LMFDB - Embedded newform 750.2.a.d.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [750,2,Mod(1,750)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(750, 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("750.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 750 = 2 \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	750.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:	$5.98878015160$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.618034$ of defining polynomial
Character	$\chi$	$=$	750.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +4.61803 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +4.61803 q^{7} -1.00000 q^{8} +1.00000 q^{9} +0.854102 q^{11} +1.00000 q^{12} +5.61803 q^{13} -4.61803 q^{14} +1.00000 q^{16} -5.70820 q^{17} -1.00000 q^{18} -7.09017 q^{19} +4.61803 q^{21} -0.854102 q^{22} +8.09017 q^{23} -1.00000 q^{24} -5.61803 q^{26} +1.00000 q^{27} +4.61803 q^{28} -7.70820 q^{29} +2.47214 q^{31} -1.00000 q^{32} +0.854102 q^{33} +5.70820 q^{34} +1.00000 q^{36} +0.618034 q^{37} +7.09017 q^{38} +5.61803 q^{39} +2.61803 q^{41} -4.61803 q^{42} -5.70820 q^{43} +0.854102 q^{44} -8.09017 q^{46} +6.38197 q^{47} +1.00000 q^{48} +14.3262 q^{49} -5.70820 q^{51} +5.61803 q^{52} +2.61803 q^{53} -1.00000 q^{54} -4.61803 q^{56} -7.09017 q^{57} +7.70820 q^{58} -4.14590 q^{59} -1.70820 q^{61} -2.47214 q^{62} +4.61803 q^{63} +1.00000 q^{64} -0.854102 q^{66} -1.23607 q^{67} -5.70820 q^{68} +8.09017 q^{69} +4.47214 q^{71} -1.00000 q^{72} -8.00000 q^{73} -0.618034 q^{74} -7.09017 q^{76} +3.94427 q^{77} -5.61803 q^{78} +3.52786 q^{79} +1.00000 q^{81} -2.61803 q^{82} +2.00000 q^{83} +4.61803 q^{84} +5.70820 q^{86} -7.70820 q^{87} -0.854102 q^{88} -4.56231 q^{89} +25.9443 q^{91} +8.09017 q^{92} +2.47214 q^{93} -6.38197 q^{94} -1.00000 q^{96} +8.18034 q^{97} -14.3262 q^{98} +0.854102 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{6} + 7 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^6 + 7 * q^7 - 2 * q^8 + 2 * q^9	$ 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{6} + 7 q^{7} - 2 q^{8} + 2 q^{9} - 5 q^{11} + 2 q^{12} + 9 q^{13} - 7 q^{14} + 2 q^{16} + 2 q^{17} - 2 q^{18} - 3 q^{19} + 7 q^{21} + 5 q^{22} + 5 q^{23} - 2 q^{24} - 9 q^{26} + 2 q^{27} + 7 q^{28} - 2 q^{29} - 4 q^{31} - 2 q^{32} - 5 q^{33} - 2 q^{34} + 2 q^{36} - q^{37} + 3 q^{38} + 9 q^{39} + 3 q^{41} - 7 q^{42} + 2 q^{43} - 5 q^{44} - 5 q^{46} + 15 q^{47} + 2 q^{48} + 13 q^{49} + 2 q^{51} + 9 q^{52} + 3 q^{53} - 2 q^{54} - 7 q^{56} - 3 q^{57} + 2 q^{58} - 15 q^{59} + 10 q^{61} + 4 q^{62} + 7 q^{63} + 2 q^{64} + 5 q^{66} + 2 q^{67} + 2 q^{68} + 5 q^{69} - 2 q^{72} - 16 q^{73} + q^{74} - 3 q^{76} - 10 q^{77} - 9 q^{78} + 16 q^{79} + 2 q^{81} - 3 q^{82} + 4 q^{83} + 7 q^{84} - 2 q^{86} - 2 q^{87} + 5 q^{88} + 11 q^{89} + 34 q^{91} + 5 q^{92} - 4 q^{93} - 15 q^{94} - 2 q^{96} - 6 q^{97} - 13 q^{98} - 5 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^6 + 7 * q^7 - 2 * q^8 + 2 * q^9 - 5 * q^11 + 2 * q^12 + 9 * q^13 - 7 * q^14 + 2 * q^16 + 2 * q^17 - 2 * q^18 - 3 * q^19 + 7 * q^21 + 5 * q^22 + 5 * q^23 - 2 * q^24 - 9 * q^26 + 2 * q^27 + 7 * q^28 - 2 * q^29 - 4 * q^31 - 2 * q^32 - 5 * q^33 - 2 * q^34 + 2 * q^36 - q^37 + 3 * q^38 + 9 * q^39 + 3 * q^41 - 7 * q^42 + 2 * q^43 - 5 * q^44 - 5 * q^46 + 15 * q^47 + 2 * q^48 + 13 * q^49 + 2 * q^51 + 9 * q^52 + 3 * q^53 - 2 * q^54 - 7 * q^56 - 3 * q^57 + 2 * q^58 - 15 * q^59 + 10 * q^61 + 4 * q^62 + 7 * q^63 + 2 * q^64 + 5 * q^66 + 2 * q^67 + 2 * q^68 + 5 * q^69 - 2 * q^72 - 16 * q^73 + q^74 - 3 * q^76 - 10 * q^77 - 9 * q^78 + 16 * q^79 + 2 * q^81 - 3 * q^82 + 4 * q^83 + 7 * q^84 - 2 * q^86 - 2 * q^87 + 5 * q^88 + 11 * q^89 + 34 * q^91 + 5 * q^92 - 4 * q^93 - 15 * q^94 - 2 * q^96 - 6 * q^97 - 13 * q^98 - 5 * 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
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	−1.00000	−0.408248
$7$	4.61803	1.74545	0.872726	−	0.488210i	$-0.162350\pi$
$7$	4.61803	1.74545	0.872726	+	0.488210i	$0.162350\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	0	0
$11$	0.854102	0.257521	0.128761	−	0.991676i	$-0.458900\pi$
$11$	0.854102	0.257521	0.128761	+	0.991676i	$0.458900\pi$
$12$	1.00000	0.288675
$13$	5.61803	1.55816	0.779081	−	0.626923i	$-0.215686\pi$
$13$	5.61803	1.55816	0.779081	+	0.626923i	$0.215686\pi$
$14$	−4.61803	−1.23422
$15$	0	0
$16$	1.00000	0.250000
$17$	−5.70820	−1.38444	−0.692221	−	0.721685i	$-0.743368\pi$
$17$	−5.70820	−1.38444	−0.692221	+	0.721685i	$0.743368\pi$
$18$	−1.00000	−0.235702
$19$	−7.09017	−1.62660	−0.813298	−	0.581847i	$-0.802330\pi$
$19$	−7.09017	−1.62660	−0.813298	+	0.581847i	$0.802330\pi$
$20$	0	0
$21$	4.61803	1.00774
$22$	−0.854102	−0.182095
$23$	8.09017	1.68692	0.843459	−	0.537194i	$-0.180516\pi$
$23$	8.09017	1.68692	0.843459	+	0.537194i	$0.180516\pi$
$24$	−1.00000	−0.204124
$25$	0	0
$26$	−5.61803	−1.10179
$27$	1.00000	0.192450
$28$	4.61803	0.872726
$29$	−7.70820	−1.43138	−0.715689	−	0.698419i	$-0.753887\pi$
$29$	−7.70820	−1.43138	−0.715689	+	0.698419i	$0.753887\pi$
$30$	0	0
$31$	2.47214	0.444009	0.222004	−	0.975046i	$-0.428740\pi$
$31$	2.47214	0.444009	0.222004	+	0.975046i	$0.428740\pi$
$32$	−1.00000	−0.176777
$33$	0.854102	0.148680
$34$	5.70820	0.978949
$35$	0	0
$36$	1.00000	0.166667
$37$	0.618034	0.101604	0.0508021	−	0.998709i	$-0.483822\pi$
$37$	0.618034	0.101604	0.0508021	+	0.998709i	$0.483822\pi$
$38$	7.09017	1.15018
$39$	5.61803	0.899605
$40$	0	0
$41$	2.61803	0.408868	0.204434	−	0.978880i	$-0.434465\pi$
$41$	2.61803	0.408868	0.204434	+	0.978880i	$0.434465\pi$
$42$	−4.61803	−0.712578
$43$	−5.70820	−0.870493	−0.435246	−	0.900311i	$-0.643339\pi$
$43$	−5.70820	−0.870493	−0.435246	+	0.900311i	$0.643339\pi$
