LMFDB - Embedded newform 1900.3.g.d.949.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1900,3,Mod(949,1900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1900, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1900.949");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1900 = 2^{2} \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1900.g (of order $2$, degree $1$, not minimal)

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:	no
Analytic conductor:	$51.7712502285$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			949.5
Character	$\chi$	$=$	1900.949
Dual form			1900.3.g.d.949.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.58743 q^{3} +1.52935i q^{7} +12.0445 q^{9} +O(q^{10})$	$q-4.58743 q^{3} +1.52935i q^{7} +12.0445 q^{9} +19.7663 q^{11} +16.2291 q^{13} -15.9769i q^{17} +(18.9164 + 1.78065i) q^{19} -7.01577i q^{21} -37.5766i q^{23} -13.9665 q^{27} -31.5765i q^{29} +38.9409i q^{31} -90.6764 q^{33} -39.1052 q^{37} -74.4499 q^{39} +69.4666i q^{41} +16.5777i q^{43} +52.0477i q^{47} +46.6611 q^{49} +73.2930i q^{51} -16.8503 q^{53} +(-86.7776 - 8.16859i) q^{57} -92.5930i q^{59} +51.5327 q^{61} +18.4202i q^{63} +48.7310 q^{67} +172.380i q^{69} -5.51515i q^{71} +62.8328i q^{73} +30.2295i q^{77} -146.361i q^{79} -44.3302 q^{81} -157.433i q^{83} +144.855i q^{87} -87.6554i q^{89} +24.8199i q^{91} -178.639i q^{93} -115.339 q^{97} +238.075 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 104 q^{9}+O(q^{10}) $ 28 * q + 104 * q^9	$ 28 q + 104 q^{9} + 8 q^{11} + 58 q^{19} + 112 q^{39} - 276 q^{49} - 100 q^{61} + 132 q^{81} - 184 q^{99}+O(q^{100}) $ 28 * q + 104 * q^9 + 8 * q^11 + 58 * q^19 + 112 * q^39 - 276 * q^49 - 100 * q^61 + 132 * q^81 - 184 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1900\mathbb{Z}\right)^\times$.

$n$	$77$	$401$	$951$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−4.58743			−1.52914			−0.764572	−	0.644539i	$-0.777049\pi$
$3$	−4.58743			−1.52914			−0.764572	+	0.644539i	$0.777049\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$			1.52935i			0.218478i	0.994016	+	0.109239i	$0.0348414\pi$
$7$			1.52935i			0.218478i	−0.994016	+	0.109239i	$0.965159\pi$
$8$		0			0
$9$	12.0445			1.33828
$10$		0			0
$11$	19.7663			1.79693			0.898467	−	0.439042i	$-0.144682\pi$
$11$	19.7663			1.79693			0.898467	+	0.439042i	$0.144682\pi$
$12$		0			0
$13$	16.2291			1.24839			0.624197	−	0.781267i	$-0.285426\pi$
$13$	16.2291			1.24839			0.624197	+	0.781267i	$0.285426\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$		−	15.9769i		−	0.939819i	−0.882715	−	0.469909i	$-0.844287\pi$
$17$		−	15.9769i		−	0.939819i	0.882715	−	0.469909i	$-0.155713\pi$
$18$		0			0
$19$	18.9164	+	1.78065i	0.995599	+	0.0937182i
$19$	18.9164	+	1.78065i	0.995599	+	0.0937182i
$20$		0			0
$21$		−	7.01577i		−	0.334084i
$22$		0			0
$23$		−	37.5766i		−	1.63377i	−0.576804	−	0.816883i	$-0.695700\pi$
$23$		−	37.5766i		−	1.63377i	0.576804	−	0.816883i	$-0.304300\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−13.9665			−0.517279
$28$		0			0
$29$		−	31.5765i		−	1.08885i	−0.838811	−	0.544423i	$-0.816749\pi$
$29$		−	31.5765i		−	1.08885i	0.838811	−	0.544423i	$-0.183251\pi$
$30$		0			0
$31$			38.9409i			1.25616i	0.778149	+	0.628080i	$0.216159\pi$
$31$			38.9409i			1.25616i	−0.778149	+	0.628080i	$0.783841\pi$
$32$		0			0
$33$	−90.6764			−2.74777
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−39.1052			−1.05690			−0.528449	−	0.848965i	$-0.677226\pi$
$37$	−39.1052			−1.05690			−0.528449	+	0.848965i	$0.677226\pi$
$38$		0			0
$39$	−74.4499			−1.90897
$40$		0			0
$41$			69.4666i			1.69431i	0.531348	+	0.847154i	$0.321686\pi$
$41$			69.4666i			1.69431i	−0.531348	+	0.847154i	$0.678314\pi$
$42$		0			0
$43$			16.5777i			0.385528i	0.981245	+	0.192764i	$0.0617452\pi$
$43$			16.5777i			0.385528i	−0.981245	+	0.192764i	$0.938255\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$			52.0477i			1.10740i	0.832717	+	0.553699i	$0.186784\pi$
$47$			52.0477i			1.10740i	−0.832717	+	0.553699i	$0.813216\pi$
$48$		0			0
$49$	46.6611			0.952267
$50$		0			0
$51$			73.2930i			1.43712i
$52$		0			0
$53$	−16.8503			−0.317931			−0.158965	−	0.987284i	$-0.550816\pi$
$53$	−16.8503			−0.317931			−0.158965	+	0.987284i	$0.550816\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−86.7776	−	8.16859i	−1.52241	−	0.143309i
$58$		0			0
$59$		−	92.5930i		−	1.56937i	−0.619893	−	0.784686i	$-0.712824\pi$
$59$		−	92.5930i		−	1.56937i	0.619893	−	0.784686i	$-0.287176\pi$
$60$		0			0
$61$	51.5327			0.844798			0.422399	−	0.906410i	$-0.361188\pi$
$61$	51.5327			0.844798			0.422399	+	0.906410i	$0.361188\pi$
$62$		0			0
$63$			18.4202i			0.292385i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	48.7310			0.727328			0.363664	−	0.931530i	$-0.381526\pi$
$67$	48.7310			0.727328			0.363664	+	0.931530i	$0.381526\pi$
$68$		0			0
$69$			172.380i			2.49826i
$70$		0			0
$71$		−	5.51515i		−	0.0776782i	−0.999245	−	0.0388391i	$-0.987634\pi$
$71$		−	5.51515i		−	0.0776782i	0.999245	−	0.0388391i	$-0.0123660\pi$
$72$		0			0
$73$			62.8328i			0.860723i	0.902657	+	0.430362i	$0.141614\pi$
