LMFDB - Embedded newform 1470.4.a.i.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1470,4,Mod(1,1470)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1470, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("1470.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1470.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:	$86.7328077084$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 210)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1470.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -5.00000 q^{5} -6.00000 q^{6} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$

\(q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -5.00000 q^{5} -6.00000 q^{6} -8.00000 q^{8} +9.00000 q^{9} +10.0000 q^{10} -44.0000 q^{11} +12.0000 q^{12} -54.0000 q^{13} -15.0000 q^{15} +16.0000 q^{16} -98.0000 q^{17} -18.0000 q^{18} +60.0000 q^{19} -20.0000 q^{20} +88.0000 q^{22} -144.000 q^{23} -24.0000 q^{24} +25.0000 q^{25} +108.000 q^{26} +27.0000 q^{27} -210.000 q^{29} +30.0000 q^{30} +208.000 q^{31} -32.0000 q^{32} -132.000 q^{33} +196.000 q^{34} +36.0000 q^{36} -226.000 q^{37} -120.000 q^{38} -162.000 q^{39} +40.0000 q^{40} +502.000 q^{41} +484.000 q^{43} -176.000 q^{44} -45.0000 q^{45} +288.000 q^{46} +232.000 q^{47} +48.0000 q^{48} -50.0000 q^{50} -294.000 q^{51} -216.000 q^{52} -530.000 q^{53} -54.0000 q^{54} +220.000 q^{55} +180.000 q^{57} +420.000 q^{58} +764.000 q^{59} -60.0000 q^{60} -814.000 q^{61} -416.000 q^{62} +64.0000 q^{64} +270.000 q^{65} +264.000 q^{66} +60.0000 q^{67} -392.000 q^{68} -432.000 q^{69} +848.000 q^{71} -72.0000 q^{72} +958.000 q^{73} +452.000 q^{74} +75.0000 q^{75} +240.000 q^{76} +324.000 q^{78} -152.000 q^{79} -80.0000 q^{80} +81.0000 q^{81} -1004.00 q^{82} -308.000 q^{83} +490.000 q^{85} -968.000 q^{86} -630.000 q^{87} +352.000 q^{88} +1094.00 q^{89} +90.0000 q^{90} -576.000 q^{92} +624.000 q^{93} -464.000 q^{94} -300.000 q^{95} -96.0000 q^{96} -554.000 q^{97} -396.000 q^{99} +O(q^{100})\)

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 $

$2$	−2.00000	−0.707107
$2$	−2.00000	−0.707107
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	4.00000	0.500000
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	−6.00000	−0.408248
$7$	0	0
$7$	0	0
$8$	−8.00000	−0.353553
$9$	9.00000	0.333333
$10$	10.0000	0.316228
$11$	−44.0000	−1.20605	−0.603023	−	0.797724i	$-0.706037\pi$
$11$	−44.0000	−1.20605	−0.603023	+	0.797724i	$0.706037\pi$
$12$	12.0000	0.288675
$13$	−54.0000	−1.15207	−0.576035	−	0.817425i	$-0.695401\pi$
$13$	−54.0000	−1.15207	−0.576035	+	0.817425i	$0.695401\pi$
$14$	0	0
$15$	−15.0000	−0.258199
$16$	16.0000	0.250000
$17$	−98.0000	−1.39815	−0.699073	−	0.715050i	$-0.746404\pi$
$17$	−98.0000	−1.39815	−0.699073	+	0.715050i	$0.746404\pi$
$18$	−18.0000	−0.235702
$19$	60.0000	0.724471	0.362235	−	0.932087i	$-0.382014\pi$
$19$	60.0000	0.724471	0.362235	+	0.932087i	$0.382014\pi$
$20$	−20.0000	−0.223607
$21$	0	0
$22$	88.0000	0.852803
$23$	−144.000	−1.30548	−0.652741	−	0.757581i	$-0.726381\pi$
$23$	−144.000	−1.30548	−0.652741	+	0.757581i	$0.726381\pi$
$24$	−24.0000	−0.204124
$25$	25.0000	0.200000
$26$	108.000	0.814636
$27$	27.0000	0.192450
$28$	0	0
$29$	−210.000	−1.34469	−0.672345	−	0.740238i	$-0.734713\pi$
$29$	−210.000	−1.34469	−0.672345	+	0.740238i	$0.734713\pi$
$30$	30.0000	0.182574
$31$	208.000	1.20509	0.602547	−	0.798084i	$-0.294153\pi$
$31$	208.000	1.20509	0.602547	+	0.798084i	$0.294153\pi$
$32$	−32.0000	−0.176777
$33$	−132.000	−0.696311
$34$	196.000	0.988639
$35$	0	0
$36$	36.0000	0.166667
$37$	−226.000	−1.00417	−0.502083	−	0.864819i	$-0.667433\pi$
$37$	−226.000	−1.00417	−0.502083	+	0.864819i	$0.667433\pi$
$38$	−120.000	−0.512278
$39$	−162.000	−0.665148
$40$	40.0000	0.158114
$41$	502.000	1.91218	0.956088	−	0.293079i	$-0.0946800\pi$
$41$	502.000	1.91218	0.956088	+	0.293079i	$0.0946800\pi$
$42$	0	0
$43$	484.000	1.71650	0.858248	−	0.513236i	$-0.171553\pi$
$43$	484.000	1.71650	0.858248	+	0.513236i	$0.171553\pi$
$44$	−176.000	−0.603023
$45$	−45.0000	−0.149071
$46$	288.000	0.923115
$47$	232.000	0.720014	0.360007	−	0.932950i	$-0.382774\pi$
$47$	232.000	0.720014	0.360007	+	0.932950i	$0.382774\pi$
$48$	48.0000	0.144338
$49$	0	0
$50$	−50.0000	−0.141421
$51$	−294.000	−0.807220
$52$	−216.000	−0.576035
$53$	−530.000	−1.37361	−0.686803	−	0.726844i	$-0.740986\pi$
$53$	−530.000	−1.37361	−0.686803	+	0.726844i	$0.740986\pi$
$54$	−54.0000	−0.136083
$55$	220.000	0.539360
$56$	0	0
$57$	180.000	0.418273
$58$	420.000	0.950840
$59$	764.000	1.68584	0.842918	−	0.538042i	$-0.180836\pi$
$59$	764.000	1.68584	0.842918	+	0.538042i	$0.180836\pi$
$60$	−60.0000	−0.129099
$61$	−814.000	−1.70856	−0.854279	−	0.519815i	$-0.826001\pi$
$61$	−814.000	−1.70856	−0.854279	+	0.519815i	$0.826001\pi$
$62$	−416.000	−0.852130
$63$	0	0
$64$	64.0000	0.125000
$65$	270.000	0.515221
$66$	264.000	0.492366
$67$	60.0000	0.109405	0.0547027	−	0.998503i	$-0.482579\pi$
$67$	60.0000	0.109405	0.0547027	+	0.998503i	$0.482579\pi$
$68$	−392.000	−0.699073
$69$	−432.000	−0.753720
$70$	0	0
$71$	848.000	1.41745	0.708726	−	0.705484i	$-0.249270\pi$
$71$	848.000	1.41745	0.708726	+	0.705484i	$0.249270\pi$
