LMFDB - Embedded newform 1573.4.a.o.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1573,4,Mod(1,1573)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1573, 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("1573.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1573 = 11^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1573.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:	$92.8100044390$
Analytic rank:	$1$
Dimension:	$34$
Twist minimal:	no (minimal twist has level 143)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	1573.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.305925 q^{2} -0.688798 q^{3} -7.90641 q^{4} -14.6552 q^{5} -0.210720 q^{6} +34.1750 q^{7} -4.86616 q^{8} -26.5256 q^{9} +O(q^{10})$	\(q+0.305925 q^{2} -0.688798 q^{3} -7.90641 q^{4} -14.6552 q^{5} -0.210720 q^{6} +34.1750 q^{7} -4.86616 q^{8} -26.5256 q^{9} -4.48337 q^{10} +5.44592 q^{12} +13.0000 q^{13} +10.4550 q^{14} +10.0944 q^{15} +61.7626 q^{16} -71.3364 q^{17} -8.11482 q^{18} -34.2450 q^{19} +115.870 q^{20} -23.5397 q^{21} -0.447054 q^{23} +3.35180 q^{24} +89.7736 q^{25} +3.97702 q^{26} +36.8683 q^{27} -270.202 q^{28} +171.089 q^{29} +3.08814 q^{30} -31.5959 q^{31} +57.8240 q^{32} -21.8236 q^{34} -500.840 q^{35} +209.722 q^{36} +268.859 q^{37} -10.4764 q^{38} -8.95437 q^{39} +71.3144 q^{40} -387.482 q^{41} -7.20136 q^{42} +452.217 q^{43} +388.736 q^{45} -0.136765 q^{46} +91.1032 q^{47} -42.5419 q^{48} +824.931 q^{49} +27.4639 q^{50} +49.1364 q^{51} -102.783 q^{52} +667.682 q^{53} +11.2789 q^{54} -166.301 q^{56} +23.5879 q^{57} +52.3404 q^{58} -331.338 q^{59} -79.8108 q^{60} +305.654 q^{61} -9.66596 q^{62} -906.511 q^{63} -476.411 q^{64} -190.517 q^{65} -835.795 q^{67} +564.015 q^{68} +0.307930 q^{69} -153.219 q^{70} -22.4572 q^{71} +129.078 q^{72} -341.797 q^{73} +82.2505 q^{74} -61.8358 q^{75} +270.755 q^{76} -2.73936 q^{78} -135.038 q^{79} -905.140 q^{80} +690.795 q^{81} -118.540 q^{82} +558.319 q^{83} +186.114 q^{84} +1045.45 q^{85} +138.344 q^{86} -117.846 q^{87} -46.9575 q^{89} +118.924 q^{90} +444.275 q^{91} +3.53459 q^{92} +21.7632 q^{93} +27.8707 q^{94} +501.866 q^{95} -39.8290 q^{96} -158.837 q^{97} +252.367 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 3 q^{2} - 29 q^{3} + 97 q^{4} - 28 q^{5} + 36 q^{6} - 36 q^{7} - 57 q^{8} + 265 q^{9}+O(q^{10}) $ 34 * q - 3 * q^2 - 29 * q^3 + 97 * q^4 - 28 * q^5 + 36 * q^6 - 36 * q^7 - 57 * q^8 + 265 * q^9	\( 34 q - 3 q^{2} - 29 q^{3} + 97 q^{4} - 28 q^{5} + 36 q^{6} - 36 q^{7} - 57 q^{8} + 265 q^{9} - 18 q^{10} - 262 q^{12} + 442 q^{13} - 231 q^{14} - 196 q^{15} + 225 q^{16} - 209 q^{17} - 190 q^{18} - 107 q^{19} - 211 q^{20} - 68 q^{21} - 632 q^{23} + 152 q^{24} + 296 q^{25} - 39 q^{26} - 920 q^{27} - 931 q^{28} - 32 q^{29} - 300 q^{30} - 290 q^{31} + 876 q^{32} - 602 q^{34} + 104 q^{35} - 611 q^{36} - 656 q^{37} - 1361 q^{38} - 377 q^{39} + 1159 q^{40} - 1121 q^{41} + 79 q^{42} + 349 q^{43} - 1024 q^{45} + 490 q^{46} - 1608 q^{47} - 1827 q^{48} + 808 q^{49} - 1322 q^{50} + 1414 q^{51} + 1261 q^{52} - 2608 q^{53} + 3131 q^{54} - 1675 q^{56} - 2150 q^{57} - 1673 q^{58} - 2011 q^{59} - 201 q^{60} - 236 q^{61} + 1396 q^{62} + 1206 q^{63} + 1331 q^{64} - 364 q^{65} - 3213 q^{67} - 1321 q^{68} - 162 q^{69} + 174 q^{70} - 3756 q^{71} - 5074 q^{72} + 823 q^{73} + 2550 q^{74} - 3063 q^{75} + 2004 q^{76} + 468 q^{78} - 2120 q^{79} - 5005 q^{80} + 710 q^{81} - 2534 q^{82} - 3843 q^{83} + 7191 q^{84} + 1582 q^{85} - 3542 q^{86} + 962 q^{87} - 3633 q^{89} - 995 q^{90} - 468 q^{91} - 2072 q^{92} - 508 q^{93} - 6309 q^{94} + 1916 q^{95} - 2150 q^{96} + 1195 q^{97} - 1487 q^{98}+O(q^{100}) \) 34 * q - 3 * q^2 - 29 * q^3 + 97 * q^4 - 28 * q^5 + 36 * q^6 - 36 * q^7 - 57 * q^8 + 265 * q^9 - 18 * q^10 - 262 * q^12 + 442 * q^13 - 231 * q^14 - 196 * q^15 + 225 * q^16 - 209 * q^17 - 190 * q^18 - 107 * q^19 - 211 * q^20 - 68 * q^21 - 632 * q^23 + 152 * q^24 + 296 * q^25 - 39 * q^26 - 920 * q^27 - 931 * q^28 - 32 * q^29 - 300 * q^30 - 290 * q^31 + 876 * q^32 - 602 * q^34 + 104 * q^35 - 611 * q^36 - 656 * q^37 - 1361 * q^38 - 377 * q^39 + 1159 * q^40 - 1121 * q^41 + 79 * q^42 + 349 * q^43 - 1024 * q^45 + 490 * q^46 - 1608 * q^47 - 1827 * q^48 + 808 * q^49 - 1322 * q^50 + 1414 * q^51 + 1261 * q^52 - 2608 * q^53 + 3131 * q^54 - 1675 * q^56 - 2150 * q^57 - 1673 * q^58 - 2011 * q^59 - 201 * q^60 - 236 * q^61 + 1396 * q^62 + 1206 * q^63 + 1331 * q^64 - 364 * q^65 - 3213 * q^67 - 1321 * q^68 - 162 * q^69 + 174 * q^70 - 3756 * q^71 - 5074 * q^72 + 823 * q^73 + 2550 * q^74 - 3063 * q^75 + 2004 * q^76 + 468 * q^78 - 2120 * q^79 - 5005 * q^80 + 710 * q^81 - 2534 * q^82 - 3843 * q^83 + 7191 * q^84 + 1582 * q^85 - 3542 * q^86 + 962 * q^87 - 3633 * q^89 - 995 * q^90 - 468 * q^91 - 2072 * q^92 - 508 * q^93 - 6309 * q^94 + 1916 * q^95 - 2150 * q^96 + 1195 * q^97 - 1487 * q^98

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 $

$2$	0.305925	0.108161	0.0540803	−	0.998537i	$-0.482777\pi$
$2$	0.305925	0.108161	0.0540803	+	0.998537i	$0.482777\pi$
$3$	−0.688798	−0.132559	−0.0662796	−	0.997801i	$-0.521113\pi$
$3$	−0.688798	−0.132559	−0.0662796	+	0.997801i	$0.521113\pi$
$4$	−7.90641	−0.988301
$5$	−14.6552	−1.31080	−0.655398	−	0.755283i	$-0.727499\pi$
$5$	−14.6552	−1.31080	−0.655398	+	0.755283i	$0.727499\pi$
$6$	−0.210720	−0.0143377
$7$	34.1750	1.84528	0.922638	−	0.385667i	$-0.126028\pi$
$7$	34.1750	1.84528	0.922638	+	0.385667i	$0.126028\pi$
$8$	−4.86616	−0.215056
$9$	−26.5256	−0.982428
$10$	−4.48337	−0.141777
$11$	0	0
$11$	0	0
$12$	5.44592	0.131008
$13$	13.0000	0.277350
$13$	13.0000	0.277350
$14$	10.4550	0.199586
$15$	10.0944	0.173758
$16$	61.7626	0.965041
$17$	−71.3364	−1.01774	−0.508871	−	0.860843i	$-0.669937\pi$
$17$	−71.3364	−1.01774	−0.508871	+	0.860843i	$0.669937\pi$
$18$	−8.11482	−0.106260
$19$	−34.2450	−0.413492	−0.206746	−	0.978395i	$-0.566287\pi$
$19$	−34.2450	−0.413492	−0.206746	+	0.978395i	$0.566287\pi$
$20$	115.870	1.29546
$21$	−23.5397	−0.244608
$22$	0	0
$23$	−0.447054	−0.00405292	−0.00202646	−	0.999998i	$-0.500645\pi$
$23$	−0.447054	−0.00405292	−0.00202646	+	0.999998i	$0.500645\pi$
$24$	3.35180	0.0285077
$25$	89.7736	0.718188
