LMFDB - Embedded newform 4025.2.a.bd.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4025,2,Mod(1,4025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4025, 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("4025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4025 = 5^{2} \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4025.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:	$32.1397868136$
Analytic rank:	$0$
Dimension:	$21$
Twist minimal:	no (minimal twist has level 805)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	4025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.30923 q^{2} -2.43985 q^{3} -0.285909 q^{4} +3.19433 q^{6} -1.00000 q^{7} +2.99279 q^{8} +2.95286 q^{9} +O(q^{10})$	\(q-1.30923 q^{2} -2.43985 q^{3} -0.285909 q^{4} +3.19433 q^{6} -1.00000 q^{7} +2.99279 q^{8} +2.95286 q^{9} +0.628746 q^{11} +0.697574 q^{12} +3.82086 q^{13} +1.30923 q^{14} -3.34644 q^{16} -5.22375 q^{17} -3.86598 q^{18} +6.31328 q^{19} +2.43985 q^{21} -0.823175 q^{22} -1.00000 q^{23} -7.30194 q^{24} -5.00239 q^{26} +0.115025 q^{27} +0.285909 q^{28} +3.73904 q^{29} +9.35403 q^{31} -1.60431 q^{32} -1.53404 q^{33} +6.83911 q^{34} -0.844247 q^{36} +7.74846 q^{37} -8.26556 q^{38} -9.32231 q^{39} +11.8024 q^{41} -3.19433 q^{42} +4.67712 q^{43} -0.179764 q^{44} +1.30923 q^{46} -11.3296 q^{47} +8.16480 q^{48} +1.00000 q^{49} +12.7452 q^{51} -1.09242 q^{52} -8.98590 q^{53} -0.150594 q^{54} -2.99279 q^{56} -15.4034 q^{57} -4.89527 q^{58} -4.34377 q^{59} -4.46944 q^{61} -12.2466 q^{62} -2.95286 q^{63} +8.79329 q^{64} +2.00842 q^{66} +6.33927 q^{67} +1.49352 q^{68} +2.43985 q^{69} +13.0698 q^{71} +8.83727 q^{72} +7.44507 q^{73} -10.1445 q^{74} -1.80502 q^{76} -0.628746 q^{77} +12.2051 q^{78} -12.1355 q^{79} -9.13921 q^{81} -15.4521 q^{82} +0.664922 q^{83} -0.697574 q^{84} -6.12344 q^{86} -9.12268 q^{87} +1.88170 q^{88} -9.82152 q^{89} -3.82086 q^{91} +0.285909 q^{92} -22.8224 q^{93} +14.8330 q^{94} +3.91426 q^{96} -12.8353 q^{97} -1.30923 q^{98} +1.85660 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q - 2 q^{2} + q^{3} + 30 q^{4} + 6 q^{6} - 21 q^{7} - 6 q^{8} + 30 q^{9}+O(q^{10}) $ 21 * q - 2 * q^2 + q^3 + 30 * q^4 + 6 * q^6 - 21 * q^7 - 6 * q^8 + 30 * q^9	$ 21 q - 2 q^{2} + q^{3} + 30 q^{4} + 6 q^{6} - 21 q^{7} - 6 q^{8} + 30 q^{9} + 7 q^{11} + 22 q^{12} + 3 q^{13} + 2 q^{14} + 56 q^{16} - 7 q^{17} + 24 q^{19} - q^{21} - 4 q^{22} - 21 q^{23} + 24 q^{24} - 2 q^{26} + 19 q^{27} - 30 q^{28} + 11 q^{29} + 46 q^{31} + 6 q^{32} + 3 q^{33} + 28 q^{34} + 58 q^{36} - 24 q^{37} + 4 q^{38} + 31 q^{39} + 14 q^{41} - 6 q^{42} - 18 q^{43} + 12 q^{44} + 2 q^{46} + 25 q^{47} + 36 q^{48} + 21 q^{49} + 17 q^{51} + 8 q^{52} - 22 q^{53} - 6 q^{54} + 6 q^{56} - 40 q^{57} - 6 q^{58} + 10 q^{59} + 38 q^{61} + 54 q^{62} - 30 q^{63} + 100 q^{64} + 38 q^{66} - 12 q^{67} - 18 q^{68} - q^{69} + 56 q^{71} - 42 q^{72} + 40 q^{73} - 20 q^{74} + 60 q^{76} - 7 q^{77} - 38 q^{78} + 49 q^{79} + 57 q^{81} - 16 q^{82} + 2 q^{83} - 22 q^{84} + 16 q^{86} + 23 q^{87} - 12 q^{88} + 28 q^{89} - 3 q^{91} - 30 q^{92} + 30 q^{93} + 66 q^{94} + 46 q^{96} + q^{97} - 2 q^{98} - 2 q^{99}+O(q^{100}) $ 21 * q - 2 * q^2 + q^3 + 30 * q^4 + 6 * q^6 - 21 * q^7 - 6 * q^8 + 30 * q^9 + 7 * q^11 + 22 * q^12 + 3 * q^13 + 2 * q^14 + 56 * q^16 - 7 * q^17 + 24 * q^19 - q^21 - 4 * q^22 - 21 * q^23 + 24 * q^24 - 2 * q^26 + 19 * q^27 - 30 * q^28 + 11 * q^29 + 46 * q^31 + 6 * q^32 + 3 * q^33 + 28 * q^34 + 58 * q^36 - 24 * q^37 + 4 * q^38 + 31 * q^39 + 14 * q^41 - 6 * q^42 - 18 * q^43 + 12 * q^44 + 2 * q^46 + 25 * q^47 + 36 * q^48 + 21 * q^49 + 17 * q^51 + 8 * q^52 - 22 * q^53 - 6 * q^54 + 6 * q^56 - 40 * q^57 - 6 * q^58 + 10 * q^59 + 38 * q^61 + 54 * q^62 - 30 * q^63 + 100 * q^64 + 38 * q^66 - 12 * q^67 - 18 * q^68 - q^69 + 56 * q^71 - 42 * q^72 + 40 * q^73 - 20 * q^74 + 60 * q^76 - 7 * q^77 - 38 * q^78 + 49 * q^79 + 57 * q^81 - 16 * q^82 + 2 * q^83 - 22 * q^84 + 16 * q^86 + 23 * q^87 - 12 * q^88 + 28 * q^89 - 3 * q^91 - 30 * q^92 + 30 * q^93 + 66 * q^94 + 46 * q^96 + q^97 - 2 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.30923	−0.925768	−0.462884	−	0.886419i	$-0.653185\pi$
$2$	−1.30923	−0.925768	−0.462884	+	0.886419i	$0.653185\pi$
$3$	−2.43985	−1.40865	−0.704323	−	0.709879i	$-0.748749\pi$
$3$	−2.43985	−1.40865	−0.704323	+	0.709879i	$0.748749\pi$
$4$	−0.285909	−0.142954
$5$	0	0
$5$	0	0
$6$	3.19433	1.30408
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	2.99279	1.05811
$9$	2.95286	0.984285
$10$	0	0
$11$	0.628746	0.189574	0.0947870	−	0.995498i	$-0.469783\pi$
$11$	0.628746	0.189574	0.0947870	+	0.995498i	$0.469783\pi$
$12$	0.697574	0.201372
$13$	3.82086	1.05972	0.529858	−	0.848087i	$-0.322245\pi$
$13$	3.82086	1.05972	0.529858	+	0.848087i	$0.322245\pi$
$14$	1.30923	0.349907
$15$	0	0
$16$	−3.34644	−0.836610
$17$	−5.22375	−1.26695	−0.633473	−	0.773765i	$-0.718371\pi$
$17$	−5.22375	−1.26695	−0.633473	+	0.773765i	$0.718371\pi$
$18$	−3.86598	−0.911219
$19$	6.31328	1.44837	0.724183	−	0.689608i	$-0.242217\pi$
$19$	6.31328	1.44837	0.724183	+	0.689608i	$0.242217\pi$
$20$	0	0
$21$	2.43985	0.532418
$22$	−0.823175	−0.175502
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−7.30194	−1.49050
$25$	0	0
$26$	−5.00239	−0.981050
$27$	0.115025	0.0221366
$28$	0.285909	0.0540317
$29$	3.73904	0.694322	0.347161	−	0.937806i	$-0.387146\pi$
$29$	3.73904	0.694322	0.347161	+	0.937806i	$0.387146\pi$
$30$	0	0
$31$	9.35403	1.68003	0.840017	−	0.542560i	$-0.182545\pi$
$31$	9.35403	1.68003	0.840017	+	0.542560i	$0.182545\pi$
$32$	−1.60431	−0.283604
$33$	−1.53404	−0.267043
$34$	6.83911	1.17290
$35$	0	0
$36$	−0.844247	−0.140708
$37$	7.74846	1.27384	0.636919	−	0.770930i	$-0.280208\pi$
