LMFDB - Embedded newform 119.4.a.e.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [119,4,Mod(1,119)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(119, 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("119.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 119 = 7 \cdot 17 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	119.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:	$7.02122729068$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 2x^{8} - 53x^{7} + 90x^{6} + 880x^{5} - 1087x^{4} - 4674x^{3} + 2515x^{2} + 1814x + 36 $ x^9 - 2x^8 - 53x^7 + 90x^6 + 880x^5 - 1087x^4 - 4674x^3 + 2515x^2 + 1814x + 36
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$5.07700$ of defining polynomial
Character	$\chi$	$=$	119.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+5.07700 q^{2} +4.79487 q^{3} +17.7759 q^{4} -7.32611 q^{5} +24.3435 q^{6} +7.00000 q^{7} +49.6323 q^{8} -4.00927 q^{9} +O(q^{10})$	\(q+5.07700 q^{2} +4.79487 q^{3} +17.7759 q^{4} -7.32611 q^{5} +24.3435 q^{6} +7.00000 q^{7} +49.6323 q^{8} -4.00927 q^{9} -37.1947 q^{10} -66.4198 q^{11} +85.2331 q^{12} +18.2269 q^{13} +35.5390 q^{14} -35.1277 q^{15} +109.776 q^{16} +17.0000 q^{17} -20.3550 q^{18} +108.594 q^{19} -130.228 q^{20} +33.5641 q^{21} -337.213 q^{22} -118.663 q^{23} +237.980 q^{24} -71.3281 q^{25} +92.5381 q^{26} -148.685 q^{27} +124.431 q^{28} +185.078 q^{29} -178.343 q^{30} +203.188 q^{31} +160.273 q^{32} -318.474 q^{33} +86.3090 q^{34} -51.2828 q^{35} -71.2684 q^{36} +198.775 q^{37} +551.331 q^{38} +87.3957 q^{39} -363.612 q^{40} -360.723 q^{41} +170.405 q^{42} +176.187 q^{43} -1180.67 q^{44} +29.3723 q^{45} -602.452 q^{46} +90.4938 q^{47} +526.360 q^{48} +49.0000 q^{49} -362.133 q^{50} +81.5127 q^{51} +324.000 q^{52} -266.272 q^{53} -754.875 q^{54} +486.599 q^{55} +347.426 q^{56} +520.693 q^{57} +939.640 q^{58} +207.117 q^{59} -624.427 q^{60} +161.076 q^{61} +1031.58 q^{62} -28.0649 q^{63} -64.5008 q^{64} -133.533 q^{65} -1616.89 q^{66} +192.619 q^{67} +302.190 q^{68} -568.974 q^{69} -260.363 q^{70} -689.688 q^{71} -198.989 q^{72} -580.427 q^{73} +1009.18 q^{74} -342.009 q^{75} +1930.36 q^{76} -464.939 q^{77} +443.708 q^{78} +186.547 q^{79} -804.229 q^{80} -604.676 q^{81} -1831.39 q^{82} +869.866 q^{83} +596.632 q^{84} -124.544 q^{85} +894.502 q^{86} +887.423 q^{87} -3296.57 q^{88} +1405.88 q^{89} +149.123 q^{90} +127.589 q^{91} -2109.35 q^{92} +974.258 q^{93} +459.437 q^{94} -795.571 q^{95} +768.487 q^{96} -479.736 q^{97} +248.773 q^{98} +266.295 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 2 q^{2} + 11 q^{3} + 38 q^{4} - 3 q^{5} + 9 q^{6} + 63 q^{7} + 24 q^{8} + 74 q^{9}+O(q^{10}) $ 9 * q + 2 * q^2 + 11 * q^3 + 38 * q^4 - 3 * q^5 + 9 * q^6 + 63 * q^7 + 24 * q^8 + 74 * q^9	\( 9 q + 2 q^{2} + 11 q^{3} + 38 q^{4} - 3 q^{5} + 9 q^{6} + 63 q^{7} + 24 q^{8} + 74 q^{9} + 134 q^{10} - 8 q^{11} + 56 q^{12} + 164 q^{13} + 14 q^{14} + 34 q^{15} + 178 q^{16} + 153 q^{17} + 98 q^{18} + 244 q^{19} - 41 q^{20} + 77 q^{21} - 80 q^{22} - 14 q^{23} + 298 q^{24} + 684 q^{25} + 326 q^{26} + 218 q^{27} + 266 q^{28} - 234 q^{29} - 335 q^{30} + 555 q^{31} - 181 q^{32} + 458 q^{33} + 34 q^{34} - 21 q^{35} - 1221 q^{36} - 364 q^{37} - 714 q^{38} - 52 q^{39} + 123 q^{40} - 45 q^{41} + 63 q^{42} - 135 q^{43} - 748 q^{44} - 844 q^{45} - 1576 q^{46} - 172 q^{47} - 949 q^{48} + 441 q^{49} - 2901 q^{50} + 187 q^{51} - 1596 q^{52} + 101 q^{53} - 1163 q^{54} + 1260 q^{55} + 168 q^{56} - 602 q^{57} + 1062 q^{58} + 280 q^{59} - 1727 q^{60} + 639 q^{61} - 1708 q^{62} + 518 q^{63} - 2390 q^{64} + 638 q^{65} - 2476 q^{66} + 35 q^{67} + 646 q^{68} + 1288 q^{69} + 938 q^{70} - 1616 q^{71} + 1335 q^{72} + 1049 q^{73} - 370 q^{74} + 1260 q^{75} + 4964 q^{76} - 56 q^{77} - 4714 q^{78} + 2304 q^{79} - 3996 q^{80} - 791 q^{81} - 215 q^{82} + 2508 q^{83} + 392 q^{84} - 51 q^{85} + 623 q^{86} + 166 q^{87} - 416 q^{88} + 2762 q^{89} + 2935 q^{90} + 1148 q^{91} - 2392 q^{92} + 2784 q^{93} - 862 q^{94} - 3462 q^{95} + 2928 q^{96} + 3107 q^{97} + 98 q^{98} - 2396 q^{99}+O(q^{100}) \) 9 * q + 2 * q^2 + 11 * q^3 + 38 * q^4 - 3 * q^5 + 9 * q^6 + 63 * q^7 + 24 * q^8 + 74 * q^9 + 134 * q^10 - 8 * q^11 + 56 * q^12 + 164 * q^13 + 14 * q^14 + 34 * q^15 + 178 * q^16 + 153 * q^17 + 98 * q^18 + 244 * q^19 - 41 * q^20 + 77 * q^21 - 80 * q^22 - 14 * q^23 + 298 * q^24 + 684 * q^25 + 326 * q^26 + 218 * q^27 + 266 * q^28 - 234 * q^29 - 335 * q^30 + 555 * q^31 - 181 * q^32 + 458 * q^33 + 34 * q^34 - 21 * q^35 - 1221 * q^36 - 364 * q^37 - 714 * q^38 - 52 * q^39 + 123 * q^40 - 45 * q^41 + 63 * q^42 - 135 * q^43 - 748 * q^44 - 844 * q^45 - 1576 * q^46 - 172 * q^47 - 949 * q^48 + 441 * q^49 - 2901 * q^50 + 187 * q^51 - 1596 * q^52 + 101 * q^53 - 1163 * q^54 + 1260 * q^55 + 168 * q^56 - 602 * q^57 + 1062 * q^58 + 280 * q^59 - 1727 * q^60 + 639 * q^61 - 1708 * q^62 + 518 * q^63 - 2390 * q^64 + 638 * q^65 - 2476 * q^66 + 35 * q^67 + 646 * q^68 + 1288 * q^69 + 938 * q^70 - 1616 * q^71 + 1335 * q^72 + 1049 * q^73 - 370 * q^74 + 1260 * q^75 + 4964 * q^76 - 56 * q^77 - 4714 * q^78 + 2304 * q^79 - 3996 * q^80 - 791 * q^81 - 215 * q^82 + 2508 * q^83 + 392 * q^84 - 51 * q^85 + 623 * q^86 + 166 * q^87 - 416 * q^88 + 2762 * q^89 + 2935 * q^90 + 1148 * q^91 - 2392 * q^92 + 2784 * q^93 - 862 * q^94 - 3462 * q^95 + 2928 * q^96 + 3107 * q^97 + 98 * q^98 - 2396 * 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 $

$2$	5.07700	1.79499	0.897495	−	0.441025i	$-0.145385\pi$
$2$	5.07700	1.79499	0.897495	+	0.441025i	$0.145385\pi$
$3$	4.79487	0.922772	0.461386	−	0.887199i	$-0.347352\pi$
$3$	4.79487	0.922772	0.461386	+	0.887199i	$0.347352\pi$
$4$	17.7759	2.22199
$5$	−7.32611	−0.655267	−0.327634	−	0.944805i	$-0.606251\pi$
$5$	−7.32611	−0.655267	−0.327634	+	0.944805i	$0.606251\pi$
$6$	24.3435	1.65637
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	49.6323	2.19346
$9$	−4.00927	−0.148491
$10$	−37.1947	−1.17620
$11$	−66.4198	−1.82058	−0.910288	−	0.413976i	$-0.864140\pi$
$11$	−66.4198	−1.82058	−0.910288	+	0.413976i	$0.864140\pi$
$12$	85.2331	2.05039
$13$	18.2269	0.388865	0.194432	−	0.980916i	$-0.437714\pi$
$13$	18.2269	0.388865	0.194432	+	0.980916i	$0.437714\pi$
$14$	35.5390	0.678442
$15$	−35.1277	−0.604662
$16$	109.776	1.71525
$17$	17.0000	0.242536
$17$	17.0000	0.242536
$18$	−20.3550	−0.266541
