	2.77758e9	0.947437	0.473718	−	0.880676i	$-0.342911\pi$
$127$	2.77758e9	0.947437	0.473718	+	0.880676i	$0.342911\pi$
$128$	2.68435e8	0.0883883
$129$	−1.95904e9	−0.622858
$130$	0	0
$131$	−5.91870e8	−0.175592	−0.0877961	−	0.996138i	$-0.527982\pi$
$131$	−5.91870e8	−0.175592	−0.0877961	+	0.996138i	$0.527982\pi$
$132$	1.67715e9	0.480827
$133$	3.16578e9	0.877299
$134$	−1.93997e9	−0.519784
$135$	3.92518e9	1.01708
$136$	4.02534e8	0.100897
$137$	4.78496e9	1.16048	0.580238	−	0.814447i	$-0.302960\pi$
$137$	4.78496e9	1.16048	0.580238	+	0.814447i	$0.302960\pi$
$138$	4.84550e9	1.13732
$139$	−9.91846e8	−0.225360	−0.112680	−	0.993631i	$-0.535944\pi$
$139$	−9.91846e8	−0.225360	−0.112680	+	0.993631i	$0.535944\pi$
$140$	2.82495e9	0.621492
$141$	−6.76033e9	−1.44039
$142$	5.86906e9	1.21135
$143$	0	0
$144$	3.77498e8	0.0731616
$145$	5.68189e8	0.106742
$146$	1.81225e9	0.330089
$147$	−2.18967e8	−0.0386767
$148$	−4.53723e9	−0.777344
$149$	7.40400e9	1.23063	0.615316	−	0.788280i	$-0.289028\pi$
$149$	7.40400e9	1.23063	0.615316	+	0.788280i	$0.289028\pi$
$150$	2.98789e9	0.481896
$151$	−8.11389e9	−1.27009	−0.635043	−	0.772477i	$-0.719017\pi$
$151$	−8.11389e9	−1.27009	−0.635043	+	0.772477i	$0.719017\pi$
$152$	−2.07689e9	−0.315586
$153$	5.66079e8	0.0835152
$154$	−4.10290e9	−0.587825
$155$	−1.07735e10	−1.49921
$156$	0	0
$157$	−1.10905e10	−1.45681	−0.728407	−	0.685145i	$-0.759739\pi$
$157$	−1.10905e10	−1.45681	−0.728407	+	0.685145i	$0.759739\pi$
$158$	4.47661e9	0.571469
$159$	6.26132e8	0.0776925
$160$	−1.85330e9	−0.223566
$161$	−1.18538e10	−1.39041
$162$	−7.48189e9	−0.853481
$163$	−7.83983e8	−0.0869886	−0.0434943	−	0.999054i	$-0.513849\pi$
$163$	−7.83983e8	−0.0869886	−0.0434943	+	0.999054i	$0.513849\pi$
$164$	4.59081e9	0.495555
$165$	−1.15792e10	−1.21618
$166$	1.20007e10	1.22664
$167$	−1.26374e10	−1.25729	−0.628643	−	0.777694i	$-0.716389\pi$
$167$	−1.26374e10	−1.25729	−0.628643	+	0.777694i	$0.716389\pi$
$168$	−4.07916e9	−0.395075
$169$	0	0
$170$	−2.77913e9	−0.255204
$171$	−2.92071e9	−0.261220
$172$	−3.14411e9	−0.273917
$173$	−3.65563e9	−0.310281	−0.155140	−	0.987892i	$-0.549583\pi$
$173$	−3.65563e9	−0.310281	−0.155140	+	0.987892i	$0.549583\pi$
$174$	−8.20451e8	−0.0678549
$175$	−7.30944e9	−0.589133
$176$	2.69169e9	0.211455
$177$	2.74397e10	2.10135
$178$	1.12709e10	0.841530
$179$	1.00526e10	0.731879	0.365939	−	0.930639i	$-0.380748\pi$
$179$	1.00526e10	0.731879	0.365939	+	0.930639i	$0.380748\pi$
$180$	−2.60627e9	−0.185052
$181$	−6.35857e9	−0.440358	−0.220179	−	0.975459i	$-0.570664\pi$
$181$	−6.35857e9	−0.440358	−0.220179	+	0.975459i	$0.570664\pi$
$182$	0	0
$183$	2.18171e10	1.43803
$184$	7.77666e9	0.500165
$185$	3.13254e10	1.96618
$186$	1.55566e10	0.953031
$187$	4.03635e9	0.241380
$188$	−1.08498e10	−0.633449
$189$	1.38656e10	0.790426
$190$	1.43390e10	0.798232
$191$	−2.56451e10	−1.39429	−0.697146	−	0.716929i	$-0.745547\pi$
$191$	−2.56451e10	−1.39429	−0.697146	+	0.716929i	$0.745547\pi$
$192$	2.67612e9	0.142118
$193$	−3.05861e10	−1.58678	−0.793389	−	0.608715i	$-0.791685\pi$
$193$	−3.05861e10	−1.58678	−0.793389	+	0.608715i	$0.791685\pi$
$194$	1.94801e10	0.987380
$195$	0	0
$196$	−3.51425e8	−0.0170091
$197$	1.73305e10	0.819811	0.409905	−	0.912128i	$-0.365562\pi$
$197$	1.73305e10	0.819811	0.409905	+	0.912128i	$0.365562\pi$
$198$	3.78530e9	0.175028
$199$	−1.44467e10	−0.653025	−0.326512	−	0.945193i	$-0.605874\pi$
$199$	−1.44467e10	−0.653025	−0.326512	+	0.945193i	$0.605874\pi$
$200$	4.79533e9	0.211926
$201$	−1.93402e10	−0.835753
$202$	−1.52419e10	−0.644107
$203$	2.00712e9	0.0829546
$204$	4.01299e9	0.162230
$205$	−3.16953e10	−1.25344
$206$	2.03746e10	0.788290
$207$	1.09362e10	0.414001
$208$	0	0
$209$	−2.08257e10	−0.754991
$210$	2.81629e10	0.999287
$211$	5.08715e10	1.76686	0.883432	−	0.468559i	$-0.155226\pi$
$211$	5.08715e10	1.76686	0.883432	+	0.468559i	$0.155226\pi$
$212$	1.00489e9	0.0341672
$213$	5.85106e10	1.94772
$214$	1.55380e10	0.506446
$215$	2.17072e10	0.692835
$216$	−9.09648e9	−0.284336
$217$	−3.80571e10	−1.16511
$218$	2.16920e10	0.650496
$219$	1.80669e10	0.530745
$220$	−1.85837e10	−0.534847
$221$	0	0
$222$	−4.52331e10	−1.24988
$223$	−2.27613e10	−0.616347	−0.308174	−	0.951330i	$-0.599718\pi$
$223$	−2.27613e10	−0.616347	−0.308174	+	0.951330i	$0.599718\pi$
$224$	−6.54675e9	−0.173744
$225$	6.74362e9	0.175417
$226$	3.51185e10	0.895465
$227$	−2.24918e10	−0.562222	−0.281111	−	0.959675i	$-0.590703\pi$
$227$	−2.24918e10	−0.562222	−0.281111	+	0.959675i	$0.590703\pi$
$228$	−2.07052e10	−0.507427
$229$	−7.10153e10	−1.70644	−0.853222	−	0.521548i	$-0.825355\pi$
$229$	−7.10153e10	−1.70644	−0.853222	+	0.521548i	$0.825355\pi$
$230$	−5.36907e10	−1.26510
$231$	−4.09032e10	−0.945155
$232$	−1.31676e9	−0.0298409
$233$	5.11111e10	1.13609	0.568046	−	0.822997i	$-0.307699\pi$
$233$	5.11111e10	1.13609	0.568046	+	0.822997i	$0.307699\pi$
$234$	0	0
$235$	7.49079e10	1.60222
$236$	4.40386e10	0.924122
$237$	4.46288e10	0.918856
$238$	−9.81722e9	−0.198332
$239$	2.14909e10	0.426054	0.213027	−	0.977046i	$-0.431668\pi$
$239$	2.14909e10	0.426054	0.213027	+	0.977046i	$0.431668\pi$
