LMFDB - Embedded newform 1849.4.a.h.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1849,4,Mod(1,1849)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1849, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1849.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1849 = 43^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1849.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:	$109.094531601$
Analytic rank:	$0$
Dimension:	$30$
Twist minimal:	no (minimal twist has level 43)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	1849.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.335126 q^{2} -1.29157 q^{3} -7.88769 q^{4} -9.09411 q^{5} -0.432838 q^{6} +17.7083 q^{7} -5.32438 q^{8} -25.3319 q^{9} +O(q^{10})$	\(q+0.335126 q^{2} -1.29157 q^{3} -7.88769 q^{4} -9.09411 q^{5} -0.432838 q^{6} +17.7083 q^{7} -5.32438 q^{8} -25.3319 q^{9} -3.04767 q^{10} +43.8496 q^{11} +10.1875 q^{12} +37.0683 q^{13} +5.93453 q^{14} +11.7457 q^{15} +61.3172 q^{16} +4.00772 q^{17} -8.48936 q^{18} +64.6443 q^{19} +71.7316 q^{20} -22.8715 q^{21} +14.6951 q^{22} -164.244 q^{23} +6.87680 q^{24} -42.2971 q^{25} +12.4226 q^{26} +67.5901 q^{27} -139.678 q^{28} -218.931 q^{29} +3.93628 q^{30} +252.111 q^{31} +63.1440 q^{32} -56.6347 q^{33} +1.34309 q^{34} -161.042 q^{35} +199.810 q^{36} +83.8311 q^{37} +21.6640 q^{38} -47.8763 q^{39} +48.4205 q^{40} -95.4155 q^{41} -7.66485 q^{42} -345.872 q^{44} +230.371 q^{45} -55.0425 q^{46} -180.589 q^{47} -79.1953 q^{48} -29.4144 q^{49} -14.1749 q^{50} -5.17625 q^{51} -292.384 q^{52} +401.262 q^{53} +22.6512 q^{54} -398.773 q^{55} -94.2859 q^{56} -83.4925 q^{57} -73.3695 q^{58} +166.969 q^{59} -92.6462 q^{60} -834.545 q^{61} +84.4889 q^{62} -448.585 q^{63} -469.376 q^{64} -337.104 q^{65} -18.9798 q^{66} -651.471 q^{67} -31.6117 q^{68} +212.132 q^{69} -53.9693 q^{70} +47.7896 q^{71} +134.876 q^{72} -763.950 q^{73} +28.0940 q^{74} +54.6295 q^{75} -509.894 q^{76} +776.503 q^{77} -16.0446 q^{78} +395.977 q^{79} -557.626 q^{80} +596.663 q^{81} -31.9762 q^{82} +423.612 q^{83} +180.404 q^{84} -36.4467 q^{85} +282.764 q^{87} -233.472 q^{88} +1229.97 q^{89} +77.2032 q^{90} +656.419 q^{91} +1295.51 q^{92} -325.618 q^{93} -60.5199 q^{94} -587.882 q^{95} -81.5548 q^{96} -374.240 q^{97} -9.85754 q^{98} -1110.79 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 6 q^{2} + 2 q^{3} + 114 q^{4} + 27 q^{5} + 8 q^{6} + 48 q^{7} + 90 q^{8} + 216 q^{9}+O(q^{10}) $ 30 * q + 6 * q^2 + 2 * q^3 + 114 * q^4 + 27 * q^5 + 8 * q^6 + 48 * q^7 + 90 * q^8 + 216 * q^9	\( 30 q + 6 q^{2} + 2 q^{3} + 114 q^{4} + 27 q^{5} + 8 q^{6} + 48 q^{7} + 90 q^{8} + 216 q^{9} - 27 q^{10} + 80 q^{11} - 36 q^{12} - 13 q^{13} + 36 q^{14} + 16 q^{15} + 318 q^{16} + 66 q^{17} + 80 q^{18} + 254 q^{19} + 312 q^{20} - 548 q^{21} + 305 q^{22} - 105 q^{23} + 123 q^{24} + 523 q^{25} + 549 q^{26} - 10 q^{27} + 578 q^{28} + 793 q^{29} + 1560 q^{30} - 359 q^{31} + 676 q^{32} + 208 q^{33} + 1007 q^{34} - 514 q^{35} + 776 q^{36} + 510 q^{37} - 2066 q^{38} + 898 q^{39} - 1248 q^{40} - 270 q^{41} - 915 q^{42} + 3256 q^{44} + 807 q^{45} + 1960 q^{46} + 1421 q^{47} - 632 q^{48} + 386 q^{49} - 141 q^{50} + 209 q^{51} + 2825 q^{52} - 21 q^{53} + 2368 q^{54} + 2258 q^{55} + 2521 q^{56} - 1723 q^{57} - 347 q^{58} + 1752 q^{59} + 2711 q^{60} + 1759 q^{61} + 395 q^{62} + 2204 q^{63} + 222 q^{64} + 1151 q^{65} + 160 q^{66} - 3001 q^{67} + 1921 q^{68} + 1660 q^{69} + 1597 q^{70} + 727 q^{71} + 9100 q^{72} + 4623 q^{73} - 2649 q^{74} + 1027 q^{75} + 874 q^{76} + 3556 q^{77} - 4979 q^{78} + 546 q^{79} + 5809 q^{80} - 410 q^{81} - 4397 q^{82} - 492 q^{83} - 10611 q^{84} - 1723 q^{85} + 5937 q^{87} + 3974 q^{88} + 5218 q^{89} + 10492 q^{90} + 1104 q^{91} + 1060 q^{92} + 1997 q^{93} - 2134 q^{94} + 6346 q^{95} - 11984 q^{96} + 2590 q^{97} + 6270 q^{98} - 2693 q^{99}+O(q^{100}) \) 30 * q + 6 * q^2 + 2 * q^3 + 114 * q^4 + 27 * q^5 + 8 * q^6 + 48 * q^7 + 90 * q^8 + 216 * q^9 - 27 * q^10 + 80 * q^11 - 36 * q^12 - 13 * q^13 + 36 * q^14 + 16 * q^15 + 318 * q^16 + 66 * q^17 + 80 * q^18 + 254 * q^19 + 312 * q^20 - 548 * q^21 + 305 * q^22 - 105 * q^23 + 123 * q^24 + 523 * q^25 + 549 * q^26 - 10 * q^27 + 578 * q^28 + 793 * q^29 + 1560 * q^30 - 359 * q^31 + 676 * q^32 + 208 * q^33 + 1007 * q^34 - 514 * q^35 + 776 * q^36 + 510 * q^37 - 2066 * q^38 + 898 * q^39 - 1248 * q^40 - 270 * q^41 - 915 * q^42 + 3256 * q^44 + 807 * q^45 + 1960 * q^46 + 1421 * q^47 - 632 * q^48 + 386 * q^49 - 141 * q^50 + 209 * q^51 + 2825 * q^52 - 21 * q^53 + 2368 * q^54 + 2258 * q^55 + 2521 * q^56 - 1723 * q^57 - 347 * q^58 + 1752 * q^59 + 2711 * q^60 + 1759 * q^61 + 395 * q^62 + 2204 * q^63 + 222 * q^64 + 1151 * q^65 + 160 * q^66 - 3001 * q^67 + 1921 * q^68 + 1660 * q^69 + 1597 * q^70 + 727 * q^71 + 9100 * q^72 + 4623 * q^73 - 2649 * q^74 + 1027 * q^75 + 874 * q^76 + 3556 * q^77 - 4979 * q^78 + 546 * q^79 + 5809 * q^80 - 410 * q^81 - 4397 * q^82 - 492 * q^83 - 10611 * q^84 - 1723 * q^85 + 5937 * q^87 + 3974 * q^88 + 5218 * q^89 + 10492 * q^90 + 1104 * q^91 + 1060 * q^92 + 1997 * q^93 - 2134 * q^94 + 6346 * q^95 - 11984 * q^96 + 2590 * q^97 + 6270 * q^98 - 2693 * 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 $

$2$	0.335126	0.118485	0.0592425	−	0.998244i	$-0.481131\pi$
$2$	0.335126	0.118485	0.0592425	+	0.998244i	$0.481131\pi$
$3$	−1.29157	−0.248562	−0.124281	−	0.992247i	$-0.539662\pi$
$3$	−1.29157	−0.248562	−0.124281	+	0.992247i	$0.539662\pi$
$4$	−7.88769	−0.985961
$5$	−9.09411	−0.813402	−0.406701	−	0.913561i	$-0.633321\pi$
$5$	−9.09411	−0.813402	−0.406701	+	0.913561i	$0.633321\pi$
$6$	−0.432838	−0.0294509
$7$	17.7083	0.956161	0.478080	−	0.878316i	$-0.341333\pi$
$7$	17.7083	0.956161	0.478080	+	0.878316i	$0.341333\pi$
$8$	−5.32438	−0.235307
$9$	−25.3319	−0.938217
$10$	−3.04767	−0.0963759
$11$	43.8496	1.20192	0.600961	−	0.799278i	$-0.294785\pi$
$11$	43.8496	1.20192	0.600961	+	0.799278i	$0.294785\pi$
$12$	10.1875	0.245073
$13$	37.0683	0.790839	0.395419	−	0.918501i	$-0.370599\pi$
$13$	37.0683	0.790839	0.395419	+	0.918501i	$0.370599\pi$
$14$	5.93453	0.113291
$15$	11.7457	0.202181
$16$	61.3172	0.958081
$17$	4.00772	0.0571774	0.0285887	−	0.999591i	$-0.490899\pi$
$17$	4.00772	0.0571774	0.0285887	+	0.999591i	$0.490899\pi$
$18$	−8.48936	−0.111165
$19$	64.6443	0.780548	0.390274	−	0.920699i	$-0.372380\pi$
