LMFDB - Embedded newform 1450.2.a.p.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1450.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$11.5783082931$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.621.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 6x - 3 $ x^3 - 6*x - 3
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 290)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.523976$ of defining polynomial
Character	$\chi$	$=$	1450.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.52398 q^{3} +1.00000 q^{4} +1.52398 q^{6} -3.67750 q^{7} -1.00000 q^{8} -0.677496 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.52398 q^{3} +1.00000 q^{4} +1.52398 q^{6} -3.67750 q^{7} -1.00000 q^{8} -0.677496 q^{9} -1.04795 q^{11} -1.52398 q^{12} +5.92692 q^{13} +3.67750 q^{14} +1.00000 q^{16} +2.72545 q^{17} +0.677496 q^{18} +7.45090 q^{19} +5.60442 q^{21} +1.04795 q^{22} -1.92692 q^{23} +1.52398 q^{24} -5.92692 q^{26} +5.60442 q^{27} -3.67750 q^{28} -1.00000 q^{29} -6.72545 q^{31} -1.00000 q^{32} +1.59706 q^{33} -2.72545 q^{34} -0.677496 q^{36} -5.35499 q^{37} -7.45090 q^{38} -9.03249 q^{39} -9.35499 q^{41} -5.60442 q^{42} +0.725449 q^{43} -1.04795 q^{44} +1.92692 q^{46} -2.09591 q^{47} -1.52398 q^{48} +6.52398 q^{49} -4.15352 q^{51} +5.92692 q^{52} +8.17635 q^{53} -5.60442 q^{54} +3.67750 q^{56} -11.3550 q^{57} +1.00000 q^{58} +2.97487 q^{59} +6.57193 q^{61} +6.72545 q^{62} +2.49149 q^{63} +1.00000 q^{64} -1.59706 q^{66} -14.4989 q^{67} +2.72545 q^{68} +2.93658 q^{69} -12.0000 q^{71} +0.677496 q^{72} +6.72545 q^{73} +5.35499 q^{74} +7.45090 q^{76} +3.85384 q^{77} +9.03249 q^{78} -11.3778 q^{79} -6.50851 q^{81} +9.35499 q^{82} -11.4509 q^{83} +5.60442 q^{84} -0.725449 q^{86} +1.52398 q^{87} +1.04795 q^{88} -1.04795 q^{89} -21.7962 q^{91} -1.92692 q^{92} +10.2494 q^{93} +2.09591 q^{94} +1.52398 q^{96} -9.92692 q^{97} -6.52398 q^{98} +0.709984 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 3 q^{6} - 3 q^{7} - 3 q^{8} + 6 q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 + 3 * q^6 - 3 * q^7 - 3 * q^8 + 6 * q^9	$ 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 3 q^{6} - 3 q^{7} - 3 q^{8} + 6 q^{9} - 3 q^{12} - 3 q^{13} + 3 q^{14} + 3 q^{16} - 3 q^{17} - 6 q^{18} - 12 q^{21} + 15 q^{23} + 3 q^{24} + 3 q^{26} - 12 q^{27} - 3 q^{28} - 3 q^{29} - 9 q^{31} - 3 q^{32} + 24 q^{33} + 3 q^{34} + 6 q^{36} - 3 q^{39} - 12 q^{41} + 12 q^{42} - 9 q^{43} - 15 q^{46} - 3 q^{48} + 18 q^{49} - 6 q^{51} - 3 q^{52} - 9 q^{53} + 12 q^{54} + 3 q^{56} - 18 q^{57} + 3 q^{58} - 15 q^{59} + 15 q^{61} + 9 q^{62} + 30 q^{63} + 3 q^{64} - 24 q^{66} - 18 q^{67} - 3 q^{68} - 9 q^{69} - 36 q^{71} - 6 q^{72} + 9 q^{73} - 30 q^{77} + 3 q^{78} + 9 q^{79} + 3 q^{81} + 12 q^{82} - 12 q^{83} - 12 q^{84} + 9 q^{86} + 3 q^{87} - 24 q^{91} + 15 q^{92} + 18 q^{93} + 3 q^{96} - 9 q^{97} - 18 q^{98} - 30 q^{99}+O(q^{100}) $ 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 + 3 * q^6 - 3 * q^7 - 3 * q^8 + 6 * q^9 - 3 * q^12 - 3 * q^13 + 3 * q^14 + 3 * q^16 - 3 * q^17 - 6 * q^18 - 12 * q^21 + 15 * q^23 + 3 * q^24 + 3 * q^26 - 12 * q^27 - 3 * q^28 - 3 * q^29 - 9 * q^31 - 3 * q^32 + 24 * q^33 + 3 * q^34 + 6 * q^36 - 3 * q^39 - 12 * q^41 + 12 * q^42 - 9 * q^43 - 15 * q^46 - 3 * q^48 + 18 * q^49 - 6 * q^51 - 3 * q^52 - 9 * q^53 + 12 * q^54 + 3 * q^56 - 18 * q^57 + 3 * q^58 - 15 * q^59 + 15 * q^61 + 9 * q^62 + 30 * q^63 + 3 * q^64 - 24 * q^66 - 18 * q^67 - 3 * q^68 - 9 * q^69 - 36 * q^71 - 6 * q^72 + 9 * q^73 - 30 * q^77 + 3 * q^78 + 9 * q^79 + 3 * q^81 + 12 * q^82 - 12 * q^83 - 12 * q^84 + 9 * q^86 + 3 * q^87 - 24 * q^91 + 15 * q^92 + 18 * q^93 + 3 * q^96 - 9 * q^97 - 18 * q^98 - 30 * 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
$3$	−1.52398	−0.879868	−0.439934	−	0.898030i	$-0.644998\pi$
$3$	−1.52398	−0.879868	−0.439934	+	0.898030i	$0.644998\pi$
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	1.52398	0.622161
$7$	−3.67750	−1.38996	−0.694981	−	0.719028i	$-0.744587\pi$
$7$	−3.67750	−1.38996	−0.694981	+	0.719028i	$0.744587\pi$
$8$	−1.00000	−0.353553
$9$	−0.677496	−0.225832
$10$	0	0
$11$	−1.04795	−0.315970	−0.157985	−	0.987442i	$-0.550500\pi$
$11$	−1.04795	−0.315970	−0.157985	+	0.987442i	$0.550500\pi$
$12$	−1.52398	−0.439934
$13$	5.92692	1.64383	0.821916	−	0.569609i	$-0.192905\pi$
$13$	5.92692	1.64383	0.821916	+	0.569609i	$0.192905\pi$
$14$	3.67750	0.982852
$15$	0	0
$16$	1.00000	0.250000
$17$	2.72545	0.661018	0.330509	−	0.943803i	$-0.392780\pi$
$17$	2.72545	0.661018	0.330509	+	0.943803i	$0.392780\pi$
$18$	0.677496	0.159687
$19$	7.45090	1.70935	0.854677	−	0.519161i	$-0.173755\pi$
$19$	7.45090	1.70935	0.854677	+	0.519161i	$0.173755\pi$
$20$	0	0
$21$	5.60442	1.22298
$22$	1.04795	0.223424
$23$	−1.92692	−0.401791	−0.200895	−	0.979613i	$-0.564385\pi$
$23$	−1.92692	−0.401791	−0.200895	+	0.979613i	$0.564385\pi$
$24$	1.52398	0.311080
$25$	0	0
$26$	−5.92692	−1.16236
$27$	5.60442	1.07857
$28$	−3.67750	−0.694981
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	0	0
$31$	−6.72545	−1.20793	−0.603963	−	0.797012i	$-0.706413\pi$
$31$	−6.72545	−1.20793	−0.603963	+	0.797012i	$0.706413\pi$
$32$	−1.00000	−0.176777
$33$	1.59706	0.278012
$34$	−2.72545	−0.467411
$35$	0	0
$36$	−0.677496	−0.112916
$37$	−5.35499	−0.880355	−0.440178	−	0.897911i	$-0.645085\pi$
$37$	−5.35499	−0.880355	−0.440178	+	0.897911i	$0.645085\pi$
$38$	−7.45090	−1.20870
$39$	−9.03249	−1.44636
$40$	0	0
$41$	−9.35499	−1.46100	−0.730502	−	0.682910i	$-0.760714\pi$
$41$	−9.35499	−1.46100	−0.730502	+	0.682910i	$0.760714\pi$
$42$	−5.60442	−0.864780
$43$	0.725449	0.110630	0.0553149	−	0.998469i	$-0.482384\pi$