$240$	−1.84761e10	−0.359468
$241$	−5.08676e10	−0.971326	−0.485663	−	0.874146i	$-0.661422\pi$
$241$	−5.08676e10	−0.971326	−0.485663	+	0.874146i	$0.661422\pi$
$242$	−1.07366e10	−0.201233
$243$	−3.08770e10	−0.568076
$244$	3.50147e10	0.632407
$245$	2.42626e9	0.0430220
$246$	4.57672e10	0.796795
$247$	0	0
$248$	2.49672e10	0.419119
$249$	1.19638e11	1.97230
$250$	2.21253e10	0.358228
$251$	4.23328e10	0.673201	0.336601	−	0.941647i	$-0.390723\pi$
$251$	4.23328e10	0.673201	0.336601	+	0.941647i	$0.390723\pi$
$252$	−9.20662e9	−0.143813
$253$	7.79792e10	1.19657
$254$	4.44413e10	0.669939
$255$	−2.77060e10	−0.410339
$256$	4.29497e9	0.0625000
$257$	6.92463e10	0.990142	0.495071	−	0.868852i	$-0.335142\pi$
$257$	6.92463e10	0.990142	0.495071	+	0.868852i	$0.335142\pi$
$258$	−3.13446e10	−0.440427
$259$	1.10656e11	1.52802
$260$	0	0
$261$	−1.85175e9	−0.0247001
$262$	−9.46991e9	−0.124162
$263$	−4.17509e10	−0.538102	−0.269051	−	0.963126i	$-0.586710\pi$
$263$	−4.17509e10	−0.538102	−0.269051	+	0.963126i	$0.586710\pi$
$264$	2.68344e10	0.339996
$265$	−6.93787e9	−0.0864211
$266$	5.06524e10	0.620344
$267$	1.12363e11	1.35308
$268$	−3.10395e10	−0.367543
$269$	−6.76023e10	−0.787184	−0.393592	−	0.919285i	$-0.628768\pi$
$269$	−6.76023e10	−0.787184	−0.393592	+	0.919285i	$0.628768\pi$
$270$	6.28028e10	0.719188
$271$	−7.29675e10	−0.821803	−0.410902	−	0.911680i	$-0.634786\pi$
$271$	−7.29675e10	−0.821803	−0.410902	+	0.911680i	$0.634786\pi$
$272$	6.44054e9	0.0713448
$273$	0	0
$274$	7.65594e10	0.820580
$275$	4.80844e10	0.506999
$276$	7.75280e10	0.804207
$277$	−1.13424e10	−0.115757	−0.0578785	−	0.998324i	$-0.518434\pi$
$277$	−1.13424e10	−0.115757	−0.0578785	+	0.998324i	$0.518434\pi$
$278$	−1.58695e10	−0.159354
$279$	3.51111e10	0.346917
$280$	4.51993e10	0.439461
$281$	−9.00245e10	−0.861355	−0.430678	−	0.902506i	$-0.641725\pi$
$281$	−9.00245e10	−0.861355	−0.430678	+	0.902506i	$0.641725\pi$
$282$	−1.08165e11	−1.01851
$283$	4.33672e10	0.401904	0.200952	−	0.979601i	$-0.435596\pi$
$283$	4.33672e10	0.401904	0.200952	+	0.979601i	$0.435596\pi$
$284$	9.39050e10	0.856557
$285$	1.42951e11	1.28346
$286$	0	0
$287$	−1.11963e11	−0.974106
$288$	6.03996e9	0.0517330
$289$	−1.08930e11	−0.918559
$290$	9.09103e9	0.0754783
$291$	1.94204e11	1.58759
$292$	2.89961e10	0.233408
$293$	4.06751e10	0.322422	0.161211	−	0.986920i	$-0.448460\pi$
$293$	4.06751e10	0.322422	0.161211	+	0.986920i	$0.448460\pi$
$294$	−3.50347e9	−0.0273486
$295$	−3.04046e11	−2.33744
$296$	−7.25957e10	−0.549665
$297$	−9.12135e10	−0.680229
$298$	1.18464e11	0.870189
$299$	0	0
$300$	4.78062e10	0.340752
$301$	7.66801e10	0.538435
$302$	−1.29822e11	−0.898086
$303$	−1.51951e11	−1.03565
$304$	−3.32303e10	−0.223153
$305$	−2.41745e11	−1.59959
$306$	9.05726e9	0.0590542
$307$	2.35037e11	1.51013	0.755063	−	0.655652i	$-0.227606\pi$
$307$	2.35037e11	1.51013	0.755063	+	0.655652i	$0.227606\pi$
$308$	−6.56465e10	−0.415655
$309$	2.03121e11	1.26748
$310$	−1.72376e11	−1.06010
$311$	1.60150e11	0.970745	0.485373	−	0.874307i	$-0.338684\pi$
$311$	1.60150e11	0.970745	0.485373	+	0.874307i	$0.338684\pi$
$312$	0	0
$313$	−2.82360e11	−1.66285	−0.831426	−	0.555635i	$-0.812475\pi$
$313$	−2.82360e11	−1.66285	−0.831426	+	0.555635i	$0.812475\pi$
$314$	−1.77449e11	−1.03012
$315$	6.35632e10	0.363754
$316$	7.16258e10	0.404089
$317$	1.27999e11	0.711936	0.355968	−	0.934498i	$-0.384151\pi$
$317$	1.27999e11	0.711936	0.355968	+	0.934498i	$0.384151\pi$
$318$	1.00181e10	0.0549369
$319$	−1.32036e10	−0.0713896
$320$	−2.96528e10	−0.158085
$321$	1.54903e11	0.814307
$322$	−1.89661e11	−0.983167
$323$	−4.98307e10	−0.254733
$324$	−1.19710e11	−0.603502
$325$	0	0
$326$	−1.25437e10	−0.0615102
$327$	2.16254e11	1.04592
$328$	7.34529e10	0.350410
$329$	2.64611e11	1.24516
$330$	−1.85267e11	−0.859972
$331$	−8.41594e10	−0.385369	−0.192684	−	0.981261i	$-0.561719\pi$
$331$	−8.41594e10	−0.385369	−0.192684	+	0.981261i	$0.561719\pi$
$332$	1.92010e11	0.867368
$333$	−1.02091e11	−0.454974
$334$	−2.02199e11	−0.889035
$335$	2.14299e11	0.929649
$336$	−6.52666e10	−0.279360
$337$	−3.35056e11	−1.41509	−0.707543	−	0.706671i	$-0.750196\pi$
$337$	−3.35056e11	−1.41509	−0.707543	+	0.706671i	$0.750196\pi$
$338$	0	0
$339$	3.50108e11	1.43980
$340$	−4.44660e10	−0.180457
$341$	2.50355e11	1.00268
$342$	−4.67314e10	−0.184710
$343$	2.60517e11	1.01628
$344$	−5.03057e10	−0.193689
$345$	−5.35260e11	−2.03413
$346$	−5.84901e10	−0.219402
$347$	1.52065e11	0.563050	0.281525	−	0.959554i	$-0.409160\pi$
$347$	1.52065e11	0.563050	0.281525	+	0.959554i	$0.409160\pi$
$348$	−1.31272e10	−0.0479806
$349$	−3.54508e11	−1.27912	−0.639561	−	0.768741i	$-0.720884\pi$
$349$	−3.54508e11	−1.27912	−0.639561	+	0.768741i	$0.720884\pi$
$350$	−1.16951e11	−0.416580
$351$	0	0
$352$	4.30671e10	0.149522
$353$	2.46472e11	0.844852	0.422426	−	0.906397i	$-0.361179\pi$
$353$	2.46472e11	0.844852	0.422426	+	0.906397i	$0.361179\pi$
$354$	4.39035e11	1.48588
$355$	−6.48328e11	−2.16654
$356$	1.80335e11	0.595052
$357$	−9.78710e10	−0.318894
$358$	1.60841e11	0.517516
$359$	2.29573e11	0.729451	0.364726	−	0.931115i	$-0.381163\pi$