$19$	64.6443	0.780548	0.390274	+	0.920699i	$0.372380\pi$
$20$	71.7316	0.801983
$21$	−22.8715	−0.237666
$22$	14.6951	0.142410
$23$	−164.244	−1.48901	−0.744506	−	0.667616i	$-0.767315\pi$
$23$	−164.244	−1.48901	−0.744506	+	0.667616i	$0.767315\pi$
$24$	6.87680	0.0584883
$25$	−42.2971	−0.338377
$26$	12.4226	0.0937025
$27$	67.5901	0.481768
$28$	−139.678	−0.942738
$29$	−218.931	−1.40188	−0.700940	−	0.713221i	$-0.747236\pi$
$29$	−218.931	−1.40188	−0.700940	+	0.713221i	$0.747236\pi$
$30$	3.93628	0.0239554
$31$	252.111	1.46066	0.730329	−	0.683095i	$-0.239367\pi$
$31$	252.111	1.46066	0.730329	+	0.683095i	$0.239367\pi$
$32$	63.1440	0.348825
$33$	−56.6347	−0.298753
$34$	1.34309	0.00677466
$35$	−161.042	−0.777744
$36$	199.810	0.925045
$37$	83.8311	0.372480	0.186240	−	0.982504i	$-0.440370\pi$
$37$	83.8311	0.372480	0.186240	+	0.982504i	$0.440370\pi$
$38$	21.6640	0.0924832
$39$	−47.8763	−0.196573
$40$	48.4205	0.191399
$41$	−95.4155	−0.363449	−0.181724	−	0.983350i	$-0.558168\pi$
$41$	−95.4155	−0.363449	−0.181724	+	0.983350i	$0.558168\pi$
$42$	−7.66485	−0.0281598
$43$	0	0
$43$	0	0
$44$	−345.872	−1.18505
$45$	230.371	0.763148
$46$	−55.0425	−0.176425
$47$	−180.589	−0.560459	−0.280229	−	0.959933i	$-0.590410\pi$
$47$	−180.589	−0.560459	−0.280229	+	0.959933i	$0.590410\pi$
$48$	−79.1953	−0.238143
$49$	−29.4144	−0.0857564
$50$	−14.1749	−0.0400925
$51$	−5.17625	−0.0142121
$52$	−292.384	−0.779737
$53$	401.262	1.03996	0.519978	−	0.854180i	$-0.325940\pi$
$53$	401.262	1.03996	0.519978	+	0.854180i	$0.325940\pi$
$54$	22.6512	0.0570822
$55$	−398.773	−0.977646
$56$	−94.2859	−0.224991
$57$	−83.4925	−0.194015
$58$	−73.3695	−0.166102
$59$	166.969	0.368433	0.184216	−	0.982886i	$-0.441025\pi$
$59$	166.969	0.368433	0.184216	+	0.982886i	$0.441025\pi$
$60$	−92.6462	−0.199343
$61$	−834.545	−1.75168	−0.875840	−	0.482602i	$-0.839692\pi$
$61$	−834.545	−1.75168	−0.875840	+	0.482602i	$0.839692\pi$
$62$	84.4889	0.173066
$63$	−448.585	−0.897086
$64$	−469.376	−0.916751
$65$	−337.104	−0.643270
$66$	−18.9798	−0.0353977
$67$	−651.471	−1.18791	−0.593955	−	0.804499i	$-0.702434\pi$
$67$	−651.471	−1.18791	−0.593955	+	0.804499i	$0.702434\pi$
$68$	−31.6117	−0.0563747
$69$	212.132	0.370112
$70$	−53.9693	−0.0921509
$71$	47.7896	0.0798814	0.0399407	−	0.999202i	$-0.487283\pi$
$71$	47.7896	0.0798814	0.0399407	+	0.999202i	$0.487283\pi$
$72$	134.876	0.220769
$73$	−763.950	−1.22484	−0.612422	−	0.790531i	$-0.709805\pi$
$73$	−763.950	−1.22484	−0.612422	+	0.790531i	$0.709805\pi$
$74$	28.0940	0.0441333
$75$	54.6295	0.0841077
$76$	−509.894	−0.769590
$77$	776.503	1.14923
$78$	−16.0446	−0.0232909
$79$	395.977	0.563936	0.281968	−	0.959424i	$-0.409013\pi$
$79$	395.977	0.563936	0.281968	+	0.959424i	$0.409013\pi$
$80$	−557.626	−0.779305
$81$	596.663	0.818467
$82$	−31.9762	−0.0430632
$83$	423.612	0.560210	0.280105	−	0.959969i	$-0.409631\pi$
$83$	423.612	0.560210	0.280105	+	0.959969i	$0.409631\pi$
$84$	180.404	0.234329
$85$	−36.4467	−0.0465082
$86$	0	0
$87$	282.764	0.348454
$88$	−233.472	−0.282820
$89$	1229.97	1.46491	0.732453	−	0.680818i	$-0.238375\pi$
$89$	1229.97	1.46491	0.732453	+	0.680818i	$0.238375\pi$
$90$	77.2032	0.0904215
$91$	656.419	0.756169
$92$	1295.51	1.46811
$93$	−325.618	−0.363065
$94$	−60.5199	−0.0664059
$95$	−587.882	−0.634900
$96$	−81.5548	−0.0867047
$97$	−374.240	−0.391736	−0.195868	−	0.980630i	$-0.562752\pi$
$97$	−374.240	−0.391736	−0.195868	+	0.980630i	$0.562752\pi$
$98$	−9.85754	−0.0101608
$99$	−1110.79	−1.12766
$100$	333.626	0.333626
$101$	−398.920	−0.393010	−0.196505	−	0.980503i	$-0.562959\pi$
$101$	−398.920	−0.393010	−0.196505	+	0.980503i	$0.562959\pi$
$102$	−1.73469	−0.00168392
$103$	261.917	0.250557	0.125279	−	0.992122i	$-0.460018\pi$
$103$	261.917	0.250557	0.125279	+	0.992122i	$0.460018\pi$
$104$	−197.366	−0.186090
$105$	207.996	0.193318
$106$	134.473	0.123219
$107$	653.246	0.590203	0.295102	−	0.955466i	$-0.404647\pi$
$107$	653.246	0.590203	0.295102	+	0.955466i	$0.404647\pi$
$108$	−533.130	−0.475004
$109$	−530.554	−0.466219	−0.233110	−	0.972450i	$-0.574890\pi$
$109$	−530.554	−0.466219	−0.233110	+	0.972450i	$0.574890\pi$
$110$	−133.639	−0.115836
$111$	−108.274	−0.0925845
$112$	1085.83	0.916080
$113$	1746.59	1.45403	0.727015	−	0.686621i	$-0.240907\pi$
$113$	1746.59	1.45403	0.727015	+	0.686621i	$0.240907\pi$
$114$	−27.9805	−0.0229878
$115$	1493.65	1.21117
$116$	1726.86	1.38220
$117$	−939.010	−0.741978
$118$	55.9557	0.0436537
$119$	70.9701	0.0546708
$120$	−62.5384	−0.0475746
$121$	591.784	0.444616
$122$	−279.678	−0.207548
$123$	123.236	0.0903396
$124$	−1988.57	−1.44015
$125$	1521.42	1.08864
$126$	−150.333	−0.106291
$127$	−1776.72	−1.24141	−0.620704	−	0.784045i	$-0.713153\pi$
$127$	−1776.72	−1.24141	−0.620704	+	0.784045i	$0.713153\pi$
$128$	−662.452	−0.457446
$129$	0	0
$130$	−112.972	−0.0762178
$131$	2525.75	1.68455	0.842273	−	0.539052i	$-0.181217\pi$
$131$	2525.75	1.68455	0.842273	+	0.539052i	$0.181217\pi$
$132$	446.717	0.294558
$133$	1144.74	0.746330
$134$	−218.325	−0.140749
$135$	−614.673	−0.391871
$136$	−21.3386	−0.0134542
$137$	845.159	0.527057	0.263529	−	0.964652i	$-0.415114\pi$
$137$	845.159	0.527057	0.263529	+	0.964652i	$0.415114\pi$
$138$	71.0911	0.0438527
$139$	−246.055	−0.150145	−0.0750724	−	0.997178i	$-0.523919\pi$
$139$	−246.055	−0.150145	−0.0750724	+	0.997178i	$0.523919\pi$
$140$	1270.25	0.766825
$141$	233.242	0.139309
$142$	16.0155	0.00946474
$143$	1625.43	0.950527
$144$	−1553.28	−0.898888
$145$	1990.98	1.14029
$146$	−256.020	−0.145126
$147$	37.9907	0.0213158
$148$	−661.234	−0.367251
$149$	714.649	0.392928	0.196464	−	0.980511i	$-0.437054\pi$
$149$	714.649	0.392928	0.196464	+	0.980511i	$0.437054\pi$
$150$	18.3078	0.00996549
$151$	1581.70	0.852431	0.426216	−	0.904622i	$-0.359846\pi$
$151$	1581.70	0.852431	0.426216	+	0.904622i	$0.359846\pi$
$152$	−344.191	−0.183668
$153$	−101.523	−0.0536448
$154$	260.226	0.136167
$155$	−2292.72	−1.18810
$156$	377.633	0.193813
$157$	−222.740	−0.113226	−0.0566132	−	0.998396i	$-0.518030\pi$
$157$	−222.740	−0.113226	−0.0566132	+	0.998396i	$0.518030\pi$
$158$	132.702	0.0668179
$159$	−518.258	−0.258494
$160$	−574.239	−0.283735
$161$	−2908.49	−1.42373
$162$	199.957	0.0969761
$163$	483.156	0.232170	0.116085	−	0.993239i	$-0.462965\pi$
$163$	483.156	0.232170	0.116085	+	0.993239i	$0.462965\pi$
$164$	752.608	0.358346
