LMFDB - Embedded newform 1450.2.a.t.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1450,2,Mod(1,1450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1450, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1450.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1450 = 2 \cdot 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1450.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:	$11.5783082931$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.3661564.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 10x^{3} + 3x^{2} + 20x + 8 $ x^5 - 2x^4 - 10x^3 + 3x^2 + 20x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 290)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$3.97530$ of defining polynomial
Character	$\chi$	$=$	1450.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +2.97530 q^{3} +1.00000 q^{4} -2.97530 q^{6} -3.57331 q^{7} -1.00000 q^{8} +5.85241 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.97530 q^{3} +1.00000 q^{4} -2.97530 q^{6} -3.57331 q^{7} -1.00000 q^{8} +5.85241 q^{9} -4.28531 q^{11} +2.97530 q^{12} -1.96909 q^{13} +3.57331 q^{14} +1.00000 q^{16} -6.37729 q^{17} -5.85241 q^{18} -7.08481 q^{19} -10.6317 q^{21} +4.28531 q^{22} -1.16960 q^{23} -2.97530 q^{24} +1.96909 q^{26} +8.48679 q^{27} -3.57331 q^{28} +1.00000 q^{29} +2.71200 q^{31} -1.00000 q^{32} -12.7501 q^{33} +6.37729 q^{34} +5.85241 q^{36} -0.803972 q^{37} +7.08481 q^{38} -5.85863 q^{39} +0.620024 q^{41} +10.6317 q^{42} +4.79059 q^{43} -4.28531 q^{44} +1.16960 q^{46} -7.80571 q^{47} +2.97530 q^{48} +5.76858 q^{49} -18.9743 q^{51} -1.96909 q^{52} -0.153799 q^{53} -8.48679 q^{54} +3.57331 q^{56} -21.0794 q^{57} -1.00000 q^{58} +6.78101 q^{59} +11.5850 q^{61} -2.71200 q^{62} -20.9125 q^{63} +1.00000 q^{64} +12.7501 q^{66} -14.9736 q^{67} -6.37729 q^{68} -3.47990 q^{69} +10.2314 q^{71} -5.85241 q^{72} +4.75154 q^{73} +0.803972 q^{74} -7.08481 q^{76} +15.3128 q^{77} +5.85863 q^{78} -4.83488 q^{79} +7.69351 q^{81} -0.620024 q^{82} -12.8390 q^{83} -10.6317 q^{84} -4.79059 q^{86} +2.97530 q^{87} +4.28531 q^{88} +8.01243 q^{89} +7.03617 q^{91} -1.16960 q^{92} +8.06901 q^{93} +7.80571 q^{94} -2.97530 q^{96} +10.1610 q^{97} -5.76858 q^{98} -25.0794 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 5 q^{2} - 3 q^{3} + 5 q^{4} + 3 q^{6} - 5 q^{7} - 5 q^{8} + 10 q^{9}+O(q^{10}) $ 5 * q - 5 * q^2 - 3 * q^3 + 5 * q^4 + 3 * q^6 - 5 * q^7 - 5 * q^8 + 10 * q^9	$ 5 q - 5 q^{2} - 3 q^{3} + 5 q^{4} + 3 q^{6} - 5 q^{7} - 5 q^{8} + 10 q^{9} - 3 q^{12} - 7 q^{13} + 5 q^{14} + 5 q^{16} - 9 q^{17} - 10 q^{18} - 4 q^{19} - 6 q^{21} - 13 q^{23} + 3 q^{24} + 7 q^{26} + 6 q^{27} - 5 q^{28} + 5 q^{29} + 5 q^{31} - 5 q^{32} - 18 q^{33} + 9 q^{34} + 10 q^{36} + 6 q^{37} + 4 q^{38} + 5 q^{39} - 4 q^{41} + 6 q^{42} - q^{43} + 13 q^{46} - 14 q^{47} - 3 q^{48} + 16 q^{49} - 32 q^{51} - 7 q^{52} - 5 q^{53} - 6 q^{54} + 5 q^{56} - 14 q^{57} - 5 q^{58} - 9 q^{59} + 5 q^{61} - 5 q^{62} - 36 q^{63} + 5 q^{64} + 18 q^{66} - 2 q^{67} - 9 q^{68} + 7 q^{69} - 6 q^{71} - 10 q^{72} - 9 q^{73} - 6 q^{74} - 4 q^{76} + 18 q^{77} - 5 q^{78} - 17 q^{79} - 3 q^{81} + 4 q^{82} - 30 q^{83} - 6 q^{84} + q^{86} - 3 q^{87} + 10 q^{89} - 22 q^{91} - 13 q^{92} + 6 q^{93} + 14 q^{94} + 3 q^{96} + 15 q^{97} - 16 q^{98} - 34 q^{99}+O(q^{100}) $ 5 * q - 5 * q^2 - 3 * q^3 + 5 * q^4 + 3 * q^6 - 5 * q^7 - 5 * q^8 + 10 * q^9 - 3 * q^12 - 7 * q^13 + 5 * q^14 + 5 * q^16 - 9 * q^17 - 10 * q^18 - 4 * q^19 - 6 * q^21 - 13 * q^23 + 3 * q^24 + 7 * q^26 + 6 * q^27 - 5 * q^28 + 5 * q^29 + 5 * q^31 - 5 * q^32 - 18 * q^33 + 9 * q^34 + 10 * q^36 + 6 * q^37 + 4 * q^38 + 5 * q^39 - 4 * q^41 + 6 * q^42 - q^43 + 13 * q^46 - 14 * q^47 - 3 * q^48 + 16 * q^49 - 32 * q^51 - 7 * q^52 - 5 * q^53 - 6 * q^54 + 5 * q^56 - 14 * q^57 - 5 * q^58 - 9 * q^59 + 5 * q^61 - 5 * q^62 - 36 * q^63 + 5 * q^64 + 18 * q^66 - 2 * q^67 - 9 * q^68 + 7 * q^69 - 6 * q^71 - 10 * q^72 - 9 * q^73 - 6 * q^74 - 4 * q^76 + 18 * q^77 - 5 * q^78 - 17 * q^79 - 3 * q^81 + 4 * q^82 - 30 * q^83 - 6 * q^84 + q^86 - 3 * q^87 + 10 * q^89 - 22 * q^91 - 13 * q^92 + 6 * q^93 + 14 * q^94 + 3 * q^96 + 15 * q^97 - 16 * q^98 - 34 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	2.97530	1.71779	0.858895	−	0.512151i	$-0.171151\pi$
$3$	2.97530	1.71779	0.858895	+	0.512151i	$0.171151\pi$
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	−2.97530	−1.21466
$7$	−3.57331	−1.35059	−0.675293	−	0.737550i	$-0.735983\pi$
$7$	−3.57331	−1.35059	−0.675293	+	0.737550i	$0.735983\pi$
$8$	−1.00000	−0.353553
$9$	5.85241	1.95080
$10$	0	0
$11$	−4.28531	−1.29207	−0.646035	−	0.763308i	$-0.723574\pi$
$11$	−4.28531	−1.29207	−0.646035	+	0.763308i	$0.723574\pi$
$12$	2.97530	0.858895
$13$	−1.96909	−0.546127	−0.273063	−	0.961996i	$-0.588037\pi$
$13$	−1.96909	−0.546127	−0.273063	+	0.961996i	$0.588037\pi$
$14$	3.57331	0.955009
$15$	0	0
$16$	1.00000	0.250000
$17$	−6.37729	−1.54672	−0.773360	−	0.633968i	$-0.781425\pi$
$17$	−6.37729	−1.54672	−0.773360	+	0.633968i	$0.781425\pi$
$18$	−5.85241	−1.37943
$19$	−7.08481	−1.62537	−0.812683	−	0.582706i	$-0.801994\pi$
$19$	−7.08481	−1.62537	−0.812683	+	0.582706i	$0.801994\pi$
$20$	0	0
$21$	−10.6317	−2.32002
$22$	4.28531	0.913632
$23$	−1.16960	−0.243877	−0.121939	−	0.992538i	$-0.538911\pi$
$23$	−1.16960	−0.243877	−0.121939	+	0.992538i	$0.538911\pi$
$24$	−2.97530	−0.607331
$25$	0	0
$26$	1.96909	0.386170
$27$	8.48679	1.63328
$28$	−3.57331	−0.675293
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	0	0
$31$	2.71200	0.487089	0.243545	−	0.969890i	$-0.421690\pi$
$31$	2.71200	0.487089	0.243545	+	0.969890i	$0.421690\pi$
$32$	−1.00000	−0.176777
$33$	−12.7501	−2.21951
$34$	6.37729	1.09370
$35$	0	0
$36$	5.85241	0.975402
