LMFDB - Embedded newform 130.4.a.e.1.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [130,4,Mod(1,130)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("130.1"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(130, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 130 = 2 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	130.a (trivial)

Newform invariants

comment:select newform

sage:traces = [2,-4,2,8,-10,-4,0,-16,38] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	yes
Analytic conductor:	$7.67024830075$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.618034$ of defining polynomial
Character	$\chi$	$=$	130.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.00000 q^{2} +7.70820 q^{3} +4.00000 q^{4} -5.00000 q^{5} -15.4164 q^{6} +17.8885 q^{7} -8.00000 q^{8} +32.4164 q^{9} +10.0000 q^{10} +38.1803 q^{11} +30.8328 q^{12} -13.0000 q^{13} -35.7771 q^{14} -38.5410 q^{15} +16.0000 q^{16} +69.7771 q^{17} -64.8328 q^{18} -152.928 q^{19} -20.0000 q^{20} +137.889 q^{21} -76.3607 q^{22} +167.125 q^{23} -61.6656 q^{24} +25.0000 q^{25} +26.0000 q^{26} +41.7508 q^{27} +71.5542 q^{28} +187.305 q^{29} +77.0820 q^{30} +91.7082 q^{31} -32.0000 q^{32} +294.302 q^{33} -139.554 q^{34} -89.4427 q^{35} +129.666 q^{36} -127.974 q^{37} +305.856 q^{38} -100.207 q^{39} +40.0000 q^{40} +239.941 q^{41} -275.777 q^{42} -203.485 q^{43} +152.721 q^{44} -162.082 q^{45} -334.249 q^{46} -333.495 q^{47} +123.331 q^{48} -23.0000 q^{49} -50.0000 q^{50} +537.856 q^{51} -52.0000 q^{52} -585.712 q^{53} -83.5016 q^{54} -190.902 q^{55} -143.108 q^{56} -1178.80 q^{57} -374.610 q^{58} -568.895 q^{59} -154.164 q^{60} +278.912 q^{61} -183.416 q^{62} +579.882 q^{63} +64.0000 q^{64} +65.0000 q^{65} -588.604 q^{66} -617.698 q^{67} +279.108 q^{68} +1288.23 q^{69} +178.885 q^{70} +319.656 q^{71} -259.331 q^{72} -241.574 q^{73} +255.947 q^{74} +192.705 q^{75} -611.712 q^{76} +682.991 q^{77} +200.413 q^{78} -60.4659 q^{79} -80.0000 q^{80} -553.420 q^{81} -479.882 q^{82} -1204.87 q^{83} +551.554 q^{84} -348.885 q^{85} +406.971 q^{86} +1443.78 q^{87} -305.443 q^{88} +557.437 q^{89} +324.164 q^{90} -232.551 q^{91} +668.498 q^{92} +706.906 q^{93} +666.991 q^{94} +764.640 q^{95} -246.663 q^{96} -241.895 q^{97} +46.0000 q^{98} +1237.67 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 4 q^{2} + 2 q^{3} + 8 q^{4} - 10 q^{5} - 4 q^{6} - 16 q^{8} + 38 q^{9} + 20 q^{10} + 54 q^{11} + 8 q^{12} - 26 q^{13} - 10 q^{15} + 32 q^{16} + 68 q^{17} - 76 q^{18} - 42 q^{19} - 40 q^{20} + 240 q^{21}+ \cdots + 1326 q^{99}+O(q^{100}) $ 2 * q - 4 * q^2 + 2 * q^3 + 8 * q^4 - 10 * q^5 - 4 * q^6 - 16 * q^8 + 38 * q^9 + 20 * q^10 + 54 * q^11 + 8 * q^12 - 26 * q^13 - 10 * q^15 + 32 * q^16 + 68 * q^17 - 76 * q^18 - 42 * q^19 - 40 * q^20 + 240 * q^21 - 108 * q^22 + 294 * q^23 - 16 * q^24 + 50 * q^25 + 52 * q^26 + 164 * q^27 + 312 * q^29 + 20 * q^30 + 170 * q^31 - 64 * q^32 + 204 * q^33 - 136 * q^34 + 152 * q^36 - 408 * q^37 + 84 * q^38 - 26 * q^39 + 80 * q^40 + 140 * q^41 - 480 * q^42 - 322 * q^43 + 216 * q^44 - 190 * q^45 - 588 * q^46 - 184 * q^47 + 32 * q^48 - 46 * q^49 - 100 * q^50 + 548 * q^51 - 104 * q^52 - 116 * q^53 - 328 * q^54 - 270 * q^55 - 1812 * q^57 - 624 * q^58 - 382 * q^59 - 40 * q^60 + 48 * q^61 - 340 * q^62 + 480 * q^63 + 128 * q^64 + 130 * q^65 - 408 * q^66 - 1620 * q^67 + 272 * q^68 + 564 * q^69 + 930 * q^71 - 304 * q^72 + 456 * q^73 + 816 * q^74 + 50 * q^75 - 168 * q^76 + 400 * q^77 + 52 * q^78 + 532 * q^79 - 160 * q^80 - 1402 * q^81 - 280 * q^82 - 120 * q^83 + 960 * q^84 - 340 * q^85 + 644 * q^86 + 732 * q^87 - 432 * q^88 + 292 * q^89 + 380 * q^90 + 1176 * q^92 + 260 * q^93 + 368 * q^94 + 210 * q^95 - 64 * q^96 - 1092 * q^97 + 92 * q^98 + 1326 * 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
$3$	7.70820	1.48344	0.741722	−	0.670707i	$-0.234009\pi$
$3$	7.70820	1.48344	0.741722	+	0.670707i	$0.234009\pi$
$4$	4.00000	0.500000
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	−15.4164	−1.04895
$7$	17.8885	0.965891	0.482945	−	0.875651i	$-0.339567\pi$
$7$	17.8885	0.965891	0.482945	+	0.875651i	$0.339567\pi$
$8$	−8.00000	−0.353553
$9$	32.4164	1.20061
$10$	10.0000	0.316228
$11$	38.1803	1.04653	0.523264	−	0.852171i	$-0.324714\pi$
$11$	38.1803	1.04653	0.523264	+	0.852171i	$0.324714\pi$
$12$	30.8328	0.741722
$13$	−13.0000	−0.277350
$13$	−13.0000	−0.277350
$14$	−35.7771	−0.682988
$15$	−38.5410	−0.663417
$16$	16.0000	0.250000
$17$	69.7771	0.995496	0.497748	−	0.867322i	$-0.334160\pi$
$17$	69.7771	0.995496	0.497748	+	0.867322i	$0.334160\pi$
$18$	−64.8328	−0.848958
$19$	−152.928	−1.84653	−0.923266	−	0.384162i	$-0.874490\pi$
$19$	−152.928	−1.84653	−0.923266	+	0.384162i	$0.874490\pi$
$20$	−20.0000	−0.223607
$21$	137.889	1.43285
$22$	−76.3607	−0.740007
$23$	167.125	1.51513	0.757563	−	0.652762i	$-0.226390\pi$
$23$	167.125	1.51513	0.757563	+	0.652762i	$0.226390\pi$
$24$	−61.6656	−0.524477
$25$	25.0000	0.200000
$26$	26.0000	0.196116
$27$	41.7508	0.297590
$28$	71.5542	0.482945
$29$	187.305	1.19937	0.599684	−	0.800237i	$-0.295293\pi$
$29$	187.305	1.19937	0.599684	+	0.800237i	$0.295293\pi$
$30$	77.0820	0.469106
$31$	91.7082	0.531332	0.265666	−	0.964065i	$-0.414408\pi$
$31$	91.7082	0.531332	0.265666	+	0.964065i	$0.414408\pi$
$32$	−32.0000	−0.176777
$33$	294.302	1.55247
$34$	−139.554	−0.703922
$35$	−89.4427	−0.431959
$36$	129.666	0.600304
$37$	−127.974	−0.568615	−0.284307	−	0.958733i	$-0.591764\pi$
$37$	−127.974	−0.568615	−0.284307	+	0.958733i	$0.591764\pi$
$38$	305.856	1.30569
$39$	−100.207	−0.411433
$40$	40.0000	0.158114
$41$	239.941	0.913964	0.456982	−	0.889476i	$-0.348930\pi$
$41$	239.941	0.913964	0.456982	+	0.889476i	$0.348930\pi$
$42$	−275.777	−1.01317
$43$	−203.485	−0.721656	−0.360828	−	0.932632i	$-0.617506\pi$
$43$	−203.485	−0.721656	−0.360828	+	0.932632i	$0.617506\pi$
$44$	152.721	0.523264
$45$	−162.082	−0.536928
$46$	−334.249	−1.07136
$47$	−333.495	−1.03501	−0.517503	−	0.855681i	$-0.673138\pi$
