LMFDB - Embedded newform 145.4.a.d.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [145,4,Mod(1,145)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(145, 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("145.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 145 = 5 \cdot 29 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	145.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:	$8.55527695083$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 2x^{6} - 36x^{5} + 95x^{4} + 249x^{3} - 970x^{2} + 810x - 171 $ x^7 - 2x^6 - 36x^5 + 95x^4 + 249x^3 - 970x^2 + 810x - 171
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-5.14097$ of defining polynomial
Character	$\chi$	$=$	145.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+5.21256 q^{2} +6.33996 q^{3} +19.1708 q^{4} -5.00000 q^{5} +33.0474 q^{6} -6.37598 q^{7} +58.2287 q^{8} +13.1951 q^{9} +O(q^{10})$	\(q+5.21256 q^{2} +6.33996 q^{3} +19.1708 q^{4} -5.00000 q^{5} +33.0474 q^{6} -6.37598 q^{7} +58.2287 q^{8} +13.1951 q^{9} -26.0628 q^{10} -61.0073 q^{11} +121.542 q^{12} -58.3202 q^{13} -33.2352 q^{14} -31.6998 q^{15} +150.154 q^{16} +56.1338 q^{17} +68.7802 q^{18} +68.4840 q^{19} -95.8542 q^{20} -40.4234 q^{21} -318.005 q^{22} +82.7426 q^{23} +369.167 q^{24} +25.0000 q^{25} -303.998 q^{26} -87.5227 q^{27} -122.233 q^{28} -29.0000 q^{29} -165.237 q^{30} +180.461 q^{31} +316.859 q^{32} -386.784 q^{33} +292.601 q^{34} +31.8799 q^{35} +252.960 q^{36} +126.378 q^{37} +356.977 q^{38} -369.748 q^{39} -291.143 q^{40} +296.186 q^{41} -210.710 q^{42} +141.910 q^{43} -1169.56 q^{44} -65.9753 q^{45} +431.301 q^{46} +207.501 q^{47} +951.971 q^{48} -302.347 q^{49} +130.314 q^{50} +355.886 q^{51} -1118.05 q^{52} +364.318 q^{53} -456.218 q^{54} +305.037 q^{55} -371.265 q^{56} +434.186 q^{57} -151.164 q^{58} -778.586 q^{59} -607.711 q^{60} -832.590 q^{61} +940.664 q^{62} -84.1314 q^{63} +450.413 q^{64} +291.601 q^{65} -2016.14 q^{66} -500.473 q^{67} +1076.13 q^{68} +524.585 q^{69} +166.176 q^{70} +1087.81 q^{71} +768.331 q^{72} +901.544 q^{73} +658.751 q^{74} +158.499 q^{75} +1312.90 q^{76} +388.981 q^{77} -1927.33 q^{78} -882.100 q^{79} -750.771 q^{80} -911.157 q^{81} +1543.89 q^{82} -1293.09 q^{83} -774.951 q^{84} -280.669 q^{85} +739.714 q^{86} -183.859 q^{87} -3552.38 q^{88} -48.0680 q^{89} -343.901 q^{90} +371.848 q^{91} +1586.25 q^{92} +1144.11 q^{93} +1081.61 q^{94} -342.420 q^{95} +2008.87 q^{96} -176.089 q^{97} -1576.00 q^{98} -804.996 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 6 q^{2} + q^{3} + 52 q^{4} - 35 q^{5} + 3 q^{6} + 17 q^{7} + 138 q^{8} + 118 q^{9}+O(q^{10}) $ 7 * q + 6 * q^2 + q^3 + 52 * q^4 - 35 * q^5 + 3 * q^6 + 17 * q^7 + 138 * q^8 + 118 * q^9	\( 7 q + 6 q^{2} + q^{3} + 52 q^{4} - 35 q^{5} + 3 q^{6} + 17 q^{7} + 138 q^{8} + 118 q^{9} - 30 q^{10} + 2 q^{11} - 77 q^{12} - 17 q^{13} + 361 q^{14} - 5 q^{15} + 372 q^{16} + 95 q^{17} + 261 q^{18} + 94 q^{19} - 260 q^{20} - 100 q^{21} + 190 q^{22} + 327 q^{23} - 117 q^{24} + 175 q^{25} - 115 q^{26} - 236 q^{27} - 67 q^{28} - 203 q^{29} - 15 q^{30} + 169 q^{31} + 890 q^{32} + 272 q^{33} + 377 q^{34} - 85 q^{35} + 2443 q^{36} - 500 q^{37} + 282 q^{38} + 1129 q^{39} - 690 q^{40} + 1208 q^{41} - 1892 q^{42} - 1517 q^{43} - 734 q^{44} - 590 q^{45} - 1413 q^{46} + 1974 q^{47} - 2637 q^{48} + 794 q^{49} + 150 q^{50} - 190 q^{51} - 2063 q^{52} - 255 q^{53} - 5052 q^{54} - 10 q^{55} + 2057 q^{56} + 94 q^{57} - 174 q^{58} + 177 q^{59} + 385 q^{60} - 705 q^{61} - 807 q^{62} + 200 q^{63} + 332 q^{64} + 85 q^{65} - 2768 q^{66} - 744 q^{67} - 2323 q^{68} + 1551 q^{69} - 1805 q^{70} + 2024 q^{71} + 6897 q^{72} - 1405 q^{73} + 82 q^{74} + 25 q^{75} - 18 q^{76} + 3402 q^{77} - 5311 q^{78} - 2157 q^{79} - 1860 q^{80} + 1099 q^{81} + 2266 q^{82} - 158 q^{83} - 4372 q^{84} - 475 q^{85} + 3033 q^{86} - 29 q^{87} - 1250 q^{88} - 2244 q^{89} - 1305 q^{90} + 3376 q^{91} + 2599 q^{92} + 586 q^{93} + 2212 q^{94} - 470 q^{95} - 5077 q^{96} - 727 q^{97} - 1567 q^{98} + 416 q^{99}+O(q^{100}) \) 7 * q + 6 * q^2 + q^3 + 52 * q^4 - 35 * q^5 + 3 * q^6 + 17 * q^7 + 138 * q^8 + 118 * q^9 - 30 * q^10 + 2 * q^11 - 77 * q^12 - 17 * q^13 + 361 * q^14 - 5 * q^15 + 372 * q^16 + 95 * q^17 + 261 * q^18 + 94 * q^19 - 260 * q^20 - 100 * q^21 + 190 * q^22 + 327 * q^23 - 117 * q^24 + 175 * q^25 - 115 * q^26 - 236 * q^27 - 67 * q^28 - 203 * q^29 - 15 * q^30 + 169 * q^31 + 890 * q^32 + 272 * q^33 + 377 * q^34 - 85 * q^35 + 2443 * q^36 - 500 * q^37 + 282 * q^38 + 1129 * q^39 - 690 * q^40 + 1208 * q^41 - 1892 * q^42 - 1517 * q^43 - 734 * q^44 - 590 * q^45 - 1413 * q^46 + 1974 * q^47 - 2637 * q^48 + 794 * q^49 + 150 * q^50 - 190 * q^51 - 2063 * q^52 - 255 * q^53 - 5052 * q^54 - 10 * q^55 + 2057 * q^56 + 94 * q^57 - 174 * q^58 + 177 * q^59 + 385 * q^60 - 705 * q^61 - 807 * q^62 + 200 * q^63 + 332 * q^64 + 85 * q^65 - 2768 * q^66 - 744 * q^67 - 2323 * q^68 + 1551 * q^69 - 1805 * q^70 + 2024 * q^71 + 6897 * q^72 - 1405 * q^73 + 82 * q^74 + 25 * q^75 - 18 * q^76 + 3402 * q^77 - 5311 * q^78 - 2157 * q^79 - 1860 * q^80 + 1099 * q^81 + 2266 * q^82 - 158 * q^83 - 4372 * q^84 - 475 * q^85 + 3033 * q^86 - 29 * q^87 - 1250 * q^88 - 2244 * q^89 - 1305 * q^90 + 3376 * q^91 + 2599 * q^92 + 586 * q^93 + 2212 * q^94 - 470 * q^95 - 5077 * q^96 - 727 * q^97 - 1567 * q^98 + 416 * 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 $

$2$	5.21256	1.84292	0.921460	−	0.388473i	$-0.126997\pi$
$2$	5.21256	1.84292	0.921460	+	0.388473i	$0.126997\pi$
$3$	6.33996	1.22013	0.610063	−	0.792353i	$-0.291144\pi$
$3$	6.33996	1.22013	0.610063	+	0.792353i	$0.291144\pi$
$4$	19.1708	2.39635
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	33.0474	2.24859
$7$	−6.37598	−0.344270	−0.172135	−	0.985073i	$-0.555067\pi$
$7$	−6.37598	−0.344270	−0.172135	+	0.985073i	$0.555067\pi$
$8$	58.2287	2.57337
$9$	13.1951	0.488706
$10$	−26.0628	−0.824179
$11$	−61.0073	−1.67222	−0.836109	−	0.548563i	$-0.815175\pi$
$11$	−61.0073	−1.67222	−0.836109	+	0.548563i	$0.815175\pi$
$12$	121.542	2.92385
$13$	−58.3202	−1.24424	−0.622120	−	0.782922i	$-0.713728\pi$
$13$	−58.3202	−1.24424	−0.622120	+	0.782922i	$0.713728\pi$
$14$	−33.2352	−0.634463
$15$	−31.6998	−0.545657
$16$	150.154	2.34616
$17$	56.1338	0.800850	0.400425	−	0.916330i	$-0.368863\pi$
$17$	56.1338	0.800850	0.400425	+	0.916330i	$0.368863\pi$
