LMFDB - Embedded newform 1900.3.g.d.949.3

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			949.3
Character	$\chi$	$=$	1900.949
Dual form			1900.3.g.d.949.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.84257 q^{3} -6.85668i q^{7} +14.4504 q^{9} +O(q^{10})$	$q-4.84257 q^{3} -6.85668i q^{7} +14.4504 q^{9} -9.59871 q^{11} +10.0805 q^{13} -27.8791i q^{17} +(-17.5630 - 7.24850i) q^{19} +33.2039i q^{21} -8.14968i q^{23} -26.3941 q^{27} -17.8174i q^{29} +20.3798i q^{31} +46.4824 q^{33} +65.1090 q^{37} -48.8154 q^{39} -16.0406i q^{41} -60.7072i q^{43} +9.60366i q^{47} +1.98597 q^{49} +135.006i q^{51} -14.7792 q^{53} +(85.0500 + 35.1013i) q^{57} +0.442058i q^{59} +65.2615 q^{61} -99.0820i q^{63} +103.423 q^{67} +39.4653i q^{69} +90.5453i q^{71} -88.8290i q^{73} +65.8153i q^{77} -86.7598i q^{79} -2.23865 q^{81} +47.4163i q^{83} +86.2817i q^{87} -58.0384i q^{89} -69.1187i q^{91} -98.6904i q^{93} -165.286 q^{97} -138.706 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−4.84257			−1.61419			−0.807094	−	0.590423i	$-0.798961\pi$
$3$	−4.84257			−1.61419			−0.807094	+	0.590423i	$0.798961\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$		−	6.85668i		−	0.979525i	−0.871856	−	0.489763i	$-0.837083\pi$
$7$		−	6.85668i		−	0.979525i	0.871856	−	0.489763i	$-0.162917\pi$
$8$		0			0
$9$	14.4504			1.60560
$10$		0			0
$11$	−9.59871			−0.872610			−0.436305	−	0.899799i	$-0.643713\pi$
$11$	−9.59871			−0.872610			−0.436305	+	0.899799i	$0.643713\pi$
$12$		0			0
$13$	10.0805			0.775422			0.387711	−	0.921781i	$-0.373266\pi$
$13$	10.0805			0.775422			0.387711	+	0.921781i	$0.373266\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$		−	27.8791i		−	1.63995i	−0.572402	−	0.819973i	$-0.693988\pi$
$17$		−	27.8791i		−	1.63995i	0.572402	−	0.819973i	$-0.306012\pi$
$18$		0			0
$19$	−17.5630	−	7.24850i	−0.924369	−	0.381500i
$19$	−17.5630	−	7.24850i	−0.924369	−	0.381500i
$20$		0			0
$21$			33.2039i			1.58114i
$22$		0			0
$23$		−	8.14968i		−	0.354334i	−0.984181	−	0.177167i	$-0.943307\pi$
$23$		−	8.14968i		−	0.354334i	0.984181	−	0.177167i	$-0.0566932\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−26.3941			−0.977561
$28$		0			0
$29$		−	17.8174i		−	0.614391i	−0.951646	−	0.307196i	$-0.900609\pi$
$29$		−	17.8174i		−	0.614391i	0.951646	−	0.307196i	$-0.0993906\pi$
$30$		0			0
$31$			20.3798i			0.657412i	0.944432	+	0.328706i	$0.106612\pi$
$31$			20.3798i			0.657412i	−0.944432	+	0.328706i	$0.893388\pi$
$32$		0			0
$33$	46.4824			1.40856
$34$		0			0
$35$		0			0
$36$		0			0
$37$	65.1090			1.75970			0.879851	−	0.475250i	$-0.157642\pi$
$37$	65.1090			1.75970			0.879851	+	0.475250i	$0.157642\pi$
$38$		0			0
$39$	−48.8154			−1.25168
$40$		0			0
$41$		−	16.0406i		−	0.391235i	−0.980680	−	0.195618i	$-0.937329\pi$
$41$		−	16.0406i		−	0.391235i	0.980680	−	0.195618i	$-0.0626712\pi$
$42$		0			0
$43$		−	60.7072i		−	1.41179i	−0.708314	−	0.705897i	$-0.750544\pi$
$43$		−	60.7072i		−	1.41179i	0.708314	−	0.705897i	$-0.249456\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$			9.60366i			0.204333i	0.994767	+	0.102167i	$0.0325775\pi$
$47$			9.60366i			0.204333i	−0.994767	+	0.102167i	$0.967423\pi$
$48$		0			0
$49$	1.98597			0.0405299
$50$		0			0
$51$			135.006i			2.64718i
$52$		0			0
$53$	−14.7792			−0.278854			−0.139427	−	0.990232i	$-0.544526\pi$
$53$	−14.7792			−0.278854			−0.139427	+	0.990232i	$0.544526\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	85.0500	+	35.1013i	1.49211	+	0.615813i
$58$		0			0
$59$			0.442058i			0.00749252i	0.999993	+	0.00374626i	$0.00119247\pi$
$59$			0.442058i			0.00749252i	−0.999993	+	0.00374626i	$0.998808\pi$
$60$		0			0
$61$	65.2615			1.06986			0.534930	−	0.844896i	$-0.320338\pi$
$61$	65.2615			1.06986			0.534930	+	0.844896i	$0.320338\pi$
$62$		0			0
$63$		−	99.0820i		−	1.57273i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	103.423			1.54363			0.771817	−	0.635845i	$-0.219348\pi$
$67$	103.423			1.54363			0.771817	+	0.635845i	$0.219348\pi$
$68$		0			0
$69$			39.4653i			0.571962i
$70$		0			0
$71$			90.5453i			1.27529i	0.770332	+	0.637643i	$0.220091\pi$
$71$			90.5453i			1.27529i	−0.770332	+	0.637643i	$0.779909\pi$
$72$		0			0
$73$		−	88.8290i		−	1.21684i	−0.793617	−	0.608418i	$-0.791804\pi$
$73$		−	88.8290i		−	1.21684i	0.793617	−	0.608418i	$-0.208196\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$			65.8153i			0.854744i
$78$		0			0
$79$		−	86.7598i		−	1.09823i	−0.835748	−	0.549113i	$-0.814966\pi$
$79$		−	86.7598i		−	1.09823i	0.835748	−	0.549113i	$-0.185034\pi$
$80$		0			0
$81$	−2.23865			−0.0276376
$82$		0			0
$83$			47.4163i			0.571281i	0.958337	+	0.285640i	$0.0922062\pi$
$83$			47.4163i			0.571281i	−0.958337	+	0.285640i	$0.907794\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$			86.2817i			0.991744i
$88$		0			0
$89$		−	58.0384i		−	0.652117i	−0.945350	−	0.326058i	$-0.894279\pi$
$89$		−	58.0384i		−	0.652117i	0.945350	−	0.326058i	$-0.105721\pi$
$90$		0			0
$91$		−	69.1187i		−	0.759546i