$37$	−0.803972	−0.132172	−0.0660861	−	0.997814i	$-0.521051\pi$
$37$	−0.803972	−0.132172	−0.0660861	+	0.997814i	$0.521051\pi$
$38$	7.08481	1.14931
$39$	−5.85863	−0.938131
$40$	0	0
$41$	0.620024	0.0968315	0.0484157	−	0.998827i	$-0.484583\pi$
$41$	0.620024	0.0968315	0.0484157	+	0.998827i	$0.484583\pi$
$42$	10.6317	1.64050
$43$	4.79059	0.730558	0.365279	−	0.930898i	$-0.380974\pi$
$43$	4.79059	0.730558	0.365279	+	0.930898i	$0.380974\pi$
$44$	−4.28531	−0.646035
$45$	0	0
$46$	1.16960	0.172447
$47$	−7.80571	−1.13858	−0.569290	−	0.822137i	$-0.692782\pi$
$47$	−7.80571	−1.13858	−0.569290	+	0.822137i	$0.692782\pi$
$48$	2.97530	0.429448
$49$	5.76858	0.824083
$50$	0	0
$51$	−18.9743	−2.65694
$52$	−1.96909	−0.273063
$53$	−0.153799	−0.0211259	−0.0105629	−	0.999944i	$-0.503362\pi$
$53$	−0.153799	−0.0211259	−0.0105629	+	0.999944i	$0.503362\pi$
$54$	−8.48679	−1.15491
$55$	0	0
$56$	3.57331	0.477504
$57$	−21.0794	−2.79204
$58$	−1.00000	−0.131306
$59$	6.78101	0.882812	0.441406	−	0.897308i	$-0.354480\pi$
$59$	6.78101	0.882812	0.441406	+	0.897308i	$0.354480\pi$
$60$	0	0
$61$	11.5850	1.48330	0.741652	−	0.670785i	$-0.234043\pi$
$61$	11.5850	1.48330	0.741652	+	0.670785i	$0.234043\pi$
$62$	−2.71200	−0.344424
$63$	−20.9125	−2.63473
$64$	1.00000	0.125000
$65$	0	0
$66$	12.7501	1.56943
$67$	−14.9736	−1.82931	−0.914657	−	0.404231i	$-0.867539\pi$
$67$	−14.9736	−1.82931	−0.914657	+	0.404231i	$0.867539\pi$
$68$	−6.37729	−0.773360
$69$	−3.47990	−0.418930
$70$	0	0
$71$	10.2314	1.21425	0.607124	−	0.794607i	$-0.292323\pi$
$71$	10.2314	1.21425	0.607124	+	0.794607i	$0.292323\pi$
$72$	−5.85241	−0.689714
$73$	4.75154	0.556125	0.278063	−	0.960563i	$-0.410308\pi$
$73$	4.75154	0.556125	0.278063	+	0.960563i	$0.410308\pi$
$74$	0.803972	0.0934598
$75$	0	0
$76$	−7.08481	−0.812683
$77$	15.3128	1.74505
$78$	5.85863	0.663359
$79$	−4.83488	−0.543967	−0.271983	−	0.962302i	$-0.587680\pi$
$79$	−4.83488	−0.543967	−0.271983	+	0.962302i	$0.587680\pi$
$80$	0	0
$81$	7.69351	0.854835
$82$	−0.620024	−0.0684702
$83$	−12.8390	−1.40927	−0.704633	−	0.709571i	$-0.748889\pi$
$83$	−12.8390	−1.40927	−0.704633	+	0.709571i	$0.748889\pi$
$84$	−10.6317	−1.16001
$85$	0	0
$86$	−4.79059	−0.516583
$87$	2.97530	0.318986
$88$	4.28531	0.456816
$89$	8.01243	0.849315	0.424658	−	0.905354i	$-0.360394\pi$
$89$	8.01243	0.849315	0.424658	+	0.905354i	$0.360394\pi$
$90$	0	0
$91$	7.03617	0.737591
$92$	−1.16960	−0.121939
$93$	8.06901	0.836717
$94$	7.80571	0.805097
$95$	0	0
$96$	−2.97530	−0.303665
$97$	10.1610	1.03169	0.515846	−	0.856681i	$-0.327478\pi$
$97$	10.1610	1.03169	0.515846	+	0.856681i	$0.327478\pi$
$98$	−5.76858	−0.582715
$99$	−25.0794	−2.52058
$100$	0	0
$101$	10.2050	1.01544	0.507718	−	0.861523i	$-0.330489\pi$
$101$	10.2050	1.01544	0.507718	+	0.861523i	$0.330489\pi$
$102$	18.9743	1.87874
$103$	3.36217	0.331284	0.165642	−	0.986186i	$-0.447030\pi$
$103$	3.36217	0.331284	0.165642	+	0.986186i	$0.447030\pi$
$104$	1.96909	0.193085
$105$	0	0
$106$	0.153799	0.0149383
$107$	8.52123	0.823778	0.411889	−	0.911234i	$-0.364869\pi$
$107$	8.52123	0.823778	0.411889	+	0.911234i	$0.364869\pi$
$108$	8.48679	0.816642
$109$	10.6221	1.01741	0.508706	−	0.860940i	$-0.330124\pi$
$109$	10.6221	1.01741	0.508706	+	0.860940i	$0.330124\pi$
$110$	0	0
$111$	−2.39206	−0.227044
$112$	−3.57331	−0.337647
$113$	−18.0211	−1.69528	−0.847639	−	0.530573i	$-0.821977\pi$
$113$	−18.0211	−1.69528	−0.847639	+	0.530573i	$0.821977\pi$
$114$	21.0794	1.97427
$115$	0	0
$116$	1.00000	0.0928477
$117$	−11.5239	−1.06539
$118$	−6.78101	−0.624242
$119$	22.7881	2.08898
$120$	0	0
$121$	7.36390	0.669446
$122$	−11.5850	−1.04885
$123$	1.84476	0.166336
$124$	2.71200	0.243545
$125$	0	0
$126$	20.9125	1.86304
$127$	15.0230	1.33307	0.666537	−	0.745472i	$-0.267776\pi$
$127$	15.0230	1.33307	0.666537	+	0.745472i	$0.267776\pi$
$128$	−1.00000	−0.0883883
$129$	14.2534	1.25495
$130$	0	0
$131$	−0.915195	−0.0799610	−0.0399805	−	0.999200i	$-0.512730\pi$
$131$	−0.915195	−0.0799610	−0.0399805	+	0.999200i	$0.512730\pi$
$132$	−12.7501	−1.10975
$133$	25.3162	2.19520
$134$	14.9736	1.29352
$135$	0	0
$136$	6.37729	0.546848
$137$	−5.94197	−0.507657	−0.253829	−	0.967249i	$-0.581690\pi$
$137$	−5.94197	−0.507657	−0.253829	+	0.967249i	$0.581690\pi$
$138$	3.47990	0.296229
$139$	−14.6897	−1.24597	−0.622983	−	0.782236i	$-0.714079\pi$
$139$	−14.6897	−1.24597	−0.622983	+	0.782236i	$0.714079\pi$
$140$	0	0
$141$	−23.2243	−1.95584
$142$	−10.2314	−0.858603
$143$	8.43816	0.705634
$144$	5.85241	0.487701
$145$	0	0
$146$	−4.75154	−0.393240
$147$	17.1633	1.41560
$148$	−0.803972	−0.0660861
$149$	−19.6945	−1.61343	−0.806717	−	0.590937i	$-0.798758\pi$
$149$	−19.6945	−1.61343	−0.806717	+	0.590937i	$0.798758\pi$
$150$	0	0
$151$	−4.58843	−0.373401	−0.186701	−	0.982417i	$-0.559779\pi$
$151$	−4.58843	−0.373401	−0.186701	+	0.982417i	$0.559779\pi$
$152$	7.08481	0.574654
$153$	−37.3225	−3.01735
$154$	−15.3128	−1.23394
$155$	0	0
$156$	−5.85863	−0.469066
$157$	6.87822	0.548942	0.274471	−	0.961595i	$-0.411497\pi$
$157$	6.87822	0.548942	0.274471	+	0.961595i	$0.411497\pi$
$158$	4.83488	0.384643
$159$	−0.457597	−0.0362898
$160$	0	0
$161$	4.17933	0.329377
$162$	−7.69351	−0.604459
$163$	−3.03333	−0.237589	−0.118794	−	0.992919i	$-0.537903\pi$
$163$	−3.03333	−0.237589	−0.118794	+	0.992919i	$0.537903\pi$
$164$	0.620024	0.0484157
$165$	0	0
$166$	12.8390	0.996502
$167$	−21.5857	−1.67035	−0.835177	−	0.549981i	$-0.814635\pi$
$167$	−21.5857	−1.67035	−0.835177	+	0.549981i	$0.814635\pi$
$168$	10.6317	0.820252
$169$	−9.12269	−0.701746
$170$	0	0
$171$	−41.4632	−3.17077
$172$	4.79059	0.365279
$173$	−21.2774	−1.61769	−0.808845	−	0.588022i	$-0.799907\pi$
$173$	−21.2774	−1.61769	−0.808845	+	0.588022i	$0.799907\pi$
$174$	−2.97530	−0.225557
$175$	0	0
$176$	−4.28531	−0.323018
