LMFDB - Embedded newform 252.4.e.a.71.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,4,Mod(71,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("252.71");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	252.e (of order $2$, degree $1$, 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:	$14.8684813214$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			71.11
Character	$\chi$	$=$	252.71
Dual form			252.4.e.a.71.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.42938 - 2.44067i) q^{2} +(-3.91377 + 6.97728i) q^{4} -15.7775i q^{5} +7.00000i q^{7} +(22.6235 - 0.420902i) q^{8} +(-38.5077 + 22.5520i) q^{10} -23.5125 q^{11} -37.7320 q^{13} +(17.0847 - 10.0056i) q^{14} +(-33.3648 - 54.6150i) q^{16} -31.9239i q^{17} -28.8804i q^{19} +(110.084 + 61.7495i) q^{20} +(33.6082 + 57.3863i) q^{22} -50.8589 q^{23} -123.929 q^{25} +(53.9332 + 92.0916i) q^{26} +(-48.8409 - 27.3964i) q^{28} +205.159i q^{29} +176.645i q^{31} +(-85.6065 + 159.498i) q^{32} +(-77.9159 + 45.6313i) q^{34} +110.442 q^{35} -338.457 q^{37} +(-70.4877 + 41.2810i) q^{38} +(-6.64077 - 356.942i) q^{40} +77.7879i q^{41} +463.054i q^{43} +(92.0225 - 164.053i) q^{44} +(72.6965 + 124.130i) q^{46} +352.149 q^{47} -49.0000 q^{49} +(177.142 + 302.471i) q^{50} +(147.675 - 263.267i) q^{52} -155.551i q^{53} +370.968i q^{55} +(2.94631 + 158.365i) q^{56} +(500.727 - 293.250i) q^{58} -761.398 q^{59} -40.2208 q^{61} +(431.132 - 252.491i) q^{62} +(511.646 - 19.0445i) q^{64} +595.317i q^{65} +838.691i q^{67} +(222.742 + 124.943i) q^{68} +(-157.864 - 269.554i) q^{70} +70.1497 q^{71} +726.789 q^{73} +(483.783 + 826.064i) q^{74} +(201.507 + 113.031i) q^{76} -164.587i q^{77} -992.308i q^{79} +(-861.687 + 526.412i) q^{80} +(189.855 - 111.188i) q^{82} -1116.85 q^{83} -503.680 q^{85} +(1130.16 - 661.878i) q^{86} +(-531.935 + 9.89644i) q^{88} -1592.19i q^{89} -264.124i q^{91} +(199.050 - 354.857i) q^{92} +(-503.353 - 859.481i) q^{94} -455.661 q^{95} -1263.10 q^{97} +(70.0394 + 119.593i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 24 q^{4} + 264 q^{10} - 468 q^{16} + 444 q^{22} - 900 q^{25} - 84 q^{28} - 432 q^{34} - 264 q^{37} + 1416 q^{40} + 180 q^{46} - 1764 q^{49} + 2736 q^{52} + 636 q^{58} - 3960 q^{61} + 1392 q^{64}+ \cdots + 5496 q^{94}+O(q^{100}) $ 36 * q - 24 * q^4 + 264 * q^10 - 468 * q^16 + 444 * q^22 - 900 * q^25 - 84 * q^28 - 432 * q^34 - 264 * q^37 + 1416 * q^40 + 180 * q^46 - 1764 * q^49 + 2736 * q^52 + 636 * q^58 - 3960 * q^61 + 1392 * q^64 - 504 * q^70 - 2520 * q^76 + 1032 * q^82 - 3144 * q^85 + 2748 * q^88 + 5496 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	−1.42938	−	2.44067i	−0.505360	−	0.862908i
$2$	−1.42938	−	2.44067i	−0.505360	−	0.862908i
$3$		0			0
$3$		0			0
$4$	−3.91377	+	6.97728i	−0.489222	+	0.872159i
$5$		−	15.7775i		−	1.41118i	−0.708619	−	0.705591i	$-0.750682\pi$
$5$		−	15.7775i		−	1.41118i	0.708619	−	0.705591i	$-0.249318\pi$
$6$		0			0
$7$			7.00000i			0.377964i
$7$			7.00000i			0.377964i
$8$	22.6235	−	0.420902i	0.999827	−	0.0186014i
$9$		0			0
$10$	−38.5077	+	22.5520i	−1.21772	+	0.713156i
$11$	−23.5125			−0.644480			−0.322240	−	0.946658i	$-0.604436\pi$
$11$	−23.5125			−0.644480			−0.322240	+	0.946658i	$0.604436\pi$
$12$		0			0
$13$	−37.7320			−0.804999			−0.402499	−	0.915420i	$-0.631858\pi$
$13$	−37.7320			−0.804999			−0.402499	+	0.915420i	$0.631858\pi$
$14$	17.0847	−	10.0056i	0.326149	−	0.191008i
$15$		0			0
$16$	−33.3648	−	54.6150i	−0.521324	−	0.853359i
$17$		−	31.9239i		−	0.455452i	−0.973725	−	0.227726i	$-0.926871\pi$
$17$		−	31.9239i		−	0.455452i	0.973725	−	0.227726i	$-0.0731291\pi$
$18$		0			0
$19$		−	28.8804i		−	0.348717i	−0.984682	−	0.174359i	$-0.944215\pi$
$19$		−	28.8804i		−	0.348717i	0.984682	−	0.174359i	$-0.0557852\pi$
$20$	110.084	+	61.7495i	1.23078	+	0.690381i
$21$		0			0
$22$	33.6082	+	57.3863i	0.325695	+	0.556127i
$23$	−50.8589			−0.461079			−0.230539	−	0.973063i	$-0.574049\pi$
$23$	−50.8589			−0.461079			−0.230539	+	0.973063i	$0.574049\pi$
$24$		0			0
$25$	−123.929			−0.991435
$26$	53.9332	+	92.0916i	0.406814	+	0.694640i
$27$		0			0
$28$	−48.8409	−	27.3964i	−0.329645	−	0.184908i
$29$			205.159i			1.31369i	0.754024	+	0.656847i	$0.228110\pi$
$29$			205.159i			1.31369i	−0.754024	+	0.656847i	$0.771890\pi$
$30$		0			0
$31$			176.645i			1.02343i	0.859156	+	0.511714i	$0.170989\pi$
$31$			176.645i			1.02343i	−0.859156	+	0.511714i	$0.829011\pi$
$32$	−85.6065	+	159.498i	−0.472914	+	0.881109i
$33$		0			0
$34$	−77.9159	+	45.6313i	−0.393014	+	0.230168i
$35$	110.442			0.533377
$36$		0			0
$37$	−338.457			−1.50384			−0.751920	−	0.659255i	$-0.770872\pi$
$37$	−338.457			−1.50384			−0.751920	+	0.659255i	$0.770872\pi$
$38$	−70.4877	+	41.2810i	−0.300911	+	0.176228i
$39$		0			0
$40$	−6.64077	−	356.942i	−0.0262500	−	1.41094i
$41$			77.7879i			0.296303i	0.988965	+	0.148152i	$0.0473323\pi$
$41$			77.7879i			0.296303i	−0.988965	+	0.148152i	$0.952668\pi$
$42$		0			0
$43$			463.054i			1.64221i	0.570775	+	0.821106i	$0.306643\pi$
$43$			463.054i			1.64221i	−0.570775	+	0.821106i	$0.693357\pi$
$44$	92.0225	−	164.053i	0.315294	−	0.562089i
$45$		0			0
$46$	72.6965	+	124.130i	0.233011	+	0.397869i
$47$	352.149			1.09290			0.546450	−	0.837492i	$-0.315979\pi$
$47$	352.149			1.09290			0.546450	+	0.837492i	$0.315979\pi$
$48$		0			0
$49$	−49.0000			−0.142857
$50$	177.142	+	302.471i	0.501032	+	0.855517i
$51$		0			0
$52$	147.675	−	263.267i	0.393823	−	0.702087i
$53$		−	155.551i		−	0.403142i	−0.979474	−	0.201571i	$-0.935395\pi$
$53$		−	155.551i		−	0.403142i	0.979474	−	0.201571i	$-0.0646048\pi$
$54$		0			0
$55$			370.968i			0.909479i
$56$	2.94631	+	158.365i	0.00703067	+	0.377899i
$57$		0			0
$58$	500.727	−	293.250i	1.13360	−	0.663889i
$59$	−761.398			−1.68010			−0.840048	−	0.542513i	$-0.817473\pi$
$59$	−761.398			−1.68010			−0.840048	+	0.542513i	$0.817473\pi$
$60$		0			0
$61$	−40.2208			−0.0844221			−0.0422110	−	0.999109i	$-0.513440\pi$
$61$	−40.2208			−0.0844221			−0.0422110	+	0.999109i	$0.513440\pi$
$62$	431.132	−	252.491i	0.883125	−	0.517200i
$63$		0			0
$64$	511.646	−	19.0445i	0.999308	−	0.0371964i
$65$			595.317i			1.13600i
$66$		0			0
$67$			838.691i			1.52929i	0.644451	+	0.764645i	$0.277086\pi$
$67$			838.691i			1.52929i	−0.644451	+	0.764645i	$0.722914\pi$
$68$	222.742	+	124.943i	0.397227	+	0.222817i
$69$		0			0
$70$	−157.864	−	269.554i	−0.269547	−	0.460255i
$71$	70.1497			0.117257			0.0586285	−	0.998280i	$-0.481327\pi$
$71$	70.1497			0.117257			0.0586285	+	0.998280i	$0.481327\pi$
$72$		0			0