$19$	108.594	1.31122	0.655609	−	0.755100i	$-0.272412\pi$
$19$	108.594	1.31122	0.655609	+	0.755100i	$0.272412\pi$
$20$	−130.228	−1.45600
$21$	33.5641	0.348775
$22$	−337.213	−3.26792
$23$	−118.663	−1.07578	−0.537891	−	0.843015i	$-0.680779\pi$
$23$	−118.663	−1.07578	−0.537891	+	0.843015i	$0.680779\pi$
$24$	237.980	2.02406
$25$	−71.3281	−0.570625
$26$	92.5381	0.698008
$27$	−148.685	−1.05980
$28$	124.431	0.839833
$29$	185.078	1.18511	0.592553	−	0.805531i	$-0.298120\pi$
$29$	185.078	1.18511	0.592553	+	0.805531i	$0.298120\pi$
$30$	−178.343	−1.08536
$31$	203.188	1.17721	0.588607	−	0.808420i	$-0.299677\pi$
$31$	203.188	1.17721	0.588607	+	0.808420i	$0.299677\pi$
$32$	160.273	0.885391
$33$	−318.474	−1.67998
$34$	86.3090	0.435349
$35$	−51.2828	−0.247668
$36$	−71.2684	−0.329946
$37$	198.775	0.883201	0.441601	−	0.897212i	$-0.354411\pi$
$37$	198.775	0.883201	0.441601	+	0.897212i	$0.354411\pi$
$38$	551.331	2.35362
$39$	87.3957	0.358834
$40$	−363.612	−1.43730
$41$	−360.723	−1.37404	−0.687019	−	0.726640i	$-0.741081\pi$
$41$	−360.723	−1.37404	−0.687019	+	0.726640i	$0.741081\pi$
$42$	170.405	0.626048
$43$	176.187	0.624844	0.312422	−	0.949943i	$-0.398860\pi$
$43$	176.187	0.624844	0.312422	+	0.949943i	$0.398860\pi$
$44$	−1180.67	−4.04530
$45$	29.3723	0.0973016
$46$	−602.452	−1.93102
$47$	90.4938	0.280848	0.140424	−	0.990091i	$-0.455153\pi$
$47$	90.4938	0.280848	0.140424	+	0.990091i	$0.455153\pi$
$48$	526.360	1.58278
$49$	49.0000	0.142857
$50$	−362.133	−1.02427
$51$	81.5127	0.223805
$52$	324.000	0.864053
$53$	−266.272	−0.690100	−0.345050	−	0.938584i	$-0.612138\pi$
$53$	−266.272	−0.690100	−0.345050	+	0.938584i	$0.612138\pi$
$54$	−754.875	−1.90232
$55$	486.599	1.19296
$56$	347.426	0.829049
$57$	520.693	1.20996
$58$	939.640	2.12725
$59$	207.117	0.457022	0.228511	−	0.973541i	$-0.426614\pi$
$59$	207.117	0.457022	0.228511	+	0.973541i	$0.426614\pi$
$60$	−624.427	−1.34355
$61$	161.076	0.338092	0.169046	−	0.985608i	$-0.445931\pi$
$61$	161.076	0.338092	0.169046	+	0.985608i	$0.445931\pi$
$62$	1031.58	2.11309
$63$	−28.0649	−0.0561245
$64$	−64.5008	−0.125978
$65$	−133.533	−0.254810
$66$	−1616.89	−3.01554
$67$	192.619	0.351227	0.175613	−	0.984459i	$-0.443809\pi$
$67$	192.619	0.351227	0.175613	+	0.984459i	$0.443809\pi$
$68$	302.190	0.538911
$69$	−568.974	−0.992701
$70$	−260.363	−0.444561
$71$	−689.688	−1.15283	−0.576415	−	0.817157i	$-0.695549\pi$
$71$	−689.688	−1.15283	−0.576415	+	0.817157i	$0.695549\pi$
$72$	−198.989	−0.325710
$73$	−580.427	−0.930600	−0.465300	−	0.885153i	$-0.654054\pi$
$73$	−580.427	−0.930600	−0.465300	+	0.885153i	$0.654054\pi$
$74$	1009.18	1.58534
$75$	−342.009	−0.526557
$76$	1930.36	2.91351
$77$	−464.939	−0.688113
$78$	443.708	0.644103
$79$	186.547	0.265673	0.132836	−	0.991138i	$-0.457592\pi$
$79$	186.547	0.265673	0.132836	+	0.991138i	$0.457592\pi$
$80$	−804.229	−1.12394
$81$	−604.676	−0.829459
$82$	−1831.39	−2.46638
$83$	869.866	1.15036	0.575182	−	0.818026i	$-0.304931\pi$
$83$	869.866	1.15036	0.575182	+	0.818026i	$0.304931\pi$
$84$	596.632	0.774974
$85$	−124.544	−0.158926
$86$	894.502	1.12159
$87$	887.423	1.09358
$88$	−3296.57	−3.99336
$89$	1405.88	1.67442	0.837211	−	0.546881i	$-0.184185\pi$
$89$	1405.88	1.67442	0.837211	+	0.546881i	$0.184185\pi$
$90$	149.123	0.174655
$91$	127.589	0.146977
$92$	−2109.35	−2.39037
$93$	974.258	1.08630
$94$	459.437	0.504120
$95$	−795.571	−0.859199
$96$	768.487	0.817014
$97$	−479.736	−0.502163	−0.251082	−	0.967966i	$-0.580786\pi$
$97$	−479.736	−0.502163	−0.251082	+	0.967966i	$0.580786\pi$
$98$	248.773	0.256427
$99$	266.295	0.270340
$100$	−1267.92	−1.26792
$101$	−195.373	−0.192479	−0.0962394	−	0.995358i	$-0.530681\pi$
$101$	−195.373	−0.192479	−0.0962394	+	0.995358i	$0.530681\pi$
$102$	413.840	0.401728
$103$	636.216	0.608623	0.304312	−	0.952573i	$-0.401574\pi$
$103$	636.216	0.608623	0.304312	+	0.952573i	$0.401574\pi$
$104$	904.644	0.852958
$105$	−245.894	−0.228541
$106$	−1351.86	−1.23872
$107$	1041.85	0.941306	0.470653	−	0.882319i	$-0.344018\pi$
$107$	1041.85	0.941306	0.470653	+	0.882319i	$0.344018\pi$
$108$	−2643.02	−2.35485
$109$	−2028.26	−1.78231	−0.891156	−	0.453697i	$-0.850105\pi$
$109$	−2028.26	−1.78231	−0.891156	+	0.453697i	$0.850105\pi$
$110$	2470.46	2.14136
$111$	953.101	0.814994
$112$	768.430	0.648302
$113$	2119.45	1.76443	0.882217	−	0.470843i	$-0.156050\pi$
$113$	2119.45	1.76443	0.882217	+	0.470843i	$0.156050\pi$
$114$	2643.56	2.17186
$115$	869.339	0.704924
$116$	3289.93	2.63329
$117$	−73.0767	−0.0577431
$118$	1051.53	0.820350
$119$	119.000	0.0916698
$120$	−1743.47	−1.32630
$121$	3080.60	2.31450
$122$	817.781	0.606873
$123$	−1729.62	−1.26792
$124$	3611.85	2.61576
$125$	1438.32	1.02918
$126$	−142.485	−0.100743
$127$	429.597	0.300162	0.150081	−	0.988674i	$-0.452047\pi$
$127$	429.597	0.300162	0.150081	+	0.988674i	$0.452047\pi$
$128$	−1609.65	−1.11152
$129$	844.794	0.576589
$130$	−677.944	−0.457382
$131$	−2207.61	−1.47237	−0.736184	−	0.676782i	$-0.763374\pi$
$131$	−2207.61	−1.47237	−0.736184	+	0.676782i	$0.763374\pi$
$132$	−5661.17	−3.73289
$133$	760.157	0.495594
$134$	977.928	0.630449
$135$	1089.28	0.694450
$136$	843.749	0.531992
$137$	2771.58	1.72841	0.864205	−	0.503141i	$-0.167822\pi$
$137$	2771.58	1.72841	0.864205	+	0.503141i	$0.167822\pi$
$138$	−2888.68	−1.78189
$139$	34.9761	0.0213427	0.0106713	−	0.999943i	$-0.496603\pi$
$139$	34.9761	0.0213427	0.0106713	+	0.999943i	$0.496603\pi$
$140$	−911.598	−0.550315
$141$	433.906	0.259159
$142$	−3501.54	−2.06932
$143$	−1210.63	−0.707958
$144$	−440.120	−0.254699
$145$	−1355.90	−0.776561
$146$	−2946.83	−1.67042
$147$	234.948	0.131825
$148$	3533.41	1.96246
$149$	−1295.62	−0.712358	−0.356179	−	0.934418i	$-0.615921\pi$
$149$	−1295.62	−0.712358	−0.356179	+	0.934418i	$0.615921\pi$
$150$	−1736.38	−0.945164
$151$	263.221	0.141858	0.0709291	−	0.997481i	$-0.477404\pi$
$151$	263.221	0.141858	0.0709291	+	0.997481i	$0.477404\pi$
$152$	5389.76	2.87610
$153$	−68.1576	−0.0360145
$154$	−2360.49	−1.23516
$155$	−1488.58	−0.771389
$156$	1553.54	0.797324
$157$	−2123.54	−1.07947	−0.539735	−	0.841835i	$-0.681476\pi$
$157$	−2123.54	−1.07947	−0.539735	+	0.841835i	$0.681476\pi$
$158$	947.097	0.476880
$159$	−1276.74	−0.636805
$160$	−1174.18	−0.580168
$161$	−830.642	−0.406607
$162$	−3069.94	−1.48887
$163$	−2532.31	−1.21685	−0.608423	−	0.793613i	$-0.708198\pi$