$359$	2.29573e11	0.729451	0.364726	+	0.931115i	$0.381163\pi$
$360$	−4.17004e10	−0.130852
$361$	−6.55836e10	−0.203242
$362$	−1.01737e11	−0.311380
$363$	−1.07037e11	−0.323559
$364$	0	0
$365$	−2.00191e11	−0.590374
$366$	3.49073e11	1.01684
$367$	5.22127e11	1.50238	0.751189	−	0.660087i	$-0.229481\pi$
$367$	5.22127e11	1.50238	0.751189	+	0.660087i	$0.229481\pi$
$368$	1.24427e11	0.353670
$369$	1.03296e11	0.290045
$370$	5.01207e11	1.39030
$371$	−2.45079e10	−0.0671620
$372$	2.48906e11	0.673895
$373$	2.20771e11	0.590543	0.295272	−	0.955413i	$-0.404590\pi$
$373$	2.20771e11	0.590543	0.295272	+	0.955413i	$0.404590\pi$
$374$	6.45815e10	0.170681
$375$	2.20574e11	0.575989
$376$	−1.73597e11	−0.447916
$377$	0	0
$378$	2.21850e11	0.558915
$379$	−1.87709e11	−0.467314	−0.233657	−	0.972319i	$-0.575069\pi$
$379$	−1.87709e11	−0.467314	−0.233657	+	0.972319i	$0.575069\pi$
$380$	2.29425e11	0.564435
$381$	4.43050e11	1.07718
$382$	−4.10321e11	−0.985913
$383$	−6.27959e11	−1.49120	−0.745601	−	0.666392i	$-0.767838\pi$
$383$	−6.27959e11	−1.49120	−0.745601	+	0.666392i	$0.767838\pi$
$384$	4.28179e10	0.100493
$385$	4.53229e11	1.05134
$386$	−4.89377e11	−1.12202
$387$	−7.07443e10	−0.160322
$388$	3.11682e11	0.698183
$389$	8.24996e11	1.82675	0.913374	−	0.407122i	$-0.133467\pi$
$389$	8.24996e11	1.82675	0.913374	+	0.407122i	$0.133467\pi$
$390$	0	0
$391$	1.86585e11	0.403720
$392$	−5.62280e9	−0.0120272
$393$	−9.44086e10	−0.199639
$394$	2.77288e11	0.579694
$395$	−4.94510e11	−1.02209
$396$	6.05648e10	0.123763
$397$	8.55547e11	1.72857	0.864284	−	0.503005i	$-0.167772\pi$
$397$	8.55547e11	1.72857	0.864284	+	0.503005i	$0.167772\pi$
$398$	−2.31147e11	−0.461758
$399$	5.04970e11	0.997442
$400$	7.67253e10	0.149854
$401$	2.36025e11	0.455835	0.227917	−	0.973680i	$-0.426808\pi$
$401$	2.36025e11	0.455835	0.227917	+	0.973680i	$0.426808\pi$
$402$	−3.09443e11	−0.590967
$403$	0	0
$404$	−2.43870e11	−0.455452
$405$	8.26489e11	1.52647
$406$	3.21139e10	0.0586578
$407$	−7.27942e11	−1.31499
$408$	6.42078e10	0.114714
$409$	2.21041e11	0.390587	0.195293	−	0.980745i	$-0.437434\pi$
$409$	2.21041e11	0.390587	0.195293	+	0.980745i	$0.437434\pi$
$410$	−5.07125e11	−0.886314
$411$	7.63245e11	1.31940
$412$	3.25993e11	0.557405
$413$	−1.07404e12	−1.81653
$414$	1.74980e11	0.292743
$415$	−1.32566e12	−2.19389
$416$	0	0
$417$	−1.58208e11	−0.256223
$418$	−3.33212e11	−0.533860
$419$	−6.43251e10	−0.101957	−0.0509786	−	0.998700i	$-0.516234\pi$
$419$	−6.43251e10	−0.101957	−0.0509786	+	0.998700i	$0.516234\pi$
$420$	4.50606e11	0.706602
$421$	4.06630e11	0.630855	0.315428	−	0.948950i	$-0.397852\pi$
$421$	4.06630e11	0.630855	0.315428	+	0.948950i	$0.397852\pi$
$422$	8.13944e11	1.24936
$423$	−2.44127e11	−0.370753
$424$	1.60783e10	0.0241598
$425$	1.15054e11	0.171061
$426$	9.36169e11	1.37725
$427$	−8.53958e11	−1.24311
$428$	2.48608e11	0.358112
$429$	0	0
$430$	3.47315e11	0.489908
$431$	−1.07838e12	−1.50530	−0.752651	−	0.658420i	$-0.771225\pi$
$431$	−1.07838e12	−1.50530	−0.752651	+	0.658420i	$0.771225\pi$
$432$	−1.45544e11	−0.201056
$433$	2.02656e11	0.277053	0.138527	−	0.990359i	$-0.455763\pi$
$433$	2.02656e11	0.277053	0.138527	+	0.990359i	$0.455763\pi$
$434$	−6.08914e11	−0.823857
$435$	9.06314e10	0.121360
$436$	3.47071e11	0.459970
$437$	−9.62693e11	−1.26276
$438$	2.89071e11	0.375293
$439$	9.26805e11	1.19096	0.595481	−	0.803369i	$-0.296961\pi$
$439$	9.26805e11	1.19096	0.595481	+	0.803369i	$0.296961\pi$
$440$	−2.97339e11	−0.378194
$441$	−7.90727e9	−0.00995527
$442$	0	0
$443$	3.93461e11	0.485383	0.242692	−	0.970103i	$-0.421970\pi$
$443$	3.93461e11	0.485383	0.242692	+	0.970103i	$0.421970\pi$
$444$	−7.23730e11	−0.883798
$445$	−1.24505e12	−1.50510
$446$	−3.64181e11	−0.435823
$447$	1.18101e12	1.39916
$448$	−1.04748e11	−0.122855
$449$	−6.50584e10	−0.0755431	−0.0377716	−	0.999286i	$-0.512026\pi$
$449$	−6.50584e10	−0.0755431	−0.0377716	+	0.999286i	$0.512026\pi$
$450$	1.07898e11	0.124039
$451$	7.36538e11	0.838302
$452$	5.61897e11	0.633189
$453$	−1.29424e12	−1.44402
$454$	−3.59869e11	−0.397551
$455$	0	0
$456$	−3.31284e11	−0.358805
$457$	−1.01701e12	−1.09069	−0.545344	−	0.838213i	$-0.683601\pi$
$457$	−1.01701e12	−1.09069	−0.545344	+	0.838213i	$0.683601\pi$
$458$	−1.13624e12	−1.20664
$459$	−2.18251e11	−0.229509
$460$	−8.59051e11	−0.894558
$461$	−1.74309e12	−1.79748	−0.898741	−	0.438480i	$-0.855517\pi$
$461$	−1.74309e12	−1.79748	−0.898741	+	0.438480i	$0.855517\pi$
$462$	−6.54451e11	−0.668326
$463$	−3.39417e11	−0.343257	−0.171629	−	0.985162i	$-0.554903\pi$
$463$	−3.39417e11	−0.343257	−0.171629	+	0.985162i	$0.554903\pi$
$464$	−2.10682e10	−0.0211007
$465$	−1.71847e12	−1.70452
$466$	8.17778e11	0.803339
$467$	4.76376e11	0.463473	0.231736	−	0.972779i	$-0.425559\pi$
$467$	4.76376e11	0.463473	0.231736	+	0.972779i	$0.425559\pi$
$468$	0	0
$469$	7.57008e11	0.722475
$470$	1.19853e12	1.13294
$471$	−1.76904e12	−1.65632
$472$	7.04617e11	0.653453
$473$	−5.04432e11	−0.463370
$474$	7.14060e11	0.649729
$475$	−5.93626e11	−0.535047
$476$	−1.57075e11	−0.140242
$477$	2.26107e10	0.0199978
$478$	3.43855e11	0.301265