$26$	3.97702	0.0299984
$27$	36.8683	0.262789
$28$	−270.202	−1.82369
$29$	171.089	1.09553	0.547766	−	0.836631i	$-0.315478\pi$
$29$	171.089	1.09553	0.547766	+	0.836631i	$0.315478\pi$
$30$	3.08814	0.0187938
$31$	−31.5959	−0.183058	−0.0915288	−	0.995802i	$-0.529175\pi$
$31$	−31.5959	−0.183058	−0.0915288	+	0.995802i	$0.529175\pi$
$32$	57.8240	0.319435
$33$	0	0
$34$	−21.8236	−0.110080
$35$	−500.840	−2.41878
$36$	209.722	0.970935
$37$	268.859	1.19460	0.597299	−	0.802019i	$-0.296241\pi$
$37$	268.859	1.19460	0.597299	+	0.802019i	$0.296241\pi$
$38$	−10.4764	−0.0447236
$39$	−8.95437	−0.0367653
$40$	71.3144	0.281895
$41$	−387.482	−1.47596	−0.737982	−	0.674820i	$-0.764221\pi$
$41$	−387.482	−1.47596	−0.737982	+	0.674820i	$0.764221\pi$
$42$	−7.20136	−0.0264570
$43$	452.217	1.60378	0.801889	−	0.597474i	$-0.203829\pi$
$43$	452.217	1.60378	0.801889	+	0.597474i	$0.203829\pi$
$44$	0	0
$45$	388.736	1.28776
$46$	−0.136765	−0.000438367 0
$47$	91.1032	0.282740	0.141370	−	0.989957i	$-0.454849\pi$
$47$	91.1032	0.282740	0.141370	+	0.989957i	$0.454849\pi$
$48$	−42.5419	−0.127925
$49$	824.931	2.40505
$50$	27.4639	0.0776798
$51$	49.1364	0.134911
$52$	−102.783	−0.274105
$53$	667.682	1.73044	0.865219	−	0.501394i	$-0.167179\pi$
$53$	667.682	1.73044	0.865219	+	0.501394i	$0.167179\pi$
$54$	11.2789	0.0284234
$55$	0	0
$56$	−166.301	−0.396838
$57$	23.5879	0.0548122
$58$	52.3404	0.118494
$59$	−331.338	−0.731128	−0.365564	−	0.930786i	$-0.619124\pi$
$59$	−331.338	−0.731128	−0.365564	+	0.930786i	$0.619124\pi$
$60$	−79.8108	−0.171725
$61$	305.654	0.641557	0.320778	−	0.947154i	$-0.396056\pi$
$61$	305.654	0.641557	0.320778	+	0.947154i	$0.396056\pi$
$62$	−9.66596	−0.0197996
$63$	−906.511	−1.81285
$64$	−476.411	−0.930490
$65$	−190.517	−0.363550
$66$	0	0
$67$	−835.795	−1.52401	−0.762004	−	0.647572i	$-0.775785\pi$
$67$	−835.795	−1.52401	−0.762004	+	0.647572i	$0.775785\pi$
$68$	564.015	1.00584
$69$	0.307930	0.000537252 0
$70$	−153.219	−0.261617
$71$	−22.4572	−0.0375378	−0.0187689	−	0.999824i	$-0.505975\pi$
$71$	−22.4572	−0.0375378	−0.0187689	+	0.999824i	$0.505975\pi$
$72$	129.078	0.211277
$73$	−341.797	−0.548005	−0.274002	−	0.961729i	$-0.588348\pi$
$73$	−341.797	−0.548005	−0.274002	+	0.961729i	$0.588348\pi$
$74$	82.2505	0.129208
$75$	−61.8358	−0.0952025
$76$	270.755	0.408655
$77$	0	0
$78$	−2.73936	−0.00397656
$79$	−135.038	−0.192316	−0.0961582	−	0.995366i	$-0.530655\pi$
$79$	−135.038	−0.192316	−0.0961582	+	0.995366i	$0.530655\pi$
$80$	−905.140	−1.26497
$81$	690.795	0.947593
$82$	−118.540	−0.159641
$83$	558.319	0.738355	0.369178	−	0.929359i	$-0.379639\pi$
$83$	558.319	0.738355	0.369178	+	0.929359i	$0.379639\pi$
$84$	186.114	0.241747
$85$	1045.45	1.33405
$86$	138.344	0.173466
$87$	−117.846	−0.145223
$88$	0	0
$89$	−46.9575	−0.0559268	−0.0279634	−	0.999609i	$-0.508902\pi$
$89$	−46.9575	−0.0559268	−0.0279634	+	0.999609i	$0.508902\pi$
$90$	118.924	0.139285
$91$	444.275	0.511788
$92$	3.53459	0.00400551
$93$	21.7632	0.0242660
$94$	27.8707	0.0305813
$95$	501.866	0.542004
$96$	−39.8290	−0.0423441
$97$	−158.837	−0.166262	−0.0831311	−	0.996539i	$-0.526492\pi$
$97$	−158.837	−0.166262	−0.0831311	+	0.996539i	$0.526492\pi$
$98$	252.367	0.260131
$99$	0	0
$100$	−709.787	−0.709787
$101$	−0.448987	−0.000442335 0	−0.000221168	−	1.00000i	$-0.500070\pi$
$101$	−0.448987	−0.000442335 0	−0.000221168		1.00000i	$0.500070\pi$
$102$	15.0320	0.0145921
$103$	528.711	0.505781	0.252891	−	0.967495i	$-0.418619\pi$
$103$	528.711	0.505781	0.252891	+	0.967495i	$0.418619\pi$
$104$	−63.2601	−0.0596458
$105$	344.977	0.320632
$106$	204.260	0.187165
$107$	−125.372	−0.113273	−0.0566364	−	0.998395i	$-0.518038\pi$
$107$	−125.372	−0.113273	−0.0566364	+	0.998395i	$0.518038\pi$
$108$	−291.496	−0.259715
$109$	−445.244	−0.391254	−0.195627	−	0.980678i	$-0.562674\pi$
$109$	−445.244	−0.391254	−0.195627	+	0.980678i	$0.562674\pi$
$110$	0	0
$111$	−185.189	−0.158355
$112$	2110.74	1.78077
$113$	−2065.99	−1.71993	−0.859963	−	0.510356i	$-0.829514\pi$
$113$	−2065.99	−1.71993	−0.859963	+	0.510356i	$0.829514\pi$
$114$	7.21612	0.00592852
$115$	6.55165	0.00531256
$116$	−1352.70	−1.08272
$117$	−344.832	−0.272477
$118$	−101.364	−0.0790793
$119$	−2437.92	−1.87802
$120$	−49.1212	−0.0373677
$121$	0	0
$122$	93.5070	0.0693912
$123$	266.897	0.195653
$124$	249.810	0.180916
$125$	516.249	0.369398
$126$	−277.324	−0.196079
$127$	−2261.70	−1.58026	−0.790131	−	0.612939i	$-0.789987\pi$
$127$	−2261.70	−1.58026	−0.790131	+	0.612939i	$0.789987\pi$
$128$	−608.338	−0.420078
$129$	−311.486	−0.212595
$130$	−58.2838	−0.0393218
$131$	−1805.98	−1.20450	−0.602249	−	0.798308i	$-0.705729\pi$
$131$	−1805.98	−1.20450	−0.602249	+	0.798308i	$0.705729\pi$
$132$	0	0
$133$	−1170.32	−0.763007
$134$	−255.690	−0.164838
$135$	−540.310	−0.344463
$136$	347.135	0.218872
$137$	1033.56	0.644547	0.322274	−	0.946647i	$-0.395553\pi$
$137$	1033.56	0.644547	0.322274	+	0.946647i	$0.395553\pi$
$138$	0.0942033	5.81096e−5 0
$139$	2326.99	1.41995	0.709973	−	0.704228i	$-0.248707\pi$
$139$	2326.99	1.41995	0.709973	+	0.704228i	$0.248707\pi$
$140$	3959.85	2.39049
$141$	−62.7517	−0.0374797
$142$	−6.87021	−0.00406011
$143$	0	0
$144$	−1638.29	−0.948083
$145$	−2507.34	−1.43602
$146$	−104.564	−0.0592726
$147$	−568.210	−0.318811
$148$	−2125.71	−1.18062
$149$	−2238.99	−1.23104	−0.615522	−	0.788120i	$-0.711055\pi$
$149$	−2238.99	−1.23104	−0.615522	+	0.788120i	$0.711055\pi$
$150$	−18.9171	−0.0102972
$151$	11.9649	0.00644826	0.00322413	−	0.999995i	$-0.498974\pi$
$151$	11.9649	0.00644826	0.00322413	+	0.999995i	$0.498974\pi$
$152$	166.642	0.0889240
$153$	1892.24	0.999859
$154$	0	0
$155$	463.042	0.239951
$156$	70.7969	0.0363352
$157$	−719.889	−0.365945	−0.182973	−	0.983118i	$-0.558572\pi$
$157$	−719.889	−0.365945	−0.182973	+	0.983118i	$0.558572\pi$
$158$	−41.3115	−0.0208011
$159$	−459.898	−0.229385
$160$	−847.420	−0.418715
$161$	−15.2781	−0.00747876
$162$	211.331	0.102492
$163$	−1478.24	−0.710335	−0.355168	−	0.934803i	$-0.615576\pi$
$163$	−1478.24	−0.710335	−0.355168	+	0.934803i	$0.615576\pi$
$164$	3063.59	1.45870
$165$	0	0
$166$	170.804	0.0798610
$167$	655.734	0.303846	0.151923	−	0.988392i	$-0.451453\pi$