$47$	−333.495	−1.03501	−0.517503	+	0.855681i	$0.673138\pi$
$48$	123.331	0.370861
$49$	−23.0000	−0.0670554
$50$	−50.0000	−0.141421
$51$	537.856	1.47676
$52$	−52.0000	−0.138675
$53$	−585.712	−1.51800	−0.758998	−	0.651094i	$-0.774311\pi$
$53$	−585.712	−1.51800	−0.758998	+	0.651094i	$0.774311\pi$
$54$	−83.5016	−0.210428
$55$	−190.902	−0.468021
$56$	−143.108	−0.341494
$57$	−1178.80	−2.73923
$58$	−374.610	−0.848081
$59$	−568.895	−1.25532	−0.627660	−	0.778488i	$-0.715987\pi$
$59$	−568.895	−1.25532	−0.627660	+	0.778488i	$0.715987\pi$
$60$	−154.164	−0.331708
$61$	278.912	0.585426	0.292713	−	0.956200i	$-0.405442\pi$
$61$	278.912	0.585426	0.292713	+	0.956200i	$0.405442\pi$
$62$	−183.416	−0.375708
$63$	579.882	1.15966
$64$	64.0000	0.125000
$65$	65.0000	0.124035
$66$	−588.604	−1.09776
$67$	−617.698	−1.12633	−0.563163	−	0.826346i	$-0.690416\pi$
$67$	−617.698	−1.12633	−0.563163	+	0.826346i	$0.690416\pi$
$68$	279.108	0.497748
$69$	1288.23	2.24760
$70$	178.885	0.305441
$71$	319.656	0.534312	0.267156	−	0.963653i	$-0.413916\pi$
$71$	319.656	0.534312	0.267156	+	0.963653i	$0.413916\pi$
$72$	−259.331	−0.424479
$73$	−241.574	−0.387317	−0.193658	−	0.981069i	$-0.562035\pi$
$73$	−241.574	−0.387317	−0.193658	+	0.981069i	$0.562035\pi$
$74$	255.947	0.402071
$75$	192.705	0.296689
$76$	−611.712	−0.923266
$77$	682.991	1.01083
$78$	200.413	0.290927
$79$	−60.4659	−0.0861133	−0.0430566	−	0.999073i	$-0.513710\pi$
$79$	−60.4659	−0.0861133	−0.0430566	+	0.999073i	$0.513710\pi$
$80$	−80.0000	−0.111803
$81$	−553.420	−0.759149
$82$	−479.882	−0.646270
$83$	−1204.87	−1.59339	−0.796695	−	0.604382i	$-0.793420\pi$
$83$	−1204.87	−1.59339	−0.796695	+	0.604382i	$0.793420\pi$
$84$	551.554	0.716423
$85$	−348.885	−0.445199
$86$	406.971	0.510288
$87$	1443.78	1.77920
$88$	−305.443	−0.370003
$89$	557.437	0.663912	0.331956	−	0.943295i	$-0.392291\pi$
$89$	557.437	0.663912	0.331956	+	0.943295i	$0.392291\pi$
$90$	324.164	0.379665
$91$	−232.551	−0.267890
$92$	668.498	0.757563
$93$	706.906	0.788201
$94$	666.991	0.731860
$95$	764.640	0.825794
$96$	−246.663	−0.262238
$97$	−241.895	−0.253203	−0.126602	−	0.991954i	$-0.540407\pi$
$97$	−241.895	−0.253203	−0.126602	+	0.991954i	$0.540407\pi$
$98$	46.0000	0.0474153
$99$	1237.67	1.25647
$100$	100.000	0.100000
$101$	−283.102	−0.278908	−0.139454	−	0.990229i	$-0.544535\pi$
$101$	−283.102	−0.278908	−0.139454	+	0.990229i	$0.544535\pi$
$102$	−1075.71	−1.04423
$103$	1932.07	1.84828	0.924138	−	0.382059i	$-0.124785\pi$
$103$	1932.07	1.84828	0.924138	+	0.382059i	$0.124785\pi$
$104$	104.000	0.0980581
$105$	−689.443	−0.640788
$106$	1171.42	1.07338
$107$	−468.547	−0.423329	−0.211664	−	0.977342i	$-0.567888\pi$
$107$	−468.547	−0.423329	−0.211664	+	0.977342i	$0.567888\pi$
$108$	167.003	0.148795
$109$	−1504.37	−1.32195	−0.660977	−	0.750406i	$-0.729858\pi$
$109$	−1504.37	−1.32195	−0.660977	+	0.750406i	$0.729858\pi$
$110$	381.803	0.330941
$111$	−986.447	−0.843508
$112$	286.217	0.241473
$113$	−1311.97	−1.09221	−0.546105	−	0.837717i	$-0.683890\pi$
$113$	−1311.97	−1.09221	−0.546105	+	0.837717i	$0.683890\pi$
$114$	2357.60	1.93693
$115$	−835.623	−0.677585
$116$	749.220	0.599684
$117$	−421.413	−0.332989
$118$	1137.79	0.887645
$119$	1248.21	0.961540
$120$	308.328	0.234553
$121$	126.738	0.0952204
$122$	−557.823	−0.413959
$123$	1849.52	1.35581
$124$	366.833	0.265666
$125$	−125.000	−0.0894427
$126$	−1159.76	−0.820000
$127$	−1857.03	−1.29752	−0.648758	−	0.760994i	$-0.724711\pi$
$127$	−1857.03	−1.29752	−0.648758	+	0.760994i	$0.724711\pi$
$128$	−128.000	−0.0883883
$129$	−1568.51	−1.07054
$130$	−130.000	−0.0877058
$131$	2023.27	1.34942	0.674708	−	0.738084i	$-0.264269\pi$
$131$	2023.27	1.34942	0.674708	+	0.738084i	$0.264269\pi$
$132$	1177.21	0.776233
$133$	−2735.66	−1.78355
$134$	1235.40	0.796433
$135$	−208.754	−0.133086
$136$	−558.217	−0.351961
$137$	−1447.75	−0.902842	−0.451421	−	0.892311i	$-0.649083\pi$
$137$	−1447.75	−0.902842	−0.451421	+	0.892311i	$0.649083\pi$
$138$	−2576.46	−1.58930
$139$	1527.02	0.931802	0.465901	−	0.884837i	$-0.345730\pi$
$139$	1527.02	0.931802	0.465901	+	0.884837i	$0.345730\pi$
$140$	−357.771	−0.215980
$141$	−2570.65	−1.53537
$142$	−639.311	−0.377816
$143$	−496.344	−0.290255
$144$	518.663	0.300152
$145$	−936.525	−0.536373
$146$	483.149	0.273874
$147$	−177.289	−0.0994730
$148$	−511.895	−0.284307
$149$	2307.18	1.26854	0.634268	−	0.773114i	$-0.281302\pi$
$149$	2307.18	1.26854	0.634268	+	0.773114i	$0.281302\pi$
$150$	−385.410	−0.209791
$151$	1093.09	0.589104	0.294552	−	0.955635i	$-0.404830\pi$
$151$	1093.09	0.589104	0.294552	+	0.955635i	$0.404830\pi$
$152$	1223.42	0.652847
$153$	2261.92	1.19520
$154$	−1365.98	−0.714766
$155$	−458.541	−0.237619
$156$	−400.827	−0.205717
$157$	−348.046	−0.176924	−0.0884622	−	0.996080i	$-0.528195\pi$
$157$	−348.046	−0.176924	−0.0884622	+	0.996080i	$0.528195\pi$
$158$	120.932	0.0608913
$159$	−4514.79	−2.25186
$160$	160.000	0.0790569
$161$	2989.62	1.46345
$162$	1106.84	0.536799
$163$	2388.98	1.14797	0.573986	−	0.818865i	$-0.305396\pi$
$163$	2388.98	1.14797	0.573986	+	0.818865i	$0.305396\pi$
$164$	959.765	0.456982
$165$	−1471.51	−0.694284
$166$	2409.73	1.12670
$167$	4264.95	1.97624	0.988118	−	0.153695i	$-0.0491173\pi$
$167$	4264.95	1.97624	0.988118	+	0.153695i	$0.0491173\pi$
$168$	−1103.11	−0.506587
$169$	169.000	0.0769231
$170$	697.771	0.314803
$171$	−4957.38	−2.21696
$172$	−813.941	−0.360828
$173$	2871.68	1.26202	0.631011	−	0.775774i	$-0.282640\pi$
$173$	2871.68	1.26202	0.631011	+	0.775774i	$0.282640\pi$
$174$	−2887.57	−1.25808
$175$	447.214	0.193178
$176$	610.885	0.261632
$177$	−4385.16	−1.86220
$178$	−1114.87	−0.469457
$179$	982.845	0.410398	0.205199	−	0.978720i	$-0.434216\pi$
$179$	982.845	0.410398	0.205199	+	0.978720i	$0.434216\pi$
$180$	−648.328	−0.268464
$181$	3342.85	1.37277	0.686386	−	0.727237i	$-0.259196\pi$
$181$	3342.85	1.37277	0.686386	+	0.727237i	$0.259196\pi$
$182$	465.102	0.189427
$183$	2149.91	0.868447
$184$	−1337.00	−0.535678
$185$	639.868	0.254292
$186$	−1413.81	−0.557342