$165$	515.042	0.243006
$166$	141.963	0.0663764
$167$	−3602.76	−1.66940	−0.834699	−	0.550706i	$-0.814359\pi$
$167$	−3602.76	−1.66940	−0.834699	+	0.550706i	$0.814359\pi$
$168$	121.777	0.0559243
$169$	−822.938	−0.374574
$170$	−12.2142	−0.00551052
$171$	−1637.56	−0.732323
$172$	0	0
$173$	3708.44	1.62975	0.814877	−	0.579634i	$-0.196804\pi$
$173$	3708.44	1.62975	0.814877	+	0.579634i	$0.196804\pi$
$174$	94.7617	0.0412866
$175$	−749.011	−0.323542
$176$	2688.73	1.15154
$177$	−215.652	−0.0915785
$178$	412.195	0.173569
$179$	−1673.56	−0.698813	−0.349407	−	0.936971i	$-0.613617\pi$
$179$	−1673.56	−0.698813	−0.349407	+	0.936971i	$0.613617\pi$
$180$	−1817.09	−0.752434
$181$	3601.76	1.47910	0.739550	−	0.673102i	$-0.235039\pi$
$181$	3601.76	1.47910	0.739550	+	0.673102i	$0.235039\pi$
$182$	219.983	0.0895947
$183$	1077.87	0.435402
$184$	874.498	0.350374
$185$	−762.370	−0.302976
$186$	−109.123	−0.0430177
$187$	175.737	0.0687227
$188$	1424.43	0.552590
$189$	1196.91	0.460647
$190$	−197.015	−0.0752261
$191$	4906.79	1.85886	0.929431	−	0.368996i	$-0.120298\pi$
$191$	4906.79	1.85886	0.929431	+	0.368996i	$0.120298\pi$
$192$	606.231	0.227870
$193$	−4150.06	−1.54781	−0.773907	−	0.633300i	$-0.781700\pi$
$193$	−4150.06	−1.54781	−0.773907	+	0.633300i	$0.781700\pi$
$194$	−125.418	−0.0464148
$195$	435.392	0.159893
$196$	232.012	0.0845525
$197$	4146.08	1.49947	0.749737	−	0.661736i	$-0.230180\pi$
$197$	4146.08	1.49947	0.749737	+	0.661736i	$0.230180\pi$
$198$	−372.255	−0.133611
$199$	4075.82	1.45190	0.725949	−	0.687749i	$-0.241401\pi$
$199$	4075.82	1.45190	0.725949	+	0.687749i	$0.241401\pi$
$200$	225.206	0.0796222
$201$	841.420	0.295269
$202$	−133.688	−0.0465658
$203$	−3876.91	−1.34042
$204$	40.8286	0.0140126
$205$	867.719	0.295630
$206$	87.7751	0.0296873
$207$	4160.61	1.39702
$208$	2272.93	0.757688
$209$	2834.62	0.938158
$210$	69.7050	0.0229052
$211$	5522.79	1.80192	0.900958	−	0.433906i	$-0.142865\pi$
$211$	5522.79	1.80192	0.900958	+	0.433906i	$0.142865\pi$
$212$	−3165.03	−1.02536
$213$	−61.7235	−0.0198555
$214$	218.920	0.0699302
$215$	0	0
$216$	−359.876	−0.113363
$217$	4464.46	1.39662
$218$	−177.803	−0.0552400
$219$	986.694	0.304450
$220$	3145.40	0.963921
$221$	148.560	0.0452181
$222$	−36.2853	−0.0109699
$223$	−4657.55	−1.39862	−0.699311	−	0.714817i	$-0.746510\pi$
$223$	−4657.55	−1.39862	−0.699311	+	0.714817i	$0.746510\pi$
$224$	1118.18	0.333533
$225$	1071.46	0.317471
$226$	585.328	0.172281
$227$	−5401.37	−1.57930	−0.789651	−	0.613557i	$-0.789738\pi$
$227$	−5401.37	−1.57930	−0.789651	+	0.613557i	$0.789738\pi$
$228$	658.563	0.191291
$229$	−2691.56	−0.776696	−0.388348	−	0.921513i	$-0.626954\pi$
$229$	−2691.56	−0.776696	−0.388348	+	0.921513i	$0.626954\pi$
$230$	500.563	0.143505
$231$	−1002.91	−0.285655
$232$	1165.67	0.329871
$233$	−1845.00	−0.518756	−0.259378	−	0.965776i	$-0.583518\pi$
$233$	−1845.00	−0.518756	−0.259378	+	0.965776i	$0.583518\pi$
$234$	−314.687	−0.0879133
$235$	1642.29	0.455878
$236$	−1317.00	−0.363260
$237$	−511.432	−0.140173
$238$	23.7839	0.00647766
$239$	−323.662	−0.0875982	−0.0437991	−	0.999040i	$-0.513946\pi$
$239$	−323.662	−0.0875982	−0.0437991	+	0.999040i	$0.513946\pi$
$240$	720.211	0.193706
$241$	3584.71	0.958140	0.479070	−	0.877777i	$-0.340974\pi$
$241$	3584.71	0.958140	0.479070	+	0.877777i	$0.340974\pi$
$242$	198.322	0.0526803
$243$	−2595.56	−0.685208
$244$	6582.63	1.72709
$245$	267.498	0.0697544
$246$	41.2994	0.0107039
$247$	2396.26	0.617288
$248$	−1342.33	−0.343703
$249$	−547.123	−0.139247
$250$	509.867	0.128987
$251$	−482.106	−0.121236	−0.0606180	−	0.998161i	$-0.519307\pi$
$251$	−482.106	−0.121236	−0.0606180	+	0.998161i	$0.519307\pi$
$252$	3538.30	0.884492
$253$	−7202.03	−1.78968
$254$	−595.426	−0.147088
$255$	47.0734	0.0115602
$256$	3533.01	0.862550
$257$	6028.15	1.46313	0.731567	−	0.681769i	$-0.238789\pi$
$257$	6028.15	1.46313	0.731567	+	0.681769i	$0.238789\pi$
$258$	0	0
$259$	1484.51	0.356151
$260$	2658.97	0.634240
$261$	5545.93	1.31527
$262$	846.443	0.199593
$263$	1326.88	0.311100	0.155550	−	0.987828i	$-0.450285\pi$
$263$	1326.88	0.311100	0.155550	+	0.987828i	$0.450285\pi$
$264$	301.545	0.0702984
$265$	−3649.13	−0.845902
$266$	383.633	0.0884288
$267$	−1588.59	−0.364121
$268$	5138.61	1.17123
$269$	3567.55	0.808614	0.404307	−	0.914623i	$-0.367513\pi$
$269$	3567.55	0.808614	0.404307	+	0.914623i	$0.367513\pi$
$270$	−205.993	−0.0464308
$271$	−6062.73	−1.35898	−0.679492	−	0.733683i	$-0.737800\pi$
$271$	−6062.73	−1.35898	−0.679492	+	0.733683i	$0.737800\pi$
$272$	245.742	0.0547806
$273$	−847.810	−0.187955
$274$	283.235	0.0624483
$275$	−1854.71	−0.406702
$276$	−1673.24	−0.364916
$277$	2432.23	0.527576	0.263788	−	0.964581i	$-0.415028\pi$
$277$	2432.23	0.527576	0.263788	+	0.964581i	$0.415028\pi$
$278$	−82.4595	−0.0177899
$279$	−6386.43	−1.37041
$280$	857.447	0.183008
$281$	−2242.41	−0.476054	−0.238027	−	0.971259i	$-0.576501\pi$
$281$	−2242.41	−0.476054	−0.238027	+	0.971259i	$0.576501\pi$
$282$	78.1656	0.0165060
$283$	−1980.23	−0.415945	−0.207973	−	0.978135i	$-0.566686\pi$
$283$	−1980.23	−0.415945	−0.207973	+	0.978135i	$0.566686\pi$
$284$	−376.949	−0.0787600
$285$	759.290	0.157812
$286$	544.724	0.112623
$287$	−1689.65	−0.347515
$288$	−1599.55	−0.327273
$289$	−4896.94	−0.996731
$290$	667.231	0.135107
$291$	483.357	0.0973708
$292$	6025.80	1.20765
$293$	3507.59	0.699370	0.349685	−	0.936867i	$-0.386289\pi$
$293$	3507.59	0.699370	0.349685	+	0.936867i	$0.386289\pi$
$294$	12.7317	0.00252560
$295$	−1518.44	−0.299684
$296$	−446.349	−0.0876469
$297$	2963.80	0.579047
$298$	239.497	0.0465561
$299$	−6088.26	−1.17757
$300$	−430.901	−0.0829269
$301$	0	0
$302$	530.070	0.101000
$303$	515.232	0.0976875
$304$	3963.81	0.747828
$305$	7589.44	1.42482
$306$	−34.0230	−0.00635610
$307$	5554.29	1.03257	0.516287	−	0.856416i	$-0.327314\pi$
$307$	5554.29	1.03257	0.516287	+	0.856416i	$0.327314\pi$
$308$	−6124.82	−1.13310
$309$	−338.283	−0.0622791
$310$	−768.351	−0.140772
$311$	4601.63	0.839018	0.419509	−	0.907751i	$-0.362202\pi$
$311$	4601.63	0.839018	0.419509	+	0.907751i	$0.362202\pi$
$312$	254.911	0.0462549
$313$	9792.73	1.76843	0.884214	−	0.467083i	$-0.154695\pi$
$313$	9792.73	1.76843	0.884214	+	0.467083i	$0.154695\pi$
$314$	−74.6458	−0.0134156
$315$	4079.49	0.729692
$316$	−3123.35	−0.556019
$317$	9324.42	1.65209	0.826044	−	0.563606i	$-0.190586\pi$
