LMFDB - Embedded newform 1734.4.a.bd.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1734,4,Mod(1,1734)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1734, 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("1734.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1734 = 2 \cdot 3 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1734.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:	$102.309311950$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 441x^{4} + 280x^{3} + 48672x^{2} + 38656x - 45712 $ x^6 - 2x^5 - 441x^4 + 280x^3 + 48672x^2 + 38656*x - 45712
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 102)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$0.650232$ of defining polynomial
Character	$\chi$	$=$	1734.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -4.06445 q^{5} -6.00000 q^{6} +33.2979 q^{7} +8.00000 q^{8} +9.00000 q^{9} -8.12889 q^{10} +5.11022 q^{11} -12.0000 q^{12} -18.3446 q^{13} +66.5957 q^{14} +12.1933 q^{15} +16.0000 q^{16} +18.0000 q^{18} -66.8279 q^{19} -16.2578 q^{20} -99.8936 q^{21} +10.2204 q^{22} -160.850 q^{23} -24.0000 q^{24} -108.480 q^{25} -36.6892 q^{26} -27.0000 q^{27} +133.191 q^{28} -170.758 q^{29} +24.3867 q^{30} -258.662 q^{31} +32.0000 q^{32} -15.3307 q^{33} -135.337 q^{35} +36.0000 q^{36} -307.851 q^{37} -133.656 q^{38} +55.0339 q^{39} -32.5156 q^{40} +280.523 q^{41} -199.787 q^{42} +328.331 q^{43} +20.4409 q^{44} -36.5800 q^{45} -321.699 q^{46} +55.5285 q^{47} -48.0000 q^{48} +765.747 q^{49} -216.961 q^{50} -73.3785 q^{52} +233.093 q^{53} -54.0000 q^{54} -20.7702 q^{55} +266.383 q^{56} +200.484 q^{57} -341.515 q^{58} +182.149 q^{59} +48.7734 q^{60} -7.28473 q^{61} -517.324 q^{62} +299.681 q^{63} +64.0000 q^{64} +74.5607 q^{65} -30.6613 q^{66} +314.116 q^{67} +482.549 q^{69} -270.675 q^{70} -96.1155 q^{71} +72.0000 q^{72} -1014.40 q^{73} -615.703 q^{74} +325.441 q^{75} -267.312 q^{76} +170.159 q^{77} +110.068 q^{78} +10.1210 q^{79} -65.0311 q^{80} +81.0000 q^{81} +561.046 q^{82} -66.0553 q^{83} -399.574 q^{84} +656.661 q^{86} +512.273 q^{87} +40.8817 q^{88} -1499.70 q^{89} -73.1600 q^{90} -610.837 q^{91} -643.398 q^{92} +775.986 q^{93} +111.057 q^{94} +271.618 q^{95} -96.0000 q^{96} +202.542 q^{97} +1531.49 q^{98} +45.9920 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 12 q^{2} - 18 q^{3} + 24 q^{4} - 14 q^{5} - 36 q^{6} - 28 q^{7} + 48 q^{8} + 54 q^{9} - 28 q^{10} - 34 q^{11} - 72 q^{12} + 34 q^{13} - 56 q^{14} + 42 q^{15} + 96 q^{16} + 108 q^{18} + 70 q^{19} - 56 q^{20}+ \cdots - 306 q^{99}+O(q^{100}) $ 6 * q + 12 * q^2 - 18 * q^3 + 24 * q^4 - 14 * q^5 - 36 * q^6 - 28 * q^7 + 48 * q^8 + 54 * q^9 - 28 * q^10 - 34 * q^11 - 72 * q^12 + 34 * q^13 - 56 * q^14 + 42 * q^15 + 96 * q^16 + 108 * q^18 + 70 * q^19 - 56 * q^20 + 84 * q^21 - 68 * q^22 - 78 * q^23 - 144 * q^24 + 188 * q^25 + 68 * q^26 - 162 * q^27 - 112 * q^28 - 280 * q^29 + 84 * q^30 - 508 * q^31 + 192 * q^32 + 102 * q^33 + 196 * q^35 + 216 * q^36 - 308 * q^37 + 140 * q^38 - 102 * q^39 - 112 * q^40 - 442 * q^41 + 168 * q^42 - 46 * q^43 - 136 * q^44 - 126 * q^45 - 156 * q^46 + 1460 * q^47 - 288 * q^48 + 1042 * q^49 + 376 * q^50 + 136 * q^52 + 476 * q^53 - 324 * q^54 - 578 * q^55 - 224 * q^56 - 210 * q^57 - 560 * q^58 + 688 * q^59 + 168 * q^60 + 84 * q^61 - 1016 * q^62 - 252 * q^63 + 384 * q^64 - 1526 * q^65 + 204 * q^66 - 1004 * q^67 + 234 * q^69 + 392 * q^70 - 332 * q^71 + 432 * q^72 - 1132 * q^73 - 616 * q^74 - 564 * q^75 + 280 * q^76 - 1548 * q^77 - 204 * q^78 - 4512 * q^79 - 224 * q^80 + 486 * q^81 - 884 * q^82 + 68 * q^83 + 336 * q^84 - 92 * q^86 + 840 * q^87 - 272 * q^88 - 2652 * q^89 - 252 * q^90 - 3052 * q^91 - 312 * q^92 + 1524 * q^93 + 2920 * q^94 + 622 * q^95 - 576 * q^96 + 1152 * q^97 + 2084 * q^98 - 306 * q^99

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 $

$2$	2.00000	0.707107
$2$	2.00000	0.707107
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	4.00000	0.500000
$5$	−4.06445	−0.363535	−0.181768	−	0.983342i	$-0.558182\pi$
$5$	−4.06445	−0.363535	−0.181768	+	0.983342i	$0.558182\pi$
$6$	−6.00000	−0.408248
$7$	33.2979	1.79792	0.898958	−	0.438036i	$-0.144326\pi$
$7$	33.2979	1.79792	0.898958	+	0.438036i	$0.144326\pi$
$8$	8.00000	0.353553
$9$	9.00000	0.333333
$10$	−8.12889	−0.257058
$11$	5.11022	0.140072	0.0700359	−	0.997544i	$-0.477689\pi$
$11$	5.11022	0.140072	0.0700359	+	0.997544i	$0.477689\pi$
$12$	−12.0000	−0.288675
$13$	−18.3446	−0.391376	−0.195688	−	0.980666i	$-0.562694\pi$
$13$	−18.3446	−0.391376	−0.195688	+	0.980666i	$0.562694\pi$
$14$	66.5957	1.27132
$15$	12.1933	0.209887
$16$	16.0000	0.250000
$17$	0	0
$17$	0	0
$18$	18.0000	0.235702
$19$	−66.8279	−0.806914	−0.403457	−	0.914998i	$-0.632192\pi$
$19$	−66.8279	−0.806914	−0.403457	+	0.914998i	$0.632192\pi$
$20$	−16.2578	−0.181768
$21$	−99.8936	−1.03803
$22$	10.2204	0.0990457
$23$	−160.850	−1.45824	−0.729118	−	0.684388i	$-0.760070\pi$
$23$	−160.850	−1.45824	−0.729118	+	0.684388i	$0.760070\pi$
$24$	−24.0000	−0.204124
$25$	−108.480	−0.867842
$26$	−36.6892	−0.276744
$27$	−27.0000	−0.192450
$28$	133.191	0.898958
$29$	−170.758	−1.09341	−0.546705	−	0.837325i	$-0.684118\pi$
$29$	−170.758	−1.09341	−0.546705	+	0.837325i	$0.684118\pi$
$30$	24.3867	0.148413
$31$	−258.662	−1.49862	−0.749308	−	0.662222i	$-0.769614\pi$
$31$	−258.662	−1.49862	−0.749308	+	0.662222i	$0.769614\pi$
$32$	32.0000	0.176777
$33$	−15.3307	−0.0808704
$34$	0	0
$35$	−135.337	−0.653605
$36$	36.0000	0.166667
$37$	−307.851	−1.36785	−0.683925	−	0.729552i	$-0.739729\pi$
$37$	−307.851	−1.36785	−0.683925	+	0.729552i	$0.739729\pi$
$38$	−133.656	−0.570575
$39$	55.0339	0.225961
$40$	−32.5156	−0.128529
$41$	280.523	1.06854	0.534272	−	0.845312i	$-0.320586\pi$
$41$	280.523	1.06854	0.534272	+	0.845312i	$0.320586\pi$
$42$	−199.787	−0.733996
$43$	328.331	1.16442	0.582209	−	0.813039i	$-0.302189\pi$
$43$	328.331	1.16442	0.582209	+	0.813039i	$0.302189\pi$