$73$	726.789			1.16526			0.582632	−	0.812736i	$-0.302023\pi$
$73$	726.789			1.16526			0.582632	+	0.812736i	$0.302023\pi$
$74$	483.783	+	826.064i	0.759981	+	1.29768i
$75$		0			0
$76$	201.507	+	113.031i	0.304137	+	0.170600i
$77$		−	164.587i		−	0.243591i
$78$		0			0
$79$		−	992.308i		−	1.41321i	−0.707610	−	0.706604i	$-0.750226\pi$
$79$		−	992.308i		−	1.41321i	0.707610	−	0.706604i	$-0.249774\pi$
$80$	−861.687	+	526.412i	−1.20424	+	0.735683i
$81$		0			0
$82$	189.855	−	111.188i	0.255682	−	0.149740i
$83$	−1116.85			−1.47700			−0.738498	−	0.674256i	$-0.764464\pi$
$83$	−1116.85			−1.47700			−0.738498	+	0.674256i	$0.764464\pi$
$84$		0			0
$85$	−503.680			−0.642726
$86$	1130.16	−	661.878i	1.41708	−	0.829909i
$87$		0			0
$88$	−531.935	+	9.89644i	−0.644368	+	0.0119882i
$89$		−	1592.19i		−	1.89631i	−0.317810	−	0.948155i	$-0.602947\pi$
$89$		−	1592.19i		−	1.89631i	0.317810	−	0.948155i	$-0.397053\pi$
$90$		0			0
$91$		−	264.124i		−	0.304261i
$92$	199.050	−	354.857i	0.225570	−	0.402134i
$93$		0			0
$94$	−503.353	−	859.481i	−0.552308	−	0.943072i
$95$	−455.661			−0.492103
$96$		0			0
$97$	−1263.10			−1.32215			−0.661075	−	0.750320i	$-0.729899\pi$
$97$	−1263.10			−1.32215			−0.661075	+	0.750320i	$0.729899\pi$
$98$	70.0394	+	119.593i	0.0721943	+	0.123273i
$99$		0			0
$100$	485.031	−	864.689i	0.485031	−	0.864689i
$101$		−	1484.69i		−	1.46269i	−0.682006	−	0.731347i	$-0.738892\pi$
$101$		−	1484.69i		−	1.46269i	0.682006	−	0.731347i	$-0.261108\pi$
$102$		0			0
$103$			1244.15i			1.19019i	0.803655	+	0.595095i	$0.202886\pi$
$103$			1244.15i			1.19019i	−0.803655	+	0.595095i	$0.797114\pi$
$104$	−853.631	+	15.8815i	−0.804859	+	0.0149741i
$105$		0			0
$106$	−379.649	+	222.341i	−0.347875	+	0.203732i
$107$	−1825.93			−1.64972			−0.824858	−	0.565340i	$-0.808745\pi$
$107$	−1825.93			−1.64972			−0.824858	+	0.565340i	$0.808745\pi$
$108$		0			0
$109$	209.445			0.184048			0.0920238	−	0.995757i	$-0.470666\pi$
$109$	209.445			0.184048			0.0920238	+	0.995757i	$0.470666\pi$
$110$	905.412	−	530.252i	0.784797	−	0.459614i
$111$		0			0
$112$	382.305	−	233.553i	0.322539	−	0.197042i
$113$		−	1021.23i		−	0.850169i	−0.905154	−	0.425084i	$-0.860244\pi$
$113$		−	1021.23i		−	0.850169i	0.905154	−	0.425084i	$-0.139756\pi$
$114$		0			0
$115$			802.426i			0.650666i
$116$	−1431.45	−	802.948i	−1.14575	−	0.642688i
$117$		0			0
$118$	1088.32	+	1858.32i	0.849054	+	1.44977i
$119$	223.467			0.172145
$120$		0			0
$121$	−778.163			−0.584646
$122$	57.4906	+	98.1659i	0.0426636	+	0.0728485i
$123$		0			0
$124$	−1232.50	−	691.347i	−0.892593	−	0.500684i
$125$		−	16.8921i		−	0.0120870i
$126$		0			0
$127$		−	2003.37i		−	1.39976i	−0.714258	−	0.699882i	$-0.753236\pi$
$127$		−	2003.37i		−	1.39976i	0.714258	−	0.699882i	$-0.246764\pi$
$128$	−777.815	−	1221.54i	−0.537108	−	0.843514i
$129$		0			0
$130$	1452.97	−	850.931i	0.980264	−	0.574089i
$131$	1168.94			0.779624			0.389812	−	0.920894i	$-0.372540\pi$
$131$	1168.94			0.779624			0.389812	+	0.920894i	$0.372540\pi$
$132$		0			0
$133$	202.163			0.131803
$134$	2046.97	−	1198.80i	1.31964	−	0.772843i
$135$		0			0
$136$	−13.4368	−	722.231i	−0.00847205	−	0.455373i
$137$		−	472.985i		−	0.294962i	−0.989065	−	0.147481i	$-0.952883\pi$
$137$		−	472.985i		−	0.294962i	0.989065	−	0.147481i	$-0.0471166\pi$
$138$		0			0
$139$			2857.76i			1.74382i	0.489662	+	0.871912i	$0.337120\pi$
$139$			2857.76i			1.74382i	−0.489662	+	0.871912i	$0.662880\pi$
$140$	−432.247	+	770.588i	−0.260939	+	0.465190i
$141$		0			0
$142$	−100.270	−	171.213i	−0.0592570	−	0.101182i
$143$	887.174			0.518805
$144$		0			0
$145$	3236.90			1.85386
$146$	−1038.85	−	1773.85i	−0.588878	−	1.00552i
$147$		0			0
$148$	1324.65	−	2361.51i	0.735711	−	1.31159i
$149$			3076.95i			1.69177i	0.533368	+	0.845883i	$0.320926\pi$
$149$			3076.95i			1.69177i	−0.533368	+	0.845883i	$0.679074\pi$
$150$		0			0
$151$		−	1309.38i		−	0.705668i	−0.935686	−	0.352834i	$-0.885218\pi$
$151$		−	1309.38i		−	0.705668i	0.935686	−	0.352834i	$-0.114782\pi$
$152$	−12.1558	−	653.376i	−0.00648662	−	0.348657i
$153$		0			0
$154$	−401.704	+	235.257i	−0.210196	+	0.123101i
$155$	2787.01			1.44424
$156$		0			0
$157$	48.9931			0.0249049			0.0124525	−	0.999922i	$-0.496036\pi$
$157$	48.9931			0.0249049			0.0124525	+	0.999922i	$0.496036\pi$
$158$	−2421.90	+	1418.38i	−1.21947	+	0.714179i
$159$		0			0
$160$	2516.47	+	1350.66i	1.24340	+	0.667367i
$161$		−	356.012i		−	0.174271i
$162$		0			0
$163$		−	1861.23i		−	0.894371i	−0.894441	−	0.447186i	$-0.852426\pi$
$163$		−	1861.23i		−	0.894371i	0.894441	−	0.447186i	$-0.147574\pi$
$164$	−542.748	−	304.444i	−0.258424	−	0.144958i
$165$		0			0
$166$	1596.40	+	2725.87i	0.746415	+	1.27451i
$167$	276.319			0.128037			0.0640186	−	0.997949i	$-0.479608\pi$
$167$	276.319			0.128037			0.0640186	+	0.997949i	$0.479608\pi$
$168$		0			0
$169$	−773.294			−0.351977
$170$	719.947	+	1229.32i	0.324808	+	0.554614i
$171$		0			0
$172$	−3230.86	−	1812.29i	−1.43227	−	0.803406i
$173$			304.273i			0.133719i	0.997762	+	0.0668597i	$0.0212980\pi$
$173$			304.273i			0.133719i	−0.997762	+	0.0668597i	$0.978702\pi$
$174$		0			0
$175$		−	867.505i		−	0.374727i
$176$	784.488	+	1284.13i	0.335983	+	0.549973i
$177$		0			0
$178$	−3886.01	+	2275.83i	−1.63634	+	0.958320i
$179$	−2828.65			−1.18113			−0.590567	−	0.806988i	$-0.701096\pi$
$179$	−2828.65			−1.18113			−0.590567	+	0.806988i	$0.701096\pi$
$180$		0			0
$181$	2289.94			0.940386			0.470193	−	0.882564i	$-0.344184\pi$
$181$	2289.94			0.940386			0.470193	+	0.882564i	$0.344184\pi$
$182$	−644.641	+	377.533i	−0.262549	+	0.153761i
$183$		0			0
$184$	−1150.61	+	21.4066i	−0.460999	+	0.00857671i
$185$			5340.01i			2.12219i
$186$		0			0
$187$			750.611i			0.293530i
$188$	−1378.23	+	2457.04i	−0.534670	+	0.953182i
$189$		0			0
$190$	651.310	+	1112.12i	0.248689	+	0.424640i
$191$	314.085			0.118986			0.0594932	−	0.998229i	$-0.481052\pi$
$191$	314.085			0.118986			0.0594932	+	0.998229i	$0.481052\pi$
$192$		0			0
$193$	−2133.16			−0.795587			−0.397793	−	0.917475i	$-0.630224\pi$
$193$	−2133.16			−0.795587			−0.397793	+	0.917475i	$0.630224\pi$
$194$	1805.45	+	3082.82i	0.668162	+	1.14089i
$195$		0			0
$196$	191.775	−	341.887i	0.0698888	−	0.124594i
$197$		−	1510.64i		−	0.546339i	−0.961966	−	0.273170i	$-0.911928\pi$
$197$		−	1510.64i		−	0.546339i	0.961966	−	0.273170i	$-0.0880720\pi$
$198$		0			0
$199$			328.162i			0.116898i	0.998290	+	0.0584492i	$0.0186156\pi$
$199$			328.162i			0.116898i	−0.998290	+	0.0584492i	$0.981384\pi$
$200$	−2803.72	+	52.1621i	−0.991263	+	0.0184421i
$201$		0			0
$202$	−3623.64	+	2122.18i	−1.26217	+	0.739187i