$167$	655.734	0.303846	0.151923	+	0.988392i	$0.451453\pi$
$168$	114.548	0.0526045
$169$	169.000	0.0769231
$170$	319.828	0.144292
$171$	908.369	0.406226
$172$	−3575.41	−1.58502
$173$	−3911.09	−1.71881	−0.859406	−	0.511294i	$-0.829166\pi$
$173$	−3911.09	−1.71881	−0.859406	+	0.511294i	$0.829166\pi$
$174$	−36.0519	−0.0157074
$175$	3068.01	1.32526
$176$	0	0
$177$	228.225	0.0969177
$178$	−14.3655	−0.00604908
$179$	−111.891	−0.0467215	−0.0233607	−	0.999727i	$-0.507437\pi$
$179$	−111.891	−0.0467215	−0.0233607	+	0.999727i	$0.507437\pi$
$180$	−3073.51	−1.27270
$181$	−4775.07	−1.96093	−0.980464	−	0.196699i	$-0.936978\pi$
$181$	−4775.07	−1.96093	−0.980464	+	0.196699i	$0.936978\pi$
$182$	135.915	0.0553553
$183$	−210.534	−0.0850442
$184$	2.17544	0.000871606 0
$185$	−3940.17	−1.56587
$186$	6.65789	0.00262462
$187$	0	0
$188$	−720.299	−0.279432
$189$	1259.97	0.484918
$190$	153.533	0.0586235
$191$	−3497.15	−1.32484	−0.662422	−	0.749131i	$-0.730471\pi$
$191$	−3497.15	−1.32484	−0.662422	+	0.749131i	$0.730471\pi$
$192$	328.151	0.123345
$193$	−2425.37	−0.904568	−0.452284	−	0.891874i	$-0.649391\pi$
$193$	−2425.37	−0.904568	−0.452284	+	0.891874i	$0.649391\pi$
$194$	−48.5921	−0.0179830
$195$	131.228	0.0481918
$196$	−6522.24	−2.37691
$197$	−2258.57	−0.816833	−0.408416	−	0.912796i	$-0.633919\pi$
$197$	−2258.57	−0.816833	−0.408416	+	0.912796i	$0.633919\pi$
$198$	0	0
$199$	3389.30	1.20734	0.603672	−	0.797233i	$-0.293704\pi$
$199$	3389.30	1.20734	0.603672	+	0.797233i	$0.293704\pi$
$200$	−436.853	−0.154451
$201$	575.694	0.202021
$202$	−0.137356	−4.78433e−5 0
$203$	5846.97	2.02156
$204$	−388.492	−0.133333
$205$	5678.61	1.93469
$206$	161.746	0.0547056
$207$	11.8584	0.00398171
$208$	802.914	0.267654
$209$	0	0
$210$	105.537	0.0346798
$211$	−3566.04	−1.16349	−0.581745	−	0.813372i	$-0.697630\pi$
$211$	−3566.04	−1.16349	−0.581745	+	0.813372i	$0.697630\pi$
$212$	−5278.97	−1.71019
$213$	15.4685	0.00497597
$214$	−38.3544	−0.0122517
$215$	−6627.31	−2.10223
$216$	−179.407	−0.0565144
$217$	−1079.79	−0.337792
$218$	−136.211	−0.0423183
$219$	235.429	0.0726431
$220$	0	0
$221$	−927.373	−0.282271
$222$	−56.6540	−0.0171278
$223$	4791.13	1.43873	0.719367	−	0.694631i	$-0.244432\pi$
$223$	4791.13	1.43873	0.719367	+	0.694631i	$0.244432\pi$
$224$	1976.14	0.589447
$225$	−2381.29	−0.705569
$226$	−632.036	−0.186028
$227$	−1452.50	−0.424695	−0.212347	−	0.977194i	$-0.568111\pi$
$227$	−1452.50	−0.424695	−0.212347	+	0.977194i	$0.568111\pi$
$228$	−186.496	−0.0541709
$229$	−3452.38	−0.996245	−0.498122	−	0.867107i	$-0.665977\pi$
$229$	−3452.38	−0.996245	−0.498122	+	0.867107i	$0.665977\pi$
$230$	2.00431	0.000574610 0
$231$	0	0
$232$	−832.547	−0.235601
$233$	−2285.07	−0.642488	−0.321244	−	0.946996i	$-0.604101\pi$
$233$	−2285.07	−0.642488	−0.321244	+	0.946996i	$0.604101\pi$
$234$	−105.493	−0.0294712
$235$	−1335.13	−0.370614
$236$	2619.69	0.722574
$237$	93.0140	0.0254933
$238$	−745.820	−0.203128
$239$	−3262.27	−0.882924	−0.441462	−	0.897280i	$-0.645540\pi$
$239$	−3262.27	−0.882924	−0.441462	+	0.897280i	$0.645540\pi$
$240$	623.459	0.167684
$241$	6064.25	1.62088	0.810441	−	0.585820i	$-0.199227\pi$
$241$	6064.25	1.62088	0.810441	+	0.585820i	$0.199227\pi$
$242$	0	0
$243$	−1471.26	−0.388401
$244$	−2416.62	−0.634051
$245$	−12089.5	−3.15253
$246$	81.6503	0.0211619
$247$	−445.185	−0.114682
$248$	153.751	0.0393677
$249$	−384.569	−0.0978758
$250$	157.933	0.0399543
$251$	5965.01	1.50003	0.750016	−	0.661419i	$-0.230046\pi$
$251$	5965.01	1.50003	0.750016	+	0.661419i	$0.230046\pi$
$252$	7167.25	1.79164
$253$	0	0
$254$	−691.909	−0.170922
$255$	−720.101	−0.176841
$256$	3625.18	0.885054
$257$	353.493	0.0857987	0.0428994	−	0.999079i	$-0.486341\pi$
$257$	353.493	0.0857987	0.0428994	+	0.999079i	$0.486341\pi$
$258$	−95.2912	−0.0229945
$259$	9188.25	2.20436
$260$	1506.31	0.359297
$261$	−4538.23	−1.07628
$262$	−552.494	−0.130279
$263$	−3095.75	−0.725825	−0.362912	−	0.931823i	$-0.618218\pi$
$263$	−3095.75	−0.725825	−0.362912	+	0.931823i	$0.618218\pi$
$264$	0	0
$265$	−9784.99	−2.26825
$266$	−358.031	−0.0825274
$267$	32.3442	0.00741361
$268$	6608.14	1.50618
$269$	−3198.61	−0.724992	−0.362496	−	0.931985i	$-0.618075\pi$
$269$	−3198.61	−0.724992	−0.362496	+	0.931985i	$0.618075\pi$
$270$	−165.294	−0.0372574
$271$	−2145.48	−0.480918	−0.240459	−	0.970659i	$-0.577298\pi$
$271$	−2145.48	−0.480918	−0.240459	+	0.970659i	$0.577298\pi$
$272$	−4405.92	−0.982163
$273$	−306.016	−0.0678422
$274$	316.191	0.0697147
$275$	0	0
$276$	−2.43462	−0.000530967 0
$277$	3574.48	0.775341	0.387671	−	0.921798i	$-0.373280\pi$
$277$	3574.48	0.775341	0.387671	+	0.921798i	$0.373280\pi$
$278$	711.883	0.153582
$279$	838.098	0.179841
$280$	2437.17	0.520174
$281$	−8311.12	−1.76441	−0.882206	−	0.470864i	$-0.843942\pi$
$281$	−8311.12	−1.76441	−0.882206	+	0.470864i	$0.843942\pi$
$282$	−19.1973	−0.00405383
$283$	8434.82	1.77172	0.885862	−	0.463949i	$-0.153568\pi$
$283$	8434.82	1.77172	0.885862	+	0.463949i	$0.153568\pi$
$284$	177.556	0.0370986
$285$	−345.684	−0.0718476
$286$	0	0
$287$	−13242.2	−2.72356
$288$	−1533.81	−0.313822
$289$	175.885	0.0357999
$290$	−767.056	−0.155321
$291$	109.406	0.0220396
$292$	2702.39	0.541594
$293$	5103.83	1.01764	0.508821	−	0.860872i	$-0.330082\pi$
$293$	5103.83	1.01764	0.508821	+	0.860872i	$0.330082\pi$
$294$	−173.830	−0.0344828
$295$	4855.81	0.958360
$296$	−1308.31	−0.256905
$297$	0	0
$298$	−684.963	−0.133151
$299$	−5.81170	−0.00112408
$300$	488.899	0.0940887
$301$	15454.5	2.95941
$302$	3.66035	0.000697448 0
$303$	0.309261	5.86356e−5 0
$304$	−2115.06	−0.399037
$305$	−4479.40	−0.840950
$306$	578.882	0.108145
$307$	5806.40	1.07944	0.539721	−	0.841844i	$-0.318530\pi$
$307$	5806.40	1.07944	0.539721	+	0.841844i	$0.318530\pi$
$308$	0	0
$309$	−364.175	−0.0670459
$310$	141.656	0.0259533
$311$	2170.92	0.395826	0.197913	−	0.980220i	$-0.436584\pi$
$311$	2170.92	0.395826	0.197913	+	0.980220i	$0.436584\pi$
$312$	43.5734	0.00790660
$313$	6455.25	1.16573	0.582863	−	0.812570i	$-0.301932\pi$
$313$	6455.25	1.16573	0.582863	+	0.812570i	$0.301932\pi$
$314$	−220.232	−0.0395809
$315$	13285.1	2.37628
$316$	1067.67	0.190066
$317$	−3928.73	−0.696086	−0.348043	−	0.937479i	$-0.613154\pi$