$43$	0.725449	0.110630	0.0553149	+	0.998469i	$0.482384\pi$
$44$	−1.04795	−0.157985
$45$	0	0
$46$	1.92692	0.284109
$47$	−2.09591	−0.305719	−0.152860	−	0.988248i	$-0.548848\pi$
$47$	−2.09591	−0.305719	−0.152860	+	0.988248i	$0.548848\pi$
$48$	−1.52398	−0.219967
$49$	6.52398	0.931997
$50$	0	0
$51$	−4.15352	−0.581609
$52$	5.92692	0.821916
$53$	8.17635	1.12311	0.561554	−	0.827440i	$-0.310204\pi$
$53$	8.17635	1.12311	0.561554	+	0.827440i	$0.310204\pi$
$54$	−5.60442	−0.762665
$55$	0	0
$56$	3.67750	0.491426
$57$	−11.3550	−1.50401
$58$	1.00000	0.131306
$59$	2.97487	0.387296	0.193648	−	0.981071i	$-0.437968\pi$
$59$	2.97487	0.387296	0.193648	+	0.981071i	$0.437968\pi$
$60$	0	0
$61$	6.57193	0.841449	0.420725	−	0.907188i	$-0.361776\pi$
$61$	6.57193	0.841449	0.420725	+	0.907188i	$0.361776\pi$
$62$	6.72545	0.854133
$63$	2.49149	0.313898
$64$	1.00000	0.125000
$65$	0	0
$66$	−1.59706	−0.196584
$67$	−14.4989	−1.77132	−0.885658	−	0.464338i	$-0.846292\pi$
$67$	−14.4989	−1.77132	−0.885658	+	0.464338i	$0.846292\pi$
$68$	2.72545	0.330509
$69$	2.93658	0.353523
$70$	0	0
$71$	−12.0000	−1.42414	−0.712069	−	0.702109i	$-0.752242\pi$
$71$	−12.0000	−1.42414	−0.712069	+	0.702109i	$0.752242\pi$
$72$	0.677496	0.0798437
$73$	6.72545	0.787154	0.393577	−	0.919292i	$-0.371237\pi$
$73$	6.72545	0.787154	0.393577	+	0.919292i	$0.371237\pi$
$74$	5.35499	0.622505
$75$	0	0
$76$	7.45090	0.854677
$77$	3.85384	0.439186
$78$	9.03249	1.02273
$79$	−11.3778	−1.28010	−0.640052	−	0.768331i	$-0.721087\pi$
$79$	−11.3778	−1.28010	−0.640052	+	0.768331i	$0.721087\pi$
$80$	0	0
$81$	−6.50851	−0.723168
$82$	9.35499	1.03309
$83$	−11.4509	−1.25690	−0.628450	−	0.777850i	$-0.716310\pi$
$83$	−11.4509	−1.25690	−0.628450	+	0.777850i	$0.716310\pi$
$84$	5.60442	0.611492
$85$	0	0
$86$	−0.725449	−0.0782271
$87$	1.52398	0.163387
$88$	1.04795	0.111712
$89$	−1.04795	−0.111083	−0.0555414	−	0.998456i	$-0.517688\pi$
$89$	−1.04795	−0.111083	−0.0555414	+	0.998456i	$0.517688\pi$
$90$	0	0
$91$	−21.7962	−2.28487
$92$	−1.92692	−0.200895
$93$	10.2494	1.06282
$94$	2.09591	0.216176
$95$	0	0
$96$	1.52398	0.155540
$97$	−9.92692	−1.00793	−0.503963	−	0.863725i	$-0.668125\pi$
$97$	−9.92692	−1.00793	−0.503963	+	0.863725i	$0.668125\pi$
$98$	−6.52398	−0.659021
$99$	0.709984	0.0713561
$100$	0	0
$101$	10.2340	1.01832	0.509159	−	0.860673i	$-0.329957\pi$
$101$	10.2340	1.01832	0.509159	+	0.860673i	$0.329957\pi$
$102$	4.15352	0.411260
$103$	6.30704	0.621451	0.310726	−	0.950500i	$-0.399428\pi$
$103$	6.30704	0.621451	0.310726	+	0.950500i	$0.399428\pi$
$104$	−5.92692	−0.581182
$105$	0	0
$106$	−8.17635	−0.794157
$107$	−9.35499	−0.904381	−0.452191	−	0.891921i	$-0.649357\pi$
$107$	−9.35499	−0.904381	−0.452191	+	0.891921i	$0.649357\pi$
$108$	5.60442	0.539285
$109$	19.4509	1.86306	0.931529	−	0.363667i	$-0.118475\pi$
$109$	19.4509	1.86306	0.931529	+	0.363667i	$0.118475\pi$
$110$	0	0
$111$	8.16088	0.774597
$112$	−3.67750	−0.347491
$113$	−16.0228	−1.50730	−0.753650	−	0.657276i	$-0.771709\pi$
$113$	−16.0228	−1.50730	−0.753650	+	0.657276i	$0.771709\pi$
$114$	11.3550	1.06349
$115$	0	0
$116$	−1.00000	−0.0928477
$117$	−4.01546	−0.371230
$118$	−2.97487	−0.273859
$119$	−10.0228	−0.918791
$120$	0	0
$121$	−9.90179	−0.900163
$122$	−6.57193	−0.594995
$123$	14.2568	1.28549
$124$	−6.72545	−0.603963
$125$	0	0
$126$	−2.49149	−0.221959
$127$	−8.00000	−0.709885	−0.354943	−	0.934888i	$-0.615500\pi$
$127$	−8.00000	−0.709885	−0.354943	+	0.934888i	$0.615500\pi$
$128$	−1.00000	−0.0883883
$129$	−1.10557	−0.0973397
$130$	0	0
$131$	2.80589	0.245152	0.122576	−	0.992459i	$-0.460885\pi$
$131$	2.80589	0.245152	0.122576	+	0.992459i	$0.460885\pi$
$132$	1.59706	0.139006
$133$	−27.4006	−2.37594
$134$	14.4989	1.25251
$135$	0	0
$136$	−2.72545	−0.233705
$137$	−13.9269	−1.18986	−0.594929	−	0.803779i	$-0.702820\pi$
$137$	−13.9269	−1.18986	−0.594929	+	0.803779i	$0.702820\pi$
$138$	−2.93658	−0.249978
$139$	−9.03249	−0.766126	−0.383063	−	0.923722i	$-0.625131\pi$
$139$	−9.03249	−0.766126	−0.383063	+	0.923722i	$0.625131\pi$
$140$	0	0
$141$	3.19411	0.268993
$142$	12.0000	1.00702
$143$	−6.21113	−0.519401
$144$	−0.677496	−0.0564580
$145$	0	0
$146$	−6.72545	−0.556602
$147$	−9.94239	−0.820034
$148$	−5.35499	−0.440178
$149$	−19.7579	−1.61863	−0.809317	−	0.587373i	$-0.800162\pi$
$149$	−19.7579	−1.61863	−0.809317	+	0.587373i	$0.800162\pi$
$150$	0	0
$151$	11.8538	0.964652	0.482326	−	0.875992i	$-0.339792\pi$
$151$	11.8538	0.964652	0.482326	+	0.875992i	$0.339792\pi$
$152$	−7.45090	−0.604348
$153$	−1.84648	−0.149279
$154$	−3.85384	−0.310551
$155$	0	0
$156$	−9.03249	−0.723178
$157$	10.0000	0.798087	0.399043	−	0.916932i	$-0.369342\pi$
$157$	10.0000	0.798087	0.399043	+	0.916932i	$0.369342\pi$
$158$	11.3778	0.905171
$159$	−12.4606	−0.988187
$160$	0	0
$161$	7.08624	0.558474
$162$	6.50851	0.511357
$163$	−5.90409	−0.462444	−0.231222	−	0.972901i	$-0.574272\pi$
$163$	−5.90409	−0.462444	−0.231222	+	0.972901i	$0.574272\pi$
$164$	−9.35499	−0.730502
$165$	0	0
$166$	11.4509	0.888762
$167$	8.93658	0.691533	0.345767	−	0.938320i	$-0.387619\pi$
$167$	8.93658	0.691533	0.345767	+	0.938320i	$0.387619\pi$
$168$	−5.60442	−0.432390
$169$	22.1284	1.70218
$170$	0	0
$171$	−5.04795	−0.386027
$172$	0.725449	0.0553149
$173$	8.97487	0.682347	0.341174	−	0.940000i	$-0.389176\pi$
$173$	8.97487	0.682347	0.341174	+	0.940000i	$0.389176\pi$
$174$	−1.52398	−0.115532
$175$	0	0
$176$	−1.04795	−0.0789924
$177$	−4.53364	−0.340769
$178$	1.04795	0.0785474
$179$	5.83102	0.435831	0.217915	−	0.975968i	$-0.430074\pi$
$179$	5.83102	0.435831	0.217915	+	0.975968i	$0.430074\pi$
$180$	0	0
$181$	7.45090	0.553821	0.276910	−	0.960896i	$-0.410689\pi$