$18$	68.7802	0.900646
$19$	68.4840	0.826911	0.413455	−	0.910524i	$-0.364322\pi$
$19$	68.4840	0.826911	0.413455	+	0.910524i	$0.364322\pi$
$20$	−95.8542	−1.07168
$21$	−40.4234	−0.420053
$22$	−318.005	−3.08176
$23$	82.7426	0.750132	0.375066	−	0.926998i	$-0.377620\pi$
$23$	82.7426	0.750132	0.375066	+	0.926998i	$0.377620\pi$
$24$	369.167	3.13983
$25$	25.0000	0.200000
$26$	−303.998	−2.29303
$27$	−87.5227	−0.623843
$28$	−122.233	−0.824994
$29$	−29.0000	−0.185695
$29$	−29.0000	−0.185695
$30$	−165.237	−1.00560
$31$	180.461	1.04554	0.522770	−	0.852474i	$-0.324899\pi$
$31$	180.461	1.04554	0.522770	+	0.852474i	$0.324899\pi$
$32$	316.859	1.75041
$33$	−386.784	−2.04032
$34$	292.601	1.47590
$35$	31.8799	0.153962
$36$	252.960	1.17111
$37$	126.378	0.561523	0.280761	−	0.959778i	$-0.409413\pi$
$37$	126.378	0.561523	0.280761	+	0.959778i	$0.409413\pi$
$38$	356.977	1.52393
$39$	−369.748	−1.51813
$40$	−291.143	−1.15085
$41$	296.186	1.12821	0.564104	−	0.825704i	$-0.309222\pi$
$41$	296.186	1.12821	0.564104	+	0.825704i	$0.309222\pi$
$42$	−210.710	−0.774124
$43$	141.910	0.503280	0.251640	−	0.967821i	$-0.419030\pi$
$43$	141.910	0.503280	0.251640	+	0.967821i	$0.419030\pi$
$44$	−1169.56	−4.00723
$45$	−65.9753	−0.218556
$46$	431.301	1.38243
$47$	207.501	0.643983	0.321991	−	0.946743i	$-0.395648\pi$
$47$	207.501	0.643983	0.321991	+	0.946743i	$0.395648\pi$
$48$	951.971	2.86261
$49$	−302.347	−0.881478
$50$	130.314	0.368584
$51$	355.886	0.977137
$52$	−1118.05	−2.98164
$53$	364.318	0.944207	0.472104	−	0.881543i	$-0.343495\pi$
$53$	364.318	0.944207	0.472104	+	0.881543i	$0.343495\pi$
$54$	−456.218	−1.14969
$55$	305.037	0.747839
$56$	−371.265	−0.885934
$57$	434.186	1.00894
$58$	−151.164	−0.342222
$59$	−778.586	−1.71802	−0.859010	−	0.511959i	$-0.828920\pi$
$59$	−778.586	−1.71802	−0.859010	+	0.511959i	$0.828920\pi$
$60$	−607.711	−1.30759
$61$	−832.590	−1.74758	−0.873789	−	0.486306i	$-0.838344\pi$
$61$	−832.590	−1.74758	−0.873789	+	0.486306i	$0.838344\pi$
$62$	940.664	1.92685
$63$	−84.1314	−0.168247
$64$	450.413	0.879713
$65$	291.601	0.556441
$66$	−2016.14	−3.76014
$67$	−500.473	−0.912574	−0.456287	−	0.889833i	$-0.650821\pi$
$67$	−500.473	−0.912574	−0.456287	+	0.889833i	$0.650821\pi$
$68$	1076.13	1.91912
$69$	524.585	0.915255
$70$	166.176	0.283740
$71$	1087.81	1.81830	0.909151	−	0.416467i	$-0.136732\pi$
$71$	1087.81	1.81830	0.909151	+	0.416467i	$0.136732\pi$
$72$	768.331	1.25762
$73$	901.544	1.44545	0.722724	−	0.691136i	$-0.242890\pi$
$73$	901.544	1.44545	0.722724	+	0.691136i	$0.242890\pi$
$74$	658.751	1.03484
$75$	158.499	0.244025
$76$	1312.90	1.98157
$77$	388.981	0.575695
$78$	−1927.33	−2.79779
$79$	−882.100	−1.25625	−0.628127	−	0.778111i	$-0.716178\pi$
$79$	−882.100	−1.25625	−0.628127	+	0.778111i	$0.716178\pi$
$80$	−750.771	−1.04923
$81$	−911.157	−1.24987
$82$	1543.89	2.07920
$83$	−1293.09	−1.71007	−0.855033	−	0.518573i	$-0.826463\pi$
$83$	−1293.09	−1.71007	−0.855033	+	0.518573i	$0.826463\pi$
$84$	−774.951	−1.00660
$85$	−280.669	−0.358151
$86$	739.714	0.927505
$87$	−183.859	−0.226572
$88$	−3552.38	−4.30323
$89$	−48.0680	−0.0572495	−0.0286247	−	0.999590i	$-0.509113\pi$
$89$	−48.0680	−0.0572495	−0.0286247	+	0.999590i	$0.509113\pi$
$90$	−343.901	−0.402781
$91$	371.848	0.428355
$92$	1586.25	1.79758
$93$	1144.11	1.27569
$94$	1081.61	1.18681
$95$	−342.420	−0.369806
$96$	2008.87	2.13572
$97$	−176.089	−0.184320	−0.0921602	−	0.995744i	$-0.529377\pi$
$97$	−176.089	−0.184320	−0.0921602	+	0.995744i	$0.529377\pi$
$98$	−1576.00	−1.62449
$99$	−804.996	−0.817223
$100$	479.271	0.479271
$101$	432.965	0.426550	0.213275	−	0.976992i	$-0.431587\pi$
$101$	432.965	0.426550	0.213275	+	0.976992i	$0.431587\pi$
$102$	1855.08	1.80079
$103$	−135.587	−0.129707	−0.0648533	−	0.997895i	$-0.520658\pi$
$103$	−135.587	−0.129707	−0.0648533	+	0.997895i	$0.520658\pi$
$104$	−3395.91	−3.20189
$105$	202.117	0.187853
$106$	1899.03	1.74010
$107$	−753.450	−0.680736	−0.340368	−	0.940292i	$-0.610552\pi$
$107$	−753.450	−0.680736	−0.340368	+	0.940292i	$0.610552\pi$
$108$	−1677.88	−1.49495
$109$	−382.704	−0.336297	−0.168149	−	0.985762i	$-0.553779\pi$
$109$	−382.704	−0.336297	−0.168149	+	0.985762i	$0.553779\pi$
$110$	1590.02	1.37821
$111$	801.228	0.685128
$112$	−957.379	−0.807713
$113$	279.853	0.232976	0.116488	−	0.993192i	$-0.462836\pi$
$113$	279.853	0.232976	0.116488	+	0.993192i	$0.462836\pi$
$114$	2263.22	1.85939
$115$	−413.713	−0.335469
$116$	−555.954	−0.444992
$117$	−769.539	−0.608068
$118$	−4058.43	−3.16617
$119$	−357.908	−0.275709
$120$	−1845.84	−1.40418
$121$	2390.89	1.79631
$122$	−4339.93	−3.22065
$123$	1877.81	1.37656
$124$	3459.59	2.50548
$125$	−125.000	−0.0894427
$126$	−438.541	−0.310066
$127$	2546.18	1.77903	0.889514	−	0.456908i	$-0.151043\pi$
$127$	2546.18	1.77903	0.889514	+	0.456908i	$0.151043\pi$
$128$	−187.061	−0.129172
$129$	899.702	0.614065
$130$	1519.99	1.02548
$131$	−1545.63	−1.03085	−0.515427	−	0.856933i	$-0.672367\pi$
$131$	−1545.63	−1.03085	−0.515427	+	0.856933i	$0.672367\pi$
$132$	−7414.97	−4.88932
$133$	−436.652	−0.284681
$134$	−2608.75	−1.68180
$135$	437.613	0.278991
$136$	3268.60	2.06088
$137$	1328.80	0.828667	0.414334	−	0.910125i	$-0.364015\pi$
$137$	1328.80	0.828667	0.414334	+	0.910125i	$0.364015\pi$
$138$	2734.43	1.68674
$139$	551.476	0.336515	0.168257	−	0.985743i	$-0.446186\pi$
$139$	551.476	0.336515	0.168257	+	0.985743i	$0.446186\pi$
$140$	611.164	0.368948
$141$	1315.55	0.785740
$142$	5670.28	3.35098
$143$	3557.96	2.08064
$144$	1981.29	1.14658
$145$	145.000	0.0830455
$146$	4699.36	2.66385
$147$	−1916.87	−1.07551
$148$	2422.76	1.34561
$149$	1481.95	0.814806	0.407403	−	0.913249i	$-0.366435\pi$
$149$	1481.95	0.814806	0.407403	+	0.913249i	$0.366435\pi$
$150$	826.186	0.449719
$151$	3075.77	1.65764	0.828818	−	0.559519i	$-0.189014\pi$
$151$	3075.77	1.65764	0.828818	+	0.559519i	$0.189014\pi$
$152$	3987.73	2.12795
$153$	740.689	0.391380
$154$	2027.59	1.06096
$155$	−902.304	−0.467580
$156$	−7088.37	−3.63797
$157$	−324.615	−0.165013	−0.0825066	−	0.996591i	$-0.526293\pi$
$157$	−324.615	−0.165013	−0.0825066	+	0.996591i	$0.526293\pi$
$158$	−4598.00	−2.31517
$159$	2309.76	1.15205
$160$	−1584.29	−0.782809
$161$	−527.565	−0.258248
$162$	−4749.46	−2.30341
$163$	−901.419	−0.433157	−0.216578	−	0.976265i	$-0.569490\pi$
$163$	−901.419	−0.433157	−0.216578	+	0.976265i	$0.569490\pi$
