LMFDB - Embedded newform 2166.4.a.o.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(\sqrt{313}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 78 $ x^2 - x - 78
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-8.34590$ 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)

$f(q)$	$=$	$q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +1.34590 q^{5} -6.00000 q^{6} -22.0377 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +1.34590 q^{5} -6.00000 q^{6} -22.0377 q^{7} +8.00000 q^{8} +9.00000 q^{9} +2.69181 q^{10} -13.3459 q^{11} -12.0000 q^{12} -24.0000 q^{13} -44.0754 q^{14} -4.03771 q^{15} +16.0000 q^{16} +117.421 q^{17} +18.0000 q^{18} +5.38361 q^{20} +66.1131 q^{21} -26.6918 q^{22} +19.4590 q^{23} -24.0000 q^{24} -123.189 q^{25} -48.0000 q^{26} -27.0000 q^{27} -88.1508 q^{28} +141.925 q^{29} -8.07542 q^{30} +116.302 q^{31} +32.0000 q^{32} +40.0377 q^{33} +234.843 q^{34} -29.6606 q^{35} +36.0000 q^{36} +84.0000 q^{37} +72.0000 q^{39} +10.7672 q^{40} +45.9246 q^{41} +132.226 q^{42} +314.566 q^{43} -53.3836 q^{44} +12.1131 q^{45} +38.9181 q^{46} -333.874 q^{47} -48.0000 q^{48} +142.661 q^{49} -246.377 q^{50} -352.264 q^{51} -96.0000 q^{52} -346.377 q^{53} -54.0000 q^{54} -17.9623 q^{55} -176.302 q^{56} +283.849 q^{58} -476.754 q^{59} -16.1508 q^{60} +504.566 q^{61} +232.603 q^{62} -198.339 q^{63} +64.0000 q^{64} -32.3017 q^{65} +80.0754 q^{66} -216.453 q^{67} +469.685 q^{68} -58.3771 q^{69} -59.3212 q^{70} -663.698 q^{71} +72.0000 q^{72} -788.113 q^{73} +168.000 q^{74} +369.566 q^{75} +294.113 q^{77} +144.000 q^{78} +1289.06 q^{79} +21.5344 q^{80} +81.0000 q^{81} +91.8492 q^{82} -789.597 q^{83} +264.453 q^{84} +158.038 q^{85} +629.131 q^{86} -425.774 q^{87} -106.767 q^{88} -386.980 q^{89} +24.2263 q^{90} +528.905 q^{91} +77.8361 q^{92} -348.905 q^{93} -667.748 q^{94} -96.0000 q^{96} +437.056 q^{97} +285.321 q^{98} -120.113 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 4 q^{2} - 6 q^{3} + 8 q^{4} - 15 q^{5} - 12 q^{6} + 9 q^{7} + 16 q^{8} + 18 q^{9}+O(q^{10}) $ 2 * q + 4 * q^2 - 6 * q^3 + 8 * q^4 - 15 * q^5 - 12 * q^6 + 9 * q^7 + 16 * q^8 + 18 * q^9	\( 2 q + 4 q^{2} - 6 q^{3} + 8 q^{4} - 15 q^{5} - 12 q^{6} + 9 q^{7} + 16 q^{8} + 18 q^{9} - 30 q^{10} - 9 q^{11} - 24 q^{12} - 48 q^{13} + 18 q^{14} + 45 q^{15} + 32 q^{16} + 111 q^{17} + 36 q^{18} - 60 q^{20} - 27 q^{21} - 18 q^{22} - 138 q^{23} - 48 q^{24} + 19 q^{25} - 96 q^{26} - 54 q^{27} + 36 q^{28} + 390 q^{29} + 90 q^{30} - 192 q^{31} + 64 q^{32} + 27 q^{33} + 222 q^{34} - 537 q^{35} + 72 q^{36} + 168 q^{37} + 144 q^{39} - 120 q^{40} + 198 q^{41} - 54 q^{42} - 167 q^{43} - 36 q^{44} - 135 q^{45} - 276 q^{46} + 93 q^{47} - 96 q^{48} + 763 q^{49} + 38 q^{50} - 333 q^{51} - 192 q^{52} - 162 q^{53} - 108 q^{54} - 89 q^{55} + 72 q^{56} + 780 q^{58} + 108 q^{59} + 180 q^{60} + 213 q^{61} - 384 q^{62} + 81 q^{63} + 128 q^{64} + 360 q^{65} + 54 q^{66} + 204 q^{67} + 444 q^{68} + 414 q^{69} - 1074 q^{70} - 1752 q^{71} + 144 q^{72} - 1417 q^{73} + 336 q^{74} - 57 q^{75} + 429 q^{77} + 288 q^{78} + 1092 q^{79} - 240 q^{80} + 162 q^{81} + 396 q^{82} - 270 q^{83} - 108 q^{84} + 263 q^{85} - 334 q^{86} - 1170 q^{87} - 72 q^{88} + 606 q^{89} - 270 q^{90} - 216 q^{91} - 552 q^{92} + 576 q^{93} + 186 q^{94} - 192 q^{96} - 612 q^{97} + 1526 q^{98} - 81 q^{99}+O(q^{100}) \) 2 * q + 4 * q^2 - 6 * q^3 + 8 * q^4 - 15 * q^5 - 12 * q^6 + 9 * q^7 + 16 * q^8 + 18 * q^9 - 30 * q^10 - 9 * q^11 - 24 * q^12 - 48 * q^13 + 18 * q^14 + 45 * q^15 + 32 * q^16 + 111 * q^17 + 36 * q^18 - 60 * q^20 - 27 * q^21 - 18 * q^22 - 138 * q^23 - 48 * q^24 + 19 * q^25 - 96 * q^26 - 54 * q^27 + 36 * q^28 + 390 * q^29 + 90 * q^30 - 192 * q^31 + 64 * q^32 + 27 * q^33 + 222 * q^34 - 537 * q^35 + 72 * q^36 + 168 * q^37 + 144 * q^39 - 120 * q^40 + 198 * q^41 - 54 * q^42 - 167 * q^43 - 36 * q^44 - 135 * q^45 - 276 * q^46 + 93 * q^47 - 96 * q^48 + 763 * q^49 + 38 * q^50 - 333 * q^51 - 192 * q^52 - 162 * q^53 - 108 * q^54 - 89 * q^55 + 72 * q^56 + 780 * q^58 + 108 * q^59 + 180 * q^60 + 213 * q^61 - 384 * q^62 + 81 * q^63 + 128 * q^64 + 360 * q^65 + 54 * q^66 + 204 * q^67 + 444 * q^68 + 414 * q^69 - 1074 * q^70 - 1752 * q^71 + 144 * q^72 - 1417 * q^73 + 336 * q^74 - 57 * q^75 + 429 * q^77 + 288 * q^78 + 1092 * q^79 - 240 * q^80 + 162 * q^81 + 396 * q^82 - 270 * q^83 - 108 * q^84 + 263 * q^85 - 334 * q^86 - 1170 * q^87 - 72 * q^88 + 606 * q^89 - 270 * q^90 - 216 * q^91 - 552 * q^92 + 576 * q^93 + 186 * q^94 - 192 * q^96 - 612 * q^97 + 1526 * q^98 - 81 * 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
$5$	1.34590	0.120381	0.0601906	−	0.998187i	$-0.480829\pi$
$5$	1.34590	0.120381	0.0601906	+	0.998187i	$0.480829\pi$
$6$	−6.00000	−0.408248
$7$	−22.0377	−1.18992	−0.594962	−	0.803754i	$-0.702833\pi$
$7$	−22.0377	−1.18992	−0.594962	+	0.803754i	$0.702833\pi$
$8$	8.00000	0.353553
$9$	9.00000	0.333333
$10$	2.69181	0.0851224
$11$	−13.3459	−0.365813	−0.182906	−	0.983130i	$-0.558551\pi$
$11$	−13.3459	−0.365813	−0.182906	+	0.983130i	$0.558551\pi$
$12$	−12.0000	−0.288675
$13$	−24.0000	−0.512031	−0.256015	−	0.966673i	$-0.582410\pi$
$13$	−24.0000	−0.512031	−0.256015	+	0.966673i	$0.582410\pi$
$14$	−44.0754	−0.841404
$15$	−4.03771	−0.0695021
$16$	16.0000	0.250000
$17$	117.421	1.67523	0.837613	−	0.546264i	$-0.183950\pi$
$17$	117.421	1.67523	0.837613	+	0.546264i	$0.183950\pi$
$18$	18.0000	0.235702
$19$	0	0
$19$	0	0
$20$	5.38361	0.0601906
$21$	66.1131	0.687003
$22$	−26.6918	−0.258669
$23$	19.4590	0.176413	0.0882063	−	0.996102i	$-0.471887\pi$
$23$	19.4590	0.176413	0.0882063	+	0.996102i	$0.471887\pi$
$24$	−24.0000	−0.204124
$25$	−123.189	−0.985508
$26$	−48.0000	−0.362061
$27$	−27.0000	−0.192450
$28$	−88.1508	−0.594962
$29$	141.925	0.908784	0.454392	−	0.890802i	$-0.349857\pi$
$29$	141.925	0.908784	0.454392	+	0.890802i	$0.349857\pi$
$30$	−8.07542	−0.0491454
$31$	116.302	0.673819	0.336910	−	0.941537i	$-0.390618\pi$
$31$	116.302	0.673819	0.336910	+	0.941537i	$0.390618\pi$
$32$	32.0000	0.176777
$33$	40.0377	0.211202
$34$	234.843	1.18456
$35$	−29.6606	−0.143245
$36$	36.0000	0.166667
