LMFDB - Embedded newform 2166.4.a.j.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2166,4,Mod(1,2166)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2166, 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("2166.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2166 = 2 \cdot 3 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2166.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:	$127.798137072$
Analytic rank:	$1$
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:	$ 1 $
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	$\chi$	$=$	2166.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -0.909830 q^{5} +6.00000 q^{6} -16.3262 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -0.909830 q^{5} +6.00000 q^{6} -16.3262 q^{7} -8.00000 q^{8} +9.00000 q^{9} +1.81966 q^{10} -1.94427 q^{11} -12.0000 q^{12} -15.0902 q^{13} +32.6525 q^{14} +2.72949 q^{15} +16.0000 q^{16} +32.0132 q^{17} -18.0000 q^{18} -3.63932 q^{20} +48.9787 q^{21} +3.88854 q^{22} -44.8885 q^{23} +24.0000 q^{24} -124.172 q^{25} +30.1803 q^{26} -27.0000 q^{27} -65.3050 q^{28} -31.1509 q^{29} -5.45898 q^{30} +299.503 q^{31} -32.0000 q^{32} +5.83282 q^{33} -64.0263 q^{34} +14.8541 q^{35} +36.0000 q^{36} +252.885 q^{37} +45.2705 q^{39} +7.27864 q^{40} -81.6475 q^{41} -97.9574 q^{42} -217.095 q^{43} -7.77709 q^{44} -8.18847 q^{45} +89.7771 q^{46} +187.743 q^{47} -48.0000 q^{48} -76.4540 q^{49} +248.344 q^{50} -96.0395 q^{51} -60.3607 q^{52} +11.8127 q^{53} +54.0000 q^{54} +1.76896 q^{55} +130.610 q^{56} +62.3018 q^{58} -244.046 q^{59} +10.9180 q^{60} +526.508 q^{61} -599.007 q^{62} -146.936 q^{63} +64.0000 q^{64} +13.7295 q^{65} -11.6656 q^{66} +210.726 q^{67} +128.053 q^{68} +134.666 q^{69} -29.7082 q^{70} +503.418 q^{71} -72.0000 q^{72} +115.265 q^{73} -505.771 q^{74} +372.517 q^{75} +31.7426 q^{77} -90.5410 q^{78} -220.492 q^{79} -14.5573 q^{80} +81.0000 q^{81} +163.295 q^{82} +200.023 q^{83} +195.915 q^{84} -29.1265 q^{85} +434.190 q^{86} +93.4528 q^{87} +15.5542 q^{88} +174.091 q^{89} +16.3769 q^{90} +246.366 q^{91} -179.554 q^{92} -898.510 q^{93} -375.485 q^{94} +96.0000 q^{96} +1105.40 q^{97} +152.908 q^{98} -17.4984 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 4 q^{2} - 6 q^{3} + 8 q^{4} - 13 q^{5} + 12 q^{6} - 17 q^{7} - 16 q^{8} + 18 q^{9}+O(q^{10}) $ 2 * q - 4 * q^2 - 6 * q^3 + 8 * q^4 - 13 * q^5 + 12 * q^6 - 17 * q^7 - 16 * q^8 + 18 * q^9	\( 2 q - 4 q^{2} - 6 q^{3} + 8 q^{4} - 13 q^{5} + 12 q^{6} - 17 q^{7} - 16 q^{8} + 18 q^{9} + 26 q^{10} + 14 q^{11} - 24 q^{12} - 19 q^{13} + 34 q^{14} + 39 q^{15} + 32 q^{16} - 12 q^{17} - 36 q^{18} - 52 q^{20} + 51 q^{21} - 28 q^{22} - 54 q^{23} + 48 q^{24} - 103 q^{25} + 38 q^{26} - 54 q^{27} - 68 q^{28} + 130 q^{29} - 78 q^{30} + 239 q^{31} - 64 q^{32} - 42 q^{33} + 24 q^{34} + 23 q^{35} + 72 q^{36} + 148 q^{37} + 57 q^{39} + 104 q^{40} - 331 q^{41} - 102 q^{42} - 224 q^{43} + 56 q^{44} - 117 q^{45} + 108 q^{46} + 333 q^{47} - 96 q^{48} - 419 q^{49} + 206 q^{50} + 36 q^{51} - 76 q^{52} + 766 q^{53} + 108 q^{54} - 191 q^{55} + 136 q^{56} - 260 q^{58} + 460 q^{59} + 156 q^{60} + 494 q^{61} - 478 q^{62} - 153 q^{63} + 128 q^{64} + 61 q^{65} + 84 q^{66} + 133 q^{67} - 48 q^{68} + 162 q^{69} - 46 q^{70} + 459 q^{71} - 144 q^{72} + 396 q^{73} - 296 q^{74} + 309 q^{75} + 21 q^{77} - 114 q^{78} - 1000 q^{79} - 208 q^{80} + 162 q^{81} + 662 q^{82} - 74 q^{83} + 204 q^{84} + 503 q^{85} + 448 q^{86} - 390 q^{87} - 112 q^{88} + 1180 q^{89} + 234 q^{90} + 249 q^{91} - 216 q^{92} - 717 q^{93} - 666 q^{94} + 192 q^{96} + 1938 q^{97} + 838 q^{98} + 126 q^{99}+O(q^{100}) \) 2 * q - 4 * q^2 - 6 * q^3 + 8 * q^4 - 13 * q^5 + 12 * q^6 - 17 * q^7 - 16 * q^8 + 18 * q^9 + 26 * q^10 + 14 * q^11 - 24 * q^12 - 19 * q^13 + 34 * q^14 + 39 * q^15 + 32 * q^16 - 12 * q^17 - 36 * q^18 - 52 * q^20 + 51 * q^21 - 28 * q^22 - 54 * q^23 + 48 * q^24 - 103 * q^25 + 38 * q^26 - 54 * q^27 - 68 * q^28 + 130 * q^29 - 78 * q^30 + 239 * q^31 - 64 * q^32 - 42 * q^33 + 24 * q^34 + 23 * q^35 + 72 * q^36 + 148 * q^37 + 57 * q^39 + 104 * q^40 - 331 * q^41 - 102 * q^42 - 224 * q^43 + 56 * q^44 - 117 * q^45 + 108 * q^46 + 333 * q^47 - 96 * q^48 - 419 * q^49 + 206 * q^50 + 36 * q^51 - 76 * q^52 + 766 * q^53 + 108 * q^54 - 191 * q^55 + 136 * q^56 - 260 * q^58 + 460 * q^59 + 156 * q^60 + 494 * q^61 - 478 * q^62 - 153 * q^63 + 128 * q^64 + 61 * q^65 + 84 * q^66 + 133 * q^67 - 48 * q^68 + 162 * q^69 - 46 * q^70 + 459 * q^71 - 144 * q^72 + 396 * q^73 - 296 * q^74 + 309 * q^75 + 21 * q^77 - 114 * q^78 - 1000 * q^79 - 208 * q^80 + 162 * q^81 + 662 * q^82 - 74 * q^83 + 204 * q^84 + 503 * q^85 + 448 * q^86 - 390 * q^87 - 112 * q^88 + 1180 * q^89 + 234 * q^90 + 249 * q^91 - 216 * q^92 - 717 * q^93 - 666 * q^94 + 192 * q^96 + 1938 * q^97 + 838 * q^98 + 126 * q^99

Display 100 coefficients 10 coefficients

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
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	4.00000	0.500000
$5$	−0.909830	−0.0813777	−0.0406888	−	0.999172i	$-0.512955\pi$
$5$	−0.909830	−0.0813777	−0.0406888	+	0.999172i	$0.512955\pi$
$6$	6.00000	0.408248
$7$	−16.3262	−0.881534	−0.440767	−	0.897622i	$-0.645293\pi$
$7$	−16.3262	−0.881534	−0.440767	+	0.897622i	$0.645293\pi$
$8$	−8.00000	−0.353553
$9$	9.00000	0.333333
$10$	1.81966	0.0575427
$11$	−1.94427	−0.0532927	−0.0266464	−	0.999645i	$-0.508483\pi$
$11$	−1.94427	−0.0532927	−0.0266464	+	0.999645i	$0.508483\pi$
$12$	−12.0000	−0.288675
$13$	−15.0902	−0.321943	−0.160972	−	0.986959i	$-0.551463\pi$
$13$	−15.0902	−0.321943	−0.160972	+	0.986959i	$0.551463\pi$
$14$	32.6525	0.623339
$15$	2.72949	0.0469834
$16$	16.0000	0.250000
$17$	32.0132	0.456725	0.228363	−	0.973576i	$-0.426663\pi$
$17$	32.0132	0.456725	0.228363	+	0.973576i	$0.426663\pi$
$18$	−18.0000	−0.235702
$19$	0	0
$19$	0	0
$20$	−3.63932	−0.0406888
$21$	48.9787	0.508954
$22$	3.88854	0.0376837
$23$	−44.8885	−0.406953	−0.203476	−	0.979080i	$-0.565224\pi$
$23$	−44.8885	−0.406953	−0.203476	+	0.979080i	$0.565224\pi$
$24$	24.0000	0.204124
$25$	−124.172	−0.993378
$26$	30.1803	0.227648
$27$	−27.0000	−0.192450
$28$	−65.3050	−0.440767
$29$	−31.1509	−0.199468	−0.0997342	−	0.995014i	$-0.531799\pi$