$317$	−3928.73	−0.696086	−0.348043	+	0.937479i	$0.613154\pi$
$318$	−140.694	−0.0248105
$319$	0	0
$320$	6981.88	1.21968
$321$	86.3561	0.0150153
$322$	−4.67394	−0.000808908 0
$323$	2442.92	0.420829
$324$	−5461.71	−0.936507
$325$	1167.06	0.199190
$326$	−452.230	−0.0768303
$327$	306.683	0.0518643
$328$	1885.55	0.317415
$329$	3113.45	0.521733
$330$	0	0
$331$	−2339.58	−0.388504	−0.194252	−	0.980952i	$-0.562228\pi$
$331$	−2339.58	−0.388504	−0.194252	+	0.980952i	$0.562228\pi$
$332$	−4414.30	−0.729718
$333$	−7131.63	−1.17361
$334$	200.605	0.0328642
$335$	12248.7	1.99767
$336$	−1453.87	−0.236057
$337$	1360.19	0.219864	0.109932	−	0.993939i	$-0.464937\pi$
$337$	1360.19	0.219864	0.109932	+	0.993939i	$0.464937\pi$
$338$	51.7013	0.00832005
$339$	1423.05	0.227992
$340$	−8265.73	−1.31845
$341$	0	0
$342$	277.892	0.0439377
$343$	16470.0	2.59270
$344$	−2200.56	−0.344902
$345$	−4.51276	−0.000704229 0
$346$	−1196.50	−0.185908
$347$	−862.670	−0.133460	−0.0667299	−	0.997771i	$-0.521257\pi$
$347$	−862.670	−0.133460	−0.0667299	+	0.997771i	$0.521257\pi$
$348$	931.737	0.143524
$349$	−7770.62	−1.19184	−0.595919	−	0.803044i	$-0.703212\pi$
$349$	−7770.62	−1.19184	−0.595919	+	0.803044i	$0.703212\pi$
$350$	938.580	0.143341
$351$	479.288	0.0728846
$352$	0	0
$353$	7053.91	1.06357	0.531787	−	0.846878i	$-0.321521\pi$
$353$	7053.91	1.06357	0.531787	+	0.846878i	$0.321521\pi$
$354$	69.8196	0.0104827
$355$	329.114	0.0492044
$356$	371.265	0.0552725
$357$	1679.24	0.248948
$358$	−34.2303	−0.00505343
$359$	3559.04	0.523229	0.261614	−	0.965172i	$-0.415745\pi$
$359$	3559.04	0.523229	0.261614	+	0.965172i	$0.415745\pi$
$360$	−1891.65	−0.276941
$361$	−5686.28	−0.829024
$362$	−1460.81	−0.212095
$363$	0	0
$364$	−3512.62	−0.505800
$365$	5009.09	0.718323
$366$	−64.4074	−0.00919844
$367$	−7294.24	−1.03748	−0.518742	−	0.854931i	$-0.673599\pi$
$367$	−7294.24	−1.03748	−0.518742	+	0.854931i	$0.673599\pi$
$368$	−27.6112	−0.00391124
$369$	10278.2	1.45003
$370$	−1205.39	−0.169366
$371$	22818.0	3.19314
$372$	−172.069	−0.0239821
$373$	2853.02	0.396043	0.198021	−	0.980198i	$-0.436548\pi$
$373$	2853.02	0.396043	0.198021	+	0.980198i	$0.436548\pi$
$374$	0	0
$375$	−355.591	−0.0489671
$376$	−443.323	−0.0608049
$377$	2224.16	0.303846
$378$	385.457	0.0524491
$379$	−2897.36	−0.392685	−0.196342	−	0.980535i	$-0.562906\pi$
$379$	−2897.36	−0.392685	−0.196342	+	0.980535i	$0.562906\pi$
$380$	−3967.96	−0.535663
$381$	1557.85	0.209478
$382$	−1069.87	−0.143296
$383$	−9981.00	−1.33161	−0.665803	−	0.746128i	$-0.731911\pi$
$383$	−9981.00	−1.33161	−0.665803	+	0.746128i	$0.731911\pi$
$384$	419.022	0.0556852
$385$	0	0
$386$	−741.979	−0.0978387
$387$	−11995.3	−1.57560
$388$	1255.83	0.164317
$389$	−11090.2	−1.44549	−0.722745	−	0.691115i	$-0.757120\pi$
$389$	−11090.2	−1.44549	−0.722745	+	0.691115i	$0.757120\pi$
$390$	40.1458	0.00521246
$391$	31.8912	0.00412483
$392$	−4014.25	−0.517220
$393$	1243.96	0.159667
$394$	−690.951	−0.0883492
$395$	1979.01	0.252088
$396$	0	0
$397$	12083.0	1.52753	0.763764	−	0.645495i	$-0.223349\pi$
$397$	12083.0	1.52753	0.763764	+	0.645495i	$0.223349\pi$
$398$	1036.87	0.130587
$399$	806.117	0.101144
$400$	5544.65	0.693081
$401$	9247.79	1.15165	0.575826	−	0.817572i	$-0.304681\pi$
$401$	9247.79	1.15165	0.575826	+	0.817572i	$0.304681\pi$
$402$	176.119	0.0218508
$403$	−410.746	−0.0507711
$404$	3.54987	0.000437161 0
$405$	−10123.7	−1.24210
$406$	1788.73	0.218653
$407$	0	0
$408$	−239.106	−0.0290135
$409$	4137.90	0.500259	0.250129	−	0.968212i	$-0.419527\pi$
$409$	4137.90	0.500259	0.250129	+	0.968212i	$0.419527\pi$
$410$	1737.23	0.209257
$411$	−711.914	−0.0854407
$412$	−4180.21	−0.499864
$413$	−11323.5	−1.34913
$414$	3.62776	0.000430664 0
$415$	−8182.26	−0.967834
$416$	751.712	0.0885955
$417$	−1602.82	−0.188227
$418$	0	0
$419$	203.401	0.0237154	0.0118577	−	0.999930i	$-0.496225\pi$
$419$	203.401	0.0237154	0.0118577	+	0.999930i	$0.496225\pi$
$420$	−2727.53	−0.316881
$421$	7008.36	0.811322	0.405661	−	0.914024i	$-0.367041\pi$
$421$	7008.36	0.811322	0.405661	+	0.914024i	$0.367041\pi$
$422$	−1090.94	−0.125844
$423$	−2416.56	−0.277771
$424$	−3249.05	−0.372141
$425$	−6404.12	−0.730931
$426$	4.73219	0.000538205 0
$427$	10445.7	1.18385
$428$	991.244	0.111948
$429$	0	0
$430$	−2027.46	−0.227378
$431$	−8751.85	−0.978101	−0.489051	−	0.872255i	$-0.662657\pi$
$431$	−8751.85	−0.978101	−0.489051	+	0.872255i	$0.662657\pi$
$432$	2277.08	0.253602
$433$	−8497.49	−0.943102	−0.471551	−	0.881839i	$-0.656306\pi$
$433$	−8497.49	−0.943102	−0.471551	+	0.881839i	$0.656306\pi$
$434$	−330.334	−0.0365358
$435$	1727.05	0.190358
$436$	3520.28	0.386677
$437$	15.3094	0.00167585
$438$	72.0236	0.00785713
$439$	−6423.10	−0.698309	−0.349154	−	0.937065i	$-0.613531\pi$
$439$	−6423.10	−0.698309	−0.349154	+	0.937065i	$0.613531\pi$
$440$	0	0
$441$	−21881.7	−2.36278
$442$	−283.706	−0.0305306
$443$	−2854.12	−0.306102	−0.153051	−	0.988218i	$-0.548910\pi$
$443$	−2854.12	−0.306102	−0.153051	+	0.988218i	$0.548910\pi$
$444$	1464.18	0.156502
$445$	688.170	0.0733087
$446$	1465.72	0.155614
$447$	1542.21	0.163186
$448$	−16281.3	−1.71701
$449$	4519.94	0.475076	0.237538	−	0.971378i	$-0.423660\pi$
$449$	4519.94	0.475076	0.237538	+	0.971378i	$0.423660\pi$
$450$	−728.496	−0.0763148
$451$	0	0
$452$	16334.5	1.69981
$453$	−8.24137	−0.000854776 0
$454$	−444.355	−0.0459353
$455$	−6510.92	−0.670850
$456$	−114.783	−0.0117877
$457$	−8462.80	−0.866243	−0.433121	−	0.901336i	$-0.642588\pi$
$457$	−8462.80	−0.866243	−0.433121	+	0.901336i	$0.642588\pi$
$458$	−1056.17	−0.107754
$459$	−2630.05	−0.267452
$460$	−51.8000	−0.00525041
$461$	−5774.23	−0.583368	−0.291684	−	0.956515i	$-0.594216\pi$
$461$	−5774.23	−0.583368	−0.291684	+	0.956515i	$0.594216\pi$
$462$	0	0
$463$	13459.1	1.35097	0.675484	−	0.737375i	$-0.263935\pi$
$463$	13459.1	1.35097	0.675484	+	0.737375i	$0.263935\pi$
$464$	10566.9	1.05723
$465$	−318.943	−0.0318078
$466$	−699.058	−0.0694919
$467$	−14715.6	−1.45815	−0.729077	−	0.684432i	$-0.760050\pi$
$467$	−14715.6	−1.45815	−0.729077	+	0.684432i	$0.760050\pi$
$468$	2726.39	0.269289
$469$	−28563.3	−2.81222
$470$	−408.449	−0.0400859
$471$	495.858	0.0485094
$472$	1612.34	0.157233
$473$	0	0
$474$	28.4553	0.00275737