$177$	20.1755	1.51649
$178$	−8.01243	−0.600557
$179$	−21.3392	−1.59497	−0.797484	−	0.603341i	$-0.793836\pi$
$179$	−21.3392	−1.59497	−0.797484	+	0.603341i	$0.793836\pi$
$180$	0	0
$181$	−2.64127	−0.196324	−0.0981620	−	0.995170i	$-0.531296\pi$
$181$	−2.64127	−0.196324	−0.0981620	+	0.995170i	$0.531296\pi$
$182$	−7.03617	−0.521556
$183$	34.4688	2.54801
$184$	1.16960	0.0862237
$185$	0	0
$186$	−8.06901	−0.591648
$187$	27.3287	1.99847
$188$	−7.80571	−0.569290
$189$	−30.3260	−2.20589
$190$	0	0
$191$	−7.52392	−0.544411	−0.272206	−	0.962239i	$-0.587753\pi$
$191$	−7.52392	−0.544411	−0.272206	+	0.962239i	$0.587753\pi$
$192$	2.97530	0.214724
$193$	0.598970	0.0431148	0.0215574	−	0.999768i	$-0.493138\pi$
$193$	0.598970	0.0431148	0.0215574	+	0.999768i	$0.493138\pi$
$194$	−10.1610	−0.729516
$195$	0	0
$196$	5.76858	0.412041
$197$	3.83151	0.272984	0.136492	−	0.990641i	$-0.456417\pi$
$197$	3.83151	0.272984	0.136492	+	0.990641i	$0.456417\pi$
$198$	25.0794	1.78232
$199$	14.8212	1.05065	0.525324	−	0.850902i	$-0.323944\pi$
$199$	14.8212	1.05065	0.525324	+	0.850902i	$0.323944\pi$
$200$	0	0
$201$	−44.5509	−3.14238
$202$	−10.2050	−0.718021
$203$	−3.57331	−0.250798
$204$	−18.9743	−1.32847
$205$	0	0
$206$	−3.36217	−0.234254
$207$	−6.84496	−0.475757
$208$	−1.96909	−0.136532
$209$	30.3606	2.10009
$210$	0	0
$211$	5.64748	0.388789	0.194394	−	0.980923i	$-0.437726\pi$
$211$	5.64748	0.388789	0.194394	+	0.980923i	$0.437726\pi$
$212$	−0.153799	−0.0105629
$213$	30.4416	2.08582
$214$	−8.52123	−0.582499
$215$	0	0
$216$	−8.48679	−0.577453
$217$	−9.69082	−0.657856
$218$	−10.6221	−0.719420
$219$	14.1373	0.955307
$220$	0	0
$221$	12.5574	0.844705
$222$	2.39206	0.160544
$223$	19.3022	1.29257	0.646287	−	0.763095i	$-0.276321\pi$
$223$	19.3022	1.29257	0.646287	+	0.763095i	$0.276321\pi$
$224$	3.57331	0.238752
$225$	0	0
$226$	18.0211	1.19874
$227$	−7.11640	−0.472332	−0.236166	−	0.971713i	$-0.575891\pi$
$227$	−7.11640	−0.472332	−0.236166	+	0.971713i	$0.575891\pi$
$228$	−21.0794	−1.39602
$229$	−20.2291	−1.33678	−0.668388	−	0.743813i	$-0.733015\pi$
$229$	−20.2291	−1.33678	−0.668388	+	0.743813i	$0.733015\pi$
$230$	0	0
$231$	45.5601	2.99763
$232$	−1.00000	−0.0656532
$233$	14.5359	0.952279	0.476140	−	0.879370i	$-0.342036\pi$
$233$	14.5359	0.952279	0.476140	+	0.879370i	$0.342036\pi$
$234$	11.5239	0.753342
$235$	0	0
$236$	6.78101	0.441406
$237$	−14.3852	−0.934421
$238$	−22.7881	−1.47713
$239$	−9.28118	−0.600350	−0.300175	−	0.953884i	$-0.597045\pi$
$239$	−9.28118	−0.600350	−0.300175	+	0.953884i	$0.597045\pi$
$240$	0	0
$241$	−12.1822	−0.784726	−0.392363	−	0.919810i	$-0.628342\pi$
$241$	−12.1822	−0.784726	−0.392363	+	0.919810i	$0.628342\pi$
$242$	−7.36390	−0.473370
$243$	−2.56986	−0.164857
$244$	11.5850	0.741652
$245$	0	0
$246$	−1.84476	−0.117617
$247$	13.9506	0.887656
$248$	−2.71200	−0.172212
$249$	−38.2000	−2.42083
$250$	0	0
$251$	−6.87028	−0.433648	−0.216824	−	0.976211i	$-0.569570\pi$
$251$	−6.87028	−0.433648	−0.216824	+	0.976211i	$0.569570\pi$
$252$	−20.9125	−1.31736
$253$	5.01208	0.315107
$254$	−15.0230	−0.942626
$255$	0	0
$256$	1.00000	0.0625000
$257$	−5.54317	−0.345773	−0.172887	−	0.984942i	$-0.555309\pi$
$257$	−5.54317	−0.345773	−0.172887	+	0.984942i	$0.555309\pi$
$258$	−14.2534	−0.887381
$259$	2.87284	0.178510
$260$	0	0
$261$	5.85241	0.362255
$262$	0.915195	0.0565409
$263$	9.71229	0.598885	0.299443	−	0.954114i	$-0.403199\pi$
$263$	9.71229	0.598885	0.299443	+	0.954114i	$0.403199\pi$
$264$	12.7501	0.784714
$265$	0	0
$266$	−25.3162	−1.55224
$267$	23.8394	1.45895
$268$	−14.9736	−0.914657
$269$	3.77507	0.230170	0.115085	−	0.993356i	$-0.463286\pi$
$269$	3.77507	0.230170	0.115085	+	0.993356i	$0.463286\pi$
$270$	0	0
$271$	−13.1352	−0.797909	−0.398955	−	0.916971i	$-0.630627\pi$
$271$	−13.1352	−0.797909	−0.398955	+	0.916971i	$0.630627\pi$
$272$	−6.37729	−0.386680
$273$	20.9347	1.26703
$274$	5.94197	0.358968
$275$	0	0
$276$	−3.47990	−0.209465
$277$	−16.7718	−1.00772	−0.503861	−	0.863785i	$-0.668088\pi$
$277$	−16.7718	−1.00772	−0.503861	+	0.863785i	$0.668088\pi$
$278$	14.6897	0.881030
$279$	15.8717	0.950216
$280$	0	0
$281$	−18.7536	−1.11875	−0.559374	−	0.828916i	$-0.688958\pi$
$281$	−18.7536	−1.11875	−0.559374	+	0.828916i	$0.688958\pi$
$282$	23.2243	1.38299
$283$	−29.2490	−1.73867	−0.869337	−	0.494219i	$-0.835454\pi$
$283$	−29.2490	−1.73867	−0.869337	+	0.494219i	$0.835454\pi$
$284$	10.2314	0.607124
$285$	0	0
$286$	−8.43816	−0.498959
$287$	−2.21554	−0.130779
$288$	−5.85241	−0.344857
$289$	23.6698	1.39234
$290$	0	0
$291$	30.2320	1.77223
$292$	4.75154	0.278063
$293$	−12.8831	−0.752636	−0.376318	−	0.926491i	$-0.622810\pi$
$293$	−12.8831	−0.752636	−0.376318	+	0.926491i	$0.622810\pi$
$294$	−17.1633	−1.00098
$295$	0	0
$296$	0.803972	0.0467299
$297$	−36.3686	−2.11032
$298$	19.6945	1.14087
$299$	2.30304	0.133188
$300$	0	0
$301$	−17.1183	−0.986682
$302$	4.58843	0.264035
$303$	30.3629	1.74431
$304$	−7.08481	−0.406341
$305$	0	0
$306$	37.3225	2.13359
$307$	−9.40469	−0.536754	−0.268377	−	0.963314i	$-0.586487\pi$
$307$	−9.40469	−0.536754	−0.268377	+	0.963314i	$0.586487\pi$
$308$	15.3128	0.872526
$309$	10.0035	0.569077
$310$	0	0
$311$	−23.9414	−1.35759	−0.678797	−	0.734326i	$-0.737498\pi$
$311$	−23.9414	−1.35759	−0.678797	+	0.734326i	$0.737498\pi$
$312$	5.85863	0.331679
$313$	−3.14215	−0.177605	−0.0888024	−	0.996049i	$-0.528304\pi$
$313$	−3.14215	−0.177605	−0.0888024	+	0.996049i	$0.528304\pi$
$314$	−6.87822	−0.388161
$315$	0	0
$316$	−4.83488	−0.271983
$317$	5.71726	0.321113	0.160557	−	0.987027i	$-0.448671\pi$
$317$	5.71726	0.321113	0.160557	+	0.987027i	$0.448671\pi$
$318$	0.457597	0.0256608
$319$	−4.28531	−0.239931
$320$	0	0
$321$	25.3532	1.41508
$322$	−4.17933	−0.232905
$323$	45.1818	2.51398
$324$	7.69351	0.427417