$29$	−31.1509	−0.199468	−0.0997342	+	0.995014i	$0.531799\pi$
$30$	−5.45898	−0.0332223
$31$	299.503	1.73524	0.867620	−	0.497229i	$-0.165649\pi$
$31$	299.503	1.73524	0.867620	+	0.497229i	$0.165649\pi$
$32$	−32.0000	−0.176777
$33$	5.83282	0.0307686
$34$	−64.0263	−0.322954
$35$	14.8541	0.0717372
$36$	36.0000	0.166667
$37$	252.885	1.12362	0.561812	−	0.827265i	$-0.310104\pi$
$37$	252.885	1.12362	0.561812	+	0.827265i	$0.310104\pi$
$38$	0	0
$39$	45.2705	0.185874
$40$	7.27864	0.0287714
$41$	−81.6475	−0.311005	−0.155502	−	0.987836i	$-0.549700\pi$
$41$	−81.6475	−0.311005	−0.155502	+	0.987836i	$0.549700\pi$
$42$	−97.9574	−0.359885
$43$	−217.095	−0.769923	−0.384962	−	0.922933i	$-0.625785\pi$
$43$	−217.095	−0.769923	−0.384962	+	0.922933i	$0.625785\pi$
$44$	−7.77709	−0.0266464
$45$	−8.18847	−0.0271259
$46$	89.7771	0.287759
$47$	187.743	0.582661	0.291331	−	0.956622i	$-0.405902\pi$
$47$	187.743	0.582661	0.291331	+	0.956622i	$0.405902\pi$
$48$	−48.0000	−0.144338
$49$	−76.4540	−0.222898
$50$	248.344	0.702424
$51$	−96.0395	−0.263690
$52$	−60.3607	−0.160972
$53$	11.8127	0.0306151	0.0153076	−	0.999883i	$-0.495127\pi$
$53$	11.8127	0.0306151	0.0153076	+	0.999883i	$0.495127\pi$
$54$	54.0000	0.136083
$55$	1.76896	0.00433684
$56$	130.610	0.311669
$57$	0	0
$58$	62.3018	0.141045
$59$	−244.046	−0.538511	−0.269255	−	0.963069i	$-0.586778\pi$
$59$	−244.046	−0.538511	−0.269255	+	0.963069i	$0.586778\pi$
$60$	10.9180	0.0234917
$61$	526.508	1.10512	0.552562	−	0.833472i	$-0.313650\pi$
$61$	526.508	1.10512	0.552562	+	0.833472i	$0.313650\pi$
$62$	−599.007	−1.22700
$63$	−146.936	−0.293845
$64$	64.0000	0.125000
$65$	13.7295	0.0261990
$66$	−11.6656	−0.0217567
$67$	210.726	0.384244	0.192122	−	0.981371i	$-0.438463\pi$
$67$	210.726	0.384244	0.192122	+	0.981371i	$0.438463\pi$
$68$	128.053	0.228363
$69$	134.666	0.234954
$70$	−29.7082	−0.0507259
$71$	503.418	0.841476	0.420738	−	0.907182i	$-0.361771\pi$
$71$	503.418	0.841476	0.420738	+	0.907182i	$0.361771\pi$
$72$	−72.0000	−0.117851
$73$	115.265	0.184806	0.0924028	−	0.995722i	$-0.470545\pi$
$73$	115.265	0.184806	0.0924028	+	0.995722i	$0.470545\pi$
$74$	−505.771	−0.794523
$75$	372.517	0.573527
$76$	0	0
$77$	31.7426	0.0469794
$78$	−90.5410	−0.131433
$79$	−220.492	−0.314016	−0.157008	−	0.987597i	$-0.550185\pi$
$79$	−220.492	−0.314016	−0.157008	+	0.987597i	$0.550185\pi$
$80$	−14.5573	−0.0203444
$81$	81.0000	0.111111
$82$	163.295	0.219913
$83$	200.023	0.264523	0.132261	−	0.991215i	$-0.457776\pi$
$83$	200.023	0.264523	0.132261	+	0.991215i	$0.457776\pi$
$84$	195.915	0.254477
$85$	−29.1265	−0.0371672
$86$	434.190	0.544418
$87$	93.4528	0.115163
$88$	15.5542	0.0188418
$89$	174.091	0.207344	0.103672	−	0.994612i	$-0.466941\pi$
$89$	174.091	0.207344	0.103672	+	0.994612i	$0.466941\pi$
$90$	16.3769	0.0191809
$91$	246.366	0.283804
$92$	−179.554	−0.203476
$93$	−898.510	−1.00184
$94$	−375.485	−0.412004
$95$	0	0
$96$	96.0000	0.102062
$97$	1105.40	1.15708	0.578538	−	0.815655i	$-0.303623\pi$
$97$	1105.40	1.15708	0.578538	+	0.815655i	$0.303623\pi$
$98$	152.908	0.157613
$99$	−17.4984	−0.0177642
$100$	−496.689	−0.496689
$101$	−896.371	−0.883092	−0.441546	−	0.897239i	$-0.645570\pi$
$101$	−896.371	−0.883092	−0.441546	+	0.897239i	$0.645570\pi$
$102$	192.079	0.186457
$103$	−161.160	−0.154170	−0.0770852	−	0.997025i	$-0.524561\pi$
$103$	−161.160	−0.154170	−0.0770852	+	0.997025i	$0.524561\pi$
$104$	120.721	0.113824
$105$	−44.5623	−0.0414175
$106$	−23.6254	−0.0216482
$107$	1121.56	1.01333	0.506663	−	0.862144i	$-0.330879\pi$
$107$	1121.56	1.01333	0.506663	+	0.862144i	$0.330879\pi$
$108$	−108.000	−0.0962250
$109$	−983.166	−0.863947	−0.431973	−	0.901886i	$-0.642183\pi$
$109$	−983.166	−0.863947	−0.431973	+	0.901886i	$0.642183\pi$
$110$	−3.53791	−0.00306661
$111$	−758.656	−0.648725
$112$	−261.220	−0.220383
$113$	500.349	0.416539	0.208270	−	0.978071i	$-0.433217\pi$
$113$	500.349	0.416539	0.208270	+	0.978071i	$0.433217\pi$
$114$	0	0
$115$	40.8409	0.0331169
$116$	−124.604	−0.0997342
$117$	−135.812	−0.107314
$118$	488.093	0.380785
$119$	−522.654	−0.402619
$120$	−21.8359	−0.0166111
$121$	−1327.22	−0.997160
$122$	−1053.02	−0.781440
$123$	244.942	0.179559
$124$	1198.01	0.867620
$125$	226.704	0.162216
$126$	293.872	0.207780
$127$	865.459	0.604701	0.302351	−	0.953197i	$-0.402229\pi$
$127$	865.459	0.604701	0.302351	+	0.953197i	$0.402229\pi$
$128$	−128.000	−0.0883883
$129$	651.286	0.444515
$130$	−27.4590	−0.0185255
$131$	−2344.79	−1.56386	−0.781930	−	0.623366i	$-0.785765\pi$
$131$	−2344.79	−1.56386	−0.781930	+	0.623366i	$0.785765\pi$
$132$	23.3313	0.0153843
$133$	0	0
$134$	−421.453	−0.271701
$135$	24.5654	0.0156611
$136$	−256.105	−0.161477
$137$	2071.28	1.29169	0.645843	−	0.763470i	$-0.276506\pi$
$137$	2071.28	1.29169	0.645843	+	0.763470i	$0.276506\pi$
$138$	−269.331	−0.166138
$139$	−1467.54	−0.895507	−0.447753	−	0.894157i	$-0.647776\pi$
$139$	−1467.54	−0.895507	−0.447753	+	0.894157i	$0.647776\pi$
$140$	59.4164	0.0358686
$141$	−563.228	−0.336400
$142$	−1006.84	−0.595013
$143$	29.3394	0.0171572
$144$	144.000	0.0833333
$145$	28.3420	0.0162323
$146$	−230.531	−0.130677
$147$	229.362	0.128690
$148$	1011.54	0.561812
$149$	−176.948	−0.0972895	−0.0486447	−	0.998816i	$-0.515490\pi$
$149$	−176.948	−0.0972895	−0.0486447	+	0.998816i	$0.515490\pi$
$150$	−745.033	−0.405545
$151$	1138.74	0.613706	0.306853	−	0.951757i	$-0.400724\pi$
$151$	1138.74	0.613706	0.306853	+	0.951757i	$0.400724\pi$
$152$	0	0
$153$	288.118	0.152242
$154$	−63.4853	−0.0332194
$155$	−272.497	−0.141210
$156$	181.082	0.0929370
$157$	−1952.19	−0.992366	−0.496183	−	0.868218i	$-0.665266\pi$
$157$	−1952.19	−0.992366	−0.496183	+	0.868218i	$0.665266\pi$
$158$	440.983	0.222043
$159$	−35.4381	−0.0176756
$160$	29.1146	0.0143857
$161$	732.861	0.358742
$162$	−162.000	−0.0785674
$163$	385.974	0.185471	0.0927357	−	0.995691i	$-0.470439\pi$
$163$	385.974	0.185471	0.0927357	+	0.995691i	$0.470439\pi$
$164$	−326.590	−0.155502
$165$	−5.30687	−0.00250387
$166$	−400.046	−0.187046
$167$	3206.11	1.48561	0.742803	−	0.669510i	$-0.233496\pi$
$167$	3206.11	1.48561	0.742803	+	0.669510i	$0.233496\pi$
$168$	−391.830	−0.179942
$169$	−1969.29	−0.896353
$170$	58.2531	0.0262812
$171$	0	0
$172$	−868.381	−0.384962
