LMFDB - Embedded newform 3750.2.a.f.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3750,2,Mod(1,3750)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3750, 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("3750.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3750 = 2 \cdot 3 \cdot 5^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3750.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:	$29.9439007580$
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:	no (minimal twist has level 150)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-0.618034$ of defining polynomial
Character	$\chi$	$=$	3750.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +0.381966 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +0.381966 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.38197 q^{11} -1.00000 q^{12} +2.47214 q^{13} +0.381966 q^{14} +1.00000 q^{16} -3.23607 q^{17} +1.00000 q^{18} +7.70820 q^{19} -0.381966 q^{21} +1.38197 q^{22} -4.47214 q^{23} -1.00000 q^{24} +2.47214 q^{26} -1.00000 q^{27} +0.381966 q^{28} -0.472136 q^{29} +4.38197 q^{31} +1.00000 q^{32} -1.38197 q^{33} -3.23607 q^{34} +1.00000 q^{36} +8.00000 q^{37} +7.70820 q^{38} -2.47214 q^{39} -7.70820 q^{41} -0.381966 q^{42} +5.70820 q^{43} +1.38197 q^{44} -4.47214 q^{46} -11.7082 q^{47} -1.00000 q^{48} -6.85410 q^{49} +3.23607 q^{51} +2.47214 q^{52} +9.09017 q^{53} -1.00000 q^{54} +0.381966 q^{56} -7.70820 q^{57} -0.472136 q^{58} -1.38197 q^{59} +7.23607 q^{61} +4.38197 q^{62} +0.381966 q^{63} +1.00000 q^{64} -1.38197 q^{66} -10.4721 q^{67} -3.23607 q^{68} +4.47214 q^{69} +14.4721 q^{71} +1.00000 q^{72} +12.4721 q^{73} +8.00000 q^{74} +7.70820 q^{76} +0.527864 q^{77} -2.47214 q^{78} -3.38197 q^{79} +1.00000 q^{81} -7.70820 q^{82} +8.85410 q^{83} -0.381966 q^{84} +5.70820 q^{86} +0.472136 q^{87} +1.38197 q^{88} +12.4721 q^{89} +0.944272 q^{91} -4.47214 q^{92} -4.38197 q^{93} -11.7082 q^{94} -1.00000 q^{96} -5.61803 q^{97} -6.85410 q^{98} +1.38197 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{6} + 3 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 + 3 * q^7 + 2 * q^8 + 2 * q^9	$ 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{6} + 3 q^{7} + 2 q^{8} + 2 q^{9} + 5 q^{11} - 2 q^{12} - 4 q^{13} + 3 q^{14} + 2 q^{16} - 2 q^{17} + 2 q^{18} + 2 q^{19} - 3 q^{21} + 5 q^{22} - 2 q^{24} - 4 q^{26} - 2 q^{27} + 3 q^{28} + 8 q^{29} + 11 q^{31} + 2 q^{32} - 5 q^{33} - 2 q^{34} + 2 q^{36} + 16 q^{37} + 2 q^{38} + 4 q^{39} - 2 q^{41} - 3 q^{42} - 2 q^{43} + 5 q^{44} - 10 q^{47} - 2 q^{48} - 7 q^{49} + 2 q^{51} - 4 q^{52} + 7 q^{53} - 2 q^{54} + 3 q^{56} - 2 q^{57} + 8 q^{58} - 5 q^{59} + 10 q^{61} + 11 q^{62} + 3 q^{63} + 2 q^{64} - 5 q^{66} - 12 q^{67} - 2 q^{68} + 20 q^{71} + 2 q^{72} + 16 q^{73} + 16 q^{74} + 2 q^{76} + 10 q^{77} + 4 q^{78} - 9 q^{79} + 2 q^{81} - 2 q^{82} + 11 q^{83} - 3 q^{84} - 2 q^{86} - 8 q^{87} + 5 q^{88} + 16 q^{89} - 16 q^{91} - 11 q^{93} - 10 q^{94} - 2 q^{96} - 9 q^{97} - 7 q^{98} + 5 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^6 + 3 * q^7 + 2 * q^8 + 2 * q^9 + 5 * q^11 - 2 * q^12 - 4 * q^13 + 3 * q^14 + 2 * q^16 - 2 * q^17 + 2 * q^18 + 2 * q^19 - 3 * q^21 + 5 * q^22 - 2 * q^24 - 4 * q^26 - 2 * q^27 + 3 * q^28 + 8 * q^29 + 11 * q^31 + 2 * q^32 - 5 * q^33 - 2 * q^34 + 2 * q^36 + 16 * q^37 + 2 * q^38 + 4 * q^39 - 2 * q^41 - 3 * q^42 - 2 * q^43 + 5 * q^44 - 10 * q^47 - 2 * q^48 - 7 * q^49 + 2 * q^51 - 4 * q^52 + 7 * q^53 - 2 * q^54 + 3 * q^56 - 2 * q^57 + 8 * q^58 - 5 * q^59 + 10 * q^61 + 11 * q^62 + 3 * q^63 + 2 * q^64 - 5 * q^66 - 12 * q^67 - 2 * q^68 + 20 * q^71 + 2 * q^72 + 16 * q^73 + 16 * q^74 + 2 * q^76 + 10 * q^77 + 4 * q^78 - 9 * q^79 + 2 * q^81 - 2 * q^82 + 11 * q^83 - 3 * q^84 - 2 * q^86 - 8 * q^87 + 5 * q^88 + 16 * q^89 - 16 * q^91 - 11 * q^93 - 10 * q^94 - 2 * q^96 - 9 * q^97 - 7 * 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
$7$	0.381966	0.144370	0.0721848	−	0.997391i	$-0.477003\pi$
$7$	0.381966	0.144370	0.0721848	+	0.997391i	$0.477003\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	0	0
$11$	1.38197	0.416678	0.208339	−	0.978057i	$-0.433194\pi$
$11$	1.38197	0.416678	0.208339	+	0.978057i	$0.433194\pi$
$12$	−1.00000	−0.288675
$13$	2.47214	0.685647	0.342824	−	0.939400i	$-0.388617\pi$
$13$	2.47214	0.685647	0.342824	+	0.939400i	$0.388617\pi$
$14$	0.381966	0.102085
$15$	0	0
$16$	1.00000	0.250000
$17$	−3.23607	−0.784862	−0.392431	−	0.919781i	$-0.628366\pi$
$17$	−3.23607	−0.784862	−0.392431	+	0.919781i	$0.628366\pi$
$18$	1.00000	0.235702
$19$	7.70820	1.76838	0.884192	−	0.467124i	$-0.154710\pi$
$19$	7.70820	1.76838	0.884192	+	0.467124i	$0.154710\pi$
$20$	0	0
$21$	−0.381966	−0.0833518
$22$	1.38197	0.294636
$23$	−4.47214	−0.932505	−0.466252	−	0.884652i	$-0.654396\pi$
$23$	−4.47214	−0.932505	−0.466252	+	0.884652i	$0.654396\pi$
$24$	−1.00000	−0.204124
$25$	0	0
$26$	2.47214	0.484826
$27$	−1.00000	−0.192450
$28$	0.381966	0.0721848
$29$	−0.472136	−0.0876734	−0.0438367	−	0.999039i	$-0.513958\pi$
$29$	−0.472136	−0.0876734	−0.0438367	+	0.999039i	$0.513958\pi$
$30$	0	0
$31$	4.38197	0.787024	0.393512	−	0.919319i	$-0.371260\pi$
$31$	4.38197	0.787024	0.393512	+	0.919319i	$0.371260\pi$
$32$	1.00000	0.176777
$33$	−1.38197	−0.240569
$34$	−3.23607	−0.554981
$35$	0	0
$36$	1.00000	0.166667
$37$	8.00000	1.31519	0.657596	−	0.753371i	$-0.271573\pi$
$37$	8.00000	1.31519	0.657596	+	0.753371i	$0.271573\pi$
$38$	7.70820	1.25044
$39$	−2.47214	−0.395859
$40$	0	0
$41$	−7.70820	−1.20382	−0.601910	−	0.798564i	$-0.705593\pi$
$41$	−7.70820	−1.20382	−0.601910	+	0.798564i	$0.705593\pi$
$42$	−0.381966	−0.0589386
$43$	5.70820	0.870493	0.435246	−	0.900311i	$-0.356661\pi$
$43$	5.70820	0.870493	0.435246	+	0.900311i	$0.356661\pi$
