LMFDB - Embedded newform 1573.4.a.o.1.14

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			1.14
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)

$f(q)$	$=$	$q-1.32200 q^{2} -9.29623 q^{3} -6.25232 q^{4} +6.03321 q^{5} +12.2896 q^{6} +36.0288 q^{7} +18.8415 q^{8} +59.4199 q^{9} +O(q^{10})$	\(q-1.32200 q^{2} -9.29623 q^{3} -6.25232 q^{4} +6.03321 q^{5} +12.2896 q^{6} +36.0288 q^{7} +18.8415 q^{8} +59.4199 q^{9} -7.97590 q^{10} +58.1230 q^{12} +13.0000 q^{13} -47.6300 q^{14} -56.0861 q^{15} +25.1101 q^{16} -6.59643 q^{17} -78.5530 q^{18} +88.7605 q^{19} -37.7216 q^{20} -334.932 q^{21} -61.7837 q^{23} -175.155 q^{24} -88.6003 q^{25} -17.1860 q^{26} -301.383 q^{27} -225.263 q^{28} -117.859 q^{29} +74.1458 q^{30} -78.4956 q^{31} -183.928 q^{32} +8.72047 q^{34} +217.369 q^{35} -371.512 q^{36} +376.305 q^{37} -117.341 q^{38} -120.851 q^{39} +113.675 q^{40} -400.726 q^{41} +442.779 q^{42} -428.122 q^{43} +358.493 q^{45} +81.6780 q^{46} +37.5800 q^{47} -233.429 q^{48} +955.072 q^{49} +117.129 q^{50} +61.3219 q^{51} -81.2802 q^{52} -253.387 q^{53} +398.428 q^{54} +678.838 q^{56} -825.138 q^{57} +155.810 q^{58} +527.766 q^{59} +350.669 q^{60} +84.3733 q^{61} +103.771 q^{62} +2140.83 q^{63} +42.2716 q^{64} +78.4318 q^{65} -513.409 q^{67} +41.2430 q^{68} +574.356 q^{69} -287.362 q^{70} -588.189 q^{71} +1119.56 q^{72} +237.358 q^{73} -497.474 q^{74} +823.649 q^{75} -554.959 q^{76} +159.765 q^{78} -286.242 q^{79} +151.494 q^{80} +1197.39 q^{81} +529.759 q^{82} -1174.54 q^{83} +2094.10 q^{84} -39.7977 q^{85} +565.977 q^{86} +1095.65 q^{87} -1451.96 q^{89} -473.927 q^{90} +468.374 q^{91} +386.292 q^{92} +729.713 q^{93} -49.6806 q^{94} +535.511 q^{95} +1709.84 q^{96} +247.047 q^{97} -1262.60 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.32200	−0.467397	−0.233698	−	0.972309i	$-0.575083\pi$
$2$	−1.32200	−0.467397	−0.233698	+	0.972309i	$0.575083\pi$
$3$	−9.29623	−1.78906	−0.894530	−	0.447007i	$-0.852490\pi$
$3$	−9.29623	−1.78906	−0.894530	+	0.447007i	$0.852490\pi$
$4$	−6.25232	−0.781540
$5$	6.03321	0.539627	0.269813	−	0.962913i	$-0.413038\pi$
$5$	6.03321	0.539627	0.269813	+	0.962913i	$0.413038\pi$
$6$	12.2896	0.836201
$7$	36.0288	1.94537	0.972685	−	0.232128i	$-0.0745688\pi$
$7$	36.0288	1.94537	0.972685	+	0.232128i	$0.0745688\pi$
$8$	18.8415	0.832686
$9$	59.4199	2.20074
$10$	−7.97590	−0.252220
$11$	0	0
$11$	0	0
$12$	58.1230	1.39822
$13$	13.0000	0.277350
$13$	13.0000	0.277350
$14$	−47.6300	−0.909260
$15$	−56.0861	−0.965425
$16$	25.1101	0.392345
$17$	−6.59643	−0.0941099	−0.0470550	−	0.998892i	$-0.514984\pi$
$17$	−6.59643	−0.0941099	−0.0470550	+	0.998892i	$0.514984\pi$
$18$	−78.5530	−1.02862
$19$	88.7605	1.07174	0.535870	−	0.844301i	$-0.319984\pi$
$19$	88.7605	1.07174	0.535870	+	0.844301i	$0.319984\pi$
$20$	−37.7216	−0.421740
$21$	−334.932	−3.48039
$22$	0	0
$23$	−61.7837	−0.560122	−0.280061	−	0.959982i	$-0.590355\pi$
$23$	−61.7837	−0.560122	−0.280061	+	0.959982i	$0.590355\pi$
$24$	−175.155	−1.48973
$25$	−88.6003	−0.708803
$26$	−17.1860	−0.129633
$27$	−301.383	−2.14819
$28$	−225.263	−1.52039
$29$	−117.859	−0.754687	−0.377344	−	0.926073i	$-0.623162\pi$
$29$	−117.859	−0.754687	−0.377344	+	0.926073i	$0.623162\pi$
$30$	74.1458	0.451237
$31$	−78.4956	−0.454782	−0.227391	−	0.973804i	$-0.573019\pi$
$31$	−78.4956	−0.454782	−0.227391	+	0.973804i	$0.573019\pi$
$32$	−183.928	−1.01607
$33$	0	0
$34$	8.72047	0.0439867
$35$	217.369	1.04977
$36$	−371.512	−1.71996
$37$	376.305	1.67200	0.836001	−	0.548727i	$-0.184887\pi$
$37$	376.305	1.67200	0.836001	+	0.548727i	$0.184887\pi$
$38$	−117.341	−0.500928
$39$	−120.851	−0.496196
$40$	113.675	0.449340
$41$	−400.726	−1.52641	−0.763205	−	0.646156i	$-0.776375\pi$
$41$	−400.726	−1.52641	−0.763205	+	0.646156i	$0.776375\pi$
$42$	442.779	1.62672
$43$	−428.122	−1.51833	−0.759163	−	0.650900i	$-0.774392\pi$
$43$	−428.122	−1.51833	−0.759163	+	0.650900i	$0.774392\pi$
$44$	0	0
$45$	358.493	1.18758
$46$	81.6780	0.261799
$47$	37.5800	0.116630	0.0583149	−	0.998298i	$-0.481427\pi$
$47$	37.5800	0.116630	0.0583149	+	0.998298i	$0.481427\pi$
$48$	−233.429	−0.701929
$49$	955.072	2.78447
$50$	117.129	0.331292
$51$	61.3219	0.168368
$52$	−81.2802	−0.216760
$53$	−253.387	−0.656704	−0.328352	−	0.944555i	$-0.606493\pi$
$53$	−253.387	−0.656704	−0.328352	+	0.944555i	$0.606493\pi$
$54$	398.428	1.00406
$55$	0	0
$56$	678.838	1.61988
$57$	−825.138	−1.91741
$58$	155.810	0.352739
$59$	527.766	1.16456	0.582282	−	0.812987i	$-0.302160\pi$
$59$	527.766	1.16456	0.582282	+	0.812987i	$0.302160\pi$
$60$	350.669	0.754519
$61$	84.3733	0.177097	0.0885483	−	0.996072i	$-0.471777\pi$
$61$	84.3733	0.177097	0.0885483	+	0.996072i	$0.471777\pi$
$62$	103.771	0.212564
$63$	2140.83	4.28125
$64$	42.2716	0.0825617
$65$	78.4318	0.149666
$66$	0	0
$67$	−513.409	−0.936163	−0.468081	−	0.883685i	$-0.655055\pi$
$67$	−513.409	−0.936163	−0.468081	+	0.883685i	$0.655055\pi$
$68$	41.2430	0.0735507
$69$	574.356	1.00209
$70$	−287.362	−0.490661
$71$	−588.189	−0.983171	−0.491586	−	0.870829i	$-0.663583\pi$
$71$	−588.189	−0.983171	−0.491586	+	0.870829i	$0.663583\pi$
$72$	1119.56	1.83252
$73$	237.358	0.380557	0.190279	−	0.981730i	$-0.439061\pi$
$73$	237.358	0.380557	0.190279	+	0.981730i	$0.439061\pi$
$74$	−497.474	−0.781489
$75$	823.649	1.26809
$76$	−554.959	−0.837608
$77$	0	0
$78$	159.765	0.231921
$79$	−286.242	−0.407655	−0.203828	−	0.979007i	$-0.565338\pi$