$325$	0	0
$326$	3.03333	0.168000
$327$	31.6040	1.74770
$328$	−0.620024	−0.0342351
$329$	27.8922	1.53775
$330$	0	0
$331$	24.0010	1.31922	0.659608	−	0.751610i	$-0.270722\pi$
$331$	24.0010	1.31922	0.659608	+	0.751610i	$0.270722\pi$
$332$	−12.8390	−0.704633
$333$	−4.70517	−0.257842
$334$	21.5857	1.18112
$335$	0	0
$336$	−10.6317	−0.580006
$337$	10.3773	0.565287	0.282643	−	0.959225i	$-0.408789\pi$
$337$	10.3773	0.565287	0.282643	+	0.959225i	$0.408789\pi$
$338$	9.12269	0.496209
$339$	−53.6181	−2.91213
$340$	0	0
$341$	−11.6218	−0.629353
$342$	41.4632	2.24207
$343$	4.40025	0.237591
$344$	−4.79059	−0.258291
$345$	0	0
$346$	21.2774	1.14388
$347$	−11.1769	−0.600005	−0.300003	−	0.953938i	$-0.596988\pi$
$347$	−11.1769	−0.600005	−0.300003	+	0.953938i	$0.596988\pi$
$348$	2.97530	0.159493
$349$	30.6661	1.64152	0.820760	−	0.571273i	$-0.193550\pi$
$349$	30.6661	1.64152	0.820760	+	0.571273i	$0.193550\pi$
$350$	0	0
$351$	−16.7112	−0.891980
$352$	4.28531	0.228408
$353$	−22.8728	−1.21740	−0.608699	−	0.793401i	$-0.708308\pi$
$353$	−22.8728	−1.21740	−0.608699	+	0.793401i	$0.708308\pi$
$354$	−20.1755	−1.07232
$355$	0	0
$356$	8.01243	0.424658
$357$	67.8013	3.58843
$358$	21.3392	1.12781
$359$	−16.7979	−0.886560	−0.443280	−	0.896383i	$-0.646185\pi$
$359$	−16.7979	−0.886560	−0.443280	+	0.896383i	$0.646185\pi$
$360$	0	0
$361$	31.1945	1.64181
$362$	2.64127	0.138822
$363$	21.9098	1.14997
$364$	7.03617	0.368796
$365$	0	0
$366$	−34.4688	−1.80171
$367$	7.12178	0.371754	0.185877	−	0.982573i	$-0.440487\pi$
$367$	7.12178	0.371754	0.185877	+	0.982573i	$0.440487\pi$
$368$	−1.16960	−0.0609694
$369$	3.62864	0.188899
$370$	0	0
$371$	0.549571	0.0285323
$372$	8.06901	0.418359
$373$	24.9332	1.29099	0.645497	−	0.763763i	$-0.276650\pi$
$373$	24.9332	1.29099	0.645497	+	0.763763i	$0.276650\pi$
$374$	−27.3287	−1.41313
$375$	0	0
$376$	7.80571	0.402549
$377$	−1.96909	−0.101413
$378$	30.3260	1.55980
$379$	0.816398	0.0419355	0.0209678	−	0.999780i	$-0.493325\pi$
$379$	0.816398	0.0419355	0.0209678	+	0.999780i	$0.493325\pi$
$380$	0	0
$381$	44.6979	2.28994
$382$	7.52392	0.384957
$383$	19.2995	0.986160	0.493080	−	0.869984i	$-0.335871\pi$
$383$	19.2995	0.986160	0.493080	+	0.869984i	$0.335871\pi$
$384$	−2.97530	−0.151833
$385$	0	0
$386$	−0.598970	−0.0304868
$387$	28.0365	1.42518
$388$	10.1610	0.515846
$389$	−0.583052	−0.0295619	−0.0147809	−	0.999891i	$-0.504705\pi$
$389$	−0.583052	−0.0295619	−0.0147809	+	0.999891i	$0.504705\pi$
$390$	0	0
$391$	7.45884	0.377210
$392$	−5.76858	−0.291357
$393$	−2.72298	−0.137356
$394$	−3.83151	−0.193029
$395$	0	0
$396$	−25.0794	−1.26029
$397$	13.7331	0.689243	0.344621	−	0.938742i	$-0.388007\pi$
$397$	13.7331	0.689243	0.344621	+	0.938742i	$0.388007\pi$
$398$	−14.8212	−0.742921
$399$	75.3234	3.77089
$400$	0	0
$401$	−23.0658	−1.15185	−0.575926	−	0.817502i	$-0.695358\pi$
$401$	−23.0658	−1.15185	−0.575926	+	0.817502i	$0.695358\pi$
$402$	44.5509	2.22200
$403$	−5.34016	−0.266012
$404$	10.2050	0.507718
$405$	0	0
$406$	3.57331	0.177341
$407$	3.44527	0.170776
$408$	18.9743	0.939370
$409$	11.0252	0.545161	0.272580	−	0.962133i	$-0.412123\pi$
$409$	11.0252	0.545161	0.272580	+	0.962133i	$0.412123\pi$
$410$	0	0
$411$	−17.6792	−0.872049
$412$	3.36217	0.165642
$413$	−24.2307	−1.19231
$414$	6.84496	0.336411
$415$	0	0
$416$	1.96909	0.0965425
$417$	−43.7063	−2.14031
$418$	−30.3606	−1.48499
$419$	29.6655	1.44926	0.724628	−	0.689141i	$-0.242012\pi$
$419$	29.6655	1.44926	0.724628	+	0.689141i	$0.242012\pi$
$420$	0	0
$421$	6.00896	0.292859	0.146429	−	0.989221i	$-0.453222\pi$
$421$	6.00896	0.292859	0.146429	+	0.989221i	$0.453222\pi$
$422$	−5.64748	−0.274915
$423$	−45.6822	−2.22115
$424$	0.153799	0.00746913
$425$	0	0
$426$	−30.4416	−1.47490
$427$	−41.3968	−2.00333
$428$	8.52123	0.411889
$429$	25.1061	1.21213
$430$	0	0
$431$	13.2050	0.636062	0.318031	−	0.948080i	$-0.396978\pi$
$431$	13.2050	0.636062	0.318031	+	0.948080i	$0.396978\pi$
$432$	8.48679	0.408321
$433$	10.2266	0.491459	0.245730	−	0.969338i	$-0.420972\pi$
$433$	10.2266	0.491459	0.245730	+	0.969338i	$0.420972\pi$
$434$	9.69082	0.465174
$435$	0	0
$436$	10.6221	0.508706
$437$	8.28635	0.396390
$438$	−14.1373	−0.675504
$439$	−6.08321	−0.290336	−0.145168	−	0.989407i	$-0.546372\pi$
$439$	−6.08321	−0.290336	−0.145168	+	0.989407i	$0.546372\pi$
$440$	0	0
$441$	33.7601	1.60762
$442$	−12.5574	−0.597296
$443$	24.1610	1.14792	0.573961	−	0.818882i	$-0.305406\pi$
$443$	24.1610	1.14792	0.573961	+	0.818882i	$0.305406\pi$
$444$	−2.39206	−0.113522
$445$	0	0
$446$	−19.3022	−0.913987
$447$	−58.5970	−2.77154
$448$	−3.57331	−0.168823
$449$	−7.55594	−0.356587	−0.178293	−	0.983977i	$-0.557058\pi$
$449$	−7.55594	−0.356587	−0.178293	+	0.983977i	$0.557058\pi$
$450$	0	0
$451$	−2.65700	−0.125113
$452$	−18.0211	−0.847639
$453$	−13.6520	−0.641425
$454$	7.11640	0.333989
$455$	0	0
$456$	21.0794	0.987135
$457$	9.62520	0.450248	0.225124	−	0.974330i	$-0.427721\pi$
$457$	9.62520	0.450248	0.225124	+	0.974330i	$0.427721\pi$
$458$	20.2291	0.945243
$459$	−54.1227	−2.52623
$460$	0	0
$461$	20.3101	0.945935	0.472967	−	0.881080i	$-0.343183\pi$
$461$	20.3101	0.945935	0.472967	+	0.881080i	$0.343183\pi$
$462$	−45.5601	−2.11965
$463$	7.72111	0.358830	0.179415	−	0.983773i	$-0.442579\pi$
$463$	7.72111	0.358830	0.179415	+	0.983773i	$0.442579\pi$
$464$	1.00000	0.0464238
$465$	0	0
$466$	−14.5359	−0.673363
$467$	−21.6688	−1.00271	−0.501357	−	0.865241i	$-0.667165\pi$
$467$	−21.6688	−1.00271	−0.501357	+	0.865241i	$0.667165\pi$
$468$	−11.5239	−0.532693
$469$	53.5053	2.47065
$470$	0	0
$471$	20.4648	0.942967
$472$	−6.78101	−0.312121
$473$	−20.5292	−0.943932
$474$	14.3852	0.660736
$475$	0	0
$476$	22.7881	1.04449
$477$	−0.900094	−0.0412125
$478$	9.28118	0.424511
$479$	−12.5672	−0.574212	−0.287106	−	0.957899i	$-0.592693\pi$