$173$	3194.72	1.40399	0.701993	−	0.712184i	$-0.252294\pi$
$173$	3194.72	1.40399	0.701993	+	0.712184i	$0.252294\pi$
$174$	−186.906	−0.0814326
$175$	2027.27	0.875696
$176$	−31.1084	−0.0133232
$177$	732.139	0.310909
$178$	−348.183	−0.146615
$179$	−2449.26	−1.02272	−0.511358	−	0.859368i	$-0.670858\pi$
$179$	−2449.26	−1.02272	−0.511358	+	0.859368i	$0.670858\pi$
$180$	−32.7539	−0.0135629
$181$	2002.67	0.822415	0.411207	−	0.911542i	$-0.365107\pi$
$181$	2002.67	0.822415	0.411207	+	0.911542i	$0.365107\pi$
$182$	−492.731	−0.200680
$183$	−1579.53	−0.638043
$184$	359.108	0.143879
$185$	−230.083	−0.0914380
$186$	1797.02	0.708408
$187$	−62.2423	−0.0243401
$188$	750.971	0.291331
$189$	440.808	0.169651
$190$	0	0
$191$	4101.97	1.55397	0.776984	−	0.629520i	$-0.216749\pi$
$191$	4101.97	1.55397	0.776984	+	0.629520i	$0.216749\pi$
$192$	−192.000	−0.0721688
$193$	−1756.55	−0.655126	−0.327563	−	0.944829i	$-0.606227\pi$
$193$	−1756.55	−0.655126	−0.327563	+	0.944829i	$0.606227\pi$
$194$	−2210.80	−0.818176
$195$	−41.1885	−0.0151260
$196$	−305.816	−0.111449
$197$	3670.57	1.32750	0.663750	−	0.747955i	$-0.268964\pi$
$197$	3670.57	1.32750	0.663750	+	0.747955i	$0.268964\pi$
$198$	34.9969	0.0125612
$199$	−2610.75	−0.930007	−0.465004	−	0.885309i	$-0.653947\pi$
$199$	−2610.75	−0.930007	−0.465004	+	0.885309i	$0.653947\pi$
$200$	993.378	0.351212
$201$	−632.179	−0.221843
$202$	1792.74	0.624440
$203$	508.577	0.175838
$204$	−384.158	−0.131845
$205$	74.2853	0.0253088
$206$	322.320	0.109015
$207$	−403.997	−0.135651
$208$	−241.443	−0.0804858
$209$	0	0
$210$	89.1246	0.0292866
$211$	3473.35	1.13325	0.566624	−	0.823976i	$-0.308249\pi$
$211$	3473.35	1.13325	0.566624	+	0.823976i	$0.308249\pi$
$212$	47.2509	0.0153076
$213$	−1510.25	−0.485826
$214$	−2243.13	−0.716529
$215$	197.520	0.0626546
$216$	216.000	0.0680414
$217$	−4889.76	−1.52967
$218$	1966.33	0.610903
$219$	−345.796	−0.106698
$220$	7.07583	0.00216842
$221$	−483.084	−0.147040
$222$	1517.31	0.458718
$223$	−2530.49	−0.759885	−0.379942	−	0.925010i	$-0.624056\pi$
$223$	−2530.49	−0.759885	−0.379942	+	0.925010i	$0.624056\pi$
$224$	522.440	0.155835
$225$	−1117.55	−0.331126
$226$	−1000.70	−0.294538
$227$	6734.59	1.96912	0.984560	−	0.175046i	$-0.0560074\pi$
$227$	6734.59	1.96912	0.984560	+	0.175046i	$0.0560074\pi$
$228$	0	0
$229$	−337.719	−0.0974546	−0.0487273	−	0.998812i	$-0.515517\pi$
$229$	−337.719	−0.0974546	−0.0487273	+	0.998812i	$0.515517\pi$
$230$	−81.6819	−0.0234172
$231$	−95.2279	−0.0271235
$232$	249.207	0.0705227
$233$	−6311.26	−1.77452	−0.887262	−	0.461265i	$-0.847396\pi$
$233$	−6311.26	−1.77452	−0.887262	+	0.461265i	$0.847396\pi$
$234$	271.623	0.0758827
$235$	−170.814	−0.0474156
$236$	−976.186	−0.269255
$237$	661.475	0.181297
$238$	1045.31	0.284695
$239$	−3275.56	−0.886519	−0.443260	−	0.896393i	$-0.646178\pi$
$239$	−3275.56	−0.886519	−0.443260	+	0.896393i	$0.646178\pi$
$240$	43.6718	0.0117459
$241$	−1668.27	−0.445904	−0.222952	−	0.974829i	$-0.571569\pi$
$241$	−1668.27	−0.445904	−0.222952	+	0.974829i	$0.571569\pi$
$242$	2654.44	0.705099
$243$	−243.000	−0.0641500
$244$	2106.03	0.552562
$245$	69.5601	0.0181389
$246$	−489.885	−0.126967
$247$	0	0
$248$	−2396.03	−0.613500
$249$	−600.070	−0.152722
$250$	−453.409	−0.114704
$251$	−2044.39	−0.514106	−0.257053	−	0.966397i	$-0.582751\pi$
$251$	−2044.39	−0.514106	−0.257053	+	0.966397i	$0.582751\pi$
$252$	−587.745	−0.146922
$253$	87.2755	0.0216876
$254$	−1730.92	−0.427588
$255$	87.3796	0.0214585
$256$	256.000	0.0625000
$257$	−5181.31	−1.25759	−0.628797	−	0.777570i	$-0.716452\pi$
$257$	−5181.31	−1.25759	−0.628797	+	0.777570i	$0.716452\pi$
$258$	−1302.57	−0.314320
$259$	−4128.67	−0.990513
$260$	54.9180	0.0130995
$261$	−280.358	−0.0664894
$262$	4689.59	1.10582
$263$	7137.93	1.67355	0.836774	−	0.547548i	$-0.184439\pi$
$263$	7137.93	1.67355	0.836774	+	0.547548i	$0.184439\pi$
$264$	−46.6625	−0.0108783
$265$	−10.7476	−0.00249139
$266$	0	0
$267$	−522.274	−0.119710
$268$	842.906	0.192122
$269$	−6395.52	−1.44960	−0.724798	−	0.688961i	$-0.758067\pi$
$269$	−6395.52	−1.44960	−0.724798	+	0.688961i	$0.758067\pi$
$270$	−49.1308	−0.0110741
$271$	−6478.86	−1.45226	−0.726131	−	0.687556i	$-0.758683\pi$
$271$	−6478.86	−1.45226	−0.726131	+	0.687556i	$0.758683\pi$
$272$	512.210	0.114181
$273$	−739.097	−0.163854
$274$	−4142.55	−0.913360
$275$	241.425	0.0529398
$276$	538.663	0.117477
$277$	3501.93	0.759606	0.379803	−	0.925067i	$-0.375992\pi$
$277$	3501.93	0.759606	0.379803	+	0.925067i	$0.375992\pi$
$278$	2935.09	0.633219
$279$	2695.53	0.578413
$280$	−118.833	−0.0253629
$281$	−1722.75	−0.365731	−0.182865	−	0.983138i	$-0.558537\pi$
$281$	−1722.75	−0.365731	−0.182865	+	0.983138i	$0.558537\pi$
$282$	1126.46	0.237870
$283$	−905.945	−0.190293	−0.0951464	−	0.995463i	$-0.530332\pi$
$283$	−905.945	−0.190293	−0.0951464	+	0.995463i	$0.530332\pi$
$284$	2013.67	0.420738
$285$	0	0
$286$	−58.6788	−0.0121320
$287$	1333.00	0.274161
$288$	−288.000	−0.0589256
$289$	−3888.16	−0.791402
$290$	−56.6841	−0.0114779
$291$	−3316.20	−0.668038
$292$	461.062	0.0924028
$293$	−6570.56	−1.31009	−0.655045	−	0.755590i	$-0.727350\pi$
$293$	−6570.56	−1.31009	−0.655045	+	0.755590i	$0.727350\pi$
$294$	−458.724	−0.0909977
$295$	222.041	0.0438228
$296$	−2023.08	−0.397261
$297$	52.4953	0.0102562
$298$	353.896	0.0687940
$299$	677.376	0.131016
$300$	1490.07	0.286763
$301$	3544.35	0.678714
$302$	−2277.49	−0.433956
$303$	2689.11	0.509853
$304$	0	0
$305$	−479.033	−0.0899323
$306$	−576.237	−0.107651
$307$	−566.581	−0.105331	−0.0526653	−	0.998612i	$-0.516772\pi$
$307$	−566.581	−0.105331	−0.0526653	+	0.998612i	$0.516772\pi$
$308$	126.971	0.0234897
$309$	483.479	0.0890103
$310$	544.995	0.0998504
$311$	3507.55	0.639534	0.319767	−	0.947496i	$-0.396395\pi$
$311$	3507.55	0.639534	0.319767	+	0.947496i	$0.396395\pi$
$312$	−362.164	−0.0657164
$313$	−321.768	−0.0581067	−0.0290534	−	0.999578i	$-0.509249\pi$
$313$	−321.768	−0.0581067	−0.0290534	+	0.999578i	$0.509249\pi$
$314$	3904.37	0.701709
$315$	133.687	0.0239124
$316$	−881.966	−0.157008
$317$	3797.03	0.672752	0.336376	−	0.941728i	$-0.390799\pi$
$317$	3797.03	0.672752	0.336376	+	0.941728i	$0.390799\pi$
$318$	70.8763	0.0124986
$319$	60.5659	0.0106302
