LMFDB - Embedded newform 4018.2.a.bp.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4018,2,Mod(1,4018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4018, 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("4018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4018 = 2 \cdot 7^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4018.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:	$32.0838915322$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.5163008.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 5x^{4} + 8x^{3} + 5x^{2} - 6x + 1 $ x^6 - 2x^5 - 5x^4 + 8x^3 + 5x^2 - 6*x + 1
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			1.1
Root			$-1.14577$ of defining polynomial
Character	$\chi$	$=$	4018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -3.30757 q^{3} +1.00000 q^{4} -3.87277 q^{5} -3.30757 q^{6} +1.00000 q^{8} +7.94005 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -3.30757 q^{3} +1.00000 q^{4} -3.87277 q^{5} -3.30757 q^{6} +1.00000 q^{8} +7.94005 q^{9} -3.87277 q^{10} -6.05768 q^{11} -3.30757 q^{12} +2.22470 q^{13} +12.8095 q^{15} +1.00000 q^{16} -4.70041 q^{17} +7.94005 q^{18} +3.59912 q^{19} -3.87277 q^{20} -6.05768 q^{22} +0.533885 q^{23} -3.30757 q^{24} +9.99839 q^{25} +2.22470 q^{26} -16.3396 q^{27} +6.98064 q^{29} +12.8095 q^{30} +9.52470 q^{31} +1.00000 q^{32} +20.0362 q^{33} -4.70041 q^{34} +7.94005 q^{36} -5.92259 q^{37} +3.59912 q^{38} -7.35835 q^{39} -3.87277 q^{40} +1.00000 q^{41} -3.00835 q^{43} -6.05768 q^{44} -30.7500 q^{45} +0.533885 q^{46} +11.6754 q^{47} -3.30757 q^{48} +9.99839 q^{50} +15.5469 q^{51} +2.22470 q^{52} -11.2204 q^{53} -16.3396 q^{54} +23.4600 q^{55} -11.9043 q^{57} +6.98064 q^{58} +6.19036 q^{59} +12.8095 q^{60} -3.60391 q^{61} +9.52470 q^{62} +1.00000 q^{64} -8.61575 q^{65} +20.0362 q^{66} +7.05464 q^{67} -4.70041 q^{68} -1.76586 q^{69} +5.41575 q^{71} +7.94005 q^{72} -5.26340 q^{73} -5.92259 q^{74} -33.0704 q^{75} +3.59912 q^{76} -7.35835 q^{78} +0.401018 q^{79} -3.87277 q^{80} +30.2242 q^{81} +1.00000 q^{82} +4.69112 q^{83} +18.2036 q^{85} -3.00835 q^{86} -23.0890 q^{87} -6.05768 q^{88} -3.68437 q^{89} -30.7500 q^{90} +0.533885 q^{92} -31.5037 q^{93} +11.6754 q^{94} -13.9386 q^{95} -3.30757 q^{96} -8.66450 q^{97} -48.0982 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} - 4 q^{3} + 6 q^{4} - 12 q^{5} - 4 q^{6} + 6 q^{8} + 18 q^{9}+O(q^{10}) $ 6 * q + 6 * q^2 - 4 * q^3 + 6 * q^4 - 12 * q^5 - 4 * q^6 + 6 * q^8 + 18 * q^9	$ 6 q + 6 q^{2} - 4 q^{3} + 6 q^{4} - 12 q^{5} - 4 q^{6} + 6 q^{8} + 18 q^{9} - 12 q^{10} - 4 q^{12} - 8 q^{13} - 4 q^{15} + 6 q^{16} - 16 q^{17} + 18 q^{18} - 12 q^{19} - 12 q^{20} + 12 q^{23} - 4 q^{24} + 14 q^{25} - 8 q^{26} - 28 q^{27} - 4 q^{30} + 4 q^{31} + 6 q^{32} + 20 q^{33} - 16 q^{34} + 18 q^{36} - 24 q^{37} - 12 q^{38} + 4 q^{39} - 12 q^{40} + 6 q^{41} + 4 q^{43} - 28 q^{45} + 12 q^{46} + 16 q^{47} - 4 q^{48} + 14 q^{50} - 16 q^{51} - 8 q^{52} - 16 q^{53} - 28 q^{54} + 12 q^{55} - 28 q^{57} - 16 q^{59} - 4 q^{60} - 32 q^{61} + 4 q^{62} + 6 q^{64} - 4 q^{65} + 20 q^{66} - 20 q^{67} - 16 q^{68} - 56 q^{69} + 12 q^{71} + 18 q^{72} - 16 q^{73} - 24 q^{74} + 4 q^{75} - 12 q^{76} + 4 q^{78} - 12 q^{80} + 42 q^{81} + 6 q^{82} - 32 q^{83} + 48 q^{85} + 4 q^{86} - 20 q^{87} - 8 q^{89} - 28 q^{90} + 12 q^{92} - 12 q^{93} + 16 q^{94} + 28 q^{95} - 4 q^{96} - 8 q^{97} - 76 q^{99}+O(q^{100}) $ 6 * q + 6 * q^2 - 4 * q^3 + 6 * q^4 - 12 * q^5 - 4 * q^6 + 6 * q^8 + 18 * q^9 - 12 * q^10 - 4 * q^12 - 8 * q^13 - 4 * q^15 + 6 * q^16 - 16 * q^17 + 18 * q^18 - 12 * q^19 - 12 * q^20 + 12 * q^23 - 4 * q^24 + 14 * q^25 - 8 * q^26 - 28 * q^27 - 4 * q^30 + 4 * q^31 + 6 * q^32 + 20 * q^33 - 16 * q^34 + 18 * q^36 - 24 * q^37 - 12 * q^38 + 4 * q^39 - 12 * q^40 + 6 * q^41 + 4 * q^43 - 28 * q^45 + 12 * q^46 + 16 * q^47 - 4 * q^48 + 14 * q^50 - 16 * q^51 - 8 * q^52 - 16 * q^53 - 28 * q^54 + 12 * q^55 - 28 * q^57 - 16 * q^59 - 4 * q^60 - 32 * q^61 + 4 * q^62 + 6 * q^64 - 4 * q^65 + 20 * q^66 - 20 * q^67 - 16 * q^68 - 56 * q^69 + 12 * q^71 + 18 * q^72 - 16 * q^73 - 24 * q^74 + 4 * q^75 - 12 * q^76 + 4 * q^78 - 12 * q^80 + 42 * q^81 + 6 * q^82 - 32 * q^83 + 48 * q^85 + 4 * q^86 - 20 * q^87 - 8 * q^89 - 28 * q^90 + 12 * q^92 - 12 * q^93 + 16 * q^94 + 28 * q^95 - 4 * q^96 - 8 * q^97 - 76 * 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
$3$	−3.30757	−1.90963	−0.954814	−	0.297203i	$-0.903946\pi$
$3$	−3.30757	−1.90963	−0.954814	+	0.297203i	$0.903946\pi$
$4$	1.00000	0.500000
$5$	−3.87277	−1.73196	−0.865979	−	0.500081i	$-0.833304\pi$
$5$	−3.87277	−1.73196	−0.865979	+	0.500081i	$0.833304\pi$
$6$	−3.30757	−1.35031
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	7.94005	2.64668
$10$	−3.87277	−1.22468
$11$	−6.05768	−1.82646	−0.913229	−	0.407446i	$-0.866419\pi$
$11$	−6.05768	−1.82646	−0.913229	+	0.407446i	$0.866419\pi$
$12$	−3.30757	−0.954814
$13$	2.22470	0.617020	0.308510	−	0.951221i	$-0.400170\pi$
$13$	2.22470	0.617020	0.308510	+	0.951221i	$0.400170\pi$
$14$	0	0
$15$	12.8095	3.30740
$16$	1.00000	0.250000
$17$	−4.70041	−1.14002	−0.570008	−	0.821639i	$-0.693060\pi$
$17$	−4.70041	−1.14002	−0.570008	+	0.821639i	$0.693060\pi$
$18$	7.94005	1.87149
$19$	3.59912	0.825694	0.412847	−	0.910800i	$-0.364534\pi$
$19$	3.59912	0.825694	0.412847	+	0.910800i	$0.364534\pi$
$20$	−3.87277	−0.865979
$21$	0	0
$22$	−6.05768	−1.29150
$23$	0.533885	0.111323	0.0556613	−	0.998450i	$-0.482273\pi$
$23$	0.533885	0.111323	0.0556613	+	0.998450i	$0.482273\pi$
$24$	−3.30757	−0.675156
$25$	9.99839	1.99968
$26$	2.22470	0.436299
$27$	−16.3396	−3.14455
$28$	0	0
$29$	6.98064	1.29627	0.648136	−	0.761525i	$-0.275549\pi$
$29$	6.98064	1.29627	0.648136	+	0.761525i	$0.275549\pi$
$30$	12.8095	2.33868
$31$	9.52470	1.71069	0.855344	−	0.518061i	$-0.173346\pi$