$92$		0			0
$93$		−	98.6904i		−	1.06119i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−165.286			−1.70397			−0.851987	−	0.523562i	$-0.824603\pi$
$97$	−165.286			−1.70397			−0.851987	+	0.523562i	$0.824603\pi$
$98$		0			0
$99$	−138.706			−1.40107
$100$		0			0
$101$	81.0614			0.802589			0.401294	−	0.915949i	$-0.368560\pi$
$101$	81.0614			0.802589			0.401294	+	0.915949i	$0.368560\pi$
$102$		0			0
$103$	−76.4480			−0.742213			−0.371107	−	0.928590i	$-0.621022\pi$
$103$	−76.4480			−0.742213			−0.371107	+	0.928590i	$0.621022\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	19.6386			0.183538			0.0917691	−	0.995780i	$-0.470748\pi$
$107$	19.6386			0.183538			0.0917691	+	0.995780i	$0.470748\pi$
$108$		0			0
$109$			101.569i			0.931830i	0.884830	+	0.465915i	$0.154275\pi$
$109$			101.569i			0.931830i	−0.884830	+	0.465915i	$0.845725\pi$
$110$		0			0
$111$	−315.295			−2.84049
$112$		0			0
$113$	126.863			1.12268			0.561341	−	0.827585i	$-0.310286\pi$
$113$	126.863			1.12268			0.561341	+	0.827585i	$0.310286\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	145.668			1.24502
$118$		0			0
$119$	−191.158			−1.60637
$120$		0			0
$121$	−28.8647			−0.238552
$122$		0			0
$123$			77.6779i			0.631528i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−62.1773			−0.489585			−0.244793	−	0.969575i	$-0.578720\pi$
$127$	−62.1773			−0.489585			−0.244793	+	0.969575i	$0.578720\pi$
$128$		0			0
$129$			293.978i			2.27890i
$130$		0			0
$131$	3.66734			0.0279949			0.0139975	−	0.999902i	$-0.495544\pi$
$131$	3.66734			0.0279949			0.0139975	+	0.999902i	$0.495544\pi$
$132$		0			0
$133$	−49.7006	+	120.424i	−0.373689	+	0.905443i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		−	223.349i		−	1.63028i	−0.579261	−	0.815142i	$-0.696659\pi$
$137$		−	223.349i		−	1.63028i	0.579261	−	0.815142i	$-0.303341\pi$
$138$		0			0
$139$	−30.4744			−0.219240			−0.109620	−	0.993974i	$-0.534963\pi$
$139$	−30.4744			−0.219240			−0.109620	+	0.993974i	$0.534963\pi$
$140$		0			0
$141$		−	46.5063i		−	0.329832i
$142$		0			0
$143$	−96.7597			−0.676642
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−9.61717			−0.0654229
$148$		0			0
$149$	−120.341			−0.807655			−0.403827	−	0.914835i	$-0.632320\pi$
$149$	−120.341			−0.807655			−0.403827	+	0.914835i	$0.632320\pi$
$150$		0			0
$151$			111.480i			0.738275i	0.929375	+	0.369138i	$0.120347\pi$
$151$			111.480i			0.738275i	−0.929375	+	0.369138i	$0.879653\pi$
$152$		0			0
$153$		−	402.865i		−	2.63311i
$154$		0			0
$155$		0			0
$156$		0			0
$157$			139.390i			0.887832i	0.896068	+	0.443916i	$0.146411\pi$
$157$			139.390i			0.887832i	−0.896068	+	0.443916i	$0.853589\pi$
$158$		0			0
$159$	71.5695			0.450123
$160$		0			0
$161$	−55.8797			−0.347079
$162$		0			0
$163$		−	163.849i		−	1.00521i	−0.864516	−	0.502605i	$-0.832375\pi$
$163$		−	163.849i		−	1.00521i	0.864516	−	0.502605i	$-0.167625\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−282.206			−1.68986			−0.844929	−	0.534878i	$-0.820357\pi$
$167$	−282.206			−1.68986			−0.844929	+	0.534878i	$0.820357\pi$
$168$		0			0
$169$	−67.3837			−0.398720
$170$		0			0
$171$	−253.793	−	104.744i	−1.48417	−	0.612538i
$172$		0			0
$173$	−244.448			−1.41300			−0.706498	−	0.707715i	$-0.749726\pi$
$173$	−244.448			−1.41300			−0.706498	+	0.707715i	$0.749726\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		−	2.14070i		−	0.0120943i
$178$		0			0
$179$		−	319.507i		−	1.78496i	−0.451090	−	0.892478i	$-0.648965\pi$
$179$		−	319.507i		−	1.78496i	0.451090	−	0.892478i	$-0.351035\pi$
$180$		0			0
$181$		−	77.1074i		−	0.426008i	−0.977051	−	0.213004i	$-0.931675\pi$
$181$		−	77.1074i		−	0.426008i	0.977051	−	0.213004i	$-0.0683247\pi$
$182$		0			0
$183$	−316.033			−1.72696
$184$		0			0
$185$		0			0
$186$		0			0
$187$			267.603i			1.43103i
$188$		0			0
$189$			180.976i			0.957546i
$190$		0			0
$191$	−73.2221			−0.383362			−0.191681	−	0.981457i	$-0.561394\pi$
$191$	−73.2221			−0.383362			−0.191681	+	0.981457i	$0.561394\pi$
$192$		0			0
$193$	−118.144			−0.612144			−0.306072	−	0.952008i	$-0.599015\pi$
$193$	−118.144			−0.612144			−0.306072	+	0.952008i	$0.599015\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	16.1635i		−	0.0820485i	−0.999158	−	0.0410242i	$-0.986938\pi$
$197$		−	16.1635i		−	0.0820485i	0.999158	−	0.0410242i	$-0.0130621\pi$
$198$		0			0
$199$	246.985			1.24113			0.620566	−	0.784154i	$-0.286903\pi$
$199$	246.985			1.24113			0.620566	+	0.784154i	$0.286903\pi$
$200$		0			0
$201$	−500.835			−2.49172
$202$		0			0
$203$	−122.168			−0.601812
$204$		0			0
$205$		0			0
$206$		0			0
$207$		−	117.766i		−	0.568920i
$208$		0			0
$209$	168.582	+	69.5763i	0.806614	+	0.332901i
$210$		0			0
$211$			86.3447i			0.409217i	0.978844	+	0.204608i	$0.0655921\pi$
$211$			86.3447i			0.409217i	−0.978844	+	0.204608i	$0.934408\pi$
$212$		0			0
$213$		−	438.472i		−	2.05855i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	139.737			0.643952
$218$		0			0
$219$			430.160i			1.96420i