$44$	20.4409	0.0700359
$45$	−36.5800	−0.121178
$46$	−321.699	−1.03113
$47$	55.5285	0.172333	0.0861666	−	0.996281i	$-0.472538\pi$
$47$	55.5285	0.172333	0.0861666	+	0.996281i	$0.472538\pi$
$48$	−48.0000	−0.144338
$49$	765.747	2.23250
$50$	−216.961	−0.613657
$51$	0	0
$52$	−73.3785	−0.195688
$53$	233.093	0.604108	0.302054	−	0.953291i	$-0.402328\pi$
$53$	233.093	0.604108	0.302054	+	0.953291i	$0.402328\pi$
$54$	−54.0000	−0.136083
$55$	−20.7702	−0.0509210
$56$	266.383	0.635659
$57$	200.484	0.465872
$58$	−341.515	−0.773157
$59$	182.149	0.401928	0.200964	−	0.979599i	$-0.435593\pi$
$59$	182.149	0.401928	0.200964	+	0.979599i	$0.435593\pi$
$60$	48.7734	0.104944
$61$	−7.28473	−0.0152904	−0.00764519	−	0.999971i	$-0.502434\pi$
$61$	−7.28473	−0.0152904	−0.00764519	+	0.999971i	$0.502434\pi$
$62$	−517.324	−1.05968
$63$	299.681	0.599305
$64$	64.0000	0.125000
$65$	74.5607	0.142279
$66$	−30.6613	−0.0571840
$67$	314.116	0.572767	0.286383	−	0.958115i	$-0.407547\pi$
$67$	314.116	0.572767	0.286383	+	0.958115i	$0.407547\pi$
$68$	0	0
$69$	482.549	0.841913
$70$	−270.675	−0.462169
$71$	−96.1155	−0.160659	−0.0803297	−	0.996768i	$-0.525597\pi$
$71$	−96.1155	−0.160659	−0.0803297	+	0.996768i	$0.525597\pi$
$72$	72.0000	0.117851
$73$	−1014.40	−1.62640	−0.813199	−	0.581985i	$-0.802276\pi$
$73$	−1014.40	−1.62640	−0.813199	+	0.581985i	$0.802276\pi$
$74$	−615.703	−0.967216
$75$	325.441	0.501049
$76$	−267.312	−0.403457
$77$	170.159	0.251837
$78$	110.068	0.159778
$79$	10.1210	0.0144140	0.00720699	−	0.999974i	$-0.497706\pi$
$79$	10.1210	0.0144140	0.00720699	+	0.999974i	$0.497706\pi$
$80$	−65.0311	−0.0908838
$81$	81.0000	0.111111
$82$	561.046	0.755575
$83$	−66.0553	−0.0873555	−0.0436778	−	0.999046i	$-0.513907\pi$
$83$	−66.0553	−0.0873555	−0.0436778	+	0.999046i	$0.513907\pi$
$84$	−399.574	−0.519013
$85$	0	0
$86$	656.661	0.823367
$87$	512.273	0.631280
$88$	40.8817	0.0495228
$89$	−1499.70	−1.78616	−0.893081	−	0.449897i	$-0.851461\pi$
$89$	−1499.70	−1.78616	−0.893081	+	0.449897i	$0.851461\pi$
$90$	−73.1600	−0.0856860
$91$	−610.837	−0.703660
$92$	−643.398	−0.729118
$93$	775.986	0.865226
$94$	111.057	0.121858
$95$	271.618	0.293342
$96$	−96.0000	−0.102062
$97$	202.542	0.212011	0.106005	−	0.994366i	$-0.466194\pi$
$97$	202.542	0.212011	0.106005	+	0.994366i	$0.466194\pi$
$98$	1531.49	1.57862
$99$	45.9920	0.0466906
$100$	−433.921	−0.433921
$101$	493.172	0.485866	0.242933	−	0.970043i	$-0.421891\pi$
$101$	493.172	0.485866	0.242933	+	0.970043i	$0.421891\pi$
$102$	0	0
$103$	−1263.90	−1.20909	−0.604544	−	0.796572i	$-0.706645\pi$
$103$	−1263.90	−1.20909	−0.604544	+	0.796572i	$0.706645\pi$
$104$	−146.757	−0.138372
$105$	406.012	0.377359
$106$	466.185	0.427169
$107$	−1710.46	−1.54539	−0.772693	−	0.634781i	$-0.781091\pi$
$107$	−1710.46	−1.54539	−0.772693	+	0.634781i	$0.781091\pi$
$108$	−108.000	−0.0962250
$109$	−1722.26	−1.51342	−0.756709	−	0.653752i	$-0.773194\pi$
$109$	−1722.26	−1.51342	−0.756709	+	0.653752i	$0.773194\pi$
$110$	−41.5404	−0.0360066
$111$	923.554	0.789729
$112$	532.766	0.449479
$113$	−1101.30	−0.916829	−0.458414	−	0.888739i	$-0.651582\pi$
$113$	−1101.30	−0.916829	−0.458414	+	0.888739i	$0.651582\pi$
$114$	400.967	0.329421
$115$	653.764	0.530120
$116$	−683.030	−0.546705
$117$	−165.102	−0.130459
$118$	364.298	0.284206
$119$	0	0
$120$	97.5467	0.0742063
$121$	−1304.89	−0.980380
$122$	−14.5695	−0.0108119
$123$	−841.569	−0.616925
$124$	−1034.65	−0.749308
$125$	948.968	0.679026
$126$	599.361	0.423773
$127$	−611.357	−0.427159	−0.213579	−	0.976926i	$-0.568512\pi$
$127$	−611.357	−0.427159	−0.213579	+	0.976926i	$0.568512\pi$
$128$	128.000	0.0883883
$129$	−984.992	−0.672277
$130$	149.121	0.100606
$131$	1944.79	1.29708	0.648538	−	0.761183i	$-0.275381\pi$
$131$	1944.79	1.29708	0.648538	+	0.761183i	$0.275381\pi$
$132$	−61.3226	−0.0404352
$133$	−2225.23	−1.45076
$134$	628.232	0.405007
$135$	109.740	0.0699624
$136$	0	0
$137$	2208.72	1.37740	0.688700	−	0.725046i	$-0.258182\pi$
$137$	2208.72	1.37740	0.688700	+	0.725046i	$0.258182\pi$
$138$	965.097	0.595323
$139$	−1342.13	−0.818981	−0.409490	−	0.912314i	$-0.634293\pi$
$139$	−1342.13	−0.818981	−0.409490	+	0.912314i	$0.634293\pi$
$140$	−541.349	−0.326803
$141$	−166.585	−0.0994966
$142$	−192.231	−0.113603
$143$	−93.7450	−0.0548207
$144$	144.000	0.0833333
$145$	694.035	0.397493
$146$	−2028.81	−1.15004
$147$	−2297.24	−1.28893
$148$	−1231.41	−0.683925
$149$	−10.3414	−0.00568590	−0.00284295	−	0.999996i	$-0.500905\pi$
$149$	−10.3414	−0.00568590	−0.00284295	+	0.999996i	$0.500905\pi$
$150$	650.882	0.354295
$151$	1952.58	1.05231	0.526155	−	0.850389i	$-0.323633\pi$
$151$	1952.58	1.05231	0.526155	+	0.850389i	$0.323633\pi$
$152$	−534.623	−0.285287
$153$	0	0
$154$	340.319	0.178076
$155$	1051.32	0.544799
$156$	220.135	0.112980
$157$	214.205	0.108888	0.0544440	−	0.998517i	$-0.482661\pi$
$157$	214.205	0.108888	0.0544440	+	0.998517i	$0.482661\pi$
$158$	20.2421	0.0101922
$159$	−699.278	−0.348782
$160$	−130.062	−0.0642645
$161$	−5355.94	−2.62179
$162$	162.000	0.0785674
$163$	1470.23	0.706484	0.353242	−	0.935532i	$-0.385079\pi$
$163$	1470.23	0.706484	0.353242	+	0.935532i	$0.385079\pi$
$164$	1122.09	0.534272
$165$	62.3106	0.0293992
$166$	−132.111	−0.0617697
$167$	3911.99	1.81269	0.906344	−	0.422540i	$-0.138862\pi$
$167$	3911.99	1.81269	0.906344	+	0.422540i	$0.138862\pi$
$168$	−799.149	−0.366998
$169$	−1860.47	−0.846825
$170$	0	0
$171$	−601.451	−0.268971
$172$	1313.32	0.582209
$173$	1615.29	0.709876	0.354938	−	0.934890i	$-0.384502\pi$
$173$	1615.29	0.709876	0.354938	+	0.934890i	$0.384502\pi$
$174$	1024.55	0.446383
$175$	−3612.16	−1.56031
$176$	81.7635	0.0350179
$177$	−546.447	−0.232053
$178$	−2999.41	−1.26301
$179$	−40.4870	−0.0169058	−0.00845290	−	0.999964i	$-0.502691\pi$
$179$	−40.4870	−0.0169058	−0.00845290	+	0.999964i	$0.502691\pi$
$180$	−146.320	−0.0605892
$181$	−1682.70	−0.691019	−0.345509	−	0.938415i	$-0.612294\pi$