$31$	9.52470	1.71069	0.855344	+	0.518061i	$0.173346\pi$
$32$	1.00000	0.176777
$33$	20.0362	3.48786
$34$	−4.70041	−0.806113
$35$	0	0
$36$	7.94005	1.32334
$37$	−5.92259	−0.973668	−0.486834	−	0.873495i	$-0.661848\pi$
$37$	−5.92259	−0.973668	−0.486834	+	0.873495i	$0.661848\pi$
$38$	3.59912	0.583854
$39$	−7.35835	−1.17828
$40$	−3.87277	−0.612339
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	−3.00835	−0.458769	−0.229385	−	0.973336i	$-0.573671\pi$
$43$	−3.00835	−0.458769	−0.229385	+	0.973336i	$0.573671\pi$
$44$	−6.05768	−0.913229
$45$	−30.7500	−4.58394
$46$	0.533885	0.0787170
$47$	11.6754	1.70303	0.851516	−	0.524329i	$-0.175684\pi$
$47$	11.6754	1.70303	0.851516	+	0.524329i	$0.175684\pi$
$48$	−3.30757	−0.477407
$49$	0	0
$50$	9.99839	1.41399
$51$	15.5469	2.17701
$52$	2.22470	0.308510
$53$	−11.2204	−1.54124	−0.770620	−	0.637295i	$-0.780053\pi$
$53$	−11.2204	−1.54124	−0.770620	+	0.637295i	$0.780053\pi$
$54$	−16.3396	−2.22353
$55$	23.4600	3.16335
$56$	0	0
$57$	−11.9043	−1.57677
$58$	6.98064	0.916603
$59$	6.19036	0.805916	0.402958	−	0.915219i	$-0.367982\pi$
$59$	6.19036	0.805916	0.402958	+	0.915219i	$0.367982\pi$
$60$	12.8095	1.65370
$61$	−3.60391	−0.461433	−0.230716	−	0.973021i	$-0.574107\pi$
$61$	−3.60391	−0.461433	−0.230716	+	0.973021i	$0.574107\pi$
$62$	9.52470	1.20964
$63$	0	0
$64$	1.00000	0.125000
$65$	−8.61575	−1.06865
$66$	20.0362	2.46629
$67$	7.05464	0.861861	0.430931	−	0.902385i	$-0.358185\pi$
$67$	7.05464	0.861861	0.430931	+	0.902385i	$0.358185\pi$
$68$	−4.70041	−0.570008
$69$	−1.76586	−0.212585
$70$	0	0
$71$	5.41575	0.642732	0.321366	−	0.946955i	$-0.395858\pi$
$71$	5.41575	0.642732	0.321366	+	0.946955i	$0.395858\pi$
$72$	7.94005	0.935743
$73$	−5.26340	−0.616035	−0.308017	−	0.951381i	$-0.599665\pi$
$73$	−5.26340	−0.616035	−0.308017	+	0.951381i	$0.599665\pi$
$74$	−5.92259	−0.688487
$75$	−33.0704	−3.81864
$76$	3.59912	0.412847
$77$	0	0
$78$	−7.35835	−0.833169
$79$	0.401018	0.0451180	0.0225590	−	0.999746i	$-0.492819\pi$
$79$	0.401018	0.0451180	0.0225590	+	0.999746i	$0.492819\pi$
$80$	−3.87277	−0.432989
$81$	30.2242	3.35824
$82$	1.00000	0.110432
$83$	4.69112	0.514917	0.257459	−	0.966289i	$-0.417115\pi$
$83$	4.69112	0.514917	0.257459	+	0.966289i	$0.417115\pi$
$84$	0	0
$85$	18.2036	1.97446
$86$	−3.00835	−0.324399
$87$	−23.0890	−2.47540
$88$	−6.05768	−0.645751
$89$	−3.68437	−0.390543	−0.195271	−	0.980749i	$-0.562559\pi$
$89$	−3.68437	−0.390543	−0.195271	+	0.980749i	$0.562559\pi$
$90$	−30.7500	−3.24134
$91$	0	0
$92$	0.533885	0.0556613
$93$	−31.5037	−3.26678
$94$	11.6754	1.20423
$95$	−13.9386	−1.43007
$96$	−3.30757	−0.337578
$97$	−8.66450	−0.879747	−0.439873	−	0.898060i	$-0.644977\pi$
$97$	−8.66450	−0.879747	−0.439873	+	0.898060i	$0.644977\pi$
$98$	0	0
$99$	−48.0982	−4.83405
$100$	9.99839	0.999839
$101$	−6.03142	−0.600149	−0.300075	−	0.953916i	$-0.597012\pi$
$101$	−6.03142	−0.600149	−0.300075	+	0.953916i	$0.597012\pi$
$102$	15.5469	1.53938
$103$	−8.47928	−0.835488	−0.417744	−	0.908565i	$-0.637179\pi$
$103$	−8.47928	−0.835488	−0.417744	+	0.908565i	$0.637179\pi$
$104$	2.22470	0.218149
$105$	0	0
$106$	−11.2204	−1.08982
$107$	3.56345	0.344492	0.172246	−	0.985054i	$-0.444898\pi$
$107$	3.56345	0.344492	0.172246	+	0.985054i	$0.444898\pi$
$108$	−16.3396	−1.57228
$109$	−4.11954	−0.394581	−0.197290	−	0.980345i	$-0.563214\pi$
$109$	−4.11954	−0.394581	−0.197290	+	0.980345i	$0.563214\pi$
$110$	23.4600	2.23683
$111$	19.5894	1.85934
$112$	0	0
$113$	−1.96493	−0.184845	−0.0924227	−	0.995720i	$-0.529461\pi$
$113$	−1.96493	−0.184845	−0.0924227	+	0.995720i	$0.529461\pi$
$114$	−11.9043	−1.11494
$115$	−2.06762	−0.192806
$116$	6.98064	0.648136
$117$	17.6642	1.63306
$118$	6.19036	0.569868
$119$	0	0
$120$	12.8095	1.16934
$121$	25.6954	2.33595
$122$	−3.60391	−0.326282
$123$	−3.30757	−0.298234
$124$	9.52470	0.855344
$125$	−19.3576	−1.73140
$126$	0	0
$127$	0.907246	0.0805050	0.0402525	−	0.999190i	$-0.487184\pi$
$127$	0.907246	0.0805050	0.0402525	+	0.999190i	$0.487184\pi$
$128$	1.00000	0.0883883
$129$	9.95034	0.876079
$130$	−8.61575	−0.755651
$131$	9.23740	0.807075	0.403538	−	0.914963i	$-0.367780\pi$
$131$	9.23740	0.807075	0.403538	+	0.914963i	$0.367780\pi$
$132$	20.0362	1.74393
$133$	0	0
$134$	7.05464	0.609428
$135$	63.2795	5.44623
$136$	−4.70041	−0.403056
$137$	−2.35366	−0.201086	−0.100543	−	0.994933i	$-0.532058\pi$
$137$	−2.35366	−0.201086	−0.100543	+	0.994933i	$0.532058\pi$
$138$	−1.76586	−0.150320
$139$	−0.333978	−0.0283276	−0.0141638	−	0.999900i	$-0.504509\pi$
$139$	−0.333978	−0.0283276	−0.0141638	+	0.999900i	$0.504509\pi$
$140$	0	0
$141$	−38.6172	−3.25216
$142$	5.41575	0.454480
$143$	−13.4765	−1.12696
$144$	7.94005	0.661670
$145$	−27.0344	−2.24509
$146$	−5.26340	−0.435602
$147$	0	0
$148$	−5.92259	−0.486834
$149$	−7.44236	−0.609702	−0.304851	−	0.952400i	$-0.598607\pi$
$149$	−7.44236	−0.609702	−0.304851	+	0.952400i	$0.598607\pi$
$150$	−33.0704	−2.70019
$151$	−7.22502	−0.587964	−0.293982	−	0.955811i	$-0.594981\pi$
$151$	−7.22502	−0.587964	−0.293982	+	0.955811i	$0.594981\pi$
$152$	3.59912	0.291927
$153$	−37.3214	−3.01726
$154$	0	0
$155$	−36.8870	−2.96284
$156$	−7.35835	−0.589139
$157$	12.8953	1.02916	0.514580	−	0.857442i	$-0.327948\pi$
$157$	12.8953	1.02916	0.514580	+	0.857442i	$0.327948\pi$
$158$	0.401018	0.0319033
$159$	37.1123	2.94320
$160$	−3.87277	−0.306170
$161$	0	0
$162$	30.2242	2.37464
$163$	6.83948	0.535709	0.267855	−	0.963459i	$-0.413685\pi$
$163$	6.83948	0.535709	0.267855	+	0.963459i	$0.413685\pi$
$164$	1.00000	0.0780869
$165$	−77.5957	−6.04082
$166$	4.69112	0.364102
$167$	−14.3011	−1.10665	−0.553327	−	0.832964i	$-0.686642\pi$
$167$	−14.3011	−1.10665	−0.553327	+	0.832964i	$0.686642\pi$
$168$	0	0
$169$	−8.05072	−0.619287
$170$	18.2036	1.39615
$171$	28.5771	2.18535
$172$	−3.00835	−0.229385
$173$	−24.8199	−1.88702	−0.943510	−	0.331344i	$-0.892498\pi$