$479$	−12.5672	−0.574212	−0.287106	+	0.957899i	$0.592693\pi$
$480$	0	0
$481$	1.58309	0.0721827
$482$	12.1822	0.554885
$483$	12.4348	0.565802
$484$	7.36390	0.334723
$485$	0	0
$486$	2.56986	0.116571
$487$	23.0673	1.04528	0.522640	−	0.852553i	$-0.324947\pi$
$487$	23.0673	1.04528	0.522640	+	0.852553i	$0.324947\pi$
$488$	−11.5850	−0.524427
$489$	−9.02506	−0.408127
$490$	0	0
$491$	−1.92280	−0.0867746	−0.0433873	−	0.999058i	$-0.513815\pi$
$491$	−1.92280	−0.0867746	−0.0433873	+	0.999058i	$0.513815\pi$
$492$	1.84476	0.0831681
$493$	−6.37729	−0.287219
$494$	−13.9506	−0.627667
$495$	0	0
$496$	2.71200	0.121772
$497$	−36.5601	−1.63995
$498$	38.2000	1.71178
$499$	6.17341	0.276360	0.138180	−	0.990407i	$-0.455875\pi$
$499$	6.17341	0.276360	0.138180	+	0.990407i	$0.455875\pi$
$500$	0	0
$501$	−64.2241	−2.86932
$502$	6.87028	0.306635
$503$	1.24751	0.0556236	0.0278118	−	0.999613i	$-0.491146\pi$
$503$	1.24751	0.0556236	0.0278118	+	0.999613i	$0.491146\pi$
$504$	20.9125	0.931518
$505$	0	0
$506$	−5.01208	−0.222814
$507$	−27.1428	−1.20545
$508$	15.0230	0.666537
$509$	1.45284	0.0643959	0.0321980	−	0.999482i	$-0.489749\pi$
$509$	1.45284	0.0643959	0.0321980	+	0.999482i	$0.489749\pi$
$510$	0	0
$511$	−16.9787	−0.751095
$512$	−1.00000	−0.0441942
$513$	−60.1273	−2.65468
$514$	5.54317	0.244499
$515$	0	0
$516$	14.2534	0.627473
$517$	33.4499	1.47112
$518$	−2.87284	−0.126225
$519$	−63.3066	−2.77885
$520$	0	0
$521$	−7.78198	−0.340935	−0.170467	−	0.985363i	$-0.554528\pi$
$521$	−7.78198	−0.340935	−0.170467	+	0.985363i	$0.554528\pi$
$522$	−5.85241	−0.256153
$523$	−43.7530	−1.91319	−0.956593	−	0.291428i	$-0.905870\pi$
$523$	−43.7530	−1.91319	−0.956593	+	0.291428i	$0.905870\pi$
$524$	−0.915195	−0.0399805
$525$	0	0
$526$	−9.71229	−0.423476
$527$	−17.2952	−0.753390
$528$	−12.7501	−0.554877
$529$	−21.6320	−0.940524
$530$	0	0
$531$	39.6853	1.72219
$532$	25.3162	1.09760
$533$	−1.22088	−0.0528822
$534$	−23.8394	−1.03163
$535$	0	0
$536$	14.9736	0.646760
$537$	−63.4906	−2.73982
$538$	−3.77507	−0.162755
$539$	−24.7202	−1.06477
$540$	0	0
$541$	−23.7821	−1.02247	−0.511237	−	0.859440i	$-0.670812\pi$
$541$	−23.7821	−1.02247	−0.511237	+	0.859440i	$0.670812\pi$
$542$	13.1352	0.564207
$543$	−7.85857	−0.337244
$544$	6.37729	0.273424
$545$	0	0
$546$	−20.9347	−0.895923
$547$	1.34974	0.0577109	0.0288554	−	0.999584i	$-0.490814\pi$
$547$	1.34974	0.0577109	0.0288554	+	0.999584i	$0.490814\pi$
$548$	−5.94197	−0.253829
$549$	67.8001	2.89364
$550$	0	0
$551$	−7.08481	−0.301823
$552$	3.47990	0.148114
$553$	17.2766	0.734674
$554$	16.7718	0.712567
$555$	0	0
$556$	−14.6897	−0.622983
$557$	11.1855	0.473944	0.236972	−	0.971516i	$-0.423845\pi$
$557$	11.1855	0.473944	0.236972	+	0.971516i	$0.423845\pi$
$558$	−15.8717	−0.671904
$559$	−9.43309	−0.398977
$560$	0	0
$561$	81.3110	3.43295
$562$	18.7536	0.791074
$563$	11.6250	0.489936	0.244968	−	0.969531i	$-0.421223\pi$
$563$	11.6250	0.489936	0.244968	+	0.969531i	$0.421223\pi$
$564$	−23.2243	−0.977920
$565$	0	0
$566$	29.2490	1.22943
$567$	−27.4913	−1.15453
$568$	−10.2314	−0.429301
$569$	−7.80019	−0.327001	−0.163500	−	0.986543i	$-0.552279\pi$
$569$	−7.80019	−0.327001	−0.163500	+	0.986543i	$0.552279\pi$
$570$	0	0
$571$	−0.723311	−0.0302696	−0.0151348	−	0.999885i	$-0.504818\pi$
$571$	−0.723311	−0.0302696	−0.0151348	+	0.999885i	$0.504818\pi$
$572$	8.43816	0.352817
$573$	−22.3859	−0.935185
$574$	2.21554	0.0924749
$575$	0	0
$576$	5.85241	0.243851
$577$	16.3827	0.682019	0.341010	−	0.940060i	$-0.389231\pi$
$577$	16.3827	0.682019	0.341010	+	0.940060i	$0.389231\pi$
$578$	−23.6698	−0.984533
$579$	1.78212	0.0740622
$580$	0	0
$581$	45.8779	1.90334
$582$	−30.2320	−1.25316
$583$	0.659076	0.0272961
$584$	−4.75154	−0.196620
$585$	0	0
$586$	12.8831	0.532194
$587$	20.0090	0.825859	0.412930	−	0.910763i	$-0.364506\pi$
$587$	20.0090	0.825859	0.412930	+	0.910763i	$0.364506\pi$
$588$	17.1633	0.707801
$589$	−19.2140	−0.791698
$590$	0	0
$591$	11.3999	0.468929
$592$	−0.803972	−0.0330430
$593$	9.60346	0.394367	0.197183	−	0.980367i	$-0.436821\pi$
$593$	9.60346	0.394367	0.197183	+	0.980367i	$0.436821\pi$
$594$	36.3686	1.49222
$595$	0	0
$596$	−19.6945	−0.806717
$597$	44.0976	1.80479
$598$	−2.30304	−0.0941781
$599$	−33.4583	−1.36707	−0.683535	−	0.729918i	$-0.739558\pi$
$599$	−33.4583	−1.36707	−0.683535	+	0.729918i	$0.739558\pi$
$600$	0	0
$601$	19.5270	0.796521	0.398260	−	0.917272i	$-0.369614\pi$
$601$	19.5270	0.796521	0.398260	+	0.917272i	$0.369614\pi$
$602$	17.1183	0.697689
$603$	−87.6316	−3.56863
$604$	−4.58843	−0.186701
$605$	0	0
$606$	−30.3629	−1.23341
$607$	34.5722	1.40324	0.701620	−	0.712551i	$-0.252460\pi$
$607$	34.5722	1.40324	0.701620	+	0.712551i	$0.252460\pi$
$608$	7.08481	0.287327
$609$	−10.6317	−0.430818
$610$	0	0
$611$	15.3701	0.621808
$612$	−37.3225	−1.50867
$613$	23.5160	0.949802	0.474901	−	0.880039i	$-0.342484\pi$
$613$	23.5160	0.949802	0.474901	+	0.880039i	$0.342484\pi$
$614$	9.40469	0.379542
$615$	0	0
$616$	−15.3128	−0.616969
$617$	−2.27144	−0.0914448	−0.0457224	−	0.998954i	$-0.514559\pi$
$617$	−2.27144	−0.0914448	−0.0457224	+	0.998954i	$0.514559\pi$
$618$	−10.0035	−0.402399
$619$	−44.5024	−1.78870	−0.894351	−	0.447365i	$-0.852362\pi$
$619$	−44.5024	−1.78870	−0.894351	+	0.447365i	$0.852362\pi$
$620$	0	0
$621$	−9.92611	−0.398321
$622$	23.9414	0.959964
$623$	−28.6309	−1.14707
$624$	−5.85863	−0.234533
$625$	0	0
$626$	3.14215	0.125586
$627$	90.3319	3.60751
$628$	6.87822	0.274471
$629$	5.12716	0.204433
$630$	0	0
$631$	−4.54577	−0.180964	−0.0904822	−	0.995898i	$-0.528841\pi$
$631$	−4.54577	−0.180964	−0.0904822	+	0.995898i	$0.528841\pi$
$632$	4.83488	0.192321
$633$	16.8030	0.667858
$634$	−5.71726	−0.227061
$635$	0	0
$636$	−0.457597	−0.0181449
$637$	−11.3588	−0.450054