$181$	−1682.70	−0.691019	−0.345509	+	0.938415i	$0.612294\pi$
$182$	−1221.67	−0.497563
$183$	21.8542	0.00882791
$184$	−1286.80	−0.515564
$185$	1251.25	0.497262
$186$	1551.97	0.611807
$187$	0	0
$188$	222.114	0.0861666
$189$	−899.042	−0.346009
$190$	543.237	0.207424
$191$	1691.14	0.640663	0.320332	−	0.947305i	$-0.396206\pi$
$191$	1691.14	0.640663	0.320332	+	0.947305i	$0.396206\pi$
$192$	−192.000	−0.0721688
$193$	−3498.79	−1.30491	−0.652456	−	0.757826i	$-0.726261\pi$
$193$	−3498.79	−1.30491	−0.652456	+	0.757826i	$0.726261\pi$
$194$	405.084	0.149914
$195$	−223.682	−0.0821447
$196$	3062.99	1.11625
$197$	4369.04	1.58011	0.790054	−	0.613037i	$-0.210052\pi$
$197$	4369.04	1.58011	0.790054	+	0.613037i	$0.210052\pi$
$198$	91.9839	0.0330152
$199$	−3358.23	−1.19628	−0.598138	−	0.801393i	$-0.704092\pi$
$199$	−3358.23	−1.19628	−0.598138	+	0.801393i	$0.704092\pi$
$200$	−867.842	−0.306829
$201$	−942.348	−0.330687
$202$	986.344	0.343559
$203$	−5685.86	−1.96586
$204$	0	0
$205$	−1140.17	−0.388454
$206$	−2527.80	−0.854954
$207$	−1447.65	−0.486079
$208$	−293.514	−0.0978439
$209$	−341.505	−0.113026
$210$	812.024	0.266833
$211$	741.004	0.241767	0.120883	−	0.992667i	$-0.461427\pi$
$211$	741.004	0.241767	0.120883	+	0.992667i	$0.461427\pi$
$212$	932.370	0.302054
$213$	288.346	0.0927567
$214$	−3420.92	−1.09275
$215$	−1334.48	−0.423307
$216$	−216.000	−0.0680414
$217$	−8612.89	−2.69438
$218$	−3444.52	−1.07015
$219$	3043.21	0.939002
$220$	−83.0808	−0.0254605
$221$	0	0
$222$	1847.11	0.558423
$223$	881.040	0.264569	0.132284	−	0.991212i	$-0.457769\pi$
$223$	881.040	0.264569	0.132284	+	0.991212i	$0.457769\pi$
$224$	1065.53	0.317830
$225$	−976.323	−0.289281
$226$	−2202.60	−0.648296
$227$	−5470.38	−1.59948	−0.799740	−	0.600347i	$-0.795029\pi$
$227$	−5470.38	−1.59948	−0.799740	+	0.600347i	$0.795029\pi$
$228$	801.935	0.232936
$229$	−4951.00	−1.42870	−0.714348	−	0.699790i	$-0.753277\pi$
$229$	−4951.00	−1.42870	−0.714348	+	0.699790i	$0.753277\pi$
$230$	1307.53	0.374852
$231$	−510.478	−0.145398
$232$	−1366.06	−0.386579
$233$	−1767.40	−0.496938	−0.248469	−	0.968640i	$-0.579927\pi$
$233$	−1767.40	−0.496938	−0.248469	+	0.968640i	$0.579927\pi$
$234$	−330.203	−0.0922481
$235$	−225.692	−0.0626492
$236$	728.595	0.200964
$237$	−30.3631	−0.00832192
$238$	0	0
$239$	2643.27	0.715392	0.357696	−	0.933838i	$-0.383562\pi$
$239$	2643.27	0.715392	0.357696	+	0.933838i	$0.383562\pi$
$240$	195.093	0.0524718
$241$	4023.54	1.07543	0.537715	−	0.843127i	$-0.319288\pi$
$241$	4023.54	1.07543	0.537715	+	0.843127i	$0.319288\pi$
$242$	−2609.77	−0.693233
$243$	−243.000	−0.0641500
$244$	−29.1389	−0.00764519
$245$	−3112.34	−0.811592
$246$	−1683.14	−0.436232
$247$	1225.93	0.315807
$248$	−2069.30	−0.529841
$249$	198.166	0.0504347
$250$	1897.94	0.480144
$251$	−380.065	−0.0955757	−0.0477879	−	0.998858i	$-0.515217\pi$
$251$	−380.065	−0.0955757	−0.0477879	+	0.998858i	$0.515217\pi$
$252$	1198.72	0.299653
$253$	−821.976	−0.204258
$254$	−1222.71	−0.302047
$255$	0	0
$256$	256.000	0.0625000
$257$	−5121.07	−1.24297	−0.621486	−	0.783426i	$-0.713471\pi$
$257$	−5121.07	−1.24297	−0.621486	+	0.783426i	$0.713471\pi$
$258$	−1969.98	−0.475371
$259$	−10250.8	−2.45928
$260$	298.243	0.0711394
$261$	−1536.82	−0.364470
$262$	3889.57	0.917171
$263$	−2525.04	−0.592016	−0.296008	−	0.955185i	$-0.595656\pi$
$263$	−2525.04	−0.592016	−0.296008	+	0.955185i	$0.595656\pi$
$264$	−122.645	−0.0285920
$265$	−947.392	−0.219614
$266$	−4450.45	−1.02584
$267$	4499.11	1.03124
$268$	1256.46	0.286383
$269$	5785.09	1.31124	0.655620	−	0.755091i	$-0.272407\pi$
$269$	5785.09	1.31124	0.655620	+	0.755091i	$0.272407\pi$
$270$	219.480	0.0494709
$271$	−1478.94	−0.331511	−0.165755	−	0.986167i	$-0.553006\pi$
$271$	−1478.94	−0.331511	−0.165755	+	0.986167i	$0.553006\pi$
$272$	0	0
$273$	1832.51	0.406258
$274$	4417.45	0.973970
$275$	−554.358	−0.121560
$276$	1930.19	0.420957
$277$	6871.97	1.49060	0.745301	−	0.666729i	$-0.232306\pi$
$277$	6871.97	1.49060	0.745301	+	0.666729i	$0.232306\pi$
$278$	−2684.27	−0.579107
$279$	−2327.96	−0.499539
$280$	−1082.70	−0.231084
$281$	−5263.80	−1.11748	−0.558740	−	0.829343i	$-0.688715\pi$
$281$	−5263.80	−1.11748	−0.558740	+	0.829343i	$0.688715\pi$
$282$	−333.171	−0.0703547
$283$	2689.55	0.564937	0.282468	−	0.959277i	$-0.408847\pi$
$283$	2689.55	0.564937	0.282468	+	0.959277i	$0.408847\pi$
$284$	−384.462	−0.0803297
$285$	−814.855	−0.169361
$286$	−187.490	−0.0387641
$287$	9340.82	1.92115
$288$	288.000	0.0589256
$289$	0	0
$290$	1388.07	0.281070
$291$	−607.626	−0.122404
$292$	−4057.62	−0.813199
$293$	6076.26	1.21153	0.605767	−	0.795642i	$-0.292867\pi$
$293$	6076.26	1.21153	0.605767	+	0.795642i	$0.292867\pi$
$294$	−4594.48	−0.911414
$295$	−740.334	−0.146115
$296$	−2462.81	−0.483608
$297$	−137.976	−0.0269568
$298$	−20.6828	−0.00402054
$299$	2950.72	0.570718
$300$	1301.76	0.250524
$301$	10932.7	2.09352
$302$	3905.16	0.744096
$303$	−1479.52	−0.280515
$304$	−1069.25	−0.201729
$305$	29.6084	0.00555859
$306$	0	0
$307$	8431.56	1.56747	0.783737	−	0.621093i	$-0.213311\pi$
$307$	8431.56	1.56747	0.783737	+	0.621093i	$0.213311\pi$
$308$	680.637	0.125919
$309$	3791.71	0.698067
$310$	2102.64	0.385231
$311$	−4926.83	−0.898312	−0.449156	−	0.893453i	$-0.648275\pi$
$311$	−4926.83	−0.898312	−0.449156	+	0.893453i	$0.648275\pi$
$312$	440.271	0.0798892
$313$	−2633.28	−0.475532	−0.237766	−	0.971322i	$-0.576415\pi$
$313$	−2633.28	−0.475532	−0.237766	+	0.971322i	$0.576415\pi$
$314$	428.410	0.0769954
$315$	−1218.04	−0.217868
$316$	40.4841	0.00720699
$317$	−11137.8	−1.97338	−0.986690	−	0.162615i	$-0.948007\pi$
$317$	−11137.8	−1.97338	−0.986690	+	0.162615i	$0.948007\pi$
$318$	−1398.56	−0.246626
$319$	−872.608	−0.153156
$320$	−260.125	−0.0454419
$321$	5131.37	0.892228
$322$	−10711.9	−1.85388
$323$	0	0
$324$	324.000	0.0555556
$325$	1990.03	0.339652
$326$	2940.45	0.499560
$327$	5166.78	0.873772
$328$	2244.18	0.377788
$329$	1848.98	0.309840
$330$	124.621	0.0207884