$44$	1.38197	0.208339
$45$	0	0
$46$	−4.47214	−0.659380
$47$	−11.7082	−1.70782	−0.853909	−	0.520423i	$-0.825774\pi$
$47$	−11.7082	−1.70782	−0.853909	+	0.520423i	$0.825774\pi$
$48$	−1.00000	−0.144338
$49$	−6.85410	−0.979157
$50$	0	0
$51$	3.23607	0.453140
$52$	2.47214	0.342824
$53$	9.09017	1.24863	0.624315	−	0.781172i	$-0.285378\pi$
$53$	9.09017	1.24863	0.624315	+	0.781172i	$0.285378\pi$
$54$	−1.00000	−0.136083
$55$	0	0
$56$	0.381966	0.0510424
$57$	−7.70820	−1.02098
$58$	−0.472136	−0.0619945
$59$	−1.38197	−0.179917	−0.0899583	−	0.995946i	$-0.528673\pi$
$59$	−1.38197	−0.179917	−0.0899583	+	0.995946i	$0.528673\pi$
$60$	0	0
$61$	7.23607	0.926484	0.463242	−	0.886232i	$-0.346686\pi$
$61$	7.23607	0.926484	0.463242	+	0.886232i	$0.346686\pi$
$62$	4.38197	0.556510
$63$	0.381966	0.0481232
$64$	1.00000	0.125000
$65$	0	0
$66$	−1.38197	−0.170108
$67$	−10.4721	−1.27938	−0.639688	−	0.768635i	$-0.720936\pi$
$67$	−10.4721	−1.27938	−0.639688	+	0.768635i	$0.720936\pi$
$68$	−3.23607	−0.392431
$69$	4.47214	0.538382
$70$	0	0
$71$	14.4721	1.71753	0.858763	−	0.512373i	$-0.171233\pi$
$71$	14.4721	1.71753	0.858763	+	0.512373i	$0.171233\pi$
$72$	1.00000	0.117851
$73$	12.4721	1.45975	0.729877	−	0.683579i	$-0.239578\pi$
$73$	12.4721	1.45975	0.729877	+	0.683579i	$0.239578\pi$
$74$	8.00000	0.929981
$75$	0	0
$76$	7.70820	0.884192
$77$	0.527864	0.0601557
$78$	−2.47214	−0.279914
$79$	−3.38197	−0.380501	−0.190250	−	0.981736i	$-0.560930\pi$
$79$	−3.38197	−0.380501	−0.190250	+	0.981736i	$0.560930\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−7.70820	−0.851229
$83$	8.85410	0.971864	0.485932	−	0.873997i	$-0.338480\pi$
$83$	8.85410	0.971864	0.485932	+	0.873997i	$0.338480\pi$
$84$	−0.381966	−0.0416759
$85$	0	0
$86$	5.70820	0.615531
$87$	0.472136	0.0506183
$88$	1.38197	0.147318
$89$	12.4721	1.32204	0.661022	−	0.750367i	$-0.270123\pi$
$89$	12.4721	1.32204	0.661022	+	0.750367i	$0.270123\pi$
$90$	0	0
$91$	0.944272	0.0989866
$92$	−4.47214	−0.466252
$93$	−4.38197	−0.454389
$94$	−11.7082	−1.20761
$95$	0	0
$96$	−1.00000	−0.102062
$97$	−5.61803	−0.570425	−0.285212	−	0.958464i	$-0.592064\pi$
$97$	−5.61803	−0.570425	−0.285212	+	0.958464i	$0.592064\pi$
$98$	−6.85410	−0.692369
$99$	1.38197	0.138893
$100$	0	0
$101$	6.61803	0.658519	0.329259	−	0.944239i	$-0.393201\pi$
$101$	6.61803	0.658519	0.329259	+	0.944239i	$0.393201\pi$
$102$	3.23607	0.320418
$103$	−1.32624	−0.130678	−0.0653391	−	0.997863i	$-0.520813\pi$
$103$	−1.32624	−0.130678	−0.0653391	+	0.997863i	$0.520813\pi$
$104$	2.47214	0.242413
$105$	0	0
$106$	9.09017	0.882915
$107$	−9.38197	−0.906989	−0.453494	−	0.891259i	$-0.649823\pi$
$107$	−9.38197	−0.906989	−0.453494	+	0.891259i	$0.649823\pi$
$108$	−1.00000	−0.0962250
$109$	12.7639	1.22256	0.611281	−	0.791413i	$-0.290654\pi$
$109$	12.7639	1.22256	0.611281	+	0.791413i	$0.290654\pi$
$110$	0	0
$111$	−8.00000	−0.759326
$112$	0.381966	0.0360924
$113$	−14.7639	−1.38887	−0.694437	−	0.719554i	$-0.744346\pi$
$113$	−14.7639	−1.38887	−0.694437	+	0.719554i	$0.744346\pi$
$114$	−7.70820	−0.721939
$115$	0	0
$116$	−0.472136	−0.0438367
$117$	2.47214	0.228549
$118$	−1.38197	−0.127220
$119$	−1.23607	−0.113310
$120$	0	0
$121$	−9.09017	−0.826379
$122$	7.23607	0.655123
$123$	7.70820	0.695025
$124$	4.38197	0.393512
$125$	0	0
$126$	0.381966	0.0340282
$127$	11.3820	1.00999	0.504993	−	0.863123i	$-0.331495\pi$
$127$	11.3820	1.00999	0.504993	+	0.863123i	$0.331495\pi$
$128$	1.00000	0.0883883
$129$	−5.70820	−0.502579
$130$	0	0
$131$	17.8885	1.56293	0.781465	−	0.623949i	$-0.214473\pi$
$131$	17.8885	1.56293	0.781465	+	0.623949i	$0.214473\pi$
$132$	−1.38197	−0.120285
$133$	2.94427	0.255301
$134$	−10.4721	−0.904655
$135$	0	0
$136$	−3.23607	−0.277491
$137$	10.1803	0.869765	0.434883	−	0.900487i	$-0.356790\pi$
$137$	10.1803	0.869765	0.434883	+	0.900487i	$0.356790\pi$
$138$	4.47214	0.380693
$139$	1.52786	0.129592	0.0647959	−	0.997899i	$-0.479360\pi$
$139$	1.52786	0.129592	0.0647959	+	0.997899i	$0.479360\pi$
$140$	0	0
$141$	11.7082	0.986009
$142$	14.4721	1.21447
$143$	3.41641	0.285694
$144$	1.00000	0.0833333
$145$	0	0
$146$	12.4721	1.03220
$147$	6.85410	0.565317
$148$	8.00000	0.657596
$149$	10.9098	0.893768	0.446884	−	0.894592i	$-0.352534\pi$
$149$	10.9098	0.893768	0.446884	+	0.894592i	$0.352534\pi$
$150$	0	0
$151$	2.67376	0.217588	0.108794	−	0.994064i	$-0.465301\pi$
$151$	2.67376	0.217588	0.108794	+	0.994064i	$0.465301\pi$
$152$	7.70820	0.625218
$153$	−3.23607	−0.261621
$154$	0.527864	0.0425365
$155$	0	0
$156$	−2.47214	−0.197929
$157$	−22.6525	−1.80786	−0.903932	−	0.427676i	$-0.859332\pi$
$157$	−22.6525	−1.80786	−0.903932	+	0.427676i	$0.859332\pi$
$158$	−3.38197	−0.269055
$159$	−9.09017	−0.720897
$160$	0	0
$161$	−1.70820	−0.134625
$162$	1.00000	0.0785674
$163$	8.47214	0.663589	0.331794	−	0.943352i	$-0.392346\pi$
$163$	8.47214	0.663589	0.331794	+	0.943352i	$0.392346\pi$
$164$	−7.70820	−0.601910
$165$	0	0
$166$	8.85410	0.687212
$167$	−1.70820	−0.132185	−0.0660924	−	0.997814i	$-0.521053\pi$
$167$	−1.70820	−0.132185	−0.0660924	+	0.997814i	$0.521053\pi$
$168$	−0.381966	−0.0294693
$169$	−6.88854	−0.529888
$170$	0	0
$171$	7.70820	0.589461
$172$	5.70820	0.435246
$173$	−6.09017	−0.463027	−0.231514	−	0.972832i	$-0.574368\pi$
$173$	−6.09017	−0.463027	−0.231514	+	0.972832i	$0.574368\pi$
$174$	0.472136	0.0357925
$175$	0	0
$176$	1.38197	0.104170
$177$	1.38197	0.103875
$178$	12.4721	0.934826
$179$	3.14590	0.235135	0.117568	−	0.993065i	$-0.462490\pi$
$179$	3.14590	0.235135	0.117568	+	0.993065i	$0.462490\pi$
$180$	0	0
$181$	24.6525	1.83240	0.916202	−	0.400717i	$-0.131239\pi$
$181$	24.6525	1.83240	0.916202	+	0.400717i	$0.131239\pi$
$182$	0.944272	0.0699941
$183$	−7.23607	−0.534906
$184$	−4.47214	−0.329690
$185$	0	0
$186$	−4.38197	−0.321301