$44$	0.854102	0.128761
$45$	0	0
$46$	−8.09017	−1.19283
$47$	6.38197	0.930905	0.465453	−	0.885073i	$-0.345892\pi$
$47$	6.38197	0.930905	0.465453	+	0.885073i	$0.345892\pi$
$48$	1.00000	0.144338
$49$	14.3262	2.04661
$50$	0	0
$51$	−5.70820	−0.799308
$52$	5.61803	0.779081
$53$	2.61803	0.359615	0.179807	−	0.983702i	$-0.442453\pi$
$53$	2.61803	0.359615	0.179807	+	0.983702i	$0.442453\pi$
$54$	−1.00000	−0.136083
$55$	0	0
$56$	−4.61803	−0.617111
$57$	−7.09017	−0.939116
$58$	7.70820	1.01214
$59$	−4.14590	−0.539750	−0.269875	−	0.962895i	$-0.586982\pi$
$59$	−4.14590	−0.539750	−0.269875	+	0.962895i	$0.586982\pi$
$60$	0	0
$61$	−1.70820	−0.218713	−0.109357	−	0.994003i	$-0.534879\pi$
$61$	−1.70820	−0.218713	−0.109357	+	0.994003i	$0.534879\pi$
$62$	−2.47214	−0.313962
$63$	4.61803	0.581818
$64$	1.00000	0.125000
$65$	0	0
$66$	−0.854102	−0.105133
$67$	−1.23607	−0.151010	−0.0755049	−	0.997145i	$-0.524057\pi$
$67$	−1.23607	−0.151010	−0.0755049	+	0.997145i	$0.524057\pi$
$68$	−5.70820	−0.692221
$69$	8.09017	0.973942
$70$	0	0
$71$	4.47214	0.530745	0.265372	−	0.964146i	$-0.414505\pi$
$71$	4.47214	0.530745	0.265372	+	0.964146i	$0.414505\pi$
$72$	−1.00000	−0.117851
$73$	−8.00000	−0.936329	−0.468165	−	0.883641i	$-0.655085\pi$
$73$	−8.00000	−0.936329	−0.468165	+	0.883641i	$0.655085\pi$
$74$	−0.618034	−0.0718450
$75$	0	0
$76$	−7.09017	−0.813298
$77$	3.94427	0.449492
$78$	−5.61803	−0.636117
$79$	3.52786	0.396916	0.198458	−	0.980109i	$-0.436407\pi$
$79$	3.52786	0.396916	0.198458	+	0.980109i	$0.436407\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−2.61803	−0.289113
$83$	2.00000	0.219529	0.109764	−	0.993958i	$-0.464990\pi$
$83$	2.00000	0.219529	0.109764	+	0.993958i	$0.464990\pi$
$84$	4.61803	0.503869
$85$	0	0
$86$	5.70820	0.615531
$87$	−7.70820	−0.826406
$88$	−0.854102	−0.0910476
$89$	−4.56231	−0.483603	−0.241802	−	0.970326i	$-0.577738\pi$
$89$	−4.56231	−0.483603	−0.241802	+	0.970326i	$0.577738\pi$
$90$	0	0
$91$	25.9443	2.71970
$92$	8.09017	0.843459
$93$	2.47214	0.256349
$94$	−6.38197	−0.658250
$95$	0	0
$96$	−1.00000	−0.102062
$97$	8.18034	0.830588	0.415294	−	0.909687i	$-0.363679\pi$
$97$	8.18034	0.830588	0.415294	+	0.909687i	$0.363679\pi$
$98$	−14.3262	−1.44717
$99$	0.854102	0.0858405
$100$	0	0
$101$	−0.291796	−0.0290348	−0.0145174	−	0.999895i	$-0.504621\pi$
$101$	−0.291796	−0.0290348	−0.0145174	+	0.999895i	$0.504621\pi$
$102$	5.70820	0.565196
$103$	14.0902	1.38835	0.694173	−	0.719808i	$-0.255770\pi$
$103$	14.0902	1.38835	0.694173	+	0.719808i	$0.255770\pi$
$104$	−5.61803	−0.550894
$105$	0	0
$106$	−2.61803	−0.254286
$107$	−2.00000	−0.193347	−0.0966736	−	0.995316i	$-0.530820\pi$
$107$	−2.00000	−0.193347	−0.0966736	+	0.995316i	$0.530820\pi$
$108$	1.00000	0.0962250
$109$	11.7082	1.12144	0.560721	−	0.828005i	$-0.310524\pi$
$109$	11.7082	1.12144	0.560721	+	0.828005i	$0.310524\pi$
$110$	0	0
$111$	0.618034	0.0586612
$112$	4.61803	0.436363
$113$	−9.70820	−0.913271	−0.456636	−	0.889654i	$-0.650946\pi$
$113$	−9.70820	−0.913271	−0.456636	+	0.889654i	$0.650946\pi$
$114$	7.09017	0.664055
$115$	0	0
$116$	−7.70820	−0.715689
$117$	5.61803	0.519387
$118$	4.14590	0.381661
$119$	−26.3607	−2.41648
$120$	0	0
$121$	−10.2705	−0.933683
$122$	1.70820	0.154654
$123$	2.61803	0.236060
$124$	2.47214	0.222004
$125$	0	0
$126$	−4.61803	−0.411407
$127$	−14.4721	−1.28419	−0.642097	−	0.766623i	$-0.721935\pi$
$127$	−14.4721	−1.28419	−0.642097	+	0.766623i	$0.721935\pi$
$128$	−1.00000	−0.0883883
$129$	−5.70820	−0.502579
$130$	0	0
$131$	−4.67376	−0.408348	−0.204174	−	0.978935i	$-0.565451\pi$
$131$	−4.67376	−0.408348	−0.204174	+	0.978935i	$0.565451\pi$
$132$	0.854102	0.0743400
$133$	−32.7426	−2.83915
$134$	1.23607	0.106780
$135$	0	0
$136$	5.70820	0.489474
$137$	−12.9443	−1.10590	−0.552952	−	0.833213i	$-0.686499\pi$
$137$	−12.9443	−1.10590	−0.552952	+	0.833213i	$0.686499\pi$
$138$	−8.09017	−0.688681
$139$	−0.381966	−0.0323979	−0.0161990	−	0.999869i	$-0.505157\pi$
$139$	−0.381966	−0.0323979	−0.0161990	+	0.999869i	$0.505157\pi$
$140$	0	0
$141$	6.38197	0.537458
$142$	−4.47214	−0.375293
$143$	4.79837	0.401260
$144$	1.00000	0.0833333
$145$	0	0
$146$	8.00000	0.662085
$147$	14.3262	1.18161
$148$	0.618034	0.0508021
$149$	17.4164	1.42681	0.713404	−	0.700753i	$-0.247153\pi$
$149$	17.4164	1.42681	0.713404	+	0.700753i	$0.247153\pi$
$150$	0	0
$151$	−13.7082	−1.11556	−0.557779	−	0.829990i	$-0.688346\pi$
$151$	−13.7082	−1.11556	−0.557779	+	0.829990i	$0.688346\pi$
$152$	7.09017	0.575089
$153$	−5.70820	−0.461481
$154$	−3.94427	−0.317838
$155$	0	0
$156$	5.61803	0.449803
$157$	10.9443	0.873448	0.436724	−	0.899596i	$-0.356139\pi$
$157$	10.9443	0.873448	0.436724	+	0.899596i	$0.356139\pi$
$158$	−3.52786	−0.280662
$159$	2.61803	0.207624
$160$	0	0
$161$	37.3607	2.94443
$162$	−1.00000	−0.0785674
$163$	−24.0000	−1.87983	−0.939913	−	0.341415i	$-0.889094\pi$
$163$	−24.0000	−1.87983	−0.939913	+	0.341415i	$0.889094\pi$
$164$	2.61803	0.204434
$165$	0	0
$166$	−2.00000	−0.155230
$167$	−13.0902	−1.01295	−0.506474	−	0.862255i	$-0.669051\pi$
$167$	−13.0902	−1.01295	−0.506474	+	0.862255i	$0.669051\pi$
$168$	−4.61803	−0.356289
$169$	18.5623	1.42787
$170$	0	0
$171$	−7.09017	−0.542199
$172$	−5.70820	−0.435246
$173$	6.61803	0.503160	0.251580	−	0.967837i	$-0.419050\pi$
$173$	6.61803	0.503160	0.251580	+	0.967837i	$0.419050\pi$
$174$	7.70820	0.584357
$175$	0	0
$176$	0.854102	0.0643804
$177$	−4.14590	−0.311625
$178$	4.56231	0.341959
$179$	−20.7984	−1.55454	−0.777272	−	0.629165i	$-0.783397\pi$
$179$	−20.7984	−1.55454	−0.777272	+	0.629165i	$0.783397\pi$
$180$	0	0
$181$	−11.5279	−0.856859	−0.428430	−	0.903575i	$-0.640933\pi$
$181$	−11.5279	−0.856859	−0.428430	+	0.903575i	$0.640933\pi$
$182$	−25.9443	−1.92312