$37$	84.0000	0.373230	0.186615	−	0.982433i	$-0.440248\pi$
$37$	84.0000	0.373230	0.186615	+	0.982433i	$0.440248\pi$
$38$	0	0
$39$	72.0000	0.295621
$40$	10.7672	0.0425612
$41$	45.9246	0.174932	0.0874660	−	0.996168i	$-0.472123\pi$
$41$	45.9246	0.174932	0.0874660	+	0.996168i	$0.472123\pi$
$42$	132.226	0.485785
$43$	314.566	1.11560	0.557800	−	0.829975i	$-0.311646\pi$
$43$	314.566	1.11560	0.557800	+	0.829975i	$0.311646\pi$
$44$	−53.3836	−0.182906
$45$	12.1131	0.0401271
$46$	38.9181	0.124742
$47$	−333.874	−1.03618	−0.518090	−	0.855326i	$-0.673357\pi$
$47$	−333.874	−1.03618	−0.518090	+	0.855326i	$0.673357\pi$
$48$	−48.0000	−0.144338
$49$	142.661	0.415920
$50$	−246.377	−0.696860
$51$	−352.264	−0.967193
$52$	−96.0000	−0.256015
$53$	−346.377	−0.897709	−0.448854	−	0.893605i	$-0.648168\pi$
$53$	−346.377	−0.897709	−0.448854	+	0.893605i	$0.648168\pi$
$54$	−54.0000	−0.136083
$55$	−17.9623	−0.0440370
$56$	−176.302	−0.420702
$57$	0	0
$58$	283.849	0.642607
$59$	−476.754	−1.05200	−0.526001	−	0.850484i	$-0.676309\pi$
$59$	−476.754	−1.05200	−0.526001	+	0.850484i	$0.676309\pi$
$60$	−16.1508	−0.0347511
$61$	504.566	1.05907	0.529533	−	0.848289i	$-0.322367\pi$
$61$	504.566	1.05907	0.529533	+	0.848289i	$0.322367\pi$
$62$	232.603	0.476462
$63$	−198.339	−0.396641
$64$	64.0000	0.125000
$65$	−32.3017	−0.0616389
$66$	80.0754	0.149342
$67$	−216.453	−0.394685	−0.197342	−	0.980335i	$-0.563231\pi$
$67$	−216.453	−0.394685	−0.197342	+	0.980335i	$0.563231\pi$
$68$	469.685	0.837613
$69$	−58.3771	−0.101852
$70$	−59.3212	−0.101289
$71$	−663.698	−1.10939	−0.554694	−	0.832055i	$-0.687165\pi$
$71$	−663.698	−1.10939	−0.554694	+	0.832055i	$0.687165\pi$
$72$	72.0000	0.117851
$73$	−788.113	−1.26358	−0.631792	−	0.775138i	$-0.717680\pi$
$73$	−788.113	−1.26358	−0.631792	+	0.775138i	$0.717680\pi$
$74$	168.000	0.263914
$75$	369.566	0.568984
$76$	0	0
$77$	294.113	0.435290
$78$	144.000	0.209036
$79$	1289.06	1.83582	0.917912	−	0.396784i	$-0.129874\pi$
$79$	1289.06	1.83582	0.917912	+	0.396784i	$0.129874\pi$
$80$	21.5344	0.0300953
$81$	81.0000	0.111111
$82$	91.8492	0.123696
$83$	−789.597	−1.04421	−0.522105	−	0.852881i	$-0.674853\pi$
$83$	−789.597	−1.04421	−0.522105	+	0.852881i	$0.674853\pi$
$84$	264.453	0.343502
$85$	158.038	0.201666
$86$	629.131	0.788848
$87$	−425.774	−0.524687
$88$	−106.767	−0.129334
$89$	−386.980	−0.460897	−0.230449	−	0.973085i	$-0.574019\pi$
$89$	−386.980	−0.460897	−0.230449	+	0.973085i	$0.574019\pi$
$90$	24.2263	0.0283741
$91$	528.905	0.609278
$92$	77.8361	0.0882063
$93$	−348.905	−0.389030
$94$	−667.748	−0.732691
$95$	0	0
$96$	−96.0000	−0.102062
$97$	437.056	0.457488	0.228744	−	0.973487i	$-0.426538\pi$
$97$	437.056	0.457488	0.228744	+	0.973487i	$0.426538\pi$
$98$	285.321	0.294100
$99$	−120.113	−0.121938
$100$	−492.754	−0.492754
$101$	−139.233	−0.137170	−0.0685850	−	0.997645i	$-0.521848\pi$
$101$	−139.233	−0.137170	−0.0685850	+	0.997645i	$0.521848\pi$
$102$	−704.528	−0.683908
$103$	−1426.11	−1.36426	−0.682131	−	0.731230i	$-0.738947\pi$
$103$	−1426.11	−1.36426	−0.682131	+	0.731230i	$0.738947\pi$
$104$	−192.000	−0.181030
$105$	88.9819	0.0827023
$106$	−692.754	−0.634776
$107$	−947.547	−0.856102	−0.428051	−	0.903755i	$-0.640800\pi$
$107$	−947.547	−0.856102	−0.428051	+	0.903755i	$0.640800\pi$
$108$	−108.000	−0.0962250
$109$	−1664.75	−1.46289	−0.731443	−	0.681903i	$-0.761153\pi$
$109$	−1664.75	−1.46289	−0.731443	+	0.681903i	$0.761153\pi$
$110$	−35.9246	−0.0311389
$111$	−252.000	−0.215485
$112$	−352.603	−0.297481
$113$	2096.04	1.74494	0.872471	−	0.488665i	$-0.162516\pi$
$113$	2096.04	1.74494	0.872471	+	0.488665i	$0.162516\pi$
$114$	0	0
$115$	26.1900	0.0212368
$116$	567.698	0.454392
$117$	−216.000	−0.170677
$118$	−953.508	−0.743878
$119$	−2587.70	−1.99339
$120$	−32.3017	−0.0245727
$121$	−1152.89	−0.866181
$122$	1009.13	0.748873
$123$	−137.774	−0.100997
$124$	465.207	0.336910
$125$	−334.038	−0.239018
$126$	−396.679	−0.280468
$127$	238.112	0.166370	0.0831850	−	0.996534i	$-0.473491\pi$
$127$	238.112	0.166370	0.0831850	+	0.996534i	$0.473491\pi$
$128$	128.000	0.0883883
$129$	−943.697	−0.644092
$130$	−64.6033	−0.0435853
$131$	−1407.26	−0.938570	−0.469285	−	0.883047i	$-0.655488\pi$
$131$	−1407.26	−0.938570	−0.469285	+	0.883047i	$0.655488\pi$
$132$	160.151	0.105601
$133$	0	0
$134$	−432.905	−0.279084
$135$	−36.3394	−0.0231674
$136$	939.371	0.592282
$137$	−863.458	−0.538468	−0.269234	−	0.963075i	$-0.586771\pi$
$137$	−863.458	−0.538468	−0.269234	+	0.963075i	$0.586771\pi$
$138$	−116.754	−0.0720201
$139$	1384.22	0.844665	0.422332	−	0.906441i	$-0.361211\pi$
$139$	1384.22	0.844665	0.422332	+	0.906441i	$0.361211\pi$
$140$	−118.642	−0.0716223
$141$	1001.62	0.598239
$142$	−1327.40	−0.784455
$143$	320.302	0.187307
$144$	144.000	0.0833333
$145$	191.017	0.109401
$146$	−1576.23	−0.893489
$147$	−427.982	−0.240132
$148$	336.000	0.186615
$149$	−1825.80	−1.00386	−0.501930	−	0.864908i	$-0.667377\pi$
$149$	−1825.80	−1.00386	−0.501930	+	0.864908i	$0.667377\pi$
$150$	739.131	0.402332
$151$	−1561.81	−0.841711	−0.420855	−	0.907128i	$-0.638270\pi$
$151$	−1561.81	−0.841711	−0.420855	+	0.907128i	$0.638270\pi$
$152$	0	0
$153$	1056.79	0.558409
$154$	588.226	0.307796
$155$	156.531	0.0811152
$156$	288.000	0.147811
$157$	−1290.45	−0.655983	−0.327991	−	0.944681i	$-0.606372\pi$
$157$	−1290.45	−0.655983	−0.327991	+	0.944681i	$0.606372\pi$
$158$	2578.11	1.29812
$159$	1039.13	0.518292
$160$	43.0689	0.0212806
$161$	−428.832	−0.209918
$162$	162.000	0.0785674
$163$	−53.5866	−0.0257499	−0.0128749	−	0.999917i	$-0.504098\pi$
$163$	−53.5866	−0.0257499	−0.0128749	+	0.999917i	$0.504098\pi$
$164$	183.698	0.0874660
$165$	53.8869	0.0254248
$166$	−1579.19	−0.738369
$167$	1169.96	0.542121	0.271061	−	0.962562i	$-0.412626\pi$
$167$	1169.96	0.542121	0.271061	+	0.962562i	$0.412626\pi$
$168$	528.905	0.242892
$169$	−1621.00	−0.737824
$170$	316.075	0.142599
$171$	0	0
$172$	1258.26	0.557800
$173$	3266.53	1.43555	0.717773	−	0.696277i	$-0.245161\pi$
$173$	3266.53	1.43555	0.717773	+	0.696277i	$0.245161\pi$
$174$	−851.547	−0.371009
$175$	2714.79	1.17268
$176$	−213.534	−0.0914532
$177$	1430.26	0.607374
