LMFDB - Embedded newform 322.4.a.f.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [322,4,Mod(1,322)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(322, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("322.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 322 = 2 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	322.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:	$18.9986150218$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 42x^{2} + 26x + 46 $ x^4 - x^3 - 42x^2 + 26x + 46
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-6.22602$ of defining polynomial
Character	$\chi$	$=$	322.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.00000 q^{2} +6.22602 q^{3} +4.00000 q^{4} -9.89045 q^{5} -12.4520 q^{6} +7.00000 q^{7} -8.00000 q^{8} +11.7633 q^{9} +19.7809 q^{10} -41.5157 q^{11} +24.9041 q^{12} +18.7390 q^{13} -14.0000 q^{14} -61.5782 q^{15} +16.0000 q^{16} -19.3383 q^{17} -23.5266 q^{18} -52.3251 q^{19} -39.5618 q^{20} +43.5821 q^{21} +83.0315 q^{22} -23.0000 q^{23} -49.8082 q^{24} -27.1789 q^{25} -37.4781 q^{26} -94.8639 q^{27} +28.0000 q^{28} -169.213 q^{29} +123.156 q^{30} -191.927 q^{31} -32.0000 q^{32} -258.478 q^{33} +38.6766 q^{34} -69.2332 q^{35} +47.0533 q^{36} +366.682 q^{37} +104.650 q^{38} +116.670 q^{39} +79.1236 q^{40} +81.0378 q^{41} -87.1643 q^{42} +202.640 q^{43} -166.063 q^{44} -116.345 q^{45} +46.0000 q^{46} +86.9907 q^{47} +99.6163 q^{48} +49.0000 q^{49} +54.3578 q^{50} -120.401 q^{51} +74.9561 q^{52} -708.249 q^{53} +189.728 q^{54} +410.609 q^{55} -56.0000 q^{56} -325.777 q^{57} +338.427 q^{58} -618.357 q^{59} -246.313 q^{60} -258.284 q^{61} +383.853 q^{62} +82.3432 q^{63} +64.0000 q^{64} -185.338 q^{65} +516.955 q^{66} -167.372 q^{67} -77.3531 q^{68} -143.198 q^{69} +138.466 q^{70} -281.024 q^{71} -94.1065 q^{72} -643.990 q^{73} -733.364 q^{74} -169.216 q^{75} -209.301 q^{76} -290.610 q^{77} -233.339 q^{78} -397.326 q^{79} -158.247 q^{80} -908.234 q^{81} -162.076 q^{82} +1439.93 q^{83} +174.329 q^{84} +191.264 q^{85} -405.280 q^{86} -1053.53 q^{87} +332.126 q^{88} -497.107 q^{89} +232.689 q^{90} +131.173 q^{91} -92.0000 q^{92} -1194.94 q^{93} -173.981 q^{94} +517.519 q^{95} -199.233 q^{96} +193.384 q^{97} -98.0000 q^{98} -488.363 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 8 q^{2} - q^{3} + 16 q^{4} - 2 q^{5} + 2 q^{6} + 28 q^{7} - 32 q^{8} - 23 q^{9} + 4 q^{10} - 66 q^{11} - 4 q^{12} - 25 q^{13} - 56 q^{14} - 4 q^{15} + 64 q^{16} - 56 q^{17} + 46 q^{18} + 4 q^{19}+ \cdots - 108 q^{99}+O(q^{100}) $ 4 * q - 8 * q^2 - q^3 + 16 * q^4 - 2 * q^5 + 2 * q^6 + 28 * q^7 - 32 * q^8 - 23 * q^9 + 4 * q^10 - 66 * q^11 - 4 * q^12 - 25 * q^13 - 56 * q^14 - 4 * q^15 + 64 * q^16 - 56 * q^17 + 46 * q^18 + 4 * q^19 - 8 * q^20 - 7 * q^21 + 132 * q^22 - 92 * q^23 + 8 * q^24 + 104 * q^25 + 50 * q^26 + 5 * q^27 + 112 * q^28 - 109 * q^29 + 8 * q^30 - 119 * q^31 - 128 * q^32 - 132 * q^33 + 112 * q^34 - 14 * q^35 - 92 * q^36 - 134 * q^37 - 8 * q^38 - 299 * q^39 + 16 * q^40 - 557 * q^41 + 14 * q^42 + 60 * q^43 - 264 * q^44 - 836 * q^45 + 184 * q^46 - 699 * q^47 - 16 * q^48 + 196 * q^49 - 208 * q^50 - 532 * q^51 - 100 * q^52 - 1002 * q^53 - 10 * q^54 - 426 * q^55 - 224 * q^56 - 64 * q^57 + 218 * q^58 - 1482 * q^59 - 16 * q^60 - 132 * q^61 + 238 * q^62 - 161 * q^63 + 256 * q^64 - 2272 * q^65 + 264 * q^66 - 380 * q^67 - 224 * q^68 + 23 * q^69 + 28 * q^70 - 173 * q^71 + 184 * q^72 - 2107 * q^73 + 268 * q^74 - 785 * q^75 + 16 * q^76 - 462 * q^77 + 598 * q^78 - 2184 * q^79 - 32 * q^80 - 560 * q^81 + 1114 * q^82 - 152 * q^83 - 28 * q^84 + 388 * q^85 - 120 * q^86 - 1493 * q^87 + 528 * q^88 + 384 * q^89 + 1672 * q^90 - 175 * q^91 - 368 * q^92 - 1891 * q^93 + 1398 * q^94 - 440 * q^95 + 32 * q^96 + 2756 * q^97 - 392 * q^98 - 108 * 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 $

$2$	−2.00000	−0.707107
$2$	−2.00000	−0.707107
$3$	6.22602	1.19820	0.599099	−	0.800675i	$-0.295526\pi$
$3$	6.22602	1.19820	0.599099	+	0.800675i	$0.295526\pi$
$4$	4.00000	0.500000
$5$	−9.89045	−0.884629	−0.442315	−	0.896860i	$-0.645843\pi$
$5$	−9.89045	−0.884629	−0.442315	+	0.896860i	$0.645843\pi$
$6$	−12.4520	−0.847254
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	−8.00000	−0.353553
$9$	11.7633	0.435678
$10$	19.7809	0.625527
$11$	−41.5157	−1.13795	−0.568976	−	0.822354i	$-0.692660\pi$
$11$	−41.5157	−1.13795	−0.568976	+	0.822354i	$0.692660\pi$
$12$	24.9041	0.599099
$13$	18.7390	0.399790	0.199895	−	0.979817i	$-0.435940\pi$
$13$	18.7390	0.399790	0.199895	+	0.979817i	$0.435940\pi$
$14$	−14.0000	−0.267261
$15$	−61.5782	−1.05996
$16$	16.0000	0.250000
$17$	−19.3383	−0.275895	−0.137948	−	0.990440i	$-0.544051\pi$
$17$	−19.3383	−0.275895	−0.137948	+	0.990440i	$0.544051\pi$
$18$	−23.5266	−0.308071
$19$	−52.3251	−0.631801	−0.315900	−	0.948792i	$-0.602307\pi$
$19$	−52.3251	−0.631801	−0.315900	+	0.948792i	$0.602307\pi$
$20$	−39.5618	−0.442315
$21$	43.5821	0.452876
$22$	83.0315	0.804653
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	−49.8082	−0.423627
$25$	−27.1789	−0.217431
$26$	−37.4781	−0.282694
$27$	−94.8639	−0.676169
$28$	28.0000	0.188982
$29$	−169.213	−1.08352	−0.541761	−	0.840533i	$-0.682242\pi$
$29$	−169.213	−1.08352	−0.541761	+	0.840533i	$0.682242\pi$
$30$	123.156	0.749506
$31$	−191.927	−1.11197	−0.555984	−	0.831193i	$-0.687659\pi$
$31$	−191.927	−1.11197	−0.555984	+	0.831193i	$0.687659\pi$
$32$	−32.0000	−0.176777
$33$	−258.478	−1.36349
$34$	38.6766	0.195088
$35$	−69.2332	−0.334358
$36$	47.0533	0.217839
$37$	366.682	1.62925	0.814623	−	0.579990i	$-0.196944\pi$
$37$	366.682	1.62925	0.814623	+	0.579990i	$0.196944\pi$
$38$	104.650	0.446750
$39$	116.670	0.479028
$40$	79.1236	0.312764
$41$	81.0378	0.308682	0.154341	−	0.988018i	$-0.450674\pi$
$41$	81.0378	0.308682	0.154341	+	0.988018i	$0.450674\pi$
$42$	−87.1643	−0.320232
$43$	202.640	0.718658	0.359329	−	0.933211i	$-0.383006\pi$
$43$	202.640	0.718658	0.359329	+	0.933211i	$0.383006\pi$
$44$	−166.063	−0.568976