$475$	−3074.30	−0.296965
$476$	19275.2	1.85605
$477$	−17710.6	−1.70003
$478$	−998.010	−0.0954977
$479$	−6719.31	−0.640946	−0.320473	−	0.947258i	$-0.603842\pi$
$479$	−6719.31	−0.640946	−0.320473	+	0.947258i	$0.603842\pi$
$480$	583.701	0.0555045
$481$	3495.16	0.331322
$482$	1855.20	0.175316
$483$	10.5235	0.000991379 0
$484$	0	0
$485$	2327.78	0.217936
$486$	−450.095	−0.0420097
$487$	7046.51	0.655663	0.327831	−	0.944736i	$-0.393682\pi$
$487$	7046.51	0.655663	0.327831	+	0.944736i	$0.393682\pi$
$488$	−1487.36	−0.137971
$489$	1018.21	0.0941615
$490$	−3698.47	−0.340979
$491$	8918.31	0.819711	0.409855	−	0.912151i	$-0.365579\pi$
$491$	8918.31	0.819711	0.409855	+	0.912151i	$0.365579\pi$
$492$	−2110.19	−0.193364
$493$	−12204.9	−1.11497
$494$	−136.193	−0.0124041
$495$	0	0
$496$	−1951.44	−0.176658
$497$	−767.475	−0.0692675
$498$	−117.649	−0.0105863
$499$	−20995.3	−1.88352	−0.941762	−	0.336279i	$-0.890831\pi$
$499$	−20995.3	−1.88352	−0.941762	+	0.336279i	$0.890831\pi$
$500$	−4081.68	−0.365076
$501$	−451.668	−0.0402776
$502$	1824.84	0.162245
$503$	13256.6	1.17511	0.587556	−	0.809184i	$-0.300090\pi$
$503$	13256.6	1.17511	0.587556	+	0.809184i	$0.300090\pi$
$504$	4411.23	0.389865
$505$	6.57997	0.000579812 0
$506$	0	0
$507$	−116.407	−0.0101969
$508$	17881.9	1.56177
$509$	−19517.8	−1.69963	−0.849816	−	0.527080i	$-0.823287\pi$
$509$	−19517.8	−1.69963	−0.849816	+	0.527080i	$0.823287\pi$
$510$	−220.297	−0.0191273
$511$	−11680.9	−1.01122
$512$	5975.74	0.515806
$513$	−1262.56	−0.108661
$514$	108.142	0.00928005
$515$	−7748.34	−0.662976
$516$	2462.74	0.210108
$517$	0	0
$518$	2810.91	0.238425
$519$	2693.95	0.227844
$520$	927.087	0.0781835
$521$	12687.5	1.06689	0.533446	−	0.845834i	$-0.320897\pi$
$521$	12687.5	1.06689	0.533446	+	0.845834i	$0.320897\pi$
$522$	−1388.36	−0.116411
$523$	12245.5	1.02382	0.511912	−	0.859038i	$-0.328937\pi$
$523$	12245.5	1.02382	0.511912	+	0.859038i	$0.328937\pi$
$524$	14278.8	1.19041
$525$	−2113.24	−0.175675
$526$	−947.065	−0.0785057
$527$	2253.94	0.186306
$528$	0	0
$529$	−12166.8	−0.999984
$530$	−2993.47	−0.245336
$531$	8788.93	0.718280
$532$	9253.06	0.754081
$533$	−5037.27	−0.409359
$534$	9.89490	0.000801861 0
$535$	1837.35	0.148478
$536$	4067.11	0.327747
$537$	77.0704	0.00619336
$538$	−978.534	−0.0784156
$539$	0	0
$540$	4271.92	0.340433
$541$	−19845.9	−1.57715	−0.788577	−	0.614936i	$-0.789182\pi$
$541$	−19845.9	−1.57715	−0.788577	+	0.614936i	$0.789182\pi$
$542$	−656.356	−0.0520164
$543$	3289.06	0.259939
$544$	−4124.96	−0.325103
$545$	6525.12	0.512854
$546$	−93.6177	−0.00733785
$547$	−18836.3	−1.47236	−0.736182	−	0.676783i	$-0.763373\pi$
$547$	−18836.3	−1.47236	−0.736182	+	0.676783i	$0.763373\pi$
$548$	−8171.75	−0.637007
$549$	−8107.64	−0.630283
$550$	0	0
$551$	−5858.95	−0.452994
$552$	−1.49844	−0.000115539 0
$553$	−4614.93	−0.354877
$554$	1093.52	0.0838615
$555$	2713.98	0.207571
$556$	−18398.1	−1.40334
$557$	−13602.5	−1.03475	−0.517377	−	0.855758i	$-0.673091\pi$
$557$	−13602.5	−1.03475	−0.517377	+	0.855758i	$0.673091\pi$
$558$	256.395	0.0194517
$559$	5878.82	0.444808
$560$	−30933.2	−2.33422
$561$	0	0
$562$	−2542.58	−0.190840
$563$	3098.00	0.231910	0.115955	−	0.993254i	$-0.463007\pi$
$563$	3098.00	0.231910	0.115955	+	0.993254i	$0.463007\pi$
$564$	496.140	0.0370413
$565$	30277.4	2.25447
$566$	2580.42	0.191631
$567$	23607.9	1.74857
$568$	109.280	0.00807272
$569$	19047.6	1.40337	0.701685	−	0.712487i	$-0.252431\pi$
$569$	19047.6	1.40337	0.701685	+	0.712487i	$0.252431\pi$
$570$	−105.753	−0.00777109
$571$	13998.3	1.02594	0.512971	−	0.858406i	$-0.328545\pi$
$571$	13998.3	1.02594	0.512971	+	0.858406i	$0.328545\pi$
$572$	0	0
$573$	2408.83	0.175620
$574$	−4051.11	−0.294582
$575$	−40.1336	−0.00291076
$576$	12637.1	0.914140
$577$	−23286.2	−1.68010	−0.840050	−	0.542508i	$-0.817475\pi$
$577$	−23286.2	−1.68010	−0.840050	+	0.542508i	$0.817475\pi$
$578$	53.8075	0.00387214
$579$	1670.59	0.119909
$580$	19824.0	1.41922
$581$	19080.6	1.36247
$582$	33.4701	0.00238382
$583$	0	0
$584$	1663.24	0.117852
$585$	5053.57	0.357161
$586$	1561.39	0.110069
$587$	−8604.88	−0.605045	−0.302522	−	0.953142i	$-0.597829\pi$
$587$	−8604.88	−0.605045	−0.302522	+	0.953142i	$0.597829\pi$
$588$	4492.50	0.315081
$589$	1082.00	0.0756929
$590$	1485.51	0.103657
$591$	1555.69	0.108279
$592$	16605.4	1.15284
$593$	818.721	0.0566962	0.0283481	−	0.999598i	$-0.490975\pi$
$593$	818.721	0.0566962	0.0283481	+	0.999598i	$0.490975\pi$
$594$	0	0
$595$	35728.1	2.46170
$596$	17702.4	1.21664
$597$	−2334.54	−0.160044
$598$	−1.77794	−0.000121581 0
$599$	13419.1	0.915340	0.457670	−	0.889122i	$-0.348684\pi$
$599$	13419.1	0.915340	0.457670	+	0.889122i	$0.348684\pi$
$600$	300.903	0.0204739
$601$	−10098.1	−0.685372	−0.342686	−	0.939450i	$-0.611337\pi$
$601$	−10098.1	−0.685372	−0.342686	+	0.939450i	$0.611337\pi$
$602$	4727.92	0.320092
$603$	22169.9	1.49723
$604$	−94.5991	−0.00637282
$605$	0	0
$606$	0.0946106	6.34207e−6 0
$607$	−7040.21	−0.470764	−0.235382	−	0.971903i	$-0.575634\pi$
$607$	−7040.21	−0.470764	−0.235382	+	0.971903i	$0.575634\pi$
$608$	−1980.18	−0.132084
$609$	−4027.38	−0.267976
$610$	−1370.36	−0.0909578
$611$	1184.34	0.0784179
$612$	−14960.8	−0.988162
$613$	−8404.65	−0.553769	−0.276885	−	0.960903i	$-0.589302\pi$
$613$	−8404.65	−0.553769	−0.276885	+	0.960903i	$0.589302\pi$
$614$	1776.32	0.116753
$615$	−3911.41	−0.256461
$616$	0	0
$617$	−4043.19	−0.263813	−0.131906	−	0.991262i	$-0.542110\pi$
$617$	−4043.19	−0.263813	−0.131906	+	0.991262i	$0.542110\pi$
$618$	−111.410	−0.00725173
$619$	−15815.9	−1.02697	−0.513486	−	0.858098i	$-0.671646\pi$
$619$	−15815.9	−1.02697	−0.513486	+	0.858098i	$0.671646\pi$
$620$	−3661.00	−0.237144
$621$	−16.4821	−0.00106506
$622$	664.139	0.0428128
$623$	−1604.77	−0.103200
$624$	−553.045	−0.0354800
$625$	−18787.4	−1.20239
$626$	1974.82	0.126086
$627$	0	0
$628$	5691.74	0.361664
$629$	−19179.4	−1.21579
$630$	4064.23	0.257020
$631$	−2383.21	−0.150355	−0.0751777	−	0.997170i	$-0.523952\pi$
$631$	−2383.21	−0.150355	−0.0751777	+	0.997170i	$0.523952\pi$
$632$	657.118	0.0413588
$633$	2456.28	0.154231
$634$	−1201.89	−0.0752892
$635$	33145.5	2.07140
$636$	3636.14	0.226702
$637$	10724.1	0.667040
$638$	0	0
