LMFDB - Embedded newform 1075.2.a.m.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1075,2,Mod(1,1075)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1075, 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("1075.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1075 = 5^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1075.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:	$8.58391821729$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.1933097.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 7x^{3} + 13x^{2} + 5x - 4 $ x^5 - 2x^4 - 7x^3 + 13x^2 + 5x - 4
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 215)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.50989$ of defining polynomial
Character	$\chi$	$=$	1075.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.50989 q^{2} +3.26173 q^{3} +4.29955 q^{4} -8.18658 q^{6} -3.13519 q^{7} -5.77162 q^{8} +7.63887 q^{9} +O(q^{10})$	\(q-2.50989 q^{2} +3.26173 q^{3} +4.29955 q^{4} -8.18658 q^{6} -3.13519 q^{7} -5.77162 q^{8} +7.63887 q^{9} -0.248163 q^{11} +14.0240 q^{12} +2.67669 q^{13} +7.86899 q^{14} +5.88703 q^{16} +0.902631 q^{17} -19.1727 q^{18} -6.19474 q^{19} -10.2261 q^{21} +0.622862 q^{22} +7.69647 q^{23} -18.8254 q^{24} -6.71819 q^{26} +15.1307 q^{27} -13.4799 q^{28} +2.32872 q^{29} +7.73623 q^{31} -3.23256 q^{32} -0.809440 q^{33} -2.26550 q^{34} +32.8437 q^{36} -3.67425 q^{37} +15.5481 q^{38} +8.73063 q^{39} +9.45452 q^{41} +25.6665 q^{42} +1.00000 q^{43} -1.06699 q^{44} -19.3173 q^{46} +9.61888 q^{47} +19.2019 q^{48} +2.82943 q^{49} +2.94414 q^{51} +11.5086 q^{52} +7.09737 q^{53} -37.9764 q^{54} +18.0951 q^{56} -20.2055 q^{57} -5.84482 q^{58} -3.26173 q^{59} -3.35338 q^{61} -19.4171 q^{62} -23.9493 q^{63} -3.66068 q^{64} +2.03161 q^{66} +0.613476 q^{67} +3.88091 q^{68} +25.1038 q^{69} -8.46512 q^{71} -44.0886 q^{72} +1.33737 q^{73} +9.22196 q^{74} -26.6346 q^{76} +0.778039 q^{77} -21.9129 q^{78} +6.65447 q^{79} +26.4357 q^{81} -23.7298 q^{82} -10.7162 q^{83} -43.9678 q^{84} -2.50989 q^{86} +7.59564 q^{87} +1.43230 q^{88} -1.34850 q^{89} -8.39193 q^{91} +33.0913 q^{92} +25.2335 q^{93} -24.1423 q^{94} -10.5437 q^{96} -4.49827 q^{97} -7.10155 q^{98} -1.89568 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 2 q^{2} + q^{3} + 8 q^{4} - 12 q^{6} - 5 q^{7} - 3 q^{8} + 18 q^{9}+O(q^{10}) $ 5 * q - 2 * q^2 + q^3 + 8 * q^4 - 12 * q^6 - 5 * q^7 - 3 * q^8 + 18 * q^9	$ 5 q - 2 q^{2} + q^{3} + 8 q^{4} - 12 q^{6} - 5 q^{7} - 3 q^{8} + 18 q^{9} - 6 q^{11} - 5 q^{13} + q^{14} + 14 q^{16} + 17 q^{17} + 5 q^{18} - 6 q^{19} + 20 q^{21} + 8 q^{22} - q^{23} - 45 q^{24} + 22 q^{26} + 22 q^{27} - 26 q^{28} + 6 q^{29} + 6 q^{31} + 7 q^{32} + 20 q^{33} + 36 q^{36} - 5 q^{37} + 16 q^{38} - 14 q^{39} + 2 q^{41} + 58 q^{42} + 5 q^{43} - 15 q^{44} - 14 q^{46} + 3 q^{48} + 18 q^{49} - 10 q^{51} + 38 q^{52} + 23 q^{53} - 56 q^{54} - 19 q^{56} - 28 q^{57} - 12 q^{58} - q^{59} + 20 q^{61} + 3 q^{62} - 26 q^{63} - 25 q^{64} + 13 q^{66} - 21 q^{67} + 48 q^{68} + 10 q^{69} + 4 q^{71} - 20 q^{72} - 5 q^{73} + 24 q^{74} + 32 q^{76} + 26 q^{77} - 88 q^{78} + 41 q^{79} + 41 q^{81} - 38 q^{82} + 7 q^{83} - 33 q^{84} - 2 q^{86} + 40 q^{87} - 12 q^{88} + 20 q^{89} - 42 q^{91} + 52 q^{92} + 36 q^{93} - 42 q^{94} + 9 q^{96} - 37 q^{97} + 26 q^{98} + 12 q^{99}+O(q^{100}) $ 5 * q - 2 * q^2 + q^3 + 8 * q^4 - 12 * q^6 - 5 * q^7 - 3 * q^8 + 18 * q^9 - 6 * q^11 - 5 * q^13 + q^14 + 14 * q^16 + 17 * q^17 + 5 * q^18 - 6 * q^19 + 20 * q^21 + 8 * q^22 - q^23 - 45 * q^24 + 22 * q^26 + 22 * q^27 - 26 * q^28 + 6 * q^29 + 6 * q^31 + 7 * q^32 + 20 * q^33 + 36 * q^36 - 5 * q^37 + 16 * q^38 - 14 * q^39 + 2 * q^41 + 58 * q^42 + 5 * q^43 - 15 * q^44 - 14 * q^46 + 3 * q^48 + 18 * q^49 - 10 * q^51 + 38 * q^52 + 23 * q^53 - 56 * q^54 - 19 * q^56 - 28 * q^57 - 12 * q^58 - q^59 + 20 * q^61 + 3 * q^62 - 26 * q^63 - 25 * q^64 + 13 * q^66 - 21 * q^67 + 48 * q^68 + 10 * q^69 + 4 * q^71 - 20 * q^72 - 5 * q^73 + 24 * q^74 + 32 * q^76 + 26 * q^77 - 88 * q^78 + 41 * q^79 + 41 * q^81 - 38 * q^82 + 7 * q^83 - 33 * q^84 - 2 * q^86 + 40 * q^87 - 12 * q^88 + 20 * q^89 - 42 * q^91 + 52 * q^92 + 36 * q^93 - 42 * q^94 + 9 * q^96 - 37 * q^97 + 26 * q^98 + 12 * 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 $

$2$	−2.50989	−1.77476	−0.887380	−	0.461038i	$-0.847477\pi$
$2$	−2.50989	−1.77476	−0.887380	+	0.461038i	$0.847477\pi$
$3$	3.26173	1.88316	0.941580	−	0.336791i	$-0.109341\pi$
$3$	3.26173	1.88316	0.941580	+	0.336791i	$0.109341\pi$
$4$	4.29955	2.14977
$5$	0	0
$5$	0	0
$6$	−8.18658	−3.34216
$7$	−3.13519	−1.18499	−0.592495	−	0.805574i	$-0.701857\pi$
$7$	−3.13519	−1.18499	−0.592495	+	0.805574i	$0.701857\pi$
$8$	−5.77162	−2.04058
$9$	7.63887	2.54629
$10$	0	0
$11$	−0.248163	−0.0748240	−0.0374120	−	0.999300i	$-0.511911\pi$
$11$	−0.248163	−0.0748240	−0.0374120	+	0.999300i	$0.511911\pi$
$12$	14.0240	4.04837
$13$	2.67669	0.742380	0.371190	−	0.928557i	$-0.378950\pi$
$13$	2.67669	0.742380	0.371190	+	0.928557i	$0.378950\pi$
$14$	7.86899	2.10308
$15$	0	0
$16$	5.88703	1.47176
$17$	0.902631	0.218920	0.109460	−	0.993991i	$-0.465088\pi$
$17$	0.902631	0.218920	0.109460	+	0.993991i	$0.465088\pi$
$18$	−19.1727	−4.51905
$19$	−6.19474	−1.42117	−0.710585	−	0.703611i	$-0.751570\pi$
$19$	−6.19474	−1.42117	−0.710585	+	0.703611i	$0.751570\pi$
$20$	0	0
$21$	−10.2261	−2.23153
$22$	0.622862	0.132795
$23$	7.69647	1.60482	0.802412	−	0.596770i	$-0.203550\pi$
$23$	7.69647	1.60482	0.802412	+	0.596770i	$0.203550\pi$
$24$	−18.8254	−3.84273
$25$	0	0
$26$	−6.71819	−1.31755
$27$	15.1307	2.91191
$28$	−13.4799	−2.54746
$29$	2.32872	0.432432	0.216216	−	0.976346i	$-0.430628\pi$
$29$	2.32872	0.432432	0.216216	+	0.976346i	$0.430628\pi$
$30$	0	0
