LMFDB - Embedded newform 2175.2.a.ba.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2175,2,Mod(1,2175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2175, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("2175.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2175 = 3 \cdot 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2175.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:	$17.3674624396$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 2x^{6} - 10x^{5} + 19x^{4} + 24x^{3} - 44x^{2} - 3x + 14 $ x^7 - 2x^6 - 10x^5 + 19x^4 + 24x^3 - 44x^2 - 3x + 14
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.26695$ of defining polynomial
Character	$\chi$	$=$	2175.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.26695 q^{2} -1.00000 q^{3} +3.13907 q^{4} +2.26695 q^{6} -0.159887 q^{7} -2.58223 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.26695 q^{2} -1.00000 q^{3} +3.13907 q^{4} +2.26695 q^{6} -0.159887 q^{7} -2.58223 q^{8} +1.00000 q^{9} -3.24930 q^{11} -3.13907 q^{12} -7.05679 q^{13} +0.362456 q^{14} -0.424361 q^{16} -7.63808 q^{17} -2.26695 q^{18} -3.99028 q^{19} +0.159887 q^{21} +7.36601 q^{22} -2.06402 q^{23} +2.58223 q^{24} +15.9974 q^{26} -1.00000 q^{27} -0.501897 q^{28} -1.00000 q^{29} +10.2044 q^{31} +6.12646 q^{32} +3.24930 q^{33} +17.3152 q^{34} +3.13907 q^{36} +4.27815 q^{37} +9.04576 q^{38} +7.05679 q^{39} -5.12330 q^{41} -0.362456 q^{42} +3.94180 q^{43} -10.1998 q^{44} +4.67903 q^{46} -5.61626 q^{47} +0.424361 q^{48} -6.97444 q^{49} +7.63808 q^{51} -22.1518 q^{52} -12.0822 q^{53} +2.26695 q^{54} +0.412864 q^{56} +3.99028 q^{57} +2.26695 q^{58} -7.06781 q^{59} +11.4310 q^{61} -23.1329 q^{62} -0.159887 q^{63} -13.0397 q^{64} -7.36601 q^{66} +14.9512 q^{67} -23.9765 q^{68} +2.06402 q^{69} +3.43347 q^{71} -2.58223 q^{72} +12.0772 q^{73} -9.69836 q^{74} -12.5258 q^{76} +0.519521 q^{77} -15.9974 q^{78} -12.7441 q^{79} +1.00000 q^{81} +11.6143 q^{82} +2.59792 q^{83} +0.501897 q^{84} -8.93586 q^{86} +1.00000 q^{87} +8.39044 q^{88} +4.33165 q^{89} +1.12829 q^{91} -6.47910 q^{92} -10.2044 q^{93} +12.7318 q^{94} -6.12646 q^{96} +3.88355 q^{97} +15.8107 q^{98} -3.24930 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 2 q^{2} - 7 q^{3} + 10 q^{4} + 2 q^{6} + q^{7} - 3 q^{8} + 7 q^{9}+O(q^{10}) $ 7 * q - 2 * q^2 - 7 * q^3 + 10 * q^4 + 2 * q^6 + q^7 - 3 * q^8 + 7 * q^9	$ 7 q - 2 q^{2} - 7 q^{3} + 10 q^{4} + 2 q^{6} + q^{7} - 3 q^{8} + 7 q^{9} + 4 q^{11} - 10 q^{12} + q^{13} + 15 q^{14} + 12 q^{16} - 8 q^{17} - 2 q^{18} + 15 q^{19} - q^{21} - 3 q^{22} - 14 q^{23} + 3 q^{24} + 6 q^{26} - 7 q^{27} + 24 q^{28} - 7 q^{29} + 5 q^{31} - 18 q^{32} - 4 q^{33} + 7 q^{34} + 10 q^{36} + 6 q^{37} + 18 q^{38} - q^{39} + 22 q^{41} - 15 q^{42} + 19 q^{43} + 15 q^{44} - 4 q^{46} - 22 q^{47} - 12 q^{48} + 12 q^{49} + 8 q^{51} - 11 q^{52} - 10 q^{53} + 2 q^{54} + 14 q^{56} - 15 q^{57} + 2 q^{58} + 6 q^{59} + 23 q^{61} - 40 q^{62} + q^{63} + 5 q^{64} + 3 q^{66} + 13 q^{67} + 7 q^{68} + 14 q^{69} + 26 q^{71} - 3 q^{72} + 24 q^{73} - 10 q^{74} + 46 q^{76} - 4 q^{77} - 6 q^{78} + 14 q^{79} + 7 q^{81} - 16 q^{82} - 10 q^{83} - 24 q^{84} + 44 q^{86} + 7 q^{87} + 66 q^{88} + 14 q^{89} + 13 q^{91} - 58 q^{92} - 5 q^{93} - 3 q^{94} + 18 q^{96} + 31 q^{97} + 59 q^{98} + 4 q^{99}+O(q^{100}) $ 7 * q - 2 * q^2 - 7 * q^3 + 10 * q^4 + 2 * q^6 + q^7 - 3 * q^8 + 7 * q^9 + 4 * q^11 - 10 * q^12 + q^13 + 15 * q^14 + 12 * q^16 - 8 * q^17 - 2 * q^18 + 15 * q^19 - q^21 - 3 * q^22 - 14 * q^23 + 3 * q^24 + 6 * q^26 - 7 * q^27 + 24 * q^28 - 7 * q^29 + 5 * q^31 - 18 * q^32 - 4 * q^33 + 7 * q^34 + 10 * q^36 + 6 * q^37 + 18 * q^38 - q^39 + 22 * q^41 - 15 * q^42 + 19 * q^43 + 15 * q^44 - 4 * q^46 - 22 * q^47 - 12 * q^48 + 12 * q^49 + 8 * q^51 - 11 * q^52 - 10 * q^53 + 2 * q^54 + 14 * q^56 - 15 * q^57 + 2 * q^58 + 6 * q^59 + 23 * q^61 - 40 * q^62 + q^63 + 5 * q^64 + 3 * q^66 + 13 * q^67 + 7 * q^68 + 14 * q^69 + 26 * q^71 - 3 * q^72 + 24 * q^73 - 10 * q^74 + 46 * q^76 - 4 * q^77 - 6 * q^78 + 14 * q^79 + 7 * q^81 - 16 * q^82 - 10 * q^83 - 24 * q^84 + 44 * q^86 + 7 * q^87 + 66 * q^88 + 14 * q^89 + 13 * q^91 - 58 * q^92 - 5 * q^93 - 3 * q^94 + 18 * q^96 + 31 * q^97 + 59 * q^98 + 4 * 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 $

$2$	−2.26695	−1.60298	−0.801489	−	0.598010i	$-0.795958\pi$
$2$	−2.26695	−1.60298	−0.801489	+	0.598010i	$0.795958\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	3.13907	1.56954
$5$	0	0
$5$	0	0
$6$	2.26695	0.925480
$7$	−0.159887	−0.0604316	−0.0302158	−	0.999543i	$-0.509619\pi$
$7$	−0.159887	−0.0604316	−0.0302158	+	0.999543i	$0.509619\pi$
$8$	−2.58223	−0.912955
$9$	1.00000	0.333333
$10$	0	0
$11$	−3.24930	−0.979701	−0.489851	−	0.871806i	$-0.662949\pi$
$11$	−3.24930	−0.979701	−0.489851	+	0.871806i	$0.662949\pi$
$12$	−3.13907	−0.906173
$13$	−7.05679	−1.95720	−0.978600	−	0.205770i	$-0.934030\pi$
$13$	−7.05679	−1.95720	−0.978600	+	0.205770i	$0.934030\pi$
$14$	0.362456	0.0968704
$15$	0	0
$16$	−0.424361	−0.106090
$17$	−7.63808	−1.85251	−0.926254	−	0.376901i	$-0.876990\pi$
$17$	−7.63808	−1.85251	−0.926254	+	0.376901i	$0.876990\pi$
$18$	−2.26695	−0.534326
$19$	−3.99028	−0.915432	−0.457716	−	0.889098i	$-0.651332\pi$
$19$	−3.99028	−0.915432	−0.457716	+	0.889098i	$0.651332\pi$
$20$	0	0
$21$	0.159887	0.0348902
$22$	7.36601	1.57044
$23$	−2.06402	−0.430377	−0.215189	−	0.976572i	$-0.569037\pi$
$23$	−2.06402	−0.430377	−0.215189	+	0.976572i	$0.569037\pi$
$24$	2.58223	0.527095
$25$	0	0
$26$	15.9974	3.13735
$27$	−1.00000	−0.192450
$28$	−0.501897	−0.0948496
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	0	0
$31$	10.2044	1.83277	0.916383	−	0.400303i	$-0.131095\pi$
$31$	10.2044	1.83277	0.916383	+	0.400303i	$0.131095\pi$
$32$	6.12646	1.08302