$331$	10177.8	1.69009	0.845045	−	0.534695i	$-0.179573\pi$
$331$	10177.8	1.69009	0.845045	+	0.534695i	$0.179573\pi$
$332$	−264.221	−0.0436778
$333$	−2770.66	−0.455950
$334$	7823.98	1.28176
$335$	−1276.71	−0.208221
$336$	−1598.30	−0.259507
$337$	−7386.32	−1.19394	−0.596971	−	0.802263i	$-0.703629\pi$
$337$	−7386.32	−1.19394	−0.596971	+	0.802263i	$0.703629\pi$
$338$	−3720.95	−0.598796
$339$	3303.90	0.529331
$340$	0	0
$341$	−1321.82	−0.209914
$342$	−1202.90	−0.190192
$343$	14076.6	2.21593
$344$	2626.64	0.411684
$345$	−1961.29	−0.306065
$346$	3230.59	0.501958
$347$	−10251.6	−1.58598	−0.792988	−	0.609237i	$-0.791476\pi$
$347$	−10251.6	−1.58598	−0.792988	+	0.609237i	$0.791476\pi$
$348$	2049.09	0.315640
$349$	11338.1	1.73901	0.869505	−	0.493924i	$-0.164438\pi$
$349$	11338.1	1.73901	0.869505	+	0.493924i	$0.164438\pi$
$350$	−7224.32	−1.10330
$351$	495.305	0.0753203
$352$	163.527	0.0247614
$353$	−4609.39	−0.694995	−0.347497	−	0.937681i	$-0.612968\pi$
$353$	−4609.39	−0.694995	−0.347497	+	0.937681i	$0.612968\pi$
$354$	−1092.89	−0.164086
$355$	390.656	0.0584053
$356$	−5998.82	−0.893081
$357$	0	0
$358$	−80.9740	−0.0119542
$359$	4521.15	0.664673	0.332336	−	0.943161i	$-0.392163\pi$
$359$	4521.15	0.664673	0.332336	+	0.943161i	$0.392163\pi$
$360$	−292.640	−0.0428430
$361$	−2393.03	−0.348889
$362$	−3365.41	−0.488624
$363$	3914.66	0.566023
$364$	−2443.35	−0.351830
$365$	4122.99	0.591253
$366$	43.7084	0.00624227
$367$	−3929.40	−0.558891	−0.279446	−	0.960161i	$-0.590151\pi$
$367$	−3929.40	−0.558891	−0.279446	+	0.960161i	$0.590151\pi$
$368$	−2573.59	−0.364559
$369$	2524.71	0.356182
$370$	2502.49	0.351617
$371$	7761.48	1.08613
$372$	3103.95	0.432613
$373$	−9797.93	−1.36010	−0.680050	−	0.733165i	$-0.738042\pi$
$373$	−9797.93	−1.36010	−0.680050	+	0.733165i	$0.738042\pi$
$374$	0	0
$375$	−2846.90	−0.392036
$376$	444.228	0.0609290
$377$	3132.48	0.427934
$378$	−1798.08	−0.244665
$379$	−10047.9	−1.36180	−0.680902	−	0.732375i	$-0.738412\pi$
$379$	−10047.9	−1.36180	−0.680902	+	0.732375i	$0.738412\pi$
$380$	1086.47	0.146671
$381$	1834.07	0.246620
$382$	3382.28	0.453017
$383$	2856.38	0.381081	0.190541	−	0.981679i	$-0.438976\pi$
$383$	2856.38	0.381081	0.190541	+	0.981679i	$0.438976\pi$
$384$	−384.000	−0.0510310
$385$	−691.603	−0.0915516
$386$	−6997.57	−0.922713
$387$	2954.98	0.388139
$388$	810.168	0.106005
$389$	5479.16	0.714150	0.357075	−	0.934076i	$-0.383774\pi$
$389$	5479.16	0.714150	0.357075	+	0.934076i	$0.383774\pi$
$390$	−447.364	−0.0580851
$391$	0	0
$392$	6125.98	0.789308
$393$	−5834.36	−0.748867
$394$	8738.08	1.11730
$395$	−41.1364	−0.00523999
$396$	183.968	0.0233453
$397$	−10647.4	−1.34604	−0.673020	−	0.739624i	$-0.735003\pi$
$397$	−10647.4	−1.34604	−0.673020	+	0.739624i	$0.735003\pi$
$398$	−6716.46	−0.845894
$399$	6675.68	0.837599
$400$	−1735.68	−0.216961
$401$	2240.43	0.279007	0.139503	−	0.990222i	$-0.455449\pi$
$401$	2240.43	0.279007	0.139503	+	0.990222i	$0.455449\pi$
$402$	−1884.70	−0.233831
$403$	4745.06	0.586522
$404$	1972.69	0.242933
$405$	−329.220	−0.0403928
$406$	−11371.7	−1.39007
$407$	−1573.19	−0.191597
$408$	0	0
$409$	−5233.25	−0.632684	−0.316342	−	0.948645i	$-0.602455\pi$
$409$	−5233.25	−0.632684	−0.316342	+	0.948645i	$0.602455\pi$
$410$	−2280.34	−0.274678
$411$	−6626.17	−0.795243
$412$	−5055.61	−0.604544
$413$	6065.17	0.722633
$414$	−2895.29	−0.343710
$415$	268.478	0.0317568
$416$	−587.028	−0.0691861
$417$	4026.40	0.472839
$418$	−683.010	−0.0799214
$419$	17057.1	1.98876	0.994382	−	0.105856i	$-0.0337582\pi$
$419$	17057.1	1.98876	0.994382	+	0.105856i	$0.0337582\pi$
$420$	1624.05	0.188680
$421$	−1995.98	−0.231065	−0.115532	−	0.993304i	$-0.536857\pi$
$421$	−1995.98	−0.231065	−0.115532	+	0.993304i	$0.536857\pi$
$422$	1482.01	0.170955
$423$	499.756	0.0574444
$424$	1864.74	0.213584
$425$	0	0
$426$	576.693	0.0655889
$427$	−242.566	−0.0274908
$428$	−6841.83	−0.772693
$429$	281.235	0.0316507
$430$	−2668.96	−0.299323
$431$	−14506.0	−1.62119	−0.810593	−	0.585610i	$-0.800855\pi$
$431$	−14506.0	−1.62119	−0.810593	+	0.585610i	$0.800855\pi$
$432$	−432.000	−0.0481125
$433$	1017.03	0.112876	0.0564378	−	0.998406i	$-0.482026\pi$
$433$	1017.03	0.112876	0.0564378	+	0.998406i	$0.482026\pi$
$434$	−17225.8	−1.90522
$435$	−2082.10	−0.229493
$436$	−6889.04	−0.756709
$437$	10749.2	1.17667
$438$	6086.43	0.663974
$439$	−1854.15	−0.201580	−0.100790	−	0.994908i	$-0.532137\pi$
$439$	−1854.15	−0.201580	−0.100790	+	0.994908i	$0.532137\pi$
$440$	−166.162	−0.0180033
$441$	6891.73	0.744166
$442$	0	0
$443$	−4297.84	−0.460941	−0.230470	−	0.973079i	$-0.574026\pi$
$443$	−4297.84	−0.460941	−0.230470	+	0.973079i	$0.574026\pi$
$444$	3694.22	0.394864
$445$	6095.47	0.649332
$446$	1762.08	0.187078
$447$	31.0242	0.00328276
$448$	2131.06	0.224739
$449$	1912.49	0.201015	0.100508	−	0.994936i	$-0.467953\pi$
$449$	1912.49	0.201015	0.100508	+	0.994936i	$0.467953\pi$
$450$	−1952.65	−0.204552
$451$	1433.53	0.149673
$452$	−4405.20	−0.458414
$453$	−5857.75	−0.607552
$454$	−10940.8	−1.13100
$455$	2482.71	0.255805
$456$	1603.87	0.164711
$457$	2234.77	0.228749	0.114374	−	0.993438i	$-0.463514\pi$
$457$	2234.77	0.228749	0.114374	+	0.993438i	$0.463514\pi$
$458$	−9902.01	−1.01024
$459$	0	0
$460$	2615.06	0.265060
$461$	149.634	0.0151174	0.00755871	−	0.999971i	$-0.497594\pi$
$461$	149.634	0.0151174	0.00755871	+	0.999971i	$0.497594\pi$
$462$	−1020.96	−0.102812
$463$	4732.09	0.474987	0.237494	−	0.971389i	$-0.423674\pi$
$463$	4732.09	0.474987	0.237494	+	0.971389i	$0.423674\pi$
$464$	−2732.12	−0.273352
$465$	−3153.95	−0.314540
$466$	−3534.81	−0.351388
$467$	−2749.01	−0.272396	−0.136198	−	0.990682i	$-0.543488\pi$
$467$	−2749.01	−0.272396	−0.136198	+	0.990682i	$0.543488\pi$
$468$	−660.406	−0.0652293
$469$	10459.4	1.02979
$470$	−451.385	−0.0442996
$471$	−642.615	−0.0628665
$472$	1457.19	0.142103
$473$	1677.84	0.163102
$474$	−60.7262	−0.00588449
$475$	7249.51	0.700274
$476$	0	0
$477$	2097.83	0.201369