$72$	−72.0000	−0.117851
$73$	958.000	1.53596	0.767982	−	0.640471i	$-0.221261\pi$
$73$	958.000	1.53596	0.767982	+	0.640471i	$0.221261\pi$
$74$	452.000	0.710053
$75$	75.0000	0.115470
$76$	240.000	0.362235
$77$	0	0
$78$	324.000	0.470330
$79$	−152.000	−0.216473	−0.108236	−	0.994125i	$-0.534520\pi$
$79$	−152.000	−0.216473	−0.108236	+	0.994125i	$0.534520\pi$
$80$	−80.0000	−0.111803
$81$	81.0000	0.111111
$82$	−1004.00	−1.35211
$83$	−308.000	−0.407318	−0.203659	−	0.979042i	$-0.565283\pi$
$83$	−308.000	−0.407318	−0.203659	+	0.979042i	$0.565283\pi$
$84$	0	0
$85$	490.000	0.625270
$86$	−968.000	−1.21375
$87$	−630.000	−0.776357
$88$	352.000	0.426401
$89$	1094.00	1.30296	0.651482	−	0.758664i	$-0.274148\pi$
$89$	1094.00	1.30296	0.651482	+	0.758664i	$0.274148\pi$
$90$	90.0000	0.105409
$91$	0	0
$92$	−576.000	−0.652741
$93$	624.000	0.695761
$94$	−464.000	−0.509127
$95$	−300.000	−0.323993
$96$	−96.0000	−0.102062
$97$	−554.000	−0.579899	−0.289949	−	0.957042i	$-0.593638\pi$
$97$	−554.000	−0.579899	−0.289949	+	0.957042i	$0.593638\pi$
$98$	0	0
$99$	−396.000	−0.402015
$100$	100.000	0.100000
$101$	−1134.00	−1.11720	−0.558600	−	0.829437i	$-0.688661\pi$
$101$	−1134.00	−1.11720	−0.558600	+	0.829437i	$0.688661\pi$
$102$	588.000	0.570791
$103$	488.000	0.466836	0.233418	−	0.972377i	$-0.425009\pi$
$103$	488.000	0.466836	0.233418	+	0.972377i	$0.425009\pi$
$104$	432.000	0.407318
$105$	0	0
$106$	1060.00	0.971286
$107$	−828.000	−0.748091	−0.374046	−	0.927410i	$-0.622030\pi$
$107$	−828.000	−0.748091	−0.374046	+	0.927410i	$0.622030\pi$
$108$	108.000	0.0962250
$109$	−42.0000	−0.0369071	−0.0184535	−	0.999830i	$-0.505874\pi$
$109$	−42.0000	−0.0369071	−0.0184535	+	0.999830i	$0.505874\pi$
$110$	−440.000	−0.381385
$111$	−678.000	−0.579756
$112$	0	0
$113$	2138.00	1.77988	0.889939	−	0.456080i	$-0.150747\pi$
$113$	2138.00	1.77988	0.889939	+	0.456080i	$0.150747\pi$
$114$	−360.000	−0.295764
$115$	720.000	0.583829
$116$	−840.000	−0.672345
$117$	−486.000	−0.384023
$118$	−1528.00	−1.19207
$119$	0	0
$120$	120.000	0.0912871
$121$	605.000	0.454545
$122$	1628.00	1.20813
$123$	1506.00	1.10400
$124$	832.000	0.602547
$125$	−125.000	−0.0894427
$126$	0	0
$127$	1072.00	0.749013	0.374506	−	0.927224i	$-0.377812\pi$
$127$	1072.00	0.749013	0.374506	+	0.927224i	$0.377812\pi$
$128$	−128.000	−0.0883883
$129$	1452.00	0.991019
$130$	−540.000	−0.364316
$131$	−1004.00	−0.669617	−0.334809	−	0.942286i	$-0.608672\pi$
$131$	−1004.00	−0.669617	−0.334809	+	0.942286i	$0.608672\pi$
$132$	−528.000	−0.348155
$133$	0	0
$134$	−120.000	−0.0773614
$135$	−135.000	−0.0860663
$136$	784.000	0.494319
$137$	642.000	0.400363	0.200182	−	0.979759i	$-0.435847\pi$
$137$	642.000	0.400363	0.200182	+	0.979759i	$0.435847\pi$
$138$	864.000	0.532961
$139$	1604.00	0.978773	0.489387	−	0.872067i	$-0.337221\pi$
$139$	1604.00	0.978773	0.489387	+	0.872067i	$0.337221\pi$
$140$	0	0
$141$	696.000	0.415701
$142$	−1696.00	−1.00229
$143$	2376.00	1.38945
$144$	144.000	0.0833333
$145$	1050.00	0.601364
$146$	−1916.00	−1.08609
$147$	0	0
$148$	−904.000	−0.502083
$149$	−2394.00	−1.31627	−0.658135	−	0.752900i	$-0.728654\pi$
$149$	−2394.00	−1.31627	−0.658135	+	0.752900i	$0.728654\pi$
$150$	−150.000	−0.0816497
$151$	800.000	0.431146	0.215573	−	0.976488i	$-0.430838\pi$
$151$	800.000	0.431146	0.215573	+	0.976488i	$0.430838\pi$
$152$	−480.000	−0.256139
$153$	−882.000	−0.466049
$154$	0	0
$155$	−1040.00	−0.538934
$156$	−648.000	−0.332574
$157$	890.000	0.452419	0.226209	−	0.974079i	$-0.427367\pi$
$157$	890.000	0.452419	0.226209	+	0.974079i	$0.427367\pi$
$158$	304.000	0.153069
$159$	−1590.00	−0.793052
$160$	160.000	0.0790569
$161$	0	0
$162$	−162.000	−0.0785674
$163$	668.000	0.320993	0.160496	−	0.987036i	$-0.448691\pi$
$163$	668.000	0.320993	0.160496	+	0.987036i	$0.448691\pi$
$164$	2008.00	0.956088
$165$	660.000	0.311400
$166$	616.000	0.288017
$167$	−816.000	−0.378108	−0.189054	−	0.981967i	$-0.560542\pi$
$167$	−816.000	−0.378108	−0.189054	+	0.981967i	$0.560542\pi$
$168$	0	0
$169$	719.000	0.327264
$170$	−980.000	−0.442133
$171$	540.000	0.241490
$172$	1936.00	0.858248
$173$	−1334.00	−0.586255	−0.293128	−	0.956073i	$-0.594696\pi$
$173$	−1334.00	−0.586255	−0.293128	+	0.956073i	$0.594696\pi$
$174$	1260.00	0.548968
$175$	0	0
$176$	−704.000	−0.301511
$177$	2292.00	0.973318
$178$	−2188.00	−0.921334
$179$	−1236.00	−0.516106	−0.258053	−	0.966131i	$-0.583081\pi$
$179$	−1236.00	−0.516106	−0.258053	+	0.966131i	$0.583081\pi$
$180$	−180.000	−0.0745356
$181$	−358.000	−0.147016	−0.0735081	−	0.997295i	$-0.523419\pi$
$181$	−358.000	−0.147016	−0.0735081	+	0.997295i	$0.523419\pi$
$182$	0	0
$183$	−2442.00	−0.986436
$184$	1152.00	0.461557
$185$	1130.00	0.449077
$186$	−1248.00	−0.491977
$187$	4312.00	1.68623
$188$	928.000	0.360007
$189$	0	0
$190$	600.000	0.229098
$191$	−888.000	−0.336405	−0.168203	−	0.985752i	$-0.553796\pi$
$191$	−888.000	−0.336405	−0.168203	+	0.985752i	$0.553796\pi$
$192$	192.000	0.0721688
$193$	−4030.00	−1.50303	−0.751517	−	0.659713i	$-0.770678\pi$
$193$	−4030.00	−1.50303	−0.751517	+	0.659713i	$0.770678\pi$
$194$	1108.00	0.410050
$195$	810.000	0.297463
$196$	0	0