$317$	9324.42	1.65209	0.826044	+	0.563606i	$0.190586\pi$
$318$	−173.682	−0.0306276
$319$	−9600.03	−1.68495
$320$	4268.56	0.745687
$321$	−843.712	−0.146702
$322$	−974.711	−0.168691
$323$	259.076	0.0446297
$324$	−4706.29	−0.806977
$325$	−1567.88	−0.267601
$326$	161.918	0.0275087
$327$	685.247	0.115885
$328$	508.028	0.0855218
$329$	−3197.93	−0.535889
$330$	172.604	0.0287926
$331$	10679.2	1.77336	0.886679	−	0.462386i	$-0.153007\pi$
$331$	10679.2	1.77336	0.886679	+	0.462386i	$0.153007\pi$
$332$	−3341.32	−0.552345
$333$	−2123.60	−0.349467
$334$	−1207.38	−0.197799
$335$	5924.56	0.966248
$336$	−1402.42	−0.227703
$337$	3164.05	0.511445	0.255722	−	0.966750i	$-0.417687\pi$
$337$	3164.05	0.511445	0.255722	+	0.966750i	$0.417687\pi$
$338$	−275.788	−0.0443813
$339$	−2255.84	−0.361417
$340$	287.480	0.0458553
$341$	11054.9	1.75560
$342$	−548.789	−0.0867693
$343$	−6594.84	−1.03816
$344$	0	0
$345$	−1929.16	−0.301050
$346$	1242.79	0.193101
$347$	3975.43	0.615021	0.307510	−	0.951545i	$-0.400504\pi$
$347$	3975.43	0.615021	0.307510	+	0.951545i	$0.400504\pi$
$348$	−2230.36	−0.343563
$349$	−3472.99	−0.532679	−0.266340	−	0.963879i	$-0.585814\pi$
$349$	−3472.99	−0.532679	−0.266340	+	0.963879i	$0.585814\pi$
$350$	−251.013	−0.0383349
$351$	2505.45	0.381001
$352$	2768.84	0.419260
$353$	−10057.9	−1.51651	−0.758257	−	0.651956i	$-0.773949\pi$
$353$	−10057.9	−1.51651	−0.758257	+	0.651956i	$0.773949\pi$
$354$	−72.2706	−0.0108507
$355$	−434.604	−0.0649757
$356$	−9701.63	−1.44434
$357$	−91.6627	−0.0135891
$358$	−560.853	−0.0827988
$359$	1092.43	0.160602	0.0803012	−	0.996771i	$-0.474412\pi$
$359$	1092.43	0.160602	0.0803012	+	0.996771i	$0.474412\pi$
$360$	−1226.58	−0.179574
$361$	−2680.12	−0.390745
$362$	1207.04	0.175251
$363$	−764.329	−0.110515
$364$	−5177.63	−0.745554
$365$	6947.45	0.996291
$366$	361.223	0.0515886
$367$	−8335.87	−1.18564	−0.592819	−	0.805336i	$-0.701985\pi$
$367$	−8335.87	−1.18564	−0.592819	+	0.805336i	$0.701985\pi$
$368$	−10071.0	−1.42659
$369$	2417.05	0.340994
$370$	−255.490	−0.0358981
$371$	7105.69	0.994365
$372$	2568.38	0.357968
$373$	3648.19	0.506423	0.253212	−	0.967411i	$-0.418513\pi$
$373$	3648.19	0.506423	0.253212	+	0.967411i	$0.418513\pi$
$374$	58.8940	0.00814261
$375$	−1965.02	−0.270595
$376$	961.522	0.131880
$377$	−8115.41	−1.10866
$378$	401.116	0.0545798
$379$	−9004.40	−1.22038	−0.610191	−	0.792254i	$-0.708907\pi$
$379$	−9004.40	−1.22038	−0.610191	+	0.792254i	$0.708907\pi$
$380$	4637.03	0.625987
$381$	2294.76	0.308567
$382$	1644.39	0.220247
$383$	3753.10	0.500716	0.250358	−	0.968153i	$-0.419452\pi$
$383$	3753.10	0.500716	0.250358	+	0.968153i	$0.419452\pi$
$384$	855.602	0.113704
$385$	−7061.61	−0.934787
$386$	−1390.79	−0.183393
$387$	0	0
$388$	2951.89	0.386236
$389$	8211.77	1.07032	0.535159	−	0.844752i	$-0.320252\pi$
$389$	8211.77	1.07032	0.535159	+	0.844752i	$0.320252\pi$
$390$	145.911	0.0189449
$391$	−658.245	−0.0851378
$392$	156.614	0.0201790
$393$	−3262.17	−0.418715
$394$	1389.46	0.177665
$395$	−3601.06	−0.458707
$396$	8761.57	1.11183
$397$	−10508.5	−1.32848	−0.664239	−	0.747520i	$-0.731244\pi$
$397$	−10508.5	−1.32848	−0.664239	+	0.747520i	$0.731244\pi$
$398$	1365.91	0.172028
$399$	−1478.51	−0.185509
$400$	−2593.54	−0.324192
$401$	2343.11	0.291794	0.145897	−	0.989300i	$-0.453393\pi$
$401$	2343.11	0.291794	0.145897	+	0.989300i	$0.453393\pi$
$402$	281.982	0.0349850
$403$	9345.33	1.15515
$404$	3146.56	0.387493
$405$	−5426.12	−0.665743
$406$	−1299.25	−0.158820
$407$	3675.96	0.447692
$408$	27.5603	0.00334421
$409$	−8034.60	−0.971358	−0.485679	−	0.874137i	$-0.661428\pi$
$409$	−8034.60	−0.971358	−0.485679	+	0.874137i	$0.661428\pi$
$410$	290.795	0.0350277
$411$	−1091.58	−0.131007
$412$	−2065.92	−0.247040
$413$	2956.75	0.352281
$414$	1394.33	0.165525
$415$	−3852.37	−0.455676
$416$	2340.64	0.275864
$417$	317.797	0.0373203
$418$	949.956	0.111158
$419$	−500.755	−0.0583854	−0.0291927	−	0.999574i	$-0.509294\pi$
$419$	−500.755	−0.0583854	−0.0291927	+	0.999574i	$0.509294\pi$
$420$	−1640.61	−0.190604
$421$	9295.11	1.07605	0.538024	−	0.842930i	$-0.319171\pi$
$421$	9295.11	1.07605	0.538024	+	0.842930i	$0.319171\pi$
$422$	1850.83	0.213500
$423$	4574.64	0.525832
$424$	−2136.47	−0.244708
$425$	−169.515	−0.0193475
$426$	−20.6852	−0.00235258
$427$	−14778.4	−1.67489
$428$	−5152.61	−0.581917
$429$	−2099.35	−0.236265
$430$	0	0
$431$	−2246.60	−0.251079	−0.125540	−	0.992089i	$-0.540066\pi$
$431$	−2246.60	−0.251079	−0.125540	+	0.992089i	$0.540066\pi$
$432$	4144.44	0.461573
$433$	−862.875	−0.0957671	−0.0478835	−	0.998853i	$-0.515248\pi$
$433$	−862.875	−0.0957671	−0.0478835	+	0.998853i	$0.515248\pi$
$434$	1496.16	0.165479
$435$	−2571.49	−0.283434
$436$	4184.85	0.459674
$437$	−10617.4	−1.16225
$438$	330.667	0.0360728
$439$	3722.96	0.404754	0.202377	−	0.979308i	$-0.435133\pi$
$439$	3722.96	0.404754	0.202377	+	0.979308i	$0.435133\pi$
$440$	2123.22	0.230046
$441$	745.122	0.0804581
$442$	49.7862	0.00535766
$443$	−3998.67	−0.428854	−0.214427	−	0.976740i	$-0.568788\pi$
$443$	−3998.67	−0.428854	−0.214427	+	0.976740i	$0.568788\pi$
$444$	854.029	0.0912847
$445$	−11185.5	−1.19156
$446$	−1560.87	−0.165716
$447$	−923.018	−0.0976672
$448$	−8311.88	−0.876561
$449$	12177.9	1.27998	0.639990	−	0.768383i	$-0.278939\pi$
$449$	12177.9	1.27998	0.639990	+	0.768383i	$0.278939\pi$
$450$	359.075	0.0376155
$451$	−4183.93	−0.436837
$452$	−13776.6	−1.43362
$453$	−2042.88	−0.211882
$454$	−1810.14	−0.187123
$455$	−5969.55	−0.615070
$456$	444.546	0.0456530
$457$	10281.4	1.05239	0.526197	−	0.850362i	$-0.323617\pi$
$457$	10281.4	1.05239	0.526197	+	0.850362i	$0.323617\pi$
$458$	−902.012	−0.0920267
$459$	270.882	0.0275462
$460$	−11781.5	−1.19416
$461$	7673.83	0.775284	0.387642	−	0.921810i	$-0.373290\pi$
$461$	7673.83	0.775284	0.387642	+	0.921810i	$0.373290\pi$
$462$	−336.100	−0.0338459
$463$	−2654.08	−0.266405	−0.133202	−	0.991089i	$-0.542526\pi$
$463$	−2654.08	−0.266405	−0.133202	+	0.991089i	$0.542526\pi$
$464$	−13424.2	−1.34311
$465$	2961.21	0.295318
$466$	−618.309	−0.0614648
$467$	−5990.23	−0.593565	−0.296782	−	0.954945i	$-0.595914\pi$
$467$	−5990.23	−0.593565	−0.296782	+	0.954945i	$0.595914\pi$
$468$	7406.62	0.731562
$469$	−11536.5	−1.13583
$470$	550.375	0.0540147
$471$	287.683	0.0281438
$472$	−889.007	−0.0866946
$473$	0	0
$474$	−171.394	−0.0166084
$475$	−2734.26	−0.264119
$476$	−559.790	−0.0539033
