LMFDB - Embedded newform 75.4.a.f.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,4,Mod(1,75)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("75.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	75.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:	$4.42514325043$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{41}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 10 $ x^2 - x - 10
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 15)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.70156$ of defining polynomial
Character	$\chi$	$=$	75.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.70156 q^{2} +3.00000 q^{3} -5.10469 q^{4} -5.10469 q^{6} +22.2094 q^{7} +22.2984 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-1.70156 q^{2} +3.00000 q^{3} -5.10469 q^{4} -5.10469 q^{6} +22.2094 q^{7} +22.2984 q^{8} +9.00000 q^{9} -1.79063 q^{11} -15.3141 q^{12} +58.2094 q^{13} -37.7906 q^{14} +2.89531 q^{16} +18.9844 q^{17} -15.3141 q^{18} +104.837 q^{19} +66.6281 q^{21} +3.04686 q^{22} -49.6125 q^{23} +66.8953 q^{24} -99.0469 q^{26} +27.0000 q^{27} -113.372 q^{28} -293.466 q^{29} +64.4187 q^{31} -183.314 q^{32} -5.37188 q^{33} -32.3031 q^{34} -45.9422 q^{36} -19.8844 q^{37} -178.388 q^{38} +174.628 q^{39} -165.581 q^{41} -113.372 q^{42} -247.350 q^{43} +9.14059 q^{44} +84.4187 q^{46} +384.544 q^{47} +8.68594 q^{48} +150.256 q^{49} +56.9531 q^{51} -297.141 q^{52} +463.528 q^{53} -45.9422 q^{54} +495.234 q^{56} +314.512 q^{57} +499.350 q^{58} -73.7906 q^{59} -137.350 q^{61} -109.612 q^{62} +199.884 q^{63} +288.758 q^{64} +9.14059 q^{66} +173.906 q^{67} -96.9093 q^{68} -148.837 q^{69} -594.281 q^{71} +200.686 q^{72} +320.231 q^{73} +33.8345 q^{74} -535.163 q^{76} -39.7687 q^{77} -297.141 q^{78} -770.469 q^{79} +81.0000 q^{81} +281.747 q^{82} +173.925 q^{83} -340.116 q^{84} +420.881 q^{86} -880.397 q^{87} -39.9282 q^{88} +1019.02 q^{89} +1292.79 q^{91} +253.256 q^{92} +193.256 q^{93} -654.325 q^{94} -549.942 q^{96} +384.375 q^{97} -255.670 q^{98} -16.1156 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 3 q^{2} + 6 q^{3} + 9 q^{4} + 9 q^{6} + 6 q^{7} + 51 q^{8} + 18 q^{9}+O(q^{10}) $ 2 * q + 3 * q^2 + 6 * q^3 + 9 * q^4 + 9 * q^6 + 6 * q^7 + 51 * q^8 + 18 * q^9	$ 2 q + 3 q^{2} + 6 q^{3} + 9 q^{4} + 9 q^{6} + 6 q^{7} + 51 q^{8} + 18 q^{9} - 42 q^{11} + 27 q^{12} + 78 q^{13} - 114 q^{14} + 25 q^{16} + 102 q^{17} + 27 q^{18} + 56 q^{19} + 18 q^{21} - 186 q^{22} - 48 q^{23} + 153 q^{24} - 6 q^{26} + 54 q^{27} - 342 q^{28} - 318 q^{29} + 52 q^{31} - 309 q^{32} - 126 q^{33} + 358 q^{34} + 81 q^{36} + 306 q^{37} - 408 q^{38} + 234 q^{39} - 408 q^{41} - 342 q^{42} + 120 q^{43} - 558 q^{44} + 92 q^{46} + 180 q^{47} + 75 q^{48} + 70 q^{49} + 306 q^{51} - 18 q^{52} + 402 q^{53} + 81 q^{54} + 30 q^{56} + 168 q^{57} + 384 q^{58} - 186 q^{59} + 340 q^{61} - 168 q^{62} + 54 q^{63} - 479 q^{64} - 558 q^{66} + 732 q^{67} + 1074 q^{68} - 144 q^{69} - 36 q^{71} + 459 q^{72} + 1332 q^{73} + 1566 q^{74} - 1224 q^{76} + 612 q^{77} - 18 q^{78} + 380 q^{79} + 162 q^{81} - 858 q^{82} - 984 q^{83} - 1026 q^{84} + 2148 q^{86} - 954 q^{87} - 1194 q^{88} + 1116 q^{89} + 972 q^{91} + 276 q^{92} + 156 q^{93} - 1616 q^{94} - 927 q^{96} - 768 q^{97} - 633 q^{98} - 378 q^{99}+O(q^{100}) $ 2 * q + 3 * q^2 + 6 * q^3 + 9 * q^4 + 9 * q^6 + 6 * q^7 + 51 * q^8 + 18 * q^9 - 42 * q^11 + 27 * q^12 + 78 * q^13 - 114 * q^14 + 25 * q^16 + 102 * q^17 + 27 * q^18 + 56 * q^19 + 18 * q^21 - 186 * q^22 - 48 * q^23 + 153 * q^24 - 6 * q^26 + 54 * q^27 - 342 * q^28 - 318 * q^29 + 52 * q^31 - 309 * q^32 - 126 * q^33 + 358 * q^34 + 81 * q^36 + 306 * q^37 - 408 * q^38 + 234 * q^39 - 408 * q^41 - 342 * q^42 + 120 * q^43 - 558 * q^44 + 92 * q^46 + 180 * q^47 + 75 * q^48 + 70 * q^49 + 306 * q^51 - 18 * q^52 + 402 * q^53 + 81 * q^54 + 30 * q^56 + 168 * q^57 + 384 * q^58 - 186 * q^59 + 340 * q^61 - 168 * q^62 + 54 * q^63 - 479 * q^64 - 558 * q^66 + 732 * q^67 + 1074 * q^68 - 144 * q^69 - 36 * q^71 + 459 * q^72 + 1332 * q^73 + 1566 * q^74 - 1224 * q^76 + 612 * q^77 - 18 * q^78 + 380 * q^79 + 162 * q^81 - 858 * q^82 - 984 * q^83 - 1026 * q^84 + 2148 * q^86 - 954 * q^87 - 1194 * q^88 + 1116 * q^89 + 972 * q^91 + 276 * q^92 + 156 * q^93 - 1616 * q^94 - 927 * q^96 - 768 * q^97 - 633 * q^98 - 378 * 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 $

$2$	−1.70156	−0.601593	−0.300797	−	0.953688i	$-0.597253\pi$
$2$	−1.70156	−0.601593	−0.300797	+	0.953688i	$0.597253\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	−5.10469	−0.638086
$5$	0	0
$5$	0	0
$6$	−5.10469	−0.347330
$7$	22.2094	1.19919	0.599597	−	0.800302i	$-0.295328\pi$
$7$	22.2094	1.19919	0.599597	+	0.800302i	$0.295328\pi$
$8$	22.2984	0.985461
$9$	9.00000	0.333333
$10$	0	0
$11$	−1.79063	−0.0490813	−0.0245407	−	0.999699i	$-0.507812\pi$
$11$	−1.79063	−0.0490813	−0.0245407	+	0.999699i	$0.507812\pi$
$12$	−15.3141	−0.368399
$13$	58.2094	1.24188	0.620938	−	0.783860i	$-0.286752\pi$
$13$	58.2094	1.24188	0.620938	+	0.783860i	$0.286752\pi$
$14$	−37.7906	−0.721426
$15$	0	0
$16$	2.89531	0.0452393
$17$	18.9844	0.270846	0.135423	−	0.990788i	$-0.456761\pi$
$17$	18.9844	0.270846	0.135423	+	0.990788i	$0.456761\pi$
$18$	−15.3141	−0.200531
$19$	104.837	1.26586	0.632931	−	0.774208i	$-0.281852\pi$
$19$	104.837	1.26586	0.632931	+	0.774208i	$0.281852\pi$
$20$	0	0
$21$	66.6281	0.692355
$22$	3.04686	0.0295270
$23$	−49.6125	−0.449779	−0.224890	−	0.974384i	$-0.572202\pi$
$23$	−49.6125	−0.449779	−0.224890	+	0.974384i	$0.572202\pi$
$24$	66.8953	0.568956
$25$	0	0
$26$	−99.0469	−0.747103
$27$	27.0000	0.192450
$28$	−113.372	−0.765188
$29$	−293.466	−1.87914	−0.939572	−	0.342350i	$-0.888777\pi$
$29$	−293.466	−1.87914	−0.939572	+	0.342350i	$0.888777\pi$
$30$	0	0
$31$	64.4187	0.373224	0.186612	−	0.982434i	$-0.440249\pi$
$31$	64.4187	0.373224	0.186612	+	0.982434i	$0.440249\pi$
$32$	−183.314	−1.01268