$173$	−24.8199	−1.88702	−0.943510	+	0.331344i	$0.892498\pi$
$174$	−23.0890	−1.75037
$175$	0	0
$176$	−6.05768	−0.456615
$177$	−20.4751	−1.53900
$178$	−3.68437	−0.276155
$179$	−24.3788	−1.82216	−0.911078	−	0.412234i	$-0.864748\pi$
$179$	−24.3788	−1.82216	−0.911078	+	0.412234i	$0.864748\pi$
$180$	−30.7500	−2.29197
$181$	−0.0528641	−0.00392936	−0.00196468	−	0.999998i	$-0.500625\pi$
$181$	−0.0528641	−0.00392936	−0.00196468	+	0.999998i	$0.500625\pi$
$182$	0	0
$183$	11.9202	0.881166
$184$	0.533885	0.0393585
$185$	22.9369	1.68635
$186$	−31.5037	−2.30996
$187$	28.4735	2.08219
$188$	11.6754	0.851516
$189$	0	0
$190$	−13.9386	−1.01121
$191$	−2.87401	−0.207956	−0.103978	−	0.994580i	$-0.533157\pi$
$191$	−2.87401	−0.207956	−0.103978	+	0.994580i	$0.533157\pi$
$192$	−3.30757	−0.238704
$193$	−7.09383	−0.510625	−0.255312	−	0.966859i	$-0.582178\pi$
$193$	−7.09383	−0.510625	−0.255312	+	0.966859i	$0.582178\pi$
$194$	−8.66450	−0.622075
$195$	28.4972	2.04073
$196$	0	0
$197$	1.52134	0.108391	0.0541954	−	0.998530i	$-0.482741\pi$
$197$	1.52134	0.108391	0.0541954	+	0.998530i	$0.482741\pi$
$198$	−48.0982	−3.41819
$199$	4.90768	0.347896	0.173948	−	0.984755i	$-0.444347\pi$
$199$	4.90768	0.347896	0.173948	+	0.984755i	$0.444347\pi$
$200$	9.99839	0.706993
$201$	−23.3337	−1.64583
$202$	−6.03142	−0.424369
$203$	0	0
$204$	15.5469	1.08850
$205$	−3.87277	−0.270486
$206$	−8.47928	−0.590779
$207$	4.23907	0.294636
$208$	2.22470	0.154255
$209$	−21.8023	−1.50810
$210$	0	0
$211$	9.33390	0.642572	0.321286	−	0.946982i	$-0.395885\pi$
$211$	9.33390	0.642572	0.321286	+	0.946982i	$0.395885\pi$
$212$	−11.2204	−0.770620
$213$	−17.9130	−1.22738
$214$	3.56345	0.243592
$215$	11.6507	0.794569
$216$	−16.3396	−1.11177
$217$	0	0
$218$	−4.11954	−0.279011
$219$	17.4091	1.17640
$220$	23.4600	1.58167
$221$	−10.4570	−0.703412
$222$	19.5894	1.31475
$223$	6.43192	0.430713	0.215357	−	0.976535i	$-0.430909\pi$
$223$	6.43192	0.430713	0.215357	+	0.976535i	$0.430909\pi$
$224$	0	0
$225$	79.3876	5.29251
$226$	−1.96493	−0.130705
$227$	−22.9617	−1.52402	−0.762011	−	0.647564i	$-0.775788\pi$
$227$	−22.9617	−1.52402	−0.762011	+	0.647564i	$0.775788\pi$
$228$	−11.9043	−0.788384
$229$	−8.12017	−0.536596	−0.268298	−	0.963336i	$-0.586461\pi$
$229$	−8.12017	−0.536596	−0.268298	+	0.963336i	$0.586461\pi$
$230$	−2.06762	−0.136335
$231$	0	0
$232$	6.98064	0.458301
$233$	−10.4623	−0.685406	−0.342703	−	0.939444i	$-0.611342\pi$
$233$	−10.4623	−0.685406	−0.342703	+	0.939444i	$0.611342\pi$
$234$	17.6642	1.15474
$235$	−45.2162	−2.94958
$236$	6.19036	0.402958
$237$	−1.32640	−0.0861586
$238$	0	0
$239$	−15.5581	−1.00637	−0.503184	−	0.864180i	$-0.667838\pi$
$239$	−15.5581	−1.00637	−0.503184	+	0.864180i	$0.667838\pi$
$240$	12.8095	0.826849
$241$	−2.30003	−0.148158	−0.0740789	−	0.997252i	$-0.523602\pi$
$241$	−2.30003	−0.148158	−0.0740789	+	0.997252i	$0.523602\pi$
$242$	25.6954	1.65177
$243$	−50.9500	−3.26845
$244$	−3.60391	−0.230716
$245$	0	0
$246$	−3.30757	−0.210883
$247$	8.00694	0.509469
$248$	9.52470	0.604819
$249$	−15.5162	−0.983301
$250$	−19.3576	−1.22428
$251$	−21.2686	−1.34246	−0.671231	−	0.741248i	$-0.734234\pi$
$251$	−21.2686	−1.34246	−0.671231	+	0.741248i	$0.734234\pi$
$252$	0	0
$253$	−3.23410	−0.203326
$254$	0.907246	0.0569257
$255$	−60.2098	−3.77048
$256$	1.00000	0.0625000
$257$	16.4453	1.02583	0.512916	−	0.858439i	$-0.328565\pi$
$257$	16.4453	1.02583	0.512916	+	0.858439i	$0.328565\pi$
$258$	9.95034	0.619481
$259$	0	0
$260$	−8.61575	−0.534326
$261$	55.4266	3.43082
$262$	9.23740	0.570688
$263$	−2.06940	−0.127604	−0.0638022	−	0.997963i	$-0.520323\pi$
$263$	−2.06940	−0.127604	−0.0638022	+	0.997963i	$0.520323\pi$
$264$	20.0362	1.23314
$265$	43.4541	2.66936
$266$	0	0
$267$	12.1863	0.745792
$268$	7.05464	0.430931
$269$	10.1884	0.621197	0.310599	−	0.950541i	$-0.399470\pi$
$269$	10.1884	0.621197	0.310599	+	0.950541i	$0.399470\pi$
$270$	63.2795	3.85107
$271$	−18.1252	−1.10103	−0.550513	−	0.834827i	$-0.685568\pi$
$271$	−18.1252	−1.10103	−0.550513	+	0.834827i	$0.685568\pi$
$272$	−4.70041	−0.285004
$273$	0	0
$274$	−2.35366	−0.142190
$275$	−60.5670	−3.65233
$276$	−1.76586	−0.106293
$277$	25.6514	1.54124	0.770622	−	0.637293i	$-0.219946\pi$
$277$	25.6514	1.54124	0.770622	+	0.637293i	$0.219946\pi$
$278$	−0.333978	−0.0200307
$279$	75.6266	4.52765
$280$	0	0
$281$	9.98688	0.595767	0.297884	−	0.954602i	$-0.403719\pi$
$281$	9.98688	0.595767	0.297884	+	0.954602i	$0.403719\pi$
$282$	−38.6172	−2.29962
$283$	10.8783	0.646647	0.323324	−	0.946288i	$-0.395200\pi$
$283$	10.8783	0.646647	0.323324	+	0.946288i	$0.395200\pi$
$284$	5.41575	0.321366
$285$	46.1028	2.73090
$286$	−13.4765	−0.796882
$287$	0	0
$288$	7.94005	0.467872
$289$	5.09381	0.299636
$290$	−27.0344	−1.58752
$291$	28.6585	1.67999
$292$	−5.26340	−0.308017
$293$	−22.7063	−1.32652	−0.663259	−	0.748390i	$-0.730827\pi$
$293$	−22.7063	−1.32652	−0.663259	+	0.748390i	$0.730827\pi$
$294$	0	0
$295$	−23.9739	−1.39581
$296$	−5.92259	−0.344243
$297$	98.9798	5.74339
$298$	−7.44236	−0.431125
$299$	1.18773	0.0686883
$300$	−33.0704	−1.90932
$301$	0	0
$302$	−7.22502	−0.415753
$303$	19.9494	1.14606
$304$	3.59912	0.206423
$305$	13.9571	0.799182
$306$	−37.3214	−2.13352
$307$	16.2095	0.925123	0.462562	−	0.886587i	$-0.346930\pi$
$307$	16.2095	0.925123	0.462562	+	0.886587i	$0.346930\pi$
$308$	0	0
$309$	28.0458	1.59547
$310$	−36.8870	−2.09504
$311$	2.08493	0.118225	0.0591127	−	0.998251i	$-0.481173\pi$
$311$	2.08493	0.118225	0.0591127	+	0.998251i	$0.481173\pi$
$312$	−7.35835	−0.416584
$313$	−26.8869	−1.51974	−0.759868	−	0.650078i	$-0.774736\pi$
$313$	−26.8869	−1.51974	−0.759868	+	0.650078i	$0.774736\pi$
$314$	12.8953	0.727727
$315$	0	0
$316$	0.401018	0.0225590
$317$	−17.2868	−0.970922	−0.485461	−	0.874258i	$-0.661348\pi$
$317$	−17.2868	−0.970922	−0.485461	+	0.874258i	$0.661348\pi$