$181$	7.45090	0.553821	0.276910	+	0.960896i	$0.410689\pi$
$182$	21.7962	1.61564
$183$	−10.0155	−0.740364
$184$	1.92692	0.142055
$185$	0	0
$186$	−10.2494	−0.751524
$187$	−2.85614	−0.208862
$188$	−2.09591	−0.152860
$189$	−20.6102	−1.49917
$190$	0	0
$191$	−22.2723	−1.61156	−0.805782	−	0.592213i	$-0.798255\pi$
$191$	−22.2723	−1.61156	−0.805782	+	0.592213i	$0.798255\pi$
$192$	−1.52398	−0.109984
$193$	−16.9749	−1.22188	−0.610939	−	0.791678i	$-0.709208\pi$
$193$	−16.9749	−1.22188	−0.610939	+	0.791678i	$0.709208\pi$
$194$	9.92692	0.712711
$195$	0	0
$196$	6.52398	0.465998
$197$	−9.43543	−0.672247	−0.336123	−	0.941818i	$-0.609116\pi$
$197$	−9.43543	−0.672247	−0.336123	+	0.941818i	$0.609116\pi$
$198$	−0.709984	−0.0504563
$199$	20.1609	1.42917	0.714583	−	0.699550i	$-0.246616\pi$
$199$	20.1609	1.42917	0.714583	+	0.699550i	$0.246616\pi$
$200$	0	0
$201$	22.0959	1.55853
$202$	−10.2340	−0.720059
$203$	3.67750	0.258110
$204$	−4.15352	−0.290805
$205$	0	0
$206$	−6.30704	−0.439432
$207$	1.30548	0.0907372
$208$	5.92692	0.410958
$209$	−7.80819	−0.540104
$210$	0	0
$211$	9.04795	0.622887	0.311443	−	0.950265i	$-0.399188\pi$
$211$	9.04795	0.622887	0.311443	+	0.950265i	$0.399188\pi$
$212$	8.17635	0.561554
$213$	18.2877	1.25305
$214$	9.35499	0.639494
$215$	0	0
$216$	−5.60442	−0.381332
$217$	24.7328	1.67897
$218$	−19.4509	−1.31738
$219$	−10.2494	−0.692592
$220$	0	0
$221$	16.1535	1.08660
$222$	−8.16088	−0.547722
$223$	−24.0228	−1.60869	−0.804344	−	0.594164i	$-0.797483\pi$
$223$	−24.0228	−1.60869	−0.804344	+	0.594164i	$0.797483\pi$
$224$	3.67750	0.245713
$225$	0	0
$226$	16.0228	1.06582
$227$	14.8059	0.982701	0.491351	−	0.870962i	$-0.336503\pi$
$227$	14.8059	0.982701	0.491351	+	0.870962i	$0.336503\pi$
$228$	−11.3550	−0.752003
$229$	−15.8693	−1.04867	−0.524337	−	0.851511i	$-0.675687\pi$
$229$	−15.8693	−1.04867	−0.524337	+	0.851511i	$0.675687\pi$
$230$	0	0
$231$	−5.87316	−0.386426
$232$	1.00000	0.0656532
$233$	1.80819	0.118458	0.0592292	−	0.998244i	$-0.481136\pi$
$233$	1.80819	0.118458	0.0592292	+	0.998244i	$0.481136\pi$
$234$	4.01546	0.262499
$235$	0	0
$236$	2.97487	0.193648
$237$	17.3395	1.12632
$238$	10.0228	0.649683
$239$	−20.3070	−1.31355	−0.656777	−	0.754085i	$-0.728081\pi$
$239$	−20.3070	−1.31355	−0.656777	+	0.754085i	$0.728081\pi$
$240$	0	0
$241$	−9.61988	−0.619671	−0.309836	−	0.950790i	$-0.600274\pi$
$241$	−9.61988	−0.619671	−0.309836	+	0.950790i	$0.600274\pi$
$242$	9.90179	0.636511
$243$	−6.89443	−0.442278
$244$	6.57193	0.420725
$245$	0	0
$246$	−14.2568	−0.908980
$247$	44.1609	2.80989
$248$	6.72545	0.427066
$249$	17.4509	1.10591
$250$	0	0
$251$	7.25909	0.458189	0.229095	−	0.973404i	$-0.426423\pi$
$251$	7.25909	0.458189	0.229095	+	0.973404i	$0.426423\pi$
$252$	2.49149	0.156949
$253$	2.01932	0.126954
$254$	8.00000	0.501965
$255$	0	0
$256$	1.00000	0.0625000
$257$	−7.25909	−0.452809	−0.226405	−	0.974033i	$-0.572697\pi$
$257$	−7.25909	−0.452809	−0.226405	+	0.974033i	$0.572697\pi$
$258$	1.10557	0.0688296
$259$	19.6930	1.22366
$260$	0	0
$261$	0.677496	0.0419359
$262$	−2.80589	−0.173348
$263$	12.0000	0.739952	0.369976	−	0.929041i	$-0.379366\pi$
$263$	12.0000	0.739952	0.369976	+	0.929041i	$0.379366\pi$
$264$	−1.59706	−0.0982920
$265$	0	0
$266$	27.4006	1.68004
$267$	1.59706	0.0977382
$268$	−14.4989	−0.885658
$269$	−19.6775	−1.19976	−0.599879	−	0.800091i	$-0.704785\pi$
$269$	−19.6775	−1.19976	−0.599879	+	0.800091i	$0.704785\pi$
$270$	0	0
$271$	−8.40294	−0.510443	−0.255221	−	0.966883i	$-0.582148\pi$
$271$	−8.40294	−0.510443	−0.255221	+	0.966883i	$0.582148\pi$
$272$	2.72545	0.165255
$273$	33.2169	2.01038
$274$	13.9269	0.841356
$275$	0	0
$276$	2.93658	0.176761
$277$	14.6141	0.878075	0.439037	−	0.898469i	$-0.355320\pi$
$277$	14.6141	0.878075	0.439037	+	0.898469i	$0.355320\pi$
$278$	9.03249	0.541733
$279$	4.55646	0.272788
$280$	0	0
$281$	16.4834	0.983316	0.491658	−	0.870788i	$-0.336391\pi$
$281$	16.4834	0.983316	0.491658	+	0.870788i	$0.336391\pi$
$282$	−3.19411	−0.190207
$283$	3.45090	0.205135	0.102567	−	0.994726i	$-0.467294\pi$
$283$	3.45090	0.205135	0.102567	+	0.994726i	$0.467294\pi$
$284$	−12.0000	−0.712069
$285$	0	0
$286$	6.21113	0.367272
$287$	34.4029	2.03074
$288$	0.677496	0.0399218
$289$	−9.57193	−0.563055
$290$	0	0
$291$	15.1284	0.886842
$292$	6.72545	0.393577
$293$	−2.64501	−0.154523	−0.0772615	−	0.997011i	$-0.524618\pi$
$293$	−2.64501	−0.154523	−0.0772615	+	0.997011i	$0.524618\pi$
$294$	9.94239	0.579852
$295$	0	0
$296$	5.35499	0.311253
$297$	−5.87316	−0.340796
$298$	19.7579	1.14455
$299$	−11.4207	−0.660477
$300$	0	0
$301$	−2.66783	−0.153771
$302$	−11.8538	−0.682112
$303$	−15.5963	−0.895985
$304$	7.45090	0.427338
$305$	0	0
$306$	1.84648	0.105556
$307$	14.9018	0.850490	0.425245	−	0.905078i	$-0.360188\pi$
$307$	14.9018	0.850490	0.425245	+	0.905078i	$0.360188\pi$
$308$	3.85384	0.219593
$309$	−9.61178	−0.546795
$310$	0	0
$311$	−23.2317	−1.31735	−0.658673	−	0.752429i	$-0.728882\pi$
$311$	−23.2317	−1.31735	−0.658673	+	0.752429i	$0.728882\pi$
$312$	9.03249	0.511364
$313$	22.9977	1.29991	0.649953	−	0.759974i	$-0.274788\pi$
$313$	22.9977	1.29991	0.649953	+	0.759974i	$0.274788\pi$
$314$	−10.0000	−0.564333
$315$	0	0
$316$	−11.3778	−0.640052
$317$	−30.6597	−1.72202	−0.861011	−	0.508586i	$-0.830168\pi$
$317$	−30.6597	−1.72202	−0.861011	+	0.508586i	$0.830168\pi$
$318$	12.4606	0.698753
$319$	1.04795	0.0586741
$320$	0	0
$321$	14.2568	0.795736
$322$	−7.08624	−0.394901
$323$	20.3070	1.12991
$324$	−6.50851	−0.361584
$325$	0	0
$326$	5.90409	0.326998
$327$	−29.6427	−1.63925
$328$	9.35499	0.516543
$329$	7.70768	0.424938
$330$	0	0
$331$	−0.856142	−0.0470578	−0.0235289	−	0.999723i	$-0.507490\pi$