$203$	−1436.12			−0.496530
$204$		0			0
$205$	1227.30			0.418138
$206$	3036.56	−	1778.36i	1.02703	−	0.601475i
$207$		0			0
$208$	1258.92	+	2060.73i	0.419665	+	0.686953i
$209$			679.050i			0.224741i
$210$		0			0
$211$		−	4199.04i		−	1.37002i	−0.728535	−	0.685009i	$-0.759798\pi$
$211$		−	4199.04i		−	1.37002i	0.728535	−	0.685009i	$-0.240202\pi$
$212$	1085.32	+	608.791i	0.351605	+	0.197226i
$213$		0			0
$214$	2609.94	+	4456.50i	0.833701	+	1.42355i
$215$	7305.84			2.31746
$216$		0			0
$217$	−1236.51			−0.386820
$218$	−299.375	−	511.187i	−0.0930104	−	0.158816i
$219$		0			0
$220$	−2588.35	−	1451.88i	−0.793210	−	0.444937i
$221$			1204.55i			0.366638i
$222$		0			0
$223$		−	1522.53i		−	0.457202i	−0.973520	−	0.228601i	$-0.926585\pi$
$223$		−	1522.53i		−	0.457202i	0.973520	−	0.228601i	$-0.0734152\pi$
$224$	−1116.48	−	599.246i	−0.333028	−	0.178745i
$225$		0			0
$226$	−2492.48	+	1459.72i	−0.733618	+	0.429642i
$227$	−1831.97			−0.535649			−0.267825	−	0.963468i	$-0.586305\pi$
$227$	−1831.97			−0.535649			−0.267825	+	0.963468i	$0.586305\pi$
$228$		0			0
$229$	417.356			0.120435			0.0602176	−	0.998185i	$-0.480821\pi$
$229$	417.356			0.120435			0.0602176	+	0.998185i	$0.480821\pi$
$230$	1958.46	−	1146.97i	0.561465	−	0.328821i
$231$		0			0
$232$	86.3519	+	4641.42i	0.0244366	+	1.31347i
$233$		−	431.598i		−	0.121352i	−0.998158	−	0.0606759i	$-0.980674\pi$
$233$		−	431.598i		−	0.121352i	0.998158	−	0.0606759i	$-0.0193256\pi$
$234$		0			0
$235$		−	5556.03i		−	1.54228i
$236$	2979.94	−	5312.49i	0.821939	−	1.46531i
$237$		0			0
$238$	−319.419	−	545.411i	−0.0869952	−	0.148545i
$239$	3365.90			0.910971			0.455485	−	0.890243i	$-0.349466\pi$
$239$	3365.90			0.910971			0.455485	+	0.890243i	$0.349466\pi$
$240$		0			0
$241$	4055.66			1.08402			0.542008	−	0.840373i	$-0.317664\pi$
$241$	4055.66			1.08402			0.542008	+	0.840373i	$0.317664\pi$
$242$	1112.29	+	1899.24i	0.295457	+	0.504496i
$243$		0			0
$244$	157.415	−	280.632i	0.0413011	−	0.0736295i
$245$			773.097i			0.201597i
$246$		0			0
$247$			1089.72i			0.280717i
$248$	74.3500	+	3996.32i	0.0190372	+	1.02325i
$249$		0			0
$250$	−41.2280	+	24.1451i	−0.0104300	+	0.00610828i
$251$	1222.93			0.307531			0.153766	−	0.988107i	$-0.450860\pi$
$251$	1222.93			0.307531			0.153766	+	0.988107i	$0.450860\pi$
$252$		0			0
$253$	1195.82			0.297156
$254$	−4889.57	+	2863.56i	−1.20787	+	0.707386i
$255$		0			0
$256$	−1869.59	+	3644.43i	−0.456442	+	0.889753i
$257$			933.046i			0.226466i	0.993568	+	0.113233i	$0.0361207\pi$
$257$			933.046i			0.226466i	−0.993568	+	0.113233i	$0.963879\pi$
$258$		0			0
$259$		−	2369.20i		−	0.568398i
$260$	−4153.69	−	2329.94i	−0.990773	−	0.555756i
$261$		0			0
$262$	−1670.85	−	2853.00i	−0.393991	−	0.672744i
$263$	2725.50			0.639018			0.319509	−	0.947583i	$-0.396482\pi$
$263$	2725.50			0.639018			0.319509	+	0.947583i	$0.396482\pi$
$264$		0			0
$265$	−2454.20			−0.568907
$266$	−288.967	−	493.414i	−0.0666078	−	0.113734i
$267$		0			0
$268$	−5851.78	−	3282.45i	−1.33379	−	0.748162i
$269$			6736.86i			1.52697i	0.645828	+	0.763483i	$0.276512\pi$
$269$			6736.86i			1.52697i	−0.645828	+	0.763483i	$0.723488\pi$
$270$		0			0
$271$			4267.63i			0.956606i	0.878195	+	0.478303i	$0.158748\pi$
$271$			4267.63i			0.956606i	−0.878195	+	0.478303i	$0.841252\pi$
$272$	−1743.52	+	1065.13i	−0.388664	+	0.237438i
$273$		0			0
$274$	−1154.40	+	676.073i	−0.254526	+	0.149062i
$275$	2913.89			0.638960
$276$		0			0
$277$	−7464.54			−1.61914			−0.809568	−	0.587026i	$-0.800299\pi$
$277$	−7464.54			−1.61914			−0.809568	+	0.587026i	$0.800299\pi$
$278$	6974.85	−	4084.80i	1.50476	−	0.881260i
$279$		0			0
$280$	2498.60	−	46.4854i	0.533284	−	0.00992155i
$281$		−	1541.92i		−	0.327343i	−0.986515	−	0.163671i	$-0.947666\pi$
$281$		−	1541.92i		−	0.327343i	0.986515	−	0.163671i	$-0.0523337\pi$
$282$		0			0
$283$		−	5.84660i		−	0.00122807i	−1.00000		0.000614036i	$-0.999805\pi$
$283$		−	5.84660i		−	0.00122807i	1.00000		0.000614036i	$-0.000195454\pi$
$284$	−274.550	+	489.454i	−0.0573646	+	0.102267i
$285$		0			0
$286$	−1268.10	−	2165.30i	−0.262184	−	0.447682i
$287$	−544.515			−0.111992
$288$		0			0
$289$	3893.86			0.792563
$290$	−4626.75	−	7900.22i	−0.936869	−	1.59971i
$291$		0			0
$292$	−2844.49	+	5071.01i	−0.570072	+	1.01630i
$293$		−	8241.62i		−	1.64328i	−0.570008	−	0.821639i	$-0.693060\pi$
$293$		−	8241.62i		−	1.64328i	0.570008	−	0.821639i	$-0.306940\pi$
$294$		0			0
$295$			12013.0i			2.37092i
$296$	−7657.09	+	142.457i	−1.50358	+	0.0279735i
$297$		0			0
$298$	7509.82	−	4398.11i	1.45984	−	0.854952i
$299$	1919.01			0.371168
$300$		0			0
$301$	−3241.38			−0.620698
$302$	−3195.77	+	1871.59i	−0.608927	+	0.356617i
$303$		0			0
$304$	−1577.30	+	963.588i	−0.297581	+	0.181795i
$305$			634.584i			0.119135i
$306$		0			0
$307$		−	9164.01i		−	1.70364i	−0.523833	−	0.851821i	$-0.675499\pi$
$307$		−	9164.01i		−	1.70364i	0.523833	−	0.851821i	$-0.324501\pi$
$308$	1148.37	+	644.158i	0.212450	+	0.119170i
$309$		0			0
$310$	−3983.68	−	6802.18i	−0.729864	−	1.24625i
$311$	−8767.25			−1.59854			−0.799269	−	0.600974i	$-0.794779\pi$
$311$	−8767.25			−1.59854			−0.799269	+	0.600974i	$0.794779\pi$
$312$		0			0
$313$	−1440.96			−0.260216			−0.130108	−	0.991500i	$-0.541532\pi$
$313$	−1440.96			−0.260216			−0.130108	+	0.991500i	$0.541532\pi$
$314$	−70.0295	−	119.576i	−0.0125860	−	0.0214907i
$315$		0			0
$316$	6923.61	+	3883.67i	1.23254	+	0.691372i
$317$			1454.49i			0.257705i	0.991664	+	0.128852i	$0.0411294\pi$
$317$			1454.49i			0.257705i	−0.991664	+	0.128852i	$0.958871\pi$
$318$		0			0
$319$		−	4823.81i		−	0.846650i
$320$	−300.475	−	8072.49i	−0.0524908	−	1.41021i
$321$		0			0
$322$	−868.910	+	508.875i	−0.150380	+	0.0880699i
$323$	−921.976			−0.158824
$324$		0			0
$325$	4676.11			0.798104
$326$	−4542.65	+	2660.39i	−0.771760	+	0.451980i
$327$		0			0
$328$	32.7410	+	1759.83i	0.00551165	+	0.296252i
$329$			2465.05i			0.413077i
$330$		0			0
$331$			240.686i			0.0399677i	0.999800	+	0.0199839i	$0.00636149\pi$
$331$			240.686i			0.0399677i	−0.999800	+	0.0199839i	$0.993639\pi$
$332$	4371.11	−	7792.59i	0.722578	−	1.28818i
$333$		0			0
$334$	−394.964	−	674.405i	−0.0647050	−	0.110484i
$335$	13232.5			2.15811
$336$		0			0
$337$	−1392.47			−0.225083			−0.112541	−	0.993647i	$-0.535899\pi$
$337$	−1392.47			−0.225083			−0.112541	+	0.993647i	$0.535899\pi$
$338$	1105.33	+	1887.36i	0.177875	+	0.303724i
$339$		0			0
$340$	1971.29	−	3514.31i	0.314436	−	0.560560i
$341$		−	4153.35i		−	0.659579i
$342$		0			0
$343$		−	343.000i		−	0.0539949i