$220$		0			0
$221$		−	281.035i		−	1.27165i
$222$		0			0
$223$	−111.083			−0.498131			−0.249065	−	0.968487i	$-0.580123\pi$
$223$	−111.083			−0.498131			−0.249065	+	0.968487i	$0.580123\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−212.064			−0.934203			−0.467101	−	0.884204i	$-0.654702\pi$
$227$	−212.064			−0.934203			−0.467101	+	0.884204i	$0.654702\pi$
$228$		0			0
$229$	121.793			0.531846			0.265923	−	0.963994i	$-0.414323\pi$
$229$	121.793			0.531846			0.265923	+	0.963994i	$0.414323\pi$
$230$		0			0
$231$		−	318.715i		−	1.37972i
$232$		0			0
$233$		−	334.305i		−	1.43478i	−0.696670	−	0.717392i	$-0.745336\pi$
$233$		−	334.305i		−	1.43478i	0.696670	−	0.717392i	$-0.254664\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$			420.140i			1.77274i
$238$		0			0
$239$	−453.267			−1.89652			−0.948258	−	0.317500i	$-0.897157\pi$
$239$	−453.267			−1.89652			−0.948258	+	0.317500i	$0.897157\pi$
$240$		0			0
$241$		−	176.552i		−	0.732582i	−0.930500	−	0.366291i	$-0.880627\pi$
$241$		−	176.552i		−	0.732582i	0.930500	−	0.366291i	$-0.119373\pi$
$242$		0			0
$243$	248.388			1.02217
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−177.044	−	73.0685i	−0.716776	−	0.295824i
$248$		0			0
$249$		−	229.616i		−	0.922154i
$250$		0			0
$251$	54.6634			0.217782			0.108891	−	0.994054i	$-0.465270\pi$
$251$	54.6634			0.217782			0.108891	+	0.994054i	$0.465270\pi$
$252$		0			0
$253$			78.2264i			0.309195i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	84.2554			0.327842			0.163921	−	0.986473i	$-0.447586\pi$
$257$	84.2554			0.327842			0.163921	+	0.986473i	$0.447586\pi$
$258$		0			0
$259$		−	446.431i		−	1.72367i
$260$		0			0
$261$		−	257.469i		−	0.986470i
$262$		0			0
$263$		−	198.029i		−	0.752962i	−0.926424	−	0.376481i	$-0.877134\pi$
$263$		−	198.029i		−	0.752962i	0.926424	−	0.376481i	$-0.122866\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$			281.055i			1.05264i
$268$		0			0
$269$			477.641i			1.77562i	0.460213	+	0.887809i	$0.347773\pi$
$269$			477.641i			1.77562i	−0.460213	+	0.887809i	$0.652227\pi$
$270$		0			0
$271$	−129.912			−0.479379			−0.239689	−	0.970850i	$-0.577046\pi$
$271$	−129.912			−0.479379			−0.239689	+	0.970850i	$0.577046\pi$
$272$		0			0
$273$			334.712i			1.22605i
$274$		0			0
$275$		0			0
$276$		0			0
$277$			468.295i			1.69059i	0.534297	+	0.845297i	$0.320577\pi$
$277$			468.295i			1.69059i	−0.534297	+	0.845297i	$0.679423\pi$
$278$		0			0
$279$			294.497i			1.05554i
$280$		0			0
$281$			386.974i			1.37713i	0.725175	+	0.688565i	$0.241759\pi$
$281$			386.974i			1.37713i	−0.725175	+	0.688565i	$0.758241\pi$
$282$		0			0
$283$			210.748i			0.744694i	0.928094	+	0.372347i	$0.121447\pi$
$283$			210.748i			0.744694i	−0.928094	+	0.372347i	$0.878553\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−109.986			−0.383225
$288$		0			0
$289$	−488.243			−1.68942
$290$		0			0
$291$	800.406			2.75054
$292$		0			0
$293$	−385.803			−1.31674			−0.658368	−	0.752697i	$-0.728753\pi$
$293$	−385.803			−1.31674			−0.658368	+	0.752697i	$0.728753\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	253.350			0.853029
$298$		0			0
$299$		−	82.1527i		−	0.274758i
$300$		0			0
$301$	−416.249			−1.38289
$302$		0			0
$303$	−392.545			−1.29553
$304$		0			0
$305$		0			0
$306$		0			0
$307$	60.4268			0.196830			0.0984150	−	0.995145i	$-0.468623\pi$
$307$	60.4268			0.196830			0.0984150	+	0.995145i	$0.468623\pi$
$308$		0			0
$309$	370.204			1.19807
$310$		0			0
$311$	244.412			0.785890			0.392945	−	0.919562i	$-0.371456\pi$
$311$	244.412			0.785890			0.392945	+	0.919562i	$0.371456\pi$
$312$		0			0
$313$			479.471i			1.53186i	0.642925	+	0.765929i	$0.277721\pi$
$313$			479.471i			1.53186i	−0.642925	+	0.765929i	$0.722279\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−87.4438			−0.275848			−0.137924	−	0.990443i	$-0.544043\pi$
$317$	−87.4438			−0.275848			−0.137924	+	0.990443i	$0.544043\pi$
$318$		0			0
$319$			171.024i			0.536124i
$320$		0			0
$321$	−95.1012			−0.296265
$322$		0			0
$323$	−202.082	+	489.641i	−0.625640	+	1.51592i
$324$		0			0
$325$		0			0
$326$		0			0
$327$		−	491.857i		−	1.50415i
$328$		0			0
$329$	65.8492			0.200149
$330$		0			0
$331$			398.587i			1.20419i	0.798425	+	0.602095i	$0.205667\pi$
$331$			398.587i			1.20419i	−0.798425	+	0.602095i	$0.794333\pi$
$332$		0			0
$333$	940.854			2.82539
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−114.633			−0.340158			−0.170079	−	0.985430i	$-0.554402\pi$
$337$	−114.633			−0.340158			−0.170079	+	0.985430i	$0.554402\pi$
$338$		0			0
$339$	−614.343			−1.81222
$340$		0			0
$341$		−	195.619i		−	0.573664i
$342$		0			0
$343$		−	349.594i		−	1.01923i
$344$		0			0
$345$		0			0
$346$		0			0
$347$		−	234.225i		−	0.674999i	−0.941326	−	0.337499i	$-0.890419\pi$
$347$		−	234.225i		−	0.674999i	0.941326	−	0.337499i	$-0.109581\pi$
$348$		0			0
$349$	163.364			0.468093			0.234046	−	0.972225i	$-0.424803\pi$
$349$	163.364			0.468093			0.234046	+	0.972225i	$0.424803\pi$
$350$		0			0