$187$	2664.11	1.04181
$188$	−1333.98	−0.517503
$189$	746.861	0.287440
$190$	−1529.28	−0.583924
$191$	16.1052	0.00610123	0.00305061	−	0.999995i	$-0.499029\pi$
$191$	16.1052	0.00610123	0.00305061	+	0.999995i	$0.499029\pi$
$192$	493.325	0.185431
$193$	−529.003	−0.197298	−0.0986489	−	0.995122i	$-0.531452\pi$
$193$	−529.003	−0.197298	−0.0986489	+	0.995122i	$0.531452\pi$
$194$	483.790	0.179042
$195$	501.033	0.183999
$196$	−92.0000	−0.0335277
$197$	−4716.72	−1.70585	−0.852924	−	0.522034i	$-0.825173\pi$
$197$	−4716.72	−1.70585	−0.852924	+	0.522034i	$0.825173\pi$
$198$	−2475.34	−0.888458
$199$	−4072.65	−1.45077	−0.725383	−	0.688346i	$-0.758337\pi$
$199$	−4072.65	−1.45077	−0.725383	+	0.688346i	$0.758337\pi$
$200$	−200.000	−0.0707107
$201$	−4761.34	−1.67084
$202$	566.204	0.197218
$203$	3350.61	1.15846
$204$	2151.42	0.738381
$205$	−1199.71	−0.408737
$206$	−3864.14	−1.30693
$207$	5417.58	1.81907
$208$	−208.000	−0.0693375
$209$	−5838.84	−1.93245
$210$	1378.89	0.453105
$211$	−4689.58	−1.53006	−0.765032	−	0.643992i	$-0.777277\pi$
$211$	−4689.58	−1.53006	−0.765032	+	0.643992i	$0.777277\pi$
$212$	−2342.85	−0.758998
$213$	2463.97	0.792622
$214$	937.094	0.299339
$215$	1017.43	0.322734
$216$	−334.006	−0.105214
$217$	1640.53	0.513208
$218$	3008.75	0.934762
$219$	−1862.10	−0.574563
$220$	−763.607	−0.234011
$221$	−907.102	−0.276101
$222$	1972.89	0.596451
$223$	2158.45	0.648164	0.324082	−	0.946029i	$-0.394945\pi$
$223$	2158.45	0.648164	0.324082	+	0.946029i	$0.394945\pi$
$224$	−572.433	−0.170747
$225$	810.410	0.240122
$226$	2623.94	0.772309
$227$	4362.74	1.27562	0.637808	−	0.770195i	$-0.279841\pi$
$227$	4362.74	1.27562	0.637808	+	0.770195i	$0.279841\pi$
$228$	−4715.20	−1.36961
$229$	−1071.83	−0.309296	−0.154648	−	0.987970i	$-0.549424\pi$
$229$	−1071.83	−0.309296	−0.154648	+	0.987970i	$0.549424\pi$
$230$	1671.25	0.479125
$231$	5264.63	1.49951
$232$	−1498.44	−0.424040
$233$	1472.88	0.414128	0.207064	−	0.978327i	$-0.433609\pi$
$233$	1472.88	0.414128	0.207064	+	0.978327i	$0.433609\pi$
$234$	842.827	0.235459
$235$	1667.48	0.462869
$236$	−2275.58	−0.627660
$237$	−466.084	−0.127744
$238$	−2496.42	−0.679912
$239$	−2380.83	−0.644363	−0.322182	−	0.946678i	$-0.604416\pi$
$239$	−2380.83	−0.644363	−0.322182	+	0.946678i	$0.604416\pi$
$240$	−616.656	−0.165854
$241$	4376.77	1.16984	0.584922	−	0.811090i	$-0.301125\pi$
$241$	4376.77	1.16984	0.584922	+	0.811090i	$0.301125\pi$
$242$	−253.477	−0.0673310
$243$	−5393.14	−1.42375
$244$	1115.65	0.292713
$245$	115.000	0.0299881
$246$	−3699.03	−0.958706
$247$	1988.06	0.512136
$248$	−733.666	−0.187854
$249$	−9287.36	−2.36370
$250$	250.000	0.0632456
$251$	1087.80	0.273551	0.136776	−	0.990602i	$-0.456326\pi$
$251$	1087.80	0.273551	0.136776	+	0.990602i	$0.456326\pi$
$252$	2319.53	0.579828
$253$	6380.87	1.58562
$254$	3714.06	0.917483
$255$	−2689.28	−0.660428
$256$	256.000	0.0625000
$257$	−5112.49	−1.24089	−0.620444	−	0.784251i	$-0.713047\pi$
$257$	−5112.49	−1.24089	−0.620444	+	0.784251i	$0.713047\pi$
$258$	3137.01	0.756984
$259$	−2289.26	−0.549220
$260$	260.000	0.0620174
$261$	6071.75	1.43997
$262$	−4046.53	−0.954182
$263$	−3790.88	−0.888805	−0.444402	−	0.895827i	$-0.646584\pi$
$263$	−3790.88	−0.888805	−0.444402	+	0.895827i	$0.646584\pi$
$264$	−2354.41	−0.548880
$265$	2928.56	0.678868
$266$	5471.32	1.26116
$267$	4296.83	0.984876
$268$	−2470.79	−0.563163
$269$	3523.30	0.798585	0.399293	−	0.916824i	$-0.369256\pi$
$269$	3523.30	0.798585	0.399293	+	0.916824i	$0.369256\pi$
$270$	417.508	0.0941063
$271$	4254.59	0.953682	0.476841	−	0.878990i	$-0.341782\pi$
$271$	4254.59	0.953682	0.476841	+	0.878990i	$0.341782\pi$
$272$	1116.43	0.248874
$273$	−1792.55	−0.397400
$274$	2895.49	0.638405
$275$	954.508	0.209306
$276$	5152.92	1.12380
$277$	−1312.77	−0.284754	−0.142377	−	0.989813i	$-0.545474\pi$
$277$	−1312.77	−0.284754	−0.142377	+	0.989813i	$0.545474\pi$
$278$	−3054.05	−0.658883
$279$	2972.85	0.637921
$280$	715.542	0.152721
$281$	3112.38	0.660743	0.330372	−	0.943851i	$-0.392826\pi$
$281$	3112.38	0.660743	0.330372	+	0.943851i	$0.392826\pi$
$282$	5141.30	1.08567
$283$	−3983.53	−0.836736	−0.418368	−	0.908278i	$-0.637398\pi$
$283$	−3983.53	−0.836736	−0.418368	+	0.908278i	$0.637398\pi$
$284$	1278.62	0.267156
$285$	5894.00	1.22502
$286$	992.689	0.205241
$287$	4292.20	0.882789
$288$	−1037.33	−0.212239
$289$	−44.1580	−0.00898800
$290$	1873.05	0.379273
$291$	−1864.57	−0.375613
$292$	−966.297	−0.193658
$293$	6710.42	1.33798	0.668988	−	0.743273i	$-0.266728\pi$
$293$	6710.42	1.33798	0.668988	+	0.743273i	$0.266728\pi$
$294$	354.577	0.0703380
$295$	2844.48	0.561396
$296$	1023.79	0.201036
$297$	1594.06	0.311437
$298$	−4614.37	−0.896990
$299$	−2172.62	−0.420220
$300$	770.820	0.148344
$301$	−3640.06	−0.697041
$302$	−2186.19	−0.416559
$303$	−2182.21	−0.413745
$304$	−2446.85	−0.461633
$305$	−1394.56	−0.261810
$306$	−4523.85	−0.845134
$307$	3883.81	0.722023	0.361011	−	0.932561i	$-0.382432\pi$
$307$	3883.81	0.722023	0.361011	+	0.932561i	$0.382432\pi$
$308$	2731.96	0.505416
$309$	14892.8	2.74181
$310$	917.082	0.168022
$311$	−9188.01	−1.67525	−0.837627	−	0.546242i	$-0.816058\pi$
$311$	−9188.01	−1.67525	−0.837627	+	0.546242i	$0.816058\pi$
$312$	801.653	0.145464
$313$	−7475.45	−1.34996	−0.674980	−	0.737836i	$-0.735848\pi$
$313$	−7475.45	−1.34996	−0.674980	+	0.737836i	$0.735848\pi$
$314$	696.093	0.125104
$315$	−2899.41	−0.518614
$316$	−241.864	−0.0430566
$317$	4668.43	0.827145	0.413572	−	0.910471i	$-0.364281\pi$
$317$	4668.43	0.827145	0.413572	+	0.910471i	$0.364281\pi$
$318$	9029.58	1.59231
$319$	7151.37	1.25517
$320$	−320.000	−0.0559017
$321$	−3611.66	−0.627985
$322$	−5979.23	−1.03481
$323$	−10670.9	−1.83821
$324$	−2213.68	−0.379574
$325$	−325.000	−0.0554700
$326$	−4777.96	−0.811738
$327$	−11596.0	−1.96104
$328$	−1919.53	−0.323135
$329$	−5965.75	−0.999703
$330$	2943.02	0.490933
$331$	1544.67	0.256503	0.128252	−	0.991742i	$-0.459063\pi$
$331$	1544.67	0.256503	0.128252	+	0.991742i	$0.459063\pi$
$332$	−4819.47	−0.796695