$37$	7.74846	1.27384	0.636919	+	0.770930i	$0.280208\pi$
$38$	−8.26556	−1.34085
$39$	−9.32231	−1.49276
$40$	0	0
$41$	11.8024	1.84323	0.921613	−	0.388111i	$-0.126872\pi$
$41$	11.8024	1.84323	0.921613	+	0.388111i	$0.126872\pi$
$42$	−3.19433	−0.492896
$43$	4.67712	0.713254	0.356627	−	0.934247i	$-0.383927\pi$
$43$	4.67712	0.713254	0.356627	+	0.934247i	$0.383927\pi$
$44$	−0.179764	−0.0271005
$45$	0	0
$46$	1.30923	0.193036
$47$	−11.3296	−1.65259	−0.826294	−	0.563240i	$-0.809555\pi$
$47$	−11.3296	−1.65259	−0.826294	+	0.563240i	$0.809555\pi$
$48$	8.16480	1.17849
$49$	1.00000	0.142857
$50$	0	0
$51$	12.7452	1.78468
$52$	−1.09242	−0.151491
$53$	−8.98590	−1.23431	−0.617154	−	0.786842i	$-0.711715\pi$
$53$	−8.98590	−1.23431	−0.617154	+	0.786842i	$0.711715\pi$
$54$	−0.150594	−0.0204933
$55$	0	0
$56$	−2.99279	−0.399928
$57$	−15.4034	−2.04024
$58$	−4.89527	−0.642781
$59$	−4.34377	−0.565511	−0.282755	−	0.959192i	$-0.591248\pi$
$59$	−4.34377	−0.565511	−0.282755	+	0.959192i	$0.591248\pi$
$60$	0	0
$61$	−4.46944	−0.572253	−0.286126	−	0.958192i	$-0.592368\pi$
$61$	−4.46944	−0.572253	−0.286126	+	0.958192i	$0.592368\pi$
$62$	−12.2466	−1.55532
$63$	−2.95286	−0.372025
$64$	8.79329	1.09916
$65$	0	0
$66$	2.00842	0.247220
$67$	6.33927	0.774465	0.387232	−	0.921982i	$-0.373431\pi$
$67$	6.33927	0.774465	0.387232	+	0.921982i	$0.373431\pi$
$68$	1.49352	0.181115
$69$	2.43985	0.293723
$70$	0	0
$71$	13.0698	1.55110	0.775552	−	0.631283i	$-0.217471\pi$
$71$	13.0698	1.55110	0.775552	+	0.631283i	$0.217471\pi$
$72$	8.83727	1.04148
$73$	7.44507	0.871379	0.435690	−	0.900097i	$-0.356505\pi$
$73$	7.44507	0.871379	0.435690	+	0.900097i	$0.356505\pi$
$74$	−10.1445	−1.17928
$75$	0	0
$76$	−1.80502	−0.207050
$77$	−0.628746	−0.0716523
$78$	12.2051	1.38195
$79$	−12.1355	−1.36535	−0.682674	−	0.730723i	$-0.739183\pi$
$79$	−12.1355	−1.36535	−0.682674	+	0.730723i	$0.739183\pi$
$80$	0	0
$81$	−9.13921	−1.01547
$82$	−15.4521	−1.70640
$83$	0.664922	0.0729846	0.0364923	−	0.999334i	$-0.488382\pi$
$83$	0.664922	0.0729846	0.0364923	+	0.999334i	$0.488382\pi$
$84$	−0.697574	−0.0761116
$85$	0	0
$86$	−6.12344	−0.660308
$87$	−9.12268	−0.978054
$88$	1.88170	0.200590
$89$	−9.82152	−1.04108	−0.520540	−	0.853837i	$-0.674269\pi$
$89$	−9.82152	−1.04108	−0.520540	+	0.853837i	$0.674269\pi$
$90$	0	0
$91$	−3.82086	−0.400535
$92$	0.285909	0.0298081
$93$	−22.8224	−2.36657
$94$	14.8330	1.52991
$95$	0	0
$96$	3.91426	0.399498
$97$	−12.8353	−1.30323	−0.651615	−	0.758550i	$-0.725908\pi$
$97$	−12.8353	−1.30323	−0.651615	+	0.758550i	$0.725908\pi$
$98$	−1.30923	−0.132253
$99$	1.85660	0.186595
$100$	0	0
$101$	−5.36565	−0.533902	−0.266951	−	0.963710i	$-0.586016\pi$
$101$	−5.36565	−0.533902	−0.266951	+	0.963710i	$0.586016\pi$
$102$	−16.6864	−1.65220
$103$	−15.8547	−1.56221	−0.781103	−	0.624402i	$-0.785343\pi$
$103$	−15.8547	−1.56221	−0.781103	+	0.624402i	$0.785343\pi$
$104$	11.4350	1.12130
$105$	0	0
$106$	11.7646	1.14268
$107$	7.81800	0.755794	0.377897	−	0.925848i	$-0.376647\pi$
$107$	7.81800	0.755794	0.377897	+	0.925848i	$0.376647\pi$
$108$	−0.0328866	−0.00316452
$109$	2.47893	0.237439	0.118719	−	0.992928i	$-0.462121\pi$
$109$	2.47893	0.237439	0.118719	+	0.992928i	$0.462121\pi$
$110$	0	0
$111$	−18.9051	−1.79439
$112$	3.34644	0.316209
$113$	−13.6363	−1.28280	−0.641400	−	0.767207i	$-0.721646\pi$
$113$	−13.6363	−1.28280	−0.641400	+	0.767207i	$0.721646\pi$
$114$	20.1667	1.88878
$115$	0	0
$116$	−1.06902	−0.0992564
$117$	11.2824	1.04306
$118$	5.68701	0.523532
$119$	5.22375	0.478861
$120$	0	0
$121$	−10.6047	−0.964062
$122$	5.85153	0.529773
$123$	−28.7961	−2.59645
$124$	−2.67440	−0.240168
$125$	0	0
$126$	3.86598	0.344409
$127$	6.56057	0.582156	0.291078	−	0.956699i	$-0.405986\pi$
$127$	6.56057	0.582156	0.291078	+	0.956699i	$0.405986\pi$
$128$	−8.30385	−0.733964
$129$	−11.4115	−1.00472
$130$	0	0
$131$	12.3861	1.08218	0.541091	−	0.840964i	$-0.318012\pi$
$131$	12.3861	1.08218	0.541091	+	0.840964i	$0.318012\pi$
$132$	0.438597	0.0381750
$133$	−6.31328	−0.547431
$134$	−8.29958	−0.716974
$135$	0	0
$136$	−15.6336	−1.34057
$137$	13.0473	1.11471	0.557354	−	0.830275i	$-0.311817\pi$
$137$	13.0473	1.11471	0.557354	+	0.830275i	$0.311817\pi$
$138$	−3.19433	−0.271919
$139$	0.384406	0.0326049	0.0163024	−	0.999867i	$-0.494811\pi$
$139$	0.384406	0.0326049	0.0163024	+	0.999867i	$0.494811\pi$
$140$	0	0
$141$	27.6424	2.32791
$142$	−17.1115	−1.43596
$143$	2.40235	0.200895
$144$	−9.88155	−0.823463
$145$	0	0
$146$	−9.74733	−0.806694
$147$	−2.43985	−0.201235
$148$	−2.21535	−0.182101
$149$	5.58914	0.457880	0.228940	−	0.973441i	$-0.426474\pi$
$149$	5.58914	0.457880	0.228940	+	0.973441i	$0.426474\pi$
$150$	0	0
$151$	−14.3563	−1.16830	−0.584149	−	0.811646i	$-0.698572\pi$
$151$	−14.3563	−1.16830	−0.584149	+	0.811646i	$0.698572\pi$
$152$	18.8943	1.53253
$153$	−15.4250	−1.24704
$154$	0.823175	0.0663333
$155$	0	0
$156$	2.66533	0.213397
$157$	6.23649	0.497726	0.248863	−	0.968539i	$-0.419943\pi$
$157$	6.23649	0.497726	0.248863	+	0.968539i	$0.419943\pi$
$158$	15.8882	1.26400
$159$	21.9242	1.73870
$160$	0	0
$161$	1.00000	0.0788110
$162$	11.9654	0.940087
$163$	21.3159	1.66959	0.834797	−	0.550558i	$-0.185585\pi$
$163$	21.3159	1.66959	0.834797	+	0.550558i	$0.185585\pi$
$164$	−3.37441	−0.263497
$165$	0	0
$166$	−0.870537	−0.0675668
$167$	18.4194	1.42533	0.712667	−	0.701502i	$-0.247487\pi$
$167$	18.4194	1.42533	0.712667	+	0.701502i	$0.247487\pi$
$168$	7.30194	0.563357
$169$	1.59896	0.122997
$170$	0	0
$171$	18.6422	1.42561
$172$	−1.33723	−0.101963
$173$	16.3836	1.24562	0.622811	−	0.782372i	$-0.285990\pi$
$173$	16.3836	1.24562	0.622811	+	0.782372i	$0.285990\pi$
$174$	11.9437	0.905451
$175$	0	0
$176$	−2.10406	−0.158600
$177$	10.5981	0.796605
$178$	12.8587	0.963798