$33$	3.24930	0.565631
$34$	17.3152	2.96953
$35$	0	0
$36$	3.13907	0.523179
$37$	4.27815	0.703323	0.351662	−	0.936127i	$-0.385617\pi$
$37$	4.27815	0.703323	0.351662	+	0.936127i	$0.385617\pi$
$38$	9.04576	1.46742
$39$	7.05679	1.12999
$40$	0	0
$41$	−5.12330	−0.800125	−0.400063	−	0.916488i	$-0.631012\pi$
$41$	−5.12330	−0.800125	−0.400063	+	0.916488i	$0.631012\pi$
$42$	−0.362456	−0.0559282
$43$	3.94180	0.601118	0.300559	−	0.953763i	$-0.402827\pi$
$43$	3.94180	0.601118	0.300559	+	0.953763i	$0.402827\pi$
$44$	−10.1998	−1.53768
$45$	0	0
$46$	4.67903	0.689885
$47$	−5.61626	−0.819215	−0.409608	−	0.912262i	$-0.634334\pi$
$47$	−5.61626	−0.819215	−0.409608	+	0.912262i	$0.634334\pi$
$48$	0.424361	0.0612513
$49$	−6.97444	−0.996348
$50$	0	0
$51$	7.63808	1.06955
$52$	−22.1518	−3.07190
$53$	−12.0822	−1.65962	−0.829808	−	0.558049i	$-0.811550\pi$
$53$	−12.0822	−1.65962	−0.829808	+	0.558049i	$0.811550\pi$
$54$	2.26695	0.308493
$55$	0	0
$56$	0.412864	0.0551713
$57$	3.99028	0.528525
$58$	2.26695	0.297665
$59$	−7.06781	−0.920151	−0.460075	−	0.887880i	$-0.652178\pi$
$59$	−7.06781	−0.920151	−0.460075	+	0.887880i	$0.652178\pi$
$60$	0	0
$61$	11.4310	1.46359	0.731796	−	0.681524i	$-0.238682\pi$
$61$	11.4310	1.46359	0.731796	+	0.681524i	$0.238682\pi$
$62$	−23.1329	−2.93788
$63$	−0.159887	−0.0201439
$64$	−13.0397	−1.62996
$65$	0	0
$66$	−7.36601	−0.906694
$67$	14.9512	1.82658	0.913289	−	0.407311i	$-0.133534\pi$
$67$	14.9512	1.82658	0.913289	+	0.407311i	$0.133534\pi$
$68$	−23.9765	−2.90758
$69$	2.06402	0.248478
$70$	0	0
$71$	3.43347	0.407478	0.203739	−	0.979025i	$-0.434691\pi$
$71$	3.43347	0.407478	0.203739	+	0.979025i	$0.434691\pi$
$72$	−2.58223	−0.304318
$73$	12.0772	1.41353	0.706764	−	0.707449i	$-0.250154\pi$
$73$	12.0772	1.41353	0.706764	+	0.707449i	$0.250154\pi$
$74$	−9.69836	−1.12741
$75$	0	0
$76$	−12.5258	−1.43680
$77$	0.519521	0.0592049
$78$	−15.9974	−1.81135
$79$	−12.7441	−1.43383	−0.716913	−	0.697163i	$-0.754446\pi$
$79$	−12.7441	−1.43383	−0.716913	+	0.697163i	$0.754446\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	11.6143	1.28258
$83$	2.59792	0.285159	0.142580	−	0.989783i	$-0.454460\pi$
$83$	2.59792	0.285159	0.142580	+	0.989783i	$0.454460\pi$
$84$	0.501897	0.0547614
$85$	0	0
$86$	−8.93586	−0.963579
$87$	1.00000	0.107211
$88$	8.39044	0.894423
$89$	4.33165	0.459154	0.229577	−	0.973290i	$-0.426266\pi$
$89$	4.33165	0.459154	0.229577	+	0.973290i	$0.426266\pi$
$90$	0	0
$91$	1.12829	0.118277
$92$	−6.47910	−0.675493
$93$	−10.2044	−1.05815
$94$	12.7318	1.31318
$95$	0	0
$96$	−6.12646	−0.625279
$97$	3.88355	0.394315	0.197158	−	0.980372i	$-0.436829\pi$
$97$	3.88355	0.394315	0.197158	+	0.980372i	$0.436829\pi$
$98$	15.8107	1.59712
$99$	−3.24930	−0.326567
$100$	0	0
$101$	15.4045	1.53280	0.766400	−	0.642363i	$-0.222046\pi$
$101$	15.4045	1.53280	0.766400	+	0.642363i	$0.222046\pi$
$102$	−17.3152	−1.71446
$103$	−7.68484	−0.757210	−0.378605	−	0.925558i	$-0.623596\pi$
$103$	−7.68484	−0.757210	−0.378605	+	0.925558i	$0.623596\pi$
$104$	18.2222	1.78684
$105$	0	0
$106$	27.3897	2.66033
$107$	4.60924	0.445592	0.222796	−	0.974865i	$-0.428482\pi$
$107$	4.60924	0.445592	0.222796	+	0.974865i	$0.428482\pi$
$108$	−3.13907	−0.302058
$109$	−14.4509	−1.38415	−0.692073	−	0.721827i	$-0.743302\pi$
$109$	−14.4509	−1.38415	−0.692073	+	0.721827i	$0.743302\pi$
$110$	0	0
$111$	−4.27815	−0.406064
$112$	0.0678498	0.00641120
$113$	4.08614	0.384392	0.192196	−	0.981357i	$-0.438439\pi$
$113$	4.08614	0.384392	0.192196	+	0.981357i	$0.438439\pi$
$114$	−9.04576	−0.847213
$115$	0	0
$116$	−3.13907	−0.291456
$117$	−7.05679	−0.652400
$118$	16.0224	1.47498
$119$	1.22123	0.111950
$120$	0	0
$121$	−0.442038	−0.0401853
$122$	−25.9136	−2.34610
$123$	5.12330	0.461952
$124$	32.0324	2.87659
$125$	0	0
$126$	0.362456	0.0322901
$127$	3.69650	0.328011	0.164006	−	0.986459i	$-0.447559\pi$
$127$	3.69650	0.328011	0.164006	+	0.986459i	$0.447559\pi$
$128$	17.3074	1.52977
$129$	−3.94180	−0.347056
$130$	0	0
$131$	−9.92811	−0.867423	−0.433712	−	0.901052i	$-0.642796\pi$
$131$	−9.92811	−0.867423	−0.433712	+	0.901052i	$0.642796\pi$
$132$	10.1998	0.887779
$133$	0.637993	0.0553210
$134$	−33.8936	−2.92797
$135$	0	0
$136$	19.7233	1.69126
$137$	−3.82810	−0.327057	−0.163528	−	0.986539i	$-0.552288\pi$
$137$	−3.82810	−0.327057	−0.163528	+	0.986539i	$0.552288\pi$
$138$	−4.67903	−0.398305
$139$	−2.06987	−0.175564	−0.0877822	−	0.996140i	$-0.527978\pi$
$139$	−2.06987	−0.175564	−0.0877822	+	0.996140i	$0.527978\pi$
$140$	0	0
$141$	5.61626	0.472974
$142$	−7.78351	−0.653177
$143$	22.9296	1.91747
$144$	−0.424361	−0.0353634
$145$	0	0
$146$	−27.3784	−2.26585
$147$	6.97444	0.575242
$148$	13.4294	1.10389
$149$	−1.46609	−0.120107	−0.0600536	−	0.998195i	$-0.519127\pi$
$149$	−1.46609	−0.120107	−0.0600536	+	0.998195i	$0.519127\pi$
$150$	0	0
$151$	−20.1279	−1.63799	−0.818995	−	0.573801i	$-0.805468\pi$
$151$	−20.1279	−1.63799	−0.818995	+	0.573801i	$0.805468\pi$
$152$	10.3038	0.835748
$153$	−7.63808	−0.617502
$154$	−1.17773	−0.0949041
$155$	0	0
$156$	22.1518	1.77356
$157$	−7.09106	−0.565928	−0.282964	−	0.959131i	$-0.591318\pi$
$157$	−7.09106	−0.565928	−0.282964	+	0.959131i	$0.591318\pi$
$158$	28.8903	2.29839
$159$	12.0822	0.958180
$160$	0	0
$161$	0.330009	0.0260084
$162$	−2.26695	−0.178109
$163$	6.58715	0.515946	0.257973	−	0.966152i	$-0.416945\pi$
$163$	6.58715	0.515946	0.257973	+	0.966152i	$0.416945\pi$
$164$	−16.0824	−1.25583
$165$	0	0
$166$	−5.88937	−0.457104
$167$	10.6638	0.825192	0.412596	−	0.910914i	$-0.364622\pi$
$167$	10.6638	0.825192	0.412596	+	0.910914i	$0.364622\pi$
$168$	−0.412864	−0.0318532
$169$	36.7983	2.83063
$170$	0	0
$171$	−3.99028	−0.305144
$172$	12.3736	0.943477
$173$	13.8799	1.05527	0.527633	−	0.849472i	$-0.323080\pi$
$173$	13.8799	1.05527	0.527633	+	0.849472i	$0.323080\pi$