$477$	−10164.7	−0.975703
$478$	−108.468	−0.0103791
$479$	9568.56	0.912732	0.456366	−	0.889792i	$-0.349151\pi$
$479$	9568.56	0.912732	0.456366	+	0.889792i	$0.349151\pi$
$480$	741.669	0.0705258
$481$	3107.48	0.294572
$482$	1201.33	0.113525
$483$	3756.52	0.353887
$484$	−4667.81	−0.438374
$485$	3403.39	0.318639
$486$	−869.841	−0.0811868
$487$	8671.51	0.806865	0.403433	−	0.915009i	$-0.367817\pi$
$487$	8671.51	0.806865	0.403433	+	0.915009i	$0.367817\pi$
$488$	4443.43	0.412182
$489$	−624.029	−0.0577088
$490$	89.6456	0.00826485
$491$	9681.68	0.889874	0.444937	−	0.895562i	$-0.353226\pi$
$491$	9681.68	0.889874	0.444937	+	0.895562i	$0.353226\pi$
$492$	−972.044	−0.0890714
$493$	−877.415	−0.0801558
$494$	803.048	0.0731393
$495$	10101.7	0.917244
$496$	15458.7	1.39943
$497$	846.275	0.0763795
$498$	−183.355	−0.0164987
$499$	1329.26	0.119250	0.0596251	−	0.998221i	$-0.481009\pi$
$499$	1329.26	0.119250	0.0596251	+	0.998221i	$0.481009\pi$
$500$	−12000.5	−1.07336
$501$	4653.20	0.414950
$502$	−161.566	−0.0143646
$503$	−13480.0	−1.19492	−0.597458	−	0.801901i	$-0.703822\pi$
$503$	−13480.0	−1.19492	−0.597458	+	0.801901i	$0.703822\pi$
$504$	2388.44	0.211090
$505$	3627.82	0.319675
$506$	−2413.59	−0.212050
$507$	1062.88	0.0931049
$508$	14014.2	1.22398
$509$	−11992.7	−1.04433	−0.522166	−	0.852844i	$-0.674876\pi$
$509$	−11992.7	−1.04433	−0.522166	+	0.852844i	$0.674876\pi$
$510$	15.7755	0.00136971
$511$	−13528.3	−1.17115
$512$	6483.62	0.559645
$513$	4369.32	0.376043
$514$	2020.19	0.173359
$515$	−2381.90	−0.203804
$516$	0	0
$517$	−7918.73	−0.673627
$518$	497.498	0.0421985
$519$	−4789.70	−0.405096
$520$	1794.87	0.151366
$521$	9919.02	0.834089	0.417044	−	0.908886i	$-0.363066\pi$
$521$	9919.02	0.834089	0.417044	+	0.908886i	$0.363066\pi$
$522$	1858.59	0.155839
$523$	20341.3	1.70069	0.850347	−	0.526223i	$-0.176392\pi$
$523$	20341.3	1.70069	0.850347	+	0.526223i	$0.176392\pi$
$524$	−19922.3	−1.66090
$525$	967.399	0.0804205
$526$	444.673	0.0368606
$527$	1010.39	0.0835166
$528$	−3472.68	−0.286229
$529$	14809.1	1.21716
$530$	−1222.92	−0.100227
$531$	−4229.64	−0.345670
$532$	−9029.38	−0.735852
$533$	−3536.89	−0.287429
$534$	−532.378	−0.0431428
$535$	−5940.70	−0.480073
$536$	3468.68	0.279523
$537$	2161.51	0.173699
$538$	1195.58	0.0958086
$539$	−1289.81	−0.103072
$540$	4848.35	0.386370
$541$	22023.6	1.75022	0.875109	−	0.483926i	$-0.160790\pi$
$541$	22023.6	1.75022	0.875109	+	0.483926i	$0.160790\pi$
$542$	−2031.78	−0.161019
$543$	−4651.92	−0.367648
$544$	253.064	0.0199449
$545$	4824.92	0.379224
$546$	−284.123	−0.0222699
$547$	6265.90	0.489782	0.244891	−	0.969551i	$-0.421248\pi$
$547$	6265.90	0.489782	0.244891	+	0.969551i	$0.421248\pi$
$548$	−6666.35	−0.519658
$549$	21140.6	1.64346
$550$	−621.561	−0.0481881
$551$	−14152.6	−1.09423
$552$	−1129.47	−0.0870898
$553$	7012.10	0.539213
$554$	815.104	0.0625098
$555$	984.653	0.0753084
$556$	1940.81	0.148037
$557$	11315.3	0.860760	0.430380	−	0.902648i	$-0.358380\pi$
$557$	11315.3	0.860760	0.430380	+	0.902648i	$0.358380\pi$
$558$	−2140.26	−0.162373
$559$	0	0
$560$	−9874.63	−0.745141
$561$	−226.976	−0.0170819
$562$	−751.491	−0.0564052
$563$	11736.5	0.878566	0.439283	−	0.898349i	$-0.355233\pi$
$563$	11736.5	0.878566	0.439283	+	0.898349i	$0.355233\pi$
$564$	−1839.74	−0.137353
$565$	−15883.7	−1.18271
$566$	−663.627	−0.0492832
$567$	10565.9	0.782587
$568$	−254.450	−0.0187966
$569$	7076.76	0.521394	0.260697	−	0.965421i	$-0.416048\pi$
$569$	7076.76	0.521394	0.260697	+	0.965421i	$0.416048\pi$
$570$	254.458	0.0186984
$571$	−6120.91	−0.448603	−0.224301	−	0.974520i	$-0.572010\pi$
$571$	−6120.91	−0.448603	−0.224301	+	0.974520i	$0.572010\pi$
$572$	−12820.9	−0.937182
$573$	−6337.45	−0.462043
$574$	−566.246	−0.0411753
$575$	6947.05	0.503847
$576$	11890.2	0.860111
$577$	10285.3	0.742087	0.371043	−	0.928616i	$-0.379000\pi$
$577$	10285.3	0.742087	0.371043	+	0.928616i	$0.379000\pi$
$578$	−1641.09	−0.118098
$579$	5360.09	0.384728
$580$	−15704.3	−1.12428
$581$	7501.46	0.535651
$582$	161.986	0.0115370
$583$	17595.2	1.24994
$584$	4067.56	0.288214
$585$	8539.46	0.603527
$586$	1175.48	0.0828648
$587$	16747.9	1.17762	0.588808	−	0.808273i	$-0.299597\pi$
$587$	16747.9	1.17762	0.588808	+	0.808273i	$0.299597\pi$
$588$	−299.659	−0.0210166
$589$	16297.5	1.14011
$590$	−508.867	−0.0355080
$591$	−5354.95	−0.372713
$592$	5140.29	0.356866
$593$	−21749.3	−1.50613	−0.753067	−	0.657944i	$-0.771426\pi$
$593$	−21749.3	−1.50613	−0.753067	+	0.657944i	$0.771426\pi$
$594$	993.246	0.0686084
$595$	−645.410	−0.0444693
$596$	−5636.93	−0.387412
$597$	−5264.20	−0.360887
$598$	−2040.33	−0.139524
$599$	−896.097	−0.0611244	−0.0305622	−	0.999533i	$-0.509730\pi$
$599$	−896.097	−0.0611244	−0.0305622	+	0.999533i	$0.509730\pi$
$600$	−290.868	−0.0197911
$601$	1801.42	0.122266	0.0611328	−	0.998130i	$-0.480529\pi$
$601$	1801.42	0.122266	0.0611328	+	0.998130i	$0.480529\pi$
$602$	0	0
$603$	16503.0	1.11452
$604$	−12476.0	−0.840464
$605$	−5381.75	−0.361652
$606$	172.668	0.0115745
$607$	12241.7	0.818575	0.409287	−	0.912406i	$-0.365777\pi$
$607$	12241.7	0.818575	0.409287	+	0.912406i	$0.365777\pi$
$608$	4081.90	0.272274
$609$	5007.29	0.333178
$610$	2543.42	0.168820
$611$	−6694.12	−0.443232
$612$	800.782	0.0528917
$613$	1830.72	0.120623	0.0603116	−	0.998180i	$-0.480791\pi$
$613$	1830.72	0.120623	0.0603116	+	0.998180i	$0.480791\pi$
$614$	1861.39	0.122344
$615$	−1120.72	−0.0734825
$616$	−4134.40	−0.270421
$617$	24568.8	1.60309	0.801543	−	0.597937i	$-0.204013\pi$
$617$	24568.8	1.60309	0.801543	+	0.597937i	$0.204013\pi$
$618$	−113.367	−0.00737914
$619$	−14277.9	−0.927106	−0.463553	−	0.886069i	$-0.653426\pi$
$619$	−14277.9	−0.927106	−0.463553	+	0.886069i	$0.653426\pi$
$620$	18084.3	1.17142
$621$	−11101.3	−0.717358
$622$	1542.13	0.0994110
$623$	21780.7	1.40069
$624$	−2935.64	−0.188333
$625$	−8548.82	−0.547125
$626$	3281.80	0.209532
$627$	−3661.11	−0.233191
$628$	1756.90	0.111637
$629$	335.972	0.0212974
$630$	1367.14	0.0864575
$631$	−26267.2	−1.65718	−0.828591	−	0.559854i	$-0.810857\pi$
$631$	−26267.2	−1.65718	−0.828591	+	0.559854i	$0.810857\pi$
$632$	−2108.33	−0.132698
$633$	−7133.06	−0.447889
$634$	3124.86	0.195748
$635$	16157.7	1.00976
$636$	4087.86	0.254865
$637$	−1090.34	−0.0678195
$638$	−3217.22	−0.199641
$639$	−1210.60	−0.0749461
$640$	6024.42	0.372088