$33$	−5.37188	−0.0283371
$34$	−32.3031	−0.162939
$35$	0	0
$36$	−45.9422	−0.212695
$37$	−19.8844	−0.0883505	−0.0441752	−	0.999024i	$-0.514066\pi$
$37$	−19.8844	−0.0883505	−0.0441752	+	0.999024i	$0.514066\pi$
$38$	−178.388	−0.761534
$39$	174.628	0.716997
$40$	0	0
$41$	−165.581	−0.630718	−0.315359	−	0.948972i	$-0.602125\pi$
$41$	−165.581	−0.630718	−0.315359	+	0.948972i	$0.602125\pi$
$42$	−113.372	−0.416516
$43$	−247.350	−0.877221	−0.438611	−	0.898677i	$-0.644529\pi$
$43$	−247.350	−0.877221	−0.438611	+	0.898677i	$0.644529\pi$
$44$	9.14059	0.0313181
$45$	0	0
$46$	84.4187	0.270584
$47$	384.544	1.19344	0.596718	−	0.802451i	$-0.296471\pi$
$47$	384.544	1.19344	0.596718	+	0.802451i	$0.296471\pi$
$48$	8.68594	0.0261189
$49$	150.256	0.438065
$50$	0	0
$51$	56.9531	0.156373
$52$	−297.141	−0.792423
$53$	463.528	1.20133	0.600665	−	0.799501i	$-0.294903\pi$
$53$	463.528	1.20133	0.600665	+	0.799501i	$0.294903\pi$
$54$	−45.9422	−0.115777
$55$	0	0
$56$	495.234	1.18176
$57$	314.512	0.730846
$58$	499.350	1.13048
$59$	−73.7906	−0.162826	−0.0814129	−	0.996680i	$-0.525943\pi$
$59$	−73.7906	−0.162826	−0.0814129	+	0.996680i	$0.525943\pi$
$60$	0	0
$61$	−137.350	−0.288293	−0.144146	−	0.989556i	$-0.546044\pi$
$61$	−137.350	−0.288293	−0.144146	+	0.989556i	$0.546044\pi$
$62$	−109.612	−0.224529
$63$	199.884	0.399731
$64$	288.758	0.563980
$65$	0	0
$66$	9.14059	0.0170474
$67$	173.906	0.317105	0.158552	−	0.987351i	$-0.449317\pi$
$67$	173.906	0.317105	0.158552	+	0.987351i	$0.449317\pi$
$68$	−96.9093	−0.172823
$69$	−148.837	−0.259680
$70$	0	0
$71$	−594.281	−0.993355	−0.496677	−	0.867935i	$-0.665447\pi$
$71$	−594.281	−0.993355	−0.496677	+	0.867935i	$0.665447\pi$
$72$	200.686	0.328487
$73$	320.231	0.513428	0.256714	−	0.966487i	$-0.417360\pi$
$73$	320.231	0.513428	0.256714	+	0.966487i	$0.417360\pi$
$74$	33.8345	0.0531510
$75$	0	0
$76$	−535.163	−0.807728
$77$	−39.7687	−0.0588580
$78$	−297.141	−0.431340
$79$	−770.469	−1.09727	−0.548636	−	0.836061i	$-0.684853\pi$
$79$	−770.469	−1.09727	−0.548636	+	0.836061i	$0.684853\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	281.747	0.379436
$83$	173.925	0.230009	0.115004	−	0.993365i	$-0.463312\pi$
$83$	173.925	0.230009	0.115004	+	0.993365i	$0.463312\pi$
$84$	−340.116	−0.441782
$85$	0	0
$86$	420.881	0.527730
$87$	−880.397	−1.08492
$88$	−39.9282	−0.0483677
$89$	1019.02	1.21367	0.606834	−	0.794829i	$-0.292439\pi$
$89$	1019.02	1.21367	0.606834	+	0.794829i	$0.292439\pi$
$90$	0	0
$91$	1292.79	1.48925
$92$	253.256	0.286998
$93$	193.256	0.215481
$94$	−654.325	−0.717962
$95$	0	0
$96$	−549.942	−0.584669
$97$	384.375	0.402344	0.201172	−	0.979556i	$-0.435525\pi$
$97$	384.375	0.402344	0.201172	+	0.979556i	$0.435525\pi$
$98$	−255.670	−0.263537
$99$	−16.1156	−0.0163604
$100$	0	0
$101$	34.4906	0.0339796	0.0169898	−	0.999856i	$-0.494592\pi$
$101$	34.4906	0.0339796	0.0169898	+	0.999856i	$0.494592\pi$
$102$	−96.9093	−0.0940730
$103$	−1756.30	−1.68013	−0.840066	−	0.542484i	$-0.817484\pi$
$103$	−1756.30	−1.68013	−0.840066	+	0.542484i	$0.817484\pi$
$104$	1297.98	1.22382
$105$	0	0
$106$	−788.722	−0.722712
$107$	−1361.74	−1.23032	−0.615159	−	0.788403i	$-0.710908\pi$
$107$	−1361.74	−1.23032	−0.615159	+	0.788403i	$0.710908\pi$
$108$	−137.827	−0.122800
$109$	321.119	0.282180	0.141090	−	0.989997i	$-0.454939\pi$
$109$	321.119	0.282180	0.141090	+	0.989997i	$0.454939\pi$
$110$	0	0
$111$	−59.6531	−0.0510092
$112$	64.3031	0.0542506
$113$	−1582.25	−1.31721	−0.658607	−	0.752487i	$-0.728854\pi$
$113$	−1582.25	−1.31721	−0.658607	+	0.752487i	$0.728854\pi$
$114$	−535.163	−0.439672
$115$	0	0
$116$	1498.05	1.19906
$117$	523.884	0.413958
$118$	125.559	0.0979549
$119$	421.631	0.324797
$120$	0	0
$121$	−1327.79	−0.997591
$122$	233.709	0.173435
$123$	−496.744	−0.364145
$124$	−328.837	−0.238149
$125$	0	0
$126$	−340.116	−0.240475
$127$	−1197.14	−0.836449	−0.418225	−	0.908344i	$-0.637348\pi$
$127$	−1197.14	−0.836449	−0.418225	+	0.908344i	$0.637348\pi$
$128$	975.173	0.673390
$129$	−742.050	−0.506464
$130$	0	0
$131$	−321.647	−0.214522	−0.107261	−	0.994231i	$-0.534208\pi$
$131$	−321.647	−0.214522	−0.107261	+	0.994231i	$0.534208\pi$
$132$	27.4218	0.0180815
$133$	2328.37	1.51801
$134$	−295.912	−0.190768
$135$	0	0
$136$	423.322	0.266909
$137$	354.291	0.220942	0.110471	−	0.993879i	$-0.464764\pi$
$137$	354.291	0.220942	0.110471	+	0.993879i	$0.464764\pi$
$138$	253.256	0.156222
$139$	77.2562	0.0471424	0.0235712	−	0.999722i	$-0.492496\pi$
$139$	77.2562	0.0471424	0.0235712	+	0.999722i	$0.492496\pi$
$140$	0	0
$141$	1153.63	0.689030
$142$	1011.21	0.597595
$143$	−104.231	−0.0609529
$144$	26.0578	0.0150798
$145$	0	0
$146$	−544.893	−0.308875
$147$	450.769	0.252917
$148$	101.503	0.0563752
$149$	−1705.38	−0.937651	−0.468826	−	0.883291i	$-0.655323\pi$
$149$	−1705.38	−0.937651	−0.468826	+	0.883291i	$0.655323\pi$
$150$	0	0
$151$	758.281	0.408663	0.204331	−	0.978902i	$-0.434498\pi$
$151$	758.281	0.408663	0.204331	+	0.978902i	$0.434498\pi$
$152$	2337.71	1.24746
$153$	170.859	0.0902821
$154$	67.6689	0.0354086
$155$	0	0
$156$	−891.422	−0.457506
$157$	−1769.05	−0.899273	−0.449636	−	0.893212i	$-0.648446\pi$
$157$	−1769.05	−0.899273	−0.449636	+	0.893212i	$0.648446\pi$
$158$	1311.00	0.660111
$159$	1390.58	0.693588
$160$	0	0
$161$	−1101.86	−0.539372
$162$	−137.827	−0.0668437
$163$	−881.719	−0.423690	−0.211845	−	0.977303i	$-0.567947\pi$
$163$	−881.719	−0.423690	−0.211845	+	0.977303i	$0.567947\pi$
$164$	845.240	0.402452
$165$	0	0
$166$	−295.944	−0.138372
$167$	−216.900	−0.100504	−0.0502522	−	0.998737i	$-0.516003\pi$
$167$	−216.900	−0.100504	−0.0502522	+	0.998737i	$0.516003\pi$
$168$	1485.70	0.682289
$169$	1191.33	0.542254
$170$	0	0
$171$	943.537	0.421954
$172$	1262.64	0.559742
$173$	4125.91	1.81322	0.906610	−	0.421970i	$-0.138661\pi$
$173$	4125.91	1.81322	0.906610	+	0.421970i	$0.138661\pi$
$174$	1498.05	0.652683
$175$	0	0
$176$	−5.18443	−0.00222040