$197$	−1714.00	−0.619886	−0.309943	−	0.950755i	$-0.600310\pi$
$197$	−1714.00	−0.619886	−0.309943	+	0.950755i	$0.600310\pi$
$198$	792.000	0.284268
$199$	4264.00	1.51893	0.759465	−	0.650549i	$-0.225461\pi$
$199$	4264.00	1.51893	0.759465	+	0.650549i	$0.225461\pi$
$200$	−200.000	−0.0707107
$201$	180.000	0.0631653
$202$	2268.00	0.789980
$203$	0	0
$204$	−1176.00	−0.403610
$205$	−2510.00	−0.855151
$206$	−976.000	−0.330103
$207$	−1296.00	−0.435161
$208$	−864.000	−0.288017
$209$	−2640.00	−0.873745
$210$	0	0
$211$	3316.00	1.08191	0.540955	−	0.841052i	$-0.318063\pi$
$211$	3316.00	1.08191	0.540955	+	0.841052i	$0.318063\pi$
$212$	−2120.00	−0.686803
$213$	2544.00	0.818366
$214$	1656.00	0.528981
$215$	−2420.00	−0.767640
$216$	−216.000	−0.0680414
$217$	0	0
$218$	84.0000	0.0260972
$219$	2874.00	0.886790
$220$	880.000	0.269680
$221$	5292.00	1.61076
$222$	1356.00	0.409949
$223$	−2128.00	−0.639020	−0.319510	−	0.947583i	$-0.603518\pi$
$223$	−2128.00	−0.639020	−0.319510	+	0.947583i	$0.603518\pi$
$224$	0	0
$225$	225.000	0.0666667
$226$	−4276.00	−1.25856
$227$	−980.000	−0.286541	−0.143271	−	0.989684i	$-0.545762\pi$
$227$	−980.000	−0.286541	−0.143271	+	0.989684i	$0.545762\pi$
$228$	720.000	0.209137
$229$	−4102.00	−1.18370	−0.591851	−	0.806047i	$-0.701603\pi$
$229$	−4102.00	−1.18370	−0.591851	+	0.806047i	$0.701603\pi$
$230$	−1440.00	−0.412830
$231$	0	0
$232$	1680.00	0.475420
$233$	2466.00	0.693361	0.346680	−	0.937983i	$-0.387309\pi$
$233$	2466.00	0.693361	0.346680	+	0.937983i	$0.387309\pi$
$234$	972.000	0.271545
$235$	−1160.00	−0.322000
$236$	3056.00	0.842918
$237$	−456.000	−0.124981
$238$	0	0
$239$	1192.00	0.322611	0.161306	−	0.986905i	$-0.448430\pi$
$239$	1192.00	0.322611	0.161306	+	0.986905i	$0.448430\pi$
$240$	−240.000	−0.0645497
$241$	3854.00	1.03012	0.515058	−	0.857155i	$-0.327770\pi$
$241$	3854.00	1.03012	0.515058	+	0.857155i	$0.327770\pi$
$242$	−1210.00	−0.321412
$243$	243.000	0.0641500
$244$	−3256.00	−0.854279
$245$	0	0
$246$	−3012.00	−0.780643
$247$	−3240.00	−0.834641
$248$	−1664.00	−0.426065
$249$	−924.000	−0.235165
$250$	250.000	0.0632456
$251$	−4020.00	−1.01092	−0.505458	−	0.862851i	$-0.668677\pi$
$251$	−4020.00	−1.01092	−0.505458	+	0.862851i	$0.668677\pi$
$252$	0	0
$253$	6336.00	1.57447
$254$	−2144.00	−0.529632
$255$	1470.00	0.361000
$256$	256.000	0.0625000
$257$	−1922.00	−0.466502	−0.233251	−	0.972417i	$-0.574936\pi$
$257$	−1922.00	−0.466502	−0.233251	+	0.972417i	$0.574936\pi$
$258$	−2904.00	−0.700756
$259$	0	0
$260$	1080.00	0.257611
$261$	−1890.00	−0.448230
$262$	2008.00	0.473491
$263$	2480.00	0.581458	0.290729	−	0.956805i	$-0.406102\pi$
$263$	2480.00	0.581458	0.290729	+	0.956805i	$0.406102\pi$
$264$	1056.00	0.246183
$265$	2650.00	0.614295
$266$	0	0
$267$	3282.00	0.752266
$268$	240.000	0.0547027
$269$	1002.00	0.227112	0.113556	−	0.993532i	$-0.463776\pi$
$269$	1002.00	0.227112	0.113556	+	0.993532i	$0.463776\pi$
$270$	270.000	0.0608581
$271$	2832.00	0.634804	0.317402	−	0.948291i	$-0.397190\pi$
$271$	2832.00	0.634804	0.317402	+	0.948291i	$0.397190\pi$
$272$	−1568.00	−0.349537
$273$	0	0
$274$	−1284.00	−0.283100
$275$	−1100.00	−0.241209
$276$	−1728.00	−0.376860
$277$	4206.00	0.912325	0.456163	−	0.889896i	$-0.349224\pi$
$277$	4206.00	0.912325	0.456163	+	0.889896i	$0.349224\pi$
$278$	−3208.00	−0.692097
$279$	1872.00	0.401698
$280$	0	0
$281$	5978.00	1.26910	0.634551	−	0.772881i	$-0.281185\pi$
$281$	5978.00	1.26910	0.634551	+	0.772881i	$0.281185\pi$
$282$	−1392.00	−0.293945
$283$	−2684.00	−0.563771	−0.281886	−	0.959448i	$-0.590960\pi$
$283$	−2684.00	−0.563771	−0.281886	+	0.959448i	$0.590960\pi$
$284$	3392.00	0.708726
$285$	−900.000	−0.187058
$286$	−4752.00	−0.982488
$287$	0	0
$288$	−288.000	−0.0589256
$289$	4691.00	0.954814
$290$	−2100.00	−0.425228
$291$	−1662.00	−0.334805
$292$	3832.00	0.767982
$293$	7490.00	1.49341	0.746707	−	0.665153i	$-0.231634\pi$
$293$	7490.00	1.49341	0.746707	+	0.665153i	$0.231634\pi$
$294$	0	0
$295$	−3820.00	−0.753929
$296$	1808.00	0.355027
$297$	−1188.00	−0.232104
$298$	4788.00	0.930743
$299$	7776.00	1.50401
$300$	300.000	0.0577350
$301$	0	0
$302$	−1600.00	−0.304866
$303$	−3402.00	−0.645016
$304$	960.000	0.181118
$305$	4070.00	0.764090
$306$	1764.00	0.329546
$307$	6860.00	1.27531	0.637656	−	0.770321i	$-0.279904\pi$
$307$	6860.00	1.27531	0.637656	+	0.770321i	$0.279904\pi$
$308$	0	0
$309$	1464.00	0.269528
$310$	2080.00	0.381084
$311$	4920.00	0.897066	0.448533	−	0.893766i	$-0.351947\pi$
$311$	4920.00	0.897066	0.448533	+	0.893766i	$0.351947\pi$
$312$	1296.00	0.235165
$313$	4558.00	0.823110	0.411555	−	0.911385i	$-0.364986\pi$
$313$	4558.00	0.823110	0.411555	+	0.911385i	$0.364986\pi$
$314$	−1780.00	−0.319908
$315$	0	0
$316$	−608.000	−0.108236
$317$	5830.00	1.03295	0.516475	−	0.856302i	$-0.327244\pi$
$317$	5830.00	1.03295	0.516475	+	0.856302i	$0.327244\pi$
$318$	3180.00	0.560772
$319$	9240.00	1.62176
$320$	−320.000	−0.0559017
$321$	−2484.00	−0.431911
$322$	0	0
$323$	−5880.00	−1.01292
$324$	324.000	0.0555556
$325$	−1350.00	−0.230414
$326$	−1336.00	−0.226976
$327$	−126.000	−0.0213083
$328$	−4016.00	−0.676056
$329$	0	0
$330$	−1320.00	−0.220193