$318$	37.1123	2.08115
$319$	−42.2864	−2.36759
$320$	−3.87277	−0.216495
$321$	−11.7864	−0.657851
$322$	0	0
$323$	−16.9173	−0.941304
$324$	30.2242	1.67912
$325$	22.2434	1.23384
$326$	6.83948	0.378804
$327$	13.6257	0.753503
$328$	1.00000	0.0552158
$329$	0	0
$330$	−77.5957	−4.27151
$331$	2.88391	0.158514	0.0792570	−	0.996854i	$-0.474745\pi$
$331$	2.88391	0.158514	0.0792570	+	0.996854i	$0.474745\pi$
$332$	4.69112	0.257459
$333$	−47.0256	−2.57699
$334$	−14.3011	−0.782522
$335$	−27.3210	−1.49271
$336$	0	0
$337$	10.9701	0.597581	0.298790	−	0.954319i	$-0.403417\pi$
$337$	10.9701	0.597581	0.298790	+	0.954319i	$0.403417\pi$
$338$	−8.05072	−0.437902
$339$	6.49917	0.352986
$340$	18.2036	0.987229
$341$	−57.6976	−3.12450
$342$	28.5771	1.54527
$343$	0	0
$344$	−3.00835	−0.162199
$345$	6.83879	0.368188
$346$	−24.8199	−1.33432
$347$	−1.96054	−0.105247	−0.0526235	−	0.998614i	$-0.516758\pi$
$347$	−1.96054	−0.105247	−0.0526235	+	0.998614i	$0.516758\pi$
$348$	−23.0890	−1.23770
$349$	−18.2795	−0.978481	−0.489241	−	0.872149i	$-0.662726\pi$
$349$	−18.2795	−0.978481	−0.489241	+	0.872149i	$0.662726\pi$
$350$	0	0
$351$	−36.3506	−1.94025
$352$	−6.05768	−0.322875
$353$	23.2747	1.23879	0.619394	−	0.785080i	$-0.287378\pi$
$353$	23.2747	1.23879	0.619394	+	0.785080i	$0.287378\pi$
$354$	−20.4751	−1.08824
$355$	−20.9740	−1.11318
$356$	−3.68437	−0.195271
$357$	0	0
$358$	−24.3788	−1.28846
$359$	12.5000	0.659723	0.329862	−	0.944029i	$-0.392998\pi$
$359$	12.5000	0.659723	0.329862	+	0.944029i	$0.392998\pi$
$360$	−30.7500	−1.62067
$361$	−6.04637	−0.318230
$362$	−0.0528641	−0.00277848
$363$	−84.9896	−4.46080
$364$	0	0
$365$	20.3840	1.06695
$366$	11.9202	0.623078
$367$	8.45799	0.441503	0.220752	−	0.975330i	$-0.429149\pi$
$367$	8.45799	0.441503	0.220752	+	0.975330i	$0.429149\pi$
$368$	0.533885	0.0278307
$369$	7.94005	0.413342
$370$	22.9369	1.19243
$371$	0	0
$372$	−31.5037	−1.63339
$373$	17.2826	0.894858	0.447429	−	0.894319i	$-0.352340\pi$
$373$	17.2826	0.894858	0.447429	+	0.894319i	$0.352340\pi$
$374$	28.4735	1.47233
$375$	64.0268	3.30633
$376$	11.6754	0.602113
$377$	15.5298	0.799825
$378$	0	0
$379$	29.5973	1.52031	0.760157	−	0.649740i	$-0.225122\pi$
$379$	29.5973	1.52031	0.760157	+	0.649740i	$0.225122\pi$
$380$	−13.9386	−0.715033
$381$	−3.00078	−0.153735
$382$	−2.87401	−0.147047
$383$	−18.2590	−0.932990	−0.466495	−	0.884524i	$-0.654483\pi$
$383$	−18.2590	−0.932990	−0.466495	+	0.884524i	$0.654483\pi$
$384$	−3.30757	−0.168789
$385$	0	0
$386$	−7.09383	−0.361066
$387$	−23.8864	−1.21422
$388$	−8.66450	−0.439873
$389$	22.9438	1.16329	0.581647	−	0.813441i	$-0.302408\pi$
$389$	22.9438	1.16329	0.581647	+	0.813441i	$0.302408\pi$
$390$	28.4972	1.44301
$391$	−2.50948	−0.126910
$392$	0	0
$393$	−30.5534	−1.54121
$394$	1.52134	0.0766439
$395$	−1.55305	−0.0781425
$396$	−48.0982	−2.41703
$397$	3.04357	0.152753	0.0763763	−	0.997079i	$-0.475665\pi$
$397$	3.04357	0.152753	0.0763763	+	0.997079i	$0.475665\pi$
$398$	4.90768	0.246000
$399$	0	0
$400$	9.99839	0.499919
$401$	20.0372	1.00061	0.500304	−	0.865850i	$-0.333221\pi$
$401$	20.0372	1.00061	0.500304	+	0.865850i	$0.333221\pi$
$402$	−23.3337	−1.16378
$403$	21.1896	1.05553
$404$	−6.03142	−0.300075
$405$	−117.051	−5.81633
$406$	0	0
$407$	35.8771	1.77836
$408$	15.5469	0.769688
$409$	−27.9562	−1.38235	−0.691173	−	0.722689i	$-0.742906\pi$
$409$	−27.9562	−1.38235	−0.691173	+	0.722689i	$0.742906\pi$
$410$	−3.87277	−0.191263
$411$	7.78489	0.384001
$412$	−8.47928	−0.417744
$413$	0	0
$414$	4.23907	0.208339
$415$	−18.1677	−0.891815
$416$	2.22470	0.109075
$417$	1.10466	0.0540952
$418$	−21.8023	−1.06638
$419$	37.3753	1.82590	0.912950	−	0.408071i	$-0.133798\pi$
$419$	37.3753	1.82590	0.912950	+	0.408071i	$0.133798\pi$
$420$	0	0
$421$	−8.99134	−0.438211	−0.219105	−	0.975701i	$-0.570314\pi$
$421$	−8.99134	−0.438211	−0.219105	+	0.975701i	$0.570314\pi$
$422$	9.33390	0.454367
$423$	92.7032	4.50738
$424$	−11.2204	−0.544910
$425$	−46.9965	−2.27966
$426$	−17.9130	−0.867888
$427$	0	0
$428$	3.56345	0.172246
$429$	44.5745	2.15208
$430$	11.6507	0.561845
$431$	0.851001	0.0409913	0.0204956	−	0.999790i	$-0.493476\pi$
$431$	0.851001	0.0409913	0.0204956	+	0.999790i	$0.493476\pi$
$432$	−16.3396	−0.786138
$433$	33.1658	1.59385	0.796923	−	0.604080i	$-0.206459\pi$
$433$	33.1658	1.59385	0.796923	+	0.604080i	$0.206459\pi$
$434$	0	0
$435$	89.4184	4.28728
$436$	−4.11954	−0.197290
$437$	1.92151	0.0919184
$438$	17.4091	0.831839
$439$	25.0468	1.19542	0.597710	−	0.801713i	$-0.296077\pi$
$439$	25.0468	1.19542	0.597710	+	0.801713i	$0.296077\pi$
$440$	23.4600	1.11841
$441$	0	0
$442$	−10.4570	−0.497388
$443$	1.65140	0.0784604	0.0392302	−	0.999230i	$-0.487509\pi$
$443$	1.65140	0.0784604	0.0392302	+	0.999230i	$0.487509\pi$
$444$	19.5894	0.929672
$445$	14.2687	0.676403
$446$	6.43192	0.304560
$447$	24.6162	1.16430
$448$	0	0
$449$	−17.7590	−0.838098	−0.419049	−	0.907964i	$-0.637636\pi$
$449$	−17.7590	−0.838098	−0.419049	+	0.907964i	$0.637636\pi$
$450$	79.3876	3.74237
$451$	−6.05768	−0.285245
$452$	−1.96493	−0.0924227
$453$	23.8973	1.12279
$454$	−22.9617	−1.07765
$455$	0	0
$456$	−11.9043	−0.557472
$457$	26.8026	1.25377	0.626886	−	0.779111i	$-0.284329\pi$
$457$	26.8026	1.25377	0.626886	+	0.779111i	$0.284329\pi$
$458$	−8.12017	−0.379431
$459$	76.8026	3.58484
$460$	−2.06762	−0.0964031
$461$	22.1793	1.03299	0.516496	−	0.856290i	$-0.327236\pi$
$461$	22.1793	1.03299	0.516496	+	0.856290i	$0.327236\pi$
$462$	0	0
$463$	−31.4496	−1.46159	−0.730794	−	0.682598i	$-0.760850\pi$
$463$	−31.4496	−1.46159	−0.730794	+	0.682598i	$0.760850\pi$
$464$	6.98064	0.324068
$465$	122.007	5.65792
$466$	−10.4623	−0.484655
$467$	−14.3411	−0.663628	−0.331814	−	0.943345i	$-0.607661\pi$
$467$	−14.3411	−0.663628	−0.331814	+	0.943345i	$0.607661\pi$
$468$	17.6642	0.816528
$469$	0	0
$470$	−45.2162	−2.08567