$351$	−266.066			−0.758023
$352$		0			0
$353$		−	671.997i		−	1.90367i	−0.306605	−	0.951837i	$-0.599193\pi$
$353$		−	671.997i		−	1.90367i	0.306605	−	0.951837i	$-0.400807\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	925.695			2.59298
$358$		0			0
$359$	−160.300			−0.446517			−0.223259	−	0.974759i	$-0.571669\pi$
$359$	−160.300			−0.446517			−0.223259	+	0.974759i	$0.571669\pi$
$360$		0			0
$361$	255.918	+	254.611i	0.708915	+	0.705294i
$362$		0			0
$363$	139.779			0.385067
$364$		0			0
$365$		0			0
$366$		0			0
$367$			34.2401i			0.0932973i	0.998911	+	0.0466487i	$0.0148541\pi$
$367$			34.2401i			0.0932973i	−0.998911	+	0.0466487i	$0.985146\pi$
$368$		0			0
$369$		−	231.794i		−	0.628169i
$370$		0			0
$371$			101.337i			0.273144i
$372$		0			0
$373$	415.310			1.11343			0.556716	−	0.830703i	$-0.312061\pi$
$373$	415.310			1.11343			0.556716	+	0.830703i	$0.312061\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	179.608i		−	0.476413i
$378$		0			0
$379$		−	514.295i		−	1.35698i	−0.734610	−	0.678489i	$-0.762635\pi$
$379$		−	514.295i		−	1.35698i	0.734610	−	0.678489i	$-0.237365\pi$
$380$		0			0
$381$	301.098			0.790283
$382$		0			0
$383$	658.940			1.72047			0.860235	−	0.509897i	$-0.170317\pi$
$383$	658.940			1.72047			0.860235	+	0.509897i	$0.170317\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		−	877.245i		−	2.26678i
$388$		0			0
$389$	284.073			0.730265			0.365133	−	0.930955i	$-0.381024\pi$
$389$	284.073			0.730265			0.365133	+	0.930955i	$0.381024\pi$
$390$		0			0
$391$	−227.206			−0.581088
$392$		0			0
$393$	−17.7593			−0.0451891
$394$		0			0
$395$		0			0
$396$		0			0
$397$			184.434i			0.464570i	0.972648	+	0.232285i	$0.0746202\pi$
$397$			184.434i			0.464570i	−0.972648	+	0.232285i	$0.925380\pi$
$398$		0			0
$399$	240.679	−	583.161i	0.603205	−	1.46156i
$400$		0			0
$401$			378.243i			0.943250i	0.881799	+	0.471625i	$0.156332\pi$
$401$			378.243i			0.943250i	−0.881799	+	0.471625i	$0.843668\pi$
$402$		0			0
$403$			205.438i			0.509772i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−624.962			−1.53553
$408$		0			0
$409$			418.384i			1.02294i	0.859300	+	0.511471i	$0.170899\pi$
$409$			418.384i			1.02294i	−0.859300	+	0.511471i	$0.829101\pi$
$410$		0			0
$411$			1081.58i			2.63159i
$412$		0			0
$413$	3.03105			0.00733911
$414$		0			0
$415$		0			0
$416$		0			0
$417$	147.574			0.353896
$418$		0			0
$419$	−695.935			−1.66094			−0.830471	−	0.557061i	$-0.811929\pi$
$419$	−695.935			−1.66094			−0.830471	+	0.557061i	$0.811929\pi$
$420$		0			0
$421$			402.866i			0.956927i	0.878108	+	0.478463i	$0.158806\pi$
$421$			402.866i			0.956927i	−0.878108	+	0.478463i	$0.841194\pi$
$422$		0			0
$423$			138.777i			0.328078i
$424$		0			0
$425$		0			0
$426$		0			0
$427$		−	447.477i		−	1.04796i
$428$		0			0
$429$	468.565			1.09223
$430$		0			0
$431$		−	245.727i		−	0.570132i	−0.958508	−	0.285066i	$-0.907984\pi$
$431$		−	245.727i		−	0.570132i	0.958508	−	0.285066i	$-0.0920156\pi$
$432$		0			0
$433$	230.070			0.531339			0.265670	−	0.964064i	$-0.414407\pi$
$433$	230.070			0.531339			0.265670	+	0.964064i	$0.414407\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−59.0729	+	143.133i	−0.135178	+	0.327535i
$438$		0			0
$439$		−	543.857i		−	1.23885i	−0.785054	−	0.619427i	$-0.787365\pi$
$439$		−	543.857i		−	1.23885i	0.785054	−	0.619427i	$-0.212635\pi$
$440$		0			0
$441$	28.6981			0.0650750
$442$		0			0
$443$			38.6987i			0.0873560i	0.999046	+	0.0436780i	$0.0139076\pi$
$443$			38.6987i			0.0873560i	−0.999046	+	0.0436780i	$0.986092\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	582.757			1.30371
$448$		0			0
$449$			103.840i			0.231270i	0.993292	+	0.115635i	$0.0368902\pi$
$449$			103.840i			0.231270i	−0.993292	+	0.115635i	$0.963110\pi$
$450$		0			0
$451$			153.970i			0.341396i
$452$		0			0
$453$		−	539.847i		−	1.19172i
$454$		0			0
$455$		0			0
$456$		0			0
$457$			93.1389i			0.203805i	0.994794	+	0.101902i	$0.0324930\pi$
$457$			93.1389i			0.203805i	−0.994794	+	0.101902i	$0.967507\pi$
$458$		0			0
$459$			735.844i			1.60315i
$460$		0			0
$461$	−117.789			−0.255507			−0.127753	−	0.991806i	$-0.540777\pi$
$461$	−117.789			−0.255507			−0.127753	+	0.991806i	$0.540777\pi$
$462$		0			0
$463$		−	93.5692i		−	0.202093i	−0.994882	−	0.101047i	$-0.967781\pi$
$463$		−	93.5692i		−	0.202093i	0.994882	−	0.101047i	$-0.0322191\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		−	351.018i		−	0.751645i	−0.926692	−	0.375823i	$-0.877360\pi$
$467$		−	351.018i		−	0.751645i	0.926692	−	0.375823i	$-0.122640\pi$
$468$		0			0
$469$		−	709.141i		−	1.51203i
$470$		0			0
$471$		−	675.004i		−	1.43313i
$472$		0			0
$473$			582.710i			1.23195i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−213.567			−0.447729
$478$		0			0
$479$	70.1471			0.146445			0.0732224	−	0.997316i	$-0.476672\pi$
$479$	70.1471			0.146445			0.0732224	+	0.997316i	$0.476672\pi$
$480$		0			0
$481$	656.331			1.36451
$482$		0			0
$483$	270.601			0.560251