$163$	−2532.31	−1.21685	−0.608423	+	0.793613i	$0.708198\pi$
$164$	−6412.19	−3.05310
$165$	2333.18	1.10083
$166$	4416.31	2.06489
$167$	−2623.95	−1.21585	−0.607925	−	0.793994i	$-0.707998\pi$
$167$	−2623.95	−1.21585	−0.607925	+	0.793994i	$0.707998\pi$
$168$	1665.86	0.765023
$169$	−1864.78	−0.848784
$170$	−632.309	−0.285270
$171$	−435.382	−0.194705
$172$	3131.89	1.38840
$173$	3635.29	1.59761	0.798804	−	0.601591i	$-0.205466\pi$
$173$	3635.29	1.59761	0.798804	+	0.601591i	$0.205466\pi$
$174$	4505.45	1.96297
$175$	−499.297	−0.215676
$176$	−7291.29	−3.12273
$177$	993.097	0.421727
$178$	7137.67	3.00557
$179$	−3428.30	−1.43153	−0.715764	−	0.698343i	$-0.753921\pi$
$179$	−3428.30	−1.43153	−0.715764	+	0.698343i	$0.753921\pi$
$180$	522.120	0.216203
$181$	3248.00	1.33382	0.666912	−	0.745137i	$-0.267616\pi$
$181$	3248.00	1.33382	0.666912	+	0.745137i	$0.267616\pi$
$182$	647.767	0.263822
$183$	772.337	0.311982
$184$	−5889.52	−2.35968
$185$	−1456.25	−0.578733
$186$	4946.31	1.94990
$187$	−1129.14	−0.441555
$188$	1608.61	0.624042
$189$	−1040.80	−0.400565
$190$	−4039.11	−1.54225
$191$	−1267.48	−0.480165	−0.240082	−	0.970753i	$-0.577174\pi$
$191$	−1267.48	−0.480165	−0.240082	+	0.970753i	$0.577174\pi$
$192$	−309.272	−0.116249
$193$	−1246.81	−0.465014	−0.232507	−	0.972595i	$-0.574693\pi$
$193$	−1246.81	−0.465014	−0.232507	+	0.972595i	$0.574693\pi$
$194$	−2435.62	−0.901378
$195$	−640.270	−0.235132
$196$	871.020	0.317427
$197$	−4194.93	−1.51714	−0.758569	−	0.651592i	$-0.774101\pi$
$197$	−4194.93	−1.51714	−0.758569	+	0.651592i	$0.774101\pi$
$198$	1351.98	0.485257
$199$	356.110	0.126854	0.0634271	−	0.997986i	$-0.479797\pi$
$199$	356.110	0.126854	0.0634271	+	0.997986i	$0.479797\pi$
$200$	−3540.18	−1.25164
$201$	923.584	0.324102
$202$	−991.909	−0.345497
$203$	1295.54	0.447928
$204$	1448.96	0.497293
$205$	2642.70	0.900362
$206$	3230.07	1.09247
$207$	475.752	0.159744
$208$	2000.87	0.666999
$209$	−7212.79	−2.38717
$210$	−1248.40	−0.410229
$211$	2273.12	0.741651	0.370825	−	0.928703i	$-0.379075\pi$
$211$	2273.12	0.741651	0.370825	+	0.928703i	$0.379075\pi$
$212$	−4733.23	−1.53339
$213$	−3306.96	−1.06380
$214$	5289.48	1.68963
$215$	−1290.77	−0.409440
$216$	−7379.59	−2.32462
$217$	1422.32	0.444945
$218$	−10297.5	−3.19923
$219$	−2783.07	−0.858732
$220$	8649.74	2.65075
$221$	309.858	0.0943136
$222$	4838.89	1.46291
$223$	2196.18	0.659494	0.329747	−	0.944069i	$-0.393037\pi$
$223$	2196.18	0.659494	0.329747	+	0.944069i	$0.393037\pi$
$224$	1121.91	0.334646
$225$	285.973	0.0847329
$226$	10760.4	3.16714
$227$	−5211.83	−1.52388	−0.761941	−	0.647646i	$-0.775753\pi$
$227$	−5211.83	−1.52388	−0.761941	+	0.647646i	$0.775753\pi$
$228$	9255.80	2.68851
$229$	−5040.10	−1.45441	−0.727203	−	0.686422i	$-0.759180\pi$
$229$	−5040.10	−1.45441	−0.727203	+	0.686422i	$0.759180\pi$
$230$	4413.63	1.26533
$231$	−2229.32	−0.634972
$232$	9185.83	2.59948
$233$	2400.43	0.674924	0.337462	−	0.941339i	$-0.390431\pi$
$233$	2400.43	0.674924	0.337462	+	0.941339i	$0.390431\pi$
$234$	−371.010	−0.103648
$235$	−662.968	−0.184031
$236$	3681.69	1.01550
$237$	894.466	0.245155
$238$	604.163	0.164546
$239$	−380.868	−0.103081	−0.0515404	−	0.998671i	$-0.516413\pi$
$239$	−380.868	−0.103081	−0.0515404	+	0.998671i	$0.516413\pi$
$240$	−3856.17	−1.03714
$241$	54.8575	0.0146626	0.00733129	−	0.999973i	$-0.497666\pi$
$241$	54.8575	0.0146626	0.00733129	+	0.999973i	$0.497666\pi$
$242$	15640.2	4.15450
$243$	1115.16	0.294394
$244$	2863.27	0.751238
$245$	−358.979	−0.0936096
$246$	−8781.28	−2.27591
$247$	1979.33	0.509887
$248$	10084.7	2.58217
$249$	4170.89	1.06152
$250$	7302.36	1.84737
$251$	−338.200	−0.0850477	−0.0425239	−	0.999095i	$-0.513540\pi$
$251$	−338.200	−0.0850477	−0.0425239	+	0.999095i	$0.513540\pi$
$252$	−498.879	−0.124708
$253$	7881.59	1.95854
$254$	2181.06	0.538788
$255$	−597.171	−0.146652
$256$	−7656.20	−1.86919
$257$	746.871	0.181278	0.0906391	−	0.995884i	$-0.471109\pi$
$257$	746.871	0.181278	0.0906391	+	0.995884i	$0.471109\pi$
$258$	4289.02	1.03497
$259$	1391.43	0.333819
$260$	−2373.66	−0.566186
$261$	−742.026	−0.175978
$262$	−11208.1	−2.64289
$263$	−7707.61	−1.80712	−0.903559	−	0.428465i	$-0.859055\pi$
$263$	−7707.61	−1.80712	−0.903559	+	0.428465i	$0.859055\pi$
$264$	−15806.6	−3.68496
$265$	1950.74	0.452200
$266$	3859.32	0.889586
$267$	6741.03	1.54511
$268$	3423.98	0.780422
$269$	−6121.56	−1.38750	−0.693751	−	0.720215i	$-0.744043\pi$
$269$	−6121.56	−1.38750	−0.693751	+	0.720215i	$0.744043\pi$
$270$	5530.30	1.24653
$271$	−8385.50	−1.87964	−0.939820	−	0.341669i	$-0.889008\pi$
$271$	−8385.50	−1.87964	−0.939820	+	0.341669i	$0.889008\pi$
$272$	1866.19	0.416008
$273$	611.770	0.135626
$274$	14071.3	3.10248
$275$	4737.60	1.03887
$276$	−10114.0	−2.20577
$277$	−2802.88	−0.607973	−0.303986	−	0.952676i	$-0.598318\pi$
$277$	−2802.88	−0.607973	−0.303986	+	0.952676i	$0.598318\pi$
$278$	177.574	0.0383099
$279$	−814.635	−0.174806
$280$	−2545.28	−0.543249
$281$	2214.20	0.470065	0.235032	−	0.971988i	$-0.424480\pi$
$281$	2214.20	0.470065	0.235032	+	0.971988i	$0.424480\pi$
$282$	2202.94	0.465188
$283$	−6154.12	−1.29267	−0.646333	−	0.763056i	$-0.723698\pi$
$283$	−6154.12	−1.29267	−0.646333	+	0.763056i	$0.723698\pi$
$284$	−12259.8	−2.56157
$285$	−3814.66	−0.792845
$286$	−6146.37	−1.27078
$287$	−2525.06	−0.519337
$288$	−642.577	−0.131473
$289$	289.000	0.0588235
$290$	−6883.90	−1.39392
$291$	−2300.27	−0.463382
$292$	−10317.6	−2.06778
$293$	1876.11	0.374074	0.187037	−	0.982353i	$-0.440112\pi$
$293$	1876.11	0.374074	0.187037	+	0.982353i	$0.440112\pi$
$294$	1192.83	0.236624
$295$	−1517.36	−0.299472
$296$	9865.67	1.93726
$297$	9875.65	1.92944
$298$	−6577.86	−1.27867
$299$	−2162.86	−0.418333
$300$	−6079.51	−1.17000
$301$	1233.31	0.236169
$302$	1336.37	0.254634
$303$	−936.788	−0.177614
$304$	11921.0	2.24906
$305$	−1180.06	−0.221541
$306$	−346.036	−0.0646456
$307$	3617.55	0.672523	0.336261	−	0.941769i	$-0.390837\pi$
$307$	3617.55	0.672523	0.336261	+	0.941769i	$0.390837\pi$
$308$	−8264.71	−1.52898
$309$	3050.57	0.561621
$310$	−7557.50	−1.38464
$311$	6683.69	1.21864	0.609320	−	0.792924i	$-0.291442\pi$
$311$	6683.69	1.21864	0.609320	+	0.792924i	$0.291442\pi$
$312$	4337.65	0.787086
$313$	6356.15	1.14783	0.573915	−	0.818915i	$-0.305424\pi$
$313$	6356.15	1.14783	0.573915	+	0.818915i	$0.305424\pi$
$314$	−10781.2	−1.93764
$315$	205.606	0.0367765
$316$	3316.04	0.590322