$45$	−116.345	−0.385414
$46$	46.0000	0.147442
$47$	86.9907	0.269977	0.134988	−	0.990847i	$-0.456900\pi$
$47$	86.9907	0.269977	0.134988	+	0.990847i	$0.456900\pi$
$48$	99.6163	0.299549
$49$	49.0000	0.142857
$50$	54.3578	0.153747
$51$	−120.401	−0.330577
$52$	74.9561	0.199895
$53$	−708.249	−1.83558	−0.917788	−	0.397071i	$-0.870027\pi$
$53$	−708.249	−1.83558	−0.917788	+	0.397071i	$0.870027\pi$
$54$	189.728	0.478124
$55$	410.609	1.00666
$56$	−56.0000	−0.133631
$57$	−325.777	−0.757022
$58$	338.427	0.766165
$59$	−618.357	−1.36446	−0.682231	−	0.731137i	$-0.738990\pi$
$59$	−618.357	−1.36446	−0.682231	+	0.731137i	$0.738990\pi$
$60$	−246.313	−0.529980
$61$	−258.284	−0.542129	−0.271064	−	0.962561i	$-0.587376\pi$
$61$	−258.284	−0.542129	−0.271064	+	0.962561i	$0.587376\pi$
$62$	383.853	0.786281
$63$	82.3432	0.164671
$64$	64.0000	0.125000
$65$	−185.338	−0.353666
$66$	516.955	0.964134
$67$	−167.372	−0.305191	−0.152596	−	0.988289i	$-0.548763\pi$
$67$	−167.372	−0.305191	−0.152596	+	0.988289i	$0.548763\pi$
$68$	−77.3531	−0.137948
$69$	−143.198	−0.249842
$70$	138.466	0.236427
$71$	−281.024	−0.469739	−0.234869	−	0.972027i	$-0.575466\pi$
$71$	−281.024	−0.469739	−0.234869	+	0.972027i	$0.575466\pi$
$72$	−94.1065	−0.154036
$73$	−643.990	−1.03251	−0.516256	−	0.856434i	$-0.672675\pi$
$73$	−643.990	−1.03251	−0.516256	+	0.856434i	$0.672675\pi$
$74$	−733.364	−1.15205
$75$	−169.216	−0.260526
$76$	−209.301	−0.315900
$77$	−290.610	−0.430105
$78$	−233.339	−0.338724
$79$	−397.326	−0.565856	−0.282928	−	0.959141i	$-0.591306\pi$
$79$	−397.326	−0.565856	−0.282928	+	0.959141i	$0.591306\pi$
$80$	−158.247	−0.221157
$81$	−908.234	−1.24586
$82$	−162.076	−0.218271
$83$	1439.93	1.90425	0.952126	−	0.305705i	$-0.0988921\pi$
$83$	1439.93	1.90425	0.952126	+	0.305705i	$0.0988921\pi$
$84$	174.329	0.226438
$85$	191.264	0.244065
$86$	−405.280	−0.508168
$87$	−1053.53	−1.29827
$88$	332.126	0.402326
$89$	−497.107	−0.592058	−0.296029	−	0.955179i	$-0.595663\pi$
$89$	−497.107	−0.592058	−0.296029	+	0.955179i	$0.595663\pi$
$90$	232.689	0.272529
$91$	131.173	0.151106
$92$	−92.0000	−0.104257
$93$	−1194.94	−1.33236
$94$	−173.981	−0.190902
$95$	517.519	0.558909
$96$	−199.233	−0.211813
$97$	193.384	0.202425	0.101212	−	0.994865i	$-0.467728\pi$
$97$	193.384	0.202425	0.101212	+	0.994865i	$0.467728\pi$
$98$	−98.0000	−0.101015
$99$	−488.363	−0.495781
$100$	−108.716	−0.108716
$101$	−1188.22	−1.17061	−0.585307	−	0.810812i	$-0.699026\pi$
$101$	−1188.22	−1.17061	−0.585307	+	0.810812i	$0.699026\pi$
$102$	240.801	0.233753
$103$	805.666	0.770725	0.385362	−	0.922765i	$-0.374076\pi$
$103$	805.666	0.770725	0.385362	+	0.922765i	$0.374076\pi$
$104$	−149.912	−0.141347
$105$	−431.047	−0.400628
$106$	1416.50	1.29795
$107$	558.186	0.504317	0.252158	−	0.967686i	$-0.418860\pi$
$107$	558.186	0.504317	0.252158	+	0.967686i	$0.418860\pi$
$108$	−379.456	−0.338085
$109$	540.293	0.474777	0.237388	−	0.971415i	$-0.423709\pi$
$109$	540.293	0.474777	0.237388	+	0.971415i	$0.423709\pi$
$110$	−821.219	−0.711820
$111$	2282.97	1.95216
$112$	112.000	0.0944911
$113$	1060.50	0.882865	0.441433	−	0.897294i	$-0.354470\pi$
$113$	1060.50	0.882865	0.441433	+	0.897294i	$0.354470\pi$
$114$	651.555	0.535295
$115$	227.480	0.184458
$116$	−676.853	−0.541761
$117$	220.433	0.174180
$118$	1236.71	0.964820
$119$	−135.368	−0.104279
$120$	492.625	0.374753
$121$	392.556	0.294933
$122$	516.568	0.383343
$123$	504.543	0.369863
$124$	−767.706	−0.555984
$125$	1505.12	1.07698
$126$	−164.686	−0.116440
$127$	345.613	0.241482	0.120741	−	0.992684i	$-0.461473\pi$
$127$	345.613	0.241482	0.120741	+	0.992684i	$0.461473\pi$
$128$	−128.000	−0.0883883
$129$	1261.64	0.861094
$130$	370.675	0.250080
$131$	1303.42	0.869316	0.434658	−	0.900596i	$-0.356869\pi$
$131$	1303.42	0.869316	0.434658	+	0.900596i	$0.356869\pi$
$132$	−1033.91	−0.681745
$133$	−366.276	−0.238798
$134$	334.745	0.215803
$135$	938.247	0.598159
$136$	154.706	0.0975438
$137$	335.747	0.209378	0.104689	−	0.994505i	$-0.466615\pi$
$137$	335.747	0.209378	0.104689	+	0.994505i	$0.466615\pi$
$138$	286.397	0.176665
$139$	−1177.75	−0.718671	−0.359335	−	0.933209i	$-0.616997\pi$
$139$	−1177.75	−0.718671	−0.359335	+	0.933209i	$0.616997\pi$
$140$	−276.933	−0.167179
$141$	541.606	0.323485
$142$	562.049	0.332156
$143$	−777.964	−0.454942
$144$	188.213	0.108920
$145$	1673.60	0.958515
$146$	1287.98	0.730096
$147$	305.075	0.171171
$148$	1466.73	0.814623
$149$	597.570	0.328556	0.164278	−	0.986414i	$-0.447471\pi$
$149$	597.570	0.328556	0.164278	+	0.986414i	$0.447471\pi$
$150$	338.433	0.184219
$151$	1732.94	0.933936	0.466968	−	0.884274i	$-0.345346\pi$
$151$	1732.94	0.933936	0.466968	+	0.884274i	$0.345346\pi$
$152$	418.601	0.223375
$153$	−227.482	−0.120202
$154$	581.220	0.304130
$155$	1898.24	0.983680
$156$	466.678	0.239514
$157$	363.093	0.184573	0.0922867	−	0.995732i	$-0.470582\pi$
$157$	363.093	0.184573	0.0922867	+	0.995732i	$0.470582\pi$
$158$	794.651	0.400121
$159$	−4409.57	−2.19938
$160$	316.495	0.156382
$161$	−161.000	−0.0788110
$162$	1816.47	0.880958
$163$	2426.28	1.16590	0.582948	−	0.812510i	$-0.301899\pi$
$163$	2426.28	1.16590	0.582948	+	0.812510i	$0.301899\pi$
$164$	324.151	0.154341
$165$	2556.46	1.20618
$166$	−2879.86	−1.34651
$167$	−3858.78	−1.78803	−0.894015	−	0.448037i	$-0.852123\pi$
$167$	−3858.78	−1.78803	−0.894015	+	0.448037i	$0.852123\pi$
$168$	−348.657	−0.160116
$169$	−1845.85	−0.840168
$170$	−382.529	−0.172580
$171$	−615.517	−0.275262
$172$	810.559	0.359329
$173$	565.736	0.248625	0.124313	−	0.992243i	$-0.460327\pi$
$173$	565.736	0.248625	0.124313	+	0.992243i	$0.460327\pi$
$174$	2107.05	0.918018
$175$	−190.252	−0.0821813
$176$	−664.252	−0.284488
$177$	−3849.90	−1.63490
$178$	994.213	0.418648
$179$	1320.44	0.551365	0.275682	−	0.961249i	$-0.411096\pi$
$179$	1320.44	0.551365	0.275682	+	0.961249i	$0.411096\pi$
$180$	−465.378	−0.192707
$181$	3238.75	1.33002	0.665011	−	0.746833i	$-0.268427\pi$
$181$	3238.75	1.33002	0.665011	+	0.746833i	$0.268427\pi$