$333$	−4148.45	−0.682683
$334$	−8529.89	−1.39741
$335$	3088.49	0.503708
$336$	2206.22	0.358211
$337$	3788.99	0.612461	0.306231	−	0.951957i	$-0.400932\pi$
$337$	3788.99	0.612461	0.306231	+	0.951957i	$0.400932\pi$
$338$	−338.000	−0.0543928
$339$	−10112.9	−1.62023
$340$	−1395.54	−0.222600
$341$	3501.45	0.556053
$342$	9914.75	1.56763
$343$	−6547.21	−1.03066
$344$	1627.88	0.255144
$345$	−6441.15	−1.00516
$346$	−5743.36	−0.892385
$347$	4545.59	0.703227	0.351614	−	0.936145i	$-0.385633\pi$
$347$	4545.59	0.703227	0.351614	+	0.936145i	$0.385633\pi$
$348$	5775.14	0.889598
$349$	1545.04	0.236975	0.118487	−	0.992956i	$-0.462195\pi$
$349$	1545.04	0.236975	0.118487	+	0.992956i	$0.462195\pi$
$350$	−894.427	−0.136598
$351$	−542.760	−0.0825367
$352$	−1221.77	−0.185002
$353$	−4271.28	−0.644015	−0.322008	−	0.946737i	$-0.604358\pi$
$353$	−4271.28	−0.644015	−0.322008	+	0.946737i	$0.604358\pi$
$354$	8770.32	1.31677
$355$	−1598.28	−0.238952
$356$	2229.75	0.331956
$357$	9621.46	1.42639
$358$	−1965.69	−0.290195
$359$	1106.68	0.162697	0.0813484	−	0.996686i	$-0.474077\pi$
$359$	1106.68	0.162697	0.0813484	+	0.996686i	$0.474077\pi$
$360$	1296.66	0.189833
$361$	16528.0	2.40968
$362$	−6685.69	−0.970697
$363$	976.925	0.141254
$364$	−930.204	−0.133945
$365$	1207.87	0.173213
$366$	−4299.82	−0.614085
$367$	83.1275	0.0118235	0.00591175	−	0.999983i	$-0.498118\pi$
$367$	83.1275	0.0118235	0.00591175	+	0.999983i	$0.498118\pi$
$368$	2673.99	0.378781
$369$	7778.03	1.09731
$370$	−1279.74	−0.179812
$371$	−10477.5	−1.46622
$372$	2827.62	0.394100
$373$	2509.17	0.348310	0.174155	−	0.984718i	$-0.444281\pi$
$373$	2509.17	0.348310	0.174155	+	0.984718i	$0.444281\pi$
$374$	−5328.23	−0.736674
$375$	−963.525	−0.132683
$376$	2667.96	0.365930
$377$	−2434.96	−0.332645
$378$	−1493.72	−0.203251
$379$	5959.76	0.807738	0.403869	−	0.914817i	$-0.367665\pi$
$379$	5959.76	0.807738	0.403869	+	0.914817i	$0.367665\pi$
$380$	3058.56	0.412897
$381$	−14314.4	−1.92479
$382$	−32.2105	−0.00431422
$383$	−2191.58	−0.292388	−0.146194	−	0.989256i	$-0.546702\pi$
$383$	−2191.58	−0.292388	−0.146194	+	0.989256i	$0.546702\pi$
$384$	−986.650	−0.131119
$385$	−3414.95	−0.452058
$386$	1058.01	0.139511
$387$	−6596.26	−0.866426
$388$	−967.579	−0.126602
$389$	−4157.52	−0.541889	−0.270944	−	0.962595i	$-0.587336\pi$
$389$	−4157.52	−0.541889	−0.270944	+	0.962595i	$0.587336\pi$
$390$	−1002.07	−0.130107
$391$	11661.5	1.50830
$392$	184.000	0.0237077
$393$	15595.7	2.00178
$394$	9433.44	1.20622
$395$	302.330	0.0385110
$396$	4950.68	0.628235
$397$	−13622.1	−1.72210	−0.861048	−	0.508524i	$-0.830191\pi$
$397$	−13622.1	−1.72210	−0.861048	+	0.508524i	$0.830191\pi$
$398$	8145.29	1.02585
$399$	−21087.0	−2.64579
$400$	400.000	0.0500000
$401$	−1679.41	−0.209142	−0.104571	−	0.994517i	$-0.533347\pi$
$401$	−1679.41	−0.209142	−0.104571	+	0.994517i	$0.533347\pi$
$402$	9522.69	1.18146
$403$	−1192.21	−0.147365
$404$	−1132.41	−0.139454
$405$	2767.10	0.339502
$406$	−6701.23	−0.819153
$407$	−4886.08	−0.595071
$408$	−4302.85	−0.522115
$409$	−15460.6	−1.86914	−0.934569	−	0.355781i	$-0.884215\pi$
$409$	−15460.6	−1.86914	−0.934569	+	0.355781i	$0.884215\pi$
$410$	2399.41	0.289021
$411$	−11159.5	−1.33932
$412$	7728.28	0.924138
$413$	−10176.7	−1.21250
$414$	−10835.2	−1.28628
$415$	6024.33	0.712585
$416$	416.000	0.0490290
$417$	11770.6	1.38228
$418$	11677.7	1.36645
$419$	−13864.6	−1.61654	−0.808271	−	0.588811i	$-0.799596\pi$
$419$	−13864.6	−1.61654	−0.808271	+	0.588811i	$0.799596\pi$
$420$	−2757.77	−0.320394
$421$	−3626.36	−0.419806	−0.209903	−	0.977722i	$-0.567315\pi$
$421$	−3626.36	−0.419806	−0.209903	+	0.977722i	$0.567315\pi$
$422$	9379.15	1.08192
$423$	−10810.7	−1.24264
$424$	4685.70	0.536692
$425$	1744.43	0.199099
$426$	−4927.94	−0.560468
$427$	4989.33	0.565458
$428$	−1874.19	−0.211664
$429$	−3825.92	−0.430577
$430$	−2034.85	−0.228208
$431$	13189.5	1.47405	0.737023	−	0.675868i	$-0.236231\pi$
$431$	13189.5	1.47405	0.737023	+	0.675868i	$0.236231\pi$
$432$	668.012	0.0743976
$433$	−3061.68	−0.339804	−0.169902	−	0.985461i	$-0.554345\pi$
$433$	−3061.68	−0.339804	−0.169902	+	0.985461i	$0.554345\pi$
$434$	−3281.05	−0.362893
$435$	−7218.92	−0.795680
$436$	−6017.50	−0.660977
$437$	−25558.0	−2.79773
$438$	3724.21	0.406277
$439$	12751.4	1.38632	0.693158	−	0.720786i	$-0.256219\pi$
$439$	12751.4	1.38632	0.693158	+	0.720786i	$0.256219\pi$
$440$	1527.21	0.165471
$441$	−745.577	−0.0805072
$442$	1814.20	0.195233
$443$	−6375.24	−0.683740	−0.341870	−	0.939747i	$-0.611060\pi$
$443$	−6375.24	−0.683740	−0.341870	+	0.939747i	$0.611060\pi$
$444$	−3945.79	−0.421754
$445$	−2787.18	−0.296910
$446$	−4316.90	−0.458321
$447$	17784.2	1.88180
$448$	1144.87	0.120736
$449$	14821.9	1.55789	0.778943	−	0.627095i	$-0.215756\pi$
$449$	14821.9	1.55789	0.778943	+	0.627095i	$0.215756\pi$
$450$	−1620.82	−0.169792
$451$	9161.04	0.956488
$452$	−5247.88	−0.546105
$453$	8425.79	0.873903
$454$	−8725.47	−0.901997
$455$	1162.76	0.119804
$456$	9430.40	0.968463
$457$	9791.53	1.00225	0.501125	−	0.865375i	$-0.332920\pi$
$457$	9791.53	1.00225	0.501125	+	0.865375i	$0.332920\pi$
$458$	2143.67	0.218705
$459$	2913.25	0.296250
$460$	−3342.49	−0.338792
$461$	7532.58	0.761013	0.380507	−	0.924778i	$-0.375750\pi$
$461$	7532.58	0.761013	0.380507	+	0.924778i	$0.375750\pi$
$462$	−10529.3	−1.06032
$463$	2045.90	0.205359	0.102679	−	0.994715i	$-0.467258\pi$
$463$	2045.90	0.205359	0.102679	+	0.994715i	$0.467258\pi$
$464$	2996.88	0.299842
$465$	−3534.53	−0.352494
$466$	−2945.77	−0.292832
$467$	17289.0	1.71315	0.856574	−	0.516023i	$-0.172588\pi$
$467$	17289.0	1.71315	0.856574	+	0.516023i	$0.172588\pi$
$468$	−1685.65	−0.166494
$469$	−11049.7	−1.08791
$470$	−3334.95	−0.327298
$471$	−2682.81	−0.262458
$472$	4551.16	0.443823
$473$	−7769.14	−0.755233
$474$	932.167	0.0903288
$475$	−3823.20	−0.369306
$476$	4992.84	0.480770
$477$	−18986.7	−1.82252
$478$	4761.65	0.455634
$479$	14488.7	1.38206	0.691028	−	0.722828i	$-0.257158\pi$
$479$	14488.7	1.38206	0.691028	+	0.722828i	$0.257158\pi$