$73$			62.8328i			0.860723i	−0.902657	+	0.430362i	$0.858386\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$			30.2295i			0.392590i
$78$		0			0
$79$		−	146.361i		−	1.85268i	−0.376692	−	0.926338i	$-0.622939\pi$
$79$		−	146.361i		−	1.85268i	0.376692	−	0.926338i	$-0.377061\pi$
$80$		0			0
$81$	−44.3302			−0.547287
$82$		0			0
$83$		−	157.433i		−	1.89678i	−0.317103	−	0.948391i	$-0.602710\pi$
$83$		−	157.433i		−	1.89678i	0.317103	−	0.948391i	$-0.397290\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$			144.855i			1.66500i
$88$		0			0
$89$		−	87.6554i		−	0.984893i	−0.870343	−	0.492446i	$-0.836103\pi$
$89$		−	87.6554i		−	0.984893i	0.870343	−	0.492446i	$-0.163897\pi$
$90$		0			0
$91$			24.8199i			0.272746i
$92$		0			0
$93$		−	178.639i		−	1.92085i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−115.339			−1.18906			−0.594531	−	0.804073i	$-0.702662\pi$
$97$	−115.339			−1.18906			−0.594531	+	0.804073i	$0.702662\pi$
$98$		0			0
$99$	238.075			2.40480
$100$		0			0
$101$	−105.886			−1.04837			−0.524186	−	0.851604i	$-0.675631\pi$
$101$	−105.886			−1.04837			−0.524186	+	0.851604i	$0.675631\pi$
$102$		0			0
$103$	−72.5992			−0.704847			−0.352423	−	0.935841i	$-0.614642\pi$
$103$	−72.5992			−0.704847			−0.352423	+	0.935841i	$0.614642\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−2.35545			−0.0220135			−0.0110068	−	0.999939i	$-0.503504\pi$
$107$	−2.35545			−0.0220135			−0.0110068	+	0.999939i	$0.503504\pi$
$108$		0			0
$109$			182.099i			1.67063i	0.549772	+	0.835315i	$0.314715\pi$
$109$			182.099i			1.67063i	−0.549772	+	0.835315i	$0.685285\pi$
$110$		0			0
$111$	179.393			1.61615
$112$		0			0
$113$	−86.4522			−0.765064			−0.382532	−	0.923942i	$-0.624948\pi$
$113$	−86.4522			−0.765064			−0.382532	+	0.923942i	$0.624948\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	195.472			1.67070
$118$		0			0
$119$	24.4342			0.205330
$120$		0			0
$121$	269.705			2.22897
$122$		0			0
$123$		−	318.673i		−	2.59084i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	119.187			0.938480			0.469240	−	0.883071i	$-0.344528\pi$
$127$	119.187			0.938480			0.469240	+	0.883071i	$0.344528\pi$
$128$		0			0
$129$		−	76.0491i		−	0.589528i
$130$		0			0
$131$	111.536			0.851423			0.425712	−	0.904859i	$-0.360024\pi$
$131$	111.536			0.851423			0.425712	+	0.904859i	$0.360024\pi$
$132$		0			0
$133$	−2.72322	+	28.9297i	−0.0204754	+	0.217516i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		−	82.0424i		−	0.598849i	−0.954120	−	0.299425i	$-0.903205\pi$
$137$		−	82.0424i		−	0.598849i	0.954120	−	0.299425i	$-0.0967947\pi$
$138$		0			0
$139$	169.587			1.22005			0.610027	−	0.792381i	$-0.291159\pi$
$139$	169.587			1.22005			0.610027	+	0.792381i	$0.291159\pi$
$140$		0			0
$141$		−	238.765i		−	1.69337i
$142$		0			0
$143$	320.789			2.24328
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−214.055			−1.45615
$148$		0			0
$149$	−67.4940			−0.452980			−0.226490	−	0.974013i	$-0.572725\pi$
$149$	−67.4940			−0.452980			−0.226490	+	0.974013i	$0.572725\pi$
$150$		0			0
$151$		−	152.293i		−	1.00856i	−0.863540	−	0.504280i	$-0.831758\pi$
$151$		−	152.293i		−	1.00856i	0.863540	−	0.504280i	$-0.168242\pi$
$152$		0			0
$153$		−	192.434i		−	1.25774i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		−	50.8926i		−	0.324157i	−0.986778	−	0.162078i	$-0.948180\pi$
$157$		−	50.8926i		−	0.324157i	0.986778	−	0.162078i	$-0.0518197\pi$
$158$		0			0
$159$	77.2997			0.486162
$160$		0			0
$161$	57.4676			0.356942
$162$		0			0
$163$			56.1081i			0.344222i	0.985078	+	0.172111i	$0.0550587\pi$
$163$			56.1081i			0.344222i	−0.985078	+	0.172111i	$0.944941\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	172.992			1.03588			0.517939	−	0.855418i	$-0.326699\pi$
$167$	172.992			1.03588			0.517939	+	0.855418i	$0.326699\pi$
$168$		0			0
$169$	94.3840			0.558485
$170$		0			0
$171$	227.839	+	21.4470i	1.33239	+	0.125421i
$172$		0			0
$173$	85.4671			0.494030			0.247015	−	0.969012i	$-0.420550\pi$
$173$	85.4671			0.494030			0.247015	+	0.969012i	$0.420550\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$			424.764i			2.39980i
$178$		0			0
$179$			181.685i			1.01500i	0.861652	+	0.507500i	$0.169430\pi$
$179$			181.685i			1.01500i	−0.861652	+	0.507500i	$0.830570\pi$
$180$		0			0
$181$			98.1169i			0.542083i	0.962568	+	0.271041i	$0.0873680\pi$
$181$			98.1169i			0.542083i	−0.962568	+	0.271041i	$0.912632\pi$
$182$		0			0
$183$	−236.403			−1.29182
$184$		0			0
$185$		0			0
$186$		0			0
$187$		−	315.804i		−	1.68879i
$188$		0			0
$189$		−	21.3596i		−	0.113014i
$190$		0			0
$191$	−150.077			−0.785741			−0.392871	−	0.919594i	$-0.628518\pi$
$191$	−150.077			−0.785741			−0.392871	+	0.919594i	$0.628518\pi$
$192$		0			0
$193$	20.0780			0.104031			0.0520156	−	0.998646i	$-0.483435\pi$
$193$	20.0780			0.104031			0.0520156	+	0.998646i	$0.483435\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			109.441i			0.555536i	0.960648	+	0.277768i	$0.0895947\pi$
$197$			109.441i			0.555536i	−0.960648	+	0.277768i	$0.910405\pi$
$198$		0			0
$199$	−29.0917			−0.146189			−0.0730947	−	0.997325i	$-0.523288\pi$
$199$	−29.0917			−0.146189			−0.0730947	+	0.997325i	$0.523288\pi$