$182$	−262.346	−0.106848
$183$	−1608.08	−0.649578
$184$	184.000	0.0737210
$185$	−3626.65	−1.44128
$186$	2389.88	0.942120
$187$	802.843	0.313956
$188$	347.963	0.134988
$189$	−664.047	−0.255568
$190$	−1035.04	−0.395208
$191$	2268.39	0.859344	0.429672	−	0.902985i	$-0.358629\pi$
$191$	2268.39	0.859344	0.429672	+	0.902985i	$0.358629\pi$
$192$	398.465	0.149775
$193$	4299.35	1.60349	0.801747	−	0.597664i	$-0.203904\pi$
$193$	4299.35	1.60349	0.801747	+	0.597664i	$0.203904\pi$
$194$	−386.768	−0.143136
$195$	−1153.91	−0.423762
$196$	196.000	0.0714286
$197$	−214.502	−0.0775768	−0.0387884	−	0.999247i	$-0.512350\pi$
$197$	−214.502	−0.0775768	−0.0387884	+	0.999247i	$0.512350\pi$
$198$	976.725	0.350570
$199$	−4983.74	−1.77532	−0.887658	−	0.460504i	$-0.847669\pi$
$199$	−4983.74	−1.77532	−0.887658	+	0.460504i	$0.847669\pi$
$200$	217.431	0.0768735
$201$	−1042.06	−0.365679
$202$	2376.43	0.827749
$203$	−1184.49	−0.409533
$204$	−481.602	−0.165289
$205$	−801.501	−0.273069
$206$	−1611.33	−0.544985
$207$	−270.556	−0.0908452
$208$	299.824	0.0999475
$209$	2172.32	0.718958
$210$	862.094	0.283286
$211$	−1863.75	−0.608083	−0.304042	−	0.952659i	$-0.598336\pi$
$211$	−1863.75	−0.608083	−0.304042	+	0.952659i	$0.598336\pi$
$212$	−2833.00	−0.917788
$213$	−1749.66	−0.562840
$214$	−1116.37	−0.356606
$215$	−2004.20	−0.635746
$216$	758.911	0.239062
$217$	−1343.49	−0.420285
$218$	−1080.59	−0.335718
$219$	−4009.49	−1.23715
$220$	1642.44	0.503332
$221$	−362.381	−0.110300
$222$	−4565.94	−1.38039
$223$	4056.06	1.21800	0.609000	−	0.793170i	$-0.291571\pi$
$223$	4056.06	1.21800	0.609000	+	0.793170i	$0.291571\pi$
$224$	−224.000	−0.0668153
$225$	−319.714	−0.0947301
$226$	−2121.01	−0.624280
$227$	3197.93	0.935040	0.467520	−	0.883983i	$-0.345148\pi$
$227$	3197.93	0.935040	0.467520	+	0.883983i	$0.345148\pi$
$228$	−1303.11	−0.378511
$229$	1986.22	0.573157	0.286579	−	0.958057i	$-0.407482\pi$
$229$	1986.22	0.573157	0.286579	+	0.958057i	$0.407482\pi$
$230$	−454.961	−0.130431
$231$	−1809.34	−0.515351
$232$	1353.71	0.383083
$233$	625.027	0.175738	0.0878688	−	0.996132i	$-0.471994\pi$
$233$	625.027	0.175738	0.0878688	+	0.996132i	$0.471994\pi$
$234$	−440.866	−0.123164
$235$	−860.378	−0.238829
$236$	−2473.43	−0.682231
$237$	−2473.76	−0.678007
$238$	270.736	0.0737362
$239$	−5688.03	−1.53945	−0.769724	−	0.638377i	$-0.779606\pi$
$239$	−5688.03	−1.53945	−0.769724	+	0.638377i	$0.779606\pi$
$240$	−985.251	−0.264990
$241$	5167.63	1.38123	0.690614	−	0.723223i	$-0.257340\pi$
$241$	5167.63	1.38123	0.690614	+	0.723223i	$0.257340\pi$
$242$	−785.111	−0.208549
$243$	−3093.36	−0.816621
$244$	−1033.14	−0.271064
$245$	−484.632	−0.126376
$246$	−1009.09	−0.261532
$247$	−980.522	−0.252588
$248$	1535.41	0.393140
$249$	8965.04	2.28167
$250$	−3010.24	−0.761536
$251$	−493.136	−0.124010	−0.0620049	−	0.998076i	$-0.519749\pi$
$251$	−493.136	−0.124010	−0.0620049	+	0.998076i	$0.519749\pi$
$252$	329.373	0.0823355
$253$	954.862	0.237279
$254$	−691.227	−0.170754
$255$	1190.82	0.292438
$256$	256.000	0.0625000
$257$	3505.77	0.850910	0.425455	−	0.904980i	$-0.360114\pi$
$257$	3505.77	0.850910	0.425455	+	0.904980i	$0.360114\pi$
$258$	−2523.28	−0.608886
$259$	2566.77	0.615797
$260$	−741.350	−0.176833
$261$	−1990.51	−0.472067
$262$	−2606.84	−0.614699
$263$	−1693.68	−0.397098	−0.198549	−	0.980091i	$-0.563623\pi$
$263$	−1693.68	−0.397098	−0.198549	+	0.980091i	$0.563623\pi$
$264$	2067.82	0.482067
$265$	7004.91	1.62380
$266$	732.552	0.168856
$267$	−3094.99	−0.709403
$268$	−669.490	−0.152596
$269$	1108.75	0.251308	0.125654	−	0.992074i	$-0.459897\pi$
$269$	1108.75	0.251308	0.125654	+	0.992074i	$0.459897\pi$
$270$	−1876.49	−0.422962
$271$	784.351	0.175815	0.0879076	−	0.996129i	$-0.471982\pi$
$271$	784.351	0.175815	0.0879076	+	0.996129i	$0.471982\pi$
$272$	−309.412	−0.0689739
$273$	816.687	0.181055
$274$	−671.493	−0.148052
$275$	1128.35	0.247426
$276$	−572.794	−0.124921
$277$	−7088.58	−1.53759	−0.768794	−	0.639497i	$-0.779143\pi$
$277$	−7088.58	−1.53759	−0.768794	+	0.639497i	$0.779143\pi$
$278$	2355.49	0.508177
$279$	−2257.69	−0.484461
$280$	553.865	0.118214
$281$	−7749.43	−1.64517	−0.822584	−	0.568644i	$-0.807468\pi$
$281$	−7749.43	−1.64517	−0.822584	+	0.568644i	$0.807468\pi$
$282$	−1083.21	−0.228739
$283$	−1837.38	−0.385939	−0.192969	−	0.981205i	$-0.561812\pi$
$283$	−1837.38	−0.385939	−0.192969	+	0.981205i	$0.561812\pi$
$284$	−1124.10	−0.234869
$285$	3222.09	0.669684
$286$	1555.93	0.321692
$287$	567.265	0.116671
$288$	−376.426	−0.0770178
$289$	−4539.03	−0.923882
$290$	−3347.19	−0.677772
$291$	1204.01	0.242545
$292$	−2575.96	−0.516256
$293$	−200.688	−0.0400147	−0.0200074	−	0.999800i	$-0.506369\pi$
$293$	−200.688	−0.0400147	−0.0200074	+	0.999800i	$0.506369\pi$
$294$	−610.150	−0.121036
$295$	6115.83	1.20704
$296$	−2933.45	−0.576026
$297$	3938.34	0.769447
$298$	−1195.14	−0.232324
$299$	−430.998	−0.0833620
$300$	−676.865	−0.130263
$301$	1418.48	0.271627
$302$	−3465.87	−0.660393
$303$	−7397.86	−1.40263
$304$	−837.202	−0.157950
$305$	2554.54	0.479583
$306$	454.965	0.0849954
$307$	−2168.79	−0.403190	−0.201595	−	0.979469i	$-0.564612\pi$
$307$	−2168.79	−0.403190	−0.201595	+	0.979469i	$0.564612\pi$
$308$	−1162.44	−0.215053
$309$	5016.09	0.923481
$310$	−3796.48	−0.695567
$311$	−9214.82	−1.68014	−0.840072	−	0.542475i	$-0.817487\pi$
$311$	−9214.82	−1.68014	−0.840072	+	0.542475i	$0.817487\pi$
$312$	−933.356	−0.169362
$313$	855.244	0.154445	0.0772224	−	0.997014i	$-0.475395\pi$
$313$	855.244	0.154445	0.0772224	+	0.997014i	$0.475395\pi$
$314$	−726.187	−0.130513
$315$	−814.412	−0.145673
$316$	−1589.30	−0.282928
$317$	−3621.69	−0.641686	−0.320843	−	0.947132i	$-0.603966\pi$
$317$	−3621.69	−0.641686	−0.320843	+	0.947132i	$0.603966\pi$
$318$	8819.15	1.55520
$319$	7025.01	1.23299
$320$	−632.989	−0.110579
$321$	3475.28	0.604271
$322$	322.000	0.0557278
$323$	1011.88	0.174311
$324$	−3632.94	−0.622931
$325$	−509.306	−0.0869268
$326$	−4852.56	−0.824413
$327$	3363.87	0.568877
$328$	−648.302	−0.109136
$329$	608.935	0.102042