$31$	7.73623	1.38947	0.694734	−	0.719266i	$-0.255522\pi$
$31$	7.73623	1.38947	0.694734	+	0.719266i	$0.255522\pi$
$32$	−3.23256	−0.571441
$33$	−0.809440	−0.140905
$34$	−2.26550	−0.388531
$35$	0	0
$36$	32.8437	5.47395
$37$	−3.67425	−0.604043	−0.302021	−	0.953301i	$-0.597661\pi$
$37$	−3.67425	−0.604043	−0.302021	+	0.953301i	$0.597661\pi$
$38$	15.5481	2.52224
$39$	8.73063	1.39802
$40$	0	0
$41$	9.45452	1.47655	0.738274	−	0.674501i	$-0.235641\pi$
$41$	9.45452	1.47655	0.738274	+	0.674501i	$0.235641\pi$
$42$	25.6665	3.96043
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	−1.06699	−0.160855
$45$	0	0
$46$	−19.3173	−2.84818
$47$	9.61888	1.40306	0.701529	−	0.712641i	$-0.252501\pi$
$47$	9.61888	1.40306	0.701529	+	0.712641i	$0.252501\pi$
$48$	19.2019	2.77155
$49$	2.82943	0.404204
$50$	0	0
$51$	2.94414	0.412262
$52$	11.5086	1.59595
$53$	7.09737	0.974899	0.487449	−	0.873151i	$-0.337927\pi$
$53$	7.09737	0.974899	0.487449	+	0.873151i	$0.337927\pi$
$54$	−37.9764	−5.16794
$55$	0	0
$56$	18.0951	2.41806
$57$	−20.2055	−2.67629
$58$	−5.84482	−0.767463
$59$	−3.26173	−0.424641	−0.212320	−	0.977200i	$-0.568102\pi$
$59$	−3.26173	−0.424641	−0.212320	+	0.977200i	$0.568102\pi$
$60$	0	0
$61$	−3.35338	−0.429356	−0.214678	−	0.976685i	$-0.568870\pi$
$61$	−3.35338	−0.429356	−0.214678	+	0.976685i	$0.568870\pi$
$62$	−19.4171	−2.46597
$63$	−23.9493	−3.01733
$64$	−3.66068	−0.457586
$65$	0	0
$66$	2.03161	0.250073
$67$	0.613476	0.0749480	0.0374740	−	0.999298i	$-0.488069\pi$
$67$	0.613476	0.0749480	0.0374740	+	0.999298i	$0.488069\pi$
$68$	3.88091	0.470629
$69$	25.1038	3.02214
$70$	0	0
$71$	−8.46512	−1.00463	−0.502313	−	0.864686i	$-0.667517\pi$
$71$	−8.46512	−1.00463	−0.502313	+	0.864686i	$0.667517\pi$
$72$	−44.0886	−5.19589
$73$	1.33737	0.156528	0.0782638	−	0.996933i	$-0.475062\pi$
$73$	1.33737	0.156528	0.0782638	+	0.996933i	$0.475062\pi$
$74$	9.22196	1.07203
$75$	0	0
$76$	−26.6346	−3.05520
$77$	0.778039	0.0886657
$78$	−21.9129	−2.48115
$79$	6.65447	0.748686	0.374343	−	0.927290i	$-0.377868\pi$
$79$	6.65447	0.748686	0.374343	+	0.927290i	$0.377868\pi$
$80$	0	0
$81$	26.4357	2.93730
$82$	−23.7298	−2.62052
$83$	−10.7162	−1.17626	−0.588131	−	0.808766i	$-0.700136\pi$
$83$	−10.7162	−1.17626	−0.588131	+	0.808766i	$0.700136\pi$
$84$	−43.9678	−4.79728
$85$	0	0
$86$	−2.50989	−0.270648
$87$	7.59564	0.814338
$88$	1.43230	0.152684
$89$	−1.34850	−0.142940	−0.0714702	−	0.997443i	$-0.522769\pi$
$89$	−1.34850	−0.142940	−0.0714702	+	0.997443i	$0.522769\pi$
$90$	0	0
$91$	−8.39193	−0.879713
$92$	33.0913	3.45001
$93$	25.2335	2.61659
$94$	−24.1423	−2.49009
$95$	0	0
$96$	−10.5437	−1.07612
$97$	−4.49827	−0.456730	−0.228365	−	0.973576i	$-0.573338\pi$
$97$	−4.49827	−0.456730	−0.228365	+	0.973576i	$0.573338\pi$
$98$	−7.10155	−0.717365
$99$	−1.89568	−0.190523
$100$	0	0
$101$	6.23256	0.620163	0.310081	−	0.950710i	$-0.399644\pi$
$101$	6.23256	0.620163	0.310081	+	0.950710i	$0.399644\pi$
$102$	−7.38946	−0.731665
$103$	−7.29211	−0.718513	−0.359256	−	0.933239i	$-0.616970\pi$
$103$	−7.29211	−0.718513	−0.359256	+	0.933239i	$0.616970\pi$
$104$	−15.4488	−1.51488
$105$	0	0
$106$	−17.8136	−1.73021
$107$	−5.69841	−0.550886	−0.275443	−	0.961317i	$-0.588825\pi$
$107$	−5.69841	−0.550886	−0.275443	+	0.961317i	$0.588825\pi$
$108$	65.0553	6.25995
$109$	13.2648	1.27053	0.635267	−	0.772292i	$-0.280890\pi$
$109$	13.2648	1.27053	0.635267	+	0.772292i	$0.280890\pi$
$110$	0	0
$111$	−11.9844	−1.13751
$112$	−18.4570	−1.74402
$113$	−8.71451	−0.819792	−0.409896	−	0.912132i	$-0.634435\pi$
$113$	−8.71451	−0.819792	−0.409896	+	0.912132i	$0.634435\pi$
$114$	50.7137	4.74977
$115$	0	0
$116$	10.0124	0.929631
$117$	20.4469	1.89031
$118$	8.18658	0.753636
$119$	−2.82992	−0.259418
$120$	0	0
$121$	−10.9384	−0.994401
$122$	8.41660	0.762004
$123$	30.8381	2.78058
$124$	33.2623	2.98704
$125$	0	0
$126$	60.1101	5.35504
$127$	−18.3875	−1.63163	−0.815815	−	0.578313i	$-0.803711\pi$
$127$	−18.3875	−1.63163	−0.815815	+	0.578313i	$0.803711\pi$
$128$	15.6530	1.38355
$129$	3.26173	0.287179
$130$	0	0
$131$	6.10277	0.533202	0.266601	−	0.963807i	$-0.414099\pi$
$131$	6.10277	0.533202	0.266601	+	0.963807i	$0.414099\pi$
$132$	−3.48023	−0.302915
$133$	19.4217	1.68407
$134$	−1.53976	−0.133015
$135$	0	0
$136$	−5.20964	−0.446723
$137$	9.57167	0.817763	0.408882	−	0.912587i	$-0.365919\pi$
$137$	9.57167	0.817763	0.408882	+	0.912587i	$0.365919\pi$
$138$	−63.0077	−5.36358
$139$	−7.86277	−0.666911	−0.333456	−	0.942766i	$-0.608215\pi$
$139$	−7.86277	−0.666911	−0.333456	+	0.942766i	$0.608215\pi$
$140$	0	0
$141$	31.3742	2.64218
$142$	21.2465	1.78297
$143$	−0.664255	−0.0555478
$144$	44.9702	3.74752
$145$	0	0
$146$	−3.35666	−0.277799
$147$	9.22881	0.761180
$148$	−15.7976	−1.29856
$149$	−1.09931	−0.0900592	−0.0450296	−	0.998986i	$-0.514338\pi$
$149$	−1.09931	−0.0900592	−0.0450296	+	0.998986i	$0.514338\pi$
$150$	0	0
$151$	7.87683	0.641007	0.320504	−	0.947247i	$-0.396148\pi$
$151$	7.87683	0.641007	0.320504	+	0.947247i	$0.396148\pi$
$152$	35.7537	2.90000
$153$	6.89508	0.557434
$154$	−1.95279	−0.157360
$155$	0	0
$156$	37.5378	3.00543
$157$	−3.04822	−0.243274	−0.121637	−	0.992575i	$-0.538814\pi$
$157$	−3.04822	−0.243274	−0.121637	+	0.992575i	$0.538814\pi$
$158$	−16.7020	−1.32874
$159$	23.1497	1.83589
$160$	0	0
$161$	−24.1299	−1.90170
$162$	−66.3506	−5.21300
$163$	−7.04394	−0.551724	−0.275862	−	0.961197i	$-0.588963\pi$
$163$	−7.04394	−0.551724	−0.275862	+	0.961197i	$0.588963\pi$
$164$	40.6502	3.17425
$165$	0	0
$166$	26.8966	2.08758
$167$	−1.89121	−0.146346	−0.0731730	−	0.997319i	$-0.523313\pi$
$167$	−1.89121	−0.146346	−0.0731730	+	0.997319i	$0.523313\pi$
$168$	59.0214	4.55360
$169$	−5.83534	−0.448873
$170$	0	0
$171$	−47.3208	−3.61871
$172$	4.29955	0.327838