$179$	−18.4771	−1.38104	−0.690521	−	0.723312i	$-0.742619\pi$
$179$	−18.4771	−1.38104	−0.690521	+	0.723312i	$0.742619\pi$
$180$	0	0
$181$	−2.16812	−0.161155	−0.0805774	−	0.996748i	$-0.525676\pi$
$181$	−2.16812	−0.161155	−0.0805774	+	0.996748i	$0.525676\pi$
$182$	5.00239	0.370802
$183$	10.9047	0.806102
$184$	−2.99279	−0.220631
$185$	0	0
$186$	29.8799	2.19090
$187$	−3.28441	−0.240180
$188$	3.23922	0.236245
$189$	−0.115025	−0.00836683
$190$	0	0
$191$	8.57543	0.620497	0.310248	−	0.950656i	$-0.399588\pi$
$191$	8.57543	0.620497	0.310248	+	0.950656i	$0.399588\pi$
$192$	−21.4543	−1.54833
$193$	−1.06484	−0.0766492	−0.0383246	−	0.999265i	$-0.512202\pi$
$193$	−1.06484	−0.0766492	−0.0383246	+	0.999265i	$0.512202\pi$
$194$	16.8044	1.20649
$195$	0	0
$196$	−0.285909	−0.0204221
$197$	−14.6832	−1.04614	−0.523068	−	0.852291i	$-0.675213\pi$
$197$	−14.6832	−1.04614	−0.523068	+	0.852291i	$0.675213\pi$
$198$	−2.43072	−0.172744
$199$	17.3921	1.23290	0.616448	−	0.787396i	$-0.288571\pi$
$199$	17.3921	1.23290	0.616448	+	0.787396i	$0.288571\pi$
$200$	0	0
$201$	−15.4668	−1.09095
$202$	7.02488	0.494269
$203$	−3.73904	−0.262429
$204$	−3.64395	−0.255128
$205$	0	0
$206$	20.7575	1.44624
$207$	−2.95286	−0.205238
$208$	−12.7863	−0.886568
$209$	3.96945	0.274573
$210$	0	0
$211$	5.89447	0.405792	0.202896	−	0.979200i	$-0.434965\pi$
$211$	5.89447	0.405792	0.202896	+	0.979200i	$0.434965\pi$
$212$	2.56915	0.176450
$213$	−31.8884	−2.18496
$214$	−10.2356	−0.699690
$215$	0	0
$216$	0.344245	0.0234229
$217$	−9.35403	−0.634993
$218$	−3.24550	−0.219813
$219$	−18.1648	−1.22747
$220$	0	0
$221$	−19.9592	−1.34260
$222$	24.7511	1.66119
$223$	−7.80931	−0.522950	−0.261475	−	0.965210i	$-0.584209\pi$
$223$	−7.80931	−0.522950	−0.261475	+	0.965210i	$0.584209\pi$
$224$	1.60431	0.107192
$225$	0	0
$226$	17.8532	1.18757
$227$	6.80942	0.451957	0.225978	−	0.974132i	$-0.427442\pi$
$227$	6.80942	0.451957	0.225978	+	0.974132i	$0.427442\pi$
$228$	4.40398	0.291661
$229$	1.86905	0.123510	0.0617552	−	0.998091i	$-0.480330\pi$
$229$	1.86905	0.123510	0.0617552	+	0.998091i	$0.480330\pi$
$230$	0	0
$231$	1.53404	0.100933
$232$	11.1901	0.734669
$233$	1.99273	0.130548	0.0652741	−	0.997867i	$-0.479208\pi$
$233$	1.99273	0.130548	0.0652741	+	0.997867i	$0.479208\pi$
$234$	−14.7713	−0.965633
$235$	0	0
$236$	1.24192	0.0808423
$237$	29.6087	1.92329
$238$	−6.83911	−0.443314
$239$	−18.0473	−1.16738	−0.583692	−	0.811975i	$-0.698392\pi$
$239$	−18.0473	−1.16738	−0.583692	+	0.811975i	$0.698392\pi$
$240$	0	0
$241$	8.91521	0.574279	0.287140	−	0.957889i	$-0.407296\pi$
$241$	8.91521	0.574279	0.287140	+	0.957889i	$0.407296\pi$
$242$	13.8840	0.892497
$243$	21.9532	1.40830
$244$	1.27785	0.0818061
$245$	0	0
$246$	37.7007	2.40371
$247$	24.1222	1.53486
$248$	27.9946	1.77766
$249$	−1.62231	−0.102810
$250$	0	0
$251$	−13.5485	−0.855172	−0.427586	−	0.903975i	$-0.640636\pi$
$251$	−13.5485	−0.855172	−0.427586	+	0.903975i	$0.640636\pi$
$252$	0.844247	0.0531826
$253$	−0.628746	−0.0395289
$254$	−8.58931	−0.538941
$255$	0	0
$256$	−6.71490	−0.419681
$257$	−11.0047	−0.686457	−0.343229	−	0.939252i	$-0.611521\pi$
$257$	−11.0047	−0.686457	−0.343229	+	0.939252i	$0.611521\pi$
$258$	14.9403	0.930140
$259$	−7.74846	−0.481466
$260$	0	0
$261$	11.0408	0.683411
$262$	−16.2163	−1.00185
$263$	−5.83413	−0.359748	−0.179874	−	0.983690i	$-0.557569\pi$
$263$	−5.83413	−0.359748	−0.179874	+	0.983690i	$0.557569\pi$
$264$	−4.59107	−0.282561
$265$	0	0
$266$	8.26556	0.506794
$267$	23.9630	1.46651
$268$	−1.81245	−0.110713
$269$	14.0654	0.857582	0.428791	−	0.903404i	$-0.358940\pi$
$269$	14.0654	0.857582	0.428791	+	0.903404i	$0.358940\pi$
$270$	0	0
$271$	19.1484	1.16318	0.581590	−	0.813482i	$-0.302431\pi$
$271$	19.1484	1.16318	0.581590	+	0.813482i	$0.302431\pi$
$272$	17.4810	1.05994
$273$	9.32231	0.564212
$274$	−17.0820	−1.03196
$275$	0	0
$276$	−0.697574	−0.0419890
$277$	19.2803	1.15844	0.579221	−	0.815171i	$-0.303357\pi$
$277$	19.2803	1.15844	0.579221	+	0.815171i	$0.303357\pi$
$278$	−0.503277	−0.0301845
$279$	27.6211	1.65363
$280$	0	0
$281$	−14.1350	−0.843221	−0.421610	−	0.906777i	$-0.638535\pi$
$281$	−14.1350	−0.843221	−0.421610	+	0.906777i	$0.638535\pi$
$282$	−36.1904	−2.15510
$283$	26.4282	1.57100	0.785498	−	0.618865i	$-0.212407\pi$
$283$	26.4282	1.57100	0.785498	+	0.618865i	$0.212407\pi$
$284$	−3.73678	−0.221737
$285$	0	0
$286$	−3.14524	−0.185982
$287$	−11.8024	−0.696674
$288$	−4.73729	−0.279147
$289$	10.2876	0.605152
$290$	0	0
$291$	31.3162	1.83579
$292$	−2.12861	−0.124567
$293$	−1.85398	−0.108311	−0.0541553	−	0.998533i	$-0.517247\pi$
$293$	−1.85398	−0.108311	−0.0541553	+	0.998533i	$0.517247\pi$
$294$	3.19433	0.186297
$295$	0	0
$296$	23.1895	1.34786
$297$	0.0723215	0.00419652
$298$	−7.31748	−0.423890
$299$	−3.82086	−0.220966
$300$	0	0
$301$	−4.67712	−0.269585
$302$	18.7957	1.08157
$303$	13.0914	0.752079
$304$	−21.1270	−1.21172
$305$	0	0
$306$	20.1949	1.15447
$307$	27.9173	1.59332	0.796662	−	0.604425i	$-0.206597\pi$
$307$	27.9173	1.59332	0.796662	+	0.604425i	$0.206597\pi$
$308$	0.179764	0.0102430
$309$	38.6830	2.20060
$310$	0	0
$311$	21.8316	1.23796	0.618979	−	0.785408i	$-0.287547\pi$
$311$	21.8316	1.23796	0.618979	+	0.785408i	$0.287547\pi$
$312$	−27.8997	−1.57951
$313$	−28.0231	−1.58396	−0.791979	−	0.610548i	$-0.790949\pi$
$313$	−28.0231	−1.58396	−0.791979	+	0.610548i	$0.790949\pi$
$314$	−8.16502	−0.460779
$315$	0	0
$316$	3.46964	0.195183
$317$	7.10927	0.399296	0.199648	−	0.979868i	$-0.436020\pi$
$317$	7.10927	0.399296	0.199648	+	0.979868i	$0.436020\pi$
$318$	−28.7039	−1.60964
$319$	2.35091	0.131625
$320$	0	0
$321$	−19.0747	−1.06465
$322$	−1.30923	−0.0729607
$323$	−32.9790	−1.83500
$324$	2.61298	0.145166
$325$	0	0
$326$	−27.9075	−1.54566
$327$	−6.04822	−0.334467