$164$	5678.14	2.70359
$165$	1933.92	0.912457
$166$	−6740.34	−3.15152
$167$	−2544.98	−1.17926	−0.589631	−	0.807673i	$-0.700727\pi$
$167$	−2544.98	−1.17926	−0.589631	+	0.807673i	$0.700727\pi$
$168$	−2353.80	−1.08095
$169$	1204.25	0.548132
$170$	−1463.01	−0.660044
$171$	903.651	0.404116
$172$	2720.53	1.20604
$173$	2230.16	0.980093	0.490046	−	0.871696i	$-0.336980\pi$
$173$	2230.16	0.980093	0.490046	+	0.871696i	$0.336980\pi$
$174$	−958.376	−0.417553
$175$	−159.399	−0.0688541
$176$	−9160.50	−3.92329
$177$	−4936.20	−2.09620
$178$	−250.558	−0.105506
$179$	2904.03	1.21261	0.606305	−	0.795232i	$-0.292651\pi$
$179$	2904.03	1.21261	0.606305	+	0.795232i	$0.292651\pi$
$180$	−1264.80	−0.523738
$181$	−2585.86	−1.06191	−0.530955	−	0.847400i	$-0.678167\pi$
$181$	−2585.86	−1.06191	−0.530955	+	0.847400i	$0.678167\pi$
$182$	1938.28	0.789423
$183$	−5278.59	−2.13226
$184$	4817.99	1.93037
$185$	−631.888	−0.251121
$186$	5963.77	2.35099
$187$	−3424.57	−1.33920
$188$	3977.97	1.54321
$189$	558.043	0.214770
$190$	−1784.89	−0.681522
$191$	2468.97	0.935333	0.467666	−	0.883905i	$-0.345095\pi$
$191$	2468.97	0.935333	0.467666	+	0.883905i	$0.345095\pi$
$192$	2855.60	1.07336
$193$	−4371.20	−1.63029	−0.815145	−	0.579258i	$-0.803343\pi$
$193$	−4371.20	−1.63029	−0.815145	+	0.579258i	$0.803343\pi$
$194$	−917.873	−0.339688
$195$	1848.74	0.678928
$196$	−5796.24	−2.11233
$197$	−1498.89	−0.542089	−0.271045	−	0.962567i	$-0.587369\pi$
$197$	−1498.89	−0.542089	−0.271045	+	0.962567i	$0.587369\pi$
$198$	−4196.09	−1.50608
$199$	−4496.34	−1.60169	−0.800847	−	0.598869i	$-0.795617\pi$
$199$	−4496.34	−1.60169	−0.800847	+	0.598869i	$0.795617\pi$
$200$	1455.72	0.514674
$201$	−3172.98	−1.11346
$202$	2256.86	0.786098
$203$	184.903	0.0639294
$204$	6822.63	2.34157
$205$	−1480.93	−0.504550
$206$	−706.756	−0.239039
$207$	1091.79	0.366594
$208$	−8757.02	−2.91918
$209$	−4178.02	−1.38278
$210$	1053.55	0.346199
$211$	4691.38	1.53065	0.765327	−	0.643641i	$-0.222577\pi$
$211$	4691.38	1.53065	0.765327	+	0.643641i	$0.222577\pi$
$212$	6984.29	2.26265
$213$	6896.68	2.21856
$214$	−3927.41	−1.25454
$215$	−709.549	−0.225074
$216$	−5096.33	−1.60538
$217$	−1150.61	−0.359948
$218$	−1994.87	−0.619769
$219$	5715.75	1.76363
$220$	5847.80	1.79209
$221$	−3273.73	−0.996449
$222$	4176.45	1.26264
$223$	2929.52	0.879709	0.439854	−	0.898069i	$-0.355030\pi$
$223$	2929.52	0.879709	0.439854	+	0.898069i	$0.355030\pi$
$224$	−2020.28	−0.602615
$225$	329.877	0.0977412
$226$	1458.75	0.429357
$227$	−815.482	−0.238438	−0.119219	−	0.992868i	$-0.538039\pi$
$227$	−815.482	−0.238438	−0.119219	+	0.992868i	$0.538039\pi$
$228$	8323.70	2.41777
$229$	−5075.40	−1.46459	−0.732297	−	0.680985i	$-0.761552\pi$
$229$	−5075.40	−1.46459	−0.732297	+	0.680985i	$0.761552\pi$
$230$	−2156.51	−0.618243
$231$	2466.12	0.702420
$232$	−1688.63	−0.477863
$233$	−1015.87	−0.285629	−0.142815	−	0.989749i	$-0.545615\pi$
$233$	−1015.87	−0.285629	−0.142815	+	0.989749i	$0.545615\pi$
$234$	−4011.27	−1.12062
$235$	−1037.51	−0.287998
$236$	−14926.1	−4.11698
$237$	−5592.48	−1.53279
$238$	−1865.62	−0.508109
$239$	−1966.75	−0.532294	−0.266147	−	0.963932i	$-0.585751\pi$
$239$	−1966.75	−0.532294	−0.266147	+	0.963932i	$0.585751\pi$
$240$	−4759.85	−1.28020
$241$	4490.20	1.20016	0.600082	−	0.799939i	$-0.295135\pi$
$241$	4490.20	1.20016	0.600082	+	0.799939i	$0.295135\pi$
$242$	12462.7	3.31046
$243$	−3413.58	−0.901159
$244$	−15961.4	−4.18781
$245$	1511.73	0.394209
$246$	9788.20	2.53688
$247$	−3994.00	−1.02888
$248$	10508.0	2.69056
$249$	−8198.16	−2.08650
$250$	−651.571	−0.164836
$251$	5919.15	1.48850	0.744250	−	0.667902i	$-0.232807\pi$
$251$	5919.15	1.48850	0.744250	+	0.667902i	$0.232807\pi$
$252$	−1612.87	−0.403180
$253$	−5047.91	−1.25438
$254$	13272.1	3.27861
$255$	−1779.43	−0.436989
$256$	−4578.37	−1.11777
$257$	752.906	0.182743	0.0913716	−	0.995817i	$-0.470875\pi$
$257$	752.906	0.182743	0.0913716	+	0.995817i	$0.470875\pi$
$258$	4689.76	1.13167
$259$	−805.780	−0.193316
$260$	5590.23	1.33343
$261$	−382.657	−0.0907505
$262$	−8056.67	−1.89978
$263$	−169.736	−0.0397961	−0.0198981	−	0.999802i	$-0.506334\pi$
$263$	−169.736	−0.0397961	−0.0198981	+	0.999802i	$0.506334\pi$
$264$	−22521.9	−5.25048
$265$	−1821.59	−0.422262
$266$	−2276.08	−0.524644
$267$	−304.749	−0.0698515
$268$	−9594.48	−2.18685
$269$	6630.15	1.50278	0.751389	−	0.659860i	$-0.229384\pi$
$269$	6630.15	1.50278	0.751389	+	0.659860i	$0.229384\pi$
$270$	2281.09	0.514158
$271$	−478.527	−0.107264	−0.0536318	−	0.998561i	$-0.517080\pi$
$271$	−478.527	−0.107264	−0.0536318	+	0.998561i	$0.517080\pi$
$272$	8428.72	1.87892
$273$	2357.50	0.522647
$274$	6926.48	1.52717
$275$	−1525.18	−0.334444
$276$	10056.7	2.19327
$277$	−6220.41	−1.34927	−0.674636	−	0.738150i	$-0.735699\pi$
$277$	−6220.41	−1.34927	−0.674636	+	0.738150i	$0.735699\pi$
$278$	2874.60	0.620170
$279$	2381.19	0.510962
$280$	1856.32	0.396202
$281$	−4153.25	−0.881716	−0.440858	−	0.897577i	$-0.645326\pi$
$281$	−4153.25	−0.881716	−0.440858	+	0.897577i	$0.645326\pi$
$282$	6857.39	1.44806
$283$	−3561.31	−0.748049	−0.374024	−	0.927419i	$-0.622022\pi$
$283$	−3561.31	−0.748049	−0.374024	+	0.927419i	$0.622022\pi$
$284$	20854.2	4.35729
$285$	−2170.93	−0.451209
$286$	18546.1	3.83445
$287$	−1888.48	−0.388409
$288$	4180.97	0.855438
$289$	−1762.00	−0.358639
$290$	755.822	0.153046
$291$	−1116.39	−0.224894
$292$	17283.4	3.46381
$293$	−1062.29	−0.211808	−0.105904	−	0.994376i	$-0.533774\pi$
$293$	−1062.29	−0.211808	−0.105904	+	0.994376i	$0.533774\pi$
$294$	−9991.79	−1.98209
$295$	3892.93	0.768322
$296$	7358.80	1.44500
$297$	5339.52	1.04320
$298$	7724.76	1.50162
$299$	−4825.57	−0.933344
$300$	3038.56	0.584771
$301$	−904.813	−0.173264
$302$	16032.7	3.05489
$303$	2744.98	0.520445
$304$	10283.2	1.94006
$305$	4162.95	0.781540
$306$	3860.89	0.721283
$307$	680.667	0.126540	0.0632699	−	0.997996i	$-0.479847\pi$
$307$	680.667	0.126540	0.0632699	+	0.997996i	$0.479847\pi$
$308$	7457.09	1.37957
$309$	−859.615	−0.158258
$310$	−4703.32	−0.861712
$311$	829.406	0.151226	0.0756130	−	0.997137i	$-0.475909\pi$
$311$	829.406	0.151226	0.0756130	+	0.997137i	$0.475909\pi$
$312$	−21529.9	−3.90670
$313$	−10589.7	−1.91236	−0.956178	−	0.292786i	$-0.905417\pi$
$313$	−10589.7	−1.91236	−0.956178	+	0.292786i	$0.905417\pi$
$314$	−1692.08	−0.304106
$315$	420.657	0.0752424