$79$	−286.242	−0.407655	−0.203828	+	0.979007i	$0.565338\pi$
$80$	151.494	0.211720
$81$	1197.39	1.64251
$82$	529.759	0.713440
$83$	−1174.54	−1.55328	−0.776641	−	0.629943i	$-0.783078\pi$
$83$	−1174.54	−1.55328	−0.776641	+	0.629943i	$0.783078\pi$
$84$	2094.10	2.72006
$85$	−39.7977	−0.0507843
$86$	565.977	0.709661
$87$	1095.65	1.35018
$88$	0	0
$89$	−1451.96	−1.72930	−0.864650	−	0.502375i	$-0.832460\pi$
$89$	−1451.96	−1.72930	−0.864650	+	0.502375i	$0.832460\pi$
$90$	−473.927	−0.555070
$91$	468.374	0.539549
$92$	386.292	0.437757
$93$	729.713	0.813632
$94$	−49.6806	−0.0545124
$95$	535.511	0.578340
$96$	1709.84	1.81781
$97$	247.047	0.258596	0.129298	−	0.991606i	$-0.458728\pi$
$97$	247.047	0.258596	0.129298	+	0.991606i	$0.458728\pi$
$98$	−1262.60	−1.30145
$99$	0	0
$100$	553.958	0.553958
$101$	−955.863	−0.941702	−0.470851	−	0.882213i	$-0.656053\pi$
$101$	−955.863	−0.941702	−0.470851	+	0.882213i	$0.656053\pi$
$102$	−81.0675	−0.0786948
$103$	−92.5846	−0.0885692	−0.0442846	−	0.999019i	$-0.514101\pi$
$103$	−92.5846	−0.0885692	−0.0442846	+	0.999019i	$0.514101\pi$
$104$	244.940	0.230946
$105$	−2020.71	−1.87811
$106$	334.977	0.306942
$107$	700.092	0.632527	0.316264	−	0.948671i	$-0.397572\pi$
$107$	700.092	0.632527	0.316264	+	0.948671i	$0.397572\pi$
$108$	1884.34	1.67890
$109$	−114.626	−0.100726	−0.0503630	−	0.998731i	$-0.516038\pi$
$109$	−114.626	−0.100726	−0.0503630	+	0.998731i	$0.516038\pi$
$110$	0	0
$111$	−3498.21	−2.99131
$112$	904.685	0.763256
$113$	477.005	0.397105	0.198553	−	0.980090i	$-0.436376\pi$
$113$	477.005	0.397105	0.198553	+	0.980090i	$0.436376\pi$
$114$	1090.83	0.896190
$115$	−372.754	−0.302257
$116$	736.894	0.589818
$117$	772.459	0.610375
$118$	−697.706	−0.544314
$119$	−237.661	−0.183079
$120$	−1056.75	−0.803897
$121$	0	0
$122$	−111.541	−0.0827744
$123$	3725.24	2.73084
$124$	490.780	0.355430
$125$	−1288.70	−0.922116
$126$	−2830.17	−2.00104
$127$	1131.87	0.790844	0.395422	−	0.918500i	$-0.370598\pi$
$127$	1131.87	0.790844	0.395422	+	0.918500i	$0.370598\pi$
$128$	1415.54	0.977478
$129$	3979.92	2.71638
$130$	−103.687	−0.0699532
$131$	−1307.33	−0.871926	−0.435963	−	0.899965i	$-0.643592\pi$
$131$	−1307.33	−0.871926	−0.435963	+	0.899965i	$0.643592\pi$
$132$	0	0
$133$	3197.93	2.08493
$134$	678.726	0.437560
$135$	−1818.31	−1.15922
$136$	−124.287	−0.0783641
$137$	338.883	0.211334	0.105667	−	0.994402i	$-0.466302\pi$
$137$	338.883	0.211334	0.105667	+	0.994402i	$0.466302\pi$
$138$	−759.297	−0.468374
$139$	1306.19	0.797047	0.398524	−	0.917158i	$-0.369523\pi$
$139$	1306.19	0.797047	0.398524	+	0.917158i	$0.369523\pi$
$140$	−1359.06	−0.820441
$141$	−349.352	−0.208658
$142$	777.584	0.459531
$143$	0	0
$144$	1492.04	0.863448
$145$	−711.071	−0.407250
$146$	−313.787	−0.177871
$147$	−8878.57	−4.98158
$148$	−2352.78	−1.30674
$149$	−1528.74	−0.840534	−0.420267	−	0.907401i	$-0.638064\pi$
$149$	−1528.74	−0.840534	−0.420267	+	0.907401i	$0.638064\pi$
$150$	−1088.86	−0.592702
$151$	−74.2771	−0.0400304	−0.0200152	−	0.999800i	$-0.506371\pi$
$151$	−74.2771	−0.0400304	−0.0200152	+	0.999800i	$0.506371\pi$
$152$	1672.38	0.892423
$153$	−391.959	−0.207111
$154$	0	0
$155$	−473.581	−0.245412
$156$	755.599	0.387797
$157$	−2119.17	−1.07725	−0.538626	−	0.842545i	$-0.681056\pi$
$157$	−2119.17	−1.07725	−0.538626	+	0.842545i	$0.681056\pi$
$158$	378.412	0.190537
$159$	2355.54	1.17488
$160$	−1109.68	−0.548297
$161$	−2225.99	−1.08964
$162$	−1582.95	−0.767703
$163$	−3094.29	−1.48689	−0.743447	−	0.668795i	$-0.766810\pi$
$163$	−3094.29	−1.48689	−0.743447	+	0.668795i	$0.766810\pi$
$164$	2505.47	1.19295
$165$	0	0
$166$	1552.74	0.725999
$167$	122.613	0.0568148	0.0284074	−	0.999596i	$-0.490956\pi$
$167$	122.613	0.0568148	0.0284074	+	0.999596i	$0.490956\pi$
$168$	−6310.63	−2.89807
$169$	169.000	0.0769231
$170$	52.6124	0.0237364
$171$	5274.14	2.35862
$172$	2676.76	1.18663
$173$	−2460.79	−1.08145	−0.540724	−	0.841200i	$-0.681850\pi$
$173$	−2460.79	−1.08145	−0.540724	+	0.841200i	$0.681850\pi$
$174$	−1448.44	−0.631071
$175$	−3192.16	−1.37888
$176$	0	0
$177$	−4906.24	−2.08348
$178$	1919.49	0.808269
$179$	1577.24	0.658594	0.329297	−	0.944226i	$-0.393188\pi$
$179$	1577.24	0.658594	0.329297	+	0.944226i	$0.393188\pi$
$180$	−2241.41	−0.928139
$181$	−2047.09	−0.840657	−0.420328	−	0.907372i	$-0.638085\pi$
$181$	−2047.09	−0.840657	−0.420328	+	0.907372i	$0.638085\pi$
$182$	−619.190	−0.252183
$183$	−784.353	−0.316836
$184$	−1164.10	−0.466406
$185$	2270.33	0.902258
$186$	−964.680	−0.380289
$187$	0	0
$188$	−234.962	−0.0911509
$189$	−10858.5	−4.17903
$190$	−707.945	−0.270314
$191$	−364.808	−0.138202	−0.0691011	−	0.997610i	$-0.522013\pi$
$191$	−364.808	−0.138202	−0.0691011	+	0.997610i	$0.522013\pi$
$192$	−392.966	−0.147708
$193$	1080.00	0.402797	0.201398	−	0.979509i	$-0.435451\pi$
$193$	1080.00	0.402797	0.201398	+	0.979509i	$0.435451\pi$
$194$	−326.595	−0.120867
$195$	−729.120	−0.267761
$196$	−5971.42	−2.17617
$197$	1266.01	0.457866	0.228933	−	0.973442i	$-0.426476\pi$
$197$	1266.01	0.457866	0.228933	+	0.973442i	$0.426476\pi$
$198$	0	0
$199$	2231.51	0.794912	0.397456	−	0.917621i	$-0.369893\pi$
$199$	2231.51	0.794912	0.397456	+	0.917621i	$0.369893\pi$
$200$	−1669.37	−0.590210
$201$	4772.77	1.67485
$202$	1263.65	0.440149
$203$	−4246.33	−1.46815
$204$	−383.404	−0.131587
$205$	−2417.66	−0.823692
$206$	122.397	0.0413970
$207$	−3671.18	−1.23268
$208$	326.431	0.108817