$478$	5286.54	0.505859
$479$	−4209.60	−0.401549	−0.200774	−	0.979638i	$-0.564346\pi$
$479$	−4209.60	−0.401549	−0.200774	+	0.979638i	$0.564346\pi$
$480$	390.187	0.0371031
$481$	5647.42	0.535343
$482$	8047.07	0.760444
$483$	16067.8	1.51369
$484$	−5219.54	−0.490190
$485$	−823.221	−0.0770733
$486$	−486.000	−0.0453609
$487$	16797.5	1.56297	0.781486	−	0.623923i	$-0.214462\pi$
$487$	16797.5	1.56297	0.781486	+	0.623923i	$0.214462\pi$
$488$	−58.2778	−0.00540597
$489$	−4410.68	−0.407889
$490$	−6224.68	−0.573882
$491$	10904.6	1.00228	0.501138	−	0.865367i	$-0.332915\pi$
$491$	10904.6	1.00228	0.501138	+	0.865367i	$0.332915\pi$
$492$	−3366.28	−0.308462
$493$	0	0
$494$	2451.87	0.223309
$495$	−186.932	−0.0169737
$496$	−4138.59	−0.374654
$497$	−3200.44	−0.288852
$498$	396.332	0.0356627
$499$	2584.19	0.231832	0.115916	−	0.993259i	$-0.463020\pi$
$499$	2584.19	0.231832	0.115916	+	0.993259i	$0.463020\pi$
$500$	3795.87	0.339513
$501$	−11736.0	−1.04656
$502$	−760.131	−0.0675823
$503$	−10948.7	−0.970537	−0.485269	−	0.874365i	$-0.661278\pi$
$503$	−10948.7	−0.970537	−0.485269	+	0.874365i	$0.661278\pi$
$504$	2397.45	0.211886
$505$	−2004.47	−0.176629
$506$	−1643.95	−0.144432
$507$	5581.42	0.488915
$508$	−2445.43	−0.213579
$509$	134.612	0.0117221	0.00586106	−	0.999983i	$-0.498134\pi$
$509$	134.612	0.0117221	0.00586106	+	0.999983i	$0.498134\pi$
$510$	0	0
$511$	−33777.5	−2.92413
$512$	512.000	0.0441942
$513$	1804.35	0.155291
$514$	−10242.1	−0.878913
$515$	5137.06	0.439546
$516$	−3939.97	−0.336138
$517$	283.763	0.0241390
$518$	−20501.6	−1.73897
$519$	−4845.88	−0.409847
$520$	596.486	0.0503031
$521$	16199.8	1.36224	0.681119	−	0.732172i	$-0.261493\pi$
$521$	16199.8	1.36224	0.681119	+	0.732172i	$0.261493\pi$
$522$	−3073.64	−0.257719
$523$	−21230.4	−1.77503	−0.887516	−	0.460778i	$-0.847571\pi$
$523$	−21230.4	−1.77503	−0.887516	+	0.460778i	$0.847571\pi$
$524$	7779.15	0.648538
$525$	10836.5	0.900844
$526$	−5050.07	−0.418619
$527$	0	0
$528$	−245.290	−0.0202176
$529$	13705.6	1.12645
$530$	−1894.78	−0.155291
$531$	1639.34	0.133976
$532$	−8900.91	−0.725382
$533$	−5146.09	−0.418202
$534$	8998.23	0.729197
$535$	6952.06	0.561802
$536$	2512.93	0.202504
$537$	121.461	0.00976057
$538$	11570.2	0.927186
$539$	3913.14	0.312710
$540$	438.960	0.0349812
$541$	−8772.55	−0.697156	−0.348578	−	0.937280i	$-0.613335\pi$
$541$	−8772.55	−0.697156	−0.348578	+	0.937280i	$0.613335\pi$
$542$	−2957.89	−0.234413
$543$	5048.11	0.398960
$544$	0	0
$545$	7000.03	0.550180
$546$	3665.02	0.287268
$547$	−8210.79	−0.641807	−0.320903	−	0.947112i	$-0.603986\pi$
$547$	−8210.79	−0.641807	−0.320903	+	0.947112i	$0.603986\pi$
$548$	8834.89	0.688700
$549$	−65.5625	−0.00509680
$550$	−1108.72	−0.0859560
$551$	11411.4	0.882288
$552$	3860.39	0.297661
$553$	337.009	0.0259151
$554$	13743.9	1.05401
$555$	−3753.74	−0.287094
$556$	−5368.54	−0.409490
$557$	−644.069	−0.0489948	−0.0244974	−	0.999700i	$-0.507799\pi$
$557$	−644.069	−0.0489948	−0.0244974	+	0.999700i	$0.507799\pi$
$558$	−4655.92	−0.353227
$559$	−6023.10	−0.455725
$560$	−2165.40	−0.163401
$561$	0	0
$562$	−10527.6	−0.790178
$563$	−22872.8	−1.71221	−0.856103	−	0.516805i	$-0.827121\pi$
$563$	−22872.8	−1.71221	−0.856103	+	0.516805i	$0.827121\pi$
$564$	−666.342	−0.0497483
$565$	4476.18	0.333299
$566$	5379.10	0.399471
$567$	2697.13	0.199768
$568$	−768.924	−0.0568016
$569$	13513.0	0.995599	0.497800	−	0.867292i	$-0.334142\pi$
$569$	13513.0	0.995599	0.497800	+	0.867292i	$0.334142\pi$
$570$	−1629.71	−0.119756
$571$	16934.7	1.24115	0.620573	−	0.784149i	$-0.286900\pi$
$571$	16934.7	1.24115	0.620573	+	0.784149i	$0.286900\pi$
$572$	−374.980	−0.0274103
$573$	−5073.43	−0.369887
$574$	18681.6	1.35846
$575$	17449.0	1.26552
$576$	576.000	0.0416667
$577$	18805.8	1.35684	0.678420	−	0.734674i	$-0.262665\pi$
$577$	18805.8	1.35684	0.678420	+	0.734674i	$0.262665\pi$
$578$	0	0
$579$	10496.4	0.753392
$580$	2776.14	0.198746
$581$	−2199.50	−0.157058
$582$	−1215.25	−0.0865530
$583$	1191.15	0.0846184
$584$	−8115.24	−0.575019
$585$	671.047	0.0474263
$586$	12152.5	0.856683
$587$	8038.76	0.565239	0.282619	−	0.959232i	$-0.408797\pi$
$587$	8038.76	0.565239	0.282619	+	0.959232i	$0.408797\pi$
$588$	−9188.97	−0.644467
$589$	17285.8	1.20925
$590$	−1480.67	−0.103319
$591$	−13107.1	−0.912276
$592$	−4925.62	−0.341963
$593$	−8124.66	−0.562630	−0.281315	−	0.959615i	$-0.590771\pi$
$593$	−8124.66	−0.562630	−0.281315	+	0.959615i	$0.590771\pi$
$594$	−275.952	−0.0190613
$595$	0	0
$596$	−41.3656	−0.00284295
$597$	10074.7	0.690670
$598$	5901.45	0.403559
$599$	−8419.51	−0.574310	−0.287155	−	0.957884i	$-0.592710\pi$
$599$	−8419.51	−0.574310	−0.287155	+	0.957884i	$0.592710\pi$
$600$	2603.53	0.177148
$601$	20305.0	1.37813	0.689067	−	0.724697i	$-0.258020\pi$
$601$	20305.0	1.37813	0.689067	+	0.724697i	$0.258020\pi$
$602$	21865.4	1.48034
$603$	2827.04	0.190922
$604$	7810.33	0.526155
$605$	5303.64	0.356403
$606$	−2959.03	−0.198354
$607$	4426.39	0.295983	0.147992	−	0.988989i	$-0.452719\pi$
$607$	4426.39	0.295983	0.147992	+	0.988989i	$0.452719\pi$
$608$	−2138.49	−0.142644
$609$	17057.6	1.13499
$610$	59.2167	0.00393052
$611$	−1018.65	−0.0674470
$612$	0	0
$613$	−8994.17	−0.592612	−0.296306	−	0.955093i	$-0.595755\pi$
$613$	−8994.17	−0.592612	−0.296306	+	0.955093i	$0.595755\pi$
$614$	16863.1	1.10837
$615$	3420.51	0.224274
$616$	1361.27	0.0890378
$617$	20223.5	1.31956	0.659779	−	0.751460i	$-0.270650\pi$
$617$	20223.5	1.31956	0.659779	+	0.751460i	$0.270650\pi$
$618$	7583.41	0.493608
$619$	−18145.5	−1.17824	−0.589118	−	0.808047i	$-0.700525\pi$
$619$	−18145.5	−1.17824	−0.589118	+	0.808047i	$0.700525\pi$
$620$	4205.27	0.272400
$621$	4342.94	0.280638
$622$	−9853.66	−0.635203
$623$	−49936.9	−3.21137
$624$	880.542	0.0564902
$625$	9703.01	0.620992
$626$	−5266.55	−0.336252
$627$	1024.52	0.0652555
$628$	856.820	0.0544440
$629$	0	0
$630$	−2436.07	−0.154056
$631$	−27551.9	−1.73823	−0.869115	−	0.494611i	$-0.835311\pi$