$331$	−0.856142	−0.0470578	−0.0235289	+	0.999723i	$0.507490\pi$
$332$	−11.4509	−0.628450
$333$	3.62799	0.198812
$334$	−8.93658	−0.488988
$335$	0	0
$336$	5.60442	0.305746
$337$	3.37046	0.183600	0.0918002	−	0.995777i	$-0.470738\pi$
$337$	3.37046	0.183600	0.0918002	+	0.995777i	$0.470738\pi$
$338$	−22.1284	−1.20363
$339$	24.4184	1.32623
$340$	0	0
$341$	7.04795	0.381668
$342$	5.04795	0.272962
$343$	1.75057	0.0945222
$344$	−0.725449	−0.0391136
$345$	0	0
$346$	−8.97487	−0.482492
$347$	−29.0627	−1.56017	−0.780083	−	0.625676i	$-0.784823\pi$
$347$	−29.0627	−1.56017	−0.780083	+	0.625676i	$0.784823\pi$
$348$	1.52398	0.0816937
$349$	−21.4006	−1.14555	−0.572775	−	0.819713i	$-0.694133\pi$
$349$	−21.4006	−1.14555	−0.572775	+	0.819713i	$0.694133\pi$
$350$	0	0
$351$	33.2169	1.77299
$352$	1.04795	0.0558561
$353$	15.3047	0.814589	0.407295	−	0.913297i	$-0.366472\pi$
$353$	15.3047	0.814589	0.407295	+	0.913297i	$0.366472\pi$
$354$	4.53364	0.240960
$355$	0	0
$356$	−1.04795	−0.0555414
$357$	15.2746	0.808415
$358$	−5.83102	−0.308179
$359$	−14.4258	−0.761363	−0.380682	−	0.924706i	$-0.624311\pi$
$359$	−14.4258	−0.761363	−0.380682	+	0.924706i	$0.624311\pi$
$360$	0	0
$361$	36.5159	1.92189
$362$	−7.45090	−0.391610
$363$	15.0901	0.792025
$364$	−21.7962	−1.14243
$365$	0	0
$366$	10.0155	0.523517
$367$	−9.75794	−0.509360	−0.254680	−	0.967025i	$-0.581970\pi$
$367$	−9.75794	−0.509360	−0.254680	+	0.967025i	$0.581970\pi$
$368$	−1.92692	−0.100448
$369$	6.33797	0.329941
$370$	0	0
$371$	−30.0685	−1.56108
$372$	10.2494	0.531408
$373$	16.7904	0.869375	0.434688	−	0.900581i	$-0.356859\pi$
$373$	16.7904	0.869375	0.434688	+	0.900581i	$0.356859\pi$
$374$	2.85614	0.147688
$375$	0	0
$376$	2.09591	0.108088
$377$	−5.92692	−0.305252
$378$	20.6102	1.06008
$379$	4.85614	0.249443	0.124722	−	0.992192i	$-0.460196\pi$
$379$	4.85614	0.249443	0.124722	+	0.992192i	$0.460196\pi$
$380$	0	0
$381$	12.1918	0.624605
$382$	22.2723	1.13955
$383$	5.32020	0.271850	0.135925	−	0.990719i	$-0.456599\pi$
$383$	5.32020	0.271850	0.135925	+	0.990719i	$0.456599\pi$
$384$	1.52398	0.0777701
$385$	0	0
$386$	16.9749	0.863998
$387$	−0.491489	−0.0249838
$388$	−9.92692	−0.503963
$389$	−23.6118	−1.19716	−0.598582	−	0.801061i	$-0.704269\pi$
$389$	−23.6118	−1.19716	−0.598582	+	0.801061i	$0.704269\pi$
$390$	0	0
$391$	−5.25172	−0.265591
$392$	−6.52398	−0.329511
$393$	−4.27611	−0.215701
$394$	9.43543	0.475350
$395$	0	0
$396$	0.709984	0.0356780
$397$	34.2413	1.71852	0.859261	−	0.511537i	$-0.170924\pi$
$397$	34.2413	1.71852	0.859261	+	0.511537i	$0.170924\pi$
$398$	−20.1609	−1.01057
$399$	41.7579	2.09051
$400$	0	0
$401$	−23.2317	−1.16013	−0.580067	−	0.814569i	$-0.696974\pi$
$401$	−23.2317	−1.16013	−0.580067	+	0.814569i	$0.696974\pi$
$402$	−22.0959	−1.10204
$403$	−39.8612	−1.98563
$404$	10.2340	0.509159
$405$	0	0
$406$	−3.67750	−0.182511
$407$	5.61178	0.278166
$408$	4.15352	0.205630
$409$	14.4989	0.716922	0.358461	−	0.933545i	$-0.383302\pi$
$409$	14.4989	0.716922	0.358461	+	0.933545i	$0.383302\pi$
$410$	0	0
$411$	21.2243	1.04692
$412$	6.30704	0.310726
$413$	−10.9401	−0.538326
$414$	−1.30548	−0.0641609
$415$	0	0
$416$	−5.92692	−0.290591
$417$	13.7653	0.674090
$418$	7.80819	0.381911
$419$	−29.1934	−1.42619	−0.713095	−	0.701068i	$-0.752707\pi$
$419$	−29.1934	−1.42619	−0.713095	+	0.701068i	$0.752707\pi$
$420$	0	0
$421$	−4.70998	−0.229551	−0.114775	−	0.993391i	$-0.536615\pi$
$421$	−4.70998	−0.229551	−0.114775	+	0.993391i	$0.536615\pi$
$422$	−9.04795	−0.440447
$423$	1.41997	0.0690412
$424$	−8.17635	−0.397078
$425$	0	0
$426$	−18.2877	−0.886043
$427$	−24.1682	−1.16958
$428$	−9.35499	−0.452191
$429$	9.46562	0.457004
$430$	0	0
$431$	−4.95205	−0.238532	−0.119266	−	0.992862i	$-0.538054\pi$
$431$	−4.95205	−0.238532	−0.119266	+	0.992862i	$0.538054\pi$
$432$	5.60442	0.269643
$433$	4.28772	0.206055	0.103027	−	0.994679i	$-0.467147\pi$
$433$	4.28772	0.206055	0.103027	+	0.994679i	$0.467147\pi$
$434$	−24.7328	−1.18721
$435$	0	0
$436$	19.4509	0.931529
$437$	−14.3573	−0.686802
$438$	10.2494	0.489736
$439$	27.2088	1.29861	0.649303	−	0.760529i	$-0.275061\pi$
$439$	27.2088	1.29861	0.649303	+	0.760529i	$0.275061\pi$
$440$	0	0
$441$	−4.41997	−0.210475
$442$	−16.1535	−0.768345
$443$	−37.3778	−1.77587	−0.887937	−	0.459965i	$-0.847862\pi$
$443$	−37.3778	−1.77587	−0.887937	+	0.459965i	$0.847862\pi$
$444$	8.16088	0.387298
$445$	0	0
$446$	24.0228	1.13751
$447$	30.1106	1.42418
$448$	−3.67750	−0.173745
$449$	−13.5468	−0.639313	−0.319657	−	0.947533i	$-0.603568\pi$
$449$	−13.5468	−0.639313	−0.319657	+	0.947533i	$0.603568\pi$
$450$	0	0
$451$	9.80359	0.461633
$452$	−16.0228	−0.753650
$453$	−18.0650	−0.848767
$454$	−14.8059	−0.694875
$455$	0	0
$456$	11.3550	0.531746
$457$	−12.9018	−0.603521	−0.301760	−	0.953384i	$-0.597574\pi$
$457$	−12.9018	−0.603521	−0.301760	+	0.953384i	$0.597574\pi$
$458$	15.8693	0.741524
$459$	15.2746	0.712955
$460$	0	0
$461$	14.2266	0.662599	0.331299	−	0.943526i	$-0.392513\pi$
$461$	14.2266	0.662599	0.331299	+	0.943526i	$0.392513\pi$
$462$	5.87316	0.273244
$463$	22.4989	1.04561	0.522805	−	0.852452i	$-0.324886\pi$
$463$	22.4989	1.04561	0.522805	+	0.852452i	$0.324886\pi$
$464$	−1.00000	−0.0464238
$465$	0	0
$466$	−1.80819	−0.0837627
$467$	−20.8863	−0.966504	−0.483252	−	0.875481i	$-0.660545\pi$
$467$	−20.8863	−0.966504	−0.483252	+	0.875481i	$0.660545\pi$
$468$	−4.01546	−0.185615
$469$	53.3195	2.46206
$470$	0	0
$471$	−15.2398	−0.702211
$472$	−2.97487	−0.136930
$473$	−0.760236	−0.0349557
$474$	−17.3395	−0.796431
$475$	0	0
$476$	−10.0228	−0.459396
$477$	−5.53944	−0.253634
$478$	20.3070	0.928822
$479$	13.6272	0.622645	0.311322	−	0.950304i	$-0.399228\pi$
$479$	13.6272	0.622645	0.311322	+	0.950304i	$0.399228\pi$