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−765.631			−1.57214			−0.786068	−	0.618140i	$-0.787887\pi$
$487$	−765.631			−1.57214			−0.786068	+	0.618140i	$0.787887\pi$
$488$		0			0
$489$			793.451i			1.62260i
$490$		0			0
$491$	244.304			0.497564			0.248782	−	0.968560i	$-0.419970\pi$
$491$	244.304			0.497564			0.248782	+	0.968560i	$0.419970\pi$
$492$		0			0
$493$	−496.731			−1.00757
$494$		0			0
$495$		0			0
$496$		0			0
$497$	620.840			1.24918
$498$		0			0
$499$	−73.0277			−0.146348			−0.0731741	−	0.997319i	$-0.523313\pi$
$499$	−73.0277			−0.146348			−0.0731741	+	0.997319i	$0.523313\pi$
$500$		0			0
$501$	1366.60			2.72775
$502$		0			0
$503$			710.302i			1.41213i	0.708147	+	0.706065i	$0.249532\pi$
$503$			710.302i			1.41213i	−0.708147	+	0.706065i	$0.750468\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	326.310			0.643609
$508$		0			0
$509$		−	936.262i		−	1.83942i	−0.392604	−	0.919708i	$-0.628426\pi$
$509$		−	936.262i		−	1.83942i	0.392604	−	0.919708i	$-0.371574\pi$
$510$		0			0
$511$	−609.072			−1.19192
$512$		0			0
$513$	463.560	+	191.318i	0.903627	+	0.372939i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		−	92.1827i		−	0.178303i
$518$		0			0
$519$	1183.76			2.28084
$520$		0			0
$521$			689.775i			1.32394i	0.749528	+	0.661972i	$0.230280\pi$
$521$			689.775i			1.32394i	−0.749528	+	0.661972i	$0.769720\pi$
$522$		0			0
$523$	−126.270			−0.241434			−0.120717	−	0.992687i	$-0.538519\pi$
$523$	−126.270			−0.241434			−0.120717	+	0.992687i	$0.538519\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	568.169			1.07812
$528$		0			0
$529$	462.583			0.874448
$530$		0			0
$531$			6.38794i			0.0120300i
$532$		0			0
$533$		−	161.698i		−	0.303373i
$534$		0			0
$535$		0			0
$536$		0			0
$537$			1547.24i			2.88126i
$538$		0			0
$539$	−19.0627			−0.0353668
$540$		0			0
$541$	952.485			1.76060			0.880300	−	0.474417i	$-0.157341\pi$
$541$	952.485			1.76060			0.880300	+	0.474417i	$0.157341\pi$
$542$		0			0
$543$			373.398i			0.687657i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	764.558			1.39773			0.698865	−	0.715254i	$-0.253689\pi$
$547$	764.558			1.39773			0.698865	+	0.715254i	$0.253689\pi$
$548$		0			0
$549$	943.057			1.71777
$550$		0			0
$551$	−129.149	+	312.926i	−0.234390	+	0.567924i
$552$		0			0
$553$	−594.884			−1.07574
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	465.851i		−	0.836358i	−0.908365	−	0.418179i	$-0.862669\pi$
$557$		−	465.851i		−	0.836358i	0.908365	−	0.418179i	$-0.137331\pi$
$558$		0			0
$559$		−	611.958i		−	1.09474i
$560$		0			0
$561$		−	1295.89i		−	2.30996i
$562$		0			0
$563$	442.560			0.786075			0.393038	−	0.919522i	$-0.371424\pi$
$563$	442.560			0.786075			0.393038	+	0.919522i	$0.371424\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$			15.3497i			0.0270718i
$568$		0			0
$569$		−	663.147i		−	1.16546i	−0.812666	−	0.582730i	$-0.801984\pi$
$569$		−	663.147i		−	1.16546i	0.812666	−	0.582730i	$-0.198016\pi$
$570$		0			0
$571$	161.428			0.282710			0.141355	−	0.989959i	$-0.454854\pi$
$571$	161.428			0.282710			0.141355	+	0.989959i	$0.454854\pi$
$572$		0			0
$573$	354.583			0.618818
$574$		0			0
$575$		0			0
$576$		0			0
$577$		−	517.669i		−	0.897174i	−0.893739	−	0.448587i	$-0.851927\pi$
$577$		−	517.669i		−	0.897174i	0.893739	−	0.448587i	$-0.148073\pi$
$578$		0			0
$579$	572.119			0.988115
$580$		0			0
$581$	325.118			0.559584
$582$		0			0
$583$	141.862			0.243331
$584$		0			0
$585$		0			0
$586$		0			0
$587$		−	389.141i		−	0.662931i	−0.943467	−	0.331466i	$-0.892457\pi$
$587$		−	389.141i		−	0.662931i	0.943467	−	0.331466i	$-0.107543\pi$
$588$		0			0
$589$	147.723	−	357.930i	0.250803	−	0.607691i
$590$		0			0
$591$			78.2730i			0.132442i
$592$		0			0
$593$			809.753i			1.36552i	0.730643	+	0.682760i	$0.239221\pi$
$593$			809.753i			1.36552i	−0.730643	+	0.682760i	$0.760779\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−1196.04			−2.00342
$598$		0			0
$599$			1074.40i			1.79366i	0.442374	+	0.896831i	$0.354136\pi$
$599$			1074.40i			1.79366i	−0.442374	+	0.896831i	$0.645864\pi$
$600$		0			0
$601$		−	1073.76i		−	1.78662i	−0.449439	−	0.893311i	$-0.648376\pi$
$601$		−	1073.76i		−	1.78662i	0.449439	−	0.893311i	$-0.351624\pi$
$602$		0			0
$603$	1494.51			2.47847
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−381.395			−0.628327			−0.314164	−	0.949369i	$-0.601724\pi$
$607$	−381.395			−0.628327			−0.314164	+	0.949369i	$0.601724\pi$
$608$		0			0
$609$	591.606			0.971438
$610$		0			0
$611$			96.8096i			0.158444i
$612$		0			0
$613$			544.647i			0.888495i	0.895904	+	0.444247i	$0.146529\pi$
$613$			544.647i			0.888495i	−0.895904	+	0.444247i	$0.853471\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$			413.071i			0.669482i	0.942310	+	0.334741i	$0.108649\pi$
$617$			413.071i			0.669482i	−0.942310	+	0.334741i	$0.891351\pi$
$618$		0			0
$619$	−1108.99			−1.79158			−0.895792	−	0.444473i	$-0.853391\pi$
$619$	−1108.99			−1.79158			−0.895792	+	0.444473i	$0.853391\pi$
$620$		0			0