$178$	−773.961	−0.325903
$179$	−2310.41	−0.964740	−0.482370	−	0.875968i	$-0.660224\pi$
$179$	−2310.41	−0.964740	−0.482370	+	0.875968i	$0.660224\pi$
$180$	48.4525	0.0200635
$181$	1230.49	0.505313	0.252657	−	0.967556i	$-0.418696\pi$
$181$	1230.49	0.505313	0.252657	+	0.967556i	$0.418696\pi$
$182$	1057.81	0.430825
$183$	−1513.70	−0.611452
$184$	155.672	0.0623712
$185$	113.056	0.0449299
$186$	−697.810	−0.275086
$187$	−1567.09	−0.612819
$188$	−1335.50	−0.518090
$189$	595.018	0.229001
$190$	0	0
$191$	−964.139	−0.365250	−0.182625	−	0.983183i	$-0.558459\pi$
$191$	−964.139	−0.365250	−0.182625	+	0.983183i	$0.558459\pi$
$192$	−192.000	−0.0721688
$193$	4716.37	1.75903	0.879513	−	0.475875i	$-0.157868\pi$
$193$	4716.37	1.75903	0.879513	+	0.475875i	$0.157868\pi$
$194$	874.112	0.323493
$195$	96.9050	0.0355872
$196$	570.642	0.207960
$197$	−206.629	−0.0747296	−0.0373648	−	0.999302i	$-0.511896\pi$
$197$	−206.629	−0.0747296	−0.0373648	+	0.999302i	$0.511896\pi$
$198$	−240.226	−0.0862229
$199$	−3490.34	−1.24333	−0.621667	−	0.783281i	$-0.713544\pi$
$199$	−3490.34	−1.24333	−0.621667	+	0.783281i	$0.713544\pi$
$200$	−985.508	−0.348430
$201$	649.358	0.227871
$202$	−278.466	−0.0969939
$203$	−3127.69	−1.08138
$204$	−1409.06	−0.483596
$205$	61.8100	0.0210585
$206$	−2852.22	−0.964679
$207$	175.131	0.0588042
$208$	−384.000	−0.128008
$209$	0	0
$210$	177.964	0.0584793
$211$	−3767.09	−1.22909	−0.614544	−	0.788883i	$-0.710660\pi$
$211$	−3767.09	−1.22909	−0.614544	+	0.788883i	$0.710660\pi$
$212$	−1385.51	−0.448854
$213$	1991.09	0.640505
$214$	−1895.09	−0.605355
$215$	423.375	0.134297
$216$	−216.000	−0.0680414
$217$	−2563.02	−0.801794
$218$	−3329.51	−1.03442
$219$	2364.34	0.729531
$220$	−71.8492	−0.0220185
$221$	−2818.11	−0.857768
$222$	−504.000	−0.152371
$223$	1457.06	0.437541	0.218771	−	0.975776i	$-0.429795\pi$
$223$	1457.06	0.437541	0.218771	+	0.975776i	$0.429795\pi$
$224$	−705.207	−0.210351
$225$	−1108.70	−0.328503
$226$	4192.07	1.23386
$227$	−1640.68	−0.479716	−0.239858	−	0.970808i	$-0.577101\pi$
$227$	−1640.68	−0.479716	−0.239858	+	0.970808i	$0.577101\pi$
$228$	0	0
$229$	1871.36	0.540012	0.270006	−	0.962859i	$-0.412974\pi$
$229$	1871.36	0.540012	0.270006	+	0.962859i	$0.412974\pi$
$230$	52.3799	0.0150167
$231$	−882.339	−0.251315
$232$	1135.40	0.321304
$233$	−5915.56	−1.66327	−0.831633	−	0.555325i	$-0.812594\pi$
$233$	−5915.56	−1.66327	−0.831633	+	0.555325i	$0.812594\pi$
$234$	−432.000	−0.120687
$235$	−449.362	−0.124737
$236$	−1907.02	−0.526001
$237$	−3867.17	−1.05991
$238$	−5175.39	−1.40954
$239$	−5243.83	−1.41923	−0.709614	−	0.704591i	$-0.751130\pi$
$239$	−5243.83	−1.41923	−0.709614	+	0.704591i	$0.751130\pi$
$240$	−64.6033	−0.0173755
$241$	784.525	0.209692	0.104846	−	0.994488i	$-0.466565\pi$
$241$	784.525	0.209692	0.104846	+	0.994488i	$0.466565\pi$
$242$	−2305.77	−0.612482
$243$	−243.000	−0.0641500
$244$	2018.26	0.529533
$245$	192.007	0.0500690
$246$	−275.547	−0.0714157
$247$	0	0
$248$	930.413	0.238231
$249$	2368.79	0.602875
$250$	−668.075	−0.169011
$251$	5853.44	1.47198	0.735988	−	0.676994i	$-0.236718\pi$
$251$	5853.44	1.47198	0.735988	+	0.676994i	$0.236718\pi$
$252$	−793.358	−0.198321
$253$	−259.698	−0.0645340
$254$	476.223	0.117641
$255$	−474.113	−0.116432
$256$	256.000	0.0625000
$257$	4142.45	1.00544	0.502722	−	0.864448i	$-0.332332\pi$
$257$	4142.45	1.00544	0.502722	+	0.864448i	$0.332332\pi$
$258$	−1887.39	−0.455442
$259$	−1851.17	−0.444116
$260$	−129.207	−0.0308195
$261$	1277.32	0.302928
$262$	−2814.51	−0.663669
$263$	−3039.91	−0.712734	−0.356367	−	0.934346i	$-0.615985\pi$
$263$	−3039.91	−0.712734	−0.356367	+	0.934346i	$0.615985\pi$
$264$	320.302	0.0746712
$265$	−466.190	−0.108067
$266$	0	0
$267$	1160.94	0.266099
$268$	−865.810	−0.197342
$269$	−1234.91	−0.279902	−0.139951	−	0.990158i	$-0.544695\pi$
$269$	−1234.91	−0.279902	−0.139951	+	0.990158i	$0.544695\pi$
$270$	−72.6788	−0.0163818
$271$	−3344.45	−0.749672	−0.374836	−	0.927091i	$-0.622301\pi$
$271$	−3344.45	−0.749672	−0.374836	+	0.927091i	$0.622301\pi$
$272$	1878.74	0.418807
$273$	−1586.72	−0.351767
$274$	−1726.92	−0.380755
$275$	1644.06	0.360512
$276$	−233.508	−0.0509259
$277$	−7247.13	−1.57198	−0.785989	−	0.618241i	$-0.787846\pi$
$277$	−7247.13	−1.57198	−0.785989	+	0.618241i	$0.787846\pi$
$278$	2768.45	0.597268
$279$	1046.72	0.224606
$280$	−237.285	−0.0506446
$281$	−772.869	−0.164076	−0.0820382	−	0.996629i	$-0.526143\pi$
$281$	−772.869	−0.164076	−0.0820382	+	0.996629i	$0.526143\pi$
$282$	2003.24	0.423019
$283$	4378.57	0.919713	0.459856	−	0.887993i	$-0.347901\pi$
$283$	4378.57	0.919713	0.459856	+	0.887993i	$0.347901\pi$
$284$	−2654.79	−0.554694
$285$	0	0
$286$	640.603	0.132446
$287$	−1012.07	−0.208156
$288$	288.000	0.0589256
$289$	8874.77	1.80638
$290$	382.033	0.0773578
$291$	−1311.17	−0.264131
$292$	−3152.45	−0.631792
$293$	3422.45	0.682395	0.341197	−	0.939992i	$-0.389168\pi$
$293$	3422.45	0.682395	0.341197	+	0.939992i	$0.389168\pi$
$294$	−855.964	−0.169799
$295$	−641.665	−0.126641
$296$	672.000	0.131957
$297$	360.339	0.0704007
$298$	−3651.60	−0.709837
$299$	−467.017	−0.0903287
$300$	1478.26	0.284492
$301$	−6932.31	−1.32748
$302$	−3123.62	−0.595179
$303$	417.698	0.0791952
$304$	0	0
$305$	679.096	0.127492
$306$	2113.58	0.394855
$307$	−6415.16	−1.19261	−0.596307	−	0.802756i	$-0.703366\pi$
$307$	−6415.16	−1.19261	−0.596307	+	0.802756i	$0.703366\pi$
$308$	1176.45	0.217645
$309$	4278.34	0.787657
$310$	313.062	0.0573571
$311$	−9933.72	−1.81122	−0.905610	−	0.424111i	$-0.860586\pi$
$311$	−9933.72	−1.81122	−0.905610	+	0.424111i	$0.860586\pi$
$312$	576.000	0.104518
$313$	−7851.66	−1.41790	−0.708949	−	0.705260i	$-0.750830\pi$
$313$	−7851.66	−1.41790	−0.708949	+	0.705260i	$0.750830\pi$
$314$	−2580.91	−0.463850
$315$	−266.946	−0.0477482
$316$	5156.22	0.917912
$317$	11205.7	1.98541	0.992704	−	0.120578i	$-0.0384748\pi$
$317$	11205.7	1.98541	0.992704	+	0.120578i	$0.0384748\pi$
$318$	2078.26	0.366488
$319$	−1894.11	−0.332445
$320$	86.1378	0.0150477
$321$	2842.64	0.494271
$322$	−857.665	−0.148434
$323$	0	0
$324$	324.000	0.0555556
$325$	2956.53	0.504611
$326$	−107.173	−0.0182079