$479$	7.63824e11	0.662954	0.331477	−	0.943463i	$-0.392453\pi$
$479$	7.63824e11	0.662954	0.331477	+	0.943463i	$0.392453\pi$
$480$	−2.95618e11	−0.254182
$481$	0	0
$482$	−8.13882e11	−0.686831
$483$	−1.89079e12	−1.58082
$484$	−1.71786e11	−0.142293
$485$	−2.15188e12	−1.76596
$486$	−4.94031e11	−0.401690
$487$	1.59493e12	1.28488	0.642440	−	0.766336i	$-0.277922\pi$
$487$	1.59493e12	1.28488	0.642440	+	0.766336i	$0.277922\pi$
$488$	5.60236e11	0.447179
$489$	−1.25052e11	−0.0989013
$490$	3.88202e10	0.0304212
$491$	−9.38889e11	−0.729034	−0.364517	−	0.931197i	$-0.618766\pi$
$491$	−9.38889e11	−0.729034	−0.364517	+	0.931197i	$0.618766\pi$
$492$	7.32276e11	0.563419
$493$	−3.15929e10	−0.0240868
$494$	0	0
$495$	−4.18144e11	−0.313042
$496$	3.99475e11	0.296362
$497$	−2.29021e12	−1.68372
$498$	1.91421e12	1.39463
$499$	8.21282e11	0.592979	0.296490	−	0.955036i	$-0.404184\pi$
$499$	8.21282e11	0.592979	0.296490	+	0.955036i	$0.404184\pi$
$500$	3.54005e11	0.253305
$501$	−2.01578e12	−1.42947
$502$	6.77324e11	0.476025
$503$	2.06643e12	1.43934	0.719671	−	0.694315i	$-0.244293\pi$
$503$	2.06643e12	1.43934	0.719671	+	0.694315i	$0.244293\pi$
$504$	−1.47306e11	−0.101691
$505$	1.68370e12	1.15200
$506$	1.24767e12	0.846100
$507$	0	0
$508$	7.11061e11	0.473718
$509$	−1.63442e12	−1.07928	−0.539638	−	0.841897i	$-0.681439\pi$
$509$	−1.63442e12	−1.07928	−0.539638	+	0.841897i	$0.681439\pi$
$510$	−4.43296e11	−0.290154
$511$	−7.07171e11	−0.458808
$512$	6.87195e10	0.0441942
$513$	1.12608e12	0.717860
$514$	1.10794e12	0.700136
$515$	−2.25068e12	−1.40988
$516$	−5.01514e11	−0.311429
$517$	−1.74072e12	−1.07157
$518$	1.77050e12	1.08047
$519$	−5.83107e11	−0.352773
$520$	0	0
$521$	−2.99302e12	−1.77967	−0.889835	−	0.456283i	$-0.849180\pi$
$521$	−2.99302e12	−1.77967	−0.889835	+	0.456283i	$0.849180\pi$
$522$	−2.96279e10	−0.0174656
$523$	1.24516e12	0.727723	0.363862	−	0.931453i	$-0.381458\pi$
$523$	1.24516e12	0.727723	0.363862	+	0.931453i	$0.381458\pi$
$524$	−1.51519e11	−0.0877961
$525$	−1.16592e12	−0.669812
$526$	−6.68014e11	−0.380496
$527$	5.99036e11	0.338302
$528$	4.29350e11	0.240413
$529$	1.80353e12	1.00132
$530$	−1.11006e11	−0.0611090
$531$	9.90895e11	0.540882
$532$	8.10439e11	0.438650
$533$	0	0
$534$	1.79782e12	0.956774
$535$	−1.71641e12	−0.905793
$536$	−4.96632e11	−0.259892
$537$	1.60348e12	0.832107
$538$	−1.08164e12	−0.556623
$539$	−5.63817e10	−0.0287732
$540$	1.00485e12	0.508542
$541$	−2.83767e12	−1.42421	−0.712104	−	0.702074i	$-0.752258\pi$
$541$	−2.83767e12	−1.42421	−0.712104	+	0.702074i	$0.752258\pi$
$542$	−1.16748e12	−0.581103
$543$	−1.01425e12	−0.500663
$544$	1.03049e11	0.0504484
$545$	−2.39621e12	−1.16343
$546$	0	0
$547$	2.73600e12	1.30669	0.653345	−	0.757060i	$-0.273365\pi$
$547$	2.73600e12	1.30669	0.653345	+	0.757060i	$0.273365\pi$
$548$	1.22495e12	0.580238
$549$	7.87853e11	0.370143
$550$	7.69351e11	0.358503
$551$	1.63005e11	0.0753389
$552$	1.24045e12	0.568660
$553$	−1.74685e12	−0.794313
$554$	−1.81479e11	−0.0818526
$555$	4.99669e12	2.23544
$556$	−2.53913e11	−0.112680
$557$	3.63597e12	1.60056	0.800279	−	0.599627i	$-0.204685\pi$
$557$	3.63597e12	1.60056	0.800279	+	0.599627i	$0.204685\pi$
$558$	5.61777e11	0.245307
$559$	0	0
$560$	7.23188e11	0.310746
$561$	6.43834e11	0.274436
$562$	−1.44039e12	−0.609070
$563$	1.81268e12	0.760385	0.380192	−	0.924907i	$-0.375858\pi$
$563$	1.81268e12	0.760385	0.380192	+	0.924907i	$0.375858\pi$
$564$	−1.73064e12	−0.720197
$565$	−3.87938e12	−1.60156
$566$	6.93876e11	0.284189
$567$	2.91956e12	1.18630
$568$	1.50248e12	0.605677
$569$	−2.53400e12	−1.01345	−0.506723	−	0.862109i	$-0.669143\pi$
$569$	−2.53400e12	−1.01345	−0.506723	+	0.862109i	$0.669143\pi$
$570$	2.28721e12	0.907547
$571$	1.44649e12	0.569446	0.284723	−	0.958610i	$-0.408098\pi$
$571$	1.44649e12	0.569446	0.284723	+	0.958610i	$0.408098\pi$
$572$	0	0
$573$	−4.09062e12	−1.58523
$574$	−1.79141e12	−0.688797
$575$	2.22276e12	0.847982
$576$	9.66394e10	0.0365808
$577$	1.45725e12	0.547321	0.273661	−	0.961826i	$-0.411766\pi$
$577$	1.45725e12	0.547321	0.273661	+	0.961826i	$0.411766\pi$
$578$	−1.74288e12	−0.649519
$579$	−4.87876e12	−1.80408
$580$	1.45456e11	0.0533712
$581$	−4.68285e12	−1.70498
$582$	3.10726e12	1.12260
$583$	1.61223e11	0.0577987
$584$	4.63937e11	0.165045
$585$	0	0
$586$	6.50801e11	0.227986
$587$	1.98221e12	0.689095	0.344547	−	0.938769i	$-0.388032\pi$
$587$	1.98221e12	0.689095	0.344547	+	0.938769i	$0.388032\pi$
$588$	−5.60555e10	−0.0193384
$589$	−3.09075e12	−1.05815
$590$	−4.86473e12	−1.65282
$591$	2.76438e12	0.932081
$592$	−1.16153e12	−0.388672
$593$	−5.30729e12	−1.76249	−0.881246	−	0.472658i	$-0.843295\pi$
$593$	−5.30729e12	−1.76249	−0.881246	+	0.472658i	$0.843295\pi$
$594$	−1.45942e12	−0.480995
$595$	1.08446e12	0.354722
$596$	1.89542e12	0.615316
$597$	−2.30438e12	−0.742454
$598$	0	0
$599$	−2.54920e12	−0.809064	−0.404532	−	0.914524i	$-0.632566\pi$
$599$	−2.54920e12	−0.809064	−0.404532	+	0.914524i	$0.632566\pi$
$600$	7.64899e11	0.240948
$601$	1.77817e12	0.555952	0.277976	−	0.960588i	$-0.410336\pi$
$601$	1.77817e12	0.555952	0.277976	+	0.960588i	$0.410336\pi$