$344$	194.900	+	10475.9i	0.0305474	+	1.64193i
$345$		0			0
$346$	742.631	−	434.920i	0.115388	−	0.0675765i
$347$	−8230.21			−1.27326			−0.636629	−	0.771170i	$-0.719672\pi$
$347$	−8230.21			−1.27326			−0.636629	+	0.771170i	$0.719672\pi$
$348$		0			0
$349$	2298.41			0.352524			0.176262	−	0.984343i	$-0.443599\pi$
$349$	2298.41			0.352524			0.176262	+	0.984343i	$0.443599\pi$
$350$	−2117.30	+	1239.99i	−0.323355	+	0.189372i
$351$		0			0
$352$	2012.82	−	3750.19i	0.304783	−	0.567857i
$353$			6796.30i			1.02473i	0.858767	+	0.512366i	$0.171231\pi$
$353$			6796.30i			1.02473i	−0.858767	+	0.512366i	$0.828769\pi$
$354$		0			0
$355$		−	1106.79i		−	0.165471i
$356$	11109.1	+	6231.46i	1.65388	+	0.927716i
$357$		0			0
$358$	4043.20	+	6903.81i	0.596899	+	1.01921i
$359$	−11252.7			−1.65430			−0.827150	−	0.561981i	$-0.810040\pi$
$359$	−11252.7			−1.65430			−0.827150	+	0.561981i	$0.810040\pi$
$360$		0			0
$361$	6024.92			0.878396
$362$	−3273.18	−	5589.00i	−0.475234	−	0.811467i
$363$		0			0
$364$	1842.87	+	1033.72i	0.265364	+	0.148851i
$365$		−	11466.9i		−	1.64440i
$366$		0			0
$367$			2173.56i			0.309152i	0.987981	+	0.154576i	$0.0494011\pi$
$367$			2173.56i			0.309152i	−0.987981	+	0.154576i	$0.950599\pi$
$368$	1696.89	+	2777.66i	0.240372	+	0.393466i
$369$		0			0
$370$	13033.2	−	7632.88i	1.83126	−	1.07247i
$371$	1088.86			0.152374
$372$		0			0
$373$	13792.9			1.91466			0.957330	−	0.288997i	$-0.0933217\pi$
$373$	13792.9			1.91466			0.957330	+	0.288997i	$0.0933217\pi$
$374$	1832.00	−	1072.90i	0.253289	−	0.148338i
$375$		0			0
$376$	7966.85	−	148.220i	1.09271	−	0.0203294i
$377$		−	7741.08i		−	1.05752i
$378$		0			0
$379$			404.932i			0.0548812i	0.999623	+	0.0274406i	$0.00873571\pi$
$379$			404.932i			0.0548812i	−0.999623	+	0.0274406i	$0.991264\pi$
$380$	1783.35	−	3179.27i	0.240748	−	0.429192i
$381$		0			0
$382$	−448.946	−	766.579i	−0.0601310	−	0.102674i
$383$	−9664.87			−1.28943			−0.644715	−	0.764423i	$-0.723024\pi$
$383$	−9664.87			−1.28943			−0.644715	+	0.764423i	$0.723024\pi$
$384$		0			0
$385$	−2596.78			−0.343751
$386$	3049.09	+	5206.35i	0.402058	+	0.686518i
$387$		0			0
$388$	4943.49	−	8813.00i	0.646824	−	1.15313i
$389$			3344.96i			0.435980i	0.975951	+	0.217990i	$0.0699500\pi$
$389$			3344.96i			0.435980i	−0.975951	+	0.217990i	$0.930050\pi$
$390$		0			0
$391$			1623.62i			0.209999i
$392$	−1108.55	+	20.6242i	−0.142832	+	0.00265734i
$393$		0			0
$394$	−3686.98	+	2159.27i	−0.471441	+	0.276098i
$395$	−15656.1			−1.99429
$396$		0			0
$397$	5442.74			0.688069			0.344035	−	0.938957i	$-0.388206\pi$
$397$	5442.74			0.688069			0.344035	+	0.938957i	$0.388206\pi$
$398$	800.937	−	469.067i	0.100873	−	0.0590759i
$399$		0			0
$400$	4134.87	+	6768.40i	0.516859	+	0.846050i
$401$		−	14165.2i		−	1.76403i	−0.471218	−	0.882017i	$-0.656186\pi$
$401$		−	14165.2i		−	1.76403i	0.471218	−	0.882017i	$-0.343814\pi$
$402$		0			0
$403$		−	6665.16i		−	0.823859i
$404$	10359.1	+	5810.73i	1.27570	+	0.715581i
$405$		0			0
$406$	2052.75	+	3505.09i	0.250927	+	0.428460i
$407$	7957.97			0.969194
$408$		0			0
$409$	9568.46			1.15680			0.578399	−	0.815754i	$-0.303678\pi$
$409$	9568.46			1.15680			0.578399	+	0.815754i	$0.303678\pi$
$410$	−1754.27	−	2995.43i	−0.211310	−	0.360814i
$411$		0			0
$412$	−8680.77	−	4869.32i	−1.03804	−	0.582267i
$413$		−	5329.79i		−	0.635016i
$414$		0			0
$415$			17621.1i			2.08431i
$416$	3230.11	−	6018.17i	0.380695	−	0.709291i
$417$		0			0
$418$	1657.34	−	970.618i	0.193931	−	0.113575i
$419$	3341.64			0.389618			0.194809	−	0.980841i	$-0.437591\pi$
$419$	3341.64			0.389618			0.194809	+	0.980841i	$0.437591\pi$
$420$		0			0
$421$	−10585.4			−1.22542			−0.612708	−	0.790309i	$-0.709920\pi$
$421$	−10585.4			−1.22542			−0.612708	+	0.790309i	$0.709920\pi$
$422$	−10248.5	+	6002.00i	−1.18220	+	0.692353i
$423$		0			0
$424$	−65.4716	−	3519.10i	−0.00749901	−	0.403073i
$425$			3956.31i			0.451551i
$426$		0			0
$427$		−	281.546i		−	0.0319085i
$428$	7146.29	−	12740.0i	0.807077	−	1.43881i
$429$		0			0
$430$	−10442.8	−	17831.2i	−1.17115	−	1.99976i
$431$	4326.10			0.483482			0.241741	−	0.970341i	$-0.422281\pi$
$431$	4326.10			0.483482			0.241741	+	0.970341i	$0.422281\pi$
$432$		0			0
$433$	−11443.7			−1.27009			−0.635046	−	0.772474i	$-0.719019\pi$
$433$	−11443.7			−1.27009			−0.635046	+	0.772474i	$0.719019\pi$
$434$	1767.44	+	3017.92i	0.195483	+	0.333790i
$435$		0			0
$436$	−819.720	+	1461.36i	−0.0900401	+	0.160519i
$437$			1468.83i			0.160786i
$438$		0			0
$439$			16418.3i			1.78497i	0.451075	+	0.892486i	$0.351041\pi$
$439$			16418.3i			1.78497i	−0.451075	+	0.892486i	$0.648959\pi$
$440$	156.141	+	8392.60i	0.0169176	+	0.909321i
$441$		0			0
$442$	2939.92	−	1721.76i	0.316375	−	0.185285i
$443$	−13807.7			−1.48087			−0.740433	−	0.672130i	$-0.765380\pi$
$443$	−13807.7			−1.48087			−0.740433	+	0.672130i	$0.765380\pi$
$444$		0			0
$445$	−25120.7			−2.67604
$446$	−3716.00	+	2176.27i	−0.394524	+	0.231052i
$447$		0			0
$448$	133.312	+	3581.52i	0.0140589	+	0.377703i
$449$		−	934.788i		−	0.0982525i	−0.998793	−	0.0491263i	$-0.984356\pi$
$449$		−	934.788i		−	0.0982525i	0.998793	−	0.0491263i	$-0.0156437\pi$
$450$		0			0
$451$		−	1828.99i		−	0.190961i
$452$	7125.39	+	3996.86i	0.741483	+	0.415921i
$453$		0			0
$454$	2618.58	+	4471.25i	0.270696	+	0.462216i
$455$	−4167.22			−0.429368
$456$		0			0
$457$	−11772.2			−1.20499			−0.602493	−	0.798124i	$-0.705826\pi$
$457$	−11772.2			−1.20499			−0.602493	+	0.798124i	$0.705826\pi$
$458$	−596.558	−	1018.63i	−0.0608632	−	0.103925i
$459$		0			0
$460$	−5598.75	−	3140.51i	−0.567485	−	0.318320i
$461$			8920.56i			0.901240i	0.892716	+	0.450620i	$0.148797\pi$
$461$			8920.56i			0.901240i	−0.892716	+	0.450620i	$0.851203\pi$
$462$		0			0
$463$		−	4574.14i		−	0.459132i	−0.973293	−	0.229566i	$-0.926269\pi$
$463$		−	4574.14i		−	0.459132i	0.973293	−	0.229566i	$-0.0737307\pi$
$464$	11204.8	−	6845.09i	1.12105	−	0.684861i
$465$		0			0
$466$	−1053.39	+	616.916i	−0.104715	+	0.0613264i
$467$	−137.173			−0.0135923			−0.00679614	−	0.999977i	$-0.502163\pi$
$467$	−137.173			−0.0135923			−0.00679614	+	0.999977i	$0.502163\pi$
$468$		0			0
$469$	−5870.84			−0.578018
$470$	−13560.5	+	7941.66i	−1.33085	+	0.779407i
$471$		0			0
$472$	−17225.5	+	320.474i	−1.67980	+	0.0312521i
$473$		−	10887.6i		−	1.05837i
$474$		0			0
$475$			3579.13i			0.345730i
$476$	−874.601	+	1559.19i	−0.0842170	+	0.150138i
$477$		0			0
$478$	−4811.14	−	8215.07i	−0.460369	−	0.786084i
$479$	10928.1			1.04242			0.521210	−	0.853428i	$-0.325481\pi$
$479$	10928.1			1.04242			0.521210	+	0.853428i	$0.325481\pi$