$173$	−7.44534	−0.566059	−0.283029	−	0.959111i	$-0.591339\pi$
$173$	−7.44534	−0.566059	−0.283029	+	0.959111i	$0.591339\pi$
$174$	−19.0642	−1.44525
$175$	0	0
$176$	−1.46094	−0.110123
$177$	−10.6389	−0.799666
$178$	3.38458	0.253685
$179$	−10.1784	−0.760771	−0.380385	−	0.924828i	$-0.624209\pi$
$179$	−10.1784	−0.760771	−0.380385	+	0.924828i	$0.624209\pi$
$180$	0	0
$181$	13.0309	0.968580	0.484290	−	0.874908i	$-0.339078\pi$
$181$	13.0309	0.968580	0.484290	+	0.874908i	$0.339078\pi$
$182$	21.0628	1.56128
$183$	−10.9378	−0.808545
$184$	−44.4211	−3.27477
$185$	0	0
$186$	−63.3333	−4.64382
$187$	−0.224000	−0.0163805
$188$	41.3569	3.01626
$189$	−47.4377	−3.45058
$190$	0	0
$191$	−13.0247	−0.942431	−0.471216	−	0.882018i	$-0.656185\pi$
$191$	−13.0247	−0.942431	−0.471216	+	0.882018i	$0.656185\pi$
$192$	−11.9402	−0.861706
$193$	−11.6569	−0.839083	−0.419541	−	0.907736i	$-0.637809\pi$
$193$	−11.6569	−0.839083	−0.419541	+	0.907736i	$0.637809\pi$
$194$	11.2902	0.810587
$195$	0	0
$196$	12.1653	0.868947
$197$	15.3026	1.09026	0.545132	−	0.838350i	$-0.316479\pi$
$197$	15.3026	1.09026	0.545132	+	0.838350i	$0.316479\pi$
$198$	4.75796	0.338133
$199$	0.718193	0.0509113	0.0254557	−	0.999676i	$-0.491896\pi$
$199$	0.718193	0.0509113	0.0254557	+	0.999676i	$0.491896\pi$
$200$	0	0
$201$	2.00099	0.141139
$202$	−15.6430	−1.10064
$203$	−7.30097	−0.512428
$204$	12.6585	0.886269
$205$	0	0
$206$	18.3024	1.27519
$207$	58.7923	4.08635
$208$	15.7577	1.09260
$209$	1.53730	0.106338
$210$	0	0
$211$	20.2812	1.39621	0.698107	−	0.715993i	$-0.254026\pi$
$211$	20.2812	1.39621	0.698107	+	0.715993i	$0.254026\pi$
$212$	30.5155	2.09581
$213$	−27.6109	−1.89187
$214$	14.3024	0.977691
$215$	0	0
$216$	−87.3287	−5.94197
$217$	−24.2546	−1.64651
$218$	−33.2931	−2.25490
$219$	4.36214	0.294766
$220$	0	0
$221$	2.41606	0.162522
$222$	30.0795	2.01881
$223$	−22.4003	−1.50003	−0.750017	−	0.661419i	$-0.769955\pi$
$223$	−22.4003	−1.50003	−0.750017	+	0.661419i	$0.769955\pi$
$224$	10.1347	0.677153
$225$	0	0
$226$	21.8725	1.45493
$227$	23.0343	1.52884	0.764419	−	0.644720i	$-0.223026\pi$
$227$	23.0343	1.52884	0.764419	+	0.644720i	$0.223026\pi$
$228$	−86.8748	−5.75342
$229$	12.6648	0.836911	0.418456	−	0.908237i	$-0.362572\pi$
$229$	12.6648	0.836911	0.418456	+	0.908237i	$0.362572\pi$
$230$	0	0
$231$	2.53775	0.166972
$232$	−13.4405	−0.882410
$233$	30.2611	1.98247	0.991236	−	0.132105i	$-0.0421737\pi$
$233$	30.2611	1.98247	0.991236	+	0.132105i	$0.0421737\pi$
$234$	−51.3194	−3.35485
$235$	0	0
$236$	−14.0240	−0.912882
$237$	21.7051	1.40990
$238$	7.10279	0.460406
$239$	18.5033	1.19688	0.598438	−	0.801169i	$-0.295788\pi$
$239$	18.5033	1.19688	0.598438	+	0.801169i	$0.295788\pi$
$240$	0	0
$241$	−16.0840	−1.03606	−0.518031	−	0.855362i	$-0.673335\pi$
$241$	−16.0840	−1.03606	−0.518031	+	0.855362i	$0.673335\pi$
$242$	27.4542	1.76482
$243$	40.8338	2.61949
$244$	−14.4180	−0.923018
$245$	0	0
$246$	−77.4002	−4.93486
$247$	−16.5814	−1.05505
$248$	−44.6506	−2.83532
$249$	−34.9535	−2.21509
$250$	0	0
$251$	−12.4459	−0.785576	−0.392788	−	0.919629i	$-0.628489\pi$
$251$	−12.4459	−0.785576	−0.392788	+	0.919629i	$0.628489\pi$
$252$	−102.971	−6.48658
$253$	−1.90998	−0.120079
$254$	46.1507	2.89575
$255$	0	0
$256$	−31.9660	−1.99788
$257$	−4.68647	−0.292334	−0.146167	−	0.989260i	$-0.546694\pi$
$257$	−4.68647	−0.292334	−0.146167	+	0.989260i	$0.546694\pi$
$258$	−8.18658	−0.509674
$259$	11.5195	0.715785
$260$	0	0
$261$	17.7888	1.10110
$262$	−15.3173	−0.946305
$263$	−17.3959	−1.07268	−0.536339	−	0.844003i	$-0.680193\pi$
$263$	−17.3959	−1.07268	−0.536339	+	0.844003i	$0.680193\pi$
$264$	4.67178	0.287528
$265$	0	0
$266$	−48.7463	−2.98883
$267$	−4.39843	−0.269180
$268$	2.63767	0.161121
$269$	−20.0133	−1.22023	−0.610115	−	0.792313i	$-0.708877\pi$
$269$	−20.0133	−1.22023	−0.610115	+	0.792313i	$0.708877\pi$
$270$	0	0
$271$	14.0575	0.853933	0.426966	−	0.904267i	$-0.359582\pi$
$271$	14.0575	0.853933	0.426966	+	0.904267i	$0.359582\pi$
$272$	5.31381	0.322197
$273$	−27.3722	−1.65664
$274$	−24.0238	−1.45133
$275$	0	0
$276$	107.935	6.49692
$277$	10.8297	0.650695	0.325347	−	0.945595i	$-0.394519\pi$
$277$	10.8297	0.650695	0.325347	+	0.945595i	$0.394519\pi$
$278$	19.7347	1.18361
$279$	59.0961	3.53799
$280$	0	0
$281$	−7.76915	−0.463469	−0.231734	−	0.972779i	$-0.574440\pi$
$281$	−7.76915	−0.463469	−0.231734	+	0.972779i	$0.574440\pi$
$282$	−78.7457	−4.68924
$283$	−7.32924	−0.435678	−0.217839	−	0.975985i	$-0.569901\pi$
$283$	−7.32924	−0.435678	−0.217839	+	0.975985i	$0.569901\pi$
$284$	−36.3962	−2.15972
$285$	0	0
$286$	1.66721	0.0985840
$287$	−29.6417	−1.74970
$288$	−24.6931	−1.45505
$289$	−16.1853	−0.952074
$290$	0	0
$291$	−14.6721	−0.860095
$292$	5.75010	0.336499
$293$	2.25307	0.131626	0.0658129	−	0.997832i	$-0.479036\pi$
$293$	2.25307	0.131626	0.0658129	+	0.997832i	$0.479036\pi$
$294$	−23.1633	−1.35091
$295$	0	0
$296$	21.2064	1.23259
$297$	−3.75488	−0.217880
$298$	2.75915	0.159834
$299$	20.6010	1.19139
$300$	0	0
$301$	−3.13519	−0.180709
$302$	−19.7700	−1.13763
$303$	20.3289	1.16787
$304$	−36.4686	−2.09162
$305$	0	0
$306$	−17.3059	−0.989312
$307$	−17.5142	−0.999586	−0.499793	−	0.866145i	$-0.666591\pi$
$307$	−17.5142	−0.999586	−0.499793	+	0.866145i	$0.666591\pi$
$308$	3.34522	0.190611
$309$	−23.7849	−1.35307
$310$	0	0
$311$	−11.8628	−0.672676	−0.336338	−	0.941741i	$-0.609188\pi$
$311$	−11.8628	−0.672676	−0.336338	+	0.941741i	$0.609188\pi$
$312$	−50.3898	−2.85276
$313$	28.1905	1.59342	0.796709	−	0.604363i	$-0.206572\pi$
$313$	28.1905	1.59342	0.796709	+	0.604363i	$0.206572\pi$
$314$	7.65069	0.431753
$315$	0	0
$316$	28.6112	1.60951
$317$	6.60104	0.370752	0.185376	−	0.982668i	$-0.440650\pi$
$317$	6.60104	0.370752	0.185376	+	0.982668i	$0.440650\pi$
$318$	−58.1032	−3.25826