$480$	0	0
$481$	−31.7386	−1.44716
$482$	9.61988	0.438174
$483$	−10.7993	−0.491384
$484$	−9.90179	−0.450082
$485$	0	0
$486$	6.89443	0.312738
$487$	−13.7808	−0.624466	−0.312233	−	0.950006i	$-0.601077\pi$
$487$	−13.7808	−0.624466	−0.312233	+	0.950006i	$0.601077\pi$
$488$	−6.57193	−0.297497
$489$	8.99770	0.406890
$490$	0	0
$491$	42.4989	1.91795	0.958973	−	0.283497i	$-0.0914946\pi$
$491$	42.4989	1.91795	0.958973	+	0.283497i	$0.0914946\pi$
$492$	14.2568	0.642746
$493$	−2.72545	−0.122748
$494$	−44.1609	−1.98689
$495$	0	0
$496$	−6.72545	−0.301982
$497$	44.1300	1.97950
$498$	−17.4509	−0.781993
$499$	−0.264890	−0.0118581	−0.00592905	−	0.999982i	$-0.501887\pi$
$499$	−0.264890	−0.0118581	−0.00592905	+	0.999982i	$0.501887\pi$
$500$	0	0
$501$	−13.6191	−0.608458
$502$	−7.25909	−0.323989
$503$	−4.19181	−0.186904	−0.0934518	−	0.995624i	$-0.529790\pi$
$503$	−4.19181	−0.186904	−0.0934518	+	0.995624i	$0.529790\pi$
$504$	−2.49149	−0.110980
$505$	0	0
$506$	−2.01932	−0.0897698
$507$	−33.7231	−1.49770
$508$	−8.00000	−0.354943
$509$	7.25909	0.321753	0.160877	−	0.986975i	$-0.448568\pi$
$509$	7.25909	0.321753	0.160877	+	0.986975i	$0.448568\pi$
$510$	0	0
$511$	−24.7328	−1.09412
$512$	−1.00000	−0.0441942
$513$	41.7579	1.84366
$514$	7.25909	0.320185
$515$	0	0
$516$	−1.10557	−0.0486699
$517$	2.19641	0.0965980
$518$	−19.6930	−0.865259
$519$	−13.6775	−0.600375
$520$	0	0
$521$	12.2916	0.538504	0.269252	−	0.963070i	$-0.413224\pi$
$521$	12.2916	0.538504	0.269252	+	0.963070i	$0.413224\pi$
$522$	−0.677496	−0.0296532
$523$	−1.16318	−0.0508623	−0.0254312	−	0.999677i	$-0.508096\pi$
$523$	−1.16318	−0.0508623	−0.0254312	+	0.999677i	$0.508096\pi$
$524$	2.80589	0.122576
$525$	0	0
$526$	−12.0000	−0.523225
$527$	−18.3299	−0.798461
$528$	1.59706	0.0695029
$529$	−19.2870	−0.838564
$530$	0	0
$531$	−2.01546	−0.0874637
$532$	−27.4006	−1.18797
$533$	−55.4463	−2.40165
$534$	−1.59706	−0.0691113
$535$	0	0
$536$	14.4989	0.626255
$537$	−8.88633	−0.383473
$538$	19.6775	0.848357
$539$	−6.83682	−0.294483
$540$	0	0
$541$	20.0302	0.861165	0.430583	−	0.902551i	$-0.358308\pi$
$541$	20.0302	0.861165	0.430583	+	0.902551i	$0.358308\pi$
$542$	8.40294	0.360937
$543$	−11.3550	−0.487289
$544$	−2.72545	−0.116853
$545$	0	0
$546$	−33.2169	−1.42155
$547$	21.0627	0.900575	0.450288	−	0.892884i	$-0.351321\pi$
$547$	21.0627	0.900575	0.450288	+	0.892884i	$0.351321\pi$
$548$	−13.9269	−0.594929
$549$	−4.45246	−0.190026
$550$	0	0
$551$	−7.45090	−0.317419
$552$	−2.93658	−0.124989
$553$	41.8419	1.77930
$554$	−14.6141	−0.620893
$555$	0	0
$556$	−9.03249	−0.383063
$557$	−5.12103	−0.216985	−0.108493	−	0.994097i	$-0.534602\pi$
$557$	−5.12103	−0.216985	−0.108493	+	0.994097i	$0.534602\pi$
$558$	−4.55646	−0.192891
$559$	4.29968	0.181857
$560$	0	0
$561$	4.35269	0.183771
$562$	−16.4834	−0.695310
$563$	−28.2340	−1.18992	−0.594960	−	0.803755i	$-0.702832\pi$
$563$	−28.2340	−1.18992	−0.594960	+	0.803755i	$0.702832\pi$
$564$	3.19411	0.134496
$565$	0	0
$566$	−3.45090	−0.145052
$567$	23.9350	1.00518
$568$	12.0000	0.503509
$569$	−4.40294	−0.184581	−0.0922905	−	0.995732i	$-0.529419\pi$
$569$	−4.40294	−0.184581	−0.0922905	+	0.995732i	$0.529419\pi$
$570$	0	0
$571$	−17.8767	−0.748115	−0.374058	−	0.927405i	$-0.622034\pi$
$571$	−17.8767	−0.748115	−0.374058	+	0.927405i	$0.622034\pi$
$572$	−6.21113	−0.259701
$573$	33.9424	1.41796
$574$	−34.4029	−1.43595
$575$	0	0
$576$	−0.677496	−0.0282290
$577$	22.9173	0.954058	0.477029	−	0.878888i	$-0.341714\pi$
$577$	22.9173	0.954058	0.477029	+	0.878888i	$0.341714\pi$
$578$	9.57193	0.398140
$579$	25.8693	1.07509
$580$	0	0
$581$	42.1106	1.74704
$582$	−15.1284	−0.627092
$583$	−8.56842	−0.354868
$584$	−6.72545	−0.278301
$585$	0	0
$586$	2.64501	0.109264
$587$	28.9018	1.19290	0.596452	−	0.802648i	$-0.296576\pi$
$587$	28.9018	1.19290	0.596452	+	0.802648i	$0.296576\pi$
$588$	−9.94239	−0.410017
$589$	−50.1106	−2.06477
$590$	0	0
$591$	14.3794	0.591489
$592$	−5.35499	−0.220089
$593$	26.0457	1.06957	0.534783	−	0.844989i	$-0.320393\pi$
$593$	26.0457	1.06957	0.534783	+	0.844989i	$0.320393\pi$
$594$	5.87316	0.240979
$595$	0	0
$596$	−19.7579	−0.809317
$597$	−30.7247	−1.25748
$598$	11.4207	0.467028
$599$	14.8863	0.608239	0.304119	−	0.952634i	$-0.401638\pi$
$599$	14.8863	0.608239	0.304119	+	0.952634i	$0.401638\pi$
$600$	0	0
$601$	−42.0457	−1.71508	−0.857539	−	0.514419i	$-0.828008\pi$
$601$	−42.0457	−1.71508	−0.857539	+	0.514419i	$0.828008\pi$
$602$	2.66783	0.108733
$603$	9.82291	0.400020
$604$	11.8538	0.482326
$605$	0	0
$606$	15.5963	0.633557
$607$	6.51817	0.264564	0.132282	−	0.991212i	$-0.457769\pi$
$607$	6.51817	0.264564	0.132282	+	0.991212i	$0.457769\pi$
$608$	−7.45090	−0.302174
$609$	−5.60442	−0.227102
$610$	0	0
$611$	−12.4223	−0.502551
$612$	−1.84648	−0.0746395
$613$	40.7904	1.64751	0.823755	−	0.566946i	$-0.191875\pi$
$613$	40.7904	1.64751	0.823755	+	0.566946i	$0.191875\pi$
$614$	−14.9018	−0.601388
$615$	0	0
$616$	−3.85384	−0.155276
$617$	−26.7254	−1.07593	−0.537963	−	0.842968i	$-0.680806\pi$
$617$	−26.7254	−1.07593	−0.537963	+	0.842968i	$0.680806\pi$
$618$	9.61178	0.386642
$619$	−46.3218	−1.86183	−0.930914	−	0.365237i	$-0.880988\pi$
$619$	−46.3218	−1.86183	−0.930914	+	0.365237i	$0.880988\pi$
$620$	0	0
$621$	−10.7993	−0.433360
$622$	23.2317	0.931505
$623$	3.85384	0.154401
$624$	−9.03249	−0.361589
$625$	0	0
$626$	−22.9977	−0.919173
$627$	11.8995	0.475220
$628$	10.0000	0.399043
$629$	−14.5948	−0.581931
$630$	0	0
$631$	1.11293	0.0443050	0.0221525	−	0.999755i	$-0.492948\pi$
$631$	1.11293	0.0443050	0.0221525	+	0.999755i	$0.492948\pi$
$632$	11.3778	0.452585
$633$	−13.7889	−0.548058
$634$	30.6597	1.21765
$635$	0	0