$177$	−221.372	−0.0940075
$178$	−1733.93	−0.730134
$179$	−3213.14	−1.34168	−0.670842	−	0.741600i	$-0.734067\pi$
$179$	−3213.14	−1.34168	−0.670842	+	0.741600i	$0.734067\pi$
$180$	0	0
$181$	3394.42	1.39395	0.696976	−	0.717095i	$-0.254529\pi$
$181$	3394.42	1.39395	0.696976	+	0.717095i	$0.254529\pi$
$182$	−2199.77	−0.895921
$183$	−412.050	−0.166446
$184$	−1106.28	−0.443240
$185$	0	0
$186$	−328.837	−0.129632
$187$	−33.9939	−0.0132935
$188$	−1962.98	−0.761514
$189$	599.653	0.230785
$190$	0	0
$191$	−3467.49	−1.31361	−0.656804	−	0.754062i	$-0.728092\pi$
$191$	−3467.49	−1.31361	−0.656804	+	0.754062i	$0.728092\pi$
$192$	866.273	0.325614
$193$	1792.14	0.668401	0.334200	−	0.942502i	$-0.391534\pi$
$193$	1792.14	0.668401	0.334200	+	0.942502i	$0.391534\pi$
$194$	−654.038	−0.242047
$195$	0	0
$196$	−767.011	−0.279523
$197$	1678.19	0.606935	0.303467	−	0.952842i	$-0.401856\pi$
$197$	1678.19	0.606935	0.303467	+	0.952842i	$0.401856\pi$
$198$	27.4218	0.00984233
$199$	3108.23	1.10722	0.553610	−	0.832776i	$-0.313250\pi$
$199$	3108.23	1.10722	0.553610	+	0.832776i	$0.313250\pi$
$200$	0	0
$201$	521.719	0.183081
$202$	−58.6878	−0.0204419
$203$	−6517.69	−2.25346
$204$	−290.728	−0.0997795
$205$	0	0
$206$	2988.46	1.01076
$207$	−446.512	−0.149926
$208$	168.534	0.0561815
$209$	−187.725	−0.0621301
$210$	0	0
$211$	−4473.27	−1.45949	−0.729745	−	0.683719i	$-0.760361\pi$
$211$	−4473.27	−1.45949	−0.729745	+	0.683719i	$0.760361\pi$
$212$	−2366.17	−0.766551
$213$	−1782.84	−0.573514
$214$	2317.08	0.740151
$215$	0	0
$216$	602.058	0.189652
$217$	1430.70	0.447568
$218$	−546.403	−0.169757
$219$	960.694	0.296428
$220$	0	0
$221$	1105.07	0.336357
$222$	101.503	0.0306868
$223$	−1753.42	−0.526535	−0.263268	−	0.964723i	$-0.584800\pi$
$223$	−1753.42	−0.526535	−0.263268	+	0.964723i	$0.584800\pi$
$224$	−4071.29	−1.21440
$225$	0	0
$226$	2692.29	0.792427
$227$	−936.900	−0.273939	−0.136970	−	0.990575i	$-0.543736\pi$
$227$	−936.900	−0.273939	−0.136970	+	0.990575i	$0.543736\pi$
$228$	−1605.49	−0.466342
$229$	−2582.06	−0.745096	−0.372548	−	0.928013i	$-0.621516\pi$
$229$	−2582.06	−0.745096	−0.372548	+	0.928013i	$0.621516\pi$
$230$	0	0
$231$	−119.306	−0.0339817
$232$	−6543.82	−1.85182
$233$	2295.01	0.645284	0.322642	−	0.946521i	$-0.395429\pi$
$233$	2295.01	0.645284	0.322642	+	0.946521i	$0.395429\pi$
$234$	−891.422	−0.249034
$235$	0	0
$236$	376.678	0.103897
$237$	−2311.41	−0.633510
$238$	−717.432	−0.195396
$239$	−2294.01	−0.620866	−0.310433	−	0.950595i	$-0.600474\pi$
$239$	−2294.01	−0.620866	−0.310433	+	0.950595i	$0.600474\pi$
$240$	0	0
$241$	382.287	0.102180	0.0510898	−	0.998694i	$-0.483731\pi$
$241$	382.287	0.102180	0.0510898	+	0.998694i	$0.483731\pi$
$242$	2259.32	0.600144
$243$	243.000	0.0641500
$244$	701.128	0.183956
$245$	0	0
$246$	845.240	0.219067
$247$	6102.52	1.57204
$248$	1436.44	0.367798
$249$	521.775	0.132796
$250$	0	0
$251$	−2259.98	−0.568322	−0.284161	−	0.958777i	$-0.591715\pi$
$251$	−2259.98	−0.568322	−0.284161	+	0.958777i	$0.591715\pi$
$252$	−1020.35	−0.255063
$253$	88.8375	0.0220758
$254$	2037.01	0.503202
$255$	0	0
$256$	−3969.38	−0.969087
$257$	−92.7843	−0.0225203	−0.0112602	−	0.999937i	$-0.503584\pi$
$257$	−92.7843	−0.0225203	−0.0112602	+	0.999937i	$0.503584\pi$
$258$	1262.64	0.304685
$259$	−441.619	−0.105949
$260$	0	0
$261$	−2641.19	−0.626382
$262$	547.302	0.129055
$263$	−568.312	−0.133246	−0.0666229	−	0.997778i	$-0.521222\pi$
$263$	−568.312	−0.133246	−0.0666229	+	0.997778i	$0.521222\pi$
$264$	−119.785	−0.0279251
$265$	0	0
$266$	−3961.87	−0.913226
$267$	3057.07	0.700711
$268$	−887.737	−0.202340
$269$	7582.41	1.71862	0.859309	−	0.511458i	$-0.170894\pi$
$269$	7582.41	1.71862	0.859309	+	0.511458i	$0.170894\pi$
$270$	0	0
$271$	7943.69	1.78061	0.890304	−	0.455366i	$-0.150492\pi$
$271$	7943.69	1.78061	0.890304	+	0.455366i	$0.150492\pi$
$272$	54.9657	0.0122529
$273$	3878.38	0.859818
$274$	−602.847	−0.132917
$275$	0	0
$276$	759.769	0.165698
$277$	6823.00	1.47998	0.739990	−	0.672618i	$-0.234830\pi$
$277$	6823.00	1.47998	0.739990	+	0.672618i	$0.234830\pi$
$278$	−131.456	−0.0283605
$279$	579.769	0.124408
$280$	0	0
$281$	3315.86	0.703942	0.351971	−	0.936011i	$-0.385512\pi$
$281$	3315.86	0.703942	0.351971	+	0.936011i	$0.385512\pi$
$282$	−1962.98	−0.414516
$283$	6602.76	1.38690	0.693451	−	0.720504i	$-0.256090\pi$
$283$	6602.76	1.38690	0.693451	+	0.720504i	$0.256090\pi$
$284$	3033.62	0.633846
$285$	0	0
$286$	177.356	0.0366688
$287$	−3677.46	−0.756353
$288$	−1649.83	−0.337559
$289$	−4552.59	−0.926642
$290$	0	0
$291$	1153.12	0.232293
$292$	−1634.68	−0.327611
$293$	5814.14	1.15927	0.579634	−	0.814877i	$-0.303195\pi$
$293$	5814.14	1.15927	0.579634	+	0.814877i	$0.303195\pi$
$294$	−767.011	−0.152153
$295$	0	0
$296$	−443.390	−0.0870660
$297$	−48.3469	−0.00944570
$298$	2901.81	0.564084
$299$	−2887.91	−0.558570
$300$	0	0
$301$	−5493.49	−1.05196
$302$	−1290.26	−0.245849
$303$	103.472	0.0196181
$304$	303.537	0.0572667
$305$	0	0
$306$	−290.728	−0.0543131
$307$	−8124.86	−1.51046	−0.755229	−	0.655462i	$-0.772474\pi$
$307$	−8124.86	−1.51046	−0.755229	+	0.655462i	$0.772474\pi$
$308$	203.007	0.0375564
$309$	−5268.91	−0.970025
$310$	0	0
$311$	7336.26	1.33762	0.668812	−	0.743432i	$-0.266803\pi$
$311$	7336.26	1.33762	0.668812	+	0.743432i	$0.266803\pi$
$312$	3893.93	0.706572
$313$	−2202.66	−0.397768	−0.198884	−	0.980023i	$-0.563732\pi$
$313$	−2202.66	−0.397768	−0.198884	+	0.980023i	$0.563732\pi$
$314$	3010.15	0.540996
$315$	0	0
$316$	3933.00	0.700154
$317$	10008.9	1.77336	0.886679	−	0.462386i	$-0.153007\pi$
$317$	10008.9	1.77336	0.886679	+	0.462386i	$0.153007\pi$
$318$	−2366.17	−0.417258
$319$	525.488	0.0922309
$320$	0	0
$321$	−4085.21	−0.710325
$322$	1874.89	0.324483
$323$	1990.27	0.342854
$324$	−413.480	−0.0708984
$325$	0	0
$326$	1500.30	0.254889
$327$	963.356	0.162917
$328$	−3692.20	−0.621548
$329$	8540.47	1.43116
$330$	0	0