$621$			215.104i			0.346383i
$622$		0			0
$623$	−397.951			−0.638765
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−816.371	−	336.928i	−1.30203	−	0.537365i
$628$		0			0
$629$		−	1815.18i		−	2.88582i
$630$		0			0
$631$	−61.5377			−0.0975241			−0.0487621	−	0.998810i	$-0.515528\pi$
$631$	−61.5377			−0.0975241			−0.0487621	+	0.998810i	$0.515528\pi$
$632$		0			0
$633$		−	418.130i		−	0.660553i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	20.0195			0.0314278
$638$		0			0
$639$			1308.42i			2.04761i
$640$		0			0
$641$		−	461.117i		−	0.719371i	−0.933074	−	0.359686i	$-0.882884\pi$
$641$		−	461.117i		−	0.719371i	0.933074	−	0.359686i	$-0.117116\pi$
$642$		0			0
$643$		−	446.784i		−	0.694843i	−0.937709	−	0.347422i	$-0.887057\pi$
$643$		−	446.784i		−	0.694843i	0.937709	−	0.347422i	$-0.112943\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			146.630i			0.226631i	0.993559	+	0.113315i	$0.0361471\pi$
$647$			146.630i			0.226631i	−0.993559	+	0.113315i	$0.963853\pi$
$648$		0			0
$649$		−	4.24319i		−	0.00653805i
$650$		0			0
$651$	−676.688			−1.03946
$652$		0			0
$653$			1257.57i			1.92583i	0.269797	+	0.962917i	$0.413044\pi$
$653$			1257.57i			1.92583i	−0.269797	+	0.962917i	$0.586956\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		−	1283.62i		−	1.95376i
$658$		0			0
$659$		−	302.508i		−	0.459041i	−0.973304	−	0.229521i	$-0.926284\pi$
$659$		−	302.508i		−	0.459041i	0.973304	−	0.229521i	$-0.0737158\pi$
$660$		0			0
$661$		−	649.086i		−	0.981976i	−0.871166	−	0.490988i	$-0.836636\pi$
$661$		−	649.086i		−	0.981976i	0.871166	−	0.490988i	$-0.163364\pi$
$662$		0			0
$663$			1360.93i			2.05268i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−145.206			−0.217700
$668$		0			0
$669$	537.928			0.804077
$670$		0			0
$671$	−626.426			−0.933571
$672$		0			0
$673$	−1130.94			−1.68044			−0.840222	−	0.542243i	$-0.817575\pi$
$673$	−1130.94			−1.68044			−0.840222	+	0.542243i	$0.817575\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−732.839			−1.08248			−0.541240	−	0.840868i	$-0.682045\pi$
$677$	−732.839			−1.08248			−0.541240	+	0.840868i	$0.682045\pi$
$678$		0			0
$679$			1133.31i			1.66909i
$680$		0			0
$681$	1026.93			1.50798
$682$		0			0
$683$	1054.81			1.54438			0.772191	−	0.635390i	$-0.219161\pi$
$683$	1054.81			1.54438			0.772191	+	0.635390i	$0.219161\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−589.789			−0.858499
$688$		0			0
$689$	−148.982			−0.216229
$690$		0			0
$691$	1062.69			1.53790			0.768951	−	0.639307i	$-0.220779\pi$
$691$	1062.69			1.53790			0.768951	+	0.639307i	$0.220779\pi$
$692$		0			0
$693$			951.060i			1.37238i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−447.199			−0.641605
$698$		0			0
$699$			1618.89i			2.31601i
$700$		0			0
$701$	−504.359			−0.719486			−0.359743	−	0.933051i	$-0.617136\pi$
$701$	−504.359			−0.719486			−0.359743	+	0.933051i	$0.617136\pi$
$702$		0			0
$703$	−1143.51	−	471.943i	−1.62661	−	0.671327i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		−	555.812i		−	0.786156i
$708$		0			0
$709$	−740.831			−1.04490			−0.522448	−	0.852671i	$-0.674981\pi$
$709$	−740.831			−1.04490			−0.522448	+	0.852671i	$0.674981\pi$
$710$		0			0
$711$		−	1253.72i		−	1.76332i
$712$		0			0
$713$	166.088			0.232943
$714$		0			0
$715$		0			0
$716$		0			0
$717$	2194.98			3.06134
$718$		0			0
$719$	−380.067			−0.528606			−0.264303	−	0.964440i	$-0.585142\pi$
$719$	−380.067			−0.528606			−0.264303	+	0.964440i	$0.585142\pi$
$720$		0			0
$721$			524.179i			0.727017i
$722$		0			0
$723$			854.966i			1.18253i
$724$		0			0
$725$		0			0
$726$		0			0
$727$		−	32.1100i		−	0.0441678i	−0.999756	−	0.0220839i	$-0.992970\pi$
$727$		−	32.1100i		−	0.0441678i	0.999756	−	0.0220839i	$-0.00703009\pi$
$728$		0			0
$729$	−1182.69			−1.62234
$730$		0			0
$731$	−1692.46			−2.31527
$732$		0			0
$733$			716.127i			0.976980i	0.872569	+	0.488490i	$0.162452\pi$
$733$			716.127i			0.976980i	−0.872569	+	0.488490i	$0.837548\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−992.732			−1.34699
$738$		0			0
$739$	487.621			0.659839			0.329919	−	0.944009i	$-0.392978\pi$
$739$	487.621			0.659839			0.329919	+	0.944009i	$0.392978\pi$
$740$		0			0
$741$	857.346	+	353.839i	1.15701	+	0.477515i
$742$		0			0
$743$	−1355.45			−1.82430			−0.912149	−	0.409858i	$-0.865578\pi$
$743$	−1355.45			−1.82430			−0.912149	+	0.409858i	$0.865578\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$			685.186i			0.917251i
$748$		0			0
$749$		−	134.655i		−	0.179780i
$750$		0			0
$751$		−	308.439i		−	0.410705i	−0.978688	−	0.205352i	$-0.934166\pi$
$751$		−	308.439i		−	0.410705i	0.978688	−	0.205352i	$-0.0658340\pi$
$752$		0			0
$753$	−264.711			−0.351542
$754$		0			0
$755$		0			0
$756$		0			0
$757$			126.540i			0.167160i	0.996501	+	0.0835800i	$0.0266354\pi$
$757$			126.540i			0.167160i	−0.996501	+	0.0835800i	$0.973365\pi$
$758$		0			0
$759$		−	378.816i		−	0.499099i
$760$		0			0
$761$	−116.745			−0.153411			−0.0767053	−	0.997054i	$-0.524440\pi$