$320$	−58.2291	−0.0101722
$321$	−3364.69	−0.585043
$322$	−1465.72	−0.253669
$323$	0	0
$324$	324.000	0.0555556
$325$	1873.78	0.319811
$326$	−771.948	−0.131148
$327$	2949.50	0.498800
$328$	653.180	0.109957
$329$	−3065.13	−0.513636
$330$	10.6137	0.00177051
$331$	−9588.45	−1.59223	−0.796116	−	0.605144i	$-0.793115\pi$
$331$	−9588.45	−1.59223	−0.796116	+	0.605144i	$0.793115\pi$
$332$	800.093	0.132261
$333$	2275.97	0.374542
$334$	−6412.22	−1.05048
$335$	−191.725	−0.0312689
$336$	783.659	0.127238
$337$	−9263.59	−1.49739	−0.748694	−	0.662916i	$-0.769319\pi$
$337$	−9263.59	−1.49739	−0.748694	+	0.662916i	$0.769319\pi$
$338$	3938.57	0.633817
$339$	−1501.05	−0.240489
$340$	−116.506	−0.0185836
$341$	−582.316	−0.0924756
$342$	0	0
$343$	6848.11	1.07803
$344$	1736.76	0.272209
$345$	−122.523	−0.0191200
$346$	−6389.43	−0.992768
$347$	−3603.50	−0.557481	−0.278740	−	0.960367i	$-0.589917\pi$
$347$	−3603.50	−0.557481	−0.278740	+	0.960367i	$0.589917\pi$
$348$	373.811	0.0575815
$349$	3751.60	0.575411	0.287706	−	0.957719i	$-0.407108\pi$
$349$	3751.60	0.575411	0.287706	+	0.957719i	$0.407108\pi$
$350$	−4054.53	−0.619211
$351$	407.435	0.0619580
$352$	62.2167	0.00942091
$353$	−8836.39	−1.33233	−0.666166	−	0.745803i	$-0.732066\pi$
$353$	−8836.39	−1.33233	−0.666166	+	0.745803i	$0.732066\pi$
$354$	−1464.28	−0.219846
$355$	−458.025	−0.0684773
$356$	696.365	0.103672
$357$	1567.96	0.232452
$358$	4898.52	0.723170
$359$	7348.14	1.08028	0.540139	−	0.841576i	$-0.318371\pi$
$359$	7348.14	1.08028	0.540139	+	0.841576i	$0.318371\pi$
$360$	65.5078	0.00959045
$361$	0	0
$362$	−4005.33	−0.581535
$363$	3981.66	0.575711
$364$	985.463	0.141902
$365$	−104.872	−0.0150390
$366$	3159.05	0.451165
$367$	−10829.4	−1.54030	−0.770150	−	0.637862i	$-0.779819\pi$
$367$	−10829.4	−1.54030	−0.770150	+	0.637862i	$0.779819\pi$
$368$	−718.217	−0.101738
$369$	−734.827	−0.103668
$370$	460.166	0.0646564
$371$	−192.857	−0.0269883
$372$	−3594.04	−0.500920
$373$	−10614.6	−1.47347	−0.736734	−	0.676183i	$-0.763633\pi$
$373$	−10614.6	−1.47347	−0.736734	+	0.676183i	$0.763633\pi$
$374$	124.485	0.0172111
$375$	−680.113	−0.0936557
$376$	−1501.94	−0.206002
$377$	470.073	0.0642174
$378$	−881.617	−0.119962
$379$	−3538.17	−0.479535	−0.239767	−	0.970830i	$-0.577071\pi$
$379$	−3538.17	−0.479535	−0.239767	+	0.970830i	$0.577071\pi$
$380$	0	0
$381$	−2596.38	−0.349124
$382$	−8203.93	−1.09882
$383$	−13138.1	−1.75280	−0.876402	−	0.481581i	$-0.840063\pi$
$383$	−13138.1	−1.75280	−0.876402	+	0.481581i	$0.840063\pi$
$384$	384.000	0.0510310
$385$	−28.8804	−0.00382307
$386$	3513.10	0.463244
$387$	−1953.86	−0.256641
$388$	4421.60	0.578538
$389$	1058.46	0.137958	0.0689792	−	0.997618i	$-0.478026\pi$
$389$	1058.46	0.137958	0.0689792	+	0.997618i	$0.478026\pi$
$390$	82.3769	0.0106957
$391$	−1437.02	−0.185866
$392$	611.632	0.0788063
$393$	7034.38	0.902895
$394$	−7341.14	−0.938684
$395$	200.610	0.0255539
$396$	−69.9938	−0.00888212
$397$	−15180.8	−1.91915	−0.959573	−	0.281461i	$-0.909181\pi$
$397$	−15180.8	−1.91915	−0.959573	+	0.281461i	$0.909181\pi$
$398$	5221.51	0.657615
$399$	0	0
$400$	−1986.76	−0.248344
$401$	1336.20	0.166400	0.0832002	−	0.996533i	$-0.473486\pi$
$401$	1336.20	0.166400	0.0832002	+	0.996533i	$0.473486\pi$
$402$	1264.36	0.156867
$403$	−4519.56	−0.558648
$404$	−3585.49	−0.441546
$405$	−73.6962	−0.00904196
$406$	−1017.15	−0.124336
$407$	−491.678	−0.0598810
$408$	768.316	0.0932287
$409$	1976.03	0.238896	0.119448	−	0.992840i	$-0.461888\pi$
$409$	1976.03	0.238896	0.119448	+	0.992840i	$0.461888\pi$
$410$	−148.571	−0.0178960
$411$	−6213.83	−0.745755
$412$	−644.639	−0.0770852
$413$	3984.36	0.474716
$414$	807.994	0.0959196
$415$	−181.987	−0.0215263
$416$	482.885	0.0569120
$417$	4402.63	0.517021
$418$	0	0
$419$	3242.90	0.378105	0.189052	−	0.981967i	$-0.439458\pi$
$419$	3242.90	0.378105	0.189052	+	0.981967i	$0.439458\pi$
$420$	−178.249	−0.0207087
$421$	−11959.4	−1.38448	−0.692241	−	0.721667i	$-0.743376\pi$
$421$	−11959.4	−1.38448	−0.692241	+	0.721667i	$0.743376\pi$
$422$	−6946.71	−0.801328
$423$	1689.68	0.194220
$424$	−94.5017	−0.0108241
$425$	−3975.14	−0.453701
$426$	3020.51	0.343531
$427$	−8595.90	−0.974204
$428$	4486.26	0.506663
$429$	−88.0182	−0.00990573
$430$	−395.039	−0.0443035
$431$	7226.13	0.807589	0.403794	−	0.914850i	$-0.367691\pi$
$431$	7226.13	0.807589	0.403794	+	0.914850i	$0.367691\pi$
$432$	−432.000	−0.0481125
$433$	−9903.01	−1.09909	−0.549547	−	0.835462i	$-0.685200\pi$
$433$	−9903.01	−1.09909	−0.549547	+	0.835462i	$0.685200\pi$
$434$	9779.53	1.08164
$435$	−85.0261	−0.00937170
$436$	−3932.66	−0.431973
$437$	0	0
$438$	691.593	0.0754465
$439$	−7077.97	−0.769506	−0.384753	−	0.923020i	$-0.625713\pi$
$439$	−7077.97	−0.769506	−0.384753	+	0.923020i	$0.625713\pi$
$440$	−14.1517	−0.00153330
$441$	−688.086	−0.0742993
$442$	966.168	0.103973
$443$	−7730.58	−0.829099	−0.414550	−	0.910027i	$-0.636061\pi$
$443$	−7730.58	−0.829099	−0.414550	+	0.910027i	$0.636061\pi$
$444$	−3034.63	−0.324362
$445$	−158.394	−0.0168732
$446$	5060.98	0.537320
$447$	530.843	0.0561701
$448$	−1044.88	−0.110192
$449$	−2353.41	−0.247359	−0.123679	−	0.992322i	$-0.539469\pi$
$449$	−2353.41	−0.247359	−0.123679	+	0.992322i	$0.539469\pi$
$450$	2235.10	0.234141
$451$	158.745	0.0165743
$452$	2001.40	0.208270
$453$	−3416.23	−0.354323
$454$	−13469.2	−1.39238
$455$	−224.151	−0.0230953
$456$	0	0
$457$	8420.95	0.861959	0.430980	−	0.902362i	$-0.358168\pi$
$457$	8420.95	0.861959	0.430980	+	0.902362i	$0.358168\pi$
$458$	675.438	0.0689108
$459$	−864.355	−0.0878968
$460$	163.364	0.0165584
$461$	−669.622	−0.0676517	−0.0338258	−	0.999428i	$-0.510769\pi$
$461$	−669.622	−0.0676517	−0.0338258	+	0.999428i	$0.510769\pi$
$462$	190.456	0.0191792
$463$	5570.89	0.559182	0.279591	−	0.960119i	$-0.409801\pi$
$463$	5570.89	0.559182	0.279591	+	0.960119i	$0.409801\pi$
$464$	−498.415	−0.0498671
$465$	817.492	0.0815275
$466$	12622.5	1.25478
$467$	−10869.8	−1.07707	−0.538537	−	0.842602i	$-0.681023\pi$
$467$	−10869.8	−1.07707	−0.538537	+	0.842602i	$0.681023\pi$
$468$	−543.246	−0.0536572
$469$	−3440.37	−0.338724
$470$	341.628	0.0335279
$471$	5856.56	0.572943
$472$	1952.37	0.190392
$473$	422.092	0.0410313
$474$	−1322.95	−0.128196
$475$	0	0
$476$	−2090.62	−0.201309