$209$	0	0
$210$	2671.38	0.877823
$211$	−927.966	−0.302767	−0.151384	−	0.988475i	$-0.548373\pi$
$211$	−927.966	−0.302767	−0.151384	+	0.988475i	$0.548373\pi$
$212$	1584.25	0.513241
$213$	5467.94	1.75895
$214$	−925.520	−0.295641
$215$	−2582.95	−0.819330
$216$	−5678.52	−1.78877
$217$	−2828.10	−0.884719
$218$	151.535	0.0470790
$219$	−2206.54	−0.680840
$220$	0	0
$221$	−85.7536	−0.0261014
$222$	4624.63	1.39813
$223$	−1020.49	−0.306443	−0.153221	−	0.988192i	$-0.548965\pi$
$223$	−1020.49	−0.306443	−0.153221	+	0.988192i	$0.548965\pi$
$224$	−6626.69	−1.97663
$225$	−5264.62	−1.55989
$226$	−630.600	−0.185606
$227$	−1666.25	−0.487192	−0.243596	−	0.969877i	$-0.578327\pi$
$227$	−1666.25	−0.487192	−0.243596	+	0.969877i	$0.578327\pi$
$228$	5159.03	1.49853
$229$	2760.09	0.796472	0.398236	−	0.917283i	$-0.369623\pi$
$229$	2760.09	0.796472	0.398236	+	0.917283i	$0.369623\pi$
$230$	492.781	0.141274
$231$	0	0
$232$	−2220.65	−0.628418
$233$	1576.29	0.443203	0.221602	−	0.975137i	$-0.428872\pi$
$233$	1576.29	0.443203	0.221602	+	0.975137i	$0.428872\pi$
$234$	−1021.19	−0.285287
$235$	226.728	0.0629366
$236$	−3299.76	−0.910154
$237$	2660.97	0.729320
$238$	314.188	0.0855704
$239$	−2956.13	−0.800069	−0.400034	−	0.916500i	$-0.631002\pi$
$239$	−2956.13	−0.800069	−0.400034	+	0.916500i	$0.631002\pi$
$240$	−1408.33	−0.378780
$241$	586.112	0.156659	0.0783294	−	0.996928i	$-0.475041\pi$
$241$	586.112	0.156659	0.0783294	+	0.996928i	$0.475041\pi$
$242$	0	0
$243$	−2993.86	−0.790354
$244$	−527.529	−0.138408
$245$	5762.15	1.50257
$246$	−4924.76	−1.27639
$247$	1153.89	0.297247
$248$	−1478.98	−0.378690
$249$	10918.8	2.77892
$250$	1703.65	0.430994
$251$	1143.71	0.287612	0.143806	−	0.989606i	$-0.454066\pi$
$251$	1143.71	0.287612	0.143806	+	0.989606i	$0.454066\pi$
$252$	−13385.1	−3.34597
$253$	0	0
$254$	−1496.33	−0.369638
$255$	369.968	0.0908561
$256$	−2209.51	−0.539432
$257$	1284.03	0.311656	0.155828	−	0.987784i	$-0.450195\pi$
$257$	1284.03	0.311656	0.155828	+	0.987784i	$0.450195\pi$
$258$	−5261.45	−1.26963
$259$	13557.8	3.25266
$260$	−490.381	−0.116970
$261$	−7003.19	−1.66087
$262$	1728.29	0.407536
$263$	7717.87	1.80952	0.904761	−	0.425919i	$-0.140049\pi$
$263$	7717.87	1.80952	0.904761	+	0.425919i	$0.140049\pi$
$264$	0	0
$265$	−1528.74	−0.354375
$266$	−4227.66	−0.974490
$267$	13497.8	3.09382
$268$	3210.00	0.731649
$269$	−558.853	−0.126669	−0.0633343	−	0.997992i	$-0.520173\pi$
$269$	−558.853	−0.126669	−0.0633343	+	0.997992i	$0.520173\pi$
$270$	2403.80	0.541817
$271$	−4877.81	−1.09338	−0.546689	−	0.837336i	$-0.684112\pi$
$271$	−4877.81	−1.09338	−0.546689	+	0.837336i	$0.684112\pi$
$272$	−165.637	−0.0369236
$273$	−4354.11	−0.965285
$274$	−448.003	−0.0987768
$275$	0	0
$276$	−3591.06	−0.783175
$277$	−3335.79	−0.723568	−0.361784	−	0.932262i	$-0.617832\pi$
$277$	−3335.79	−0.723568	−0.361784	+	0.932262i	$0.617832\pi$
$278$	−1726.78	−0.372538
$279$	−4664.20	−1.00086
$280$	4095.57	0.874133
$281$	2494.83	0.529640	0.264820	−	0.964298i	$-0.414687\pi$
$281$	2494.83	0.529640	0.264820	+	0.964298i	$0.414687\pi$
$282$	461.843	0.0975260
$283$	−3416.89	−0.717713	−0.358857	−	0.933393i	$-0.616833\pi$
$283$	−3416.89	−0.717713	−0.358857	+	0.933393i	$0.616833\pi$
$284$	3677.54	0.768388
$285$	−4978.23	−1.03468
$286$	0	0
$287$	−14437.7	−2.96943
$288$	−10929.0	−2.23610
$289$	−4869.49	−0.991143
$290$	940.034	0.190347
$291$	−2296.60	−0.462643
$292$	−1484.04	−0.297421
$293$	−2434.79	−0.485467	−0.242733	−	0.970093i	$-0.578044\pi$
$293$	−2434.79	−0.485467	−0.242733	+	0.970093i	$0.578044\pi$
$294$	11737.5	2.32837
$295$	3184.13	0.628431
$296$	7090.16	1.39225
$297$	0	0
$298$	2021.00	0.392863
$299$	−803.188	−0.155350
$300$	−5149.72	−0.991064
$301$	−15424.7	−2.95371
$302$	98.1942	0.0187101
$303$	8885.92	1.68476
$304$	2228.78	0.420492
$305$	509.042	0.0955661
$306$	518.169	0.0968032
$307$	5713.36	1.06215	0.531073	−	0.847326i	$-0.321789\pi$
$307$	5713.36	1.06215	0.531073	+	0.847326i	$0.321789\pi$
$308$	0	0
$309$	860.688	0.158456
$310$	626.073	0.114705
$311$	−4734.08	−0.863166	−0.431583	−	0.902073i	$-0.642045\pi$
$311$	−4734.08	−0.863166	−0.431583	+	0.902073i	$0.642045\pi$
$312$	−2277.02	−0.413176
$313$	−9724.92	−1.75618	−0.878091	−	0.478493i	$-0.841183\pi$
$313$	−9724.92	−1.75618	−0.878091	+	0.478493i	$0.841183\pi$
$314$	2801.54	0.503504
$315$	12916.1	2.31028
$316$	1789.68	0.318599
$317$	1587.18	0.281215	0.140607	−	0.990065i	$-0.455094\pi$
$317$	1587.18	0.281215	0.140607	+	0.990065i	$0.455094\pi$
$318$	−3114.02	−0.549137
$319$	0	0
$320$	255.033	0.0445525
$321$	−6508.21	−1.13163
$322$	2942.76	0.509296
$323$	−585.502	−0.100861
$324$	−7486.46	−1.28369
$325$	−1151.80	−0.196587
$326$	4090.65	0.694969
$327$	1065.59	0.180205
$328$	−7550.29	−1.27102
$329$	1353.96	0.226888
$330$	0	0
$331$	174.315	0.0289462	0.0144731	−	0.999895i	$-0.495393\pi$
$331$	174.315	0.0289462	0.0144731	+	0.999895i	$0.495393\pi$
$332$	7343.60	1.21395
$333$	22360.0	3.67964
$334$	−162.094	−0.0265551
$335$	−3097.51	−0.505179
$336$	−8410.16	−1.36551
$337$	8435.89	1.36360	0.681798	−	0.731540i	$-0.261198\pi$
$337$	8435.89	1.36360	0.681798	+	0.731540i	$0.261198\pi$
$338$	−223.418	−0.0359536
$339$	−4434.35	−0.710445
$340$	248.828	0.0396899
$341$	0	0
$342$	−6972.41	−1.10241
$343$	22052.2	3.47145
$344$	−8066.48	−1.26429
$345$	3465.21	0.540756
$346$	3253.16	0.505465
$347$	−10168.2	−1.57307	−0.786537	−	0.617543i	$-0.788128\pi$