$327$	4994.26	0.844597
$328$	367.397	0.0618478
$329$	7357.81	1.23298
$330$	107.774	0.0179780
$331$	−6622.11	−1.09965	−0.549825	−	0.835280i	$-0.685306\pi$
$331$	−6622.11	−1.09965	−0.549825	+	0.835280i	$0.685306\pi$
$332$	−3158.39	−0.522105
$333$	756.000	0.124410
$334$	2339.92	0.383338
$335$	−291.324	−0.0475126
$336$	1057.81	0.171751
$337$	8357.96	1.35100	0.675500	−	0.737360i	$-0.263928\pi$
$337$	8357.96	1.35100	0.675500	+	0.737360i	$0.263928\pi$
$338$	−3242.00	−0.521721
$339$	−6288.11	−1.00744
$340$	632.151	0.100833
$341$	−1552.15	−0.246492
$342$	0	0
$343$	4415.02	0.695011
$344$	2516.53	0.394424
$345$	−78.5699	−0.0122610
$346$	6533.06	1.01508
$347$	−9382.86	−1.45158	−0.725790	−	0.687916i	$-0.758526\pi$
$347$	−9382.86	−1.45158	−0.725790	+	0.687916i	$0.758526\pi$
$348$	−1703.09	−0.262343
$349$	2359.05	0.361826	0.180913	−	0.983499i	$-0.442095\pi$
$349$	2359.05	0.361826	0.180913	+	0.983499i	$0.442095\pi$
$350$	5429.59	0.829210
$351$	648.000	0.0985404
$352$	−427.069	−0.0646672
$353$	6399.46	0.964897	0.482449	−	0.875924i	$-0.339748\pi$
$353$	6399.46	0.964897	0.482449	+	0.875924i	$0.339748\pi$
$354$	2860.53	0.429478
$355$	−893.274	−0.133549
$356$	−1547.92	−0.230449
$357$	7763.09	1.15089
$358$	−4620.83	−0.682174
$359$	−5487.16	−0.806688	−0.403344	−	0.915048i	$-0.632152\pi$
$359$	−5487.16	−0.806688	−0.403344	+	0.915048i	$0.632152\pi$
$360$	96.9050	0.0141871
$361$	0	0
$362$	2460.98	0.357311
$363$	3458.66	0.500090
$364$	2115.62	0.304639
$365$	−1060.72	−0.152112
$366$	−3027.39	−0.432362
$367$	5102.79	0.725786	0.362893	−	0.931831i	$-0.381789\pi$
$367$	5102.79	0.725786	0.362893	+	0.931831i	$0.381789\pi$
$368$	311.344	0.0441031
$369$	413.321	0.0583107
$370$	226.112	0.0317702
$371$	7633.36	1.06821
$372$	−1395.62	−0.194515
$373$	−10092.1	−1.40094	−0.700471	−	0.713681i	$-0.747027\pi$
$373$	−10092.1	−1.40094	−0.700471	+	0.713681i	$0.747027\pi$
$374$	−3134.19	−0.433329
$375$	1002.11	0.137997
$376$	−2670.99	−0.366345
$377$	−3406.19	−0.465325
$378$	1190.04	0.161928
$379$	13109.1	1.77669	0.888347	−	0.459173i	$-0.151854\pi$
$379$	13109.1	1.77669	0.888347	+	0.459173i	$0.151854\pi$
$380$	0	0
$381$	−714.335	−0.0960538
$382$	−1928.28	−0.258270
$383$	−8116.82	−1.08290	−0.541449	−	0.840733i	$-0.682124\pi$
$383$	−8116.82	−1.08290	−0.541449	+	0.840733i	$0.682124\pi$
$384$	−384.000	−0.0510310
$385$	395.848	0.0524007
$386$	9432.75	1.24382
$387$	2831.09	0.371867
$388$	1748.22	0.228744
$389$	−3446.20	−0.449175	−0.224587	−	0.974454i	$-0.572103\pi$
$389$	−3446.20	−0.449175	−0.224587	+	0.974454i	$0.572103\pi$
$390$	193.810	0.0251640
$391$	2284.91	0.295531
$392$	1141.28	0.147050
$393$	4221.77	0.541884
$394$	−413.259	−0.0528418
$395$	1734.94	0.220999
$396$	−480.453	−0.0609688
$397$	−14087.1	−1.78089	−0.890444	−	0.455094i	$-0.849606\pi$
$397$	−14087.1	−1.78089	−0.890444	+	0.455094i	$0.849606\pi$
$398$	−6980.68	−0.879170
$399$	0	0
$400$	−1971.02	−0.246377
$401$	−2131.58	−0.265452	−0.132726	−	0.991153i	$-0.542373\pi$
$401$	−2131.58	−0.265452	−0.132726	+	0.991153i	$0.542373\pi$
$402$	1298.72	0.161129
$403$	−2791.24	−0.345016
$404$	−556.931	−0.0685850
$405$	109.018	0.0133757
$406$	−6255.39	−0.764654
$407$	−1121.06	−0.136532
$408$	−2818.11	−0.341954
$409$	−14884.4	−1.79948	−0.899741	−	0.436423i	$-0.856245\pi$
$409$	−14884.4	−1.79948	−0.899741	+	0.436423i	$0.856245\pi$
$410$	123.620	0.0148906
$411$	2590.37	0.310885
$412$	−5704.45	−0.682131
$413$	10506.6	1.25180
$414$	350.263	0.0415808
$415$	−1062.72	−0.125703
$416$	−768.000	−0.0905151
$417$	−4152.67	−0.487667
$418$	0	0
$419$	1612.99	0.188067	0.0940333	−	0.995569i	$-0.470024\pi$
$419$	1612.99	0.188067	0.0940333	+	0.995569i	$0.470024\pi$
$420$	355.927	0.0413511
$421$	5278.49	0.611063	0.305532	−	0.952182i	$-0.401166\pi$
$421$	5278.49	0.611063	0.305532	+	0.952182i	$0.401166\pi$
$422$	−7534.19	−0.869096
$423$	−3004.86	−0.345394
$424$	−2771.02	−0.317388
$425$	−14465.0	−1.65095
$426$	3982.19	0.452905
$427$	−11119.5	−1.26021
$428$	−3790.19	−0.428051
$429$	−960.905	−0.108142
$430$	846.750	0.0949625
$431$	8961.96	1.00158	0.500791	−	0.865568i	$-0.333042\pi$
$431$	8961.96	1.00158	0.500791	+	0.865568i	$0.333042\pi$
$432$	−432.000	−0.0481125
$433$	−14224.7	−1.57875	−0.789374	−	0.613913i	$-0.789594\pi$
$433$	−14224.7	−1.57875	−0.789374	+	0.613913i	$0.789594\pi$
$434$	−5126.04	−0.566954
$435$	−573.050	−0.0631624
$436$	−6659.02	−0.731443
$437$	0	0
$438$	4728.68	0.515856
$439$	−17545.0	−1.90747	−0.953735	−	0.300649i	$-0.902797\pi$
$439$	−17545.0	−1.90747	−0.953735	+	0.300649i	$0.902797\pi$
$440$	−143.698	−0.0155694
$441$	1283.95	0.138640
$442$	−5636.22	−0.606534
$443$	7476.66	0.801866	0.400933	−	0.916107i	$-0.368686\pi$
$443$	7476.66	0.801866	0.400933	+	0.916107i	$0.368686\pi$
$444$	−1008.00	−0.107742
$445$	−520.838	−0.0554834
$446$	2914.11	0.309388
$447$	5477.40	0.579579
$448$	−1410.41	−0.148741
$449$	4604.04	0.483915	0.241958	−	0.970287i	$-0.422211\pi$
$449$	4604.04	0.483915	0.241958	+	0.970287i	$0.422211\pi$
$450$	−2217.39	−0.232287
$451$	−612.905	−0.0639924
$452$	8384.15	0.872471
$453$	4685.43	0.485962
$454$	−3281.35	−0.339210
$455$	711.855	0.0733456
$456$	0	0
$457$	3233.71	0.330999	0.165499	−	0.986210i	$-0.447076\pi$
$457$	3233.71	0.330999	0.165499	+	0.986210i	$0.447076\pi$
$458$	3742.71	0.381846
$459$	−3170.38	−0.322398
$460$	104.760	0.0106184
$461$	−16608.6	−1.67796	−0.838979	−	0.544164i	$-0.816847\pi$
$461$	−16608.6	−1.67796	−0.838979	+	0.544164i	$0.816847\pi$
$462$	−1764.68	−0.177706
$463$	−7651.85	−0.768060	−0.384030	−	0.923321i	$-0.625464\pi$
$463$	−7651.85	−0.768060	−0.384030	+	0.923321i	$0.625464\pi$
$464$	2270.79	0.227196
$465$	−469.592	−0.0468319
$466$	−11831.1	−1.17611
$467$	−2926.73	−0.290006	−0.145003	−	0.989431i	$-0.546319\pi$
$467$	−2926.73	−0.290006	−0.145003	+	0.989431i	$0.546319\pi$
$468$	−864.000	−0.0853385
$469$	4770.12	0.469645
$470$	−898.724	−0.0882022
$471$	3871.36	0.378732
$472$	−3814.03	−0.371939
$473$	−4198.16	−0.408101
$474$	−7734.34	−0.749472
$475$	0	0
$476$	−10350.8	−0.996697
$477$	−3117.39	−0.299236
$478$	−10487.7	−1.00355
$479$	−13156.0	−1.25493	−0.627467	−	0.778643i	$-0.715908\pi$