$631$	−27551.9	−1.73823	−0.869115	+	0.494611i	$0.835311\pi$
$632$	80.9683	0.00509611
$633$	−2223.01	−0.139584
$634$	−22275.6	−1.39539
$635$	2484.83	0.155287
$636$	−2797.11	−0.174391
$637$	−14047.3	−0.873746
$638$	−1745.22	−0.108297
$639$	−865.039	−0.0535531
$640$	−520.249	−0.0321323
$641$	−24470.4	−1.50784	−0.753918	−	0.656969i	$-0.771838\pi$
$641$	−24470.4	−1.50784	−0.753918	+	0.656969i	$0.771838\pi$
$642$	10262.7	0.630901
$643$	−10096.8	−0.619255	−0.309627	−	0.950858i	$-0.600204\pi$
$643$	−10096.8	−0.619255	−0.309627	+	0.950858i	$0.600204\pi$
$644$	−21423.8	−1.31089
$645$	4003.45	0.244396
$646$	0	0
$647$	13578.2	0.825059	0.412529	−	0.910944i	$-0.364645\pi$
$647$	13578.2	0.825059	0.412529	+	0.910944i	$0.364645\pi$
$648$	648.000	0.0392837
$649$	930.820	0.0562988
$650$	3980.06	0.240170
$651$	25838.7	1.55560
$652$	5880.90	0.353242
$653$	9939.36	0.595646	0.297823	−	0.954621i	$-0.403739\pi$
$653$	9939.36	0.595646	0.297823	+	0.954621i	$0.403739\pi$
$654$	10333.6	0.617850
$655$	−7904.48	−0.471532
$656$	4488.37	0.267136
$657$	−9129.64	−0.542133
$658$	3697.96	0.219090
$659$	18058.7	1.06748	0.533739	−	0.845649i	$-0.320787\pi$
$659$	18058.7	1.06748	0.533739	+	0.845649i	$0.320787\pi$
$660$	249.242	0.0146996
$661$	−19648.0	−1.15615	−0.578076	−	0.815983i	$-0.696196\pi$
$661$	−19648.0	−1.15615	−0.578076	+	0.815983i	$0.696196\pi$
$662$	20355.5	1.19507
$663$	0	0
$664$	−528.442	−0.0308848
$665$	9044.31	0.527404
$666$	−5541.33	−0.322405
$667$	27466.3	1.59445
$668$	15648.0	0.906344
$669$	−2643.12	−0.152749
$670$	−2553.41	−0.147234
$671$	−37.2265	−0.00214175
$672$	−3196.59	−0.183499
$673$	17883.0	1.02428	0.512138	−	0.858903i	$-0.328854\pi$
$673$	17883.0	1.02428	0.512138	+	0.858903i	$0.328854\pi$
$674$	−14772.6	−0.844245
$675$	2928.97	0.167016
$676$	−7441.90	−0.423413
$677$	26725.2	1.51718	0.758590	−	0.651568i	$-0.225888\pi$
$677$	26725.2	1.51718	0.758590	+	0.651568i	$0.225888\pi$
$678$	6607.80	0.374294
$679$	6744.22	0.381177
$680$	0	0
$681$	16411.1	0.923460
$682$	−2643.64	−0.148431
$683$	−24279.3	−1.36020	−0.680102	−	0.733117i	$-0.738065\pi$
$683$	−24279.3	−1.36020	−0.680102	+	0.733117i	$0.738065\pi$
$684$	−2405.80	−0.134486
$685$	−8977.23	−0.500734
$686$	28153.2	1.56690
$687$	14853.0	0.824859
$688$	5253.29	0.291104
$689$	−4275.99	−0.236433
$690$	−3922.58	−0.216421
$691$	11137.8	0.613174	0.306587	−	0.951843i	$-0.400813\pi$
$691$	11137.8	0.613174	0.306587	+	0.951843i	$0.400813\pi$
$692$	6461.18	0.354938
$693$	1531.43	0.0839457
$694$	−20503.2	−1.12145
$695$	5455.03	0.297728
$696$	4098.18	0.223191
$697$	0	0
$698$	22676.2	1.22967
$699$	5302.21	0.286907
$700$	−14448.6	−0.780153
$701$	−1650.56	−0.0889312	−0.0444656	−	0.999011i	$-0.514159\pi$
$701$	−1650.56	−0.0889312	−0.0444656	+	0.999011i	$0.514159\pi$
$702$	990.610	0.0532595
$703$	20573.1	1.10374
$704$	327.054	0.0175090
$705$	677.077	0.0361705
$706$	−9218.78	−0.491435
$707$	16421.6	0.873546
$708$	−2185.79	−0.116027
$709$	−14166.7	−0.750410	−0.375205	−	0.926942i	$-0.622428\pi$
$709$	−14166.7	−0.750410	−0.375205	+	0.926942i	$0.622428\pi$
$710$	781.312	0.0412988
$711$	91.0893	0.00480466
$712$	−11997.6	−0.631503
$713$	41605.7	2.18534
$714$	0	0
$715$	381.022	0.0199292
$716$	−161.948	−0.00845290
$717$	−7929.80	−0.413032
$718$	9042.31	0.469994
$719$	−9795.69	−0.508091	−0.254046	−	0.967192i	$-0.581761\pi$
$719$	−9795.69	−0.508091	−0.254046	+	0.967192i	$0.581761\pi$
$720$	−585.280	−0.0302946
$721$	−42085.2	−2.17384
$722$	−4786.06	−0.246702
$723$	−12070.6	−0.620900
$724$	−6730.81	−0.345509
$725$	18523.8	0.948907
$726$	7829.31	0.400238
$727$	−8021.85	−0.409235	−0.204618	−	0.978842i	$-0.565595\pi$
$727$	−8021.85	−0.409235	−0.204618	+	0.978842i	$0.565595\pi$
$728$	−4886.69	−0.248781
$729$	729.000	0.0370370
$730$	8245.99	0.418079
$731$	0	0
$732$	87.4167	0.00441395
$733$	−11391.4	−0.574014	−0.287007	−	0.957928i	$-0.592660\pi$
$733$	−11391.4	−0.574014	−0.287007	+	0.957928i	$0.592660\pi$
$734$	−7858.80	−0.395196
$735$	9337.02	0.468573
$736$	−5147.18	−0.257782
$737$	1605.20	0.0802284
$738$	5049.42	0.251858
$739$	15410.0	0.767072	0.383536	−	0.923526i	$-0.374706\pi$
$739$	15410.0	0.767072	0.383536	+	0.923526i	$0.374706\pi$
$740$	5004.98	0.248631
$741$	−3677.80	−0.182331
$742$	15523.0	0.768013
$743$	28940.7	1.42898	0.714489	−	0.699647i	$-0.246659\pi$
$743$	28940.7	1.42898	0.714489	+	0.699647i	$0.246659\pi$
$744$	6207.89	0.305904
$745$	42.0320	0.00206703
$746$	−19595.9	−0.961737
$747$	−594.497	−0.0291185
$748$	0	0
$749$	−56954.6	−2.77847
$750$	−5693.81	−0.277211
$751$	−9470.96	−0.460187	−0.230093	−	0.973169i	$-0.573903\pi$
$751$	−9470.96	−0.460187	−0.230093	+	0.973169i	$0.573903\pi$
$752$	888.455	0.0430833
$753$	1140.20	0.0551807
$754$	6264.97	0.302595
$755$	−7936.16	−0.382552
$756$	−3596.17	−0.173004
$757$	−1463.59	−0.0702710	−0.0351355	−	0.999383i	$-0.511186\pi$
$757$	−1463.59	−0.0702710	−0.0351355	+	0.999383i	$0.511186\pi$
$758$	−20095.7	−0.962940
$759$	2465.93	0.117928
$760$	2172.95	0.103712
$761$	37987.0	1.80950	0.904748	−	0.425947i	$-0.140059\pi$
$761$	37987.0	1.80950	0.904748	+	0.425947i	$0.140059\pi$
$762$	3668.14	0.174387
$763$	−57347.5	−2.72100
$764$	6764.57	0.320332
$765$	0	0
$766$	5712.75	0.269465
$767$	−3341.45	−0.157305
$768$	−768.000	−0.0360844
$769$	−29701.4	−1.39280	−0.696398	−	0.717655i	$-0.745215\pi$
$769$	−29701.4	−1.39280	−0.696398	+	0.717655i	$0.745215\pi$
$770$	−1383.21	−0.0647368
$771$	15363.2	0.717630
$772$	−13995.1	−0.652456
$773$	22444.2	1.04432	0.522161	−	0.852847i	$-0.325126\pi$
$773$	22444.2	1.04432	0.522161	+	0.852847i	$0.325126\pi$
$774$	5909.95	0.274456
$775$	28059.7	1.30056
$776$	1620.34	0.0749571
$777$	30752.4	1.41987
$778$	10958.3	0.504980
$779$	−18746.8	−0.862224
$780$	−894.729	−0.0410723
$781$	−491.171	−0.0225038
$782$	0	0
$783$	4610.45	0.210427
$784$	12252.0	0.558125
$785$	−870.624	−0.0395846
$786$	−11668.7	−0.529529
$787$	40576.5	1.83786	0.918931	−	0.394418i	$-0.129054\pi$