$200$		0			0
$201$	−223.550			−1.11219
$202$		0			0
$203$	48.2914			0.237889
$204$		0			0
$205$		0			0
$206$		0			0
$207$		−	452.592i		−	2.18643i
$208$		0			0
$209$	373.906	+	35.1967i	1.78902	+	0.168405i
$210$		0			0
$211$		−	134.671i		−	0.638249i	−0.947713	−	0.319125i	$-0.896611\pi$
$211$		−	134.671i		−	0.638249i	0.947713	−	0.319125i	$-0.103389\pi$
$212$		0			0
$213$			25.3004i			0.118781i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−59.5541			−0.274443
$218$		0			0
$219$		−	288.241i		−	1.31617i
$220$		0			0
$221$		−	259.291i		−	1.17326i
$222$		0			0
$223$	201.645			0.904236			0.452118	−	0.891958i	$-0.350669\pi$
$223$	201.645			0.904236			0.452118	+	0.891958i	$0.350669\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	435.566			1.91879			0.959396	−	0.282064i	$-0.0910189\pi$
$227$	435.566			1.91879			0.959396	+	0.282064i	$0.0910189\pi$
$228$		0			0
$229$	−336.632			−1.47001			−0.735003	−	0.678063i	$-0.762819\pi$
$229$	−336.632			−1.47001			−0.735003	+	0.678063i	$0.762819\pi$
$230$		0			0
$231$		−	138.676i		−	0.600327i
$232$		0			0
$233$		−	270.736i		−	1.16196i	−0.813919	−	0.580979i	$-0.802670\pi$
$233$		−	270.736i		−	1.16196i	0.813919	−	0.580979i	$-0.197330\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$			671.423i			2.83301i
$238$		0			0
$239$	−111.441			−0.466279			−0.233139	−	0.972443i	$-0.574900\pi$
$239$	−111.441			−0.466279			−0.233139	+	0.972443i	$0.574900\pi$
$240$		0			0
$241$		−	269.049i		−	1.11639i	−0.829711	−	0.558194i	$-0.811495\pi$
$241$		−	269.049i		−	1.11639i	0.829711	−	0.558194i	$-0.188505\pi$
$242$		0			0
$243$	329.061			1.35416
$244$		0			0
$245$		0			0
$246$		0			0
$247$	306.996	+	28.8983i	1.24290	+	0.116997i
$248$		0			0
$249$			722.213i			2.90045i
$250$		0			0
$251$	−69.8084			−0.278121			−0.139061	−	0.990284i	$-0.544408\pi$
$251$	−69.8084			−0.278121			−0.139061	+	0.990284i	$0.544408\pi$
$252$		0			0
$253$		−	742.749i		−	2.93577i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	205.201			0.798448			0.399224	−	0.916853i	$-0.369280\pi$
$257$	205.201			0.798448			0.399224	+	0.916853i	$0.369280\pi$
$258$		0			0
$259$		−	59.8054i		−	0.230909i
$260$		0			0
$261$		−	380.324i		−	1.45718i
$262$		0			0
$263$			369.721i			1.40578i	0.711297	+	0.702892i	$0.248108\pi$
$263$			369.721i			1.40578i	−0.711297	+	0.702892i	$0.751892\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$			402.113i			1.50604i
$268$		0			0
$269$		−	56.1803i		−	0.208849i	−0.994533	−	0.104424i	$-0.966700\pi$
$269$		−	56.1803i		−	0.208849i	0.994533	−	0.104424i	$-0.0333000\pi$
$270$		0			0
$271$	−108.318			−0.399697			−0.199849	−	0.979827i	$-0.564045\pi$
$271$	−108.318			−0.399697			−0.199849	+	0.979827i	$0.564045\pi$
$272$		0			0
$273$		−	113.860i		−	0.417068i
$274$		0			0
$275$		0			0
$276$		0			0
$277$			186.564i			0.673517i	0.941591	+	0.336758i	$0.109331\pi$
$277$			186.564i			0.673517i	−0.941591	+	0.336758i	$0.890669\pi$
$278$		0			0
$279$			469.025i			1.68109i
$280$		0			0
$281$			136.711i			0.486516i	0.969962	+	0.243258i	$0.0782161\pi$
$281$			136.711i			0.486516i	−0.969962	+	0.243258i	$0.921784\pi$
$282$		0			0
$283$		−	100.842i		−	0.356332i	−0.984000	−	0.178166i	$-0.942984\pi$
$283$		−	100.842i		−	0.356332i	0.984000	−	0.178166i	$-0.0570163\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−106.238			−0.370169
$288$		0			0
$289$	33.7382			0.116741
$290$		0			0
$291$	529.110			1.81825
$292$		0			0
$293$	−345.837			−1.18033			−0.590165	−	0.807283i	$-0.700937\pi$
$293$	−345.837			−1.18033			−0.590165	+	0.807283i	$0.700937\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−276.066			−0.929515
$298$		0			0
$299$		−	609.835i		−	2.03958i
$300$		0			0
$301$	−25.3531			−0.0842294
$302$		0			0
$303$	485.743			1.60311
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−212.148			−0.691035			−0.345518	−	0.938412i	$-0.612297\pi$
$307$	−212.148			−0.691035			−0.345518	+	0.938412i	$0.612297\pi$
$308$		0			0
$309$	333.044			1.07781
$310$		0			0
$311$	534.396			1.71832			0.859158	−	0.511711i	$-0.170988\pi$
$311$	534.396			1.71832			0.859158	+	0.511711i	$0.170988\pi$
$312$		0			0
$313$		−	242.134i		−	0.773590i	−0.922166	−	0.386795i	$-0.873582\pi$
$313$		−	242.134i		−	0.773590i	0.922166	−	0.386795i	$-0.126418\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−448.993			−1.41638			−0.708191	−	0.706021i	$-0.750488\pi$
$317$	−448.993			−1.41638			−0.708191	+	0.706021i	$0.750488\pi$
$318$		0			0
$319$		−	624.150i		−	1.95658i
$320$		0			0
$321$	10.8055			0.0336619
$322$		0			0
$323$	28.4492	−	302.225i	0.0880781	−	0.935682i
$324$		0			0
$325$		0			0
$326$		0			0
$327$		−	835.365i		−	2.55463i
$328$		0			0
$329$	−79.5989			−0.241942
$330$		0			0
$331$			444.084i			1.34164i	0.741618	+	0.670822i	$0.234059\pi$
$331$			444.084i			1.34164i	−0.741618	+	0.670822i	$0.765941\pi$
$332$		0			0
$333$	−471.004			−1.41443
$334$		0			0
$335$		0			0
$336$		0			0
$337$	517.271			1.53493			0.767464	−	0.641092i	$-0.221518\pi$
$337$	517.271			1.53493			0.767464	+	0.641092i	$0.221518\pi$
$338$		0			0
$339$	396.593			1.16989
$340$		0			0
$341$			769.717i			2.25723i