$187$	−4.47214	−0.327035
$188$	−11.7082	−0.853909
$189$	−0.381966	−0.0277839
$190$	0	0
$191$	17.7082	1.28132	0.640660	−	0.767824i	$-0.278661\pi$
$191$	17.7082	1.28132	0.640660	+	0.767824i	$0.278661\pi$
$192$	−1.00000	−0.0721688
$193$	11.1459	0.802299	0.401150	−	0.916013i	$-0.368611\pi$
$193$	11.1459	0.802299	0.401150	+	0.916013i	$0.368611\pi$
$194$	−5.61803	−0.403351
$195$	0	0
$196$	−6.85410	−0.489579
$197$	−5.90983	−0.421058	−0.210529	−	0.977588i	$-0.567519\pi$
$197$	−5.90983	−0.421058	−0.210529	+	0.977588i	$0.567519\pi$
$198$	1.38197	0.0982120
$199$	−18.5066	−1.31190	−0.655948	−	0.754806i	$-0.727731\pi$
$199$	−18.5066	−1.31190	−0.655948	+	0.754806i	$0.727731\pi$
$200$	0	0
$201$	10.4721	0.738648
$202$	6.61803	0.465643
$203$	−0.180340	−0.0126574
$204$	3.23607	0.226570
$205$	0	0
$206$	−1.32624	−0.0924034
$207$	−4.47214	−0.310835
$208$	2.47214	0.171412
$209$	10.6525	0.736847
$210$	0	0
$211$	23.4164	1.61205	0.806026	−	0.591880i	$-0.201614\pi$
$211$	23.4164	1.61205	0.806026	+	0.591880i	$0.201614\pi$
$212$	9.09017	0.624315
$213$	−14.4721	−0.991614
$214$	−9.38197	−0.641338
$215$	0	0
$216$	−1.00000	−0.0680414
$217$	1.67376	0.113622
$218$	12.7639	0.864483
$219$	−12.4721	−0.842789
$220$	0	0
$221$	−8.00000	−0.538138
$222$	−8.00000	−0.536925
$223$	3.09017	0.206933	0.103467	−	0.994633i	$-0.467007\pi$
$223$	3.09017	0.206933	0.103467	+	0.994633i	$0.467007\pi$
$224$	0.381966	0.0255212
$225$	0	0
$226$	−14.7639	−0.982082
$227$	11.2705	0.748050	0.374025	−	0.927419i	$-0.377977\pi$
$227$	11.2705	0.748050	0.374025	+	0.927419i	$0.377977\pi$
$228$	−7.70820	−0.510488
$229$	−14.4721	−0.956346	−0.478173	−	0.878266i	$-0.658701\pi$
$229$	−14.4721	−0.956346	−0.478173	+	0.878266i	$0.658701\pi$
$230$	0	0
$231$	−0.527864	−0.0347309
$232$	−0.472136	−0.0309972
$233$	−12.6525	−0.828891	−0.414446	−	0.910074i	$-0.636024\pi$
$233$	−12.6525	−0.828891	−0.414446	+	0.910074i	$0.636024\pi$
$234$	2.47214	0.161609
$235$	0	0
$236$	−1.38197	−0.0899583
$237$	3.38197	0.219682
$238$	−1.23607	−0.0801224
$239$	25.7082	1.66293	0.831463	−	0.555581i	$-0.187504\pi$
$239$	25.7082	1.66293	0.831463	+	0.555581i	$0.187504\pi$
$240$	0	0
$241$	−10.5623	−0.680378	−0.340189	−	0.940357i	$-0.610491\pi$
$241$	−10.5623	−0.680378	−0.340189	+	0.940357i	$0.610491\pi$
$242$	−9.09017	−0.584338
$243$	−1.00000	−0.0641500
$244$	7.23607	0.463242
$245$	0	0
$246$	7.70820	0.491457
$247$	19.0557	1.21249
$248$	4.38197	0.278255
$249$	−8.85410	−0.561106
$250$	0	0
$251$	−6.56231	−0.414209	−0.207105	−	0.978319i	$-0.566404\pi$
$251$	−6.56231	−0.414209	−0.207105	+	0.978319i	$0.566404\pi$
$252$	0.381966	0.0240616
$253$	−6.18034	−0.388555
$254$	11.3820	0.714168
$255$	0	0
$256$	1.00000	0.0625000
$257$	−22.0000	−1.37232	−0.686161	−	0.727450i	$-0.740706\pi$
$257$	−22.0000	−1.37232	−0.686161	+	0.727450i	$0.740706\pi$
$258$	−5.70820	−0.355377
$259$	3.05573	0.189874
$260$	0	0
$261$	−0.472136	−0.0292245
$262$	17.8885	1.10516
$263$	1.70820	0.105332	0.0526662	−	0.998612i	$-0.483228\pi$
$263$	1.70820	0.105332	0.0526662	+	0.998612i	$0.483228\pi$
$264$	−1.38197	−0.0850541
$265$	0	0
$266$	2.94427	0.180525
$267$	−12.4721	−0.763282
$268$	−10.4721	−0.639688
$269$	2.09017	0.127440	0.0637200	−	0.997968i	$-0.479704\pi$
$269$	2.09017	0.127440	0.0637200	+	0.997968i	$0.479704\pi$
$270$	0	0
$271$	11.0344	0.670295	0.335147	−	0.942166i	$-0.391214\pi$
$271$	11.0344	0.670295	0.335147	+	0.942166i	$0.391214\pi$
$272$	−3.23607	−0.196215
$273$	−0.944272	−0.0571499
$274$	10.1803	0.615017
$275$	0	0
$276$	4.47214	0.269191
$277$	−0.944272	−0.0567358	−0.0283679	−	0.999598i	$-0.509031\pi$
$277$	−0.944272	−0.0567358	−0.0283679	+	0.999598i	$0.509031\pi$
$278$	1.52786	0.0916352
$279$	4.38197	0.262341
$280$	0	0
$281$	−29.8885	−1.78300	−0.891501	−	0.453020i	$-0.850347\pi$
$281$	−29.8885	−1.78300	−0.891501	+	0.453020i	$0.850347\pi$
$282$	11.7082	0.697213
$283$	31.4164	1.86751	0.933756	−	0.357911i	$-0.116511\pi$
$283$	31.4164	1.86751	0.933756	+	0.357911i	$0.116511\pi$
$284$	14.4721	0.858763
$285$	0	0
$286$	3.41641	0.202016
$287$	−2.94427	−0.173795
$288$	1.00000	0.0589256
$289$	−6.52786	−0.383992
$290$	0	0
$291$	5.61803	0.329335
$292$	12.4721	0.729877
$293$	−10.9098	−0.637359	−0.318680	−	0.947863i	$-0.603239\pi$
$293$	−10.9098	−0.637359	−0.318680	+	0.947863i	$0.603239\pi$
$294$	6.85410	0.399739
$295$	0	0
$296$	8.00000	0.464991
$297$	−1.38197	−0.0801898
$298$	10.9098	0.631989
$299$	−11.0557	−0.639369
$300$	0	0
$301$	2.18034	0.125673
$302$	2.67376	0.153858
$303$	−6.61803	−0.380196
$304$	7.70820	0.442096
$305$	0	0
$306$	−3.23607	−0.184994
$307$	10.0000	0.570730	0.285365	−	0.958419i	$-0.407885\pi$
$307$	10.0000	0.570730	0.285365	+	0.958419i	$0.407885\pi$
$308$	0.527864	0.0300778
$309$	1.32624	0.0754470
$310$	0	0
$311$	−18.9443	−1.07423	−0.537116	−	0.843509i	$-0.680486\pi$
$311$	−18.9443	−1.07423	−0.537116	+	0.843509i	$0.680486\pi$
$312$	−2.47214	−0.139957
$313$	17.2705	0.976187	0.488093	−	0.872791i	$-0.337693\pi$
$313$	17.2705	0.976187	0.488093	+	0.872791i	$0.337693\pi$
$314$	−22.6525	−1.27835
$315$	0	0
$316$	−3.38197	−0.190250
$317$	−0.437694	−0.0245833	−0.0122917	−	0.999924i	$-0.503913\pi$
$317$	−0.437694	−0.0245833	−0.0122917	+	0.999924i	$0.503913\pi$
$318$	−9.09017	−0.509751
$319$	−0.652476	−0.0365316
$320$	0	0
$321$	9.38197	0.523650
$322$	−1.70820	−0.0951945
$323$	−24.9443	−1.38794
$324$	1.00000	0.0555556
$325$	0	0
$326$	8.47214	0.469228
$327$	−12.7639	−0.705847
$328$	−7.70820	−0.425614
$329$	−4.47214	−0.246557
$330$	0	0
$331$	−18.0000	−0.989369	−0.494685	−	0.869072i	$-0.664716\pi$
$331$	−18.0000	−0.989369	−0.494685	+	0.869072i	$0.664716\pi$
$332$	8.85410	0.485932
$333$	8.00000	0.438397
$334$	−1.70820	−0.0934688
$335$	0	0
$336$	−0.381966	−0.0208380