$638$	4.28531	0.169657
$639$	59.8786	2.36876
$640$	0	0
$641$	23.9841	0.947316	0.473658	−	0.880709i	$-0.342933\pi$
$641$	23.9841	0.947316	0.473658	+	0.880709i	$0.342933\pi$
$642$	−25.3532	−1.00061
$643$	32.2295	1.27101	0.635504	−	0.772097i	$-0.280792\pi$
$643$	32.2295	1.27101	0.635504	+	0.772097i	$0.280792\pi$
$644$	4.17933	0.164689
$645$	0	0
$646$	−45.1818	−1.77766
$647$	−7.46610	−0.293523	−0.146761	−	0.989172i	$-0.546885\pi$
$647$	−7.46610	−0.293523	−0.146761	+	0.989172i	$0.546885\pi$
$648$	−7.69351	−0.302230
$649$	−29.0587	−1.14066
$650$	0	0
$651$	−28.8331	−1.13006
$652$	−3.03333	−0.118794
$653$	19.1646	0.749968	0.374984	−	0.927031i	$-0.377648\pi$
$653$	19.1646	0.749968	0.374984	+	0.927031i	$0.377648\pi$
$654$	−31.6040	−1.23581
$655$	0	0
$656$	0.620024	0.0242079
$657$	27.8080	1.08489
$658$	−27.8922	−1.08735
$659$	11.8789	0.462737	0.231368	−	0.972866i	$-0.425680\pi$
$659$	11.8789	0.462737	0.231368	+	0.972866i	$0.425680\pi$
$660$	0	0
$661$	24.2933	0.944898	0.472449	−	0.881358i	$-0.343370\pi$
$661$	24.2933	0.944898	0.472449	+	0.881358i	$0.343370\pi$
$662$	−24.0010	−0.932827
$663$	37.3621	1.45103
$664$	12.8390	0.498251
$665$	0	0
$666$	4.70517	0.182322
$667$	−1.16960	−0.0452869
$668$	−21.5857	−0.835177
$669$	57.4299	2.22037
$670$	0	0
$671$	−49.6453	−1.91653
$672$	10.6317	0.410126
$673$	−9.70226	−0.373995	−0.186997	−	0.982360i	$-0.559876\pi$
$673$	−9.70226	−0.373995	−0.186997	+	0.982360i	$0.559876\pi$
$674$	−10.3773	−0.399718
$675$	0	0
$676$	−9.12269	−0.350873
$677$	−19.0883	−0.733622	−0.366811	−	0.930295i	$-0.619550\pi$
$677$	−19.0883	−0.733622	−0.366811	+	0.930295i	$0.619550\pi$
$678$	53.6181	2.05919
$679$	−36.3084	−1.39339
$680$	0	0
$681$	−21.1734	−0.811367
$682$	11.6218	0.445020
$683$	−26.9984	−1.03307	−0.516533	−	0.856267i	$-0.672778\pi$
$683$	−26.9984	−1.03307	−0.516533	+	0.856267i	$0.672778\pi$
$684$	−41.4632	−1.58539
$685$	0	0
$686$	−4.40025	−0.168002
$687$	−60.1876	−2.29630
$688$	4.79059	0.182640
$689$	0.302843	0.0115374
$690$	0	0
$691$	−42.2469	−1.60715	−0.803574	−	0.595205i	$-0.797071\pi$
$691$	−42.2469	−1.60715	−0.803574	+	0.595205i	$0.797071\pi$
$692$	−21.2774	−0.808845
$693$	89.6167	3.40426
$694$	11.1769	0.424268
$695$	0	0
$696$	−2.97530	−0.112778
$697$	−3.95407	−0.149771
$698$	−30.6661	−1.16073
$699$	43.2487	1.63582
$700$	0	0
$701$	25.6110	0.967314	0.483657	−	0.875258i	$-0.339308\pi$
$701$	25.6110	0.967314	0.483657	+	0.875258i	$0.339308\pi$
$702$	16.7112	0.630725
$703$	5.69598	0.214828
$704$	−4.28531	−0.161509
$705$	0	0
$706$	22.8728	0.860831
$707$	−36.4657	−1.37143
$708$	20.1755	0.758243
$709$	−21.9912	−0.825896	−0.412948	−	0.910755i	$-0.635501\pi$
$709$	−21.9912	−0.825896	−0.412948	+	0.910755i	$0.635501\pi$
$710$	0	0
$711$	−28.2957	−1.06117
$712$	−8.01243	−0.300278
$713$	−3.17194	−0.118790
$714$	−67.8013	−2.53740
$715$	0	0
$716$	−21.3392	−0.797484
$717$	−27.6143	−1.03127
$718$	16.7979	0.626892
$719$	−23.4948	−0.876209	−0.438104	−	0.898924i	$-0.644350\pi$
$719$	−23.4948	−0.876209	−0.438104	+	0.898924i	$0.644350\pi$
$720$	0	0
$721$	−12.0141	−0.447428
$722$	−31.1945	−1.16094
$723$	−36.2458	−1.34800
$724$	−2.64127	−0.0981620
$725$	0	0
$726$	−21.9098	−0.813150
$727$	−38.7492	−1.43713	−0.718564	−	0.695461i	$-0.755200\pi$
$727$	−38.7492	−1.43713	−0.718564	+	0.695461i	$0.755200\pi$
$728$	−7.03617	−0.260778
$729$	−30.7266	−1.13802
$730$	0	0
$731$	−30.5510	−1.12997
$732$	34.4688	1.27400
$733$	37.1432	1.37192	0.685958	−	0.727642i	$-0.259384\pi$
$733$	37.1432	1.37192	0.685958	+	0.727642i	$0.259384\pi$
$734$	−7.12178	−0.262870
$735$	0	0
$736$	1.16960	0.0431118
$737$	64.1665	2.36360
$738$	−3.62864	−0.133572
$739$	−5.90085	−0.217066	−0.108533	−	0.994093i	$-0.534615\pi$
$739$	−5.90085	−0.217066	−0.108533	+	0.994093i	$0.534615\pi$
$740$	0	0
$741$	41.5072	1.52481
$742$	−0.549571	−0.0201754
$743$	32.8955	1.20682	0.603409	−	0.797432i	$-0.293809\pi$
$743$	32.8955	1.20682	0.603409	+	0.797432i	$0.293809\pi$
$744$	−8.06901	−0.295824
$745$	0	0
$746$	−24.9332	−0.912870
$747$	−75.1393	−2.74920
$748$	27.3287	0.999235
$749$	−30.4490	−1.11258
$750$	0	0
$751$	−1.34780	−0.0491820	−0.0245910	−	0.999698i	$-0.507828\pi$
$751$	−1.34780	−0.0491820	−0.0245910	+	0.999698i	$0.507828\pi$
$752$	−7.80571	−0.284645
$753$	−20.4411	−0.744916
$754$	1.96909	0.0717099
$755$	0	0
$756$	−30.3260	−1.10295
$757$	22.6414	0.822916	0.411458	−	0.911429i	$-0.365020\pi$
$757$	22.6414	0.822916	0.411458	+	0.911429i	$0.365020\pi$
$758$	−0.816398	−0.0296529
$759$	14.9124	0.541288
$760$	0	0
$761$	−44.3522	−1.60777	−0.803883	−	0.594788i	$-0.797236\pi$
$761$	−44.3522	−1.60777	−0.803883	+	0.594788i	$0.797236\pi$
$762$	−44.6979	−1.61923
$763$	−37.9561	−1.37410
$764$	−7.52392	−0.272206
$765$	0	0
$766$	−19.2995	−0.697320
$767$	−13.3524	−0.482127
$768$	2.97530	0.107362
$769$	41.3268	1.49028	0.745140	−	0.666908i	$-0.232382\pi$
$769$	41.3268	1.49028	0.745140	+	0.666908i	$0.232382\pi$
$770$	0	0
$771$	−16.4926	−0.593966
$772$	0.598970	0.0215574
$773$	−9.43767	−0.339449	−0.169725	−	0.985492i	$-0.554288\pi$
$773$	−9.43767	−0.339449	−0.169725	+	0.985492i	$0.554288\pi$
$774$	−28.0365	−1.00775
$775$	0	0
$776$	−10.1610	−0.364758
$777$	8.54757	0.306642
$778$	0.583052	0.0209034
$779$	−4.39275	−0.157387
$780$	0	0
$781$	−43.8449	−1.56889
$782$	−7.45884	−0.266728
$783$	8.48679	0.303293
$784$	5.76858	0.206021
$785$	0	0
$786$	2.72298	0.0971255
$787$	4.73128	0.168652	0.0843259	−	0.996438i	$-0.473126\pi$
$787$	4.73128	0.168652	0.0843259	+	0.996438i	$0.473126\pi$
$788$	3.83151	0.136492
$789$	28.8970	1.02876
$790$	0	0
$791$	64.3949	2.28962
$792$	25.0794	0.891159
$793$	−22.8118	−0.810072
$794$	−13.7331	−0.487368
$795$	0	0
$796$	14.8212	0.525324
$797$	49.4209	1.75058	0.875288	−	0.483601i	$-0.160672\pi$