$331$	5020.00	0.833608	0.416804	−	0.908996i	$-0.363150\pi$
$331$	5020.00	0.833608	0.416804	+	0.908996i	$0.363150\pi$
$332$	−1232.00	−0.203659
$333$	−2034.00	−0.334722
$334$	1632.00	0.267362
$335$	−300.000	−0.0489276
$336$	0	0
$337$	−3662.00	−0.591934	−0.295967	−	0.955198i	$-0.595642\pi$
$337$	−3662.00	−0.591934	−0.295967	+	0.955198i	$0.595642\pi$
$338$	−1438.00	−0.231411
$339$	6414.00	1.02761
$340$	1960.00	0.312635
$341$	−9152.00	−1.45340
$342$	−1080.00	−0.170759
$343$	0	0
$344$	−3872.00	−0.606873
$345$	2160.00	0.337074
$346$	2668.00	0.414545
$347$	−860.000	−0.133047	−0.0665234	−	0.997785i	$-0.521191\pi$
$347$	−860.000	−0.133047	−0.0665234	+	0.997785i	$0.521191\pi$
$348$	−2520.00	−0.388179
$349$	3458.00	0.530380	0.265190	−	0.964196i	$-0.414565\pi$
$349$	3458.00	0.530380	0.265190	+	0.964196i	$0.414565\pi$
$350$	0	0
$351$	−1458.00	−0.221716
$352$	1408.00	0.213201
$353$	−2994.00	−0.451429	−0.225715	−	0.974193i	$-0.572472\pi$
$353$	−2994.00	−0.451429	−0.225715	+	0.974193i	$0.572472\pi$
$354$	−4584.00	−0.688240
$355$	−4240.00	−0.633904
$356$	4376.00	0.651482
$357$	0	0
$358$	2472.00	0.364942
$359$	1760.00	0.258744	0.129372	−	0.991596i	$-0.458704\pi$
$359$	1760.00	0.258744	0.129372	+	0.991596i	$0.458704\pi$
$360$	360.000	0.0527046
$361$	−3259.00	−0.475142
$362$	716.000	0.103956
$363$	1815.00	0.262432
$364$	0	0
$365$	−4790.00	−0.686904
$366$	4884.00	0.697516
$367$	608.000	0.0864778	0.0432389	−	0.999065i	$-0.486232\pi$
$367$	608.000	0.0864778	0.0432389	+	0.999065i	$0.486232\pi$
$368$	−2304.00	−0.326370
$369$	4518.00	0.637392
$370$	−2260.00	−0.317545
$371$	0	0
$372$	2496.00	0.347881
$373$	−7090.00	−0.984199	−0.492100	−	0.870539i	$-0.663770\pi$
$373$	−7090.00	−0.984199	−0.492100	+	0.870539i	$0.663770\pi$
$374$	−8624.00	−1.19234
$375$	−375.000	−0.0516398
$376$	−1856.00	−0.254564
$377$	11340.0	1.54918
$378$	0	0
$379$	14268.0	1.93377	0.966884	−	0.255217i	$-0.0821469\pi$
$379$	14268.0	1.93377	0.966884	+	0.255217i	$0.0821469\pi$
$380$	−1200.00	−0.161997
$381$	3216.00	0.432443
$382$	1776.00	0.237875
$383$	4104.00	0.547532	0.273766	−	0.961796i	$-0.411731\pi$
$383$	4104.00	0.547532	0.273766	+	0.961796i	$0.411731\pi$
$384$	−384.000	−0.0510310
$385$	0	0
$386$	8060.00	1.06281
$387$	4356.00	0.572165
$388$	−2216.00	−0.289949
$389$	15110.0	1.96943	0.984714	−	0.174180i	$-0.0557273\pi$
$389$	15110.0	1.96943	0.984714	+	0.174180i	$0.0557273\pi$
$390$	−1620.00	−0.210338
$391$	14112.0	1.82525
$392$	0	0
$393$	−3012.00	−0.386604
$394$	3428.00	0.438325
$395$	760.000	0.0968095
$396$	−1584.00	−0.201008
$397$	10682.0	1.35041	0.675207	−	0.737628i	$-0.264054\pi$
$397$	10682.0	1.35041	0.675207	+	0.737628i	$0.264054\pi$
$398$	−8528.00	−1.07405
$399$	0	0
$400$	400.000	0.0500000
$401$	−10526.0	−1.31083	−0.655416	−	0.755268i	$-0.727507\pi$
$401$	−10526.0	−1.31083	−0.655416	+	0.755268i	$0.727507\pi$
$402$	−360.000	−0.0446646
$403$	−11232.0	−1.38835
$404$	−4536.00	−0.558600
$405$	−405.000	−0.0496904
$406$	0	0
$407$	9944.00	1.21107
$408$	2352.00	0.285395
$409$	6.00000	0.000725381 0	0.000362691	−	1.00000i	$-0.499885\pi$
$409$	6.00000	0.000725381 0	0.000362691		1.00000i	$0.499885\pi$
$410$	5020.00	0.604683
$411$	1926.00	0.231150
$412$	1952.00	0.233418
$413$	0	0
$414$	2592.00	0.307705
$415$	1540.00	0.182158
$416$	1728.00	0.203659
$417$	4812.00	0.565095
$418$	5280.00	0.617831
$419$	15108.0	1.76151	0.880757	−	0.473569i	$-0.157035\pi$
$419$	15108.0	1.76151	0.880757	+	0.473569i	$0.157035\pi$
$420$	0	0
$421$	10094.0	1.16853	0.584265	−	0.811563i	$-0.301383\pi$
$421$	10094.0	1.16853	0.584265	+	0.811563i	$0.301383\pi$
$422$	−6632.00	−0.765025
$423$	2088.00	0.240005
$424$	4240.00	0.485643
$425$	−2450.00	−0.279629
$426$	−5088.00	−0.578672
$427$	0	0
$428$	−3312.00	−0.374046
$429$	7128.00	0.802198
$430$	4840.00	0.542804
$431$	−12696.0	−1.41890	−0.709449	−	0.704757i	$-0.751056\pi$
$431$	−12696.0	−1.41890	−0.709449	+	0.704757i	$0.751056\pi$
$432$	432.000	0.0481125
$433$	−12122.0	−1.34537	−0.672686	−	0.739928i	$-0.734860\pi$
$433$	−12122.0	−1.34537	−0.672686	+	0.739928i	$0.734860\pi$
$434$	0	0
$435$	3150.00	0.347198
$436$	−168.000	−0.0184535
$437$	−8640.00	−0.945783
$438$	−5748.00	−0.627055
$439$	8552.00	0.929760	0.464880	−	0.885374i	$-0.346097\pi$
$439$	8552.00	0.929760	0.464880	+	0.885374i	$0.346097\pi$
$440$	−1760.00	−0.190693
$441$	0	0
$442$	−10584.0	−1.13898
$443$	−3548.00	−0.380520	−0.190260	−	0.981734i	$-0.560933\pi$
$443$	−3548.00	−0.380520	−0.190260	+	0.981734i	$0.560933\pi$
$444$	−2712.00	−0.289878
$445$	−5470.00	−0.582703
$446$	4256.00	0.451855
$447$	−7182.00	−0.759948
$448$	0	0
$449$	−16686.0	−1.75381	−0.876905	−	0.480663i	$-0.840396\pi$
$449$	−16686.0	−1.75381	−0.876905	+	0.480663i	$0.840396\pi$
$450$	−450.000	−0.0471405
$451$	−22088.0	−2.30617
$452$	8552.00	0.889939
$453$	2400.00	0.248922
$454$	1960.00	0.202615
$455$	0	0
$456$	−1440.00	−0.147882
$457$	778.000	0.0796352	0.0398176	−	0.999207i	$-0.487322\pi$
$457$	778.000	0.0796352	0.0398176	+	0.999207i	$0.487322\pi$
$458$	8204.00	0.837004
$459$	−2646.00	−0.269073
$460$	2880.00	0.291915
$461$	−838.000	−0.0846628	−0.0423314	−	0.999104i	$-0.513479\pi$
$461$	−838.000	−0.0846628	−0.0423314	+	0.999104i	$0.513479\pi$