$479$	−13156.0	−1.25493	−0.627467	+	0.778643i	$0.715908\pi$
$480$	−129.207	−0.0122864
$481$	−2016.00	−0.191105
$482$	1569.05	0.148274
$483$	1286.50	0.121196
$484$	−4611.55	−0.433090
$485$	588.235	0.0550729
$486$	−486.000	−0.0453609
$487$	20380.9	1.89640	0.948200	−	0.317674i	$-0.102902\pi$
$487$	20380.9	1.89640	0.948200	+	0.317674i	$0.102902\pi$
$488$	4036.53	0.374436
$489$	160.760	0.0148667
$490$	384.015	0.0354041
$491$	355.381	0.0326642	0.0163321	−	0.999867i	$-0.494801\pi$
$491$	355.381	0.0326642	0.0163321	+	0.999867i	$0.494801\pi$
$492$	−551.095	−0.0504985
$493$	16665.0	1.52242
$494$	0	0
$495$	−161.661	−0.0146790
$496$	1860.83	0.168455
$497$	14626.4	1.32009
$498$	4737.58	0.426297
$499$	−5863.92	−0.526063	−0.263031	−	0.964787i	$-0.584722\pi$
$499$	−5863.92	−0.526063	−0.263031	+	0.964787i	$0.584722\pi$
$500$	−1336.15	−0.119509
$501$	−3509.88	−0.312994
$502$	11706.9	1.04084
$503$	1969.51	0.174585	0.0872925	−	0.996183i	$-0.472179\pi$
$503$	1969.51	0.174585	0.0872925	+	0.996183i	$0.472179\pi$
$504$	−1586.72	−0.140234
$505$	−187.394	−0.0165127
$506$	−519.397	−0.0456324
$507$	4863.00	0.425983
$508$	952.447	0.0831850
$509$	15121.6	1.31681	0.658403	−	0.752666i	$-0.271232\pi$
$509$	15121.6	1.31681	0.658403	+	0.752666i	$0.271232\pi$
$510$	−948.226	−0.0823297
$511$	17368.2	1.50357
$512$	512.000	0.0441942
$513$	0	0
$514$	8284.90	0.710956
$515$	−1919.41	−0.164232
$516$	−3774.79	−0.322046
$517$	4455.85	0.379048
$518$	−3702.34	−0.314037
$519$	−9799.58	−0.828813
$520$	−258.413	−0.0217926
$521$	−2375.36	−0.199744	−0.0998718	−	0.995000i	$-0.531843\pi$
$521$	−2375.36	−0.199744	−0.0998718	+	0.995000i	$0.531843\pi$
$522$	2554.64	0.214202
$523$	8971.32	0.750073	0.375037	−	0.927010i	$-0.377630\pi$
$523$	8971.32	0.750073	0.375037	+	0.927010i	$0.377630\pi$
$524$	−5629.03	−0.469285
$525$	−8144.38	−0.677047
$526$	−6079.83	−0.503979
$527$	13656.3	1.12880
$528$	640.603	0.0528005
$529$	−11788.3	−0.968879
$530$	−932.380	−0.0764151
$531$	−4290.79	−0.350667
$532$	0	0
$533$	−1102.19	−0.0895706
$534$	2321.88	0.188160
$535$	−1275.31	−0.103059
$536$	−1731.62	−0.139542
$537$	6931.24	0.556993
$538$	−2469.82	−0.197921
$539$	−1903.93	−0.152149
$540$	−145.358	−0.0115837
$541$	6089.62	0.483943	0.241971	−	0.970283i	$-0.422206\pi$
$541$	6089.62	0.483943	0.241971	+	0.970283i	$0.422206\pi$
$542$	−6688.91	−0.530098
$543$	−3691.47	−0.291743
$544$	3757.48	0.296141
$545$	−2240.60	−0.176104
$546$	−3173.43	−0.248737
$547$	−16296.4	−1.27383	−0.636913	−	0.770936i	$-0.719789\pi$
$547$	−16296.4	−1.27383	−0.636913	+	0.770936i	$0.719789\pi$
$548$	−3453.83	−0.269234
$549$	4541.09	0.353022
$550$	3288.12	0.254920
$551$	0	0
$552$	−467.017	−0.0360101
$553$	−28407.8	−2.18449
$554$	−14494.3	−1.11156
$555$	−339.168	−0.0259403
$556$	5536.90	0.422332
$557$	4317.00	0.328397	0.164199	−	0.986427i	$-0.447496\pi$
$557$	4317.00	0.328397	0.164199	+	0.986427i	$0.447496\pi$
$558$	2093.43	0.158821
$559$	−7549.58	−0.571222
$560$	−474.570	−0.0358111
$561$	4701.28	0.353811
$562$	−1545.74	−0.116020
$563$	−347.095	−0.0259828	−0.0129914	−	0.999916i	$-0.504135\pi$
$563$	−347.095	−0.0259828	−0.0129914	+	0.999916i	$0.504135\pi$
$564$	4006.49	0.299120
$565$	2821.06	0.210058
$566$	8757.13	0.650335
$567$	−1785.05	−0.132214
$568$	−5309.59	−0.392228
$569$	19907.4	1.46672	0.733359	−	0.679842i	$-0.237951\pi$
$569$	19907.4	1.46672	0.733359	+	0.679842i	$0.237951\pi$
$570$	0	0
$571$	5475.55	0.401304	0.200652	−	0.979663i	$-0.435694\pi$
$571$	5475.55	0.401304	0.200652	+	0.979663i	$0.435694\pi$
$572$	1281.21	0.0936537
$573$	2892.42	0.210877
$574$	−2024.15	−0.147188
$575$	−2397.13	−0.173856
$576$	576.000	0.0416667
$577$	13139.8	0.948036	0.474018	−	0.880515i	$-0.342803\pi$
$577$	13139.8	0.948036	0.474018	+	0.880515i	$0.342803\pi$
$578$	17749.5	1.27731
$579$	−14149.1	−1.01557
$580$	764.067	0.0547003
$581$	17400.9	1.24253
$582$	−2622.34	−0.186769
$583$	4622.72	0.328393
$584$	−6304.91	−0.446745
$585$	−290.715	−0.0205463
$586$	6844.90	0.482526
$587$	−20553.0	−1.44517	−0.722583	−	0.691284i	$-0.757045\pi$
$587$	−20553.0	−1.44517	−0.722583	+	0.691284i	$0.757045\pi$
$588$	−1711.93	−0.120066
$589$	0	0
$590$	−1283.33	−0.0895489
$591$	619.888	0.0431452
$592$	1344.00	0.0933075
$593$	5656.53	0.391713	0.195857	−	0.980633i	$-0.437251\pi$
$593$	5656.53	0.391713	0.195857	+	0.980633i	$0.437251\pi$
$594$	720.679	0.0497808
$595$	−3482.79	−0.239967
$596$	−7303.19	−0.501930
$597$	10471.0	0.717840
$598$	−934.033	−0.0638720
$599$	14889.7	1.01565	0.507826	−	0.861460i	$-0.330449\pi$
$599$	14889.7	1.01565	0.507826	+	0.861460i	$0.330449\pi$
$600$	2956.53	0.201166
$601$	21752.9	1.47640	0.738202	−	0.674580i	$-0.235675\pi$
$601$	21752.9	1.47640	0.738202	+	0.674580i	$0.235675\pi$
$602$	−13864.6	−0.938670
$603$	−1948.07	−0.131562
$604$	−6247.24	−0.420855
$605$	−1551.67	−0.104272
$606$	835.397	0.0559995
$607$	10498.8	0.702031	0.351016	−	0.936370i	$-0.385836\pi$
$607$	10498.8	0.702031	0.351016	+	0.936370i	$0.385836\pi$
$608$	0	0
$609$	9383.08	0.624337
$610$	1358.19	0.0901502
$611$	8012.97	0.530557
$612$	4227.17	0.279204
$613$	17849.1	1.17605	0.588025	−	0.808843i	$-0.299906\pi$
$613$	17849.1	1.17605	0.588025	+	0.808843i	$0.299906\pi$
$614$	−12830.3	−0.843306
$615$	−185.430	−0.0121582
$616$	2352.91	0.153898
$617$	−13199.6	−0.861257	−0.430629	−	0.902529i	$-0.641708\pi$
$617$	−13199.6	−0.861257	−0.430629	+	0.902529i	$0.641708\pi$
$618$	8556.67	0.556958
$619$	−4791.54	−0.311128	−0.155564	−	0.987826i	$-0.549720\pi$
$619$	−4791.54	−0.311128	−0.155564	+	0.987826i	$0.549720\pi$
$620$	626.123	0.0405576
$621$	−525.394	−0.0339506
$622$	−19867.4	−1.28073
$623$	8528.16	0.548433
$624$	1152.00	0.0739053
$625$	14949.0	0.956735
$626$	−15703.3	−1.00261
$627$	0	0
$628$	−5161.81	−0.327991
$629$	9863.39	0.625245
$630$	−533.891	−0.0337631
$631$	5386.40	0.339825	0.169912	−	0.985459i	$-0.445652\pi$
$631$	5386.40	0.339825	0.169912	+	0.985459i	$0.445652\pi$
$632$	10312.4	0.649062
$633$	11301.3	0.709614
$634$	22411.4	1.40390
$635$	320.475	0.0200278
$636$	4156.53	0.259146
$637$	−3423.85	−0.212964
$638$	−3788.22	−0.235074