$174$	−2.26695	−0.171857
$175$	0	0
$176$	1.37888	0.103937
$177$	7.06781	0.531249
$178$	−9.81965	−0.736014
$179$	−11.1105	−0.830439	−0.415219	−	0.909721i	$-0.636295\pi$
$179$	−11.1105	−0.830439	−0.415219	+	0.909721i	$0.636295\pi$
$180$	0	0
$181$	10.9453	0.813557	0.406778	−	0.913527i	$-0.366652\pi$
$181$	10.9453	0.813557	0.406778	+	0.913527i	$0.366652\pi$
$182$	−2.55777	−0.189595
$183$	−11.4310	−0.845005
$184$	5.32976	0.392915
$185$	0	0
$186$	23.1329	1.69619
$187$	24.8184	1.81490
$188$	−17.6298	−1.28579
$189$	0.159887	0.0116301
$190$	0	0
$191$	18.1472	1.31309	0.656544	−	0.754287i	$-0.272017\pi$
$191$	18.1472	1.31309	0.656544	+	0.754287i	$0.272017\pi$
$192$	13.0397	0.941058
$193$	17.3305	1.24747	0.623737	−	0.781634i	$-0.285614\pi$
$193$	17.3305	1.24747	0.623737	+	0.781634i	$0.285614\pi$
$194$	−8.80383	−0.632078
$195$	0	0
$196$	−21.8933	−1.56381
$197$	10.4273	0.742915	0.371458	−	0.928450i	$-0.378858\pi$
$197$	10.4273	0.742915	0.371458	+	0.928450i	$0.378858\pi$
$198$	7.36601	0.523480
$199$	11.5570	0.819256	0.409628	−	0.912253i	$-0.365659\pi$
$199$	11.5570	0.819256	0.409628	+	0.912253i	$0.365659\pi$
$200$	0	0
$201$	−14.9512	−1.05458
$202$	−34.9212	−2.45704
$203$	0.159887	0.0112219
$204$	23.9765	1.67869
$205$	0	0
$206$	17.4212	1.21379
$207$	−2.06402	−0.143459
$208$	2.99463	0.207640
$209$	12.9656	0.896850
$210$	0	0
$211$	−21.1616	−1.45682	−0.728412	−	0.685140i	$-0.759741\pi$
$211$	−21.1616	−1.45682	−0.728412	+	0.685140i	$0.759741\pi$
$212$	−37.9269	−2.60483
$213$	−3.43347	−0.235257
$214$	−10.4489	−0.714274
$215$	0	0
$216$	2.58223	0.175698
$217$	−1.63155	−0.110757
$218$	32.7595	2.21876
$219$	−12.0772	−0.816101
$220$	0	0
$221$	53.9003	3.62573
$222$	9.69836	0.650911
$223$	−9.46925	−0.634108	−0.317054	−	0.948408i	$-0.602694\pi$
$223$	−9.46925	−0.634108	−0.317054	+	0.948408i	$0.602694\pi$
$224$	−0.979541	−0.0654483
$225$	0	0
$226$	−9.26310	−0.616172
$227$	−22.4030	−1.48694	−0.743471	−	0.668768i	$-0.766822\pi$
$227$	−22.4030	−1.48694	−0.743471	+	0.668768i	$0.766822\pi$
$228$	12.5258	0.829539
$229$	2.03117	0.134223	0.0671117	−	0.997745i	$-0.478622\pi$
$229$	2.03117	0.134223	0.0671117	+	0.997745i	$0.478622\pi$
$230$	0	0
$231$	−0.519521	−0.0341820
$232$	2.58223	0.169532
$233$	−11.0704	−0.725249	−0.362624	−	0.931935i	$-0.618119\pi$
$233$	−11.0704	−0.725249	−0.362624	+	0.931935i	$0.618119\pi$
$234$	15.9974	1.04578
$235$	0	0
$236$	−22.1864	−1.44421
$237$	12.7441	0.827820
$238$	−2.76847	−0.179453
$239$	−2.24098	−0.144957	−0.0724786	−	0.997370i	$-0.523091\pi$
$239$	−2.24098	−0.144957	−0.0724786	+	0.997370i	$0.523091\pi$
$240$	0	0
$241$	14.4838	0.932986	0.466493	−	0.884525i	$-0.345517\pi$
$241$	14.4838	0.932986	0.466493	+	0.884525i	$0.345517\pi$
$242$	1.00208	0.0644161
$243$	−1.00000	−0.0641500
$244$	35.8828	2.29716
$245$	0	0
$246$	−11.6143	−0.740499
$247$	28.1585	1.79168
$248$	−26.3501	−1.67323
$249$	−2.59792	−0.164637
$250$	0	0
$251$	−16.2044	−1.02281	−0.511407	−	0.859339i	$-0.670875\pi$
$251$	−16.2044	−1.02281	−0.511407	+	0.859339i	$0.670875\pi$
$252$	−0.501897	−0.0316165
$253$	6.70661	0.421641
$254$	−8.37978	−0.525794
$255$	0	0
$256$	−13.1557	−0.822232
$257$	3.36942	0.210178	0.105089	−	0.994463i	$-0.466487\pi$
$257$	3.36942	0.210178	0.105089	+	0.994463i	$0.466487\pi$
$258$	8.93586	0.556323
$259$	−0.684020	−0.0425029
$260$	0	0
$261$	−1.00000	−0.0618984
$262$	22.5066	1.39046
$263$	−1.79671	−0.110790	−0.0553950	−	0.998465i	$-0.517642\pi$
$263$	−1.79671	−0.110790	−0.0553950	+	0.998465i	$0.517642\pi$
$264$	−8.39044	−0.516396
$265$	0	0
$266$	−1.44630	−0.0886783
$267$	−4.33165	−0.265093
$268$	46.9329	2.86688
$269$	−0.117055	−0.00713699	−0.00356849	−	0.999994i	$-0.501136\pi$
$269$	−0.117055	−0.00713699	−0.00356849	+	0.999994i	$0.501136\pi$
$270$	0	0
$271$	−4.06294	−0.246806	−0.123403	−	0.992357i	$-0.539381\pi$
$271$	−4.06294	−0.246806	−0.123403	+	0.992357i	$0.539381\pi$
$272$	3.24131	0.196533
$273$	−1.12829	−0.0682871
$274$	8.67813	0.524265
$275$	0	0
$276$	6.47910	0.389996
$277$	12.5436	0.753674	0.376837	−	0.926279i	$-0.377012\pi$
$277$	12.5436	0.753674	0.376837	+	0.926279i	$0.377012\pi$
$278$	4.69231	0.281426
$279$	10.2044	0.610922
$280$	0	0
$281$	−2.83163	−0.168921	−0.0844605	−	0.996427i	$-0.526917\pi$
$281$	−2.83163	−0.168921	−0.0844605	+	0.996427i	$0.526917\pi$
$282$	−12.7318	−0.758167
$283$	−28.2249	−1.67780	−0.838898	−	0.544288i	$-0.816800\pi$
$283$	−28.2249	−1.67780	−0.838898	+	0.544288i	$0.816800\pi$
$284$	10.7779	0.639551
$285$	0	0
$286$	−51.9804	−3.07366
$287$	0.819148	0.0483528
$288$	6.12646	0.361005
$289$	41.3403	2.43178
$290$	0	0
$291$	−3.88355	−0.227658
$292$	37.9112	2.21859
$293$	−21.9337	−1.28138	−0.640691	−	0.767799i	$-0.721352\pi$
$293$	−21.9337	−1.28138	−0.640691	+	0.767799i	$0.721352\pi$
$294$	−15.8107	−0.922100
$295$	0	0
$296$	−11.0472	−0.642103
$297$	3.24930	0.188544
$298$	3.32357	0.192529
$299$	14.5653	0.842335
$300$	0	0
$301$	−0.630241	−0.0363265
$302$	45.6291	2.62566
$303$	−15.4045	−0.884963
$304$	1.69332	0.0971185
$305$	0	0
$306$	17.3152	0.989843
$307$	0.461574	0.0263434	0.0131717	−	0.999913i	$-0.495807\pi$
$307$	0.461574	0.0263434	0.0131717	+	0.999913i	$0.495807\pi$
$308$	1.63081	0.0929243
$309$	7.68484	0.437175
$310$	0	0
$311$	27.5507	1.56226	0.781128	−	0.624371i	$-0.214645\pi$
$311$	27.5507	1.56226	0.781128	+	0.624371i	$0.214645\pi$
$312$	−18.2222	−1.03163
$313$	−14.9121	−0.842882	−0.421441	−	0.906856i	$-0.638476\pi$
$313$	−14.9121	−0.842882	−0.421441	+	0.906856i	$0.638476\pi$
$314$	16.0751	0.907170
$315$	0	0
$316$	−40.0048	−2.25044
$317$	22.9266	1.28769	0.643843	−	0.765157i	$-0.277339\pi$
$317$	22.9266	1.28769	0.643843	+	0.765157i	$0.277339\pi$
$318$	−27.3897	−1.53594
$319$	3.24930	0.181926
$320$	0	0
$321$	−4.60924	−0.257263
$322$	−0.748115	−0.0416908