$480$		0			0
$481$	12770.7			1.21059
$482$	−5797.06	−	9898.53i	−0.547819	−	0.935406i
$483$		0			0
$484$	3045.55	−	5429.46i	0.286021	−	0.509904i
$485$			19928.6i			1.86579i
$486$		0			0
$487$			9011.53i			0.838504i	0.907870	+	0.419252i	$0.137708\pi$
$487$			9011.53i			0.838504i	−0.907870	+	0.419252i	$0.862292\pi$
$488$	−909.936	+	16.9290i	−0.0844075	+	0.00157037i
$489$		0			0
$490$	1886.88	−	1105.05i	0.173960	−	0.101879i
$491$	−6797.47			−0.624777			−0.312388	−	0.949954i	$-0.601129\pi$
$491$	−6797.47			−0.624777			−0.312388	+	0.949954i	$0.601129\pi$
$492$		0			0
$493$	6549.49			0.598325
$494$	2659.64	−	1557.61i	0.242233	−	0.141863i
$495$		0			0
$496$	9647.43	−	5893.70i	0.873352	−	0.533538i
$497$			491.048i			0.0443189i
$498$		0			0
$499$			709.640i			0.0636630i	0.999493	+	0.0318315i	$0.0101340\pi$
$499$			709.640i			0.0636630i	−0.999493	+	0.0318315i	$0.989866\pi$
$500$	117.861	+	66.1117i	0.0105418	+	0.00591321i
$501$		0			0
$502$	−1748.02	−	2984.76i	−0.155414	−	0.265371i
$503$	1150.21			0.101959			0.0509795	−	0.998700i	$-0.483766\pi$
$503$	1150.21			0.101959			0.0509795	+	0.998700i	$0.483766\pi$
$504$		0			0
$505$	−23424.7			−2.06413
$506$	−1709.27	−	2918.60i	−0.150171	−	0.256418i
$507$		0			0
$508$	13978.0	+	7840.73i	1.22082	+	0.684795i
$509$			3194.56i			0.278186i	0.990279	+	0.139093i	$0.0444186\pi$
$509$			3194.56i			0.278186i	−0.990279	+	0.139093i	$0.955581\pi$
$510$		0			0
$511$			5087.52i			0.440428i
$512$	11567.2	−	646.207i	0.998443	−	0.0557784i
$513$		0			0
$514$	2277.26	−	1333.67i	0.195420	−	0.114447i
$515$	19629.6			1.67958
$516$		0			0
$517$	−8279.90			−0.704352
$518$	−5782.45	+	3386.48i	−0.490475	+	0.287246i
$519$		0			0
$520$	250.570	+	13468.2i	0.0211312	+	1.13580i
$521$			6422.65i			0.540079i	0.962849	+	0.270040i	$0.0870368\pi$
$521$			6422.65i			0.540079i	−0.962849	+	0.270040i	$0.912963\pi$
$522$		0			0
$523$			8840.42i			0.739129i	0.929205	+	0.369565i	$0.120493\pi$
$523$			8840.42i			0.739129i	−0.929205	+	0.369565i	$0.879507\pi$
$524$	−4574.97	+	8156.02i	−0.381409	+	0.679957i
$525$		0			0
$526$	−3895.77	−	6652.07i	−0.322934	−	0.551414i
$527$	5639.19			0.466123
$528$		0			0
$529$	−9580.37			−0.787406
$530$	3507.98	+	5989.91i	0.287503	+	0.490915i
$531$		0			0
$532$	−791.220	+	1410.55i	−0.0644807	+	0.114953i
$533$		−	2935.10i		−	0.238524i
$534$		0			0
$535$			28808.6i			2.32805i
$536$	353.007	+	18974.1i	0.0284469	+	1.52903i
$537$		0			0
$538$	16442.5	−	9629.51i	1.31763	−	0.771668i
$539$	1152.11			0.0920686
$540$		0			0
$541$	13395.6			1.06455			0.532275	−	0.846571i	$-0.321337\pi$
$541$	13395.6			1.06455			0.532275	+	0.846571i	$0.321337\pi$
$542$	10415.9	−	6100.05i	0.825463	−	0.483431i
$543$		0			0
$544$	5091.79	+	2732.90i	0.401303	+	0.215390i
$545$		−	3304.52i		−	0.259725i
$546$		0			0
$547$		−	16033.9i		−	1.25331i	−0.779297	−	0.626655i	$-0.784423\pi$
$547$		−	16033.9i		−	1.25331i	0.779297	−	0.626655i	$-0.215577\pi$
$548$	3300.15	+	1851.16i	0.257254	+	0.144302i
$549$		0			0
$550$	−4165.04	−	7111.85i	−0.322905	−	0.551364i
$551$	5925.09			0.458108
$552$		0			0
$553$	6946.15			0.534142
$554$	10669.6	+	18218.5i	0.818247	+	1.39717i
$555$		0			0
$556$	−19939.3	−	11184.6i	−1.52089	−	0.853117i
$557$		−	19550.5i		−	1.48722i	−0.668613	−	0.743610i	$-0.733112\pi$
$557$		−	19550.5i		−	1.48722i	0.668613	−	0.743610i	$-0.266888\pi$
$558$		0			0
$559$		−	17472.0i		−	1.32198i
$560$	−3684.89	−	6031.81i	−0.278062	−	0.455162i
$561$		0			0
$562$	−3763.33	+	2203.98i	−0.282467	+	0.165426i
$563$	−5558.55			−0.416101			−0.208051	−	0.978118i	$-0.566712\pi$
$563$	−5558.55			−0.416101			−0.208051	+	0.978118i	$0.566712\pi$
$564$		0			0
$565$	−16112.4			−1.19974
$566$	−14.2696	+	8.35698i	−0.00105971	+	0.000620619i
$567$		0			0
$568$	1587.03	−	29.5261i	0.117237	−	0.00218114i
$569$			24053.5i			1.77219i	0.463502	+	0.886096i	$0.346593\pi$
$569$			24053.5i			1.77219i	−0.463502	+	0.886096i	$0.653407\pi$
$570$		0			0
$571$		−	7034.11i		−	0.515531i	−0.966207	−	0.257766i	$-0.917014\pi$
$571$		−	7034.11i		−	0.515531i	0.966207	−	0.257766i	$-0.0829862\pi$
$572$	−3472.20	+	6190.06i	−0.253811	+	0.452481i
$573$		0			0
$574$	778.317	+	1328.98i	0.0565964	+	0.0966389i
$575$	6302.91			0.457130
$576$		0			0
$577$	21687.4			1.56475			0.782373	−	0.622810i	$-0.214009\pi$
$577$	21687.4			1.56475			0.782373	+	0.622810i	$0.214009\pi$
$578$	−5565.79	−	9503.65i	−0.400530	−	0.683909i
$579$		0			0
$580$	−12668.5	+	22584.8i	−0.906950	+	1.61686i
$581$		−	7817.97i		−	0.558252i
$582$		0			0
$583$			3657.39i			0.259817i
$584$	16442.5	−	305.907i	1.16506	−	0.0216755i
$585$		0			0
$586$	−20115.1	+	11780.4i	−1.41800	+	0.830448i
$587$	−19803.0			−1.39243			−0.696215	−	0.717833i	$-0.745134\pi$
$587$	−19803.0			−1.39243			−0.696215	+	0.717833i	$0.745134\pi$
$588$		0			0
$589$	5101.57			0.356887
$590$	29319.7	−	17171.0i	2.04589	−	1.19817i
$591$		0			0
$592$	11292.5	+	18484.8i	0.783988	+	1.28331i
$593$			2320.01i			0.160660i	0.996768	+	0.0803301i	$0.0255974\pi$
$593$			2320.01i			0.160660i	−0.996768	+	0.0803301i	$0.974403\pi$
$594$		0			0
$595$		−	3525.76i		−	0.242928i
$596$	−21468.7	−	12042.5i	−1.47549	−	0.827649i
$597$		0			0
$598$	−2742.98	−	4683.68i	−0.187574	−	0.320284i
$599$	9216.77			0.628693			0.314346	−	0.949308i	$-0.398215\pi$
$599$	9216.77			0.628693			0.314346	+	0.949308i	$0.398215\pi$
$600$		0			0
$601$	3122.88			0.211955			0.105977	−	0.994369i	$-0.466203\pi$
$601$	3122.88			0.211955			0.105977	+	0.994369i	$0.466203\pi$
$602$	4633.15	+	7911.15i	0.313676	+	0.535605i
$603$		0			0
$604$	9135.90	+	5124.62i	0.615455	+	0.345228i
$605$			12277.5i			0.825041i
$606$		0			0
$607$		−	13819.8i		−	0.924099i	−0.886854	−	0.462049i	$-0.847114\pi$
$607$		−	13819.8i		−	0.924099i	0.886854	−	0.462049i	$-0.152886\pi$
$608$	4606.36	+	2472.35i	0.307258	+	0.164913i
$609$		0			0
$610$	1548.81	−	907.058i	0.102803	−	0.0602061i
$611$	−13287.3			−0.879782
$612$		0			0
$613$	21961.3			1.44700			0.723498	−	0.690327i	$-0.242533\pi$
$613$	21961.3			1.44700			0.723498	+	0.690327i	$0.242533\pi$
$614$	−22366.4	+	13098.8i	−1.47009	+	0.860953i
$615$		0			0
$616$	−69.2751	−	3723.54i	−0.00453112	−	0.243548i
$617$		−	8350.99i		−	0.544892i	−0.962171	−	0.272446i	$-0.912167\pi$
$617$		−	8350.99i		−	0.544892i	0.962171	−	0.272446i	$-0.0878326\pi$
$618$		0			0
$619$			9479.90i			0.615556i	0.951458	+	0.307778i	$0.0995854\pi$
$619$			9479.90i			0.615556i	−0.951458	+	0.307778i	$0.900415\pi$
$620$	−10907.7	+	19445.7i	−0.706556	+	1.25961i
$621$		0			0
$622$	12531.7	+	21398.0i	0.807837	+	1.37939i