$316$	−16910.6	−3.01043
$317$	6086.97	1.07848	0.539241	−	0.842152i	$-0.318711\pi$
$317$	6086.97	1.07848	0.539241	+	0.842152i	$0.318711\pi$
$318$	12039.8	2.12314
$319$	1769.21	0.310523
$320$	−2252.07	−0.393420
$321$	−4776.84	−0.830583
$322$	−2749.97	−0.475931
$323$	3844.27	0.662231
$324$	−17467.6	−2.99514
$325$	−1458.00	−0.248848
$326$	−4698.70	−0.798273
$327$	−2426.33	−0.410325
$328$	17246.5	2.90330
$329$	−1323.02	−0.221704
$330$	10080.7	1.68159
$331$	5241.06	0.870316	0.435158	−	0.900354i	$-0.356693\pi$
$331$	5241.06	0.870316	0.435158	+	0.900354i	$0.356693\pi$
$332$	−24789.7	−4.09792
$333$	1667.56	0.274420
$334$	−13265.9	−2.17328
$335$	2502.36	0.408116
$336$	−6069.74	−0.985511
$337$	−6647.79	−1.07457	−0.537283	−	0.843402i	$-0.680549\pi$
$337$	−6647.79	−1.07457	−0.537283	+	0.843402i	$0.680549\pi$
$338$	6277.21	1.01016
$339$	1774.26	0.284261
$340$	−5380.66	−0.858256
$341$	−11009.4	−1.74837
$342$	4710.34	0.744754
$343$	4114.72	0.647737
$344$	8263.22	1.29512
$345$	−2622.92	−0.409314
$346$	11624.9	1.80623
$347$	−4066.40	−0.629094	−0.314547	−	0.949242i	$-0.601853\pi$
$347$	−4066.40	−0.629094	−0.314547	+	0.949242i	$0.601853\pi$
$348$	−3524.73	−0.542946
$349$	−4087.38	−0.626912	−0.313456	−	0.949603i	$-0.601487\pi$
$349$	−4087.38	−0.626912	−0.313456	+	0.949603i	$0.601487\pi$
$350$	−830.880	−0.126893
$351$	5104.34	0.776209
$352$	−19330.7	−2.92707
$353$	−1812.11	−0.273226	−0.136613	−	0.990625i	$-0.543622\pi$
$353$	−1812.11	−0.273226	−0.136613	+	0.990625i	$0.543622\pi$
$354$	−25730.3	−3.86313
$355$	−5439.05	−0.813169
$356$	−921.504	−0.137190
$357$	−2269.12	−0.336399
$358$	15137.4	2.23474
$359$	12501.8	1.83793	0.918967	−	0.394333i	$-0.129025\pi$
$359$	12501.8	1.83793	0.918967	+	0.394333i	$0.129025\pi$
$360$	−3841.66	−0.562425
$361$	−2168.94	−0.316218
$362$	−13479.0	−1.95702
$363$	15158.2	2.19173
$364$	7128.64	1.02649
$365$	−4507.72	−0.646424
$366$	−27515.0	−3.92959
$367$	−5366.63	−0.763312	−0.381656	−	0.924304i	$-0.624646\pi$
$367$	−5366.63	−0.763312	−0.381656	+	0.924304i	$0.624646\pi$
$368$	12424.1	1.75993
$369$	3908.20	0.551363
$370$	−3293.76	−0.462795
$371$	−2322.89	−0.325063
$372$	21933.6	3.05700
$373$	1807.46	0.250903	0.125451	−	0.992100i	$-0.459962\pi$
$373$	1807.46	0.250903	0.125451	+	0.992100i	$0.459962\pi$
$374$	−17850.8	−2.46803
$375$	−792.495	−0.109131
$376$	12082.5	1.65721
$377$	1691.29	0.231049
$378$	2908.83	0.395805
$379$	6151.37	0.833706	0.416853	−	0.908974i	$-0.363133\pi$
$379$	6151.37	0.833706	0.416853	+	0.908974i	$0.363133\pi$
$380$	−6564.48	−0.886186
$381$	16142.6	2.17064
$382$	12869.7	1.72374
$383$	−1284.92	−0.171426	−0.0857130	−	0.996320i	$-0.527317\pi$
$383$	−1284.92	−0.171426	−0.0857130	+	0.996320i	$0.527317\pi$
$384$	−1185.96	−0.157606
$385$	−1944.91	−0.257459
$386$	−22785.2	−3.00449
$387$	1872.51	0.245956
$388$	−3375.76	−0.441697
$389$	7789.62	1.01529	0.507647	−	0.861565i	$-0.330515\pi$
$389$	7789.62	1.01529	0.507647	+	0.861565i	$0.330515\pi$
$390$	9636.67	1.25121
$391$	4644.66	0.600743
$392$	−17605.3	−2.26837
$393$	−9799.20	−1.25777
$394$	−7813.07	−0.999027
$395$	4410.50	0.561814
$396$	−15432.4	−1.95836
$397$	−7666.16	−0.969152	−0.484576	−	0.874749i	$-0.661026\pi$
$397$	−7666.16	−0.969152	−0.484576	+	0.874749i	$0.661026\pi$
$398$	−23437.5	−2.95179
$399$	−2768.36	−0.347346
$400$	3753.85	0.469232
$401$	2382.60	0.296711	0.148356	−	0.988934i	$-0.452602\pi$
$401$	2382.60	0.296711	0.148356	+	0.988934i	$0.452602\pi$
$402$	−16539.3	−2.05201
$403$	−10524.5	−1.30090
$404$	8300.29	1.02217
$405$	4555.79	0.558960
$406$	963.820	0.117817
$407$	−7709.95	−0.938988
$408$	20722.8	2.51453
$409$	2636.65	0.318763	0.159381	−	0.987217i	$-0.449050\pi$
$409$	2636.65	0.318763	0.159381	+	0.987217i	$0.449050\pi$
$410$	−7719.45	−0.929846
$411$	8424.56	1.01108
$412$	−2599.31	−0.310823
$413$	4964.24	0.591463
$414$	5691.05	0.675604
$415$	6465.47	0.764765
$416$	−18479.3	−2.17793
$417$	3496.33	0.410591
$418$	−21778.2	−2.54834
$419$	−6602.97	−0.769871	−0.384936	−	0.922943i	$-0.625776\pi$
$419$	−6602.97	−0.769871	−0.384936	+	0.922943i	$0.625776\pi$
$420$	3874.75	0.450163
$421$	15883.7	1.83878	0.919390	−	0.393347i	$-0.128683\pi$
$421$	15883.7	1.83878	0.919390	+	0.393347i	$0.128683\pi$
$422$	24454.1	2.82087
$423$	2738.00	0.314718
$424$	21213.8	2.42979
$425$	1403.35	0.160170
$426$	35949.4	4.08862
$427$	5308.57	0.601639
$428$	−14444.3	−1.63128
$429$	22557.3	2.53864
$430$	−3698.57	−0.414793
$431$	−1219.60	−0.136301	−0.0681507	−	0.997675i	$-0.521710\pi$
$431$	−1219.60	−0.136301	−0.0681507	+	0.997675i	$0.521710\pi$
$432$	−13141.9	−1.46363
$433$	−11053.2	−1.22675	−0.613377	−	0.789790i	$-0.710189\pi$
$433$	−11053.2	−1.22675	−0.613377	+	0.789790i	$0.710189\pi$
$434$	−5997.65	−0.663356
$435$	919.294	0.101326
$436$	−7336.76	−0.805888
$437$	5666.55	0.620292
$438$	29793.7	3.25023
$439$	2683.07	0.291699	0.145850	−	0.989307i	$-0.453408\pi$
$439$	2683.07	0.291699	0.145850	+	0.989307i	$0.453408\pi$
$440$	17761.9	1.92446
$441$	−3989.49	−0.430784
$442$	−17064.6	−1.83638
$443$	8012.04	0.859285	0.429643	−	0.902999i	$-0.358640\pi$
$443$	8012.04	0.859285	0.429643	+	0.902999i	$0.358640\pi$
$444$	15360.2	1.64181
$445$	240.340	0.0256027
$446$	15270.3	1.62123
$447$	9395.50	0.994165
$448$	−2871.82	−0.302859
$449$	−1841.49	−0.193553	−0.0967765	−	0.995306i	$-0.530853\pi$
$449$	−1841.49	−0.193553	−0.0967765	+	0.995306i	$0.530853\pi$
$450$	1719.50	0.180129
$451$	−18069.5	−1.88661
$452$	5365.01	0.558294
$453$	19500.3	2.02252
$454$	−4250.75	−0.439422
$455$	−1859.24	−0.191566
$456$	25282.1	2.59636
$457$	−5983.60	−0.612475	−0.306238	−	0.951955i	$-0.599070\pi$
$457$	−5983.60	−0.612475	−0.306238	+	0.951955i	$0.599070\pi$
$458$	−26455.9	−2.69913
$459$	−4912.98	−0.499604
$460$	−7931.23	−0.803903
$461$	−1961.26	−0.198146	−0.0990728	−	0.995080i	$-0.531588\pi$
$461$	−1961.26	−0.198146	−0.0990728	+	0.995080i	$0.531588\pi$
$462$	12854.8	1.29450
$463$	10864.9	1.09057	0.545286	−	0.838250i	$-0.316421\pi$
$463$	10864.9	1.09057	0.545286	+	0.838250i	$0.316421\pi$
$464$	−4354.47	−0.435671
$465$	−5720.57	−0.570506
$466$	−5295.27	−0.526392
$467$	8762.37	0.868253	0.434126	−	0.900852i	$-0.357057\pi$
$467$	8762.37	0.868253	0.434126	+	0.900852i	$0.357057\pi$
$468$	−14752.7	−1.45715
$469$	3191.00	0.314172
$470$	−5408.07	−0.530757
$471$	−2058.04	−0.201337
$472$	−45336.0	−4.42110