$477$	106.314	0.0102050
$478$	6551.11	0.626864
$479$	−2435.33	−0.232303	−0.116151	−	0.993232i	$-0.537056\pi$
$479$	−2435.33	−0.232303	−0.116151	+	0.993232i	$0.537056\pi$
$480$	−87.3437	−0.00830557
$481$	−3816.08	−0.361743
$482$	3336.55	0.315302
$483$	−2198.58	−0.207120
$484$	−5308.88	−0.498580
$485$	−1005.73	−0.0941602
$486$	486.000	0.0453609
$487$	−10685.2	−0.994233	−0.497116	−	0.867684i	$-0.665608\pi$
$487$	−10685.2	−0.994233	−0.497116	+	0.867684i	$0.665608\pi$
$488$	−4212.07	−0.390720
$489$	−1157.92	−0.107082
$490$	−139.120	−0.0128261
$491$	−9068.91	−0.833552	−0.416776	−	0.909009i	$-0.636840\pi$
$491$	−9068.91	−0.833552	−0.416776	+	0.909009i	$0.636840\pi$
$492$	979.769	0.0897793
$493$	−997.239	−0.0911022
$494$	0	0
$495$	15.9206	0.00144561
$496$	4792.06	0.433810
$497$	−8218.93	−0.741789
$498$	1200.14	0.107991
$499$	−9085.54	−0.815080	−0.407540	−	0.913187i	$-0.633613\pi$
$499$	−9085.54	−0.815080	−0.407540	+	0.913187i	$0.633613\pi$
$500$	906.817	0.0811082
$501$	−9618.33	−0.857716
$502$	4088.77	0.363528
$503$	−229.914	−0.0203804	−0.0101902	−	0.999948i	$-0.503244\pi$
$503$	−229.914	−0.0203804	−0.0101902	+	0.999948i	$0.503244\pi$
$504$	1175.49	0.103890
$505$	815.546	0.0718640
$506$	−174.551	−0.0153355
$507$	5907.86	0.517509
$508$	3461.84	0.302351
$509$	−9812.78	−0.854507	−0.427253	−	0.904132i	$-0.640519\pi$
$509$	−9812.78	−0.854507	−0.427253	+	0.904132i	$0.640519\pi$
$510$	−174.759	−0.0151735
$511$	−1881.85	−0.162912
$512$	−512.000	−0.0441942
$513$	0	0
$514$	10362.6	0.889253
$515$	146.628	0.0125460
$516$	2605.14	0.222258
$517$	−365.023	−0.0310516
$518$	8257.34	0.700399
$519$	−9584.15	−0.810592
$520$	−109.836	−0.00926274
$521$	−8772.27	−0.737658	−0.368829	−	0.929497i	$-0.620241\pi$
$521$	−8772.27	−0.737658	−0.368829	+	0.929497i	$0.620241\pi$
$522$	560.717	0.0470151
$523$	4563.38	0.381535	0.190767	−	0.981635i	$-0.438902\pi$
$523$	4563.38	0.381535	0.190767	+	0.981635i	$0.438902\pi$
$524$	−9379.18	−0.781930
$525$	−6081.80	−0.505583
$526$	−14275.9	−1.18338
$527$	9588.05	0.792528
$528$	93.3251	0.00769214
$529$	−10152.0	−0.834390
$530$	21.4951	0.00176168
$531$	−2196.42	−0.179504
$532$	0	0
$533$	1232.07	0.100126
$534$	1044.55	0.0846480
$535$	−1020.43	−0.0824620
$536$	−1685.81	−0.135851
$537$	7347.78	0.590466
$538$	12791.0	1.02502
$539$	148.647	0.0118788
$540$	98.2616	0.00783057
$541$	−5541.69	−0.440399	−0.220200	−	0.975455i	$-0.570671\pi$
$541$	−5541.69	−0.440399	−0.220200	+	0.975455i	$0.570671\pi$
$542$	12957.7	1.02690
$543$	−6008.00	−0.474821
$544$	−1024.42	−0.0807384
$545$	894.514	0.0703060
$546$	1478.19	0.115862
$547$	−482.902	−0.0377466	−0.0188733	−	0.999822i	$-0.506008\pi$
$547$	−482.902	−0.0377466	−0.0188733	+	0.999822i	$0.506008\pi$
$548$	8285.10	0.645843
$549$	4738.58	0.368374
$550$	−482.849	−0.0374341
$551$	0	0
$552$	−1077.33	−0.0830688
$553$	3599.80	0.276815
$554$	−7003.87	−0.537123
$555$	690.248	0.0527917
$556$	−5870.18	−0.447753
$557$	−9850.15	−0.749308	−0.374654	−	0.927165i	$-0.622238\pi$
$557$	−9850.15	−0.749308	−0.374654	+	0.927165i	$0.622238\pi$
$558$	−5391.06	−0.409000
$559$	3276.00	0.247872
$560$	237.666	0.0179343
$561$	186.727	0.0140528
$562$	3445.49	0.258611
$563$	15083.7	1.12913	0.564567	−	0.825387i	$-0.309043\pi$
$563$	15083.7	1.12913	0.564567	+	0.825387i	$0.309043\pi$
$564$	−2252.91	−0.168200
$565$	−455.233	−0.0338970
$566$	1811.89	0.134557
$567$	−1322.43	−0.0979482
$568$	−4027.35	−0.297507
$569$	−354.846	−0.0261439	−0.0130720	−	0.999915i	$-0.504161\pi$
$569$	−354.846	−0.0261439	−0.0130720	+	0.999915i	$0.504161\pi$
$570$	0	0
$571$	10394.6	0.761821	0.380910	−	0.924612i	$-0.375611\pi$
$571$	10394.6	0.761821	0.380910	+	0.924612i	$0.375611\pi$
$572$	117.358	0.00857861
$573$	−12305.9	−0.897184
$574$	−2665.99	−0.193861
$575$	5573.91	0.404258
$576$	576.000	0.0416667
$577$	1289.40	0.0930303	0.0465151	−	0.998918i	$-0.485188\pi$
$577$	1289.40	0.0930303	0.0465151	+	0.998918i	$0.485188\pi$
$578$	7776.32	0.559606
$579$	5269.65	0.378237
$580$	113.368	0.00811613
$581$	−3265.63	−0.233186
$582$	6632.40	0.472374
$583$	−22.9671	−0.00163156
$584$	−922.124	−0.0653386
$585$	123.565	0.00873299
$586$	13141.1	0.926373
$587$	19612.9	1.37906	0.689531	−	0.724256i	$-0.257817\pi$
$587$	19612.9	1.37906	0.689531	+	0.724256i	$0.257817\pi$
$588$	917.447	0.0643451
$589$	0	0
$590$	−444.082	−0.0309874
$591$	−11011.7	−0.766432
$592$	4046.17	0.280906
$593$	7358.41	0.509568	0.254784	−	0.966998i	$-0.417996\pi$
$593$	7358.41	0.509568	0.254784	+	0.966998i	$0.417996\pi$
$594$	−104.991	−0.00725222
$595$	475.527	0.0327642
$596$	−707.791	−0.0486447
$597$	7832.26	0.536940
$598$	−1354.75	−0.0926420
$599$	−16712.6	−1.13999	−0.569997	−	0.821647i	$-0.693056\pi$
$599$	−16712.6	−1.13999	−0.569997	+	0.821647i	$0.693056\pi$
$600$	−2980.13	−0.202772
$601$	−8181.83	−0.555314	−0.277657	−	0.960680i	$-0.589558\pi$
$601$	−8181.83	−0.555314	−0.277657	+	0.960680i	$0.589558\pi$
$602$	−7088.70	−0.479923
$603$	1896.54	0.128081
$604$	4554.97	0.306853
$605$	1207.54	0.0811466
$606$	−5378.23	−0.360521
$607$	−19171.1	−1.28193	−0.640966	−	0.767569i	$-0.721466\pi$
$607$	−19171.1	−1.28193	−0.640966	+	0.767569i	$0.721466\pi$
$608$	0	0
$609$	−1525.73	−0.101520
$610$	958.067	0.0635918
$611$	−2833.07	−0.187584
$612$	1152.47	0.0761209
$613$	−23387.4	−1.54096	−0.770481	−	0.637463i	$-0.779984\pi$
$613$	−23387.4	−1.54096	−0.770481	+	0.637463i	$0.779984\pi$
$614$	1133.16	0.0744800
$615$	−222.856	−0.0146121
$616$	−253.941	−0.0166097
$617$	29646.2	1.93438	0.967189	−	0.254056i	$-0.0817649\pi$
$617$	29646.2	1.93438	0.967189	+	0.254056i	$0.0817649\pi$
$618$	−966.959	−0.0629398
$619$	17042.8	1.10663	0.553317	−	0.832971i	$-0.313362\pi$
$619$	17042.8	1.10663	0.553317	+	0.832971i	$0.313362\pi$
$620$	−1089.99	−0.0706049
$621$	1211.99	0.0783181
$622$	−7015.11	−0.452219
$623$	−2842.26	−0.182781
$624$	724.328	0.0464685
$625$	15315.3	0.980177
$626$	643.536	0.0410876
$627$	0	0
$628$	−7808.75	−0.496183
$629$	8095.66	0.513188
$630$	−267.374	−0.0169086
$631$	−12936.7	−0.816170	−0.408085	−	0.912944i	$-0.633803\pi$
$631$	−12936.7	−0.816170	−0.408085	+	0.912944i	$0.633803\pi$
$632$	1763.93	0.111021
$633$	−10420.1	−0.654282
$634$	−7594.05	−0.475707
$635$	−787.421	−0.0492092