$331$	−8695.94	−1.44402	−0.722012	−	0.691881i	$-0.756782\pi$
$331$	−8695.94	−1.44402	−0.722012	+	0.691881i	$0.756782\pi$
$332$	−887.832	−0.146765
$333$	−178.959	−0.0294502
$334$	369.069	0.0604627
$335$	0	0
$336$	192.909	0.0313216
$337$	−7400.61	−1.19625	−0.598126	−	0.801402i	$-0.704088\pi$
$337$	−7400.61	−1.19625	−0.598126	+	0.801402i	$0.704088\pi$
$338$	−2027.12	−0.326216
$339$	−4746.74	−0.760494
$340$	0	0
$341$	−115.350	−0.0183183
$342$	−1605.49	−0.253845
$343$	−4280.72	−0.673869
$344$	−5515.52	−0.864467
$345$	0	0
$346$	−7020.49	−1.09082
$347$	7841.44	1.21311	0.606557	−	0.795040i	$-0.292550\pi$
$347$	7841.44	1.21311	0.606557	+	0.795040i	$0.292550\pi$
$348$	4494.15	0.692275
$349$	−4961.26	−0.760946	−0.380473	−	0.924792i	$-0.624239\pi$
$349$	−4961.26	−0.760946	−0.380473	+	0.924792i	$0.624239\pi$
$350$	0	0
$351$	1571.65	0.238999
$352$	328.247	0.0497035
$353$	−12163.0	−1.83392	−0.916959	−	0.398981i	$-0.869364\pi$
$353$	−12163.0	−1.83392	−0.916959	+	0.398981i	$0.869364\pi$
$354$	376.678	0.0565543
$355$	0	0
$356$	−5201.80	−0.774424
$357$	1264.89	0.187522
$358$	5467.36	0.807148
$359$	5193.79	0.763559	0.381779	−	0.924253i	$-0.375311\pi$
$359$	5193.79	0.763559	0.381779	+	0.924253i	$0.375311\pi$
$360$	0	0
$361$	4131.90	0.602406
$362$	−5775.81	−0.838591
$363$	−3983.38	−0.575959
$364$	−6599.31	−0.950268
$365$	0	0
$366$	701.128	0.100133
$367$	−6086.09	−0.865644	−0.432822	−	0.901479i	$-0.642482\pi$
$367$	−6086.09	−0.865644	−0.432822	+	0.901479i	$0.642482\pi$
$368$	−143.644	−0.0203477
$369$	−1490.23	−0.210239
$370$	0	0
$371$	10294.7	1.44063
$372$	−986.512	−0.137495
$373$	−10581.9	−1.46893	−0.734466	−	0.678646i	$-0.762567\pi$
$373$	−10581.9	−1.46893	−0.734466	+	0.678646i	$0.762567\pi$
$374$	57.8428	0.00799727
$375$	0	0
$376$	8574.72	1.17608
$377$	−17082.4	−2.33366
$378$	−1020.35	−0.138839
$379$	11655.2	1.57964	0.789822	−	0.613336i	$-0.210173\pi$
$379$	11655.2	1.57964	0.789822	+	0.613336i	$0.210173\pi$
$380$	0	0
$381$	−3591.42	−0.482924
$382$	5900.16	0.790257
$383$	6364.97	0.849177	0.424588	−	0.905387i	$-0.360419\pi$
$383$	6364.97	0.849177	0.424588	+	0.905387i	$0.360419\pi$
$384$	2925.52	0.388782
$385$	0	0
$386$	−3049.44	−0.402105
$387$	−2226.15	−0.292407
$388$	−1962.11	−0.256730
$389$	6134.33	0.799545	0.399773	−	0.916614i	$-0.369089\pi$
$389$	6134.33	0.799545	0.399773	+	0.916614i	$0.369089\pi$
$390$	0	0
$391$	−941.862	−0.121821
$392$	3350.48	0.431696
$393$	−964.941	−0.123855
$394$	−2855.55	−0.365128
$395$	0	0
$396$	82.2653	0.0104394
$397$	9746.46	1.23214	0.616072	−	0.787690i	$-0.288723\pi$
$397$	9746.46	1.23214	0.616072	+	0.787690i	$0.288723\pi$
$398$	−5288.85	−0.666096
$399$	6985.12	0.876425
$400$	0	0
$401$	−1306.44	−0.162695	−0.0813474	−	0.996686i	$-0.525922\pi$
$401$	−1306.44	−0.162695	−0.0813474	+	0.996686i	$0.525922\pi$
$402$	−887.737	−0.110140
$403$	3749.77	0.463498
$404$	−176.063	−0.0216819
$405$	0	0
$406$	11090.2	1.35566
$407$	35.6055	0.00433636
$408$	1269.97	0.154100
$409$	−3876.93	−0.468709	−0.234354	−	0.972151i	$-0.575298\pi$
$409$	−3876.93	−0.468709	−0.234354	+	0.972151i	$0.575298\pi$
$410$	0	0
$411$	1062.87	0.127561
$412$	8965.38	1.07207
$413$	−1638.84	−0.195260
$414$	759.769	0.0901947
$415$	0	0
$416$	−10670.6	−1.25762
$417$	231.769	0.0272177
$418$	319.426	0.0373771
$419$	−16022.5	−1.86814	−0.934071	−	0.357088i	$-0.883770\pi$
$419$	−16022.5	−1.86814	−0.934071	+	0.357088i	$0.883770\pi$
$420$	0	0
$421$	−8119.73	−0.939980	−0.469990	−	0.882672i	$-0.655742\pi$
$421$	−8119.73	−0.939980	−0.469990	+	0.882672i	$0.655742\pi$
$422$	7611.54	0.878019
$423$	3460.89	0.397812
$424$	10336.0	1.18386
$425$	0	0
$426$	3033.62	0.345022
$427$	−3050.46	−0.345719
$428$	6951.24	0.785049
$429$	−312.694	−0.0351911
$430$	0	0
$431$	−5713.99	−0.638592	−0.319296	−	0.947655i	$-0.603446\pi$
$431$	−5713.99	−0.638592	−0.319296	+	0.947655i	$0.603446\pi$
$432$	78.1735	0.00870630
$433$	6251.34	0.693811	0.346906	−	0.937900i	$-0.387232\pi$
$433$	6251.34	0.693811	0.346906	+	0.937900i	$0.387232\pi$
$434$	−2434.42	−0.269254
$435$	0	0
$436$	−1639.21	−0.180055
$437$	−5201.25	−0.569358
$438$	−1634.68	−0.178329
$439$	−4230.97	−0.459984	−0.229992	−	0.973192i	$-0.573870\pi$
$439$	−4230.97	−0.459984	−0.229992	+	0.973192i	$0.573870\pi$
$440$	0	0
$441$	1352.31	0.146022
$442$	−1880.34	−0.202350
$443$	6314.29	0.677203	0.338601	−	0.940930i	$-0.390046\pi$
$443$	6314.29	0.677203	0.338601	+	0.940930i	$0.390046\pi$
$444$	304.510	0.0325482
$445$	0	0
$446$	2983.55	0.316760
$447$	−5116.13	−0.541353
$448$	6413.13	0.676321
$449$	−9349.71	−0.982717	−0.491358	−	0.870957i	$-0.663499\pi$
$449$	−9349.71	−0.982717	−0.491358	+	0.870957i	$0.663499\pi$
$450$	0	0
$451$	296.494	0.0309565
$452$	8076.87	0.840496
$453$	2274.84	0.235941
$454$	1594.19	0.164800
$455$	0	0
$456$	7013.14	0.720220
$457$	−9547.46	−0.977268	−0.488634	−	0.872489i	$-0.662505\pi$
$457$	−9547.46	−0.977268	−0.488634	+	0.872489i	$0.662505\pi$
$458$	4393.53	0.448245
$459$	512.578	0.0521244
$460$	0	0
$461$	6237.23	0.630145	0.315073	−	0.949068i	$-0.397971\pi$
$461$	6237.23	0.630145	0.315073	+	0.949068i	$0.397971\pi$
$462$	203.007	0.0204431
$463$	6469.98	0.649428	0.324714	−	0.945812i	$-0.394732\pi$
$463$	6469.98	0.649428	0.324714	+	0.945812i	$0.394732\pi$
$464$	−849.675	−0.0850111
$465$	0	0
$466$	−3905.10	−0.388198
$467$	7206.64	0.714097	0.357049	−	0.934086i	$-0.383783\pi$
$467$	7206.64	0.714097	0.357049	+	0.934086i	$0.383783\pi$
$468$	−2674.27	−0.264141
$469$	3862.35	0.380270
$470$	0	0
$471$	−5307.16	−0.519195
$472$	−1645.42	−0.160458
$473$	442.912	0.0430552
$474$	3933.00	0.381115
$475$	0	0
$476$	−2152.29	−0.207248
$477$	4171.75	0.400443
$478$	3903.39	0.373509
$479$	−10851.8	−1.03514	−0.517571	−	0.855640i	$-0.673164\pi$
$479$	−10851.8	−1.03514	−0.517571	+	0.855640i	$0.673164\pi$
$480$	0	0
$481$	−1157.46	−0.109720
$482$	−650.485	−0.0614705
$483$	−3305.59	−0.311407
$484$	6777.97	0.636549
$485$	0	0
$486$	−413.480	−0.0385922
