LMFDB - Embedded newform 4025.2.a.bd.1.7

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			1.7
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)

$f(q)$	$=$	$q-1.50084 q^{2} +0.816695 q^{3} +0.252529 q^{4} -1.22573 q^{6} -1.00000 q^{7} +2.62268 q^{8} -2.33301 q^{9} +O(q^{10})$	\(q-1.50084 q^{2} +0.816695 q^{3} +0.252529 q^{4} -1.22573 q^{6} -1.00000 q^{7} +2.62268 q^{8} -2.33301 q^{9} -5.57614 q^{11} +0.206239 q^{12} -4.04443 q^{13} +1.50084 q^{14} -4.44129 q^{16} -6.57649 q^{17} +3.50148 q^{18} +0.0315796 q^{19} -0.816695 q^{21} +8.36892 q^{22} -1.00000 q^{23} +2.14193 q^{24} +6.07006 q^{26} -4.35544 q^{27} -0.252529 q^{28} -6.35790 q^{29} +1.36927 q^{31} +1.42032 q^{32} -4.55401 q^{33} +9.87028 q^{34} -0.589153 q^{36} +2.86325 q^{37} -0.0473961 q^{38} -3.30307 q^{39} -4.54127 q^{41} +1.22573 q^{42} -1.93731 q^{43} -1.40814 q^{44} +1.50084 q^{46} -1.87483 q^{47} -3.62718 q^{48} +1.00000 q^{49} -5.37099 q^{51} -1.02134 q^{52} -1.12976 q^{53} +6.53684 q^{54} -2.62268 q^{56} +0.0257909 q^{57} +9.54221 q^{58} +5.50239 q^{59} +12.8429 q^{61} -2.05506 q^{62} +2.33301 q^{63} +6.75090 q^{64} +6.83485 q^{66} +1.66458 q^{67} -1.66075 q^{68} -0.816695 q^{69} +10.4018 q^{71} -6.11873 q^{72} -7.21105 q^{73} -4.29728 q^{74} +0.00797478 q^{76} +5.57614 q^{77} +4.95739 q^{78} +5.58626 q^{79} +3.44196 q^{81} +6.81573 q^{82} -11.1128 q^{83} -0.206239 q^{84} +2.90759 q^{86} -5.19247 q^{87} -14.6244 q^{88} +16.6306 q^{89} +4.04443 q^{91} -0.252529 q^{92} +1.11828 q^{93} +2.81383 q^{94} +1.15997 q^{96} +13.8986 q^{97} -1.50084 q^{98} +13.0092 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.50084	−1.06126	−0.530628	−	0.847605i	$-0.678044\pi$
$2$	−1.50084	−1.06126	−0.530628	+	0.847605i	$0.678044\pi$
$3$	0.816695	0.471519	0.235760	−	0.971811i	$-0.424242\pi$
$3$	0.816695	0.471519	0.235760	+	0.971811i	$0.424242\pi$
$4$	0.252529	0.126265
$5$	0	0
$5$	0	0
$6$	−1.22573	−0.500403
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	2.62268	0.927257
$9$	−2.33301	−0.777670
$10$	0	0
$11$	−5.57614	−1.68127	−0.840635	−	0.541601i	$-0.817818\pi$
$11$	−5.57614	−1.68127	−0.840635	+	0.541601i	$0.817818\pi$
$12$	0.206239	0.0595362
$13$	−4.04443	−1.12172	−0.560862	−	0.827909i	$-0.689530\pi$
$13$	−4.04443	−1.12172	−0.560862	+	0.827909i	$0.689530\pi$
$14$	1.50084	0.401117
$15$	0	0
$16$	−4.44129	−1.11032
$17$	−6.57649	−1.59503	−0.797516	−	0.603297i	$-0.793853\pi$
$17$	−6.57649	−1.59503	−0.797516	+	0.603297i	$0.793853\pi$
$18$	3.50148	0.825307
$19$	0.0315796	0.00724487	0.00362243	−	0.999993i	$-0.498847\pi$
$19$	0.0315796	0.00724487	0.00362243	+	0.999993i	$0.498847\pi$
$20$	0	0
$21$	−0.816695	−0.178218
$22$	8.36892	1.78426
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	2.14193	0.437220
$25$	0	0
$26$	6.07006	1.19044
$27$	−4.35544	−0.838205
$28$	−0.252529	−0.0477235
$29$	−6.35790	−1.18063	−0.590317	−	0.807172i	$-0.700997\pi$
$29$	−6.35790	−1.18063	−0.590317	+	0.807172i	$0.700997\pi$
$30$	0	0
$31$	1.36927	0.245929	0.122964	−	0.992411i	$-0.460760\pi$
$31$	1.36927	0.245929	0.122964	+	0.992411i	$0.460760\pi$
$32$	1.42032	0.251079
$33$	−4.55401	−0.792752
$34$	9.87028	1.69274
$35$	0	0
$36$	−0.589153	−0.0981921
$37$	2.86325	0.470715	0.235357	−	0.971909i	$-0.424374\pi$
$37$	2.86325	0.470715	0.235357	+	0.971909i	$0.424374\pi$
$38$	−0.0473961	−0.00768866
$39$	−3.30307	−0.528914
$40$	0	0
$41$	−4.54127	−0.709227	−0.354613	−	0.935013i	$-0.615388\pi$
$41$	−4.54127	−0.709227	−0.354613	+	0.935013i	$0.615388\pi$
$42$	1.22573	0.189134
$43$	−1.93731	−0.295437	−0.147718	−	0.989029i	$-0.547193\pi$
$43$	−1.93731	−0.295437	−0.147718	+	0.989029i	$0.547193\pi$
$44$	−1.40814	−0.212285
$45$	0	0
$46$	1.50084	0.221287
$47$	−1.87483	−0.273472	−0.136736	−	0.990608i	$-0.543661\pi$
$47$	−1.87483	−0.273472	−0.136736	+	0.990608i	$0.543661\pi$
$48$	−3.62718	−0.523538
$49$	1.00000	0.142857
$50$	0	0
$51$	−5.37099	−0.752089
$52$	−1.02134	−0.141634
$53$	−1.12976	−0.155184	−0.0775919	−	0.996985i	$-0.524723\pi$
$53$	−1.12976	−0.155184	−0.0775919	+	0.996985i	$0.524723\pi$
$54$	6.53684	0.889551
$55$	0	0
$56$	−2.62268	−0.350470
$57$	0.0257909	0.00341609
$58$	9.54221	1.25295
$59$	5.50239	0.716350	0.358175	−	0.933654i	$-0.383399\pi$
$59$	5.50239	0.716350	0.358175	+	0.933654i	$0.383399\pi$
$60$	0	0
$61$	12.8429	1.64437	0.822185	−	0.569221i	$-0.192755\pi$
$61$	12.8429	1.64437	0.822185	+	0.569221i	$0.192755\pi$
$62$	−2.05506	−0.260993
$63$	2.33301	0.293931
$64$	6.75090	0.843863
$65$	0	0
$66$	6.83485	0.841312
$67$	1.66458	0.203361	0.101680	−	0.994817i	$-0.467578\pi$
$67$	1.66458	0.203361	0.101680	+	0.994817i	$0.467578\pi$
$68$	−1.66075	−0.201396
$69$	−0.816695	−0.0983186
$70$	0	0
$71$	10.4018	1.23446	0.617231	−	0.786782i	$-0.288254\pi$
$71$	10.4018	1.23446	0.617231	+	0.786782i	$0.288254\pi$
$72$	−6.11873	−0.721100
$73$	−7.21105	−0.843990	−0.421995	−	0.906598i	$-0.638670\pi$
$73$	−7.21105	−0.843990	−0.421995	+	0.906598i	$0.638670\pi$
$74$	−4.29728	−0.499549
$75$	0	0
$76$	0.00797478	0.000914770 0
$77$	5.57614	0.635461
$78$	4.95739	0.561313
$79$	5.58626	0.628504	0.314252	−	0.949340i	$-0.398246\pi$
$79$	5.58626	0.628504	0.314252	+	0.949340i	$0.398246\pi$
$80$	0	0