$473$	−8657.53	−0.841594
$474$	−29151.2	−2.82480
$475$	1712.10	0.165382
$476$	−6861.39	−0.660696
$477$	4807.21	0.461440
$478$	−10251.8	−0.980975
$479$	19725.6	1.88160	0.940798	−	0.338969i	$-0.110078\pi$
$479$	19725.6	1.88160	0.940798	+	0.338969i	$0.110078\pi$
$480$	−10044.4	−0.955125
$481$	−7370.36	−0.698669
$482$	23405.5	2.21181
$483$	−3344.74	−0.315095
$484$	45835.4	4.30460
$485$	880.443	0.0824306
$486$	−17793.5	−1.66076
$487$	7534.19	0.701041	0.350520	−	0.936555i	$-0.386005\pi$
$487$	7534.19	0.701041	0.350520	+	0.936555i	$0.386005\pi$
$488$	−48480.6	−4.49716
$489$	−5714.96	−0.528506
$490$	7880.01	0.726495
$491$	19428.1	1.78570	0.892849	−	0.450356i	$-0.148703\pi$
$491$	19428.1	1.78570	0.892849	+	0.450356i	$0.148703\pi$
$492$	35999.2	3.29872
$493$	−1627.88	−0.148714
$494$	−20819.0	−1.89613
$495$	4024.98	0.365473
$496$	27096.9	2.45300
$497$	−6935.86	−0.625987
$498$	−42733.4	−3.84524
$499$	−10255.2	−0.920011	−0.460005	−	0.887916i	$-0.652153\pi$
$499$	−10255.2	−0.920011	−0.460005	+	0.887916i	$0.652153\pi$
$500$	−2396.35	−0.214336
$501$	−16135.1	−1.43885
$502$	30853.9	2.74318
$503$	7473.22	0.662454	0.331227	−	0.943551i	$-0.392537\pi$
$503$	7473.22	0.662454	0.331227	+	0.943551i	$0.392537\pi$
$504$	−4898.86	−0.432962
$505$	−2164.82	−0.190759
$506$	−26312.5	−2.31173
$507$	7634.87	0.668789
$508$	48812.3	4.26318
$509$	8947.08	0.779121	0.389560	−	0.921001i	$-0.372627\pi$
$509$	8947.08	0.779121	0.389560	+	0.921001i	$0.372627\pi$
$510$	−9275.39	−0.805336
$511$	−5748.22	−0.497625
$512$	−22368.6	−1.93078
$513$	−5993.90	−0.515862
$514$	3924.57	0.336781
$515$	677.935	0.0580065
$516$	17248.0	1.47152
$517$	−12659.1	−1.07688
$518$	−4200.18	−0.356265
$519$	14139.1	1.19584
$520$	16979.5	1.43193
$521$	−10606.3	−0.891879	−0.445940	−	0.895063i	$-0.647130\pi$
$521$	−10606.3	−0.891879	−0.445940	+	0.895063i	$0.647130\pi$
$522$	−1994.62	−0.167246
$523$	−20727.8	−1.73301	−0.866503	−	0.499172i	$-0.833638\pi$
$523$	−20727.8	−1.73301	−0.866503	+	0.499172i	$0.833638\pi$
$524$	−29630.9	−2.47029
$525$	−1010.59	−0.0840106
$526$	−884.760	−0.0733410
$527$	10130.0	0.837320
$528$	−58077.2	−4.78690
$529$	−5320.66	−0.437302
$530$	−9495.17	−0.778196
$531$	−10273.5	−0.839607
$532$	−8370.99	−0.682196
$533$	−17273.7	−1.40376
$534$	−1588.53	−0.128731
$535$	3767.25	0.304434
$536$	−29141.9	−2.34839
$537$	18411.4	1.47954
$538$	34560.1	2.76950
$539$	18445.4	1.47402
$540$	8389.41	0.668561
$541$	−4680.36	−0.371949	−0.185974	−	0.982555i	$-0.559544\pi$
$541$	−4680.36	−0.371949	−0.185974	+	0.982555i	$0.559544\pi$
$542$	−2494.35	−0.197678
$543$	−16394.3	−1.29566
$544$	17786.5	1.40182
$545$	1913.52	0.150397
$546$	12288.6	0.963196
$547$	8552.59	0.668524	0.334262	−	0.942480i	$-0.391513\pi$
$547$	8552.59	0.668524	0.334262	+	0.942480i	$0.391513\pi$
$548$	25474.3	1.98578
$549$	−10986.1	−0.854052
$550$	−7950.11	−0.616353
$551$	−1986.04	−0.153553
$552$	30545.9	2.35529
$553$	5624.25	0.432491
$554$	−32424.3	−2.48660
$555$	−4006.14	−0.306399
$556$	10572.3	0.806409
$557$	10564.2	0.803629	0.401814	−	0.915721i	$-0.368380\pi$
$557$	10564.2	0.803629	0.401814	+	0.915721i	$0.368380\pi$
$558$	12412.1	0.941662
$559$	−8276.21	−0.626201
$560$	4786.90	0.361220
$561$	−21711.6	−1.63399
$562$	−21649.1	−1.62493
$563$	16624.5	1.24447	0.622236	−	0.782829i	$-0.286224\pi$
$563$	16624.5	1.24447	0.622236	+	0.782829i	$0.286224\pi$
$564$	25220.2	1.88291
$565$	−1399.26	−0.104190
$566$	−18563.5	−1.37859
$567$	5809.52	0.430294
$568$	63341.8	4.67916
$569$	−9400.24	−0.692581	−0.346290	−	0.938127i	$-0.612559\pi$
$569$	−9400.24	−0.692581	−0.346290	+	0.938127i	$0.612559\pi$
$570$	−11316.1	−0.831543
$571$	8882.86	0.651026	0.325513	−	0.945537i	$-0.394463\pi$
$571$	8882.86	0.651026	0.325513	+	0.945537i	$0.394463\pi$
$572$	68209.0	4.98595
$573$	15653.2	1.14122
$574$	−9843.81	−0.715806
$575$	2068.57	0.150026
$576$	5943.23	0.429921
$577$	17503.7	1.26289	0.631447	−	0.775419i	$-0.282461\pi$
$577$	17503.7	1.26289	0.631447	+	0.775419i	$0.282461\pi$
$578$	−9184.51	−0.660944
$579$	−27713.2	−1.98916
$580$	2779.77	0.199006
$581$	8244.74	0.588725
$582$	−5819.28	−0.414462
$583$	−22226.1	−1.57892
$584$	52495.7	3.71967
$585$	3847.70	0.271936
$586$	−5537.26	−0.390345
$587$	−9109.83	−0.640550	−0.320275	−	0.947325i	$-0.603775\pi$
$587$	−9109.83	−0.640550	−0.320275	+	0.947325i	$0.603775\pi$
$588$	−36747.9	−2.57731
$589$	12358.7	0.864568
$590$	20292.1	1.41596
$591$	−9502.91	−0.661417
$592$	18976.1	1.31742
$593$	15168.7	1.05043	0.525213	−	0.850971i	$-0.323986\pi$
$593$	15168.7	1.05043	0.525213	+	0.850971i	$0.323986\pi$
$594$	27832.6	1.92254
$595$	1789.54	0.123301
$596$	28410.2	1.95256
$597$	−28506.6	−1.95427
$598$	−25153.6	−1.72008
$599$	9963.96	0.679660	0.339830	−	0.940487i	$-0.389630\pi$
$599$	9963.96	0.679660	0.339830	+	0.940487i	$0.389630\pi$
$600$	9229.18	0.627966
$601$	−15546.7	−1.05518	−0.527589	−	0.849499i	$-0.676904\pi$
$601$	−15546.7	−1.05518	−0.527589	+	0.849499i	$0.676904\pi$
$602$	−4716.40	−0.319312
$603$	−6603.77	−0.445981
$604$	58965.1	3.97228
$605$	−11954.5	−0.803335
$606$	14308.4	0.959138
$607$	−13532.0	−0.904856	−0.452428	−	0.891801i	$-0.649442\pi$
$607$	−13532.0	−0.904856	−0.452428	+	0.891801i	$0.649442\pi$
$608$	21699.7	1.44744
$609$	1172.28	0.0780019
$610$	21699.6	1.44032
$611$	−12101.5	−0.801269
$612$	14199.6	0.937886
$613$	3618.68	0.238429	0.119215	−	0.992868i	$-0.461962\pi$
$613$	3618.68	0.238429	0.119215	+	0.992868i	$0.461962\pi$
$614$	3548.02	0.233203
$615$	−9389.05	−0.615615
$616$	22649.9	1.48148
$617$	−17669.4	−1.15291	−0.576455	−	0.817129i	$-0.695564\pi$
$617$	−17669.4	−1.15291	−0.576455	+	0.817129i	$0.695564\pi$
$618$	−4480.80	−0.291657
$619$	−20897.7	−1.35695	−0.678474	−	0.734624i	$-0.737358\pi$
$619$	−20897.7	−1.35695	−0.678474	+	0.734624i	$0.737358\pi$
$620$	−17297.9	−1.12049
$621$	−7241.86	−0.467964
$622$	4323.33	0.278697
$623$	306.481	0.0197093
$624$	−55519.1	−3.56177
$625$	625.000	0.0400000
$626$	−55199.7	−3.52432
$627$	−26488.5	−1.68716
$628$	−6223.14	−0.395430
$629$	7094.05	0.449695
$630$	2192.70	0.138666
$631$	−10549.0	−0.665529	−0.332765	−	0.943010i	$-0.607981\pi$
$631$	−10549.0	−0.665529	−0.332765	+	0.943010i	$0.607981\pi$
$632$	−51363.5	−3.23280
$633$	29743.2	1.86759
$634$	31728.7	1.98755
$635$	−12730.9	−0.795605
$636$	44280.1	2.76072
$637$	17632.9	1.09677
$638$	9222.13	0.572269