$337$	12.0902	0.658594	0.329297	−	0.944226i	$-0.393188\pi$
$337$	12.0902	0.658594	0.329297	+	0.944226i	$0.393188\pi$
$338$	−6.88854	−0.374687
$339$	14.7639	0.801867
$340$	0	0
$341$	6.05573	0.327936
$342$	7.70820	0.416812
$343$	−5.29180	−0.285730
$344$	5.70820	0.307766
$345$	0	0
$346$	−6.09017	−0.327410
$347$	0.437694	0.0234967	0.0117483	−	0.999931i	$-0.496260\pi$
$347$	0.437694	0.0234967	0.0117483	+	0.999931i	$0.496260\pi$
$348$	0.472136	0.0253091
$349$	7.88854	0.422264	0.211132	−	0.977458i	$-0.432285\pi$
$349$	7.88854	0.422264	0.211132	+	0.977458i	$0.432285\pi$
$350$	0	0
$351$	−2.47214	−0.131953
$352$	1.38197	0.0736590
$353$	−8.76393	−0.466457	−0.233229	−	0.972422i	$-0.574929\pi$
$353$	−8.76393	−0.466457	−0.233229	+	0.972422i	$0.574929\pi$
$354$	1.38197	0.0734507
$355$	0	0
$356$	12.4721	0.661022
$357$	1.23607	0.0654197
$358$	3.14590	0.166266
$359$	−0.180340	−0.00951798	−0.00475899	−	0.999989i	$-0.501515\pi$
$359$	−0.180340	−0.00951798	−0.00475899	+	0.999989i	$0.501515\pi$
$360$	0	0
$361$	40.4164	2.12718
$362$	24.6525	1.29571
$363$	9.09017	0.477110
$364$	0.944272	0.0494933
$365$	0	0
$366$	−7.23607	−0.378235
$367$	−28.3820	−1.48153	−0.740763	−	0.671766i	$-0.765536\pi$
$367$	−28.3820	−1.48153	−0.740763	+	0.671766i	$0.765536\pi$
$368$	−4.47214	−0.233126
$369$	−7.70820	−0.401273
$370$	0	0
$371$	3.47214	0.180264
$372$	−4.38197	−0.227194
$373$	−20.4721	−1.06001	−0.530004	−	0.847995i	$-0.677809\pi$
$373$	−20.4721	−1.06001	−0.530004	+	0.847995i	$0.677809\pi$
$374$	−4.47214	−0.231249
$375$	0	0
$376$	−11.7082	−0.603805
$377$	−1.16718	−0.0601130
$378$	−0.381966	−0.0196462
$379$	2.18034	0.111997	0.0559983	−	0.998431i	$-0.482166\pi$
$379$	2.18034	0.111997	0.0559983	+	0.998431i	$0.482166\pi$
$380$	0	0
$381$	−11.3820	−0.583116
$382$	17.7082	0.906031
$383$	−20.0000	−1.02195	−0.510976	−	0.859595i	$-0.670716\pi$
$383$	−20.0000	−1.02195	−0.510976	+	0.859595i	$0.670716\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	11.1459	0.567311
$387$	5.70820	0.290164
$388$	−5.61803	−0.285212
$389$	−14.6180	−0.741164	−0.370582	−	0.928800i	$-0.620842\pi$
$389$	−14.6180	−0.741164	−0.370582	+	0.928800i	$0.620842\pi$
$390$	0	0
$391$	14.4721	0.731887
$392$	−6.85410	−0.346184
$393$	−17.8885	−0.902358
$394$	−5.90983	−0.297733
$395$	0	0
$396$	1.38197	0.0694464
$397$	−35.2361	−1.76845	−0.884224	−	0.467063i	$-0.845312\pi$
$397$	−35.2361	−1.76845	−0.884224	+	0.467063i	$0.845312\pi$
$398$	−18.5066	−0.927651
$399$	−2.94427	−0.147398
$400$	0	0
$401$	12.2918	0.613823	0.306912	−	0.951738i	$-0.400704\pi$
$401$	12.2918	0.613823	0.306912	+	0.951738i	$0.400704\pi$
$402$	10.4721	0.522303
$403$	10.8328	0.539621
$404$	6.61803	0.329259
$405$	0	0
$406$	−0.180340	−0.00895012
$407$	11.0557	0.548012
$408$	3.23607	0.160209
$409$	−18.7984	−0.929520	−0.464760	−	0.885437i	$-0.653859\pi$
$409$	−18.7984	−0.929520	−0.464760	+	0.885437i	$0.653859\pi$
$410$	0	0
$411$	−10.1803	−0.502159
$412$	−1.32624	−0.0653391
$413$	−0.527864	−0.0259745
$414$	−4.47214	−0.219793
$415$	0	0
$416$	2.47214	0.121206
$417$	−1.52786	−0.0748198
$418$	10.6525	0.521030
$419$	8.09017	0.395231	0.197615	−	0.980280i	$-0.436680\pi$
$419$	8.09017	0.395231	0.197615	+	0.980280i	$0.436680\pi$
$420$	0	0
$421$	−27.2361	−1.32740	−0.663702	−	0.747997i	$-0.731016\pi$
$421$	−27.2361	−1.32740	−0.663702	+	0.747997i	$0.731016\pi$
$422$	23.4164	1.13989
$423$	−11.7082	−0.569272
$424$	9.09017	0.441458
$425$	0	0
$426$	−14.4721	−0.701177
$427$	2.76393	0.133756
$428$	−9.38197	−0.453494
$429$	−3.41641	−0.164946
$430$	0	0
$431$	−36.8328	−1.77417	−0.887087	−	0.461602i	$-0.847275\pi$
$431$	−36.8328	−1.77417	−0.887087	+	0.461602i	$0.847275\pi$
$432$	−1.00000	−0.0481125
$433$	−22.5066	−1.08160	−0.540799	−	0.841152i	$-0.681878\pi$
$433$	−22.5066	−1.08160	−0.540799	+	0.841152i	$0.681878\pi$
$434$	1.67376	0.0803432
$435$	0	0
$436$	12.7639	0.611281
$437$	−34.4721	−1.64903
$438$	−12.4721	−0.595942
$439$	14.5066	0.692361	0.346181	−	0.938168i	$-0.387478\pi$
$439$	14.5066	0.692361	0.346181	+	0.938168i	$0.387478\pi$
$440$	0	0
$441$	−6.85410	−0.326386
$442$	−8.00000	−0.380521
$443$	14.3820	0.683308	0.341654	−	0.939826i	$-0.389013\pi$
$443$	14.3820	0.683308	0.341654	+	0.939826i	$0.389013\pi$
$444$	−8.00000	−0.379663
$445$	0	0
$446$	3.09017	0.146324
$447$	−10.9098	−0.516017
$448$	0.381966	0.0180462
$449$	−14.2918	−0.674472	−0.337236	−	0.941420i	$-0.609492\pi$
$449$	−14.2918	−0.674472	−0.337236	+	0.941420i	$0.609492\pi$
$450$	0	0
$451$	−10.6525	−0.501605
$452$	−14.7639	−0.694437
$453$	−2.67376	−0.125624
$454$	11.2705	0.528951
$455$	0	0
$456$	−7.70820	−0.360970
$457$	7.09017	0.331664	0.165832	−	0.986154i	$-0.446969\pi$
$457$	7.09017	0.331664	0.165832	+	0.986154i	$0.446969\pi$
$458$	−14.4721	−0.676239
$459$	3.23607	0.151047
$460$	0	0
$461$	−12.5623	−0.585085	−0.292542	−	0.956253i	$-0.594501\pi$
$461$	−12.5623	−0.585085	−0.292542	+	0.956253i	$0.594501\pi$
$462$	−0.527864	−0.0245585
$463$	30.8328	1.43292	0.716461	−	0.697627i	$-0.245761\pi$
$463$	30.8328	1.43292	0.716461	+	0.697627i	$0.245761\pi$
$464$	−0.472136	−0.0219184
$465$	0	0
$466$	−12.6525	−0.586115
$467$	26.3262	1.21823	0.609117	−	0.793081i	$-0.291524\pi$
$467$	26.3262	1.21823	0.609117	+	0.793081i	$0.291524\pi$
$468$	2.47214	0.114275
$469$	−4.00000	−0.184703
$470$	0	0
$471$	22.6525	1.04377
$472$	−1.38197	−0.0636101
$473$	7.88854	0.362716
$474$	3.38197	0.155339
$475$	0	0
$476$	−1.23607	−0.0566551
$477$	9.09017	0.416210
$478$	25.7082	1.17587
$479$	11.1246	0.508296	0.254148	−	0.967165i	$-0.418205\pi$
$479$	11.1246	0.508296	0.254148	+	0.967165i	$0.418205\pi$
$480$	0	0
$481$	19.7771	0.901758
$482$	−10.5623	−0.481100
$483$	1.70820	0.0777260
$484$	−9.09017	−0.413190
$485$	0	0
$486$	−1.00000	−0.0453609
$487$	−6.79837	−0.308064	−0.154032	−	0.988066i	$-0.549226\pi$
