LMFDB - Embedded newform 1859.4.a.g.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1859,4,Mod(1,1859)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1859, 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("1859.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1859 = 11 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1859.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$109.684550701$
Analytic rank:	$1$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 93 x^{15} - 7 x^{14} + 3449 x^{13} + 406 x^{12} - 65242 x^{11} - 7942 x^{10} + 669163 x^{9} + \cdots - 2210688 $ x^17 - 93x^15 - 7x^14 + 3449x^13 + 406x^12 - 65242x^11 - 7942x^10 + 669163x^9 + 59532x^8 - 3663297x^7 - 79027x^6 + 9967603x^5 - 984554x^4 - 12177120x^3 + 3207432x^2 + 5215872*x - 2210688
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	no (minimal twist has level 143)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$1.71387$ of defining polynomial
Character	$\chi$	$=$	1859.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.71387 q^{2} +7.58218 q^{3} -5.06264 q^{4} +12.0244 q^{5} -12.9949 q^{6} +1.14865 q^{7} +22.3877 q^{8} +30.4895 q^{9} +O(q^{10})$	\(q-1.71387 q^{2} +7.58218 q^{3} -5.06264 q^{4} +12.0244 q^{5} -12.9949 q^{6} +1.14865 q^{7} +22.3877 q^{8} +30.4895 q^{9} -20.6082 q^{10} +11.0000 q^{11} -38.3858 q^{12} -1.96864 q^{14} +91.1710 q^{15} +2.13141 q^{16} -13.4913 q^{17} -52.2551 q^{18} -96.5360 q^{19} -60.8750 q^{20} +8.70928 q^{21} -18.8526 q^{22} -65.4896 q^{23} +169.748 q^{24} +19.5855 q^{25} +26.4578 q^{27} -5.81520 q^{28} -100.762 q^{29} -156.255 q^{30} -259.433 q^{31} -182.755 q^{32} +83.4040 q^{33} +23.1223 q^{34} +13.8118 q^{35} -154.357 q^{36} -51.8065 q^{37} +165.451 q^{38} +269.198 q^{40} -204.693 q^{41} -14.9266 q^{42} -419.761 q^{43} -55.6890 q^{44} +366.617 q^{45} +112.241 q^{46} +183.789 q^{47} +16.1607 q^{48} -341.681 q^{49} -33.5670 q^{50} -102.293 q^{51} +183.031 q^{53} -45.3453 q^{54} +132.268 q^{55} +25.7157 q^{56} -731.954 q^{57} +172.693 q^{58} -739.589 q^{59} -461.566 q^{60} +620.222 q^{61} +444.636 q^{62} +35.0218 q^{63} +296.167 q^{64} -142.944 q^{66} -795.028 q^{67} +68.3015 q^{68} -496.554 q^{69} -23.6717 q^{70} +417.489 q^{71} +682.589 q^{72} -231.438 q^{73} +88.7898 q^{74} +148.501 q^{75} +488.727 q^{76} +12.6352 q^{77} +1173.74 q^{79} +25.6289 q^{80} -622.608 q^{81} +350.819 q^{82} -141.928 q^{83} -44.0919 q^{84} -162.224 q^{85} +719.417 q^{86} -763.995 q^{87} +246.265 q^{88} -1273.83 q^{89} -628.335 q^{90} +331.550 q^{92} -1967.07 q^{93} -314.991 q^{94} -1160.79 q^{95} -1385.68 q^{96} +210.784 q^{97} +585.597 q^{98} +335.384 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q - 6 q^{3} + 50 q^{4} - 24 q^{5} + 16 q^{6} - 62 q^{7} - 21 q^{8} + 135 q^{9}+O(q^{10}) $ 17 * q - 6 * q^3 + 50 * q^4 - 24 * q^5 + 16 * q^6 - 62 * q^7 - 21 * q^8 + 135 * q^9	\( 17 q - 6 q^{3} + 50 q^{4} - 24 q^{5} + 16 q^{6} - 62 q^{7} - 21 q^{8} + 135 q^{9} + 2 q^{10} + 187 q^{11} - 127 q^{12} - 148 q^{15} + 126 q^{16} - 74 q^{17} + 90 q^{18} - 159 q^{19} - 222 q^{20} - 184 q^{21} - 215 q^{23} + 214 q^{24} + 95 q^{25} - 192 q^{27} - 358 q^{28} - 157 q^{29} + 829 q^{30} - 394 q^{31} - 553 q^{32} - 66 q^{33} - 702 q^{34} + 58 q^{35} - 700 q^{36} + 88 q^{37} - 1318 q^{38} + 733 q^{40} - 512 q^{41} + 337 q^{42} + 927 q^{43} + 550 q^{44} - 1482 q^{45} - 1361 q^{46} - 143 q^{47} - 178 q^{48} + 1835 q^{49} - 583 q^{50} - 568 q^{51} + 106 q^{53} - 67 q^{54} - 264 q^{55} + 2059 q^{56} + 1298 q^{57} - 1690 q^{58} - 266 q^{59} + 37 q^{60} - 624 q^{61} + 643 q^{62} - 2360 q^{63} - 1589 q^{64} + 176 q^{66} - 676 q^{67} - 413 q^{68} + 764 q^{69} - 1061 q^{70} - 763 q^{71} - 1366 q^{72} - 2374 q^{73} - 1649 q^{74} + 2420 q^{75} - 2101 q^{76} - 682 q^{77} + 2164 q^{79} - 1013 q^{80} + 537 q^{81} + 3152 q^{82} + 777 q^{83} - 3381 q^{84} - 1690 q^{85} + 2894 q^{86} - 4200 q^{87} - 231 q^{88} - 1687 q^{89} - 5399 q^{90} + 5542 q^{92} - 4310 q^{93} + 1777 q^{94} + 1124 q^{95} - 3465 q^{96} - 2047 q^{97} + 1553 q^{98} + 1485 q^{99}+O(q^{100}) \) 17 * q - 6 * q^3 + 50 * q^4 - 24 * q^5 + 16 * q^6 - 62 * q^7 - 21 * q^8 + 135 * q^9 + 2 * q^10 + 187 * q^11 - 127 * q^12 - 148 * q^15 + 126 * q^16 - 74 * q^17 + 90 * q^18 - 159 * q^19 - 222 * q^20 - 184 * q^21 - 215 * q^23 + 214 * q^24 + 95 * q^25 - 192 * q^27 - 358 * q^28 - 157 * q^29 + 829 * q^30 - 394 * q^31 - 553 * q^32 - 66 * q^33 - 702 * q^34 + 58 * q^35 - 700 * q^36 + 88 * q^37 - 1318 * q^38 + 733 * q^40 - 512 * q^41 + 337 * q^42 + 927 * q^43 + 550 * q^44 - 1482 * q^45 - 1361 * q^46 - 143 * q^47 - 178 * q^48 + 1835 * q^49 - 583 * q^50 - 568 * q^51 + 106 * q^53 - 67 * q^54 - 264 * q^55 + 2059 * q^56 + 1298 * q^57 - 1690 * q^58 - 266 * q^59 + 37 * q^60 - 624 * q^61 + 643 * q^62 - 2360 * q^63 - 1589 * q^64 + 176 * q^66 - 676 * q^67 - 413 * q^68 + 764 * q^69 - 1061 * q^70 - 763 * q^71 - 1366 * q^72 - 2374 * q^73 - 1649 * q^74 + 2420 * q^75 - 2101 * q^76 - 682 * q^77 + 2164 * q^79 - 1013 * q^80 + 537 * q^81 + 3152 * q^82 + 777 * q^83 - 3381 * q^84 - 1690 * q^85 + 2894 * q^86 - 4200 * q^87 - 231 * q^88 - 1687 * q^89 - 5399 * q^90 + 5542 * q^92 - 4310 * q^93 + 1777 * q^94 + 1124 * q^95 - 3465 * q^96 - 2047 * q^97 + 1553 * q^98 + 1485 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.71387	−0.605946	−0.302973	−	0.952999i	$-0.597979\pi$
$2$	−1.71387	−0.605946	−0.302973	+	0.952999i	$0.597979\pi$
$3$	7.58218	1.45919	0.729596	−	0.683879i	$-0.239708\pi$
$3$	7.58218	1.45919	0.729596	+	0.683879i	$0.239708\pi$
$4$	−5.06264	−0.632830
$5$	12.0244	1.07549	0.537746	−	0.843107i	$-0.319276\pi$
$5$	12.0244	1.07549	0.537746	+	0.843107i	$0.319276\pi$
$6$	−12.9949	−0.884191
$7$	1.14865	0.0620213	0.0310107	−	0.999519i	$-0.490127\pi$
$7$	1.14865	0.0620213	0.0310107	+	0.999519i	$0.490127\pi$
$8$	22.3877	0.989406
$9$	30.4895	1.12924
$10$	−20.6082	−0.651690
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	−38.3858	−0.923420
$13$	0	0
$13$	0	0
$14$	−1.96864	−0.0375816
$15$	91.1710	1.56935
$16$	2.13141	0.0333033
$17$	−13.4913	−0.192477	−0.0962387	−	0.995358i	$-0.530681\pi$
$17$	−13.4913	−0.192477	−0.0962387	+	0.995358i	$0.530681\pi$