$323$	30.4781	1.69584
$324$	3.13907	0.174393
$325$	0	0
$326$	−14.9328	−0.827049
$327$	14.4509	0.799137
$328$	13.2295	0.730478
$329$	0.897966	0.0495065
$330$	0	0
$331$	−3.23147	−0.177618	−0.0888088	−	0.996049i	$-0.528306\pi$
$331$	−3.23147	−0.177618	−0.0888088	+	0.996049i	$0.528306\pi$
$332$	8.15507	0.447568
$333$	4.27815	0.234441
$334$	−24.1744	−1.32277
$335$	0	0
$336$	−0.0678498	−0.00370151
$337$	−28.8026	−1.56898	−0.784489	−	0.620143i	$-0.787075\pi$
$337$	−28.8026	−1.56898	−0.784489	+	0.620143i	$0.787075\pi$
$338$	−83.4199	−4.53744
$339$	−4.08614	−0.221929
$340$	0	0
$341$	−33.1572	−1.79556
$342$	9.04576	0.489139
$343$	2.23433	0.120642
$344$	−10.1786	−0.548794
$345$	0	0
$346$	−31.4650	−1.69157
$347$	16.4175	0.881337	0.440669	−	0.897670i	$-0.354741\pi$
$347$	16.4175	0.881337	0.440669	+	0.897670i	$0.354741\pi$
$348$	3.13907	0.168272
$349$	−18.2107	−0.974796	−0.487398	−	0.873180i	$-0.662054\pi$
$349$	−18.2107	−0.974796	−0.487398	+	0.873180i	$0.662054\pi$
$350$	0	0
$351$	7.05679	0.376663
$352$	−19.9067	−1.06103
$353$	18.8790	1.00483	0.502414	−	0.864627i	$-0.332445\pi$
$353$	18.8790	1.00483	0.502414	+	0.864627i	$0.332445\pi$
$354$	−16.0224	−0.851581
$355$	0	0
$356$	13.5974	0.720660
$357$	−1.22123	−0.0646343
$358$	25.1870	1.33117
$359$	14.4500	0.762640	0.381320	−	0.924443i	$-0.375470\pi$
$359$	14.4500	0.762640	0.381320	+	0.924443i	$0.375470\pi$
$360$	0	0
$361$	−3.07770	−0.161984
$362$	−24.8125	−1.30411
$363$	0.442038	0.0232010
$364$	3.54178	0.185640
$365$	0	0
$366$	25.9136	1.35452
$367$	21.1171	1.10231	0.551153	−	0.834404i	$-0.314188\pi$
$367$	21.1171	1.10231	0.551153	+	0.834404i	$0.314188\pi$
$368$	0.875889	0.0456589
$369$	−5.12330	−0.266708
$370$	0	0
$371$	1.93178	0.100293
$372$	−32.0324	−1.66080
$373$	17.1185	0.886361	0.443181	−	0.896432i	$-0.353850\pi$
$373$	17.1185	0.886361	0.443181	+	0.896432i	$0.353850\pi$
$374$	−56.2622	−2.90925
$375$	0	0
$376$	14.5025	0.747907
$377$	7.05679	0.363443
$378$	−0.362456	−0.0186427
$379$	−0.206688	−0.0106169	−0.00530844	−	0.999986i	$-0.501690\pi$
$379$	−0.206688	−0.0106169	−0.00530844	+	0.999986i	$0.501690\pi$
$380$	0	0
$381$	−3.69650	−0.189377
$382$	−41.1389	−2.10485
$383$	−16.3701	−0.836474	−0.418237	−	0.908338i	$-0.637352\pi$
$383$	−16.3701	−0.836474	−0.418237	+	0.908338i	$0.637352\pi$
$384$	−17.3074	−0.883215
$385$	0	0
$386$	−39.2873	−1.99967
$387$	3.94180	0.200373
$388$	12.1908	0.618892
$389$	11.7627	0.596393	0.298197	−	0.954504i	$-0.403615\pi$
$389$	11.7627	0.596393	0.298197	+	0.954504i	$0.403615\pi$
$390$	0	0
$391$	15.7651	0.797277
$392$	18.0096	0.909621
$393$	9.92811	0.500807
$394$	−23.6382	−1.19088
$395$	0	0
$396$	−10.1998	−0.512559
$397$	4.96134	0.249002	0.124501	−	0.992219i	$-0.460267\pi$
$397$	4.96134	0.249002	0.124501	+	0.992219i	$0.460267\pi$
$398$	−26.1992	−1.31325
$399$	−0.637993	−0.0319396
$400$	0	0
$401$	36.1967	1.80758	0.903789	−	0.427979i	$-0.140774\pi$
$401$	36.1967	1.80758	0.903789	+	0.427979i	$0.140774\pi$
$402$	33.8936	1.69046
$403$	−72.0103	−3.58709
$404$	48.3557	2.40579
$405$	0	0
$406$	−0.362456	−0.0179884
$407$	−13.9010	−0.689047
$408$	−19.7233	−0.976447
$409$	−16.1607	−0.799094	−0.399547	−	0.916713i	$-0.630832\pi$
$409$	−16.1607	−0.799094	−0.399547	+	0.916713i	$0.630832\pi$
$410$	0	0
$411$	3.82810	0.188826
$412$	−24.1233	−1.18847
$413$	1.13005	0.0556061
$414$	4.67903	0.229962
$415$	0	0
$416$	−43.2331	−2.11968
$417$	2.06987	0.101362
$418$	−29.3924	−1.43763
$419$	−33.5544	−1.63924	−0.819621	−	0.572906i	$-0.805816\pi$
$419$	−33.5544	−1.63924	−0.819621	+	0.572906i	$0.805816\pi$
$420$	0	0
$421$	26.9847	1.31515	0.657577	−	0.753388i	$-0.271582\pi$
$421$	26.9847	1.31515	0.657577	+	0.753388i	$0.271582\pi$
$422$	47.9723	2.33526
$423$	−5.61626	−0.273072
$424$	31.1990	1.51515
$425$	0	0
$426$	7.78351	0.377112
$427$	−1.82767	−0.0884471
$428$	14.4687	0.699373
$429$	−22.9296	−1.10705
$430$	0	0
$431$	0.832366	0.0400937	0.0200468	−	0.999799i	$-0.493618\pi$
$431$	0.832366	0.0400937	0.0200468	+	0.999799i	$0.493618\pi$
$432$	0.424361	0.0204171
$433$	22.5647	1.08439	0.542195	−	0.840253i	$-0.317593\pi$
$433$	22.5647	1.08439	0.542195	+	0.840253i	$0.317593\pi$
$434$	3.69865	0.177541
$435$	0	0
$436$	−45.3625	−2.17247
$437$	8.23600	0.393981
$438$	27.3784	1.30819
$439$	23.9583	1.14347	0.571734	−	0.820439i	$-0.306271\pi$
$439$	23.9583	1.14347	0.571734	+	0.820439i	$0.306271\pi$
$440$	0	0
$441$	−6.97444	−0.332116
$442$	−122.190	−5.81196
$443$	−17.4925	−0.831092	−0.415546	−	0.909572i	$-0.636409\pi$
$443$	−17.4925	−0.831092	−0.415546	+	0.909572i	$0.636409\pi$
$444$	−13.4294	−0.637332
$445$	0	0
$446$	21.4663	1.01646
$447$	1.46609	0.0693439
$448$	2.08487	0.0985010
$449$	4.22200	0.199249	0.0996243	−	0.995025i	$-0.468236\pi$
$449$	4.22200	0.199249	0.0996243	+	0.995025i	$0.468236\pi$
$450$	0	0
$451$	16.6471	0.783884
$452$	12.8267	0.603318
$453$	20.1279	0.945694
$454$	50.7866	2.38353
$455$	0	0
$456$	−10.3038	−0.482520
$457$	1.28562	0.0601389	0.0300694	−	0.999548i	$-0.490427\pi$
$457$	1.28562	0.0601389	0.0300694	+	0.999548i	$0.490427\pi$
$458$	−4.60456	−0.215157
$459$	7.63808	0.356515
$460$	0	0
$461$	−23.8534	−1.11097	−0.555483	−	0.831528i	$-0.687466\pi$
$461$	−23.8534	−1.11097	−0.555483	+	0.831528i	$0.687466\pi$
$462$	1.17773	0.0547929
$463$	−14.1402	−0.657152	−0.328576	−	0.944478i	$-0.606569\pi$
$463$	−14.1402	−0.657152	−0.328576	+	0.944478i	$0.606569\pi$
$464$	0.424361	0.0197005
$465$	0	0
$466$	25.0962	1.16256
$467$	−7.06487	−0.326923	−0.163462	−	0.986550i	$-0.552266\pi$
$467$	−7.06487	−0.326923	−0.163462	+	0.986550i	$0.552266\pi$
$468$	−22.1518	−1.02397
$469$	−2.39050	−0.110383
$470$	0	0
$471$	7.09106	0.326739
$472$	18.2507	0.840056
$473$	−12.8081	−0.588916
$474$	−28.8903	−1.32698
$475$	0	0
$476$	3.83353	0.175710
$477$	−12.0822	−0.553205