$183$	−1.70820	−0.126274
$184$	−8.09017	−0.596415
$185$	0	0
$186$	−2.47214	−0.181266
$187$	−4.87539	−0.356524
$188$	6.38197	0.465453
$189$	4.61803	0.335913
$190$	0	0
$191$	−4.00000	−0.289430	−0.144715	−	0.989473i	$-0.546227\pi$
$191$	−4.00000	−0.289430	−0.144715	+	0.989473i	$0.546227\pi$
$192$	1.00000	0.0721688
$193$	−3.70820	−0.266922	−0.133461	−	0.991054i	$-0.542609\pi$
$193$	−3.70820	−0.266922	−0.133461	+	0.991054i	$0.542609\pi$
$194$	−8.18034	−0.587314
$195$	0	0
$196$	14.3262	1.02330
$197$	2.94427	0.209771	0.104885	−	0.994484i	$-0.466552\pi$
$197$	2.94427	0.209771	0.104885	+	0.994484i	$0.466552\pi$
$198$	−0.854102	−0.0606984
$199$	−9.23607	−0.654727	−0.327364	−	0.944898i	$-0.606160\pi$
$199$	−9.23607	−0.654727	−0.327364	+	0.944898i	$0.606160\pi$
$200$	0	0
$201$	−1.23607	−0.0871855
$202$	0.291796	0.0205307
$203$	−35.5967	−2.49840
$204$	−5.70820	−0.399654
$205$	0	0
$206$	−14.0902	−0.981709
$207$	8.09017	0.562306
$208$	5.61803	0.389541
$209$	−6.05573	−0.418883
$210$	0	0
$211$	−2.43769	−0.167818	−0.0839089	−	0.996473i	$-0.526740\pi$
$211$	−2.43769	−0.167818	−0.0839089	+	0.996473i	$0.526740\pi$
$212$	2.61803	0.179807
$213$	4.47214	0.306426
$214$	2.00000	0.136717
$215$	0	0
$216$	−1.00000	−0.0680414
$217$	11.4164	0.774996
$218$	−11.7082	−0.792980
$219$	−8.00000	−0.540590
$220$	0	0
$221$	−32.0689	−2.15719
$222$	−0.618034	−0.0414797
$223$	−11.0557	−0.740346	−0.370173	−	0.928963i	$-0.620702\pi$
$223$	−11.0557	−0.740346	−0.370173	+	0.928963i	$0.620702\pi$
$224$	−4.61803	−0.308555
$225$	0	0
$226$	9.70820	0.645780
$227$	15.2361	1.01125	0.505627	−	0.862752i	$-0.331261\pi$
$227$	15.2361	1.01125	0.505627	+	0.862752i	$0.331261\pi$
$228$	−7.09017	−0.469558
$229$	−27.2361	−1.79981	−0.899905	−	0.436086i	$-0.856364\pi$
$229$	−27.2361	−1.79981	−0.899905	+	0.436086i	$0.856364\pi$
$230$	0	0
$231$	3.94427	0.259514
$232$	7.70820	0.506068
$233$	6.47214	0.424004	0.212002	−	0.977269i	$-0.432002\pi$
$233$	6.47214	0.424004	0.212002	+	0.977269i	$0.432002\pi$
$234$	−5.61803	−0.367262
$235$	0	0
$236$	−4.14590	−0.269875
$237$	3.52786	0.229159
$238$	26.3607	1.70871
$239$	−24.9443	−1.61351	−0.806755	−	0.590886i	$-0.798778\pi$
$239$	−24.9443	−1.61351	−0.806755	+	0.590886i	$0.798778\pi$
$240$	0	0
$241$	3.90983	0.251854	0.125927	−	0.992039i	$-0.459809\pi$
$241$	3.90983	0.251854	0.125927	+	0.992039i	$0.459809\pi$
$242$	10.2705	0.660213
$243$	1.00000	0.0641500
$244$	−1.70820	−0.109357
$245$	0	0
$246$	−2.61803	−0.166920
$247$	−39.8328	−2.53450
$248$	−2.47214	−0.156981
$249$	2.00000	0.126745
$250$	0	0
$251$	−24.0000	−1.51487	−0.757433	−	0.652913i	$-0.773547\pi$
$251$	−24.0000	−1.51487	−0.757433	+	0.652913i	$0.773547\pi$
$252$	4.61803	0.290909
$253$	6.90983	0.434417
$254$	14.4721	0.908063
$255$	0	0
$256$	1.00000	0.0625000
$257$	26.4721	1.65129	0.825643	−	0.564193i	$-0.190812\pi$
$257$	26.4721	1.65129	0.825643	+	0.564193i	$0.190812\pi$
$258$	5.70820	0.355377
$259$	2.85410	0.177345
$260$	0	0
$261$	−7.70820	−0.477126
$262$	4.67376	0.288746
$263$	9.67376	0.596510	0.298255	−	0.954486i	$-0.403595\pi$
$263$	9.67376	0.596510	0.298255	+	0.954486i	$0.403595\pi$
$264$	−0.854102	−0.0525663
$265$	0	0
$266$	32.7426	2.00758
$267$	−4.56231	−0.279209
$268$	−1.23607	−0.0755049
$269$	17.4164	1.06190	0.530949	−	0.847404i	$-0.321836\pi$
$269$	17.4164	1.06190	0.530949	+	0.847404i	$0.321836\pi$
$270$	0	0
$271$	17.4164	1.05797	0.528986	−	0.848631i	$-0.322573\pi$
$271$	17.4164	1.05797	0.528986	+	0.848631i	$0.322573\pi$
$272$	−5.70820	−0.346111
$273$	25.9443	1.57022
$274$	12.9443	0.781992
$275$	0	0
$276$	8.09017	0.486971
$277$	−28.4508	−1.70945	−0.854723	−	0.519084i	$-0.826273\pi$
$277$	−28.4508	−1.70945	−0.854723	+	0.519084i	$0.826273\pi$
$278$	0.381966	0.0229088
$279$	2.47214	0.148003
$280$	0	0
$281$	−13.5066	−0.805735	−0.402867	−	0.915258i	$-0.631986\pi$
$281$	−13.5066	−0.805735	−0.402867	+	0.915258i	$0.631986\pi$
$282$	−6.38197	−0.380041
$283$	−14.1803	−0.842934	−0.421467	−	0.906844i	$-0.638485\pi$
$283$	−14.1803	−0.842934	−0.421467	+	0.906844i	$0.638485\pi$
$284$	4.47214	0.265372
$285$	0	0
$286$	−4.79837	−0.283734
$287$	12.0902	0.713660
$288$	−1.00000	−0.0589256
$289$	15.5836	0.916682
$290$	0	0
$291$	8.18034	0.479540
$292$	−8.00000	−0.468165
$293$	3.79837	0.221903	0.110952	−	0.993826i	$-0.464610\pi$
$293$	3.79837	0.221903	0.110952	+	0.993826i	$0.464610\pi$
$294$	−14.3262	−0.835523
$295$	0	0
$296$	−0.618034	−0.0359225
$297$	0.854102	0.0495600
$298$	−17.4164	−1.00891
$299$	45.4508	2.62849
$300$	0	0
$301$	−26.3607	−1.51940
$302$	13.7082	0.788818
$303$	−0.291796	−0.0167632
$304$	−7.09017	−0.406649
$305$	0	0
$306$	5.70820	0.326316
$307$	16.1803	0.923461	0.461730	−	0.887020i	$-0.347229\pi$
$307$	16.1803	0.923461	0.461730	+	0.887020i	$0.347229\pi$
$308$	3.94427	0.224746
$309$	14.0902	0.801562
$310$	0	0
$311$	−8.94427	−0.507183	−0.253592	−	0.967311i	$-0.581612\pi$
$311$	−8.94427	−0.507183	−0.253592	+	0.967311i	$0.581612\pi$
$312$	−5.61803	−0.318059
$313$	13.7082	0.774833	0.387417	−	0.921905i	$-0.373367\pi$
$313$	13.7082	0.774833	0.387417	+	0.921905i	$0.373367\pi$
$314$	−10.9443	−0.617621
$315$	0	0
$316$	3.52786	0.198458
$317$	17.1459	0.963010	0.481505	−	0.876443i	$-0.340090\pi$
$317$	17.1459	0.963010	0.481505	+	0.876443i	$0.340090\pi$
$318$	−2.61803	−0.146812
$319$	−6.58359	−0.368610
$320$	0	0
$321$	−2.00000	−0.111629
$322$	−37.3607	−2.08203
$323$	40.4721	2.25193
$324$	1.00000	0.0555556
$325$	0	0
$326$	24.0000	1.32924
$327$	11.7082	0.647465
$328$	−2.61803	−0.144557
$329$	29.4721	1.62485
$330$	0	0
$331$	−2.47214	−0.135881	−0.0679404	−	0.997689i	$-0.521643\pi$
$331$	−2.47214	−0.135881	−0.0679404	+	0.997689i	$0.521643\pi$
$332$	2.00000	0.109764
$333$	0.618034	0.0338681
$334$	13.0902	0.716262