$487$	−6.79837	−0.308064	−0.154032	+	0.988066i	$0.549226\pi$
$488$	7.23607	0.327561
$489$	−8.47214	−0.383123
$490$	0	0
$491$	8.27051	0.373243	0.186621	−	0.982432i	$-0.440246\pi$
$491$	8.27051	0.373243	0.186621	+	0.982432i	$0.440246\pi$
$492$	7.70820	0.347513
$493$	1.52786	0.0688115
$494$	19.0557	0.857358
$495$	0	0
$496$	4.38197	0.196756
$497$	5.52786	0.247959
$498$	−8.85410	−0.396762
$499$	−13.5967	−0.608674	−0.304337	−	0.952564i	$-0.598435\pi$
$499$	−13.5967	−0.608674	−0.304337	+	0.952564i	$0.598435\pi$
$500$	0	0
$501$	1.70820	0.0763169
$502$	−6.56231	−0.292890
$503$	−11.8885	−0.530084	−0.265042	−	0.964237i	$-0.585386\pi$
$503$	−11.8885	−0.530084	−0.265042	+	0.964237i	$0.585386\pi$
$504$	0.381966	0.0170141
$505$	0	0
$506$	−6.18034	−0.274750
$507$	6.88854	0.305931
$508$	11.3820	0.504993
$509$	20.5066	0.908938	0.454469	−	0.890763i	$-0.349829\pi$
$509$	20.5066	0.908938	0.454469	+	0.890763i	$0.349829\pi$
$510$	0	0
$511$	4.76393	0.210744
$512$	1.00000	0.0441942
$513$	−7.70820	−0.340326
$514$	−22.0000	−0.970378
$515$	0	0
$516$	−5.70820	−0.251290
$517$	−16.1803	−0.711611
$518$	3.05573	0.134261
$519$	6.09017	0.267329
$520$	0	0
$521$	−8.18034	−0.358387	−0.179194	−	0.983814i	$-0.557349\pi$
$521$	−8.18034	−0.358387	−0.179194	+	0.983814i	$0.557349\pi$
$522$	−0.472136	−0.0206648
$523$	28.9443	1.26564	0.632822	−	0.774297i	$-0.281896\pi$
$523$	28.9443	1.26564	0.632822	+	0.774297i	$0.281896\pi$
$524$	17.8885	0.781465
$525$	0	0
$526$	1.70820	0.0744812
$527$	−14.1803	−0.617705
$528$	−1.38197	−0.0601424
$529$	−3.00000	−0.130435
$530$	0	0
$531$	−1.38197	−0.0599722
$532$	2.94427	0.127650
$533$	−19.0557	−0.825395
$534$	−12.4721	−0.539722
$535$	0	0
$536$	−10.4721	−0.452327
$537$	−3.14590	−0.135756
$538$	2.09017	0.0901136
$539$	−9.47214	−0.407994
$540$	0	0
$541$	−3.81966	−0.164220	−0.0821100	−	0.996623i	$-0.526166\pi$
$541$	−3.81966	−0.164220	−0.0821100	+	0.996623i	$0.526166\pi$
$542$	11.0344	0.473970
$543$	−24.6525	−1.05794
$544$	−3.23607	−0.138745
$545$	0	0
$546$	−0.944272	−0.0404111
$547$	−3.70820	−0.158551	−0.0792757	−	0.996853i	$-0.525261\pi$
$547$	−3.70820	−0.158551	−0.0792757	+	0.996853i	$0.525261\pi$
$548$	10.1803	0.434883
$549$	7.23607	0.308828
$550$	0	0
$551$	−3.63932	−0.155040
$552$	4.47214	0.190347
$553$	−1.29180	−0.0549328
$554$	−0.944272	−0.0401183
$555$	0	0
$556$	1.52786	0.0647959
$557$	−2.67376	−0.113291	−0.0566455	−	0.998394i	$-0.518040\pi$
$557$	−2.67376	−0.113291	−0.0566455	+	0.998394i	$0.518040\pi$
$558$	4.38197	0.185503
$559$	14.1115	0.596851
$560$	0	0
$561$	4.47214	0.188814
$562$	−29.8885	−1.26077
$563$	−12.2705	−0.517140	−0.258570	−	0.965992i	$-0.583251\pi$
$563$	−12.2705	−0.517140	−0.258570	+	0.965992i	$0.583251\pi$
$564$	11.7082	0.493004
$565$	0	0
$566$	31.4164	1.32053
$567$	0.381966	0.0160411
$568$	14.4721	0.607237
$569$	43.7771	1.83523	0.917615	−	0.397469i	$-0.130111\pi$
$569$	43.7771	1.83523	0.917615	+	0.397469i	$0.130111\pi$
$570$	0	0
$571$	−27.8885	−1.16710	−0.583550	−	0.812077i	$-0.698337\pi$
$571$	−27.8885	−1.16710	−0.583550	+	0.812077i	$0.698337\pi$
$572$	3.41641	0.142847
$573$	−17.7082	−0.739771
$574$	−2.94427	−0.122892
$575$	0	0
$576$	1.00000	0.0416667
$577$	−37.9787	−1.58107	−0.790537	−	0.612414i	$-0.790199\pi$
$577$	−37.9787	−1.58107	−0.790537	+	0.612414i	$0.790199\pi$
$578$	−6.52786	−0.271523
$579$	−11.1459	−0.463208
$580$	0	0
$581$	3.38197	0.140308
$582$	5.61803	0.232875
$583$	12.5623	0.520278
$584$	12.4721	0.516101
$585$	0	0
$586$	−10.9098	−0.450681
$587$	−30.0344	−1.23965	−0.619827	−	0.784738i	$-0.712797\pi$
$587$	−30.0344	−1.23965	−0.619827	+	0.784738i	$0.712797\pi$
$588$	6.85410	0.282658
$589$	33.7771	1.39176
$590$	0	0
$591$	5.90983	0.243098
$592$	8.00000	0.328798
$593$	0	0		−	1.00000i	$-0.5\pi$
$593$	0	0			1.00000i	$0.5\pi$
$594$	−1.38197	−0.0567028
$595$	0	0
$596$	10.9098	0.446884
$597$	18.5066	0.757424
$598$	−11.0557	−0.452102
$599$	−8.47214	−0.346162	−0.173081	−	0.984908i	$-0.555372\pi$
$599$	−8.47214	−0.346162	−0.173081	+	0.984908i	$0.555372\pi$
$600$	0	0
$601$	−41.2705	−1.68346	−0.841730	−	0.539899i	$-0.818462\pi$
$601$	−41.2705	−1.68346	−0.841730	+	0.539899i	$0.818462\pi$
$602$	2.18034	0.0888640
$603$	−10.4721	−0.426458
$604$	2.67376	0.108794
$605$	0	0
$606$	−6.61803	−0.268839
$607$	−13.5623	−0.550477	−0.275239	−	0.961376i	$-0.588757\pi$
$607$	−13.5623	−0.550477	−0.275239	+	0.961376i	$0.588757\pi$
$608$	7.70820	0.312609
$609$	0.180340	0.00730774
$610$	0	0
$611$	−28.9443	−1.17096
$612$	−3.23607	−0.130810
$613$	−32.2492	−1.30253	−0.651267	−	0.758849i	$-0.725762\pi$
$613$	−32.2492	−1.30253	−0.651267	+	0.758849i	$0.725762\pi$
$614$	10.0000	0.403567
$615$	0	0
$616$	0.527864	0.0212682
$617$	37.8885	1.52534	0.762668	−	0.646791i	$-0.223889\pi$
$617$	37.8885	1.52534	0.762668	+	0.646791i	$0.223889\pi$
$618$	1.32624	0.0533491
$619$	17.4164	0.700025	0.350012	−	0.936745i	$-0.386177\pi$
$619$	17.4164	0.700025	0.350012	+	0.936745i	$0.386177\pi$
$620$	0	0
$621$	4.47214	0.179461
$622$	−18.9443	−0.759596
$623$	4.76393	0.190863
$624$	−2.47214	−0.0989646
$625$	0	0
$626$	17.2705	0.690268
$627$	−10.6525	−0.425419
$628$	−22.6525	−0.903932
$629$	−25.8885	−1.03224
$630$	0	0
$631$	37.5279	1.49396	0.746980	−	0.664846i	$-0.231503\pi$
$631$	37.5279	1.49396	0.746980	+	0.664846i	$0.231503\pi$
$632$	−3.38197	−0.134527
$633$	−23.4164	−0.930719
$634$	−0.437694	−0.0173831
$635$	0	0
$636$	−9.09017	−0.360449
$637$	−16.9443	−0.671356
$638$	−0.652476	−0.0258318
$639$	14.4721	0.572509
$640$	0	0
$641$	−36.1803	−1.42904	−0.714519	−	0.699616i	$-0.753354\pi$
$641$	−36.1803	−1.42904	−0.714519	+	0.699616i	$0.753354\pi$
$642$	9.38197	0.370277
$643$	−13.8885	−0.547711	−0.273855	−	0.961771i	$-0.588299\pi$