$487$	12757.1	1.18702	0.593510	−	0.804827i	$-0.297742\pi$
$487$	12757.1	1.18702	0.593510	+	0.804827i	$0.297742\pi$
$488$	−3062.69	−0.284101
$489$	−2645.16	−0.244618
$490$	0	0
$491$	−7016.52	−0.644911	−0.322455	−	0.946585i	$-0.604508\pi$
$491$	−7016.52	−0.644911	−0.322455	+	0.946585i	$0.604508\pi$
$492$	2535.72	0.232356
$493$	−5571.26	−0.508960
$494$	−10383.8	−0.945729
$495$	0	0
$496$	186.512	0.0168844
$497$	−13198.6	−1.19122
$498$	−887.832	−0.0798890
$499$	11372.3	1.02023	0.510113	−	0.860107i	$-0.329604\pi$
$499$	11372.3	1.02023	0.510113	+	0.860107i	$0.329604\pi$
$500$	0	0
$501$	−650.700	−0.0580262
$502$	3845.50	0.341899
$503$	−5587.37	−0.495285	−0.247643	−	0.968851i	$-0.579656\pi$
$503$	−5587.37	−0.495285	−0.247643	+	0.968851i	$0.579656\pi$
$504$	4457.11	0.393919
$505$	0	0
$506$	−151.163	−0.0132806
$507$	3573.99	0.313070
$508$	6111.03	0.533726
$509$	16256.7	1.41565	0.707825	−	0.706388i	$-0.249676\pi$
$509$	16256.7	1.41565	0.707825	+	0.706388i	$0.249676\pi$
$510$	0	0
$511$	7112.14	0.615699
$512$	−1047.24	−0.0903943
$513$	2830.61	0.243615
$514$	157.878	0.0135481
$515$	0	0
$516$	3787.93	0.323167
$517$	−688.574	−0.0585754
$518$	751.442	0.0637384
$519$	12377.7	1.04686
$520$	0	0
$521$	19748.4	1.66064	0.830320	−	0.557286i	$-0.188157\pi$
$521$	19748.4	1.66064	0.830320	+	0.557286i	$0.188157\pi$
$522$	4494.15	0.376827
$523$	−7843.44	−0.655774	−0.327887	−	0.944717i	$-0.606337\pi$
$523$	−7843.44	−0.655774	−0.327887	+	0.944717i	$0.606337\pi$
$524$	1641.91	0.136884
$525$	0	0
$526$	967.019	0.0801597
$527$	1222.95	0.101086
$528$	−15.5533	−0.00128195
$529$	−9705.60	−0.797699
$530$	0	0
$531$	−664.116	−0.0542753
$532$	−11885.6	−0.968622
$533$	−9638.38	−0.783273
$534$	−5201.80	−0.421543
$535$	0	0
$536$	3877.84	0.312495
$537$	−9639.42	−0.774622
$538$	−12902.0	−1.03391
$539$	−269.053	−0.0215008
$540$	0	0
$541$	7383.29	0.586751	0.293376	−	0.955997i	$-0.405221\pi$
$541$	7383.29	0.586751	0.293376	+	0.955997i	$0.405221\pi$
$542$	−13516.7	−1.07120
$543$	10183.3	0.804798
$544$	−3480.10	−0.274280
$545$	0	0
$546$	−6599.31	−0.517260
$547$	−3354.90	−0.262240	−0.131120	−	0.991367i	$-0.541857\pi$
$547$	−3354.90	−0.262240	−0.131120	+	0.991367i	$0.541857\pi$
$548$	−1808.54	−0.140980
$549$	−1236.15	−0.0960976
$550$	0	0
$551$	−30766.2	−2.37874
$552$	−3318.84	−0.255905
$553$	−17111.6	−1.31584
$554$	−11609.8	−0.890346
$555$	0	0
$556$	−394.369	−0.0300809
$557$	20771.8	1.58012	0.790061	−	0.613028i	$-0.210049\pi$
$557$	20771.8	1.58012	0.790061	+	0.613028i	$0.210049\pi$
$558$	−986.512	−0.0748430
$559$	−14398.1	−1.08940
$560$	0	0
$561$	−101.982	−0.00767500
$562$	−5642.15	−0.423487
$563$	7194.86	0.538592	0.269296	−	0.963057i	$-0.413209\pi$
$563$	7194.86	0.538592	0.269296	+	0.963057i	$0.413209\pi$
$564$	−5888.93	−0.439660
$565$	0	0
$566$	−11235.0	−0.834350
$567$	1798.96	0.133244
$568$	−13251.5	−0.978913
$569$	11549.5	0.850931	0.425466	−	0.904975i	$-0.360110\pi$
$569$	11549.5	0.850931	0.425466	+	0.904975i	$0.360110\pi$
$570$	0	0
$571$	1482.54	0.108655	0.0543277	−	0.998523i	$-0.482698\pi$
$571$	1482.54	0.108655	0.0543277	+	0.998523i	$0.482698\pi$
$572$	532.068	0.0388932
$573$	−10402.5	−0.758412
$574$	6257.42	0.455017
$575$	0	0
$576$	2598.82	0.187993
$577$	−15264.0	−1.10130	−0.550649	−	0.834737i	$-0.685620\pi$
$577$	−15264.0	−1.10130	−0.550649	+	0.834737i	$0.685620\pi$
$578$	7746.52	0.557462
$579$	5376.43	0.385901
$580$	0	0
$581$	3862.76	0.275825
$582$	−1962.11	−0.139746
$583$	−830.006	−0.0589628
$584$	7140.66	0.505963
$585$	0	0
$586$	−9893.12	−0.697408
$587$	1736.89	0.122128	0.0610639	−	0.998134i	$-0.480551\pi$
$587$	1736.89	0.122128	0.0610639	+	0.998134i	$0.480551\pi$
$588$	−2301.03	−0.161383
$589$	6753.50	0.472450
$590$	0	0
$591$	5034.57	0.350414
$592$	−57.5714	−0.00399691
$593$	−11764.8	−0.814707	−0.407353	−	0.913271i	$-0.633548\pi$
$593$	−11764.8	−0.814707	−0.407353	+	0.913271i	$0.633548\pi$
$594$	82.2653	0.00568247
$595$	0	0
$596$	8705.42	0.598302
$597$	9324.69	0.639253
$598$	4913.96	0.336032
$599$	−9451.99	−0.644737	−0.322369	−	0.946614i	$-0.604479\pi$
$599$	−9451.99	−0.644737	−0.322369	+	0.946614i	$0.604479\pi$
$600$	0	0
$601$	−3131.93	−0.212569	−0.106285	−	0.994336i	$-0.533895\pi$
$601$	−3131.93	−0.212569	−0.106285	+	0.994336i	$0.533895\pi$
$602$	9347.51	0.632851
$603$	1565.16	0.105702
$604$	−3870.79	−0.260762
$605$	0	0
$606$	−176.063	−0.0118021
$607$	22700.8	1.51795	0.758975	−	0.651120i	$-0.225700\pi$
$607$	22700.8	1.51795	0.758975	+	0.651120i	$0.225700\pi$
$608$	−19218.2	−1.28191
$609$	−19553.1	−1.30103
$610$	0	0
$611$	22384.0	1.48210
$612$	−872.184	−0.0576077
$613$	28911.6	1.90494	0.952471	−	0.304629i	$-0.0985325\pi$
$613$	28911.6	1.90494	0.952471	+	0.304629i	$0.0985325\pi$
$614$	13825.0	0.908681
$615$	0	0
$616$	−886.780	−0.0580023
$617$	−5566.87	−0.363231	−0.181616	−	0.983370i	$-0.558133\pi$
$617$	−5566.87	−0.363231	−0.181616	+	0.983370i	$0.558133\pi$
$618$	8965.38	0.583560
$619$	4150.32	0.269492	0.134746	−	0.990880i	$-0.456978\pi$
$619$	4150.32	0.269492	0.134746	+	0.990880i	$0.456978\pi$
$620$	0	0
$621$	−1339.54	−0.0865600
$622$	−12483.1	−0.804705
$623$	22631.9	1.45542
$624$	505.603	0.0324364
$625$	0	0
$626$	3747.96	0.239295
$627$	−563.175	−0.0358709
$628$	9030.46	0.573813
$629$	−377.492	−0.0239294
$630$	0	0
$631$	−4090.09	−0.258041	−0.129021	−	0.991642i	$-0.541183\pi$
$631$	−4090.09	−0.258041	−0.129021	+	0.991642i	$0.541183\pi$
$632$	−17180.2	−1.08132
$633$	−13419.8	−0.842637
$634$	−17030.7	−1.06684
$635$	0	0
$636$	−7098.50	−0.442569
$637$	8746.32	0.544022
$638$	−894.150	−0.0554855
$639$	−5348.53	−0.331118
$640$	0	0
$641$	3909.35	0.240890	0.120445	−	0.992720i	$-0.461568\pi$
$641$	3909.35	0.240890	0.120445	+	0.992720i	$0.461568\pi$
$642$	6951.24	0.427327
$643$	30539.5	1.87303	0.936516	−	0.350624i	$-0.114031\pi$
$643$	30539.5	1.87303	0.936516	+	0.350624i	$0.114031\pi$
$644$	5624.66	0.344166
$645$	0	0