$319$	−0.577901	−0.0323563
$320$	0	0
$321$	−18.5867	−1.03741
$322$	60.5634	3.37507
$323$	−5.59156	−0.311123
$324$	113.661	6.31453
$325$	0	0
$326$	17.6795	0.979178
$327$	43.2661	2.39262
$328$	−54.5679	−3.01301
$329$	−30.1570	−1.66261
$330$	0	0
$331$	−9.68209	−0.532176	−0.266088	−	0.963949i	$-0.585731\pi$
$331$	−9.68209	−0.532176	−0.266088	+	0.963949i	$0.585731\pi$
$332$	−46.0750	−2.52870
$333$	−28.0671	−1.53807
$334$	4.74672	0.259729
$335$	0	0
$336$	−60.2016	−3.28427
$337$	−29.2544	−1.59359	−0.796794	−	0.604251i	$-0.793473\pi$
$337$	−29.2544	−1.59359	−0.796794	+	0.604251i	$0.793473\pi$
$338$	14.6461	0.796641
$339$	−28.4244	−1.54380
$340$	0	0
$341$	−1.91985	−0.103966
$342$	118.770	6.42234
$343$	13.0756	0.706013
$344$	−5.77162	−0.311185
$345$	0	0
$346$	18.6870	1.00462
$347$	−8.34899	−0.448197	−0.224099	−	0.974566i	$-0.571944\pi$
$347$	−8.34899	−0.448197	−0.224099	+	0.974566i	$0.571944\pi$
$348$	32.6578	1.75064
$349$	−22.2663	−1.19189	−0.595944	−	0.803026i	$-0.703222\pi$
$349$	−22.2663	−1.19189	−0.595944	+	0.803026i	$0.703222\pi$
$350$	0	0
$351$	40.5002	2.16174
$352$	0.802202	0.0427575
$353$	−18.3351	−0.975880	−0.487940	−	0.872877i	$-0.662252\pi$
$353$	−18.3351	−0.975880	−0.487940	+	0.872877i	$0.662252\pi$
$354$	26.7024	1.41922
$355$	0	0
$356$	−5.79793	−0.307290
$357$	−9.23043	−0.488526
$358$	25.5467	1.35019
$359$	−28.8857	−1.52453	−0.762265	−	0.647265i	$-0.775913\pi$
$359$	−28.8857	−1.52453	−0.762265	+	0.647265i	$0.775913\pi$
$360$	0	0
$361$	19.3748	1.01973
$362$	−32.7061	−1.71900
$363$	−35.6781	−1.87262
$364$	−36.0815	−1.89119
$365$	0	0
$366$	27.4527	1.43497
$367$	−22.7231	−1.18613	−0.593067	−	0.805153i	$-0.702083\pi$
$367$	−22.7231	−1.18613	−0.593067	+	0.805153i	$0.702083\pi$
$368$	45.3093	2.36191
$369$	72.2218	3.75972
$370$	0	0
$371$	−22.2516	−1.15525
$372$	108.493	5.62508
$373$	30.1880	1.56308	0.781539	−	0.623857i	$-0.214435\pi$
$373$	30.1880	1.56308	0.781539	+	0.623857i	$0.214435\pi$
$374$	0.562214	0.0290714
$375$	0	0
$376$	−55.5165	−2.86304
$377$	6.23325	0.321029
$378$	119.063	6.12396
$379$	14.7592	0.758128	0.379064	−	0.925370i	$-0.376246\pi$
$379$	14.7592	0.758128	0.379064	+	0.925370i	$0.376246\pi$
$380$	0	0
$381$	−59.9751	−3.07262
$382$	32.6905	1.67259
$383$	14.0955	0.720248	0.360124	−	0.932904i	$-0.382734\pi$
$383$	14.0955	0.720248	0.360124	+	0.932904i	$0.382734\pi$
$384$	51.0559	2.60544
$385$	0	0
$386$	29.2576	1.48917
$387$	7.63887	0.388305
$388$	−19.3405	−0.981867
$389$	30.9837	1.57094	0.785468	−	0.618902i	$-0.212422\pi$
$389$	30.9837	1.57094	0.785468	+	0.618902i	$0.212422\pi$
$390$	0	0
$391$	6.94707	0.351328
$392$	−16.3304	−0.824808
$393$	19.9056	1.00410
$394$	−38.4078	−1.93496
$395$	0	0
$396$	−8.15059	−0.409582
$397$	−31.0726	−1.55949	−0.779744	−	0.626099i	$-0.784651\pi$
$397$	−31.0726	−1.55949	−0.779744	+	0.626099i	$0.784651\pi$
$398$	−1.80259	−0.0903554
$399$	63.3483	3.17138
$400$	0	0
$401$	−4.92956	−0.246170	−0.123085	−	0.992396i	$-0.539279\pi$
$401$	−4.92956	−0.246170	−0.123085	+	0.992396i	$0.539279\pi$
$402$	−5.02227	−0.250488
$403$	20.7075	1.03151
$404$	26.7972	1.33321
$405$	0	0
$406$	18.3246	0.909437
$407$	0.911813	0.0451969
$408$	−16.9924	−0.841251
$409$	−7.61888	−0.376729	−0.188365	−	0.982099i	$-0.560319\pi$
$409$	−7.61888	−0.376729	−0.188365	+	0.982099i	$0.560319\pi$
$410$	0	0
$411$	31.2202	1.53998
$412$	−31.3528	−1.54464
$413$	10.2261	0.503195
$414$	−147.562	−7.25229
$415$	0	0
$416$	−8.65256	−0.424226
$417$	−25.6462	−1.25590
$418$	−3.85847	−0.188724
$419$	21.8373	1.06682	0.533410	−	0.845857i	$-0.320910\pi$
$419$	21.8373	1.06682	0.533410	+	0.845857i	$0.320910\pi$
$420$	0	0
$421$	−13.5012	−0.658009	−0.329005	−	0.944328i	$-0.606713\pi$
$421$	−13.5012	−0.658009	−0.329005	+	0.944328i	$0.606713\pi$
$422$	−50.9036	−2.47795
$423$	73.4773	3.57259
$424$	−40.9633	−1.98935
$425$	0	0
$426$	69.3004	3.35761
$427$	10.5135	0.508783
$428$	−24.5006	−1.18428
$429$	−2.16662	−0.104605
$430$	0	0
$431$	−7.29975	−0.351617	−0.175808	−	0.984424i	$-0.556254\pi$
$431$	−7.29975	−0.351617	−0.175808	+	0.984424i	$0.556254\pi$
$432$	89.0749	4.28562
$433$	−10.1310	−0.486865	−0.243433	−	0.969918i	$-0.578274\pi$
$433$	−10.1310	−0.486865	−0.243433	+	0.969918i	$0.578274\pi$
$434$	60.8763	2.92216
$435$	0	0
$436$	57.0326	2.73136
$437$	−47.6776	−2.28073
$438$	−10.9485	−0.523140
$439$	−17.6650	−0.843103	−0.421552	−	0.906804i	$-0.638514\pi$
$439$	−17.6650	−0.843103	−0.421552	+	0.906804i	$0.638514\pi$
$440$	0	0
$441$	21.6136	1.02922
$442$	−6.06405	−0.288437
$443$	−36.7934	−1.74811	−0.874054	−	0.485828i	$-0.838518\pi$
$443$	−36.7934	−1.74811	−0.874054	+	0.485828i	$0.838518\pi$
$444$	−51.5275	−2.44539
$445$	0	0
$446$	56.2223	2.66220
$447$	−3.58566	−0.169596
$448$	11.4769	0.542235
$449$	0.788959	0.0372333	0.0186166	−	0.999827i	$-0.494074\pi$
$449$	0.788959	0.0372333	0.0186166	+	0.999827i	$0.494074\pi$
$450$	0	0
$451$	−2.34626	−0.110481
$452$	−37.4685	−1.76237
$453$	25.6921	1.20712
$454$	−57.8135	−2.71332
$455$	0	0
$456$	116.619	5.46117
$457$	−23.7442	−1.11070	−0.555352	−	0.831615i	$-0.687417\pi$
$457$	−23.7442	−1.11070	−0.555352	+	0.831615i	$0.687417\pi$
$458$	−31.7872	−1.48532
$459$	13.6575	0.637475
$460$	0	0
$461$	10.5205	0.489988	0.244994	−	0.969525i	$-0.421214\pi$
$461$	10.5205	0.489988	0.244994	+	0.969525i	$0.421214\pi$
$462$	−6.36947	−0.296335
$463$	33.7411	1.56808	0.784042	−	0.620708i	$-0.213155\pi$
$463$	33.7411	1.56808	0.784042	+	0.620708i	$0.213155\pi$
$464$	13.7092	0.636435
$465$	0	0
$466$	−75.9521	−3.51841
$467$	−19.2665	−0.891548	−0.445774	−	0.895146i	$-0.647071\pi$
$467$	−19.2665	−0.891548	−0.445774	+	0.895146i	$0.647071\pi$
$468$	87.9123	4.06375
$469$	−1.92336	−0.0888127
$470$	0	0
$471$	−9.94245	−0.458124
$472$	18.8254	0.866511