$643$	−13.8885	−0.547711	−0.273855	+	0.961771i	$0.588299\pi$
$644$	−1.70820	−0.0673127
$645$	0	0
$646$	−24.9443	−0.981419
$647$	−5.05573	−0.198761	−0.0993806	−	0.995049i	$-0.531686\pi$
$647$	−5.05573	−0.198761	−0.0993806	+	0.995049i	$0.531686\pi$
$648$	1.00000	0.0392837
$649$	−1.90983	−0.0749674
$650$	0	0
$651$	−1.67376	−0.0655999
$652$	8.47214	0.331794
$653$	2.85410	0.111690	0.0558448	−	0.998439i	$-0.482215\pi$
$653$	2.85410	0.111690	0.0558448	+	0.998439i	$0.482215\pi$
$654$	−12.7639	−0.499109
$655$	0	0
$656$	−7.70820	−0.300955
$657$	12.4721	0.486584
$658$	−4.47214	−0.174342
$659$	−18.3820	−0.716060	−0.358030	−	0.933710i	$-0.616551\pi$
$659$	−18.3820	−0.716060	−0.358030	+	0.933710i	$0.616551\pi$
$660$	0	0
$661$	−21.5279	−0.837337	−0.418668	−	0.908139i	$-0.637503\pi$
$661$	−21.5279	−0.837337	−0.418668	+	0.908139i	$0.637503\pi$
$662$	−18.0000	−0.699590
$663$	8.00000	0.310694
$664$	8.85410	0.343606
$665$	0	0
$666$	8.00000	0.309994
$667$	2.11146	0.0817559
$668$	−1.70820	−0.0660924
$669$	−3.09017	−0.119473
$670$	0	0
$671$	10.0000	0.386046
$672$	−0.381966	−0.0147347
$673$	24.4508	0.942511	0.471255	−	0.881997i	$-0.343801\pi$
$673$	24.4508	0.942511	0.471255	+	0.881997i	$0.343801\pi$
$674$	12.0902	0.465696
$675$	0	0
$676$	−6.88854	−0.264944
$677$	17.9098	0.688331	0.344165	−	0.938909i	$-0.388162\pi$
$677$	17.9098	0.688331	0.344165	+	0.938909i	$0.388162\pi$
$678$	14.7639	0.567005
$679$	−2.14590	−0.0823520
$680$	0	0
$681$	−11.2705	−0.431887
$682$	6.05573	0.231886
$683$	−4.50658	−0.172439	−0.0862197	−	0.996276i	$-0.527479\pi$
$683$	−4.50658	−0.172439	−0.0862197	+	0.996276i	$0.527479\pi$
$684$	7.70820	0.294731
$685$	0	0
$686$	−5.29180	−0.202042
$687$	14.4721	0.552146
$688$	5.70820	0.217623
$689$	22.4721	0.856120
$690$	0	0
$691$	6.76393	0.257312	0.128656	−	0.991689i	$-0.458934\pi$
$691$	6.76393	0.257312	0.128656	+	0.991689i	$0.458934\pi$
$692$	−6.09017	−0.231514
$693$	0.527864	0.0200519
$694$	0.437694	0.0166146
$695$	0	0
$696$	0.472136	0.0178963
$697$	24.9443	0.944832
$698$	7.88854	0.298586
$699$	12.6525	0.478561
$700$	0	0
$701$	−12.8328	−0.484689	−0.242344	−	0.970190i	$-0.577916\pi$
$701$	−12.8328	−0.484689	−0.242344	+	0.970190i	$0.577916\pi$
$702$	−2.47214	−0.0933048
$703$	61.6656	2.32576
$704$	1.38197	0.0520848
$705$	0	0
$706$	−8.76393	−0.329835
$707$	2.52786	0.0950701
$708$	1.38197	0.0519375
$709$	−30.2918	−1.13763	−0.568816	−	0.822465i	$-0.692598\pi$
$709$	−30.2918	−1.13763	−0.568816	+	0.822465i	$0.692598\pi$
$710$	0	0
$711$	−3.38197	−0.126834
$712$	12.4721	0.467413
$713$	−19.5967	−0.733904
$714$	1.23607	0.0462587
$715$	0	0
$716$	3.14590	0.117568
$717$	−25.7082	−0.960090
$718$	−0.180340	−0.00673022
$719$	−43.4164	−1.61916	−0.809579	−	0.587010i	$-0.800305\pi$
$719$	−43.4164	−1.61916	−0.809579	+	0.587010i	$0.800305\pi$
$720$	0	0
$721$	−0.506578	−0.0188659
$722$	40.4164	1.50414
$723$	10.5623	0.392816
$724$	24.6525	0.916202
$725$	0	0
$726$	9.09017	0.337368
$727$	−35.4164	−1.31352	−0.656761	−	0.754099i	$-0.728074\pi$
$727$	−35.4164	−1.31352	−0.656761	+	0.754099i	$0.728074\pi$
$728$	0.944272	0.0349970
$729$	1.00000	0.0370370
$730$	0	0
$731$	−18.4721	−0.683217
$732$	−7.23607	−0.267453
$733$	−0.111456	−0.00411673	−0.00205836	−	0.999998i	$-0.500655\pi$
$733$	−0.111456	−0.00411673	−0.00205836	+	0.999998i	$0.500655\pi$
$734$	−28.3820	−1.04760
$735$	0	0
$736$	−4.47214	−0.164845
$737$	−14.4721	−0.533088
$738$	−7.70820	−0.283743
$739$	−25.8197	−0.949792	−0.474896	−	0.880042i	$-0.657514\pi$
$739$	−25.8197	−0.949792	−0.474896	+	0.880042i	$0.657514\pi$
$740$	0	0
$741$	−19.0557	−0.700030
$742$	3.47214	0.127466
$743$	37.0132	1.35788	0.678940	−	0.734193i	$-0.262439\pi$
$743$	37.0132	1.35788	0.678940	+	0.734193i	$0.262439\pi$
$744$	−4.38197	−0.160651
$745$	0	0
$746$	−20.4721	−0.749538
$747$	8.85410	0.323955
$748$	−4.47214	−0.163517
$749$	−3.58359	−0.130942
$750$	0	0
$751$	0.201626	0.00735744	0.00367872	−	0.999993i	$-0.498829\pi$
$751$	0.201626	0.00735744	0.00367872	+	0.999993i	$0.498829\pi$
$752$	−11.7082	−0.426954
$753$	6.56231	0.239144
$754$	−1.16718	−0.0425063
$755$	0	0
$756$	−0.381966	−0.0138920
$757$	23.1246	0.840478	0.420239	−	0.907413i	$-0.361946\pi$
$757$	23.1246	0.840478	0.420239	+	0.907413i	$0.361946\pi$
$758$	2.18034	0.0791935
$759$	6.18034	0.224332
$760$	0	0
$761$	−25.4164	−0.921344	−0.460672	−	0.887570i	$-0.652392\pi$
$761$	−25.4164	−0.921344	−0.460672	+	0.887570i	$0.652392\pi$
$762$	−11.3820	−0.412325
$763$	4.87539	0.176501
$764$	17.7082	0.640660
$765$	0	0
$766$	−20.0000	−0.722629
$767$	−3.41641	−0.123359
$768$	−1.00000	−0.0360844
$769$	−35.6869	−1.28690	−0.643452	−	0.765487i	$-0.722498\pi$
$769$	−35.6869	−1.28690	−0.643452	+	0.765487i	$0.722498\pi$
$770$	0	0
$771$	22.0000	0.792311
$772$	11.1459	0.401150
$773$	−7.85410	−0.282492	−0.141246	−	0.989974i	$-0.545111\pi$
$773$	−7.85410	−0.282492	−0.141246	+	0.989974i	$0.545111\pi$
$774$	5.70820	0.205177
$775$	0	0
$776$	−5.61803	−0.201676
$777$	−3.05573	−0.109624
$778$	−14.6180	−0.524082
$779$	−59.4164	−2.12881
$780$	0	0
$781$	20.0000	0.715656
$782$	14.4721	0.517523
$783$	0.472136	0.0168728
$784$	−6.85410	−0.244789
$785$	0	0
$786$	−17.8885	−0.638063
$787$	−30.0689	−1.07184	−0.535920	−	0.844269i	$-0.680035\pi$
$787$	−30.0689	−1.07184	−0.535920	+	0.844269i	$0.680035\pi$
$788$	−5.90983	−0.210529
$789$	−1.70820	−0.0608137
$790$	0	0
$791$	−5.63932	−0.200511
$792$	1.38197	0.0491060
$793$	17.8885	0.635241
$794$	−35.2361	−1.25048
$795$	0	0
$796$	−18.5066	−0.655948
$797$	−36.5066	−1.29313	−0.646565	−	0.762859i	$-0.723795\pi$
$797$	−36.5066	−1.29313	−0.646565	+	0.762859i	$0.723795\pi$
$798$	−2.94427	−0.104226
$799$	37.8885	1.34040
$800$	0	0
$801$	12.4721	0.440681
$802$	12.2918	0.434038
$803$	17.2361	0.608248
$804$	10.4721	0.369324
$805$	0	0