$335$	0	0
$336$	4.61803	0.251934
$337$	32.8328	1.78852	0.894259	−	0.447550i	$-0.147703\pi$
$337$	32.8328	1.78852	0.894259	+	0.447550i	$0.147703\pi$
$338$	−18.5623	−1.00966
$339$	−9.70820	−0.527277
$340$	0	0
$341$	2.11146	0.114342
$342$	7.09017	0.383392
$343$	33.8328	1.82680
$344$	5.70820	0.307766
$345$	0	0
$346$	−6.61803	−0.355788
$347$	8.18034	0.439144	0.219572	−	0.975596i	$-0.429534\pi$
$347$	8.18034	0.439144	0.219572	+	0.975596i	$0.429534\pi$
$348$	−7.70820	−0.413203
$349$	−20.0000	−1.07058	−0.535288	−	0.844670i	$-0.679797\pi$
$349$	−20.0000	−1.07058	−0.535288	+	0.844670i	$0.679797\pi$
$350$	0	0
$351$	5.61803	0.299868
$352$	−0.854102	−0.0455238
$353$	31.1246	1.65660	0.828298	−	0.560288i	$-0.189309\pi$
$353$	31.1246	1.65660	0.828298	+	0.560288i	$0.189309\pi$
$354$	4.14590	0.220352
$355$	0	0
$356$	−4.56231	−0.241802
$357$	−26.3607	−1.39516
$358$	20.7984	1.09923
$359$	9.41641	0.496979	0.248489	−	0.968635i	$-0.420066\pi$
$359$	9.41641	0.496979	0.248489	+	0.968635i	$0.420066\pi$
$360$	0	0
$361$	31.2705	1.64582
$362$	11.5279	0.605891
$363$	−10.2705	−0.539062
$364$	25.9443	1.35985
$365$	0	0
$366$	1.70820	0.0892892
$367$	−11.4164	−0.595932	−0.297966	−	0.954577i	$-0.596308\pi$
$367$	−11.4164	−0.595932	−0.297966	+	0.954577i	$0.596308\pi$
$368$	8.09017	0.421729
$369$	2.61803	0.136289
$370$	0	0
$371$	12.0902	0.627690
$372$	2.47214	0.128174
$373$	−3.67376	−0.190220	−0.0951101	−	0.995467i	$-0.530320\pi$
$373$	−3.67376	−0.190220	−0.0951101	+	0.995467i	$0.530320\pi$
$374$	4.87539	0.252100
$375$	0	0
$376$	−6.38197	−0.329125
$377$	−43.3050	−2.23032
$378$	−4.61803	−0.237526
$379$	−28.9230	−1.48567	−0.742837	−	0.669472i	$-0.766520\pi$
$379$	−28.9230	−1.48567	−0.742837	+	0.669472i	$0.766520\pi$
$380$	0	0
$381$	−14.4721	−0.741430
$382$	4.00000	0.204658
$383$	−2.03444	−0.103955	−0.0519776	−	0.998648i	$-0.516552\pi$
$383$	−2.03444	−0.103955	−0.0519776	+	0.998648i	$0.516552\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	3.70820	0.188743
$387$	−5.70820	−0.290164
$388$	8.18034	0.415294
$389$	32.5410	1.64990	0.824948	−	0.565209i	$-0.191205\pi$
$389$	32.5410	1.64990	0.824948	+	0.565209i	$0.191205\pi$
$390$	0	0
$391$	−46.1803	−2.33544
$392$	−14.3262	−0.723584
$393$	−4.67376	−0.235760
$394$	−2.94427	−0.148330
$395$	0	0
$396$	0.854102	0.0429202
$397$	7.67376	0.385135	0.192568	−	0.981284i	$-0.438319\pi$
$397$	7.67376	0.385135	0.192568	+	0.981284i	$0.438319\pi$
$398$	9.23607	0.462962
$399$	−32.7426	−1.63918
$400$	0	0
$401$	14.3262	0.715418	0.357709	−	0.933833i	$-0.383558\pi$
$401$	14.3262	0.715418	0.357709	+	0.933833i	$0.383558\pi$
$402$	1.23607	0.0616495
$403$	13.8885	0.691838
$404$	−0.291796	−0.0145174
$405$	0	0
$406$	35.5967	1.76664
$407$	0.527864	0.0261652
$408$	5.70820	0.282598
$409$	1.85410	0.0916794	0.0458397	−	0.998949i	$-0.485404\pi$
$409$	1.85410	0.0916794	0.0458397	+	0.998949i	$0.485404\pi$
$410$	0	0
$411$	−12.9443	−0.638494
$412$	14.0902	0.694173
$413$	−19.1459	−0.942108
$414$	−8.09017	−0.397610
$415$	0	0
$416$	−5.61803	−0.275447
$417$	−0.381966	−0.0187050
$418$	6.05573	0.296195
$419$	−17.8885	−0.873913	−0.436956	−	0.899483i	$-0.643944\pi$
$419$	−17.8885	−0.873913	−0.436956	+	0.899483i	$0.643944\pi$
$420$	0	0
$421$	15.1246	0.737128	0.368564	−	0.929602i	$-0.379849\pi$
$421$	15.1246	0.737128	0.368564	+	0.929602i	$0.379849\pi$
$422$	2.43769	0.118665
$423$	6.38197	0.310302
$424$	−2.61803	−0.127143
$425$	0	0
$426$	−4.47214	−0.216676
$427$	−7.88854	−0.381753
$428$	−2.00000	−0.0966736
$429$	4.79837	0.231668
$430$	0	0
$431$	12.7639	0.614817	0.307408	−	0.951578i	$-0.400538\pi$
$431$	12.7639	0.614817	0.307408	+	0.951578i	$0.400538\pi$
$432$	1.00000	0.0481125
$433$	−6.36068	−0.305675	−0.152837	−	0.988251i	$-0.548841\pi$
$433$	−6.36068	−0.305675	−0.152837	+	0.988251i	$0.548841\pi$
$434$	−11.4164	−0.548005
$435$	0	0
$436$	11.7082	0.560721
$437$	−57.3607	−2.74393
$438$	8.00000	0.382255
$439$	−1.34752	−0.0643138	−0.0321569	−	0.999483i	$-0.510238\pi$
$439$	−1.34752	−0.0643138	−0.0321569	+	0.999483i	$0.510238\pi$
$440$	0	0
$441$	14.3262	0.682202
$442$	32.0689	1.52536
$443$	27.1246	1.28873	0.644365	−	0.764718i	$-0.277122\pi$
$443$	27.1246	1.28873	0.644365	+	0.764718i	$0.277122\pi$
$444$	0.618034	0.0293306
$445$	0	0
$446$	11.0557	0.523504
$447$	17.4164	0.823768
$448$	4.61803	0.218182
$449$	−3.56231	−0.168116	−0.0840578	−	0.996461i	$-0.526788\pi$
$449$	−3.56231	−0.168116	−0.0840578	+	0.996461i	$0.526788\pi$
$450$	0	0
$451$	2.23607	0.105292
$452$	−9.70820	−0.456636
$453$	−13.7082	−0.644068
$454$	−15.2361	−0.715064
$455$	0	0
$456$	7.09017	0.332028
$457$	−1.88854	−0.0883424	−0.0441712	−	0.999024i	$-0.514065\pi$
$457$	−1.88854	−0.0883424	−0.0441712	+	0.999024i	$0.514065\pi$
$458$	27.2361	1.27266
$459$	−5.70820	−0.266436
$460$	0	0
$461$	−29.5967	−1.37846	−0.689229	−	0.724544i	$-0.742051\pi$
$461$	−29.5967	−1.37846	−0.689229	+	0.724544i	$0.742051\pi$
$462$	−3.94427	−0.183504
$463$	−32.9443	−1.53105	−0.765525	−	0.643406i	$-0.777521\pi$
$463$	−32.9443	−1.53105	−0.765525	+	0.643406i	$0.777521\pi$
$464$	−7.70820	−0.357844
$465$	0	0
$466$	−6.47214	−0.299816
$467$	16.7639	0.775742	0.387871	−	0.921714i	$-0.373211\pi$
$467$	16.7639	0.775742	0.387871	+	0.921714i	$0.373211\pi$
$468$	5.61803	0.259694
$469$	−5.70820	−0.263580
$470$	0	0
$471$	10.9443	0.504285
$472$	4.14590	0.190830
$473$	−4.87539	−0.224171
$474$	−3.52786	−0.162040
$475$	0	0
$476$	−26.3607	−1.20824
$477$	2.61803	0.119872
$478$	24.9443	1.14092
$479$	31.1246	1.42212	0.711060	−	0.703131i	$-0.248215\pi$
$479$	31.1246	1.42212	0.711060	+	0.703131i	$0.248215\pi$
$480$	0	0
$481$	3.47214	0.158316
$482$	−3.90983	−0.178088
$483$	37.3607	1.69997
$484$	−10.2705	−0.466841
$485$	0	0