$18$	−52.2551	−0.684258
$19$	−96.5360	−1.16563	−0.582813	−	0.812606i	$-0.698048\pi$
$19$	−96.5360	−1.16563	−0.582813	+	0.812606i	$0.698048\pi$
$20$	−60.8750	−0.680604
$21$	8.70928	0.0905010
$22$	−18.8526	−0.182700
$23$	−65.4896	−0.593719	−0.296859	−	0.954921i	$-0.595939\pi$
$23$	−65.4896	−0.593719	−0.296859	+	0.954921i	$0.595939\pi$
$24$	169.748	1.44373
$25$	19.5855	0.156684
$26$	0	0
$27$	26.4578	0.188585
$28$	−5.81520	−0.0392489
$29$	−100.762	−0.645208	−0.322604	−	0.946534i	$-0.604558\pi$
$29$	−100.762	−0.645208	−0.322604	+	0.946534i	$0.604558\pi$
$30$	−156.255	−0.950941
$31$	−259.433	−1.50308	−0.751542	−	0.659686i	$-0.770689\pi$
$31$	−259.433	−1.50308	−0.751542	+	0.659686i	$0.770689\pi$
$32$	−182.755	−1.00959
$33$	83.4040	0.439963
$34$	23.1223	0.116631
$35$	13.8118	0.0667035
$36$	−154.357	−0.714616
$37$	−51.8065	−0.230188	−0.115094	−	0.993355i	$-0.536717\pi$
$37$	−51.8065	−0.230188	−0.115094	+	0.993355i	$0.536717\pi$
$38$	165.451	0.706306
$39$	0	0
$40$	269.198	1.06410
$41$	−204.693	−0.779701	−0.389851	−	0.920878i	$-0.627473\pi$
$41$	−204.693	−0.779701	−0.389851	+	0.920878i	$0.627473\pi$
$42$	−14.9266	−0.0548387
$43$	−419.761	−1.48867	−0.744337	−	0.667805i	$-0.767234\pi$
$43$	−419.761	−1.48867	−0.744337	+	0.667805i	$0.767234\pi$
$44$	−55.6890	−0.190805
$45$	366.617	1.21449
$46$	112.241	0.359761
$47$	183.789	0.570390	0.285195	−	0.958469i	$-0.407942\pi$
$47$	183.789	0.570390	0.285195	+	0.958469i	$0.407942\pi$
$48$	16.1607	0.0485959
$49$	−341.681	−0.996153
$50$	−33.5670	−0.0949419
$51$	−102.293	−0.280861
$52$	0	0
$53$	183.031	0.474362	0.237181	−	0.971465i	$-0.423776\pi$
$53$	183.031	0.474362	0.237181	+	0.971465i	$0.423776\pi$
$54$	−45.3453	−0.114273
$55$	132.268	0.324273
$56$	25.7157	0.0613643
$57$	−731.954	−1.70087
$58$	172.693	0.390961
$59$	−739.589	−1.63197	−0.815986	−	0.578072i	$-0.803805\pi$
$59$	−739.589	−1.63197	−0.815986	+	0.578072i	$0.803805\pi$
$60$	−461.566	−0.993131
$61$	620.222	1.30182	0.650912	−	0.759153i	$-0.274387\pi$
$61$	620.222	1.30182	0.650912	+	0.759153i	$0.274387\pi$
$62$	444.636	0.910787
$63$	35.0218	0.0700369
$64$	296.167	0.578451
$65$	0	0
$66$	−142.944	−0.266594
$67$	−795.028	−1.44967	−0.724837	−	0.688920i	$-0.758085\pi$
$67$	−795.028	−1.44967	−0.724837	+	0.688920i	$0.758085\pi$
$68$	68.3015	0.121805
$69$	−496.554	−0.866350
$70$	−23.6717	−0.0404187
$71$	417.489	0.697843	0.348922	−	0.937152i	$-0.386548\pi$
$71$	417.489	0.697843	0.348922	+	0.937152i	$0.386548\pi$
$72$	682.589	1.11728
$73$	−231.438	−0.371065	−0.185533	−	0.982638i	$-0.559401\pi$
$73$	−231.438	−0.371065	−0.185533	+	0.982638i	$0.559401\pi$
$74$	88.7898	0.139481
$75$	148.501	0.228632
$76$	488.727	0.737643
$77$	12.6352	0.0187001
$78$	0	0
$79$	1173.74	1.67159	0.835797	−	0.549038i	$-0.185006\pi$
$79$	1173.74	1.67159	0.835797	+	0.549038i	$0.185006\pi$
$80$	25.6289	0.0358174
$81$	−622.608	−0.854057
$82$	350.819	0.472457
$83$	−141.928	−0.187694	−0.0938471	−	0.995587i	$-0.529916\pi$
$83$	−141.928	−0.187694	−0.0938471	+	0.995587i	$0.529916\pi$
$84$	−44.0919	−0.0572717
$85$	−162.224	−0.207008
$86$	719.417	0.902055
$87$	−763.995	−0.941482
$88$	246.265	0.298317
$89$	−1273.83	−1.51715	−0.758573	−	0.651588i	$-0.774103\pi$
$89$	−1273.83	−1.51715	−0.758573	+	0.651588i	$0.774103\pi$
$90$	−628.335	−0.735914
$91$	0	0
$92$	331.550	0.375723
$93$	−1967.07	−2.19329
$94$	−314.991	−0.345626
$95$	−1160.79	−1.25362
$96$	−1385.68	−1.47318
$97$	210.784	0.220638	0.110319	−	0.993896i	$-0.464813\pi$
$97$	210.784	0.220638	0.110319	+	0.993896i	$0.464813\pi$
$98$	585.597	0.603615
$99$	335.384	0.340479
$100$	−99.1542	−0.0991542
$101$	553.209	0.545014	0.272507	−	0.962154i	$-0.412147\pi$
$101$	553.209	0.545014	0.272507	+	0.962154i	$0.412147\pi$
$102$	175.318	0.170187
$103$	1285.96	1.23019	0.615095	−	0.788453i	$-0.289118\pi$
$103$	1285.96	1.23019	0.615095	+	0.788453i	$0.289118\pi$
$104$	0	0
$105$	104.724	0.0973331
$106$	−313.692	−0.287438
$107$	609.473	0.550654	0.275327	−	0.961351i	$-0.411214\pi$
$107$	609.473	0.550654	0.275327	+	0.961351i	$0.411214\pi$
$108$	−133.946	−0.119342
$109$	696.768	0.612277	0.306139	−	0.951987i	$-0.400963\pi$
$109$	696.768	0.612277	0.306139	+	0.951987i	$0.400963\pi$
$110$	−226.691	−0.196492
$111$	−392.806	−0.335888
$112$	2.44825	0.00206551
$113$	−136.391	−0.113545	−0.0567724	−	0.998387i	$-0.518081\pi$
$113$	−136.391	−0.113545	−0.0567724	+	0.998387i	$0.518081\pi$
$114$	1254.48	1.03064
$115$	−787.472	−0.638540
$116$	510.121	0.408307
$117$	0	0
$118$	1267.56	0.988886
$119$	−15.4968	−0.0119377
$120$	2041.11	1.55272
$121$	121.000	0.0909091
$122$	−1062.98	−0.788835
$123$	−1552.02	−1.13773
$124$	1313.42	0.951196
$125$	−1267.54	−0.906980
$126$	−60.0229	−0.0424386
$127$	821.003	0.573640	0.286820	−	0.957985i	$-0.407402\pi$
$127$	821.003	0.573640	0.286820	+	0.957985i	$0.407402\pi$
$128$	954.444	0.659076
$129$	−3182.70	−2.17226
$130$	0	0
$131$	424.367	0.283032	0.141516	−	0.989936i	$-0.454802\pi$
$131$	424.367	0.283032	0.141516	+	0.989936i	$0.454802\pi$
$132$	−422.244	−0.278422
$133$	−110.886	−0.0722936
$134$	1362.58	0.878424
$135$	318.138	0.202822
$136$	−302.039	−0.190438
$137$	167.562	0.104495	0.0522475	−	0.998634i	$-0.483362\pi$
$137$	167.562	0.104495	0.0522475	+	0.998634i	$0.483362\pi$
$138$	851.031	0.524961
$139$	−432.639	−0.264000	−0.132000	−	0.991250i	$-0.542140\pi$
$139$	−432.639	−0.264000	−0.132000	+	0.991250i	$0.542140\pi$
$140$	−69.9242	−0.0422119
$141$	1393.52	0.832309
$142$	−715.524	−0.422855
$143$	0	0
$144$	64.9856	0.0376074
$145$	−1211.60	−0.693916
$146$	396.655	0.224845
$147$	−2590.68	−1.45358
$148$	262.278	0.145670
$149$	−380.350	−0.209124	−0.104562	−	0.994518i	$-0.533344\pi$
$149$	−380.350	−0.209124	−0.104562	+	0.994518i	$0.533344\pi$
$150$	−254.511	−0.138538
$151$	−2099.11	−1.13128	−0.565641	−	0.824652i	$-0.691371\pi$
$151$	−2099.11	−1.13128	−0.565641	+	0.824652i	$0.691371\pi$
$152$	−2161.22	−1.15328
$153$	−411.342	−0.217353
$154$	−21.6551	−0.0113313
$155$	−3119.52	−1.61655
$156$	0	0
$157$	−562.141	−0.285756	−0.142878	−	0.989740i	$-0.545636\pi$
$157$	−562.141	−0.285756	−0.142878	+	0.989740i	$0.545636\pi$
$158$	−2011.64	−1.01290
$159$	1387.77	0.692186
$160$	−2197.51	−1.08580
$161$	−75.2247	−0.0368232