$462$	0	0
$463$	−7456.00	−0.748401	−0.374201	−	0.927348i	$-0.622083\pi$
$463$	−7456.00	−0.748401	−0.374201	+	0.927348i	$0.622083\pi$
$464$	−3360.00	−0.336173
$465$	−3120.00	−0.311154
$466$	−4932.00	−0.490280
$467$	−10724.0	−1.06263	−0.531314	−	0.847175i	$-0.678302\pi$
$467$	−10724.0	−1.06263	−0.531314	+	0.847175i	$0.678302\pi$
$468$	−1944.00	−0.192012
$469$	0	0
$470$	2320.00	0.227689
$471$	2670.00	0.261204
$472$	−6112.00	−0.596033
$473$	−21296.0	−2.07017
$474$	912.000	0.0883746
$475$	1500.00	0.144894
$476$	0	0
$477$	−4770.00	−0.457869
$478$	−2384.00	−0.228121
$479$	−768.000	−0.0732585	−0.0366292	−	0.999329i	$-0.511662\pi$
$479$	−768.000	−0.0732585	−0.0366292	+	0.999329i	$0.511662\pi$
$480$	480.000	0.0456435
$481$	12204.0	1.15687
$482$	−7708.00	−0.728402
$483$	0	0
$484$	2420.00	0.227273
$485$	2770.00	0.259339
$486$	−486.000	−0.0453609
$487$	−10744.0	−0.999707	−0.499853	−	0.866110i	$-0.666613\pi$
$487$	−10744.0	−0.999707	−0.499853	+	0.866110i	$0.666613\pi$
$488$	6512.00	0.604066
$489$	2004.00	0.185325
$490$	0	0
$491$	3540.00	0.325373	0.162686	−	0.986678i	$-0.447984\pi$
$491$	3540.00	0.325373	0.162686	+	0.986678i	$0.447984\pi$
$492$	6024.00	0.551998
$493$	20580.0	1.88007
$494$	6480.00	0.590180
$495$	1980.00	0.179787
$496$	3328.00	0.301273
$497$	0	0
$498$	1848.00	0.166287
$499$	15732.0	1.41134	0.705672	−	0.708538i	$-0.250645\pi$
$499$	15732.0	1.41134	0.705672	+	0.708538i	$0.250645\pi$
$500$	−500.000	−0.0447214
$501$	−2448.00	−0.218301
$502$	8040.00	0.714826
$503$	8496.00	0.753117	0.376559	−	0.926393i	$-0.377107\pi$
$503$	8496.00	0.753117	0.376559	+	0.926393i	$0.377107\pi$
$504$	0	0
$505$	5670.00	0.499627
$506$	−12672.0	−1.11332
$507$	2157.00	0.188946
$508$	4288.00	0.374506
$509$	−17638.0	−1.53593	−0.767967	−	0.640489i	$-0.778732\pi$
$509$	−17638.0	−1.53593	−0.767967	+	0.640489i	$0.778732\pi$
$510$	−2940.00	−0.255265
$511$	0	0
$512$	−512.000	−0.0441942
$513$	1620.00	0.139424
$514$	3844.00	0.329867
$515$	−2440.00	−0.208775
$516$	5808.00	0.495510
$517$	−10208.0	−0.868370
$518$	0	0
$519$	−4002.00	−0.338475
$520$	−2160.00	−0.182158
$521$	−1802.00	−0.151530	−0.0757649	−	0.997126i	$-0.524140\pi$
$521$	−1802.00	−0.151530	−0.0757649	+	0.997126i	$0.524140\pi$
$522$	3780.00	0.316947
$523$	−9196.00	−0.768859	−0.384429	−	0.923154i	$-0.625602\pi$
$523$	−9196.00	−0.768859	−0.384429	+	0.923154i	$0.625602\pi$
$524$	−4016.00	−0.334809
$525$	0	0
$526$	−4960.00	−0.411153
$527$	−20384.0	−1.68490
$528$	−2112.00	−0.174078
$529$	8569.00	0.704282
$530$	−5300.00	−0.434372
$531$	6876.00	0.561945
$532$	0	0
$533$	−27108.0	−2.20296
$534$	−6564.00	−0.531933
$535$	4140.00	0.334557
$536$	−480.000	−0.0386807
$537$	−3708.00	−0.297974
$538$	−2004.00	−0.160592
$539$	0	0
$540$	−540.000	−0.0430331
$541$	−5130.00	−0.407682	−0.203841	−	0.979004i	$-0.565343\pi$
$541$	−5130.00	−0.407682	−0.203841	+	0.979004i	$0.565343\pi$
$542$	−5664.00	−0.448874
$543$	−1074.00	−0.0848798
$544$	3136.00	0.247160
$545$	210.000	0.0165053
$546$	0	0
$547$	5916.00	0.462431	0.231216	−	0.972903i	$-0.425730\pi$
$547$	5916.00	0.462431	0.231216	+	0.972903i	$0.425730\pi$
$548$	2568.00	0.200182
$549$	−7326.00	−0.569519
$550$	2200.00	0.170561
$551$	−12600.0	−0.974189
$552$	3456.00	0.266480
$553$	0	0
$554$	−8412.00	−0.645111
$555$	3390.00	0.259275
$556$	6416.00	0.489387
$557$	24166.0	1.83832	0.919162	−	0.393880i	$-0.128867\pi$
$557$	24166.0	1.83832	0.919162	+	0.393880i	$0.128867\pi$
$558$	−3744.00	−0.284043
$559$	−26136.0	−1.97752
$560$	0	0
$561$	12936.0	0.973544
$562$	−11956.0	−0.897390
$563$	−15572.0	−1.16569	−0.582843	−	0.812585i	$-0.698060\pi$
$563$	−15572.0	−1.16569	−0.582843	+	0.812585i	$0.698060\pi$
$564$	2784.00	0.207850
$565$	−10690.0	−0.795985
$566$	5368.00	0.398646
$567$	0	0
$568$	−6784.00	−0.501145
$569$	−12294.0	−0.905784	−0.452892	−	0.891565i	$-0.649608\pi$
$569$	−12294.0	−0.905784	−0.452892	+	0.891565i	$0.649608\pi$
$570$	1800.00	0.132270
$571$	−4740.00	−0.347395	−0.173698	−	0.984799i	$-0.555572\pi$
$571$	−4740.00	−0.347395	−0.173698	+	0.984799i	$0.555572\pi$
$572$	9504.00	0.694724
$573$	−2664.00	−0.194224
$574$	0	0
$575$	−3600.00	−0.261096
$576$	576.000	0.0416667
$577$	−12442.0	−0.897690	−0.448845	−	0.893610i	$-0.648165\pi$
$577$	−12442.0	−0.897690	−0.448845	+	0.893610i	$0.648165\pi$
$578$	−9382.00	−0.675155
$579$	−12090.0	−0.867778
$580$	4200.00	0.300682
$581$	0	0
$582$	3324.00	0.236743
$583$	23320.0	1.65663
$584$	−7664.00	−0.543046
$585$	2430.00	0.171740
$586$	−14980.0	−1.05600
$587$	22036.0	1.54944	0.774722	−	0.632303i	$-0.217890\pi$
$587$	22036.0	1.54944	0.774722	+	0.632303i	$0.217890\pi$
$588$	0	0
$589$	12480.0	0.873055
$590$	7640.00	0.533108
$591$	−5142.00	−0.357891
$592$	−3616.00	−0.251042
$593$	−9666.00	−0.669368	−0.334684	−	0.942330i	$-0.608630\pi$
$593$	−9666.00	−0.669368	−0.334684	+	0.942330i	$0.608630\pi$
$594$	2376.00	0.164122
$595$	0	0
$596$	−9576.00	−0.658135
$597$	12792.0	0.876954
$598$	−15552.0	−1.06349
$599$	−4800.00	−0.327417	−0.163708	−	0.986509i	$-0.552346\pi$
$599$	−4800.00	−0.327417	−0.163708	+	0.986509i	$0.552346\pi$
$600$	−600.000	−0.0408248