$639$	14353.7	0.888615
$640$	935.307	0.0577676
$641$	−3620.31	−0.223079	−0.111540	−	0.993760i	$-0.535578\pi$
$641$	−3620.31	−0.223079	−0.111540	+	0.993760i	$0.535578\pi$
$642$	−24899.6	−1.53070
$643$	7456.81	0.457337	0.228669	−	0.973504i	$-0.426563\pi$
$643$	7456.81	0.457337	0.228669	+	0.973504i	$0.426563\pi$
$644$	−10113.9	−0.618854
$645$	−4498.51	−0.274618
$646$	20038.5	1.22044
$647$	−23585.7	−1.43315	−0.716576	−	0.697509i	$-0.754292\pi$
$647$	−23585.7	−1.43315	−0.716576	+	0.697509i	$0.754292\pi$
$648$	−53055.5	−3.21638
$649$	47499.4	2.87290
$650$	−7599.95	−0.458607
$651$	−7294.85	−0.439182
$652$	−17280.9	−1.03800
$653$	−11910.8	−0.713791	−0.356895	−	0.934144i	$-0.616165\pi$
$653$	−11910.8	−0.713791	−0.356895	+	0.934144i	$0.616165\pi$
$654$	−12647.4	−0.756196
$655$	7728.13	0.461012
$656$	44473.6	2.64696
$657$	11895.9	0.706400
$658$	−6896.35	−0.408583
$659$	2497.06	0.147605	0.0738024	−	0.997273i	$-0.476487\pi$
$659$	2497.06	0.147605	0.0738024	+	0.997273i	$0.476487\pi$
$660$	37074.8	2.18657
$661$	19274.6	1.13418	0.567091	−	0.823655i	$-0.308069\pi$
$661$	19274.6	1.13418	0.567091	+	0.823655i	$0.308069\pi$
$662$	27319.3	1.60392
$663$	−20755.3	−1.21579
$664$	−75295.2	−4.40063
$665$	2183.26	0.127313
$666$	8692.27	0.505733
$667$	−2399.54	−0.139296
$668$	−48789.4	−2.82593
$669$	18573.0	1.07336
$670$	13043.7	0.752125
$671$	50794.1	2.92233
$672$	−12808.5	−0.735266
$673$	−10560.6	−0.604875	−0.302438	−	0.953169i	$-0.597800\pi$
$673$	−10560.6	−0.604875	−0.302438	+	0.953169i	$0.597800\pi$
$674$	−34652.1	−1.98034
$675$	−2188.07	−0.124769
$676$	23086.4	1.31352
$677$	−3316.76	−0.188292	−0.0941459	−	0.995558i	$-0.530012\pi$
$677$	−3316.76	−0.188292	−0.0941459	+	0.995558i	$0.530012\pi$
$678$	9248.42	0.523869
$679$	1122.74	0.0634561
$680$	−16343.0	−0.921654
$681$	−5170.12	−0.290924
$682$	−57387.4	−3.22211
$683$	28395.1	1.59079	0.795393	−	0.606094i	$-0.207265\pi$
$683$	28395.1	1.59079	0.795393	+	0.606094i	$0.207265\pi$
$684$	17323.7	0.968406
$685$	−6644.02	−0.370591
$686$	21448.2	1.19373
$687$	−32177.9	−1.78699
$688$	21308.3	1.18077
$689$	−21247.1	−1.17482
$690$	−13672.2	−0.754334
$691$	13485.0	0.742391	0.371196	−	0.928555i	$-0.378948\pi$
$691$	13485.0	0.742391	0.371196	+	0.928555i	$0.378948\pi$
$692$	42754.0	2.34865
$693$	5132.63	0.281346
$694$	−21196.4	−1.15937
$695$	−2757.38	−0.150494
$696$	−10705.9	−0.583052
$697$	16626.1	0.903526
$698$	−21305.7	−1.15535
$699$	−6440.55	−0.348503
$700$	−3055.82	−0.164999
$701$	−14838.8	−0.799505	−0.399753	−	0.916623i	$-0.630904\pi$
$701$	−14838.8	−0.799505	−0.399753	+	0.916623i	$0.630904\pi$
$702$	26606.7	1.43049
$703$	8654.84	0.464329
$704$	−27478.5	−1.47107
$705$	−6577.75	−0.351394
$706$	−9445.72	−0.503533
$707$	−2760.57	−0.146849
$708$	−94631.0	−5.02324
$709$	10329.0	0.547130	0.273565	−	0.961853i	$-0.411797\pi$
$709$	10329.0	0.547130	0.273565	+	0.961853i	$0.411797\pi$
$710$	−28351.4	−1.49861
$711$	−11639.4	−0.613939
$712$	−2798.94	−0.147324
$713$	14931.8	0.784293
$714$	−11827.9	−0.619957
$715$	−17789.8	−0.930490
$716$	55672.7	2.90584
$717$	−12469.1	−0.649465
$718$	65166.3	3.38717
$719$	15242.7	0.790624	0.395312	−	0.918547i	$-0.370637\pi$
$719$	15242.7	0.790624	0.395312	+	0.918547i	$0.370637\pi$
$720$	−9906.47	−0.512767
$721$	864.499	0.0446541
$722$	−11305.8	−0.582765
$723$	28467.7	1.46435
$724$	−49573.2	−2.54471
$725$	−725.000	−0.0371391
$726$	79012.9	4.03918
$727$	−25276.3	−1.28947	−0.644735	−	0.764406i	$-0.723032\pi$
$727$	−25276.3	−1.28947	−0.644735	+	0.764406i	$0.723032\pi$
$728$	21652.2	1.10231
$729$	2959.25	0.150346
$730$	−23496.8	−1.19131
$731$	7965.94	0.403052
$732$	−101195.	−5.10966
$733$	2020.15	0.101795	0.0508977	−	0.998704i	$-0.483792\pi$
$733$	2020.15	0.101795	0.0508977	+	0.998704i	$0.483792\pi$
$734$	−27973.9	−1.40672
$735$	9584.33	0.480984
$736$	26217.7	1.31304
$737$	30532.5	1.52602
$738$	20371.7	1.01612
$739$	−13269.9	−0.660540	−0.330270	−	0.943886i	$-0.607140\pi$
$739$	−13269.9	−0.660540	−0.330270	+	0.943886i	$0.607140\pi$
$740$	−12113.8	−0.601774
$741$	−25321.8	−1.25536
$742$	−12108.2	−0.599064
$743$	−19031.0	−0.939675	−0.469837	−	0.882753i	$-0.655687\pi$
$743$	−19031.0	−0.939675	−0.469837	+	0.882753i	$0.655687\pi$
$744$	66620.3	3.28282
$745$	−7409.75	−0.364392
$746$	9421.50	0.462394
$747$	−17062.5	−0.835720
$748$	−65651.9	−3.20919
$749$	4803.98	0.234357
$750$	−4130.93	−0.201120
$751$	38291.2	1.86054	0.930271	−	0.366872i	$-0.119571\pi$
$751$	38291.2	1.86054	0.930271	+	0.366872i	$0.119571\pi$
$752$	31157.2	1.51089
$753$	37527.1	1.81616
$754$	8815.94	0.425806
$755$	−15378.9	−0.741317
$756$	10698.1	0.514666
$757$	17281.3	0.829723	0.414861	−	0.909885i	$-0.363830\pi$
$757$	17281.3	0.829723	0.414861	+	0.909885i	$0.363830\pi$
$758$	32064.4	1.53645
$759$	−32003.5	−1.53051
$760$	−19938.7	−0.951647
$761$	−4698.24	−0.223799	−0.111899	−	0.993720i	$-0.535693\pi$
$761$	−4698.24	−0.223799	−0.111899	+	0.993720i	$0.535693\pi$
$762$	84144.6	4.00031
$763$	2440.11	0.115777
$764$	47332.3	2.24139
$765$	−3703.45	−0.175031
$766$	−6697.71	−0.315924
$767$	45407.3	2.13763
$768$	−29026.7	−1.36382
$769$	10247.2	0.480523	0.240262	−	0.970708i	$-0.422767\pi$
$769$	10247.2	0.480523	0.240262	+	0.970708i	$0.422767\pi$
$770$	−10137.9	−0.474476
$771$	4773.40	0.222970
$772$	−83799.5	−3.90675
$773$	8085.14	0.376200	0.188100	−	0.982150i	$-0.439767\pi$
$773$	8085.14	0.376200	0.188100	+	0.982150i	$0.439767\pi$
$774$	9760.58	0.453277
$775$	4511.52	0.209108
$776$	−10253.4	−0.474324
$777$	−5108.61	−0.235869
$778$	40603.9	1.87110
$779$	20284.0	0.932928
$780$	35441.8	1.62695
$781$	−66364.4	−3.04060
$782$	24210.6	1.10712
$783$	2538.16	0.115845
$784$	−45398.6	−2.06809
$785$	1623.07	0.0737962
$786$	−51079.0	−2.31797
$787$	18275.2	0.827754	0.413877	−	0.910333i	$-0.364174\pi$
$787$	18275.2	0.827754	0.413877	+	0.910333i	$0.364174\pi$
$788$	−28735.0	−1.29904
$789$	−1076.12	−0.0485562
$790$	22990.0	1.03538
$791$	−1784.34	−0.0802069
$792$	−46873.8	−2.10302
$793$	48556.8	2.17440
$794$	−39960.3	−1.78607
$795$	−11548.8	−0.515213
$796$	−86198.6	−3.83822
$797$	9583.07	0.425910	0.212955	−	0.977062i	$-0.431691\pi$
$797$	9583.07	0.425910	0.212955	+	0.977062i	$0.431691\pi$
$798$	−14430.2	−0.640132
$799$	11647.8	0.515734
$800$	7921.47	0.350083
$801$	−634.261	−0.0279782
$802$	12419.5	0.546816
$803$	−55000.8	−2.41711
$804$	−60828.6	−2.66823