$602$	1.22688e12	0.380731
$603$	−6.98408e11	−0.215120
$604$	−2.07716e12	−0.635043
$605$	1.18602e12	0.359910
$606$	−2.43122e12	−0.732315
$607$	−6.45909e11	−0.193118	−0.0965588	−	0.995327i	$-0.530784\pi$
$607$	−6.45909e11	−0.193118	−0.0965588	+	0.995327i	$0.530784\pi$
$608$	−5.31685e11	−0.157793
$609$	3.20154e11	0.0943150
$610$	−3.86791e12	−1.13108
$611$	0	0
$612$	1.44916e11	0.0417576
$613$	−2.63173e12	−0.752782	−0.376391	−	0.926461i	$-0.622835\pi$
$613$	−2.63173e12	−0.752782	−0.376391	+	0.926461i	$0.622835\pi$
$614$	3.76059e12	1.06782
$615$	−5.05569e12	−1.42509
$616$	−1.05034e12	−0.293913
$617$	−3.85338e12	−1.07043	−0.535216	−	0.844716i	$-0.679770\pi$
$617$	−3.85338e12	−1.07043	−0.535216	+	0.844716i	$0.679770\pi$
$618$	3.24993e12	0.896244
$619$	6.18414e12	1.69306	0.846529	−	0.532343i	$-0.178688\pi$
$619$	6.18414e12	1.69306	0.846529	+	0.532343i	$0.178688\pi$
$620$	−2.75801e12	−0.749606
$621$	−4.21645e12	−1.13772
$622$	2.56240e12	0.686421
$623$	−4.39810e12	−1.16969
$624$	0	0
$625$	−4.73067e12	−1.24012
$626$	−4.51776e12	−1.17581
$627$	−3.32189e12	−0.858384
$628$	−2.83918e12	−0.728407
$629$	−1.74178e12	−0.443676
$630$	1.01701e12	0.257213
$631$	−1.63522e8	−4.10623e−5 0	−2.05311e−5	−	1.00000i	$-0.500007\pi$
$631$	−1.63522e8	−4.10623e−5 0	−2.05311e−5		1.00000i	$0.500007\pi$
$632$	1.14601e12	0.285734
$633$	8.11447e12	2.00883
$634$	2.04799e12	0.503415
$635$	−4.90922e12	−1.19820
$636$	1.60290e11	0.0388462
$637$	0	0
$638$	−2.11258e11	−0.0504801
$639$	2.11292e12	0.501337
$640$	−4.74445e11	−0.111783
$641$	2.70983e11	0.0633988	0.0316994	−	0.999497i	$-0.489908\pi$
$641$	2.70983e11	0.0633988	0.0316994	+	0.999497i	$0.489908\pi$
$642$	2.47845e12	0.575802
$643$	−1.80868e12	−0.417265	−0.208632	−	0.977994i	$-0.566901\pi$
$643$	−1.80868e12	−0.417265	−0.208632	+	0.977994i	$0.566901\pi$
$644$	−3.03458e12	−0.695204
$645$	3.46249e12	0.787716
$646$	−7.97292e11	−0.180124
$647$	−4.85979e12	−1.09031	−0.545153	−	0.838337i	$-0.683528\pi$
$647$	−4.85979e12	−1.09031	−0.545153	+	0.838337i	$0.683528\pi$
$648$	−1.91536e12	−0.426741
$649$	7.06544e12	1.56328
$650$	0	0
$651$	−6.07045e12	−1.32467
$652$	−2.00700e11	−0.0434943
$653$	−5.49983e10	−0.0118369	−0.00591847	−	0.999982i	$-0.501884\pi$
$653$	−5.49983e10	−0.0118369	−0.00591847	+	0.999982i	$0.501884\pi$
$654$	3.46006e12	0.739578
$655$	1.04610e12	0.222068
$656$	1.17525e12	0.247777
$657$	6.52429e11	0.136612
$658$	4.23377e12	0.880463
$659$	5.88872e12	1.21629	0.608144	−	0.793827i	$-0.291914\pi$
$659$	5.88872e12	1.21629	0.608144	+	0.793827i	$0.291914\pi$
$660$	−2.96427e12	−0.608092
$661$	−5.52398e12	−1.12550	−0.562750	−	0.826627i	$-0.690257\pi$
$661$	−5.52398e12	−1.12550	−0.562750	+	0.826627i	$0.690257\pi$
$662$	−1.34655e12	−0.272497
$663$	0	0
$664$	3.07217e12	0.613322
$665$	−5.59533e12	−1.10950
$666$	−1.63345e12	−0.321715
$667$	−6.10352e11	−0.119403
$668$	−3.23518e12	−0.628643
$669$	−3.63064e12	−0.700754
$670$	3.42879e12	0.657361
$671$	5.61768e12	1.06981
$672$	−1.04427e12	−0.197537
$673$	6.15531e12	1.15660	0.578298	−	0.815825i	$-0.303717\pi$
$673$	6.15531e12	1.15660	0.578298	+	0.815825i	$0.303717\pi$
$674$	−5.36089e12	−1.00062
$675$	−2.59999e12	−0.482064
$676$	0	0
$677$	5.73319e12	1.04893	0.524466	−	0.851432i	$-0.324265\pi$
$677$	5.73319e12	1.04893	0.524466	+	0.851432i	$0.324265\pi$
$678$	5.60173e12	1.01810
$679$	−7.60147e12	−1.37241
$680$	−7.11457e11	−0.127602
$681$	−3.58765e12	−0.639216
$682$	4.00568e12	0.709000
$683$	3.72368e12	0.654756	0.327378	−	0.944894i	$-0.393835\pi$
$683$	3.72368e12	0.654756	0.327378	+	0.944894i	$0.393835\pi$
$684$	−7.47702e11	−0.130610
$685$	−8.45715e12	−1.46763
$686$	4.16827e12	0.718617
$687$	−1.13276e13	−1.94013
$688$	−8.04891e11	−0.136959
$689$	0	0
$690$	−8.56415e12	−1.43835
$691$	1.21804e11	0.0203240	0.0101620	−	0.999948i	$-0.496765\pi$
$691$	1.21804e11	0.0203240	0.0101620	+	0.999948i	$0.496765\pi$
$692$	−9.35842e11	−0.155140
$693$	−1.47709e12	−0.243280
$694$	2.43304e12	0.398137
$695$	1.75303e12	0.285009
$696$	−2.10035e11	−0.0339274
$697$	1.76235e12	0.282842
$698$	−5.67213e12	−0.904475
$699$	8.15269e12	1.29168
$700$	−1.87122e12	−0.294566
$701$	7.48411e12	1.17060	0.585300	−	0.810816i	$-0.300977\pi$
$701$	7.48411e12	1.17060	0.585300	+	0.810816i	$0.300977\pi$
$702$	0	0
$703$	8.98681e12	1.38774
$704$	6.89074e11	0.105728
$705$	1.19485e13	1.82164
$706$	3.94354e12	0.597400
$707$	5.94764e12	0.895277
$708$	7.02455e12	1.05068
$709$	−2.03611e12	−0.302616	−0.151308	−	0.988487i	$-0.548349\pi$
$709$	−2.03611e12	−0.302616	−0.151308	+	0.988487i	$0.548349\pi$
$710$	−1.03732e13	−1.53198
$711$	1.61162e12	0.236511
$712$	2.88536e12	0.420765
$713$	1.15729e13	1.67703
$714$	−1.56594e12	−0.225492
$715$	0	0
$716$	2.57346e12	0.365939
$717$	3.42800e12	0.484400
$718$	3.67317e12	0.515800
$719$	1.45945e12	0.203661	0.101831	−	0.994802i	$-0.467530\pi$
$719$	1.45945e12	0.203661	0.101831	+	0.994802i	$0.467530\pi$
$720$	−6.67206e11	−0.0925260
$721$	−7.95050e12	−1.09569
$722$	−1.04934e12	−0.143714
$723$	−8.11385e12	−1.10435
$724$	−1.62779e12	−0.220179