$471$	−42.6523	−1.96532
$472$	6.19036	0.284934
$473$	18.2236	0.837923
$474$	−1.32640	−0.0609234
$475$	35.9853	1.65112
$476$	0	0
$477$	−89.0904	−4.07917
$478$	−15.5581	−0.711609
$479$	−12.2351	−0.559037	−0.279518	−	0.960140i	$-0.590175\pi$
$479$	−12.2351	−0.559037	−0.279518	+	0.960140i	$0.590175\pi$
$480$	12.8095	0.584671
$481$	−13.1760	−0.600772
$482$	−2.30003	−0.104763
$483$	0	0
$484$	25.6954	1.16797
$485$	33.5557	1.52368
$486$	−50.9500	−2.31114
$487$	5.21478	0.236304	0.118152	−	0.992996i	$-0.462303\pi$
$487$	5.21478	0.236304	0.118152	+	0.992996i	$0.462303\pi$
$488$	−3.60391	−0.163141
$489$	−22.6221	−1.02301
$490$	0	0
$491$	8.94577	0.403717	0.201858	−	0.979415i	$-0.435302\pi$
$491$	8.94577	0.403717	0.201858	+	0.979415i	$0.435302\pi$
$492$	−3.30757	−0.149117
$493$	−32.8118	−1.47777
$494$	8.00694	0.360249
$495$	186.274	8.37238
$496$	9.52470	0.427672
$497$	0	0
$498$	−15.5162	−0.695299
$499$	14.3264	0.641337	0.320669	−	0.947191i	$-0.396092\pi$
$499$	14.3264	0.641337	0.320669	+	0.947191i	$0.396092\pi$
$500$	−19.3576	−0.865699
$501$	47.3020	2.11330
$502$	−21.2686	−0.949264
$503$	41.7063	1.85959	0.929795	−	0.368077i	$-0.119984\pi$
$503$	41.7063	1.85959	0.929795	+	0.368077i	$0.119984\pi$
$504$	0	0
$505$	23.3583	1.03943
$506$	−3.23410	−0.143773
$507$	26.6284	1.18261
$508$	0.907246	0.0402525
$509$	6.39637	0.283514	0.141757	−	0.989901i	$-0.454725\pi$
$509$	6.39637	0.283514	0.141757	+	0.989901i	$0.454725\pi$
$510$	−60.2098	−2.66613
$511$	0	0
$512$	1.00000	0.0441942
$513$	−58.8080	−2.59644
$514$	16.4453	0.725373
$515$	32.8383	1.44703
$516$	9.95034	0.438039
$517$	−70.7258	−3.11052
$518$	0	0
$519$	82.0936	3.60351
$520$	−8.61575	−0.377826
$521$	11.9458	0.523353	0.261677	−	0.965156i	$-0.415725\pi$
$521$	11.9458	0.523353	0.261677	+	0.965156i	$0.415725\pi$
$522$	55.4266	2.42596
$523$	−24.1939	−1.05792	−0.528962	−	0.848645i	$-0.677419\pi$
$523$	−24.1939	−1.05792	−0.528962	+	0.848645i	$0.677419\pi$
$524$	9.23740	0.403538
$525$	0	0
$526$	−2.06940	−0.0902299
$527$	−44.7700	−1.95021
$528$	20.0362	0.871964
$529$	−22.7150	−0.987607
$530$	43.4541	1.88752
$531$	49.1517	2.13300
$532$	0	0
$533$	2.22470	0.0963623
$534$	12.1863	0.527354
$535$	−13.8004	−0.596645
$536$	7.05464	0.304714
$537$	80.6346	3.47964
$538$	10.1884	0.439253
$539$	0	0
$540$	63.2795	2.72311
$541$	−42.3740	−1.82180	−0.910901	−	0.412624i	$-0.864612\pi$
$541$	−42.3740	−1.82180	−0.910901	+	0.412624i	$0.864612\pi$
$542$	−18.1252	−0.778543
$543$	0.174852	0.00750362
$544$	−4.70041	−0.201528
$545$	15.9541	0.683397
$546$	0	0
$547$	−19.5275	−0.834935	−0.417467	−	0.908692i	$-0.637082\pi$
$547$	−19.5275	−0.834935	−0.417467	+	0.908692i	$0.637082\pi$
$548$	−2.35366	−0.100543
$549$	−28.6152	−1.22127
$550$	−60.5670	−2.58259
$551$	25.1241	1.07032
$552$	−1.76586	−0.0751601
$553$	0	0
$554$	25.6514	1.08982
$555$	−75.8653	−3.22030
$556$	−0.333978	−0.0141638
$557$	−13.3280	−0.564724	−0.282362	−	0.959308i	$-0.591118\pi$
$557$	−13.3280	−0.564724	−0.282362	+	0.959308i	$0.591118\pi$
$558$	75.6266	3.20153
$559$	−6.69267	−0.283070
$560$	0	0
$561$	−94.1783	−3.97621
$562$	9.98688	0.421271
$563$	−17.1983	−0.724822	−0.362411	−	0.932018i	$-0.618046\pi$
$563$	−17.1983	−0.724822	−0.362411	+	0.932018i	$0.618046\pi$
$564$	−38.6172	−1.62608
$565$	7.60975	0.320145
$566$	10.8783	0.457249
$567$	0	0
$568$	5.41575	0.227240
$569$	−8.77605	−0.367911	−0.183956	−	0.982935i	$-0.558890\pi$
$569$	−8.77605	−0.367911	−0.183956	+	0.982935i	$0.558890\pi$
$570$	46.1028	1.93104
$571$	38.2957	1.60262	0.801312	−	0.598247i	$-0.204136\pi$
$571$	38.2957	1.60262	0.801312	+	0.598247i	$0.204136\pi$
$572$	−13.4765	−0.563480
$573$	9.50599	0.397118
$574$	0	0
$575$	5.33799	0.222609
$576$	7.94005	0.330835
$577$	44.6215	1.85762	0.928808	−	0.370561i	$-0.120835\pi$
$577$	44.6215	1.85762	0.928808	+	0.370561i	$0.120835\pi$
$578$	5.09381	0.211875
$579$	23.4634	0.975104
$580$	−27.0344	−1.12254
$581$	0	0
$582$	28.6585	1.18793
$583$	67.9695	2.81501
$584$	−5.26340	−0.217801
$585$	−68.4094	−2.82838
$586$	−22.7063	−0.937989
$587$	5.54935	0.229046	0.114523	−	0.993421i	$-0.463466\pi$
$587$	5.54935	0.229046	0.114523	+	0.993421i	$0.463466\pi$
$588$	0	0
$589$	34.2805	1.41250
$590$	−23.9739	−0.986988
$591$	−5.03194	−0.206986
$592$	−5.92259	−0.243417
$593$	−23.8376	−0.978893	−0.489446	−	0.872033i	$-0.662801\pi$
$593$	−23.8376	−0.978893	−0.489446	+	0.872033i	$0.662801\pi$
$594$	98.9798	4.06119
$595$	0	0
$596$	−7.44236	−0.304851
$597$	−16.2325	−0.664353
$598$	1.18773	0.0485700
$599$	−23.6738	−0.967286	−0.483643	−	0.875265i	$-0.660687\pi$
$599$	−23.6738	−0.967286	−0.483643	+	0.875265i	$0.660687\pi$
$600$	−33.0704	−1.35009
$601$	36.6358	1.49441	0.747203	−	0.664595i	$-0.231396\pi$
$601$	36.6358	1.49441	0.747203	+	0.664595i	$0.231396\pi$
$602$	0	0
$603$	56.0141	2.28107
$604$	−7.22502	−0.293982
$605$	−99.5127	−4.04577
$606$	19.9494	0.810388
$607$	−16.6639	−0.676369	−0.338184	−	0.941080i	$-0.609813\pi$
$607$	−16.6639	−0.676369	−0.338184	+	0.941080i	$0.609813\pi$
$608$	3.59912	0.145963
$609$	0	0
$610$	13.9571	0.565107
$611$	25.9742	1.05080
$612$	−37.3214	−1.50863
$613$	−13.3045	−0.537363	−0.268682	−	0.963229i	$-0.586588\pi$
$613$	−13.3045	−0.537363	−0.268682	+	0.963229i	$0.586588\pi$
$614$	16.2095	0.654161
$615$	12.8095	0.516528
$616$	0	0
$617$	−14.9486	−0.601810	−0.300905	−	0.953654i	$-0.597289\pi$
$617$	−14.9486	−0.601810	−0.300905	+	0.953654i	$0.597289\pi$
$618$	28.0458	1.12817
$619$	−14.9047	−0.599071	−0.299535	−	0.954085i	$-0.596832\pi$
$619$	−14.9047	−0.599071	−0.299535	+	0.954085i	$0.596832\pi$
$620$	−36.8870	−1.48142
$621$	−8.72345	−0.350060
$622$	2.08493	0.0835980
$623$	0	0
$624$	−7.35835	−0.294570
$625$	24.9758	0.999032
$626$	−26.8869	−1.07462
$627$	72.1126	2.87990
$628$	12.8953	0.514580
$629$	27.8386	1.11000
$630$	0	0
$631$	18.3314	0.729763	0.364882	−	0.931054i	$-0.381109\pi$