$486$	−1.00000	−0.0453609
$487$	11.7984	0.534635	0.267318	−	0.963608i	$-0.413863\pi$
$487$	11.7984	0.534635	0.267318	+	0.963608i	$0.413863\pi$
$488$	1.70820	0.0773268
$489$	−24.0000	−1.08532
$490$	0	0
$491$	−18.0344	−0.813883	−0.406941	−	0.913454i	$-0.633405\pi$
$491$	−18.0344	−0.813883	−0.406941	+	0.913454i	$0.633405\pi$
$492$	2.61803	0.118030
$493$	44.0000	1.98166
$494$	39.8328	1.79216
$495$	0	0
$496$	2.47214	0.111002
$497$	20.6525	0.926390
$498$	−2.00000	−0.0896221
$499$	−7.61803	−0.341030	−0.170515	−	0.985355i	$-0.554543\pi$
$499$	−7.61803	−0.341030	−0.170515	+	0.985355i	$0.554543\pi$
$500$	0	0
$501$	−13.0902	−0.584826
$502$	24.0000	1.07117
$503$	−36.8541	−1.64324	−0.821622	−	0.570033i	$-0.806930\pi$
$503$	−36.8541	−1.64324	−0.821622	+	0.570033i	$0.806930\pi$
$504$	−4.61803	−0.205704
$505$	0	0
$506$	−6.90983	−0.307179
$507$	18.5623	0.824381
$508$	−14.4721	−0.642097
$509$	25.7082	1.13950	0.569748	−	0.821819i	$-0.307041\pi$
$509$	25.7082	1.13950	0.569748	+	0.821819i	$0.307041\pi$
$510$	0	0
$511$	−36.9443	−1.63432
$512$	−1.00000	−0.0441942
$513$	−7.09017	−0.313039
$514$	−26.4721	−1.16764
$515$	0	0
$516$	−5.70820	−0.251290
$517$	5.45085	0.239728
$518$	−2.85410	−0.125402
$519$	6.61803	0.290499
$520$	0	0
$521$	−10.0902	−0.442058	−0.221029	−	0.975267i	$-0.570942\pi$
$521$	−10.0902	−0.442058	−0.221029	+	0.975267i	$0.570942\pi$
$522$	7.70820	0.337379
$523$	−12.3607	−0.540495	−0.270247	−	0.962791i	$-0.587105\pi$
$523$	−12.3607	−0.540495	−0.270247	+	0.962791i	$0.587105\pi$
$524$	−4.67376	−0.204174
$525$	0	0
$526$	−9.67376	−0.421796
$527$	−14.1115	−0.614705
$528$	0.854102	0.0371700
$529$	42.4508	1.84569
$530$	0	0
$531$	−4.14590	−0.179917
$532$	−32.7426	−1.41957
$533$	14.7082	0.637083
$534$	4.56231	0.197430
$535$	0	0
$536$	1.23607	0.0533900
$537$	−20.7984	−0.897516
$538$	−17.4164	−0.750875
$539$	12.2361	0.527045
$540$	0	0
$541$	13.4164	0.576816	0.288408	−	0.957508i	$-0.406874\pi$
$541$	13.4164	0.576816	0.288408	+	0.957508i	$0.406874\pi$
$542$	−17.4164	−0.748099
$543$	−11.5279	−0.494708
$544$	5.70820	0.244737
$545$	0	0
$546$	−25.9443	−1.11031
$547$	−5.23607	−0.223878	−0.111939	−	0.993715i	$-0.535706\pi$
$547$	−5.23607	−0.223878	−0.111939	+	0.993715i	$0.535706\pi$
$548$	−12.9443	−0.552952
$549$	−1.70820	−0.0729044
$550$	0	0
$551$	54.6525	2.32827
$552$	−8.09017	−0.344340
$553$	16.2918	0.692798
$554$	28.4508	1.20876
$555$	0	0
$556$	−0.381966	−0.0161990
$557$	−42.4508	−1.79870	−0.899350	−	0.437229i	$-0.855960\pi$
$557$	−42.4508	−1.79870	−0.899350	+	0.437229i	$0.855960\pi$
$558$	−2.47214	−0.104654
$559$	−32.0689	−1.35637
$560$	0	0
$561$	−4.87539	−0.205839
$562$	13.5066	0.569741
$563$	−10.9443	−0.461246	−0.230623	−	0.973043i	$-0.574076\pi$
$563$	−10.9443	−0.461246	−0.230623	+	0.973043i	$0.574076\pi$
$564$	6.38197	0.268729
$565$	0	0
$566$	14.1803	0.596044
$567$	4.61803	0.193939
$568$	−4.47214	−0.187647
$569$	−36.9230	−1.54789	−0.773946	−	0.633252i	$-0.781720\pi$
$569$	−36.9230	−1.54789	−0.773946	+	0.633252i	$0.781720\pi$
$570$	0	0
$571$	−29.2705	−1.22493	−0.612466	−	0.790497i	$-0.709823\pi$
$571$	−29.2705	−1.22493	−0.612466	+	0.790497i	$0.709823\pi$
$572$	4.79837	0.200630
$573$	−4.00000	−0.167102
$574$	−12.0902	−0.504634
$575$	0	0
$576$	1.00000	0.0416667
$577$	4.76393	0.198325	0.0991625	−	0.995071i	$-0.468384\pi$
$577$	4.76393	0.198325	0.0991625	+	0.995071i	$0.468384\pi$
$578$	−15.5836	−0.648192
$579$	−3.70820	−0.154108
$580$	0	0
$581$	9.23607	0.383177
$582$	−8.18034	−0.339086
$583$	2.23607	0.0926085
$584$	8.00000	0.331042
$585$	0	0
$586$	−3.79837	−0.156909
$587$	20.7639	0.857019	0.428510	−	0.903537i	$-0.359039\pi$
$587$	20.7639	0.857019	0.428510	+	0.903537i	$0.359039\pi$
$588$	14.3262	0.590804
$589$	−17.5279	−0.722223
$590$	0	0
$591$	2.94427	0.121111
$592$	0.618034	0.0254010
$593$	−31.3050	−1.28554	−0.642770	−	0.766059i	$-0.722215\pi$
$593$	−31.3050	−1.28554	−0.642770	+	0.766059i	$0.722215\pi$
$594$	−0.854102	−0.0350442
$595$	0	0
$596$	17.4164	0.713404
$597$	−9.23607	−0.378007
$598$	−45.4508	−1.85862
$599$	−11.2361	−0.459093	−0.229547	−	0.973298i	$-0.573724\pi$
$599$	−11.2361	−0.459093	−0.229547	+	0.973298i	$0.573724\pi$
$600$	0	0
$601$	30.5623	1.24666	0.623331	−	0.781958i	$-0.285779\pi$
$601$	30.5623	1.24666	0.623331	+	0.781958i	$0.285779\pi$
$602$	26.3607	1.07438
$603$	−1.23607	−0.0503366
$604$	−13.7082	−0.557779
$605$	0	0
$606$	0.291796	0.0118534
$607$	36.9787	1.50092	0.750460	−	0.660916i	$-0.229832\pi$
$607$	36.9787	1.50092	0.750460	+	0.660916i	$0.229832\pi$
$608$	7.09017	0.287544
$609$	−35.5967	−1.44245
$610$	0	0
$611$	35.8541	1.45050
$612$	−5.70820	−0.230740
$613$	10.7426	0.433891	0.216946	−	0.976184i	$-0.430391\pi$
$613$	10.7426	0.433891	0.216946	+	0.976184i	$0.430391\pi$
$614$	−16.1803	−0.652985
$615$	0	0
$616$	−3.94427	−0.158919
$617$	14.4721	0.582626	0.291313	−	0.956628i	$-0.405908\pi$
$617$	14.4721	0.582626	0.291313	+	0.956628i	$0.405908\pi$
$618$	−14.0902	−0.566790
$619$	−5.14590	−0.206831	−0.103416	−	0.994638i	$-0.532977\pi$
$619$	−5.14590	−0.206831	−0.103416	+	0.994638i	$0.532977\pi$
$620$	0	0
$621$	8.09017	0.324647
$622$	8.94427	0.358633
$623$	−21.0689	−0.844107
$624$	5.61803	0.224901
$625$	0	0
$626$	−13.7082	−0.547890
$627$	−6.05573	−0.241842
$628$	10.9443	0.436724
$629$	−3.52786	−0.140665
$630$	0	0
$631$	20.2918	0.807804	0.403902	−	0.914802i	$-0.367654\pi$
$631$	20.2918	0.807804	0.403902	+	0.914802i	$0.367654\pi$
$632$	−3.52786	−0.140331
$633$	−2.43769	−0.0968896
$634$	−17.1459	−0.680951
$635$	0	0
$636$	2.61803	0.103812
$637$	80.4853	3.18894
$638$	6.58359	0.260647
$639$	4.47214	0.176915
$640$	0	0
$641$	−35.8541	−1.41615	−0.708076	−	0.706136i	$-0.750437\pi$
$641$	−35.8541	−1.41615	−0.708076	+	0.706136i	$0.750437\pi$