$328$	35.3221	1.95034
$329$	11.3296	0.624619
$330$	0	0
$331$	−19.3052	−1.06111	−0.530556	−	0.847650i	$-0.678017\pi$
$331$	−19.3052	−1.06111	−0.530556	+	0.847650i	$0.678017\pi$
$332$	−0.190107	−0.0104335
$333$	22.8801	1.25382
$334$	−24.1153	−1.31953
$335$	0	0
$336$	−8.16480	−0.445426
$337$	−14.9549	−0.814645	−0.407323	−	0.913284i	$-0.633538\pi$
$337$	−14.9549	−0.814645	−0.407323	+	0.913284i	$0.633538\pi$
$338$	−2.09341	−0.113867
$339$	33.2706	1.80701
$340$	0	0
$341$	5.88131	0.318491
$342$	−24.4070	−1.31978
$343$	−1.00000	−0.0539949
$344$	13.9976	0.754702
$345$	0	0
$346$	−21.4500	−1.15316
$347$	−17.6990	−0.950134	−0.475067	−	0.879950i	$-0.657576\pi$
$347$	−17.6990	−0.950134	−0.475067	+	0.879950i	$0.657576\pi$
$348$	2.60826	0.139817
$349$	13.5736	0.726577	0.363288	−	0.931677i	$-0.381654\pi$
$349$	13.5736	0.726577	0.363288	+	0.931677i	$0.381654\pi$
$350$	0	0
$351$	0.439494	0.0234584
$352$	−1.00870	−0.0537640
$353$	−4.11726	−0.219140	−0.109570	−	0.993979i	$-0.534947\pi$
$353$	−4.11726	−0.219140	−0.109570	+	0.993979i	$0.534947\pi$
$354$	−13.8754	−0.737471
$355$	0	0
$356$	2.80806	0.148827
$357$	−12.7452	−0.674545
$358$	24.1908	1.27852
$359$	20.5900	1.08670	0.543349	−	0.839507i	$-0.317156\pi$
$359$	20.5900	1.08670	0.543349	+	0.839507i	$0.317156\pi$
$360$	0	0
$361$	20.8575	1.09776
$362$	2.83857	0.149192
$363$	25.8738	1.35802
$364$	1.09242	0.0572582
$365$	0	0
$366$	−14.2769	−0.746263
$367$	−29.9430	−1.56301	−0.781506	−	0.623898i	$-0.785548\pi$
$367$	−29.9430	−1.56301	−0.781506	+	0.623898i	$0.785548\pi$
$368$	3.34644	0.174445
$369$	34.8508	1.81426
$370$	0	0
$371$	8.98590	0.466525
$372$	6.52513	0.338312
$373$	5.96338	0.308772	0.154386	−	0.988011i	$-0.450660\pi$
$373$	5.96338	0.308772	0.154386	+	0.988011i	$0.450660\pi$
$374$	4.30006	0.222351
$375$	0	0
$376$	−33.9070	−1.74862
$377$	14.2863	0.735784
$378$	0.150594	0.00774574
$379$	−8.27953	−0.425291	−0.212645	−	0.977129i	$-0.568208\pi$
$379$	−8.27953	−0.425291	−0.212645	+	0.977129i	$0.568208\pi$
$380$	0	0
$381$	−16.0068	−0.820053
$382$	−11.2272	−0.574436
$383$	20.5433	1.04971	0.524856	−	0.851191i	$-0.324119\pi$
$383$	20.5433	1.04971	0.524856	+	0.851191i	$0.324119\pi$
$384$	20.2601	1.03390
$385$	0	0
$386$	1.39413	0.0709593
$387$	13.8109	0.702046
$388$	3.66973	0.186303
$389$	−16.6648	−0.844940	−0.422470	−	0.906377i	$-0.638837\pi$
$389$	−16.6648	−0.844940	−0.422470	+	0.906377i	$0.638837\pi$
$390$	0	0
$391$	5.22375	0.264176
$392$	2.99279	0.151159
$393$	−30.2203	−1.52441
$394$	19.2238	0.968479
$395$	0	0
$396$	−0.530817	−0.0266746
$397$	27.1661	1.36343	0.681713	−	0.731620i	$-0.261235\pi$
$397$	27.1661	1.36343	0.681713	+	0.731620i	$0.261235\pi$
$398$	−22.7704	−1.14137
$399$	15.4034	0.771137
$400$	0	0
$401$	−16.8298	−0.840442	−0.420221	−	0.907422i	$-0.638047\pi$
$401$	−16.8298	−0.840442	−0.420221	+	0.907422i	$0.638047\pi$
$402$	20.2497	1.00996
$403$	35.7404	1.78036
$404$	1.53409	0.0763236
$405$	0	0
$406$	4.89527	0.242948
$407$	4.87181	0.241487
$408$	38.1435	1.88839
$409$	5.93014	0.293226	0.146613	−	0.989194i	$-0.453163\pi$
$409$	5.93014	0.293226	0.146613	+	0.989194i	$0.453163\pi$
$410$	0	0
$411$	−31.8335	−1.57023
$412$	4.53299	0.223324
$413$	4.34377	0.213743
$414$	3.86598	0.190002
$415$	0	0
$416$	−6.12983	−0.300540
$417$	−0.937892	−0.0459287
$418$	−5.19694	−0.254190
$419$	−8.80187	−0.430000	−0.215000	−	0.976614i	$-0.568975\pi$
$419$	−8.80187	−0.430000	−0.215000	+	0.976614i	$0.568975\pi$
$420$	0	0
$421$	32.3755	1.57789	0.788944	−	0.614465i	$-0.210628\pi$
$421$	32.3755	1.57789	0.788944	+	0.614465i	$0.210628\pi$
$422$	−7.71723	−0.375669
$423$	−33.4546	−1.62662
$424$	−26.8929	−1.30603
$425$	0	0
$426$	41.7494	2.02276
$427$	4.46944	0.216291
$428$	−2.23523	−0.108044
$429$	−5.86137	−0.282989
$430$	0	0
$431$	−24.9639	−1.20247	−0.601234	−	0.799073i	$-0.705324\pi$
$431$	−24.9639	−1.20247	−0.601234	+	0.799073i	$0.705324\pi$
$432$	−0.384924	−0.0185197
$433$	6.73110	0.323476	0.161738	−	0.986834i	$-0.448290\pi$
$433$	6.73110	0.323476	0.161738	+	0.986834i	$0.448290\pi$
$434$	12.2466	0.587856
$435$	0	0
$436$	−0.708749	−0.0339429
$437$	−6.31328	−0.302005
$438$	23.7820	1.13635
$439$	33.5221	1.59992	0.799960	−	0.600053i	$-0.204854\pi$
$439$	33.5221	1.59992	0.799960	+	0.600053i	$0.204854\pi$
$440$	0	0
$441$	2.95286	0.140612
$442$	26.1313	1.24294
$443$	16.6280	0.790021	0.395010	−	0.918677i	$-0.370741\pi$
$443$	16.6280	0.790021	0.395010	+	0.918677i	$0.370741\pi$
$444$	5.40512	0.256516
$445$	0	0
$446$	10.2242	0.484130
$447$	−13.6366	−0.644991
$448$	−8.79329	−0.415444
$449$	−27.0942	−1.27865	−0.639327	−	0.768935i	$-0.720787\pi$
$449$	−27.0942	−1.27865	−0.639327	+	0.768935i	$0.720787\pi$
$450$	0	0
$451$	7.42071	0.349428
$452$	3.89875	0.183382
$453$	35.0272	1.64572
$454$	−8.91511	−0.418407
$455$	0	0
$456$	−46.0992	−2.15879
$457$	3.72601	0.174296	0.0871478	−	0.996195i	$-0.472225\pi$
$457$	3.72601	0.174296	0.0871478	+	0.996195i	$0.472225\pi$
$458$	−2.44703	−0.114342
$459$	−0.600862	−0.0280458
$460$	0	0
$461$	−0.955542	−0.0445040	−0.0222520	−	0.999752i	$-0.507084\pi$
$461$	−0.955542	−0.0445040	−0.0222520	+	0.999752i	$0.507084\pi$
$462$	−2.00842	−0.0934402
$463$	12.6141	0.586225	0.293113	−	0.956078i	$-0.405309\pi$
$463$	12.6141	0.586225	0.293113	+	0.956078i	$0.405309\pi$
$464$	−12.5125	−0.580877
$465$	0	0
$466$	−2.60895	−0.120857
$467$	22.3659	1.03497	0.517486	−	0.855692i	$-0.326868\pi$
$467$	22.3659	1.03497	0.517486	+	0.855692i	$0.326868\pi$
$468$	−3.22575	−0.149110
$469$	−6.33927	−0.292720
$470$	0	0
$471$	−15.2161	−0.701121
$472$	−13.0000	−0.598373
$473$	2.94072	0.135215
$474$	−38.7647	−1.78052
$475$	0	0
$476$	−1.49352	−0.0684552
$477$	−26.5341	−1.21491
$478$	23.6281	1.08073