$480$	1233.31	0.117277
$481$	1663.66	0.157705
$482$	−8753.54	−0.827205
$483$	23044.6	2.17094
$484$	506.953	0.0476102
$485$	1209.47	0.113236
$486$	10786.3	1.00674
$487$	−3451.25	−0.321132	−0.160566	−	0.987025i	$-0.551332\pi$
$487$	−3451.25	−0.321132	−0.160566	+	0.987025i	$0.551332\pi$
$488$	−2231.29	−0.206979
$489$	18414.7	1.70295
$490$	−230.000	−0.0212048
$491$	−20328.9	−1.86849	−0.934246	−	0.356630i	$-0.883926\pi$
$491$	−20328.9	−1.86849	−0.934246	+	0.356630i	$0.883926\pi$
$492$	7398.06	0.677907
$493$	13069.6	1.19397
$494$	−3976.13	−0.362135
$495$	−6188.35	−0.561910
$496$	1467.33	0.132833
$497$	5718.17	0.516087
$498$	18574.7	1.67139
$499$	−4756.36	−0.426701	−0.213351	−	0.976976i	$-0.568438\pi$
$499$	−4756.36	−0.426701	−0.213351	+	0.976976i	$0.568438\pi$
$500$	−500.000	−0.0447214
$501$	32875.1	2.93164
$502$	−2175.60	−0.193430
$503$	18875.2	1.67317	0.836583	−	0.547840i	$-0.184550\pi$
$503$	18875.2	1.67317	0.836583	+	0.547840i	$0.184550\pi$
$504$	−4639.06	−0.410000
$505$	1415.51	0.124731
$506$	−12761.7	−1.12120
$507$	1302.69	0.114111
$508$	−7428.11	−0.648758
$509$	13108.3	1.14148	0.570740	−	0.821131i	$-0.306657\pi$
$509$	13108.3	1.14148	0.570740	+	0.821131i	$0.306657\pi$
$510$	5378.56	0.466993
$511$	−4321.41	−0.374106
$512$	−512.000	−0.0441942
$513$	−6384.86	−0.549510
$514$	10225.0	0.877440
$515$	−9660.34	−0.826574
$516$	−6274.02	−0.535268
$517$	−12733.0	−1.08316
$518$	4578.53	0.388357
$519$	22135.5	1.87214
$520$	−520.000	−0.0438529
$521$	−1065.58	−0.0896047	−0.0448023	−	0.998996i	$-0.514266\pi$
$521$	−1065.58	−0.0896047	−0.0448023	+	0.998996i	$0.514266\pi$
$522$	−12143.5	−1.01821
$523$	11752.4	0.982591	0.491296	−	0.870993i	$-0.336524\pi$
$523$	11752.4	0.982591	0.491296	+	0.870993i	$0.336524\pi$
$524$	8093.06	0.674708
$525$	3447.21	0.286569
$526$	7581.76	0.628480
$527$	6399.13	0.528938
$528$	4708.83	0.388116
$529$	15763.6	1.29561
$530$	−5857.12	−0.480032
$531$	−18441.5	−1.50715
$532$	−10942.6	−0.891774
$533$	−3119.24	−0.253488
$534$	−8593.67	−0.696413
$535$	2342.74	0.189318
$536$	4941.59	0.398216
$537$	7575.97	0.608803
$538$	−7046.60	−0.564685
$539$	−878.148	−0.0701753
$540$	−835.016	−0.0665432
$541$	−11910.5	−0.946532	−0.473266	−	0.880920i	$-0.656925\pi$
$541$	−11910.5	−0.946532	−0.473266	+	0.880920i	$0.656925\pi$
$542$	−8509.17	−0.674355
$543$	25767.3	2.03643
$544$	−2232.87	−0.175980
$545$	7521.87	0.591196
$546$	3585.10	0.281004
$547$	−22283.2	−1.74180	−0.870898	−	0.491464i	$-0.836462\pi$
$547$	−22283.2	−1.74180	−0.870898	+	0.491464i	$0.836462\pi$
$548$	−5790.98	−0.451421
$549$	9041.32	0.702867
$550$	−1909.02	−0.148001
$551$	−28644.2	−2.21467
$552$	−10305.8	−0.794648
$553$	−1081.65	−0.0831760
$554$	2625.54	0.201351
$555$	4932.24	0.377228
$556$	6108.09	0.465901
$557$	8012.19	0.609493	0.304746	−	0.952434i	$-0.401428\pi$
$557$	8012.19	0.609493	0.304746	+	0.952434i	$0.401428\pi$
$558$	−5945.70	−0.451078
$559$	2645.31	0.200151
$560$	−1431.08	−0.107990
$561$	20535.5	1.54547
$562$	−6224.76	−0.467216
$563$	−1086.28	−0.0813167	−0.0406583	−	0.999173i	$-0.512946\pi$
$563$	−1086.28	−0.0813167	−0.0406583	+	0.999173i	$0.512946\pi$
$564$	−10282.6	−0.767687
$565$	6559.84	0.488451
$566$	7967.06	0.591661
$567$	−9899.87	−0.733255
$568$	−2557.24	−0.188908
$569$	1084.26	0.0798850	0.0399425	−	0.999202i	$-0.487283\pi$
$569$	1084.26	0.0798850	0.0399425	+	0.999202i	$0.487283\pi$
$570$	−11788.0	−0.866219
$571$	14671.2	1.07525	0.537627	−	0.843183i	$-0.319321\pi$
$571$	14671.2	1.07525	0.537627	+	0.843183i	$0.319321\pi$
$572$	−1985.38	−0.145127
$573$	124.143	0.00905083
$574$	−8584.40	−0.624226
$575$	4178.12	0.303025
$576$	2074.65	0.150076
$577$	25311.7	1.82624	0.913118	−	0.407696i	$-0.133668\pi$
$577$	25311.7	1.82624	0.913118	+	0.407696i	$0.133668\pi$
$578$	88.3161	0.00635548
$579$	−4077.66	−0.292680
$580$	−3746.10	−0.268187
$581$	−21553.3	−1.53904
$582$	3729.15	0.265598
$583$	−22362.7	−1.58862
$584$	1932.59	0.136937
$585$	2107.07	0.148917
$586$	−13420.8	−0.946092
$587$	−11336.2	−0.797093	−0.398546	−	0.917148i	$-0.630485\pi$
$587$	−11336.2	−0.797093	−0.398546	+	0.917148i	$0.630485\pi$
$588$	−709.155	−0.0497365
$589$	−14024.8	−0.981120
$590$	−5688.95	−0.396967
$591$	−36357.4	−2.53053
$592$	−2047.58	−0.142154
$593$	−9575.02	−0.663067	−0.331534	−	0.943443i	$-0.607566\pi$
$593$	−9575.02	−0.663067	−0.331534	+	0.943443i	$0.607566\pi$
$594$	−3188.12	−0.220219
$595$	−6241.05	−0.430014
$596$	9228.73	0.634268
$597$	−31392.8	−2.15213
$598$	4345.24	0.297141
$599$	15495.6	1.05698	0.528491	−	0.848939i	$-0.322758\pi$
$599$	15495.6	1.05698	0.528491	+	0.848939i	$0.322758\pi$
$600$	−1541.64	−0.104895
$601$	11100.9	0.753433	0.376717	−	0.926329i	$-0.377053\pi$
$601$	11100.9	0.753433	0.376717	+	0.926329i	$0.377053\pi$
$602$	7280.11	0.492882
$603$	−20023.6	−1.35228
$604$	4372.37	0.294552
$605$	−633.692	−0.0425839
$606$	4364.42	0.292562
$607$	25928.7	1.73379	0.866897	−	0.498487i	$-0.166111\pi$
$607$	25928.7	1.73379	0.866897	+	0.498487i	$0.166111\pi$
$608$	4893.70	0.326424
$609$	25827.2	1.71851
$610$	2789.12	0.185128
$611$	4335.44	0.287059
$612$	9047.69	0.597600
$613$	−14208.7	−0.936188	−0.468094	−	0.883679i	$-0.655059\pi$
$613$	−14208.7	−0.936188	−0.468094	+	0.883679i	$0.655059\pi$
$614$	−7767.63	−0.510547
$615$	−9247.58	−0.606339
$616$	−5463.93	−0.357383
$617$	−21425.7	−1.39800	−0.699000	−	0.715121i	$-0.746371\pi$
$617$	−21425.7	−1.39800	−0.699000	+	0.715121i	$0.746371\pi$
$618$	−29785.6	−1.93876
$619$	22816.0	1.48151	0.740755	−	0.671776i	$-0.234468\pi$
$619$	22816.0	1.48151	0.740755	+	0.671776i	$0.234468\pi$
$620$	−1834.16	−0.118809
$621$	6977.58	0.450887
$622$	18376.0	1.18458
$623$	9971.73	0.641266
$624$	−1603.31	−0.102858
$625$	625.000	0.0400000
$626$	14950.9	0.954565
$627$	−45007.0	−2.86668
$628$	−1392.19	−0.0884622
$629$	−8929.63	−0.566054
$630$	5798.82	0.366715
$631$	27919.5	1.76142	0.880710	−	0.473656i	$-0.157066\pi$
$631$	27919.5	1.76142	0.880710	+	0.473656i	$0.157066\pi$
$632$	483.727	0.0304456