$787$	40576.5	1.83786	0.918931	+	0.394418i	$0.129054\pi$
$788$	17476.2	0.790054
$789$	7575.11	0.341801
$790$	−82.2728	−0.00370523
$791$	−36671.0	−1.64838
$792$	367.936	0.0165076
$793$	133.636	0.00598428
$794$	−21294.8	−0.951794
$795$	2842.18	0.126794
$796$	−13432.9	−0.598138
$797$	10014.0	0.445063	0.222531	−	0.974926i	$-0.428568\pi$
$797$	10014.0	0.445063	0.222531	+	0.974926i	$0.428568\pi$
$798$	13351.4	0.592272
$799$	0	0
$800$	−3471.37	−0.153414
$801$	−13497.3	−0.595387
$802$	4480.86	0.197288
$803$	−5183.83	−0.227812
$804$	−3769.39	−0.165344
$805$	21768.9	0.953111
$806$	9490.12	0.414733
$807$	−17355.3	−0.757044
$808$	3945.38	0.171780
$809$	−2763.14	−0.120082	−0.0600412	−	0.998196i	$-0.519123\pi$
$809$	−2763.14	−0.120082	−0.0600412	+	0.998196i	$0.519123\pi$
$810$	−658.440	−0.0285620
$811$	−29392.1	−1.27262	−0.636311	−	0.771432i	$-0.719541\pi$
$811$	−29392.1	−1.27262	−0.636311	+	0.771432i	$0.719541\pi$
$812$	−22743.4	−0.982929
$813$	4436.83	0.191398
$814$	−3146.38	−0.135480
$815$	−5975.65	−0.256832
$816$	0	0
$817$	−21941.6	−0.939585
$818$	−10466.5	−0.447375
$819$	−5497.53	−0.234553
$820$	−4560.68	−0.194227
$821$	40619.0	1.72669	0.863346	−	0.504612i	$-0.168364\pi$
$821$	40619.0	1.72669	0.863346	+	0.504612i	$0.168364\pi$
$822$	−13252.3	−0.562322
$823$	−8061.18	−0.341428	−0.170714	−	0.985321i	$-0.554607\pi$
$823$	−8061.18	−0.341428	−0.170714	+	0.985321i	$0.554607\pi$
$824$	−10111.2	−0.427477
$825$	1663.07	0.0701828
$826$	12130.3	0.510979
$827$	−14281.4	−0.600499	−0.300249	−	0.953861i	$-0.597070\pi$
$827$	−14281.4	−0.600499	−0.300249	+	0.953861i	$0.597070\pi$
$828$	−5790.58	−0.243039
$829$	19975.7	0.836894	0.418447	−	0.908241i	$-0.362575\pi$
$829$	19975.7	0.836894	0.418447	+	0.908241i	$0.362575\pi$
$830$	536.956	0.0224554
$831$	−20615.9	−0.860599
$832$	−1174.06	−0.0489220
$833$	0	0
$834$	8052.81	0.334348
$835$	−15900.1	−0.658976
$836$	−1366.02	−0.0565129
$837$	6983.88	0.288409
$838$	34114.1	1.40627
$839$	−9994.18	−0.411248	−0.205624	−	0.978631i	$-0.565922\pi$
$839$	−9994.18	−0.411248	−0.205624	+	0.978631i	$0.565922\pi$
$840$	3248.10	0.133417
$841$	4769.14	0.195545
$842$	−3991.97	−0.163388
$843$	15791.4	0.645178
$844$	2964.02	0.120883
$845$	7561.80	0.307851
$846$	999.512	0.0406193
$847$	−43449.9	−1.76264
$848$	3729.48	0.151027
$849$	−8068.65	−0.326166
$850$	0	0
$851$	49517.7	1.99465
$852$	1153.39	0.0463783
$853$	32464.2	1.30311	0.651556	−	0.758601i	$-0.274117\pi$
$853$	32464.2	1.30311	0.651556	+	0.758601i	$0.274117\pi$
$854$	−485.131	−0.0194389
$855$	2444.57	0.0977806
$856$	−13683.7	−0.546376
$857$	12018.3	0.479038	0.239519	−	0.970892i	$-0.423010\pi$
$857$	12018.3	0.479038	0.239519	+	0.970892i	$0.423010\pi$
$858$	562.470	0.0223804
$859$	17465.0	0.693711	0.346855	−	0.937919i	$-0.387249\pi$
$859$	17465.0	0.693711	0.346855	+	0.937919i	$0.387249\pi$
$860$	−5337.93	−0.211653
$861$	−28022.5	−1.10918
$862$	−29012.1	−1.14635
$863$	−40272.5	−1.58852	−0.794259	−	0.607579i	$-0.792141\pi$
$863$	−40272.5	−1.58852	−0.794259	+	0.607579i	$0.792141\pi$
$864$	−864.000	−0.0340207
$865$	−6565.28	−0.258065
$866$	2034.05	0.0798152
$867$	0	0
$868$	−34451.6	−1.34719
$869$	51.7207	0.00201899
$870$	−4164.21	−0.162276
$871$	−5762.34	−0.224167
$872$	−13778.1	−0.535074
$873$	1822.88	0.0706702
$874$	21498.5	0.832033
$875$	31598.6	1.22083
$876$	12172.9	0.469501
$877$	14757.2	0.568205	0.284103	−	0.958794i	$-0.408304\pi$
$877$	14757.2	0.568205	0.284103	+	0.958794i	$0.408304\pi$
$878$	−3708.30	−0.142539
$879$	−18228.8	−0.699479
$880$	−332.323	−0.0127302
$881$	−16991.8	−0.649794	−0.324897	−	0.945749i	$-0.605330\pi$
$881$	−16991.8	−0.649794	−0.324897	+	0.945749i	$0.605330\pi$
$882$	13783.5	0.526205
$883$	5494.09	0.209389	0.104695	−	0.994504i	$-0.466613\pi$
$883$	5494.09	0.209389	0.104695	+	0.994504i	$0.466613\pi$
$884$	0	0
$885$	2221.00	0.0843595
$886$	−8595.68	−0.325934
$887$	13528.4	0.512108	0.256054	−	0.966662i	$-0.417578\pi$
$887$	13528.4	0.512108	0.256054	+	0.966662i	$0.417578\pi$
$888$	7388.43	0.279211
$889$	−20356.9	−0.767996
$890$	12190.9	0.459147
$891$	413.928	0.0155635
$892$	3524.16	0.132284
$893$	−3710.85	−0.139058
$894$	62.0483	0.00232126
$895$	164.557	0.00614585
$896$	4262.13	0.158915
$897$	−8852.17	−0.329504
$898$	3824.97	0.142139
$899$	44168.5	1.63860
$900$	−3905.29	−0.144640
$901$	0	0
$902$	2867.07	0.105835
$903$	−32798.1	−1.20870
$904$	−8810.41	−0.324148
$905$	6839.26	0.251210
$906$	−11715.5	−0.429604
$907$	12119.6	0.443687	0.221844	−	0.975082i	$-0.428793\pi$
$907$	12119.6	0.443687	0.221844	+	0.975082i	$0.428793\pi$
$908$	−21881.5	−0.799740
$909$	4438.55	0.161955
$910$	4965.43	0.180882
$911$	−32615.9	−1.18618	−0.593092	−	0.805134i	$-0.702093\pi$
$911$	−32615.9	−1.18618	−0.593092	+	0.805134i	$0.702093\pi$
$912$	3207.74	0.116468
$913$	−337.557	−0.0122360
$914$	4469.54	0.161750
$915$	−88.8251	−0.00320925
$916$	−19804.0	−0.714348
$917$	64757.2	2.33203
$918$	0	0
$919$	−46742.5	−1.67780	−0.838898	−	0.544289i	$-0.816800\pi$
$919$	−46742.5	−1.67780	−0.838898	+	0.544289i	$0.816800\pi$
$920$	5230.11	0.187426
$921$	−25294.7	−0.904981
$922$	299.267	0.0106896
$923$	1763.20	0.0628781
$924$	−2041.91	−0.0726991
$925$	33395.8	1.18708
$926$	9464.19	0.335867
$927$	−11375.1	−0.403029
$928$	−5464.24	−0.193289
$929$	9938.02	0.350975	0.175488	−	0.984482i	$-0.443850\pi$
$929$	9938.02	0.350975	0.175488	+	0.984482i	$0.443850\pi$
$930$	−6307.91	−0.222413
$931$	−51173.3	−1.80144
$932$	−7069.61	−0.248469
$933$	14780.5	0.518641
$934$	−5498.02	−0.192613
$935$	0	0
$936$	−1320.81	−0.0461241
$937$	18865.1	0.657733	0.328867	−	0.944376i	$-0.393333\pi$
$937$	18865.1	0.657733	0.328867	+	0.944376i	$0.393333\pi$
$938$	20918.8	0.728169
$939$	7899.83	0.274549
$940$	−902.770	−0.0313246
$941$	36061.9	1.24929	0.624647	−	0.780907i	$-0.285243\pi$
$941$	36061.9	1.24929	0.624647	+	0.780907i	$0.285243\pi$
$942$	−1285.23	−0.0444533
$943$	−45122.0	−1.55819
$944$	2914.38	0.100482