$642$	2.00000	0.0789337
$643$	−32.9443	−1.29920	−0.649598	−	0.760278i	$-0.725063\pi$
$643$	−32.9443	−1.29920	−0.649598	+	0.760278i	$0.725063\pi$
$644$	37.3607	1.47222
$645$	0	0
$646$	−40.4721	−1.59235
$647$	8.14590	0.320248	0.160124	−	0.987097i	$-0.448811\pi$
$647$	8.14590	0.320248	0.160124	+	0.987097i	$0.448811\pi$
$648$	−1.00000	−0.0392837
$649$	−3.54102	−0.138997
$650$	0	0
$651$	11.4164	0.447444
$652$	−24.0000	−0.939913
$653$	18.8541	0.737818	0.368909	−	0.929466i	$-0.379731\pi$
$653$	18.8541	0.737818	0.368909	+	0.929466i	$0.379731\pi$
$654$	−11.7082	−0.457827
$655$	0	0
$656$	2.61803	0.102217
$657$	−8.00000	−0.312110
$658$	−29.4721	−1.14894
$659$	−23.5066	−0.915686	−0.457843	−	0.889033i	$-0.651378\pi$
$659$	−23.5066	−0.915686	−0.457843	+	0.889033i	$0.651378\pi$
$660$	0	0
$661$	−41.1246	−1.59956	−0.799781	−	0.600292i	$-0.795051\pi$
$661$	−41.1246	−1.59956	−0.799781	+	0.600292i	$0.795051\pi$
$662$	2.47214	0.0960823
$663$	−32.0689	−1.24545
$664$	−2.00000	−0.0776151
$665$	0	0
$666$	−0.618034	−0.0239483
$667$	−62.3607	−2.41462
$668$	−13.0902	−0.506474
$669$	−11.0557	−0.427439
$670$	0	0
$671$	−1.45898	−0.0563233
$672$	−4.61803	−0.178145
$673$	−18.4721	−0.712049	−0.356024	−	0.934477i	$-0.615868\pi$
$673$	−18.4721	−0.712049	−0.356024	+	0.934477i	$0.615868\pi$
$674$	−32.8328	−1.26467
$675$	0	0
$676$	18.5623	0.713935
$677$	17.7426	0.681905	0.340953	−	0.940080i	$-0.389250\pi$
$677$	17.7426	0.681905	0.340953	+	0.940080i	$0.389250\pi$
$678$	9.70820	0.372841
$679$	37.7771	1.44975
$680$	0	0
$681$	15.2361	0.583847
$682$	−2.11146	−0.0808518
$683$	5.88854	0.225319	0.112659	−	0.993634i	$-0.464063\pi$
$683$	5.88854	0.225319	0.112659	+	0.993634i	$0.464063\pi$
$684$	−7.09017	−0.271099
$685$	0	0
$686$	−33.8328	−1.29174
$687$	−27.2361	−1.03912
$688$	−5.70820	−0.217623
$689$	14.7082	0.560338
$690$	0	0
$691$	1.88854	0.0718436	0.0359218	−	0.999355i	$-0.488563\pi$
$691$	1.88854	0.0718436	0.0359218	+	0.999355i	$0.488563\pi$
$692$	6.61803	0.251580
$693$	3.94427	0.149831
$694$	−8.18034	−0.310521
$695$	0	0
$696$	7.70820	0.292179
$697$	−14.9443	−0.566055
$698$	20.0000	0.757011
$699$	6.47214	0.244799
$700$	0	0
$701$	−4.29180	−0.162099	−0.0810495	−	0.996710i	$-0.525827\pi$
$701$	−4.29180	−0.162099	−0.0810495	+	0.996710i	$0.525827\pi$
$702$	−5.61803	−0.212039
$703$	−4.38197	−0.165269
$704$	0.854102	0.0321902
$705$	0	0
$706$	−31.1246	−1.17139
$707$	−1.34752	−0.0506789
$708$	−4.14590	−0.155812
$709$	−12.6525	−0.475174	−0.237587	−	0.971366i	$-0.576356\pi$
$709$	−12.6525	−0.475174	−0.237587	+	0.971366i	$0.576356\pi$
$710$	0	0
$711$	3.52786	0.132305
$712$	4.56231	0.170980
$713$	20.0000	0.749006
$714$	26.3607	0.986524
$715$	0	0
$716$	−20.7984	−0.777272
$717$	−24.9443	−0.931561
$718$	−9.41641	−0.351417
$719$	47.8885	1.78594	0.892971	−	0.450115i	$-0.148617\pi$
$719$	47.8885	1.78594	0.892971	+	0.450115i	$0.148617\pi$
$720$	0	0
$721$	65.0689	2.42329
$722$	−31.2705	−1.16377
$723$	3.90983	0.145408
$724$	−11.5279	−0.428430
$725$	0	0
$726$	10.2705	0.381174
$727$	−28.3262	−1.05056	−0.525281	−	0.850929i	$-0.676040\pi$
$727$	−28.3262	−1.05056	−0.525281	+	0.850929i	$0.676040\pi$
$728$	−25.9443	−0.961559
$729$	1.00000	0.0370370
$730$	0	0
$731$	32.5836	1.20515
$732$	−1.70820	−0.0631370
$733$	−46.9230	−1.73314	−0.866570	−	0.499056i	$-0.833680\pi$
$733$	−46.9230	−1.73314	−0.866570	+	0.499056i	$0.833680\pi$
$734$	11.4164	0.421387
$735$	0	0
$736$	−8.09017	−0.298208
$737$	−1.05573	−0.0388882
$738$	−2.61803	−0.0963712
$739$	7.67376	0.282284	0.141142	−	0.989989i	$-0.454923\pi$
$739$	7.67376	0.282284	0.141142	+	0.989989i	$0.454923\pi$
$740$	0	0
$741$	−39.8328	−1.46330
$742$	−12.0902	−0.443844
$743$	−44.8541	−1.64554	−0.822769	−	0.568376i	$-0.807572\pi$
$743$	−44.8541	−1.64554	−0.822769	+	0.568376i	$0.807572\pi$
$744$	−2.47214	−0.0906329
$745$	0	0
$746$	3.67376	0.134506
$747$	2.00000	0.0731762
$748$	−4.87539	−0.178262
$749$	−9.23607	−0.337479
$750$	0	0
$751$	54.0689	1.97300	0.986501	−	0.163756i	$-0.0523611\pi$
$751$	54.0689	1.97300	0.986501	+	0.163756i	$0.0523611\pi$
$752$	6.38197	0.232726
$753$	−24.0000	−0.874609
$754$	43.3050	1.57707
$755$	0	0
$756$	4.61803	0.167956
$757$	27.3262	0.993189	0.496595	−	0.867983i	$-0.334584\pi$
$757$	27.3262	0.993189	0.496595	+	0.867983i	$0.334584\pi$
$758$	28.9230	1.05053
$759$	6.90983	0.250811
$760$	0	0
$761$	25.9656	0.941251	0.470625	−	0.882333i	$-0.344028\pi$
$761$	25.9656	0.941251	0.470625	+	0.882333i	$0.344028\pi$
$762$	14.4721	0.524270
$763$	54.0689	1.95743
$764$	−4.00000	−0.144715
$765$	0	0
$766$	2.03444	0.0735074
$767$	−23.2918	−0.841018
$768$	1.00000	0.0360844
$769$	27.3262	0.985409	0.492705	−	0.870197i	$-0.336008\pi$
$769$	27.3262	0.985409	0.492705	+	0.870197i	$0.336008\pi$
$770$	0	0
$771$	26.4721	0.953371
$772$	−3.70820	−0.133461
$773$	−9.05573	−0.325712	−0.162856	−	0.986650i	$-0.552071\pi$
$773$	−9.05573	−0.325712	−0.162856	+	0.986650i	$0.552071\pi$
$774$	5.70820	0.205177
$775$	0	0
$776$	−8.18034	−0.293657
$777$	2.85410	0.102390
$778$	−32.5410	−1.16665
$779$	−18.5623	−0.665064
$780$	0	0
$781$	3.81966	0.136678
$782$	46.1803	1.65141
$783$	−7.70820	−0.275469
$784$	14.3262	0.511651
$785$	0	0
$786$	4.67376	0.166708
$787$	−37.4164	−1.33375	−0.666875	−	0.745169i	$-0.732369\pi$
$787$	−37.4164	−1.33375	−0.666875	+	0.745169i	$0.732369\pi$
$788$	2.94427	0.104885
$789$	9.67376	0.344395
$790$	0	0
$791$	−44.8328	−1.59407
$792$	−0.854102	−0.0303492
$793$	−9.59675	−0.340791
$794$	−7.67376	−0.272332
$795$	0	0
$796$	−9.23607	−0.327364
$797$	48.8673	1.73097	0.865484	−	0.500937i	$-0.167011\pi$
$797$	48.8673	1.73097	0.865484	+	0.500937i	$0.167011\pi$
$798$	32.7426	1.15908
$799$	−36.4296	−1.28879
$800$	0	0
$801$	−4.56231	−0.161201
$802$	−14.3262	−0.505877