$601$	6150.00	0.417411	0.208705	−	0.977979i	$-0.433075\pi$
$601$	6150.00	0.417411	0.208705	+	0.977979i	$0.433075\pi$
$602$	0	0
$603$	540.000	0.0364685
$604$	3200.00	0.215573
$605$	−3025.00	−0.203279
$606$	6804.00	0.456095
$607$	9920.00	0.663328	0.331664	−	0.943397i	$-0.392390\pi$
$607$	9920.00	0.663328	0.331664	+	0.943397i	$0.392390\pi$
$608$	−1920.00	−0.128070
$609$	0	0
$610$	−8140.00	−0.540293
$611$	−12528.0	−0.829507
$612$	−3528.00	−0.233024
$613$	−17442.0	−1.14923	−0.574613	−	0.818425i	$-0.694847\pi$
$613$	−17442.0	−1.14923	−0.574613	+	0.818425i	$0.694847\pi$
$614$	−13720.0	−0.901782
$615$	−7530.00	−0.493722
$616$	0	0
$617$	27746.0	1.81039	0.905196	−	0.424994i	$-0.139724\pi$
$617$	27746.0	1.81039	0.905196	+	0.424994i	$0.139724\pi$
$618$	−2928.00	−0.190585
$619$	−28172.0	−1.82929	−0.914643	−	0.404262i	$-0.867528\pi$
$619$	−28172.0	−1.82929	−0.914643	+	0.404262i	$0.867528\pi$
$620$	−4160.00	−0.269467
$621$	−3888.00	−0.251240
$622$	−9840.00	−0.634322
$623$	0	0
$624$	−2592.00	−0.166287
$625$	625.000	0.0400000
$626$	−9116.00	−0.582027
$627$	−7920.00	−0.504457
$628$	3560.00	0.226209
$629$	22148.0	1.40397
$630$	0	0
$631$	30752.0	1.94012	0.970062	−	0.242859i	$-0.0780852\pi$
$631$	30752.0	1.94012	0.970062	+	0.242859i	$0.0780852\pi$
$632$	1216.00	0.0765346
$633$	9948.00	0.624641
$634$	−11660.0	−0.730407
$635$	−5360.00	−0.334969
$636$	−6360.00	−0.396526
$637$	0	0
$638$	−18480.0	−1.14676
$639$	7632.00	0.472484
$640$	640.000	0.0395285
$641$	1154.00	0.0711080	0.0355540	−	0.999368i	$-0.488680\pi$
$641$	1154.00	0.0711080	0.0355540	+	0.999368i	$0.488680\pi$
$642$	4968.00	0.305407
$643$	−20308.0	−1.24552	−0.622760	−	0.782413i	$-0.713989\pi$
$643$	−20308.0	−1.24552	−0.622760	+	0.782413i	$0.713989\pi$
$644$	0	0
$645$	−7260.00	−0.443197
$646$	11760.0	0.716240
$647$	−12256.0	−0.744719	−0.372359	−	0.928089i	$-0.621451\pi$
$647$	−12256.0	−0.744719	−0.372359	+	0.928089i	$0.621451\pi$
$648$	−648.000	−0.0392837
$649$	−33616.0	−2.03319
$650$	2700.00	0.162927
$651$	0	0
$652$	2672.00	0.160496
$653$	4838.00	0.289932	0.144966	−	0.989437i	$-0.453693\pi$
$653$	4838.00	0.289932	0.144966	+	0.989437i	$0.453693\pi$
$654$	252.000	0.0150672
$655$	5020.00	0.299462
$656$	8032.00	0.478044
$657$	8622.00	0.511988
$658$	0	0
$659$	−5588.00	−0.330315	−0.165157	−	0.986267i	$-0.552813\pi$
$659$	−5588.00	−0.330315	−0.165157	+	0.986267i	$0.552813\pi$
$660$	2640.00	0.155700
$661$	−9430.00	−0.554893	−0.277447	−	0.960741i	$-0.589488\pi$
$661$	−9430.00	−0.554893	−0.277447	+	0.960741i	$0.589488\pi$
$662$	−10040.0	−0.589450
$663$	15876.0	0.929974
$664$	2464.00	0.144009
$665$	0	0
$666$	4068.00	0.236684
$667$	30240.0	1.75547
$668$	−3264.00	−0.189054
$669$	−6384.00	−0.368938
$670$	600.000	0.0345970
$671$	35816.0	2.06060
$672$	0	0
$673$	−16430.0	−0.941055	−0.470527	−	0.882385i	$-0.655936\pi$
$673$	−16430.0	−0.941055	−0.470527	+	0.882385i	$0.655936\pi$
$674$	7324.00	0.418561
$675$	675.000	0.0384900
$676$	2876.00	0.163632
$677$	−12606.0	−0.715639	−0.357820	−	0.933791i	$-0.616480\pi$
$677$	−12606.0	−0.715639	−0.357820	+	0.933791i	$0.616480\pi$
$678$	−12828.0	−0.726632
$679$	0	0
$680$	−3920.00	−0.221066
$681$	−2940.00	−0.165435
$682$	18304.0	1.02771
$683$	23444.0	1.31341	0.656706	−	0.754147i	$-0.271949\pi$
$683$	23444.0	1.31341	0.656706	+	0.754147i	$0.271949\pi$
$684$	2160.00	0.120745
$685$	−3210.00	−0.179048
$686$	0	0
$687$	−12306.0	−0.683411
$688$	7744.00	0.429124
$689$	28620.0	1.58249
$690$	−4320.00	−0.238347
$691$	−14980.0	−0.824698	−0.412349	−	0.911026i	$-0.635291\pi$
$691$	−14980.0	−0.824698	−0.412349	+	0.911026i	$0.635291\pi$
$692$	−5336.00	−0.293128
$693$	0	0
$694$	1720.00	0.0940783
$695$	−8020.00	−0.437721
$696$	5040.00	0.274484
$697$	−49196.0	−2.67350
$698$	−6916.00	−0.375035
$699$	7398.00	0.400312
$700$	0	0
$701$	−25298.0	−1.36304	−0.681521	−	0.731799i	$-0.738681\pi$
$701$	−25298.0	−1.36304	−0.681521	+	0.731799i	$0.738681\pi$
$702$	2916.00	0.156777
$703$	−13560.0	−0.727489
$704$	−2816.00	−0.150756
$705$	−3480.00	−0.185907
$706$	5988.00	0.319209
$707$	0	0
$708$	9168.00	0.486659
$709$	−25634.0	−1.35784	−0.678918	−	0.734215i	$-0.737551\pi$
$709$	−25634.0	−1.35784	−0.678918	+	0.734215i	$0.737551\pi$
$710$	8480.00	0.448238
$711$	−1368.00	−0.0721575
$712$	−8752.00	−0.460667
$713$	−29952.0	−1.57323
$714$	0	0
$715$	−11880.0	−0.621380
$716$	−4944.00	−0.258053
$717$	3576.00	0.186260
$718$	−3520.00	−0.182960
$719$	8448.00	0.438188	0.219094	−	0.975704i	$-0.429690\pi$
$719$	8448.00	0.438188	0.219094	+	0.975704i	$0.429690\pi$
$720$	−720.000	−0.0372678
$721$	0	0
$722$	6518.00	0.335976
$723$	11562.0	0.594738
$724$	−1432.00	−0.0735081
$725$	−5250.00	−0.268938
$726$	−3630.00	−0.185567
$727$	23112.0	1.17906	0.589530	−	0.807746i	$-0.299313\pi$
$727$	23112.0	1.17906	0.589530	+	0.807746i	$0.299313\pi$
$728$	0	0
$729$	729.000	0.0370370
$730$	9580.00	0.485715
$731$	−47432.0	−2.39991
$732$	−9768.00	−0.493218
$733$	−10582.0	−0.533227	−0.266613	−	0.963804i	$-0.585905\pi$
$733$	−10582.0	−0.533227	−0.266613	+	0.963804i	$0.585905\pi$
$734$	−1216.00	−0.0611490
$735$	0	0
$736$	4608.00	0.230779
$737$	−2640.00	−0.131948
$738$	−9036.00	−0.450704