$479$	3.79714	0.173496	0.0867480	−	0.996230i	$-0.472353\pi$
$479$	3.79714	0.173496	0.0867480	+	0.996230i	$0.472353\pi$
$480$	0	0
$481$	29.6058	1.34991
$482$	−11.6721	−0.531649
$483$	−2.43985	−0.111017
$484$	3.03197	0.137817
$485$	0	0
$486$	−28.7419	−1.30376
$487$	−18.8808	−0.855572	−0.427786	−	0.903880i	$-0.640706\pi$
$487$	−18.8808	−0.855572	−0.427786	+	0.903880i	$0.640706\pi$
$488$	−13.3761	−0.605506
$489$	−52.0076	−2.35187
$490$	0	0
$491$	23.8550	1.07656	0.538281	−	0.842766i	$-0.319074\pi$
$491$	23.8550	1.07656	0.538281	+	0.842766i	$0.319074\pi$
$492$	8.23305	0.371174
$493$	−19.5318	−0.879668
$494$	−31.5815	−1.42092
$495$	0	0
$496$	−31.3027	−1.40553
$497$	−13.0698	−0.586263
$498$	2.12398	0.0951777
$499$	−12.3128	−0.551194	−0.275597	−	0.961273i	$-0.588876\pi$
$499$	−12.3128	−0.551194	−0.275597	+	0.961273i	$0.588876\pi$
$500$	0	0
$501$	−44.9405	−2.00779
$502$	17.7381	0.791691
$503$	7.19133	0.320645	0.160323	−	0.987065i	$-0.448747\pi$
$503$	7.19133	0.320645	0.160323	+	0.987065i	$0.448747\pi$
$504$	−8.83727	−0.393643
$505$	0	0
$506$	0.823175	0.0365946
$507$	−3.90122	−0.173259
$508$	−1.87572	−0.0832218
$509$	−9.23659	−0.409405	−0.204702	−	0.978824i	$-0.565623\pi$
$509$	−9.23659	−0.409405	−0.204702	+	0.978824i	$0.565623\pi$
$510$	0	0
$511$	−7.44507	−0.329350
$512$	25.3991	1.12249
$513$	0.726185	0.0320618
$514$	14.4078	0.635500
$515$	0	0
$516$	3.26264	0.143630
$517$	−7.12342	−0.313288
$518$	10.1445	0.445725
$519$	−39.9735	−1.75464
$520$	0	0
$521$	29.3783	1.28709	0.643543	−	0.765410i	$-0.277464\pi$
$521$	29.3783	1.28709	0.643543	+	0.765410i	$0.277464\pi$
$522$	−14.4550	−0.632680
$523$	−1.16498	−0.0509408	−0.0254704	−	0.999676i	$-0.508108\pi$
$523$	−1.16498	−0.0509408	−0.0254704	+	0.999676i	$0.508108\pi$
$524$	−3.54131	−0.154703
$525$	0	0
$526$	7.63823	0.333043
$527$	−48.8631	−2.12851
$528$	5.13359	0.223411
$529$	1.00000	0.0434783
$530$	0	0
$531$	−12.8265	−0.556624
$532$	1.80502	0.0782577
$533$	45.0953	1.95329
$534$	−31.3732	−1.35765
$535$	0	0
$536$	18.9721	0.819469
$537$	45.0813	1.94540
$538$	−18.4149	−0.793922
$539$	0.628746	0.0270820
$540$	0	0
$541$	10.3706	0.445865	0.222933	−	0.974834i	$-0.428437\pi$
$541$	10.3706	0.445865	0.222933	+	0.974834i	$0.428437\pi$
$542$	−25.0697	−1.07683
$543$	5.28987	0.227010
$544$	8.38050	0.359311
$545$	0	0
$546$	−12.2051	−0.522329
$547$	10.9361	0.467593	0.233796	−	0.972286i	$-0.424885\pi$
$547$	10.9361	0.467593	0.233796	+	0.972286i	$0.424885\pi$
$548$	−3.73034	−0.159352
$549$	−13.1976	−0.563260
$550$	0	0
$551$	23.6056	1.00563
$552$	7.30194	0.310791
$553$	12.1355	0.516053
$554$	−25.2424	−1.07245
$555$	0	0
$556$	−0.109905	−0.00466101
$557$	−39.3272	−1.66635	−0.833174	−	0.553010i	$-0.813479\pi$
$557$	−39.3272	−1.66635	−0.833174	+	0.553010i	$0.813479\pi$
$558$	−36.1625	−1.53088
$559$	17.8706	0.755847
$560$	0	0
$561$	8.01347	0.338329
$562$	18.5060	0.780627
$563$	11.4104	0.480889	0.240445	−	0.970663i	$-0.422707\pi$
$563$	11.4104	0.480889	0.240445	+	0.970663i	$0.422707\pi$
$564$	−7.90321	−0.332785
$565$	0	0
$566$	−34.6007	−1.45438
$567$	9.13921	0.383811
$568$	39.1153	1.64124
$569$	−0.348795	−0.0146223	−0.00731113	−	0.999973i	$-0.502327\pi$
$569$	−0.348795	−0.0146223	−0.00731113	+	0.999973i	$0.502327\pi$
$570$	0	0
$571$	13.9035	0.581843	0.290922	−	0.956747i	$-0.406038\pi$
$571$	13.9035	0.581843	0.290922	+	0.956747i	$0.406038\pi$
$572$	−0.686853	−0.0287188
$573$	−20.9228	−0.874061
$574$	15.4521	0.644958
$575$	0	0
$576$	25.9653	1.08189
$577$	−16.6456	−0.692966	−0.346483	−	0.938056i	$-0.612624\pi$
$577$	−16.6456	−0.692966	−0.346483	+	0.938056i	$0.612624\pi$
$578$	−13.4688	−0.560230
$579$	2.59806	0.107972
$580$	0	0
$581$	−0.664922	−0.0275856
$582$	−41.0003	−1.69952
$583$	−5.64985	−0.233993
$584$	22.2815	0.922015
$585$	0	0
$586$	2.42729	0.100270
$587$	27.5783	1.13828	0.569140	−	0.822241i	$-0.307276\pi$
$587$	27.5783	1.13828	0.569140	+	0.822241i	$0.307276\pi$
$588$	0.697574	0.0287675
$589$	59.0546	2.43330
$590$	0	0
$591$	35.8248	1.47364
$592$	−25.9297	−1.06571
$593$	42.5956	1.74919	0.874597	−	0.484851i	$-0.161126\pi$
$593$	42.5956	1.74919	0.874597	+	0.484851i	$0.161126\pi$
$594$	−0.0946856	−0.00388500
$595$	0	0
$596$	−1.59798	−0.0654559
$597$	−42.4342	−1.73671
$598$	5.00239	0.204563
$599$	27.6938	1.13154	0.565770	−	0.824563i	$-0.308579\pi$
$599$	27.6938	1.13154	0.565770	+	0.824563i	$0.308579\pi$
$600$	0	0
$601$	−3.66015	−0.149301	−0.0746503	−	0.997210i	$-0.523784\pi$
$601$	−3.66015	−0.149301	−0.0746503	+	0.997210i	$0.523784\pi$
$602$	6.12344	0.249573
$603$	18.7189	0.762294
$604$	4.10459	0.167013
$605$	0	0
$606$	−17.1396	−0.696251
$607$	38.1079	1.54675	0.773376	−	0.633947i	$-0.218566\pi$
$607$	38.1079	1.54675	0.773376	+	0.633947i	$0.218566\pi$
$608$	−10.1284	−0.410762
$609$	9.12268	0.369670
$610$	0	0
$611$	−43.2887	−1.75127
$612$	4.41014	0.178269
$613$	−12.1715	−0.491603	−0.245801	−	0.969320i	$-0.579051\pi$
$613$	−12.1715	−0.491603	−0.245801	+	0.969320i	$0.579051\pi$
$614$	−36.5502	−1.47505
$615$	0	0
$616$	−1.88170	−0.0758160
$617$	31.7184	1.27694	0.638468	−	0.769648i	$-0.279568\pi$
$617$	31.7184	1.27694	0.638468	+	0.769648i	$0.279568\pi$
$618$	−50.6450	−2.03724
$619$	7.79002	0.313107	0.156554	−	0.987669i	$-0.449962\pi$
$619$	7.79002	0.313107	0.156554	+	0.987669i	$0.449962\pi$
$620$	0	0
$621$	−0.115025	−0.00461579
$622$	−28.5827	−1.14606
$623$	9.82152	0.393491
$624$	31.1965	1.24886
$625$	0	0
$626$	36.6887	1.46638
$627$	−9.68485	−0.386776
$628$	−1.78307	−0.0711522
$629$	−40.4760	−1.61388
$630$	0	0
$631$	19.6785	0.783390	0.391695	−	0.920095i	$-0.371889\pi$
$631$	19.6785	0.783390	0.391695	+	0.920095i	$0.371889\pi$
$632$	−36.3189	−1.44469
$633$	−14.3816	−0.571617
$634$	−9.30769	−0.369655
$635$	0	0
$636$	−6.26833	−0.248556
$637$	3.82086	0.151388