$330$	−5112.92	−0.852901
$331$	2886.49	0.479323	0.239662	−	0.970856i	$-0.422964\pi$
$331$	2886.49	0.479323	0.239662	+	0.970856i	$0.422964\pi$
$332$	5759.72	0.952126
$333$	4313.39	0.709827
$334$	7717.55	1.26433
$335$	1655.39	0.269981
$336$	697.314	0.113219
$337$	−2056.69	−0.332448	−0.166224	−	0.986088i	$-0.553158\pi$
$337$	−2056.69	−0.332448	−0.166224	+	0.986088i	$0.553158\pi$
$338$	3691.70	0.594088
$339$	6602.72	1.05785
$340$	765.058	0.122033
$341$	7967.97	1.26537
$342$	1231.03	0.194639
$343$	343.000	0.0539949
$344$	−1621.12	−0.254084
$345$	1416.30	0.221017
$346$	−1131.47	−0.175804
$347$	3641.32	0.563332	0.281666	−	0.959513i	$-0.409113\pi$
$347$	3641.32	0.563332	0.281666	+	0.959513i	$0.409113\pi$
$348$	−4214.10	−0.649137
$349$	7487.45	1.14841	0.574204	−	0.818713i	$-0.305312\pi$
$349$	7487.45	1.14841	0.574204	+	0.818713i	$0.305312\pi$
$350$	380.505	0.0581109
$351$	−1777.66	−0.270326
$352$	1328.50	0.201163
$353$	11902.3	1.79460	0.897302	−	0.441416i	$-0.145524\pi$
$353$	11902.3	1.79460	0.897302	+	0.441416i	$0.145524\pi$
$354$	7699.81	1.15605
$355$	2779.46	0.415545
$356$	−1988.43	−0.296029
$357$	−842.804	−0.124946
$358$	−2640.88	−0.389874
$359$	−4802.20	−0.705991	−0.352995	−	0.935625i	$-0.614837\pi$
$359$	−4802.20	−0.705991	−0.352995	+	0.935625i	$0.614837\pi$
$360$	930.756	0.136264
$361$	−4121.08	−0.600828
$362$	−6477.49	−0.940468
$363$	2444.06	0.353388
$364$	524.693	0.0755532
$365$	6369.35	0.913390
$366$	3216.16	0.459321
$367$	−9127.37	−1.29822	−0.649108	−	0.760697i	$-0.724857\pi$
$367$	−9127.37	−1.29822	−0.649108	+	0.760697i	$0.724857\pi$
$368$	−368.000	−0.0521286
$369$	953.273	0.134486
$370$	7253.30	1.01914
$371$	−4957.74	−0.693782
$372$	−4779.75	−0.666179
$373$	−12900.8	−1.79083	−0.895413	−	0.445237i	$-0.853120\pi$
$373$	−12900.8	−1.79083	−0.895413	+	0.445237i	$0.853120\pi$
$374$	−1605.69	−0.222000
$375$	9370.90	1.29043
$376$	−695.926	−0.0954511
$377$	−3170.89	−0.433181
$378$	1328.09	0.180714
$379$	−1830.25	−0.248058	−0.124029	−	0.992279i	$-0.539582\pi$
$379$	−1830.25	−0.248058	−0.124029	+	0.992279i	$0.539582\pi$
$380$	2070.08	0.279455
$381$	2151.80	0.289343
$382$	−4536.78	−0.607648
$383$	−8010.59	−1.06873	−0.534363	−	0.845255i	$-0.679448\pi$
$383$	−8010.59	−1.06873	−0.534363	+	0.845255i	$0.679448\pi$
$384$	−796.930	−0.105907
$385$	2874.27	0.380484
$386$	−8598.70	−1.13384
$387$	2383.72	0.313104
$388$	773.537	0.101212
$389$	4424.06	0.576629	0.288315	−	0.957536i	$-0.406905\pi$
$389$	4424.06	0.576629	0.288315	+	0.957536i	$0.406905\pi$
$390$	2307.83	0.299645
$391$	444.780	0.0575282
$392$	−392.000	−0.0505076
$393$	8115.12	1.04161
$394$	429.004	0.0548551
$395$	3929.73	0.500573
$396$	−1953.45	−0.247890
$397$	−6976.76	−0.881999	−0.440999	−	0.897507i	$-0.645376\pi$
$397$	−6976.76	−0.881999	−0.440999	+	0.897507i	$0.645376\pi$
$398$	9967.48	1.25534
$399$	−2280.44	−0.286127
$400$	−434.862	−0.0543578
$401$	−9824.95	−1.22353	−0.611764	−	0.791040i	$-0.709540\pi$
$401$	−9824.95	−1.22353	−0.611764	+	0.791040i	$0.709540\pi$
$402$	2084.13	0.258574
$403$	−3596.52	−0.444554
$404$	−4752.87	−0.585307
$405$	8982.85	1.10213
$406$	2368.99	0.289583
$407$	−15223.1	−1.85400
$408$	963.204	0.116877
$409$	8036.27	0.971559	0.485780	−	0.874081i	$-0.338536\pi$
$409$	8036.27	0.971559	0.485780	+	0.874081i	$0.338536\pi$
$410$	1603.00	0.193089
$411$	2090.36	0.250876
$412$	3222.66	0.385362
$413$	−4328.50	−0.515718
$414$	541.112	0.0642373
$415$	−14241.6	−1.68456
$416$	−599.649	−0.0706736
$417$	−7332.68	−0.861110
$418$	−4344.63	−0.508380
$419$	4471.23	0.521322	0.260661	−	0.965430i	$-0.416060\pi$
$419$	4471.23	0.521322	0.260661	+	0.965430i	$0.416060\pi$
$420$	−1724.19	−0.200314
$421$	−8709.07	−1.00820	−0.504102	−	0.863644i	$-0.668177\pi$
$421$	−8709.07	−1.00820	−0.504102	+	0.863644i	$0.668177\pi$
$422$	3727.49	0.429980
$423$	1023.30	0.117623
$424$	5665.99	0.648974
$425$	525.593	0.0599883
$426$	3499.33	0.397988
$427$	−1807.99	−0.204905
$428$	2232.75	0.252158
$429$	−4843.62	−0.545110
$430$	4008.40	0.449540
$431$	−11847.9	−1.32411	−0.662056	−	0.749455i	$-0.730316\pi$
$431$	−11847.9	−1.32411	−0.662056	+	0.749455i	$0.730316\pi$
$432$	−1517.82	−0.169042
$433$	6306.04	0.699882	0.349941	−	0.936772i	$-0.386202\pi$
$433$	6306.04	0.699882	0.349941	+	0.936772i	$0.386202\pi$
$434$	2686.97	0.297186
$435$	10419.8	1.14849
$436$	2161.17	0.237388
$437$	1203.48	0.131740
$438$	8018.99	0.874799
$439$	−26.8997	−0.00292449	−0.00146225	−	0.999999i	$-0.500465\pi$
$439$	−26.8997	−0.00292449	−0.00146225	+	0.999999i	$0.500465\pi$
$440$	−3284.88	−0.355910
$441$	576.402	0.0622398
$442$	724.761	0.0779941
$443$	−12573.3	−1.34848	−0.674241	−	0.738512i	$-0.735529\pi$
$443$	−12573.3	−1.34848	−0.674241	+	0.738512i	$0.735529\pi$
$444$	9131.87	0.976080
$445$	4916.61	0.523752
$446$	−8112.13	−0.861256
$447$	3720.48	0.393675
$448$	448.000	0.0472456
$449$	2972.66	0.312446	0.156223	−	0.987722i	$-0.450068\pi$
$449$	2972.66	0.312446	0.156223	+	0.987722i	$0.450068\pi$
$450$	639.428	0.0669843
$451$	−3364.34	−0.351266
$452$	4242.01	0.441433
$453$	10789.3	1.11904
$454$	−6395.86	−0.661173
$455$	−1297.36	−0.133673
$456$	2606.22	0.267648
$457$	11841.7	1.21210	0.606050	−	0.795426i	$-0.292753\pi$
$457$	11841.7	1.21210	0.606050	+	0.795426i	$0.292753\pi$
$458$	−3972.44	−0.405284
$459$	1834.50	0.186552
$460$	909.922	0.0922290
$461$	−5145.33	−0.519831	−0.259915	−	0.965631i	$-0.583695\pi$
$461$	−5145.33	−0.519831	−0.259915	+	0.965631i	$0.583695\pi$
$462$	3618.69	0.364408
$463$	−10743.6	−1.07840	−0.539200	−	0.842177i	$-0.681273\pi$
$463$	−10743.6	−1.07840	−0.539200	+	0.842177i	$0.681273\pi$
$464$	−2707.41	−0.270880
$465$	11818.5	1.17864
$466$	−1250.05	−0.124265
$467$	−6047.05	−0.599195	−0.299597	−	0.954066i	$-0.596852\pi$
$467$	−6047.05	−0.599195	−0.299597	+	0.954066i	$0.596852\pi$
$468$	881.732	0.0870899
$469$	−1171.61	−0.115351
$470$	1720.76	0.168878
$471$	2260.63	0.221155
$472$	4946.86	0.482410
$473$	−8412.74	−0.817797
$474$	4947.51	0.479424
$475$	1422.14	0.137373