$806$	10.8328	0.381570
$807$	−2.09017	−0.0735775
$808$	6.61803	0.232822
$809$	22.8328	0.802759	0.401380	−	0.915912i	$-0.368531\pi$
$809$	22.8328	0.802759	0.401380	+	0.915912i	$0.368531\pi$
$810$	0	0
$811$	7.70820	0.270672	0.135336	−	0.990800i	$-0.456789\pi$
$811$	7.70820	0.270672	0.135336	+	0.990800i	$0.456789\pi$
$812$	−0.180340	−0.00632869
$813$	−11.0344	−0.386995
$814$	11.0557	0.387503
$815$	0	0
$816$	3.23607	0.113285
$817$	44.0000	1.53937
$818$	−18.7984	−0.657270
$819$	0.944272	0.0329955
$820$	0	0
$821$	−33.9098	−1.18346	−0.591731	−	0.806136i	$-0.701555\pi$
$821$	−33.9098	−1.18346	−0.591731	+	0.806136i	$0.701555\pi$
$822$	−10.1803	−0.355080
$823$	32.0344	1.11665	0.558325	−	0.829622i	$-0.311444\pi$
$823$	32.0344	1.11665	0.558325	+	0.829622i	$0.311444\pi$
$824$	−1.32624	−0.0462017
$825$	0	0
$826$	−0.527864	−0.0183667
$827$	−43.1033	−1.49885	−0.749425	−	0.662090i	$-0.769670\pi$
$827$	−43.1033	−1.49885	−0.749425	+	0.662090i	$0.769670\pi$
$828$	−4.47214	−0.155417
$829$	−9.88854	−0.343443	−0.171722	−	0.985146i	$-0.554933\pi$
$829$	−9.88854	−0.343443	−0.171722	+	0.985146i	$0.554933\pi$
$830$	0	0
$831$	0.944272	0.0327564
$832$	2.47214	0.0857059
$833$	22.1803	0.768503
$834$	−1.52786	−0.0529056
$835$	0	0
$836$	10.6525	0.368424
$837$	−4.38197	−0.151463
$838$	8.09017	0.279470
$839$	−38.3607	−1.32436	−0.662179	−	0.749346i	$-0.730368\pi$
$839$	−38.3607	−1.32436	−0.662179	+	0.749346i	$0.730368\pi$
$840$	0	0
$841$	−28.7771	−0.992313
$842$	−27.2361	−0.938617
$843$	29.8885	1.02942
$844$	23.4164	0.806026
$845$	0	0
$846$	−11.7082	−0.402536
$847$	−3.47214	−0.119304
$848$	9.09017	0.312158
$849$	−31.4164	−1.07821
$850$	0	0
$851$	−35.7771	−1.22642
$852$	−14.4721	−0.495807
$853$	5.59675	0.191629	0.0958145	−	0.995399i	$-0.469454\pi$
$853$	5.59675	0.191629	0.0958145	+	0.995399i	$0.469454\pi$
$854$	2.76393	0.0945798
$855$	0	0
$856$	−9.38197	−0.320669
$857$	42.0689	1.43705	0.718523	−	0.695503i	$-0.244819\pi$
$857$	42.0689	1.43705	0.718523	+	0.695503i	$0.244819\pi$
$858$	−3.41641	−0.116634
$859$	−15.7082	−0.535957	−0.267979	−	0.963425i	$-0.586356\pi$
$859$	−15.7082	−0.535957	−0.267979	+	0.963425i	$0.586356\pi$
$860$	0	0
$861$	2.94427	0.100341
$862$	−36.8328	−1.25453
$863$	12.1803	0.414624	0.207312	−	0.978275i	$-0.433529\pi$
$863$	12.1803	0.414624	0.207312	+	0.978275i	$0.433529\pi$
$864$	−1.00000	−0.0340207
$865$	0	0
$866$	−22.5066	−0.764805
$867$	6.52786	0.221698
$868$	1.67376	0.0568112
$869$	−4.67376	−0.158547
$870$	0	0
$871$	−25.8885	−0.877200
$872$	12.7639	0.432241
$873$	−5.61803	−0.190142
$874$	−34.4721	−1.16604
$875$	0	0
$876$	−12.4721	−0.421394
$877$	3.12461	0.105511	0.0527553	−	0.998607i	$-0.483200\pi$
$877$	3.12461	0.105511	0.0527553	+	0.998607i	$0.483200\pi$
$878$	14.5066	0.489573
$879$	10.9098	0.367979
$880$	0	0
$881$	25.5967	0.862376	0.431188	−	0.902262i	$-0.358095\pi$
$881$	25.5967	0.862376	0.431188	+	0.902262i	$0.358095\pi$
$882$	−6.85410	−0.230790
$883$	28.0689	0.944593	0.472297	−	0.881440i	$-0.343425\pi$
$883$	28.0689	0.944593	0.472297	+	0.881440i	$0.343425\pi$
$884$	−8.00000	−0.269069
$885$	0	0
$886$	14.3820	0.483172
$887$	−3.41641	−0.114712	−0.0573559	−	0.998354i	$-0.518267\pi$
$887$	−3.41641	−0.114712	−0.0573559	+	0.998354i	$0.518267\pi$
$888$	−8.00000	−0.268462
$889$	4.34752	0.145811
$890$	0	0
$891$	1.38197	0.0462976
$892$	3.09017	0.103467
$893$	−90.2492	−3.02008
$894$	−10.9098	−0.364879
$895$	0	0
$896$	0.381966	0.0127606
$897$	11.0557	0.369140
$898$	−14.2918	−0.476923
$899$	−2.06888	−0.0690011
$900$	0	0
$901$	−29.4164	−0.980003
$902$	−10.6525	−0.354689
$903$	−2.18034	−0.0725572
$904$	−14.7639	−0.491041
$905$	0	0
$906$	−2.67376	−0.0888298
$907$	21.5279	0.714821	0.357410	−	0.933947i	$-0.383660\pi$
$907$	21.5279	0.714821	0.357410	+	0.933947i	$0.383660\pi$
$908$	11.2705	0.374025
$909$	6.61803	0.219506
$910$	0	0
$911$	−4.18034	−0.138501	−0.0692504	−	0.997599i	$-0.522061\pi$
$911$	−4.18034	−0.138501	−0.0692504	+	0.997599i	$0.522061\pi$
$912$	−7.70820	−0.255244
$913$	12.2361	0.404955
$914$	7.09017	0.234522
$915$	0	0
$916$	−14.4721	−0.478173
$917$	6.83282	0.225639
$918$	3.23607	0.106806
$919$	48.7214	1.60717	0.803585	−	0.595190i	$-0.202923\pi$
$919$	48.7214	1.60717	0.803585	+	0.595190i	$0.202923\pi$
$920$	0	0
$921$	−10.0000	−0.329511
$922$	−12.5623	−0.413718
$923$	35.7771	1.17762
$924$	−0.527864	−0.0173655
$925$	0	0
$926$	30.8328	1.01323
$927$	−1.32624	−0.0435594
$928$	−0.472136	−0.0154986
$929$	57.0132	1.87054	0.935270	−	0.353934i	$-0.115156\pi$
$929$	57.0132	1.87054	0.935270	+	0.353934i	$0.115156\pi$
$930$	0	0
$931$	−52.8328	−1.73153
$932$	−12.6525	−0.414446
$933$	18.9443	0.620208
$934$	26.3262	0.861421
$935$	0	0
$936$	2.47214	0.0808043
$937$	51.6869	1.68854	0.844269	−	0.535920i	$-0.180035\pi$
$937$	51.6869	1.68854	0.844269	+	0.535920i	$0.180035\pi$
$938$	−4.00000	−0.130605
$939$	−17.2705	−0.563602
$940$	0	0
$941$	−24.5623	−0.800708	−0.400354	−	0.916360i	$-0.631113\pi$
$941$	−24.5623	−0.800708	−0.400354	+	0.916360i	$0.631113\pi$
$942$	22.6525	0.738058
$943$	34.4721	1.12257
$944$	−1.38197	−0.0449792
$945$	0	0
$946$	7.88854	0.256479
$947$	−13.4377	−0.436666	−0.218333	−	0.975874i	$-0.570062\pi$
$947$	−13.4377	−0.436666	−0.218333	+	0.975874i	$0.570062\pi$
$948$	3.38197	0.109841
$949$	30.8328	1.00088
$950$	0	0
$951$	0.437694	0.0141932
$952$	−1.23607	−0.0400612
$953$	−57.3050	−1.85629	−0.928145	−	0.372219i	$-0.878597\pi$
$953$	−57.3050	−1.85629	−0.928145	+	0.372219i	$0.878597\pi$
$954$	9.09017	0.294305
$955$	0	0
$956$	25.7082	0.831463
$957$	0.652476	0.0210915
$958$	11.1246	0.359420
$959$	3.88854	0.125568
$960$	0	0
$961$	−11.7984	−0.380593
$962$	19.7771	0.637639
$963$	−9.38197	−0.302330
$964$	−10.5623	−0.340189
$965$	0	0
$966$	1.70820	0.0549606