$473$	−0.248163	−0.0114105
$474$	−54.4773	−2.50223
$475$	0	0
$476$	−12.1674	−0.557691
$477$	54.2158	2.48237
$478$	−46.4412	−2.12417
$479$	−9.69667	−0.443052	−0.221526	−	0.975154i	$-0.571104\pi$
$479$	−9.69667	−0.443052	−0.221526	+	0.975154i	$0.571104\pi$
$480$	0	0
$481$	−9.83482	−0.448429
$482$	40.3691	1.83876
$483$	−78.7052	−3.58121
$484$	−47.0303	−2.13774
$485$	0	0
$486$	−102.488	−4.64897
$487$	0.683509	0.0309728	0.0154864	−	0.999880i	$-0.495070\pi$
$487$	0.683509	0.0309728	0.0154864	+	0.999880i	$0.495070\pi$
$488$	19.3544	0.876133
$489$	−22.9754	−1.03898
$490$	0	0
$491$	−29.1038	−1.31344	−0.656718	−	0.754137i	$-0.728056\pi$
$491$	−29.1038	−1.31344	−0.656718	+	0.754137i	$0.728056\pi$
$492$	132.590	5.97761
$493$	2.10197	0.0946680
$494$	41.6174	1.87246
$495$	0	0
$496$	45.5434	2.04496
$497$	26.5398	1.19047
$498$	87.7294	3.93125
$499$	30.7637	1.37717	0.688586	−	0.725155i	$-0.258232\pi$
$499$	30.7637	1.37717	0.688586	+	0.725155i	$0.258232\pi$
$500$	0	0
$501$	−6.16860	−0.275593
$502$	31.2378	1.39421
$503$	−4.02345	−0.179397	−0.0896983	−	0.995969i	$-0.528590\pi$
$503$	−4.02345	−0.179397	−0.0896983	+	0.995969i	$0.528590\pi$
$504$	138.226	6.15709
$505$	0	0
$506$	4.79384	0.213112
$507$	−19.0333	−0.845298
$508$	−79.0581	−3.50764
$509$	12.8168	0.568094	0.284047	−	0.958810i	$-0.408323\pi$
$509$	12.8168	0.568094	0.284047	+	0.958810i	$0.408323\pi$
$510$	0	0
$511$	−4.19292	−0.185484
$512$	48.9252	2.16221
$513$	−93.7308	−4.13832
$514$	11.7625	0.518823
$515$	0	0
$516$	14.0240	0.617370
$517$	−2.38705	−0.104982
$518$	−28.9126	−1.27035
$519$	−24.2847	−1.06598
$520$	0	0
$521$	−10.8754	−0.476460	−0.238230	−	0.971209i	$-0.576567\pi$
$521$	−10.8754	−0.476460	−0.238230	+	0.971209i	$0.576567\pi$
$522$	−44.6478	−1.95418
$523$	35.9454	1.57178	0.785892	−	0.618364i	$-0.212204\pi$
$523$	35.9454	1.57178	0.785892	+	0.618364i	$0.212204\pi$
$524$	26.2392	1.14626
$525$	0	0
$526$	43.6618	1.90375
$527$	6.98296	0.304183
$528$	−4.76520	−0.207379
$529$	36.2356	1.57546
$530$	0	0
$531$	−24.9159	−1.08126
$532$	83.5045	3.62038
$533$	25.3068	1.09616
$534$	11.0396	0.477729
$535$	0	0
$536$	−3.54075	−0.152937
$537$	−33.1992	−1.43265
$538$	50.2311	2.16562
$539$	−0.702159	−0.0302441
$540$	0	0
$541$	26.1499	1.12427	0.562135	−	0.827045i	$-0.309980\pi$
$541$	26.1499	1.12427	0.562135	+	0.827045i	$0.309980\pi$
$542$	−35.2828	−1.51553
$543$	42.5033	1.82399
$544$	−2.91781	−0.125100
$545$	0	0
$546$	68.7012	2.94014
$547$	−0.231141	−0.00988287	−0.00494143	−	0.999988i	$-0.501573\pi$
$547$	−0.231141	−0.00988287	−0.00494143	+	0.999988i	$0.501573\pi$
$548$	41.1539	1.75801
$549$	−25.6160	−1.09326
$550$	0	0
$551$	−14.4258	−0.614559
$552$	−144.889	−6.16690
$553$	−20.8630	−0.887186
$554$	−27.1814	−1.15483
$555$	0	0
$556$	−33.8064	−1.43371
$557$	3.96726	0.168098	0.0840491	−	0.996462i	$-0.473215\pi$
$557$	3.96726	0.168098	0.0840491	+	0.996462i	$0.473215\pi$
$558$	−148.325	−6.27908
$559$	2.67669	0.113212
$560$	0	0
$561$	−0.730626	−0.0308470
$562$	19.4997	0.822546
$563$	−12.1492	−0.512026	−0.256013	−	0.966673i	$-0.582409\pi$
$563$	−12.1492	−0.512026	−0.256013	+	0.966673i	$0.582409\pi$
$564$	134.895	5.68009
$565$	0	0
$566$	18.3956	0.773225
$567$	−82.8809	−3.48067
$568$	48.8574	2.05001
$569$	−42.4665	−1.78029	−0.890143	−	0.455681i	$-0.849396\pi$
$569$	−42.4665	−1.78029	−0.890143	+	0.455681i	$0.849396\pi$
$570$	0	0
$571$	−23.4374	−0.980824	−0.490412	−	0.871491i	$-0.663154\pi$
$571$	−23.4374	−0.980824	−0.490412	+	0.871491i	$0.663154\pi$
$572$	−2.85600	−0.119415
$573$	−42.4829	−1.77475
$574$	74.3975	3.10529
$575$	0	0
$576$	−27.9635	−1.16514
$577$	41.0241	1.70785	0.853927	−	0.520393i	$-0.174214\pi$
$577$	41.0241	1.70785	0.853927	+	0.520393i	$0.174214\pi$
$578$	40.6232	1.68970
$579$	−38.0217	−1.58013
$580$	0	0
$581$	33.5975	1.39386
$582$	36.8254	1.52646
$583$	−1.76130	−0.0729458
$584$	−7.71880	−0.319406
$585$	0	0
$586$	−5.65496	−0.233604
$587$	29.4970	1.21747	0.608735	−	0.793374i	$-0.291677\pi$
$587$	29.4970	1.21747	0.608735	+	0.793374i	$0.291677\pi$
$588$	39.6797	1.63637
$589$	−47.9239	−1.97467
$590$	0	0
$591$	49.9129	2.05314
$592$	−21.6304	−0.889004
$593$	−17.7334	−0.728223	−0.364111	−	0.931355i	$-0.618627\pi$
$593$	−17.7334	−0.728223	−0.364111	+	0.931355i	$0.618627\pi$
$594$	9.42435	0.386686
$595$	0	0
$596$	−4.72655	−0.193607
$597$	2.34255	0.0958742
$598$	−51.7064	−2.11443
$599$	−16.9852	−0.693997	−0.346998	−	0.937866i	$-0.612799\pi$
$599$	−16.9852	−0.693997	−0.346998	+	0.937866i	$0.612799\pi$
$600$	0	0
$601$	5.70922	0.232884	0.116442	−	0.993197i	$-0.462851\pi$
$601$	5.70922	0.232884	0.116442	+	0.993197i	$0.462851\pi$
$602$	7.86899	0.320716
$603$	4.68626	0.190839
$604$	33.8668	1.37802
$605$	0	0
$606$	−51.0233	−2.07268
$607$	−4.37105	−0.177415	−0.0887077	−	0.996058i	$-0.528274\pi$
$607$	−4.37105	−0.177415	−0.0887077	+	0.996058i	$0.528274\pi$
$608$	20.0249	0.812116
$609$	−23.8138	−0.964983
$610$	0	0
$611$	25.7467	1.04160
$612$	29.6457	1.19836
$613$	−35.0848	−1.41706	−0.708532	−	0.705679i	$-0.750642\pi$
$613$	−35.0848	−1.41706	−0.708532	+	0.705679i	$0.750642\pi$
$614$	43.9586	1.77403
$615$	0	0
$616$	−4.49054	−0.180929
$617$	−23.0537	−0.928108	−0.464054	−	0.885807i	$-0.653606\pi$
$617$	−23.0537	−0.928108	−0.464054	+	0.885807i	$0.653606\pi$
$618$	59.6974	2.40138
$619$	−29.3047	−1.17785	−0.588927	−	0.808186i	$-0.700449\pi$
$619$	−29.3047	−1.17785	−0.588927	+	0.808186i	$0.700449\pi$
$620$	0	0
$621$	116.453	4.67310
$622$	29.7743	1.19384
$623$	4.22780	0.169383
$624$	51.3974	2.05754
$625$	0	0
$626$	−70.7550	−2.82794
$627$	5.01427	0.200251
$628$	−13.1060	−0.522985
$629$	−3.31649	−0.132237
$630$	0	0
$631$	−31.7883	−1.26547	−0.632737	−	0.774367i	$-0.718069\pi$
$631$	−31.7883	−1.26547	−0.632737	+	0.774367i	$0.718069\pi$