$636$	−12.4606	−0.494093
$637$	38.6671	1.53205
$638$	−1.04795	−0.0414888
$639$	8.12995	0.321616
$640$	0	0
$641$	29.7386	1.17460	0.587302	−	0.809368i	$-0.300190\pi$
$641$	29.7386	1.17460	0.587302	+	0.809368i	$0.300190\pi$
$642$	−14.2568	−0.562670
$643$	8.24206	0.325035	0.162518	−	0.986706i	$-0.448039\pi$
$643$	8.24206	0.325035	0.162518	+	0.986706i	$0.448039\pi$
$644$	7.08624	0.279237
$645$	0	0
$646$	−20.3070	−0.798970
$647$	50.2065	1.97382	0.986911	−	0.161264i	$-0.0515571\pi$
$647$	50.2065	1.97382	0.986911	+	0.161264i	$0.0515571\pi$
$648$	6.50851	0.255678
$649$	−3.11753	−0.122374
$650$	0	0
$651$	−37.6922	−1.47727
$652$	−5.90409	−0.231222
$653$	−22.8515	−0.894250	−0.447125	−	0.894471i	$-0.647552\pi$
$653$	−22.8515	−0.894250	−0.447125	+	0.894471i	$0.647552\pi$
$654$	29.6427	1.15912
$655$	0	0
$656$	−9.35499	−0.365251
$657$	−4.55646	−0.177765
$658$	−7.70768	−0.300477
$659$	32.7556	1.27598	0.637989	−	0.770045i	$-0.279766\pi$
$659$	32.7556	1.27598	0.637989	+	0.770045i	$0.279766\pi$
$660$	0	0
$661$	5.85384	0.227688	0.113844	−	0.993499i	$-0.463684\pi$
$661$	5.85384	0.227688	0.113844	+	0.993499i	$0.463684\pi$
$662$	0.856142	0.0332749
$663$	−24.6176	−0.956068
$664$	11.4509	0.444381
$665$	0	0
$666$	−3.62799	−0.140582
$667$	1.92692	0.0746107
$668$	8.93658	0.345767
$669$	36.6102	1.41543
$670$	0	0
$671$	−6.88707	−0.265872
$672$	−5.60442	−0.216195
$673$	−47.9645	−1.84889	−0.924447	−	0.381310i	$-0.875473\pi$
$673$	−47.9645	−1.84889	−0.924447	+	0.381310i	$0.875473\pi$
$674$	−3.37046	−0.129825
$675$	0	0
$676$	22.1284	0.851092
$677$	−10.1152	−0.388760	−0.194380	−	0.980926i	$-0.562269\pi$
$677$	−10.1152	−0.388760	−0.194380	+	0.980926i	$0.562269\pi$
$678$	−24.4184	−0.937783
$679$	36.5062	1.40098
$680$	0	0
$681$	−22.5638	−0.864648
$682$	−7.04795	−0.269880
$683$	28.6404	1.09589	0.547947	−	0.836513i	$-0.315409\pi$
$683$	28.6404	1.09589	0.547947	+	0.836513i	$0.315409\pi$
$684$	−5.04795	−0.193013
$685$	0	0
$686$	−1.75057	−0.0668373
$687$	24.1844	0.922694
$688$	0.725449	0.0276575
$689$	48.4606	1.84620
$690$	0	0
$691$	−31.9343	−1.21484	−0.607419	−	0.794382i	$-0.707795\pi$
$691$	−31.9343	−1.21484	−0.607419	+	0.794382i	$0.707795\pi$
$692$	8.97487	0.341174
$693$	−2.61096	−0.0991823
$694$	29.0627	1.10320
$695$	0	0
$696$	−1.52398	−0.0577662
$697$	−25.4966	−0.965751
$698$	21.4006	0.810026
$699$	−2.75564	−0.104228
$700$	0	0
$701$	25.0480	0.946048	0.473024	−	0.881050i	$-0.343162\pi$
$701$	25.0480	0.946048	0.473024	+	0.881050i	$0.343162\pi$
$702$	−33.2169	−1.25369
$703$	−39.8995	−1.50484
$704$	−1.04795	−0.0394962
$705$	0	0
$706$	−15.3047	−0.576001
$707$	−37.6353	−1.41542
$708$	−4.53364	−0.170385
$709$	40.3334	1.51475	0.757376	−	0.652979i	$-0.226481\pi$
$709$	40.3334	1.51475	0.757376	+	0.652979i	$0.226481\pi$
$710$	0	0
$711$	7.70843	0.289089
$712$	1.04795	0.0392737
$713$	12.9594	0.485334
$714$	−15.2746	−0.571636
$715$	0	0
$716$	5.83102	0.217915
$717$	30.9474	1.15575
$718$	14.4258	0.538365
$719$	−19.4702	−0.726117	−0.363058	−	0.931766i	$-0.618267\pi$
$719$	−19.4702	−0.726117	−0.363058	+	0.931766i	$0.618267\pi$
$720$	0	0
$721$	−23.1941	−0.863794
$722$	−36.5159	−1.35898
$723$	14.6605	0.545229
$724$	7.45090	0.276910
$725$	0	0
$726$	−15.0901	−0.560046
$727$	−28.9668	−1.07432	−0.537159	−	0.843481i	$-0.680503\pi$
$727$	−28.9668	−1.07432	−0.537159	+	0.843481i	$0.680503\pi$
$728$	21.7962	0.807822
$729$	30.0325	1.11231
$730$	0	0
$731$	1.97717	0.0731284
$732$	−10.0155	−0.370182
$733$	−45.2088	−1.66983	−0.834913	−	0.550382i	$-0.814482\pi$
$733$	−45.2088	−1.66983	−0.834913	+	0.550382i	$0.814482\pi$
$734$	9.75794	0.360172
$735$	0	0
$736$	1.92692	0.0710273
$737$	15.1941	0.559682
$738$	−6.33797	−0.233304
$739$	−18.3070	−0.673435	−0.336718	−	0.941606i	$-0.609317\pi$
$739$	−18.3070	−0.673435	−0.336718	+	0.941606i	$0.609317\pi$
$740$	0	0
$741$	−67.3001	−2.47233
$742$	30.0685	1.10385
$743$	−33.9041	−1.24382	−0.621910	−	0.783088i	$-0.713643\pi$
$743$	−33.9041	−1.24382	−0.621910	+	0.783088i	$0.713643\pi$
$744$	−10.2494	−0.375762
$745$	0	0
$746$	−16.7904	−0.614741
$747$	7.75794	0.283848
$748$	−2.85614	−0.104431
$749$	34.4029	1.25706
$750$	0	0
$751$	−22.4989	−0.820995	−0.410497	−	0.911862i	$-0.634645\pi$
$751$	−22.4989	−0.820995	−0.410497	+	0.911862i	$0.634645\pi$
$752$	−2.09591	−0.0764298
$753$	−11.0627	−0.403146
$754$	5.92692	0.215846
$755$	0	0
$756$	−20.6102	−0.749586
$757$	−10.6450	−0.386899	−0.193450	−	0.981110i	$-0.561968\pi$
$757$	−10.6450	−0.386899	−0.193450	+	0.981110i	$0.561968\pi$
$758$	−4.85614	−0.176383
$759$	−3.07740	−0.111703
$760$	0	0
$761$	−39.3852	−1.42771	−0.713856	−	0.700293i	$-0.753053\pi$
$761$	−39.3852	−1.42771	−0.713856	+	0.700293i	$0.753053\pi$
$762$	−12.1918	−0.441663
$763$	−71.5306	−2.58958
$764$	−22.2723	−0.805782
$765$	0	0
$766$	−5.32020	−0.192227
$767$	17.6318	0.636649
$768$	−1.52398	−0.0549918
$769$	4.75564	0.171493	0.0857463	−	0.996317i	$-0.472673\pi$
$769$	4.75564	0.171493	0.0857463	+	0.996317i	$0.472673\pi$
$770$	0	0
$771$	11.0627	0.398413
$772$	−16.9749	−0.610939
$773$	−53.8995	−1.93863	−0.969315	−	0.245822i	$-0.920942\pi$
$773$	−53.8995	−1.93863	−0.969315	+	0.245822i	$0.920942\pi$
$774$	0.491489	0.0176662
$775$	0	0
$776$	9.92692	0.356356
$777$	−30.0116	−1.07666
$778$	23.6118	0.846523
$779$	−69.7031	−2.49737
$780$	0	0
$781$	12.5754	0.449984
$782$	5.25172	0.187801
$783$	−5.60442	−0.200286
$784$	6.52398	0.232999
$785$	0	0
$786$	4.27611	0.152524
$787$	−12.0650	−0.430070	−0.215035	−	0.976606i	$-0.568987\pi$
$787$	−12.0650	−0.430070	−0.215035	+	0.976606i	$0.568987\pi$
$788$	−9.43543	−0.336123
$789$	−18.2877	−0.651060
$790$	0	0
$791$	58.9239	2.09509
$792$	−0.709984	−0.0252282