$805$	2637.83	0.115492
$806$	−54859.7	−2.39746
$807$	42034.8	1.83358
$808$	25211.0	1.09767
$809$	−23688.5	−1.02947	−0.514735	−	0.857349i	$-0.672110\pi$
$809$	−23688.5	−1.02947	−0.514735	+	0.857349i	$0.672110\pi$
$810$	23747.3	1.03012
$811$	−37691.0	−1.63195	−0.815974	−	0.578088i	$-0.803799\pi$
$811$	−37691.0	−1.63195	−0.815974	+	0.578088i	$0.803799\pi$
$812$	3544.75	0.153197
$813$	−3033.84	−0.130875
$814$	−40188.6	−1.73048
$815$	4507.09	0.193714
$816$	53437.7	2.29252
$817$	9718.55	0.416168
$818$	13743.7	0.587454
$819$	4906.56	0.209340
$820$	−28390.7	−1.20908
$821$	35720.0	1.51844	0.759218	−	0.650836i	$-0.225582\pi$
$821$	35720.0	1.51844	0.759218	+	0.650836i	$0.225582\pi$
$822$	43913.6	1.86334
$823$	2501.23	0.105939	0.0529693	−	0.998596i	$-0.483131\pi$
$823$	2501.23	0.105939	0.0529693	+	0.998596i	$0.483131\pi$
$824$	−7895.05	−0.333783
$825$	−9669.60	−0.408063
$826$	25876.4	1.09002
$827$	−21356.3	−0.897983	−0.448991	−	0.893536i	$-0.648217\pi$
$827$	−21356.3	−0.897983	−0.448991	+	0.893536i	$0.648217\pi$
$828$	20930.6	0.878489
$829$	−21251.7	−0.890353	−0.445176	−	0.895443i	$-0.646859\pi$
$829$	−21251.7	−0.890353	−0.445176	+	0.895443i	$0.646859\pi$
$830$	33701.7	1.40940
$831$	−39437.2	−1.64628
$832$	−26268.2	−1.09457
$833$	−16971.9	−0.705932
$834$	18224.9	0.756685
$835$	12724.9	0.527382
$836$	−80096.2	−3.31362
$837$	−15794.4	−0.652252
$838$	−34418.4	−1.41881
$839$	−18259.4	−0.751354	−0.375677	−	0.926751i	$-0.622590\pi$
$839$	−18259.4	−0.751354	−0.375677	+	0.926751i	$0.622590\pi$
$840$	11769.0	0.483416
$841$	841.000	0.0344828
$842$	82795.1	3.38873
$843$	−26331.4	−1.07580
$844$	89937.7	3.66799
$845$	−6021.23	−0.245132
$846$	14272.0	0.580001
$847$	−15244.3	−0.618417
$848$	54703.9	2.21526
$849$	−22578.5	−0.912713
$850$	7315.03	0.295180
$851$	10456.8	0.421216
$852$	132215.	5.31645
$853$	−28424.6	−1.14096	−0.570481	−	0.821311i	$-0.693243\pi$
$853$	−28424.6	−1.14096	−0.570481	+	0.821311i	$0.693243\pi$
$854$	27671.3	1.10877
$855$	−4518.26	−0.180726
$856$	−43872.4	−1.75178
$857$	−9320.80	−0.371520	−0.185760	−	0.982595i	$-0.559475\pi$
$857$	−9320.80	−0.371520	−0.185760	+	0.982595i	$0.559475\pi$
$858$	117581.	4.67851
$859$	21132.4	0.839380	0.419690	−	0.907668i	$-0.362139\pi$
$859$	21132.4	0.839380	0.419690	+	0.907668i	$0.362139\pi$
$860$	−13602.6	−0.539356
$861$	−11972.9	−0.473907
$862$	−6357.23	−0.251193
$863$	21301.0	0.840203	0.420102	−	0.907477i	$-0.361994\pi$
$863$	21301.0	0.840203	0.420102	+	0.907477i	$0.361994\pi$
$864$	−27732.3	−1.09198
$865$	−11150.8	−0.438311
$866$	−57615.7	−2.26081
$867$	−11171.0	−0.437585
$868$	−22058.2	−0.862564
$869$	53814.6	2.10073
$870$	4791.88	0.186736
$871$	29187.7	1.13546
$872$	−22284.4	−0.865417
$873$	−2323.50	−0.0900785
$874$	29537.2	1.14315
$875$	796.997	0.0307925
$876$	109576.	4.22628
$877$	11419.6	0.439697	0.219848	−	0.975534i	$-0.429444\pi$
$877$	11419.6	0.439697	0.219848	+	0.975534i	$0.429444\pi$
$878$	13985.7	0.537578
$879$	−6734.88	−0.258432
$880$	45802.5	1.75455
$881$	15004.2	0.573784	0.286892	−	0.957963i	$-0.407378\pi$
$881$	15004.2	0.573784	0.286892	+	0.957963i	$0.407378\pi$
$882$	−20795.5	−0.793900
$883$	−4234.36	−0.161379	−0.0806894	−	0.996739i	$-0.525712\pi$
$883$	−4234.36	−0.161379	−0.0806894	+	0.996739i	$0.525712\pi$
$884$	−62760.2	−2.38784
$885$	24681.0	0.937449
$886$	41763.3	1.58359
$887$	50237.9	1.90172	0.950860	−	0.309622i	$-0.100202\pi$
$887$	50237.9	1.90172	0.950860	+	0.309622i	$0.100202\pi$
$888$	46654.5	1.76309
$889$	−16234.4	−0.612467
$890$	1252.79	0.0471838
$891$	55587.2	2.09006
$892$	56161.3	2.10809
$893$	14210.5	0.532516
$894$	48974.6	1.83217
$895$	−14520.1	−0.542296
$896$	1192.70	0.0444702
$897$	−30593.9	−1.13880
$898$	−9598.89	−0.356703
$899$	−5233.37	−0.194152
$900$	6324.01	0.234223
$901$	20450.6	0.756168
$902$	−94188.6	−3.47687
$903$	−5736.48	−0.211404
$904$	16295.5	0.599534
$905$	12929.3	0.474901
$906$	101646.	3.72735
$907$	−31312.6	−1.14633	−0.573164	−	0.819441i	$-0.694284\pi$
$907$	−31312.6	−1.14633	−0.573164	+	0.819441i	$0.694284\pi$
$908$	−15633.5	−0.571382
$909$	5713.00	0.208458
$910$	−9691.41	−0.353041
$911$	872.220	0.0317211	0.0158606	−	0.999874i	$-0.494951\pi$
$911$	872.220	0.0317211	0.0158606	+	0.999874i	$0.494951\pi$
$912$	65194.8	2.36712
$913$	78888.2	2.85960
$914$	−31189.9	−1.12874
$915$	26392.9	0.953577
$916$	−97299.7	−3.50969
$917$	9854.87	0.354893
$918$	−25609.2	−0.920731
$919$	−26902.3	−0.965641	−0.482820	−	0.875719i	$-0.660388\pi$
$919$	−26902.3	−0.965641	−0.482820	+	0.875719i	$0.660388\pi$
$920$	−24090.0	−0.863286
$921$	4315.40	0.154394
$922$	−10223.2	−0.365166
$923$	−63441.3	−2.26240
$924$	47277.7	1.68325
$925$	3159.44	0.112305
$926$	56634.0	2.00984
$927$	−1789.08	−0.0633884
$928$	−9188.90	−0.325044
$929$	−45849.6	−1.61924	−0.809621	−	0.586952i	$-0.800328\pi$
$929$	−45849.6	−1.61924	−0.809621	+	0.586952i	$0.800328\pi$
$930$	−29818.9	−1.05140
$931$	−20705.9	−0.728904
$932$	−19475.0	−0.684469
$933$	5258.40	0.184515
$934$	45674.4	1.60012
$935$	17122.9	0.598906
$936$	−44809.2	−1.56478
$937$	22736.8	0.792722	0.396361	−	0.918095i	$-0.370273\pi$
$937$	22736.8	0.792722	0.396361	+	0.918095i	$0.370273\pi$
$938$	16633.3	0.578994
$939$	−67138.5	−2.33331
$940$	−19889.9	−0.690145
$941$	−46907.0	−1.62500	−0.812500	−	0.582961i	$-0.801894\pi$
$941$	−46907.0	−1.62500	−0.812500	+	0.582961i	$0.801894\pi$
$942$	−10727.7	−0.371048
$943$	24507.2	0.846305
$944$	−116908.	−4.03075
$945$	−2790.21	−0.0960483
$946$	−45128.0	−1.55099
$947$	14219.4	0.487928	0.243964	−	0.969784i	$-0.421552\pi$
$947$	14219.4	0.487928	0.243964	+	0.969784i	$0.421552\pi$
$948$	−107212.	−3.67310
$949$	−52578.2	−1.79848
$950$	8924.43	0.304786
$951$	38591.2	1.31588
$952$	−20840.5	−0.709501
$953$	−50695.8	−1.72319	−0.861594	−	0.507597i	$-0.830534\pi$
$953$	−50695.8	−1.72319	−0.861594	+	0.507597i	$0.830534\pi$
$954$	25057.9	0.850397
$955$	−12344.9	−0.418294
$956$	−37704.1	−1.27556
$957$	11216.7	0.378877
$958$	102821.	3.46763
$959$	−8472.42	−0.285286
$960$	−14278.0	−0.480021
$961$	2775.13	0.0931533
$962$	−38418.5	−1.28759
$963$	−9941.82	−0.332680
$964$	86080.9	2.87602
$965$	21856.0	0.729087
$966$	−17434.7	−0.580695
$967$	−15022.8	−0.499586	−0.249793	−	0.968299i	$-0.580362\pi$
$967$	−15022.8	−0.499586	−0.249793	+	0.968299i	$0.580362\pi$
$968$	139218.	4.62257
$969$	24372.5	0.808006