$641$	−17181.9	−1.05873	−0.529364	−	0.848395i	$-0.677570\pi$
$641$	−17181.9	−1.05873	−0.529364	+	0.848395i	$0.677570\pi$
$642$	−282.750	−0.0173820
$643$	15337.5	0.940669	0.470334	−	0.882488i	$-0.344133\pi$
$643$	15337.5	0.940669	0.470334	+	0.882488i	$0.344133\pi$
$644$	22941.3	1.40375
$645$	0	0
$646$	86.8232	0.00528795
$647$	−24411.4	−1.48332	−0.741661	−	0.670775i	$-0.765962\pi$
$647$	−24411.4	−1.48332	−0.741661	+	0.670775i	$0.765962\pi$
$648$	−3176.86	−0.192591
$649$	7321.52	0.442827
$650$	−525.438	−0.0317067
$651$	−5766.16	−0.347148
$652$	−3810.99	−0.228911
$653$	25578.8	1.53289	0.766444	−	0.642311i	$-0.222024\pi$
$653$	25578.8	1.53289	0.766444	+	0.642311i	$0.222024\pi$
$654$	229.644	0.0137306
$655$	−22969.4	−1.37021
$656$	−5850.61	−0.348213
$657$	19352.3	1.14917
$658$	−1071.71	−0.0634947
$659$	−4495.86	−0.265757	−0.132878	−	0.991132i	$-0.542422\pi$
$659$	−4495.86	−0.265757	−0.132878	+	0.991132i	$0.542422\pi$
$660$	−4062.49	−0.239595
$661$	−22583.3	−1.32888	−0.664438	−	0.747344i	$-0.731329\pi$
$661$	−22583.3	−1.32888	−0.664438	+	0.747344i	$0.731329\pi$
$662$	3578.87	0.210116
$663$	−191.875	−0.0112395
$664$	−2255.47	−0.131821
$665$	−10410.4	−0.607066
$666$	−711.673	−0.0414066
$667$	35958.2	2.08741
$668$	28417.4	1.64596
$669$	6015.55	0.347645
$670$	1985.47	0.114486
$671$	−36594.4	−2.10538
$672$	−1444.20	−0.0829036
$673$	−31153.9	−1.78439	−0.892194	−	0.451652i	$-0.850835\pi$
$673$	−31153.9	−1.78439	−0.892194	+	0.451652i	$0.850835\pi$
$674$	1060.36	0.0605985
$675$	−2858.87	−0.163019
$676$	6491.08	0.369315
$677$	−397.335	−0.0225566	−0.0112783	−	0.999936i	$-0.503590\pi$
$677$	−397.335	−0.0225566	−0.0112783	+	0.999936i	$0.503590\pi$
$678$	−755.991	−0.0428225
$679$	−6627.18	−0.374562
$680$	194.056	0.0109437
$681$	6976.23	0.392555
$682$	3704.80	0.208012
$683$	15704.1	0.879795	0.439897	−	0.898048i	$-0.355015\pi$
$683$	15704.1	0.879795	0.439897	+	0.898048i	$0.355015\pi$
$684$	12916.6	0.722042
$685$	−7685.97	−0.428709
$686$	−2210.10	−0.123006
$687$	3476.33	0.193057
$688$	0	0
$689$	14874.1	0.822437
$690$	−646.511	−0.0356699
$691$	−14244.7	−0.784218	−0.392109	−	0.919919i	$-0.628254\pi$
$691$	−14244.7	−0.784218	−0.392109	+	0.919919i	$0.628254\pi$
$692$	−29251.0	−1.60687
$693$	−19670.3	−1.07823
$694$	1332.27	0.0728707
$695$	2237.65	0.122128
$696$	−1505.55	−0.0819936
$697$	−382.399	−0.0207810
$698$	−1163.89	−0.0631145
$699$	2382.95	0.128943
$700$	5907.97	0.319000
$701$	32762.5	1.76522	0.882612	−	0.470102i	$-0.155783\pi$
$701$	32762.5	1.76522	0.882612	+	0.470102i	$0.155783\pi$
$702$	839.643	0.0451429
$703$	5419.20	0.290738
$704$	−20581.9	−1.10186
$705$	−2121.13	−0.113314
$706$	−3370.67	−0.179684
$707$	−7064.21	−0.375781
$708$	1701.00	0.0902928
$709$	24243.6	1.28419	0.642094	−	0.766626i	$-0.278066\pi$
$709$	24243.6	1.28419	0.642094	+	0.766626i	$0.278066\pi$
$710$	−145.647	−0.00769865
$711$	−10030.8	−0.529094
$712$	−6548.83	−0.344702
$713$	−41407.7	−2.17494
$714$	−30.7186	−0.00161010
$715$	−14781.8	−0.773161
$716$	13200.5	0.689003
$717$	418.032	0.0217736
$718$	366.102	0.0190290
$719$	−20394.0	−1.05781	−0.528907	−	0.848680i	$-0.677398\pi$
$719$	−20394.0	−1.05781	−0.528907	+	0.848680i	$0.677398\pi$
$720$	14125.7	0.731157
$721$	4638.11	0.239573
$722$	−898.177	−0.0462974
$723$	−4629.90	−0.238157
$724$	−28409.6	−1.45833
$725$	9260.15	0.474363
$726$	−256.147	−0.0130943
$727$	−90.5236	−0.00461807	−0.00230903	−	0.999997i	$-0.500735\pi$
$727$	−90.5236	−0.00461807	−0.00230903	+	0.999997i	$0.500735\pi$
$728$	−3495.02	−0.177932
$729$	−12757.5	−0.648150
$730$	2328.27	0.118045
$731$	0	0
$732$	−8501.91	−0.429289
$733$	−13786.2	−0.694684	−0.347342	−	0.937738i	$-0.612916\pi$
$733$	−13786.2	−0.694684	−0.347342	+	0.937738i	$0.612916\pi$
$734$	−2793.57	−0.140480
$735$	−345.492	−0.0173383
$736$	−10371.0	−0.519404
$737$	−28566.7	−1.42777
$738$	810.016	0.0404026
$739$	310.287	0.0154453	0.00772265	−	0.999970i	$-0.497542\pi$
$739$	310.287	0.0154453	0.00772265	+	0.999970i	$0.497542\pi$
$740$	6013.34	0.298723
$741$	−3094.93	−0.153435
$742$	2381.30	0.117817
$743$	−5921.60	−0.292386	−0.146193	−	0.989256i	$-0.546702\pi$
$743$	−5921.60	−0.292386	−0.146193	+	0.989256i	$0.546702\pi$
$744$	1733.71	0.0854315
$745$	−6499.10	−0.319609
$746$	1222.60	0.0600035
$747$	−10730.9	−0.525598
$748$	−1386.16	−0.0677579
$749$	11567.9	0.564329
$750$	−658.528	−0.0320614
$751$	−9530.23	−0.463067	−0.231533	−	0.972827i	$-0.574374\pi$
$751$	−9530.23	−0.463067	−0.231533	+	0.972827i	$0.574374\pi$
$752$	−11073.2	−0.536965
$753$	622.673	0.0301347
$754$	−2719.69	−0.131360
$755$	−14384.2	−0.693370
$756$	−9440.85	−0.454181
$757$	−1036.49	−0.0497649	−0.0248824	−	0.999690i	$-0.507921\pi$
$757$	−1036.49	−0.0497649	−0.0248824	+	0.999690i	$0.507921\pi$
$758$	−3017.61	−0.144597
$759$	9301.91	0.444846
$760$	3130.11	0.149396
$761$	24351.6	1.15998	0.579991	−	0.814623i	$-0.303056\pi$
$761$	24351.6	1.15998	0.579991	+	0.814623i	$0.303056\pi$
$762$	769.034	0.0365606
$763$	−9395.24	−0.445781
$764$	−38703.2	−1.83277
$765$	923.262	0.0436348
$766$	1257.76	0.0593273
$767$	6189.27	0.291371
$768$	−4563.12	−0.214398
$769$	38787.7	1.81888	0.909441	−	0.415834i	$-0.136510\pi$
$769$	38787.7	1.81888	0.909441	+	0.415834i	$0.136510\pi$
$770$	−2366.53	−0.110758
$771$	−7785.77	−0.363680
$772$	32734.4	1.52608
$773$	240.472	0.0111891	0.00559456	−	0.999984i	$-0.498219\pi$
$773$	240.472	0.0111891	0.00559456	+	0.999984i	$0.498219\pi$
$774$	0	0
$775$	−10663.5	−0.494253
$776$	1992.60	0.0921780
$777$	−1917.35	−0.0885257
$778$	2751.98	0.126816
$779$	−6168.06	−0.283689
$780$	−3434.24	−0.157648
$781$	2095.55	0.0960112
$782$	−220.595	−0.0100875
$783$	−14797.6	−0.675380
$784$	−1803.61	−0.0821616
$785$	2025.62	0.0920987
$786$	−1093.24	−0.0496114
$787$	2542.32	0.115151	0.0575756	−	0.998341i	$-0.481663\pi$
$787$	2542.32	0.115151	0.0575756	+	0.998341i	$0.481663\pi$
$788$	−32703.0	−1.47842
$789$	−1713.76	−0.0773277
$790$	−1206.81	−0.0543498
$791$	30929.2	1.39029
$792$	5914.27	0.265346
$793$	−30935.2	−1.38530
$794$	−3521.67	−0.157405
$795$	4713.09	0.210259
$796$	−32148.8	−1.43151
$797$	32508.4	1.44480	0.722400	−	0.691476i	$-0.243039\pi$
$797$	32508.4	1.44480	0.722400	+	0.691476i	$0.243039\pi$
$798$	−495.488	−0.0219801
$799$	−723.749	−0.0320455
$800$	−2670.81	−0.118034
$801$	−31157.4	−1.37440
$802$	785.236	0.0345731
$803$	−33498.9	−1.47217
$804$	−6636.86	−0.291124