$761$	−116.745			−0.153411			−0.0767053	+	0.997054i	$0.524440\pi$
$762$		0			0
$763$	696.429			0.912751
$764$		0			0
$765$		0			0
$766$		0			0
$767$			4.45617i			0.00580987i
$768$		0			0
$769$	−178.462			−0.232071			−0.116035	−	0.993245i	$-0.537019\pi$
$769$	−178.462			−0.232071			−0.116035	+	0.993245i	$0.537019\pi$
$770$		0			0
$771$	−408.012			−0.529199
$772$		0			0
$773$	−757.415			−0.979838			−0.489919	−	0.871768i	$-0.662974\pi$
$773$	−757.415			−0.979838			−0.489919	+	0.871768i	$0.662974\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$			2161.87i			2.78233i
$778$		0			0
$779$	−116.271	+	281.722i	−0.149256	+	0.361646i
$780$		0			0
$781$		−	869.119i		−	1.11283i
$782$		0			0
$783$			470.274i			0.600605i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−394.797			−0.501649			−0.250824	−	0.968033i	$-0.580702\pi$
$787$	−394.797			−0.501649			−0.250824	+	0.968033i	$0.580702\pi$
$788$		0			0
$789$			958.969i			1.21542i
$790$		0			0
$791$		−	869.859i		−	1.09970i
$792$		0			0
$793$	657.868			0.829594
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−1395.92			−1.75147			−0.875736	−	0.482790i	$-0.839623\pi$
$797$	−1395.92			−1.75147			−0.875736	+	0.482790i	$0.839623\pi$
$798$		0			0
$799$	267.741			0.335095
$800$		0			0
$801$		−	838.680i		−	1.04704i
$802$		0			0
$803$			852.644i			1.06182i
$804$		0			0
$805$		0			0
$806$		0			0
$807$		−	2313.01i		−	2.86618i
$808$		0			0
$809$	1037.98			1.28304			0.641520	−	0.767106i	$-0.278304\pi$
$809$	1037.98			1.28304			0.641520	+	0.767106i	$0.278304\pi$
$810$		0			0
$811$			856.583i			1.05621i	0.849180	+	0.528103i	$0.177097\pi$
$811$			856.583i			1.05621i	−0.849180	+	0.528103i	$0.822903\pi$
$812$		0			0
$813$	629.106			0.773808
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−440.036	+	1066.20i	−0.538600	+	1.30502i
$818$		0			0
$819$		−	998.796i		−	1.21953i
$820$		0			0
$821$	−1246.94			−1.51881			−0.759403	−	0.650620i	$-0.774509\pi$
$821$	−1246.94			−1.51881			−0.759403	+	0.650620i	$0.774509\pi$
$822$		0			0
$823$			565.419i			0.687021i	0.939149	+	0.343511i	$0.111616\pi$
$823$			565.419i			0.687021i	−0.939149	+	0.343511i	$0.888384\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	385.248			0.465838			0.232919	−	0.972496i	$-0.425172\pi$
$827$	385.248			0.465838			0.232919	+	0.972496i	$0.425172\pi$
$828$		0			0
$829$		−	291.671i		−	0.351835i	−0.984405	−	0.175918i	$-0.943711\pi$
$829$		−	291.671i		−	0.351835i	0.984405	−	0.175918i	$-0.0562892\pi$
$830$		0			0
$831$		−	2267.75i		−	2.72894i
$832$		0			0
$833$		−	55.3669i		−	0.0664669i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		−	537.906i		−	0.642660i
$838$		0			0
$839$			681.986i			0.812855i	0.913683	+	0.406428i	$0.133226\pi$
$839$			681.986i			0.812855i	−0.913683	+	0.406428i	$0.866774\pi$
$840$		0			0
$841$	523.542			0.622523
$842$		0			0
$843$		−	1873.94i		−	2.22295i
$844$		0			0
$845$		0			0
$846$		0			0
$847$			197.916i			0.233667i
$848$		0			0
$849$		−	1020.56i		−	1.20208i
$850$		0			0
$851$		−	530.617i		−	0.623522i
$852$		0			0
$853$		−	1226.89i		−	1.43833i	−0.694842	−	0.719163i	$-0.744526\pi$
$853$		−	1226.89i		−	1.43833i	0.694842	−	0.719163i	$-0.255474\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−1490.25			−1.73891			−0.869455	−	0.494011i	$-0.835530\pi$
$857$	−1490.25			−1.73891			−0.869455	+	0.494011i	$0.835530\pi$
$858$		0			0
$859$	353.772			0.411842			0.205921	−	0.978569i	$-0.433981\pi$
$859$	353.772			0.411842			0.205921	+	0.978569i	$0.433981\pi$
$860$		0			0
$861$	532.612			0.618597
$862$		0			0
$863$	−191.399			−0.221783			−0.110892	−	0.993833i	$-0.535371\pi$
$863$	−191.399			−0.221783			−0.110892	+	0.993833i	$0.535371\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	2364.35			2.72705
$868$		0			0
$869$			832.782i			0.958323i
$870$		0			0
$871$	1042.56			1.19697
$872$		0			0
$873$	−2388.45			−2.73591
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−215.594			−0.245831			−0.122915	−	0.992417i	$-0.539224\pi$
$877$	−215.594			−0.245831			−0.122915	+	0.992417i	$0.539224\pi$
$878$		0			0
$879$	1868.28			2.12546
$880$		0			0
$881$	−738.673			−0.838448			−0.419224	−	0.907883i	$-0.637698\pi$
$881$	−738.673			−0.838448			−0.419224	+	0.907883i	$0.637698\pi$
$882$		0			0
$883$		−	676.569i		−	0.766216i	−0.923703	−	0.383108i	$-0.874854\pi$
$883$		−	676.569i		−	0.766216i	0.923703	−	0.383108i	$-0.125146\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−947.023			−1.06767			−0.533835	−	0.845589i	$-0.679250\pi$
$887$	−947.023			−1.06767			−0.533835	+	0.845589i	$0.679250\pi$
$888$		0			0
$889$			426.330i			0.479561i
$890$		0			0
$891$	21.4881			0.0241169
$892$		0			0
$893$	69.6121	−	168.669i	0.0779531	−	0.188879i
$894$		0			0
$895$		0			0
$896$		0			0
$897$			397.830i			0.443512i
$898$		0			0
$899$	363.113			0.403908
$900$		0			0
$901$			412.032i			0.457305i
$902$		0			0
$903$	2015.72			2.23224
$904$		0			0
$905$		0			0
$906$		0			0