$793$	38.9513	1.38320
$794$	−34.2413	−1.21518
$795$	0	0
$796$	20.1609	0.714583
$797$	−35.1129	−1.24376	−0.621882	−	0.783111i	$-0.713632\pi$
$797$	−35.1129	−1.24376	−0.621882	+	0.783111i	$0.713632\pi$
$798$	−41.7579	−1.47821
$799$	−5.71228	−0.202086
$800$	0	0
$801$	0.709984	0.0250860
$802$	23.2317	0.820338
$803$	−7.04795	−0.248717
$804$	22.0959	0.779263
$805$	0	0
$806$	39.8612	1.40405
$807$	29.9880	1.05563
$808$	−10.2340	−0.360029
$809$	41.4006	1.45557	0.727785	−	0.685806i	$-0.240550\pi$
$809$	41.4006	1.45557	0.727785	+	0.685806i	$0.240550\pi$
$810$	0	0
$811$	2.70613	0.0950250	0.0475125	−	0.998871i	$-0.484871\pi$
$811$	2.70613	0.0950250	0.0475125	+	0.998871i	$0.484871\pi$
$812$	3.67750	0.129055
$813$	12.8059	0.449122
$814$	−5.61178	−0.196693
$815$	0	0
$816$	−4.15352	−0.145402
$817$	5.40524	0.189106
$818$	−14.4989	−0.506940
$819$	14.7669	0.515996
$820$	0	0
$821$	−27.1439	−0.947327	−0.473664	−	0.880706i	$-0.657069\pi$
$821$	−27.1439	−0.947327	−0.473664	+	0.880706i	$0.657069\pi$
$822$	−21.2243	−0.740282
$823$	50.7247	1.76815	0.884076	−	0.467343i	$-0.154789\pi$
$823$	50.7247	1.76815	0.884076	+	0.467343i	$0.154789\pi$
$824$	−6.30704	−0.219716
$825$	0	0
$826$	10.9401	0.380654
$827$	13.0781	0.454772	0.227386	−	0.973805i	$-0.426982\pi$
$827$	13.0781	0.454772	0.227386	+	0.973805i	$0.426982\pi$
$828$	1.30548	0.0453686
$829$	−9.48109	−0.329292	−0.164646	−	0.986353i	$-0.552648\pi$
$829$	−9.48109	−0.329292	−0.164646	+	0.986353i	$0.552648\pi$
$830$	0	0
$831$	−22.2715	−0.772590
$832$	5.92692	0.205479
$833$	17.7808	0.616067
$834$	−13.7653	−0.476653
$835$	0	0
$836$	−7.80819	−0.270052
$837$	−37.6922	−1.30283
$838$	29.1934	1.00847
$839$	14.2065	0.490464	0.245232	−	0.969464i	$-0.421136\pi$
$839$	14.2065	0.490464	0.245232	+	0.969464i	$0.421136\pi$
$840$	0	0
$841$	1.00000	0.0344828
$842$	4.70998	0.162317
$843$	−25.1203	−0.865189
$844$	9.04795	0.311443
$845$	0	0
$846$	−1.41997	−0.0488195
$847$	36.4138	1.25119
$848$	8.17635	0.280777
$849$	−5.25909	−0.180491
$850$	0	0
$851$	10.3186	0.353719
$852$	18.2877	0.626527
$853$	39.7727	1.36179	0.680895	−	0.732381i	$-0.261591\pi$
$853$	39.7727	1.36179	0.680895	+	0.732381i	$0.261591\pi$
$854$	24.1682	0.827020
$855$	0	0
$856$	9.35499	0.319747
$857$	−38.0457	−1.29961	−0.649807	−	0.760099i	$-0.725150\pi$
$857$	−38.0457	−1.29961	−0.649807	+	0.760099i	$0.725150\pi$
$858$	−9.46562	−0.323151
$859$	−39.4509	−1.34605	−0.673024	−	0.739621i	$-0.735005\pi$
$859$	−39.4509	−1.34605	−0.673024	+	0.739621i	$0.735005\pi$
$860$	0	0
$861$	−52.4293	−1.78678
$862$	4.95205	0.168667
$863$	29.4428	1.00224	0.501122	−	0.865377i	$-0.332921\pi$
$863$	29.4428	1.00224	0.501122	+	0.865377i	$0.332921\pi$
$864$	−5.60442	−0.190666
$865$	0	0
$866$	−4.28772	−0.145703
$867$	14.5874	0.495414
$868$	24.7328	0.839486
$869$	11.9234	0.404474
$870$	0	0
$871$	−85.9335	−2.91175
$872$	−19.4509	−0.658691
$873$	6.72545	0.227622
$874$	14.3573	0.485643
$875$	0	0
$876$	−10.2494	−0.346296
$877$	2.49535	0.0842618	0.0421309	−	0.999112i	$-0.486585\pi$
$877$	2.49535	0.0842618	0.0421309	+	0.999112i	$0.486585\pi$
$878$	−27.2088	−0.918254
$879$	4.03093	0.135960
$880$	0	0
$881$	−42.0604	−1.41705	−0.708525	−	0.705686i	$-0.750639\pi$
$881$	−42.0604	−1.41705	−0.708525	+	0.705686i	$0.750639\pi$
$882$	4.41997	0.148828
$883$	−13.8391	−0.465723	−0.232862	−	0.972510i	$-0.574809\pi$
$883$	−13.8391	−0.465723	−0.232862	+	0.972510i	$0.574809\pi$
$884$	16.1535	0.543302
$885$	0	0
$886$	37.3778	1.25573
$887$	−6.70998	−0.225299	−0.112650	−	0.993635i	$-0.535934\pi$
$887$	−6.70998	−0.225299	−0.112650	+	0.993635i	$0.535934\pi$
$888$	−8.16088	−0.273861
$889$	29.4200	0.986714
$890$	0	0
$891$	6.82061	0.228499
$892$	−24.0228	−0.804344
$893$	−15.6164	−0.522582
$894$	−30.1106	−1.00705
$895$	0	0
$896$	3.67750	0.122857
$897$	17.4049	0.581132
$898$	13.5468	0.452063
$899$	6.72545	0.224306
$900$	0	0
$901$	22.2842	0.742395
$902$	−9.80359	−0.326424
$903$	4.06572	0.135299
$904$	16.0228	0.532911
$905$	0	0
$906$	18.0650	0.600169
$907$	5.07814	0.168617	0.0843085	−	0.996440i	$-0.473132\pi$
$907$	5.07814	0.168617	0.0843085	+	0.996440i	$0.473132\pi$
$908$	14.8059	0.491351
$909$	−6.93347	−0.229969
$910$	0	0
$911$	14.7637	0.489145	0.244572	−	0.969631i	$-0.421352\pi$
$911$	14.7637	0.489145	0.244572	+	0.969631i	$0.421352\pi$
$912$	−11.3550	−0.376001
$913$	12.0000	0.397142
$914$	12.9018	0.426753
$915$	0	0
$916$	−15.8693	−0.524337
$917$	−10.3186	−0.340752
$918$	−15.2746	−0.504135
$919$	44.0000	1.45143	0.725713	−	0.687998i	$-0.241510\pi$
$919$	44.0000	1.45143	0.725713	+	0.687998i	$0.241510\pi$
$920$	0	0
$921$	−22.7100	−0.748319
$922$	−14.2266	−0.468528
$923$	−71.1231	−2.34104
$924$	−5.87316	−0.193213
$925$	0	0
$926$	−22.4989	−0.739358
$927$	−4.27299	−0.140344
$928$	1.00000	0.0328266
$929$	−15.4857	−0.508069	−0.254034	−	0.967195i	$-0.581758\pi$
$929$	−15.4857	−0.508069	−0.254034	+	0.967195i	$0.581758\pi$
$930$	0	0
$931$	48.6095	1.59311
$932$	1.80819	0.0592292
$933$	35.4045	1.15909
$934$	20.8863	0.683422
$935$	0	0
$936$	4.01546	0.131250
$937$	−6.35269	−0.207533	−0.103767	−	0.994602i	$-0.533090\pi$
$937$	−6.35269	−0.207533	−0.103767	+	0.994602i	$0.533090\pi$
$938$	−53.3195	−1.74094
$939$	−35.0480	−1.14375
$940$	0	0
$941$	29.4006	0.958434	0.479217	−	0.877697i	$-0.340921\pi$
$941$	29.4006	0.958434	0.479217	+	0.877697i	$0.340921\pi$
$942$	15.2398	0.496538
$943$	18.0263	0.587018
$944$	2.97487	0.0968239
$945$	0	0
$946$	0.760236	0.0247174
$947$	−5.90760	−0.191971	−0.0959856	−	0.995383i	$-0.530600\pi$
$947$	−5.90760	−0.191971	−0.0959856	+	0.995383i	$0.530600\pi$
$948$	17.3395	0.563162
$949$	39.8612	1.29395
$950$	0	0
$951$	46.7247	1.51515