$636$	−141.753	−0.00883782
$637$	1153.70	0.0717604
$638$	−121.132	−0.00751669
$639$	4530.76	0.280492
$640$	116.458	0.00719284
$641$	30925.1	1.90557	0.952783	−	0.303650i	$-0.0982055\pi$
$641$	30925.1	1.90557	0.952783	+	0.303650i	$0.0982055\pi$
$642$	6729.39	0.413688
$643$	−2848.23	−0.174686	−0.0873430	−	0.996178i	$-0.527838\pi$
$643$	−2848.23	−0.174686	−0.0873430	+	0.996178i	$0.527838\pi$
$644$	2931.44	0.179371
$645$	−592.559	−0.0361736
$646$	0	0
$647$	14856.5	0.902733	0.451367	−	0.892339i	$-0.350937\pi$
$647$	14856.5	0.902733	0.451367	+	0.892339i	$0.350937\pi$
$648$	−648.000	−0.0392837
$649$	474.493	0.0286987
$650$	−3747.56	−0.226141
$651$	14669.3	0.883157
$652$	1543.90	0.0927357
$653$	−697.326	−0.0417894	−0.0208947	−	0.999782i	$-0.506651\pi$
$653$	−697.326	−0.0417894	−0.0208947	+	0.999782i	$0.506651\pi$
$654$	−5898.99	−0.352705
$655$	2133.36	0.127263
$656$	−1306.36	−0.0777512
$657$	1037.39	0.0616018
$658$	6130.26	0.363195
$659$	2792.41	0.165064	0.0825319	−	0.996588i	$-0.473699\pi$
$659$	2792.41	0.165064	0.0825319	+	0.996588i	$0.473699\pi$
$660$	−21.2275	−0.00125194
$661$	−28297.2	−1.66510	−0.832551	−	0.553949i	$-0.813120\pi$
$661$	−28297.2	−1.66510	−0.832551	+	0.553949i	$0.813120\pi$
$662$	19176.9	1.12588
$663$	1449.25	0.0848933
$664$	−1600.19	−0.0935230
$665$	0	0
$666$	−4551.94	−0.264841
$667$	1398.32	0.0811741
$668$	12824.4	0.742803
$669$	7591.48	0.438720
$670$	383.450	0.0221104
$671$	−1023.68	−0.0588950
$672$	−1567.32	−0.0899712
$673$	19162.8	1.09758	0.548790	−	0.835960i	$-0.315089\pi$
$673$	19162.8	1.09758	0.548790	+	0.835960i	$0.315089\pi$
$674$	18527.2	1.05881
$675$	3352.65	0.191176
$676$	−7877.15	−0.448176
$677$	14029.7	0.796463	0.398232	−	0.917285i	$-0.369624\pi$
$677$	14029.7	0.796463	0.398232	+	0.917285i	$0.369624\pi$
$678$	3002.10	0.170051
$679$	−18047.0	−1.02000
$680$	233.012	0.0131406
$681$	−20203.8	−1.13687
$682$	1164.63	0.0653901
$683$	6578.33	0.368540	0.184270	−	0.982876i	$-0.441008\pi$
$683$	6578.33	0.368540	0.184270	+	0.982876i	$0.441008\pi$
$684$	0	0
$685$	−1884.51	−0.105114
$686$	−13696.2	−0.762279
$687$	1013.16	0.0562654
$688$	−3473.52	−0.192481
$689$	−178.256	−0.00985633
$690$	245.046	0.0135199
$691$	28001.9	1.54159	0.770797	−	0.637080i	$-0.219858\pi$
$691$	28001.9	1.54159	0.770797	+	0.637080i	$0.219858\pi$
$692$	12778.9	0.701993
$693$	285.684	0.0156598
$694$	7206.99	0.394198
$695$	1335.22	0.0728743
$696$	−747.622	−0.0407163
$697$	−2613.79	−0.142044
$698$	−7503.20	−0.406877
$699$	18933.8	1.02452
$700$	8109.06	0.437848
$701$	1649.54	0.0888762	0.0444381	−	0.999012i	$-0.485850\pi$
$701$	1649.54	0.0888762	0.0444381	+	0.999012i	$0.485850\pi$
$702$	−814.869	−0.0438109
$703$	0	0
$704$	−124.433	−0.00666159
$705$	512.442	0.0273754
$706$	17672.8	0.942102
$707$	14634.4	0.778476
$708$	2928.56	0.155455
$709$	12138.8	0.642993	0.321496	−	0.946911i	$-0.395814\pi$
$709$	12138.8	0.642993	0.321496	+	0.946911i	$0.395814\pi$
$710$	916.050	0.0484208
$711$	−1984.42	−0.104672
$712$	−1392.73	−0.0733073
$713$	−13444.3	−0.706160
$714$	−3135.93	−0.164368
$715$	−26.6939	−0.00139622
$716$	−9797.04	−0.511358
$717$	9826.67	0.511832
$718$	−14696.3	−0.763872
$719$	−17081.4	−0.885994	−0.442997	−	0.896523i	$-0.646085\pi$
$719$	−17081.4	−0.885994	−0.442997	+	0.896523i	$0.646085\pi$
$720$	−131.016	−0.00678147
$721$	2631.13	0.135906
$722$	0	0
$723$	5004.82	0.257443
$724$	8010.67	0.411207
$725$	3868.08	0.198147
$726$	−7963.32	−0.407089
$727$	−8523.48	−0.434826	−0.217413	−	0.976080i	$-0.569762\pi$
$727$	−8523.48	−0.434826	−0.217413	+	0.976080i	$0.569762\pi$
$728$	−1970.93	−0.100340
$729$	729.000	0.0370370
$730$	209.744	0.0106342
$731$	−6949.90	−0.351644
$732$	−6318.10	−0.319022
$733$	19655.2	0.990425	0.495212	−	0.868772i	$-0.335090\pi$
$733$	19655.2	0.990425	0.495212	+	0.868772i	$0.335090\pi$
$734$	21658.8	1.08916
$735$	−208.680	−0.0104725
$736$	1436.43	0.0719397
$737$	−409.709	−0.0204774
$738$	1469.65	0.0733045
$739$	−844.721	−0.0420481	−0.0210241	−	0.999779i	$-0.506693\pi$
$739$	−844.721	−0.0420481	−0.0210241	+	0.999779i	$0.506693\pi$
$740$	−920.331	−0.0457190
$741$	0	0
$742$	385.714	0.0190836
$743$	23692.3	1.16983	0.584916	−	0.811094i	$-0.301127\pi$
$743$	23692.3	1.16983	0.584916	+	0.811094i	$0.301127\pi$
$744$	7188.08	0.354204
$745$	160.992	0.00791719
$746$	21229.2	1.04190
$747$	1800.21	0.0881743
$748$	−248.969	−0.0121701
$749$	−18310.9	−0.893280
$750$	1360.23	0.0662246
$751$	8581.33	0.416960	0.208480	−	0.978027i	$-0.433148\pi$
$751$	8581.33	0.416960	0.208480	+	0.978027i	$0.433148\pi$
$752$	3003.88	0.145665
$753$	6133.16	0.296819
$754$	−940.145	−0.0454086
$755$	−1036.06	−0.0499420
$756$	1763.23	0.0848256
$757$	−19326.7	−0.927926	−0.463963	−	0.885855i	$-0.653573\pi$
$757$	−19326.7	−0.927926	−0.463963	+	0.885855i	$0.653573\pi$
$758$	7076.34	0.339082
$759$	−261.827	−0.0125213
$760$	0	0
$761$	−26601.6	−1.26716	−0.633580	−	0.773677i	$-0.718415\pi$
$761$	−26601.6	−1.26716	−0.633580	+	0.773677i	$0.718415\pi$
$762$	5192.75	0.246868
$763$	16051.4	0.761598
$764$	16407.9	0.776984
$765$	−262.139	−0.0123891
$766$	26276.1	1.23942
$767$	3682.70	0.173370
$768$	−768.000	−0.0360844
$769$	−24235.8	−1.13650	−0.568248	−	0.822857i	$-0.692379\pi$
$769$	−24235.8	−1.13650	−0.568248	+	0.822857i	$0.692379\pi$
$770$	57.7608	0.00270332
$771$	15543.9	0.726072
$772$	−7026.20	−0.327563
$773$	11054.8	0.514377	0.257188	−	0.966361i	$-0.417204\pi$
$773$	11054.8	0.514377	0.257188	+	0.966361i	$0.417204\pi$
$774$	3907.71	0.181473
$775$	−37190.0	−1.72375
$776$	−8843.20	−0.409088
$777$	12386.0	0.571873
$778$	−2116.91	−0.0975514
$779$	0	0
$780$	−164.754	−0.00756299
$781$	−978.782	−0.0448445
$782$	2874.05	0.131427
$783$	841.075	0.0383877
$784$	−1223.26	−0.0557245
$785$	1776.16	0.0807565
$786$	−14068.8	−0.638443
$787$	34632.5	1.56863	0.784316	−	0.620361i	$-0.213014\pi$
$787$	34632.5	1.56863	0.784316	+	0.620361i	$0.213014\pi$
$788$	14682.3	0.663750
$789$	−21413.8	−0.966224
$790$	−401.220	−0.0180693
$791$	−8168.82	−0.367193
$792$	139.988	0.00628061
$793$	−7945.10	−0.355787
$794$	30361.5	1.35704
$795$	32.2427	0.00143840
$796$	−10443.0	−0.465004
$797$	−21904.6	−0.973526	−0.486763	−	0.873534i	$-0.661822\pi$