$633$	−36148.2	−2.26977
$634$	−9336.85	−0.584880
$635$	9285.14	0.580267
$636$	−18059.2	−1.12593
$637$	299.000	0.0185978
$638$	−14302.7	−0.887540
$639$	10362.1	0.641499
$640$	640.000	0.0395285
$641$	−27914.7	−1.72007	−0.860033	−	0.510238i	$-0.829557\pi$
$641$	−27914.7	−1.72007	−0.860033	+	0.510238i	$0.829557\pi$
$642$	7223.32	0.444052
$643$	−25491.8	−1.56345	−0.781726	−	0.623622i	$-0.785661\pi$
$643$	−25491.8	−1.56345	−0.781726	+	0.623622i	$0.785661\pi$
$644$	11958.5	0.731723
$645$	7842.53	0.478759
$646$	21341.7	1.29981
$647$	−30447.3	−1.85009	−0.925045	−	0.379857i	$-0.875973\pi$
$647$	−30447.3	−1.85009	−0.925045	+	0.379857i	$0.875973\pi$
$648$	4427.36	0.268400
$649$	−21720.6	−1.31373
$650$	650.000	0.0392232
$651$	12645.5	0.761316
$652$	9555.92	0.573986
$653$	14357.5	0.860418	0.430209	−	0.902729i	$-0.358440\pi$
$653$	14357.5	0.860418	0.430209	+	0.902729i	$0.358440\pi$
$654$	23192.1	1.38667
$655$	−10116.3	−0.603478
$656$	3839.06	0.228491
$657$	−7830.97	−0.465016
$658$	11931.5	0.706897
$659$	−7815.23	−0.461970	−0.230985	−	0.972957i	$-0.574195\pi$
$659$	−7815.23	−0.461970	−0.230985	+	0.972957i	$0.574195\pi$
$660$	−5886.04	−0.347142
$661$	−16755.3	−0.985938	−0.492969	−	0.870047i	$-0.664088\pi$
$661$	−16755.3	−0.985938	−0.492969	+	0.870047i	$0.664088\pi$
$662$	−3089.34	−0.181375
$663$	−6992.13	−0.409580
$664$	9638.93	0.563348
$665$	13678.3	0.797626
$666$	8296.89	0.482730
$667$	31303.3	1.81719
$668$	17059.8	0.988118
$669$	16637.8	0.961516
$670$	−6176.98	−0.356176
$671$	10648.9	0.612665
$672$	−4412.43	−0.253294
$673$	−15704.8	−0.899517	−0.449758	−	0.893150i	$-0.648490\pi$
$673$	−15704.8	−0.899517	−0.449758	+	0.893150i	$0.648490\pi$
$674$	−7577.98	−0.433076
$675$	1043.77	0.0595181
$676$	676.000	0.0384615
$677$	12623.1	0.716608	0.358304	−	0.933605i	$-0.383355\pi$
$677$	12623.1	0.716608	0.358304	+	0.933605i	$0.383355\pi$
$678$	20225.8	1.14568
$679$	−4327.14	−0.244566
$680$	2791.08	0.157402
$681$	33628.9	1.89231
$682$	−7002.90	−0.393189
$683$	6822.45	0.382216	0.191108	−	0.981569i	$-0.438792\pi$
$683$	6822.45	0.382216	0.191108	+	0.981569i	$0.438792\pi$
$684$	−19829.5	−1.10848
$685$	7238.73	0.403763
$686$	13094.4	0.728786
$687$	−8261.91	−0.458823
$688$	−3255.76	−0.180414
$689$	7614.26	0.421016
$690$	12882.3	0.710755
$691$	−26024.5	−1.43273	−0.716365	−	0.697725i	$-0.754196\pi$
$691$	−26024.5	−1.43273	−0.716365	+	0.697725i	$0.754196\pi$
$692$	11486.7	0.631011
$693$	22140.1	1.21361
$694$	−9091.17	−0.497257
$695$	−7635.12	−0.416714
$696$	−11550.3	−0.629040
$697$	16742.4	0.909847
$698$	−3090.09	−0.167567
$699$	11353.3	0.614335
$700$	1788.85	0.0965891
$701$	−3921.15	−0.211269	−0.105635	−	0.994405i	$-0.533687\pi$
$701$	−3921.15	−0.211269	−0.105635	+	0.994405i	$0.533687\pi$
$702$	1085.52	0.0583623
$703$	19570.8	1.04996
$704$	2443.54	0.130816
$705$	12853.3	0.686640
$706$	8542.56	0.455387
$707$	−5064.29	−0.269395
$708$	−17540.6	−0.931099
$709$	−28145.7	−1.49088	−0.745440	−	0.666572i	$-0.767761\pi$
$709$	−28145.7	−1.49088	−0.745440	+	0.666572i	$0.767761\pi$
$710$	3196.56	0.168964
$711$	−1960.09	−0.103388
$712$	−4459.49	−0.234728
$713$	15326.7	0.805034
$714$	−19242.9	−1.00861
$715$	2481.72	0.129806
$716$	3931.38	0.205199
$717$	−18351.9	−0.955877
$718$	−2213.35	−0.115044
$719$	24216.6	1.25609	0.628043	−	0.778179i	$-0.283856\pi$
$719$	24216.6	1.25609	0.628043	+	0.778179i	$0.283856\pi$
$720$	−2593.31	−0.134232
$721$	34561.9	1.78523
$722$	−33056.0	−1.70390
$723$	33737.0	1.73540
$724$	13371.4	0.686386
$725$	4682.62	0.239873
$726$	−1953.85	−0.0998818
$727$	−12683.1	−0.647027	−0.323513	−	0.946224i	$-0.604864\pi$
$727$	−12683.1	−0.647027	−0.323513	+	0.946224i	$0.604864\pi$
$728$	1860.41	0.0947134
$729$	−26629.1	−1.35290
$730$	−2415.74	−0.122480
$731$	−14198.6	−0.718406
$732$	8599.63	0.434224
$733$	−19816.4	−0.998546	−0.499273	−	0.866445i	$-0.666400\pi$
$733$	−19816.4	−0.998546	−0.499273	+	0.866445i	$0.666400\pi$
$734$	−166.255	−0.00836047
$735$	886.443	0.0444857
$736$	−5347.99	−0.267839
$737$	−23583.9	−1.17873
$738$	−15556.1	−0.775917
$739$	19586.7	0.974976	0.487488	−	0.873130i	$-0.337913\pi$
$739$	19586.7	0.974976	0.487488	+	0.873130i	$0.337913\pi$
$740$	2559.47	0.127146
$741$	15324.4	0.759725
$742$	20955.1	1.03677
$743$	12246.4	0.604680	0.302340	−	0.953200i	$-0.402232\pi$
$743$	12246.4	0.604680	0.302340	+	0.953200i	$0.402232\pi$
$744$	−5655.24	−0.278671
$745$	−11535.9	−0.567306
$746$	−5018.33	−0.246293
$747$	−39057.5	−1.91304
$748$	10656.5	0.520907
$749$	−8381.63	−0.408889
$750$	1927.05	0.0938213
$751$	−6566.74	−0.319073	−0.159537	−	0.987192i	$-0.551000\pi$
$751$	−6566.74	−0.319073	−0.159537	+	0.987192i	$0.551000\pi$
$752$	−5335.93	−0.258752
$753$	8384.99	0.405798
$754$	4869.93	0.235215
$755$	−5465.47	−0.263455
$756$	2987.44	0.143720
$757$	7608.85	0.365321	0.182661	−	0.983176i	$-0.441529\pi$
$757$	7608.85	0.365321	0.182661	+	0.983176i	$0.441529\pi$
$758$	−11919.5	−0.571157
$759$	49185.1	2.35218
$760$	−6117.12	−0.291962
$761$	5763.27	0.274532	0.137266	−	0.990534i	$-0.456169\pi$
$761$	5763.27	0.274532	0.137266	+	0.990534i	$0.456169\pi$
$762$	28628.7	1.36104
$763$	−26911.1	−1.27686
$764$	64.4210	0.00305061
$765$	−11309.6	−0.534510
$766$	4383.16	0.206749
$767$	7395.64	0.348163
$768$	1973.30	0.0927153
$769$	−11841.4	−0.555282	−0.277641	−	0.960685i	$-0.589553\pi$
$769$	−11841.4	−0.555282	−0.277641	+	0.960685i	$0.589553\pi$
$770$	6829.91	0.319653
$771$	−39408.1	−1.84079
$772$	−2116.01	−0.0986489
$773$	−5247.85	−0.244181	−0.122091	−	0.992519i	$-0.538960\pi$
$773$	−5247.85	−0.244181	−0.122091	+	0.992519i	$0.538960\pi$
$774$	13192.5	0.612656
$775$	2292.71	0.106266
$776$	1935.16	0.0895208
$777$	−17646.1	−0.814737
$778$	8315.05	0.383173
$779$	−36693.7	−1.68766
$780$	2004.13	0.0919993
$781$	12204.6	0.559172
$782$	−23322.9	−1.06653
$783$	7820.13	0.356920
$784$	−368.000	−0.0167638
$785$	1740.23	0.0791230
$786$	−31191.5	−1.41548
$787$	33333.8	1.50981	0.754905	−	0.655835i	$-0.227683\pi$
$787$	33333.8	1.50981	0.754905	+	0.655835i	$0.227683\pi$