$347$	−10168.2	−1.57307	−0.786537	+	0.617543i	$0.788128\pi$
$348$	−6850.34	−1.05522
$349$	4975.52	0.763133	0.381567	−	0.924341i	$-0.375385\pi$
$349$	4975.52	0.763133	0.381567	+	0.924341i	$0.375385\pi$
$350$	4220.03	0.644486
$351$	−3917.98	−0.595801
$352$	0	0
$353$	2850.33	0.429767	0.214884	−	0.976640i	$-0.431063\pi$
$353$	2850.33	0.429767	0.214884	+	0.976640i	$0.431063\pi$
$354$	6486.04	0.973811
$355$	−3548.67	−0.530546
$356$	9078.13	1.35152
$357$	2209.35	0.327539
$358$	−2085.11	−0.307825
$359$	−3744.17	−0.550445	−0.275222	−	0.961381i	$-0.588752\pi$
$359$	−3744.17	−0.550445	−0.275222	+	0.961381i	$0.588752\pi$
$360$	6754.56	0.988879
$361$	1019.43	0.148626
$362$	2706.25	0.392920
$363$	0	0
$364$	−2928.42	−0.421679
$365$	1432.03	0.205359
$366$	1036.91	0.148088
$367$	11185.1	1.59089	0.795447	−	0.606023i	$-0.207236\pi$
$367$	11185.1	1.59089	0.795447	+	0.606023i	$0.207236\pi$
$368$	−1551.39	−0.219761
$369$	−23811.1	−3.35923
$370$	−3001.37	−0.421713
$371$	−9129.21	−1.27753
$372$	−4562.40	−0.635886
$373$	3784.06	0.525285	0.262643	−	0.964893i	$-0.415406\pi$
$373$	3784.06	0.525285	0.262643	+	0.964893i	$0.415406\pi$
$374$	0	0
$375$	11980.0	1.64972
$376$	708.064	0.0971160
$377$	−1532.17	−0.209313
$378$	14354.9	1.95327
$379$	1670.65	0.226426	0.113213	−	0.993571i	$-0.463886\pi$
$379$	1670.65	0.226426	0.113213	+	0.993571i	$0.463886\pi$
$380$	−3348.19	−0.451996
$381$	−10522.1	−1.41487
$382$	482.276	0.0645953
$383$	10684.7	1.42549	0.712745	−	0.701423i	$-0.247452\pi$
$383$	10684.7	1.42549	0.712745	+	0.701423i	$0.247452\pi$
$384$	−13159.2	−1.74877
$385$	0	0
$386$	−1427.75	−0.188266
$387$	−25439.0	−3.34144
$388$	−1544.61	−0.202103
$389$	5999.95	0.782030	0.391015	−	0.920384i	$-0.372124\pi$
$389$	5999.95	0.782030	0.391015	+	0.920384i	$0.372124\pi$
$390$	963.895	0.125151
$391$	407.552	0.0527130
$392$	17995.0	2.31859
$393$	12153.3	1.55993
$394$	−1673.66	−0.214005
$395$	−1726.96	−0.219982
$396$	0	0
$397$	5240.95	0.662558	0.331279	−	0.943533i	$-0.392520\pi$
$397$	5240.95	0.662558	0.331279	+	0.943533i	$0.392520\pi$
$398$	−2950.05	−0.371539
$399$	−29728.7	−3.73007
$400$	−2224.76	−0.278095
$401$	13887.2	1.72941	0.864704	−	0.502282i	$-0.167506\pi$
$401$	13887.2	1.72941	0.864704	+	0.502282i	$0.167506\pi$
$402$	−6309.59	−0.782820
$403$	−1020.44	−0.126134
$404$	5976.36	0.735978
$405$	7224.10	0.886342
$406$	5613.64	0.686207
$407$	0	0
$408$	1155.40	0.140198
$409$	−4738.73	−0.572897	−0.286449	−	0.958096i	$-0.592475\pi$
$409$	−4738.73	−0.572897	−0.286449	+	0.958096i	$0.592475\pi$
$410$	3196.15	0.384991
$411$	−3150.34	−0.378089
$412$	578.868	0.0692204
$413$	19014.8	2.26551
$414$	4853.30	0.576151
$415$	−7086.25	−0.838193
$416$	−2391.06	−0.281806
$417$	−12142.6	−1.42597
$418$	0	0
$419$	−14656.1	−1.70882	−0.854411	−	0.519597i	$-0.826082\pi$
$419$	−14656.1	−1.70882	−0.854411	+	0.519597i	$0.826082\pi$
$420$	12634.2	1.46782
$421$	−3527.59	−0.408371	−0.204185	−	0.978932i	$-0.565455\pi$
$421$	−3527.59	−0.408371	−0.204185	+	0.978932i	$0.565455\pi$
$422$	1226.77	0.141512
$423$	2233.00	0.256672
$424$	−4774.20	−0.546829
$425$	584.446	0.0667054
$426$	−7228.60	−0.822129
$427$	3039.86	0.344518
$428$	−4377.20	−0.494345
$429$	0	0
$430$	3414.66	0.382952
$431$	−7465.38	−0.834326	−0.417163	−	0.908832i	$-0.636976\pi$
$431$	−7465.38	−0.834326	−0.417163	+	0.908832i	$0.636976\pi$
$432$	−7567.75	−0.842833
$433$	−11865.2	−1.31687	−0.658433	−	0.752639i	$-0.728781\pi$
$433$	−11865.2	−1.31687	−0.658433	+	0.752639i	$0.728781\pi$
$434$	3738.74	0.413515
$435$	6610.28	0.728594
$436$	716.676	0.0787214
$437$	−5483.95	−0.600305
$438$	2917.04	0.318222
$439$	−8869.81	−0.964311	−0.482156	−	0.876086i	$-0.660146\pi$
$439$	−8869.81	−0.964311	−0.482156	+	0.876086i	$0.660146\pi$
$440$	0	0
$441$	56750.3	6.12788
$442$	113.366	0.0121997
$443$	11010.8	1.18091	0.590453	−	0.807072i	$-0.298949\pi$
$443$	11010.8	1.18091	0.590453	+	0.807072i	$0.298949\pi$
$444$	21872.0	2.33783
$445$	−8760.00	−0.933177
$446$	1349.08	0.143230
$447$	14211.5	1.50377
$448$	1522.99	0.160613
$449$	17337.6	1.82230	0.911148	−	0.412079i	$-0.135197\pi$
$449$	17337.6	1.82230	0.911148	+	0.412079i	$0.135197\pi$
$450$	6959.82	0.729087
$451$	0	0
$452$	−2982.39	−0.310354
$453$	690.497	0.0716167
$454$	2202.77	0.227712
$455$	2825.80	0.291155
$456$	−15546.9	−1.59660
$457$	12931.3	1.32363	0.661815	−	0.749667i	$-0.269787\pi$
$457$	12931.3	1.32363	0.661815	+	0.749667i	$0.269787\pi$
$458$	−3648.84	−0.372268
$459$	1988.05	0.202166
$460$	2330.58	0.236226
$461$	129.042	0.0130370	0.00651852	−	0.999979i	$-0.497925\pi$
$461$	129.042	0.0130370	0.00651852	+	0.999979i	$0.497925\pi$
$462$	0	0
$463$	−13928.2	−1.39806	−0.699028	−	0.715094i	$-0.746384\pi$
$463$	−13928.2	−1.39806	−0.699028	+	0.715094i	$0.746384\pi$
$464$	−2959.46	−0.296098
$465$	4402.52	0.439058
$466$	−2083.85	−0.207152
$467$	−5052.35	−0.500631	−0.250316	−	0.968164i	$-0.580534\pi$
$467$	−5052.35	−0.500631	−0.250316	+	0.968164i	$0.580534\pi$
$468$	−4829.66	−0.477032
$469$	−18497.5	−1.82118
$470$	−299.734	−0.0294164
$471$	19700.3	1.92727
$472$	9943.93	0.969717
$473$	0	0
$474$	−3517.80	−0.340882
$475$	−7864.21	−0.759652
$476$	1485.93	0.143083
$477$	−15056.2	−1.44523
$478$	3908.00	0.373950
$479$	−13048.6	−1.24469	−0.622345	−	0.782743i	$-0.713820\pi$
$479$	−13048.6	−1.24469	−0.622345	+	0.782743i	$0.713820\pi$
$480$	10315.8	0.980937
$481$	4891.96	0.463730
$482$	−774.839	−0.0732219