$632$	−38.4070	−1.52775
$633$	66.1517	2.62929
$634$	−16.5679	−0.657995
$635$	0	0
$636$	99.5332	3.94675
$637$	7.57349	0.300073
$638$	1.45047	0.0574246
$639$	−64.6639	−2.55807
$640$	0	0
$641$	42.7217	1.68740	0.843702	−	0.536811i	$-0.180371\pi$
$641$	42.7217	1.68740	0.843702	+	0.536811i	$0.180371\pi$
$642$	46.6505	1.84115
$643$	5.88234	0.231977	0.115988	−	0.993251i	$-0.462996\pi$
$643$	5.88234	0.231977	0.115988	+	0.993251i	$0.462996\pi$
$644$	−103.748	−4.08823
$645$	0	0
$646$	14.0342	0.552169
$647$	−39.6468	−1.55868	−0.779338	−	0.626604i	$-0.784445\pi$
$647$	−39.6468	−1.55868	−0.779338	+	0.626604i	$0.784445\pi$
$648$	−152.577	−5.99377
$649$	0.809440	0.0317733
$650$	0	0
$651$	−79.1118	−3.10064
$652$	−30.2858	−1.18608
$653$	39.0899	1.52971	0.764854	−	0.644204i	$-0.222811\pi$
$653$	39.0899	1.52971	0.764854	+	0.644204i	$0.222811\pi$
$654$	−108.593	−4.24633
$655$	0	0
$656$	55.6590	2.17312
$657$	10.2160	0.398564
$658$	75.6908	2.95074
$659$	−49.9625	−1.94626	−0.973131	−	0.230254i	$-0.926044\pi$
$659$	−49.9625	−1.94626	−0.973131	+	0.230254i	$0.926044\pi$
$660$	0	0
$661$	−12.3002	−0.478421	−0.239210	−	0.970968i	$-0.576889\pi$
$661$	−12.3002	−0.478421	−0.239210	+	0.970968i	$0.576889\pi$
$662$	24.3010	0.944485
$663$	7.88053	0.306055
$664$	61.8501	2.40025
$665$	0	0
$666$	70.4453	2.72970
$667$	17.9229	0.693977
$668$	−8.13134	−0.314611
$669$	−73.0636	−2.82480
$670$	0	0
$671$	0.832184	0.0321261
$672$	33.0566	1.27519
$673$	−14.3751	−0.554118	−0.277059	−	0.960853i	$-0.589360\pi$
$673$	−14.3751	−0.554118	−0.277059	+	0.960853i	$0.589360\pi$
$674$	73.4253	2.82824
$675$	0	0
$676$	−25.0893	−0.964975
$677$	19.8543	0.763062	0.381531	−	0.924356i	$-0.375397\pi$
$677$	19.8543	0.763062	0.381531	+	0.924356i	$0.375397\pi$
$678$	71.3420	2.73987
$679$	14.1029	0.541221
$680$	0	0
$681$	75.1315	2.87905
$682$	4.81861	0.184514
$683$	−33.8908	−1.29680	−0.648398	−	0.761302i	$-0.724561\pi$
$683$	−33.8908	−1.29680	−0.648398	+	0.761302i	$0.724561\pi$
$684$	−203.458	−7.77941
$685$	0	0
$686$	−32.8182	−1.25300
$687$	41.3090	1.57604
$688$	5.88703	0.224441
$689$	18.9974	0.723745
$690$	0	0
$691$	14.3619	0.546354	0.273177	−	0.961964i	$-0.411926\pi$
$691$	14.3619	0.546354	0.273177	+	0.961964i	$0.411926\pi$
$692$	−32.0116	−1.21690
$693$	5.94333	0.225769
$694$	20.9551	0.795443
$695$	0	0
$696$	−43.8391	−1.66172
$697$	8.53394	0.323246
$698$	55.8860	2.11532
$699$	98.7035	3.73331
$700$	0	0
$701$	11.8354	0.447015	0.223508	−	0.974702i	$-0.428249\pi$
$701$	11.8354	0.447015	0.223508	+	0.974702i	$0.428249\pi$
$702$	−101.651	−3.83657
$703$	22.7610	0.858448
$704$	0.908446	0.0342384
$705$	0	0
$706$	46.0192	1.73195
$707$	−19.5403	−0.734887
$708$	−45.7423	−1.71910
$709$	−22.9382	−0.861462	−0.430731	−	0.902480i	$-0.641744\pi$
$709$	−22.9382	−0.861462	−0.430731	+	0.902480i	$0.641744\pi$
$710$	0	0
$711$	50.8326	1.90637
$712$	7.78301	0.291681
$713$	59.5417	2.22985
$714$	23.1674	0.867017
$715$	0	0
$716$	−43.7626	−1.63549
$717$	60.3526	2.25391
$718$	72.5000	2.70567
$719$	40.1157	1.49606	0.748032	−	0.663663i	$-0.230999\pi$
$719$	40.1157	1.49606	0.748032	+	0.663663i	$0.230999\pi$
$720$	0	0
$721$	22.8622	0.851431
$722$	−48.6286	−1.80977
$723$	−52.4616	−1.95107
$724$	56.0270	2.08223
$725$	0	0
$726$	89.5482	3.32345
$727$	−10.3290	−0.383082	−0.191541	−	0.981485i	$-0.561348\pi$
$727$	−10.3290	−0.383082	−0.191541	+	0.981485i	$0.561348\pi$
$728$	48.4350	1.79512
$729$	53.8817	1.99562
$730$	0	0
$731$	0.902631	0.0333850
$732$	−47.0276	−1.73819
$733$	27.0182	0.997938	0.498969	−	0.866620i	$-0.333712\pi$
$733$	27.0182	0.997938	0.498969	+	0.866620i	$0.333712\pi$
$734$	57.0324	2.10510
$735$	0	0
$736$	−24.8793	−0.917063
$737$	−0.152242	−0.00560791
$738$	−181.269	−6.67260
$739$	20.7027	0.761560	0.380780	−	0.924666i	$-0.375655\pi$
$739$	20.7027	0.761560	0.380780	+	0.924666i	$0.375655\pi$
$740$	0	0
$741$	−54.0839	−1.98682
$742$	55.8491	2.05029
$743$	−40.3655	−1.48087	−0.740433	−	0.672130i	$-0.765380\pi$
$743$	−40.3655	−1.48087	−0.740433	+	0.672130i	$0.765380\pi$
$744$	−145.638	−5.33935
$745$	0	0
$746$	−75.7686	−2.77409
$747$	−81.8600	−2.99510
$748$	−0.963098	−0.0352143
$749$	17.8656	0.652795
$750$	0	0
$751$	9.23655	0.337046	0.168523	−	0.985698i	$-0.446100\pi$
$751$	9.23655	0.337046	0.168523	+	0.985698i	$0.446100\pi$
$752$	56.6266	2.06496
$753$	−40.5950	−1.47936
$754$	−15.6448	−0.569749
$755$	0	0
$756$	−203.961	−7.41798
$757$	−10.6745	−0.387973	−0.193986	−	0.981004i	$-0.562142\pi$
$757$	−10.6745	−0.387973	−0.193986	+	0.981004i	$0.562142\pi$
$758$	−37.0439	−1.34550
$759$	−6.22983	−0.226129
$760$	0	0
$761$	−21.3301	−0.773217	−0.386608	−	0.922244i	$-0.626353\pi$
$761$	−21.3301	−0.773217	−0.386608	+	0.922244i	$0.626353\pi$
$762$	150.531	5.45316
$763$	−41.5876	−1.50557
$764$	−56.0002	−2.02601
$765$	0	0
$766$	−35.3782	−1.27827
$767$	−8.73063	−0.315245
$768$	−104.265	−3.76232
$769$	25.6062	0.923385	0.461692	−	0.887040i	$-0.347242\pi$
$769$	25.6062	0.923385	0.461692	+	0.887040i	$0.347242\pi$
$770$	0	0
$771$	−15.2860	−0.550512
$772$	−50.1195	−1.80384
$773$	21.4476	0.771416	0.385708	−	0.922621i	$-0.373957\pi$
$773$	21.4476	0.771416	0.385708	+	0.922621i	$0.373957\pi$
$774$	−19.1727	−0.689149
$775$	0	0
$776$	25.9623	0.931992
$777$	37.5734	1.34794
$778$	−77.7657	−2.78803
$779$	−58.5683	−2.09843
$780$	0	0
$781$	2.10073	0.0751700
$782$	−17.4364	−0.623524
$783$	35.2351	1.25920
$784$	16.6569	0.594890
$785$	0	0
$786$	−49.9608	−1.78204
$787$	43.6900	1.55738	0.778691	−	0.627408i	$-0.215884\pi$
$787$	43.6900	1.55738	0.778691	+	0.627408i	$0.215884\pi$
$788$	65.7943	2.34382
$789$	−56.7407	−2.02002
$790$	0	0
$791$	27.3217	0.971446
$792$	10.9412	0.388777
$793$	−8.97594	−0.318745
$794$	77.9888	2.76772
$795$	0	0
$796$	3.08791	0.109448