$342$		0			0
$343$			146.299i			0.426527i
$344$		0			0
$345$		0			0
$346$		0			0
$347$			30.8683i			0.0889576i	0.999010	+	0.0444788i	$0.0141627\pi$
$347$			30.8683i			0.0889576i	−0.999010	+	0.0444788i	$0.985837\pi$
$348$		0			0
$349$	156.386			0.448097			0.224049	−	0.974578i	$-0.428073\pi$
$349$	156.386			0.448097			0.224049	+	0.974578i	$0.428073\pi$
$350$		0			0
$351$	−226.664			−0.645767
$352$		0			0
$353$			569.039i			1.61201i	0.591909	+	0.806005i	$0.298374\pi$
$353$			569.039i			1.61201i	−0.591909	+	0.806005i	$0.701626\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−112.090			−0.313978
$358$		0			0
$359$	339.420			0.945459			0.472729	−	0.881208i	$-0.343269\pi$
$359$	339.420			0.945459			0.472729	+	0.881208i	$0.343269\pi$
$360$		0			0
$361$	354.659	+	67.3667i	0.982434	+	0.186611i
$362$		0			0
$363$	−1237.25			−3.40841
$364$		0			0
$365$		0			0
$366$		0			0
$367$		−	72.4587i		−	0.197435i	−0.995115	−	0.0987176i	$-0.968526\pi$
$367$		−	72.4587i		−	0.197435i	0.995115	−	0.0987176i	$-0.0314740\pi$
$368$		0			0
$369$			836.692i			2.26746i
$370$		0			0
$371$		−	25.7700i		−	0.0694608i
$372$		0			0
$373$	480.589			1.28844			0.644221	−	0.764840i	$-0.277182\pi$
$373$	480.589			1.28844			0.644221	+	0.764840i	$0.277182\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	512.459i		−	1.35931i
$378$		0			0
$379$		−	343.159i		−	0.905433i	−0.891654	−	0.452717i	$-0.850455\pi$
$379$		−	343.159i		−	0.905433i	0.891654	−	0.452717i	$-0.149545\pi$
$380$		0			0
$381$	−546.762			−1.43507
$382$		0			0
$383$	380.989			0.994751			0.497375	−	0.867536i	$-0.334297\pi$
$383$	380.989			0.994751			0.497375	+	0.867536i	$0.334297\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$			199.671i			0.515945i
$388$		0			0
$389$	−153.297			−0.394081			−0.197040	−	0.980395i	$-0.563133\pi$
$389$	−153.297			−0.394081			−0.197040	+	0.980395i	$0.563133\pi$
$390$		0			0
$391$	−600.358			−1.53544
$392$		0			0
$393$	−511.666			−1.30195
$394$		0			0
$395$		0			0
$396$		0			0
$397$			410.383i			1.03371i	0.856073	+	0.516855i	$0.172897\pi$
$397$			410.383i			1.03371i	−0.856073	+	0.516855i	$0.827103\pi$
$398$		0			0
$399$	12.4926	−	132.713i	0.0313098	−	0.332614i
$400$		0			0
$401$		−	96.2006i		−	0.239902i	−0.992780	−	0.119951i	$-0.961726\pi$
$401$		−	96.2006i		−	0.239902i	0.992780	−	0.119951i	$-0.0382737\pi$
$402$		0			0
$403$			631.977i			1.56818i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−772.964			−1.89918
$408$		0			0
$409$		−	804.488i		−	1.96696i	−0.181008	−	0.983482i	$-0.557936\pi$
$409$		−	804.488i		−	1.96696i	0.181008	−	0.983482i	$-0.442064\pi$
$410$		0			0
$411$			376.364i			0.915727i
$412$		0			0
$413$	141.607			0.342873
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−777.970			−1.86564
$418$		0			0
$419$	−105.005			−0.250609			−0.125304	−	0.992118i	$-0.539991\pi$
$419$	−105.005			−0.250609			−0.125304	+	0.992118i	$0.539991\pi$
$420$		0			0
$421$			228.201i			0.542045i	0.962573	+	0.271023i	$0.0873618\pi$
$421$			228.201i			0.542045i	−0.962573	+	0.271023i	$0.912638\pi$
$422$		0			0
$423$			626.890i			1.48201i
$424$		0			0
$425$		0			0
$426$		0			0
$427$			78.8113i			0.184570i
$428$		0			0
$429$	−1471.60			−3.43030
$430$		0			0
$431$		−	182.455i		−	0.423329i	−0.977342	−	0.211665i	$-0.932112\pi$
$431$		−	182.455i		−	0.423329i	0.977342	−	0.211665i	$-0.0678884\pi$
$432$		0			0
$433$	29.9156			0.0690890			0.0345445	−	0.999403i	$-0.489002\pi$
$433$	29.9156			0.0690890			0.0345445	+	0.999403i	$0.489002\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	66.9106	−	710.813i	0.153113	−	1.62657i
$438$		0			0
$439$			497.696i			1.13370i	0.823820	+	0.566852i	$0.191839\pi$
$439$			497.696i			1.13370i	−0.823820	+	0.566852i	$0.808161\pi$
$440$		0			0
$441$	562.011			1.27440
$442$		0			0
$443$			348.602i			0.786912i	0.919343	+	0.393456i	$0.128721\pi$
$443$			348.602i			0.786912i	−0.919343	+	0.393456i	$0.871279\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	309.624			0.692672
$448$		0			0
$449$		−	285.726i		−	0.636360i	−0.948030	−	0.318180i	$-0.896928\pi$
$449$		−	285.726i		−	0.636360i	0.948030	−	0.318180i	$-0.103072\pi$
$450$		0			0
$451$			1373.10i			3.04456i
$452$		0			0
$453$			698.632i			1.54223i
$454$		0			0
$455$		0			0
$456$		0			0
$457$			394.636i			0.863535i	0.901985	+	0.431768i	$0.142110\pi$
$457$			394.636i			0.863535i	−0.901985	+	0.431768i	$0.857890\pi$
$458$		0			0
$459$			223.142i			0.486148i
$460$		0			0
$461$	−15.9653			−0.0346318			−0.0173159	−	0.999850i	$-0.505512\pi$
$461$	−15.9653			−0.0346318			−0.0173159	+	0.999850i	$0.505512\pi$
$462$		0			0
$463$		−	291.052i		−	0.628623i	−0.949320	−	0.314311i	$-0.898226\pi$
$463$		−	291.052i		−	0.628623i	0.949320	−	0.314311i	$-0.101774\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		−	592.490i		−	1.26871i	−0.773040	−	0.634357i	$-0.781265\pi$
$467$		−	592.490i		−	1.26871i	0.773040	−	0.634357i	$-0.218735\pi$
$468$		0			0
$469$			74.5265i			0.158905i
$470$		0			0
$471$			233.466i			0.495682i
$472$		0			0
$473$			327.679i			0.692768i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−202.954			−0.425480