$739$	27124.0	1.35017	0.675083	−	0.737742i	$-0.264108\pi$
$739$	27124.0	1.35017	0.675083	+	0.737742i	$0.264108\pi$
$740$	4520.00	0.224539
$741$	−9720.00	−0.481880
$742$	0	0
$743$	11616.0	0.573553	0.286776	−	0.957998i	$-0.407416\pi$
$743$	11616.0	0.573553	0.286776	+	0.957998i	$0.407416\pi$
$744$	−4992.00	−0.245989
$745$	11970.0	0.588654
$746$	14180.0	0.695934
$747$	−2772.00	−0.135773
$748$	17248.0	0.843114
$749$	0	0
$750$	750.000	0.0365148
$751$	1544.00	0.0750218	0.0375109	−	0.999296i	$-0.488057\pi$
$751$	1544.00	0.0750218	0.0375109	+	0.999296i	$0.488057\pi$
$752$	3712.00	0.180004
$753$	−12060.0	−0.583653
$754$	−22680.0	−1.09543
$755$	−4000.00	−0.192814
$756$	0	0
$757$	−39506.0	−1.89679	−0.948395	−	0.317091i	$-0.897294\pi$
$757$	−39506.0	−1.89679	−0.948395	+	0.317091i	$0.897294\pi$
$758$	−28536.0	−1.36738
$759$	19008.0	0.909021
$760$	2400.00	0.114549
$761$	26022.0	1.23955	0.619774	−	0.784780i	$-0.287224\pi$
$761$	26022.0	1.23955	0.619774	+	0.784780i	$0.287224\pi$
$762$	−6432.00	−0.305783
$763$	0	0
$764$	−3552.00	−0.168203
$765$	4410.00	0.208423
$766$	−8208.00	−0.387163
$767$	−41256.0	−1.94220
$768$	768.000	0.0360844
$769$	27230.0	1.27690	0.638452	−	0.769662i	$-0.279575\pi$
$769$	27230.0	1.27690	0.638452	+	0.769662i	$0.279575\pi$
$770$	0	0
$771$	−5766.00	−0.269335
$772$	−16120.0	−0.751517
$773$	4866.00	0.226414	0.113207	−	0.993571i	$-0.463888\pi$
$773$	4866.00	0.226414	0.113207	+	0.993571i	$0.463888\pi$
$774$	−8712.00	−0.404582
$775$	5200.00	0.241019
$776$	4432.00	0.205025
$777$	0	0
$778$	−30220.0	−1.39260
$779$	30120.0	1.38532
$780$	3240.00	0.148732
$781$	−37312.0	−1.70951
$782$	−28224.0	−1.29065
$783$	−5670.00	−0.258786
$784$	0	0
$785$	−4450.00	−0.202328
$786$	6024.00	0.273370
$787$	5852.00	0.265059	0.132529	−	0.991179i	$-0.457690\pi$
$787$	5852.00	0.265059	0.132529	+	0.991179i	$0.457690\pi$
$788$	−6856.00	−0.309943
$789$	7440.00	0.335705
$790$	−1520.00	−0.0684546
$791$	0	0
$792$	3168.00	0.142134
$793$	43956.0	1.96838
$794$	−21364.0	−0.954887
$795$	7950.00	0.354663
$796$	17056.0	0.759465
$797$	−16326.0	−0.725592	−0.362796	−	0.931869i	$-0.618178\pi$
$797$	−16326.0	−0.725592	−0.362796	+	0.931869i	$0.618178\pi$
$798$	0	0
$799$	−22736.0	−1.00669
$800$	−800.000	−0.0353553
$801$	9846.00	0.434321
$802$	21052.0	0.926898
$803$	−42152.0	−1.85244
$804$	720.000	0.0315826
$805$	0	0
$806$	22464.0	0.981713
$807$	3006.00	0.131123
$808$	9072.00	0.394990
$809$	7578.00	0.329330	0.164665	−	0.986350i	$-0.447346\pi$
$809$	7578.00	0.329330	0.164665	+	0.986350i	$0.447346\pi$
$810$	810.000	0.0351364
$811$	−6860.00	−0.297025	−0.148512	−	0.988911i	$-0.547449\pi$
$811$	−6860.00	−0.297025	−0.148512	+	0.988911i	$0.547449\pi$
$812$	0	0
$813$	8496.00	0.366504
$814$	−19888.0	−0.856356
$815$	−3340.00	−0.143552
$816$	−4704.00	−0.201805
$817$	29040.0	1.24355
$818$	−12.0000	−0.000512922 0
$819$	0	0
$820$	−10040.0	−0.427576
$821$	−25722.0	−1.09343	−0.546714	−	0.837320i	$-0.684121\pi$
$821$	−25722.0	−1.09343	−0.546714	+	0.837320i	$0.684121\pi$
$822$	−3852.00	−0.163448
$823$	−21320.0	−0.902999	−0.451500	−	0.892271i	$-0.649111\pi$
$823$	−21320.0	−0.902999	−0.451500	+	0.892271i	$0.649111\pi$
$824$	−3904.00	−0.165051
$825$	−3300.00	−0.139262
$826$	0	0
$827$	−22156.0	−0.931608	−0.465804	−	0.884888i	$-0.654235\pi$
$827$	−22156.0	−0.931608	−0.465804	+	0.884888i	$0.654235\pi$
$828$	−5184.00	−0.217580
$829$	45394.0	1.90181	0.950904	−	0.309486i	$-0.100157\pi$
$829$	45394.0	1.90181	0.950904	+	0.309486i	$0.100157\pi$
$830$	−3080.00	−0.128805
$831$	12618.0	0.526731
$832$	−3456.00	−0.144009
$833$	0	0
$834$	−9624.00	−0.399583
$835$	4080.00	0.169095
$836$	−10560.0	−0.436872
$837$	5616.00	0.231920
$838$	−30216.0	−1.24558
$839$	31048.0	1.27759	0.638794	−	0.769378i	$-0.279434\pi$
$839$	31048.0	1.27759	0.638794	+	0.769378i	$0.279434\pi$
$840$	0	0
$841$	19711.0	0.808192
$842$	−20188.0	−0.826276
$843$	17934.0	0.732716
$844$	13264.0	0.540955
$845$	−3595.00	−0.146357
$846$	−4176.00	−0.169709
$847$	0	0
$848$	−8480.00	−0.343401
$849$	−8052.00	−0.325493
$850$	4900.00	0.197728
$851$	32544.0	1.31092
$852$	10176.0	0.409183
$853$	16354.0	0.656448	0.328224	−	0.944600i	$-0.393550\pi$
$853$	16354.0	0.656448	0.328224	+	0.944600i	$0.393550\pi$
$854$	0	0
$855$	−2700.00	−0.107998
$856$	6624.00	0.264490
$857$	−11274.0	−0.449373	−0.224686	−	0.974431i	$-0.572136\pi$
$857$	−11274.0	−0.449373	−0.224686	+	0.974431i	$0.572136\pi$
$858$	−14256.0	−0.567240
$859$	21204.0	0.842225	0.421112	−	0.907008i	$-0.361640\pi$
$859$	21204.0	0.842225	0.421112	+	0.907008i	$0.361640\pi$
$860$	−9680.00	−0.383820
$861$	0	0
$862$	25392.0	1.00331
$863$	−31304.0	−1.23476	−0.617382	−	0.786664i	$-0.711807\pi$
$863$	−31304.0	−1.23476	−0.617382	+	0.786664i	$0.711807\pi$
$864$	−864.000	−0.0340207
$865$	6670.00	0.262181
$866$	24244.0	0.951322
$867$	14073.0	0.551262
$868$	0	0
$869$	6688.00	0.261076
$870$	−6300.00	−0.245506
$871$	−3240.00	−0.126043
$872$	336.000	0.0130486
$873$	−4986.00	−0.193300
$874$	17280.0	0.668770
$875$	0	0
$876$	11496.0	0.443395
$877$	23894.0	0.920003	0.460002	−	0.887918i	$-0.347849\pi$
$877$	23894.0	0.920003	0.460002	+	0.887918i	$0.347849\pi$
$878$	−17104.0	−0.657440