$162$	1067.07	0.517512
$163$	−1832.39	−0.880515	−0.440258	−	0.897872i	$-0.645113\pi$
$163$	−1832.39	−0.880515	−0.440258	+	0.897872i	$0.645113\pi$
$164$	1036.29	0.493418
$165$	1002.88	0.473177
$166$	243.247	0.113733
$167$	3981.22	1.84477	0.922383	−	0.386276i	$-0.126239\pi$
$167$	3981.22	1.84477	0.922383	+	0.386276i	$0.126239\pi$
$168$	194.981	0.0895422
$169$	0	0
$170$	278.032	0.125436
$171$	−2943.33	−1.31627
$172$	2125.10	0.942077
$173$	672.880	0.295712	0.147856	−	0.989009i	$-0.452763\pi$
$173$	672.880	0.295712	0.147856	+	0.989009i	$0.452763\pi$
$174$	1309.39	0.570487
$175$	22.4969	0.00971774
$176$	23.4455	0.0100413
$177$	−5607.70	−2.38136
$178$	2183.19	0.919308
$179$	−2818.83	−1.17704	−0.588518	−	0.808484i	$-0.700288\pi$
$179$	−2818.83	−1.17704	−0.588518	+	0.808484i	$0.700288\pi$
$180$	−1856.05	−0.768565
$181$	1142.57	0.469207	0.234604	−	0.972091i	$-0.424621\pi$
$181$	1142.57	0.469207	0.234604	+	0.972091i	$0.424621\pi$
$182$	0	0
$183$	4702.64	1.89961
$184$	−1466.16	−0.587429
$185$	−622.941	−0.247565
$186$	3371.31	1.32901
$187$	−148.404	−0.0580341
$188$	−930.456	−0.360960
$189$	30.3908	0.0116963
$190$	1989.44	0.759627
$191$	2491.00	0.943678	0.471839	−	0.881685i	$-0.343590\pi$
$191$	2491.00	0.943678	0.471839	+	0.881685i	$0.343590\pi$
$192$	2245.59	0.844071
$193$	−4279.33	−1.59602	−0.798012	−	0.602641i	$-0.794115\pi$
$193$	−4279.33	−1.59602	−0.798012	+	0.602641i	$0.794115\pi$
$194$	−361.258	−0.133695
$195$	0	0
$196$	1729.81	0.630395
$197$	213.659	0.0772718	0.0386359	−	0.999253i	$-0.487699\pi$
$197$	213.659	0.0772718	0.0386359	+	0.999253i	$0.487699\pi$
$198$	−574.806	−0.206312
$199$	5018.25	1.78761	0.893806	−	0.448455i	$-0.148025\pi$
$199$	5018.25	1.78761	0.893806	+	0.448455i	$0.148025\pi$
$200$	438.474	0.155024
$201$	−6028.05	−2.11535
$202$	−948.130	−0.330249
$203$	−115.740	−0.0400166
$204$	517.874	0.177737
$205$	−2461.31	−0.838563
$206$	−2203.98	−0.745428
$207$	−1996.74	−0.670451
$208$	0	0
$209$	−1061.90	−0.351449
$210$	−179.483	−0.0589786
$211$	1856.32	0.605660	0.302830	−	0.953045i	$-0.402069\pi$
$211$	1856.32	0.605660	0.302830	+	0.953045i	$0.402069\pi$
$212$	−926.619	−0.300191
$213$	3165.48	1.01829
$214$	−1044.56	−0.333666
$215$	−5047.36	−1.60106
$216$	592.329	0.186588
$217$	−297.998	−0.0932232
$218$	−1194.17	−0.371007
$219$	−1754.80	−0.541455
$220$	−669.625	−0.205210
$221$	0	0
$222$	673.221	0.203530
$223$	4633.46	1.39139	0.695693	−	0.718339i	$-0.255097\pi$
$223$	4633.46	1.39139	0.695693	+	0.718339i	$0.255097\pi$
$224$	−209.921	−0.0626159
$225$	597.151	0.176934
$226$	233.756	0.0688020
$227$	2509.04	0.733617	0.366809	−	0.930296i	$-0.380450\pi$
$227$	2509.04	0.733617	0.366809	+	0.930296i	$0.380450\pi$
$228$	3705.62	1.07636
$229$	1069.34	0.308578	0.154289	−	0.988026i	$-0.450691\pi$
$229$	1069.34	0.308578	0.154289	+	0.988026i	$0.450691\pi$
$230$	1349.63	0.386921
$231$	95.8021	0.0272871
$232$	−2255.83	−0.638373
$233$	−4014.76	−1.12882	−0.564411	−	0.825494i	$-0.690897\pi$
$233$	−4014.76	−1.12882	−0.564411	+	0.825494i	$0.690897\pi$
$234$	0	0
$235$	2209.94	0.613450
$236$	3744.27	1.03276
$237$	8899.50	2.43918
$238$	26.5595	0.00723360
$239$	−3129.33	−0.846942	−0.423471	−	0.905910i	$-0.639189\pi$
$239$	−3129.33	−0.846942	−0.423471	+	0.905910i	$0.639189\pi$
$240$	194.323	0.0522645
$241$	5179.34	1.38436	0.692179	−	0.721725i	$-0.256651\pi$
$241$	5179.34	1.38436	0.692179	+	0.721725i	$0.256651\pi$
$242$	−207.379	−0.0550860
$243$	−5435.09	−1.43482
$244$	−3139.96	−0.823833
$245$	−4108.49	−1.07136
$246$	2659.97	0.689405
$247$	0	0
$248$	−5808.12	−1.48716
$249$	−1076.12	−0.273882
$250$	2172.41	0.549581
$251$	5277.32	1.32710	0.663549	−	0.748133i	$-0.269049\pi$
$251$	5277.32	1.32710	0.663549	+	0.748133i	$0.269049\pi$
$252$	−177.302	−0.0443215
$253$	−720.386	−0.179013
$254$	−1407.10	−0.347594
$255$	−1230.01	−0.302064
$256$	−4005.13	−0.977816
$257$	4437.31	1.07701	0.538505	−	0.842622i	$-0.318989\pi$
$257$	4437.31	1.07701	0.538505	+	0.842622i	$0.318989\pi$
$258$	5454.75	1.31627
$259$	−59.5076	−0.0142765
$260$	0	0
$261$	−3072.18	−0.728594
$262$	−727.312	−0.171502
$263$	−4055.35	−0.950811	−0.475405	−	0.879767i	$-0.657699\pi$
$263$	−4055.35	−0.950811	−0.475405	+	0.879767i	$0.657699\pi$
$264$	1867.22	0.435302
$265$	2200.83	0.510173
$266$	190.045	0.0438060
$267$	−9658.43	−2.21381
$268$	4024.94	0.917397
$269$	−6812.19	−1.54404	−0.772020	−	0.635598i	$-0.780754\pi$
$269$	−6812.19	−1.54404	−0.772020	+	0.635598i	$0.780754\pi$
$270$	−545.249	−0.122899
$271$	−874.626	−0.196051	−0.0980254	−	0.995184i	$-0.531253\pi$
$271$	−874.626	−0.196051	−0.0980254	+	0.995184i	$0.531253\pi$
$272$	−28.7554	−0.00641013
$273$	0	0
$274$	−287.181	−0.0633183
$275$	215.440	0.0472420
$276$	2513.88	0.548252
$277$	4575.21	0.992411	0.496205	−	0.868205i	$-0.334726\pi$
$277$	4575.21	0.992411	0.496205	+	0.868205i	$0.334726\pi$
$278$	741.489	0.159970
$279$	−7909.98	−1.69734
$280$	309.215	0.0659968
$281$	2100.40	0.445906	0.222953	−	0.974829i	$-0.428430\pi$
$281$	2100.40	0.445906	0.222953	+	0.974829i	$0.428430\pi$
$282$	−2388.32	−0.504334
$283$	−4771.16	−1.00218	−0.501088	−	0.865396i	$-0.667067\pi$
$283$	−4771.16	−1.00218	−0.501088	+	0.865396i	$0.667067\pi$
$284$	−2113.60	−0.441616
$285$	−8801.28	−1.82927
$286$	0	0
$287$	−235.121	−0.0483581
$288$	−5572.09	−1.14006
$289$	−4730.99	−0.962952
$290$	2076.53	0.420476
$291$	1598.20	0.321953
$292$	1171.69	0.234821
$293$	−7427.38	−1.48093	−0.740464	−	0.672096i	$-0.765394\pi$
$293$	−7427.38	−1.48093	−0.740464	+	0.672096i	$0.765394\pi$
$294$	4440.10	0.880790
$295$	−8893.09	−1.75517
$296$	−1159.83	−0.227749
$297$	291.036	0.0568606
$298$	651.871	0.126718
$299$	0	0
$300$	−751.805	−0.144685
$301$	−482.159	−0.0923295
$302$	3597.62	0.685495
$303$	4194.53	0.795279
$304$	−205.758	−0.0388192
$305$	7457.78	1.40010
$306$	704.988	0.131704
$307$	9166.55	1.70411	0.852057	−	0.523449i	$-0.175355\pi$
$307$	9166.55	1.70411	0.852057	+	0.523449i	$0.175355\pi$
$308$	−63.9672	−0.0118340
$309$	9750.40	1.79508
$310$	5346.46	0.979544
$311$	−7571.27	−1.38047	−0.690237	−	0.723584i	$-0.742494\pi$
$311$	−7571.27	−1.38047	−0.690237	+	0.723584i	$0.742494\pi$
$312$	0	0
$313$	4911.34	0.886918	0.443459	−	0.896295i	$-0.353751\pi$