$478$	5.08020	0.232363
$479$	22.9561	1.04889	0.524444	−	0.851445i	$-0.324273\pi$
$479$	22.9561	1.04889	0.524444	+	0.851445i	$0.324273\pi$
$480$	0	0
$481$	−30.1900	−1.37654
$482$	−32.8342	−1.49556
$483$	−0.330009	−0.0150159
$484$	−1.38759	−0.0630723
$485$	0	0
$486$	2.26695	0.102831
$487$	27.0319	1.22493	0.612467	−	0.790496i	$-0.290177\pi$
$487$	27.0319	1.22493	0.612467	+	0.790496i	$0.290177\pi$
$488$	−29.5175	−1.33619
$489$	−6.58715	−0.297881
$490$	0	0
$491$	−11.5498	−0.521235	−0.260617	−	0.965442i	$-0.583926\pi$
$491$	−11.5498	−0.521235	−0.260617	+	0.965442i	$0.583926\pi$
$492$	16.0824	0.725051
$493$	7.63808	0.344002
$494$	−63.8340	−2.87203
$495$	0	0
$496$	−4.33036	−0.194439
$497$	−0.548966	−0.0246245
$498$	5.88937	0.263909
$499$	3.77942	0.169190	0.0845950	−	0.996415i	$-0.473040\pi$
$499$	3.77942	0.169190	0.0845950	+	0.996415i	$0.473040\pi$
$500$	0	0
$501$	−10.6638	−0.476425
$502$	36.7346	1.63955
$503$	14.7684	0.658489	0.329244	−	0.944245i	$-0.393206\pi$
$503$	14.7684	0.658489	0.329244	+	0.944245i	$0.393206\pi$
$504$	0.412864	0.0183904
$505$	0	0
$506$	−15.2036	−0.675881
$507$	−36.7983	−1.63427
$508$	11.6036	0.514826
$509$	−42.4182	−1.88015	−0.940077	−	0.340962i	$-0.889247\pi$
$509$	−42.4182	−1.88015	−0.940077	+	0.340962i	$0.889247\pi$
$510$	0	0
$511$	−1.93098	−0.0854217
$512$	−4.79143	−0.211753
$513$	3.99028	0.176175
$514$	−7.63831	−0.336911
$515$	0	0
$516$	−12.3736	−0.544717
$517$	18.2489	0.802586
$518$	1.55064	0.0681312
$519$	−13.8799	−0.609258
$520$	0	0
$521$	20.3409	0.891152	0.445576	−	0.895244i	$-0.352999\pi$
$521$	20.3409	0.891152	0.445576	+	0.895244i	$0.352999\pi$
$522$	2.26695	0.0992218
$523$	−1.52190	−0.0665481	−0.0332740	−	0.999446i	$-0.510593\pi$
$523$	−1.52190	−0.0665481	−0.0332740	+	0.999446i	$0.510593\pi$
$524$	−31.1651	−1.36145
$525$	0	0
$526$	4.07306	0.177594
$527$	−77.9421	−3.39521
$528$	−1.37888	−0.0600080
$529$	−18.7398	−0.814775
$530$	0	0
$531$	−7.06781	−0.306717
$532$	2.00271	0.0868283
$533$	36.1540	1.56601
$534$	9.81965	0.424938
$535$	0	0
$536$	−38.6074	−1.66758
$537$	11.1105	0.479454
$538$	0.265359	0.0114404
$539$	22.6620	0.976123
$540$	0	0
$541$	−9.40679	−0.404430	−0.202215	−	0.979341i	$-0.564814\pi$
$541$	−9.40679	−0.404430	−0.202215	+	0.979341i	$0.564814\pi$
$542$	9.21049	0.395624
$543$	−10.9453	−0.469707
$544$	−46.7944	−2.00629
$545$	0	0
$546$	2.55777	0.109463
$547$	−19.7232	−0.843304	−0.421652	−	0.906758i	$-0.638550\pi$
$547$	−19.7232	−0.843304	−0.421652	+	0.906758i	$0.638550\pi$
$548$	−12.0167	−0.513328
$549$	11.4310	0.487864
$550$	0	0
$551$	3.99028	0.169991
$552$	−5.32976	−0.226850
$553$	2.03762	0.0866483
$554$	−28.4358	−1.20812
$555$	0	0
$556$	−6.49749	−0.275555
$557$	−9.01986	−0.382184	−0.191092	−	0.981572i	$-0.561203\pi$
$557$	−9.01986	−0.382184	−0.191092	+	0.981572i	$0.561203\pi$
$558$	−23.1329	−0.979294
$559$	−27.8164	−1.17651
$560$	0	0
$561$	−24.8184	−1.04784
$562$	6.41918	0.270777
$563$	−17.5283	−0.738728	−0.369364	−	0.929285i	$-0.620424\pi$
$563$	−17.5283	−0.738728	−0.369364	+	0.929285i	$0.620424\pi$
$564$	17.6298	0.742350
$565$	0	0
$566$	63.9845	2.68947
$567$	−0.159887	−0.00671462
$568$	−8.86599	−0.372009
$569$	32.3981	1.35820	0.679099	−	0.734046i	$-0.262371\pi$
$569$	32.3981	1.35820	0.679099	+	0.734046i	$0.262371\pi$
$570$	0	0
$571$	−11.8393	−0.495458	−0.247729	−	0.968829i	$-0.579684\pi$
$571$	−11.8393	−0.495458	−0.247729	+	0.968829i	$0.579684\pi$
$572$	71.9778	3.00954
$573$	−18.1472	−0.758112
$574$	−1.85697	−0.0775085
$575$	0	0
$576$	−13.0397	−0.543320
$577$	0.192778	0.00802545	0.00401273	−	0.999992i	$-0.498723\pi$
$577$	0.192778	0.00802545	0.00401273	+	0.999992i	$0.498723\pi$
$578$	−93.7165	−3.89809
$579$	−17.3305	−0.720229
$580$	0	0
$581$	−0.415374	−0.0172326
$582$	8.80383	0.364931
$583$	39.2587	1.62593
$584$	−31.1861	−1.29049
$585$	0	0
$586$	49.7227	2.05403
$587$	−34.5089	−1.42433	−0.712167	−	0.702010i	$-0.752286\pi$
$587$	−34.5089	−1.42433	−0.712167	+	0.702010i	$0.752286\pi$
$588$	21.8933	0.902863
$589$	−40.7184	−1.67777
$590$	0	0
$591$	−10.4273	−0.428922
$592$	−1.81548	−0.0746158
$593$	−2.42748	−0.0996846	−0.0498423	−	0.998757i	$-0.515872\pi$
$593$	−2.42748	−0.0996846	−0.0498423	+	0.998757i	$0.515872\pi$
$594$	−7.36601	−0.302231
$595$	0	0
$596$	−4.60218	−0.188513
$597$	−11.5570	−0.472997
$598$	−33.0189	−1.35024
$599$	29.3312	1.19844	0.599220	−	0.800585i	$-0.295478\pi$
$599$	29.3312	1.19844	0.599220	+	0.800585i	$0.295478\pi$
$600$	0	0
$601$	29.5631	1.20590	0.602952	−	0.797778i	$-0.293991\pi$
$601$	29.5631	1.20590	0.602952	+	0.797778i	$0.293991\pi$
$602$	1.42873	0.0582306
$603$	14.9512	0.608860
$604$	−63.1831	−2.57089
$605$	0	0
$606$	34.9212	1.41858
$607$	−33.1756	−1.34656	−0.673278	−	0.739390i	$-0.735114\pi$
$607$	−33.1756	−1.34656	−0.673278	+	0.739390i	$0.735114\pi$
$608$	−24.4463	−0.991427
$609$	−0.159887	−0.00647894
$610$	0	0
$611$	39.6327	1.60337
$612$	−23.9765	−0.969193
$613$	13.9979	0.565371	0.282686	−	0.959213i	$-0.408775\pi$
$613$	13.9979	0.565371	0.282686	+	0.959213i	$0.408775\pi$
$614$	−1.04637	−0.0422279
$615$	0	0
$616$	−1.34152	−0.0540514
$617$	29.9344	1.20511	0.602556	−	0.798077i	$-0.294149\pi$
$617$	29.9344	1.20511	0.602556	+	0.798077i	$0.294149\pi$
$618$	−17.4212	−0.700782
$619$	−14.9032	−0.599009	−0.299505	−	0.954095i	$-0.596821\pi$
$619$	−14.9032	−0.599009	−0.299505	+	0.954095i	$0.596821\pi$
$620$	0	0
$621$	2.06402	0.0828261
$622$	−62.4561	−2.50426
$623$	−0.692574	−0.0277474
$624$	−2.99463	−0.119881
$625$	0	0
$626$	33.8050	1.35112
$627$	−12.9656	−0.517796
$628$	−22.2594	−0.888245
$629$	−32.6769	−1.30291
$630$	0	0
$631$	−28.8643	−1.14907	−0.574534	−	0.818480i	$-0.694817\pi$
$631$	−28.8643	−1.14907	−0.574534	+	0.818480i	$0.694817\pi$
$632$	32.9082	1.30902
$633$	21.1616	0.841097
$634$	−51.9735	−2.06413