$483$	20693.3	1.94944
$484$	0	0
$485$	1490.48	0.139545
$486$	3957.88	0.369409
$487$	−11495.6	−1.06964	−0.534822	−	0.844965i	$-0.679621\pi$
$487$	−11495.6	−1.06964	−0.534822	+	0.844965i	$0.679621\pi$
$488$	1589.72	0.147466
$489$	28765.2	2.66014
$490$	−7617.56	−0.702298
$491$	−5879.01	−0.540358	−0.270179	−	0.962810i	$-0.587083\pi$
$491$	−5879.01	−0.540358	−0.270179	+	0.962810i	$0.587083\pi$
$492$	−23291.4	−2.13426
$493$	777.451	0.0710236
$494$	−1525.44	−0.138932
$495$	0	0
$496$	−1971.03	−0.178431
$497$	−21191.7	−1.91263
$498$	−14434.6	−1.29886
$499$	−16052.9	−1.44013	−0.720067	−	0.693905i	$-0.755889\pi$
$499$	−16052.9	−1.44013	−0.720067	+	0.693905i	$0.755889\pi$
$500$	8057.34	0.720671
$501$	−1139.84	−0.101645
$502$	−1511.99	−0.134429
$503$	−6011.33	−0.532867	−0.266433	−	0.963853i	$-0.585845\pi$
$503$	−6011.33	−0.532867	−0.266433	+	0.963853i	$0.585845\pi$
$504$	40336.5	3.56494
$505$	−5766.93	−0.508168
$506$	0	0
$507$	−1571.06	−0.137620
$508$	−7076.81	−0.618076
$509$	20592.7	1.79323	0.896617	−	0.442807i	$-0.146017\pi$
$509$	20592.7	1.79323	0.896617	+	0.442807i	$0.146017\pi$
$510$	−489.097	−0.0424659
$511$	8551.72	0.740325
$512$	−8403.34	−0.725349
$513$	−26750.9	−2.30230
$514$	−1697.49	−0.145667
$515$	−558.582	−0.0477943
$516$	−24883.8	−2.12296
$517$	0	0
$518$	−17923.4	−1.52029
$519$	22876.1	1.93478
$520$	1477.78	0.124625
$521$	11884.8	0.999391	0.499695	−	0.866201i	$-0.333445\pi$
$521$	11884.8	0.999391	0.499695	+	0.866201i	$0.333445\pi$
$522$	9258.21	0.776285
$523$	−7451.05	−0.622967	−0.311483	−	0.950252i	$-0.600826\pi$
$523$	−7451.05	−0.622967	−0.311483	+	0.950252i	$0.600826\pi$
$524$	8173.87	0.681445
$525$	29675.1	2.46691
$526$	−10203.0	−0.845765
$527$	517.791	0.0427995
$528$	0	0
$529$	−8349.77	−0.686264
$530$	2020.99	0.165634
$531$	31359.8	2.56290
$532$	−19994.5	−1.62946
$533$	−5209.43	−0.423350
$534$	−17844.0	−1.44604
$535$	4223.80	0.341329
$536$	−9673.42	−0.779530
$537$	−14662.4	−1.17827
$538$	738.803	0.0592045
$539$	0	0
$540$	11368.6	0.905979
$541$	16438.2	1.30635	0.653175	−	0.757207i	$-0.273437\pi$
$541$	16438.2	1.30635	0.653175	+	0.757207i	$0.273437\pi$
$542$	6448.45	0.511042
$543$	19030.2	1.50399
$544$	1213.27	0.0956220
$545$	−691.560	−0.0543545
$546$	5756.13	0.451171
$547$	−20234.5	−1.58165	−0.790826	−	0.612042i	$-0.790348\pi$
$547$	−20234.5	−1.58165	−0.790826	+	0.612042i	$0.790348\pi$
$548$	−2118.81	−0.165166
$549$	5013.45	0.389743
$550$	0	0
$551$	−10461.3	−0.808828
$552$	10821.7	0.834428
$553$	−10313.0	−0.793041
$554$	4409.91	0.338194
$555$	−21105.5	−1.61419
$556$	−8166.72	−0.622925
$557$	17902.9	1.36188	0.680942	−	0.732338i	$-0.261571\pi$
$557$	17902.9	1.36188	0.680942	+	0.732338i	$0.261571\pi$
$558$	6166.07	0.467797
$559$	−5565.59	−0.421108
$560$	5458.16	0.411874
$561$	0	0
$562$	−3298.16	−0.247552
$563$	−20216.7	−1.51338	−0.756688	−	0.653776i	$-0.773184\pi$
$563$	−20216.7	−1.51338	−0.756688	+	0.653776i	$0.773184\pi$
$564$	2184.26	0.163074
$565$	2877.87	0.214289
$566$	4517.12	0.335457
$567$	43140.4	3.19529
$568$	−11082.4	−0.818673
$569$	−5690.09	−0.419228	−0.209614	−	0.977784i	$-0.567221\pi$
$569$	−5690.09	−0.419228	−0.209614	+	0.977784i	$0.567221\pi$
$570$	6581.22	0.483608
$571$	−8664.74	−0.635041	−0.317520	−	0.948251i	$-0.602850\pi$
$571$	−8664.74	−0.635041	−0.317520	+	0.948251i	$0.602850\pi$
$572$	0	0
$573$	3391.34	0.247252
$574$	19086.5	1.38790
$575$	5474.06	0.397016
$576$	2511.77	0.181697
$577$	2133.42	0.153926	0.0769632	−	0.997034i	$-0.475478\pi$
$577$	2133.42	0.153926	0.0769632	+	0.997034i	$0.475478\pi$
$578$	6437.45	0.463257
$579$	−10039.9	−0.720628
$580$	4445.84	0.318282
$581$	−42317.2	−3.02171
$582$	3036.10	0.216238
$583$	0	0
$584$	4472.19	0.316885
$585$	4660.41	0.329375
$586$	3218.79	0.226906
$587$	−20738.1	−1.45818	−0.729090	−	0.684417i	$-0.760057\pi$
$587$	−20738.1	−1.45818	−0.729090	+	0.684417i	$0.760057\pi$
$588$	55511.7	3.89330
$589$	−6967.31	−0.487408
$590$	−4209.41	−0.293727
$591$	−11769.1	−0.819149
$592$	9449.04	0.656002
$593$	−9506.42	−0.658317	−0.329158	−	0.944275i	$-0.606765\pi$
$593$	−9506.42	−0.658317	−0.329158	+	0.944275i	$0.606765\pi$
$594$	0	0
$595$	−1433.86	−0.0987942
$596$	9558.19	0.656911
$597$	−20744.6	−1.42215
$598$	1061.81	0.0726100
$599$	−719.765	−0.0490965	−0.0245482	−	0.999699i	$-0.507815\pi$
$599$	−719.765	−0.0490965	−0.0245482	+	0.999699i	$0.507815\pi$
$600$	15518.8	1.05592
$601$	18994.4	1.28918	0.644589	−	0.764529i	$-0.277029\pi$
$601$	18994.4	1.28918	0.644589	+	0.764529i	$0.277029\pi$
$602$	20391.4	1.38055
$603$	−30506.7	−2.06025
$604$	464.404	0.0312853
$605$	0	0
$606$	−11747.2	−0.787453
$607$	11663.5	0.779913	0.389956	−	0.920833i	$-0.372490\pi$
$607$	11663.5	0.779913	0.389956	+	0.920833i	$0.372490\pi$
$608$	−16325.5	−1.08896
$609$	39474.8	2.62660
$610$	−672.952	−0.0446673
$611$	488.539	0.0323473
$612$	2450.65	0.161866
$613$	−1008.56	−0.0664526	−0.0332263	−	0.999448i	$-0.510578\pi$
$613$	−1008.56	−0.0664526	−0.0332263	+	0.999448i	$0.510578\pi$
$614$	−7553.05	−0.496443
$615$	22475.2	1.47364
$616$	0	0
$617$	14098.4	0.919904	0.459952	−	0.887944i	$-0.347867\pi$
$617$	14098.4	0.919904	0.459952	+	0.887944i	$0.347867\pi$
$618$	−1137.83	−0.0740617
$619$	27010.3	1.75386	0.876928	−	0.480622i	$-0.159589\pi$
$619$	27010.3	1.75386	0.876928	+	0.480622i	$0.159589\pi$
$620$	2960.98	0.191800
$621$	18620.6	1.20325
$622$	6258.44	0.403441
$623$	−52312.4	−3.36413