$313$	4911.34	0.886918	0.443459	+	0.896295i	$0.353751\pi$
$314$	963.438	0.173153
$315$	421.115	0.0753242
$316$	−5942.21	−1.05783
$317$	−4342.41	−0.769382	−0.384691	−	0.923045i	$-0.625692\pi$
$317$	−4342.41	−0.769382	−0.384691	+	0.923045i	$0.625692\pi$
$318$	−2378.47	−0.419427
$319$	−1108.38	−0.194537
$320$	3561.22	0.622120
$321$	4621.13	0.803509
$322$	128.926	0.0223129
$323$	1302.39	0.224357
$324$	3152.04	0.540473
$325$	0	0
$326$	3140.49	0.533544
$327$	5283.02	0.893430
$328$	−4582.62	−0.771441
$329$	211.109	0.0353764
$330$	−1718.81	−0.286719
$331$	7714.14	1.28099	0.640495	−	0.767963i	$-0.278729\pi$
$331$	7714.14	1.28099	0.640495	+	0.767963i	$0.278729\pi$
$332$	718.530	0.118778
$333$	−1579.55	−0.259937
$334$	−6823.30	−1.11783
$335$	−9559.71	−1.55911
$336$	18.5630	0.00301398
$337$	−1241.33	−0.200652	−0.100326	−	0.994955i	$-0.531989\pi$
$337$	−1241.33	−0.200652	−0.100326	+	0.994955i	$0.531989\pi$
$338$	0	0
$339$	−1034.14	−0.165684
$340$	821.282	0.131001
$341$	−2853.77	−0.453197
$342$	5044.50	0.797589
$343$	−786.459	−0.123804
$344$	−9397.49	−1.47290
$345$	−5970.75	−0.931752
$346$	−1153.23	−0.179185
$347$	−7892.11	−1.22095	−0.610476	−	0.792035i	$-0.709022\pi$
$347$	−7892.11	−1.22095	−0.610476	+	0.792035i	$0.709022\pi$
$348$	3867.83	0.595798
$349$	12310.9	1.88822	0.944108	−	0.329636i	$-0.106926\pi$
$349$	12310.9	1.88822	0.944108	+	0.329636i	$0.106926\pi$
$350$	−38.5568	−0.00588842
$351$	0	0
$352$	−2010.30	−0.304402
$353$	8589.06	1.29504	0.647520	−	0.762048i	$-0.275806\pi$
$353$	8589.06	1.29504	0.647520	+	0.762048i	$0.275806\pi$
$354$	9610.89	1.44297
$355$	5020.05	0.750525
$356$	6448.95	0.960095
$357$	−117.499	−0.0174194
$358$	4831.12	0.713220
$359$	3701.05	0.544105	0.272053	−	0.962282i	$-0.412298\pi$
$359$	3701.05	0.544105	0.272053	+	0.962282i	$0.412298\pi$
$360$	8207.71	1.20162
$361$	2460.21	0.358683
$362$	−1958.22	−0.284314
$363$	917.444	0.132654
$364$	0	0
$365$	−2782.89	−0.399078
$366$	−8059.72	−1.15106
$367$	9787.49	1.39211	0.696053	−	0.717991i	$-0.254938\pi$
$367$	9787.49	1.39211	0.696053	+	0.717991i	$0.254938\pi$
$368$	−139.585	−0.0197728
$369$	−6241.00	−0.880469
$370$	1067.64	0.150011
$371$	210.238	0.0294206
$372$	9958.56	1.38798
$373$	1477.98	0.205166	0.102583	−	0.994724i	$-0.467289\pi$
$373$	1477.98	0.205166	0.102583	+	0.994724i	$0.467289\pi$
$374$	254.346	0.0351655
$375$	−9610.74	−1.32346
$376$	4114.61	0.564348
$377$	0	0
$378$	−52.0859	−0.00708733
$379$	−13264.6	−1.79778	−0.898889	−	0.438177i	$-0.855624\pi$
$379$	−13264.6	−1.79778	−0.898889	+	0.438177i	$0.855624\pi$
$380$	5876.64	0.793329
$381$	6224.99	0.837050
$382$	−4269.26	−0.571818
$383$	−2321.46	−0.309716	−0.154858	−	0.987937i	$-0.549492\pi$
$383$	−2321.46	−0.309716	−0.154858	+	0.987937i	$0.549492\pi$
$384$	7236.77	0.961718
$385$	151.930	0.0201118
$386$	7334.23	0.967104
$387$	−12798.3	−1.68107
$388$	−1067.12	−0.139626
$389$	−7014.06	−0.914209	−0.457104	−	0.889413i	$-0.651113\pi$
$389$	−7014.06	−0.914209	−0.457104	+	0.889413i	$0.651113\pi$
$390$	0	0
$391$	883.539	0.114277
$392$	−7649.45	−0.985600
$393$	3217.63	0.412997
$394$	−366.184	−0.0468225
$395$	14113.5	1.79779
$396$	−1697.93	−0.215465
$397$	7033.39	0.889158	0.444579	−	0.895740i	$-0.353353\pi$
$397$	7033.39	0.889158	0.444579	+	0.895740i	$0.353353\pi$
$398$	−8600.65	−1.08320
$399$	−840.759	−0.105490
$400$	41.7447	0.00521809
$401$	−8022.65	−0.999083	−0.499541	−	0.866290i	$-0.666498\pi$
$401$	−8022.65	−0.999083	−0.499541	+	0.866290i	$0.666498\pi$
$402$	10331.3	1.28179
$403$	0	0
$404$	−2800.70	−0.344901
$405$	−7486.47	−0.918532
$406$	198.364	0.0242479
$407$	−569.872	−0.0694042
$408$	−2290.11	−0.277886
$409$	319.613	0.0386402	0.0193201	−	0.999813i	$-0.493850\pi$
$409$	319.613	0.0386402	0.0193201	+	0.999813i	$0.493850\pi$
$410$	4218.37	0.508123
$411$	1270.49	0.152478
$412$	−6510.36	−0.778501
$413$	−849.530	−0.101217
$414$	3422.17	0.406257
$415$	−1706.59	−0.201864
$416$	0	0
$417$	−3280.35	−0.385226
$418$	1819.96	0.212959
$419$	−12257.4	−1.42915	−0.714573	−	0.699561i	$-0.753379\pi$
$419$	−12257.4	−1.42915	−0.714573	+	0.699561i	$0.753379\pi$
$420$	−530.178	−0.0615953
$421$	−13918.5	−1.61127	−0.805636	−	0.592411i	$-0.798176\pi$
$421$	−13918.5	−1.61127	−0.805636	+	0.592411i	$0.798176\pi$
$422$	−3181.50	−0.366997
$423$	5603.62	0.644107
$424$	4097.64	0.469337
$425$	−264.233	−0.0301581
$426$	−5425.23	−0.617027
$427$	712.419	0.0807409
$428$	−3085.54	−0.348470
$429$	0	0
$430$	8650.54	0.970153
$431$	−1697.27	−0.189686	−0.0948432	−	0.995492i	$-0.530235\pi$
$431$	−1697.27	−0.189686	−0.0948432	+	0.995492i	$0.530235\pi$
$432$	56.3924	0.00628051
$433$	−11237.9	−1.24725	−0.623627	−	0.781722i	$-0.714341\pi$
$433$	−11237.9	−1.24725	−0.623627	+	0.781722i	$0.714341\pi$
$434$	510.731	0.0564882
$435$	−9186.56	−1.01256
$436$	−3527.48	−0.387467
$437$	6322.11	0.692054
$438$	3007.51	0.328092
$439$	16627.3	1.80770	0.903848	−	0.427853i	$-0.140730\pi$
$439$	16627.3	1.80770	0.903848	+	0.427853i	$0.140730\pi$
$440$	2961.18	0.320838
$441$	−10417.7	−1.12490
$442$	0	0
$443$	−12257.4	−1.31460	−0.657301	−	0.753628i	$-0.728302\pi$
$443$	−12257.4	−1.31460	−0.657301	+	0.753628i	$0.728302\pi$
$444$	1988.64	0.212560
$445$	−15317.0	−1.63168
$446$	−7941.16	−0.843105
$447$	−2883.88	−0.305152
$448$	340.193	0.0358763
$449$	−6503.86	−0.683599	−0.341799	−	0.939773i	$-0.611036\pi$
$449$	−6503.86	−0.683599	−0.341799	+	0.939773i	$0.611036\pi$
$450$	−1023.44	−0.107212
$451$	−2251.63	−0.235089
$452$	690.497	0.0718545
$453$	−15915.9	−1.65076
$454$	−4300.18	−0.444532
$455$	0	0
$456$	−16386.8	−1.68285
$457$	−6475.67	−0.662842	−0.331421	−	0.943483i	$-0.607528\pi$
$457$	−6475.67	−0.662842	−0.331421	+	0.943483i	$0.607528\pi$
$458$	−1832.72	−0.186981
$459$	−356.950	−0.0362984
$460$	3986.68	0.404087
$461$	−14619.6	−1.47702	−0.738508	−	0.674245i	$-0.764469\pi$
$461$	−14619.6	−1.47702	−0.738508	+	0.674245i	$0.764469\pi$
$462$	−164.193	−0.0165345
$463$	−10624.1	−1.06640	−0.533198	−	0.845990i	$-0.679010\pi$
$463$	−10624.1	−1.06640	−0.533198	+	0.845990i	$0.679010\pi$
$464$	−214.765	−0.0214875
$465$	−23652.8	−2.35886
$466$	6880.79	0.684005
$467$	5675.39	0.562368	0.281184	−	0.959654i	$-0.409273\pi$