$317$	9717.27	1.72169	0.860846	−	0.508866i	$-0.169935\pi$
$317$	9717.27	1.72169	0.860846	+	0.508866i	$0.169935\pi$
$318$	−6482.00	−1.14306
$319$	−12292.8	−2.15758
$320$	472.540	0.0825493
$321$	4995.54	0.868611
$322$	−4217.17	−0.729856
$323$	1846.10	0.318017
$324$	−10748.7	−1.84305
$325$	−1300.09	−0.221896
$326$	−12856.5	−2.18423
$327$	−9725.23	−1.64467
$328$	−17903.5	−3.01389
$329$	633.457	0.106151
$330$	11845.5	1.97599
$331$	7474.63	1.24122	0.620609	−	0.784120i	$-0.286886\pi$
$331$	7474.63	1.24122	0.620609	+	0.784120i	$0.286886\pi$
$332$	15462.7	2.55609
$333$	−796.943	−0.131148
$334$	−13321.8	−2.18244
$335$	−1411.15	−0.230147
$336$	3684.52	0.598235
$337$	9472.86	1.53122	0.765608	−	0.643308i	$-0.222438\pi$
$337$	9472.86	1.53122	0.765608	+	0.643308i	$0.222438\pi$
$338$	−9467.48	−1.52356
$339$	10162.5	1.62817
$340$	−2213.88	−0.353131
$341$	−13495.7	−2.14321
$342$	−2210.43	−0.349493
$343$	343.000	0.0539949
$344$	8744.57	1.37057
$345$	4168.36	0.650485
$346$	18456.4	2.86769
$347$	−819.647	−0.126804	−0.0634019	−	0.997988i	$-0.520195\pi$
$347$	−819.647	−0.126804	−0.0634019	+	0.997988i	$0.520195\pi$
$348$	15774.8	2.42993
$349$	9535.34	1.46251	0.731254	−	0.682106i	$-0.238936\pi$
$349$	9535.34	1.46251	0.731254	+	0.682106i	$0.238936\pi$
$350$	−2534.93	−0.387136
$351$	−2710.08	−0.412117
$352$	−10645.3	−1.61192
$353$	−7063.20	−1.06497	−0.532487	−	0.846438i	$-0.678743\pi$
$353$	−7063.20	−1.06497	−0.532487	+	0.846438i	$0.678743\pi$
$354$	5041.95	0.756996
$355$	5052.73	0.755411
$356$	24990.9	3.72055
$357$	570.589	0.0845904
$358$	−17405.5	−2.56958
$359$	−2455.98	−0.361063	−0.180531	−	0.983569i	$-0.557782\pi$
$359$	−2455.98	−0.361063	−0.180531	+	0.983569i	$0.557782\pi$
$360$	1457.82	0.213427
$361$	4933.64	0.719294
$362$	16490.1	2.39420
$363$	14771.0	2.13575
$364$	2268.00	0.326581
$365$	4252.27	0.609792
$366$	3921.15	0.560005
$367$	−54.8495	−0.00780142	−0.00390071	−	0.999992i	$-0.501242\pi$
$367$	−54.8495	−0.00780142	−0.00390071	+	0.999992i	$0.501242\pi$
$368$	−13026.3	−1.84523
$369$	1446.24	0.204033
$370$	−7393.38	−1.03882
$371$	−1863.90	−0.260833
$372$	17318.3	2.41375
$373$	−3763.69	−0.522458	−0.261229	−	0.965277i	$-0.584128\pi$
$373$	−3763.69	−0.522458	−0.261229	+	0.965277i	$0.584128\pi$
$374$	−5732.63	−0.792586
$375$	6896.56	0.949698
$376$	4491.41	0.616029
$377$	3373.40	0.460846
$378$	−5284.12	−0.719011
$379$	−5747.82	−0.779012	−0.389506	−	0.921024i	$-0.627354\pi$
$379$	−5747.82	−0.779012	−0.389506	+	0.921024i	$0.627354\pi$
$380$	−14142.0	−1.90913
$381$	2059.86	0.276981
$382$	−6434.98	−0.861891
$383$	−2495.41	−0.332923	−0.166462	−	0.986048i	$-0.553234\pi$
$383$	−2495.41	−0.332923	−0.166462	+	0.986048i	$0.553234\pi$
$384$	−7718.07	−1.02568
$385$	3406.19	0.450898
$386$	−6330.07	−0.834695
$387$	−706.382	−0.0927840
$388$	−8527.75	−1.11580
$389$	−3985.85	−0.519513	−0.259756	−	0.965674i	$-0.583642\pi$
$389$	−3985.85	−0.519513	−0.259756	+	0.965674i	$0.583642\pi$
$390$	−3250.65	−0.422059
$391$	−2017.27	−0.260915
$392$	2431.98	0.313351
$393$	−10585.2	−1.35866
$394$	−21297.6	−2.72325
$395$	−1366.66	−0.174087
$396$	4733.64	0.600692
$397$	8121.38	1.02670	0.513351	−	0.858179i	$-0.328404\pi$
$397$	8121.38	1.02670	0.513351	+	0.858179i	$0.328404\pi$
$398$	1807.97	0.227702
$399$	3644.85	0.457320
$400$	−7830.09	−0.978762
$401$	1631.38	0.203160	0.101580	−	0.994827i	$-0.467610\pi$
$401$	1631.38	0.203160	0.101580	+	0.994827i	$0.467610\pi$
$402$	4689.03	0.581760
$403$	3703.49	0.457777
$404$	−3472.94	−0.427686
$405$	4429.92	0.543517
$406$	6577.48	0.804026
$407$	−13202.6	−1.60794
$408$	4045.66	0.490907
$409$	12302.1	1.48728	0.743642	−	0.668578i	$-0.233097\pi$
$409$	12302.1	1.48728	0.743642	+	0.668578i	$0.233097\pi$
$410$	13417.0	1.61614
$411$	13289.4	1.59493
$412$	11309.3	1.35235
$413$	1449.82	0.172738
$414$	2415.39	0.286739
$415$	−6372.73	−0.753795
$416$	2921.28	0.344297
$417$	167.706	0.0196944
$418$	−36619.3	−4.28495
$419$	−6248.80	−0.728577	−0.364288	−	0.931286i	$-0.618688\pi$
$419$	−6248.80	−0.728577	−0.364288	+	0.931286i	$0.618688\pi$
$420$	−4370.99	−0.507815
$421$	3396.34	0.393177	0.196588	−	0.980486i	$-0.437014\pi$
$421$	3396.34	0.393177	0.196588	+	0.980486i	$0.437014\pi$
$422$	11540.6	1.33126
$423$	−362.814	−0.0417036
$424$	−13215.7	−1.51370
$425$	−1212.58	−0.138397
$426$	−16789.4	−1.90951
$427$	1127.53	0.127787
$428$	18519.9	2.09157
$429$	−5804.81	−0.653284
$430$	−6553.22	−0.734941
$431$	−1651.50	−0.184571	−0.0922855	−	0.995733i	$-0.529417\pi$
$431$	−1651.50	−0.184571	−0.0922855	+	0.995733i	$0.529417\pi$
$432$	−16322.0	−1.81781
$433$	−2241.40	−0.248764	−0.124382	−	0.992234i	$-0.539695\pi$
$433$	−2241.40	−0.248764	−0.124382	+	0.992234i	$0.539695\pi$
$434$	7221.09	0.798672
$435$	−6501.36	−0.716589
$436$	−36054.2	−3.96028
$437$	−12886.1	−1.41058
$438$	−14129.6	−1.54142
$439$	892.152	0.0969934	0.0484967	−	0.998823i	$-0.484557\pi$
$439$	892.152	0.0969934	0.0484967	+	0.998823i	$0.484557\pi$
$440$	24151.0	2.61672
$441$	−196.454	−0.0212131
$442$	1573.15	0.169292
$443$	8787.23	0.942424	0.471212	−	0.882020i	$-0.343817\pi$
$443$	8787.23	0.942424	0.471212	+	0.882020i	$0.343817\pi$
$444$	16942.2	1.81091
$445$	−10299.7	−1.09719
$446$	11150.0	1.18379
$447$	−6212.32	−0.657344
$448$	−451.505	−0.0476152
$449$	9036.46	0.949793	0.474896	−	0.880042i	$-0.342486\pi$
$449$	9036.46	0.949793	0.474896	+	0.880042i	$0.342486\pi$
$450$	1451.89	0.152095
$451$	23959.2	2.50154
$452$	37675.1	3.92055
$453$	1262.11	0.130903
$454$	−26460.4	−2.73535
$455$	−934.728	−0.0963093
$456$	25843.2	2.65399
$457$	264.011	0.0270239	0.0135120	−	0.999909i	$-0.495699\pi$
$457$	264.011	0.0270239	0.0135120	+	0.999909i	$0.495699\pi$
$458$	−25588.6	−2.61064
$459$	−2527.65	−0.257038
$460$	15453.3	1.56633
$461$	18243.6	1.84315	0.921573	−	0.388206i	$-0.126905\pi$
$461$	18243.6	1.84315	0.921573	+	0.388206i	$0.126905\pi$
$462$	−11318.3	−1.13977
$463$	−10229.0	−1.02674	−0.513369	−	0.858168i	$-0.671603\pi$
$463$	−10229.0	−1.02674	−0.513369	+	0.858168i	$0.671603\pi$
$464$	20317.0	2.03275
$465$	−7137.52	−0.711817
$466$	12187.0	1.21148
$467$	−126.156	−0.0125006	−0.00625031	−	0.999980i	$-0.501990\pi$
$467$	−126.156	−0.0125006	−0.00625031	+	0.999980i	$0.501990\pi$
$468$	−1299.00	−0.128304
$469$	1348.34	0.132751
$470$	−3365.89	−0.330333
$471$	−10182.1	−0.996106
$472$	10279.7	1.00246
$473$	−11702.3	−1.13758
$474$	4541.20	0.440052