$476$	−541.472	−0.0521393
$477$	−8331.36	−0.799720
$478$	11376.1	1.08855
$479$	−1039.14	−0.0991223	−0.0495612	−	0.998771i	$-0.515782\pi$
$479$	−1039.14	−0.0991223	−0.0495612	+	0.998771i	$0.515782\pi$
$480$	1970.50	0.187376
$481$	6871.26	0.651357
$482$	−10335.3	−0.976676
$483$	−1002.39	−0.0944312
$484$	1570.22	0.147466
$485$	−1912.66	−0.179071
$486$	6186.71	0.577438
$487$	4060.20	0.377793	0.188896	−	0.981997i	$-0.439509\pi$
$487$	4060.20	0.377793	0.188896	+	0.981997i	$0.439509\pi$
$488$	2066.27	0.191671
$489$	15106.1	1.39697
$490$	969.265	0.0893610
$491$	7755.82	0.712862	0.356431	−	0.934322i	$-0.383993\pi$
$491$	7755.82	0.712862	0.356431	+	0.934322i	$0.383993\pi$
$492$	2018.17	0.184931
$493$	3272.29	0.298939
$494$	1961.04	0.178606
$495$	4830.13	0.438582
$496$	−3070.83	−0.277992
$497$	−1967.17	−0.177545
$498$	−17930.1	−1.61339
$499$	12482.6	1.11984	0.559919	−	0.828547i	$-0.310832\pi$
$499$	12482.6	1.11984	0.559919	+	0.828547i	$0.310832\pi$
$500$	6020.47	0.538488
$501$	−24024.8	−2.14241
$502$	986.272	0.0876882
$503$	7263.00	0.643819	0.321910	−	0.946770i	$-0.395675\pi$
$503$	7263.00	0.643819	0.321910	+	0.946770i	$0.395675\pi$
$504$	−658.746	−0.0582200
$505$	11752.0	1.03556
$506$	−1909.72	−0.167782
$507$	−11492.3	−1.00669
$508$	1382.45	0.120741
$509$	−9298.85	−0.809753	−0.404876	−	0.914371i	$-0.632685\pi$
$509$	−9298.85	−0.809753	−0.404876	+	0.914371i	$0.632685\pi$
$510$	−2381.63	−0.206785
$511$	−4507.93	−0.390253
$512$	−512.000	−0.0441942
$513$	4963.77	0.427204
$514$	−7011.54	−0.601684
$515$	−7968.40	−0.681805
$516$	5046.56	0.430547
$517$	−3611.48	−0.307220
$518$	−5133.55	−0.435434
$519$	3522.28	0.297902
$520$	1482.70	0.125040
$521$	17700.1	1.48840	0.744200	−	0.667957i	$-0.232831\pi$
$521$	17700.1	1.48840	0.744200	+	0.667957i	$0.232831\pi$
$522$	3981.02	0.333802
$523$	−4985.36	−0.416815	−0.208408	−	0.978042i	$-0.566828\pi$
$523$	−4985.36	−0.416815	−0.208408	+	0.978042i	$0.566828\pi$
$524$	5213.68	0.434658
$525$	−1184.51	−0.0984694
$526$	3387.36	0.280791
$527$	3711.53	0.306787
$528$	−4135.64	−0.340873
$529$	529.000	0.0434783
$530$	−14009.8	−1.14820
$531$	−7273.93	−0.594467
$532$	−1465.10	−0.119399
$533$	1518.57	0.123408
$534$	6189.99	0.501624
$535$	−5520.72	−0.446133
$536$	1338.98	0.107901
$537$	8221.08	0.660644
$538$	−2217.51	−0.177702
$539$	−2034.27	−0.162564
$540$	3752.99	0.299079
$541$	15877.9	1.26182	0.630910	−	0.775856i	$-0.282682\pi$
$541$	15877.9	1.26182	0.630910	+	0.775856i	$0.282682\pi$
$542$	−1568.70	−0.124320
$543$	20164.5	1.59363
$544$	618.825	0.0487719
$545$	−5343.74	−0.420001
$546$	−1633.37	−0.128026
$547$	−8542.53	−0.667737	−0.333869	−	0.942620i	$-0.608354\pi$
$547$	−8542.53	−0.667737	−0.333869	+	0.942620i	$0.608354\pi$
$548$	1342.99	0.104689
$549$	−3038.27	−0.236194
$550$	−2256.70	−0.174957
$551$	8854.11	0.684569
$552$	1145.59	0.0883323
$553$	−2781.28	−0.213873
$554$	14177.2	1.08724
$555$	−22579.6	−1.72694
$556$	−4710.99	−0.359335
$557$	−14999.9	−1.14106	−0.570528	−	0.821278i	$-0.693261\pi$
$557$	−14999.9	−1.14106	−0.570528	+	0.821278i	$0.693261\pi$
$558$	4515.39	0.342565
$559$	3797.27	0.287312
$560$	−1107.73	−0.0835896
$561$	4998.51	0.376181
$562$	15498.9	1.16331
$563$	19048.3	1.42592	0.712959	−	0.701206i	$-0.247355\pi$
$563$	19048.3	1.42592	0.712959	+	0.701206i	$0.247355\pi$
$564$	2166.42	0.161743
$565$	−10488.9	−0.781008
$566$	3674.75	0.272900
$567$	−6357.64	−0.470892
$568$	2248.20	0.166078
$569$	−4524.55	−0.333355	−0.166678	−	0.986011i	$-0.553304\pi$
$569$	−4524.55	−0.333355	−0.166678	+	0.986011i	$0.553304\pi$
$570$	−6444.17	−0.473538
$571$	−21959.6	−1.60942	−0.804712	−	0.593666i	$-0.797680\pi$
$571$	−21959.6	−1.60942	−0.804712	+	0.593666i	$0.797680\pi$
$572$	−3111.86	−0.227471
$573$	14123.0	1.02966
$574$	−1134.53	−0.0824988
$575$	625.115	0.0453375
$576$	752.852	0.0544598
$577$	6815.71	0.491753	0.245877	−	0.969301i	$-0.420924\pi$
$577$	6815.71	0.491753	0.245877	+	0.969301i	$0.420924\pi$
$578$	9078.06	0.653283
$579$	26767.9	1.92130
$580$	6694.39	0.479257
$581$	10079.5	0.719740
$582$	−2408.03	−0.171505
$583$	29403.5	2.08880
$584$	5151.92	0.365048
$585$	−2180.18	−0.154085
$586$	401.376	0.0282947
$587$	−10153.0	−0.713898	−0.356949	−	0.934124i	$-0.616183\pi$
$587$	−10153.0	−0.713898	−0.356949	+	0.934124i	$0.616183\pi$
$588$	1220.30	0.0855856
$589$	10042.6	0.702542
$590$	−12231.7	−0.853508
$591$	−1335.49	−0.0929523
$592$	5866.91	0.407312
$593$	5891.25	0.407968	0.203984	−	0.978974i	$-0.434611\pi$
$593$	5891.25	0.407968	0.203984	+	0.978974i	$0.434611\pi$
$594$	−7876.69	−0.544081
$595$	1338.85	0.0922479
$596$	2390.28	0.164278
$597$	−31028.8	−2.12718
$598$	861.995	0.0589458
$599$	−26348.6	−1.79728	−0.898642	−	0.438683i	$-0.855445\pi$
$599$	−26348.6	−1.79728	−0.898642	+	0.438683i	$0.855445\pi$
$600$	1353.73	0.0921097
$601$	−11213.6	−0.761088	−0.380544	−	0.924763i	$-0.624263\pi$
$601$	−11213.6	−0.761088	−0.380544	+	0.924763i	$0.624263\pi$
$602$	−2836.96	−0.192069
$603$	−1968.85	−0.132965
$604$	6931.74	0.466968
$605$	−3882.55	−0.260906
$606$	14795.7	0.991807
$607$	−17937.3	−1.19943	−0.599713	−	0.800215i	$-0.704719\pi$
$607$	−17937.3	−1.19943	−0.599713	+	0.800215i	$0.704719\pi$
$608$	1674.40	0.111688
$609$	−7374.68	−0.490701
$610$	−5109.09	−0.339116
$611$	1630.12	0.107934
$612$	−909.929	−0.0601008
$613$	6735.03	0.443761	0.221880	−	0.975074i	$-0.428781\pi$
$613$	6735.03	0.443761	0.221880	+	0.975074i	$0.428781\pi$
$614$	4337.57	0.285098
$615$	−4990.16	−0.327191
$616$	2324.88	0.152065
$617$	21561.2	1.40684	0.703421	−	0.710773i	$-0.251655\pi$
$617$	21561.2	1.40684	0.703421	+	0.710773i	$0.251655\pi$
$618$	−10032.2	−0.652999
$619$	−811.525	−0.0526946	−0.0263473	−	0.999653i	$-0.508388\pi$
$619$	−811.525	−0.0526946	−0.0263473	+	0.999653i	$0.508388\pi$
$620$	7592.96	0.491840
$621$	2181.87	0.140991
$622$	18429.6	1.18804
$623$	−3479.75	−0.223777
$624$	1866.71	0.119757
$625$	−11488.9	−0.735292
$626$	−1710.49	−0.109209
$627$	13524.9	0.861454
$628$	1452.37	0.0922867