$803$	−6.83282	−0.241125
$804$	−1.23607	−0.0435928
$805$	0	0
$806$	−13.8885	−0.489203
$807$	17.4164	0.613087
$808$	0.291796	0.0102653
$809$	30.6738	1.07843	0.539216	−	0.842167i	$-0.318721\pi$
$809$	30.6738	1.07843	0.539216	+	0.842167i	$0.318721\pi$
$810$	0	0
$811$	30.2705	1.06294	0.531471	−	0.847077i	$-0.321640\pi$
$811$	30.2705	1.06294	0.531471	+	0.847077i	$0.321640\pi$
$812$	−35.5967	−1.24920
$813$	17.4164	0.610820
$814$	−0.527864	−0.0185016
$815$	0	0
$816$	−5.70820	−0.199827
$817$	40.4721	1.41594
$818$	−1.85410	−0.0648272
$819$	25.9443	0.906566
$820$	0	0
$821$	5.88854	0.205512	0.102756	−	0.994707i	$-0.467234\pi$
$821$	5.88854	0.205512	0.102756	+	0.994707i	$0.467234\pi$
$822$	12.9443	0.451483
$823$	29.9230	1.04305	0.521525	−	0.853236i	$-0.325363\pi$
$823$	29.9230	1.04305	0.521525	+	0.853236i	$0.325363\pi$
$824$	−14.0902	−0.490854
$825$	0	0
$826$	19.1459	0.666171
$827$	28.1803	0.979926	0.489963	−	0.871743i	$-0.337010\pi$
$827$	28.1803	0.979926	0.489963	+	0.871743i	$0.337010\pi$
$828$	8.09017	0.281153
$829$	50.3607	1.74910	0.874549	−	0.484937i	$-0.161157\pi$
$829$	50.3607	1.74910	0.874549	+	0.484937i	$0.161157\pi$
$830$	0	0
$831$	−28.4508	−0.986949
$832$	5.61803	0.194770
$833$	−81.7771	−2.83341
$834$	0.381966	0.0132264
$835$	0	0
$836$	−6.05573	−0.209442
$837$	2.47214	0.0854495
$838$	17.8885	0.617949
$839$	54.6525	1.88681	0.943407	−	0.331639i	$-0.107601\pi$
$839$	54.6525	1.88681	0.943407	+	0.331639i	$0.107601\pi$
$840$	0	0
$841$	30.4164	1.04884
$842$	−15.1246	−0.521229
$843$	−13.5066	−0.465191
$844$	−2.43769	−0.0839089
$845$	0	0
$846$	−6.38197	−0.219417
$847$	−47.4296	−1.62970
$848$	2.61803	0.0899037
$849$	−14.1803	−0.486668
$850$	0	0
$851$	5.00000	0.171398
$852$	4.47214	0.153213
$853$	14.7295	0.504328	0.252164	−	0.967684i	$-0.418858\pi$
$853$	14.7295	0.504328	0.252164	+	0.967684i	$0.418858\pi$
$854$	7.88854	0.269940
$855$	0	0
$856$	2.00000	0.0683586
$857$	−9.70820	−0.331626	−0.165813	−	0.986157i	$-0.553025\pi$
$857$	−9.70820	−0.331626	−0.165813	+	0.986157i	$0.553025\pi$
$858$	−4.79837	−0.163814
$859$	28.0344	0.956523	0.478261	−	0.878218i	$-0.341267\pi$
$859$	28.0344	0.956523	0.478261	+	0.878218i	$0.341267\pi$
$860$	0	0
$861$	12.0902	0.412032
$862$	−12.7639	−0.434741
$863$	−18.0344	−0.613900	−0.306950	−	0.951726i	$-0.599308\pi$
$863$	−18.0344	−0.613900	−0.306950	+	0.951726i	$0.599308\pi$
$864$	−1.00000	−0.0340207
$865$	0	0
$866$	6.36068	0.216145
$867$	15.5836	0.529247
$868$	11.4164	0.387498
$869$	3.01316	0.102214
$870$	0	0
$871$	−6.94427	−0.235298
$872$	−11.7082	−0.396490
$873$	8.18034	0.276863
$874$	57.3607	1.94025
$875$	0	0
$876$	−8.00000	−0.270295
$877$	37.9787	1.28245	0.641225	−	0.767353i	$-0.278427\pi$
$877$	37.9787	1.28245	0.641225	+	0.767353i	$0.278427\pi$
$878$	1.34752	0.0454767
$879$	3.79837	0.128116
$880$	0	0
$881$	53.1591	1.79097	0.895487	−	0.445088i	$-0.146827\pi$
$881$	53.1591	1.79097	0.895487	+	0.445088i	$0.146827\pi$
$882$	−14.3262	−0.482390
$883$	19.4164	0.653414	0.326707	−	0.945126i	$-0.394061\pi$
$883$	19.4164	0.653414	0.326707	+	0.945126i	$0.394061\pi$
$884$	−32.0689	−1.07859
$885$	0	0
$886$	−27.1246	−0.911269
$887$	2.03444	0.0683099	0.0341549	−	0.999417i	$-0.489126\pi$
$887$	2.03444	0.0683099	0.0341549	+	0.999417i	$0.489126\pi$
$888$	−0.618034	−0.0207399
$889$	−66.8328	−2.24150
$890$	0	0
$891$	0.854102	0.0286135
$892$	−11.0557	−0.370173
$893$	−45.2492	−1.51421
$894$	−17.4164	−0.582492
$895$	0	0
$896$	−4.61803	−0.154278
$897$	45.4508	1.51756
$898$	3.56231	0.118876
$899$	−19.0557	−0.635544
$900$	0	0
$901$	−14.9443	−0.497866
$902$	−2.23607	−0.0744529
$903$	−26.3607	−0.877228
$904$	9.70820	0.322890
$905$	0	0
$906$	13.7082	0.455425
$907$	14.6525	0.486527	0.243264	−	0.969960i	$-0.421782\pi$
$907$	14.6525	0.486527	0.243264	+	0.969960i	$0.421782\pi$
$908$	15.2361	0.505627
$909$	−0.291796	−0.00967826
$910$	0	0
$911$	−46.9443	−1.55533	−0.777667	−	0.628677i	$-0.783597\pi$
$911$	−46.9443	−1.55533	−0.777667	+	0.628677i	$0.783597\pi$
$912$	−7.09017	−0.234779
$913$	1.70820	0.0565333
$914$	1.88854	0.0624675
$915$	0	0
$916$	−27.2361	−0.899905
$917$	−21.5836	−0.712753
$918$	5.70820	0.188399
$919$	41.2361	1.36025	0.680126	−	0.733095i	$-0.261925\pi$
$919$	41.2361	1.36025	0.680126	+	0.733095i	$0.261925\pi$
$920$	0	0
$921$	16.1803	0.533160
$922$	29.5967	0.974717
$923$	25.1246	0.826987
$924$	3.94427	0.129757
$925$	0	0
$926$	32.9443	1.08262
$927$	14.0902	0.462782
$928$	7.70820	0.253034
$929$	−58.8115	−1.92954	−0.964772	−	0.263088i	$-0.915259\pi$
$929$	−58.8115	−1.92954	−0.964772	+	0.263088i	$0.915259\pi$
$930$	0	0
$931$	−101.575	−3.32900
$932$	6.47214	0.212002
$933$	−8.94427	−0.292822
$934$	−16.7639	−0.548533
$935$	0	0
$936$	−5.61803	−0.183631
$937$	−24.6525	−0.805361	−0.402681	−	0.915341i	$-0.631921\pi$
$937$	−24.6525	−0.805361	−0.402681	+	0.915341i	$0.631921\pi$
$938$	5.70820	0.186379
$939$	13.7082	0.447350
$940$	0	0
$941$	4.18034	0.136275	0.0681376	−	0.997676i	$-0.478294\pi$
$941$	4.18034	0.136275	0.0681376	+	0.997676i	$0.478294\pi$
$942$	−10.9443	−0.356584
$943$	21.1803	0.689727
$944$	−4.14590	−0.134937
$945$	0	0
$946$	4.87539	0.158513
$947$	−21.8885	−0.711282	−0.355641	−	0.934623i	$-0.615737\pi$
$947$	−21.8885	−0.711282	−0.355641	+	0.934623i	$0.615737\pi$
$948$	3.52786	0.114580
$949$	−44.9443	−1.45895
$950$	0	0
$951$	17.1459	0.555994
$952$	26.3607	0.854355
$953$	44.5410	1.44283	0.721413	−	0.692506i	$-0.243493\pi$
$953$	44.5410	1.44283	0.721413	+	0.692506i	$0.243493\pi$
$954$	−2.61803	−0.0847620
$955$	0	0
$956$	−24.9443	−0.806755
$957$	−6.58359	−0.212817
$958$	−31.1246	−1.00559
$959$	−59.7771	−1.93030
$960$	0	0
$961$	−24.8885	−0.802856
$962$	−3.47214	−0.111946
$963$	−2.00000	−0.0644491
$964$	3.90983	0.125927