$475$	−7745.80	−0.748214
$476$	2115.33	0.203689
$477$	1067.56	0.102474
$478$	−1933.67	−0.185029
$479$	10801.7	1.03036	0.515178	−	0.857083i	$-0.327726\pi$
$479$	10801.7	1.03036	0.515178	+	0.857083i	$0.327726\pi$
$480$	−5630.02	−0.535362
$481$	3623.06	0.343446
$482$	278.511	0.0263192
$483$	−3982.82	−0.375206
$484$	54760.4	5.14279
$485$	3514.60	0.329051
$486$	5661.69	0.528435
$487$	8950.44	0.832819	0.416410	−	0.909177i	$-0.363288\pi$
$487$	8950.44	0.832819	0.416410	+	0.909177i	$0.363288\pi$
$488$	7994.56	0.741592
$489$	−12142.1	−1.12287
$490$	−1822.54	−0.168028
$491$	−21349.5	−1.96230	−0.981148	−	0.193256i	$-0.938095\pi$
$491$	−21349.5	−1.96230	−0.981148	+	0.193256i	$0.938095\pi$
$492$	−30745.6	−2.81731
$493$	3146.32	0.287431
$494$	10049.1	0.915241
$495$	−1950.91	−0.177145
$496$	22305.1	2.01921
$497$	−4827.81	−0.435728
$498$	21175.6	1.90542
$499$	−14963.0	−1.34235	−0.671177	−	0.741297i	$-0.734211\pi$
$499$	−14963.0	−1.34235	−0.671177	+	0.741297i	$0.734211\pi$
$500$	25567.5	2.28682
$501$	−12581.5	−1.12195
$502$	−1717.04	−0.152660
$503$	16391.5	1.45300	0.726500	−	0.687166i	$-0.241146\pi$
$503$	16391.5	1.45300	0.726500	+	0.687166i	$0.241146\pi$
$504$	−1392.92	−0.123107
$505$	1431.33	0.126125
$506$	40014.8	3.51556
$507$	−8941.36	−0.783234
$508$	7636.48	0.666957
$509$	−12842.0	−1.11830	−0.559149	−	0.829067i	$-0.688872\pi$
$509$	−12842.0	−1.11830	−0.559149	+	0.829067i	$0.688872\pi$
$510$	−3031.84	−0.263239
$511$	−4062.99	−0.351734
$512$	−25993.3	−2.24366
$513$	−16146.3	−1.38962
$514$	3791.86	0.325393
$515$	−4660.99	−0.398811
$516$	15017.0	1.28117
$517$	−6010.58	−0.511306
$518$	7064.27	0.599201
$519$	17430.7	1.47423
$520$	−6627.52	−0.558916
$521$	16837.2	1.41583	0.707917	−	0.706295i	$-0.249635\pi$
$521$	16837.2	1.41583	0.707917	+	0.706295i	$0.249635\pi$
$522$	−3767.27	−0.315879
$523$	−786.412	−0.0657503	−0.0328752	−	0.999459i	$-0.510466\pi$
$523$	−786.412	−0.0657503	−0.0328752	+	0.999459i	$0.510466\pi$
$524$	−39242.4	−3.27158
$525$	−2394.06	−0.199020
$526$	−39131.5	−3.24376
$527$	3454.19	0.285516
$528$	−34960.7	−2.88157
$529$	1913.94	0.157306
$530$	9903.90	0.811694
$531$	−830.386	−0.0678638
$532$	13512.5	1.10120
$533$	−6574.88	−0.534315
$534$	34224.2	2.77346
$535$	−7632.73	−0.616807
$536$	9560.14	0.770401
$537$	−16438.3	−1.32097
$538$	−31079.1	−2.49055
$539$	−3254.57	−0.260082
$540$	19363.0	1.54306
$541$	−1247.36	−0.0991280	−0.0495640	−	0.998771i	$-0.515783\pi$
$541$	−1247.36	−0.0991280	−0.0495640	+	0.998771i	$0.515783\pi$
$542$	−42573.2	−3.37394
$543$	15573.7	1.23082
$544$	2724.64	0.214739
$545$	14859.3	1.16789
$546$	3105.95	0.243448
$547$	5521.05	0.431559	0.215780	−	0.976442i	$-0.430771\pi$
$547$	5521.05	0.431559	0.215780	+	0.976442i	$0.430771\pi$
$548$	49267.4	3.84051
$549$	−645.796	−0.0502038
$550$	24052.8	1.86475
$551$	20098.3	1.55393
$552$	−28239.5	−2.17745
$553$	1305.83	0.100415
$554$	−14230.2	−1.09130
$555$	−6982.52	−0.534039
$556$	621.732	0.0474232
$557$	67.0735	0.00510233	0.00255116	−	0.999997i	$-0.499188\pi$
$557$	67.0735	0.00510233	0.00255116	+	0.999997i	$0.499188\pi$
$558$	−4135.90	−0.313775
$559$	3211.35	0.242980
$560$	−5629.60	−0.424811
$561$	−5414.06	−0.407454
$562$	11241.5	0.843761
$563$	17988.7	1.34660	0.673298	−	0.739372i	$-0.264877\pi$
$563$	17988.7	1.34660	0.673298	+	0.739372i	$0.264877\pi$
$564$	7713.07	0.575849
$565$	−15527.3	−1.15618
$566$	−31244.4	−2.32032
$567$	−4232.73	−0.313506
$568$	−34230.8	−2.52868
$569$	−10639.7	−0.783898	−0.391949	−	0.919987i	$-0.628199\pi$
$569$	−10639.7	−0.783898	−0.391949	+	0.919987i	$0.628199\pi$
$570$	−19367.0	−1.42315
$571$	10244.8	0.750846	0.375423	−	0.926854i	$-0.377497\pi$
$571$	10244.8	0.750846	0.375423	+	0.926854i	$0.377497\pi$
$572$	−21520.1	−1.57307
$573$	−6077.39	−0.443083
$574$	−12819.7	−0.932205
$575$	8464.02	0.613868
$576$	258.601	0.0187067
$577$	9418.23	0.679525	0.339763	−	0.940511i	$-0.389653\pi$
$577$	9418.23	0.679525	0.339763	+	0.940511i	$0.389653\pi$
$578$	1467.25	0.105588
$579$	−5978.30	−0.429102
$580$	−24102.4	−1.72551
$581$	6089.06	0.434796
$582$	−11678.5	−0.831767
$583$	17685.8	1.25638
$584$	−28807.9	−2.04123
$585$	535.368	0.0378371
$586$	9525.03	0.671460
$587$	−267.085	−0.0187799	−0.00938995	−	0.999956i	$-0.502989\pi$
$587$	−267.085	−0.0187799	−0.00938995	+	0.999956i	$0.502989\pi$
$588$	4176.42	0.292913
$589$	22065.0	1.54358
$590$	−7703.63	−0.537548
$591$	−20114.1	−1.39997
$592$	21820.7	1.51491
$593$	18306.6	1.26773	0.633863	−	0.773445i	$-0.281468\pi$
$593$	18306.6	1.26773	0.633863	+	0.773445i	$0.281468\pi$
$594$	50138.7	3.46332
$595$	−871.807	−0.0600683
$596$	−23030.8	−1.58285
$597$	1707.50	0.117058
$598$	−10980.9	−0.750904
$599$	−19303.2	−1.31670	−0.658352	−	0.752710i	$-0.728746\pi$
$599$	−19303.2	−1.31670	−0.658352	+	0.752710i	$0.728746\pi$
$600$	−16974.7	−1.15498
$601$	3205.40	0.217556	0.108778	−	0.994066i	$-0.465306\pi$
$601$	3205.40	0.217556	0.108778	+	0.994066i	$0.465306\pi$
$602$	6261.52	0.423921
$603$	−772.263	−0.0521542
$604$	4678.98	0.315207
$605$	−22568.8	−1.51661
$606$	−4756.07	−0.318815
$607$	950.480	0.0635565	0.0317783	−	0.999495i	$-0.489883\pi$
$607$	950.480	0.0635565	0.0317783	+	0.999495i	$0.489883\pi$
$608$	17404.7	1.16094
$609$	6211.96	0.413336
$610$	−5991.16	−0.397664
$611$	1649.42	0.109212
$612$	−1211.56	−0.0800237
$613$	−11755.8	−0.774570	−0.387285	−	0.921960i	$-0.626587\pi$
$613$	−11755.8	−0.774570	−0.387285	+	0.921960i	$0.626587\pi$
$614$	18366.3	1.20717
$615$	12671.4	0.830829
$616$	−23076.0	−1.50935
$617$	4887.71	0.318917	0.159458	−	0.987205i	$-0.449025\pi$
$617$	4887.71	0.318917	0.159458	+	0.987205i	$0.449025\pi$
$618$	15487.7	1.00810
$619$	20570.0	1.33567	0.667833	−	0.744311i	$-0.267222\pi$
$619$	20570.0	1.33567	0.667833	+	0.744311i	$0.267222\pi$
$620$	−26460.8	−1.71402
$621$	17643.5	1.14011
$622$	33933.1	2.18745
$623$	9841.19	0.632872
$624$	9593.92	0.615488
$625$	−1621.29	−0.103762
$626$	32270.2	2.06034
$627$	−34584.4	−2.20282
$628$	−37747.8	−2.39857
$629$	3379.18	0.214208
$630$	1043.86	0.0660135
$631$	9937.24	0.626934	0.313467	−	0.949599i	$-0.398510\pi$
$631$	9937.24	0.626934	0.313467	+	0.949599i	$0.398510\pi$
$632$	9258.74	0.582742
$633$	10899.3	0.684375
$634$	49334.6	3.09042
$635$	−3147.28	−0.196686
$636$	−22695.2	−1.41497
$637$	893.120	0.0555521
$638$	−62410.7	−3.87283
$639$	2765.14	0.171185
$640$	11792.5	0.728343