$797$	46.8097	1.65809	0.829043	−	0.559185i	$-0.188886\pi$
$797$	46.8097	1.65809	0.829043	+	0.559185i	$0.188886\pi$
$798$	−158.997	−5.62844
$799$	8.68230	0.307158
$800$	0	0
$801$	−10.3010	−0.363968
$802$	12.3726	0.436893
$803$	−0.331886	−0.0117120
$804$	8.60336	0.303417
$805$	0	0
$806$	−51.9735	−1.83069
$807$	−65.2778	−2.29789
$808$	−35.9720	−1.26549
$809$	2.62610	0.0923288	0.0461644	−	0.998934i	$-0.485300\pi$
$809$	2.62610	0.0923288	0.0461644	+	0.998934i	$0.485300\pi$
$810$	0	0
$811$	36.1962	1.27102	0.635510	−	0.772093i	$-0.280790\pi$
$811$	36.1962	1.27102	0.635510	+	0.772093i	$0.280790\pi$
$812$	−31.3909	−1.10160
$813$	45.8518	1.60809
$814$	−2.28855	−0.0802136
$815$	0	0
$816$	17.3322	0.606749
$817$	−6.19474	−0.216726
$818$	19.1226	0.668604
$819$	−64.1048	−2.24000
$820$	0	0
$821$	−31.4660	−1.09817	−0.549085	−	0.835767i	$-0.685024\pi$
$821$	−31.4660	−1.09817	−0.549085	+	0.835767i	$0.685024\pi$
$822$	−78.3592	−2.73309
$823$	43.9257	1.53115	0.765577	−	0.643344i	$-0.222454\pi$
$823$	43.9257	1.53115	0.765577	+	0.643344i	$0.222454\pi$
$824$	42.0873	1.46618
$825$	0	0
$826$	−25.6665	−0.893051
$827$	−28.7775	−1.00069	−0.500346	−	0.865825i	$-0.666794\pi$
$827$	−28.7775	−1.00069	−0.500346	+	0.865825i	$0.666794\pi$
$828$	252.780	8.78472
$829$	31.2180	1.08425	0.542123	−	0.840299i	$-0.317621\pi$
$829$	31.2180	1.08425	0.542123	+	0.840299i	$0.317621\pi$
$830$	0	0
$831$	35.3236	1.22536
$832$	−9.79851	−0.339702
$833$	2.55393	0.0884883
$834$	64.3692	2.22892
$835$	0	0
$836$	6.60972	0.228602
$837$	117.055	4.04600
$838$	−54.8092	−1.89335
$839$	−16.8160	−0.580554	−0.290277	−	0.956943i	$-0.593747\pi$
$839$	−16.8160	−0.580554	−0.290277	+	0.956943i	$0.593747\pi$
$840$	0	0
$841$	−23.5771	−0.813003
$842$	33.8866	1.16781
$843$	−25.3408	−0.872785
$844$	87.2000	3.00155
$845$	0	0
$846$	−184.420	−6.34049
$847$	34.2940	1.17836
$848$	41.7824	1.43481
$849$	−23.9060	−0.820452
$850$	0	0
$851$	−28.2787	−0.969383
$852$	−118.715	−4.06709
$853$	20.6282	0.706295	0.353148	−	0.935568i	$-0.385111\pi$
$853$	20.6282	0.706295	0.353148	+	0.935568i	$0.385111\pi$
$854$	−26.3877	−0.902967
$855$	0	0
$856$	32.8891	1.12412
$857$	32.8803	1.12317	0.561585	−	0.827419i	$-0.310192\pi$
$857$	32.8803	1.12317	0.561585	+	0.827419i	$0.310192\pi$
$858$	5.43797	0.185649
$859$	−43.1433	−1.47203	−0.736016	−	0.676964i	$-0.763295\pi$
$859$	−43.1433	−1.47203	−0.736016	+	0.676964i	$0.763295\pi$
$860$	0	0
$861$	−96.6833	−3.29496
$862$	18.3216	0.624036
$863$	45.6650	1.55445	0.777227	−	0.629221i	$-0.216626\pi$
$863$	45.6650	1.55445	0.777227	+	0.629221i	$0.216626\pi$
$864$	−48.9109	−1.66398
$865$	0	0
$866$	25.4277	0.864070
$867$	−52.7919	−1.79291
$868$	−104.284	−3.53962
$869$	−1.65139	−0.0560197
$870$	0	0
$871$	1.64208	0.0556399
$872$	−76.5592	−2.59262
$873$	−34.3617	−1.16297
$874$	119.666	4.04775
$875$	0	0
$876$	18.7553	0.633681
$877$	−15.9707	−0.539294	−0.269647	−	0.962959i	$-0.586907\pi$
$877$	−15.9707	−0.539294	−0.269647	+	0.962959i	$0.586907\pi$
$878$	44.3372	1.49631
$879$	7.34891	0.247872
$880$	0	0
$881$	13.7670	0.463823	0.231912	−	0.972737i	$-0.425502\pi$
$881$	13.7670	0.463823	0.231912	+	0.972737i	$0.425502\pi$
$882$	−54.2478	−1.82662
$883$	−12.0482	−0.405455	−0.202728	−	0.979235i	$-0.564981\pi$
$883$	−12.0482	−0.405455	−0.202728	+	0.979235i	$0.564981\pi$
$884$	10.3880	0.349385
$885$	0	0
$886$	92.3475	3.10247
$887$	14.1405	0.474791	0.237395	−	0.971413i	$-0.423706\pi$
$887$	14.1405	0.474791	0.237395	+	0.971413i	$0.423706\pi$
$888$	69.1694	2.32117
$889$	57.6484	1.93347
$890$	0	0
$891$	−6.56036	−0.219780
$892$	−96.3111	−3.22474
$893$	−59.5864	−1.99398
$894$	8.99961	0.300992
$895$	0	0
$896$	−49.0753	−1.63949
$897$	67.1950	2.24358
$898$	−1.98020	−0.0660802
$899$	18.0155	0.600850
$900$	0	0
$901$	6.40630	0.213425
$902$	5.88886	0.196078
$903$	−10.2261	−0.340305
$904$	50.2968	1.67285
$905$	0	0
$906$	−64.4843	−2.14235
$907$	−2.93772	−0.0975455	−0.0487727	−	0.998810i	$-0.515531\pi$
$907$	−2.93772	−0.0975455	−0.0487727	+	0.998810i	$0.515531\pi$
$908$	99.0370	3.28666
$909$	47.6097	1.57911
$910$	0	0
$911$	1.04732	0.0346992	0.0173496	−	0.999849i	$-0.494477\pi$
$911$	1.04732	0.0346992	0.0173496	+	0.999849i	$0.494477\pi$
$912$	−118.951	−3.93885
$913$	2.65938	0.0880125
$914$	59.5952	1.97124
$915$	0	0
$916$	54.4528	1.79917
$917$	−19.1334	−0.631839
$918$	−34.2787	−1.13137
$919$	15.7325	0.518966	0.259483	−	0.965748i	$-0.416448\pi$
$919$	15.7325	0.518966	0.259483	+	0.965748i	$0.416448\pi$
$920$	0	0
$921$	−57.1264	−1.88238
$922$	−26.4053	−0.869611
$923$	−22.6585	−0.745813
$924$	10.9112	0.358952
$925$	0	0
$926$	−84.6866	−2.78297
$927$	−55.7034	−1.82954
$928$	−7.52772	−0.247109
$929$	−26.5084	−0.869711	−0.434855	−	0.900500i	$-0.643201\pi$
$929$	−26.5084	−0.869711	−0.434855	+	0.900500i	$0.643201\pi$
$930$	0	0
$931$	−17.5275	−0.574442
$932$	130.109	4.26187
$933$	−38.6931	−1.26676
$934$	48.3568	1.58228
$935$	0	0
$936$	−118.011	−3.85732
$937$	−25.7747	−0.842021	−0.421011	−	0.907056i	$-0.638324\pi$
$937$	−25.7747	−0.842021	−0.421011	+	0.907056i	$0.638324\pi$
$938$	4.82743	0.157621
$939$	91.9496	3.00066
$940$	0	0
$941$	−33.5036	−1.09219	−0.546093	−	0.837725i	$-0.683885\pi$
$941$	−33.5036	−1.09219	−0.546093	+	0.837725i	$0.683885\pi$
$942$	24.9545	0.813060
$943$	72.7664	2.36960
$944$	−19.2019	−0.624968
$945$	0	0
$946$	0.622862	0.0202510
$947$	12.5066	0.406411	0.203205	−	0.979136i	$-0.434864\pi$
$947$	12.5066	0.406411	0.203205	+	0.979136i	$0.434864\pi$
$948$	93.3220	3.03096
$949$	3.57973	0.116203
$950$	0	0
$951$	21.5308	0.698184
$952$	16.3332	0.529363
$953$	−13.3246	−0.431628	−0.215814	−	0.976435i	$-0.569240\pi$
$953$	−13.3246	−0.431628	−0.215814	+	0.976435i	$0.569240\pi$
$954$	−136.076	−4.40562
$955$	0	0
$956$	79.5557	2.57302
$957$	−1.88496	−0.0609320