$646$	−3386.58	−0.206259
$647$	−12707.7	−0.772167	−0.386083	−	0.922464i	$-0.626172\pi$
$647$	−12707.7	−0.772167	−0.386083	+	0.922464i	$0.626172\pi$
$648$	1806.17	0.109496
$649$	132.132	0.00799170
$650$	0	0
$651$	4292.10	0.258403
$652$	4500.90	0.270351
$653$	12777.6	0.765737	0.382869	−	0.923803i	$-0.374936\pi$
$653$	12777.6	0.765737	0.382869	+	0.923803i	$0.374936\pi$
$654$	−1639.21	−0.0980095
$655$	0	0
$656$	−479.410	−0.0285332
$657$	2882.08	0.171143
$658$	−14532.1	−0.860976
$659$	23563.5	1.39287	0.696435	−	0.717620i	$-0.254768\pi$
$659$	23563.5	1.39287	0.696435	+	0.717620i	$0.254768\pi$
$660$	0	0
$661$	−4361.31	−0.256634	−0.128317	−	0.991733i	$-0.540958\pi$
$661$	−4361.31	−0.256634	−0.128317	+	0.991733i	$0.540958\pi$
$662$	14796.7	0.868715
$663$	3315.21	0.194196
$664$	3878.25	0.226665
$665$	0	0
$666$	304.510	0.0177170
$667$	14559.6	0.845200
$668$	1107.21	0.0641304
$669$	−5260.25	−0.303995
$670$	0	0
$671$	245.943	0.0141498
$672$	−12213.9	−0.701131
$673$	−8203.52	−0.469870	−0.234935	−	0.972011i	$-0.575488\pi$
$673$	−8203.52	−0.469870	−0.234935	+	0.972011i	$0.575488\pi$
$674$	12592.6	0.719657
$675$	0	0
$676$	−6081.37	−0.346004
$677$	28057.1	1.59279	0.796397	−	0.604774i	$-0.206737\pi$
$677$	28057.1	1.59279	0.796397	+	0.604774i	$0.206737\pi$
$678$	8076.87	0.457508
$679$	8536.73	0.482488
$680$	0	0
$681$	−2810.70	−0.158159
$682$	196.275	0.0110202
$683$	−3344.62	−0.187377	−0.0936885	−	0.995602i	$-0.529866\pi$
$683$	−3344.62	−0.187377	−0.0936885	+	0.995602i	$0.529866\pi$
$684$	−4816.46	−0.269243
$685$	0	0
$686$	7283.91	0.405395
$687$	−7746.17	−0.430182
$688$	−716.156	−0.0396849
$689$	26981.7	1.49190
$690$	0	0
$691$	12964.8	0.713757	0.356879	−	0.934151i	$-0.383841\pi$
$691$	12964.8	0.713757	0.356879	+	0.934151i	$0.383841\pi$
$692$	−21061.5	−1.15699
$693$	−357.918	−0.0196193
$694$	−13342.7	−0.729801
$695$	0	0
$696$	−19631.5	−1.06915
$697$	−3143.46	−0.170828
$698$	8441.90	0.457780
$699$	6885.03	0.372555
$700$	0	0
$701$	−16162.1	−0.870806	−0.435403	−	0.900236i	$-0.643394\pi$
$701$	−16162.1	−0.870806	−0.435403	+	0.900236i	$0.643394\pi$
$702$	−2674.27	−0.143780
$703$	−2084.63	−0.111839
$704$	−517.058	−0.0276809
$705$	0	0
$706$	20696.2	1.10327
$707$	766.014	0.0407481
$708$	1130.03	0.0599849
$709$	−14244.4	−0.754529	−0.377265	−	0.926105i	$-0.623135\pi$
$709$	−14244.4	−0.754529	−0.377265	+	0.926105i	$0.623135\pi$
$710$	0	0
$711$	−6934.22	−0.365757
$712$	22722.7	1.19602
$713$	−3195.97	−0.167868
$714$	−2152.29	−0.112812
$715$	0	0
$716$	16402.1	0.856109
$717$	−6882.02	−0.358457
$718$	−8837.55	−0.459352
$719$	−27638.5	−1.43358	−0.716790	−	0.697289i	$-0.754389\pi$
$719$	−27638.5	−1.43358	−0.716790	+	0.697289i	$0.754389\pi$
$720$	0	0
$721$	−39006.4	−2.01480
$722$	−7030.68	−0.362403
$723$	1146.86	0.0589934
$724$	−17327.4	−0.889460
$725$	0	0
$726$	6777.97	0.346493
$727$	−2525.52	−0.128840	−0.0644199	−	0.997923i	$-0.520520\pi$
$727$	−2525.52	−0.128840	−0.0644199	+	0.997923i	$0.520520\pi$
$728$	28827.3	1.46760
$729$	729.000	0.0370370
$730$	0	0
$731$	−4695.79	−0.237592
$732$	2103.39	0.106207
$733$	−8400.27	−0.423289	−0.211645	−	0.977347i	$-0.567882\pi$
$733$	−8400.27	−0.423289	−0.211645	+	0.977347i	$0.567882\pi$
$734$	10355.9	0.520765
$735$	0	0
$736$	9094.67	0.455481
$737$	−311.401	−0.0155639
$738$	2535.72	0.126479
$739$	−19689.1	−0.980074	−0.490037	−	0.871702i	$-0.663017\pi$
$739$	−19689.1	−0.980074	−0.490037	+	0.871702i	$0.663017\pi$
$740$	0	0
$741$	18307.6	0.907619
$742$	−17517.0	−0.866671
$743$	−22526.6	−1.11227	−0.556137	−	0.831091i	$-0.687717\pi$
$743$	−22526.6	−1.11227	−0.556137	+	0.831091i	$0.687717\pi$
$744$	4309.31	0.212348
$745$	0	0
$746$	18005.8	0.883699
$747$	1565.32	0.0766696
$748$	173.528	0.00848239
$749$	−30243.3	−1.47539
$750$	0	0
$751$	34691.1	1.68562	0.842808	−	0.538215i	$-0.180901\pi$
$751$	34691.1	1.68562	0.842808	+	0.538215i	$0.180901\pi$
$752$	1113.37	0.0539902
$753$	−6779.95	−0.328121
$754$	29066.8	1.40392
$755$	0	0
$756$	−3061.04	−0.147261
$757$	6619.98	0.317843	0.158922	−	0.987291i	$-0.449198\pi$
$757$	6619.98	0.317843	0.158922	+	0.987291i	$0.449198\pi$
$758$	−19832.0	−0.950303
$759$	266.512	0.0127454
$760$	0	0
$761$	−29368.7	−1.39897	−0.699483	−	0.714649i	$-0.746586\pi$
$761$	−29368.7	−1.39897	−0.699483	+	0.714649i	$0.746586\pi$
$762$	6111.03	0.290524
$763$	7131.84	0.338388
$764$	17700.5	0.838194
$765$	0	0
$766$	−10830.4	−0.510859
$767$	−4295.31	−0.202209
$768$	−11908.1	−0.559503
$769$	32677.4	1.53235	0.766174	−	0.642633i	$-0.222158\pi$
$769$	32677.4	1.53235	0.766174	+	0.642633i	$0.222158\pi$
$770$	0	0
$771$	−278.353	−0.0130021
$772$	−9148.33	−0.426497
$773$	−28047.5	−1.30504	−0.652522	−	0.757770i	$-0.726289\pi$
$773$	−28047.5	−1.30504	−0.652522	+	0.757770i	$0.726289\pi$
$774$	3787.93	0.175910
$775$	0	0
$776$	8570.96	0.396494
$777$	−1324.86	−0.0611699
$778$	−10438.0	−0.481001
$779$	−17359.1	−0.798402
$780$	0	0
$781$	1064.14	0.0487552
$782$	1602.64	0.0732867
$783$	−7923.57	−0.361642
$784$	435.039	0.0198177
$785$	0	0
$786$	1641.91	0.0745100
$787$	−22172.1	−1.00426	−0.502128	−	0.864793i	$-0.667449\pi$
$787$	−22172.1	−1.00426	−0.502128	+	0.864793i	$0.667449\pi$
$788$	−8566.64	−0.387276
$789$	−1704.94	−0.0769295
$790$	0	0
$791$	−35140.7	−1.57960
$792$	−359.354	−0.0161226
$793$	−7995.06	−0.358024
$794$	−16584.2	−0.741249
$795$	0	0
$796$	−15866.5	−0.706501
$797$	−24170.3	−1.07422	−0.537112	−	0.843511i	$-0.680485\pi$
$797$	−24170.3	−1.07422	−0.537112	+	0.843511i	$0.680485\pi$
$798$	−11885.6	−0.527251
$799$	7300.32	0.323238
$800$	0	0
$801$	9171.22	0.404556
$802$	2222.99	0.0978761
$803$	−573.415	−0.0251997
$804$	−2663.21	−0.116821
$805$	0	0
$806$	−6380.47	−0.278837
$807$	22747.2	0.992244
$808$	769.085	0.0334856
$809$	15304.2	0.665102	0.332551	−	0.943085i	$-0.392091\pi$
$809$	15304.2	0.665102	0.332551	+	0.943085i	$0.392091\pi$
$810$	0	0
$811$	−27002.2	−1.16914	−0.584572	−	0.811342i	$-0.698738\pi$