$641$	177.615	0.0109444	0.00547220	−	0.999985i	$-0.498258\pi$
$641$	177.615	0.0109444	0.00547220	+	0.999985i	$0.498258\pi$
$642$	25362.4	1.55915
$643$	−8991.83	−0.551482	−0.275741	−	0.961232i	$-0.588923\pi$
$643$	−8991.83	−0.551482	−0.275741	+	0.961232i	$0.588923\pi$
$644$	−14765.4	−0.903477
$645$	−6189.05	−0.377820
$646$	9372.63	0.570838
$647$	−21581.8	−1.31139	−0.655694	−	0.755027i	$-0.727624\pi$
$647$	−21581.8	−1.31139	−0.655694	+	0.755027i	$0.727624\pi$
$648$	−30011.4	−1.81938
$649$	−13756.7	−0.832043
$650$	−6600.57	−0.398301
$651$	6819.81	0.410583
$652$	−45014.1	−2.70382
$653$	−5526.75	−0.331208	−0.165604	−	0.986192i	$-0.552957\pi$
$653$	−5526.75	−0.331208	−0.165604	+	0.986192i	$0.552957\pi$
$654$	−49375.0	−2.95216
$655$	16173.2	0.964794
$656$	−39598.7	−2.35681
$657$	2327.09	0.138186
$658$	3216.06	0.190540
$659$	−12087.6	−0.714518	−0.357259	−	0.934005i	$-0.616289\pi$
$659$	−12087.6	−0.714518	−0.357259	+	0.934005i	$0.616289\pi$
$660$	41474.3	2.44604
$661$	9070.48	0.533738	0.266869	−	0.963733i	$-0.414011\pi$
$661$	9070.48	0.533738	0.266869	+	0.963733i	$0.414011\pi$
$662$	37948.7	2.22797
$663$	1485.73	0.0870299
$664$	43173.4	2.52327
$665$	−5569.00	−0.324747
$666$	−4046.08	−0.235409
$667$	−21961.9	−1.27492
$668$	−46643.0	−2.70161
$669$	10530.4	0.608563
$670$	−7164.41	−0.413112
$671$	−10698.6	−0.615523
$672$	5379.41	0.308802
$673$	−6704.31	−0.384000	−0.192000	−	0.981395i	$-0.561497\pi$
$673$	−6704.31	−0.384000	−0.192000	+	0.981395i	$0.561497\pi$
$674$	48093.7	2.74852
$675$	10605.4	0.604746
$676$	−33148.1	−1.88599
$677$	−23305.7	−1.32306	−0.661531	−	0.749918i	$-0.730093\pi$
$677$	−23305.7	−1.32306	−0.661531	+	0.749918i	$0.730093\pi$
$678$	51594.9	2.92255
$679$	−3358.15	−0.189800
$680$	−6181.40	−0.348597
$681$	−24990.0	−1.40620
$682$	−68517.7	−3.84703
$683$	32236.3	1.80599	0.902993	−	0.429656i	$-0.141365\pi$
$683$	32236.3	1.80599	0.902993	+	0.429656i	$0.141365\pi$
$684$	−7739.31	−0.432632
$685$	−20304.9	−1.13257
$686$	1741.41	0.0969203
$687$	−24166.6	−1.34209
$688$	19341.1	1.07176
$689$	−4853.32	−0.268355
$690$	21162.8	1.16761
$691$	20511.6	1.12923	0.564615	−	0.825354i	$-0.309025\pi$
$691$	20511.6	1.12923	0.564615	+	0.825354i	$0.309025\pi$
$692$	64620.6	3.54987
$693$	1864.06	0.102179
$694$	−4161.34	−0.227612
$695$	−256.239	−0.0139852
$696$	44044.8	2.39873
$697$	−6132.30	−0.333253
$698$	48410.9	2.62519
$699$	11509.7	0.622801
$700$	−8875.45	−0.479229
$701$	156.066	0.00840876	0.00420438	−	0.999991i	$-0.498662\pi$
$701$	156.066	0.00840876	0.00420438	+	0.999991i	$0.498662\pi$
$702$	−13759.1	−0.739746
$703$	21585.8	1.15807
$704$	4284.13	0.229353
$705$	−3178.84	−0.169819
$706$	−35859.8	−1.91162
$707$	−1367.61	−0.0727501
$708$	17653.2	0.937073
$709$	26197.1	1.38766	0.693832	−	0.720136i	$-0.255921\pi$
$709$	26197.1	1.38766	0.693832	+	0.720136i	$0.255921\pi$
$710$	25652.7	1.35596
$711$	−747.916	−0.0394501
$712$	69777.3	3.67277
$713$	−24110.9	−1.26642
$714$	2896.88	0.151839
$715$	8869.21	0.463902
$716$	−60941.2	−3.18084
$717$	−1826.21	−0.0951201
$718$	−12469.0	−0.648104
$719$	24146.4	1.25245	0.626223	−	0.779644i	$-0.284600\pi$
$719$	24146.4	1.25245	0.626223	+	0.779644i	$0.284600\pi$
$720$	3224.37	0.166896
$721$	4453.51	0.230038
$722$	25048.1	1.29113
$723$	263.034	0.0135302
$724$	57736.2	2.96374
$725$	−13201.2	−0.676251
$726$	74992.5	3.83366
$727$	−8131.80	−0.414844	−0.207422	−	0.978252i	$-0.566507\pi$
$727$	−8131.80	−0.414844	−0.207422	+	0.978252i	$0.566507\pi$
$728$	6332.51	0.322388
$729$	21673.3	1.10112
$730$	21588.8	1.09457
$731$	2995.18	0.151547
$732$	13729.0	0.693221
$733$	−11437.3	−0.576324	−0.288162	−	0.957582i	$-0.593044\pi$
$733$	−11437.3	−0.576324	−0.288162	+	0.957582i	$0.593044\pi$
$734$	−278.471	−0.0140035
$735$	−1721.26	−0.0863803
$736$	−19018.5	−0.952487
$737$	−12793.7	−0.639435
$738$	7342.54	0.366237
$739$	17643.7	0.878259	0.439130	−	0.898424i	$-0.355287\pi$
$739$	17643.7	0.878259	0.439130	+	0.898424i	$0.355287\pi$
$740$	−25886.2	−1.28594
$741$	9490.64	0.470509
$742$	−9463.04	−0.468193
$743$	14897.3	0.735572	0.367786	−	0.929910i	$-0.380116\pi$
$743$	14897.3	0.735572	0.367786	+	0.929910i	$0.380116\pi$
$744$	48354.7	2.38275
$745$	9491.85	0.466785
$746$	−19108.3	−0.937806
$747$	−3487.52	−0.170819
$748$	−20071.4	−0.981129
$749$	7292.97	0.355780
$750$	35013.8	1.70470
$751$	−28967.2	−1.40750	−0.703748	−	0.710450i	$-0.748492\pi$
$751$	−28967.2	−1.40750	−0.703748	+	0.710450i	$0.748492\pi$
$752$	9934.02	0.481724
$753$	−1621.62	−0.0784797
$754$	17126.7	0.827214
$755$	−1928.38	−0.0929550
$756$	−18501.1	−0.890051
$757$	9672.67	0.464411	0.232206	−	0.972667i	$-0.425406\pi$
$757$	9672.67	0.464411	0.232206	+	0.972667i	$0.425406\pi$
$758$	−29181.7	−1.39832
$759$	37791.1	1.80729
$760$	−39486.0	−1.88462
$761$	26635.9	1.26879	0.634397	−	0.773008i	$-0.281249\pi$
$761$	26635.9	1.26879	0.634397	+	0.773008i	$0.281249\pi$
$762$	10457.9	0.497179
$763$	−14197.8	−0.673651
$764$	−22530.6	−1.06692
$765$	499.330	0.0235991
$766$	−12669.2	−0.597594
$767$	3775.10	0.177720
$768$	−36710.4	−1.72484
$769$	5359.11	0.251306	0.125653	−	0.992074i	$-0.459897\pi$
$769$	5359.11	0.251306	0.125653	+	0.992074i	$0.459897\pi$
$770$	17293.2	0.809357
$771$	3581.14	0.167279
$772$	−22163.3	−1.03326
$773$	−20526.5	−0.955093	−0.477546	−	0.878607i	$-0.658474\pi$
$773$	−20526.5	−0.955093	−0.477546	+	0.878607i	$0.658474\pi$
$774$	−3586.30	−0.166546
$775$	−14493.0	−0.671747
$776$	−23810.4	−1.10147
$777$	6671.70	0.308039
$778$	−20236.1	−0.932520
$779$	−39172.4	−1.80166
$780$	−11381.4	−0.522460
$781$	45808.9	2.09881
$782$	−10241.7	−0.468340
$783$	−27518.3	−1.25597
$784$	5379.01	0.245035
$785$	15557.3	0.707342
$786$	−53741.1	−2.43878
$787$	−7742.83	−0.350701	−0.175351	−	0.984506i	$-0.556106\pi$
$787$	−7742.83	−0.350701	−0.175351	+	0.984506i	$0.556106\pi$
$788$	−74568.7	−3.37107
$789$	−36957.0	−1.66756
$790$	−6938.54	−0.312484
$791$	14836.1	0.666893
$792$	13216.8	0.592979
$793$	2935.92	0.131472
$794$	41232.2	1.84292
$795$	9353.53	0.417277
$796$	6330.19	0.281869
$797$	−37478.3	−1.66568	−0.832842	−	0.553510i	$-0.813288\pi$
$797$	−37478.3	−1.66568	−0.832842	+	0.553510i	$0.813288\pi$
$798$	18504.9	0.820886
$799$	1538.39	0.0681158
$800$	−11432.0	−0.505226
$801$	−5636.57	−0.248637
$802$	8282.50	0.364670
$803$	38551.8	1.69423
$804$	16417.5	0.720152
$805$	6085.37	0.266436
$806$	18802.6	0.821705