$635$	0	0
$636$	37.9269	1.50390
$637$	49.2171	1.95005
$638$	−7.36601	−0.291623
$639$	3.43347	0.135826
$640$	0	0
$641$	44.0167	1.73856	0.869278	−	0.494324i	$-0.164585\pi$
$641$	44.0167	1.73856	0.869278	+	0.494324i	$0.164585\pi$
$642$	10.4489	0.412386
$643$	29.6239	1.16825	0.584125	−	0.811663i	$-0.301438\pi$
$643$	29.6239	1.16825	0.584125	+	0.811663i	$0.301438\pi$
$644$	1.03592	0.0408211
$645$	0	0
$646$	−69.0923	−2.71840
$647$	39.3943	1.54875	0.774375	−	0.632727i	$-0.218064\pi$
$647$	39.3943	1.54875	0.774375	+	0.632727i	$0.218064\pi$
$648$	−2.58223	−0.101439
$649$	22.9654	0.901473
$650$	0	0
$651$	1.63155	0.0639455
$652$	20.6776	0.809796
$653$	−22.3518	−0.874692	−0.437346	−	0.899293i	$-0.644082\pi$
$653$	−22.3518	−0.874692	−0.437346	+	0.899293i	$0.644082\pi$
$654$	−32.7595	−1.28100
$655$	0	0
$656$	2.17413	0.0848855
$657$	12.0772	0.471176
$658$	−2.03565	−0.0793577
$659$	42.1979	1.64380	0.821898	−	0.569634i	$-0.192915\pi$
$659$	42.1979	1.64380	0.821898	+	0.569634i	$0.192915\pi$
$660$	0	0
$661$	8.38035	0.325958	0.162979	−	0.986630i	$-0.447890\pi$
$661$	8.38035	0.325958	0.162979	+	0.986630i	$0.447890\pi$
$662$	7.32559	0.284717
$663$	−53.9003	−2.09332
$664$	−6.70843	−0.260337
$665$	0	0
$666$	−9.69836	−0.375804
$667$	2.06402	0.0799191
$668$	33.4746	1.29517
$669$	9.46925	0.366102
$670$	0	0
$671$	−37.1428	−1.43388
$672$	0.979541	0.0377866
$673$	3.13725	0.120932	0.0604660	−	0.998170i	$-0.480741\pi$
$673$	3.13725	0.120932	0.0604660	+	0.998170i	$0.480741\pi$
$674$	65.2941	2.51504
$675$	0	0
$676$	115.512	4.44279
$677$	−16.2776	−0.625600	−0.312800	−	0.949819i	$-0.601267\pi$
$677$	−16.2776	−0.625600	−0.312800	+	0.949819i	$0.601267\pi$
$678$	9.26310	0.355747
$679$	−0.620929	−0.0238291
$680$	0	0
$681$	22.4030	0.858486
$682$	75.1658	2.87825
$683$	1.78249	0.0682050	0.0341025	−	0.999418i	$-0.489143\pi$
$683$	1.78249	0.0682050	0.0341025	+	0.999418i	$0.489143\pi$
$684$	−12.5258	−0.478935
$685$	0	0
$686$	−5.06512	−0.193387
$687$	−2.03117	−0.0774939
$688$	−1.67275	−0.0637728
$689$	85.2614	3.24820
$690$	0	0
$691$	−20.8504	−0.793187	−0.396594	−	0.917994i	$-0.629808\pi$
$691$	−20.8504	−0.793187	−0.396594	+	0.917994i	$0.629808\pi$
$692$	43.5699	1.65628
$693$	0.519521	0.0197350
$694$	−37.2177	−1.41276
$695$	0	0
$696$	−2.58223	−0.0978791
$697$	39.1322	1.48224
$698$	41.2828	1.56258
$699$	11.0704	0.418722
$700$	0	0
$701$	32.5504	1.22941	0.614707	−	0.788756i	$-0.289274\pi$
$701$	32.5504	1.22941	0.614707	+	0.788756i	$0.289274\pi$
$702$	−15.9974	−0.603783
$703$	−17.0710	−0.643845
$704$	42.3698	1.59687
$705$	0	0
$706$	−42.7978	−1.61072
$707$	−2.46297	−0.0926295
$708$	22.1864	0.833815
$709$	5.93195	0.222779	0.111390	−	0.993777i	$-0.464470\pi$
$709$	5.93195	0.222779	0.111390	+	0.993777i	$0.464470\pi$
$710$	0	0
$711$	−12.7441	−0.477942
$712$	−11.1853	−0.419187
$713$	−21.0621	−0.788781
$714$	2.76847	0.103607
$715$	0	0
$716$	−34.8767	−1.30340
$717$	2.24098	0.0836911
$718$	−32.7574	−1.22250
$719$	−13.5279	−0.504505	−0.252252	−	0.967661i	$-0.581171\pi$
$719$	−13.5279	−0.504505	−0.252252	+	0.967661i	$0.581171\pi$
$720$	0	0
$721$	1.22871	0.0457594
$722$	6.97701	0.259657
$723$	−14.4838	−0.538660
$724$	34.3581	1.27691
$725$	0	0
$726$	−1.00208	−0.0371907
$727$	12.7407	0.472525	0.236263	−	0.971689i	$-0.424077\pi$
$727$	12.7407	0.472525	0.236263	+	0.971689i	$0.424077\pi$
$728$	−2.91350	−0.107981
$729$	1.00000	0.0370370
$730$	0	0
$731$	−30.1078	−1.11358
$732$	−35.8828	−1.32627
$733$	−30.9422	−1.14288	−0.571438	−	0.820645i	$-0.693614\pi$
$733$	−30.9422	−1.14288	−0.571438	+	0.820645i	$0.693614\pi$
$734$	−47.8716	−1.76697
$735$	0	0
$736$	−12.6451	−0.466105
$737$	−48.5809	−1.78950
$738$	11.6143	0.427528
$739$	35.0047	1.28767	0.643834	−	0.765166i	$-0.277343\pi$
$739$	35.0047	1.28767	0.643834	+	0.765166i	$0.277343\pi$
$740$	0	0
$741$	−28.1585	−1.03443
$742$	−4.37926	−0.160768
$743$	12.5515	0.460468	0.230234	−	0.973135i	$-0.426051\pi$
$743$	12.5515	0.460468	0.230234	+	0.973135i	$0.426051\pi$
$744$	26.3501	0.966041
$745$	0	0
$746$	−38.8068	−1.42082
$747$	2.59792	0.0950530
$748$	77.9069	2.84856
$749$	−0.736956	−0.0269278
$750$	0	0
$751$	−33.8278	−1.23439	−0.617197	−	0.786809i	$-0.711732\pi$
$751$	−33.8278	−1.23439	−0.617197	+	0.786809i	$0.711732\pi$
$752$	2.38332	0.0869108
$753$	16.2044	0.590522
$754$	−15.9974	−0.582591
$755$	0	0
$756$	0.501897	0.0182538
$757$	6.60568	0.240088	0.120044	−	0.992769i	$-0.461697\pi$
$757$	6.60568	0.240088	0.120044	+	0.992769i	$0.461697\pi$
$758$	0.468553	0.0170186
$759$	−6.70661	−0.243435
$760$	0	0
$761$	−22.8638	−0.828814	−0.414407	−	0.910092i	$-0.636011\pi$
$761$	−22.8638	−0.828814	−0.414407	+	0.910092i	$0.636011\pi$
$762$	8.37978	0.303568
$763$	2.31051	0.0836461
$764$	56.9656	2.06094
$765$	0	0
$766$	37.1103	1.34085
$767$	49.8760	1.80092
$768$	13.1557	0.474716
$769$	−35.0078	−1.26241	−0.631206	−	0.775615i	$-0.717440\pi$
$769$	−35.0078	−1.26241	−0.631206	+	0.775615i	$0.717440\pi$
$770$	0	0
$771$	−3.36942	−0.121347
$772$	54.4016	1.95796
$773$	−17.7019	−0.636691	−0.318346	−	0.947975i	$-0.603127\pi$
$773$	−17.7019	−0.636691	−0.318346	+	0.947975i	$0.603127\pi$
$774$	−8.93586	−0.321193
$775$	0	0
$776$	−10.0282	−0.359992
$777$	0.684020	0.0245391
$778$	−26.6655	−0.956005
$779$	20.4434	0.732460
$780$	0	0
$781$	−11.1564	−0.399206
$782$	−35.7388	−1.27802
$783$	1.00000	0.0357371
$784$	2.95968	0.105703
$785$	0	0
$786$	−22.5066	−0.802782
$787$	−5.13176	−0.182928	−0.0914638	−	0.995808i	$-0.529155\pi$
$787$	−5.13176	−0.182928	−0.0914638	+	0.995808i	$0.529155\pi$
$788$	32.7321	1.16603
$789$	1.79671	0.0639647
$790$	0	0
$791$	−0.653321	−0.0232294
$792$	8.39044	0.298141
$793$	−80.6662	−2.86454
$794$	−11.2471	−0.399145
$795$	0	0
$796$	36.2783	1.28585
$797$	−27.5492	−0.975842	−0.487921	−	0.872888i	$-0.662245\pi$