$624$	−3034.58	−0.194680
$625$	3300.06	0.211204
$626$	12856.3	0.820834
$627$	0	0
$628$	13249.8	0.841915
$629$	−2482.27	−0.157352
$630$	−17075.0	−1.07982
$631$	−15225.6	−0.960576	−0.480288	−	0.877111i	$-0.659468\pi$
$631$	−15225.6	−0.960576	−0.480288	+	0.877111i	$0.659468\pi$
$632$	−5393.25	−0.339449
$633$	8626.59	0.541669
$634$	−2098.25	−0.131439
$635$	6828.81	0.426761
$636$	−14727.6	−0.918219
$637$	12415.9	0.772272
$638$	0	0
$639$	−34950.1	−2.16370
$640$	8540.25	0.527474
$641$	−13695.8	−0.843917	−0.421959	−	0.906615i	$-0.638657\pi$
$641$	−13695.8	−0.843917	−0.421959	+	0.906615i	$0.638657\pi$
$642$	8603.85	0.528920
$643$	−19128.5	−1.17318	−0.586590	−	0.809884i	$-0.699530\pi$
$643$	−19128.5	−1.17318	−0.586590	+	0.809884i	$0.699530\pi$
$644$	13917.6	0.851600
$645$	24011.7	1.46583
$646$	774.033	0.0471423
$647$	−14217.4	−0.863898	−0.431949	−	0.901898i	$-0.642174\pi$
$647$	−14217.4	−0.863898	−0.431949	+	0.901898i	$0.642174\pi$
$648$	22560.6	1.36769
$649$	0	0
$650$	1522.68	0.0918839
$651$	26290.7	1.58282
$652$	19346.5	1.16207
$653$	−16277.4	−0.975471	−0.487736	−	0.872991i	$-0.662177\pi$
$653$	−16277.4	−0.975471	−0.487736	+	0.872991i	$0.662177\pi$
$654$	−1408.70	−0.0842272
$655$	−7887.43	−0.470515
$656$	−10062.3	−0.598880
$657$	14103.8	0.837506
$658$	−1789.93	−0.106047
$659$	−4939.36	−0.291973	−0.145986	−	0.989287i	$-0.546636\pi$
$659$	−4939.36	−0.291973	−0.145986	+	0.989287i	$0.546636\pi$
$660$	0	0
$661$	4799.96	0.282446	0.141223	−	0.989978i	$-0.454897\pi$
$661$	4799.96	0.282446	0.141223	+	0.989978i	$0.454897\pi$
$662$	−230.444	−0.0135294
$663$	797.185	0.0466970
$664$	−22130.1	−1.29340
$665$	19293.8	1.12508
$666$	−29559.9	−1.71985
$667$	7281.79	0.422717
$668$	−766.616	−0.0444031
$669$	9486.67	0.548245
$670$	4094.90	0.236119
$671$	0	0
$672$	61603.3	3.53631
$673$	4002.05	0.229224	0.114612	−	0.993410i	$-0.463438\pi$
$673$	4002.05	0.229224	0.114612	+	0.993410i	$0.463438\pi$
$674$	−11152.2	−0.637341
$675$	26702.6	1.52264
$676$	−1056.64	−0.0601185
$677$	8983.22	0.509975	0.254988	−	0.966944i	$-0.417929\pi$
$677$	8983.22	0.509975	0.254988	+	0.966944i	$0.417929\pi$
$678$	5862.20	0.332060
$679$	8900.78	0.503064
$680$	−749.849	−0.0422874
$681$	15489.8	0.871616
$682$	0	0
$683$	−4513.00	−0.252833	−0.126417	−	0.991977i	$-0.540348\pi$
$683$	−4513.00	−0.252833	−0.126417	+	0.991977i	$0.540348\pi$
$684$	−32975.6	−1.84335
$685$	2044.55	0.114041
$686$	−29153.0	−1.62254
$687$	−25658.4	−1.42494
$688$	−10750.2	−0.595708
$689$	−3294.03	−0.182137
$690$	−4581.00	−0.252747
$691$	−27122.3	−1.49317	−0.746584	−	0.665291i	$-0.768307\pi$
$691$	−27122.3	−1.49317	−0.746584	+	0.665291i	$0.768307\pi$
$692$	15385.7	0.845195
$693$	0	0
$694$	13442.3	0.735250
$695$	7880.52	0.430108
$696$	20643.7	1.12428
$697$	2643.36	0.143650
$698$	−6577.63	−0.356686
$699$	−14653.6	−0.792917
$700$	19958.4	1.07765
$701$	−10355.4	−0.557940	−0.278970	−	0.960300i	$-0.589993\pi$
$701$	−10355.4	−0.557940	−0.278970	+	0.960300i	$0.589993\pi$
$702$	5179.56	0.278476
$703$	33401.0	1.79195
$704$	0	0
$705$	−2107.71	−0.112597
$706$	−3768.13	−0.200872
$707$	−34438.6	−1.83196
$708$	30675.4	1.62832
$709$	24576.0	1.30179	0.650895	−	0.759168i	$-0.274394\pi$
$709$	24576.0	1.30179	0.650895	+	0.759168i	$0.274394\pi$
$710$	4691.33	0.247975
$711$	−17008.5	−0.897143
$712$	−27357.2	−1.43996
$713$	4849.75	0.254733
$714$	−2920.76	−0.153091
$715$	0	0
$716$	−9861.41	−0.514718
$717$	27480.9	1.43137
$718$	4949.79	0.257276
$719$	15654.8	0.811995	0.405997	−	0.913874i	$-0.366924\pi$
$719$	15654.8	0.811995	0.405997	+	0.913874i	$0.366924\pi$
$720$	9001.79	0.465940
$721$	−3335.71	−0.172300
$722$	−1347.68	−0.0694674
$723$	−5448.63	−0.280272
$724$	12799.1	0.657007
$725$	10442.4	0.534924
$726$	0	0
$727$	−36590.3	−1.86665	−0.933327	−	0.359027i	$-0.883109\pi$
$727$	−36590.3	−1.86665	−0.933327	+	0.359027i	$0.883109\pi$
$728$	8824.89	0.449275
$729$	−4497.89	−0.228516
$730$	−1893.14	−0.0959841
$731$	2824.08	0.142890
$732$	4904.03	0.247620
$733$	10935.3	0.551031	0.275516	−	0.961297i	$-0.411151\pi$
$733$	10935.3	0.551031	0.275516	+	0.961297i	$0.411151\pi$
$734$	−14786.7	−0.743579
$735$	−53566.3	−2.68819
$736$	11363.7	0.569121
$737$	0	0
$738$	31478.2	1.57009
$739$	−19040.2	−0.947776	−0.473888	−	0.880585i	$-0.657150\pi$
$739$	−19040.2	−0.947776	−0.473888	+	0.880585i	$0.657150\pi$
$740$	−14194.8	−0.705151
$741$	−10726.8	−0.531793
$742$	12068.8	0.597115
$743$	−4602.95	−0.227276	−0.113638	−	0.993522i	$-0.536250\pi$
$743$	−4602.95	−0.227276	−0.113638	+	0.993522i	$0.536250\pi$
$744$	13748.9	0.677500
$745$	−9223.23	−0.453575
$746$	−5002.52	−0.245517
$747$	−69791.0	−3.41837
$748$	0	0
$749$	25223.4	1.23050
$750$	−15837.6	−0.771075
$751$	−5651.68	−0.274611	−0.137305	−	0.990529i	$-0.543844\pi$
$751$	−5651.68	−0.274611	−0.137305	+	0.990529i	$0.543844\pi$
$752$	943.636	0.0457591
$753$	−10632.2	−0.514554
$754$	2025.53	0.0978321
$755$	−448.130	−0.0216015
$756$	67890.6	3.26608
$757$	−26393.1	−1.26721	−0.633603	−	0.773659i	$-0.718425\pi$
$757$	−26393.1	−1.26721	−0.633603	+	0.773659i	$0.718425\pi$
$758$	−2208.60	−0.105831
$759$	0	0
$760$	10089.9	0.481576
$761$	−8242.84	−0.392645	−0.196322	−	0.980539i	$-0.562900\pi$
$761$	−8242.84	−0.392645	−0.196322	+	0.980539i	$0.562900\pi$
$762$	13910.2	0.661305
$763$	−4129.82	−0.195949
$764$	2280.90	0.108011
$765$	−2364.77	−0.111763
$766$	−14125.1	−0.666269
$767$	6860.96	0.322992