$631$	18.3314	0.729763	0.364882	+	0.931054i	$0.381109\pi$
$632$	0.401018	0.0159516
$633$	−30.8726	−1.22707
$634$	−17.2868	−0.686545
$635$	−3.51356	−0.139431
$636$	37.1123	1.47160
$637$	0	0
$638$	−42.2864	−1.67414
$639$	43.0013	1.70111
$640$	−3.87277	−0.153085
$641$	−3.53353	−0.139566	−0.0697829	−	0.997562i	$-0.522231\pi$
$641$	−3.53353	−0.139566	−0.0697829	+	0.997562i	$0.522231\pi$
$642$	−11.7864	−0.465171
$643$	−7.20916	−0.284301	−0.142151	−	0.989845i	$-0.545402\pi$
$643$	−7.20916	−0.284301	−0.142151	+	0.989845i	$0.545402\pi$
$644$	0	0
$645$	−38.5354	−1.51733
$646$	−16.9173	−0.665602
$647$	−41.9515	−1.64928	−0.824642	−	0.565654i	$-0.808624\pi$
$647$	−41.9515	−1.64928	−0.824642	+	0.565654i	$0.808624\pi$
$648$	30.2242	1.18732
$649$	−37.4992	−1.47197
$650$	22.2434	0.872457
$651$	0	0
$652$	6.83948	0.267855
$653$	−44.2064	−1.72993	−0.864965	−	0.501833i	$-0.832659\pi$
$653$	−44.2064	−1.72993	−0.864965	+	0.501833i	$0.832659\pi$
$654$	13.6257	0.532807
$655$	−35.7744	−1.39782
$656$	1.00000	0.0390434
$657$	−41.7917	−1.63045
$658$	0	0
$659$	46.7615	1.82157	0.910785	−	0.412880i	$-0.135477\pi$
$659$	46.7615	1.82157	0.910785	+	0.412880i	$0.135477\pi$
$660$	−77.5957	−3.02041
$661$	−4.68047	−0.182049	−0.0910247	−	0.995849i	$-0.529014\pi$
$661$	−4.68047	−0.182049	−0.0910247	+	0.995849i	$0.529014\pi$
$662$	2.88391	0.112086
$663$	34.5872	1.34326
$664$	4.69112	0.182051
$665$	0	0
$666$	−47.0256	−1.82221
$667$	3.72686	0.144304
$668$	−14.3011	−0.553327
$669$	−21.2740	−0.822502
$670$	−27.3210	−1.05550
$671$	21.8313	0.842788
$672$	0	0
$673$	−36.0725	−1.39049	−0.695247	−	0.718771i	$-0.744705\pi$
$673$	−36.0725	−1.39049	−0.695247	+	0.718771i	$0.744705\pi$
$674$	10.9701	0.422553
$675$	−163.369	−6.28809
$676$	−8.05072	−0.309643
$677$	−39.0587	−1.50115	−0.750575	−	0.660786i	$-0.770223\pi$
$677$	−39.0587	−1.50115	−0.750575	+	0.660786i	$0.770223\pi$
$678$	6.49917	0.249599
$679$	0	0
$680$	18.2036	0.698077
$681$	75.9475	2.91032
$682$	−57.6976	−2.20935
$683$	5.38884	0.206198	0.103099	−	0.994671i	$-0.467124\pi$
$683$	5.38884	0.206198	0.103099	+	0.994671i	$0.467124\pi$
$684$	28.5771	1.09267
$685$	9.11518	0.348273
$686$	0	0
$687$	26.8581	1.02470
$688$	−3.00835	−0.114692
$689$	−24.9620	−0.950975
$690$	6.83879	0.260348
$691$	−42.1815	−1.60466	−0.802331	−	0.596880i	$-0.796407\pi$
$691$	−42.1815	−1.60466	−0.802331	+	0.596880i	$0.796407\pi$
$692$	−24.8199	−0.943510
$693$	0	0
$694$	−1.96054	−0.0744209
$695$	1.29342	0.0490622
$696$	−23.0890	−0.875185
$697$	−4.70041	−0.178041
$698$	−18.2795	−0.691891
$699$	34.6047	1.30887
$700$	0	0
$701$	−5.46425	−0.206382	−0.103191	−	0.994662i	$-0.532905\pi$
$701$	−5.46425	−0.206382	−0.103191	+	0.994662i	$0.532905\pi$
$702$	−36.3506	−1.37196
$703$	−21.3161	−0.803951
$704$	−6.05768	−0.228307
$705$	149.556	5.63260
$706$	23.2747	0.875955
$707$	0	0
$708$	−20.4751	−0.769500
$709$	−48.2902	−1.81358	−0.906789	−	0.421585i	$-0.861474\pi$
$709$	−48.2902	−1.81358	−0.906789	+	0.421585i	$0.861474\pi$
$710$	−20.9740	−0.787140
$711$	3.18410	0.119413
$712$	−3.68437	−0.138078
$713$	5.08510	0.190438
$714$	0	0
$715$	52.1914	1.95185
$716$	−24.3788	−0.911078
$717$	51.4594	1.92179
$718$	12.5000	0.466495
$719$	−52.1574	−1.94514	−0.972571	−	0.232606i	$-0.925275\pi$
$719$	−52.1574	−1.94514	−0.972571	+	0.232606i	$0.925275\pi$
$720$	−30.7500	−1.14599
$721$	0	0
$722$	−6.04637	−0.225023
$723$	7.60752	0.282927
$724$	−0.0528641	−0.00196468
$725$	69.7951	2.59212
$726$	−84.9896	−3.15426
$727$	−31.3575	−1.16299	−0.581493	−	0.813551i	$-0.697531\pi$
$727$	−31.3575	−1.16299	−0.581493	+	0.813551i	$0.697531\pi$
$728$	0	0
$729$	77.8484	2.88327
$730$	20.3840	0.754445
$731$	14.1405	0.523004
$732$	11.9202	0.440583
$733$	5.43860	0.200879	0.100440	−	0.994943i	$-0.467975\pi$
$733$	5.43860	0.200879	0.100440	+	0.994943i	$0.467975\pi$
$734$	8.45799	0.312190
$735$	0	0
$736$	0.533885	0.0196793
$737$	−42.7347	−1.57415
$738$	7.94005	0.292277
$739$	48.4786	1.78331	0.891656	−	0.452713i	$-0.149544\pi$
$739$	48.4786	1.78331	0.891656	+	0.452713i	$0.149544\pi$
$740$	22.9369	0.843175
$741$	−26.4835	−0.972897
$742$	0	0
$743$	−2.55894	−0.0938786	−0.0469393	−	0.998898i	$-0.514947\pi$
$743$	−2.55894	−0.0938786	−0.0469393	+	0.998898i	$0.514947\pi$
$744$	−31.5037	−1.15498
$745$	28.8226	1.05598
$746$	17.2826	0.632760
$747$	37.2477	1.36282
$748$	28.4735	1.04110
$749$	0	0
$750$	64.0268	2.33793
$751$	30.6177	1.11726	0.558629	−	0.829418i	$-0.311328\pi$
$751$	30.6177	1.11726	0.558629	+	0.829418i	$0.311328\pi$
$752$	11.6754	0.425758
$753$	70.3475	2.56360
$754$	15.5298	0.565562
$755$	27.9809	1.01833
$756$	0	0
$757$	14.9086	0.541861	0.270930	−	0.962599i	$-0.412669\pi$
$757$	14.9086	0.541861	0.270930	+	0.962599i	$0.412669\pi$
$758$	29.5973	1.07502
$759$	10.6970	0.388278
$760$	−13.9386	−0.505605
$761$	−35.1656	−1.27475	−0.637376	−	0.770553i	$-0.719980\pi$
$761$	−35.1656	−1.27475	−0.637376	+	0.770553i	$0.719980\pi$
$762$	−3.00078	−0.108707
$763$	0	0
$764$	−2.87401	−0.103978
$765$	144.538	5.22576
$766$	−18.2590	−0.659723
$767$	13.7717	0.497266
$768$	−3.30757	−0.119352
$769$	−25.9354	−0.935256	−0.467628	−	0.883925i	$-0.654891\pi$
$769$	−25.9354	−0.935256	−0.467628	+	0.883925i	$0.654891\pi$
$770$	0	0
$771$	−54.3942	−1.95896
$772$	−7.09383	−0.255312
$773$	39.6671	1.42673	0.713364	−	0.700794i	$-0.247171\pi$
$773$	39.6671	1.42673	0.713364	+	0.700794i	$0.247171\pi$
$774$	−23.8864	−0.858580
$775$	95.2317	3.42082
$776$	−8.66450	−0.311037
$777$	0	0
$778$	22.9438	0.822574
$779$	3.59912	0.128952
$780$	28.4972	1.02036
$781$	−32.8069	−1.17392
$782$	−2.50948	−0.0897387
$783$	−114.061	−4.07619
$784$	0	0
$785$	−49.9408	−1.78246
$786$	−30.5534	−1.08980
$787$	−4.36654	−0.155650	−0.0778252	−	0.996967i	$-0.524798\pi$
$787$	−4.36654	−0.155650	−0.0778252	+	0.996967i	$0.524798\pi$
$788$	1.52134	0.0541954