$478$		0			0
$479$	−198.971			−0.415389			−0.207695	−	0.978194i	$-0.566596\pi$
$479$	−198.971			−0.415389			−0.207695	+	0.978194i	$0.566596\pi$
$480$		0			0
$481$	−634.643			−1.31942
$482$		0			0
$483$	−263.629			−0.545815
$484$		0			0
$485$		0			0
$486$		0			0
$487$	136.234			0.279741			0.139871	−	0.990170i	$-0.455331\pi$
$487$	136.234			0.279741			0.139871	+	0.990170i	$0.455331\pi$
$488$		0			0
$489$		−	257.392i		−	0.526364i
$490$		0			0
$491$	220.115			0.448299			0.224149	−	0.974555i	$-0.428040\pi$
$491$	220.115			0.448299			0.224149	+	0.974555i	$0.428040\pi$
$492$		0			0
$493$	−504.495			−1.02332
$494$		0			0
$495$		0			0
$496$		0			0
$497$	8.43457			0.0169710
$498$		0			0
$499$	−929.974			−1.86367			−0.931837	−	0.362877i	$-0.881795\pi$
$499$	−929.974			−1.86367			−0.931837	+	0.362877i	$0.881795\pi$
$500$		0			0
$501$	−793.587			−1.58401
$502$		0			0
$503$		−	606.816i		−	1.20639i	−0.797593	−	0.603196i	$-0.793893\pi$
$503$		−	606.816i		−	1.20639i	0.797593	−	0.603196i	$-0.206107\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−432.980			−0.854004
$508$		0			0
$509$		−	342.999i		−	0.673869i	−0.941528	−	0.336935i	$-0.890610\pi$
$509$		−	342.999i		−	0.673869i	0.941528	−	0.336935i	$-0.109390\pi$
$510$		0			0
$511$	−96.0931			−0.188049
$512$		0			0
$513$	−264.196	−	24.8694i	−0.515002	−	0.0484784i
$514$		0			0
$515$		0			0
$516$		0			0
$517$			1028.79i			1.98992i
$518$		0			0
$519$	−392.074			−0.755442
$520$		0			0
$521$		−	303.047i		−	0.581664i	−0.956774	−	0.290832i	$-0.906068\pi$
$521$		−	303.047i		−	0.581664i	0.956774	−	0.290832i	$-0.0939320\pi$
$522$		0			0
$523$	839.474			1.60511			0.802556	−	0.596576i	$-0.203473\pi$
$523$	839.474			1.60511			0.802556	+	0.596576i	$0.203473\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	622.156			1.18056
$528$		0			0
$529$	−883.001			−1.66919
$530$		0			0
$531$		−	1115.24i		−	2.10026i
$532$		0			0
$533$			1127.38i			2.11516i
$534$		0			0
$535$		0			0
$536$		0			0
$537$		−	833.468i		−	1.55208i
$538$		0			0
$539$	922.316			1.71116
$540$		0			0
$541$	−673.205			−1.24437			−0.622186	−	0.782869i	$-0.713755\pi$
$541$	−673.205			−1.24437			−0.622186	+	0.782869i	$0.713755\pi$
$542$		0			0
$543$		−	450.105i		−	0.828922i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	393.199			0.718828			0.359414	−	0.933178i	$-0.382977\pi$
$547$	393.199			0.718828			0.359414	+	0.933178i	$0.382977\pi$
$548$		0			0
$549$	620.686			1.13058
$550$		0			0
$551$	56.2266	−	597.313i	0.102045	−	1.08405i
$552$		0			0
$553$	223.837			0.404769
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	62.2937i		−	0.111838i	−0.998435	−	0.0559189i	$-0.982191\pi$
$557$		−	62.2937i		−	0.111838i	0.998435	−	0.0559189i	$-0.0178088\pi$
$558$		0			0
$559$			269.042i			0.481291i
$560$		0			0
$561$			1448.73i			2.58240i
$562$		0			0
$563$	−763.894			−1.35683			−0.678414	−	0.734680i	$-0.737332\pi$
$563$	−763.894			−1.35683			−0.678414	+	0.734680i	$0.737332\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$		−	67.7962i		−	0.119570i
$568$		0			0
$569$			344.276i			0.605055i	0.953141	+	0.302527i	$0.0978304\pi$
$569$			344.276i			0.605055i	−0.953141	+	0.302527i	$0.902170\pi$
$570$		0			0
$571$	−394.946			−0.691675			−0.345837	−	0.938294i	$-0.612405\pi$
$571$	−394.946			−0.691675			−0.345837	+	0.938294i	$0.612405\pi$
$572$		0			0
$573$	688.466			1.20151
$574$		0			0
$575$		0			0
$576$		0			0
$577$			491.043i			0.851027i	0.904952	+	0.425514i	$0.139907\pi$
$577$			491.043i			0.851027i	−0.904952	+	0.425514i	$0.860093\pi$
$578$		0			0
$579$	−92.1065			−0.159079
$580$		0			0
$581$	240.769			0.414405
$582$		0			0
$583$	−333.068			−0.571300
$584$		0			0
$585$		0			0
$586$		0			0
$587$		−	99.3437i		−	0.169240i	−0.996413	−	0.0846198i	$-0.973032\pi$
$587$		−	99.3437i		−	0.169240i	0.996413	−	0.0846198i	$-0.0269676\pi$
$588$		0			0
$589$	−69.3400	+	736.621i	−0.117725	+	1.25063i
$590$		0			0
$591$		−	502.052i		−	0.849495i
$592$		0			0
$593$		−	879.094i		−	1.48245i	−0.671256	−	0.741226i	$-0.734245\pi$
$593$		−	879.094i		−	1.48245i	0.671256	−	0.741226i	$-0.265755\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	133.456			0.223545
$598$		0			0
$599$		−	14.4131i		−	0.0240620i	−0.999928	−	0.0120310i	$-0.996170\pi$
$599$		−	14.4131i		−	0.0240620i	0.999928	−	0.0120310i	$-0.00382967\pi$
$600$		0			0
$601$		−	485.996i		−	0.808645i	−0.914617	−	0.404322i	$-0.867507\pi$
$601$		−	485.996i		−	0.808645i	0.914617	−	0.404322i	$-0.132493\pi$
$602$		0			0
$603$	586.941			0.973368
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−249.106			−0.410389			−0.205195	−	0.978721i	$-0.565783\pi$
$607$	−249.106			−0.410389			−0.205195	+	0.978721i	$0.565783\pi$
$608$		0			0
$609$	−221.533			−0.363766
$610$		0			0
$611$			844.688i			1.38247i
$612$		0			0
$613$			439.644i			0.717200i	0.933491	+	0.358600i	$0.116746\pi$
$613$			439.644i			0.717200i	−0.933491	+	0.358600i	$0.883254\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	31.6889i		−	0.0513597i	−0.999670	−	0.0256798i	$-0.991825\pi$
$617$		−	31.6889i		−	0.0513597i	0.999670	−	0.0256798i	$-0.00817505\pi$
$618$		0			0