$639$	−5973.28	−0.369796
$640$	172.276	0.0106403
$641$	5652.27	0.348286	0.174143	−	0.984720i	$-0.444285\pi$
$641$	5652.27	0.348286	0.174143	+	0.984720i	$0.444285\pi$
$642$	5685.28	0.349502
$643$	12944.9	0.793930	0.396965	−	0.917834i	$-0.370063\pi$
$643$	12944.9	0.793930	0.396965	+	0.917834i	$0.370063\pi$
$644$	−1715.33	−0.104959
$645$	−1270.12	−0.0775366
$646$	0	0
$647$	8544.45	0.519191	0.259596	−	0.965717i	$-0.416411\pi$
$647$	8544.45	0.519191	0.259596	+	0.965717i	$0.416411\pi$
$648$	648.000	0.0392837
$649$	6362.72	0.384836
$650$	5913.05	0.356814
$651$	7689.07	0.462916
$652$	−214.346	−0.0128749
$653$	30248.6	1.81274	0.906371	−	0.422482i	$-0.138841\pi$
$653$	30248.6	1.81274	0.906371	+	0.422482i	$0.138841\pi$
$654$	9988.53	0.597221
$655$	−1894.03	−0.112986
$656$	734.793	0.0437330
$657$	−7093.02	−0.421195
$658$	14715.6	0.871846
$659$	12834.6	0.758674	0.379337	−	0.925259i	$-0.376152\pi$
$659$	12834.6	0.758674	0.379337	+	0.925259i	$0.376152\pi$
$660$	215.547	0.0127124
$661$	9620.28	0.566090	0.283045	−	0.959107i	$-0.408655\pi$
$661$	9620.28	0.566090	0.283045	+	0.959107i	$0.408655\pi$
$662$	−13244.2	−0.777570
$663$	8454.34	0.495233
$664$	−6316.77	−0.369184
$665$	0	0
$666$	1512.00	0.0879712
$667$	2761.71	0.160321
$668$	4679.84	0.271061
$669$	−4371.17	−0.252615
$670$	−582.648	−0.0335965
$671$	−6733.88	−0.387420
$672$	2115.62	0.121446
$673$	−31365.1	−1.79649	−0.898244	−	0.439496i	$-0.855157\pi$
$673$	−31365.1	−1.79649	−0.898244	+	0.439496i	$0.855157\pi$
$674$	16715.9	0.955302
$675$	3326.09	0.189661
$676$	−6484.00	−0.368912
$677$	−26018.7	−1.47707	−0.738537	−	0.674213i	$-0.764483\pi$
$677$	−26018.7	−1.47707	−0.738537	+	0.674213i	$0.764483\pi$
$678$	−12576.2	−0.712370
$679$	−9631.71	−0.544376
$680$	1264.30	0.0712996
$681$	4922.03	0.276964
$682$	−3104.30	−0.174296
$683$	−2478.27	−0.138841	−0.0694206	−	0.997587i	$-0.522115\pi$
$683$	−2478.27	−0.138841	−0.0694206	+	0.997587i	$0.522115\pi$
$684$	0	0
$685$	−1162.13	−0.0648215
$686$	8830.04	0.491447
$687$	−5614.07	−0.311776
$688$	5033.05	0.278900
$689$	8313.05	0.459655
$690$	−157.140	−0.00866987
$691$	−26246.8	−1.44497	−0.722485	−	0.691386i	$-0.757000\pi$
$691$	−26246.8	−1.44497	−0.722485	+	0.691386i	$0.757000\pi$
$692$	13066.1	0.717773
$693$	2647.02	0.145097
$694$	−18765.7	−1.02642
$695$	1863.03	0.101682
$696$	−3406.19	−0.185505
$697$	5392.53	0.293051
$698$	4718.11	0.255850
$699$	17746.7	0.960288
$700$	10859.2	0.586340
$701$	4888.87	0.263410	0.131705	−	0.991289i	$-0.457955\pi$
$701$	4888.87	0.263410	0.131705	+	0.991289i	$0.457955\pi$
$702$	1296.00	0.0696786
$703$	0	0
$704$	−854.138	−0.0457266
$705$	1348.09	0.0720168
$706$	12798.9	0.682285
$707$	3068.37	0.163222
$708$	5721.05	0.303687
$709$	7622.74	0.403777	0.201889	−	0.979408i	$-0.435292\pi$
$709$	7622.74	0.403777	0.201889	+	0.979408i	$0.435292\pi$
$710$	−1786.55	−0.0944337
$711$	11601.5	0.611941
$712$	−3095.84	−0.162952
$713$	2263.12	0.118870
$714$	15526.2	0.813799
$715$	431.095	0.0225483
$716$	−9241.65	−0.482370
$717$	15731.5	0.819391
$718$	−10974.3	−0.570415
$719$	24010.0	1.24537	0.622686	−	0.782472i	$-0.286041\pi$
$719$	24010.0	1.24537	0.622686	+	0.782472i	$0.286041\pi$
$720$	193.810	0.0100318
$721$	31428.2	1.62337
$722$	0	0
$723$	−2353.58	−0.121066
$724$	4921.97	0.252657
$725$	−17483.5	−0.895614
$726$	6917.32	0.353617
$727$	15340.9	0.782617	0.391308	−	0.920260i	$-0.372023\pi$
$727$	15340.9	0.782617	0.391308	+	0.920260i	$0.372023\pi$
$728$	4231.24	0.215412
$729$	729.000	0.0370370
$730$	−2121.45	−0.107559
$731$	36936.7	1.86888
$732$	−6054.79	−0.305726
$733$	−8115.88	−0.408959	−0.204480	−	0.978871i	$-0.565550\pi$
$733$	−8115.88	−0.408959	−0.204480	+	0.978871i	$0.565550\pi$
$734$	10205.6	0.513208
$735$	−576.022	−0.0289073
$736$	622.689	0.0311856
$737$	2888.75	0.144381
$738$	826.642	0.0412319
$739$	28266.5	1.40704	0.703518	−	0.710677i	$-0.251611\pi$
$739$	28266.5	1.40704	0.703518	+	0.710677i	$0.251611\pi$
$740$	452.223	0.0224650
$741$	0	0
$742$	15266.7	0.755335
$743$	−37073.5	−1.83054	−0.915272	−	0.402836i	$-0.868025\pi$
$743$	−37073.5	−1.83054	−0.915272	+	0.402836i	$0.868025\pi$
$744$	−2791.24	−0.137543
$745$	−2457.35	−0.120846
$746$	−20184.3	−0.990615
$747$	−7106.37	−0.348070
$748$	−6268.37	−0.306410
$749$	20881.8	1.01870
$750$	2004.23	0.0975787
$751$	−12820.2	−0.622924	−0.311462	−	0.950259i	$-0.600819\pi$
$751$	−12820.2	−0.622924	−0.311462	+	0.950259i	$0.600819\pi$
$752$	−5341.98	−0.259045
$753$	−17560.3	−0.849846
$754$	−6812.38	−0.329035
$755$	−2102.04	−0.101326
$756$	2380.07	0.114501
$757$	22427.5	1.07681	0.538403	−	0.842688i	$-0.319028\pi$
$757$	22427.5	1.07681	0.538403	+	0.842688i	$0.319028\pi$
$758$	26218.1	1.25631
$759$	779.095	0.0372587
$760$	0	0
$761$	−28274.0	−1.34682	−0.673410	−	0.739269i	$-0.735171\pi$
$761$	−28274.0	−1.34682	−0.673410	+	0.739269i	$0.735171\pi$
$762$	−1428.67	−0.0679203
$763$	36687.4	1.74072
$764$	−3856.56	−0.182625
$765$	1422.34	0.0672219
$766$	−16233.6	−0.765725
$767$	11442.1	0.538657
$768$	−768.000	−0.0360844
$769$	16813.8	0.788452	0.394226	−	0.919013i	$-0.371013\pi$
$769$	16813.8	0.788452	0.394226	+	0.919013i	$0.371013\pi$
$770$	791.695	0.0370529
$771$	−12427.3	−0.580493
$772$	18865.5	0.879513
$773$	−490.142	−0.0228062	−0.0114031	−	0.999935i	$-0.503630\pi$
$773$	−490.142	−0.0228062	−0.0114031	+	0.999935i	$0.503630\pi$
$774$	5662.18	0.262949
$775$	−14327.0	−0.664055
$776$	3496.45	0.161746
$777$	5553.50	0.256410
$778$	−6892.39	−0.317615
$779$	0	0
$780$	387.620	0.0177936
$781$	8857.65	0.405828
$782$	4569.81	0.208972
$783$	−3831.96	−0.174896
$784$	2282.57	0.103980
$785$	−1736.82	−0.0789680
$786$	8443.54	0.383170
$787$	−41200.3	−1.86611	−0.933057	−	0.359729i	$-0.882869\pi$
$787$	−41200.3	−1.86611	−0.933057	+	0.359729i	$0.882869\pi$
$788$	−826.518	−0.0373648
$789$	9119.74	0.411497
$790$	3469.89	0.156270
$791$	−46191.8	−2.07635
$792$	−960.905	−0.0431115
$793$	−12109.6	−0.542274
$794$	−28174.2	−1.25928
$795$	1398.57	0.0623927
$796$	−13961.4	−0.621667
$797$	−8996.71	−0.399849	−0.199925	−	0.979811i	$-0.564070\pi$
$797$	−8996.71	−0.399849	−0.199925	+	0.979811i	$0.564070\pi$