$623$	11145.3			0.716737
$624$		0			0
$625$	−15757.7			−1.00849
$626$	2059.67	+	3516.90i	0.131503	+	0.224543i
$627$		0			0
$628$	−191.748	+	341.838i	−0.0121840	+	0.0217211i
$629$			10804.9i			0.684927i
$630$		0			0
$631$		−	12675.6i		−	0.799693i	−0.916582	−	0.399846i	$-0.869063\pi$
$631$		−	12675.6i		−	0.799693i	0.916582	−	0.399846i	$-0.130937\pi$
$632$	−417.664	−	22449.5i	−0.0262876	−	1.41296i
$633$		0			0
$634$	3549.94	−	2079.02i	0.222376	−	0.130234i
$635$	−31608.1			−1.97532
$636$		0			0
$637$	1848.87			0.115000
$638$	−11773.3	+	6895.03i	−0.730581	+	0.427863i
$639$		0			0
$640$	−19272.8	+	12272.0i	−1.19035	+	0.757957i
$641$			415.766i			0.0256190i	0.999918	+	0.0128095i	$0.00407750\pi$
$641$			415.766i			0.0256190i	−0.999918	+	0.0128095i	$0.995922\pi$
$642$		0			0
$643$			1748.72i			0.107252i	0.998561	+	0.0536258i	$0.0170778\pi$
$643$			1748.72i			0.107252i	−0.998561	+	0.0536258i	$0.982922\pi$
$644$	2484.00	+	1393.35i	0.151992	+	0.0852574i
$645$		0			0
$646$	1317.85	+	2250.24i	0.0802633	+	0.137051i
$647$	17144.4			1.04175			0.520877	−	0.853632i	$-0.325605\pi$
$647$	17144.4			1.04175			0.520877	+	0.853632i	$0.325605\pi$
$648$		0			0
$649$	17902.4			1.08279
$650$	−6683.91	−	11412.8i	−0.403330	−	0.688690i
$651$		0			0
$652$	12986.3	+	7284.42i	0.780034	+	0.437546i
$653$			13708.4i			0.821520i	0.911743	+	0.410760i	$0.134737\pi$
$653$			13708.4i			0.821520i	−0.911743	+	0.410760i	$0.865263\pi$
$654$		0			0
$655$		−	18442.9i		−	1.10019i
$656$	4248.38	−	2595.37i	0.252853	−	0.154470i
$657$		0			0
$658$	6016.37	−	3523.47i	0.356448	−	0.208753i
$659$	−3117.98			−0.184308			−0.0921542	−	0.995745i	$-0.529375\pi$
$659$	−3117.98			−0.184308			−0.0921542	+	0.995745i	$0.529375\pi$
$660$		0			0
$661$	21138.9			1.24389			0.621944	−	0.783062i	$-0.286343\pi$
$661$	21138.9			1.24389			0.621944	+	0.783062i	$0.286343\pi$
$662$	587.437	−	344.031i	0.0344885	−	0.0201981i
$663$		0			0
$664$	−25267.1	+	470.085i	−1.47674	+	0.0274742i
$665$		−	3189.62i		−	0.185998i
$666$		0			0
$667$		−	10434.2i		−	0.605717i
$668$	−1081.45	+	1927.96i	−0.0626386	+	0.111669i
$669$		0			0
$670$	−18914.1	−	32296.1i	−1.09062	−	1.86225i
$671$	945.691			0.0544083
$672$		0			0
$673$	−2307.32			−0.132156			−0.0660778	−	0.997814i	$-0.521049\pi$
$673$	−2307.32			−0.132156			−0.0660778	+	0.997814i	$0.521049\pi$
$674$	1990.37	+	3398.58i	0.113748	+	0.194226i
$675$		0			0
$676$	3026.50	−	5395.48i	0.172195	−	0.306980i
$677$		−	3314.25i		−	0.188149i	−0.995565	−	0.0940746i	$-0.970011\pi$
$677$		−	3314.25i		−	0.188149i	0.995565	−	0.0940746i	$-0.0299892\pi$
$678$		0			0
$679$		−	8841.71i		−	0.499725i
$680$	−11395.0	+	212.000i	−0.642615	+	0.0119556i
$681$		0			0
$682$	−10137.0	+	5936.70i	−0.569157	+	0.333325i
$683$	−24300.2			−1.36138			−0.680690	−	0.732571i	$-0.738320\pi$
$683$	−24300.2			−1.36138			−0.680690	+	0.732571i	$0.738320\pi$
$684$		0			0
$685$	−7462.52			−0.416246
$686$	−837.151	+	490.276i	−0.0465927	+	0.0272869i
$687$		0			0
$688$	25289.7	−	15449.7i	1.40140	−	0.856125i
$689$			5869.25i			0.324529i
$690$		0			0
$691$		−	24627.2i		−	1.35580i	−0.735152	−	0.677902i	$-0.762889\pi$
$691$		−	24627.2i		−	1.35580i	0.735152	−	0.677902i	$-0.237111\pi$
$692$	−2123.00	−	1190.86i	−0.116625	−	0.0654184i
$693$		0			0
$694$	11764.1	+	20087.3i	0.643455	+	1.09871i
$695$	45088.2			2.46085
$696$		0			0
$697$	2483.29			0.134952
$698$	−3285.28	−	5609.66i	−0.178152	−	0.304196i
$699$		0			0
$700$	6052.83	+	3395.22i	0.326822	+	0.183325i
$701$			11630.1i			0.626625i	0.949650	+	0.313313i	$0.101439\pi$
$701$			11630.1i			0.626625i	−0.949650	+	0.313313i	$0.898561\pi$
$702$		0			0
$703$			9774.79i			0.524414i
$704$	−12030.1	+	447.784i	−0.644034	+	0.0239723i
$705$		0			0
$706$	16587.6	−	9714.47i	0.884251	−	0.517859i
$707$	10392.8			0.552846
$708$		0			0
$709$	22039.3			1.16742			0.583711	−	0.811961i	$-0.301600\pi$
$709$	22039.3			1.16742			0.583711	+	0.811961i	$0.301600\pi$
$710$	−2701.31	+	1582.01i	−0.142786	+	0.0836224i
$711$		0			0
$712$	−670.154	−	36020.8i	−0.0352740	−	1.89598i
$713$		−	8983.95i		−	0.471881i
$714$		0			0
$715$		−	13997.4i		−	0.732129i
$716$	11070.7	−	19736.3i	0.577837	−	1.03014i
$717$		0			0
$718$	16084.3	+	27464.1i	0.836018	+	1.42751i
$719$	30873.4			1.60137			0.800684	−	0.599087i	$-0.204470\pi$
$719$	30873.4			1.60137			0.800684	+	0.599087i	$0.204470\pi$
$720$		0			0
$721$	−8709.04			−0.449850
$722$	−8611.87	−	14704.9i	−0.443907	−	0.757976i
$723$		0			0
$724$	−8962.31	+	15977.5i	−0.460057	+	0.820167i
$725$		−	25425.3i		−	1.30244i
$726$		0			0
$727$			4726.44i			0.241120i	0.992706	+	0.120560i	$0.0384690\pi$
$727$			4726.44i			0.241120i	−0.992706	+	0.120560i	$0.961531\pi$
$728$	−111.170	−	5975.41i	−0.00565968	−	0.304208i
$729$		0			0
$730$	−27987.0	+	16390.5i	−1.41897	+	0.831014i
$731$	14782.5			0.747949
$732$		0			0
$733$	−13188.7			−0.664580			−0.332290	−	0.943177i	$-0.607821\pi$
$733$	−13188.7			−0.664580			−0.332290	+	0.943177i	$0.607821\pi$
$734$	5304.94	−	3106.83i	0.266770	−	0.156233i
$735$		0			0
$736$	4353.85	−	8111.88i	0.218051	−	0.406261i
$737$		−	19719.7i		−	0.985597i
$738$		0			0
$739$			16007.0i			0.796786i	0.917215	+	0.398393i	$0.130432\pi$
$739$			16007.0i			0.796786i	−0.917215	+	0.398393i	$0.869568\pi$
$740$	−37258.7	−	20899.6i	−1.85089	−	1.03822i
$741$		0			0
$742$	−1556.38	−	2657.54i	−0.0770036	−	0.131484i
$743$	−8589.38			−0.424110			−0.212055	−	0.977258i	$-0.568016\pi$
$743$	−8589.38			−0.424110			−0.212055	+	0.977258i	$0.568016\pi$
$744$		0			0
$745$	48546.5			2.38739
$746$	−19715.2	−	33663.9i	−0.967593	−	1.65218i
$747$		0			0
$748$	−5237.22	−	2937.72i	−0.256005	−	0.143601i
$749$		−	12781.5i		−	0.623534i
$750$		0			0
$751$		−	15818.0i		−	0.768585i	−0.923211	−	0.384292i	$-0.874445\pi$
$751$		−	15818.0i		−	0.768585i	0.923211	−	0.384292i	$-0.125555\pi$
$752$	−11749.4	−	19232.6i	−0.569755	−	0.932635i
$753$		0			0
$754$	−18893.5	+	11064.9i	−0.912545	+	0.534430i
$755$	−20658.7			−0.995826
$756$		0			0
$757$	−10993.9			−0.527846			−0.263923	−	0.964544i	$-0.585016\pi$
$757$	−10993.9			−0.527846			−0.263923	+	0.964544i	$0.585016\pi$
$758$	988.307	−	578.800i	0.0473574	−	0.0277348i
$759$		0			0
$760$	−10308.6	+	191.788i	−0.492018	+	0.00915381i
$761$			15944.5i			0.759508i	0.925087	+	0.379754i	$0.123991\pi$
$761$			15944.5i			0.759508i	−0.925087	+	0.379754i	$0.876009\pi$
$762$		0			0
$763$			1466.12i			0.0695635i
$764$	−1229.26	+	2191.46i	−0.0582107	+	0.103775i
$765$		0			0
$766$	13814.7	+	23588.8i	0.651627	+	1.11266i
$767$	28729.1			1.35247