$797$	−27.5492	−0.975842	−0.487921	+	0.872888i	$0.662245\pi$
$798$	1.44630	0.0511984
$799$	42.8974	1.51760
$800$	0	0
$801$	4.33165	0.153051
$802$	−82.0562	−2.89751
$803$	−39.2424	−1.38484
$804$	−46.9329	−1.65520
$805$	0	0
$806$	163.244	5.75002
$807$	0.117055	0.00412054
$808$	−39.7778	−1.39938
$809$	−5.51555	−0.193917	−0.0969583	−	0.995288i	$-0.530911\pi$
$809$	−5.51555	−0.193917	−0.0969583	+	0.995288i	$0.530911\pi$
$810$	0	0
$811$	−17.1711	−0.602959	−0.301479	−	0.953473i	$-0.597480\pi$
$811$	−17.1711	−0.602959	−0.301479	+	0.953473i	$0.597480\pi$
$812$	0.501897	0.0176131
$813$	4.06294	0.142493
$814$	31.5129	1.10453
$815$	0	0
$816$	−3.24131	−0.113468
$817$	−15.7288	−0.550283
$818$	36.6355	1.28093
$819$	1.12829	0.0394256
$820$	0	0
$821$	6.53740	0.228157	0.114078	−	0.993472i	$-0.463609\pi$
$821$	6.53740	0.228157	0.114078	+	0.993472i	$0.463609\pi$
$822$	−8.67813	−0.302684
$823$	35.8588	1.24996	0.624979	−	0.780641i	$-0.285107\pi$
$823$	35.8588	1.24996	0.624979	+	0.780641i	$0.285107\pi$
$824$	19.8440	0.691299
$825$	0	0
$826$	−2.56177	−0.0891354
$827$	2.36177	0.0821269	0.0410635	−	0.999157i	$-0.486925\pi$
$827$	2.36177	0.0821269	0.0410635	+	0.999157i	$0.486925\pi$
$828$	−6.47910	−0.225164
$829$	54.0332	1.87665	0.938325	−	0.345754i	$-0.112377\pi$
$829$	54.0332	1.87665	0.938325	+	0.345754i	$0.112377\pi$
$830$	0	0
$831$	−12.5436	−0.435134
$832$	92.0182	3.19016
$833$	53.2713	1.84574
$834$	−4.69231	−0.162481
$835$	0	0
$836$	40.7000	1.40764
$837$	−10.2044	−0.352716
$838$	76.0663	2.62767
$839$	27.6639	0.955063	0.477532	−	0.878615i	$-0.341532\pi$
$839$	27.6639	0.955063	0.477532	+	0.878615i	$0.341532\pi$
$840$	0	0
$841$	1.00000	0.0344828
$842$	−61.1730	−2.10816
$843$	2.83163	0.0975266
$844$	−66.4278	−2.28654
$845$	0	0
$846$	12.7318	0.437728
$847$	0.0706761	0.00242846
$848$	5.12721	0.176069
$849$	28.2249	0.968676
$850$	0	0
$851$	−8.83017	−0.302694
$852$	−10.7779	−0.369245
$853$	−16.7180	−0.572413	−0.286207	−	0.958168i	$-0.592394\pi$
$853$	−16.7180	−0.572413	−0.286207	+	0.958168i	$0.592394\pi$
$854$	4.14324	0.141779
$855$	0	0
$856$	−11.9021	−0.406805
$857$	50.6304	1.72950	0.864750	−	0.502202i	$-0.167477\pi$
$857$	50.6304	1.72950	0.864750	+	0.502202i	$0.167477\pi$
$858$	51.9804	1.77458
$859$	−23.0473	−0.786363	−0.393182	−	0.919461i	$-0.628626\pi$
$859$	−23.0473	−0.786363	−0.393182	+	0.919461i	$0.628626\pi$
$860$	0	0
$861$	−0.819148	−0.0279165
$862$	−1.88693	−0.0642692
$863$	−45.4971	−1.54874	−0.774370	−	0.632733i	$-0.781933\pi$
$863$	−45.4971	−1.54874	−0.774370	+	0.632733i	$0.781933\pi$
$864$	−6.12646	−0.208426
$865$	0	0
$866$	−51.1531	−1.73825
$867$	−41.3403	−1.40399
$868$	−5.12156	−0.173837
$869$	41.4095	1.40472
$870$	0	0
$871$	−105.507	−3.57498
$872$	37.3155	1.26366
$873$	3.88355	0.131438
$874$	−18.6706	−0.631543
$875$	0	0
$876$	−37.9112	−1.28090
$877$	−6.44199	−0.217531	−0.108765	−	0.994067i	$-0.534690\pi$
$877$	−6.44199	−0.217531	−0.108765	+	0.994067i	$0.534690\pi$
$878$	−54.3124	−1.83295
$879$	21.9337	0.739806
$880$	0	0
$881$	−43.3346	−1.45998	−0.729990	−	0.683458i	$-0.760475\pi$
$881$	−43.3346	−1.45998	−0.729990	+	0.683458i	$0.760475\pi$
$882$	15.8107	0.532375
$883$	24.6736	0.830333	0.415166	−	0.909745i	$-0.363723\pi$
$883$	24.6736	0.830333	0.415166	+	0.909745i	$0.363723\pi$
$884$	169.197	5.69072
$885$	0	0
$886$	39.6546	1.33222
$887$	−37.1527	−1.24747	−0.623733	−	0.781637i	$-0.714385\pi$
$887$	−37.1527	−1.24747	−0.623733	+	0.781637i	$0.714385\pi$
$888$	11.0472	0.370718
$889$	−0.591021	−0.0198222
$890$	0	0
$891$	−3.24930	−0.108856
$892$	−29.7247	−0.995255
$893$	22.4104	0.749936
$894$	−3.32357	−0.111157
$895$	0	0
$896$	−2.76723	−0.0924466
$897$	−14.5653	−0.486322
$898$	−9.57108	−0.319391
$899$	−10.2044	−0.340336
$900$	0	0
$901$	92.2847	3.07445
$902$	−37.7383	−1.25655
$903$	0.630241	0.0209731
$904$	−10.5514	−0.350933
$905$	0	0
$906$	−45.6291	−1.51593
$907$	−7.49457	−0.248853	−0.124427	−	0.992229i	$-0.539709\pi$
$907$	−7.49457	−0.248853	−0.124427	+	0.992229i	$0.539709\pi$
$908$	−70.3248	−2.33381
$909$	15.4045	0.510934
$910$	0	0
$911$	48.6818	1.61290	0.806449	−	0.591303i	$-0.201386\pi$
$911$	48.6818	1.61290	0.806449	+	0.591303i	$0.201386\pi$
$912$	−1.69332	−0.0560714
$913$	−8.44143	−0.279371
$914$	−2.91444	−0.0964012
$915$	0	0
$916$	6.37598	0.210668
$917$	1.58737	0.0524197
$918$	−17.3152	−0.571486
$919$	−26.1563	−0.862816	−0.431408	−	0.902157i	$-0.641983\pi$
$919$	−26.1563	−0.862816	−0.431408	+	0.902157i	$0.641983\pi$
$920$	0	0
$921$	−0.461574	−0.0152094
$922$	54.0746	1.78085
$923$	−24.2293	−0.797515
$924$	−1.63081	−0.0536498
$925$	0	0
$926$	32.0552	1.05340
$927$	−7.68484	−0.252403
$928$	−6.12646	−0.201111
$929$	−8.15366	−0.267513	−0.133756	−	0.991014i	$-0.542704\pi$
$929$	−8.15366	−0.267513	−0.133756	+	0.991014i	$0.542704\pi$
$930$	0	0
$931$	27.8299	0.912089
$932$	−34.7509	−1.13830
$933$	−27.5507	−0.901968
$934$	16.0157	0.524051
$935$	0	0
$936$	18.2222	0.595612
$937$	−41.9169	−1.36936	−0.684682	−	0.728842i	$-0.740059\pi$
$937$	−41.9169	−1.36936	−0.684682	+	0.728842i	$0.740059\pi$
$938$	5.41915	0.176941
$939$	14.9121	0.486638
$940$	0	0
$941$	14.4789	0.471998	0.235999	−	0.971753i	$-0.424164\pi$
$941$	14.4789	0.471998	0.235999	+	0.971753i	$0.424164\pi$
$942$	−16.0751	−0.523755
$943$	10.5746	0.344356
$944$	2.99931	0.0976191
$945$	0	0
$946$	29.0353	0.944020
$947$	−1.83838	−0.0597392	−0.0298696	−	0.999554i	$-0.509509\pi$
$947$	−1.83838	−0.0597392	−0.0298696	+	0.999554i	$0.509509\pi$
$948$	40.0048	1.29929
$949$	−85.2262	−2.76656
$950$	0	0
$951$	−22.9266	−0.743446
$952$	−3.15349	−0.102205
$953$	49.5140	1.60391	0.801957	−	0.597382i	$-0.203792\pi$
$953$	49.5140	1.60391	0.801957	+	0.597382i	$0.203792\pi$
$954$	27.3897	0.886776
$955$	0	0
$956$	−7.03461	−0.227516
$957$	−3.24930	−0.105035