$958$	24.3376	0.786312
$959$	−30.0090	−0.969042
$960$	0	0
$961$	28.8493	0.930623
$962$	24.6843	0.795854
$963$	−43.5294	−1.40272
$964$	−69.1540	−2.22730
$965$	0	0
$966$	197.541	6.35579
$967$	35.1437	1.13014	0.565072	−	0.825042i	$-0.308848\pi$
$967$	35.1437	1.13014	0.565072	+	0.825042i	$0.308848\pi$
$968$	63.1324	2.02915
$969$	−18.2382	−0.585894
$970$	0	0
$971$	54.0062	1.73314	0.866571	−	0.499054i	$-0.166319\pi$
$971$	54.0062	1.73314	0.866571	+	0.499054i	$0.166319\pi$
$972$	175.567	5.63131
$973$	24.6513	0.790284
$974$	−1.71553	−0.0549692
$975$	0	0
$976$	−19.7414	−0.631907
$977$	−0.447973	−0.0143319	−0.00716596	−	0.999974i	$-0.502281\pi$
$977$	−0.447973	−0.0143319	−0.00716596	+	0.999974i	$0.502281\pi$
$978$	57.6658	1.84395
$979$	0.334647	0.0106954
$980$	0	0
$981$	101.328	3.23515
$982$	73.0473	2.33103
$983$	−43.5886	−1.39026	−0.695130	−	0.718884i	$-0.744653\pi$
$983$	−43.5886	−1.39026	−0.695130	+	0.718884i	$0.744653\pi$
$984$	−177.986	−5.67397
$985$	0	0
$986$	−5.27572	−0.168013
$987$	−98.3640	−3.13096
$988$	−71.2925	−2.26812
$989$	7.69647	0.244733
$990$	0	0
$991$	−47.3742	−1.50489	−0.752445	−	0.658655i	$-0.771126\pi$
$991$	−47.3742	−1.50489	−0.752445	+	0.658655i	$0.771126\pi$
$992$	−25.0078	−0.794000
$993$	−31.5803	−1.00217
$994$	−66.6119	−2.11280
$995$	0	0
$996$	−150.284	−4.76194
$997$	9.73338	0.308259	0.154130	−	0.988051i	$-0.450743\pi$
$997$	9.73338	0.308259	0.154130	+	0.988051i	$0.450743\pi$
$998$	−77.2135	−2.44415
$999$	−55.5940	−1.75892

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1075.2.a.m.1.1		5
3.2	odd	2		9675.2.a.ch.1.5		5
5.2	odd	4		1075.2.b.h.474.1		10
5.3	odd	4		1075.2.b.h.474.10		10
5.4	even	2		215.2.a.c.1.5	✓	5
15.14	odd	2		1935.2.a.u.1.1		5
20.19	odd	2		3440.2.a.w.1.5		5
215.214	odd	2		9245.2.a.l.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
215.2.a.c.1.5	✓	5	5.4	even	2
1075.2.a.m.1.1		5	1.1	even	1	trivial
1075.2.b.h.474.1		10	5.2	odd	4
1075.2.b.h.474.10		10	5.3	odd	4
1935.2.a.u.1.1		5	15.14	odd	2
3440.2.a.w.1.5		5	20.19	odd	2
9245.2.a.l.1.1		5	215.214	odd	2
9675.2.a.ch.1.5		5	3.2	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:	\( N \)	\(=\)	\( 1075 = 5^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1075.a (trivial)

\(f(q)\)	\(=\)	\(q-2.50989 q^{2} +3.26173 q^{3} +4.29955 q^{4} -8.18658 q^{6} -3.13519 q^{7} -5.77162 q^{8} +7.63887 q^{9} +O(q^{10})\)	\(q-2.50989 q^{2} +3.26173 q^{3} +4.29955 q^{4} -8.18658 q^{6} -3.13519 q^{7} -5.77162 q^{8} +7.63887 q^{9} -0.248163 q^{11} +14.0240 q^{12} +2.67669 q^{13} +7.86899 q^{14} +5.88703 q^{16} +0.902631 q^{17} -19.1727 q^{18} -6.19474 q^{19} -10.2261 q^{21} +0.622862 q^{22} +7.69647 q^{23} -18.8254 q^{24} -6.71819 q^{26} +15.1307 q^{27} -13.4799 q^{28} +2.32872 q^{29} +7.73623 q^{31} -3.23256 q^{32} -0.809440 q^{33} -2.26550 q^{34} +32.8437 q^{36} -3.67425 q^{37} +15.5481 q^{38} +8.73063 q^{39} +9.45452 q^{41} +25.6665 q^{42} +1.00000 q^{43} -1.06699 q^{44} -19.3173 q^{46} +9.61888 q^{47} +19.2019 q^{48} +2.82943 q^{49} +2.94414 q^{51} +11.5086 q^{52} +7.09737 q^{53} -37.9764 q^{54} +18.0951 q^{56} -20.2055 q^{57} -5.84482 q^{58} -3.26173 q^{59} -3.35338 q^{61} -19.4171 q^{62} -23.9493 q^{63} -3.66068 q^{64} +2.03161 q^{66} +0.613476 q^{67} +3.88091 q^{68} +25.1038 q^{69} -8.46512 q^{71} -44.0886 q^{72} +1.33737 q^{73} +9.22196 q^{74} -26.6346 q^{76} +0.778039 q^{77} -21.9129 q^{78} +6.65447 q^{79} +26.4357 q^{81} -23.7298 q^{82} -10.7162 q^{83} -43.9678 q^{84} -2.50989 q^{86} +7.59564 q^{87} +1.43230 q^{88} -1.34850 q^{89} -8.39193 q^{91} +33.0913 q^{92} +25.2335 q^{93} -24.1423 q^{94} -10.5437 q^{96} -4.49827 q^{97} -7.10155 q^{98} -1.89568 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 2 q^{2} + q^{3} + 8 q^{4} - 12 q^{6} - 5 q^{7} - 3 q^{8} + 18 q^{9}+O(q^{10}) \) 5 * q - 2 * q^2 + q^3 + 8 * q^4 - 12 * q^6 - 5 * q^7 - 3 * q^8 + 18 * q^9	\( 5 q - 2 q^{2} + q^{3} + 8 q^{4} - 12 q^{6} - 5 q^{7} - 3 q^{8} + 18 q^{9} - 6 q^{11} - 5 q^{13} + q^{14} + 14 q^{16} + 17 q^{17} + 5 q^{18} - 6 q^{19} + 20 q^{21} + 8 q^{22} - q^{23} - 45 q^{24} + 22 q^{26} + 22 q^{27} - 26 q^{28} + 6 q^{29} + 6 q^{31} + 7 q^{32} + 20 q^{33} + 36 q^{36} - 5 q^{37} + 16 q^{38} - 14 q^{39} + 2 q^{41} + 58 q^{42} + 5 q^{43} - 15 q^{44} - 14 q^{46} + 3 q^{48} + 18 q^{49} - 10 q^{51} + 38 q^{52} + 23 q^{53} - 56 q^{54} - 19 q^{56} - 28 q^{57} - 12 q^{58} - q^{59} + 20 q^{61} + 3 q^{62} - 26 q^{63} - 25 q^{64} + 13 q^{66} - 21 q^{67} + 48 q^{68} + 10 q^{69} + 4 q^{71} - 20 q^{72} - 5 q^{73} + 24 q^{74} + 32 q^{76} + 26 q^{77} - 88 q^{78} + 41 q^{79} + 41 q^{81} - 38 q^{82} + 7 q^{83} - 33 q^{84} - 2 q^{86} + 40 q^{87} - 12 q^{88} + 20 q^{89} - 42 q^{91} + 52 q^{92} + 36 q^{93} - 42 q^{94} + 9 q^{96} - 37 q^{97} + 26 q^{98} + 12 q^{99}+O(q^{100}) \) 5 * q - 2 * q^2 + q^3 + 8 * q^4 - 12 * q^6 - 5 * q^7 - 3 * q^8 + 18 * q^9 - 6 * q^11 - 5 * q^13 + q^14 + 14 * q^16 + 17 * q^17 + 5 * q^18 - 6 * q^19 + 20 * q^21 + 8 * q^22 - q^23 - 45 * q^24 + 22 * q^26 + 22 * q^27 - 26 * q^28 + 6 * q^29 + 6 * q^31 + 7 * q^32 + 20 * q^33 + 36 * q^36 - 5 * q^37 + 16 * q^38 - 14 * q^39 + 2 * q^41 + 58 * q^42 + 5 * q^43 - 15 * q^44 - 14 * q^46 + 3 * q^48 + 18 * q^49 - 10 * q^51 + 38 * q^52 + 23 * q^53 - 56 * q^54 - 19 * q^56 - 28 * q^57 - 12 * q^58 - q^59 + 20 * q^61 + 3 * q^62 - 26 * q^63 - 25 * q^64 + 13 * q^66 - 21 * q^67 + 48 * q^68 + 10 * q^69 + 4 * q^71 - 20 * q^72 - 5 * q^73 + 24 * q^74 + 32 * q^76 + 26 * q^77 - 88 * q^78 + 41 * q^79 + 41 * q^81 - 38 * q^82 + 7 * q^83 - 33 * q^84 - 2 * q^86 + 40 * q^87 - 12 * q^88 + 20 * q^89 - 42 * q^91 + 52 * q^92 + 36 * q^93 - 42 * q^94 + 9 * q^96 - 37 * q^97 + 26 * q^98 + 12 * q^99

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