$638$	−3.07788	−0.121855
$639$	38.5934	1.52673
$640$	0	0
$641$	18.1661	0.717518	0.358759	−	0.933430i	$-0.383200\pi$
$641$	18.1661	0.717518	0.358759	+	0.933430i	$0.383200\pi$
$642$	24.9733	0.985616
$643$	−2.57373	−0.101498	−0.0507489	−	0.998711i	$-0.516161\pi$
$643$	−2.57373	−0.101498	−0.0507489	+	0.998711i	$0.516161\pi$
$644$	−0.285909	−0.0112664
$645$	0	0
$646$	43.1772	1.69878
$647$	31.4065	1.23472	0.617358	−	0.786683i	$-0.288203\pi$
$647$	31.4065	1.23472	0.617358	+	0.786683i	$0.288203\pi$
$648$	−27.3517	−1.07448
$649$	−2.73113	−0.107206
$650$	0	0
$651$	22.8224	0.894481
$652$	−6.09442	−0.238676
$653$	−33.2819	−1.30242	−0.651210	−	0.758897i	$-0.725738\pi$
$653$	−33.2819	−1.30242	−0.651210	+	0.758897i	$0.725738\pi$
$654$	7.91852	0.309639
$655$	0	0
$656$	−39.4960	−1.54206
$657$	21.9842	0.857685
$658$	−14.8330	−0.578252
$659$	−14.6865	−0.572104	−0.286052	−	0.958214i	$-0.592343\pi$
$659$	−14.6865	−0.572104	−0.286052	+	0.958214i	$0.592343\pi$
$660$	0	0
$661$	−22.9211	−0.891529	−0.445764	−	0.895150i	$-0.647068\pi$
$661$	−22.9211	−0.891529	−0.445764	+	0.895150i	$0.647068\pi$
$662$	25.2751	0.982343
$663$	48.6974	1.89125
$664$	1.98997	0.0772258
$665$	0	0
$666$	−29.9554	−1.16075
$667$	−3.73904	−0.144776
$668$	−5.26626	−0.203758
$669$	19.0535	0.736652
$670$	0	0
$671$	−2.81014	−0.108484
$672$	−3.91426	−0.150996
$673$	−3.43383	−0.132364	−0.0661821	−	0.997808i	$-0.521082\pi$
$673$	−3.43383	−0.132364	−0.0661821	+	0.997808i	$0.521082\pi$
$674$	19.5795	0.754172
$675$	0	0
$676$	−0.457157	−0.0175830
$677$	−34.2453	−1.31615	−0.658076	−	0.752951i	$-0.728630\pi$
$677$	−34.2453	−1.31615	−0.658076	+	0.752951i	$0.728630\pi$
$678$	−43.5590	−1.67287
$679$	12.8353	0.492575
$680$	0	0
$681$	−16.6139	−0.636648
$682$	−7.70001	−0.294849
$683$	−30.1049	−1.15193	−0.575966	−	0.817474i	$-0.695374\pi$
$683$	−30.1049	−1.15193	−0.575966	+	0.817474i	$0.695374\pi$
$684$	−5.32997	−0.203797
$685$	0	0
$686$	1.30923	0.0499868
$687$	−4.56020	−0.173983
$688$	−15.6517	−0.596715
$689$	−34.3339	−1.30802
$690$	0	0
$691$	−15.3245	−0.582972	−0.291486	−	0.956575i	$-0.594150\pi$
$691$	−15.3245	−0.582972	−0.291486	+	0.956575i	$0.594150\pi$
$692$	−4.68422	−0.178067
$693$	−1.85660	−0.0705263
$694$	23.1722	0.879603
$695$	0	0
$696$	−27.3023	−1.03489
$697$	−61.6528	−2.33527
$698$	−17.7710	−0.672641
$699$	−4.86196	−0.183896
$700$	0	0
$701$	−24.2372	−0.915427	−0.457713	−	0.889100i	$-0.651331\pi$
$701$	−24.2372	−0.915427	−0.457713	+	0.889100i	$0.651331\pi$
$702$	−0.575400	−0.0217171
$703$	48.9182	1.84498
$704$	5.52875	0.208372
$705$	0	0
$706$	5.39046	0.202872
$707$	5.36565	0.201796
$708$	−3.03010	−0.113878
$709$	−31.8046	−1.19445	−0.597223	−	0.802075i	$-0.703729\pi$
$709$	−31.8046	−1.19445	−0.597223	+	0.802075i	$0.703729\pi$
$710$	0	0
$711$	−35.8343	−1.34389
$712$	−29.3937	−1.10158
$713$	−9.35403	−0.350311
$714$	16.6864	0.624472
$715$	0	0
$716$	5.28276	0.197426
$717$	44.0327	1.64443
$718$	−26.9571	−1.00603
$719$	−50.9964	−1.90185	−0.950923	−	0.309428i	$-0.899862\pi$
$719$	−50.9964	−1.90185	−0.950923	+	0.309428i	$0.899862\pi$
$720$	0	0
$721$	15.8547	0.590459
$722$	−27.3073	−1.01627
$723$	−21.7518	−0.808957
$724$	0.619883	0.0230378
$725$	0	0
$726$	−33.8748	−1.25721
$727$	−15.8310	−0.587138	−0.293569	−	0.955938i	$-0.594843\pi$
$727$	−15.8310	−0.587138	−0.293569	+	0.955938i	$0.594843\pi$
$728$	−11.4350	−0.423810
$729$	−26.1448	−0.968327
$730$	0	0
$731$	−24.4321	−0.903654
$732$	−3.11776	−0.115236
$733$	−2.47144	−0.0912846	−0.0456423	−	0.998958i	$-0.514533\pi$
$733$	−2.47144	−0.0912846	−0.0456423	+	0.998958i	$0.514533\pi$
$734$	39.2024	1.44699
$735$	0	0
$736$	1.60431	0.0591355
$737$	3.98579	0.146818
$738$	−45.6278	−1.67958
$739$	19.3932	0.713391	0.356696	−	0.934221i	$-0.383903\pi$
$739$	19.3932	0.713391	0.356696	+	0.934221i	$0.383903\pi$
$740$	0	0
$741$	−58.8544	−2.16207
$742$	−11.7646	−0.431894
$743$	−31.3151	−1.14884	−0.574420	−	0.818561i	$-0.694772\pi$
$743$	−31.3151	−1.14884	−0.574420	+	0.818561i	$0.694772\pi$
$744$	−68.3026	−2.50410
$745$	0	0
$746$	−7.80745	−0.285851
$747$	1.96342	0.0718377
$748$	0.939043	0.0343348
$749$	−7.81800	−0.285663
$750$	0	0
$751$	−6.79796	−0.248061	−0.124031	−	0.992278i	$-0.539582\pi$
$751$	−6.79796	−0.248061	−0.124031	+	0.992278i	$0.539582\pi$
$752$	37.9137	1.38257
$753$	33.0562	1.20464
$754$	−18.7041	−0.681165
$755$	0	0
$756$	0.0328866	0.00119608
$757$	−21.9855	−0.799075	−0.399538	−	0.916717i	$-0.630829\pi$
$757$	−21.9855	−0.799075	−0.399538	+	0.916717i	$0.630829\pi$
$758$	10.8398	0.393720
$759$	1.53404	0.0556823
$760$	0	0
$761$	10.4750	0.379717	0.189858	−	0.981811i	$-0.439197\pi$
$761$	10.4750	0.379717	0.189858	+	0.981811i	$0.439197\pi$
$762$	20.9566	0.759178
$763$	−2.47893	−0.0897434
$764$	−2.45179	−0.0887027
$765$	0	0
$766$	−26.8959	−0.971790
$767$	−16.5969	−0.599281
$768$	16.3833	0.591183
$769$	−42.1758	−1.52090	−0.760449	−	0.649397i	$-0.775021\pi$
$769$	−42.1758	−1.52090	−0.760449	+	0.649397i	$0.775021\pi$
$770$	0	0
$771$	26.8499	0.966976
$772$	0.304448	0.0109573
$773$	37.2574	1.34006	0.670028	−	0.742336i	$-0.266282\pi$
$773$	37.2574	1.34006	0.670028	+	0.742336i	$0.266282\pi$
$774$	−18.0816	−0.649931
$775$	0	0
$776$	−38.4134	−1.37896
$777$	18.9051	0.678215
$778$	21.8181	0.782218
$779$	74.5119	2.66966
$780$	0	0
$781$	8.21761	0.294049
$782$	−6.83911	−0.244566
$783$	0.430083	0.0153699
$784$	−3.34644	−0.119516
$785$	0	0
$786$	39.5654	1.41125
$787$	23.1561	0.825425	0.412712	−	0.910861i	$-0.364581\pi$
$787$	23.1561	0.825425	0.412712	+	0.910861i	$0.364581\pi$
$788$	4.19806	0.149550
$789$	14.2344	0.506757
$790$	0	0
$791$	13.6363	0.484853
$792$	5.55640	0.197438
$793$	−17.0771	−0.606425
$794$	−35.5667	−1.26222
$795$	0	0
$796$	−4.97256	−0.176248