$725$	−3.76362e11	−0.0505923
$726$	−1.71259e12	−0.228791
$727$	−8.61854e10	−0.0114427	−0.00572135	−	0.999984i	$-0.501821\pi$
$727$	−8.61854e10	−0.0114427	−0.00572135	+	0.999984i	$0.501821\pi$
$728$	0	0
$729$	4.27897e12	0.561133
$730$	−3.20306e12	−0.417457
$731$	−1.20698e12	−0.156341
$732$	5.58517e12	0.719013
$733$	6.94903e12	0.889111	0.444556	−	0.895751i	$-0.353362\pi$
$733$	6.94903e12	0.889111	0.444556	+	0.895751i	$0.353362\pi$
$734$	8.35404e12	1.06234
$735$	3.87011e11	0.0489137
$736$	1.99083e12	0.250082
$737$	−4.97990e12	−0.621752
$738$	1.65274e12	0.205093
$739$	−2.94805e12	−0.363609	−0.181804	−	0.983335i	$-0.558194\pi$
$739$	−2.94805e12	−0.363609	−0.181804	+	0.983335i	$0.558194\pi$
$740$	8.01931e12	0.983092
$741$	0	0
$742$	−3.92127e11	−0.0474907
$743$	1.30043e13	1.56544	0.782719	−	0.622375i	$-0.213832\pi$
$743$	1.30043e13	1.56544	0.782719	+	0.622375i	$0.213832\pi$
$744$	3.98250e12	0.476516
$745$	−1.30862e13	−1.55636
$746$	3.53233e12	0.417577
$747$	4.32035e12	0.507664
$748$	1.03330e12	0.120690
$749$	−6.06319e12	−0.703936
$750$	3.52919e12	0.407285
$751$	−1.57055e12	−0.180166	−0.0900829	−	0.995934i	$-0.528713\pi$
$751$	−1.57055e12	−0.180166	−0.0900829	+	0.995934i	$0.528713\pi$
$752$	−2.77755e12	−0.316725
$753$	6.75246e12	0.765394
$754$	0	0
$755$	1.43408e13	1.60625
$756$	3.54960e12	0.395213
$757$	−9.58378e12	−1.06073	−0.530366	−	0.847769i	$-0.677945\pi$
$757$	−9.58378e12	−1.06073	−0.530366	+	0.847769i	$0.677945\pi$
$758$	−3.00335e12	−0.330441
$759$	1.24384e13	1.36043
$760$	3.67080e12	0.399116
$761$	7.11276e12	0.768789	0.384395	−	0.923169i	$-0.374410\pi$
$761$	7.11276e12	0.768789	0.384395	+	0.923169i	$0.374410\pi$
$762$	7.08879e12	0.761684
$763$	−8.46456e12	−0.904157
$764$	−6.56514e12	−0.697146
$765$	−1.00051e12	−0.105620
$766$	−1.00473e13	−1.05444
$767$	0	0
$768$	6.85086e11	0.0710591
$769$	1.73274e13	1.78676	0.893379	−	0.449304i	$-0.148328\pi$
$769$	1.73274e13	1.78676	0.893379	+	0.449304i	$0.148328\pi$
$770$	7.25166e12	0.743411
$771$	1.10454e13	1.12574
$772$	−7.83004e12	−0.793389
$773$	9.87303e12	0.994587	0.497294	−	0.867582i	$-0.334327\pi$
$773$	9.87303e12	0.994587	0.497294	+	0.867582i	$0.334327\pi$
$774$	−1.13191e12	−0.113365
$775$	7.13623e12	0.710577
$776$	4.98691e12	0.493690
$777$	1.76507e13	1.73727
$778$	1.31999e13	1.29171
$779$	−9.09293e12	−0.884678
$780$	0	0
$781$	1.50659e13	1.44899
$782$	2.98535e12	0.285473
$783$	7.13938e11	0.0678786
$784$	−8.99647e10	−0.00850453
$785$	1.96019e13	1.84240
$786$	−1.51054e12	−0.141166
$787$	6.54652e12	0.608309	0.304155	−	0.952623i	$-0.401626\pi$
$787$	6.54652e12	0.608309	0.304155	+	0.952623i	$0.401626\pi$
$788$	4.43661e12	0.409905
$789$	−6.65964e12	−0.611793
$790$	−7.91216e12	−0.722725
$791$	−1.37038e13	−1.24465
$792$	9.69036e11	0.0875138
$793$	0	0
$794$	1.36887e13	1.22228
$795$	−1.10665e12	−0.0982562
$796$	−3.69836e12	−0.326512
$797$	4.91818e12	0.431760	0.215880	−	0.976420i	$-0.430738\pi$
$797$	4.91818e12	0.431760	0.215880	+	0.976420i	$0.430738\pi$
$798$	8.07952e12	0.705298
$799$	−4.16509e12	−0.361547
$800$	1.22760e12	0.105963
$801$	4.05764e12	0.348279
$802$	3.77639e12	0.322324
$803$	4.65205e12	0.394843
$804$	−4.95108e12	−0.417877
$805$	2.09510e13	1.75842
$806$	0	0
$807$	−1.07832e13	−0.894986
$808$	−3.90193e12	−0.322053
$809$	8.28568e12	0.680080	0.340040	−	0.940411i	$-0.389559\pi$
$809$	8.28568e12	0.680080	0.340040	+	0.940411i	$0.389559\pi$
$810$	1.32238e13	1.07938
$811$	2.06397e13	1.67537	0.837684	−	0.546155i	$-0.183909\pi$
$811$	2.06397e13	1.67537	0.837684	+	0.546155i	$0.183909\pi$
$812$	5.13822e11	0.0414773
$813$	−1.16390e13	−0.934346
$814$	−1.16471e13	−0.929837
$815$	1.38565e12	0.110013
$816$	1.02733e12	0.0811152
$817$	6.22747e12	0.489004
$818$	3.53665e12	0.276187
$819$	0	0
$820$	−8.11400e12	−0.626719
$821$	1.24767e9	9.58422e−5 0	4.79211e−5	−	1.00000i	$-0.499985\pi$
$821$	1.24767e9	9.58422e−5 0	4.79211e−5		1.00000i	$0.499985\pi$
$822$	1.22119e13	0.932955
$823$	1.23070e13	0.935090	0.467545	−	0.883969i	$-0.345139\pi$
$823$	1.23070e13	0.935090	0.467545	+	0.883969i	$0.345139\pi$
$824$	5.21589e12	0.394145
$825$	7.66990e12	0.576431
$826$	−1.71846e13	−1.28448
$827$	−5.07786e12	−0.377490	−0.188745	−	0.982026i	$-0.560442\pi$
$827$	−5.07786e12	−0.377490	−0.188745	+	0.982026i	$0.560442\pi$
$828$	2.79967e12	0.207000
$829$	−1.95629e13	−1.43859	−0.719295	−	0.694705i	$-0.755535\pi$
$829$	−1.95629e13	−1.43859	−0.719295	+	0.694705i	$0.755535\pi$
$830$	−2.12105e13	−1.55131
$831$	−1.80922e12	−0.131610
$832$	0	0
$833$	−1.34907e11	−0.00970806
$834$	−2.53133e12	−0.181177
$835$	2.23359e13	1.59006
$836$	−5.33139e12	−0.377496
$837$	−1.35370e13	−0.953364
$838$	−1.02920e12	−0.0720946
$839$	1.50732e13	1.05021	0.525107	−	0.851036i	$-0.324025\pi$
$839$	1.50732e13	1.05021	0.525107	+	0.851036i	$0.324025\pi$
$840$	7.20970e12	0.499643
$841$	−1.44038e13	−0.992876
$842$	6.50608e12	0.446082
$843$	−1.43597e13	−0.979315
$844$	1.30231e13	0.883432
$845$	0	0
$846$	−3.90604e12	−0.262162
$847$	4.18961e12	0.279704
$848$	2.57253e11	0.0170836
$849$	6.91747e12	0.456944
$850$	1.84086e12	0.120958