$789$	6.84468	0.243677
$790$	−1.55305	−0.0552551
$791$	0	0
$792$	−48.0982	−1.70910
$793$	−8.01760	−0.284713
$794$	3.04357	0.108012
$795$	−143.728	−5.09749
$796$	4.90768	0.173948
$797$	−10.4561	−0.370375	−0.185187	−	0.982703i	$-0.559289\pi$
$797$	−10.4561	−0.370375	−0.185187	+	0.982703i	$0.559289\pi$
$798$	0	0
$799$	−54.8791	−1.94148
$800$	9.99839	0.353496
$801$	−29.2541	−1.03364
$802$	20.0372	0.707537
$803$	31.8840	1.12516
$804$	−23.3337	−0.822917
$805$	0	0
$806$	21.1896	0.746371
$807$	−33.6989	−1.18626
$808$	−6.03142	−0.212185
$809$	−41.8027	−1.46971	−0.734853	−	0.678226i	$-0.762749\pi$
$809$	−41.8027	−1.46971	−0.734853	+	0.678226i	$0.762749\pi$
$810$	−117.051	−4.11277
$811$	−49.9521	−1.75406	−0.877028	−	0.480439i	$-0.840477\pi$
$811$	−49.9521	−1.75406	−0.877028	+	0.480439i	$0.840477\pi$
$812$	0	0
$813$	59.9504	2.10255
$814$	35.8771	1.25749
$815$	−26.4878	−0.927826
$816$	15.5469	0.544252
$817$	−10.8274	−0.378803
$818$	−27.9562	−0.977466
$819$	0	0
$820$	−3.87277	−0.135243
$821$	−4.12898	−0.144102	−0.0720512	−	0.997401i	$-0.522954\pi$
$821$	−4.12898	−0.144102	−0.0720512	+	0.997401i	$0.522954\pi$
$822$	7.78489	0.271529
$823$	−11.8683	−0.413703	−0.206851	−	0.978372i	$-0.566322\pi$
$823$	−11.8683	−0.413703	−0.206851	+	0.978372i	$0.566322\pi$
$824$	−8.47928	−0.295390
$825$	200.330	6.97459
$826$	0	0
$827$	−53.8557	−1.87274	−0.936372	−	0.351008i	$-0.885839\pi$
$827$	−53.8557	−1.87274	−0.936372	+	0.351008i	$0.885839\pi$
$828$	4.23907	0.147318
$829$	37.5271	1.30337	0.651686	−	0.758489i	$-0.274062\pi$
$829$	37.5271	1.30337	0.651686	+	0.758489i	$0.274062\pi$
$830$	−18.1677	−0.630609
$831$	−84.8439	−2.94320
$832$	2.22470	0.0771275
$833$	0	0
$834$	1.10466	0.0382511
$835$	55.3850	1.91668
$836$	−21.8023	−0.754048
$837$	−155.630	−5.37934
$838$	37.3753	1.29111
$839$	19.0531	0.657786	0.328893	−	0.944367i	$-0.393324\pi$
$839$	19.0531	0.657786	0.328893	+	0.944367i	$0.393324\pi$
$840$	0	0
$841$	19.7293	0.680320
$842$	−8.99134	−0.309862
$843$	−33.0324	−1.13769
$844$	9.33390	0.321286
$845$	31.1786	1.07258
$846$	92.7032	3.18720
$847$	0	0
$848$	−11.2204	−0.385310
$849$	−35.9808	−1.23486
$850$	−46.9965	−1.61197
$851$	−3.16198	−0.108391
$852$	−17.9130	−0.613689
$853$	−25.5388	−0.874430	−0.437215	−	0.899357i	$-0.644035\pi$
$853$	−25.5388	−0.874430	−0.437215	+	0.899357i	$0.644035\pi$
$854$	0	0
$855$	−110.673	−3.78493
$856$	3.56345	0.121796
$857$	−31.6247	−1.08028	−0.540139	−	0.841576i	$-0.681628\pi$
$857$	−31.6247	−1.08028	−0.540139	+	0.841576i	$0.681628\pi$
$858$	44.5745	1.52175
$859$	−53.3239	−1.81939	−0.909694	−	0.415280i	$-0.863684\pi$
$859$	−53.3239	−1.81939	−0.909694	+	0.415280i	$0.863684\pi$
$860$	11.6507	0.397284
$861$	0	0
$862$	0.851001	0.0289852
$863$	−2.73115	−0.0929694	−0.0464847	−	0.998919i	$-0.514802\pi$
$863$	−2.73115	−0.0929694	−0.0464847	+	0.998919i	$0.514802\pi$
$864$	−16.3396	−0.555883
$865$	96.1218	3.26824
$866$	33.1658	1.12702
$867$	−16.8482	−0.572193
$868$	0	0
$869$	−2.42924	−0.0824062
$870$	89.4184	3.03157
$871$	15.6944	0.531785
$872$	−4.11954	−0.139505
$873$	−68.7965	−2.32841
$874$	1.92151	0.0649962
$875$	0	0
$876$	17.4091	0.588199
$877$	−23.0478	−0.778269	−0.389135	−	0.921181i	$-0.627226\pi$
$877$	−23.0478	−0.778269	−0.389135	+	0.921181i	$0.627226\pi$
$878$	25.0468	0.845289
$879$	75.1028	2.53316
$880$	23.4600	0.790837
$881$	−34.5243	−1.16315	−0.581576	−	0.813492i	$-0.697564\pi$
$881$	−34.5243	−1.16315	−0.581576	+	0.813492i	$0.697564\pi$
$882$	0	0
$883$	6.11188	0.205681	0.102841	−	0.994698i	$-0.467207\pi$
$883$	6.11188	0.205681	0.102841	+	0.994698i	$0.467207\pi$
$884$	−10.4570	−0.351706
$885$	79.2953	2.66548
$886$	1.65140	0.0554799
$887$	5.64372	0.189498	0.0947488	−	0.995501i	$-0.469795\pi$
$887$	5.64372	0.189498	0.0947488	+	0.995501i	$0.469795\pi$
$888$	19.5894	0.657377
$889$	0	0
$890$	14.2687	0.478289
$891$	−183.088	−6.13369
$892$	6.43192	0.215357
$893$	42.0211	1.40618
$894$	24.6162	0.823288
$895$	94.4135	3.15590
$896$	0	0
$897$	−3.92851	−0.131169
$898$	−17.7590	−0.592625
$899$	66.4885	2.21752
$900$	79.3876	2.64625
$901$	52.7404	1.75704
$902$	−6.05768	−0.201699
$903$	0	0
$904$	−1.96493	−0.0653527
$905$	0.204731	0.00680548
$906$	23.8973	0.793934
$907$	−21.1256	−0.701464	−0.350732	−	0.936476i	$-0.614067\pi$
$907$	−21.1256	−0.701464	−0.350732	+	0.936476i	$0.614067\pi$
$908$	−22.9617	−0.762011
$909$	−47.8898	−1.58840
$910$	0	0
$911$	−26.5810	−0.880667	−0.440333	−	0.897834i	$-0.645140\pi$
$911$	−26.5810	−0.880667	−0.440333	+	0.897834i	$0.645140\pi$
$912$	−11.9043	−0.394192
$913$	−28.4173	−0.940475
$914$	26.8026	0.886551
$915$	−46.1642	−1.52614
$916$	−8.12017	−0.268298
$917$	0	0
$918$	76.8026	2.53486
$919$	20.1647	0.665172	0.332586	−	0.943073i	$-0.392079\pi$
$919$	20.1647	0.665172	0.332586	+	0.943073i	$0.392079\pi$
$920$	−2.06762	−0.0681673
$921$	−53.6140	−1.76664
$922$	22.1793	0.730435
$923$	12.0484	0.396578
$924$	0	0
$925$	−59.2163	−1.94702
$926$	−31.4496	−1.03350
$927$	−67.3259	−2.21127
$928$	6.98064	0.229151
$929$	20.0618	0.658205	0.329102	−	0.944294i	$-0.393254\pi$
$929$	20.0618	0.658205	0.329102	+	0.944294i	$0.393254\pi$
$930$	122.007	4.00075
$931$	0	0
$932$	−10.4623	−0.342703
$933$	−6.89606	−0.225767
$934$	−14.3411	−0.469256
$935$	−110.272	−3.60627
$936$	17.6642	0.577372
$937$	18.2309	0.595578	0.297789	−	0.954632i	$-0.403751\pi$
$937$	18.2309	0.595578	0.297789	+	0.954632i	$0.403751\pi$
$938$	0	0
$939$	88.9303	2.90213
$940$	−45.2162	−1.47479
$941$	16.5589	0.539805	0.269902	−	0.962888i	$-0.413009\pi$
$941$	16.5589	0.539805	0.269902	+	0.962888i	$0.413009\pi$
$942$	−42.6523	−1.38969
$943$	0.533885	0.0173857
$944$	6.19036	0.201479
$945$	0	0
$946$	18.2236	0.592501
$947$	57.4355	1.86640	0.933201	−	0.359354i	$-0.117003\pi$
$947$	57.4355	1.86640	0.933201	+	0.359354i	$0.117003\pi$
$948$	−1.32640	−0.0430793