$768$		0			0
$769$	−21870.6			−1.02558			−0.512792	−	0.858513i	$-0.671389\pi$
$769$	−21870.6			−1.02558			−0.512792	+	0.858513i	$0.671389\pi$
$770$	3711.77	+	6337.88i	0.173718	+	0.296625i
$771$		0			0
$772$	8348.70	−	14883.6i	0.389218	−	0.693878i
$773$		−	19936.1i		−	0.927620i	−0.885935	−	0.463810i	$-0.846482\pi$
$773$		−	19936.1i		−	0.927620i	0.885935	−	0.463810i	$-0.153518\pi$
$774$		0			0
$775$		−	21891.4i		−	1.01466i
$776$	−28575.8	+	531.641i	−1.32192	+	0.0245938i
$777$		0			0
$778$	8163.95	−	4781.20i	0.376211	−	0.220327i
$779$	2246.55			0.103326
$780$		0			0
$781$	−1649.39			−0.0755697
$782$	3962.72	−	2320.76i	0.181210	−	0.106125i
$783$		0			0
$784$	1634.87	+	2676.13i	0.0744749	+	0.121908i
$785$		−	772.988i		−	0.0351454i
$786$		0			0
$787$			27000.3i			1.22294i	0.791266	+	0.611472i	$0.209422\pi$
$787$			27000.3i			1.22294i	−0.791266	+	0.611472i	$0.790578\pi$
$788$	10540.2	+	5912.31i	0.476495	+	0.267281i
$789$		0			0
$790$	22378.5	+	38211.5i	1.00784	+	1.72089i
$791$	7148.60			0.321334
$792$		0			0
$793$	1517.61			0.0679597
$794$	−7779.72	−	13284.0i	−0.347723	−	0.593741i
$795$		0			0
$796$	−2289.68	−	1284.35i	−0.101954	−	0.0571893i
$797$		−	16938.8i		−	0.752826i	−0.926452	−	0.376413i	$-0.877157\pi$
$797$		−	16938.8i		−	0.752826i	0.926452	−	0.376413i	$-0.122843\pi$
$798$		0			0
$799$		−	11242.0i		−	0.497763i
$800$	10609.2	−	19766.5i	0.468863	−	0.873562i
$801$		0			0
$802$	−34572.7	+	20247.4i	−1.52220	+	0.891473i
$803$	−17088.6			−0.750989
$804$		0			0
$805$	−5616.98			−0.245929
$806$	−16267.5	+	9527.01i	−0.710915	+	0.416346i
$807$		0			0
$808$	−624.908	−	33588.9i	−0.0272081	−	1.46244i
$809$			9479.48i			0.411966i	0.978556	+	0.205983i	$0.0660392\pi$
$809$			9479.48i			0.411966i	−0.978556	+	0.205983i	$0.933961\pi$
$810$		0			0
$811$		−	32925.6i		−	1.42562i	−0.701359	−	0.712808i	$-0.747423\pi$
$811$		−	32925.6i		−	1.42562i	0.701359	−	0.712808i	$-0.252577\pi$
$812$	5620.63	−	10020.2i	0.242913	−	0.433053i
$813$		0			0
$814$	−11374.9	−	19422.8i	−0.489792	−	0.836326i
$815$	−29365.5			−1.26212
$816$		0			0
$817$	13373.2			0.572667
$818$	−13676.9	−	23353.5i	−0.584599	−	0.998210i
$819$		0			0
$820$	−4803.37	+	8563.20i	−0.204562	+	0.364683i
$821$			9381.63i			0.398808i	0.979917	+	0.199404i	$0.0639006\pi$
$821$			9381.63i			0.398808i	−0.979917	+	0.199404i	$0.936099\pi$
$822$		0			0
$823$			35540.1i			1.50529i	0.658428	+	0.752644i	$0.271222\pi$
$823$			35540.1i			1.50529i	−0.658428	+	0.752644i	$0.728778\pi$
$824$	523.664	+	28147.0i	0.0221392	+	1.18999i
$825$		0			0
$826$	−13008.3	+	7618.27i	−0.547961	+	0.320912i
$827$	−1743.92			−0.0733278			−0.0366639	−	0.999328i	$-0.511673\pi$
$827$	−1743.92			−0.0733278			−0.0366639	+	0.999328i	$0.511673\pi$
$828$		0			0
$829$	−43358.5			−1.81653			−0.908264	−	0.418398i	$-0.862592\pi$
$829$	−43358.5			−1.81653			−0.908264	+	0.418398i	$0.862592\pi$
$830$	43007.5	−	25187.2i	1.79857	−	1.05333i
$831$		0			0
$832$	−19305.4	+	718.589i	−0.804442	+	0.0299430i
$833$			1564.27i			0.0650646i
$834$		0			0
$835$		−	4359.62i		−	0.180684i
$836$	−4737.92	−	2657.65i	−0.196010	−	0.109948i
$837$		0			0
$838$	−4776.46	−	8155.86i	−0.196898	−	0.336205i
$839$	13882.5			0.571248			0.285624	−	0.958342i	$-0.407799\pi$
$839$	13882.5			0.571248			0.285624	+	0.958342i	$0.407799\pi$
$840$		0			0
$841$	−17701.4			−0.725794
$842$	15130.5	+	25835.5i	0.619277	+	1.05742i
$843$		0			0
$844$	29297.9	+	16434.1i	1.19487	+	0.670242i
$845$			12200.6i			0.496704i
$846$		0			0
$847$		−	5447.14i		−	0.220975i
$848$	−8495.40	+	5189.92i	−0.344025	+	0.210168i
$849$		0			0
$850$	9656.06	−	5655.05i	0.389647	−	0.228196i
$851$	17213.6			0.693388
$852$		0			0
$853$	26331.9			1.05696			0.528480	−	0.848946i	$-0.322762\pi$
$853$	26331.9			1.05696			0.528480	+	0.848946i	$0.322762\pi$
$854$	−687.161	+	402.434i	−0.0275342	+	0.0161253i
$855$		0			0
$856$	−41309.0	+	768.538i	−1.64943	+	0.0306870i
$857$			23177.4i			0.923832i	0.886924	+	0.461916i	$0.152838\pi$
$857$			23177.4i			0.923832i	−0.886924	+	0.461916i	$0.847162\pi$
$858$		0			0
$859$		−	27339.6i		−	1.08593i	−0.839755	−	0.542965i	$-0.817302\pi$
$859$		−	27339.6i		−	1.08593i	0.839755	−	0.542965i	$-0.182698\pi$
$860$	−28593.4	+	50974.9i	−1.13375	+	2.02120i
$861$		0			0
$862$	−6183.62	−	10558.6i	−0.244333	−	0.417201i
$863$	−10007.4			−0.394736			−0.197368	−	0.980330i	$-0.563239\pi$
$863$	−10007.4			−0.394736			−0.197368	+	0.980330i	$0.563239\pi$
$864$		0			0
$865$	4800.67			0.188702
$866$	16357.4	+	27930.4i	0.641854	+	1.09597i
$867$		0			0
$868$	4839.43	−	8627.48i	0.189241	−	0.337368i
$869$			23331.6i			0.910784i
$870$		0			0
$871$		−	31645.5i		−	1.23108i
$872$	4738.38	−	88.1557i	0.184016	−	0.00342354i
$873$		0			0
$874$	3584.93	−	2099.50i	0.138744	−	0.0812549i
$875$	118.244			0.00456845
$876$		0			0
$877$	33763.4			1.30001			0.650005	−	0.759930i	$-0.274767\pi$
$877$	33763.4			1.30001			0.650005	+	0.759930i	$0.274767\pi$
$878$	40071.7	−	23467.9i	1.54027	−	0.902054i
$879$		0			0
$880$	20260.4	−	12377.3i	0.776111	−	0.474133i
$881$			2440.72i			0.0933372i	0.998910	+	0.0466686i	$0.0148605\pi$
$881$			2440.72i			0.0933372i	−0.998910	+	0.0466686i	$0.985140\pi$
$882$		0			0
$883$		−	11198.0i		−	0.426777i	−0.976967	−	0.213388i	$-0.931550\pi$
$883$		−	11198.0i		−	0.426777i	0.976967	−	0.213388i	$-0.0684499\pi$
$884$	−8404.51	−	4714.35i	−0.319767	−	0.179367i
$885$		0			0
$886$	19736.4	+	33700.1i	0.748371	+	1.27785i
$887$	−40801.1			−1.54449			−0.772247	−	0.635322i	$-0.780867\pi$
$887$	−40801.1			−1.54449			−0.772247	+	0.635322i	$0.780867\pi$
$888$		0			0
$889$	14023.6			0.529061
$890$	35906.9	+	61311.5i	1.35236	+	2.30917i
$891$		0			0
$892$	10623.1	+	5958.83i	0.398753	+	0.223673i
$893$		−	10170.2i		−	0.381112i
$894$		0			0
$895$			44629.0i			1.66680i
$896$	8550.77	−	5444.71i	0.318818	−	0.203008i
$897$		0			0
$898$	−2281.51	+	1336.16i	−0.0847829	+	0.0496529i
$899$	−36240.3			−1.34447
$900$		0			0
$901$	−4965.79			−0.183612
$902$	−4463.96	+	2614.31i	−0.164782	+	0.0965043i
$903$		0			0
$904$	−429.837	−	23103.8i	−0.0158143	−	0.850022i
$905$		−	36129.5i		−	1.32706i
$906$		0			0
$907$			13257.2i			0.485334i	0.970110	+	0.242667i	$0.0780222\pi$
$907$			13257.2i			0.485334i	−0.970110	+	0.242667i	$0.921978\pi$
$908$	7169.93	−	12782.2i	0.262051	−	0.467172i
$909$		0			0
$910$	5956.52	+	10170.8i	0.216985	+	0.370505i
$911$	10748.9			0.390919			0.195460	−	0.980712i	$-0.437380\pi$
$911$	10748.9			0.390919			0.195460	+	0.980712i	$0.437380\pi$
$912$		0			0
$913$	26260.0			0.951894