$467$	5675.39	0.562368	0.281184	+	0.959654i	$0.409273\pi$
$468$	0	0
$469$	−913.210	−0.0899107
$470$	−3787.56	−0.371718
$471$	−4262.25	−0.416973
$472$	−16557.7	−1.61468
$473$	−4617.37	−0.448852
$474$	−15252.6	−1.47801
$475$	−1890.71	−0.182635
$476$	78.4545	0.00755453
$477$	5580.51	0.535669
$478$	5363.27	0.513201
$479$	−12268.0	−1.17023	−0.585115	−	0.810950i	$-0.698951\pi$
$479$	−12268.0	−1.17023	−0.585115	+	0.810950i	$0.698951\pi$
$480$	−16661.9	−1.58439
$481$	0	0
$482$	−8876.73	−0.838846
$483$	−570.368	−0.0537321
$484$	−612.579	−0.0575300
$485$	2534.55	0.237295
$486$	9315.05	0.869422
$487$	−2012.00	−0.187213	−0.0936064	−	0.995609i	$-0.529840\pi$
$487$	−2012.00	−0.187213	−0.0936064	+	0.995609i	$0.529840\pi$
$488$	13885.3	1.28803
$489$	−13893.5	−1.28484
$490$	7041.44	0.649183
$491$	10888.7	1.00081	0.500407	−	0.865790i	$-0.333184\pi$
$491$	10888.7	1.00081	0.500407	+	0.865790i	$0.333184\pi$
$492$	7857.33	0.719991
$493$	1359.41	0.124188
$494$	0	0
$495$	4032.78	0.366182
$496$	−552.958	−0.0500576
$497$	479.550	0.0432812
$498$	1844.34	0.165957
$499$	−12983.5	−1.16478	−0.582388	−	0.812911i	$-0.697882\pi$
$499$	−12983.5	−1.16478	−0.582388	+	0.812911i	$0.697882\pi$
$500$	6417.11	0.573964
$501$	30186.3	2.69187
$502$	−9044.66	−0.804149
$503$	−17173.0	−1.52228	−0.761138	−	0.648590i	$-0.775359\pi$
$503$	−17173.0	−1.52228	−0.761138	+	0.648590i	$0.775359\pi$
$504$	784.057	0.0692950
$505$	6651.99	0.586158
$506$	1234.65	0.108472
$507$	0	0
$508$	−4156.44	−0.363016
$509$	−2131.91	−0.185649	−0.0928245	−	0.995682i	$-0.529590\pi$
$509$	−2131.91	−0.185649	−0.0928245	+	0.995682i	$0.529590\pi$
$510$	2108.09	0.183035
$511$	−265.841	−0.0230139
$512$	−771.264	−0.0665730
$513$	−2554.13	−0.219820
$514$	−7604.98	−0.652609
$515$	15462.9	1.32306
$516$	16112.9	1.37467
$517$	2021.68	0.171979
$518$	101.989	0.00865081
$519$	5101.90	0.431500
$520$	0	0
$521$	13036.6	1.09624	0.548122	−	0.836398i	$-0.315343\pi$
$521$	13036.6	1.09624	0.548122	+	0.836398i	$0.315343\pi$
$522$	5265.33	0.441489
$523$	13914.1	1.16333	0.581666	−	0.813428i	$-0.302401\pi$
$523$	13914.1	1.16333	0.581666	+	0.813428i	$0.302401\pi$
$524$	−2148.42	−0.179111
$525$	170.575	0.0141800
$526$	6950.35	0.576140
$527$	3500.09	0.289310
$528$	177.768	0.0146522
$529$	−7878.11	−0.647498
$530$	−3771.94	−0.309137
$531$	−22549.7	−1.84289
$532$	561.377	0.0457496
$533$	0	0
$534$	16553.3	1.34145
$535$	7328.53	0.592224
$536$	−17798.9	−1.43432
$537$	−21372.9	−1.71752
$538$	11675.2	0.935604
$539$	−3758.49	−0.300352
$540$	−1610.62	−0.128352
$541$	−14823.1	−1.17799	−0.588997	−	0.808135i	$-0.700477\pi$
$541$	−14823.1	−1.17799	−0.588997	+	0.808135i	$0.700477\pi$
$542$	1499.00	0.118796
$543$	8663.16	0.684663
$544$	2465.59	0.194323
$545$	8378.19	0.658500
$546$	0	0
$547$	15016.3	1.17377	0.586883	−	0.809672i	$-0.300355\pi$
$547$	15016.3	1.17377	0.586883	+	0.809672i	$0.300355\pi$
$548$	−848.307	−0.0661275
$549$	18910.2	1.47007
$550$	−369.237	−0.0286261
$551$	9727.16	0.752071
$552$	−11116.7	−0.857172
$553$	1348.22	0.103674
$554$	−7841.33	−0.601347
$555$	−4723.25	−0.361245
$556$	2190.30	0.167067
$557$	−16833.8	−1.28056	−0.640280	−	0.768142i	$-0.721182\pi$
$557$	−16833.8	−1.28056	−0.640280	+	0.768142i	$0.721182\pi$
$558$	13556.7	1.02850
$559$	0	0
$560$	29.4386	0.00222144
$561$	−1125.23	−0.0846829
$562$	−3599.82	−0.270195
$563$	−6064.83	−0.454000	−0.227000	−	0.973895i	$-0.572892\pi$
$563$	−6064.83	−0.454000	−0.227000	+	0.973895i	$0.572892\pi$
$564$	−7054.88	−0.526710
$565$	−1640.01	−0.122117
$566$	8177.16	0.607265
$567$	−715.159	−0.0529698
$568$	9346.63	0.690451
$569$	9627.30	0.709310	0.354655	−	0.934997i	$-0.384598\pi$
$569$	9627.30	0.709310	0.354655	+	0.934997i	$0.384598\pi$
$570$	15084.3	1.10844
$571$	−15965.2	−1.17009	−0.585047	−	0.811000i	$-0.698924\pi$
$571$	−15965.2	−1.17009	−0.585047	+	0.811000i	$0.698924\pi$
$572$	0	0
$573$	18887.2	1.37701
$574$	402.968	0.0293024
$575$	−1282.65	−0.0930262
$576$	9029.98	0.653210
$577$	−14746.2	−1.06394	−0.531969	−	0.846764i	$-0.678548\pi$
$577$	−14746.2	−1.06394	−0.531969	+	0.846764i	$0.678548\pi$
$578$	8108.31	0.583497
$579$	−32446.6	−2.32891
$580$	6133.89	0.439131
$581$	−163.026	−0.0116410
$582$	−2739.12	−0.195086
$583$	2013.34	0.143026
$584$	−5181.36	−0.367134
$585$	0	0
$586$	12729.6	0.897362
$587$	8722.18	0.613293	0.306646	−	0.951824i	$-0.400793\pi$
$587$	8722.18	0.613293	0.306646	+	0.951824i	$0.400793\pi$
$588$	13115.7	0.919868
$589$	25044.7	1.75203
$590$	15241.6	1.06354
$591$	1620.00	0.112754
$592$	−110.421	−0.00766600
$593$	11043.5	0.764758	0.382379	−	0.924006i	$-0.375105\pi$
$593$	11043.5	0.764758	0.382379	+	0.924006i	$0.375105\pi$
$594$	−498.799	−0.0344545
$595$	−186.339	−0.0128389
$596$	1925.57	0.132340
$597$	38049.3	2.60847
$598$	0	0
$599$	16196.7	1.10481	0.552403	−	0.833577i	$-0.313711\pi$
$599$	16196.7	1.10481	0.552403	+	0.833577i	$0.313711\pi$
$600$	3324.59	0.226210
$601$	−17497.4	−1.18758	−0.593788	−	0.804622i	$-0.702368\pi$
$601$	−17497.4	−1.18758	−0.593788	+	0.804622i	$0.702368\pi$
$602$	826.359	0.0559467
$603$	−24240.0	−1.63703
$604$	10627.1	0.715909
$605$	1454.95	0.0977720
$606$	−7188.90	−0.481896
$607$	−1022.95	−0.0684026	−0.0342013	−	0.999415i	$-0.510889\pi$
$607$	−1022.95	−0.0684026	−0.0342013	+	0.999415i	$0.510889\pi$
$608$	17642.4	1.17680
$609$	−877.564	−0.0583919
$610$	−12781.7	−0.848386
$611$	0	0
$612$	2082.48	0.137548
$613$	1693.48	0.111581	0.0557903	−	0.998443i	$-0.482232\pi$
$613$	1693.48	0.111581	0.0557903	+	0.998443i	$0.482232\pi$
$614$	−15710.3	−1.03260
$615$	−18662.1	−1.22362
$616$	282.872	0.0185020
$617$	7260.34	0.473728	0.236864	−	0.971543i	$-0.423880\pi$
$617$	7260.34	0.473728	0.236864	+	0.971543i	$0.423880\pi$
$618$	−16710.9	−1.08772
$619$	−24727.9	−1.60565	−0.802826	−	0.596213i	$-0.796671\pi$
$619$	−24727.9	−1.60565	−0.802826	+	0.596213i	$0.796671\pi$
$620$	15793.0	1.02300
$621$	−1732.71	−0.111967
$622$	12976.2	0.836492
$623$	−1463.19	−0.0940954
$624$	0	0
$625$	−17689.6	−1.13213
$626$	−8417.41	−0.537424
$627$	−8051.49	−0.512832
$628$	2845.92	0.180835
$629$	698.936	0.0443059
$630$	−721.737	−0.0456424
$631$	20569.6	1.29772	0.648861	−	0.760907i	$-0.275246\pi$
$631$	20569.6	1.29772	0.648861	+	0.760907i	$0.275246\pi$