$639$	595.690	0.0368781
$640$	8915.29	0.550637
$641$	−8484.01	−0.522774	−0.261387	−	0.965234i	$-0.584180\pi$
$641$	−8484.01	−0.522774	−0.261387	+	0.965234i	$0.584180\pi$
$642$	26.4185	0.00162407
$643$	22333.6	1.36975	0.684876	−	0.728660i	$-0.259856\pi$
$643$	22333.6	1.36975	0.684876	+	0.728660i	$0.259856\pi$
$644$	120.795	0.00739127
$645$	4564.87	0.278669
$646$	747.349	0.0455171
$647$	14270.5	0.867127	0.433564	−	0.901123i	$-0.357256\pi$
$647$	14270.5	0.867127	0.433564	+	0.901123i	$0.357256\pi$
$648$	−3361.52	−0.203786
$649$	0	0
$650$	357.031	0.0215445
$651$	743.756	0.0447774
$652$	11687.6	0.702025
$653$	18905.3	1.13296	0.566480	−	0.824076i	$-0.308305\pi$
$653$	18905.3	1.13296	0.566480	+	0.824076i	$0.308305\pi$
$654$	93.8220	0.00560968
$655$	26466.9	1.57885
$656$	−23931.9	−1.42437
$657$	9066.37	0.538375
$658$	952.481	0.0564310
$659$	−26044.7	−1.53954	−0.769771	−	0.638320i	$-0.779630\pi$
$659$	−26044.7	−1.53954	−0.769771	+	0.638320i	$0.779630\pi$
$660$	0	0
$661$	−3995.86	−0.235130	−0.117565	−	0.993065i	$-0.537509\pi$
$661$	−3995.86	−0.235130	−0.117565	+	0.993065i	$0.537509\pi$
$662$	−715.735	−0.0420209
$663$	638.773	0.0374176
$664$	−2716.87	−0.158788
$665$	17151.3	1.00015
$666$	−2181.74	−0.126938
$667$	−76.4861	−0.00444011
$668$	−5184.51	−0.300291
$669$	−3300.12	−0.190717
$670$	3747.18	0.216069
$671$	0	0
$672$	−1361.16	−0.0781366
$673$	22260.2	1.27499	0.637493	−	0.770456i	$-0.279971\pi$
$673$	22260.2	1.27499	0.637493	+	0.770456i	$0.279971\pi$
$674$	416.115	0.0237806
$675$	3309.80	0.188732
$676$	−1336.18	−0.0760232
$677$	17406.9	0.988188	0.494094	−	0.869408i	$-0.335500\pi$
$677$	17406.9	0.988188	0.494094	+	0.869408i	$0.335500\pi$
$678$	435.345	0.0246598
$679$	−5428.25	−0.306800
$680$	−5087.31	−0.286896
$681$	1000.48	0.0562972
$682$	0	0
$683$	9089.96	0.509250	0.254625	−	0.967040i	$-0.418048\pi$
$683$	9089.96	0.509250	0.254625	+	0.967040i	$0.418048\pi$
$684$	−7181.94	−0.401474
$685$	−15147.0	−0.844871
$686$	5038.57	0.280428
$687$	2377.99	0.132061
$688$	27930.1	1.54771
$689$	8679.87	0.479937
$690$	−1.38056	−7.61698e−5 0
$691$	32723.1	1.80152	0.900758	−	0.434322i	$-0.143012\pi$
$691$	32723.1	1.80152	0.900758	+	0.434322i	$0.143012\pi$
$692$	30922.7	1.69870
$693$	0	0
$694$	−263.912	−0.0144351
$695$	−34102.4	−1.86126
$696$	573.457	0.0312311
$697$	27641.6	1.50215
$698$	−2377.22	−0.128910
$699$	1573.95	0.0851677
$700$	−24257.0	−1.30975
$701$	−19683.3	−1.06053	−0.530263	−	0.847833i	$-0.677907\pi$
$701$	−19683.3	−1.06053	−0.530263	+	0.847833i	$0.677907\pi$
$702$	146.626	0.00788325
$703$	−9207.08	−0.493957
$704$	0	0
$705$	919.635	0.0491283
$706$	2157.96	0.115037
$707$	−15.3441	−0.000816231 0
$708$	−1804.44	−0.0957839
$709$	−1882.05	−0.0996926	−0.0498463	−	0.998757i	$-0.515873\pi$
$709$	−1882.05	−0.0996926	−0.0498463	+	0.998757i	$0.515873\pi$
$710$	100.684	0.00532198
$711$	3581.96	0.188937
$712$	228.503	0.0120274
$713$	14.1251	0.000741919 0
$714$	513.719	0.0269264
$715$	0	0
$716$	884.658	0.0461749
$717$	2247.05	0.117040
$718$	1088.80	0.0565928
$719$	−27322.8	−1.41720	−0.708601	−	0.705609i	$-0.750673\pi$
$719$	−27322.8	−1.41720	−0.708601	+	0.705609i	$0.750673\pi$
$720$	24009.4	1.24274
$721$	18068.7	0.933306
$722$	−1739.57	−0.0896678
$723$	−4177.04	−0.214863
$724$	37753.6	1.93799
$725$	15359.3	0.786799
$726$	0	0
$727$	24485.6	1.24913	0.624567	−	0.780971i	$-0.285276\pi$
$727$	24485.6	1.24913	0.624567	+	0.780971i	$0.285276\pi$
$728$	−2161.91	−0.110063
$729$	−17638.1	−0.896107
$730$	1532.40	0.0776943
$731$	−32259.5	−1.63223
$732$	1664.57	0.0840493
$733$	32212.7	1.62320	0.811599	−	0.584215i	$-0.198598\pi$
$733$	32212.7	1.62320	0.811599	+	0.584215i	$0.198598\pi$
$734$	−2231.49	−0.112215
$735$	8327.21	0.417896
$736$	−25.8505	−0.00129465
$737$	0	0
$738$	3144.35	0.156836
$739$	−15419.1	−0.767525	−0.383762	−	0.923432i	$-0.625372\pi$
$739$	−15419.1	−0.767525	−0.383762	+	0.923432i	$0.625372\pi$
$740$	31152.6	1.54756
$741$	306.643	0.0152022
$742$	6980.60	0.345372
$743$	31968.4	1.57848	0.789238	−	0.614087i	$-0.210476\pi$
$743$	31968.4	1.57848	0.789238	+	0.614087i	$0.210476\pi$
$744$	−105.903	−0.00521854
$745$	32812.8	1.61365
$746$	872.810	0.0428363
$747$	−14809.7	−0.725381
$748$	0	0
$749$	−4284.59	−0.209020
$750$	−108.784	−0.00529631
$751$	−10809.5	−0.525224	−0.262612	−	0.964901i	$-0.584584\pi$
$751$	−10809.5	−0.525224	−0.262612	+	0.964901i	$0.584584\pi$
$752$	5626.77	0.272855
$753$	−4108.69	−0.198843
$754$	680.425	0.0328642
$755$	−175.347	−0.00845235
$756$	−9961.87	−0.479246
$757$	28992.8	1.39202	0.696011	−	0.718031i	$-0.254956\pi$
$757$	28992.8	1.39202	0.696011	+	0.718031i	$0.254956\pi$
$758$	−886.374	−0.0424730
$759$	0	0
$760$	−2442.16	−0.116561
$761$	−19344.2	−0.921456	−0.460728	−	0.887541i	$-0.652412\pi$
$761$	−19344.2	−0.921456	−0.460728	+	0.887541i	$0.652412\pi$
$762$	476.585	0.0226573
$763$	−15216.2	−0.721972
$764$	27649.9	1.30935
$765$	−27731.0	−1.31061
$766$	−3053.43	−0.144027
$767$	−4307.39	−0.202778
$768$	−2497.02	−0.117322
$769$	−13583.4	−0.636971	−0.318485	−	0.947928i	$-0.603174\pi$
$769$	−13583.4	−0.636971	−0.318485	+	0.947928i	$0.603174\pi$
$770$	0	0
$771$	−243.485	−0.0113734
$772$	19175.9	0.893986
$773$	11540.8	0.536991	0.268495	−	0.963281i	$-0.413474\pi$
$773$	11540.8	0.536991	0.268495	+	0.963281i	$0.413474\pi$
$774$	−3669.66	−0.170418
$775$	−2836.47	−0.131470
$776$	772.926	0.0357557
$777$	−6328.84	−0.292209
$778$	−3392.76	−0.156345
$779$	13269.3	0.610299
$780$	−1037.54	−0.0476281
$781$	0	0
$782$	9.75632	0.000446145 0
$783$	6307.76	0.287894
$784$	50949.9	2.32097
$785$	10550.1	0.479680
$786$	380.556	0.0172697
$787$	−18172.1	−0.823083	−0.411542	−	0.911391i	$-0.635009\pi$
$787$	−18172.1	−0.823083	−0.411542	+	0.911391i	$0.635009\pi$
$788$	17857.1	0.807277
$789$	2132.34	0.0962147
$790$	605.427	0.0272660
$791$	−70605.1	−3.17374
$792$	0	0
$793$	3973.50	0.177936
$794$	3696.49	0.165219
$795$	6739.88	0.300678
$796$	−26797.2	−1.19322
$797$	26306.5	1.16916	0.584582	−	0.811335i	$-0.301259\pi$
$797$	26306.5	1.16916	0.584582	+	0.811335i	$0.301259\pi$
$798$	246.611	0.0109398
$799$	−6498.97	−0.287756
$800$	5191.07	0.229415
$801$	1245.57	0.0549441
$802$	2829.13	0.124563
$803$	0	0