$967$	22.0902	0.710372	0.355186	−	0.934796i	$-0.384418\pi$
$967$	22.0902	0.710372	0.355186	+	0.934796i	$0.384418\pi$
$968$	−9.09017	−0.292169
$969$	24.9443	0.801325
$970$	0	0
$971$	37.2148	1.19428	0.597140	−	0.802137i	$-0.296304\pi$
$971$	37.2148	1.19428	0.597140	+	0.802137i	$0.296304\pi$
$972$	−1.00000	−0.0320750
$973$	0.583592	0.0187091
$974$	−6.79837	−0.217834
$975$	0	0
$976$	7.23607	0.231621
$977$	−5.23607	−0.167517	−0.0837583	−	0.996486i	$-0.526692\pi$
$977$	−5.23607	−0.167517	−0.0837583	+	0.996486i	$0.526692\pi$
$978$	−8.47214	−0.270909
$979$	17.2361	0.550867
$980$	0	0
$981$	12.7639	0.407521
$982$	8.27051	0.263923
$983$	17.8197	0.568359	0.284179	−	0.958771i	$-0.408279\pi$
$983$	17.8197	0.568359	0.284179	+	0.958771i	$0.408279\pi$
$984$	7.70820	0.245729
$985$	0	0
$986$	1.52786	0.0486571
$987$	4.47214	0.142350
$988$	19.0557	0.606243
$989$	−25.5279	−0.811739
$990$	0	0
$991$	−26.4508	−0.840239	−0.420119	−	0.907469i	$-0.638012\pi$
$991$	−26.4508	−0.840239	−0.420119	+	0.907469i	$0.638012\pi$
$992$	4.38197	0.139128
$993$	18.0000	0.571213
$994$	5.52786	0.175333
$995$	0	0
$996$	−8.85410	−0.280553
$997$	43.5967	1.38072	0.690361	−	0.723465i	$-0.257452\pi$
$997$	43.5967	1.38072	0.690361	+	0.723465i	$0.257452\pi$
$998$	−13.5967	−0.430398
$999$	−8.00000	−0.253109

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3750.2.a.f.1.1		2
5.2	odd	4		3750.2.c.b.1249.3		4
5.3	odd	4		3750.2.c.b.1249.2		4
5.4	even	2		3750.2.a.d.1.2		2
25.2	odd	20		750.2.h.b.649.2		8
25.9	even	10		750.2.g.b.151.1		4
25.11	even	5		150.2.g.a.121.1	yes	4
25.12	odd	20		750.2.h.b.349.1		8
25.13	odd	20		750.2.h.b.349.2		8
25.14	even	10		750.2.g.b.601.1		4
25.16	even	5		150.2.g.a.31.1	✓	4
25.23	odd	20		750.2.h.b.649.1		8
75.11	odd	10		450.2.h.c.271.1		4
75.41	odd	10		450.2.h.c.181.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.g.a.31.1	✓	4	25.16	even	5
150.2.g.a.121.1	yes	4	25.11	even	5
450.2.h.c.181.1		4	75.41	odd	10
450.2.h.c.271.1		4	75.11	odd	10
750.2.g.b.151.1		4	25.9	even	10
750.2.g.b.601.1		4	25.14	even	10
750.2.h.b.349.1		8	25.12	odd	20
750.2.h.b.349.2		8	25.13	odd	20
750.2.h.b.649.1		8	25.23	odd	20
750.2.h.b.649.2		8	25.2	odd	20
3750.2.a.d.1.2		2	5.4	even	2
3750.2.a.f.1.1		2	1.1	even	1	trivial
3750.2.c.b.1249.2		4	5.3	odd	4
3750.2.c.b.1249.3		4	5.2	odd	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:	\( N \)	\(=\)	\( 3750 = 2 \cdot 3 \cdot 5^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3750.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +0.381966 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +0.381966 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.38197 q^{11} -1.00000 q^{12} +2.47214 q^{13} +0.381966 q^{14} +1.00000 q^{16} -3.23607 q^{17} +1.00000 q^{18} +7.70820 q^{19} -0.381966 q^{21} +1.38197 q^{22} -4.47214 q^{23} -1.00000 q^{24} +2.47214 q^{26} -1.00000 q^{27} +0.381966 q^{28} -0.472136 q^{29} +4.38197 q^{31} +1.00000 q^{32} -1.38197 q^{33} -3.23607 q^{34} +1.00000 q^{36} +8.00000 q^{37} +7.70820 q^{38} -2.47214 q^{39} -7.70820 q^{41} -0.381966 q^{42} +5.70820 q^{43} +1.38197 q^{44} -4.47214 q^{46} -11.7082 q^{47} -1.00000 q^{48} -6.85410 q^{49} +3.23607 q^{51} +2.47214 q^{52} +9.09017 q^{53} -1.00000 q^{54} +0.381966 q^{56} -7.70820 q^{57} -0.472136 q^{58} -1.38197 q^{59} +7.23607 q^{61} +4.38197 q^{62} +0.381966 q^{63} +1.00000 q^{64} -1.38197 q^{66} -10.4721 q^{67} -3.23607 q^{68} +4.47214 q^{69} +14.4721 q^{71} +1.00000 q^{72} +12.4721 q^{73} +8.00000 q^{74} +7.70820 q^{76} +0.527864 q^{77} -2.47214 q^{78} -3.38197 q^{79} +1.00000 q^{81} -7.70820 q^{82} +8.85410 q^{83} -0.381966 q^{84} +5.70820 q^{86} +0.472136 q^{87} +1.38197 q^{88} +12.4721 q^{89} +0.944272 q^{91} -4.47214 q^{92} -4.38197 q^{93} -11.7082 q^{94} -1.00000 q^{96} -5.61803 q^{97} -6.85410 q^{98} +1.38197 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{6} + 3 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^6 + 3 * q^7 + 2 * q^8 + 2 * q^9	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{6} + 3 q^{7} + 2 q^{8} + 2 q^{9} + 5 q^{11} - 2 q^{12} - 4 q^{13} + 3 q^{14} + 2 q^{16} - 2 q^{17} + 2 q^{18} + 2 q^{19} - 3 q^{21} + 5 q^{22} - 2 q^{24} - 4 q^{26} - 2 q^{27} + 3 q^{28} + 8 q^{29} + 11 q^{31} + 2 q^{32} - 5 q^{33} - 2 q^{34} + 2 q^{36} + 16 q^{37} + 2 q^{38} + 4 q^{39} - 2 q^{41} - 3 q^{42} - 2 q^{43} + 5 q^{44} - 10 q^{47} - 2 q^{48} - 7 q^{49} + 2 q^{51} - 4 q^{52} + 7 q^{53} - 2 q^{54} + 3 q^{56} - 2 q^{57} + 8 q^{58} - 5 q^{59} + 10 q^{61} + 11 q^{62} + 3 q^{63} + 2 q^{64} - 5 q^{66} - 12 q^{67} - 2 q^{68} + 20 q^{71} + 2 q^{72} + 16 q^{73} + 16 q^{74} + 2 q^{76} + 10 q^{77} + 4 q^{78} - 9 q^{79} + 2 q^{81} - 2 q^{82} + 11 q^{83} - 3 q^{84} - 2 q^{86} - 8 q^{87} + 5 q^{88} + 16 q^{89} - 16 q^{91} - 11 q^{93} - 10 q^{94} - 2 q^{96} - 9 q^{97} - 7 q^{98} + 5 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^6 + 3 * q^7 + 2 * q^8 + 2 * q^9 + 5 * q^11 - 2 * q^12 - 4 * q^13 + 3 * q^14 + 2 * q^16 - 2 * q^17 + 2 * q^18 + 2 * q^19 - 3 * q^21 + 5 * q^22 - 2 * q^24 - 4 * q^26 - 2 * q^27 + 3 * q^28 + 8 * q^29 + 11 * q^31 + 2 * q^32 - 5 * q^33 - 2 * q^34 + 2 * q^36 + 16 * q^37 + 2 * q^38 + 4 * q^39 - 2 * q^41 - 3 * q^42 - 2 * q^43 + 5 * q^44 - 10 * q^47 - 2 * q^48 - 7 * q^49 + 2 * q^51 - 4 * q^52 + 7 * q^53 - 2 * q^54 + 3 * q^56 - 2 * q^57 + 8 * q^58 - 5 * q^59 + 10 * q^61 + 11 * q^62 + 3 * q^63 + 2 * q^64 - 5 * q^66 - 12 * q^67 - 2 * q^68 + 20 * q^71 + 2 * q^72 + 16 * q^73 + 16 * q^74 + 2 * q^76 + 10 * q^77 + 4 * q^78 - 9 * q^79 + 2 * q^81 - 2 * q^82 + 11 * q^83 - 3 * q^84 - 2 * q^86 - 8 * q^87 + 5 * q^88 + 16 * q^89 - 16 * q^91 - 11 * q^93 - 10 * q^94 - 2 * q^96 - 9 * q^97 - 7 * q^98 + 5 * q^99

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