$807$	−29352.0	−1.28035
$808$	−9696.82	−0.422194
$809$	2530.29	0.109963	0.0549816	−	0.998487i	$-0.482490\pi$
$809$	2530.29	0.109963	0.0549816	+	0.998487i	$0.482490\pi$
$810$	22490.7	0.975608
$811$	−6892.52	−0.298433	−0.149216	−	0.988805i	$-0.547675\pi$
$811$	−6892.52	−0.298433	−0.149216	+	0.988805i	$0.547675\pi$
$812$	23029.5	0.995291
$813$	−40207.3	−1.73448
$814$	−67029.7	−2.88623
$815$	18552.0	0.797360
$816$	8948.12	0.383881
$817$	19132.9	0.819307
$818$	62457.7	2.66966
$819$	−511.537	−0.0218248
$820$	46976.4	2.00059
$821$	−4058.72	−0.172534	−0.0862669	−	0.996272i	$-0.527494\pi$
$821$	−4058.72	−0.172534	−0.0862669	+	0.996272i	$0.527494\pi$
$822$	67470.0	2.86288
$823$	−27099.0	−1.14777	−0.573883	−	0.818937i	$-0.694564\pi$
$823$	−27099.0	−1.14777	−0.573883	+	0.818937i	$0.694564\pi$
$824$	31576.8	1.33499
$825$	22716.2	0.958637
$826$	7360.72	0.310063
$827$	−21817.4	−0.917372	−0.458686	−	0.888598i	$-0.651680\pi$
$827$	−21817.4	−0.917372	−0.458686	+	0.888598i	$0.651680\pi$
$828$	8456.93	0.354950
$829$	−45114.9	−1.89012	−0.945058	−	0.326902i	$-0.893995\pi$
$829$	−45114.9	−1.89012	−0.945058	+	0.326902i	$0.893995\pi$
$830$	−32354.3	−1.35306
$831$	−13439.4	−0.561020
$832$	−1175.65	−0.0489884
$833$	833.000	0.0346479
$834$	851.442	0.0353513
$835$	19223.3	0.796707
$836$	−128214.	−5.30427
$837$	−30211.0	−1.24761
$838$	−31725.1	−1.30779
$839$	7800.25	0.320971	0.160485	−	0.987038i	$-0.448694\pi$
$839$	7800.25	0.320971	0.160485	+	0.987038i	$0.448694\pi$
$840$	−12204.3	−0.501295
$841$	9864.79	0.404477
$842$	17243.2	0.705748
$843$	10616.8	0.433763
$844$	40406.9	1.64794
$845$	13661.6	0.556180
$846$	−1842.01	−0.0748575
$847$	21564.2	0.874798
$848$	−29230.2	−1.18369
$849$	−29508.2	−1.19284
$850$	−6156.26	−0.248421
$851$	−23587.3	−0.950132
$852$	−58784.2	−2.36375
$853$	23921.4	0.960203	0.480102	−	0.877213i	$-0.340600\pi$
$853$	23921.4	0.960203	0.480102	+	0.877213i	$0.340600\pi$
$854$	5724.47	0.229376
$855$	3189.66	0.127584
$856$	51709.5	2.06471
$857$	−11013.6	−0.438992	−0.219496	−	0.975613i	$-0.570441\pi$
$857$	−11013.6	−0.438992	−0.219496	+	0.975613i	$0.570441\pi$
$858$	−29471.0	−1.17264
$859$	−35649.5	−1.41600	−0.708001	−	0.706212i	$-0.750403\pi$
$859$	−35649.5	−1.41600	−0.708001	+	0.706212i	$0.750403\pi$
$860$	−22944.6	−0.909771
$861$	−12107.3	−0.479230
$862$	−8384.68	−0.331303
$863$	−6069.25	−0.239397	−0.119699	−	0.992810i	$-0.538193\pi$
$863$	−6069.25	−0.239397	−0.119699	+	0.992810i	$0.538193\pi$
$864$	−23830.2	−0.938334
$865$	−26632.6	−1.04686
$866$	−11379.6	−0.446529
$867$	1385.72	0.0542807
$868$	25282.9	0.988663
$869$	−12390.4	−0.483677
$870$	−33007.4	−1.28627
$871$	3510.86	0.136580
$872$	−100667.	−3.90943
$873$	1923.39	0.0745669
$874$	−65422.7	−2.53198
$875$	10068.2	0.388993
$876$	−49471.6	−1.90809
$877$	16180.1	0.622990	0.311495	−	0.950248i	$-0.399170\pi$
$877$	16180.1	0.622990	0.311495	+	0.950248i	$0.399170\pi$
$878$	4529.45	0.174102
$879$	8995.72	0.345185
$880$	53416.8	2.04623
$881$	−12851.3	−0.491452	−0.245726	−	0.969339i	$-0.579026\pi$
$881$	−12851.3	−0.491452	−0.245726	+	0.969339i	$0.579026\pi$
$882$	−997.397	−0.0380772
$883$	24797.8	0.945089	0.472544	−	0.881307i	$-0.343336\pi$
$883$	24797.8	0.945089	0.472544	+	0.881307i	$0.343336\pi$
$884$	5508.01	0.209564
$885$	−7275.54	−0.276344
$886$	44612.8	1.69164
$887$	43596.8	1.65032	0.825162	−	0.564896i	$-0.191084\pi$
$887$	43596.8	1.65032	0.825162	+	0.564896i	$0.191084\pi$
$888$	47304.6	1.78765
$889$	3007.18	0.113451
$890$	−52291.4	−1.96945
$891$	40162.5	1.51009
$892$	39039.1	1.46539
$893$	9827.08	0.368254
$894$	−31539.9	−1.17993
$895$	25116.1	0.938033
$896$	−11267.6	−0.420115
$897$	−10370.6	−0.386027
$898$	45878.1	1.70487
$899$	37605.6	1.39512
$900$	5083.44	0.188276
$901$	−4526.63	−0.167374
$902$	121641.	4.49024
$903$	5913.56	0.217930
$904$	105193.	3.87021
$905$	−23795.2	−0.874011
$906$	6407.72	0.234969
$907$	−17874.8	−0.654380	−0.327190	−	0.944959i	$-0.606102\pi$
$907$	−17874.8	−0.654380	−0.327190	+	0.944959i	$0.606102\pi$
$908$	−92645.0	−3.38605
$909$	783.303	0.0285814
$910$	−4745.61	−0.172874
$911$	−10895.0	−0.396234	−0.198117	−	0.980178i	$-0.563483\pi$
$911$	−10895.0	−0.396234	−0.198117	+	0.980178i	$0.563483\pi$
$912$	57159.5	2.07537
$913$	−57776.3	−2.09432
$914$	1340.38	0.0485076
$915$	−5658.22	−0.204432
$916$	−89592.3	−3.23167
$917$	−15453.3	−0.556503
$918$	−12832.9	−0.461381
$919$	−27545.1	−0.988717	−0.494358	−	0.869258i	$-0.664597\pi$
$919$	−27545.1	−0.988717	−0.494358	+	0.869258i	$0.664597\pi$
$920$	43147.3	1.54622
$921$	17345.7	0.620585
$922$	92622.8	3.30843
$923$	−12570.9	−0.448295
$924$	−39628.2	−1.41090
$925$	−14178.3	−0.503977
$926$	−51932.4	−1.84299
$927$	−2550.76	−0.0903753
$928$	29662.9	1.04928
$929$	24943.5	0.880915	0.440458	−	0.897773i	$-0.354816\pi$
$929$	24943.5	0.880915	0.440458	+	0.897773i	$0.354816\pi$
$930$	−36237.2	−1.27770
$931$	5321.10	0.187317
$932$	42669.8	1.49967
$933$	32047.4	1.12453
$934$	−640.492	−0.0224385
$935$	8272.18	0.289336
$936$	−3626.96	−0.126657
$937$	6018.07	0.209821	0.104910	−	0.994482i	$-0.466544\pi$
$937$	6018.07	0.209821	0.104910	+	0.994482i	$0.466544\pi$
$938$	6845.50	0.238287
$939$	30476.9	1.05919
$940$	−11784.9	−0.408914
$941$	−4808.69	−0.166587	−0.0832937	−	0.996525i	$-0.526544\pi$
$941$	−4808.69	−0.166587	−0.0832937	+	0.996525i	$0.526544\pi$
$942$	−51694.4	−1.78800
$943$	42804.6	1.47816
$944$	22736.4	0.783905
$945$	7624.99	0.262477
$946$	−59412.7	−2.04194
$947$	30253.2	1.03812	0.519058	−	0.854739i	$-0.326283\pi$
$947$	30253.2	1.03812	0.519058	+	0.854739i	$0.326283\pi$
$948$	15900.0	0.544733
$949$	−10579.4	−0.361878
$950$	−39325.4	−1.34304
$951$	46593.0	1.58873
$952$	5906.24	0.201074
$953$	39446.8	1.34083	0.670413	−	0.741988i	$-0.266117\pi$
$953$	39446.8	1.34083	0.670413	+	0.741988i	$0.266117\pi$
$954$	5419.98	0.183940
$955$	9285.68	0.314636
$956$	−6770.28	−0.229044
$957$	−58942.5	−1.99095
$958$	54840.0	1.84948
$959$	19401.1	0.653277
$960$	2265.76	0.0761742
$961$	11494.3	0.385832
$962$	18394.3	0.616482
$963$	−4177.07	−0.139776
$964$	975.142	0.0325801
$965$	9134.30	0.304708
$966$	−20220.7	−0.673491
$967$	−38959.3	−1.29560	−0.647800	−	0.761810i	$-0.724311\pi$
$967$	−38959.3	−1.29560	−0.647800	+	0.761810i	$0.724311\pi$
$968$	152897.	5.07675
$969$	8851.78	0.293457
$970$	17843.6	0.590644
$971$	−29621.3	−0.978982	−0.489491	−	0.872008i	$-0.662817\pi$