$952$	10.0228	0.324842
$953$	24.2877	0.786756	0.393378	−	0.919377i	$-0.371306\pi$
$953$	24.2877	0.786756	0.393378	+	0.919377i	$0.371306\pi$
$954$	5.53944	0.179346
$955$	0	0
$956$	−20.3070	−0.656777
$957$	−1.59706	−0.0516255
$958$	−13.6272	−0.440276
$959$	51.2162	1.65386
$960$	0	0
$961$	14.2317	0.459086
$962$	31.7386	1.02329
$963$	6.33797	0.204238
$964$	−9.61988	−0.309836
$965$	0	0
$966$	10.7993	0.347461
$967$	−15.9691	−0.513531	−0.256765	−	0.966474i	$-0.582657\pi$
$967$	−15.9691	−0.513531	−0.256765	+	0.966474i	$0.582657\pi$
$968$	9.90179	0.318256
$969$	−30.9474	−0.994175
$970$	0	0
$971$	35.4509	1.13767	0.568837	−	0.822450i	$-0.307394\pi$
$971$	35.4509	1.13767	0.568837	+	0.822450i	$0.307394\pi$
$972$	−6.89443	−0.221139
$973$	33.2169	1.06489
$974$	13.7808	0.441564
$975$	0	0
$976$	6.57193	0.210362
$977$	5.23976	0.167635	0.0838175	−	0.996481i	$-0.473289\pi$
$977$	5.23976	0.167635	0.0838175	+	0.996481i	$0.473289\pi$
$978$	−8.99770	−0.287715
$979$	1.09821	0.0350988
$980$	0	0
$981$	−13.1779	−0.420738
$982$	−42.4989	−1.35619
$983$	26.9165	0.858504	0.429252	−	0.903185i	$-0.358777\pi$
$983$	26.9165	0.858504	0.429252	+	0.903185i	$0.358777\pi$
$984$	−14.2568	−0.454490
$985$	0	0
$986$	2.72545	0.0867960
$987$	−11.7463	−0.373890
$988$	44.1609	1.40494
$989$	−1.39788	−0.0444501
$990$	0	0
$991$	−31.3550	−0.996024	−0.498012	−	0.867170i	$-0.665936\pi$
$991$	−31.3550	−0.996024	−0.498012	+	0.867170i	$0.665936\pi$
$992$	6.72545	0.213533
$993$	1.30474	0.0414047
$994$	−44.1300	−1.39972
$995$	0	0
$996$	17.4509	0.552953
$997$	−50.6597	−1.60441	−0.802205	−	0.597049i	$-0.796340\pi$
$997$	−50.6597	−1.60441	−0.802205	+	0.597049i	$0.796340\pi$
$998$	0.264890	0.00838495
$999$	−30.0116	−0.949525

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1450.2.a.p.1.2		3
5.2	odd	4		1450.2.b.l.349.2		6
5.3	odd	4		1450.2.b.l.349.5		6
5.4	even	2		290.2.a.e.1.2	✓	3
15.14	odd	2		2610.2.a.x.1.3		3
20.19	odd	2		2320.2.a.l.1.2		3
40.19	odd	2		9280.2.a.by.1.2		3
40.29	even	2		9280.2.a.bf.1.2		3
145.144	even	2		8410.2.a.v.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
290.2.a.e.1.2	✓	3	5.4	even	2
1450.2.a.p.1.2		3	1.1	even	1	trivial
1450.2.b.l.349.2		6	5.2	odd	4
1450.2.b.l.349.5		6	5.3	odd	4
2320.2.a.l.1.2		3	20.19	odd	2
2610.2.a.x.1.3		3	15.14	odd	2
8410.2.a.v.1.2		3	145.144	even	2
9280.2.a.bf.1.2		3	40.29	even	2
9280.2.a.by.1.2		3	40.19	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.52398 q^{3} +1.00000 q^{4} +1.52398 q^{6} -3.67750 q^{7} -1.00000 q^{8} -0.677496 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.52398 q^{3} +1.00000 q^{4} +1.52398 q^{6} -3.67750 q^{7} -1.00000 q^{8} -0.677496 q^{9} -1.04795 q^{11} -1.52398 q^{12} +5.92692 q^{13} +3.67750 q^{14} +1.00000 q^{16} +2.72545 q^{17} +0.677496 q^{18} +7.45090 q^{19} +5.60442 q^{21} +1.04795 q^{22} -1.92692 q^{23} +1.52398 q^{24} -5.92692 q^{26} +5.60442 q^{27} -3.67750 q^{28} -1.00000 q^{29} -6.72545 q^{31} -1.00000 q^{32} +1.59706 q^{33} -2.72545 q^{34} -0.677496 q^{36} -5.35499 q^{37} -7.45090 q^{38} -9.03249 q^{39} -9.35499 q^{41} -5.60442 q^{42} +0.725449 q^{43} -1.04795 q^{44} +1.92692 q^{46} -2.09591 q^{47} -1.52398 q^{48} +6.52398 q^{49} -4.15352 q^{51} +5.92692 q^{52} +8.17635 q^{53} -5.60442 q^{54} +3.67750 q^{56} -11.3550 q^{57} +1.00000 q^{58} +2.97487 q^{59} +6.57193 q^{61} +6.72545 q^{62} +2.49149 q^{63} +1.00000 q^{64} -1.59706 q^{66} -14.4989 q^{67} +2.72545 q^{68} +2.93658 q^{69} -12.0000 q^{71} +0.677496 q^{72} +6.72545 q^{73} +5.35499 q^{74} +7.45090 q^{76} +3.85384 q^{77} +9.03249 q^{78} -11.3778 q^{79} -6.50851 q^{81} +9.35499 q^{82} -11.4509 q^{83} +5.60442 q^{84} -0.725449 q^{86} +1.52398 q^{87} +1.04795 q^{88} -1.04795 q^{89} -21.7962 q^{91} -1.92692 q^{92} +10.2494 q^{93} +2.09591 q^{94} +1.52398 q^{96} -9.92692 q^{97} -6.52398 q^{98} +0.709984 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 3 q^{6} - 3 q^{7} - 3 q^{8} + 6 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 + 3 * q^6 - 3 * q^7 - 3 * q^8 + 6 * q^9	\( 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 3 q^{6} - 3 q^{7} - 3 q^{8} + 6 q^{9} - 3 q^{12} - 3 q^{13} + 3 q^{14} + 3 q^{16} - 3 q^{17} - 6 q^{18} - 12 q^{21} + 15 q^{23} + 3 q^{24} + 3 q^{26} - 12 q^{27} - 3 q^{28} - 3 q^{29} - 9 q^{31} - 3 q^{32} + 24 q^{33} + 3 q^{34} + 6 q^{36} - 3 q^{39} - 12 q^{41} + 12 q^{42} - 9 q^{43} - 15 q^{46} - 3 q^{48} + 18 q^{49} - 6 q^{51} - 3 q^{52} - 9 q^{53} + 12 q^{54} + 3 q^{56} - 18 q^{57} + 3 q^{58} - 15 q^{59} + 15 q^{61} + 9 q^{62} + 30 q^{63} + 3 q^{64} - 24 q^{66} - 18 q^{67} - 3 q^{68} - 9 q^{69} - 36 q^{71} - 6 q^{72} + 9 q^{73} - 30 q^{77} + 3 q^{78} + 9 q^{79} + 3 q^{81} + 12 q^{82} - 12 q^{83} - 12 q^{84} + 9 q^{86} + 3 q^{87} - 24 q^{91} + 15 q^{92} + 18 q^{93} + 3 q^{96} - 9 q^{97} - 18 q^{98} - 30 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 + 3 * q^6 - 3 * q^7 - 3 * q^8 + 6 * q^9 - 3 * q^12 - 3 * q^13 + 3 * q^14 + 3 * q^16 - 3 * q^17 - 6 * q^18 - 12 * q^21 + 15 * q^23 + 3 * q^24 + 3 * q^26 - 12 * q^27 - 3 * q^28 - 3 * q^29 - 9 * q^31 - 3 * q^32 + 24 * q^33 + 3 * q^34 + 6 * q^36 - 3 * q^39 - 12 * q^41 + 12 * q^42 - 9 * q^43 - 15 * q^46 - 3 * q^48 + 18 * q^49 - 6 * q^51 - 3 * q^52 - 9 * q^53 + 12 * q^54 + 3 * q^56 - 18 * q^57 + 3 * q^58 - 15 * q^59 + 15 * q^61 + 9 * q^62 + 30 * q^63 + 3 * q^64 - 24 * q^66 - 18 * q^67 - 3 * q^68 - 9 * q^69 - 36 * q^71 - 6 * q^72 + 9 * q^73 - 30 * q^77 + 3 * q^78 + 9 * q^79 + 3 * q^81 + 12 * q^82 - 12 * q^83 - 12 * q^84 + 9 * q^86 + 3 * q^87 - 24 * q^91 + 15 * q^92 + 18 * q^93 + 3 * q^96 - 9 * q^97 - 18 * q^98 - 30 * q^99

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