$797$	−21904.6	−0.973526	−0.486763	+	0.873534i	$0.661822\pi$
$798$	0	0
$799$	6010.23	0.266116
$800$	3973.51	0.175606
$801$	1566.82	0.0691148
$802$	−2672.40	−0.117663
$803$	−224.107	−0.00984879
$804$	−2528.72	−0.110922
$805$	−666.779	−0.0291936
$806$	9039.12	0.395024
$807$	19186.6	0.836925
$808$	7170.97	0.312220
$809$	33327.8	1.44838	0.724192	−	0.689598i	$-0.242213\pi$
$809$	33327.8	1.44838	0.724192	+	0.689598i	$0.242213\pi$
$810$	147.392	0.00639363
$811$	−1389.76	−0.0601738	−0.0300869	−	0.999547i	$-0.509578\pi$
$811$	−1389.76	−0.0601738	−0.0300869	+	0.999547i	$0.509578\pi$
$812$	2034.31	0.0879191
$813$	19436.6	0.838464
$814$	983.356	0.0423423
$815$	−351.171	−0.0150932
$816$	−1536.63	−0.0659226
$817$	0	0
$818$	−3952.06	−0.168925
$819$	2217.29	0.0946013
$820$	297.141	0.0126544
$821$	−11572.6	−0.491943	−0.245972	−	0.969277i	$-0.579107\pi$
$821$	−11572.6	−0.491943	−0.245972	+	0.969277i	$0.579107\pi$
$822$	12427.7	0.527329
$823$	26073.3	1.10432	0.552162	−	0.833737i	$-0.313803\pi$
$823$	26073.3	1.10432	0.552162	+	0.833737i	$0.313803\pi$
$824$	1289.28	0.0545074
$825$	−724.274	−0.0305648
$826$	−7968.72	−0.335675
$827$	−44795.6	−1.88355	−0.941775	−	0.336245i	$-0.890843\pi$
$827$	−44795.6	−1.88355	−0.941775	+	0.336245i	$0.890843\pi$
$828$	−1615.99	−0.0678254
$829$	−12346.2	−0.517250	−0.258625	−	0.965978i	$-0.583269\pi$
$829$	−12346.2	−0.517250	−0.258625	+	0.965978i	$0.583269\pi$
$830$	363.974	0.0152214
$831$	−10505.8	−0.438559
$832$	−965.771	−0.0402429
$833$	−2447.53	−0.101803
$834$	−8805.26	−0.365589
$835$	−2917.02	−0.120895
$836$	0	0
$837$	−8086.59	−0.333947
$838$	−6485.79	−0.267360
$839$	7050.38	0.290115	0.145057	−	0.989423i	$-0.453663\pi$
$839$	7050.38	0.290115	0.145057	+	0.989423i	$0.453663\pi$
$840$	356.498	0.0146433
$841$	−23418.6	−0.960212
$842$	23918.8	0.978976
$843$	5168.24	0.211155
$844$	13893.4	0.566624
$845$	1791.72	0.0729431
$846$	−3379.37	−0.137335
$847$	21668.5	0.879030
$848$	189.003	0.00765378
$849$	2717.84	0.109866
$850$	7950.29	0.320815
$851$	−11351.7	−0.457262
$852$	−6041.02	−0.242913
$853$	6590.63	0.264547	0.132274	−	0.991213i	$-0.457772\pi$
$853$	6590.63	0.264547	0.132274	+	0.991213i	$0.457772\pi$
$854$	17191.8	0.688866
$855$	0	0
$856$	−8972.52	−0.358264
$857$	−41470.4	−1.65298	−0.826489	−	0.562954i	$-0.809665\pi$
$857$	−41470.4	−1.65298	−0.826489	+	0.562954i	$0.809665\pi$
$858$	176.036	0.00700441
$859$	33928.2	1.34763	0.673816	−	0.738899i	$-0.264654\pi$
$859$	33928.2	1.34763	0.673816	+	0.738899i	$0.264654\pi$
$860$	790.079	0.0313273
$861$	−3998.99	−0.158287
$862$	−14452.3	−0.571051
$863$	6042.42	0.238339	0.119169	−	0.992874i	$-0.461977\pi$
$863$	6042.42	0.238339	0.119169	+	0.992874i	$0.461977\pi$
$864$	864.000	0.0340207
$865$	−2906.65	−0.114253
$866$	19806.0	0.777177
$867$	11664.5	0.456916
$868$	−19559.1	−0.764836
$869$	428.695	0.0167347
$870$	170.052	0.00662680
$871$	−3179.90	−0.123705
$872$	7865.32	0.305451
$873$	9948.60	0.385692
$874$	0	0
$875$	−3701.23	−0.142999
$876$	−1383.19	−0.0533488
$877$	23546.2	0.906611	0.453306	−	0.891355i	$-0.350245\pi$
$877$	23546.2	0.906611	0.453306	+	0.891355i	$0.350245\pi$
$878$	14155.9	0.544123
$879$	19711.7	0.756381
$880$	28.3033	0.00108421
$881$	−39700.3	−1.51820	−0.759101	−	0.650973i	$-0.774361\pi$
$881$	−39700.3	−1.51820	−0.759101	+	0.650973i	$0.774361\pi$
$882$	1376.17	0.0525375
$883$	−41792.3	−1.59278	−0.796389	−	0.604785i	$-0.793259\pi$
$883$	−41792.3	−1.59278	−0.796389	+	0.604785i	$0.793259\pi$
$884$	−1932.34	−0.0735198
$885$	−666.122	−0.0253011
$886$	15461.2	0.586262
$887$	3207.98	0.121435	0.0607177	−	0.998155i	$-0.480661\pi$
$887$	3207.98	0.121435	0.0607177	+	0.998155i	$0.480661\pi$
$888$	6069.25	0.229359
$889$	−14129.7	−0.533065
$890$	316.787	0.0119312
$891$	−157.486	−0.00592141
$892$	−10122.0	−0.379942
$893$	0	0
$894$	−1061.69	−0.0397183
$895$	2228.41	0.0832263
$896$	2089.76	0.0779173
$897$	−2032.13	−0.0756419
$898$	4706.81	0.174909
$899$	−9329.81	−0.346125
$900$	−4470.20	−0.165563
$901$	378.162	0.0139827
$902$	−317.490	−0.0117198
$903$	−10633.0	−0.391856
$904$	−4002.80	−0.147269
$905$	−1822.09	−0.0669262
$906$	6832.46	0.250544
$907$	−51184.8	−1.87383	−0.936915	−	0.349558i	$-0.886332\pi$
$907$	−51184.8	−1.87383	−0.936915	+	0.349558i	$0.886332\pi$
$908$	26938.4	0.984560
$909$	−8067.34	−0.294364
$910$	448.302	0.0163308
$911$	−15160.8	−0.551372	−0.275686	−	0.961248i	$-0.588905\pi$
$911$	−15160.8	−0.551372	−0.275686	+	0.961248i	$0.588905\pi$
$912$	0	0
$913$	−388.900	−0.0140971
$914$	−16841.9	−0.609497
$915$	1437.10	0.0519225
$916$	−1350.88	−0.0487273
$917$	38281.7	1.37860
$918$	1728.71	0.0621524
$919$	33318.2	1.19594	0.597969	−	0.801519i	$-0.295974\pi$
$919$	33318.2	1.19594	0.597969	+	0.801519i	$0.295974\pi$
$920$	−326.728	−0.0117086
$921$	1699.74	0.0608127
$922$	1339.24	0.0478369
$923$	−7596.67	−0.270907
$924$	−380.912	−0.0135618
$925$	−31401.3	−1.11618
$926$	−11141.8	−0.395401
$927$	−1450.44	−0.0513901
$928$	996.830	0.0352613
$929$	14464.8	0.510843	0.255421	−	0.966830i	$-0.417786\pi$
$929$	14464.8	0.510843	0.255421	+	0.966830i	$0.417786\pi$
$930$	−1634.98	−0.0576486
$931$	0	0
$932$	−25245.0	−0.887262
$933$	−10522.7	−0.369235
$934$	21739.6	0.761606
$935$	56.6299	0.00198074
$936$	1086.49	0.0379414
$937$	16046.8	0.559475	0.279737	−	0.960077i	$-0.409753\pi$
$937$	16046.8	0.559475	0.279737	+	0.960077i	$0.409753\pi$
$938$	6880.74	0.239514
$939$	965.304	0.0335479
$940$	−683.256	−0.0237078
$941$	−19129.4	−0.662700	−0.331350	−	0.943508i	$-0.607504\pi$
$941$	−19129.4	−0.662700	−0.331350	+	0.943508i	$0.607504\pi$
$942$	−11713.1	−0.405132
$943$	3665.04	0.126564
$944$	−3904.74	−0.134628
$945$	−401.061	−0.0138058
$946$	−844.184	−0.0290135
$947$	−41617.7	−1.42808	−0.714041	−	0.700104i	$-0.753137\pi$
$947$	−41617.7	−1.42808	−0.714041	+	0.700104i	$0.753137\pi$
$948$	2645.90	0.0906485
$949$	−1739.38	−0.0594969
$950$	0	0
$951$	−11391.1	−0.388413
$952$	4181.24	0.142347
$953$	36269.8	1.23284	0.616419	−	0.787419i	$-0.288583\pi$
$953$	36269.8	1.23284	0.616419	+	0.787419i	$0.288583\pi$
$954$	−212.629	−0.00721605
$955$	−3732.09	−0.126458
$956$	−13102.2	−0.443260
$957$	−181.698	−0.00613736
$958$	4870.66	0.164263
$959$	−33816.1	−1.13867
$960$	174.687	0.00587293
$961$	59911.3	2.01105