$851$	−3.36499e13	−2.19939
$852$	1.49787e13	0.973859
$853$	−5.33191e12	−0.344835	−0.172418	−	0.985024i	$-0.555158\pi$
$853$	−5.33191e12	−0.344835	−0.172418	+	0.985024i	$0.555158\pi$
$854$	−1.36633e13	−0.879015
$855$	5.16220e12	0.330360
$856$	3.97773e12	0.253223
$857$	−7.95292e12	−0.503631	−0.251816	−	0.967775i	$-0.581028\pi$
$857$	−7.95292e12	−0.503631	−0.251816	+	0.967775i	$0.581028\pi$
$858$	0	0
$859$	4.62716e12	0.289965	0.144982	−	0.989434i	$-0.453687\pi$
$859$	4.62716e12	0.289965	0.144982	+	0.989434i	$0.453687\pi$
$860$	5.55703e12	0.346418
$861$	−1.78591e13	−1.10751
$862$	−1.72541e13	−1.06441
$863$	−6.60844e12	−0.405556	−0.202778	−	0.979225i	$-0.564997\pi$
$863$	−6.60844e12	−0.405556	−0.202778	+	0.979225i	$0.564997\pi$
$864$	−2.32870e12	−0.142168
$865$	6.46113e12	0.392406
$866$	3.24249e12	0.195906
$867$	−1.73753e13	−1.04435
$868$	−9.74262e12	−0.582555
$869$	1.14915e13	0.683575
$870$	1.45010e12	0.0858147
$871$	0	0
$872$	5.55314e12	0.325248
$873$	7.01304e12	0.408641
$874$	−1.54031e13	−0.892907
$875$	−8.63366e12	−0.497919
$876$	4.62514e12	0.265373
$877$	−3.39068e12	−0.193548	−0.0967739	−	0.995306i	$-0.530852\pi$
$877$	−3.39068e12	−0.193548	−0.0967739	+	0.995306i	$0.530852\pi$
$878$	1.48289e13	0.842138
$879$	6.48805e12	0.366576
$880$	−4.75742e12	−0.267423
$881$	1.20785e13	0.675495	0.337748	−	0.941237i	$-0.390335\pi$
$881$	1.20785e13	0.675495	0.337748	+	0.941237i	$0.390335\pi$
$882$	−1.26516e11	−0.00703944
$883$	5.33631e12	0.295405	0.147702	−	0.989032i	$-0.452812\pi$
$883$	5.33631e12	0.295405	0.147702	+	0.989032i	$0.452812\pi$
$884$	0	0
$885$	−4.84981e13	−2.65754
$886$	6.29538e12	0.343218
$887$	1.35083e13	0.732731	0.366366	−	0.930471i	$-0.380602\pi$
$887$	1.35083e13	0.732731	0.366366	+	0.930471i	$0.380602\pi$
$888$	−1.15797e13	−0.624940
$889$	−1.73417e13	−0.931182
$890$	−1.99207e13	−1.06427
$891$	−1.92060e13	−1.02091
$892$	−5.82690e12	−0.308174
$893$	2.14900e13	1.13085
$894$	1.88961e13	0.989358
$895$	−1.77674e13	−0.925593
$896$	−1.67597e12	−0.0868719
$897$	0	0
$898$	−1.04093e12	−0.0534170
$899$	−1.95955e12	−0.100055
$900$	1.72637e12	0.0877085
$901$	3.85765e11	0.0195012
$902$	1.17846e13	0.592769
$903$	1.22312e13	0.612172
$904$	8.99035e12	0.447732
$905$	1.12384e13	0.556912
$906$	−2.07078e13	−1.02108
$907$	2.95151e13	1.44814	0.724071	−	0.689726i	$-0.242269\pi$
$907$	2.95151e13	1.44814	0.724071	+	0.689726i	$0.242269\pi$
$908$	−5.75790e12	−0.281111
$909$	−5.48723e12	−0.266573
$910$	0	0
$911$	−2.98046e12	−0.143368	−0.0716838	−	0.997427i	$-0.522837\pi$
$911$	−2.98046e12	−0.143368	−0.0716838	+	0.997427i	$0.522837\pi$
$912$	−5.30054e12	−0.253713
$913$	3.08057e13	1.46728
$914$	−1.62721e13	−0.771232
$915$	−3.85605e13	−1.81864
$916$	−1.81799e13	−0.853222
$917$	3.69532e12	0.172580
$918$	−3.49201e12	−0.162287
$919$	−3.51732e13	−1.62664	−0.813321	−	0.581815i	$-0.802343\pi$
$919$	−3.51732e13	−1.62664	−0.813321	+	0.581815i	$0.802343\pi$
$920$	−1.37448e13	−0.632548
$921$	3.74905e13	1.71693
$922$	−2.78894e13	−1.27101
$923$	0	0
$924$	−1.04712e13	−0.472578
$925$	−2.07496e13	−0.931906
$926$	−5.43068e12	−0.242720
$927$	7.33505e12	0.326245
$928$	−3.37091e11	−0.0149204
$929$	2.56701e13	1.13072	0.565361	−	0.824843i	$-0.308737\pi$
$929$	2.56701e13	1.13072	0.565361	+	0.824843i	$0.308737\pi$
$930$	−2.74955e13	−1.20528
$931$	6.96060e11	0.0303650
$932$	1.30844e13	0.568046
$933$	2.55454e13	1.10368
$934$	7.62202e12	0.327725
$935$	−7.13402e12	−0.305268
$936$	0	0
$937$	3.44586e11	0.0146039	0.00730197	−	0.999973i	$-0.497676\pi$
$937$	3.44586e11	0.0146039	0.00730197	+	0.999973i	$0.497676\pi$
$938$	1.21121e13	0.510867
$939$	−4.50390e13	−1.89057
$940$	1.91764e13	0.801111
$941$	−1.04276e13	−0.433542	−0.216771	−	0.976223i	$-0.569552\pi$
$941$	−1.04276e13	−0.433542	−0.216771	+	0.976223i	$0.569552\pi$
$942$	−2.83047e13	−1.17119
$943$	3.40473e13	1.40210
$944$	1.12739e13	0.462061
$945$	−2.45067e13	−0.999636
$946$	−8.07092e12	−0.327652
$947$	−3.05879e13	−1.23588	−0.617939	−	0.786226i	$-0.712032\pi$
$947$	−3.05879e13	−1.23588	−0.617939	+	0.786226i	$0.712032\pi$
$948$	1.14250e13	0.459428
$949$	0	0
$950$	−9.49802e12	−0.378335
$951$	2.04171e13	0.809433
$952$	−2.51321e12	−0.0991658
$953$	−3.43552e13	−1.34919	−0.674596	−	0.738187i	$-0.735682\pi$
$953$	−3.43552e13	−1.34919	−0.674596	+	0.738187i	$0.735682\pi$
$954$	3.61772e11	0.0141406
$955$	4.53262e13	1.76333
$956$	5.50167e12	0.213027
$957$	−2.10610e12	−0.0811661
$958$	1.22212e13	0.468780
$959$	−2.98747e13	−1.14057
$960$	−4.72989e12	−0.179734
$961$	1.07156e13	0.405286
$962$	0	0
$963$	5.59384e12	0.209600
$964$	−1.30221e13	−0.485663
$965$	5.40592e13	2.00677
$966$	−3.02527e13	−1.11781
$967$	−5.29016e13	−1.94558	−0.972791	−	0.231685i	$-0.925576\pi$
$967$	−5.29016e13	−1.94558	−0.972791	+	0.231685i	$0.925576\pi$
$968$	−2.74858e12	−0.100616
$969$	−7.94845e12	−0.289618
$970$	−3.44301e13	−1.24872
$971$	3.46593e13	1.25122	0.625610	−	0.780136i	$-0.284850\pi$
$971$	3.46593e13	1.25122	0.625610	+	0.780136i	$0.284850\pi$
$972$	−7.90450e12	−0.284038
$973$	6.19255e12	0.221494
$974$	2.55190e13	0.908547