$907$	1224.31			1.34985			0.674925	−	0.737886i	$-0.264176\pi$
$907$	1224.31			1.34985			0.674925	+	0.737886i	$0.264176\pi$
$908$		0			0
$909$	1171.37			1.28864
$910$		0			0
$911$			1146.43i			1.25844i	0.777229	+	0.629218i	$0.216625\pi$
$911$			1146.43i			1.25844i	−0.777229	+	0.629218i	$0.783375\pi$
$912$		0			0
$913$		−	455.135i		−	0.498505i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		−	25.1457i		−	0.0274217i
$918$		0			0
$919$	1510.92			1.64409			0.822043	−	0.569425i	$-0.192834\pi$
$919$	1510.92			1.64409			0.822043	+	0.569425i	$0.192834\pi$
$920$		0			0
$921$	−292.621			−0.317721
$922$		0			0
$923$			912.742i			0.988886i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−1104.71			−1.19170
$928$		0			0
$929$	−350.718			−0.377522			−0.188761	−	0.982023i	$-0.560447\pi$
$929$	−350.718			−0.377522			−0.188761	+	0.982023i	$0.560447\pi$
$930$		0			0
$931$	−34.8795	−	14.3953i	−0.0374646	−	0.0154622i
$932$		0			0
$933$	−1183.58			−1.26858
$934$		0			0
$935$		0			0
$936$		0			0
$937$			1152.96i			1.23048i	0.788338	+	0.615242i	$0.210942\pi$
$937$			1152.96i			1.23048i	−0.788338	+	0.615242i	$0.789058\pi$
$938$		0			0
$939$		−	2321.87i		−	2.47271i
$940$		0			0
$941$			765.775i			0.813788i	0.913475	+	0.406894i	$0.133388\pi$
$941$			765.775i			0.813788i	−0.913475	+	0.406894i	$0.866612\pi$
$942$		0			0
$943$	−130.726			−0.138628
$944$		0			0
$945$		0			0
$946$		0			0
$947$		−	242.099i		−	0.255648i	−0.991797	−	0.127824i	$-0.959201\pi$
$947$		−	242.099i		−	0.255648i	0.991797	−	0.127824i	$-0.0407993\pi$
$948$		0			0
$949$		−	895.440i		−	0.943562i
$950$		0			0
$951$	423.453			0.445271
$952$		0			0
$953$	402.050			0.421878			0.210939	−	0.977499i	$-0.432348\pi$
$953$	402.050			0.421878			0.210939	+	0.977499i	$0.432348\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		−	828.193i		−	0.865406i
$958$		0			0
$959$	−1531.43			−1.59690
$960$		0			0
$961$	545.665			0.567810
$962$		0			0
$963$	283.786			0.294690
$964$		0			0
$965$		0			0
$966$		0			0
$967$		−	1022.23i		−	1.05711i	−0.848898	−	0.528557i	$-0.822733\pi$
$967$		−	1022.23i		−	1.05711i	0.848898	−	0.528557i	$-0.177267\pi$
$968$		0			0
$969$	978.593	−	2371.12i	1.00990	−	2.44697i
$970$		0			0
$971$			1739.87i			1.79183i	0.444226	+	0.895915i	$0.353479\pi$
$971$			1739.87i			1.79183i	−0.444226	+	0.895915i	$0.646521\pi$
$972$		0			0
$973$			208.953i			0.214752i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	1454.92			1.48917			0.744585	−	0.667528i	$-0.232648\pi$
$977$	1454.92			1.48917			0.744585	+	0.667528i	$0.232648\pi$
$978$		0			0
$979$			557.094i			0.569044i
$980$		0			0
$981$			1467.72i			1.49615i
$982$		0			0
$983$	785.609			0.799195			0.399597	−	0.916691i	$-0.369150\pi$
$983$	785.609			0.799195			0.399597	+	0.916691i	$0.369150\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−318.879			−0.323079
$988$		0			0
$989$	−494.744			−0.500246
$990$		0			0
$991$		−	1039.65i		−	1.04909i	−0.851383	−	0.524544i	$-0.824236\pi$
$991$		−	1039.65i		−	1.04909i	0.851383	−	0.524544i	$-0.175764\pi$
$992$		0			0
$993$		−	1930.18i		−	1.94379i
$994$		0			0
$995$		0			0
$996$		0			0
$997$			1628.52i			1.63342i	0.577050	+	0.816709i	$0.304204\pi$
$997$			1628.52i			1.63342i	−0.577050	+	0.816709i	$0.695796\pi$
$998$		0			0
$999$	−1718.50			−1.72022

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1900.3.g.d.949.3		28
5.2	odd	4		1900.3.e.h.1101.13	yes	14
5.3	odd	4		1900.3.e.g.1101.2	✓	14
5.4	even	2	inner	1900.3.g.d.949.26		28
19.18	odd	2	inner	1900.3.g.d.949.25		28
95.18	even	4		1900.3.e.g.1101.13	yes	14
95.37	even	4		1900.3.e.h.1101.2	yes	14
95.94	odd	2	inner	1900.3.g.d.949.4		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1900.3.e.g.1101.2	✓	14	5.3	odd	4
1900.3.e.g.1101.13	yes	14	95.18	even	4
1900.3.e.h.1101.2	yes	14	95.37	even	4
1900.3.e.h.1101.13	yes	14	5.2	odd	4
1900.3.g.d.949.3		28	1.1	even	1	trivial
1900.3.g.d.949.4		28	95.94	odd	2	inner
1900.3.g.d.949.25		28	19.18	odd	2	inner
1900.3.g.d.949.26		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)

\(f(q)\)	\(=\)	\(q-4.84257 q^{3} -6.85668i q^{7} +14.4504 q^{9} +O(q^{10})\)	\(q-4.84257 q^{3} -6.85668i q^{7} +14.4504 q^{9} -9.59871 q^{11} +10.0805 q^{13} -27.8791i q^{17} +(-17.5630 - 7.24850i) q^{19} +33.2039i q^{21} -8.14968i q^{23} -26.3941 q^{27} -17.8174i q^{29} +20.3798i q^{31} +46.4824 q^{33} +65.1090 q^{37} -48.8154 q^{39} -16.0406i q^{41} -60.7072i q^{43} +9.60366i q^{47} +1.98597 q^{49} +135.006i q^{51} -14.7792 q^{53} +(85.0500 + 35.1013i) q^{57} +0.442058i q^{59} +65.2615 q^{61} -99.0820i q^{63} +103.423 q^{67} +39.4653i q^{69} +90.5453i q^{71} -88.8290i q^{73} +65.8153i q^{77} -86.7598i q^{79} -2.23865 q^{81} +47.4163i q^{83} +86.2817i q^{87} -58.0384i q^{89} -69.1187i q^{91} -98.6904i q^{93} -165.286 q^{97} -138.706 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 104 q^{9}+O(q^{10}) \) 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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