$811$	−27002.2	−1.16914	−0.584572	+	0.811342i	$0.698738\pi$
$812$	33270.7	1.43790
$813$	23831.1	1.02803
$814$	−60.5849	−0.00260872
$815$	0	0
$816$	164.897	0.00707421
$817$	−25931.5	−1.11044
$818$	6596.84	0.281972
$819$	11635.1	0.496416
$820$	0	0
$821$	25061.4	1.06535	0.532673	−	0.846321i	$-0.321188\pi$
$821$	25061.4	1.06535	0.532673	+	0.846321i	$0.321188\pi$
$822$	−1808.54	−0.0767398
$823$	−24896.4	−1.05448	−0.527238	−	0.849718i	$-0.676772\pi$
$823$	−24896.4	−1.05448	−0.527238	+	0.849718i	$0.676772\pi$
$824$	−39162.8	−1.65571
$825$	0	0
$826$	2788.59	0.117467
$827$	−20063.2	−0.843612	−0.421806	−	0.906686i	$-0.638604\pi$
$827$	−20063.2	−0.843612	−0.421806	+	0.906686i	$0.638604\pi$
$828$	2279.31	0.0956659
$829$	−13884.2	−0.581687	−0.290844	−	0.956771i	$-0.593936\pi$
$829$	−13884.2	−0.581687	−0.290844	+	0.956771i	$0.593936\pi$
$830$	0	0
$831$	20469.0	0.854467
$832$	16808.4	0.700393
$833$	2852.52	0.118648
$834$	−394.369	−0.0163740
$835$	0	0
$836$	958.277	0.0396444
$837$	1739.31	0.0718270
$838$	27263.3	1.12386
$839$	−13678.1	−0.562838	−0.281419	−	0.959585i	$-0.590805\pi$
$839$	−13678.1	−0.562838	−0.281419	+	0.959585i	$0.590805\pi$
$840$	0	0
$841$	61733.1	2.53118
$842$	13816.2	0.565485
$843$	9947.59	0.406421
$844$	22834.6	0.931280
$845$	0	0
$846$	−5888.93	−0.239321
$847$	−29489.5	−1.19630
$848$	1342.06	0.0543473
$849$	19808.3	0.800728
$850$	0	0
$851$	986.512	0.0397382
$852$	9100.86	0.365951
$853$	29802.9	1.19629	0.598143	−	0.801390i	$-0.295906\pi$
$853$	29802.9	1.19629	0.598143	+	0.801390i	$0.295906\pi$
$854$	5190.54	0.207982
$855$	0	0
$856$	−30364.6	−1.21243
$857$	22045.2	0.878706	0.439353	−	0.898314i	$-0.355208\pi$
$857$	22045.2	0.878706	0.439353	+	0.898314i	$0.355208\pi$
$858$	532.068	0.0211708
$859$	33609.5	1.33497	0.667487	−	0.744622i	$-0.267370\pi$
$859$	33609.5	1.33497	0.667487	+	0.744622i	$0.267370\pi$
$860$	0	0
$861$	−11032.4	−0.436681
$862$	9722.70	0.384172
$863$	33775.6	1.33226	0.666128	−	0.745838i	$-0.267951\pi$
$863$	33775.6	1.33226	0.666128	+	0.745838i	$0.267951\pi$
$864$	−4949.48	−0.194890
$865$	0	0
$866$	−10637.0	−0.417392
$867$	−13657.8	−0.534997
$868$	−7303.27	−0.285587
$869$	1379.62	0.0538556
$870$	0	0
$871$	10123.0	0.393805
$872$	7160.44	0.278077
$873$	3459.37	0.134115
$874$	8850.25	0.342522
$875$	0	0
$876$	−4904.04	−0.189146
$877$	12637.0	0.486570	0.243285	−	0.969955i	$-0.421775\pi$
$877$	12637.0	0.486570	0.243285	+	0.969955i	$0.421775\pi$
$878$	7199.25	0.276723
$879$	17442.4	0.669304
$880$	0	0
$881$	−6579.45	−0.251609	−0.125804	−	0.992055i	$-0.540151\pi$
$881$	−6579.45	−0.251609	−0.125804	+	0.992055i	$0.540151\pi$
$882$	−2301.03	−0.0878456
$883$	−50442.1	−1.92244	−0.961219	−	0.275786i	$-0.911062\pi$
$883$	−50442.1	−1.92244	−0.961219	+	0.275786i	$0.911062\pi$
$884$	−5641.03	−0.214625
$885$	0	0
$886$	−10744.2	−0.407401
$887$	984.823	0.0372797	0.0186399	−	0.999826i	$-0.494066\pi$
$887$	984.823	0.0372797	0.0186399	+	0.999826i	$0.494066\pi$
$888$	−1330.17	−0.0502676
$889$	−26587.7	−1.00306
$890$	0	0
$891$	−145.041	−0.00545348
$892$	8950.64	0.335975
$893$	40314.6	1.51072
$894$	8705.42	0.325674
$895$	0	0
$896$	21658.0	0.807525
$897$	−8663.74	−0.322490
$898$	15909.1	0.591196
$899$	−18904.7	−0.701342
$900$	0	0
$901$	8799.79	0.325376
$902$	−504.503	−0.0186232
$903$	−16480.5	−0.607348
$904$	−35281.6	−1.29806
$905$	0	0
$906$	−3870.79	−0.141941
$907$	43679.9	1.59908	0.799541	−	0.600612i	$-0.205076\pi$
$907$	43679.9	1.59908	0.799541	+	0.600612i	$0.205076\pi$
$908$	4782.58	0.174797
$909$	310.415	0.0113265
$910$	0	0
$911$	−10364.3	−0.376930	−0.188465	−	0.982080i	$-0.560351\pi$
$911$	−10364.3	−0.376930	−0.188465	+	0.982080i	$0.560351\pi$
$912$	910.612	0.0330629
$913$	−311.435	−0.0112891
$914$	16245.6	0.587918
$915$	0	0
$916$	13180.6	0.475435
$917$	−7143.58	−0.257254
$918$	−872.184	−0.0313577
$919$	11451.9	0.411059	0.205530	−	0.978651i	$-0.434108\pi$
$919$	11451.9	0.411059	0.205530	+	0.978651i	$0.434108\pi$
$920$	0	0
$921$	−24374.6	−0.872063
$922$	−10613.0	−0.379091
$923$	−34592.7	−1.23362
$924$	609.020	0.0216832
$925$	0	0
$926$	−11009.1	−0.390692
$927$	−15806.7	−0.560044
$928$	53796.4	1.90297
$929$	−27701.8	−0.978326	−0.489163	−	0.872192i	$-0.662698\pi$
$929$	−27701.8	−0.978326	−0.489163	+	0.872192i	$0.662698\pi$
$930$	0	0
$931$	15752.5	0.554529
$932$	−11715.3	−0.411746
$933$	22008.8	0.772277
$934$	−12262.5	−0.429596
$935$	0	0
$936$	11681.8	0.407940
$937$	−5878.01	−0.204937	−0.102469	−	0.994736i	$-0.532674\pi$
$937$	−5878.01	−0.204937	−0.102469	+	0.994736i	$0.532674\pi$
$938$	−6572.03	−0.228768
$939$	−6607.97	−0.229652
$940$	0	0
$941$	−28786.0	−0.997234	−0.498617	−	0.866823i	$-0.666159\pi$
$941$	−28786.0	−0.997234	−0.498617	+	0.866823i	$0.666159\pi$
$942$	9030.46	0.312344
$943$	8214.90	0.283684
$944$	−213.647	−0.00736612
$945$	0	0
$946$	−753.642	−0.0259017
$947$	−1695.04	−0.0581641	−0.0290821	−	0.999577i	$-0.509258\pi$
$947$	−1695.04	−0.0581641	−0.0290821	+	0.999577i	$0.509258\pi$
$948$	11799.0	0.404234
$949$	18640.5	0.637613
$950$	0	0
$951$	30026.6	1.02385
$952$	9401.72	0.320075
$953$	31929.4	1.08530	0.542651	−	0.839958i	$-0.317420\pi$
$953$	31929.4	1.08530	0.542651	+	0.839958i	$0.317420\pi$
$954$	−7098.50	−0.240904
$955$	0	0
$956$	11710.2	0.396166
$957$	1576.46	0.0532495
$958$	18465.1	0.622735
$959$	7868.57	0.264952
$960$	0	0
$961$	−25641.2	−0.860704
$962$	1969.48	0.0660069
$963$	−12255.6	−0.410106
$964$	−1951.46	−0.0651994
$965$	0	0
$966$	5624.66	0.187340
$967$	−10897.1	−0.362385	−0.181193	−	0.983448i	$-0.557996\pi$
$967$	−10897.1	−0.362385	−0.181193	+	0.983448i	$0.557996\pi$
$968$	−29607.7	−0.983087
$969$	5970.82	0.197947
$970$	0	0
$971$	7041.97	0.232737	0.116368	−	0.993206i	$-0.462875\pi$
$971$	7041.97	0.232737	0.116368	+	0.993206i	$0.462875\pi$
$972$	−1240.44	−0.0409332
$973$	1715.81	0.0565328
$974$	−21707.0	−0.714103
$975$	0	0
$976$	−397.671	−0.0130422