$975$	0	0
$976$	8.96377e12	0.316204
$977$	−1.48680e13	−0.522069	−0.261035	−	0.965329i	$-0.584064\pi$
$977$	−1.48680e13	−0.522069	−0.261035	+	0.965329i	$0.584064\pi$
$978$	−2.00084e12	−0.0699338
$979$	2.89325e13	1.00661
$980$	6.21124e11	0.0215110
$981$	7.80932e12	0.269217
$982$	−1.50222e13	−0.515505
$983$	−1.71439e13	−0.585624	−0.292812	−	0.956170i	$-0.594591\pi$
$983$	−1.71439e13	−0.585624	−0.292812	+	0.956170i	$0.594591\pi$
$984$	1.17164e13	0.398398
$985$	−3.06307e13	−1.03680
$986$	−5.05487e11	−0.0170319
$987$	4.22079e13	1.41568
$988$	0	0
$989$	−2.33180e13	−0.775010
$990$	−6.69030e12	−0.221354
$991$	3.48129e13	1.14659	0.573296	−	0.819348i	$-0.305664\pi$
$991$	3.48129e13	1.14659	0.573296	+	0.819348i	$0.305664\pi$
$992$	6.39160e12	0.209560
$993$	−1.34242e13	−0.438144
$994$	−3.66433e13	−1.19057
$995$	2.55337e13	0.825868
$996$	3.06274e13	0.986151
$997$	−3.63962e13	−1.16662	−0.583308	−	0.812251i	$-0.698242\pi$
$997$	−3.63962e13	−1.16662	−0.583308	+	0.812251i	$0.698242\pi$
$998$	1.31405e13	0.419300
$999$	3.93609e13	1.25032

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	338.10.a.f.1.3		3
13.12	even	2		26.10.a.d.1.3	✓	3
39.38	odd	2		234.10.a.l.1.1		3
52.51	odd	2		208.10.a.e.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.10.a.d.1.3	✓	3	13.12	even	2
208.10.a.e.1.1		3	52.51	odd	2
234.10.a.l.1.1		3	39.38	odd	2
338.10.a.f.1.3		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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 338 = 2 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	338.a (trivial)

\(f(q)\)	\(=\)	\(q+16.0000 q^{2} +159.509 q^{3} +256.000 q^{4} -1767.44 q^{5} +2552.15 q^{6} -6243.46 q^{7} +4096.00 q^{8} +5760.16 q^{9} -28279.1 q^{10} +41072.0 q^{11} +40834.3 q^{12} -99895.4 q^{14} -281924. q^{15} +65536.0 q^{16} +98274.9 q^{17} +92162.5 q^{18} -507054. q^{19} -452466. q^{20} -995890. q^{21} +657152. q^{22} +1.89860e6 q^{23} +653349. q^{24} +1.17074e6 q^{25} -2.22082e6 q^{27} -1.59833e6 q^{28} -321475. q^{29} -4.51078e6 q^{30} +6.09551e6 q^{31} +1.04858e6 q^{32} +6.55136e6 q^{33} +1.57240e6 q^{34} +1.10350e7 q^{35} +1.47460e6 q^{36} -1.77236e7 q^{37} -8.11287e6 q^{38} -7.23945e6 q^{40} +1.79328e7 q^{41} -1.59342e7 q^{42} -1.22817e7 q^{43} +1.05144e7 q^{44} -1.01808e7 q^{45} +3.03776e7 q^{46} -4.23821e7 q^{47} +1.04536e7 q^{48} -1.37275e6 q^{49} +1.87318e7 q^{50} +1.56757e7 q^{51} +3.92537e6 q^{53} -3.55331e7 q^{54} -7.25925e7 q^{55} -2.55732e7 q^{56} -8.08798e7 q^{57} -5.14360e6 q^{58} +1.72026e8 q^{59} -7.21724e7 q^{60} +1.36776e8 q^{61} +9.75281e7 q^{62} -3.59633e7 q^{63} +1.67772e7 q^{64} +1.04822e8 q^{66} -1.21248e8 q^{67} +2.51584e7 q^{68} +3.02844e8 q^{69} +1.76560e8 q^{70} +3.66817e8 q^{71} +2.35936e7 q^{72} +1.13266e8 q^{73} -2.83577e8 q^{74} +1.86743e8 q^{75} -1.29806e8 q^{76} -2.56432e8 q^{77} +2.79788e8 q^{79} -1.15831e8 q^{80} -4.67618e8 q^{81} +2.86926e8 q^{82} +7.50041e8 q^{83} -2.54948e8 q^{84} -1.73695e8 q^{85} -1.96507e8 q^{86} -5.12782e7 q^{87} +1.68231e8 q^{88} +7.04433e8 q^{89} -1.62892e8 q^{90} +4.86041e8 q^{92} +9.72289e8 q^{93} -6.78113e8 q^{94} +8.96190e8 q^{95} +1.67257e8 q^{96} +1.21751e9 q^{97} -2.19641e7 q^{98} +2.36581e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 48 q^{2} + 768 q^{4} - 248 q^{5} + 2956 q^{7} + 12288 q^{8} - 20863 q^{9} - 3968 q^{10} + 31324 q^{11} + 47296 q^{14} - 392140 q^{15} + 196608 q^{16} + 905228 q^{17} - 333808 q^{18} - 1726316 q^{19}+ \cdots + 304026580 q^{99}+O(q^{100}) \) 3 * q + 48 * q^2 + 768 * q^4 - 248 * q^5 + 2956 * q^7 + 12288 * q^8 - 20863 * q^9 - 3968 * q^10 + 31324 * q^11 + 47296 * q^14 - 392140 * q^15 + 196608 * q^16 + 905228 * q^17 - 333808 * q^18 - 1726316 * q^19 - 63488 * q^20 - 1771246 * q^21 + 501184 * q^22 + 2135256 * q^23 + 4074295 * q^25 + 3038724 * q^27 + 756736 * q^28 + 372426 * q^29 - 6274240 * q^30 + 1444776 * q^31 + 3145728 * q^32 + 7719476 * q^33 + 14483648 * q^34 - 3459436 * q^35 - 5340928 * q^36 + 2809672 * q^37 - 27621056 * q^38 - 1015808 * q^40 + 7424806 * q^41 - 28339936 * q^42 + 36070040 * q^43 + 8018944 * q^44 - 32156162 * q^45 + 34164096 * q^46 - 7032884 * q^47 + 41844597 * q^49 + 65188720 * q^50 - 47158124 * q^51 - 15011674 * q^53 + 48619584 * q^54 + 121479136 * q^55 + 12107776 * q^56 + 14804300 * q^57 + 5958816 * q^58 + 40286396 * q^59 - 100387840 * q^60 + 230710478 * q^61 + 23116416 * q^62 - 151778040 * q^63 + 50331648 * q^64 + 123511616 * q^66 - 201453084 * q^67 + 231738368 * q^68 + 268135008 * q^69 - 55350976 * q^70 + 99165572 * q^71 - 85454848 * q^72 + 350942946 * q^73 + 44954752 * q^74 - 28166788 * q^75 - 441936896 * q^76 - 1066624588 * q^77 + 138794592 * q^79 - 16252928 * q^80 - 363498349 * q^81 + 118796896 * q^82 + 1364469516 * q^83 - 453438976 * q^84 + 1225485962 * q^85 + 577120640 * q^86 - 93372576 * q^87 + 128303104 * q^88 + 709437058 * q^89 - 514498592 * q^90 + 546625536 * q^92 + 1382471232 * q^93 - 112526144 * q^94 - 833387824 * q^95 + 362189698 * q^97 + 669513552 * q^98 + 304026580 * q^99

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