$629$	−7091.00	−0.449502
$630$	1628.82	0.103006
$631$	−6015.69	−0.379526	−0.189763	−	0.981830i	$-0.560772\pi$
$631$	−6015.69	−0.379526	−0.189763	+	0.981830i	$0.560772\pi$
$632$	3178.60	0.200060
$633$	−11603.7	−0.728604
$634$	7243.39	0.453741
$635$	−3418.27	−0.213622
$636$	−17638.3	−1.09969
$637$	918.212	0.0571129
$638$	−14050.0	−0.871859
$639$	−3305.78	−0.204655
$640$	1265.98	0.0781909
$641$	−28011.7	−1.72604	−0.863022	−	0.505166i	$-0.831431\pi$
$641$	−28011.7	−1.72604	−0.863022	+	0.505166i	$0.831431\pi$
$642$	−6950.56	−0.427284
$643$	−8896.79	−0.545653	−0.272827	−	0.962063i	$-0.587959\pi$
$643$	−8896.79	−0.545653	−0.272827	+	0.962063i	$0.587959\pi$
$644$	−644.000	−0.0394055
$645$	−12478.2	−0.761749
$646$	−2023.76	−0.123256
$647$	−15429.8	−0.937570	−0.468785	−	0.883312i	$-0.655308\pi$
$647$	−15429.8	−0.937570	−0.468785	+	0.883312i	$0.655308\pi$
$648$	7265.87	0.440479
$649$	25671.6	1.55269
$650$	1018.61	0.0614666
$651$	−8364.57	−0.503584
$652$	9705.12	0.582948
$653$	11711.0	0.701820	0.350910	−	0.936409i	$-0.385872\pi$
$653$	11711.0	0.701820	0.350910	+	0.936409i	$0.385872\pi$
$654$	−6727.75	−0.402257
$655$	−12891.4	−0.769022
$656$	1296.60	0.0771706
$657$	−7575.46	−0.449843
$658$	−1217.87	−0.0721543
$659$	10814.5	0.639258	0.319629	−	0.947543i	$-0.396442\pi$
$659$	10814.5	0.639258	0.319629	+	0.947543i	$0.396442\pi$
$660$	10225.8	0.603092
$661$	4122.46	0.242580	0.121290	−	0.992617i	$-0.461297\pi$
$661$	4122.46	0.242580	0.121290	+	0.992617i	$0.461297\pi$
$662$	−5772.99	−0.338933
$663$	−2256.19	−0.132162
$664$	−11519.4	−0.673255
$665$	3622.64	0.211248
$666$	−8626.79	−0.501924
$667$	3891.91	0.225930
$668$	−15435.1	−0.894015
$669$	25253.1	1.45941
$670$	−3310.78	−0.190905
$671$	10722.8	0.616916
$672$	−1394.63	−0.0800580
$673$	−21192.2	−1.21382	−0.606909	−	0.794771i	$-0.707591\pi$
$673$	−21192.2	−1.21382	−0.606909	+	0.794771i	$0.707591\pi$
$674$	4113.38	0.235077
$675$	2578.30	0.147020
$676$	−7383.40	−0.420084
$677$	−29376.9	−1.66772	−0.833860	−	0.551976i	$-0.813874\pi$
$677$	−29376.9	−1.66772	−0.833860	+	0.551976i	$0.813874\pi$
$678$	−13205.4	−0.748011
$679$	1353.69	0.0765093
$680$	−1530.12	−0.0862901
$681$	19910.4	1.12036
$682$	−15935.9	−0.894749
$683$	−2923.77	−0.163800	−0.0818998	−	0.996641i	$-0.526099\pi$
$683$	−2923.77	−0.163800	−0.0818998	+	0.996641i	$0.526099\pi$
$684$	−2462.07	−0.137631
$685$	−3320.69	−0.185222
$686$	−686.000	−0.0381802
$687$	12366.2	0.686756
$688$	3242.24	0.179664
$689$	−13271.9	−0.733845
$690$	−2832.60	−0.156283
$691$	−19904.1	−1.09579	−0.547893	−	0.836548i	$-0.684570\pi$
$691$	−19904.1	−1.09579	−0.547893	+	0.836548i	$0.684570\pi$
$692$	2262.94	0.124313
$693$	−3418.54	−0.187387
$694$	−7282.64	−0.398336
$695$	11648.5	0.635757
$696$	8428.20	0.459009
$697$	−1567.13	−0.0851641
$698$	−14974.9	−0.812047
$699$	3891.43	0.210569
$700$	−761.009	−0.0410906
$701$	−15700.8	−0.845949	−0.422974	−	0.906142i	$-0.639014\pi$
$701$	−15700.8	−0.845949	−0.422974	+	0.906142i	$0.639014\pi$
$702$	3555.31	0.191149
$703$	−19186.7	−1.02936
$704$	−2657.01	−0.142244
$705$	−5356.73	−0.286165
$706$	−23804.6	−1.26898
$707$	−8317.52	−0.442451
$708$	−15399.6	−0.817448
$709$	−11130.6	−0.589588	−0.294794	−	0.955561i	$-0.595251\pi$
$709$	−11130.6	−0.589588	−0.294794	+	0.955561i	$0.595251\pi$
$710$	−5558.92	−0.293835
$711$	−4673.87	−0.246531
$712$	3976.85	0.209324
$713$	4414.31	0.231862
$714$	1685.61	0.0883505
$715$	7694.42	0.402455
$716$	5281.76	0.275682
$717$	−35413.8	−1.84456
$718$	9604.41	0.499211
$719$	26480.8	1.37353	0.686766	−	0.726879i	$-0.259030\pi$
$719$	26480.8	1.37353	0.686766	+	0.726879i	$0.259030\pi$
$720$	−1861.51	−0.0963534
$721$	5639.66	0.291307
$722$	8242.16	0.424850
$723$	32173.7	1.65498
$724$	12955.0	0.665011
$725$	4599.03	0.235591
$726$	−4888.12	−0.249883
$727$	15809.9	0.806542	0.403271	−	0.915081i	$-0.367873\pi$
$727$	15809.9	0.806542	0.403271	+	0.915081i	$0.367873\pi$
$728$	−1049.39	−0.0534242
$729$	5263.02	0.267389
$730$	−12738.7	−0.645864
$731$	−3918.71	−0.198274
$732$	−6432.32	−0.324789
$733$	−16659.7	−0.839481	−0.419740	−	0.907644i	$-0.637879\pi$
$733$	−16659.7	−0.839481	−0.419740	+	0.907644i	$0.637879\pi$
$734$	18254.7	0.917977
$735$	−3017.33	−0.151423
$736$	736.000	0.0368605
$737$	6948.59	0.347292
$738$	−1906.55	−0.0950961
$739$	−36041.7	−1.79407	−0.897033	−	0.441963i	$-0.854282\pi$
$739$	−36041.7	−1.79407	−0.897033	+	0.441963i	$0.854282\pi$
$740$	−14506.6	−0.720640
$741$	−6104.75	−0.302650
$742$	9915.49	0.490578
$743$	−14639.2	−0.722828	−0.361414	−	0.932405i	$-0.617706\pi$
$743$	−14639.2	−0.722828	−0.361414	+	0.932405i	$0.617706\pi$
$744$	9559.51	0.471060
$745$	−5910.24	−0.290650
$746$	25801.6	1.26631
$747$	16938.4	0.829642
$748$	3211.37	0.156978
$749$	3907.30	0.190614
$750$	−18741.8	−0.912471
$751$	−15263.2	−0.741629	−0.370814	−	0.928707i	$-0.620921\pi$
$751$	−15263.2	−0.741629	−0.370814	+	0.928707i	$0.620921\pi$
$752$	1391.85	0.0674941
$753$	−3070.27	−0.148588
$754$	6341.79	0.306305
$755$	−17139.5	−0.826187
$756$	−2656.19	−0.127784
$757$	−25812.5	−1.23933	−0.619663	−	0.784868i	$-0.712731\pi$
$757$	−25812.5	−1.23933	−0.619663	+	0.784868i	$0.712731\pi$
$758$	3660.51	0.175403
$759$	5944.99	0.284307
$760$	−4140.16	−0.197604
$761$	8641.54	0.411637	0.205818	−	0.978590i	$-0.434014\pi$
$761$	8641.54	0.411637	0.205818	+	0.978590i	$0.434014\pi$
$762$	−4303.59	−0.204597
$763$	3782.05	0.179449
$764$	9073.55	0.429672
$765$	2249.90	0.106334
$766$	16021.2	0.755703
$767$	−11587.4	−0.545498
$768$	1593.86	0.0748874
$769$	7300.25	0.342333	0.171166	−	0.985242i	$-0.445246\pi$
$769$	7300.25	0.342333	0.171166	+	0.985242i	$0.445246\pi$
$770$	−5748.53	−0.269042
$771$	21827.0	1.01956
$772$	17197.4	0.801747
$773$	16068.9	0.747684	0.373842	−	0.927492i	$-0.378040\pi$
$773$	16068.9	0.747684	0.373842	+	0.927492i	$0.378040\pi$
$774$	−4767.43	−0.221398
$775$	5216.35	0.241777
$776$	−1547.07	−0.0715679
$777$	15980.8	0.737847
$778$	−8848.12	−0.407739
$779$	−4240.31	−0.195026
$780$	−4615.66	−0.211881