$81$	3.44196	0.382440
$82$	6.81573	0.752671
$83$	−11.1128	−1.21979	−0.609894	−	0.792483i	$-0.708788\pi$
$83$	−11.1128	−1.21979	−0.609894	+	0.792483i	$0.708788\pi$
$84$	−0.206239	−0.0225026
$85$	0	0
$86$	2.90759	0.313534
$87$	−5.19247	−0.556691
$88$	−14.6244	−1.55897
$89$	16.6306	1.76284	0.881418	−	0.472337i	$-0.156590\pi$
$89$	16.6306	1.76284	0.881418	+	0.472337i	$0.156590\pi$
$90$	0	0
$91$	4.04443	0.423972
$92$	−0.252529	−0.0263280
$93$	1.11828	0.115960
$94$	2.81383	0.290224
$95$	0	0
$96$	1.15997	0.118388
$97$	13.8986	1.41119	0.705597	−	0.708614i	$-0.250679\pi$
$97$	13.8986	1.41119	0.705597	+	0.708614i	$0.250679\pi$
$98$	−1.50084	−0.151608
$99$	13.0092	1.30747
$100$	0	0
$101$	8.56886	0.852634	0.426317	−	0.904574i	$-0.359811\pi$
$101$	8.56886	0.852634	0.426317	+	0.904574i	$0.359811\pi$
$102$	8.06101	0.798159
$103$	−7.41286	−0.730411	−0.365205	−	0.930927i	$-0.619001\pi$
$103$	−7.41286	−0.730411	−0.365205	+	0.930927i	$0.619001\pi$
$104$	−10.6072	−1.04013
$105$	0	0
$106$	1.69559	0.164690
$107$	3.54317	0.342532	0.171266	−	0.985225i	$-0.445214\pi$
$107$	3.54317	0.342532	0.171266	+	0.985225i	$0.445214\pi$
$108$	−1.09988	−0.105836
$109$	−12.4712	−1.19452	−0.597261	−	0.802047i	$-0.703744\pi$
$109$	−12.4712	−1.19452	−0.597261	+	0.802047i	$0.703744\pi$
$110$	0	0
$111$	2.33840	0.221951
$112$	4.44129	0.419662
$113$	9.56214	0.899530	0.449765	−	0.893147i	$-0.351508\pi$
$113$	9.56214	0.899530	0.449765	+	0.893147i	$0.351508\pi$
$114$	−0.0387082	−0.00362535
$115$	0	0
$116$	−1.60556	−0.149072
$117$	9.43569	0.872330
$118$	−8.25822	−0.760231
$119$	6.57649	0.602866
$120$	0	0
$121$	20.0934	1.82667
$122$	−19.2752	−1.74510
$123$	−3.70883	−0.334414
$124$	0.345781	0.0310521
$125$	0	0
$126$	−3.50148	−0.311937
$127$	−16.6954	−1.48148	−0.740739	−	0.671793i	$-0.765524\pi$
$127$	−16.6954	−1.48148	−0.740739	+	0.671793i	$0.765524\pi$
$128$	−12.9727	−1.14663
$129$	−1.58219	−0.139304
$130$	0	0
$131$	−1.51048	−0.131972	−0.0659858	−	0.997821i	$-0.521019\pi$
$131$	−1.51048	−0.131972	−0.0659858	+	0.997821i	$0.521019\pi$
$132$	−1.15002	−0.100096
$133$	−0.0315796	−0.00273830
$134$	−2.49827	−0.215818
$135$	0	0
$136$	−17.2480	−1.47901
$137$	−5.80267	−0.495756	−0.247878	−	0.968791i	$-0.579733\pi$
$137$	−5.80267	−0.495756	−0.247878	+	0.968791i	$0.579733\pi$
$138$	1.22573	0.104341
$139$	−7.01912	−0.595354	−0.297677	−	0.954667i	$-0.596212\pi$
$139$	−7.01912	−0.595354	−0.297677	+	0.954667i	$0.596212\pi$
$140$	0	0
$141$	−1.53117	−0.128947
$142$	−15.6114	−1.31008
$143$	22.5523	1.88592
$144$	10.3616	0.863464
$145$	0	0
$146$	10.8227	0.895689
$147$	0.816695	0.0673599
$148$	0.723053	0.0594346
$149$	−21.2940	−1.74447	−0.872235	−	0.489087i	$-0.837330\pi$
$149$	−21.2940	−1.74447	−0.872235	+	0.489087i	$0.837330\pi$
$150$	0	0
$151$	2.55312	0.207770	0.103885	−	0.994589i	$-0.466873\pi$
$151$	2.55312	0.207770	0.103885	+	0.994589i	$0.466873\pi$
$152$	0.0828233	0.00671785
$153$	15.3430	1.24041
$154$	−8.36892	−0.674386
$155$	0	0
$156$	−0.834121	−0.0667831
$157$	−7.81119	−0.623401	−0.311700	−	0.950180i	$-0.600899\pi$
$157$	−7.81119	−0.623401	−0.311700	+	0.950180i	$0.600899\pi$
$158$	−8.38410	−0.667003
$159$	−0.922666	−0.0731722
$160$	0	0
$161$	1.00000	0.0788110
$162$	−5.16584	−0.405866
$163$	−23.2397	−1.82027	−0.910137	−	0.414307i	$-0.864024\pi$
$163$	−23.2397	−1.82027	−0.910137	+	0.414307i	$0.864024\pi$
$164$	−1.14680	−0.0895502
$165$	0	0
$166$	16.6786	1.29451
$167$	−10.4503	−0.808672	−0.404336	−	0.914611i	$-0.632497\pi$
$167$	−10.4503	−0.808672	−0.404336	+	0.914611i	$0.632497\pi$
$168$	−2.14193	−0.165253
$169$	3.35743	0.258264
$170$	0	0
$171$	−0.0736756	−0.00563411
$172$	−0.489226	−0.0373032
$173$	−11.1955	−0.851177	−0.425588	−	0.904917i	$-0.639933\pi$
$173$	−11.1955	−0.851177	−0.425588	+	0.904917i	$0.639933\pi$
$174$	7.79308	0.590792
$175$	0	0
$176$	24.7653	1.86675
$177$	4.49377	0.337773
$178$	−24.9599	−1.87082
$179$	−6.43423	−0.480917	−0.240458	−	0.970659i	$-0.577298\pi$
$179$	−6.43423	−0.480917	−0.240458	+	0.970659i	$0.577298\pi$
$180$	0	0
$181$	−16.3430	−1.21476	−0.607382	−	0.794410i	$-0.707780\pi$
$181$	−16.3430	−1.21476	−0.607382	+	0.794410i	$0.707780\pi$
$182$	−6.07006	−0.449942
$183$	10.4888	0.775352
$184$	−2.62268	−0.193346
$185$	0	0
$186$	−1.67836	−0.123063
$187$	36.6714	2.68168
$188$	−0.473449	−0.0345298
$189$	4.35544	0.316812
$190$	0	0
$191$	15.4727	1.11957	0.559783	−	0.828639i	$-0.310884\pi$
$191$	15.4727	1.11957	0.559783	+	0.828639i	$0.310884\pi$
$192$	5.51343	0.397898
$193$	17.7528	1.27787	0.638936	−	0.769260i	$-0.279375\pi$
$193$	17.7528	1.27787	0.638936	+	0.769260i	$0.279375\pi$
$194$	−20.8597	−1.49764
$195$	0	0
$196$	0.252529	0.0180378
$197$	12.4152	0.884546	0.442273	−	0.896880i	$-0.354172\pi$
$197$	12.4152	0.884546	0.442273	+	0.896880i	$0.354172\pi$
$198$	−19.5248	−1.38756
$199$	13.7043	0.971473	0.485736	−	0.874105i	$-0.338552\pi$
$199$	13.7043	0.971473	0.485736	+	0.874105i	$0.338552\pi$
$200$	0	0
$201$	1.35945	0.0958885
$202$	−12.8605	−0.904863
$203$	6.35790	0.446237
$204$	−1.35633	−0.0949621
$205$	0	0
$206$	11.1255	0.775153
$207$	2.33301	0.162155
$208$	17.9625	1.24547
$209$	−0.176093	−0.0121806
$210$	0	0
$211$	16.4605	1.13319	0.566595	−	0.823996i	$-0.308260\pi$