$768$	20540.1	0.965076
$769$	4560.19	0.213842	0.106921	−	0.994268i	$-0.465901\pi$
$769$	4560.19	0.213842	0.106921	+	0.994268i	$0.465901\pi$
$770$	0	0
$771$	−11936.6	−0.557572
$772$	−6752.48	−0.314802
$773$	5465.11	0.254290	0.127145	−	0.991884i	$-0.459419\pi$
$773$	5465.11	0.254290	0.127145	+	0.991884i	$0.459419\pi$
$774$	33630.3	1.56178
$775$	6954.74	0.322350
$776$	4654.74	0.215329
$777$	−126036.	−5.81921
$778$	−7931.93	−0.365518
$779$	−35568.6	−1.63591
$780$	4558.69	0.209266
$781$	0	0
$782$	−538.783	−0.0246379
$783$	35520.8	1.62121
$784$	23981.9	1.09247
$785$	−12785.4	−0.581314
$786$	−16066.6	−0.729106
$787$	19324.8	0.875291	0.437645	−	0.899148i	$-0.355813\pi$
$787$	19324.8	0.875291	0.437645	+	0.899148i	$0.355813\pi$
$788$	−7915.51	−0.357840
$789$	−71747.1	−3.23735
$790$	2283.04	0.102819
$791$	17185.9	0.772516
$792$	0	0
$793$	1096.85	0.0491177
$794$	−6928.52	−0.309678
$795$	14211.5	0.633999
$796$	−13952.1	−0.621255
$797$	3344.13	0.148626	0.0743132	−	0.997235i	$-0.476324\pi$
$797$	3344.13	0.148626	0.0743132	+	0.997235i	$0.476324\pi$
$798$	39301.3	1.74342
$799$	−247.893	−0.0109760
$800$	16296.1	0.720191
$801$	−86275.5	−3.80573
$802$	−18358.8	−0.808320
$803$	0	0
$804$	−29840.9	−1.30896
$805$	−13429.9	−0.588001
$806$	1349.02	0.0589545
$807$	5195.23	0.226618
$808$	−18009.9	−0.784143
$809$	1161.36	0.0504712	0.0252356	−	0.999682i	$-0.491966\pi$
$809$	1161.36	0.0504712	0.0252356	+	0.999682i	$0.491966\pi$
$810$	−9550.25	−0.414273
$811$	31312.5	1.35577	0.677885	−	0.735168i	$-0.262897\pi$
$811$	31312.5	1.35577	0.677885	+	0.735168i	$0.262897\pi$
$812$	26549.4	1.14742
$813$	45345.2	1.95612
$814$	0	0
$815$	−18668.5	−0.802368
$816$	1539.80	0.0660585
$817$	−38000.3	−1.62725
$818$	6264.59	0.267770
$819$	27830.7	1.18741
$820$	15116.0	0.643749
$821$	−23995.1	−1.02002	−0.510008	−	0.860169i	$-0.670358\pi$
$821$	−23995.1	−1.02002	−0.510008	+	0.860169i	$0.670358\pi$
$822$	4164.74	0.176718
$823$	39059.3	1.65434	0.827170	−	0.561952i	$-0.189950\pi$
$823$	39059.3	1.65434	0.827170	+	0.561952i	$0.189950\pi$
$824$	−1744.44	−0.0737504
$825$	0	0
$826$	−25137.5	−1.05889
$827$	4216.07	0.177276	0.0886379	−	0.996064i	$-0.471749\pi$
$827$	4216.07	0.177276	0.0886379	+	0.996064i	$0.471749\pi$
$828$	22953.4	0.963389
$829$	16917.1	0.708753	0.354376	−	0.935103i	$-0.384693\pi$
$829$	16917.1	0.708753	0.354376	+	0.935103i	$0.384693\pi$
$830$	9368.00	0.391769
$831$	31010.3	1.29451
$832$	549.531	0.0228985
$833$	−6300.06	−0.262046
$834$	16052.6	0.666492
$835$	739.750	0.0306588
$836$	0	0
$837$	23657.2	0.976958
$838$	19375.3	0.798699
$839$	−26025.6	−1.07092	−0.535462	−	0.844559i	$-0.679862\pi$
$839$	−26025.6	−1.07092	−0.535462	+	0.844559i	$0.679862\pi$
$840$	−38073.4	−1.56388
$841$	−10498.2	−0.430447
$842$	4663.47	0.190871
$843$	−23192.5	−0.947559
$844$	5801.94	0.236625
$845$	1019.61	0.0415098
$846$	−2952.02	−0.119967
$847$	0	0
$848$	−6362.56	−0.257655
$849$	31764.2	1.28403
$850$	−772.636	−0.0311779
$851$	−23249.5	−0.936525
$852$	−34187.3	−1.37469
$853$	−1334.36	−0.0535610	−0.0267805	−	0.999641i	$-0.508526\pi$
$853$	−1334.36	−0.0535610	−0.0267805	+	0.999641i	$0.508526\pi$
$854$	−4018.70	−0.161027
$855$	31820.0	1.27277
$856$	13190.8	0.526697
$857$	−48316.4	−1.92585	−0.962927	−	0.269764i	$-0.913054\pi$
$857$	−48316.4	−1.92585	−0.962927	+	0.269764i	$0.913054\pi$
$858$	0	0
$859$	20702.0	0.822287	0.411144	−	0.911571i	$-0.365129\pi$
$859$	20702.0	0.822287	0.411144	+	0.911571i	$0.365129\pi$
$860$	16149.5	0.640339
$861$	134216.	5.31250
$862$	9869.22	0.389962
$863$	20748.5	0.818411	0.409205	−	0.912442i	$-0.365806\pi$
$863$	20748.5	0.818411	0.409205	+	0.912442i	$0.365806\pi$
$864$	55432.7	2.18271
$865$	−14846.5	−0.583578
$866$	15685.7	0.615499
$867$	45267.9	1.77322
$868$	17682.2	0.691443
$869$	0	0
$870$	−8738.77	−0.340543
$871$	−6674.32	−0.259645
$872$	−2159.72	−0.0838732
$873$	14679.5	0.569101
$874$	7249.78	0.280580
$875$	−46430.1	−1.79386
$876$	13796.0	0.532104
$877$	−46708.4	−1.79844	−0.899219	−	0.437500i	$-0.855864\pi$
$877$	−46708.4	−1.79844	−0.899219	+	0.437500i	$0.855864\pi$
$878$	11725.9	0.450716
$879$	22634.4	0.868530
$880$	0	0
$881$	47664.2	1.82276	0.911378	−	0.411571i	$-0.135020\pi$
$881$	47664.2	1.82276	0.911378	+	0.411571i	$0.135020\pi$
$882$	−75023.8	−2.86415
$883$	−32896.3	−1.25374	−0.626868	−	0.779125i	$-0.715664\pi$
$883$	−32896.3	−1.25374	−0.626868	+	0.779125i	$0.715664\pi$
$884$	536.159	0.0203993
$885$	−29600.4	−1.12430
$886$	−14556.3	−0.551952
$887$	19896.0	0.753147	0.376573	−	0.926387i	$-0.377102\pi$
$887$	19896.0	0.753147	0.376573	+	0.926387i	$0.377102\pi$
$888$	−65911.8	−2.49083
$889$	40779.9	1.53848
$890$	11580.7	0.436164
$891$	0	0
$892$	6380.40	0.239497
$893$	3335.62	0.124997
$894$	−18787.6	−0.702855
$895$	9515.82	0.355395
$896$	51000.1	1.90156
$897$	7466.62	0.277930
$898$	−22920.2	−0.851736
$899$	9251.44	0.343218
$900$	32916.1	1.21912
$901$	1671.45	0.0618024
$902$	0	0
$903$	143392.	5.28436
$904$	8987.51	0.330664
$905$	−12350.5	−0.453641
$906$	−912.836	−0.0334734
$907$	−52885.8	−1.93610	−0.968050	−	0.250756i	$-0.919321\pi$
$907$	−52885.8	−1.93610	−0.968050	+	0.250756i	$0.919321\pi$
$908$	10417.9	0.380760
$909$	−56797.3	−2.07244
$910$	−3735.70	−0.136085
$911$	−19826.6	−0.721058	−0.360529	−	0.932748i	$-0.617404\pi$
$911$	−19826.6	−0.721058	−0.360529	+	0.932748i	$0.617404\pi$
$912$	−20719.3	−0.752285
$913$	0	0
$914$	−17095.1	−0.618660