$632$	26277.3	1.65389
$633$	14075.0	0.883774
$634$	7442.34	0.466204
$635$	9872.04	0.616945
$636$	−7025.79	−0.438036
$637$	0	0
$638$	1899.63	0.117879
$639$	12729.0	0.788032
$640$	11476.6	0.708831
$641$	1396.87	0.0860737	0.0430368	−	0.999073i	$-0.486297\pi$
$641$	1396.87	0.0860737	0.0430368	+	0.999073i	$0.486297\pi$
$642$	−7920.04	−0.486883
$643$	18509.3	1.13520	0.567602	−	0.823303i	$-0.307871\pi$
$643$	18509.3	1.13520	0.567602	+	0.823303i	$0.307871\pi$
$644$	380.836	0.0233028
$645$	−38270.0	−2.33625
$646$	−2232.14	−0.135948
$647$	3353.00	0.203740	0.101870	−	0.994798i	$-0.467517\pi$
$647$	3353.00	0.203740	0.101870	+	0.994798i	$0.467517\pi$
$648$	−13938.8	−0.845010
$649$	−8135.48	−0.492058
$650$	0	0
$651$	−2259.48	−0.136031
$652$	9276.74	0.557216
$653$	−22765.2	−1.36427	−0.682136	−	0.731225i	$-0.738949\pi$
$653$	−22765.2	−1.36427	−0.682136	+	0.731225i	$0.738949\pi$
$654$	−9054.42	−0.541370
$655$	5102.75	0.304398
$656$	−436.286	−0.0259666
$657$	−7056.42	−0.419021
$658$	−361.814	−0.0214362
$659$	33170.2	1.96074	0.980371	−	0.197162i	$-0.0631724\pi$
$659$	33170.2	1.96074	0.980371	+	0.197162i	$0.0631724\pi$
$660$	−5077.22	−0.299440
$661$	−8204.77	−0.482796	−0.241398	−	0.970426i	$-0.577606\pi$
$661$	−8204.77	−0.482796	−0.241398	+	0.970426i	$0.577606\pi$
$662$	−13221.1	−0.776210
$663$	0	0
$664$	−3177.44	−0.185706
$665$	−1333.34	−0.0777513
$666$	2707.15	0.157508
$667$	6598.87	0.383072
$668$	−20155.5	−1.16742
$669$	35131.7	2.03030
$670$	16384.1	0.944738
$671$	6822.44	0.392515
$672$	−1591.66	−0.0913685
$673$	26068.7	1.49313	0.746563	−	0.665315i	$-0.231703\pi$
$673$	26068.7	1.49313	0.746563	+	0.665315i	$0.231703\pi$
$674$	2127.49	0.121584
$675$	518.189	0.0295483
$676$	0	0
$677$	−12640.8	−0.717618	−0.358809	−	0.933411i	$-0.616817\pi$
$677$	−12640.8	−0.717618	−0.358809	+	0.933411i	$0.616817\pi$
$678$	1772.38	0.100395
$679$	242.118	0.0136843
$680$	−3631.83	−0.204815
$681$	19024.0	1.07049
$682$	4890.99	0.274613
$683$	−9229.09	−0.517044	−0.258522	−	0.966005i	$-0.583235\pi$
$683$	−9229.09	−0.517044	−0.258522	+	0.966005i	$0.583235\pi$
$684$	14901.0	0.832975
$685$	2014.83	0.112384
$686$	1347.89	0.0750185
$687$	8107.96	0.450274
$688$	−894.683	−0.0495777
$689$	0	0
$690$	10233.1	0.564591
$691$	−3657.76	−0.201371	−0.100686	−	0.994918i	$-0.532104\pi$
$691$	−3657.76	−0.201371	−0.100686	+	0.994918i	$0.532104\pi$
$692$	−3406.55	−0.187135
$693$	385.239	0.0211169
$694$	13526.1	0.739831
$695$	−5202.22	−0.283930
$696$	−17104.1	−0.931508
$697$	2761.58	0.150075
$698$	−21099.3	−1.14416
$699$	−30440.6	−1.64717
$700$	−113.894	−0.00614968
$701$	26747.1	1.44112	0.720559	−	0.693394i	$-0.243885\pi$
$701$	26747.1	1.44112	0.720559	+	0.693394i	$0.243885\pi$
$702$	0	0
$703$	5001.20	0.268313
$704$	3257.84	0.174410
$705$	16756.2	0.895141
$706$	−14720.6	−0.784724
$707$	635.444	0.0338025
$708$	28389.8	1.50699
$709$	−8825.09	−0.467466	−0.233733	−	0.972301i	$-0.575094\pi$
$709$	−8825.09	−0.467466	−0.233733	+	0.972301i	$0.575094\pi$
$710$	−8603.72	−0.454778
$711$	35786.7	1.88763
$712$	−28518.2	−1.50107
$713$	16990.2	0.892409
$714$	201.379	0.0105552
$715$	0	0
$716$	14270.7	0.744863
$717$	−23727.1	−1.23585
$718$	−6343.12	−0.329698
$719$	26633.2	1.38143	0.690716	−	0.723126i	$-0.257296\pi$
$719$	26633.2	1.38143	0.690716	+	0.723126i	$0.257296\pi$
$720$	781.410	0.0404465
$721$	1477.12	0.0762980
$722$	−4216.49	−0.217343
$723$	39270.7	2.02004
$724$	−5784.41	−0.296928
$725$	−1973.47	−0.101094
$726$	−1572.38	−0.0803810
$727$	6013.99	0.306804	0.153402	−	0.988164i	$-0.450977\pi$
$727$	6013.99	0.306804	0.153402	+	0.988164i	$0.450977\pi$
$728$	0	0
$729$	−24399.4	−1.23962
$730$	4769.53	0.241819
$731$	5663.11	0.286536
$732$	−23807.7	−1.20213
$733$	−11746.5	−0.591908	−0.295954	−	0.955202i	$-0.595638\pi$
$733$	−11746.5	−0.591908	−0.295954	+	0.955202i	$0.595638\pi$
$734$	−16774.5	−0.843540
$735$	−31151.3	−1.56331
$736$	11968.5	0.599410
$737$	−8745.31	−0.437093
$738$	10696.3	0.533517
$739$	−16976.0	−0.845021	−0.422510	−	0.906358i	$-0.638851\pi$
$739$	−16976.0	−0.845021	−0.422510	+	0.906358i	$0.638851\pi$
$740$	3153.72	0.156666
$741$	0	0
$742$	−360.322	−0.0178273
$743$	24921.6	1.23053	0.615266	−	0.788320i	$-0.289049\pi$
$743$	24921.6	1.23053	0.615266	+	0.788320i	$0.289049\pi$
$744$	−44038.2	−2.17005
$745$	−4573.47	−0.224911
$746$	−2533.07	−0.124320
$747$	−4327.31	−0.211952
$748$	751.316	0.0367257
$749$	700.071	0.0341523
$750$	16471.6	0.801943
$751$	25657.3	1.24667	0.623335	−	0.781955i	$-0.285777\pi$
$751$	25657.3	1.24667	0.623335	+	0.781955i	$0.285777\pi$
$752$	391.729	0.0189959
$753$	40013.6	1.93649
$754$	0	0
$755$	−25240.5	−1.21668
$756$	−153.858	−0.00740178
$757$	−41083.2	−1.97252	−0.986259	−	0.165207i	$-0.947171\pi$
$757$	−41083.2	−1.97252	−0.986259	+	0.165207i	$0.947171\pi$
$758$	22733.9	1.08936
$759$	−5462.10	−0.261214
$760$	−25987.3	−1.24034
$761$	8750.87	0.416844	0.208422	−	0.978039i	$-0.433167\pi$
$761$	8750.87	0.416844	0.208422	+	0.978039i	$0.433167\pi$
$762$	−10668.8	−0.507207
$763$	800.343	0.0379742
$764$	−12611.0	−0.597188
$765$	−4946.13	−0.233762
$766$	3978.70	0.187671
$767$	0	0
$768$	−30367.6	−1.42682
$769$	3787.13	0.177591	0.0887953	−	0.996050i	$-0.471698\pi$
$769$	3787.13	0.177591	0.0887953	+	0.996050i	$0.471698\pi$
$770$	−260.389	−0.0121867
$771$	33644.5	1.57156
$772$	21664.7	1.01001
$773$	39001.3	1.81472	0.907361	−	0.420352i	$-0.138093\pi$
$773$	39001.3	1.81472	0.907361	+	0.420352i	$0.138093\pi$
$774$	21934.6	1.01864
$775$	−5081.13	−0.235509
$776$	4718.98	0.218301
$777$	−451.197	−0.0208322
$778$	12021.2	0.553961
$779$	19760.3	0.908840
$780$	0	0
$781$	4592.38	0.210408
$782$	−1514.27	−0.0692459
$783$	−2665.94	−0.121677
$784$	−728.261	−0.0331752
$785$	−6759.39	−0.307329
$786$	−5514.61	−0.250254
$787$	12795.8	0.579568	0.289784	−	0.957092i	$-0.406417\pi$
$787$	12795.8	0.579568	0.289784	+	0.957092i	$0.406417\pi$
$788$	−1081.68	−0.0488999
$789$	−30748.4	−1.38742
$790$	−24188.7	−1.08936
$791$	−156.665	−0.00704219
$792$	7508.48	0.336872
$793$	0	0
$794$	−12054.3	−0.538782
$795$	16687.1	0.744440
$796$	−25405.6	−1.13125
$797$	−22658.2	−1.00702	−0.503510	−	0.863989i	$-0.667958\pi$
$797$	−22658.2	−1.00702	−0.503510	+	0.863989i	$0.667958\pi$