$798$	0	0
$799$	−39203.9	−1.73584
$800$	−3942.03	−0.174215
$801$	−3482.82	−0.153632
$802$	−4263.17	−0.187703
$803$	10518.1	0.462235
$804$	2597.43	0.113936
$805$	−577.167	−0.0252701
$806$	−5582.48	−0.243963
$807$	3704.72	0.161602
$808$	−1113.86	−0.0484970
$809$	31171.6	1.35468	0.677339	−	0.735671i	$-0.263133\pi$
$809$	31171.6	1.35468	0.677339	+	0.735671i	$0.263133\pi$
$810$	218.036	0.00945804
$811$	18189.3	0.787564	0.393782	−	0.919204i	$-0.371167\pi$
$811$	18189.3	0.787564	0.393782	+	0.919204i	$0.371167\pi$
$812$	−12510.8	−0.540692
$813$	10033.4	0.432823
$814$	−2242.11	−0.0965430
$815$	−72.1224	−0.00309980
$816$	−5636.22	−0.241798
$817$	0	0
$818$	−29768.9	−1.27243
$819$	4760.15	0.203093
$820$	247.240	0.0105293
$821$	−28437.2	−1.20885	−0.604425	−	0.796662i	$-0.706597\pi$
$821$	−28437.2	−1.20885	−0.604425	+	0.796662i	$0.706597\pi$
$822$	5180.75	0.219829
$823$	−13699.1	−0.580222	−0.290111	−	0.956993i	$-0.593692\pi$
$823$	−13699.1	−0.580222	−0.290111	+	0.956993i	$0.593692\pi$
$824$	−11408.9	−0.482339
$825$	−4932.19	−0.208141
$826$	21013.1	0.885158
$827$	15865.6	0.667110	0.333555	−	0.942731i	$-0.391752\pi$
$827$	15865.6	0.667110	0.333555	+	0.942731i	$0.391752\pi$
$828$	700.525	0.0294021
$829$	27992.1	1.17275	0.586374	−	0.810041i	$-0.300555\pi$
$829$	27992.1	1.17275	0.586374	+	0.810041i	$0.300555\pi$
$830$	−2125.44	−0.0888857
$831$	21741.4	0.907582
$832$	−1536.00	−0.0640039
$833$	16751.4	0.696761
$834$	−8305.35	−0.344833
$835$	1574.65	0.0652612
$836$	0	0
$837$	−3140.15	−0.129677
$838$	3225.99	0.132983
$839$	7115.02	0.292774	0.146387	−	0.989227i	$-0.453235\pi$
$839$	7115.02	0.292774	0.146387	+	0.989227i	$0.453235\pi$
$840$	711.855	0.0292397
$841$	−4246.41	−0.174112
$842$	10557.0	0.432087
$843$	2318.61	0.0947296
$844$	−15068.4	−0.614544
$845$	−2181.71	−0.0888202
$846$	−6009.73	−0.244230
$847$	25407.0	1.03069
$848$	−5542.03	−0.224427
$849$	−13135.7	−0.530996
$850$	−28929.9	−1.16740
$851$	1634.56	0.0658425
$852$	7964.38	0.320253
$853$	−7865.82	−0.315733	−0.157867	−	0.987460i	$-0.550462\pi$
$853$	−7865.82	−0.315733	−0.157867	+	0.987460i	$0.550462\pi$
$854$	−22238.9	−0.891102
$855$	0	0
$856$	−7580.38	−0.302678
$857$	30763.9	1.22623	0.613113	−	0.789995i	$-0.289917\pi$
$857$	30763.9	1.22623	0.613113	+	0.789995i	$0.289917\pi$
$858$	−1921.81	−0.0764680
$859$	−30061.8	−1.19406	−0.597029	−	0.802220i	$-0.703652\pi$
$859$	−30061.8	−1.19406	−0.597029	+	0.802220i	$0.703652\pi$
$860$	1693.50	0.0671487
$861$	3036.22	0.120179
$862$	17923.9	0.708226
$863$	29791.8	1.17512	0.587558	−	0.809182i	$-0.300089\pi$
$863$	29791.8	1.17512	0.587558	+	0.809182i	$0.300089\pi$
$864$	−864.000	−0.0340207
$865$	4396.43	0.172813
$866$	−28449.5	−1.11634
$867$	−26624.3	−1.04292
$868$	−10252.1	−0.400897
$869$	−17203.6	−0.671568
$870$	−1146.10	−0.0446626
$871$	5194.86	0.202091
$872$	−13318.0	−0.517208
$873$	3933.50	0.152496
$874$	0	0
$875$	7361.43	0.284413
$876$	9457.36	0.364765
$877$	9351.32	0.360059	0.180030	−	0.983661i	$-0.442381\pi$
$877$	9351.32	0.360059	0.180030	+	0.983661i	$0.442381\pi$
$878$	−35090.1	−1.34878
$879$	−10267.3	−0.393981
$880$	−287.397	−0.0110092
$881$	24493.2	0.936660	0.468330	−	0.883554i	$-0.344856\pi$
$881$	24493.2	0.936660	0.468330	+	0.883554i	$0.344856\pi$
$882$	2567.89	0.0980333
$883$	29912.2	1.14001	0.570004	−	0.821642i	$-0.306942\pi$
$883$	29912.2	1.14001	0.570004	+	0.821642i	$0.306942\pi$
$884$	−11272.4	−0.428884
$885$	1924.99	0.0731164
$886$	14953.3	0.567005
$887$	966.961	0.0366036	0.0183018	−	0.999833i	$-0.494174\pi$
$887$	966.961	0.0366036	0.0183018	+	0.999833i	$0.494174\pi$
$888$	−2016.00	−0.0761853
$889$	−5247.44	−0.197968
$890$	−1041.68	−0.0392327
$891$	−1081.02	−0.0406459
$892$	5828.22	0.218771
$893$	0	0
$894$	10954.8	0.409824
$895$	−3109.59	−0.116137
$896$	−2820.83	−0.105175
$897$	1401.05	0.0521513
$898$	9208.07	0.342180
$899$	16506.1	0.612356
$900$	−4434.79	−0.164251
$901$	−40672.1	−1.50387
$902$	−1225.81	−0.0452495
$903$	20796.9	0.766421
$904$	16768.3	0.616930
$905$	1656.12	0.0608302
$906$	9370.86	0.343627
$907$	−20917.0	−0.765751	−0.382876	−	0.923800i	$-0.625066\pi$
$907$	−20917.0	−0.765751	−0.382876	+	0.923800i	$0.625066\pi$
$908$	−6562.70	−0.239858
$909$	−1253.09	−0.0457234
$910$	1423.71	0.0518632
$911$	−10252.8	−0.372878	−0.186439	−	0.982467i	$-0.559695\pi$
$911$	−10252.8	−0.372878	−0.186439	+	0.982467i	$0.559695\pi$
$912$	0	0
$913$	10537.9	0.381986
$914$	6467.41	0.234051
$915$	−2037.29	−0.0736073
$916$	7485.42	0.270006
$917$	31012.7	1.11683
$918$	−6340.75	−0.227969
$919$	44690.2	1.60413	0.802063	−	0.597239i	$-0.203736\pi$
$919$	44690.2	1.60413	0.802063	+	0.597239i	$0.203736\pi$
$920$	209.520	0.00750833
$921$	19245.5	0.688556
$922$	−33217.2	−1.18650
$923$	15928.8	0.568041
$924$	−3529.36	−0.125657
$925$	−10347.8	−0.367821
$926$	−15303.7	−0.543100
$927$	−12835.0	−0.454754
$928$	4541.59	0.160652
$929$	−42448.9	−1.49914	−0.749571	−	0.661924i	$-0.769740\pi$
$929$	−42448.9	−1.49914	−0.749571	+	0.661924i	$0.769740\pi$
$930$	−939.185	−0.0331151
$931$	0	0
$932$	−23662.2	−0.831633
$933$	29801.2	1.04571
$934$	−5853.46	−0.205066
$935$	−2109.16	−0.0737720
$936$	−1728.00	−0.0603434
$937$	10877.9	0.379259	0.189629	−	0.981856i	$-0.439271\pi$
$937$	10877.9	0.379259	0.189629	+	0.981856i	$0.439271\pi$
$938$	9540.23	0.332089
$939$	23555.0	0.818624
$940$	−1797.45	−0.0623684
$941$	55427.2	1.92017	0.960083	−	0.279715i	$-0.0902401\pi$
$941$	55427.2	1.92017	0.960083	+	0.279715i	$0.0902401\pi$
$942$	7742.72	0.267804
$943$	893.648	0.0308602
$944$	−7628.07	−0.263000
$945$	800.837	0.0275674
$946$	−8396.32	−0.288571
$947$	19072.1	0.654445	0.327222	−	0.944947i	$-0.393887\pi$
$947$	19072.1	0.654445	0.327222	+	0.944947i	$0.393887\pi$
$948$	−15468.7	−0.529957
$949$	18914.7	0.646994
$950$	0	0
$951$	−33617.1	−1.14628
$952$	−20701.6	−0.704771
$953$	−32018.9	−1.08835	−0.544173	−	0.838973i	$-0.683156\pi$
$953$	−32018.9	−1.08835	−0.544173	+	0.838973i	$0.683156\pi$
$954$	−6234.79	−0.211592
$955$	−1297.64	−0.0439692
$956$	−20975.3	−0.709614
$957$	5682.34	0.191937
$958$	−26312.0	−0.887372
$959$	19028.6	0.640737
$960$	−258.413	−0.00868777