$915$	−4732.17	−0.170973
$916$	−17257.0	−0.622474
$917$	−47101.6	−1.69622
$918$	−2628.20	−0.0944919
$919$	13416.6	0.481582	0.240791	−	0.970577i	$-0.422593\pi$
$919$	13416.6	0.481582	0.240791	+	0.970577i	$0.422593\pi$
$920$	−7023.27	−0.251685
$921$	−53112.7	−1.90024
$922$	−170.593	−0.00609347
$923$	−7646.45	−0.272683
$924$	0	0
$925$	−33340.7	−1.18512
$926$	18413.1	0.653447
$927$	−5501.37	−0.194918
$928$	21677.6	0.766813
$929$	−1948.41	−0.0688107	−0.0344054	−	0.999408i	$-0.510954\pi$
$929$	−1948.41	−0.0688107	−0.0344054	+	0.999408i	$0.510954\pi$
$930$	−5820.12	−0.205214
$931$	84772.7	2.98422
$932$	−9855.48	−0.346381
$933$	44009.1	1.54426
$934$	6679.19	0.233993
$935$	0	0
$936$	14554.3	0.508251
$937$	32919.5	1.14774	0.573871	−	0.818946i	$-0.305441\pi$
$937$	32919.5	1.14774	0.573871	+	0.818946i	$0.305441\pi$
$938$	24453.7	0.851215
$939$	90405.1	3.14192
$940$	−1417.58	−0.0491875
$941$	44018.5	1.52493	0.762466	−	0.647028i	$-0.223988\pi$
$941$	44018.5	1.52493	0.762466	+	0.647028i	$0.223988\pi$
$942$	−26043.8	−0.900799
$943$	24758.3	0.854975
$944$	13252.3	0.456911
$945$	−65511.4	−2.25512
$946$	0	0
$947$	−48871.4	−1.67699	−0.838493	−	0.544912i	$-0.816563\pi$
$947$	−48871.4	−1.67699	−0.838493	+	0.544912i	$0.816563\pi$
$948$	−16637.3	−0.569993
$949$	3085.66	0.105548
$950$	10396.5	0.355059
$951$	−14754.8	−0.503110
$952$	−4477.90	−0.152447
$953$	40622.7	1.38080	0.690398	−	0.723430i	$-0.257436\pi$
$953$	40622.7	1.38080	0.690398	+	0.723430i	$0.257436\pi$
$954$	19904.3	0.675498
$955$	−2200.97	−0.0745776
$956$	18482.7	0.625286
$957$	0	0
$958$	17250.3	0.581765
$959$	12209.5	0.411123
$960$	−2370.85	−0.0797071
$961$	−23629.4	−0.793174
$962$	−6467.16	−0.216746
$963$	41599.4	1.39203
$964$	−3664.56	−0.122435
$965$	6515.84	0.217360
$966$	−27356.5	−0.911162
$967$	45285.3	1.50598	0.752988	−	0.658034i	$-0.228612\pi$
$967$	45285.3	1.50598	0.752988	+	0.658034i	$0.228612\pi$
$968$	0	0
$969$	5442.96	0.180447
$970$	−1970.42	−0.0652230
$971$	1578.09	0.0521560	0.0260780	−	0.999660i	$-0.491698\pi$
$971$	1578.09	0.0521560	0.0260780	+	0.999660i	$0.491698\pi$
$972$	18718.6	0.617694
$973$	47060.4	1.55055
$974$	15197.2	0.499948
$975$	10707.4	0.351705
$976$	2118.62	0.0694830
$977$	−25921.5	−0.848825	−0.424413	−	0.905469i	$-0.639519\pi$
$977$	−25921.5	−0.848825	−0.424413	+	0.905469i	$0.639519\pi$
$978$	−38027.6	−1.24334
$979$	0	0
$980$	−36026.8	−1.17432
$981$	−6811.04	−0.221672
$982$	7772.04	0.252562
$983$	−12805.3	−0.415488	−0.207744	−	0.978183i	$-0.566612\pi$
$983$	−12805.3	−0.415488	−0.207744	+	0.978183i	$0.566612\pi$
$984$	70189.2	2.27393
$985$	7638.11	0.247077
$986$	−1027.79	−0.0331962
$987$	−12586.7	−0.405917
$988$	−7214.47	−0.232311
$989$	26451.0	0.850447
$990$	0	0
$991$	42905.7	1.37532	0.687661	−	0.726032i	$-0.258638\pi$
$991$	42905.7	1.37532	0.687661	+	0.726032i	$0.258638\pi$
$992$	14437.5	0.462089
$993$	−1620.47	−0.0517866
$994$	28015.4	0.893959
$995$	13463.2	0.428956
$996$	−68267.8	−2.17183
$997$	9223.69	0.292996	0.146498	−	0.989211i	$-0.453200\pi$
$997$	9223.69	0.292996	0.146498	+	0.989211i	$0.453200\pi$
$998$	21221.9	0.673114
$999$	−113412.	−3.59178

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1573.4.a.o.1.14		34
11.5	even	5		143.4.h.a.14.10	✓	68
11.9	even	5		143.4.h.a.92.10	yes	68
11.10	odd	2		1573.4.a.p.1.21		34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.h.a.14.10	✓	68	11.5	even	5
143.4.h.a.92.10	yes	68	11.9	even	5
1573.4.a.o.1.14		34	1.1	even	1	trivial
1573.4.a.p.1.21		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)

\(f(q)\)	\(=\)	\(q-1.32200 q^{2} -9.29623 q^{3} -6.25232 q^{4} +6.03321 q^{5} +12.2896 q^{6} +36.0288 q^{7} +18.8415 q^{8} +59.4199 q^{9} +O(q^{10})\)	\(q-1.32200 q^{2} -9.29623 q^{3} -6.25232 q^{4} +6.03321 q^{5} +12.2896 q^{6} +36.0288 q^{7} +18.8415 q^{8} +59.4199 q^{9} -7.97590 q^{10} +58.1230 q^{12} +13.0000 q^{13} -47.6300 q^{14} -56.0861 q^{15} +25.1101 q^{16} -6.59643 q^{17} -78.5530 q^{18} +88.7605 q^{19} -37.7216 q^{20} -334.932 q^{21} -61.7837 q^{23} -175.155 q^{24} -88.6003 q^{25} -17.1860 q^{26} -301.383 q^{27} -225.263 q^{28} -117.859 q^{29} +74.1458 q^{30} -78.4956 q^{31} -183.928 q^{32} +8.72047 q^{34} +217.369 q^{35} -371.512 q^{36} +376.305 q^{37} -117.341 q^{38} -120.851 q^{39} +113.675 q^{40} -400.726 q^{41} +442.779 q^{42} -428.122 q^{43} +358.493 q^{45} +81.6780 q^{46} +37.5800 q^{47} -233.429 q^{48} +955.072 q^{49} +117.129 q^{50} +61.3219 q^{51} -81.2802 q^{52} -253.387 q^{53} +398.428 q^{54} +678.838 q^{56} -825.138 q^{57} +155.810 q^{58} +527.766 q^{59} +350.669 q^{60} +84.3733 q^{61} +103.771 q^{62} +2140.83 q^{63} +42.2716 q^{64} +78.4318 q^{65} -513.409 q^{67} +41.2430 q^{68} +574.356 q^{69} -287.362 q^{70} -588.189 q^{71} +1119.56 q^{72} +237.358 q^{73} -497.474 q^{74} +823.649 q^{75} -554.959 q^{76} +159.765 q^{78} -286.242 q^{79} +151.494 q^{80} +1197.39 q^{81} +529.759 q^{82} -1174.54 q^{83} +2094.10 q^{84} -39.7977 q^{85} +565.977 q^{86} +1095.65 q^{87} -1451.96 q^{89} -473.927 q^{90} +468.374 q^{91} +386.292 q^{92} +729.713 q^{93} -49.6806 q^{94} +535.511 q^{95} +1709.84 q^{96} +247.047 q^{97} -1262.60 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 3 q^{2} - 29 q^{3} + 97 q^{4} - 28 q^{5} + 36 q^{6} - 36 q^{7} - 57 q^{8} + 265 q^{9}+O(q^{10}) \) 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

Related objects

Downloads

Learn more