$958$	−52.0403	−1.68135
$959$	0.612063	0.0197646
$960$	0	0
$961$	73.1299	2.35903
$962$	68.4393	2.20657
$963$	4.60924	0.148531
$964$	45.4658	1.46436
$965$	0	0
$966$	0.748115	0.0240702
$967$	−5.90299	−0.189827	−0.0949137	−	0.995486i	$-0.530258\pi$
$967$	−5.90299	−0.189827	−0.0949137	+	0.995486i	$0.530258\pi$
$968$	1.14144	0.0366874
$969$	−30.4781	−0.979096
$970$	0	0
$971$	−35.7964	−1.14876	−0.574380	−	0.818588i	$-0.694757\pi$
$971$	−35.7964	−1.14876	−0.574380	+	0.818588i	$0.694757\pi$
$972$	−3.13907	−0.100686
$973$	0.330946	0.0106096
$974$	−61.2801	−1.96354
$975$	0	0
$976$	−4.85088	−0.155273
$977$	1.79673	0.0574825	0.0287412	−	0.999587i	$-0.490850\pi$
$977$	1.79673	0.0574825	0.0287412	+	0.999587i	$0.490850\pi$
$978$	14.9328	0.477497
$979$	−14.0748	−0.449834
$980$	0	0
$981$	−14.4509	−0.461382
$982$	26.1828	0.835528
$983$	−6.24151	−0.199073	−0.0995365	−	0.995034i	$-0.531736\pi$
$983$	−6.24151	−0.199073	−0.0995365	+	0.995034i	$0.531736\pi$
$984$	−13.2295	−0.421742
$985$	0	0
$986$	−17.3152	−0.551427
$987$	−0.897966	−0.0285826
$988$	88.3917	2.81211
$989$	−8.13593	−0.258708
$990$	0	0
$991$	41.0410	1.30371	0.651855	−	0.758344i	$-0.273991\pi$
$991$	41.0410	1.30371	0.651855	+	0.758344i	$0.273991\pi$
$992$	62.5169	1.98491
$993$	3.23147	0.102548
$994$	1.24448	0.0394725
$995$	0	0
$996$	−8.15507	−0.258403
$997$	−29.8910	−0.946657	−0.473329	−	0.880886i	$-0.656948\pi$
$997$	−29.8910	−0.946657	−0.473329	+	0.880886i	$0.656948\pi$
$998$	−8.56776	−0.271208
$999$	−4.27815	−0.135355

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2175.2.a.ba.1.2	✓	7
3.2	odd	2		6525.2.a.bx.1.6		7
5.2	odd	4		2175.2.c.o.349.3		14
5.3	odd	4		2175.2.c.o.349.12		14
5.4	even	2		2175.2.a.bb.1.6	yes	7
15.14	odd	2		6525.2.a.bu.1.2		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2175.2.a.ba.1.2	✓	7	1.1	even	1	trivial
2175.2.a.bb.1.6	yes	7	5.4	even	2
2175.2.c.o.349.3		14	5.2	odd	4
2175.2.c.o.349.12		14	5.3	odd	4
6525.2.a.bu.1.2		7	15.14	odd	2
6525.2.a.bx.1.6		7	3.2	odd	2

Overview	Random
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Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2175 = 3 \cdot 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2175.a (trivial)

\(f(q)\)	\(=\)	\(q-2.26695 q^{2} -1.00000 q^{3} +3.13907 q^{4} +2.26695 q^{6} -0.159887 q^{7} -2.58223 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.26695 q^{2} -1.00000 q^{3} +3.13907 q^{4} +2.26695 q^{6} -0.159887 q^{7} -2.58223 q^{8} +1.00000 q^{9} -3.24930 q^{11} -3.13907 q^{12} -7.05679 q^{13} +0.362456 q^{14} -0.424361 q^{16} -7.63808 q^{17} -2.26695 q^{18} -3.99028 q^{19} +0.159887 q^{21} +7.36601 q^{22} -2.06402 q^{23} +2.58223 q^{24} +15.9974 q^{26} -1.00000 q^{27} -0.501897 q^{28} -1.00000 q^{29} +10.2044 q^{31} +6.12646 q^{32} +3.24930 q^{33} +17.3152 q^{34} +3.13907 q^{36} +4.27815 q^{37} +9.04576 q^{38} +7.05679 q^{39} -5.12330 q^{41} -0.362456 q^{42} +3.94180 q^{43} -10.1998 q^{44} +4.67903 q^{46} -5.61626 q^{47} +0.424361 q^{48} -6.97444 q^{49} +7.63808 q^{51} -22.1518 q^{52} -12.0822 q^{53} +2.26695 q^{54} +0.412864 q^{56} +3.99028 q^{57} +2.26695 q^{58} -7.06781 q^{59} +11.4310 q^{61} -23.1329 q^{62} -0.159887 q^{63} -13.0397 q^{64} -7.36601 q^{66} +14.9512 q^{67} -23.9765 q^{68} +2.06402 q^{69} +3.43347 q^{71} -2.58223 q^{72} +12.0772 q^{73} -9.69836 q^{74} -12.5258 q^{76} +0.519521 q^{77} -15.9974 q^{78} -12.7441 q^{79} +1.00000 q^{81} +11.6143 q^{82} +2.59792 q^{83} +0.501897 q^{84} -8.93586 q^{86} +1.00000 q^{87} +8.39044 q^{88} +4.33165 q^{89} +1.12829 q^{91} -6.47910 q^{92} -10.2044 q^{93} +12.7318 q^{94} -6.12646 q^{96} +3.88355 q^{97} +15.8107 q^{98} -3.24930 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 2 q^{2} - 7 q^{3} + 10 q^{4} + 2 q^{6} + q^{7} - 3 q^{8} + 7 q^{9}+O(q^{10}) \) 7 * q - 2 * q^2 - 7 * q^3 + 10 * q^4 + 2 * q^6 + q^7 - 3 * q^8 + 7 * q^9	\( 7 q - 2 q^{2} - 7 q^{3} + 10 q^{4} + 2 q^{6} + q^{7} - 3 q^{8} + 7 q^{9} + 4 q^{11} - 10 q^{12} + q^{13} + 15 q^{14} + 12 q^{16} - 8 q^{17} - 2 q^{18} + 15 q^{19} - q^{21} - 3 q^{22} - 14 q^{23} + 3 q^{24} + 6 q^{26} - 7 q^{27} + 24 q^{28} - 7 q^{29} + 5 q^{31} - 18 q^{32} - 4 q^{33} + 7 q^{34} + 10 q^{36} + 6 q^{37} + 18 q^{38} - q^{39} + 22 q^{41} - 15 q^{42} + 19 q^{43} + 15 q^{44} - 4 q^{46} - 22 q^{47} - 12 q^{48} + 12 q^{49} + 8 q^{51} - 11 q^{52} - 10 q^{53} + 2 q^{54} + 14 q^{56} - 15 q^{57} + 2 q^{58} + 6 q^{59} + 23 q^{61} - 40 q^{62} + q^{63} + 5 q^{64} + 3 q^{66} + 13 q^{67} + 7 q^{68} + 14 q^{69} + 26 q^{71} - 3 q^{72} + 24 q^{73} - 10 q^{74} + 46 q^{76} - 4 q^{77} - 6 q^{78} + 14 q^{79} + 7 q^{81} - 16 q^{82} - 10 q^{83} - 24 q^{84} + 44 q^{86} + 7 q^{87} + 66 q^{88} + 14 q^{89} + 13 q^{91} - 58 q^{92} - 5 q^{93} - 3 q^{94} + 18 q^{96} + 31 q^{97} + 59 q^{98} + 4 q^{99}+O(q^{100}) \) 7 * q - 2 * q^2 - 7 * q^3 + 10 * q^4 + 2 * q^6 + q^7 - 3 * q^8 + 7 * q^9 + 4 * q^11 - 10 * q^12 + q^13 + 15 * q^14 + 12 * q^16 - 8 * q^17 - 2 * q^18 + 15 * q^19 - q^21 - 3 * q^22 - 14 * q^23 + 3 * q^24 + 6 * q^26 - 7 * q^27 + 24 * q^28 - 7 * q^29 + 5 * q^31 - 18 * q^32 - 4 * q^33 + 7 * q^34 + 10 * q^36 + 6 * q^37 + 18 * q^38 - q^39 + 22 * q^41 - 15 * q^42 + 19 * q^43 + 15 * q^44 - 4 * q^46 - 22 * q^47 - 12 * q^48 + 12 * q^49 + 8 * q^51 - 11 * q^52 - 10 * q^53 + 2 * q^54 + 14 * q^56 - 15 * q^57 + 2 * q^58 + 6 * q^59 + 23 * q^61 - 40 * q^62 + q^63 + 5 * q^64 + 3 * q^66 + 13 * q^67 + 7 * q^68 + 14 * q^69 + 26 * q^71 - 3 * q^72 + 24 * q^73 - 10 * q^74 + 46 * q^76 - 4 * q^77 - 6 * q^78 + 14 * q^79 + 7 * q^81 - 16 * q^82 - 10 * q^83 - 24 * q^84 + 44 * q^86 + 7 * q^87 + 66 * q^88 + 14 * q^89 + 13 * q^91 - 58 * q^92 - 5 * q^93 - 3 * q^94 + 18 * q^96 + 31 * q^97 + 59 * q^98 + 4 * q^99

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