$797$	−20.0507	−0.710233	−0.355117	−	0.934822i	$-0.615559\pi$
$797$	−20.0507	−0.710233	−0.355117	+	0.934822i	$0.615559\pi$
$798$	−20.1667	−0.713893
$799$	59.1828	2.09374
$800$	0	0
$801$	−29.0015	−1.02472
$802$	22.0342	0.778054
$803$	4.68106	0.165191
$804$	4.42211	0.155956
$805$	0	0
$806$	−46.7926	−1.64820
$807$	−34.3174	−1.20803
$808$	−16.0582	−0.564927
$809$	12.9001	0.453542	0.226771	−	0.973948i	$-0.427183\pi$
$809$	12.9001	0.453542	0.226771	+	0.973948i	$0.427183\pi$
$810$	0	0
$811$	−18.6560	−0.655101	−0.327550	−	0.944834i	$-0.606223\pi$
$811$	−18.6560	−0.655101	−0.327550	+	0.944834i	$0.606223\pi$
$812$	1.06902	0.0375154
$813$	−46.7191	−1.63851
$814$	−6.37834	−0.223561
$815$	0	0
$816$	−42.6509	−1.49308
$817$	29.5280	1.03305
$818$	−7.76393	−0.271460
$819$	−11.2824	−0.394240
$820$	0	0
$821$	2.18263	0.0761741	0.0380871	−	0.999274i	$-0.487874\pi$
$821$	2.18263	0.0761741	0.0380871	+	0.999274i	$0.487874\pi$
$822$	41.6774	1.45367
$823$	4.78338	0.166738	0.0833691	−	0.996519i	$-0.473432\pi$
$823$	4.78338	0.166738	0.0833691	+	0.996519i	$0.473432\pi$
$824$	−47.4497	−1.65299
$825$	0	0
$826$	−5.68701	−0.197876
$827$	34.3352	1.19395	0.596977	−	0.802259i	$-0.296368\pi$
$827$	34.3352	1.19395	0.596977	+	0.802259i	$0.296368\pi$
$828$	0.844247	0.0293396
$829$	16.8054	0.583677	0.291838	−	0.956468i	$-0.405733\pi$
$829$	16.8054	0.583677	0.291838	+	0.956468i	$0.405733\pi$
$830$	0	0
$831$	−47.0410	−1.63184
$832$	33.5979	1.16480
$833$	−5.22375	−0.180992
$834$	1.22792	0.0425193
$835$	0	0
$836$	−1.13490	−0.0392514
$837$	1.07595	0.0371902
$838$	11.5237	0.398080
$839$	28.1603	0.972203	0.486101	−	0.873902i	$-0.338419\pi$
$839$	28.1603	0.972203	0.486101	+	0.873902i	$0.338419\pi$
$840$	0	0
$841$	−15.0196	−0.517917
$842$	−42.3871	−1.46076
$843$	34.4871	1.18780
$844$	−1.68528	−0.0580098
$845$	0	0
$846$	43.7998	1.50587
$847$	10.6047	0.364381
$848$	30.0708	1.03263
$849$	−64.4809	−2.21298
$850$	0	0
$851$	−7.74846	−0.265614
$852$	9.11718	0.312349
$853$	−34.8933	−1.19472	−0.597362	−	0.801972i	$-0.703785\pi$
$853$	−34.8933	−1.19472	−0.597362	+	0.801972i	$0.703785\pi$
$854$	−5.85153	−0.200235
$855$	0	0
$856$	23.3976	0.799714
$857$	−29.9098	−1.02170	−0.510849	−	0.859670i	$-0.670669\pi$
$857$	−29.9098	−1.02170	−0.510849	+	0.859670i	$0.670669\pi$
$858$	7.67390	0.261982
$859$	−20.7246	−0.707114	−0.353557	−	0.935413i	$-0.615028\pi$
$859$	−20.7246	−0.707114	−0.353557	+	0.935413i	$0.615028\pi$
$860$	0	0
$861$	28.7961	0.981367
$862$	32.6835	1.11321
$863$	−13.2072	−0.449577	−0.224788	−	0.974408i	$-0.572169\pi$
$863$	−13.2072	−0.449577	−0.224788	+	0.974408i	$0.572169\pi$
$864$	−0.184535	−0.00627802
$865$	0	0
$866$	−8.81258	−0.299464
$867$	−25.1001	−0.852445
$868$	2.67440	0.0907751
$869$	−7.63014	−0.258835
$870$	0	0
$871$	24.2214	0.820712
$872$	7.41892	0.251236
$873$	−37.9009	−1.28275
$874$	8.26556	0.279587
$875$	0	0
$876$	5.19348	0.175472
$877$	2.35884	0.0796523	0.0398262	−	0.999207i	$-0.487320\pi$
$877$	2.35884	0.0796523	0.0398262	+	0.999207i	$0.487320\pi$
$878$	−43.8882	−1.48115
$879$	4.52343	0.152571
$880$	0	0
$881$	5.91705	0.199350	0.0996752	−	0.995020i	$-0.468220\pi$
$881$	5.91705	0.199350	0.0996752	+	0.995020i	$0.468220\pi$
$882$	−3.86598	−0.130174
$883$	25.1410	0.846062	0.423031	−	0.906115i	$-0.360966\pi$
$883$	25.1410	0.846062	0.423031	+	0.906115i	$0.360966\pi$
$884$	5.70652	0.191931
$885$	0	0
$886$	−21.7699	−0.731375
$887$	16.4801	0.553347	0.276674	−	0.960964i	$-0.410768\pi$
$887$	16.4801	0.553347	0.276674	+	0.960964i	$0.410768\pi$
$888$	−56.5788	−1.89866
$889$	−6.56057	−0.220034
$890$	0	0
$891$	−5.74624	−0.192506
$892$	2.23275	0.0747580
$893$	−71.5267	−2.39355
$894$	17.8535	0.597112
$895$	0	0
$896$	8.30385	0.277412
$897$	9.32231	0.311263
$898$	35.4726	1.18374
$899$	34.9751	1.16648
$900$	0	0
$901$	46.9401	1.56380
$902$	−9.71544	−0.323489
$903$	11.4115	0.379750
$904$	−40.8107	−1.35734
$905$	0	0
$906$	−45.8587	−1.52355
$907$	36.1515	1.20039	0.600195	−	0.799854i	$-0.295090\pi$
$907$	36.1515	1.20039	0.600195	+	0.799854i	$0.295090\pi$
$908$	−1.94687	−0.0646092
$909$	−15.8440	−0.525512
$910$	0	0
$911$	0.974249	0.0322783	0.0161392	−	0.999870i	$-0.494863\pi$
$911$	0.974249	0.0322783	0.0161392	+	0.999870i	$0.494863\pi$
$912$	51.5467	1.70688
$913$	0.418067	0.0138360
$914$	−4.87822	−0.161357
$915$	0	0
$916$	−0.534379	−0.0176564
$917$	−12.3861	−0.409026
$918$	0.786668	0.0259639
$919$	49.0533	1.61812	0.809059	−	0.587727i	$-0.199977\pi$
$919$	49.0533	1.61812	0.809059	+	0.587727i	$0.199977\pi$
$920$	0	0
$921$	−68.1139	−2.24443
$922$	1.25103	0.0412004
$923$	49.9380	1.64373
$924$	−0.438597	−0.0144288
$925$	0	0
$926$	−16.5148	−0.542708
$927$	−46.8166	−1.53766
$928$	−5.99857	−0.196913
$929$	21.5115	0.705771	0.352886	−	0.935667i	$-0.385201\pi$
$929$	21.5115	0.705771	0.352886	+	0.935667i	$0.385201\pi$
$930$	0	0
$931$	6.31328	0.206909
$932$	−0.569739	−0.0186624
$933$	−53.2658	−1.74384
$934$	−29.2822	−0.958143
$935$	0	0
$936$	33.7660	1.10367
$937$	13.5932	0.444069	0.222034	−	0.975039i	$-0.428730\pi$
$937$	13.5932	0.444069	0.222034	+	0.975039i	$0.428730\pi$
$938$	8.29958	0.270991
$939$	68.3720	2.23124
$940$	0	0
$941$	−40.2193	−1.31111	−0.655557	−	0.755146i	$-0.727566\pi$
$941$	−40.2193	−1.31111	−0.655557	+	0.755146i	$0.727566\pi$
$942$	19.9214	0.649075
$943$	−11.8024	−0.384339
$944$	14.5362	0.473112
$945$	0	0
$946$	−3.85009	−0.125177
$947$	−19.4964	−0.633549	−0.316775	−	0.948501i	$-0.602600\pi$
$947$	−19.4964	−0.633549	−0.316775	+	0.948501i	$0.602600\pi$
$948$	−8.46540	−0.274943
$949$	28.4465	0.923414
$950$	0	0
$951$	−17.3455	−0.562467
$952$	15.6336	0.506687
$953$	−4.40749	−0.142773	−0.0713864	−	0.997449i	$-0.522742\pi$
$953$	−4.40749	−0.142773	−0.0713864	+	0.997449i	$0.522742\pi$