$211$	16.4605	1.13319	0.566595	+	0.823996i	$0.308260\pi$
$212$	−0.285296	−0.0195942
$213$	8.49508	0.582073
$214$	−5.31775	−0.363514
$215$	0	0
$216$	−11.4229	−0.777232
$217$	−1.36927	−0.0929523
$218$	18.7173	1.26769
$219$	−5.88923	−0.397957
$220$	0	0
$221$	26.5982	1.78919
$222$	−3.50957	−0.235547
$223$	−14.8249	−0.992749	−0.496374	−	0.868108i	$-0.665336\pi$
$223$	−14.8249	−0.992749	−0.496374	+	0.868108i	$0.665336\pi$
$224$	−1.42032	−0.0948988
$225$	0	0
$226$	−14.3513	−0.954632
$227$	−18.2901	−1.21396	−0.606979	−	0.794718i	$-0.707619\pi$
$227$	−18.2901	−1.21396	−0.606979	+	0.794718i	$0.707619\pi$
$228$	0.00651296	0.000431332 0
$229$	26.0017	1.71824	0.859120	−	0.511774i	$-0.171011\pi$
$229$	26.0017	1.71824	0.859120	+	0.511774i	$0.171011\pi$
$230$	0	0
$231$	4.55401	0.299632
$232$	−16.6747	−1.09475
$233$	9.49697	0.622167	0.311084	−	0.950383i	$-0.399308\pi$
$233$	9.49697	0.622167	0.311084	+	0.950383i	$0.399308\pi$
$234$	−14.1615	−0.925766
$235$	0	0
$236$	1.38951	0.0904496
$237$	4.56228	0.296352
$238$	−9.87028	−0.639795
$239$	−26.3213	−1.70258	−0.851291	−	0.524694i	$-0.824180\pi$
$239$	−26.3213	−1.70258	−0.851291	+	0.524694i	$0.824180\pi$
$240$	0	0
$241$	−11.2193	−0.722701	−0.361351	−	0.932430i	$-0.617684\pi$
$241$	−11.2193	−0.722701	−0.361351	+	0.932430i	$0.617684\pi$
$242$	−30.1570	−1.93857
$243$	15.8774	1.01853
$244$	3.24322	0.207626
$245$	0	0
$246$	5.56637	0.354899
$247$	−0.127722	−0.00812674
$248$	3.59116	0.228039
$249$	−9.07578	−0.575154
$250$	0	0
$251$	−6.14342	−0.387769	−0.193885	−	0.981024i	$-0.562109\pi$
$251$	−6.14342	−0.387769	−0.193885	+	0.981024i	$0.562109\pi$
$252$	0.589153	0.0371131
$253$	5.57614	0.350569
$254$	25.0572	1.57223
$255$	0	0
$256$	5.96814	0.373009
$257$	22.3978	1.39714	0.698568	−	0.715544i	$-0.253821\pi$
$257$	22.3978	1.39714	0.698568	+	0.715544i	$0.253821\pi$
$258$	2.37462	0.147837
$259$	−2.86325	−0.177913
$260$	0	0
$261$	14.8330	0.918142
$262$	2.26700	0.140056
$263$	−20.5242	−1.26558	−0.632789	−	0.774324i	$-0.718090\pi$
$263$	−20.5242	−1.26558	−0.632789	+	0.774324i	$0.718090\pi$
$264$	−11.9437	−0.735085
$265$	0	0
$266$	0.0473961	0.00290604
$267$	13.5821	0.831211
$268$	0.420355	0.0256772
$269$	−18.4098	−1.12246	−0.561232	−	0.827658i	$-0.689673\pi$
$269$	−18.4098	−1.12246	−0.561232	+	0.827658i	$0.689673\pi$
$270$	0	0
$271$	4.23951	0.257532	0.128766	−	0.991675i	$-0.458898\pi$
$271$	4.23951	0.257532	0.128766	+	0.991675i	$0.458898\pi$
$272$	29.2081	1.77100
$273$	3.30307	0.199911
$274$	8.70890	0.526124
$275$	0	0
$276$	−0.206239	−0.0124141
$277$	3.50266	0.210454	0.105227	−	0.994448i	$-0.466443\pi$
$277$	3.50266	0.210454	0.105227	+	0.994448i	$0.466443\pi$
$278$	10.5346	0.631823
$279$	−3.19452	−0.191251
$280$	0	0
$281$	−17.7739	−1.06030	−0.530151	−	0.847903i	$-0.677865\pi$
$281$	−17.7739	−1.06030	−0.530151	+	0.847903i	$0.677865\pi$
$282$	2.29804	0.136846
$283$	24.4579	1.45387	0.726934	−	0.686707i	$-0.240944\pi$
$283$	24.4579	1.45387	0.726934	+	0.686707i	$0.240944\pi$
$284$	2.62675	0.155869
$285$	0	0
$286$	−33.8475	−2.00145
$287$	4.54127	0.268063
$288$	−3.31361	−0.195256
$289$	26.2502	1.54413
$290$	0	0
$291$	11.3510	0.665405
$292$	−1.82100	−0.106566
$293$	1.58615	0.0926639	0.0463320	−	0.998926i	$-0.485247\pi$
$293$	1.58615	0.0926639	0.0463320	+	0.998926i	$0.485247\pi$
$294$	−1.22573	−0.0714861
$295$	0	0
$296$	7.50938	0.436474
$297$	24.2866	1.40925
$298$	31.9589	1.85133
$299$	4.04443	0.233896
$300$	0	0
$301$	1.93731	0.111665
$302$	−3.83183	−0.220497
$303$	6.99815	0.402033
$304$	−0.140254	−0.00804413
$305$	0	0
$306$	−23.0274	−1.31639
$307$	9.24426	0.527598	0.263799	−	0.964578i	$-0.415024\pi$
$307$	9.24426	0.527598	0.263799	+	0.964578i	$0.415024\pi$
$308$	1.40814	0.0802361
$309$	−6.05405	−0.344403
$310$	0	0
$311$	−19.4611	−1.10354	−0.551768	−	0.833998i	$-0.686047\pi$
$311$	−19.4611	−1.10354	−0.551768	+	0.833998i	$0.686047\pi$
$312$	−8.66289	−0.490439
$313$	−25.4236	−1.43702	−0.718512	−	0.695514i	$-0.755177\pi$
$313$	−25.4236	−1.43702	−0.718512	+	0.695514i	$0.755177\pi$
$314$	11.7234	0.661588
$315$	0	0
$316$	1.41069	0.0793577
$317$	6.44839	0.362178	0.181089	−	0.983467i	$-0.442038\pi$
$317$	6.44839	0.362178	0.181089	+	0.983467i	$0.442038\pi$
$318$	1.38478	0.0776544
$319$	35.4526	1.98496
$320$	0	0
$321$	2.89369	0.161510
$322$	−1.50084	−0.0836387
$323$	−0.207683	−0.0115558
$324$	0.869194	0.0482886
$325$	0	0
$326$	34.8791	1.93178
$327$	−10.1851	−0.563240
$328$	−11.9103	−0.657636
$329$	1.87483	0.103363
$330$	0	0
$331$	23.7887	1.30755	0.653774	−	0.756690i	$-0.273185\pi$
$331$	23.7887	1.30755	0.653774	+	0.756690i	$0.273185\pi$
$332$	−2.80631	−0.154016
$333$	−6.67998	−0.366061
$334$	15.6843	0.858208
$335$	0	0
$336$	3.62718	0.197879
$337$	−18.0792	−0.984838	−0.492419	−	0.870358i	$-0.663887\pi$
$337$	−18.0792	−0.984838	−0.492419	+	0.870358i	$0.663887\pi$
$338$	−5.03897	−0.274084
$339$	7.80935	0.424146
$340$	0	0
$341$	−7.63526	−0.413473
$342$	0.110575	0.00597924
$343$	−1.00000	−0.0539949
$344$	−5.08094	−0.273946
$345$	0	0
$346$	16.8027	0.903316
$347$	3.93025	0.210987	0.105494	−	0.994420i	$-0.466358\pi$
$347$	3.93025	0.210987	0.105494	+	0.994420i	$0.466358\pi$
$348$	−1.31125	−0.0702904