$945$	3654.11	0.125786
$946$	3355.68	0.115330
$947$	−52177.2	−1.79042	−0.895212	−	0.445640i	$-0.852976\pi$
$947$	−52177.2	−1.79042	−0.895212	+	0.445640i	$0.852976\pi$
$948$	−121.452	−0.00416096
$949$	18608.9	0.636533
$950$	14499.0	0.495169
$951$	33413.4	1.13933
$952$	0	0
$953$	−38749.7	−1.31713	−0.658566	−	0.752523i	$-0.728836\pi$
$953$	−38749.7	−1.31713	−0.658566	+	0.752523i	$0.728836\pi$
$954$	4195.67	0.142390
$955$	−6873.55	−0.232904
$956$	10573.1	0.357696
$957$	2617.83	0.0884245
$958$	−8419.21	−0.283938
$959$	73545.7	2.47645
$960$	780.374	0.0262359
$961$	37115.1	1.24585
$962$	11294.8	0.378545
$963$	−15394.1	−0.515128
$964$	16094.1	0.537715
$965$	14220.6	0.474382
$966$	32135.7	1.07034
$967$	−52687.2	−1.75213	−0.876063	−	0.482197i	$-0.839839\pi$
$967$	−52687.2	−1.75213	−0.876063	+	0.482197i	$0.839839\pi$
$968$	−10439.1	−0.346617
$969$	0	0
$970$	−1646.44	−0.0544991
$971$	4339.06	0.143406	0.0717030	−	0.997426i	$-0.477157\pi$
$971$	4339.06	0.143406	0.0717030	+	0.997426i	$0.477157\pi$
$972$	−972.000	−0.0320750
$973$	−44690.2	−1.47246
$974$	33595.0	1.10519
$975$	−5970.09	−0.196098
$976$	−116.556	−0.00382260
$977$	−23529.5	−0.770498	−0.385249	−	0.922813i	$-0.625884\pi$
$977$	−23529.5	−0.770498	−0.385249	+	0.922813i	$0.625884\pi$
$978$	−8821.35	−0.288421
$979$	−7663.82	−0.250191
$980$	−12449.4	−0.405796
$981$	−15500.3	−0.504473
$982$	21809.2	0.708717
$983$	−25016.8	−0.811712	−0.405856	−	0.913937i	$-0.633027\pi$
$983$	−25016.8	−0.811712	−0.405856	+	0.913937i	$0.633027\pi$
$984$	−6732.55	−0.218116
$985$	−17757.7	−0.574425
$986$	0	0
$987$	−5546.94	−0.178886
$988$	4903.73	0.157903
$989$	−52811.8	−1.69800
$990$	−373.864	−0.0120022
$991$	48058.4	1.54049	0.770246	−	0.637747i	$-0.220134\pi$
$991$	48058.4	1.54049	0.770246	+	0.637747i	$0.220134\pi$
$992$	−8277.19	−0.264920
$993$	−30533.3	−0.975774
$994$	−6400.88	−0.204249
$995$	13649.4	0.434888
$996$	792.663	0.0252174
$997$	27283.0	0.866662	0.433331	−	0.901235i	$-0.357338\pi$
$997$	27283.0	0.866662	0.433331	+	0.901235i	$0.357338\pi$
$998$	5168.38	0.163930
$999$	8311.99	0.263243

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1734.4.a.bd.1.3		6
17.2	even	8		102.4.f.c.55.2	yes	12
17.9	even	8		102.4.f.c.13.2	✓	12
17.16	even	2		1734.4.a.be.1.4		6
51.2	odd	8		306.4.g.g.55.3		12
51.26	odd	8		306.4.g.g.217.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
102.4.f.c.13.2	✓	12	17.9	even	8
102.4.f.c.55.2	yes	12	17.2	even	8
306.4.g.g.55.3		12	51.2	odd	8
306.4.g.g.217.3		12	51.26	odd	8
1734.4.a.bd.1.3		6	1.1	even	1	trivial
1734.4.a.be.1.4		6	17.16	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:	\( N \)	\(=\)	\( 1734 = 2 \cdot 3 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1734.a (trivial)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -4.06445 q^{5} -6.00000 q^{6} +33.2979 q^{7} +8.00000 q^{8} +9.00000 q^{9} -8.12889 q^{10} +5.11022 q^{11} -12.0000 q^{12} -18.3446 q^{13} +66.5957 q^{14} +12.1933 q^{15} +16.0000 q^{16} +18.0000 q^{18} -66.8279 q^{19} -16.2578 q^{20} -99.8936 q^{21} +10.2204 q^{22} -160.850 q^{23} -24.0000 q^{24} -108.480 q^{25} -36.6892 q^{26} -27.0000 q^{27} +133.191 q^{28} -170.758 q^{29} +24.3867 q^{30} -258.662 q^{31} +32.0000 q^{32} -15.3307 q^{33} -135.337 q^{35} +36.0000 q^{36} -307.851 q^{37} -133.656 q^{38} +55.0339 q^{39} -32.5156 q^{40} +280.523 q^{41} -199.787 q^{42} +328.331 q^{43} +20.4409 q^{44} -36.5800 q^{45} -321.699 q^{46} +55.5285 q^{47} -48.0000 q^{48} +765.747 q^{49} -216.961 q^{50} -73.3785 q^{52} +233.093 q^{53} -54.0000 q^{54} -20.7702 q^{55} +266.383 q^{56} +200.484 q^{57} -341.515 q^{58} +182.149 q^{59} +48.7734 q^{60} -7.28473 q^{61} -517.324 q^{62} +299.681 q^{63} +64.0000 q^{64} +74.5607 q^{65} -30.6613 q^{66} +314.116 q^{67} +482.549 q^{69} -270.675 q^{70} -96.1155 q^{71} +72.0000 q^{72} -1014.40 q^{73} -615.703 q^{74} +325.441 q^{75} -267.312 q^{76} +170.159 q^{77} +110.068 q^{78} +10.1210 q^{79} -65.0311 q^{80} +81.0000 q^{81} +561.046 q^{82} -66.0553 q^{83} -399.574 q^{84} +656.661 q^{86} +512.273 q^{87} +40.8817 q^{88} -1499.70 q^{89} -73.1600 q^{90} -610.837 q^{91} -643.398 q^{92} +775.986 q^{93} +111.057 q^{94} +271.618 q^{95} -96.0000 q^{96} +202.542 q^{97} +1531.49 q^{98} +45.9920 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 12 q^{2} - 18 q^{3} + 24 q^{4} - 14 q^{5} - 36 q^{6} - 28 q^{7} + 48 q^{8} + 54 q^{9} - 28 q^{10} - 34 q^{11} - 72 q^{12} + 34 q^{13} - 56 q^{14} + 42 q^{15} + 96 q^{16} + 108 q^{18} + 70 q^{19} - 56 q^{20}+ \cdots - 306 q^{99}+O(q^{100}) \) 6 * q + 12 * q^2 - 18 * q^3 + 24 * q^4 - 14 * q^5 - 36 * q^6 - 28 * q^7 + 48 * q^8 + 54 * q^9 - 28 * q^10 - 34 * q^11 - 72 * q^12 + 34 * q^13 - 56 * q^14 + 42 * q^15 + 96 * q^16 + 108 * q^18 + 70 * q^19 - 56 * q^20 + 84 * q^21 - 68 * q^22 - 78 * q^23 - 144 * q^24 + 188 * q^25 + 68 * q^26 - 162 * q^27 - 112 * q^28 - 280 * q^29 + 84 * q^30 - 508 * q^31 + 192 * q^32 + 102 * q^33 + 196 * q^35 + 216 * q^36 - 308 * q^37 + 140 * q^38 - 102 * q^39 - 112 * q^40 - 442 * q^41 + 168 * q^42 - 46 * q^43 - 136 * q^44 - 126 * q^45 - 156 * q^46 + 1460 * q^47 - 288 * q^48 + 1042 * q^49 + 376 * q^50 + 136 * q^52 + 476 * q^53 - 324 * q^54 - 578 * q^55 - 224 * q^56 - 210 * q^57 - 560 * q^58 + 688 * q^59 + 168 * q^60 + 84 * q^61 - 1016 * q^62 - 252 * q^63 + 384 * q^64 - 1526 * q^65 + 204 * q^66 - 1004 * q^67 + 234 * q^69 + 392 * q^70 - 332 * q^71 + 432 * q^72 - 1132 * q^73 - 616 * q^74 - 564 * q^75 + 280 * q^76 - 1548 * q^77 - 204 * q^78 - 4512 * q^79 - 224 * q^80 + 486 * q^81 - 884 * q^82 + 68 * q^83 + 336 * q^84 - 92 * q^86 + 840 * q^87 - 272 * q^88 - 2652 * q^89 - 252 * q^90 - 3052 * q^91 - 312 * q^92 + 1524 * q^93 + 2920 * q^94 + 622 * q^95 - 576 * q^96 + 1152 * q^97 + 2084 * q^98 - 306 * q^99

Introduction

L-functions

Modular forms

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Database

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