$781$	11666.9	0.534540
$782$	−889.561	−0.0406786
$783$	16052.2	0.732644
$784$	784.000	0.0357143
$785$	−3591.16	−0.163279
$786$	−16230.2	−0.736531
$787$	−754.116	−0.0341567	−0.0170783	−	0.999854i	$-0.505436\pi$
$787$	−754.116	−0.0341567	−0.0170783	+	0.999854i	$0.505436\pi$
$788$	−858.007	−0.0387884
$789$	−10544.9	−0.475802
$790$	−7859.46	−0.353958
$791$	7423.52	0.333692
$792$	3906.90	0.175285
$793$	−4839.99	−0.216738
$794$	13953.5	0.623667
$795$	43612.7	1.94564
$796$	−19935.0	−0.887658
$797$	−6159.16	−0.273737	−0.136869	−	0.990589i	$-0.543704\pi$
$797$	−6159.16	−0.273737	−0.136869	+	0.990589i	$0.543704\pi$
$798$	4560.88	0.202323
$799$	−1682.25	−0.0744853
$800$	869.725	0.0384368
$801$	−5847.62	−0.257947
$802$	19649.9	0.865165
$803$	26735.7	1.17495
$804$	−4168.26	−0.182840
$805$	1592.36	0.0697185
$806$	7193.03	0.314347
$807$	6903.13	0.301117
$808$	9505.74	0.413875
$809$	−1676.54	−0.0728602	−0.0364301	−	0.999336i	$-0.511599\pi$
$809$	−1676.54	−0.0728602	−0.0364301	+	0.999336i	$0.511599\pi$
$810$	−17965.7	−0.779321
$811$	16726.0	0.724205	0.362102	−	0.932138i	$-0.382059\pi$
$811$	16726.0	0.724205	0.362102	+	0.932138i	$0.382059\pi$
$812$	−4737.97	−0.204766
$813$	4883.39	0.210662
$814$	30446.1	1.31098
$815$	−23997.0	−1.03139
$816$	−1926.41	−0.0826443
$817$	−10603.2	−0.454048
$818$	−16072.5	−0.686996
$819$	1543.03	0.0658338
$820$	−3206.00	−0.136535
$821$	−11588.4	−0.492617	−0.246309	−	0.969191i	$-0.579218\pi$
$821$	−11588.4	−0.492617	−0.246309	+	0.969191i	$0.579218\pi$
$822$	−4180.73	−0.177396
$823$	−42240.5	−1.78908	−0.894538	−	0.446991i	$-0.852496\pi$
$823$	−42240.5	−1.78908	−0.894538	+	0.446991i	$0.852496\pi$
$824$	−6445.33	−0.272492
$825$	7025.14	0.296465
$826$	8657.00	0.364668
$827$	30885.9	1.29868	0.649341	−	0.760498i	$-0.275045\pi$
$827$	30885.9	1.29868	0.649341	+	0.760498i	$0.275045\pi$
$828$	−1082.22	−0.0454226
$829$	11743.9	0.492017	0.246008	−	0.969268i	$-0.420881\pi$
$829$	11743.9	0.492017	0.246008	+	0.969268i	$0.420881\pi$
$830$	28483.1	1.19116
$831$	−44133.7	−1.84233
$832$	1199.30	0.0499738
$833$	−947.576	−0.0394136
$834$	14665.4	0.608897
$835$	38165.0	1.58174
$836$	8689.26	0.359479
$837$	18206.9	0.751879
$838$	−8942.46	−0.368630
$839$	30404.4	1.25110	0.625552	−	0.780183i	$-0.284874\pi$
$839$	30404.4	1.25110	0.625552	+	0.780183i	$0.284874\pi$
$840$	3448.38	0.141643
$841$	4244.15	0.174019
$842$	17418.1	0.712908
$843$	−48248.1	−1.97124
$844$	−7454.98	−0.304042
$845$	18256.3	0.743237
$846$	−2046.60	−0.0831720
$847$	2747.89	0.111474
$848$	−11332.0	−0.458894
$849$	−11439.5	−0.462431
$850$	−1051.19	−0.0424181
$851$	−8433.68	−0.339721
$852$	−6998.65	−0.281420
$853$	1256.30	0.0504276	0.0252138	−	0.999682i	$-0.491973\pi$
$853$	1256.30	0.0504276	0.0252138	+	0.999682i	$0.491973\pi$
$854$	3615.97	0.144890
$855$	6087.74	0.243505
$856$	−4465.49	−0.178303
$857$	−7524.50	−0.299921	−0.149960	−	0.988692i	$-0.547915\pi$
$857$	−7524.50	−0.299921	−0.149960	+	0.988692i	$0.547915\pi$
$858$	9687.24	0.385451
$859$	32543.0	1.29261	0.646306	−	0.763078i	$-0.276313\pi$
$859$	32543.0	1.29261	0.646306	+	0.763078i	$0.276313\pi$
$860$	−8016.80	−0.317873
$861$	3531.80	0.139795
$862$	23695.8	0.936288
$863$	17286.5	0.681852	0.340926	−	0.940090i	$-0.389259\pi$
$863$	17286.5	0.681852	0.340926	+	0.940090i	$0.389259\pi$
$864$	3035.64	0.119531
$865$	−5595.39	−0.219941
$866$	−12612.1	−0.494891
$867$	−28260.1	−1.10699
$868$	−5373.94	−0.210142
$869$	16495.3	0.643916
$870$	−20839.7	−0.812105
$871$	−3136.40	−0.122012
$872$	−4322.34	−0.167859
$873$	2274.84	0.0881920
$874$	−2406.96	−0.0931539
$875$	10535.8	0.407058
$876$	−16038.0	−0.618577
$877$	−10416.4	−0.401068	−0.200534	−	0.979687i	$-0.564268\pi$
$877$	−10416.4	−0.401068	−0.200534	+	0.979687i	$0.564268\pi$
$878$	53.7994	0.00206793
$879$	−1249.49	−0.0479456
$880$	6569.75	0.251666
$881$	48386.4	1.85037	0.925186	−	0.379514i	$-0.123909\pi$
$881$	48386.4	1.85037	0.925186	+	0.379514i	$0.123909\pi$
$882$	−1152.80	−0.0440102
$883$	4310.85	0.164294	0.0821471	−	0.996620i	$-0.473822\pi$
$883$	4310.85	0.164294	0.0821471	+	0.996620i	$0.473822\pi$
$884$	−1449.52	−0.0551501
$885$	38077.3	1.44628
$886$	25146.7	0.953521
$887$	4359.56	0.165028	0.0825139	−	0.996590i	$-0.473705\pi$
$887$	4359.56	0.165028	0.0825139	+	0.996590i	$0.473705\pi$
$888$	−18263.7	−0.690193
$889$	2419.29	0.0912716
$890$	−9833.22	−0.370349
$891$	37706.0	1.41773
$892$	16224.3	0.609000
$893$	−4551.80	−0.170571
$894$	−7440.96	−0.278370
$895$	−13059.8	−0.487753
$896$	−896.000	−0.0334077
$897$	−2683.40	−0.0998842
$898$	−5945.32	−0.220933
$899$	32476.5	1.20484
$900$	−1278.86	−0.0473650
$901$	13696.3	0.506427
$902$	6728.69	0.248382
$903$	8831.48	0.325463
$904$	−8484.03	−0.312140
$905$	−32032.7	−1.17658
$906$	−21578.6	−0.791281
$907$	−50399.3	−1.84507	−0.922537	−	0.385908i	$-0.873888\pi$
$907$	−50399.3	−1.84507	−0.922537	+	0.385908i	$0.873888\pi$
$908$	12791.7	0.467520
$909$	−13977.4	−0.510011
$910$	2594.73	0.0945212
$911$	46810.4	1.70241	0.851206	−	0.524832i	$-0.175872\pi$
$911$	46810.4	1.70241	0.851206	+	0.524832i	$0.175872\pi$
$912$	−5212.44	−0.189256
$913$	−59779.8	−2.16695
$914$	−23683.3	−0.857085
$915$	15904.6	0.574635
$916$	7944.88	0.286579
$917$	9123.94	0.328570
$918$	−3669.01	−0.131912
$919$	19768.2	0.709569	0.354785	−	0.934948i	$-0.384554\pi$
$919$	19768.2	0.709569	0.354785	+	0.934948i	$0.384554\pi$
$920$	−1819.84	−0.0652157
$921$	−13502.9	−0.483101
$922$	10290.7	0.367576
$923$	−5266.12	−0.187797
$924$	−7237.38	−0.257676
$925$	−9966.01	−0.354249
$926$	21487.3	0.762545
$927$	9477.30	0.335788
$928$	5414.83	0.191541
$929$	30117.9	1.06366	0.531828	−	0.846852i	$-0.321505\pi$
$929$	30117.9	1.06366	0.531828	+	0.846852i	$0.321505\pi$
$930$	−23637.0	−0.833427
$931$	−2563.93	−0.0902572
$932$	2500.11	0.0878688
$933$	−57371.7	−2.01314
$934$	12094.1	0.423695
$935$	−7940.48	−0.277734
$936$	−1763.46	−0.0615819
$937$	−54880.6	−1.91342	−0.956708	−	0.291049i	$-0.905996\pi$
$937$	−54880.6	−1.91342	−0.956708	+	0.291049i	$0.905996\pi$