$961$	−16264.9	−0.545968
$962$	−4032.00	−0.135132
$963$	−8527.93	−0.285367
$964$	3138.10	0.104846
$965$	6347.78	0.211754
$966$	2572.99	0.0856985
$967$	−32394.5	−1.07729	−0.538643	−	0.842534i	$-0.681063\pi$
$967$	−32394.5	−1.07729	−0.538643	+	0.842534i	$0.681063\pi$
$968$	−9223.09	−0.306241
$969$	0	0
$970$	1176.47	0.0389424
$971$	48474.3	1.60208	0.801038	−	0.598614i	$-0.204282\pi$
$971$	48474.3	1.60208	0.801038	+	0.598614i	$0.204282\pi$
$972$	−972.000	−0.0320750
$973$	−30505.1	−1.00509
$974$	40761.8	1.34096
$975$	−8869.58	−0.291337
$976$	8073.05	0.264766
$977$	−56371.2	−1.84593	−0.922966	−	0.384881i	$-0.874242\pi$
$977$	−56371.2	−1.84593	−0.922966	+	0.384881i	$0.874242\pi$
$978$	321.520	0.0105123
$979$	5164.60	0.168602
$980$	768.029	0.0250345
$981$	−14982.8	−0.487629
$982$	710.762	0.0230971
$983$	39132.0	1.26970	0.634852	−	0.772634i	$-0.281061\pi$
$983$	39132.0	1.26970	0.634852	+	0.772634i	$0.281061\pi$
$984$	−1102.19	−0.0357079
$985$	−278.103	−0.00899604
$986$	33329.9	1.07651
$987$	−22073.4	−0.711860
$988$	0	0
$989$	6121.14	0.196806
$990$	−323.321	−0.0103796
$991$	15342.6	0.491799	0.245899	−	0.969295i	$-0.420917\pi$
$991$	15342.6	0.491799	0.245899	+	0.969295i	$0.420917\pi$
$992$	3721.65	0.119116
$993$	19866.3	0.634883
$994$	29252.8	0.933443
$995$	−4697.66	−0.149674
$996$	9475.16	0.301438
$997$	3913.40	0.124312	0.0621558	−	0.998066i	$-0.480202\pi$
$997$	3913.40	0.124312	0.0621558	+	0.998066i	$0.480202\pi$
$998$	−11727.8	−0.371982
$999$	−2268.00	−0.0718282

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2166.4.a.m.1.2	✓	2	19.18	odd	2
2166.4.a.o.1.2	yes	2	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2166 = 2 \cdot 3 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2166.a (trivial)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +1.34590 q^{5} -6.00000 q^{6} -22.0377 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +1.34590 q^{5} -6.00000 q^{6} -22.0377 q^{7} +8.00000 q^{8} +9.00000 q^{9} +2.69181 q^{10} -13.3459 q^{11} -12.0000 q^{12} -24.0000 q^{13} -44.0754 q^{14} -4.03771 q^{15} +16.0000 q^{16} +117.421 q^{17} +18.0000 q^{18} +5.38361 q^{20} +66.1131 q^{21} -26.6918 q^{22} +19.4590 q^{23} -24.0000 q^{24} -123.189 q^{25} -48.0000 q^{26} -27.0000 q^{27} -88.1508 q^{28} +141.925 q^{29} -8.07542 q^{30} +116.302 q^{31} +32.0000 q^{32} +40.0377 q^{33} +234.843 q^{34} -29.6606 q^{35} +36.0000 q^{36} +84.0000 q^{37} +72.0000 q^{39} +10.7672 q^{40} +45.9246 q^{41} +132.226 q^{42} +314.566 q^{43} -53.3836 q^{44} +12.1131 q^{45} +38.9181 q^{46} -333.874 q^{47} -48.0000 q^{48} +142.661 q^{49} -246.377 q^{50} -352.264 q^{51} -96.0000 q^{52} -346.377 q^{53} -54.0000 q^{54} -17.9623 q^{55} -176.302 q^{56} +283.849 q^{58} -476.754 q^{59} -16.1508 q^{60} +504.566 q^{61} +232.603 q^{62} -198.339 q^{63} +64.0000 q^{64} -32.3017 q^{65} +80.0754 q^{66} -216.453 q^{67} +469.685 q^{68} -58.3771 q^{69} -59.3212 q^{70} -663.698 q^{71} +72.0000 q^{72} -788.113 q^{73} +168.000 q^{74} +369.566 q^{75} +294.113 q^{77} +144.000 q^{78} +1289.06 q^{79} +21.5344 q^{80} +81.0000 q^{81} +91.8492 q^{82} -789.597 q^{83} +264.453 q^{84} +158.038 q^{85} +629.131 q^{86} -425.774 q^{87} -106.767 q^{88} -386.980 q^{89} +24.2263 q^{90} +528.905 q^{91} +77.8361 q^{92} -348.905 q^{93} -667.748 q^{94} -96.0000 q^{96} +437.056 q^{97} +285.321 q^{98} -120.113 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 4 q^{2} - 6 q^{3} + 8 q^{4} - 15 q^{5} - 12 q^{6} + 9 q^{7} + 16 q^{8} + 18 q^{9}+O(q^{10}) \) 2 * q + 4 * q^2 - 6 * q^3 + 8 * q^4 - 15 * q^5 - 12 * q^6 + 9 * q^7 + 16 * q^8 + 18 * q^9	\( 2 q + 4 q^{2} - 6 q^{3} + 8 q^{4} - 15 q^{5} - 12 q^{6} + 9 q^{7} + 16 q^{8} + 18 q^{9} - 30 q^{10} - 9 q^{11} - 24 q^{12} - 48 q^{13} + 18 q^{14} + 45 q^{15} + 32 q^{16} + 111 q^{17} + 36 q^{18} - 60 q^{20} - 27 q^{21} - 18 q^{22} - 138 q^{23} - 48 q^{24} + 19 q^{25} - 96 q^{26} - 54 q^{27} + 36 q^{28} + 390 q^{29} + 90 q^{30} - 192 q^{31} + 64 q^{32} + 27 q^{33} + 222 q^{34} - 537 q^{35} + 72 q^{36} + 168 q^{37} + 144 q^{39} - 120 q^{40} + 198 q^{41} - 54 q^{42} - 167 q^{43} - 36 q^{44} - 135 q^{45} - 276 q^{46} + 93 q^{47} - 96 q^{48} + 763 q^{49} + 38 q^{50} - 333 q^{51} - 192 q^{52} - 162 q^{53} - 108 q^{54} - 89 q^{55} + 72 q^{56} + 780 q^{58} + 108 q^{59} + 180 q^{60} + 213 q^{61} - 384 q^{62} + 81 q^{63} + 128 q^{64} + 360 q^{65} + 54 q^{66} + 204 q^{67} + 444 q^{68} + 414 q^{69} - 1074 q^{70} - 1752 q^{71} + 144 q^{72} - 1417 q^{73} + 336 q^{74} - 57 q^{75} + 429 q^{77} + 288 q^{78} + 1092 q^{79} - 240 q^{80} + 162 q^{81} + 396 q^{82} - 270 q^{83} - 108 q^{84} + 263 q^{85} - 334 q^{86} - 1170 q^{87} - 72 q^{88} + 606 q^{89} - 270 q^{90} - 216 q^{91} - 552 q^{92} + 576 q^{93} + 186 q^{94} - 192 q^{96} - 612 q^{97} + 1526 q^{98} - 81 q^{99}+O(q^{100}) \) 2 * q + 4 * q^2 - 6 * q^3 + 8 * q^4 - 15 * q^5 - 12 * q^6 + 9 * q^7 + 16 * q^8 + 18 * q^9 - 30 * q^10 - 9 * q^11 - 24 * q^12 - 48 * q^13 + 18 * q^14 + 45 * q^15 + 32 * q^16 + 111 * q^17 + 36 * q^18 - 60 * q^20 - 27 * q^21 - 18 * q^22 - 138 * q^23 - 48 * q^24 + 19 * q^25 - 96 * q^26 - 54 * q^27 + 36 * q^28 + 390 * q^29 + 90 * q^30 - 192 * q^31 + 64 * q^32 + 27 * q^33 + 222 * q^34 - 537 * q^35 + 72 * q^36 + 168 * q^37 + 144 * q^39 - 120 * q^40 + 198 * q^41 - 54 * q^42 - 167 * q^43 - 36 * q^44 - 135 * q^45 - 276 * q^46 + 93 * q^47 - 96 * q^48 + 763 * q^49 + 38 * q^50 - 333 * q^51 - 192 * q^52 - 162 * q^53 - 108 * q^54 - 89 * q^55 + 72 * q^56 + 780 * q^58 + 108 * q^59 + 180 * q^60 + 213 * q^61 - 384 * q^62 + 81 * q^63 + 128 * q^64 + 360 * q^65 + 54 * q^66 + 204 * q^67 + 444 * q^68 + 414 * q^69 - 1074 * q^70 - 1752 * q^71 + 144 * q^72 - 1417 * q^73 + 336 * q^74 - 57 * q^75 + 429 * q^77 + 288 * q^78 + 1092 * q^79 - 240 * q^80 + 162 * q^81 + 396 * q^82 - 270 * q^83 - 108 * q^84 + 263 * q^85 - 334 * q^86 - 1170 * q^87 - 72 * q^88 + 606 * q^89 - 270 * q^90 - 216 * q^91 - 552 * q^92 + 576 * q^93 + 186 * q^94 - 192 * q^96 - 612 * q^97 + 1526 * q^98 - 81 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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