$954$	34.7393	1.12473
$955$	0	0
$956$	5.15988	0.166883
$957$	−5.73585	−0.185414
$958$	−4.97135	−0.160617
$959$	−13.0473	−0.421320
$960$	0	0
$961$	56.4979	1.82251
$962$	−38.7609	−1.24970
$963$	23.0854	0.743917
$964$	−2.54894	−0.0820958
$965$	0	0
$966$	3.19433	0.102776
$967$	26.2533	0.844248	0.422124	−	0.906538i	$-0.361285\pi$
$967$	26.2533	0.844248	0.422124	+	0.906538i	$0.361285\pi$
$968$	−31.7375	−1.02008
$969$	80.4637	2.58487
$970$	0	0
$971$	−12.9386	−0.415219	−0.207610	−	0.978212i	$-0.566568\pi$
$971$	−12.9386	−0.415219	−0.207610	+	0.978212i	$0.566568\pi$
$972$	−6.27661	−0.201323
$973$	−0.384406	−0.0123235
$974$	24.7194	0.792061
$975$	0	0
$976$	14.9567	0.478752
$977$	−16.1001	−0.515088	−0.257544	−	0.966267i	$-0.582913\pi$
$977$	−16.1001	−0.515088	−0.257544	+	0.966267i	$0.582913\pi$
$978$	68.0901	2.17728
$979$	−6.17525	−0.197362
$980$	0	0
$981$	7.31993	0.233707
$982$	−31.2318	−0.996645
$983$	0.218755	0.00697722	0.00348861	−	0.999994i	$-0.498890\pi$
$983$	0.218755	0.00697722	0.00348861	+	0.999994i	$0.498890\pi$
$984$	−86.1805	−2.74733
$985$	0	0
$986$	25.5717	0.814369
$987$	−27.6424	−0.879868
$988$	−6.89674	−0.219414
$989$	−4.67712	−0.148724
$990$	0	0
$991$	−3.61978	−0.114986	−0.0574930	−	0.998346i	$-0.518311\pi$
$991$	−3.61978	−0.114986	−0.0574930	+	0.998346i	$0.518311\pi$
$992$	−15.0067	−0.476464
$993$	47.1019	1.49473
$994$	17.1115	0.542743
$995$	0	0
$996$	0.463832	0.0146971
$997$	60.8850	1.92825	0.964124	−	0.265452i	$-0.0855211\pi$
$997$	60.8850	1.92825	0.964124	+	0.265452i	$0.0855211\pi$
$998$	16.1203	0.510278
$999$	0.891266	0.0281984

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4025.2.a.bd.1.8		21
5.2	odd	4		805.2.c.c.484.14	✓	42
5.3	odd	4		805.2.c.c.484.29	yes	42
5.4	even	2		4025.2.a.be.1.14		21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
805.2.c.c.484.14	✓	42	5.2	odd	4
805.2.c.c.484.29	yes	42	5.3	odd	4
4025.2.a.bd.1.8		21	1.1	even	1	trivial
4025.2.a.be.1.14		21	5.4	even	2

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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:	\( N \)	\(=\)	\( 4025 = 5^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4025.a (trivial)

\(f(q)\)	\(=\)	\(q-1.30923 q^{2} -2.43985 q^{3} -0.285909 q^{4} +3.19433 q^{6} -1.00000 q^{7} +2.99279 q^{8} +2.95286 q^{9} +O(q^{10})\)	\(q-1.30923 q^{2} -2.43985 q^{3} -0.285909 q^{4} +3.19433 q^{6} -1.00000 q^{7} +2.99279 q^{8} +2.95286 q^{9} +0.628746 q^{11} +0.697574 q^{12} +3.82086 q^{13} +1.30923 q^{14} -3.34644 q^{16} -5.22375 q^{17} -3.86598 q^{18} +6.31328 q^{19} +2.43985 q^{21} -0.823175 q^{22} -1.00000 q^{23} -7.30194 q^{24} -5.00239 q^{26} +0.115025 q^{27} +0.285909 q^{28} +3.73904 q^{29} +9.35403 q^{31} -1.60431 q^{32} -1.53404 q^{33} +6.83911 q^{34} -0.844247 q^{36} +7.74846 q^{37} -8.26556 q^{38} -9.32231 q^{39} +11.8024 q^{41} -3.19433 q^{42} +4.67712 q^{43} -0.179764 q^{44} +1.30923 q^{46} -11.3296 q^{47} +8.16480 q^{48} +1.00000 q^{49} +12.7452 q^{51} -1.09242 q^{52} -8.98590 q^{53} -0.150594 q^{54} -2.99279 q^{56} -15.4034 q^{57} -4.89527 q^{58} -4.34377 q^{59} -4.46944 q^{61} -12.2466 q^{62} -2.95286 q^{63} +8.79329 q^{64} +2.00842 q^{66} +6.33927 q^{67} +1.49352 q^{68} +2.43985 q^{69} +13.0698 q^{71} +8.83727 q^{72} +7.44507 q^{73} -10.1445 q^{74} -1.80502 q^{76} -0.628746 q^{77} +12.2051 q^{78} -12.1355 q^{79} -9.13921 q^{81} -15.4521 q^{82} +0.664922 q^{83} -0.697574 q^{84} -6.12344 q^{86} -9.12268 q^{87} +1.88170 q^{88} -9.82152 q^{89} -3.82086 q^{91} +0.285909 q^{92} -22.8224 q^{93} +14.8330 q^{94} +3.91426 q^{96} -12.8353 q^{97} -1.30923 q^{98} +1.85660 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q - 2 q^{2} + q^{3} + 30 q^{4} + 6 q^{6} - 21 q^{7} - 6 q^{8} + 30 q^{9}+O(q^{10}) \) 21 * q - 2 * q^2 + q^3 + 30 * q^4 + 6 * q^6 - 21 * q^7 - 6 * q^8 + 30 * q^9	\( 21 q - 2 q^{2} + q^{3} + 30 q^{4} + 6 q^{6} - 21 q^{7} - 6 q^{8} + 30 q^{9} + 7 q^{11} + 22 q^{12} + 3 q^{13} + 2 q^{14} + 56 q^{16} - 7 q^{17} + 24 q^{19} - q^{21} - 4 q^{22} - 21 q^{23} + 24 q^{24} - 2 q^{26} + 19 q^{27} - 30 q^{28} + 11 q^{29} + 46 q^{31} + 6 q^{32} + 3 q^{33} + 28 q^{34} + 58 q^{36} - 24 q^{37} + 4 q^{38} + 31 q^{39} + 14 q^{41} - 6 q^{42} - 18 q^{43} + 12 q^{44} + 2 q^{46} + 25 q^{47} + 36 q^{48} + 21 q^{49} + 17 q^{51} + 8 q^{52} - 22 q^{53} - 6 q^{54} + 6 q^{56} - 40 q^{57} - 6 q^{58} + 10 q^{59} + 38 q^{61} + 54 q^{62} - 30 q^{63} + 100 q^{64} + 38 q^{66} - 12 q^{67} - 18 q^{68} - q^{69} + 56 q^{71} - 42 q^{72} + 40 q^{73} - 20 q^{74} + 60 q^{76} - 7 q^{77} - 38 q^{78} + 49 q^{79} + 57 q^{81} - 16 q^{82} + 2 q^{83} - 22 q^{84} + 16 q^{86} + 23 q^{87} - 12 q^{88} + 28 q^{89} - 3 q^{91} - 30 q^{92} + 30 q^{93} + 66 q^{94} + 46 q^{96} + q^{97} - 2 q^{98} - 2 q^{99}+O(q^{100}) \) 21 * q - 2 * q^2 + q^3 + 30 * q^4 + 6 * q^6 - 21 * q^7 - 6 * q^8 + 30 * q^9 + 7 * q^11 + 22 * q^12 + 3 * q^13 + 2 * q^14 + 56 * q^16 - 7 * q^17 + 24 * q^19 - q^21 - 4 * q^22 - 21 * q^23 + 24 * q^24 - 2 * q^26 + 19 * q^27 - 30 * q^28 + 11 * q^29 + 46 * q^31 + 6 * q^32 + 3 * q^33 + 28 * q^34 + 58 * q^36 - 24 * q^37 + 4 * q^38 + 31 * q^39 + 14 * q^41 - 6 * q^42 - 18 * q^43 + 12 * q^44 + 2 * q^46 + 25 * q^47 + 36 * q^48 + 21 * q^49 + 17 * q^51 + 8 * q^52 - 22 * q^53 - 6 * q^54 + 6 * q^56 - 40 * q^57 - 6 * q^58 + 10 * q^59 + 38 * q^61 + 54 * q^62 - 30 * q^63 + 100 * q^64 + 38 * q^66 - 12 * q^67 - 18 * q^68 - q^69 + 56 * q^71 - 42 * q^72 + 40 * q^73 - 20 * q^74 + 60 * q^76 - 7 * q^77 - 38 * q^78 + 49 * q^79 + 57 * q^81 - 16 * q^82 + 2 * q^83 - 22 * q^84 + 16 * q^86 + 23 * q^87 - 12 * q^88 + 28 * q^89 - 3 * q^91 - 30 * q^92 + 30 * q^93 + 66 * q^94 + 46 * q^96 + q^97 - 2 * q^98 - 2 * q^99

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