$965$	0	0
$966$	−37.3607	−1.20206
$967$	−1.68692	−0.0542476	−0.0271238	−	0.999632i	$-0.508635\pi$
$967$	−1.68692	−0.0542476	−0.0271238	+	0.999632i	$0.508635\pi$
$968$	10.2705	0.330107
$969$	40.4721	1.30015
$970$	0	0
$971$	−40.2705	−1.29234	−0.646171	−	0.763193i	$-0.723631\pi$
$971$	−40.2705	−1.29234	−0.646171	+	0.763193i	$0.723631\pi$
$972$	1.00000	0.0320750
$973$	−1.76393	−0.0565491
$974$	−11.7984	−0.378044
$975$	0	0
$976$	−1.70820	−0.0546783
$977$	−53.3050	−1.70538	−0.852688	−	0.522420i	$-0.825029\pi$
$977$	−53.3050	−1.70538	−0.852688	+	0.522420i	$0.825029\pi$
$978$	24.0000	0.767435
$979$	−3.89667	−0.124538
$980$	0	0
$981$	11.7082	0.373814
$982$	18.0344	0.575502
$983$	29.2148	0.931807	0.465903	−	0.884836i	$-0.345729\pi$
$983$	29.2148	0.931807	0.465903	+	0.884836i	$0.345729\pi$
$984$	−2.61803	−0.0834599
$985$	0	0
$986$	−44.0000	−1.40125
$987$	29.4721	0.938108
$988$	−39.8328	−1.26725
$989$	−46.1803	−1.46845
$990$	0	0
$991$	51.8885	1.64829	0.824147	−	0.566376i	$-0.191655\pi$
$991$	51.8885	1.64829	0.824147	+	0.566376i	$0.191655\pi$
$992$	−2.47214	−0.0784904
$993$	−2.47214	−0.0784509
$994$	−20.6525	−0.655057
$995$	0	0
$996$	2.00000	0.0633724
$997$	−7.09017	−0.224548	−0.112274	−	0.993677i	$-0.535813\pi$
$997$	−7.09017	−0.224548	−0.112274	+	0.993677i	$0.535813\pi$
$998$	7.61803	0.241145
$999$	0.618034	0.0195537

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.a.d.1.2	✓	2
3.2	odd	2		2250.2.a.p.1.2		2
4.3	odd	2		6000.2.a.a.1.1		2
5.2	odd	4		750.2.c.a.499.2		4
5.3	odd	4		750.2.c.a.499.3		4
5.4	even	2		750.2.a.e.1.1	yes	2
15.2	even	4		2250.2.c.g.1999.4		4
15.8	even	4		2250.2.c.g.1999.1		4
15.14	odd	2		2250.2.a.a.1.1		2
20.3	even	4		6000.2.f.k.1249.2		4
20.7	even	4		6000.2.f.k.1249.3		4
20.19	odd	2		6000.2.a.bb.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
750.2.a.d.1.2	✓	2	1.1	even	1	trivial
750.2.a.e.1.1	yes	2	5.4	even	2
750.2.c.a.499.2		4	5.2	odd	4
750.2.c.a.499.3		4	5.3	odd	4
2250.2.a.a.1.1		2	15.14	odd	2
2250.2.a.p.1.2		2	3.2	odd	2
2250.2.c.g.1999.1		4	15.8	even	4
2250.2.c.g.1999.4		4	15.2	even	4
6000.2.a.a.1.1		2	4.3	odd	2
6000.2.a.bb.1.2		2	20.19	odd	2
6000.2.f.k.1249.2		4	20.3	even	4
6000.2.f.k.1249.3		4	20.7	even	4

Overview	Random
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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:	\( N \)	\(=\)	\( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	750.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +4.61803 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +4.61803 q^{7} -1.00000 q^{8} +1.00000 q^{9} +0.854102 q^{11} +1.00000 q^{12} +5.61803 q^{13} -4.61803 q^{14} +1.00000 q^{16} -5.70820 q^{17} -1.00000 q^{18} -7.09017 q^{19} +4.61803 q^{21} -0.854102 q^{22} +8.09017 q^{23} -1.00000 q^{24} -5.61803 q^{26} +1.00000 q^{27} +4.61803 q^{28} -7.70820 q^{29} +2.47214 q^{31} -1.00000 q^{32} +0.854102 q^{33} +5.70820 q^{34} +1.00000 q^{36} +0.618034 q^{37} +7.09017 q^{38} +5.61803 q^{39} +2.61803 q^{41} -4.61803 q^{42} -5.70820 q^{43} +0.854102 q^{44} -8.09017 q^{46} +6.38197 q^{47} +1.00000 q^{48} +14.3262 q^{49} -5.70820 q^{51} +5.61803 q^{52} +2.61803 q^{53} -1.00000 q^{54} -4.61803 q^{56} -7.09017 q^{57} +7.70820 q^{58} -4.14590 q^{59} -1.70820 q^{61} -2.47214 q^{62} +4.61803 q^{63} +1.00000 q^{64} -0.854102 q^{66} -1.23607 q^{67} -5.70820 q^{68} +8.09017 q^{69} +4.47214 q^{71} -1.00000 q^{72} -8.00000 q^{73} -0.618034 q^{74} -7.09017 q^{76} +3.94427 q^{77} -5.61803 q^{78} +3.52786 q^{79} +1.00000 q^{81} -2.61803 q^{82} +2.00000 q^{83} +4.61803 q^{84} +5.70820 q^{86} -7.70820 q^{87} -0.854102 q^{88} -4.56231 q^{89} +25.9443 q^{91} +8.09017 q^{92} +2.47214 q^{93} -6.38197 q^{94} -1.00000 q^{96} +8.18034 q^{97} -14.3262 q^{98} +0.854102 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{6} + 7 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^6 + 7 * q^7 - 2 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{6} + 7 q^{7} - 2 q^{8} + 2 q^{9} - 5 q^{11} + 2 q^{12} + 9 q^{13} - 7 q^{14} + 2 q^{16} + 2 q^{17} - 2 q^{18} - 3 q^{19} + 7 q^{21} + 5 q^{22} + 5 q^{23} - 2 q^{24} - 9 q^{26} + 2 q^{27} + 7 q^{28} - 2 q^{29} - 4 q^{31} - 2 q^{32} - 5 q^{33} - 2 q^{34} + 2 q^{36} - q^{37} + 3 q^{38} + 9 q^{39} + 3 q^{41} - 7 q^{42} + 2 q^{43} - 5 q^{44} - 5 q^{46} + 15 q^{47} + 2 q^{48} + 13 q^{49} + 2 q^{51} + 9 q^{52} + 3 q^{53} - 2 q^{54} - 7 q^{56} - 3 q^{57} + 2 q^{58} - 15 q^{59} + 10 q^{61} + 4 q^{62} + 7 q^{63} + 2 q^{64} + 5 q^{66} + 2 q^{67} + 2 q^{68} + 5 q^{69} - 2 q^{72} - 16 q^{73} + q^{74} - 3 q^{76} - 10 q^{77} - 9 q^{78} + 16 q^{79} + 2 q^{81} - 3 q^{82} + 4 q^{83} + 7 q^{84} - 2 q^{86} - 2 q^{87} + 5 q^{88} + 11 q^{89} + 34 q^{91} + 5 q^{92} - 4 q^{93} - 15 q^{94} - 2 q^{96} - 6 q^{97} - 13 q^{98} - 5 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^6 + 7 * q^7 - 2 * q^8 + 2 * q^9 - 5 * q^11 + 2 * q^12 + 9 * q^13 - 7 * q^14 + 2 * q^16 + 2 * q^17 - 2 * q^18 - 3 * q^19 + 7 * q^21 + 5 * q^22 + 5 * q^23 - 2 * q^24 - 9 * q^26 + 2 * q^27 + 7 * q^28 - 2 * q^29 - 4 * q^31 - 2 * q^32 - 5 * q^33 - 2 * q^34 + 2 * q^36 - q^37 + 3 * q^38 + 9 * q^39 + 3 * q^41 - 7 * q^42 + 2 * q^43 - 5 * q^44 - 5 * q^46 + 15 * q^47 + 2 * q^48 + 13 * q^49 + 2 * q^51 + 9 * q^52 + 3 * q^53 - 2 * q^54 - 7 * q^56 - 3 * q^57 + 2 * q^58 - 15 * q^59 + 10 * q^61 + 4 * q^62 + 7 * q^63 + 2 * q^64 + 5 * q^66 + 2 * q^67 + 2 * q^68 + 5 * q^69 - 2 * q^72 - 16 * q^73 + q^74 - 3 * q^76 - 10 * q^77 - 9 * q^78 + 16 * q^79 + 2 * q^81 - 3 * q^82 + 4 * q^83 + 7 * q^84 - 2 * q^86 - 2 * q^87 + 5 * q^88 + 11 * q^89 + 34 * q^91 + 5 * q^92 - 4 * q^93 - 15 * q^94 - 2 * q^96 - 6 * q^97 - 13 * q^98 - 5 * q^99

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