$349$	−9.77290	−0.523131	−0.261566	−	0.965186i	$-0.584239\pi$
$349$	−9.77290	−0.523131	−0.261566	+	0.965186i	$0.584239\pi$
$350$	0	0
$351$	17.6153	0.940235
$352$	−7.91989	−0.422131
$353$	−23.1310	−1.23114	−0.615570	−	0.788082i	$-0.711074\pi$
$353$	−23.1310	−1.23114	−0.615570	+	0.788082i	$0.711074\pi$
$354$	−6.74445	−0.358463
$355$	0	0
$356$	4.19970	0.222584
$357$	5.37099	0.284263
$358$	9.65677	0.510376
$359$	6.64008	0.350450	0.175225	−	0.984528i	$-0.443935\pi$
$359$	6.64008	0.350450	0.175225	+	0.984528i	$0.443935\pi$
$360$	0	0
$361$	−18.9990	−0.999948
$362$	24.5282	1.28918
$363$	16.4102	0.861311
$364$	1.02134	0.0535326
$365$	0	0
$366$	−15.7420	−0.822847
$367$	12.6692	0.661325	0.330662	−	0.943749i	$-0.392728\pi$
$367$	12.6692	0.661325	0.330662	+	0.943749i	$0.392728\pi$
$368$	4.44129	0.231518
$369$	10.5948	0.551544
$370$	0	0
$371$	1.12976	0.0586540
$372$	0.282398	0.0146416
$373$	6.00241	0.310793	0.155396	−	0.987852i	$-0.450335\pi$
$373$	6.00241	0.310793	0.155396	+	0.987852i	$0.450335\pi$
$374$	−55.0381	−2.84595
$375$	0	0
$376$	−4.91708	−0.253579
$377$	25.7141	1.32434
$378$	−6.53684	−0.336219
$379$	31.3566	1.61068	0.805340	−	0.592814i	$-0.201983\pi$
$379$	31.3566	1.61068	0.805340	+	0.592814i	$0.201983\pi$
$380$	0	0
$381$	−13.6351	−0.698545
$382$	−23.2221	−1.18815
$383$	−5.53739	−0.282948	−0.141474	−	0.989942i	$-0.545184\pi$
$383$	−5.53739	−0.282948	−0.141474	+	0.989942i	$0.545184\pi$
$384$	−10.5947	−0.540660
$385$	0	0
$386$	−26.6441	−1.35615
$387$	4.51976	0.229752
$388$	3.50981	0.178184
$389$	8.20381	0.415950	0.207975	−	0.978134i	$-0.433313\pi$
$389$	8.20381	0.415950	0.207975	+	0.978134i	$0.433313\pi$
$390$	0	0
$391$	6.57649	0.332587
$392$	2.62268	0.132465
$393$	−1.23361	−0.0622272
$394$	−18.6333	−0.938730
$395$	0	0
$396$	3.28520	0.165087
$397$	−9.62114	−0.482871	−0.241436	−	0.970417i	$-0.577618\pi$
$397$	−9.62114	−0.482871	−0.241436	+	0.970417i	$0.577618\pi$
$398$	−20.5680	−1.03098
$399$	−0.0257909	−0.00129116
$400$	0	0
$401$	26.8333	1.33999	0.669996	−	0.742365i	$-0.266296\pi$
$401$	26.8333	1.33999	0.669996	+	0.742365i	$0.266296\pi$
$402$	−2.04033	−0.101762
$403$	−5.53793	−0.275864
$404$	2.16389	0.107657
$405$	0	0
$406$	−9.54221	−0.473572
$407$	−15.9659	−0.791399
$408$	−14.0864	−0.697380
$409$	36.4908	1.80436	0.902178	−	0.431365i	$-0.141968\pi$
$409$	36.4908	1.80436	0.902178	+	0.431365i	$0.141968\pi$
$410$	0	0
$411$	−4.73902	−0.233758
$412$	−1.87196	−0.0922250
$413$	−5.50239	−0.270755
$414$	−3.50148	−0.172088
$415$	0	0
$416$	−5.74437	−0.281641
$417$	−5.73248	−0.280721
$418$	0.264287	0.0129267
$419$	−11.8204	−0.577465	−0.288733	−	0.957410i	$-0.593234\pi$
$419$	−11.8204	−0.577465	−0.288733	+	0.957410i	$0.593234\pi$
$420$	0	0
$421$	−10.0249	−0.488583	−0.244291	−	0.969702i	$-0.578555\pi$
$421$	−10.0249	−0.488583	−0.244291	+	0.969702i	$0.578555\pi$
$422$	−24.7047	−1.20261
$423$	4.37400	0.212671
$424$	−2.96299	−0.143895
$425$	0	0
$426$	−12.7498	−0.617728
$427$	−12.8429	−0.621513
$428$	0.894754	0.0432496
$429$	18.4184	0.889248
$430$	0	0
$431$	−27.9864	−1.34806	−0.674029	−	0.738705i	$-0.735438\pi$
$431$	−27.9864	−1.34806	−0.674029	+	0.738705i	$0.735438\pi$
$432$	19.3438	0.930678
$433$	17.0989	0.821719	0.410859	−	0.911699i	$-0.365229\pi$
$433$	17.0989	0.821719	0.410859	+	0.911699i	$0.365229\pi$
$434$	2.05506	0.0986462
$435$	0	0
$436$	−3.14933	−0.150826
$437$	−0.0315796	−0.00151066
$438$	8.83881	0.422335
$439$	24.6894	1.17836	0.589180	−	0.808002i	$-0.299451\pi$
$439$	24.6894	1.17836	0.589180	+	0.808002i	$0.299451\pi$
$440$	0	0
$441$	−2.33301	−0.111096
$442$	−39.9197	−1.89878
$443$	22.3512	1.06194	0.530968	−	0.847392i	$-0.321828\pi$
$443$	22.3512	1.06194	0.530968	+	0.847392i	$0.321828\pi$
$444$	0.590514	0.0280246
$445$	0	0
$446$	22.2499	1.05356
$447$	−17.3907	−0.822551
$448$	−6.75090	−0.318950
$449$	−14.0885	−0.664878	−0.332439	−	0.943125i	$-0.607871\pi$
$449$	−14.0885	−0.664878	−0.332439	+	0.943125i	$0.607871\pi$
$450$	0	0
$451$	25.3228	1.19240
$452$	2.41472	0.113579
$453$	2.08512	0.0979675
$454$	27.4506	1.28832
$455$	0	0
$456$	0.0676414	0.00316760
$457$	−29.8888	−1.39814	−0.699070	−	0.715054i	$-0.746402\pi$
$457$	−29.8888	−1.39814	−0.699070	+	0.715054i	$0.746402\pi$
$458$	−39.0245	−1.82349
$459$	28.6435	1.33697
$460$	0	0
$461$	−29.6760	−1.38215	−0.691074	−	0.722784i	$-0.742862\pi$
$461$	−29.6760	−1.38215	−0.691074	+	0.722784i	$0.742862\pi$
$462$	−6.83485	−0.317986
$463$	−13.0213	−0.605153	−0.302576	−	0.953125i	$-0.597847\pi$
$463$	−13.0213	−0.605153	−0.302576	+	0.953125i	$0.597847\pi$
$464$	28.2373	1.31088
$465$	0	0
$466$	−14.2535	−0.660279
$467$	−9.14341	−0.423107	−0.211553	−	0.977366i	$-0.567852\pi$
$467$	−9.14341	−0.423107	−0.211553	+	0.977366i	$0.567852\pi$
$468$	2.38279	0.110144
$469$	−1.66458	−0.0768631
$470$	0	0
$471$	−6.37936	−0.293945
$472$	14.4310	0.664241
$473$	10.8027	0.496709
$474$	−6.84726	−0.314505
$475$	0	0
$476$	1.66075	0.0761206
$477$	2.63573	0.120682
$478$	39.5041	1.80688
$479$	−9.02717	−0.412462	−0.206231	−	0.978503i	$-0.566120\pi$
$479$	−9.02717	−0.412462	−0.206231	+	0.978503i	$0.566120\pi$
$480$	0	0
$481$	−11.5802	−0.528012
$482$	16.8385	0.766971
$483$	0.816695	0.0371609