$962$	7632.17	0.255791
$963$	10094.1	0.337775
$964$	−6673.09	−0.222952
$965$	1598.16	0.0533126
$966$	4397.17	0.146456
$967$	28249.4	0.939442	0.469721	−	0.882815i	$-0.344354\pi$
$967$	28249.4	0.939442	0.469721	+	0.882815i	$0.344354\pi$
$968$	10617.8	0.352549
$969$	0	0
$970$	2011.45	0.0665813
$971$	11234.1	0.371285	0.185643	−	0.982617i	$-0.440563\pi$
$971$	11234.1	0.371285	0.185643	+	0.982617i	$0.440563\pi$
$972$	−972.000	−0.0320750
$973$	23959.5	0.789420
$974$	21370.3	0.703029
$975$	−5621.34	−0.184643
$976$	8424.14	0.276281
$977$	10338.6	0.338547	0.169273	−	0.985569i	$-0.445858\pi$
$977$	10338.6	0.338547	0.169273	+	0.985569i	$0.445858\pi$
$978$	2315.84	0.0757184
$979$	−338.481	−0.0110499
$980$	278.240	0.00906945
$981$	−8848.49	−0.287982
$982$	18137.8	0.589410
$983$	35054.0	1.13739	0.568693	−	0.822550i	$-0.307449\pi$
$983$	35054.0	1.13739	0.568693	+	0.822550i	$0.307449\pi$
$984$	−1959.54	−0.0634836
$985$	−3339.60	−0.108029
$986$	1994.48	0.0644190
$987$	9195.39	0.296548
$988$	0	0
$989$	9745.09	0.313322
$990$	−31.8412	−0.00102220
$991$	25256.8	0.809595	0.404798	−	0.914406i	$-0.367342\pi$
$991$	25256.8	0.809595	0.404798	+	0.914406i	$0.367342\pi$
$992$	−9584.11	−0.306750
$993$	28765.3	0.919275
$994$	16437.9	0.524524
$995$	2375.34	0.0756818
$996$	−2400.28	−0.0763612
$997$	−39035.2	−1.23998	−0.619989	−	0.784611i	$-0.712863\pi$
$997$	−39035.2	−1.23998	−0.619989	+	0.784611i	$0.712863\pi$
$998$	18171.1	0.576348
$999$	−6827.91	−0.216242

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2166.4.a.j.1.2	✓	2
19.18	odd	2		2166.4.a.p.1.2	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2166.4.a.j.1.2	✓	2	1.1	even	1	trivial
2166.4.a.p.1.2	yes	2	19.18	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:	\( N \)	\(=\)	\( 2166 = 2 \cdot 3 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2166.a (trivial)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -0.909830 q^{5} +6.00000 q^{6} -16.3262 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -0.909830 q^{5} +6.00000 q^{6} -16.3262 q^{7} -8.00000 q^{8} +9.00000 q^{9} +1.81966 q^{10} -1.94427 q^{11} -12.0000 q^{12} -15.0902 q^{13} +32.6525 q^{14} +2.72949 q^{15} +16.0000 q^{16} +32.0132 q^{17} -18.0000 q^{18} -3.63932 q^{20} +48.9787 q^{21} +3.88854 q^{22} -44.8885 q^{23} +24.0000 q^{24} -124.172 q^{25} +30.1803 q^{26} -27.0000 q^{27} -65.3050 q^{28} -31.1509 q^{29} -5.45898 q^{30} +299.503 q^{31} -32.0000 q^{32} +5.83282 q^{33} -64.0263 q^{34} +14.8541 q^{35} +36.0000 q^{36} +252.885 q^{37} +45.2705 q^{39} +7.27864 q^{40} -81.6475 q^{41} -97.9574 q^{42} -217.095 q^{43} -7.77709 q^{44} -8.18847 q^{45} +89.7771 q^{46} +187.743 q^{47} -48.0000 q^{48} -76.4540 q^{49} +248.344 q^{50} -96.0395 q^{51} -60.3607 q^{52} +11.8127 q^{53} +54.0000 q^{54} +1.76896 q^{55} +130.610 q^{56} +62.3018 q^{58} -244.046 q^{59} +10.9180 q^{60} +526.508 q^{61} -599.007 q^{62} -146.936 q^{63} +64.0000 q^{64} +13.7295 q^{65} -11.6656 q^{66} +210.726 q^{67} +128.053 q^{68} +134.666 q^{69} -29.7082 q^{70} +503.418 q^{71} -72.0000 q^{72} +115.265 q^{73} -505.771 q^{74} +372.517 q^{75} +31.7426 q^{77} -90.5410 q^{78} -220.492 q^{79} -14.5573 q^{80} +81.0000 q^{81} +163.295 q^{82} +200.023 q^{83} +195.915 q^{84} -29.1265 q^{85} +434.190 q^{86} +93.4528 q^{87} +15.5542 q^{88} +174.091 q^{89} +16.3769 q^{90} +246.366 q^{91} -179.554 q^{92} -898.510 q^{93} -375.485 q^{94} +96.0000 q^{96} +1105.40 q^{97} +152.908 q^{98} -17.4984 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 4 q^{2} - 6 q^{3} + 8 q^{4} - 13 q^{5} + 12 q^{6} - 17 q^{7} - 16 q^{8} + 18 q^{9}+O(q^{10}) \) 2 * q - 4 * q^2 - 6 * q^3 + 8 * q^4 - 13 * q^5 + 12 * q^6 - 17 * q^7 - 16 * q^8 + 18 * q^9	\( 2 q - 4 q^{2} - 6 q^{3} + 8 q^{4} - 13 q^{5} + 12 q^{6} - 17 q^{7} - 16 q^{8} + 18 q^{9} + 26 q^{10} + 14 q^{11} - 24 q^{12} - 19 q^{13} + 34 q^{14} + 39 q^{15} + 32 q^{16} - 12 q^{17} - 36 q^{18} - 52 q^{20} + 51 q^{21} - 28 q^{22} - 54 q^{23} + 48 q^{24} - 103 q^{25} + 38 q^{26} - 54 q^{27} - 68 q^{28} + 130 q^{29} - 78 q^{30} + 239 q^{31} - 64 q^{32} - 42 q^{33} + 24 q^{34} + 23 q^{35} + 72 q^{36} + 148 q^{37} + 57 q^{39} + 104 q^{40} - 331 q^{41} - 102 q^{42} - 224 q^{43} + 56 q^{44} - 117 q^{45} + 108 q^{46} + 333 q^{47} - 96 q^{48} - 419 q^{49} + 206 q^{50} + 36 q^{51} - 76 q^{52} + 766 q^{53} + 108 q^{54} - 191 q^{55} + 136 q^{56} - 260 q^{58} + 460 q^{59} + 156 q^{60} + 494 q^{61} - 478 q^{62} - 153 q^{63} + 128 q^{64} + 61 q^{65} + 84 q^{66} + 133 q^{67} - 48 q^{68} + 162 q^{69} - 46 q^{70} + 459 q^{71} - 144 q^{72} + 396 q^{73} - 296 q^{74} + 309 q^{75} + 21 q^{77} - 114 q^{78} - 1000 q^{79} - 208 q^{80} + 162 q^{81} + 662 q^{82} - 74 q^{83} + 204 q^{84} + 503 q^{85} + 448 q^{86} - 390 q^{87} - 112 q^{88} + 1180 q^{89} + 234 q^{90} + 249 q^{91} - 216 q^{92} - 717 q^{93} - 666 q^{94} + 192 q^{96} + 1938 q^{97} + 838 q^{98} + 126 q^{99}+O(q^{100}) \) 2 * q - 4 * q^2 - 6 * q^3 + 8 * q^4 - 13 * q^5 + 12 * q^6 - 17 * q^7 - 16 * q^8 + 18 * q^9 + 26 * q^10 + 14 * q^11 - 24 * q^12 - 19 * q^13 + 34 * q^14 + 39 * q^15 + 32 * q^16 - 12 * q^17 - 36 * q^18 - 52 * q^20 + 51 * q^21 - 28 * q^22 - 54 * q^23 + 48 * q^24 - 103 * q^25 + 38 * q^26 - 54 * q^27 - 68 * q^28 + 130 * q^29 - 78 * q^30 + 239 * q^31 - 64 * q^32 - 42 * q^33 + 24 * q^34 + 23 * q^35 + 72 * q^36 + 148 * q^37 + 57 * q^39 + 104 * q^40 - 331 * q^41 - 102 * q^42 - 224 * q^43 + 56 * q^44 - 117 * q^45 + 108 * q^46 + 333 * q^47 - 96 * q^48 - 419 * q^49 + 206 * q^50 + 36 * q^51 - 76 * q^52 + 766 * q^53 + 108 * q^54 - 191 * q^55 + 136 * q^56 - 260 * q^58 + 460 * q^59 + 156 * q^60 + 494 * q^61 - 478 * q^62 - 153 * q^63 + 128 * q^64 + 61 * q^65 + 84 * q^66 + 133 * q^67 - 48 * q^68 + 162 * q^69 - 46 * q^70 + 459 * q^71 - 144 * q^72 + 396 * q^73 - 296 * q^74 + 309 * q^75 + 21 * q^77 - 114 * q^78 - 1000 * q^79 - 208 * q^80 + 162 * q^81 + 662 * q^82 - 74 * q^83 + 204 * q^84 + 503 * q^85 + 448 * q^86 - 390 * q^87 - 112 * q^88 + 1180 * q^89 + 234 * q^90 + 249 * q^91 - 216 * q^92 - 717 * q^93 - 666 * q^94 + 192 * q^96 + 1938 * q^97 + 838 * q^98 + 126 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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