$938$	2343.21	0.0815657
$939$	5324.77	0.185056
$940$	−3441.51	−0.119415
$941$	42264.7	1.46417	0.732087	−	0.681211i	$-0.238546\pi$
$941$	42264.7	1.46417	0.732087	+	0.681211i	$0.238546\pi$
$942$	−4521.25	−0.156380
$943$	−1863.87	−0.0643647
$944$	−9893.72	−0.341115
$945$	6567.73	0.226083
$946$	16825.5	0.578270
$947$	16330.6	0.560373	0.280186	−	0.959946i	$-0.409604\pi$
$947$	16330.6	0.560373	0.280186	+	0.959946i	$0.409604\pi$
$948$	−9895.03	−0.339004
$949$	−12067.7	−0.412788
$950$	−2844.28	−0.0971375
$951$	−22548.7	−0.768867
$952$	1082.94	0.0368681
$953$	−55484.1	−1.88595	−0.942973	−	0.332868i	$-0.891984\pi$
$953$	−55484.1	−1.88595	−0.942973	+	0.332868i	$0.891984\pi$
$954$	16662.7	0.565488
$955$	−22435.4	−0.760201
$956$	−22752.1	−0.769724
$957$	43737.9	1.47737
$958$	2078.28	0.0700901
$959$	2350.23	0.0791374
$960$	−3941.00	−0.132495
$961$	7044.81	0.236474
$962$	−13742.5	−0.460579
$963$	6566.12	0.219720
$964$	20670.5	0.690614
$965$	−42522.6	−1.41850
$966$	2004.78	0.0667730
$967$	49602.8	1.64956	0.824778	−	0.565457i	$-0.191300\pi$
$967$	49602.8	1.64956	0.824778	+	0.565457i	$0.191300\pi$
$968$	−3140.45	−0.104275
$969$	6299.97	0.208859
$970$	3825.31	0.126622
$971$	45053.6	1.48902	0.744510	−	0.667611i	$-0.232683\pi$
$971$	45053.6	1.48902	0.744510	+	0.667611i	$0.232683\pi$
$972$	−12373.4	−0.408311
$973$	−8244.23	−0.271632
$974$	−8120.39	−0.267140
$975$	−3170.95	−0.104156
$976$	−4132.54	−0.135532
$977$	−7977.63	−0.261235	−0.130618	−	0.991433i	$-0.541696\pi$
$977$	−7977.63	−0.261235	−0.130618	+	0.991433i	$0.541696\pi$
$978$	−30212.1	−0.987810
$979$	20637.7	0.673733
$980$	−1938.53	−0.0631878
$981$	6355.64	0.206850
$982$	−15511.6	−0.504070
$983$	745.180	0.0241786	0.0120893	−	0.999927i	$-0.496152\pi$
$983$	745.180	0.0241786	0.0120893	+	0.999927i	$0.496152\pi$
$984$	−4036.34	−0.130766
$985$	2121.52	0.0686267
$986$	−6544.59	−0.211382
$987$	3791.24	0.122266
$988$	−3922.09	−0.126294
$989$	−4660.72	−0.149850
$990$	−9660.26	−0.310124
$991$	−30814.7	−0.987752	−0.493876	−	0.869532i	$-0.664420\pi$
$991$	−30814.7	−0.987752	−0.493876	+	0.869532i	$0.664420\pi$
$992$	6141.65	0.196570
$993$	17971.4	0.574324
$994$	3934.34	0.125543
$995$	49291.4	1.57050
$996$	35860.2	1.14084
$997$	37297.4	1.18477	0.592387	−	0.805654i	$-0.298186\pi$
$997$	37297.4	1.18477	0.592387	+	0.805654i	$0.298186\pi$
$998$	−24965.3	−0.791845
$999$	−34784.9	−1.10165

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	322.4.a.f.1.4	✓	4
7.6	odd	2		2254.4.a.j.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.4.a.f.1.4	✓	4	1.1	even	1	trivial
2254.4.a.j.1.1		4	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 322 = 2 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	322.a (trivial)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} +6.22602 q^{3} +4.00000 q^{4} -9.89045 q^{5} -12.4520 q^{6} +7.00000 q^{7} -8.00000 q^{8} +11.7633 q^{9} +19.7809 q^{10} -41.5157 q^{11} +24.9041 q^{12} +18.7390 q^{13} -14.0000 q^{14} -61.5782 q^{15} +16.0000 q^{16} -19.3383 q^{17} -23.5266 q^{18} -52.3251 q^{19} -39.5618 q^{20} +43.5821 q^{21} +83.0315 q^{22} -23.0000 q^{23} -49.8082 q^{24} -27.1789 q^{25} -37.4781 q^{26} -94.8639 q^{27} +28.0000 q^{28} -169.213 q^{29} +123.156 q^{30} -191.927 q^{31} -32.0000 q^{32} -258.478 q^{33} +38.6766 q^{34} -69.2332 q^{35} +47.0533 q^{36} +366.682 q^{37} +104.650 q^{38} +116.670 q^{39} +79.1236 q^{40} +81.0378 q^{41} -87.1643 q^{42} +202.640 q^{43} -166.063 q^{44} -116.345 q^{45} +46.0000 q^{46} +86.9907 q^{47} +99.6163 q^{48} +49.0000 q^{49} +54.3578 q^{50} -120.401 q^{51} +74.9561 q^{52} -708.249 q^{53} +189.728 q^{54} +410.609 q^{55} -56.0000 q^{56} -325.777 q^{57} +338.427 q^{58} -618.357 q^{59} -246.313 q^{60} -258.284 q^{61} +383.853 q^{62} +82.3432 q^{63} +64.0000 q^{64} -185.338 q^{65} +516.955 q^{66} -167.372 q^{67} -77.3531 q^{68} -143.198 q^{69} +138.466 q^{70} -281.024 q^{71} -94.1065 q^{72} -643.990 q^{73} -733.364 q^{74} -169.216 q^{75} -209.301 q^{76} -290.610 q^{77} -233.339 q^{78} -397.326 q^{79} -158.247 q^{80} -908.234 q^{81} -162.076 q^{82} +1439.93 q^{83} +174.329 q^{84} +191.264 q^{85} -405.280 q^{86} -1053.53 q^{87} +332.126 q^{88} -497.107 q^{89} +232.689 q^{90} +131.173 q^{91} -92.0000 q^{92} -1194.94 q^{93} -173.981 q^{94} +517.519 q^{95} -199.233 q^{96} +193.384 q^{97} -98.0000 q^{98} -488.363 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 8 q^{2} - q^{3} + 16 q^{4} - 2 q^{5} + 2 q^{6} + 28 q^{7} - 32 q^{8} - 23 q^{9} + 4 q^{10} - 66 q^{11} - 4 q^{12} - 25 q^{13} - 56 q^{14} - 4 q^{15} + 64 q^{16} - 56 q^{17} + 46 q^{18} + 4 q^{19}+ \cdots - 108 q^{99}+O(q^{100}) \) 4 * q - 8 * q^2 - q^3 + 16 * q^4 - 2 * q^5 + 2 * q^6 + 28 * q^7 - 32 * q^8 - 23 * q^9 + 4 * q^10 - 66 * q^11 - 4 * q^12 - 25 * q^13 - 56 * q^14 - 4 * q^15 + 64 * q^16 - 56 * q^17 + 46 * q^18 + 4 * q^19 - 8 * q^20 - 7 * q^21 + 132 * q^22 - 92 * q^23 + 8 * q^24 + 104 * q^25 + 50 * q^26 + 5 * q^27 + 112 * q^28 - 109 * q^29 + 8 * q^30 - 119 * q^31 - 128 * q^32 - 132 * q^33 + 112 * q^34 - 14 * q^35 - 92 * q^36 - 134 * q^37 - 8 * q^38 - 299 * q^39 + 16 * q^40 - 557 * q^41 + 14 * q^42 + 60 * q^43 - 264 * q^44 - 836 * q^45 + 184 * q^46 - 699 * q^47 - 16 * q^48 + 196 * q^49 - 208 * q^50 - 532 * q^51 - 100 * q^52 - 1002 * q^53 - 10 * q^54 - 426 * q^55 - 224 * q^56 - 64 * q^57 + 218 * q^58 - 1482 * q^59 - 16 * q^60 - 132 * q^61 + 238 * q^62 - 161 * q^63 + 256 * q^64 - 2272 * q^65 + 264 * q^66 - 380 * q^67 - 224 * q^68 + 23 * q^69 + 28 * q^70 - 173 * q^71 + 184 * q^72 - 2107 * q^73 + 268 * q^74 - 785 * q^75 + 16 * q^76 - 462 * q^77 + 598 * q^78 - 2184 * q^79 - 32 * q^80 - 560 * q^81 + 1114 * q^82 - 152 * q^83 - 28 * q^84 + 388 * q^85 - 120 * q^86 - 1493 * q^87 + 528 * q^88 + 384 * q^89 + 1672 * q^90 - 175 * q^91 - 368 * q^92 - 1891 * q^93 + 1398 * q^94 - 440 * q^95 + 32 * q^96 + 2756 * q^97 - 392 * q^98 - 108 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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