$804$	−4551.67	−0.199658
$805$	223.903	0.00980314
$806$	−125.657	−0.00549143
$807$	2203.20	0.0961043
$808$	2.18484	9.51269e−5 0
$809$	−3583.22	−0.155722	−0.0778612	−	0.996964i	$-0.524809\pi$
$809$	−3583.22	−0.155722	−0.0778612	+	0.996964i	$0.524809\pi$
$810$	−3097.09	−0.134347
$811$	−7797.73	−0.337627	−0.168813	−	0.985648i	$-0.553994\pi$
$811$	−7797.73	−0.337627	−0.168813	+	0.985648i	$0.553994\pi$
$812$	−46228.5	−1.99791
$813$	1477.80	0.0637501
$814$	0	0
$815$	21663.8	0.931105
$816$	3034.79	0.130195
$817$	−15486.2	−0.663149
$818$	1265.88	0.0541083
$819$	−11784.6	−0.502795
$820$	−44897.4	−1.91206
$821$	−14347.6	−0.609910	−0.304955	−	0.952367i	$-0.598641\pi$
$821$	−14347.6	−0.609910	−0.304955	+	0.952367i	$0.598641\pi$
$822$	−217.792	−0.00924132
$823$	18701.5	0.792094	0.396047	−	0.918230i	$-0.370382\pi$
$823$	18701.5	0.792094	0.396047	+	0.918230i	$0.370382\pi$
$824$	−2572.79	−0.108771
$825$	0	0
$826$	−3464.13	−0.145923
$827$	23452.6	0.986129	0.493064	−	0.869993i	$-0.335877\pi$
$827$	23452.6	0.986129	0.493064	+	0.869993i	$0.335877\pi$
$828$	−93.7571	−0.00393512
$829$	−45997.8	−1.92710	−0.963552	−	0.267523i	$-0.913795\pi$
$829$	−45997.8	−1.92710	−0.963552	+	0.267523i	$0.913795\pi$
$830$	−2503.15	−0.104682
$831$	−2462.09	−0.102779
$832$	−6193.34	−0.258072
$833$	−58847.6	−2.44772
$834$	−490.344	−0.0203588
$835$	−9609.89	−0.398280
$836$	0	0
$837$	−1164.89	−0.0481055
$838$	62.2252	0.00256508
$839$	25300.8	1.04110	0.520549	−	0.853832i	$-0.325727\pi$
$839$	25300.8	1.04110	0.520549	+	0.853832i	$0.325727\pi$
$840$	−1678.72	−0.0689538
$841$	4882.46	0.200191
$842$	2144.03	0.0877531
$843$	5724.68	0.233889
$844$	28194.6	1.14988
$845$	−2476.72	−0.100831
$846$	−739.286	−0.0300439
$847$	0	0
$848$	41237.8	1.66994
$849$	−5809.88	−0.234858
$850$	−1959.18	−0.0790580
$851$	−120.194	−0.00484161
$852$	−122.300	−0.00491776
$853$	6318.70	0.253632	0.126816	−	0.991926i	$-0.459524\pi$
$853$	6318.70	0.253632	0.126816	+	0.991926i	$0.459524\pi$
$854$	3195.60	0.128046
$855$	−13312.3	−0.532480
$856$	610.081	0.0243600
$857$	4103.08	0.163545	0.0817727	−	0.996651i	$-0.473942\pi$
$857$	4103.08	0.163545	0.0817727	+	0.996651i	$0.473942\pi$
$858$	0	0
$859$	13794.1	0.547903	0.273952	−	0.961743i	$-0.411669\pi$
$859$	13794.1	0.547903	0.273952	+	0.961743i	$0.411669\pi$
$860$	52398.2	2.07763
$861$	9121.20	0.361033
$862$	−2677.41	−0.105792
$863$	−38958.4	−1.53669	−0.768343	−	0.640038i	$-0.778918\pi$
$863$	−38958.4	−1.53669	−0.768343	+	0.640038i	$0.778918\pi$
$864$	2131.87	0.0839442
$865$	57317.6	2.25301
$866$	−2599.59	−0.102007
$867$	−121.149	−0.00474561
$868$	8537.26	0.333840
$869$	0	0
$870$	528.346	0.0205892
$871$	−10865.3	−0.422684
$872$	2166.63	0.0841415
$873$	4213.24	0.163341
$874$	4.68352	0.000181261 0
$875$	17642.8	0.681641
$876$	−1861.40	−0.0717933
$877$	−26250.6	−1.01074	−0.505371	−	0.862902i	$-0.668644\pi$
$877$	−26250.6	−1.01074	−0.505371	+	0.862902i	$0.668644\pi$
$878$	−1964.98	−0.0755296
$879$	−3515.51	−0.134898
$880$	0	0
$881$	−25051.6	−0.958013	−0.479007	−	0.877811i	$-0.659003\pi$
$881$	−25051.6	−0.958013	−0.479007	+	0.877811i	$0.659003\pi$
$882$	−6694.16	−0.255560
$883$	8742.61	0.333196	0.166598	−	0.986025i	$-0.446722\pi$
$883$	8742.61	0.333196	0.166598	+	0.986025i	$0.446722\pi$
$884$	7332.20	0.278969
$885$	−3344.67	−0.127039
$886$	−873.146	−0.0331082
$887$	10536.1	0.398837	0.199418	−	0.979914i	$-0.436095\pi$
$887$	10536.1	0.398837	0.199418	+	0.979914i	$0.436095\pi$
$888$	901.161	0.0340552
$889$	−77293.5	−2.91602
$890$	210.528	0.00792912
$891$	0	0
$892$	−37880.6	−1.42190
$893$	−3119.83	−0.116911
$894$	471.801	0.0176503
$895$	1639.78	0.0612423
$896$	−20789.9	−0.775160
$897$	4.00309	0.000149007 0
$898$	1382.76	0.0513845
$899$	−5405.71	−0.200546
$900$	18827.5	0.697314
$901$	−47630.1	−1.76114
$902$	0	0
$903$	−10645.0	−0.392297
$904$	10053.4	0.369881
$905$	69979.3	2.57038
$906$	−2.52124	−9.24531e−5 0
$907$	−28350.6	−1.03789	−0.518945	−	0.854808i	$-0.673675\pi$
$907$	−28350.6	−1.03789	−0.518945	+	0.854808i	$0.673675\pi$
$908$	11484.1	0.419727
$909$	11.9096	0.000434563 0
$910$	−1991.85	−0.0725596
$911$	22306.3	0.811242	0.405621	−	0.914041i	$-0.367055\pi$
$911$	22306.3	0.811242	0.405621	+	0.914041i	$0.367055\pi$
$912$	1456.85	0.0528960
$913$	0	0
$914$	−2588.98	−0.0936934
$915$	3085.40	0.111476
$916$	27296.0	0.984590
$917$	−61719.4	−2.22263
$918$	−804.597	−0.0289277
$919$	−26178.9	−0.939676	−0.469838	−	0.882753i	$-0.655688\pi$
$919$	−26178.9	−0.939676	−0.469838	+	0.882753i	$0.655688\pi$
$920$	−31.8814	−0.00114250
$921$	−3999.43	−0.143090
$922$	−1766.48	−0.0630975
$923$	−291.944	−0.0104111
$924$	0	0
$925$	24136.4	0.857946
$926$	4117.47	0.146122
$927$	−14024.4	−0.496893
$928$	9893.05	0.349952
$929$	−41492.7	−1.46537	−0.732686	−	0.680566i	$-0.761734\pi$
$929$	−41492.7	−1.46537	−0.732686	+	0.680566i	$0.761734\pi$
$930$	−97.5724	−0.00344035
$931$	−28249.8	−0.994467
$932$	18066.7	0.634972
$933$	−1495.33	−0.0524703
$934$	−4501.87	−0.157715
$935$	0	0
$936$	1678.01	0.0585977
$937$	−31458.3	−1.09679	−0.548397	−	0.836218i	$-0.684762\pi$
$937$	−31458.3	−1.09679	−0.548397	+	0.836218i	$0.684762\pi$
$938$	−8738.21	−0.304171
$939$	−4446.36	−0.154528
$940$	10556.1	0.366279
$941$	−17257.1	−0.597837	−0.298919	−	0.954279i	$-0.596626\pi$
$941$	−17257.1	−0.597837	−0.298919	+	0.954279i	$0.596626\pi$
$942$	151.695	0.00524681
$943$	173.225	0.00598197
$944$	−20464.3	−0.705568
$945$	−18465.1	−0.635630
$946$	0	0
$947$	−44293.2	−1.51989	−0.759946	−	0.649987i	$-0.774774\pi$
$947$	−44293.2	−1.51989	−0.759946	+	0.649987i	$0.774774\pi$
$948$	−735.407	−0.0251951
$949$	−4443.37	−0.151989
$950$	−940.504	−0.0321200
$951$	2706.10	0.0922726
$952$	11863.3	0.403879
$953$	45913.5	1.56063	0.780317	−	0.625384i	$-0.215058\pi$
$953$	45913.5	1.56063	0.780317	+	0.625384i	$0.215058\pi$
$954$	−5418.12	−0.183877
$955$	51251.3	1.73660
$956$	25792.9	0.872595
$957$	0	0
$958$	−2055.60	−0.0693251
$959$	35321.9	1.18937
$960$	−4809.10	−0.161680
$961$	−28792.7	−0.966490
$962$	1069.26	0.0358360
$963$	3325.57	0.111282
$964$	−47946.4	−1.60192
$965$	35544.1	1.18571
$966$	3.21940	0.000107228 0
$967$	−18404.6	−0.612050	−0.306025	−	0.952023i	$-0.598999\pi$