$798$	1440.96	0.0639214
$799$	−2479.54	−0.109787
$800$	−3579.34	−0.158186
$801$	−38838.5	−1.71322
$802$	13749.8	0.605390
$803$	−2545.82	−0.111880
$804$	30517.8	1.33866
$805$	−904.530	−0.0396031
$806$	0	0
$807$	−51651.3	−2.25305
$808$	12385.1	0.539240
$809$	37998.1	1.65135	0.825675	−	0.564146i	$-0.190795\pi$
$809$	37998.1	1.65135	0.825675	+	0.564146i	$0.190795\pi$
$810$	12830.9	0.556581
$811$	1289.52	0.0558339	0.0279169	−	0.999610i	$-0.491113\pi$
$811$	1289.52	0.0558339	0.0279169	+	0.999610i	$0.491113\pi$
$812$	585.951	0.0253237
$813$	−6631.57	−0.286076
$814$	976.688	0.0420552
$815$	−22033.4	−0.946987
$816$	−218.029	−0.00935360
$817$	40522.1	1.73524
$818$	−547.777	−0.0234139
$819$	0	0
$820$	12460.7	0.530667
$821$	37353.1	1.58786	0.793929	−	0.608010i	$-0.208032\pi$
$821$	37353.1	1.58786	0.793929	+	0.608010i	$0.208032\pi$
$822$	−2177.45	−0.0923935
$823$	−18764.4	−0.794757	−0.397379	−	0.917655i	$-0.630080\pi$
$823$	−18764.4	−0.794757	−0.397379	+	0.917655i	$0.630080\pi$
$824$	28789.7	1.21716
$825$	1633.51	0.0689351
$826$	1455.99	0.0613320
$827$	−2725.13	−0.114585	−0.0572926	−	0.998357i	$-0.518247\pi$
$827$	−2725.13	−0.114585	−0.0572926	+	0.998357i	$0.518247\pi$
$828$	10108.8	0.424281
$829$	18577.8	0.778327	0.389164	−	0.921169i	$-0.372764\pi$
$829$	18577.8	0.778327	0.389164	+	0.921169i	$0.372764\pi$
$830$	2924.89	0.122318
$831$	34690.1	1.44812
$832$	0	0
$833$	4609.71	0.191737
$834$	5622.10	0.233426
$835$	47871.7	1.98403
$836$	5376.00	0.222408
$837$	−6864.03	−0.283460
$838$	21007.6	0.865984
$839$	−25333.2	−1.04243	−0.521214	−	0.853426i	$-0.674521\pi$
$839$	−25333.2	−1.04243	−0.521214	+	0.853426i	$0.674521\pi$
$840$	2344.52	0.0963020
$841$	−14236.0	−0.583707
$842$	23854.5	0.976343
$843$	15925.6	0.650662
$844$	−9397.88	−0.383280
$845$	0	0
$846$	−9603.90	−0.390294
$847$	138.987	0.00563830
$848$	390.114	0.0157978
$849$	−36175.8	−1.46237
$850$	452.862	0.0182742
$851$	3392.79	0.136667
$852$	−16025.7	−0.644402
$853$	−16957.1	−0.680657	−0.340329	−	0.940307i	$-0.610538\pi$
$853$	−16957.1	−0.680657	−0.340329	+	0.940307i	$0.610538\pi$
$854$	−1221.00	−0.0489246
$855$	−35391.7	−1.41564
$856$	13644.7	0.544820
$857$	34328.5	1.36831	0.684153	−	0.729339i	$-0.260172\pi$
$857$	34328.5	1.36831	0.684153	+	0.729339i	$0.260172\pi$
$858$	0	0
$859$	49595.5	1.96994	0.984969	−	0.172730i	$-0.0552588\pi$
$859$	49595.5	1.96994	0.984969	+	0.172730i	$0.0552588\pi$
$860$	25553.0	1.01320
$861$	−1782.73	−0.0705637
$862$	2908.91	0.114940
$863$	−40368.3	−1.59230	−0.796149	−	0.605100i	$-0.793133\pi$
$863$	−40368.3	−1.59230	−0.796149	+	0.605100i	$0.793133\pi$
$864$	−4835.29	−0.190393
$865$	8090.96	0.318036
$866$	19260.4	0.755768
$867$	−35871.2	−1.40513
$868$	1508.66	0.0589944
$869$	12911.1	0.504005
$870$	15744.6	0.613554
$871$	0	0
$872$	15599.0	0.605791
$873$	6426.70	0.249153
$874$	−10835.3	−0.419347
$875$	−1455.96	−0.0562521
$876$	8883.94	0.342649
$877$	17469.2	0.672624	0.336312	−	0.941751i	$-0.390820\pi$
$877$	17469.2	0.672624	0.336312	+	0.941751i	$0.390820\pi$
$878$	−28497.1	−1.09537
$879$	−56315.7	−2.16096
$880$	281.917	0.0107994
$881$	−20477.8	−0.783106	−0.391553	−	0.920156i	$-0.628062\pi$
$881$	−20477.8	−0.783106	−0.391553	+	0.920156i	$0.628062\pi$
$882$	17854.6	0.681626
$883$	−35816.4	−1.36503	−0.682514	−	0.730873i	$-0.739113\pi$
$883$	−35816.4	−1.36503	−0.682514	+	0.730873i	$0.739113\pi$
$884$	0	0
$885$	−67429.1	−2.56113
$886$	21007.7	0.796577
$887$	41513.2	1.57145	0.785725	−	0.618576i	$-0.212290\pi$
$887$	41513.2	1.57145	0.785725	+	0.618576i	$0.212290\pi$
$888$	−8794.04	−0.332329
$889$	943.046	0.0355779
$890$	26251.4	0.988708
$891$	−6848.69	−0.257508
$892$	−23457.5	−0.880511
$893$	−17742.2	−0.664861
$894$	4942.61	0.184905
$895$	−33894.7	−1.26589
$896$	1096.32	0.0408768
$897$	0	0
$898$	11146.8	0.414224
$899$	26141.0	0.969801
$900$	−3023.16	−0.111969
$901$	−2469.32	−0.0913040
$902$	3859.01	0.142451
$903$	−3655.82	−0.134726
$904$	−3053.47	−0.112342
$905$	13738.7	0.504629
$906$	27277.8	1.00027
$907$	−708.287	−0.0259297	−0.0129649	−	0.999916i	$-0.504127\pi$
$907$	−708.287	−0.0259297	−0.0129649	+	0.999916i	$0.504127\pi$
$908$	−12702.4	−0.464255
$909$	16867.1	0.615451
$910$	0	0
$911$	9545.67	0.347159	0.173580	−	0.984820i	$-0.444467\pi$
$911$	9545.67	0.347159	0.173580	+	0.984820i	$0.444467\pi$
$912$	−1560.09	−0.0566446
$913$	−1561.21	−0.0565919
$914$	11098.5	0.401646
$915$	56546.2	2.04302
$916$	−5413.70	−0.195277
$917$	487.450	0.0175540
$918$	611.766	0.0219949
$919$	−8045.50	−0.288789	−0.144394	−	0.989520i	$-0.546123\pi$
$919$	−8045.50	−0.288789	−0.144394	+	0.989520i	$0.546123\pi$
$920$	−17629.7	−0.631776
$921$	69502.5	2.48663
$922$	25056.2	0.894992
$923$	0	0
$924$	−485.011	−0.0172681
$925$	−1014.66	−0.0360667
$926$	18208.3	0.646179
$927$	39208.3	1.38918
$928$	18414.7	0.651393
$929$	48885.7	1.72647	0.863234	−	0.504804i	$-0.168435\pi$
$929$	48885.7	1.72647	0.863234	+	0.504804i	$0.168435\pi$
$930$	40537.9	1.42934
$931$	32984.5	1.16114
$932$	20325.3	0.714352
$933$	−57406.7	−2.01437
$934$	−9726.90	−0.340764
$935$	−1784.47	−0.0624153
$936$	0	0
$937$	4864.24	0.169592	0.0847960	−	0.996398i	$-0.472976\pi$
$937$	4864.24	0.169592	0.0847960	+	0.996398i	$0.472976\pi$
$938$	1565.13	0.0544810
$939$	37238.7	1.29418
$940$	−11188.1	−0.388210
$941$	54095.1	1.87402	0.937009	−	0.349305i	$-0.113582\pi$
$941$	54095.1	1.87402	0.937009	+	0.349305i	$0.113582\pi$
$942$	7304.96	0.252663
$943$	13405.3	0.462923
$944$	−1576.37	−0.0543500
$945$	365.430	0.0125793
$946$	7913.59	0.271980
$947$	−55632.7	−1.90900	−0.954498	−	0.298219i	$-0.903608\pi$
$947$	−55632.7	−1.90900	−0.954498	+	0.298219i	$0.903608\pi$
$948$	−45055.0	−1.54358
$949$	0	0
$950$	3240.43	0.110667
$951$	−32924.9	−1.12268
$952$	−346.937	−0.0118112
$953$	−25538.7	−0.868079	−0.434040	−	0.900894i	$-0.642912\pi$
$953$	−25538.7	−0.868079	−0.434040	+	0.900894i	$0.642912\pi$
$954$	−9564.29	−0.324586
$955$	29952.7	1.01492
$956$	15842.6	0.535970
$957$	−8403.95	−0.283867
$958$	21025.8	0.709096
$959$	192.471	0.00648092
$960$	27001.8	0.907792
$961$	37514.6	1.25926
$962$	0	0
$963$	18582.5	0.621820
$964$	−26221.1	−0.876064
$965$	−51456.2	−1.71651
$966$	977.538	0.0325588