$484$	5.07416	0.230644
$485$	0	0
$486$	−23.8294	−1.08092
$487$	32.3124	1.46421	0.732107	−	0.681189i	$-0.238537\pi$
$487$	32.3124	1.46421	0.732107	+	0.681189i	$0.238537\pi$
$488$	33.6829	1.52475
$489$	−18.9798	−0.858294
$490$	0	0
$491$	20.5131	0.925742	0.462871	−	0.886426i	$-0.346819\pi$
$491$	20.5131	0.925742	0.462871	+	0.886426i	$0.346819\pi$
$492$	−0.936588	−0.0422246
$493$	41.8127	1.88315
$494$	0.191690	0.00862455
$495$	0	0
$496$	−6.08133	−0.273060
$497$	−10.4018	−0.466583
$498$	13.6213	0.610386
$499$	24.9439	1.11664	0.558322	−	0.829624i	$-0.311445\pi$
$499$	24.9439	1.11664	0.558322	+	0.829624i	$0.311445\pi$
$500$	0	0
$501$	−8.53474	−0.381304
$502$	9.22031	0.411523
$503$	18.3089	0.816353	0.408177	−	0.912903i	$-0.366165\pi$
$503$	18.3089	0.816353	0.408177	+	0.912903i	$0.366165\pi$
$504$	6.11873	0.272550
$505$	0	0
$506$	−8.36892	−0.372044
$507$	2.74200	0.121776
$508$	−4.21607	−0.187058
$509$	15.6600	0.694118	0.347059	−	0.937843i	$-0.387180\pi$
$509$	15.6600	0.694118	0.347059	+	0.937843i	$0.387180\pi$
$510$	0	0
$511$	7.21105	0.318998
$512$	16.9881	0.750776
$513$	−0.137543	−0.00607269
$514$	−33.6156	−1.48272
$515$	0	0
$516$	−0.399549	−0.0175892
$517$	10.4543	0.459781
$518$	4.29728	0.188812
$519$	−9.14330	−0.401346
$520$	0	0
$521$	−21.8013	−0.955131	−0.477566	−	0.878596i	$-0.658481\pi$
$521$	−21.8013	−0.955131	−0.477566	+	0.878596i	$0.658481\pi$
$522$	−22.2621	−0.974384
$523$	−24.7544	−1.08244	−0.541218	−	0.840883i	$-0.682036\pi$
$523$	−24.7544	−1.08244	−0.541218	+	0.840883i	$0.682036\pi$
$524$	−0.381441	−0.0166633
$525$	0	0
$526$	30.8036	1.34310
$527$	−9.00501	−0.392264
$528$	20.2257	0.880209
$529$	1.00000	0.0434783
$530$	0	0
$531$	−12.8371	−0.557084
$532$	−0.00797478	−0.000345751 0
$533$	18.3668	0.795557
$534$	−20.3846	−0.882128
$535$	0	0
$536$	4.36566	0.188568
$537$	−5.25481	−0.226762
$538$	27.6302	1.19122
$539$	−5.57614	−0.240182
$540$	0	0
$541$	25.9715	1.11660	0.558302	−	0.829638i	$-0.311453\pi$
$541$	25.9715	1.11660	0.558302	+	0.829638i	$0.311453\pi$
$542$	−6.36283	−0.273307
$543$	−13.3472	−0.572785
$544$	−9.34069	−0.400479
$545$	0	0
$546$	−4.95739	−0.212157
$547$	18.5380	0.792626	0.396313	−	0.918115i	$-0.370289\pi$
$547$	18.5380	0.792626	0.396313	+	0.918115i	$0.370289\pi$
$548$	−1.46534	−0.0625964
$549$	−29.9627	−1.27878
$550$	0	0
$551$	−0.200780	−0.00855353
$552$	−2.14193	−0.0911666
$553$	−5.58626	−0.237552
$554$	−5.25694	−0.223346
$555$	0	0
$556$	−1.77253	−0.0751721
$557$	0.901162	0.0381834	0.0190917	−	0.999818i	$-0.493923\pi$
$557$	0.901162	0.0381834	0.0190917	+	0.999818i	$0.493923\pi$
$558$	4.79448	0.202967
$559$	7.83531	0.331398
$560$	0	0
$561$	29.9494	1.26446
$562$	26.6758	1.12525
$563$	38.6739	1.62991	0.814955	−	0.579525i	$-0.196762\pi$
$563$	38.6739	1.62991	0.814955	+	0.579525i	$0.196762\pi$
$564$	−0.386664	−0.0162815
$565$	0	0
$566$	−36.7074	−1.54293
$567$	−3.44196	−0.144549
$568$	27.2805	1.14466
$569$	12.1566	0.509631	0.254816	−	0.966990i	$-0.417985\pi$
$569$	12.1566	0.509631	0.254816	+	0.966990i	$0.417985\pi$
$570$	0	0
$571$	−43.6516	−1.82676	−0.913382	−	0.407104i	$-0.866539\pi$
$571$	−43.6516	−1.82676	−0.913382	+	0.407104i	$0.866539\pi$
$572$	5.69512	0.238125
$573$	12.6365	0.527897
$574$	−6.81573	−0.284483
$575$	0	0
$576$	−15.7499	−0.656247
$577$	9.86386	0.410638	0.205319	−	0.978695i	$-0.434177\pi$
$577$	9.86386	0.410638	0.205319	+	0.978695i	$0.434177\pi$
$578$	−39.3974	−1.63872
$579$	14.4986	0.602541
$580$	0	0
$581$	11.1128	0.461037
$582$	−17.0360	−0.706165
$583$	6.29968	0.260906
$584$	−18.9123	−0.782595
$585$	0	0
$586$	−2.38056	−0.0983401
$587$	−42.5969	−1.75816	−0.879080	−	0.476674i	$-0.841842\pi$
$587$	−42.5969	−1.75816	−0.879080	+	0.476674i	$0.841842\pi$
$588$	0.206239	0.00850517
$589$	0.0432411	0.00178172
$590$	0	0
$591$	10.1394	0.417080
$592$	−12.7165	−0.522645
$593$	9.47386	0.389045	0.194522	−	0.980898i	$-0.437684\pi$
$593$	9.47386	0.389045	0.194522	+	0.980898i	$0.437684\pi$
$594$	−36.4503	−1.49558
$595$	0	0
$596$	−5.37735	−0.220265
$597$	11.1922	0.458068
$598$	−6.07006	−0.248223
$599$	38.5320	1.57438	0.787188	−	0.616713i	$-0.211536\pi$
$599$	38.5320	1.57438	0.787188	+	0.616713i	$0.211536\pi$
$600$	0	0
$601$	36.3755	1.48379	0.741895	−	0.670517i	$-0.233927\pi$
$601$	36.3755	1.48379	0.741895	+	0.670517i	$0.233927\pi$
$602$	−2.90759	−0.118505
$603$	−3.88348	−0.158147
$604$	0.644737	0.0262340
$605$	0	0
$606$	−10.5031	−0.426660
$607$	15.4526	0.627202	0.313601	−	0.949555i	$-0.398465\pi$
$607$	15.4526	0.627202	0.313601	+	0.949555i	$0.398465\pi$
$608$	0.0448531	0.00181903
$609$	5.19247	0.210410
$610$	0	0
$611$	7.58263	0.306760
$612$	3.87456	0.156620
$613$	33.8611	1.36764	0.683818	−	0.729653i	$-0.260318\pi$
$613$	33.8611	1.36764	0.683818	+	0.729653i	$0.260318\pi$
$614$	−13.8742	−0.559916
$615$	0	0
$616$	14.6244	0.589235
$617$	45.4881	1.83128	0.915640	−	0.401998i	$-0.131684\pi$
$617$	45.4881	1.83128	0.915640	+	0.401998i	$0.131684\pi$
$618$	9.08617	0.365500
$619$	1.72666	0.0694001	0.0347001	−	0.999398i	$-0.488952\pi$
$619$	1.72666	0.0694001	0.0347001	+	0.999398i	$0.488952\pi$
$620$	0	0
$621$	4.35544	0.174778
$622$	29.2080	1.17113
$623$	−16.6306	−0.666289
$624$	14.6699	0.587265
$625$	0	0