$619$	590.945			0.954677			0.477339	−	0.878719i	$-0.341602\pi$
$619$	590.945			0.954677			0.477339	+	0.878719i	$0.341602\pi$
$620$		0			0
$621$			524.814i			0.845112i
$622$		0			0
$623$	134.055			0.215177
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−1715.27	−	161.462i	−2.73568	−	0.257516i
$628$		0			0
$629$			624.781i			0.993293i
$630$		0			0
$631$	−144.511			−0.229019			−0.114509	−	0.993422i	$-0.536530\pi$
$631$	−144.511			−0.229019			−0.114509	+	0.993422i	$0.536530\pi$
$632$		0			0
$633$			617.792i			0.975975i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	757.268			1.18880
$638$		0			0
$639$		−	66.4273i		−	0.103955i
$640$		0			0
$641$		−	41.9005i		−	0.0653674i	−0.999466	−	0.0326837i	$-0.989595\pi$
$641$		−	41.9005i		−	0.0653674i	0.999466	−	0.0326837i	$-0.0104054\pi$
$642$		0			0
$643$			847.463i			1.31798i	0.752150	+	0.658992i	$0.229017\pi$
$643$			847.463i			1.31798i	−0.752150	+	0.658992i	$0.770983\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	828.509i		−	1.28054i	−0.768150	−	0.640269i	$-0.778823\pi$
$647$		−	828.509i		−	1.28054i	0.768150	−	0.640269i	$-0.221177\pi$
$648$		0			0
$649$		−	1830.22i		−	2.82006i
$650$		0			0
$651$	273.200			0.419663
$652$		0			0
$653$			376.647i			0.576795i	0.957511	+	0.288397i	$0.0931224\pi$
$653$			376.647i			0.576795i	−0.957511	+	0.288397i	$0.906878\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$			756.791i			1.15189i
$658$		0			0
$659$		−	656.057i		−	0.995534i	−0.867311	−	0.497767i	$-0.834154\pi$
$659$		−	656.057i		−	0.995534i	0.867311	−	0.497767i	$-0.165846\pi$
$660$		0			0
$661$		−	837.563i		−	1.26712i	−0.773696	−	0.633558i	$-0.781594\pi$
$661$		−	837.563i		−	1.26712i	0.773696	−	0.633558i	$-0.218406\pi$
$662$		0			0
$663$			1189.48i			1.79409i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−1186.54			−1.77892
$668$		0			0
$669$	−925.030			−1.38271
$670$		0			0
$671$	1018.61			1.51805
$672$		0			0
$673$	383.937			0.570486			0.285243	−	0.958455i	$-0.407926\pi$
$673$	383.937			0.570486			0.285243	+	0.958455i	$0.407926\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	597.994			0.883300			0.441650	−	0.897187i	$-0.354393\pi$
$677$	597.994			0.883300			0.441650	+	0.897187i	$0.354393\pi$
$678$		0			0
$679$		−	176.393i		−	0.259784i
$680$		0			0
$681$	−1998.13			−2.93411
$682$		0			0
$683$	−814.772			−1.19293			−0.596466	−	0.802639i	$-0.703429\pi$
$683$	−814.772			−1.19293			−0.596466	+	0.802639i	$0.703429\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	1544.27			2.24785
$688$		0			0
$689$	−273.466			−0.396903
$690$		0			0
$691$	183.046			0.264900			0.132450	−	0.991190i	$-0.457716\pi$
$691$	183.046			0.264900			0.132450	+	0.991190i	$0.457716\pi$
$692$		0			0
$693$			364.099i			0.525396i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	1109.86			1.59234
$698$		0			0
$699$			1241.98i			1.77680i
$700$		0			0
$701$	20.2332			0.0288633			0.0144317	−	0.999896i	$-0.495406\pi$
$701$	20.2332			0.0288633			0.0144317	+	0.999896i	$0.495406\pi$
$702$		0			0
$703$	−739.729	−	69.6325i	−1.05225	−	0.0990506i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		−	161.936i		−	0.229046i
$708$		0			0
$709$	−348.032			−0.490877			−0.245438	−	0.969412i	$-0.578932\pi$
$709$	−348.032			−0.490877			−0.245438	+	0.969412i	$0.578932\pi$
$710$		0			0
$711$		−	1762.85i		−	2.47940i
$712$		0			0
$713$	1463.27			2.05227
$714$		0			0
$715$		0			0
$716$		0			0
$717$	511.226			0.713007
$718$		0			0
$719$	1282.72			1.78403			0.892014	−	0.452007i	$-0.149292\pi$
$719$	1282.72			1.78403			0.892014	+	0.452007i	$0.149292\pi$
$720$		0			0
$721$		−	111.029i		−	0.153993i
$722$		0			0
$723$			1234.25i			1.70712i
$724$		0			0
$725$		0			0
$726$		0			0
$727$		−	203.759i		−	0.280274i	−0.990132	−	0.140137i	$-0.955246\pi$
$727$		−	203.759i		−	0.280274i	0.990132	−	0.140137i	$-0.0447543\pi$
$728$		0			0
$729$	−1110.57			−1.52342
$730$		0			0
$731$	264.861			0.362327
$732$		0			0
$733$		−	350.631i		−	0.478350i	−0.970976	−	0.239175i	$-0.923123\pi$
$733$		−	350.631i		−	0.478350i	0.970976	−	0.239175i	$-0.0768770\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	963.229			1.30696
$738$		0			0
$739$	−1288.92			−1.74415			−0.872073	−	0.489375i	$-0.837225\pi$
$739$	−1288.92			−1.74415			−0.872073	+	0.489375i	$0.837225\pi$
$740$		0			0
$741$	−1408.32	−	132.569i	−1.90057	−	0.178905i
$742$		0			0
$743$	1222.62			1.64551			0.822757	−	0.568393i	$-0.192435\pi$
$743$	1222.62			1.64551			0.822757	+	0.568393i	$0.192435\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$		−	1896.20i		−	2.53843i
$748$		0			0
$749$		−	3.60229i		−	0.00480947i
$750$		0			0
$751$		−	1256.47i		−	1.67306i	−0.547919	−	0.836531i	$-0.684580\pi$
$751$		−	1256.47i		−	1.67306i	0.547919	−	0.836531i	$-0.315420\pi$
$752$		0			0
$753$	320.241			0.425287
$754$		0			0
$755$		0			0
$756$		0			0
$757$		−	680.666i		−	0.899162i	−0.893240	−	0.449581i	$-0.851573\pi$
$757$		−	680.666i		−	0.899162i	0.893240	−	0.449581i	$-0.148427\pi$
$758$		0			0
$759$			3407.31i			4.48921i
$760$		0			0
$761$	656.481			0.862656			0.431328	−	0.902195i	$-0.358045\pi$
$761$	656.481			0.862656			0.431328	+	0.902195i	$0.358045\pi$