$977$	−37607.6	−1.23150	−0.615749	−	0.787943i	$-0.711146\pi$
$977$	−37607.6	−1.23150	−0.615749	+	0.787943i	$0.711146\pi$
$978$	4500.90	0.147160
$979$	−1824.69	−0.0595684
$980$	0	0
$981$	2890.07	0.0940599
$982$	11939.0	0.387974
$983$	−25297.7	−0.820826	−0.410413	−	0.911900i	$-0.634615\pi$
$983$	−25297.7	−0.820826	−0.410413	+	0.911900i	$0.634615\pi$
$984$	−11076.6	−0.358851
$985$	0	0
$986$	9479.85	0.306187
$987$	25621.4	0.826281
$988$	−31151.5	−1.00310
$989$	12271.6	0.394556
$990$	0	0
$991$	−41686.5	−1.33624	−0.668120	−	0.744053i	$-0.732901\pi$
$991$	−41686.5	−1.33624	−0.668120	+	0.744053i	$0.732901\pi$
$992$	−11808.9	−0.377955
$993$	−26087.8	−0.833708
$994$	22458.3	0.716633
$995$	0	0
$996$	−2663.50	−0.0847351
$997$	25465.9	0.808939	0.404470	−	0.914551i	$-0.367456\pi$
$997$	25465.9	0.808939	0.404470	+	0.914551i	$0.367456\pi$
$998$	−19350.6	−0.613761
$999$	−536.878	−0.0170031

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.4.a.f.1.1		2
3.2	odd	2		225.4.a.i.1.2		2
4.3	odd	2		1200.4.a.bn.1.1		2
5.2	odd	4		15.4.b.a.4.2	✓	4
5.3	odd	4		15.4.b.a.4.3	yes	4
5.4	even	2		75.4.a.c.1.2		2
15.2	even	4		45.4.b.b.19.3		4
15.8	even	4		45.4.b.b.19.2		4
15.14	odd	2		225.4.a.o.1.1		2
20.3	even	4		240.4.f.f.49.1		4
20.7	even	4		240.4.f.f.49.3		4
20.19	odd	2		1200.4.a.bt.1.2		2
40.3	even	4		960.4.f.p.769.4		4
40.13	odd	4		960.4.f.q.769.2		4
40.27	even	4		960.4.f.p.769.2		4
40.37	odd	4		960.4.f.q.769.4		4
60.23	odd	4		720.4.f.j.289.4		4
60.47	odd	4		720.4.f.j.289.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.4.b.a.4.2	✓	4	5.2	odd	4
15.4.b.a.4.3	yes	4	5.3	odd	4
45.4.b.b.19.2		4	15.8	even	4
45.4.b.b.19.3		4	15.2	even	4
75.4.a.c.1.2		2	5.4	even	2
75.4.a.f.1.1		2	1.1	even	1	trivial
225.4.a.i.1.2		2	3.2	odd	2
225.4.a.o.1.1		2	15.14	odd	2
240.4.f.f.49.1		4	20.3	even	4
240.4.f.f.49.3		4	20.7	even	4
720.4.f.j.289.3		4	60.47	odd	4
720.4.f.j.289.4		4	60.23	odd	4
960.4.f.p.769.2		4	40.27	even	4
960.4.f.p.769.4		4	40.3	even	4
960.4.f.q.769.2		4	40.13	odd	4
960.4.f.q.769.4		4	40.37	odd	4
1200.4.a.bn.1.1		2	4.3	odd	2
1200.4.a.bt.1.2		2	20.19	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	75.a (trivial)

\(f(q)\)	\(=\)	\(q-1.70156 q^{2} +3.00000 q^{3} -5.10469 q^{4} -5.10469 q^{6} +22.2094 q^{7} +22.2984 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-1.70156 q^{2} +3.00000 q^{3} -5.10469 q^{4} -5.10469 q^{6} +22.2094 q^{7} +22.2984 q^{8} +9.00000 q^{9} -1.79063 q^{11} -15.3141 q^{12} +58.2094 q^{13} -37.7906 q^{14} +2.89531 q^{16} +18.9844 q^{17} -15.3141 q^{18} +104.837 q^{19} +66.6281 q^{21} +3.04686 q^{22} -49.6125 q^{23} +66.8953 q^{24} -99.0469 q^{26} +27.0000 q^{27} -113.372 q^{28} -293.466 q^{29} +64.4187 q^{31} -183.314 q^{32} -5.37188 q^{33} -32.3031 q^{34} -45.9422 q^{36} -19.8844 q^{37} -178.388 q^{38} +174.628 q^{39} -165.581 q^{41} -113.372 q^{42} -247.350 q^{43} +9.14059 q^{44} +84.4187 q^{46} +384.544 q^{47} +8.68594 q^{48} +150.256 q^{49} +56.9531 q^{51} -297.141 q^{52} +463.528 q^{53} -45.9422 q^{54} +495.234 q^{56} +314.512 q^{57} +499.350 q^{58} -73.7906 q^{59} -137.350 q^{61} -109.612 q^{62} +199.884 q^{63} +288.758 q^{64} +9.14059 q^{66} +173.906 q^{67} -96.9093 q^{68} -148.837 q^{69} -594.281 q^{71} +200.686 q^{72} +320.231 q^{73} +33.8345 q^{74} -535.163 q^{76} -39.7687 q^{77} -297.141 q^{78} -770.469 q^{79} +81.0000 q^{81} +281.747 q^{82} +173.925 q^{83} -340.116 q^{84} +420.881 q^{86} -880.397 q^{87} -39.9282 q^{88} +1019.02 q^{89} +1292.79 q^{91} +253.256 q^{92} +193.256 q^{93} -654.325 q^{94} -549.942 q^{96} +384.375 q^{97} -255.670 q^{98} -16.1156 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 3 q^{2} + 6 q^{3} + 9 q^{4} + 9 q^{6} + 6 q^{7} + 51 q^{8} + 18 q^{9}+O(q^{10}) \) 2 * q + 3 * q^2 + 6 * q^3 + 9 * q^4 + 9 * q^6 + 6 * q^7 + 51 * q^8 + 18 * q^9	\( 2 q + 3 q^{2} + 6 q^{3} + 9 q^{4} + 9 q^{6} + 6 q^{7} + 51 q^{8} + 18 q^{9} - 42 q^{11} + 27 q^{12} + 78 q^{13} - 114 q^{14} + 25 q^{16} + 102 q^{17} + 27 q^{18} + 56 q^{19} + 18 q^{21} - 186 q^{22} - 48 q^{23} + 153 q^{24} - 6 q^{26} + 54 q^{27} - 342 q^{28} - 318 q^{29} + 52 q^{31} - 309 q^{32} - 126 q^{33} + 358 q^{34} + 81 q^{36} + 306 q^{37} - 408 q^{38} + 234 q^{39} - 408 q^{41} - 342 q^{42} + 120 q^{43} - 558 q^{44} + 92 q^{46} + 180 q^{47} + 75 q^{48} + 70 q^{49} + 306 q^{51} - 18 q^{52} + 402 q^{53} + 81 q^{54} + 30 q^{56} + 168 q^{57} + 384 q^{58} - 186 q^{59} + 340 q^{61} - 168 q^{62} + 54 q^{63} - 479 q^{64} - 558 q^{66} + 732 q^{67} + 1074 q^{68} - 144 q^{69} - 36 q^{71} + 459 q^{72} + 1332 q^{73} + 1566 q^{74} - 1224 q^{76} + 612 q^{77} - 18 q^{78} + 380 q^{79} + 162 q^{81} - 858 q^{82} - 984 q^{83} - 1026 q^{84} + 2148 q^{86} - 954 q^{87} - 1194 q^{88} + 1116 q^{89} + 972 q^{91} + 276 q^{92} + 156 q^{93} - 1616 q^{94} - 927 q^{96} - 768 q^{97} - 633 q^{98} - 378 q^{99}+O(q^{100}) \) 2 * q + 3 * q^2 + 6 * q^3 + 9 * q^4 + 9 * q^6 + 6 * q^7 + 51 * q^8 + 18 * q^9 - 42 * q^11 + 27 * q^12 + 78 * q^13 - 114 * q^14 + 25 * q^16 + 102 * q^17 + 27 * q^18 + 56 * q^19 + 18 * q^21 - 186 * q^22 - 48 * q^23 + 153 * q^24 - 6 * q^26 + 54 * q^27 - 342 * q^28 - 318 * q^29 + 52 * q^31 - 309 * q^32 - 126 * q^33 + 358 * q^34 + 81 * q^36 + 306 * q^37 - 408 * q^38 + 234 * q^39 - 408 * q^41 - 342 * q^42 + 120 * q^43 - 558 * q^44 + 92 * q^46 + 180 * q^47 + 75 * q^48 + 70 * q^49 + 306 * q^51 - 18 * q^52 + 402 * q^53 + 81 * q^54 + 30 * q^56 + 168 * q^57 + 384 * q^58 - 186 * q^59 + 340 * q^61 - 168 * q^62 + 54 * q^63 - 479 * q^64 - 558 * q^66 + 732 * q^67 + 1074 * q^68 - 144 * q^69 - 36 * q^71 + 459 * q^72 + 1332 * q^73 + 1566 * q^74 - 1224 * q^76 + 612 * q^77 - 18 * q^78 + 380 * q^79 + 162 * q^81 - 858 * q^82 - 984 * q^83 - 1026 * q^84 + 2148 * q^86 - 954 * q^87 - 1194 * q^88 + 1116 * q^89 + 972 * q^91 + 276 * q^92 + 156 * q^93 - 1616 * q^94 - 927 * q^96 - 768 * q^97 - 633 * q^98 - 378 * q^99

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