$970$	4589.36	0.151913
$971$	15417.1	0.509534	0.254767	−	0.967003i	$-0.418001\pi$
$971$	15417.1	0.509534	0.254767	+	0.967003i	$0.418001\pi$
$972$	−65441.3	−2.15950
$973$	−3516.20	−0.115852
$974$	39272.5	1.29196
$975$	−9243.69	−0.303626
$976$	−125017.	−4.10009
$977$	35120.3	1.15005	0.575024	−	0.818136i	$-0.304993\pi$
$977$	35120.3	1.15005	0.575024	+	0.818136i	$0.304993\pi$
$978$	−29789.6	−0.973994
$979$	2932.50	0.0957336
$980$	28981.2	0.944664
$981$	−5049.81	−0.164351
$982$	101270.	3.29090
$983$	2757.23	0.0894628	0.0447314	−	0.998999i	$-0.485757\pi$
$983$	2757.23	0.0894628	0.0447314	+	0.998999i	$0.485757\pi$
$984$	109342.	3.54239
$985$	7494.46	0.242430
$986$	−8485.43	−0.274068
$987$	−8387.92	−0.270507
$988$	−76568.3	−2.46555
$989$	11742.0	0.377526
$990$	20980.5	0.673538
$991$	14086.1	0.451525	0.225762	−	0.974182i	$-0.427513\pi$
$991$	14086.1	0.451525	0.225762	+	0.974182i	$0.427513\pi$
$992$	57180.6	1.83013
$993$	33228.1	1.06189
$994$	−36153.6	−1.15364
$995$	22481.7	0.716299
$996$	−157166.	−4.99998
$997$	−20962.8	−0.665897	−0.332948	−	0.942945i	$-0.608043\pi$
$997$	−20962.8	−0.665897	−0.332948	+	0.942945i	$0.608043\pi$
$998$	−53455.9	−1.69551
$999$	−11060.9	−0.350302

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	145.4.a.d.1.6	✓	7
3.2	odd	2		1305.4.a.l.1.2		7
4.3	odd	2		2320.4.a.s.1.2		7
5.4	even	2		725.4.a.f.1.2		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
145.4.a.d.1.6	✓	7	1.1	even	1	trivial
725.4.a.f.1.2		7	5.4	even	2
1305.4.a.l.1.2		7	3.2	odd	2
2320.4.a.s.1.2		7	4.3	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:	\( N \)	\(=\)	\( 145 = 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	145.a (trivial)

\(f(q)\)	\(=\)	\(q+5.21256 q^{2} +6.33996 q^{3} +19.1708 q^{4} -5.00000 q^{5} +33.0474 q^{6} -6.37598 q^{7} +58.2287 q^{8} +13.1951 q^{9} +O(q^{10})\)	\(q+5.21256 q^{2} +6.33996 q^{3} +19.1708 q^{4} -5.00000 q^{5} +33.0474 q^{6} -6.37598 q^{7} +58.2287 q^{8} +13.1951 q^{9} -26.0628 q^{10} -61.0073 q^{11} +121.542 q^{12} -58.3202 q^{13} -33.2352 q^{14} -31.6998 q^{15} +150.154 q^{16} +56.1338 q^{17} +68.7802 q^{18} +68.4840 q^{19} -95.8542 q^{20} -40.4234 q^{21} -318.005 q^{22} +82.7426 q^{23} +369.167 q^{24} +25.0000 q^{25} -303.998 q^{26} -87.5227 q^{27} -122.233 q^{28} -29.0000 q^{29} -165.237 q^{30} +180.461 q^{31} +316.859 q^{32} -386.784 q^{33} +292.601 q^{34} +31.8799 q^{35} +252.960 q^{36} +126.378 q^{37} +356.977 q^{38} -369.748 q^{39} -291.143 q^{40} +296.186 q^{41} -210.710 q^{42} +141.910 q^{43} -1169.56 q^{44} -65.9753 q^{45} +431.301 q^{46} +207.501 q^{47} +951.971 q^{48} -302.347 q^{49} +130.314 q^{50} +355.886 q^{51} -1118.05 q^{52} +364.318 q^{53} -456.218 q^{54} +305.037 q^{55} -371.265 q^{56} +434.186 q^{57} -151.164 q^{58} -778.586 q^{59} -607.711 q^{60} -832.590 q^{61} +940.664 q^{62} -84.1314 q^{63} +450.413 q^{64} +291.601 q^{65} -2016.14 q^{66} -500.473 q^{67} +1076.13 q^{68} +524.585 q^{69} +166.176 q^{70} +1087.81 q^{71} +768.331 q^{72} +901.544 q^{73} +658.751 q^{74} +158.499 q^{75} +1312.90 q^{76} +388.981 q^{77} -1927.33 q^{78} -882.100 q^{79} -750.771 q^{80} -911.157 q^{81} +1543.89 q^{82} -1293.09 q^{83} -774.951 q^{84} -280.669 q^{85} +739.714 q^{86} -183.859 q^{87} -3552.38 q^{88} -48.0680 q^{89} -343.901 q^{90} +371.848 q^{91} +1586.25 q^{92} +1144.11 q^{93} +1081.61 q^{94} -342.420 q^{95} +2008.87 q^{96} -176.089 q^{97} -1576.00 q^{98} -804.996 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 6 q^{2} + q^{3} + 52 q^{4} - 35 q^{5} + 3 q^{6} + 17 q^{7} + 138 q^{8} + 118 q^{9}+O(q^{10}) \) 7 * q + 6 * q^2 + q^3 + 52 * q^4 - 35 * q^5 + 3 * q^6 + 17 * q^7 + 138 * q^8 + 118 * q^9	\( 7 q + 6 q^{2} + q^{3} + 52 q^{4} - 35 q^{5} + 3 q^{6} + 17 q^{7} + 138 q^{8} + 118 q^{9} - 30 q^{10} + 2 q^{11} - 77 q^{12} - 17 q^{13} + 361 q^{14} - 5 q^{15} + 372 q^{16} + 95 q^{17} + 261 q^{18} + 94 q^{19} - 260 q^{20} - 100 q^{21} + 190 q^{22} + 327 q^{23} - 117 q^{24} + 175 q^{25} - 115 q^{26} - 236 q^{27} - 67 q^{28} - 203 q^{29} - 15 q^{30} + 169 q^{31} + 890 q^{32} + 272 q^{33} + 377 q^{34} - 85 q^{35} + 2443 q^{36} - 500 q^{37} + 282 q^{38} + 1129 q^{39} - 690 q^{40} + 1208 q^{41} - 1892 q^{42} - 1517 q^{43} - 734 q^{44} - 590 q^{45} - 1413 q^{46} + 1974 q^{47} - 2637 q^{48} + 794 q^{49} + 150 q^{50} - 190 q^{51} - 2063 q^{52} - 255 q^{53} - 5052 q^{54} - 10 q^{55} + 2057 q^{56} + 94 q^{57} - 174 q^{58} + 177 q^{59} + 385 q^{60} - 705 q^{61} - 807 q^{62} + 200 q^{63} + 332 q^{64} + 85 q^{65} - 2768 q^{66} - 744 q^{67} - 2323 q^{68} + 1551 q^{69} - 1805 q^{70} + 2024 q^{71} + 6897 q^{72} - 1405 q^{73} + 82 q^{74} + 25 q^{75} - 18 q^{76} + 3402 q^{77} - 5311 q^{78} - 2157 q^{79} - 1860 q^{80} + 1099 q^{81} + 2266 q^{82} - 158 q^{83} - 4372 q^{84} - 475 q^{85} + 3033 q^{86} - 29 q^{87} - 1250 q^{88} - 2244 q^{89} - 1305 q^{90} + 3376 q^{91} + 2599 q^{92} + 586 q^{93} + 2212 q^{94} - 470 q^{95} - 5077 q^{96} - 727 q^{97} - 1567 q^{98} + 416 q^{99}+O(q^{100}) \) 7 * q + 6 * q^2 + q^3 + 52 * q^4 - 35 * q^5 + 3 * q^6 + 17 * q^7 + 138 * q^8 + 118 * q^9 - 30 * q^10 + 2 * q^11 - 77 * q^12 - 17 * q^13 + 361 * q^14 - 5 * q^15 + 372 * q^16 + 95 * q^17 + 261 * q^18 + 94 * q^19 - 260 * q^20 - 100 * q^21 + 190 * q^22 + 327 * q^23 - 117 * q^24 + 175 * q^25 - 115 * q^26 - 236 * q^27 - 67 * q^28 - 203 * q^29 - 15 * q^30 + 169 * q^31 + 890 * q^32 + 272 * q^33 + 377 * q^34 - 85 * q^35 + 2443 * q^36 - 500 * q^37 + 282 * q^38 + 1129 * q^39 - 690 * q^40 + 1208 * q^41 - 1892 * q^42 - 1517 * q^43 - 734 * q^44 - 590 * q^45 - 1413 * q^46 + 1974 * q^47 - 2637 * q^48 + 794 * q^49 + 150 * q^50 - 190 * q^51 - 2063 * q^52 - 255 * q^53 - 5052 * q^54 - 10 * q^55 + 2057 * q^56 + 94 * q^57 - 174 * q^58 + 177 * q^59 + 385 * q^60 - 705 * q^61 - 807 * q^62 + 200 * q^63 + 332 * q^64 + 85 * q^65 - 2768 * q^66 - 744 * q^67 - 2323 * q^68 + 1551 * q^69 - 1805 * q^70 + 2024 * q^71 + 6897 * q^72 - 1405 * q^73 + 82 * q^74 + 25 * q^75 - 18 * q^76 + 3402 * q^77 - 5311 * q^78 - 2157 * q^79 - 1860 * q^80 + 1099 * q^81 + 2266 * q^82 - 158 * q^83 - 4372 * q^84 - 475 * q^85 + 3033 * q^86 - 29 * q^87 - 1250 * q^88 - 2244 * q^89 - 1305 * q^90 + 3376 * q^91 + 2599 * q^92 + 586 * q^93 + 2212 * q^94 - 470 * q^95 - 5077 * q^96 - 727 * q^97 - 1567 * q^98 + 416 * q^99

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