$788$	−18866.9	−0.852924
$789$	−29220.9	−1.31849
$790$	−604.659	−0.0272314
$791$	−23469.2	−1.05495
$792$	−9901.36	−0.444229
$793$	−3625.85	−0.162368
$794$	27244.1	1.21771
$795$	22573.9	1.00706
$796$	−16290.6	−0.725383
$797$	6999.18	0.311071	0.155535	−	0.987830i	$-0.450290\pi$
$797$	6999.18	0.311071	0.155535	+	0.987830i	$0.450290\pi$
$798$	42174.0	1.87086
$799$	−23270.3	−1.03034
$800$	−800.000	−0.0353553
$801$	18070.1	0.797098
$802$	3358.82	0.147886
$803$	−9223.39	−0.405338
$804$	−19045.4	−0.835421
$805$	−14948.1	−0.654473
$806$	2384.41	0.104203
$807$	27158.3	1.18466
$808$	2264.82	0.0986089
$809$	10977.3	0.477058	0.238529	−	0.971135i	$-0.423335\pi$
$809$	10977.3	0.477058	0.238529	+	0.971135i	$0.423335\pi$
$810$	−5534.20	−0.240064
$811$	31470.2	1.36260	0.681299	−	0.732005i	$-0.261415\pi$
$811$	31470.2	1.36260	0.681299	+	0.732005i	$0.261415\pi$
$812$	13402.5	0.579229
$813$	32795.2	1.41473
$814$	9772.16	0.420779
$815$	−11944.9	−0.513388
$816$	8605.70	0.369191
$817$	31118.6	1.33256
$818$	30921.2	1.32168
$819$	−7538.47	−0.321631
$820$	−4798.82	−0.204369
$821$	970.042	0.0412359	0.0206180	−	0.999787i	$-0.493437\pi$
$821$	970.042	0.0412359	0.0206180	+	0.999787i	$0.493437\pi$
$822$	22319.0	0.947039
$823$	−2108.31	−0.0892964	−0.0446482	−	0.999003i	$-0.514217\pi$
$823$	−2108.31	−0.0892964	−0.0446482	+	0.999003i	$0.514217\pi$
$824$	−15456.6	−0.653464
$825$	7357.55	0.310493
$826$	20353.4	0.857368
$827$	35137.2	1.47744	0.738719	−	0.674013i	$-0.235431\pi$
$827$	35137.2	1.47744	0.738719	+	0.674013i	$0.235431\pi$
$828$	21670.3	0.909536
$829$	−20626.9	−0.864175	−0.432088	−	0.901832i	$-0.642223\pi$
$829$	−20626.9	−0.864175	−0.432088	+	0.901832i	$0.642223\pi$
$830$	−12048.7	−0.503874
$831$	−10119.1	−0.422416
$832$	−832.000	−0.0346688
$833$	−1604.87	−0.0667534
$834$	−23541.2	−0.977417
$835$	−21324.7	−0.883800
$836$	−23355.4	−0.966223
$837$	3828.89	0.158119
$838$	27729.2	1.14307
$839$	−36738.4	−1.51174	−0.755870	−	0.654722i	$-0.772786\pi$
$839$	−36738.4	−1.51174	−0.755870	+	0.654722i	$0.772786\pi$
$840$	5515.54	0.226553
$841$	10694.1	0.438482
$842$	7252.73	0.296847
$843$	23990.8	0.980176
$844$	−18758.3	−0.765032
$845$	−845.000	−0.0344010
$846$	21621.4	0.878677
$847$	2267.16	0.0919725
$848$	−9371.39	−0.379499
$849$	−30705.8	−1.24125
$850$	−3488.85	−0.140784
$851$	−21387.6	−0.861523
$852$	9855.88	0.396311
$853$	−14073.1	−0.564893	−0.282446	−	0.959283i	$-0.591146\pi$
$853$	−14073.1	−0.564893	−0.282446	+	0.959283i	$0.591146\pi$
$854$	−9978.65	−0.399839
$855$	24786.9	0.991454
$856$	3748.38	0.149669
$857$	48358.8	1.92754	0.963772	−	0.266726i	$-0.0859420\pi$
$857$	48358.8	1.92754	0.963772	+	0.266726i	$0.0859420\pi$
$858$	7651.85	0.304464
$859$	25856.3	1.02702	0.513508	−	0.858085i	$-0.328346\pi$
$859$	25856.3	1.02702	0.513508	+	0.858085i	$0.328346\pi$
$860$	4069.71	0.161367
$861$	33085.1	1.30957
$862$	−26378.9	−1.04231
$863$	−15097.4	−0.595507	−0.297754	−	0.954643i	$-0.596237\pi$
$863$	−15097.4	−0.595507	−0.297754	+	0.954643i	$0.596237\pi$
$864$	−1336.02	−0.0526070
$865$	−14358.4	−0.564394
$866$	6123.36	0.240277
$867$	−340.379	−0.0133332
$868$	6562.10	0.256604
$869$	−2308.61	−0.0901199
$870$	14437.8	0.562631
$871$	8030.08	0.312387
$872$	12035.0	0.467381
$873$	−7841.36	−0.303997
$874$	51116.1	1.97829
$875$	−2236.07	−0.0863919
$876$	−7448.42	−0.287282
$877$	8455.97	0.325585	0.162792	−	0.986660i	$-0.447950\pi$
$877$	8455.97	0.325585	0.162792	+	0.986660i	$0.447950\pi$
$878$	−25502.9	−0.980273
$879$	51725.3	1.98481
$880$	−3054.43	−0.117005
$881$	−5047.67	−0.193031	−0.0965154	−	0.995331i	$-0.530770\pi$
$881$	−5047.67	−0.193031	−0.0965154	+	0.995331i	$0.530770\pi$
$882$	1491.15	0.0569272
$883$	−25885.9	−0.986558	−0.493279	−	0.869871i	$-0.664202\pi$
$883$	−25885.9	−0.986558	−0.493279	+	0.869871i	$0.664202\pi$
$884$	−3628.41	−0.138050
$885$	21925.8	0.832800
$886$	12750.5	0.483477
$887$	12787.6	0.484065	0.242032	−	0.970268i	$-0.422186\pi$
$887$	12787.6	0.484065	0.242032	+	0.970268i	$0.422186\pi$
$888$	7891.58	0.298225
$889$	−33219.5	−1.25326
$890$	5574.37	0.209947
$891$	−21129.7	−0.794470
$892$	8633.81	0.324082
$893$	51000.8	1.91117
$894$	−35568.5	−1.33063
$895$	−4914.23	−0.183536
$896$	−2289.73	−0.0853735
$897$	−16747.0	−0.623373
$898$	−29643.9	−1.10159
$899$	17177.4	0.637262
$900$	3241.64	0.120061
$901$	−40869.3	−1.51116
$902$	−18322.1	−0.676339
$903$	−28058.3	−1.03402
$904$	10495.8	0.386154
$905$	−16714.2	−0.613923
$906$	−16851.6	−0.617943
$907$	−4778.50	−0.174937	−0.0874683	−	0.996167i	$-0.527878\pi$
$907$	−4778.50	−0.174937	−0.0874683	+	0.996167i	$0.527878\pi$
$908$	17450.9	0.637808
$909$	−9177.15	−0.334859
$910$	−2325.51	−0.0847142
$911$	−581.524	−0.0211490	−0.0105745	−	0.999944i	$-0.503366\pi$
$911$	−581.524	−0.0211490	−0.0105745	+	0.999944i	$0.503366\pi$
$912$	−18860.8	−0.684807
$913$	−46002.2	−1.66753
$914$	−19583.1	−0.708698
$915$	−10749.5	−0.388381
$916$	−4287.33	−0.154648
$917$	36193.3	1.30339
$918$	−5826.50	−0.209480
$919$	11885.1	0.426610	0.213305	−	0.976986i	$-0.431577\pi$
$919$	11885.1	0.426610	0.213305	+	0.976986i	$0.431577\pi$
$920$	6684.98	0.239562
$921$	29937.2	1.07108
$922$	−15065.2	−0.538117
$923$	−4155.52	−0.148191
$924$	21058.5	0.749756
$925$	−3199.34	−0.113723
$926$	−4091.80	−0.145210
$927$	62630.7	2.21905
$928$	−5993.76	−0.212020
$929$	15219.6	0.537502	0.268751	−	0.963210i	$-0.413389\pi$
$929$	15219.6	0.537502	0.268751	+	0.963210i	$0.413389\pi$
$930$	7069.06	0.249251
$931$	3517.34	0.123820
$932$	5891.53	0.207064
$933$	−70823.1	−2.48515
$934$	−34578.0	−1.21138
$935$	−13320.6	−0.465913
$936$	3371.31	0.117729
$937$	−48722.0	−1.69870	−0.849349	−	0.527832i	$-0.823005\pi$
$937$	−48722.0	−1.69870	−0.849349	+	0.527832i	$0.823005\pi$
$938$	22099.4	0.769267
$939$	−57622.3	−2.00259
$940$	6669.91	0.231434
$941$	−27151.1	−0.940597	−0.470299	−	0.882507i	$-0.655854\pi$
$941$	−27151.1	−0.940597	−0.470299	+	0.882507i	$0.655854\pi$
$942$	5365.63	0.185585
$943$	40100.1	1.38477