$626$	38.1568	1.52505
$627$	−0.143814	−0.00574338
$628$	−1.97255	−0.0787134
$629$	−18.8301	−0.750806
$630$	0	0
$631$	−37.8555	−1.50700	−0.753502	−	0.657446i	$-0.771637\pi$
$631$	−37.8555	−1.50700	−0.753502	+	0.657446i	$0.771637\pi$
$632$	14.6510	0.582785
$633$	13.4432	0.534321
$634$	−9.67803	−0.384363
$635$	0	0
$636$	−0.233000	−0.00923905
$637$	−4.04443	−0.160246
$638$	−53.2088	−2.10656
$639$	−24.2674	−0.960004
$640$	0	0
$641$	−37.6517	−1.48715	−0.743577	−	0.668650i	$-0.766872\pi$
$641$	−37.6517	−1.48715	−0.743577	+	0.668650i	$0.766872\pi$
$642$	−4.34298	−0.171404
$643$	−34.8532	−1.37448	−0.687238	−	0.726433i	$-0.741177\pi$
$643$	−34.8532	−1.37448	−0.687238	+	0.726433i	$0.741177\pi$
$644$	0.252529	0.00995104
$645$	0	0
$646$	0.311700	0.0122637
$647$	5.50383	0.216378	0.108189	−	0.994130i	$-0.465495\pi$
$647$	5.50383	0.216378	0.108189	+	0.994130i	$0.465495\pi$
$648$	9.02715	0.354620
$649$	−30.6821	−1.20438
$650$	0	0
$651$	−1.11828	−0.0438288
$652$	−5.86870	−0.229836
$653$	−31.9836	−1.25162	−0.625808	−	0.779977i	$-0.715230\pi$
$653$	−31.9836	−1.25162	−0.625808	+	0.779977i	$0.715230\pi$
$654$	15.2863	0.597742
$655$	0	0
$656$	20.1691	0.787470
$657$	16.8234	0.656345
$658$	−2.81383	−0.109694
$659$	−12.6793	−0.493915	−0.246958	−	0.969026i	$-0.579431\pi$
$659$	−12.6793	−0.493915	−0.246958	+	0.969026i	$0.579431\pi$
$660$	0	0
$661$	14.9284	0.580647	0.290323	−	0.956929i	$-0.406237\pi$
$661$	14.9284	0.580647	0.290323	+	0.956929i	$0.406237\pi$
$662$	−35.7032	−1.38764
$663$	21.7226	0.843636
$664$	−29.1453	−1.13106
$665$	0	0
$666$	10.0256	0.388484
$667$	6.35790	0.246179
$668$	−2.63901	−0.102107
$669$	−12.1074	−0.468100
$670$	0	0
$671$	−71.6141	−2.76463
$672$	−1.15997	−0.0447466
$673$	−35.8357	−1.38136	−0.690682	−	0.723158i	$-0.742690\pi$
$673$	−35.8357	−1.38136	−0.690682	+	0.723158i	$0.742690\pi$
$674$	27.1341	1.04517
$675$	0	0
$676$	0.847848	0.0326095
$677$	3.09993	0.119140	0.0595700	−	0.998224i	$-0.481027\pi$
$677$	3.09993	0.119140	0.0595700	+	0.998224i	$0.481027\pi$
$678$	−11.7206	−0.450127
$679$	−13.8986	−0.533381
$680$	0	0
$681$	−14.9374	−0.572404
$682$	11.4593	0.438800
$683$	21.9949	0.841610	0.420805	−	0.907151i	$-0.361748\pi$
$683$	21.9949	0.841610	0.420805	+	0.907151i	$0.361748\pi$
$684$	−0.0186052	−0.000711389 0
$685$	0	0
$686$	1.50084	0.0573024
$687$	21.2355	0.810183
$688$	8.60414	0.328030
$689$	4.56922	0.174073
$690$	0	0
$691$	26.7812	1.01881	0.509403	−	0.860528i	$-0.329866\pi$
$691$	26.7812	1.01881	0.509403	+	0.860528i	$0.329866\pi$
$692$	−2.82718	−0.107473
$693$	−13.0092	−0.494178
$694$	−5.89869	−0.223911
$695$	0	0
$696$	−13.6182	−0.516196
$697$	29.8656	1.13124
$698$	14.6676	0.555176
$699$	7.75613	0.293364
$700$	0	0
$701$	−16.1107	−0.608493	−0.304246	−	0.952593i	$-0.598405\pi$
$701$	−16.1107	−0.608493	−0.304246	+	0.952593i	$0.598405\pi$
$702$	−26.4378	−0.997830
$703$	0.0904203	0.00341027
$704$	−37.6440	−1.41876
$705$	0	0
$706$	34.7161	1.30656
$707$	−8.56886	−0.322265
$708$	1.13481	0.0426487
$709$	−51.1562	−1.92121	−0.960606	−	0.277913i	$-0.910357\pi$
$709$	−51.1562	−1.92121	−0.960606	+	0.277913i	$0.910357\pi$
$710$	0	0
$711$	−13.0328	−0.488768
$712$	43.6166	1.63460
$713$	−1.36927	−0.0512797
$714$	−8.06101	−0.301676
$715$	0	0
$716$	−1.62483	−0.0607227
$717$	−21.4965	−0.802800
$718$	−9.96572	−0.371917
$719$	23.1532	0.863467	0.431734	−	0.902001i	$-0.357902\pi$
$719$	23.1532	0.863467	0.431734	+	0.902001i	$0.357902\pi$
$720$	0	0
$721$	7.41286	0.276069
$722$	28.5145	1.06120
$723$	−9.16278	−0.340767
$724$	−4.12708	−0.153382
$725$	0	0
$726$	−24.6291	−0.914071
$727$	15.4927	0.574593	0.287297	−	0.957842i	$-0.407243\pi$
$727$	15.4927	0.574593	0.287297	+	0.957842i	$0.407243\pi$
$728$	10.6072	0.393131
$729$	2.64110	0.0978184
$730$	0	0
$731$	12.7407	0.471231
$732$	2.64872	0.0978995
$733$	3.41564	0.126159	0.0630797	−	0.998008i	$-0.479908\pi$
$733$	3.41564	0.126159	0.0630797	+	0.998008i	$0.479908\pi$
$734$	−19.0144	−0.701835
$735$	0	0
$736$	−1.42032	−0.0523535
$737$	−9.28193	−0.341904
$738$	−15.9012	−0.585330
$739$	17.9699	0.661033	0.330516	−	0.943800i	$-0.392777\pi$
$739$	17.9699	0.661033	0.330516	+	0.943800i	$0.392777\pi$
$740$	0	0
$741$	−0.104310	−0.00383191
$742$	−1.69559	−0.0622469
$743$	−1.24775	−0.0457755	−0.0228877	−	0.999738i	$-0.507286\pi$
$743$	−1.24775	−0.0457755	−0.0228877	+	0.999738i	$0.507286\pi$
$744$	2.93289	0.107525
$745$	0	0
$746$	−9.00867	−0.329831
$747$	25.9263	0.948593
$748$	9.26061	0.338601
$749$	−3.54317	−0.129465
$750$	0	0
$751$	47.7360	1.74191	0.870956	−	0.491361i	$-0.163501\pi$
$751$	47.7360	1.74191	0.870956	+	0.491361i	$0.163501\pi$
$752$	8.32666	0.303642
$753$	−5.01731	−0.182841
$754$	−38.5928	−1.40547
$755$	0	0
$756$	1.09988	0.0400021
$757$	−2.61944	−0.0952052	−0.0476026	−	0.998866i	$-0.515158\pi$
$757$	−2.61944	−0.0952052	−0.0476026	+	0.998866i	$0.515158\pi$
$758$	−47.0613	−1.70934
$759$	4.55401	0.165300
$760$	0	0
$761$	27.4578	0.995346	0.497673	−	0.867365i	$-0.334188\pi$
$761$	27.4578	0.995346	0.497673	+	0.867365i	$0.334188\pi$
$762$	20.4641	0.741335
$763$	12.4712	0.451487
$764$	3.90731	0.141362
$765$	0	0
$766$	8.31076	0.300280
$767$	−22.2540	−0.803547
$768$	4.87415	0.175881