$971$	−29621.3	−0.978982	−0.489491	+	0.872008i	$0.662817\pi$
$972$	19823.1	0.654141
$973$	244.833	0.00806678
$974$	45441.4	1.49490
$975$	−6233.77	−0.204759
$976$	17682.2	0.579912
$977$	553.794	0.0181345	0.00906726	−	0.999959i	$-0.497114\pi$
$977$	553.794	0.0181345	0.00906726	+	0.999959i	$0.497114\pi$
$978$	−61645.4	−2.01554
$979$	−93378.6	−3.04841
$980$	−6381.19	−0.207999
$981$	8131.84	0.264658
$982$	−108391.	−3.52230
$983$	19096.6	0.619621	0.309811	−	0.950798i	$-0.399734\pi$
$983$	19096.6	0.619621	0.309811	+	0.950798i	$0.399734\pi$
$984$	−85845.0	−2.78114
$985$	30732.5	0.994131
$986$	15973.9	0.515935
$987$	3037.34	0.0979530
$988$	35184.5	1.13296
$989$	−20906.9	−0.672196
$990$	−9904.75	−0.317973
$991$	−19252.5	−0.617130	−0.308565	−	0.951203i	$-0.599849\pi$
$991$	−19252.5	−0.617130	−0.308565	+	0.951203i	$0.599849\pi$
$992$	32565.5	1.04229
$993$	35839.9	1.14536
$994$	−24510.8	−0.782128
$995$	−2608.90	−0.0831235
$996$	74141.3	2.35869
$997$	−1878.65	−0.0596765	−0.0298382	−	0.999555i	$-0.509499\pi$
$997$	−1878.65	−0.0596765	−0.0298382	+	0.999555i	$0.509499\pi$
$998$	−75967.0	−2.40951
$999$	−29555.0	−0.936013

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	119.4.a.e.1.9	✓	9
3.2	odd	2		1071.4.a.r.1.1		9
4.3	odd	2		1904.4.a.s.1.4		9
7.6	odd	2		833.4.a.g.1.9		9
17.16	even	2		2023.4.a.h.1.9		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
119.4.a.e.1.9	✓	9	1.1	even	1	trivial
833.4.a.g.1.9		9	7.6	odd	2
1071.4.a.r.1.1		9	3.2	odd	2
1904.4.a.s.1.4		9	4.3	odd	2
2023.4.a.h.1.9		9	17.16	even	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:	\( N \)	\(=\)	\( 119 = 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	119.a (trivial)

\(f(q)\)	\(=\)	\(q+5.07700 q^{2} +4.79487 q^{3} +17.7759 q^{4} -7.32611 q^{5} +24.3435 q^{6} +7.00000 q^{7} +49.6323 q^{8} -4.00927 q^{9} +O(q^{10})\)	\(q+5.07700 q^{2} +4.79487 q^{3} +17.7759 q^{4} -7.32611 q^{5} +24.3435 q^{6} +7.00000 q^{7} +49.6323 q^{8} -4.00927 q^{9} -37.1947 q^{10} -66.4198 q^{11} +85.2331 q^{12} +18.2269 q^{13} +35.5390 q^{14} -35.1277 q^{15} +109.776 q^{16} +17.0000 q^{17} -20.3550 q^{18} +108.594 q^{19} -130.228 q^{20} +33.5641 q^{21} -337.213 q^{22} -118.663 q^{23} +237.980 q^{24} -71.3281 q^{25} +92.5381 q^{26} -148.685 q^{27} +124.431 q^{28} +185.078 q^{29} -178.343 q^{30} +203.188 q^{31} +160.273 q^{32} -318.474 q^{33} +86.3090 q^{34} -51.2828 q^{35} -71.2684 q^{36} +198.775 q^{37} +551.331 q^{38} +87.3957 q^{39} -363.612 q^{40} -360.723 q^{41} +170.405 q^{42} +176.187 q^{43} -1180.67 q^{44} +29.3723 q^{45} -602.452 q^{46} +90.4938 q^{47} +526.360 q^{48} +49.0000 q^{49} -362.133 q^{50} +81.5127 q^{51} +324.000 q^{52} -266.272 q^{53} -754.875 q^{54} +486.599 q^{55} +347.426 q^{56} +520.693 q^{57} +939.640 q^{58} +207.117 q^{59} -624.427 q^{60} +161.076 q^{61} +1031.58 q^{62} -28.0649 q^{63} -64.5008 q^{64} -133.533 q^{65} -1616.89 q^{66} +192.619 q^{67} +302.190 q^{68} -568.974 q^{69} -260.363 q^{70} -689.688 q^{71} -198.989 q^{72} -580.427 q^{73} +1009.18 q^{74} -342.009 q^{75} +1930.36 q^{76} -464.939 q^{77} +443.708 q^{78} +186.547 q^{79} -804.229 q^{80} -604.676 q^{81} -1831.39 q^{82} +869.866 q^{83} +596.632 q^{84} -124.544 q^{85} +894.502 q^{86} +887.423 q^{87} -3296.57 q^{88} +1405.88 q^{89} +149.123 q^{90} +127.589 q^{91} -2109.35 q^{92} +974.258 q^{93} +459.437 q^{94} -795.571 q^{95} +768.487 q^{96} -479.736 q^{97} +248.773 q^{98} +266.295 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 2 q^{2} + 11 q^{3} + 38 q^{4} - 3 q^{5} + 9 q^{6} + 63 q^{7} + 24 q^{8} + 74 q^{9}+O(q^{10}) \) 9 * q + 2 * q^2 + 11 * q^3 + 38 * q^4 - 3 * q^5 + 9 * q^6 + 63 * q^7 + 24 * q^8 + 74 * q^9	\( 9 q + 2 q^{2} + 11 q^{3} + 38 q^{4} - 3 q^{5} + 9 q^{6} + 63 q^{7} + 24 q^{8} + 74 q^{9} + 134 q^{10} - 8 q^{11} + 56 q^{12} + 164 q^{13} + 14 q^{14} + 34 q^{15} + 178 q^{16} + 153 q^{17} + 98 q^{18} + 244 q^{19} - 41 q^{20} + 77 q^{21} - 80 q^{22} - 14 q^{23} + 298 q^{24} + 684 q^{25} + 326 q^{26} + 218 q^{27} + 266 q^{28} - 234 q^{29} - 335 q^{30} + 555 q^{31} - 181 q^{32} + 458 q^{33} + 34 q^{34} - 21 q^{35} - 1221 q^{36} - 364 q^{37} - 714 q^{38} - 52 q^{39} + 123 q^{40} - 45 q^{41} + 63 q^{42} - 135 q^{43} - 748 q^{44} - 844 q^{45} - 1576 q^{46} - 172 q^{47} - 949 q^{48} + 441 q^{49} - 2901 q^{50} + 187 q^{51} - 1596 q^{52} + 101 q^{53} - 1163 q^{54} + 1260 q^{55} + 168 q^{56} - 602 q^{57} + 1062 q^{58} + 280 q^{59} - 1727 q^{60} + 639 q^{61} - 1708 q^{62} + 518 q^{63} - 2390 q^{64} + 638 q^{65} - 2476 q^{66} + 35 q^{67} + 646 q^{68} + 1288 q^{69} + 938 q^{70} - 1616 q^{71} + 1335 q^{72} + 1049 q^{73} - 370 q^{74} + 1260 q^{75} + 4964 q^{76} - 56 q^{77} - 4714 q^{78} + 2304 q^{79} - 3996 q^{80} - 791 q^{81} - 215 q^{82} + 2508 q^{83} + 392 q^{84} - 51 q^{85} + 623 q^{86} + 166 q^{87} - 416 q^{88} + 2762 q^{89} + 2935 q^{90} + 1148 q^{91} - 2392 q^{92} + 2784 q^{93} - 862 q^{94} - 3462 q^{95} + 2928 q^{96} + 3107 q^{97} + 98 q^{98} - 2396 q^{99}+O(q^{100}) \) 9 * q + 2 * q^2 + 11 * q^3 + 38 * q^4 - 3 * q^5 + 9 * q^6 + 63 * q^7 + 24 * q^8 + 74 * q^9 + 134 * q^10 - 8 * q^11 + 56 * q^12 + 164 * q^13 + 14 * q^14 + 34 * q^15 + 178 * q^16 + 153 * q^17 + 98 * q^18 + 244 * q^19 - 41 * q^20 + 77 * q^21 - 80 * q^22 - 14 * q^23 + 298 * q^24 + 684 * q^25 + 326 * q^26 + 218 * q^27 + 266 * q^28 - 234 * q^29 - 335 * q^30 + 555 * q^31 - 181 * q^32 + 458 * q^33 + 34 * q^34 - 21 * q^35 - 1221 * q^36 - 364 * q^37 - 714 * q^38 - 52 * q^39 + 123 * q^40 - 45 * q^41 + 63 * q^42 - 135 * q^43 - 748 * q^44 - 844 * q^45 - 1576 * q^46 - 172 * q^47 - 949 * q^48 + 441 * q^49 - 2901 * q^50 + 187 * q^51 - 1596 * q^52 + 101 * q^53 - 1163 * q^54 + 1260 * q^55 + 168 * q^56 - 602 * q^57 + 1062 * q^58 + 280 * q^59 - 1727 * q^60 + 639 * q^61 - 1708 * q^62 + 518 * q^63 - 2390 * q^64 + 638 * q^65 - 2476 * q^66 + 35 * q^67 + 646 * q^68 + 1288 * q^69 + 938 * q^70 - 1616 * q^71 + 1335 * q^72 + 1049 * q^73 - 370 * q^74 + 1260 * q^75 + 4964 * q^76 - 56 * q^77 - 4714 * q^78 + 2304 * q^79 - 3996 * q^80 - 791 * q^81 - 215 * q^82 + 2508 * q^83 + 392 * q^84 - 51 * q^85 + 623 * q^86 + 166 * q^87 - 416 * q^88 + 2762 * q^89 + 2935 * q^90 + 1148 * q^91 - 2392 * q^92 + 2784 * q^93 - 862 * q^94 - 3462 * q^95 + 2928 * q^96 + 3107 * q^97 + 98 * q^98 - 2396 * q^99

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