$967$	−18404.6	−0.612050	−0.306025	+	0.952023i	$0.598999\pi$
$968$	0	0
$969$	−1682.68	−0.0557847
$970$	712.125	0.0235721
$971$	17632.1	0.582741	0.291370	−	0.956610i	$-0.405889\pi$
$971$	17632.1	0.582741	0.291370	+	0.956610i	$0.405889\pi$
$972$	11632.4	0.383857
$973$	79524.8	2.62019
$974$	2155.70	0.0709170
$975$	−803.866	−0.0264044
$976$	18878.0	0.619128
$977$	2400.97	0.0786220	0.0393110	−	0.999227i	$-0.487484\pi$
$977$	2400.97	0.0786220	0.0393110	+	0.999227i	$0.487484\pi$
$978$	311.495	0.0101846
$979$	0	0
$980$	95584.4	3.11565
$981$	11810.4	0.384379
$982$	2728.33	0.0886605
$983$	655.628	0.0212729	0.0106365	−	0.999943i	$-0.496614\pi$
$983$	655.628	0.0212729	0.0106365	+	0.999943i	$0.496614\pi$
$984$	−1298.76	−0.0420763
$985$	33099.6	1.07070
$986$	−3733.77	−0.120596
$987$	−2144.54	−0.0691605
$988$	3519.82	0.113340
$989$	−202.165	−0.00649999
$990$	0	0
$991$	−35827.9	−1.14845	−0.574224	−	0.818698i	$-0.694696\pi$
$991$	−35827.9	−1.14845	−0.574224	+	0.818698i	$0.694696\pi$
$992$	−1827.00	−0.0584751
$993$	1611.50	0.0514998
$994$	−234.790	−0.00749202
$995$	−49670.8	−1.58258
$996$	3040.56	0.0967308
$997$	−45335.2	−1.44010	−0.720050	−	0.693922i	$-0.755881\pi$
$997$	−45335.2	−1.44010	−0.720050	+	0.693922i	$0.755881\pi$
$998$	−6422.98	−0.203723
$999$	9912.36	0.313927

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1573.4.a.o.1.18		34
11.3	even	5		143.4.h.a.53.9	yes	68
11.4	even	5		143.4.h.a.27.9	✓	68
11.10	odd	2		1573.4.a.p.1.17		34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.h.a.27.9	✓	68	11.4	even	5
143.4.h.a.53.9	yes	68	11.3	even	5
1573.4.a.o.1.18		34	1.1	even	1	trivial
1573.4.a.p.1.17		34	11.10	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:	\( N \)	\(=\)	\( 1573 = 11^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1573.a (trivial)

\(f(q)\)	\(=\)	\(q+0.305925 q^{2} -0.688798 q^{3} -7.90641 q^{4} -14.6552 q^{5} -0.210720 q^{6} +34.1750 q^{7} -4.86616 q^{8} -26.5256 q^{9} +O(q^{10})\)	\(q+0.305925 q^{2} -0.688798 q^{3} -7.90641 q^{4} -14.6552 q^{5} -0.210720 q^{6} +34.1750 q^{7} -4.86616 q^{8} -26.5256 q^{9} -4.48337 q^{10} +5.44592 q^{12} +13.0000 q^{13} +10.4550 q^{14} +10.0944 q^{15} +61.7626 q^{16} -71.3364 q^{17} -8.11482 q^{18} -34.2450 q^{19} +115.870 q^{20} -23.5397 q^{21} -0.447054 q^{23} +3.35180 q^{24} +89.7736 q^{25} +3.97702 q^{26} +36.8683 q^{27} -270.202 q^{28} +171.089 q^{29} +3.08814 q^{30} -31.5959 q^{31} +57.8240 q^{32} -21.8236 q^{34} -500.840 q^{35} +209.722 q^{36} +268.859 q^{37} -10.4764 q^{38} -8.95437 q^{39} +71.3144 q^{40} -387.482 q^{41} -7.20136 q^{42} +452.217 q^{43} +388.736 q^{45} -0.136765 q^{46} +91.1032 q^{47} -42.5419 q^{48} +824.931 q^{49} +27.4639 q^{50} +49.1364 q^{51} -102.783 q^{52} +667.682 q^{53} +11.2789 q^{54} -166.301 q^{56} +23.5879 q^{57} +52.3404 q^{58} -331.338 q^{59} -79.8108 q^{60} +305.654 q^{61} -9.66596 q^{62} -906.511 q^{63} -476.411 q^{64} -190.517 q^{65} -835.795 q^{67} +564.015 q^{68} +0.307930 q^{69} -153.219 q^{70} -22.4572 q^{71} +129.078 q^{72} -341.797 q^{73} +82.2505 q^{74} -61.8358 q^{75} +270.755 q^{76} -2.73936 q^{78} -135.038 q^{79} -905.140 q^{80} +690.795 q^{81} -118.540 q^{82} +558.319 q^{83} +186.114 q^{84} +1045.45 q^{85} +138.344 q^{86} -117.846 q^{87} -46.9575 q^{89} +118.924 q^{90} +444.275 q^{91} +3.53459 q^{92} +21.7632 q^{93} +27.8707 q^{94} +501.866 q^{95} -39.8290 q^{96} -158.837 q^{97} +252.367 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 3 q^{2} - 29 q^{3} + 97 q^{4} - 28 q^{5} + 36 q^{6} - 36 q^{7} - 57 q^{8} + 265 q^{9}+O(q^{10}) \) 34 * q - 3 * q^2 - 29 * q^3 + 97 * q^4 - 28 * q^5 + 36 * q^6 - 36 * q^7 - 57 * q^8 + 265 * q^9	\( 34 q - 3 q^{2} - 29 q^{3} + 97 q^{4} - 28 q^{5} + 36 q^{6} - 36 q^{7} - 57 q^{8} + 265 q^{9} - 18 q^{10} - 262 q^{12} + 442 q^{13} - 231 q^{14} - 196 q^{15} + 225 q^{16} - 209 q^{17} - 190 q^{18} - 107 q^{19} - 211 q^{20} - 68 q^{21} - 632 q^{23} + 152 q^{24} + 296 q^{25} - 39 q^{26} - 920 q^{27} - 931 q^{28} - 32 q^{29} - 300 q^{30} - 290 q^{31} + 876 q^{32} - 602 q^{34} + 104 q^{35} - 611 q^{36} - 656 q^{37} - 1361 q^{38} - 377 q^{39} + 1159 q^{40} - 1121 q^{41} + 79 q^{42} + 349 q^{43} - 1024 q^{45} + 490 q^{46} - 1608 q^{47} - 1827 q^{48} + 808 q^{49} - 1322 q^{50} + 1414 q^{51} + 1261 q^{52} - 2608 q^{53} + 3131 q^{54} - 1675 q^{56} - 2150 q^{57} - 1673 q^{58} - 2011 q^{59} - 201 q^{60} - 236 q^{61} + 1396 q^{62} + 1206 q^{63} + 1331 q^{64} - 364 q^{65} - 3213 q^{67} - 1321 q^{68} - 162 q^{69} + 174 q^{70} - 3756 q^{71} - 5074 q^{72} + 823 q^{73} + 2550 q^{74} - 3063 q^{75} + 2004 q^{76} + 468 q^{78} - 2120 q^{79} - 5005 q^{80} + 710 q^{81} - 2534 q^{82} - 3843 q^{83} + 7191 q^{84} + 1582 q^{85} - 3542 q^{86} + 962 q^{87} - 3633 q^{89} - 995 q^{90} - 468 q^{91} - 2072 q^{92} - 508 q^{93} - 6309 q^{94} + 1916 q^{95} - 2150 q^{96} + 1195 q^{97} - 1487 q^{98}+O(q^{100}) \) 34 * q - 3 * q^2 - 29 * q^3 + 97 * q^4 - 28 * q^5 + 36 * q^6 - 36 * q^7 - 57 * q^8 + 265 * q^9 - 18 * q^10 - 262 * q^12 + 442 * q^13 - 231 * q^14 - 196 * q^15 + 225 * q^16 - 209 * q^17 - 190 * q^18 - 107 * q^19 - 211 * q^20 - 68 * q^21 - 632 * q^23 + 152 * q^24 + 296 * q^25 - 39 * q^26 - 920 * q^27 - 931 * q^28 - 32 * q^29 - 300 * q^30 - 290 * q^31 + 876 * q^32 - 602 * q^34 + 104 * q^35 - 611 * q^36 - 656 * q^37 - 1361 * q^38 - 377 * q^39 + 1159 * q^40 - 1121 * q^41 + 79 * q^42 + 349 * q^43 - 1024 * q^45 + 490 * q^46 - 1608 * q^47 - 1827 * q^48 + 808 * q^49 - 1322 * q^50 + 1414 * q^51 + 1261 * q^52 - 2608 * q^53 + 3131 * q^54 - 1675 * q^56 - 2150 * q^57 - 1673 * q^58 - 2011 * q^59 - 201 * q^60 - 236 * q^61 + 1396 * q^62 + 1206 * q^63 + 1331 * q^64 - 364 * q^65 - 3213 * q^67 - 1321 * q^68 - 162 * q^69 + 174 * q^70 - 3756 * q^71 - 5074 * q^72 + 823 * q^73 + 2550 * q^74 - 3063 * q^75 + 2004 * q^76 + 468 * q^78 - 2120 * q^79 - 5005 * q^80 + 710 * q^81 - 2534 * q^82 - 3843 * q^83 + 7191 * q^84 + 1582 * q^85 - 3542 * q^86 + 962 * q^87 - 3633 * q^89 - 995 * q^90 - 468 * q^91 - 2072 * q^92 - 508 * q^93 - 6309 * q^94 + 1916 * q^95 - 2150 * q^96 + 1195 * q^97 - 1487 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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