$762$		0			0
$763$	−278.492			−0.364996
$764$		0			0
$765$		0			0
$766$		0			0
$767$		−	1502.70i		−	1.95919i
$768$		0			0
$769$	429.894			0.559030			0.279515	−	0.960141i	$-0.409826\pi$
$769$	429.894			0.559030			0.279515	+	0.960141i	$0.409826\pi$
$770$		0			0
$771$	−941.346			−1.22094
$772$		0			0
$773$	1410.12			1.82422			0.912111	−	0.409943i	$-0.134451\pi$
$773$	1410.12			1.82422			0.912111	+	0.409943i	$0.134451\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$			274.353i			0.353093i
$778$		0			0
$779$	−123.695	+	1314.06i	−0.158787	+	1.68685i
$780$		0			0
$781$		−	109.014i		−	0.139582i
$782$		0			0
$783$			441.014i			0.563236i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−696.889			−0.885501			−0.442750	−	0.896645i	$-0.645997\pi$
$787$	−696.889			−0.885501			−0.442750	+	0.896645i	$0.645997\pi$
$788$		0			0
$789$		−	1696.07i		−	2.14964i
$790$		0			0
$791$		−	132.215i		−	0.167150i
$792$		0			0
$793$	836.330			1.05464
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−1145.32			−1.43704			−0.718520	−	0.695506i	$-0.755180\pi$
$797$	−1145.32			−1.43704			−0.718520	+	0.695506i	$0.755180\pi$
$798$		0			0
$799$	831.562			1.04075
$800$		0			0
$801$		−	1055.77i		−	1.31806i
$802$		0			0
$803$			1241.97i			1.54666i
$804$		0			0
$805$		0			0
$806$		0			0
$807$			257.723i			0.319360i
$808$		0			0
$809$	−355.323			−0.439212			−0.219606	−	0.975589i	$-0.570477\pi$
$809$	−355.323			−0.439212			−0.219606	+	0.975589i	$0.570477\pi$
$810$		0			0
$811$			108.258i			0.133487i	0.997770	+	0.0667437i	$0.0212610\pi$
$811$			108.258i			0.133487i	−0.997770	+	0.0667437i	$0.978739\pi$
$812$		0			0
$813$	496.901			0.611195
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−29.5190	+	313.590i	−0.0361310	+	0.383831i
$818$		0			0
$819$			298.944i			0.365011i
$820$		0			0
$821$	−470.491			−0.573071			−0.286535	−	0.958070i	$-0.592504\pi$
$821$	−470.491			−0.573071			−0.286535	+	0.958070i	$0.592504\pi$
$822$		0			0
$823$			986.856i			1.19910i	0.800339	+	0.599548i	$0.204653\pi$
$823$			986.856i			1.19910i	−0.800339	+	0.599548i	$0.795347\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	1180.91			1.42794			0.713972	−	0.700174i	$-0.246894\pi$
$827$	1180.91			1.42794			0.713972	+	0.700174i	$0.246894\pi$
$828$		0			0
$829$			357.631i			0.431401i	0.976460	+	0.215701i	$0.0692035\pi$
$829$			357.631i			0.431401i	−0.976460	+	0.215701i	$0.930797\pi$
$830$		0			0
$831$		−	855.850i		−	1.02990i
$832$		0			0
$833$		−	745.500i		−	0.894959i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		−	543.869i		−	0.649784i
$838$		0			0
$839$		−	1334.94i		−	1.59111i	−0.605884	−	0.795553i	$-0.707181\pi$
$839$		−	1334.94i		−	1.59111i	0.605884	−	0.795553i	$-0.292819\pi$
$840$		0			0
$841$	−156.076			−0.185584
$842$		0			0
$843$		−	627.152i		−	0.743952i
$844$		0			0
$845$		0			0
$846$		0			0
$847$			412.473i			0.486981i
$848$		0			0
$849$			462.605i			0.544882i
$850$		0			0
$851$			1469.44i			1.72672i
$852$		0			0
$853$		−	1346.94i		−	1.57906i	−0.613713	−	0.789529i	$-0.710325\pi$
$853$		−	1346.94i		−	1.57906i	0.613713	−	0.789529i	$-0.289675\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	10.3502			0.0120773			0.00603863	−	0.999982i	$-0.498078\pi$
$857$	10.3502			0.0120773			0.00603863	+	0.999982i	$0.498078\pi$
$858$		0			0
$859$	−1026.42			−1.19490			−0.597449	−	0.801907i	$-0.703819\pi$
$859$	−1026.42			−1.19490			−0.597449	+	0.801907i	$0.703819\pi$
$860$		0			0
$861$	487.362			0.566041
$862$		0			0
$863$	−1145.76			−1.32764			−0.663822	−	0.747891i	$-0.731067\pi$
$863$	−1145.76			−1.32764			−0.663822	+	0.747891i	$0.731067\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−154.772			−0.178514
$868$		0			0
$869$		−	2893.02i		−	3.32914i
$870$		0			0
$871$	790.860			0.907991
$872$		0			0
$873$	−1389.20			−1.59130
$874$		0			0
$875$		0			0
$876$		0			0
$877$	1242.23			1.41645			0.708225	−	0.705987i	$-0.249496\pi$
$877$	1242.23			1.41645			0.708225	+	0.705987i	$0.249496\pi$
$878$		0			0
$879$	1586.50			1.80489
$880$		0			0
$881$	−1102.73			−1.25168			−0.625842	−	0.779950i	$-0.715244\pi$
$881$	−1102.73			−1.25168			−0.625842	+	0.779950i	$0.715244\pi$
$882$		0			0
$883$			597.580i			0.676761i	0.941009	+	0.338381i	$0.109879\pi$
$883$			597.580i			0.676761i	−0.941009	+	0.338381i	$0.890121\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	327.216			0.368902			0.184451	−	0.982842i	$-0.440949\pi$
$887$	327.216			0.368902			0.184451	+	0.982842i	$0.440949\pi$
$888$		0			0
$889$			182.278i			0.205037i
$890$		0			0
$891$	−876.243			−0.983438
$892$		0			0
$893$	−92.6785	+	984.554i	−0.103783	+	1.10252i
$894$		0			0
$895$		0			0
$896$		0			0
$897$			2797.57i			3.11881i
$898$		0			0
$899$	1229.62			1.36776
$900$		0			0
$901$			269.216i			0.298797i
$902$		0			0
$903$	116.305			0.128799
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−253.226			−0.279190			−0.139595	−	0.990209i	$-0.544580\pi$
$907$	−253.226			−0.279190			−0.139595	+	0.990209i	$0.544580\pi$
$908$		0			0
$909$	−1275.34			−1.40302
$910$		0			0
$911$		−	1122.92i		−	1.23263i	−0.787500	−	0.616314i	$-0.788625\pi$