$797$	49.4209	1.75058	0.875288	+	0.483601i	$0.160672\pi$
$798$	−75.3234	−2.66642
$799$	49.7792	1.76106
$800$	0	0
$801$	46.8920	1.65685
$802$	23.0658	0.814483
$803$	−20.3618	−0.718553
$804$	−44.5509	−1.57119
$805$	0	0
$806$	5.34016	0.188099
$807$	11.2320	0.395384
$808$	−10.2050	−0.359011
$809$	9.40397	0.330626	0.165313	−	0.986241i	$-0.447137\pi$
$809$	9.40397	0.330626	0.165313	+	0.986241i	$0.447137\pi$
$810$	0	0
$811$	−30.4674	−1.06986	−0.534928	−	0.844898i	$-0.679661\pi$
$811$	−30.4674	−1.06986	−0.534928	+	0.844898i	$0.679661\pi$
$812$	−3.57331	−0.125399
$813$	−39.0813	−1.37064
$814$	−3.44527	−0.120757
$815$	0	0
$816$	−18.9743	−0.664235
$817$	−33.9404	−1.18742
$818$	−11.0252	−0.385487
$819$	41.1786	1.43890
$820$	0	0
$821$	−4.45249	−0.155393	−0.0776965	−	0.996977i	$-0.524757\pi$
$821$	−4.45249	−0.155393	−0.0776965	+	0.996977i	$0.524757\pi$
$822$	17.6792	0.616631
$823$	−41.6982	−1.45351	−0.726754	−	0.686897i	$-0.758972\pi$
$823$	−41.6982	−1.45351	−0.726754	+	0.686897i	$0.758972\pi$
$824$	−3.36217	−0.117127
$825$	0	0
$826$	24.2307	0.843093
$827$	−36.6838	−1.27562	−0.637811	−	0.770193i	$-0.720160\pi$
$827$	−36.6838	−1.27562	−0.637811	+	0.770193i	$0.720160\pi$
$828$	−6.84496	−0.237879
$829$	−20.5010	−0.712028	−0.356014	−	0.934481i	$-0.615864\pi$
$829$	−20.5010	−0.712028	−0.356014	+	0.934481i	$0.615864\pi$
$830$	0	0
$831$	−49.9012	−1.73105
$832$	−1.96909	−0.0682658
$833$	−36.7879	−1.27462
$834$	43.7063	1.51343
$835$	0	0
$836$	30.3606	1.05004
$837$	23.0162	0.795555
$838$	−29.6655	−1.02478
$839$	−7.92763	−0.273692	−0.136846	−	0.990592i	$-0.543697\pi$
$839$	−7.92763	−0.273692	−0.136846	+	0.990592i	$0.543697\pi$
$840$	0	0
$841$	1.00000	0.0344828
$842$	−6.00896	−0.207082
$843$	−55.7977	−1.92177
$844$	5.64748	0.194394
$845$	0	0
$846$	45.6822	1.57059
$847$	−26.3136	−0.904144
$848$	−0.153799	−0.00528147
$849$	−87.0247	−2.98668
$850$	0	0
$851$	0.940321	0.0322338
$852$	30.4416	1.04291
$853$	−21.7893	−0.746051	−0.373026	−	0.927821i	$-0.621680\pi$
$853$	−21.7893	−0.746051	−0.373026	+	0.927821i	$0.621680\pi$
$854$	41.3968	1.41657
$855$	0	0
$856$	−8.52123	−0.291250
$857$	35.4888	1.21227	0.606137	−	0.795360i	$-0.292718\pi$
$857$	35.4888	1.21227	0.606137	+	0.795360i	$0.292718\pi$
$858$	−25.1061	−0.857106
$859$	45.7040	1.55940	0.779699	−	0.626154i	$-0.215372\pi$
$859$	45.7040	1.55940	0.779699	+	0.626154i	$0.215372\pi$
$860$	0	0
$861$	−6.59190	−0.224651
$862$	−13.2050	−0.449764
$863$	−6.68814	−0.227667	−0.113833	−	0.993500i	$-0.536313\pi$
$863$	−6.68814	−0.227667	−0.113833	+	0.993500i	$0.536313\pi$
$864$	−8.48679	−0.288726
$865$	0	0
$866$	−10.2266	−0.347514
$867$	70.4247	2.39175
$868$	−9.69082	−0.328928
$869$	20.7190	0.702844
$870$	0	0
$871$	29.4843	0.999037
$872$	−10.6221	−0.359710
$873$	59.4663	2.01263
$874$	−8.28635	−0.280290
$875$	0	0
$876$	14.1373	0.477654
$877$	42.3173	1.42895	0.714476	−	0.699660i	$-0.246665\pi$
$877$	42.3173	1.42895	0.714476	+	0.699660i	$0.246665\pi$
$878$	6.08321	0.205298
$879$	−38.3310	−1.29287
$880$	0	0
$881$	47.1413	1.58823	0.794115	−	0.607768i	$-0.207935\pi$
$881$	47.1413	1.58823	0.794115	+	0.607768i	$0.207935\pi$
$882$	−33.7601	−1.13676
$883$	−9.20502	−0.309773	−0.154887	−	0.987932i	$-0.549501\pi$
$883$	−9.20502	−0.309773	−0.154887	+	0.987932i	$0.549501\pi$
$884$	12.5574	0.422352
$885$	0	0
$886$	−24.1610	−0.811704
$887$	−38.8554	−1.30464	−0.652319	−	0.757944i	$-0.726204\pi$
$887$	−38.8554	−1.30464	−0.652319	+	0.757944i	$0.726204\pi$
$888$	2.39206	0.0802722
$889$	−53.6818	−1.80043
$890$	0	0
$891$	−32.9691	−1.10451
$892$	19.3022	0.646287
$893$	55.3019	1.85061
$894$	58.5970	1.95978
$895$	0	0
$896$	3.57331	0.119376
$897$	6.85222	0.228789
$898$	7.55594	0.252145
$899$	2.71200	0.0904502
$900$	0	0
$901$	0.980819	0.0326758
$902$	2.65700	0.0884683
$903$	−50.9320	−1.69491
$904$	18.0211	0.599371
$905$	0	0
$906$	13.6520	0.453556
$907$	−6.01838	−0.199837	−0.0999185	−	0.994996i	$-0.531858\pi$
$907$	−6.01838	−0.199837	−0.0999185	+	0.994996i	$0.531858\pi$
$908$	−7.11640	−0.236166
$909$	59.7239	1.98092
$910$	0	0
$911$	36.6978	1.21585	0.607925	−	0.793994i	$-0.292002\pi$
$911$	36.6978	1.21585	0.607925	+	0.793994i	$0.292002\pi$
$912$	−21.0794	−0.698010
$913$	55.0193	1.82087
$914$	−9.62520	−0.318373
$915$	0	0
$916$	−20.2291	−0.668388
$917$	3.27028	0.107994
$918$	54.1227	1.78632
$919$	−46.9029	−1.54719	−0.773593	−	0.633683i	$-0.781542\pi$
$919$	−46.9029	−1.54719	−0.773593	+	0.633683i	$0.781542\pi$
$920$	0	0
$921$	−27.9818	−0.922031
$922$	−20.3101	−0.668877
$923$	−20.1466	−0.663133
$924$	45.5601	1.49882
$925$	0	0
$926$	−7.72111	−0.253731
$927$	19.6768	0.646271
$928$	−1.00000	−0.0328266
$929$	−56.0417	−1.83867	−0.919334	−	0.393477i	$-0.871272\pi$
$929$	−56.0417	−1.83867	−0.919334	+	0.393477i	$0.871272\pi$
$930$	0	0
$931$	−40.8693	−1.33944
$932$	14.5359	0.476140
$933$	−71.2329	−2.33206
$934$	21.6688	0.709025
$935$	0	0
$936$	11.5239	0.376671
$937$	−47.8181	−1.56215	−0.781075	−	0.624437i	$-0.785328\pi$
$937$	−47.8181	−1.56215	−0.781075	+	0.624437i	$0.785328\pi$
$938$	−53.5053	−1.74701
$939$	−9.34884	−0.305088
$940$	0	0
$941$	−28.2680	−0.921510	−0.460755	−	0.887527i	$-0.652421\pi$
$941$	−28.2680	−0.921510	−0.460755	+	0.887527i	$0.652421\pi$
$942$	−20.4648	−0.666779
$943$	−0.725177	−0.0236150
$944$	6.78101	0.220703
$945$	0	0
$946$	20.5292	0.667461
$947$	42.6499	1.38594	0.692968	−	0.720969i	$-0.256303\pi$
$947$	42.6499	1.38594	0.692968	+	0.720969i	$0.256303\pi$
$948$	−14.3852	−0.467211
$949$	−9.35619	−0.303715
$950$	0	0
$951$	17.0106	0.551605
$952$	−22.7881	−0.738565
$953$	56.4371	1.82818	0.914089	−	0.405513i	$-0.132907\pi$
$953$	56.4371	1.82818	0.914089	+	0.405513i	$0.132907\pi$
$954$	0.900094	0.0291416
$955$	0	0
$956$	−9.28118	−0.300175
$957$	−12.7501	−0.412152