$805$	26450.2	1.15807
$806$	3131.86	0.136867
$807$	−4607.73	−0.200991
$808$	2124.00	0.0924778
$809$	−38942.7	−1.69240	−0.846202	−	0.532863i	$-0.821116\pi$
$809$	−38942.7	−1.69240	−0.846202	+	0.532863i	$0.821116\pi$
$810$	−1818.43	−0.0788806
$811$	−14126.6	−0.611654	−0.305827	−	0.952087i	$-0.598933\pi$
$811$	−14126.6	−0.611654	−0.305827	+	0.952087i	$0.598933\pi$
$812$	30579.9	1.32160
$813$	7830.43	0.337792
$814$	1231.91	0.0530447
$815$	−4393.88	−0.188848
$816$	−317.393	−0.0136164
$817$	0	0
$818$	−2692.60	−0.115091
$819$	−16628.3	−0.709451
$820$	−6844.30	−0.291480
$821$	−28063.8	−1.19298	−0.596488	−	0.802622i	$-0.703438\pi$
$821$	−28063.8	−1.19298	−0.596488	+	0.802622i	$0.703438\pi$
$822$	−365.817	−0.0155223
$823$	631.388	0.0267422	0.0133711	−	0.999911i	$-0.495744\pi$
$823$	631.388	0.0267422	0.0133711	+	0.999911i	$0.495744\pi$
$824$	−1394.54	−0.0589578
$825$	2395.48	0.101091
$826$	990.883	0.0417400
$827$	−20884.8	−0.878156	−0.439078	−	0.898449i	$-0.644695\pi$
$827$	−20884.8	−0.878156	−0.439078	+	0.898449i	$0.644695\pi$
$828$	−32817.6	−1.37740
$829$	8989.33	0.376613	0.188307	−	0.982110i	$-0.439700\pi$
$829$	8989.33	0.376613	0.188307	+	0.982110i	$0.439700\pi$
$830$	−1291.03	−0.0539907
$831$	−3141.39	−0.131136
$832$	−17399.0	−0.725002
$833$	−117.885	−0.00490332
$834$	106.502	0.00442190
$835$	32763.9	1.35789
$836$	−22358.6	−0.924987
$837$	17040.2	0.703698
$838$	−167.816	−0.00691779
$839$	−1016.74	−0.0418378	−0.0209189	−	0.999781i	$-0.506659\pi$
$839$	−1016.74	−0.0418378	−0.0209189	+	0.999781i	$0.506659\pi$
$840$	−1107.45	−0.0454889
$841$	23541.8	0.965265
$842$	3115.03	0.127495
$843$	2896.23	0.118329
$844$	−43562.0	−1.77662
$845$	7483.90	0.304679
$846$	1533.08	0.0623031
$847$	10479.5	0.425124
$848$	24604.3	0.996361
$849$	2557.60	0.103388
$850$	−56.8089	−0.00229239
$851$	−13768.8	−0.554627
$852$	486.856	0.0195768
$853$	12089.1	0.485256	0.242628	−	0.970119i	$-0.421991\pi$
$853$	12089.1	0.485256	0.242628	+	0.970119i	$0.421991\pi$
$854$	−4952.63	−0.198449
$855$	14892.2	0.595673
$856$	−3478.13	−0.138879
$857$	41301.6	1.64625	0.823124	−	0.567861i	$-0.192229\pi$
$857$	41301.6	1.64625	0.823124	+	0.567861i	$0.192229\pi$
$858$	−703.548	−0.0279939
$859$	−4731.49	−0.187935	−0.0939676	−	0.995575i	$-0.529955\pi$
$859$	−4731.49	−0.187935	−0.0939676	+	0.995575i	$0.529955\pi$
$860$	0	0
$861$	2182.30	0.0863792
$862$	−752.896	−0.0297491
$863$	8461.51	0.333758	0.166879	−	0.985977i	$-0.446631\pi$
$863$	8461.51	0.333758	0.166879	+	0.985977i	$0.446631\pi$
$864$	4267.91	0.168052
$865$	−33725.0	−1.32565
$866$	−289.172	−0.0113470
$867$	6324.73	0.247750
$868$	−35214.3	−1.37702
$869$	17363.4	0.677807
$870$	−861.774	−0.0335826
$871$	−24149.0	−0.939445
$872$	2824.87	0.109704
$873$	9480.20	0.367533
$874$	−3558.18	−0.137709
$875$	26941.8	1.04091
$876$	−7782.73	−0.300176
$877$	−13680.9	−0.526764	−0.263382	−	0.964692i	$-0.584838\pi$
$877$	−13680.9	−0.526764	−0.263382	+	0.964692i	$0.584838\pi$
$878$	1247.66	0.0479573
$879$	−4530.29	−0.173837
$880$	−24451.6	−0.936664
$881$	−5367.01	−0.205243	−0.102622	−	0.994720i	$-0.532723\pi$
$881$	−5367.01	−0.205243	−0.102622	+	0.994720i	$0.532723\pi$
$882$	249.710	0.00953307
$883$	−15908.7	−0.606307	−0.303154	−	0.952942i	$-0.598040\pi$
$883$	−15908.7	−0.606307	−0.303154	+	0.952942i	$0.598040\pi$
$884$	−1171.79	−0.0445833
$885$	1961.16	0.0744902
$886$	−1340.06	−0.0508128
$887$	5562.07	0.210548	0.105274	−	0.994443i	$-0.466428\pi$
$887$	5562.07	0.210548	0.105274	+	0.994443i	$0.466428\pi$
$888$	576.490	0.0217857
$889$	−31462.8	−1.18699
$890$	−3748.55	−0.141182
$891$	26163.4	0.983734
$892$	36737.3	1.37899
$893$	−11674.0	−0.437465
$894$	−309.327	−0.0115721
$895$	15219.5	0.568416
$896$	−11730.9	−0.437392
$897$	7863.40	0.292699
$898$	4081.13	0.151658
$899$	−55194.9	−2.04767
$900$	−8451.37	−0.313014
$901$	1608.15	0.0594619
$902$	−1402.14	−0.0517586
$903$	0	0
$904$	−9299.51	−0.342143
$905$	−32754.8	−1.20310
$906$	−684.621	−0.0251049
$907$	−38211.2	−1.39888	−0.699438	−	0.714693i	$-0.746566\pi$
$907$	−38211.2	−1.39888	−0.699438	+	0.714693i	$0.746566\pi$
$908$	42604.3	1.55713
$909$	10105.4	0.368728
$910$	−2000.55	−0.0728765
$911$	47699.5	1.73475	0.867374	−	0.497658i	$-0.165806\pi$
$911$	47699.5	1.73475	0.867374	+	0.497658i	$0.165806\pi$
$912$	−5119.52	−0.185882
$913$	18575.2	0.673328
$914$	3445.57	0.124693
$915$	−9802.28	−0.354157
$916$	21230.2	0.765792
$917$	44726.8	1.61070
$918$	90.7798	0.00326381
$919$	2057.55	0.0738544	0.0369272	−	0.999318i	$-0.488243\pi$
$919$	2057.55	0.0738544	0.0369272	+	0.999318i	$0.488243\pi$
$920$	−7952.78	−0.284995
$921$	−7173.74	−0.256659
$922$	2571.70	0.0918595
$923$	1771.48	0.0631733
$924$	7910.62	0.281645
$925$	−3545.81	−0.126038
$926$	−889.450	−0.0315650
$927$	−6634.83	−0.235077
$928$	−13824.2	−0.489010
$929$	2749.08	0.0970875	0.0485438	−	0.998821i	$-0.484542\pi$
$929$	2749.08	0.0970875	0.0485438	+	0.998821i	$0.484542\pi$
$930$	992.378	0.0349907
$931$	−1901.48	−0.0669370
$932$	14552.8	0.511473
$933$	−5943.32	−0.208548
$934$	−2007.48	−0.0703285
$935$	−1598.17	−0.0558992
$936$	4999.64	0.174592
$937$	8237.93	0.287216	0.143608	−	0.989635i	$-0.454130\pi$
$937$	8237.93	0.287216	0.143608	+	0.989635i	$0.454130\pi$
$938$	−3866.18	−0.134579
$939$	−12648.0	−0.439564
$940$	−12953.9	−0.449478
$941$	−22326.8	−0.773466	−0.386733	−	0.922192i	$-0.626396\pi$
$941$	−22326.8	−0.773466	−0.386733	+	0.922192i	$0.626396\pi$
$942$	96.4102	0.00333462
$943$	15671.4	0.541179
$944$	10238.1	0.352988
$945$	−10884.8	−0.374692
$946$	0	0
$947$	−41921.8	−1.43852	−0.719258	−	0.694743i	$-0.755518\pi$
$947$	−41921.8	−1.43852	−0.719258	+	0.694743i	$0.755518\pi$
$948$	4034.02	0.138205
$949$	−28318.4	−0.968654
$950$	−916.323	−0.0312941
$951$	−12043.1	−0.410647
$952$	−377.872	−0.0128644
$953$	32671.5	1.11053	0.555264	−	0.831674i	$-0.312617\pi$
$953$	32671.5	1.11053	0.555264	+	0.831674i	$0.312617\pi$
$954$	−3406.46	−0.115606
$955$	−44622.9	−1.51200
$956$	2552.95	0.0863684
$957$	12399.1	0.418815
$958$	3206.67	0.108145
$959$	14966.4	0.503951
$960$	−5513.14	−0.185350
$961$	33768.8	1.13352
$962$	1041.40	0.0349023
$963$	−16547.9	−0.553738
$964$	−28275.1	−0.944689
$965$	37741.1	1.25899
$966$	1258.91	0.0419303
$967$	47736.7	1.58750	0.793748	−	0.608246i	$-0.208127\pi$
$967$	47736.7	1.58750	0.793748	+	0.608246i	$0.208127\pi$
$968$	−3150.88	−0.104621