$911$		−	1122.92i		−	1.23263i	0.787500	−	0.616314i	$-0.211375\pi$
$912$		0			0
$913$		−	3111.86i		−	3.40839i
$914$		0			0
$915$		0			0
$916$		0			0
$917$			170.578i			0.186017i
$918$		0			0
$919$	−967.325			−1.05258			−0.526292	−	0.850304i	$-0.676418\pi$
$919$	−967.325			−1.05258			−0.526292	+	0.850304i	$0.676418\pi$
$920$		0			0
$921$	973.213			1.05669
$922$		0			0
$923$		−	89.5060i		−	0.0969729i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−874.423			−0.943282
$928$		0			0
$929$	−374.642			−0.403275			−0.201637	−	0.979460i	$-0.564626\pi$
$929$	−374.642			−0.403275			−0.201637	+	0.979460i	$0.564626\pi$
$930$		0			0
$931$	882.659	+	83.0869i	0.948076	+	0.0892448i
$932$		0			0
$933$	−2451.51			−2.62755
$934$		0			0
$935$		0			0
$936$		0			0
$937$			310.678i			0.331567i	0.986162	+	0.165783i	$0.0530153\pi$
$937$			310.678i			0.331567i	−0.986162	+	0.165783i	$0.946985\pi$
$938$		0			0
$939$			1110.77i			1.18293i
$940$		0			0
$941$		−	118.112i		−	0.125518i	−0.998029	−	0.0627589i	$-0.980010\pi$
$941$		−	118.112i		−	0.125518i	0.998029	−	0.0627589i	$-0.0199899\pi$
$942$		0			0
$943$	2610.32			2.76810
$944$		0			0
$945$		0			0
$946$		0			0
$947$			553.081i			0.584034i	0.956413	+	0.292017i	$0.0943265\pi$
$947$			553.081i			0.584034i	−0.956413	+	0.292017i	$0.905674\pi$
$948$		0			0
$949$			1019.72i			1.07452i
$950$		0			0
$951$	2059.72			2.16585
$952$		0			0
$953$	375.463			0.393980			0.196990	−	0.980406i	$-0.436883\pi$
$953$	375.463			0.393980			0.196990	+	0.980406i	$0.436883\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$			2863.24i			2.99189i
$958$		0			0
$959$	125.471			0.130835
$960$		0			0
$961$	−555.396			−0.577936
$962$		0			0
$963$	−28.3702			−0.0294603
$964$		0			0
$965$		0			0
$966$		0			0
$967$			1280.32i			1.32401i	0.749500	+	0.662004i	$0.230294\pi$
$967$			1280.32i			1.32401i	−0.749500	+	0.662004i	$0.769706\pi$
$968$		0			0
$969$	−130.509	+	1386.44i	−0.134684	+	1.43079i
$970$		0			0
$971$		−	487.041i		−	0.501587i	−0.968041	−	0.250793i	$-0.919309\pi$
$971$		−	487.041i		−	0.501587i	0.968041	−	0.250793i	$-0.0806915\pi$
$972$		0			0
$973$			259.358i			0.266555i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−85.6576			−0.0876741			−0.0438371	−	0.999039i	$-0.513958\pi$
$977$	−85.6576			−0.0876741			−0.0438371	+	0.999039i	$0.513958\pi$
$978$		0			0
$979$		−	1732.62i		−	1.76979i
$980$		0			0
$981$			2193.29i			2.23577i
$982$		0			0
$983$	220.950			0.224771			0.112386	−	0.993665i	$-0.464151\pi$
$983$	220.950			0.224771			0.112386	+	0.993665i	$0.464151\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	365.155			0.369964
$988$		0			0
$989$	622.934			0.629862
$990$		0			0
$991$			1569.41i			1.58367i	0.610737	+	0.791834i	$0.290873\pi$
$991$			1569.41i			1.58367i	−0.610737	+	0.791834i	$0.709127\pi$
$992$		0			0
$993$		−	2037.21i		−	2.05157i
$994$		0			0
$995$		0			0
$996$		0			0
$997$		−	1821.95i		−	1.82743i	−0.406355	−	0.913715i	$-0.633200\pi$
$997$		−	1821.95i		−	1.82743i	0.406355	−	0.913715i	$-0.366800\pi$
$998$		0			0
$999$	546.164			0.546711

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1900.3.g.d.949.5		28
5.2	odd	4		1900.3.e.g.1101.12	yes	14
5.3	odd	4		1900.3.e.h.1101.3	yes	14
5.4	even	2	inner	1900.3.g.d.949.24		28
19.18	odd	2	inner	1900.3.g.d.949.23		28
95.18	even	4		1900.3.e.h.1101.12	yes	14
95.37	even	4		1900.3.e.g.1101.3	✓	14
95.94	odd	2	inner	1900.3.g.d.949.6		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1900.3.e.g.1101.3	✓	14	95.37	even	4
1900.3.e.g.1101.12	yes	14	5.2	odd	4
1900.3.e.h.1101.3	yes	14	5.3	odd	4
1900.3.e.h.1101.12	yes	14	95.18	even	4
1900.3.g.d.949.5		28	1.1	even	1	trivial
1900.3.g.d.949.6		28	95.94	odd	2	inner
1900.3.g.d.949.23		28	19.18	odd	2	inner
1900.3.g.d.949.24		28	5.4	even	2	inner

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:	\( N \)	\(=\)	\( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1900.g (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-4.58743 q^{3} +1.52935i q^{7} +12.0445 q^{9} +O(q^{10})\)	\(q-4.58743 q^{3} +1.52935i q^{7} +12.0445 q^{9} +19.7663 q^{11} +16.2291 q^{13} -15.9769i q^{17} +(18.9164 + 1.78065i) q^{19} -7.01577i q^{21} -37.5766i q^{23} -13.9665 q^{27} -31.5765i q^{29} +38.9409i q^{31} -90.6764 q^{33} -39.1052 q^{37} -74.4499 q^{39} +69.4666i q^{41} +16.5777i q^{43} +52.0477i q^{47} +46.6611 q^{49} +73.2930i q^{51} -16.8503 q^{53} +(-86.7776 - 8.16859i) q^{57} -92.5930i q^{59} +51.5327 q^{61} +18.4202i q^{63} +48.7310 q^{67} +172.380i q^{69} -5.51515i q^{71} +62.8328i q^{73} +30.2295i q^{77} -146.361i q^{79} -44.3302 q^{81} -157.433i q^{83} +144.855i q^{87} -87.6554i q^{89} +24.8199i q^{91} -178.639i q^{93} -115.339 q^{97} +238.075 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 104 q^{9}+O(q^{10}) \) 28 * q + 104 * q^9	\( 28 q + 104 q^{9} + 8 q^{11} + 58 q^{19} + 112 q^{39} - 276 q^{49} - 100 q^{61} + 132 q^{81} - 184 q^{99}+O(q^{100}) \) 28 * q + 104 * q^9 + 8 * q^11 + 58 * q^19 + 112 * q^39 - 276 * q^49 - 100 * q^61 + 132 * q^81 - 184 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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