$944$	−9102.33	−0.313830
$945$	−3734.30	−0.128547
$946$	15538.3	0.534031
$947$	26266.5	0.901317	0.450659	−	0.892696i	$-0.351189\pi$
$947$	26266.5	0.901317	0.450659	+	0.892696i	$0.351189\pi$
$948$	−1864.33	−0.0638721
$949$	3140.47	0.107422
$950$	7646.40	0.261139
$951$	35985.2	1.22702
$952$	−9985.68	−0.339956
$953$	−27675.9	−0.940725	−0.470363	−	0.882473i	$-0.655877\pi$
$953$	−27675.9	−0.940725	−0.470363	+	0.882473i	$0.655877\pi$
$954$	37973.4	1.28871
$955$	−80.5262	−0.00272855
$956$	−9523.30	−0.322182
$957$	55124.2	1.86198
$958$	−28977.4	−0.977261
$959$	−25898.1	−0.872046
$960$	−2466.63	−0.0829271
$961$	−21380.6	−0.717687
$962$	−3327.32	−0.111515
$963$	−15188.6	−0.508252
$964$	17507.1	0.584922
$965$	2645.02	0.0882343
$966$	−46089.1	−1.53509
$967$	−1676.34	−0.0557471	−0.0278736	−	0.999611i	$-0.508874\pi$
$967$	−1676.34	−0.0557471	−0.0278736	+	0.999611i	$0.508874\pi$
$968$	−1013.91	−0.0336655
$969$	−82253.3	−2.72689
$970$	−2418.95	−0.0800698
$971$	12176.4	0.402431	0.201215	−	0.979547i	$-0.435511\pi$
$971$	12176.4	0.402431	0.201215	+	0.979547i	$0.435511\pi$
$972$	−21572.6	−0.711873
$973$	27316.2	0.900018
$974$	6902.51	0.227075
$975$	−2505.17	−0.0822867
$976$	4462.59	0.146357
$977$	−4710.79	−0.154259	−0.0771297	−	0.997021i	$-0.524576\pi$
$977$	−4710.79	−0.154259	−0.0771297	+	0.997021i	$0.524576\pi$
$978$	−36829.5	−1.20417
$979$	21283.1	0.694802
$980$	460.000	0.0149940
$981$	−48766.4	−1.58715
$982$	40657.8	1.32122
$983$	4834.94	0.156878	0.0784388	−	0.996919i	$-0.475006\pi$
$983$	4834.94	0.156878	0.0784388	+	0.996919i	$0.475006\pi$
$984$	−14796.1	−0.479353
$985$	23583.6	0.762879
$986$	−26139.2	−0.844261
$987$	−45985.2	−1.48300
$988$	7952.26	0.256068
$989$	−34007.4	−1.09340
$990$	12376.7	0.397330
$991$	28637.9	0.917973	0.458987	−	0.888443i	$-0.348213\pi$
$991$	28637.9	0.917973	0.458987	+	0.888443i	$0.348213\pi$
$992$	−2934.66	−0.0939270
$993$	11906.6	0.380509
$994$	−11436.3	−0.364928
$995$	20363.2	0.648802
$996$	−37149.4	−1.18185
$997$	−27133.9	−0.861924	−0.430962	−	0.902370i	$-0.641826\pi$
$997$	−27133.9	−0.861924	−0.430962	+	0.902370i	$0.641826\pi$
$998$	9512.72	0.301723
$999$	−5343.00	−0.169214

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	130.4.a.e.1.2	✓	2
3.2	odd	2		1170.4.a.z.1.2		2
4.3	odd	2		1040.4.a.j.1.1		2
5.2	odd	4		650.4.b.k.599.1		4
5.3	odd	4		650.4.b.k.599.4		4
5.4	even	2		650.4.a.s.1.1		2
13.12	even	2		1690.4.a.t.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.4.a.e.1.2	✓	2	1.1	even	1	trivial
650.4.a.s.1.1		2	5.4	even	2
650.4.b.k.599.1		4	5.2	odd	4
650.4.b.k.599.4		4	5.3	odd	4
1040.4.a.j.1.1		2	4.3	odd	2
1170.4.a.z.1.2		2	3.2	odd	2
1690.4.a.t.1.2		2	13.12	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 130 = 2 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	130.a (trivial)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} +7.70820 q^{3} +4.00000 q^{4} -5.00000 q^{5} -15.4164 q^{6} +17.8885 q^{7} -8.00000 q^{8} +32.4164 q^{9} +10.0000 q^{10} +38.1803 q^{11} +30.8328 q^{12} -13.0000 q^{13} -35.7771 q^{14} -38.5410 q^{15} +16.0000 q^{16} +69.7771 q^{17} -64.8328 q^{18} -152.928 q^{19} -20.0000 q^{20} +137.889 q^{21} -76.3607 q^{22} +167.125 q^{23} -61.6656 q^{24} +25.0000 q^{25} +26.0000 q^{26} +41.7508 q^{27} +71.5542 q^{28} +187.305 q^{29} +77.0820 q^{30} +91.7082 q^{31} -32.0000 q^{32} +294.302 q^{33} -139.554 q^{34} -89.4427 q^{35} +129.666 q^{36} -127.974 q^{37} +305.856 q^{38} -100.207 q^{39} +40.0000 q^{40} +239.941 q^{41} -275.777 q^{42} -203.485 q^{43} +152.721 q^{44} -162.082 q^{45} -334.249 q^{46} -333.495 q^{47} +123.331 q^{48} -23.0000 q^{49} -50.0000 q^{50} +537.856 q^{51} -52.0000 q^{52} -585.712 q^{53} -83.5016 q^{54} -190.902 q^{55} -143.108 q^{56} -1178.80 q^{57} -374.610 q^{58} -568.895 q^{59} -154.164 q^{60} +278.912 q^{61} -183.416 q^{62} +579.882 q^{63} +64.0000 q^{64} +65.0000 q^{65} -588.604 q^{66} -617.698 q^{67} +279.108 q^{68} +1288.23 q^{69} +178.885 q^{70} +319.656 q^{71} -259.331 q^{72} -241.574 q^{73} +255.947 q^{74} +192.705 q^{75} -611.712 q^{76} +682.991 q^{77} +200.413 q^{78} -60.4659 q^{79} -80.0000 q^{80} -553.420 q^{81} -479.882 q^{82} -1204.87 q^{83} +551.554 q^{84} -348.885 q^{85} +406.971 q^{86} +1443.78 q^{87} -305.443 q^{88} +557.437 q^{89} +324.164 q^{90} -232.551 q^{91} +668.498 q^{92} +706.906 q^{93} +666.991 q^{94} +764.640 q^{95} -246.663 q^{96} -241.895 q^{97} +46.0000 q^{98} +1237.67 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 4 q^{2} + 2 q^{3} + 8 q^{4} - 10 q^{5} - 4 q^{6} - 16 q^{8} + 38 q^{9} + 20 q^{10} + 54 q^{11} + 8 q^{12} - 26 q^{13} - 10 q^{15} + 32 q^{16} + 68 q^{17} - 76 q^{18} - 42 q^{19} - 40 q^{20} + 240 q^{21}+ \cdots + 1326 q^{99}+O(q^{100}) \) 2 * q - 4 * q^2 + 2 * q^3 + 8 * q^4 - 10 * q^5 - 4 * q^6 - 16 * q^8 + 38 * q^9 + 20 * q^10 + 54 * q^11 + 8 * q^12 - 26 * q^13 - 10 * q^15 + 32 * q^16 + 68 * q^17 - 76 * q^18 - 42 * q^19 - 40 * q^20 + 240 * q^21 - 108 * q^22 + 294 * q^23 - 16 * q^24 + 50 * q^25 + 52 * q^26 + 164 * q^27 + 312 * q^29 + 20 * q^30 + 170 * q^31 - 64 * q^32 + 204 * q^33 - 136 * q^34 + 152 * q^36 - 408 * q^37 + 84 * q^38 - 26 * q^39 + 80 * q^40 + 140 * q^41 - 480 * q^42 - 322 * q^43 + 216 * q^44 - 190 * q^45 - 588 * q^46 - 184 * q^47 + 32 * q^48 - 46 * q^49 - 100 * q^50 + 548 * q^51 - 104 * q^52 - 116 * q^53 - 328 * q^54 - 270 * q^55 - 1812 * q^57 - 624 * q^58 - 382 * q^59 - 40 * q^60 + 48 * q^61 - 340 * q^62 + 480 * q^63 + 128 * q^64 + 130 * q^65 - 408 * q^66 - 1620 * q^67 + 272 * q^68 + 564 * q^69 + 930 * q^71 - 304 * q^72 + 456 * q^73 + 816 * q^74 + 50 * q^75 - 168 * q^76 + 400 * q^77 + 52 * q^78 + 532 * q^79 - 160 * q^80 - 1402 * q^81 - 280 * q^82 - 120 * q^83 + 960 * q^84 - 340 * q^85 + 644 * q^86 + 732 * q^87 - 432 * q^88 + 292 * q^89 + 380 * q^90 + 1176 * q^92 + 260 * q^93 + 368 * q^94 + 210 * q^95 - 64 * q^96 - 1092 * q^97 + 92 * q^98 + 1326 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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