$879$	22470.0	0.862223
$880$	3520.00	0.134840
$881$	−15458.0	−0.591139	−0.295569	−	0.955321i	$-0.595509\pi$
$881$	−15458.0	−0.591139	−0.295569	+	0.955321i	$0.595509\pi$
$882$	0	0
$883$	−24276.0	−0.925201	−0.462600	−	0.886567i	$-0.653084\pi$
$883$	−24276.0	−0.925201	−0.462600	+	0.886567i	$0.653084\pi$
$884$	21168.0	0.805381
$885$	−11460.0	−0.435281
$886$	7096.00	0.269069
$887$	−80.0000	−0.00302834	−0.00151417	−	0.999999i	$-0.500482\pi$
$887$	−80.0000	−0.00302834	−0.00151417	+	0.999999i	$0.500482\pi$
$888$	5424.00	0.204975
$889$	0	0
$890$	10940.0	0.412033
$891$	−3564.00	−0.134005
$892$	−8512.00	−0.319510
$893$	13920.0	0.521629
$894$	14364.0	0.537365
$895$	6180.00	0.230810
$896$	0	0
$897$	23328.0	0.868338
$898$	33372.0	1.24013
$899$	−43680.0	−1.62048
$900$	900.000	0.0333333
$901$	51940.0	1.92050
$902$	44176.0	1.63071
$903$	0	0
$904$	−17104.0	−0.629282
$905$	1790.00	0.0657476
$906$	−4800.00	−0.176015
$907$	21716.0	0.795003	0.397502	−	0.917601i	$-0.369877\pi$
$907$	21716.0	0.795003	0.397502	+	0.917601i	$0.369877\pi$
$908$	−3920.00	−0.143271
$909$	−10206.0	−0.372400
$910$	0	0
$911$	26760.0	0.973214	0.486607	−	0.873621i	$-0.338234\pi$
$911$	26760.0	0.973214	0.486607	+	0.873621i	$0.338234\pi$
$912$	2880.00	0.104568
$913$	13552.0	0.491244
$914$	−1556.00	−0.0563106
$915$	12210.0	0.441148
$916$	−16408.0	−0.591851
$917$	0	0
$918$	5292.00	0.190264
$919$	11984.0	0.430159	0.215079	−	0.976597i	$-0.430999\pi$
$919$	11984.0	0.430159	0.215079	+	0.976597i	$0.430999\pi$
$920$	−5760.00	−0.206415
$921$	20580.0	0.736302
$922$	1676.00	0.0598656
$923$	−45792.0	−1.63300
$924$	0	0
$925$	−5650.00	−0.200833
$926$	14912.0	0.529199
$927$	4392.00	0.155612
$928$	6720.00	0.237710
$929$	28622.0	1.01083	0.505413	−	0.862878i	$-0.331340\pi$
$929$	28622.0	1.01083	0.505413	+	0.862878i	$0.331340\pi$
$930$	6240.00	0.220019
$931$	0	0
$932$	9864.00	0.346680
$933$	14760.0	0.517921
$934$	21448.0	0.751392
$935$	−21560.0	−0.754104
$936$	3888.00	0.135773
$937$	−17474.0	−0.609232	−0.304616	−	0.952475i	$-0.598528\pi$
$937$	−17474.0	−0.609232	−0.304616	+	0.952475i	$0.598528\pi$
$938$	0	0
$939$	13674.0	0.475223
$940$	−4640.00	−0.161000
$941$	−6998.00	−0.242432	−0.121216	−	0.992626i	$-0.538679\pi$
$941$	−6998.00	−0.242432	−0.121216	+	0.992626i	$0.538679\pi$
$942$	−5340.00	−0.184699
$943$	−72288.0	−2.49631
$944$	12224.0	0.421459
$945$	0	0
$946$	42592.0	1.46383
$947$	44204.0	1.51683	0.758414	−	0.651773i	$-0.225974\pi$
$947$	44204.0	1.51683	0.758414	+	0.651773i	$0.225974\pi$
$948$	−1824.00	−0.0624903
$949$	−51732.0	−1.76954
$950$	−3000.00	−0.102456
$951$	17490.0	0.596374
$952$	0	0
$953$	−30.0000	−0.00101972	−0.000509861	−	1.00000i	$-0.500162\pi$
$953$	−30.0000	−0.00101972	−0.000509861		1.00000i	$0.500162\pi$
$954$	9540.00	0.323762
$955$	4440.00	0.150445
$956$	4768.00	0.161306
$957$	27720.0	0.936322
$958$	1536.00	0.0518016
$959$	0	0
$960$	−960.000	−0.0322749
$961$	13473.0	0.452251
$962$	−24408.0	−0.818031
$963$	−7452.00	−0.249364
$964$	15416.0	0.515058
$965$	20150.0	0.672178
$966$	0	0
$967$	20104.0	0.668564	0.334282	−	0.942473i	$-0.391506\pi$
$967$	20104.0	0.668564	0.334282	+	0.942473i	$0.391506\pi$
$968$	−4840.00	−0.160706
$969$	−17640.0	−0.584807
$970$	−5540.00	−0.183380
$971$	18156.0	0.600055	0.300028	−	0.953930i	$-0.403004\pi$
$971$	18156.0	0.600055	0.300028	+	0.953930i	$0.403004\pi$
$972$	972.000	0.0320750
$973$	0	0
$974$	21488.0	0.706899
$975$	−4050.00	−0.133030
$976$	−13024.0	−0.427139
$977$	13002.0	0.425763	0.212882	−	0.977078i	$-0.431715\pi$
$977$	13002.0	0.425763	0.212882	+	0.977078i	$0.431715\pi$
$978$	−4008.00	−0.131045
$979$	−48136.0	−1.57143
$980$	0	0
$981$	−378.000	−0.0123024
$982$	−7080.00	−0.230073
$983$	−11264.0	−0.365479	−0.182739	−	0.983161i	$-0.558496\pi$
$983$	−11264.0	−0.365479	−0.182739	+	0.983161i	$0.558496\pi$
$984$	−12048.0	−0.390321
$985$	8570.00	0.277221
$986$	−41160.0	−1.32941
$987$	0	0
$988$	−12960.0	−0.417320
$989$	−69696.0	−2.24085
$990$	−3960.00	−0.127128
$991$	−10424.0	−0.334137	−0.167068	−	0.985945i	$-0.553430\pi$
$991$	−10424.0	−0.334137	−0.167068	+	0.985945i	$0.553430\pi$
$992$	−6656.00	−0.213032
$993$	15060.0	0.481284
$994$	0	0
$995$	−21320.0	−0.679286
$996$	−3696.00	−0.117583
$997$	9730.00	0.309079	0.154540	−	0.987987i	$-0.450611\pi$
$997$	9730.00	0.309079	0.154540	+	0.987987i	$0.450611\pi$
$998$	−31464.0	−0.997971
$999$	−6102.00	−0.193252

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.4.a.i.1.1		1
7.6	odd	2		210.4.a.b.1.1	✓	1
21.20	even	2		630.4.a.n.1.1		1
28.27	even	2		1680.4.a.x.1.1		1
35.13	even	4		1050.4.g.k.799.2		2
35.27	even	4		1050.4.g.k.799.1		2
35.34	odd	2		1050.4.a.w.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.4.a.b.1.1	✓	1	7.6	odd	2
630.4.a.n.1.1		1	21.20	even	2
1050.4.a.w.1.1		1	35.34	odd	2
1050.4.g.k.799.1		2	35.27	even	4
1050.4.g.k.799.2		2	35.13	even	4
1470.4.a.i.1.1		1	1.1	even	1	trivial
1680.4.a.x.1.1		1	28.27	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:	\( N \)	\(=\)	\( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1470.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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