$914$	16826.8	+	28732.0i	0.608953	+	1.03979i
$915$		0			0
$916$	−1633.44	+	2912.01i	−0.0589195	+	0.105039i
$917$			8182.58i			0.294670i
$918$		0			0
$919$			36773.1i			1.31995i	0.751289	+	0.659973i	$0.229432\pi$
$919$			36773.1i			1.31995i	−0.751289	+	0.659973i	$0.770568\pi$
$920$	337.742	+	18153.7i	0.0121033	+	0.650554i
$921$		0			0
$922$	21772.2	−	12750.8i	0.777688	−	0.455451i
$923$	−2646.89			−0.0943917
$924$		0			0
$925$	41944.8			1.49096
$926$	−11164.0	+	6538.16i	−0.396189	+	0.232027i
$927$		0			0
$928$	−32722.5	−	17563.0i	−1.15751	−	0.621264i
$929$			48989.7i			1.73014i	0.501651	+	0.865070i	$0.332726\pi$
$929$			48989.7i			1.73014i	−0.501651	+	0.865070i	$0.667274\pi$
$930$		0			0
$931$			1415.14i			0.0498167i
$932$	3011.38	+	1689.18i	0.105838	+	0.0593679i
$933$		0			0
$934$	196.071	+	334.794i	0.00686900	+	0.0117289i
$935$	11842.8			0.414224
$936$		0			0
$937$	−36515.8			−1.27313			−0.636564	−	0.771224i	$-0.719645\pi$
$937$	−36515.8			−1.27313			−0.636564	+	0.771224i	$0.719645\pi$
$938$	8391.63	+	14328.8i	0.292107	+	0.498776i
$939$		0			0
$940$	38766.0	+	21745.1i	1.34511	+	0.754517i
$941$			5560.99i			0.192650i	0.995350	+	0.0963248i	$0.0307087\pi$
$941$			5560.99i			0.192650i	−0.995350	+	0.0963248i	$0.969291\pi$
$942$		0			0
$943$		−	3956.21i		−	0.136619i
$944$	25403.9	+	41583.7i	0.875874	+	1.43372i
$945$		0			0
$946$	−26573.0	+	15562.4i	−0.913279	+	0.534860i
$947$	42010.7			1.44157			0.720783	−	0.693160i	$-0.243782\pi$
$947$	42010.7			1.44157			0.720783	+	0.693160i	$0.243782\pi$
$948$		0			0
$949$	−27423.2			−0.938035
$950$	8735.49	−	5115.92i	0.298333	−	0.174718i
$951$		0			0
$952$	5055.62	−	94.0578i	0.172115	−	0.00320213i
$953$		−	34345.1i		−	1.16742i	−0.811964	−	0.583708i	$-0.801601\pi$
$953$		−	34345.1i		−	1.16742i	0.811964	−	0.583708i	$-0.198399\pi$
$954$		0			0
$955$		−	4955.48i		−	0.167911i
$956$	−13173.4	+	23484.8i	−0.445667	+	0.794512i
$957$		0			0
$958$	−15620.4	−	26672.0i	−0.526798	−	0.899513i
$959$	3310.90			0.111485
$960$		0			0
$961$	−1412.29			−0.0474064
$962$	−18254.1	−	31169.1i	−0.611783	−	1.04463i
$963$		0			0
$964$	−15872.9	+	28297.4i	−0.530324	+	0.945435i
$965$			33655.9i			1.12272i
$966$		0			0
$967$		−	10449.5i		−	0.347499i	−0.984790	−	0.173750i	$-0.944412\pi$
$967$		−	10449.5i		−	0.347499i	0.984790	−	0.173750i	$-0.0555884\pi$
$968$	−17604.8	+	327.530i	−0.584544	+	0.0108752i
$969$		0			0
$970$	48639.1	−	28485.4i	1.61001	−	0.942898i
$971$	−17540.5			−0.579713			−0.289857	−	0.957070i	$-0.593608\pi$
$971$	−17540.5			−0.579713			−0.289857	+	0.957070i	$0.593608\pi$
$972$		0			0
$973$	−20004.3			−0.659104
$974$	21994.2	−	12880.9i	0.723552	−	0.423747i
$975$		0			0
$976$	1341.96	+	2196.66i	0.0440113	+	0.0720423i
$977$			42272.5i			1.38425i	0.721776	+	0.692127i	$0.243326\pi$
$977$			42272.5i			1.38425i	−0.721776	+	0.692127i	$0.756674\pi$
$978$		0			0
$979$			37436.3i			1.22213i
$980$	−5394.11	−	3025.73i	−0.175825	−	0.0986258i
$981$		0			0
$982$	9716.13	+	16590.4i	0.315737	+	0.539125i
$983$	20775.1			0.674084			0.337042	−	0.941490i	$-0.390574\pi$
$983$	20775.1			0.674084			0.337042	+	0.941490i	$0.390574\pi$
$984$		0			0
$985$	−23834.1			−0.770984
$986$	−9361.68	−	15985.2i	−0.302370	−	0.516300i
$987$		0			0
$988$	−7603.26	−	4264.91i	−0.244830	−	0.137333i
$989$		−	23550.4i		−	0.757190i
$990$		0			0
$991$			12344.0i			0.395683i	0.980234	+	0.197841i	$0.0633931\pi$
$991$			12344.0i			0.395683i	−0.980234	+	0.197841i	$0.936607\pi$
$992$	−28174.4	−	15121.9i	−0.901752	−	0.483993i
$993$		0			0
$994$	1198.49	−	701.892i	0.0382432	−	0.0223970i
$995$	5177.58			0.164965
$996$		0			0
$997$	−50011.2			−1.58864			−0.794319	−	0.607501i	$-0.792172\pi$
$997$	−50011.2			−1.58864			−0.794319	+	0.607501i	$0.792172\pi$
$998$	1732.00	−	1014.34i	0.0549354	−	0.0321728i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.4.e.a.71.11	✓	36
3.2	odd	2	inner	252.4.e.a.71.26	yes	36
4.3	odd	2	inner	252.4.e.a.71.25	yes	36
12.11	even	2	inner	252.4.e.a.71.12	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.4.e.a.71.11	✓	36	1.1	even	1	trivial
252.4.e.a.71.12	yes	36	12.11	even	2	inner
252.4.e.a.71.25	yes	36	4.3	odd	2	inner
252.4.e.a.71.26	yes	36	3.2	odd	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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	252.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.42938 - 2.44067i) q^{2} +(-3.91377 + 6.97728i) q^{4} -15.7775i q^{5} +7.00000i q^{7} +(22.6235 - 0.420902i) q^{8} +(-38.5077 + 22.5520i) q^{10} -23.5125 q^{11} -37.7320 q^{13} +(17.0847 - 10.0056i) q^{14} +(-33.3648 - 54.6150i) q^{16} -31.9239i q^{17} -28.8804i q^{19} +(110.084 + 61.7495i) q^{20} +(33.6082 + 57.3863i) q^{22} -50.8589 q^{23} -123.929 q^{25} +(53.9332 + 92.0916i) q^{26} +(-48.8409 - 27.3964i) q^{28} +205.159i q^{29} +176.645i q^{31} +(-85.6065 + 159.498i) q^{32} +(-77.9159 + 45.6313i) q^{34} +110.442 q^{35} -338.457 q^{37} +(-70.4877 + 41.2810i) q^{38} +(-6.64077 - 356.942i) q^{40} +77.7879i q^{41} +463.054i q^{43} +(92.0225 - 164.053i) q^{44} +(72.6965 + 124.130i) q^{46} +352.149 q^{47} -49.0000 q^{49} +(177.142 + 302.471i) q^{50} +(147.675 - 263.267i) q^{52} -155.551i q^{53} +370.968i q^{55} +(2.94631 + 158.365i) q^{56} +(500.727 - 293.250i) q^{58} -761.398 q^{59} -40.2208 q^{61} +(431.132 - 252.491i) q^{62} +(511.646 - 19.0445i) q^{64} +595.317i q^{65} +838.691i q^{67} +(222.742 + 124.943i) q^{68} +(-157.864 - 269.554i) q^{70} +70.1497 q^{71} +726.789 q^{73} +(483.783 + 826.064i) q^{74} +(201.507 + 113.031i) q^{76} -164.587i q^{77} -992.308i q^{79} +(-861.687 + 526.412i) q^{80} +(189.855 - 111.188i) q^{82} -1116.85 q^{83} -503.680 q^{85} +(1130.16 - 661.878i) q^{86} +(-531.935 + 9.89644i) q^{88} -1592.19i q^{89} -264.124i q^{91} +(199.050 - 354.857i) q^{92} +(-503.353 - 859.481i) q^{94} -455.661 q^{95} -1263.10 q^{97} +(70.0394 + 119.593i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 24 q^{4} + 264 q^{10} - 468 q^{16} + 444 q^{22} - 900 q^{25} - 84 q^{28} - 432 q^{34} - 264 q^{37} + 1416 q^{40} + 180 q^{46} - 1764 q^{49} + 2736 q^{52} + 636 q^{58} - 3960 q^{61} + 1392 q^{64}+ \cdots + 5496 q^{94}+O(q^{100}) \) 36 * q - 24 * q^4 + 264 * q^10 - 468 * q^16 + 444 * q^22 - 900 * q^25 - 84 * q^28 - 432 * q^34 - 264 * q^37 + 1416 * q^40 + 180 * q^46 - 1764 * q^49 + 2736 * q^52 + 636 * q^58 - 3960 * q^61 + 1392 * q^64 - 504 * q^70 - 2520 * q^76 + 1032 * q^82 - 3144 * q^85 + 2748 * q^88 + 5496 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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