$769$	−15.8642	−0.572077	−0.286038	−	0.958218i	$-0.592338\pi$
$769$	−15.8642	−0.572077	−0.286038	+	0.958218i	$0.592338\pi$
$770$	0	0
$771$	18.2922	0.658777
$772$	4.48309	0.161350
$773$	−44.2624	−1.59201	−0.796004	−	0.605292i	$-0.793056\pi$
$773$	−44.2624	−1.59201	−0.796004	+	0.605292i	$0.793056\pi$
$774$	−6.78344	−0.243826
$775$	0	0
$776$	36.4517	1.30854
$777$	−2.33840	−0.0838896
$778$	−12.3126	−0.441429
$779$	−0.143412	−0.00513826
$780$	0	0
$781$	−58.0018	−2.07547
$782$	−9.87028	−0.352960
$783$	27.6915	0.989613
$784$	−4.44129	−0.158617
$785$	0	0
$786$	1.85145	0.0660390
$787$	−13.2515	−0.472367	−0.236183	−	0.971709i	$-0.575897\pi$
$787$	−13.2515	−0.472367	−0.236183	+	0.971709i	$0.575897\pi$
$788$	3.13520	0.111687
$789$	−16.7620	−0.596744
$790$	0	0
$791$	−9.56214	−0.339990
$792$	34.1189	1.21236
$793$	−51.9424	−1.84453
$794$	14.4398	0.512450
$795$	0	0
$796$	3.46074	0.122663
$797$	−22.6458	−0.802156	−0.401078	−	0.916044i	$-0.631364\pi$
$797$	−22.6458	−0.802156	−0.401078	+	0.916044i	$0.631364\pi$
$798$	0.0387082	0.00137025
$799$	12.3298	0.436197
$800$	0	0
$801$	−38.7992	−1.37090
$802$	−40.2726	−1.42207
$803$	40.2099	1.41898
$804$	0.343302	0.0121073
$805$	0	0
$806$	8.31156	0.292762
$807$	−15.0352	−0.529264
$808$	22.4734	0.790610
$809$	−1.76330	−0.0619942	−0.0309971	−	0.999519i	$-0.509868\pi$
$809$	−1.76330	−0.0619942	−0.0309971	+	0.999519i	$0.509868\pi$
$810$	0	0
$811$	−18.9434	−0.665194	−0.332597	−	0.943069i	$-0.607925\pi$
$811$	−18.9434	−0.665194	−0.332597	+	0.943069i	$0.607925\pi$
$812$	1.60556	0.0563440
$813$	3.46239	0.121431
$814$	23.9623	0.839877
$815$	0	0
$816$	23.8541	0.835060
$817$	−0.0611795	−0.00214040
$818$	−54.7670	−1.91488
$819$	−9.43569	−0.329710
$820$	0	0
$821$	−52.4982	−1.83220	−0.916099	−	0.400952i	$-0.868679\pi$
$821$	−52.4982	−1.83220	−0.916099	+	0.400952i	$0.868679\pi$
$822$	7.11252	0.248078
$823$	31.5761	1.10067	0.550336	−	0.834943i	$-0.314500\pi$
$823$	31.5761	1.10067	0.550336	+	0.834943i	$0.314500\pi$
$824$	−19.4416	−0.677279
$825$	0	0
$826$	8.25822	0.287340
$827$	−0.407237	−0.0141610	−0.00708050	−	0.999975i	$-0.502254\pi$
$827$	−0.407237	−0.0141610	−0.00708050	+	0.999975i	$0.502254\pi$
$828$	0.589153	0.0204745
$829$	46.9030	1.62901	0.814504	−	0.580158i	$-0.197009\pi$
$829$	46.9030	1.62901	0.814504	+	0.580158i	$0.197009\pi$
$830$	0	0
$831$	2.86060	0.0992333
$832$	−27.3036	−0.946581
$833$	−6.57649	−0.227862
$834$	8.60355	0.297917
$835$	0	0
$836$	−0.0444685	−0.00153798
$837$	−5.96379	−0.206139
$838$	17.7406	0.612838
$839$	42.3064	1.46058	0.730289	−	0.683138i	$-0.239385\pi$
$839$	42.3064	1.46058	0.730289	+	0.683138i	$0.239385\pi$
$840$	0	0
$841$	11.4229	0.393895
$842$	15.0458	0.518511
$843$	−14.5159	−0.499953
$844$	4.15676	0.143082
$845$	0	0
$846$	−6.56468	−0.225698
$847$	−20.0934	−0.690417
$848$	5.01757	0.172304
$849$	19.9746	0.685527
$850$	0	0
$851$	−2.86325	−0.0981508
$852$	2.14525	0.0734952
$853$	0.228036	0.00780779	0.00390390	−	0.999992i	$-0.498757\pi$
$853$	0.228036	0.00780779	0.00390390	+	0.999992i	$0.498757\pi$
$854$	19.2752	0.659585
$855$	0	0
$856$	9.29261	0.317615
$857$	−25.4818	−0.870440	−0.435220	−	0.900324i	$-0.643329\pi$
$857$	−25.4818	−0.870440	−0.435220	+	0.900324i	$0.643329\pi$
$858$	−27.6431	−0.943720
$859$	−47.1913	−1.61015	−0.805073	−	0.593175i	$-0.797874\pi$
$859$	−47.1913	−1.61015	−0.805073	+	0.593175i	$0.797874\pi$
$860$	0	0
$861$	3.70883	0.126397
$862$	42.0032	1.43063
$863$	−1.79277	−0.0610267	−0.0305133	−	0.999534i	$-0.509714\pi$
$863$	−1.79277	−0.0610267	−0.0305133	+	0.999534i	$0.509714\pi$
$864$	−6.18610	−0.210456
$865$	0	0
$866$	−25.6627	−0.872054
$867$	21.4384	0.728087
$868$	−0.345781	−0.0117366
$869$	−31.1498	−1.05668
$870$	0	0
$871$	−6.73227	−0.228114
$872$	−32.7079	−1.10763
$873$	−32.4257	−1.09744
$874$	0.0473961	0.00160320
$875$	0	0
$876$	−1.48720	−0.0502479
$877$	32.3361	1.09191	0.545957	−	0.837813i	$-0.316166\pi$
$877$	32.3361	1.09191	0.545957	+	0.837813i	$0.316166\pi$
$878$	−37.0549	−1.25054
$879$	1.29540	0.0436928
$880$	0	0
$881$	47.1294	1.58783	0.793914	−	0.608030i	$-0.208040\pi$
$881$	47.1294	1.58783	0.793914	+	0.608030i	$0.208040\pi$
$882$	3.50148	0.117901
$883$	53.7694	1.80948	0.904742	−	0.425960i	$-0.140064\pi$
$883$	53.7694	1.80948	0.904742	+	0.425960i	$0.140064\pi$
$884$	6.71681	0.225911
$885$	0	0
$886$	−33.5456	−1.12699
$887$	−13.4916	−0.453005	−0.226502	−	0.974011i	$-0.572729\pi$
$887$	−13.4916	−0.453005	−0.226502	+	0.974011i	$0.572729\pi$
$888$	6.13287	0.205806
$889$	16.6954	0.559946
$890$	0	0
$891$	−19.1928	−0.642984
$892$	−3.74372	−0.125349
$893$	−0.0592065	−0.00198127
$894$	26.1007	0.872938
$895$	0	0
$896$	12.9727	0.433387
$897$	3.30307	0.110286
$898$	21.1446	0.705605
$899$	−8.70570	−0.290351
$900$	0	0
$901$	7.42983	0.247523
$902$	−38.0055	−1.26544
$903$	1.58219	0.0526520
$904$	25.0784	0.834096
$905$	0	0
$906$	−3.12944	−0.103969
$907$	−32.7055	−1.08597	−0.542985	−	0.839742i	$-0.682706\pi$
$907$	−32.7055	−1.08597	−0.542985	+	0.839742i	$0.682706\pi$
$908$	−4.61878	−0.153280
$909$	−19.9912	−0.663067
$910$	0	0
$911$	0.0799151	0.00264771	0.00132385	−	0.999999i	$-0.499579\pi$
$911$	0.0799151	0.00264771	0.00132385	+	0.999999i	$0.499579\pi$