$969$	−334.615	−0.0110933
$970$	1140.56	0.0377539
$971$	−15380.7	−0.508332	−0.254166	−	0.967161i	$-0.581801\pi$
$971$	−15380.7	−0.508332	−0.254166	+	0.967161i	$0.581801\pi$
$972$	20473.0	0.675589
$973$	−4357.23	−0.143563
$974$	2906.05	0.0956014
$975$	2025.03	0.0665156
$976$	−51171.9	−1.67825
$977$	20896.4	0.684274	0.342137	−	0.939650i	$-0.388849\pi$
$977$	20896.4	0.684274	0.342137	+	0.939650i	$0.388849\pi$
$978$	−209.128	−0.00683762
$979$	53933.7	1.76070
$980$	−2109.94	−0.0687752
$981$	13439.9	0.437415
$982$	3244.58	0.105437
$983$	−29285.6	−0.950220	−0.475110	−	0.879926i	$-0.657592\pi$
$983$	−29285.6	−0.950220	−0.475110	+	0.879926i	$0.657592\pi$
$984$	−656.153	−0.0212575
$985$	−37705.0	−1.21968
$986$	−294.045	−0.00949725
$987$	4130.34	0.133202
$988$	−18900.9	−0.608622
$989$	0	0
$990$	3385.33	0.108680
$991$	6717.36	0.215322	0.107661	−	0.994188i	$-0.465664\pi$
$991$	6717.36	0.215322	0.107661	+	0.994188i	$0.465664\pi$
$992$	15919.3	0.509514
$993$	−13792.9	−0.440790
$994$	283.609	0.00904982
$995$	−37066.0	−1.18098
$996$	4315.54	0.137292
$997$	52598.2	1.67081	0.835407	−	0.549632i	$-0.185232\pi$
$997$	52598.2	1.67081	0.835407	+	0.549632i	$0.185232\pi$
$998$	445.469	0.0141293
$999$	5666.16	0.179449

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.4.a.h.1.16		30
43.21	even	7		43.4.e.a.11.6	yes	60
43.41	even	7		43.4.e.a.4.6	✓	60
43.42	odd	2		1849.4.a.g.1.15		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.4.e.a.4.6	✓	60	43.41	even	7
43.4.e.a.11.6	yes	60	43.21	even	7
1849.4.a.g.1.15		30	43.42	odd	2
1849.4.a.h.1.16		30	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1849 = 43^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1849.a (trivial)

\(f(q)\)	\(=\)	\(q+0.335126 q^{2} -1.29157 q^{3} -7.88769 q^{4} -9.09411 q^{5} -0.432838 q^{6} +17.7083 q^{7} -5.32438 q^{8} -25.3319 q^{9} +O(q^{10})\)	\(q+0.335126 q^{2} -1.29157 q^{3} -7.88769 q^{4} -9.09411 q^{5} -0.432838 q^{6} +17.7083 q^{7} -5.32438 q^{8} -25.3319 q^{9} -3.04767 q^{10} +43.8496 q^{11} +10.1875 q^{12} +37.0683 q^{13} +5.93453 q^{14} +11.7457 q^{15} +61.3172 q^{16} +4.00772 q^{17} -8.48936 q^{18} +64.6443 q^{19} +71.7316 q^{20} -22.8715 q^{21} +14.6951 q^{22} -164.244 q^{23} +6.87680 q^{24} -42.2971 q^{25} +12.4226 q^{26} +67.5901 q^{27} -139.678 q^{28} -218.931 q^{29} +3.93628 q^{30} +252.111 q^{31} +63.1440 q^{32} -56.6347 q^{33} +1.34309 q^{34} -161.042 q^{35} +199.810 q^{36} +83.8311 q^{37} +21.6640 q^{38} -47.8763 q^{39} +48.4205 q^{40} -95.4155 q^{41} -7.66485 q^{42} -345.872 q^{44} +230.371 q^{45} -55.0425 q^{46} -180.589 q^{47} -79.1953 q^{48} -29.4144 q^{49} -14.1749 q^{50} -5.17625 q^{51} -292.384 q^{52} +401.262 q^{53} +22.6512 q^{54} -398.773 q^{55} -94.2859 q^{56} -83.4925 q^{57} -73.3695 q^{58} +166.969 q^{59} -92.6462 q^{60} -834.545 q^{61} +84.4889 q^{62} -448.585 q^{63} -469.376 q^{64} -337.104 q^{65} -18.9798 q^{66} -651.471 q^{67} -31.6117 q^{68} +212.132 q^{69} -53.9693 q^{70} +47.7896 q^{71} +134.876 q^{72} -763.950 q^{73} +28.0940 q^{74} +54.6295 q^{75} -509.894 q^{76} +776.503 q^{77} -16.0446 q^{78} +395.977 q^{79} -557.626 q^{80} +596.663 q^{81} -31.9762 q^{82} +423.612 q^{83} +180.404 q^{84} -36.4467 q^{85} +282.764 q^{87} -233.472 q^{88} +1229.97 q^{89} +77.2032 q^{90} +656.419 q^{91} +1295.51 q^{92} -325.618 q^{93} -60.5199 q^{94} -587.882 q^{95} -81.5548 q^{96} -374.240 q^{97} -9.85754 q^{98} -1110.79 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 6 q^{2} + 2 q^{3} + 114 q^{4} + 27 q^{5} + 8 q^{6} + 48 q^{7} + 90 q^{8} + 216 q^{9}+O(q^{10}) \) 30 * q + 6 * q^2 + 2 * q^3 + 114 * q^4 + 27 * q^5 + 8 * q^6 + 48 * q^7 + 90 * q^8 + 216 * q^9	\( 30 q + 6 q^{2} + 2 q^{3} + 114 q^{4} + 27 q^{5} + 8 q^{6} + 48 q^{7} + 90 q^{8} + 216 q^{9} - 27 q^{10} + 80 q^{11} - 36 q^{12} - 13 q^{13} + 36 q^{14} + 16 q^{15} + 318 q^{16} + 66 q^{17} + 80 q^{18} + 254 q^{19} + 312 q^{20} - 548 q^{21} + 305 q^{22} - 105 q^{23} + 123 q^{24} + 523 q^{25} + 549 q^{26} - 10 q^{27} + 578 q^{28} + 793 q^{29} + 1560 q^{30} - 359 q^{31} + 676 q^{32} + 208 q^{33} + 1007 q^{34} - 514 q^{35} + 776 q^{36} + 510 q^{37} - 2066 q^{38} + 898 q^{39} - 1248 q^{40} - 270 q^{41} - 915 q^{42} + 3256 q^{44} + 807 q^{45} + 1960 q^{46} + 1421 q^{47} - 632 q^{48} + 386 q^{49} - 141 q^{50} + 209 q^{51} + 2825 q^{52} - 21 q^{53} + 2368 q^{54} + 2258 q^{55} + 2521 q^{56} - 1723 q^{57} - 347 q^{58} + 1752 q^{59} + 2711 q^{60} + 1759 q^{61} + 395 q^{62} + 2204 q^{63} + 222 q^{64} + 1151 q^{65} + 160 q^{66} - 3001 q^{67} + 1921 q^{68} + 1660 q^{69} + 1597 q^{70} + 727 q^{71} + 9100 q^{72} + 4623 q^{73} - 2649 q^{74} + 1027 q^{75} + 874 q^{76} + 3556 q^{77} - 4979 q^{78} + 546 q^{79} + 5809 q^{80} - 410 q^{81} - 4397 q^{82} - 492 q^{83} - 10611 q^{84} - 1723 q^{85} + 5937 q^{87} + 3974 q^{88} + 5218 q^{89} + 10492 q^{90} + 1104 q^{91} + 1060 q^{92} + 1997 q^{93} - 2134 q^{94} + 6346 q^{95} - 11984 q^{96} + 2590 q^{97} + 6270 q^{98} - 2693 q^{99}+O(q^{100}) \) 30 * q + 6 * q^2 + 2 * q^3 + 114 * q^4 + 27 * q^5 + 8 * q^6 + 48 * q^7 + 90 * q^8 + 216 * q^9 - 27 * q^10 + 80 * q^11 - 36 * q^12 - 13 * q^13 + 36 * q^14 + 16 * q^15 + 318 * q^16 + 66 * q^17 + 80 * q^18 + 254 * q^19 + 312 * q^20 - 548 * q^21 + 305 * q^22 - 105 * q^23 + 123 * q^24 + 523 * q^25 + 549 * q^26 - 10 * q^27 + 578 * q^28 + 793 * q^29 + 1560 * q^30 - 359 * q^31 + 676 * q^32 + 208 * q^33 + 1007 * q^34 - 514 * q^35 + 776 * q^36 + 510 * q^37 - 2066 * q^38 + 898 * q^39 - 1248 * q^40 - 270 * q^41 - 915 * q^42 + 3256 * q^44 + 807 * q^45 + 1960 * q^46 + 1421 * q^47 - 632 * q^48 + 386 * q^49 - 141 * q^50 + 209 * q^51 + 2825 * q^52 - 21 * q^53 + 2368 * q^54 + 2258 * q^55 + 2521 * q^56 - 1723 * q^57 - 347 * q^58 + 1752 * q^59 + 2711 * q^60 + 1759 * q^61 + 395 * q^62 + 2204 * q^63 + 222 * q^64 + 1151 * q^65 + 160 * q^66 - 3001 * q^67 + 1921 * q^68 + 1660 * q^69 + 1597 * q^70 + 727 * q^71 + 9100 * q^72 + 4623 * q^73 - 2649 * q^74 + 1027 * q^75 + 874 * q^76 + 3556 * q^77 - 4979 * q^78 + 546 * q^79 + 5809 * q^80 - 410 * q^81 - 4397 * q^82 - 492 * q^83 - 10611 * q^84 - 1723 * q^85 + 5937 * q^87 + 3974 * q^88 + 5218 * q^89 + 10492 * q^90 + 1104 * q^91 + 1060 * q^92 + 1997 * q^93 - 2134 * q^94 + 6346 * q^95 - 11984 * q^96 + 2590 * q^97 + 6270 * q^98 - 2693 * q^99

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