$967$	24631.1	0.819112	0.409556	−	0.912285i	$-0.365684\pi$
$967$	24631.1	0.819112	0.409556	+	0.912285i	$0.365684\pi$
$968$	2708.91	0.0899460
$969$	9874.99	0.327379
$970$	−4343.90	−0.143788
$971$	46966.6	1.55225	0.776123	−	0.630582i	$-0.217184\pi$
$971$	46966.6	1.55225	0.776123	+	0.630582i	$0.217184\pi$
$972$	27515.9	0.907996
$973$	−496.952	−0.0163736
$974$	3448.32	0.113441
$975$	0	0
$976$	1321.95	0.0433550
$977$	28486.7	0.932825	0.466412	−	0.884567i	$-0.345546\pi$
$977$	28486.7	0.932825	0.466412	+	0.884567i	$0.345546\pi$
$978$	23811.7	0.778543
$979$	−14012.2	−0.457437
$980$	20799.8	0.677986
$981$	21244.1	0.691408
$982$	−18661.8	−0.606439
$983$	−22432.7	−0.727867	−0.363933	−	0.931425i	$-0.618566\pi$
$983$	−22432.7	−0.727867	−0.363933	+	0.931425i	$0.618566\pi$
$984$	−34746.2	−1.12568
$985$	2569.11	0.0831052
$986$	−2329.85	−0.0752511
$987$	1600.67	0.0516209
$988$	0	0
$989$	27490.0	0.883853
$990$	−6911.68	−0.221886
$991$	26569.1	0.851659	0.425829	−	0.904803i	$-0.359982\pi$
$991$	26569.1	0.851659	0.425829	+	0.904803i	$0.359982\pi$
$992$	47412.6	1.51749
$993$	58490.0	1.86921
$994$	−821.887	−0.0262260
$995$	60341.3	1.92256
$996$	5448.02	0.173321
$997$	−32095.2	−1.01952	−0.509762	−	0.860315i	$-0.670267\pi$
$997$	−32095.2	−1.01952	−0.509762	+	0.860315i	$0.670267\pi$
$998$	22252.2	0.705791
$999$	−1370.69	−0.0434100

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.4.a.g.1.6		17
13.3	even	3		143.4.e.b.100.12	✓	34
13.9	even	3		143.4.e.b.133.12	yes	34
13.12	even	2		1859.4.a.h.1.12		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.e.b.100.12	✓	34	13.3	even	3
143.4.e.b.133.12	yes	34	13.9	even	3
1859.4.a.g.1.6		17	1.1	even	1	trivial
1859.4.a.h.1.12		17	13.12	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1859 = 11 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1859.a (trivial)

\(f(q)\)	\(=\)	\(q-1.71387 q^{2} +7.58218 q^{3} -5.06264 q^{4} +12.0244 q^{5} -12.9949 q^{6} +1.14865 q^{7} +22.3877 q^{8} +30.4895 q^{9} +O(q^{10})\)	\(q-1.71387 q^{2} +7.58218 q^{3} -5.06264 q^{4} +12.0244 q^{5} -12.9949 q^{6} +1.14865 q^{7} +22.3877 q^{8} +30.4895 q^{9} -20.6082 q^{10} +11.0000 q^{11} -38.3858 q^{12} -1.96864 q^{14} +91.1710 q^{15} +2.13141 q^{16} -13.4913 q^{17} -52.2551 q^{18} -96.5360 q^{19} -60.8750 q^{20} +8.70928 q^{21} -18.8526 q^{22} -65.4896 q^{23} +169.748 q^{24} +19.5855 q^{25} +26.4578 q^{27} -5.81520 q^{28} -100.762 q^{29} -156.255 q^{30} -259.433 q^{31} -182.755 q^{32} +83.4040 q^{33} +23.1223 q^{34} +13.8118 q^{35} -154.357 q^{36} -51.8065 q^{37} +165.451 q^{38} +269.198 q^{40} -204.693 q^{41} -14.9266 q^{42} -419.761 q^{43} -55.6890 q^{44} +366.617 q^{45} +112.241 q^{46} +183.789 q^{47} +16.1607 q^{48} -341.681 q^{49} -33.5670 q^{50} -102.293 q^{51} +183.031 q^{53} -45.3453 q^{54} +132.268 q^{55} +25.7157 q^{56} -731.954 q^{57} +172.693 q^{58} -739.589 q^{59} -461.566 q^{60} +620.222 q^{61} +444.636 q^{62} +35.0218 q^{63} +296.167 q^{64} -142.944 q^{66} -795.028 q^{67} +68.3015 q^{68} -496.554 q^{69} -23.6717 q^{70} +417.489 q^{71} +682.589 q^{72} -231.438 q^{73} +88.7898 q^{74} +148.501 q^{75} +488.727 q^{76} +12.6352 q^{77} +1173.74 q^{79} +25.6289 q^{80} -622.608 q^{81} +350.819 q^{82} -141.928 q^{83} -44.0919 q^{84} -162.224 q^{85} +719.417 q^{86} -763.995 q^{87} +246.265 q^{88} -1273.83 q^{89} -628.335 q^{90} +331.550 q^{92} -1967.07 q^{93} -314.991 q^{94} -1160.79 q^{95} -1385.68 q^{96} +210.784 q^{97} +585.597 q^{98} +335.384 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 6 q^{3} + 50 q^{4} - 24 q^{5} + 16 q^{6} - 62 q^{7} - 21 q^{8} + 135 q^{9}+O(q^{10}) \) 17 * q - 6 * q^3 + 50 * q^4 - 24 * q^5 + 16 * q^6 - 62 * q^7 - 21 * q^8 + 135 * q^9	\( 17 q - 6 q^{3} + 50 q^{4} - 24 q^{5} + 16 q^{6} - 62 q^{7} - 21 q^{8} + 135 q^{9} + 2 q^{10} + 187 q^{11} - 127 q^{12} - 148 q^{15} + 126 q^{16} - 74 q^{17} + 90 q^{18} - 159 q^{19} - 222 q^{20} - 184 q^{21} - 215 q^{23} + 214 q^{24} + 95 q^{25} - 192 q^{27} - 358 q^{28} - 157 q^{29} + 829 q^{30} - 394 q^{31} - 553 q^{32} - 66 q^{33} - 702 q^{34} + 58 q^{35} - 700 q^{36} + 88 q^{37} - 1318 q^{38} + 733 q^{40} - 512 q^{41} + 337 q^{42} + 927 q^{43} + 550 q^{44} - 1482 q^{45} - 1361 q^{46} - 143 q^{47} - 178 q^{48} + 1835 q^{49} - 583 q^{50} - 568 q^{51} + 106 q^{53} - 67 q^{54} - 264 q^{55} + 2059 q^{56} + 1298 q^{57} - 1690 q^{58} - 266 q^{59} + 37 q^{60} - 624 q^{61} + 643 q^{62} - 2360 q^{63} - 1589 q^{64} + 176 q^{66} - 676 q^{67} - 413 q^{68} + 764 q^{69} - 1061 q^{70} - 763 q^{71} - 1366 q^{72} - 2374 q^{73} - 1649 q^{74} + 2420 q^{75} - 2101 q^{76} - 682 q^{77} + 2164 q^{79} - 1013 q^{80} + 537 q^{81} + 3152 q^{82} + 777 q^{83} - 3381 q^{84} - 1690 q^{85} + 2894 q^{86} - 4200 q^{87} - 231 q^{88} - 1687 q^{89} - 5399 q^{90} + 5542 q^{92} - 4310 q^{93} + 1777 q^{94} + 1124 q^{95} - 3465 q^{96} - 2047 q^{97} + 1553 q^{98} + 1485 q^{99}+O(q^{100}) \) 17 * q - 6 * q^3 + 50 * q^4 - 24 * q^5 + 16 * q^6 - 62 * q^7 - 21 * q^8 + 135 * q^9 + 2 * q^10 + 187 * q^11 - 127 * q^12 - 148 * q^15 + 126 * q^16 - 74 * q^17 + 90 * q^18 - 159 * q^19 - 222 * q^20 - 184 * q^21 - 215 * q^23 + 214 * q^24 + 95 * q^25 - 192 * q^27 - 358 * q^28 - 157 * q^29 + 829 * q^30 - 394 * q^31 - 553 * q^32 - 66 * q^33 - 702 * q^34 + 58 * q^35 - 700 * q^36 + 88 * q^37 - 1318 * q^38 + 733 * q^40 - 512 * q^41 + 337 * q^42 + 927 * q^43 + 550 * q^44 - 1482 * q^45 - 1361 * q^46 - 143 * q^47 - 178 * q^48 + 1835 * q^49 - 583 * q^50 - 568 * q^51 + 106 * q^53 - 67 * q^54 - 264 * q^55 + 2059 * q^56 + 1298 * q^57 - 1690 * q^58 - 266 * q^59 + 37 * q^60 - 624 * q^61 + 643 * q^62 - 2360 * q^63 - 1589 * q^64 + 176 * q^66 - 676 * q^67 - 413 * q^68 + 764 * q^69 - 1061 * q^70 - 763 * q^71 - 1366 * q^72 - 2374 * q^73 - 1649 * q^74 + 2420 * q^75 - 2101 * q^76 - 682 * q^77 + 2164 * q^79 - 1013 * q^80 + 537 * q^81 + 3152 * q^82 + 777 * q^83 - 3381 * q^84 - 1690 * q^85 + 2894 * q^86 - 4200 * q^87 - 231 * q^88 - 1687 * q^89 - 5399 * q^90 + 5542 * q^92 - 4310 * q^93 + 1777 * q^94 + 1124 * q^95 - 3465 * q^96 - 2047 * q^97 + 1553 * q^98 + 1485 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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