$912$	−0.114545	−0.00379296
$913$	61.9666	2.05080
$914$	44.8584	1.48378
$915$	0	0
$916$	6.56618	0.216953
$917$	1.51048	0.0498806
$918$	−42.9894	−1.41886
$919$	42.9841	1.41792	0.708958	−	0.705251i	$-0.249166\pi$
$919$	42.9841	1.41792	0.708958	+	0.705251i	$0.249166\pi$
$920$	0	0
$921$	7.54974	0.248773
$922$	44.5389	1.46681
$923$	−42.0692	−1.38473
$924$	1.15002	0.0378329
$925$	0	0
$926$	19.5430	0.642222
$927$	17.2943	0.568018
$928$	−9.03023	−0.296432
$929$	23.3398	0.765754	0.382877	−	0.923799i	$-0.374933\pi$
$929$	23.3398	0.765754	0.382877	+	0.923799i	$0.374933\pi$
$930$	0	0
$931$	0.0315796	0.00103498
$932$	2.39826	0.0785577
$933$	−15.8938	−0.520339
$934$	13.7228	0.449024
$935$	0	0
$936$	24.7468	0.808874
$937$	−11.7697	−0.384500	−0.192250	−	0.981346i	$-0.561578\pi$
$937$	−11.7697	−0.384500	−0.192250	+	0.981346i	$0.561578\pi$
$938$	2.49827	0.0815714
$939$	−20.7633	−0.677585
$940$	0	0
$941$	−4.51567	−0.147207	−0.0736034	−	0.997288i	$-0.523450\pi$
$941$	−4.51567	−0.147207	−0.0736034	+	0.997288i	$0.523450\pi$
$942$	9.57442	0.311951
$943$	4.54127	0.147884
$944$	−24.4377	−0.795379
$945$	0	0
$946$	−16.2132	−0.527135
$947$	19.0220	0.618133	0.309066	−	0.951040i	$-0.399983\pi$
$947$	19.0220	0.618133	0.309066	+	0.951040i	$0.399983\pi$
$948$	1.15211	0.0374187
$949$	29.1646	0.946723
$950$	0	0
$951$	5.26637	0.170774
$952$	17.2480	0.559012
$953$	−43.3856	−1.40540	−0.702699	−	0.711488i	$-0.748022\pi$
$953$	−43.3856	−1.40540	−0.702699	+	0.711488i	$0.748022\pi$
$954$	−3.95582	−0.128074
$955$	0	0
$956$	−6.64689	−0.214976
$957$	28.9540	0.935949
$958$	13.5484	0.437728
$959$	5.80267	0.187378
$960$	0	0
$961$	−29.1251	−0.939519
$962$	17.3801	0.560356
$963$	−8.26625	−0.266376
$964$	−2.83321	−0.0912515
$965$	0	0
$966$	−1.22573	−0.0394373
$967$	41.0523	1.32015	0.660076	−	0.751199i	$-0.270524\pi$
$967$	41.0523	1.32015	0.660076	+	0.751199i	$0.270524\pi$
$968$	52.6985	1.69379
$969$	−0.169614	−0.00544878
$970$	0	0
$971$	−38.5361	−1.23668	−0.618341	−	0.785910i	$-0.712195\pi$
$971$	−38.5361	−1.23668	−0.618341	+	0.785910i	$0.712195\pi$
$972$	4.00949	0.128605
$973$	7.01912	0.225023
$974$	−48.4958	−1.55391
$975$	0	0
$976$	−57.0392	−1.82578
$977$	−37.5284	−1.20064	−0.600320	−	0.799760i	$-0.704960\pi$
$977$	−37.5284	−1.20064	−0.600320	+	0.799760i	$0.704960\pi$
$978$	28.4856	0.910870
$979$	−92.7344	−2.96380
$980$	0	0
$981$	29.0953	0.928943
$982$	−30.7869	−0.982449
$983$	−48.9074	−1.55990	−0.779952	−	0.625839i	$-0.784757\pi$
$983$	−48.9074	−1.55990	−0.779952	+	0.625839i	$0.784757\pi$
$984$	−9.72708	−0.310088
$985$	0	0
$986$	−62.7543	−1.99850
$987$	1.53117	0.0487375
$988$	−0.0322534	−0.00102612
$989$	1.93731	0.0616028
$990$	0	0
$991$	−8.69537	−0.276217	−0.138109	−	0.990417i	$-0.544102\pi$
$991$	−8.69537	−0.276217	−0.138109	+	0.990417i	$0.544102\pi$
$992$	1.94480	0.0617474
$993$	19.4282	0.616534
$994$	15.6114	0.495164
$995$	0	0
$996$	−2.29190	−0.0726215
$997$	−13.9339	−0.441290	−0.220645	−	0.975354i	$-0.570816\pi$
$997$	−13.9339	−0.441290	−0.220645	+	0.975354i	$0.570816\pi$
$998$	−37.4369	−1.18505
$999$	−12.4707	−0.394556

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4025.2.a.bd.1.7		21
5.2	odd	4		805.2.c.c.484.13	✓	42
5.3	odd	4		805.2.c.c.484.30	yes	42
5.4	even	2		4025.2.a.be.1.15		21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
805.2.c.c.484.13	✓	42	5.2	odd	4
805.2.c.c.484.30	yes	42	5.3	odd	4
4025.2.a.bd.1.7		21	1.1	even	1	trivial
4025.2.a.be.1.15		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)

\(f(q)\)	\(=\)	\(q-1.50084 q^{2} +0.816695 q^{3} +0.252529 q^{4} -1.22573 q^{6} -1.00000 q^{7} +2.62268 q^{8} -2.33301 q^{9} +O(q^{10})\)	\(q-1.50084 q^{2} +0.816695 q^{3} +0.252529 q^{4} -1.22573 q^{6} -1.00000 q^{7} +2.62268 q^{8} -2.33301 q^{9} -5.57614 q^{11} +0.206239 q^{12} -4.04443 q^{13} +1.50084 q^{14} -4.44129 q^{16} -6.57649 q^{17} +3.50148 q^{18} +0.0315796 q^{19} -0.816695 q^{21} +8.36892 q^{22} -1.00000 q^{23} +2.14193 q^{24} +6.07006 q^{26} -4.35544 q^{27} -0.252529 q^{28} -6.35790 q^{29} +1.36927 q^{31} +1.42032 q^{32} -4.55401 q^{33} +9.87028 q^{34} -0.589153 q^{36} +2.86325 q^{37} -0.0473961 q^{38} -3.30307 q^{39} -4.54127 q^{41} +1.22573 q^{42} -1.93731 q^{43} -1.40814 q^{44} +1.50084 q^{46} -1.87483 q^{47} -3.62718 q^{48} +1.00000 q^{49} -5.37099 q^{51} -1.02134 q^{52} -1.12976 q^{53} +6.53684 q^{54} -2.62268 q^{56} +0.0257909 q^{57} +9.54221 q^{58} +5.50239 q^{59} +12.8429 q^{61} -2.05506 q^{62} +2.33301 q^{63} +6.75090 q^{64} +6.83485 q^{66} +1.66458 q^{67} -1.66075 q^{68} -0.816695 q^{69} +10.4018 q^{71} -6.11873 q^{72} -7.21105 q^{73} -4.29728 q^{74} +0.00797478 q^{76} +5.57614 q^{77} +4.95739 q^{78} +5.58626 q^{79} +3.44196 q^{81} +6.81573 q^{82} -11.1128 q^{83} -0.206239 q^{84} +2.90759 q^{86} -5.19247 q^{87} -14.6244 q^{88} +16.6306 q^{89} +4.04443 q^{91} -0.252529 q^{92} +1.11828 q^{93} +2.81383 q^{94} +1.15997 q^{96} +13.8986 q^{97} -1.50084 q^{98} +13.0092 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q - 2 q^{2} + q^{3} + 30 q^{4} + 6 q^{6} - 21 q^{7} - 6 q^{8} + 30 q^{9}+O(q^{10}) \) 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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