$949$	−11.7095	−0.380106
$950$	35.9853	1.16752
$951$	57.1773	1.85410
$952$	0	0
$953$	56.6818	1.83610	0.918052	−	0.396460i	$-0.129761\pi$
$953$	56.6818	1.83610	0.918052	+	0.396460i	$0.129761\pi$
$954$	−89.0904	−2.88441
$955$	11.1304	0.360171
$956$	−15.5581	−0.503184
$957$	139.866	4.52121
$958$	−12.2351	−0.395299
$959$	0	0
$960$	12.8095	0.413424
$961$	59.7200	1.92645
$962$	−13.1760	−0.424810
$963$	28.2939	0.911759
$964$	−2.30003	−0.0740789
$965$	27.4728	0.884380
$966$	0	0
$967$	−35.7547	−1.14979	−0.574896	−	0.818226i	$-0.694958\pi$
$967$	−35.7547	−1.14979	−0.574896	+	0.818226i	$0.694958\pi$
$968$	25.6954	0.825883
$969$	55.9552	1.79754
$970$	33.5557	1.07741
$971$	19.6443	0.630414	0.315207	−	0.949023i	$-0.397926\pi$
$971$	19.6443	0.630414	0.315207	+	0.949023i	$0.397926\pi$
$972$	−50.9500	−1.63422
$973$	0	0
$974$	5.21478	0.167092
$975$	−73.5716	−2.35618
$976$	−3.60391	−0.115358
$977$	−27.9407	−0.893904	−0.446952	−	0.894558i	$-0.647490\pi$
$977$	−27.9407	−0.893904	−0.446952	+	0.894558i	$0.647490\pi$
$978$	−22.6221	−0.723374
$979$	22.3187	0.713310
$980$	0	0
$981$	−32.7094	−1.04433
$982$	8.94577	0.285471
$983$	58.7479	1.87377	0.936883	−	0.349643i	$-0.113697\pi$
$983$	58.7479	1.87377	0.936883	+	0.349643i	$0.113697\pi$
$984$	−3.30757	−0.105442
$985$	−5.89180	−0.187728
$986$	−32.8118	−1.04494
$987$	0	0
$988$	8.00694	0.254735
$989$	−1.60611	−0.0510714
$990$	186.274	5.92016
$991$	−36.0677	−1.14573	−0.572864	−	0.819650i	$-0.694168\pi$
$991$	−36.0677	−1.14573	−0.572864	+	0.819650i	$0.694168\pi$
$992$	9.52470	0.302410
$993$	−9.53874	−0.302703
$994$	0	0
$995$	−19.0064	−0.602542
$996$	−15.5162	−0.491651
$997$	30.5916	0.968845	0.484423	−	0.874834i	$-0.339030\pi$
$997$	30.5916	0.968845	0.484423	+	0.874834i	$0.339030\pi$
$998$	14.3264	0.453494
$999$	96.7725	3.06175

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4018.2.a.bp.1.1	✓	6
7.6	odd	2		4018.2.a.bq.1.6	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4018.2.a.bp.1.1	✓	6	1.1	even	1	trivial
4018.2.a.bq.1.6	yes	6	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4018 = 2 \cdot 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4018.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -3.30757 q^{3} +1.00000 q^{4} -3.87277 q^{5} -3.30757 q^{6} +1.00000 q^{8} +7.94005 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -3.30757 q^{3} +1.00000 q^{4} -3.87277 q^{5} -3.30757 q^{6} +1.00000 q^{8} +7.94005 q^{9} -3.87277 q^{10} -6.05768 q^{11} -3.30757 q^{12} +2.22470 q^{13} +12.8095 q^{15} +1.00000 q^{16} -4.70041 q^{17} +7.94005 q^{18} +3.59912 q^{19} -3.87277 q^{20} -6.05768 q^{22} +0.533885 q^{23} -3.30757 q^{24} +9.99839 q^{25} +2.22470 q^{26} -16.3396 q^{27} +6.98064 q^{29} +12.8095 q^{30} +9.52470 q^{31} +1.00000 q^{32} +20.0362 q^{33} -4.70041 q^{34} +7.94005 q^{36} -5.92259 q^{37} +3.59912 q^{38} -7.35835 q^{39} -3.87277 q^{40} +1.00000 q^{41} -3.00835 q^{43} -6.05768 q^{44} -30.7500 q^{45} +0.533885 q^{46} +11.6754 q^{47} -3.30757 q^{48} +9.99839 q^{50} +15.5469 q^{51} +2.22470 q^{52} -11.2204 q^{53} -16.3396 q^{54} +23.4600 q^{55} -11.9043 q^{57} +6.98064 q^{58} +6.19036 q^{59} +12.8095 q^{60} -3.60391 q^{61} +9.52470 q^{62} +1.00000 q^{64} -8.61575 q^{65} +20.0362 q^{66} +7.05464 q^{67} -4.70041 q^{68} -1.76586 q^{69} +5.41575 q^{71} +7.94005 q^{72} -5.26340 q^{73} -5.92259 q^{74} -33.0704 q^{75} +3.59912 q^{76} -7.35835 q^{78} +0.401018 q^{79} -3.87277 q^{80} +30.2242 q^{81} +1.00000 q^{82} +4.69112 q^{83} +18.2036 q^{85} -3.00835 q^{86} -23.0890 q^{87} -6.05768 q^{88} -3.68437 q^{89} -30.7500 q^{90} +0.533885 q^{92} -31.5037 q^{93} +11.6754 q^{94} -13.9386 q^{95} -3.30757 q^{96} -8.66450 q^{97} -48.0982 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} - 4 q^{3} + 6 q^{4} - 12 q^{5} - 4 q^{6} + 6 q^{8} + 18 q^{9}+O(q^{10}) \) 6 * q + 6 * q^2 - 4 * q^3 + 6 * q^4 - 12 * q^5 - 4 * q^6 + 6 * q^8 + 18 * q^9	\( 6 q + 6 q^{2} - 4 q^{3} + 6 q^{4} - 12 q^{5} - 4 q^{6} + 6 q^{8} + 18 q^{9} - 12 q^{10} - 4 q^{12} - 8 q^{13} - 4 q^{15} + 6 q^{16} - 16 q^{17} + 18 q^{18} - 12 q^{19} - 12 q^{20} + 12 q^{23} - 4 q^{24} + 14 q^{25} - 8 q^{26} - 28 q^{27} - 4 q^{30} + 4 q^{31} + 6 q^{32} + 20 q^{33} - 16 q^{34} + 18 q^{36} - 24 q^{37} - 12 q^{38} + 4 q^{39} - 12 q^{40} + 6 q^{41} + 4 q^{43} - 28 q^{45} + 12 q^{46} + 16 q^{47} - 4 q^{48} + 14 q^{50} - 16 q^{51} - 8 q^{52} - 16 q^{53} - 28 q^{54} + 12 q^{55} - 28 q^{57} - 16 q^{59} - 4 q^{60} - 32 q^{61} + 4 q^{62} + 6 q^{64} - 4 q^{65} + 20 q^{66} - 20 q^{67} - 16 q^{68} - 56 q^{69} + 12 q^{71} + 18 q^{72} - 16 q^{73} - 24 q^{74} + 4 q^{75} - 12 q^{76} + 4 q^{78} - 12 q^{80} + 42 q^{81} + 6 q^{82} - 32 q^{83} + 48 q^{85} + 4 q^{86} - 20 q^{87} - 8 q^{89} - 28 q^{90} + 12 q^{92} - 12 q^{93} + 16 q^{94} + 28 q^{95} - 4 q^{96} - 8 q^{97} - 76 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 - 4 * q^3 + 6 * q^4 - 12 * q^5 - 4 * q^6 + 6 * q^8 + 18 * q^9 - 12 * q^10 - 4 * q^12 - 8 * q^13 - 4 * q^15 + 6 * q^16 - 16 * q^17 + 18 * q^18 - 12 * q^19 - 12 * q^20 + 12 * q^23 - 4 * q^24 + 14 * q^25 - 8 * q^26 - 28 * q^27 - 4 * q^30 + 4 * q^31 + 6 * q^32 + 20 * q^33 - 16 * q^34 + 18 * q^36 - 24 * q^37 - 12 * q^38 + 4 * q^39 - 12 * q^40 + 6 * q^41 + 4 * q^43 - 28 * q^45 + 12 * q^46 + 16 * q^47 - 4 * q^48 + 14 * q^50 - 16 * q^51 - 8 * q^52 - 16 * q^53 - 28 * q^54 + 12 * q^55 - 28 * q^57 - 16 * q^59 - 4 * q^60 - 32 * q^61 + 4 * q^62 + 6 * q^64 - 4 * q^65 + 20 * q^66 - 20 * q^67 - 16 * q^68 - 56 * q^69 + 12 * q^71 + 18 * q^72 - 16 * q^73 - 24 * q^74 + 4 * q^75 - 12 * q^76 + 4 * q^78 - 12 * q^80 + 42 * q^81 + 6 * q^82 - 32 * q^83 + 48 * q^85 + 4 * q^86 - 20 * q^87 - 8 * q^89 - 28 * q^90 + 12 * q^92 - 12 * q^93 + 16 * q^94 + 28 * q^95 - 4 * q^96 - 8 * q^97 - 76 * q^99

Introduction

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