$958$	12.5672	0.406029
$959$	21.2325	0.685635
$960$	0	0
$961$	−23.6451	−0.762744
$962$	−1.58309	−0.0510409
$963$	49.8698	1.60703
$964$	−12.1822	−0.392363
$965$	0	0
$966$	−12.4348	−0.400082
$967$	−27.1418	−0.872822	−0.436411	−	0.899748i	$-0.643751\pi$
$967$	−27.1418	−0.872822	−0.436411	+	0.899748i	$0.643751\pi$
$968$	−7.36390	−0.236685
$969$	134.430	4.31850
$970$	0	0
$971$	18.3551	0.589043	0.294521	−	0.955645i	$-0.404840\pi$
$971$	18.3551	0.589043	0.294521	+	0.955645i	$0.404840\pi$
$972$	−2.56986	−0.0824284
$973$	52.4910	1.68278
$974$	−23.0673	−0.739125
$975$	0	0
$976$	11.5850	0.370826
$977$	−30.6656	−0.981081	−0.490540	−	0.871419i	$-0.663201\pi$
$977$	−30.6656	−0.981081	−0.490540	+	0.871419i	$0.663201\pi$
$978$	9.02506	0.288590
$979$	−34.3358	−1.09738
$980$	0	0
$981$	62.1650	1.98477
$982$	1.92280	0.0613589
$983$	−17.0958	−0.545273	−0.272636	−	0.962117i	$-0.587896\pi$
$983$	−17.0958	−0.545273	−0.272636	+	0.962117i	$0.587896\pi$
$984$	−1.84476	−0.0588087
$985$	0	0
$986$	6.37729	0.203094
$987$	82.9878	2.64153
$988$	13.9506	0.443828
$989$	−5.60305	−0.178167
$990$	0	0
$991$	53.7601	1.70774	0.853872	−	0.520483i	$-0.174248\pi$
$991$	53.7601	1.70774	0.853872	+	0.520483i	$0.174248\pi$
$992$	−2.71200	−0.0861060
$993$	71.4103	2.26614
$994$	36.5601	1.15962
$995$	0	0
$996$	−38.2000	−1.21041
$997$	60.5248	1.91684	0.958420	−	0.285360i	$-0.0921132\pi$
$997$	60.5248	1.91684	0.958420	+	0.285360i	$0.0921132\pi$
$998$	−6.17341	−0.195416
$999$	−6.82314	−0.215875

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1450.2.a.t.1.5		5
5.2	odd	4		290.2.b.b.59.1	✓	10
5.3	odd	4		290.2.b.b.59.10	yes	10
5.4	even	2		1450.2.a.u.1.1		5
15.2	even	4		2610.2.e.i.2089.8		10
15.8	even	4		2610.2.e.i.2089.3		10
20.3	even	4		2320.2.d.h.929.1		10
20.7	even	4		2320.2.d.h.929.10		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
290.2.b.b.59.1	✓	10	5.2	odd	4
290.2.b.b.59.10	yes	10	5.3	odd	4
1450.2.a.t.1.5		5	1.1	even	1	trivial
1450.2.a.u.1.1		5	5.4	even	2
2320.2.d.h.929.1		10	20.3	even	4
2320.2.d.h.929.10		10	20.7	even	4
2610.2.e.i.2089.3		10	15.8	even	4
2610.2.e.i.2089.8		10	15.2	even	4

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:	\( N \)	\(=\)	\( 1450 = 2 \cdot 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1450.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.97530 q^{3} +1.00000 q^{4} -2.97530 q^{6} -3.57331 q^{7} -1.00000 q^{8} +5.85241 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.97530 q^{3} +1.00000 q^{4} -2.97530 q^{6} -3.57331 q^{7} -1.00000 q^{8} +5.85241 q^{9} -4.28531 q^{11} +2.97530 q^{12} -1.96909 q^{13} +3.57331 q^{14} +1.00000 q^{16} -6.37729 q^{17} -5.85241 q^{18} -7.08481 q^{19} -10.6317 q^{21} +4.28531 q^{22} -1.16960 q^{23} -2.97530 q^{24} +1.96909 q^{26} +8.48679 q^{27} -3.57331 q^{28} +1.00000 q^{29} +2.71200 q^{31} -1.00000 q^{32} -12.7501 q^{33} +6.37729 q^{34} +5.85241 q^{36} -0.803972 q^{37} +7.08481 q^{38} -5.85863 q^{39} +0.620024 q^{41} +10.6317 q^{42} +4.79059 q^{43} -4.28531 q^{44} +1.16960 q^{46} -7.80571 q^{47} +2.97530 q^{48} +5.76858 q^{49} -18.9743 q^{51} -1.96909 q^{52} -0.153799 q^{53} -8.48679 q^{54} +3.57331 q^{56} -21.0794 q^{57} -1.00000 q^{58} +6.78101 q^{59} +11.5850 q^{61} -2.71200 q^{62} -20.9125 q^{63} +1.00000 q^{64} +12.7501 q^{66} -14.9736 q^{67} -6.37729 q^{68} -3.47990 q^{69} +10.2314 q^{71} -5.85241 q^{72} +4.75154 q^{73} +0.803972 q^{74} -7.08481 q^{76} +15.3128 q^{77} +5.85863 q^{78} -4.83488 q^{79} +7.69351 q^{81} -0.620024 q^{82} -12.8390 q^{83} -10.6317 q^{84} -4.79059 q^{86} +2.97530 q^{87} +4.28531 q^{88} +8.01243 q^{89} +7.03617 q^{91} -1.16960 q^{92} +8.06901 q^{93} +7.80571 q^{94} -2.97530 q^{96} +10.1610 q^{97} -5.76858 q^{98} -25.0794 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 5 q^{2} - 3 q^{3} + 5 q^{4} + 3 q^{6} - 5 q^{7} - 5 q^{8} + 10 q^{9}+O(q^{10}) \) 5 * q - 5 * q^2 - 3 * q^3 + 5 * q^4 + 3 * q^6 - 5 * q^7 - 5 * q^8 + 10 * q^9	\( 5 q - 5 q^{2} - 3 q^{3} + 5 q^{4} + 3 q^{6} - 5 q^{7} - 5 q^{8} + 10 q^{9} - 3 q^{12} - 7 q^{13} + 5 q^{14} + 5 q^{16} - 9 q^{17} - 10 q^{18} - 4 q^{19} - 6 q^{21} - 13 q^{23} + 3 q^{24} + 7 q^{26} + 6 q^{27} - 5 q^{28} + 5 q^{29} + 5 q^{31} - 5 q^{32} - 18 q^{33} + 9 q^{34} + 10 q^{36} + 6 q^{37} + 4 q^{38} + 5 q^{39} - 4 q^{41} + 6 q^{42} - q^{43} + 13 q^{46} - 14 q^{47} - 3 q^{48} + 16 q^{49} - 32 q^{51} - 7 q^{52} - 5 q^{53} - 6 q^{54} + 5 q^{56} - 14 q^{57} - 5 q^{58} - 9 q^{59} + 5 q^{61} - 5 q^{62} - 36 q^{63} + 5 q^{64} + 18 q^{66} - 2 q^{67} - 9 q^{68} + 7 q^{69} - 6 q^{71} - 10 q^{72} - 9 q^{73} - 6 q^{74} - 4 q^{76} + 18 q^{77} - 5 q^{78} - 17 q^{79} - 3 q^{81} + 4 q^{82} - 30 q^{83} - 6 q^{84} + q^{86} - 3 q^{87} + 10 q^{89} - 22 q^{91} - 13 q^{92} + 6 q^{93} + 14 q^{94} + 3 q^{96} + 15 q^{97} - 16 q^{98} - 34 q^{99}+O(q^{100}) \) 5 * q - 5 * q^2 - 3 * q^3 + 5 * q^4 + 3 * q^6 - 5 * q^7 - 5 * q^8 + 10 * q^9 - 3 * q^12 - 7 * q^13 + 5 * q^14 + 5 * q^16 - 9 * q^17 - 10 * q^18 - 4 * q^19 - 6 * q^21 - 13 * q^23 + 3 * q^24 + 7 * q^26 + 6 * q^27 - 5 * q^28 + 5 * q^29 + 5 * q^31 - 5 * q^32 - 18 * q^33 + 9 * q^34 + 10 * q^36 + 6 * q^37 + 4 * q^38 + 5 * q^39 - 4 * q^41 + 6 * q^42 - q^43 + 13 * q^46 - 14 * q^47 - 3 * q^48 + 16 * q^49 - 32 * q^51 - 7 * q^52 - 5 * q^53 - 6 * q^54 + 5 * q^56 - 14 * q^57 - 5 * q^58 - 9 * q^59 + 5 * q^61 - 5 * q^62 - 36 * q^63 + 5 * q^64 + 18 * q^66 - 2 * q^67 - 9 * q^68 + 7 * q^69 - 6 * q^71 - 10 * q^72 - 9 * q^73 - 6 * q^74 - 4 * q^76 + 18 * q^77 - 5 * q^78 - 17 * q^79 - 3 * q^81 + 4 * q^82 - 30 * q^83 - 6 * q^84 + q^86 - 3 * q^87 + 10 * q^89 - 22 * q^91 - 13 * q^92 + 6 * q^93 + 14 * q^94 + 3 * q^96 + 15 * q^97 - 16 * q^98 - 34 * q^99

Introduction

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