LMFDB - Embedded newform 363.4.d.d.362.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [363,4,Mod(362,363)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(363, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("363.362");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 363 = 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	363.d (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:	$21.4176933321$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	no (minimal twist has level 33)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			362.18
Character	$\chi$	$=$	363.362
Dual form			363.4.d.d.362.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.05192 q^{2} +(-1.20902 - 5.05354i) q^{3} -6.89347 q^{4} +12.2895i q^{5} +(1.27179 + 5.31590i) q^{6} -22.4006i q^{7} +15.6667 q^{8} +(-24.0765 + 12.2197i) q^{9} +O(q^{10})$	\(q-1.05192 q^{2} +(-1.20902 - 5.05354i) q^{3} -6.89347 q^{4} +12.2895i q^{5} +(1.27179 + 5.31590i) q^{6} -22.4006i q^{7} +15.6667 q^{8} +(-24.0765 + 12.2197i) q^{9} -12.9275i q^{10} +(8.33435 + 34.8364i) q^{12} +79.2941i q^{13} +23.5636i q^{14} +(62.1054 - 14.8582i) q^{15} +38.6677 q^{16} -33.3165 q^{17} +(25.3265 - 12.8541i) q^{18} +36.1195i q^{19} -84.7171i q^{20} +(-113.202 + 27.0828i) q^{21} -134.233i q^{23} +(-18.9414 - 79.1723i) q^{24} -26.0312 q^{25} -83.4108i q^{26} +(90.8616 + 106.898i) q^{27} +154.418i q^{28} +108.399 q^{29} +(-65.3297 + 15.6296i) q^{30} +31.3155 q^{31} -166.009 q^{32} +35.0462 q^{34} +275.292 q^{35} +(165.971 - 84.2360i) q^{36} +7.96593 q^{37} -37.9947i q^{38} +(400.716 - 95.8682i) q^{39} +192.535i q^{40} -7.43487 q^{41} +(119.080 - 28.4889i) q^{42} -74.3056i q^{43} +(-150.173 - 295.888i) q^{45} +141.202i q^{46} -512.670i q^{47} +(-46.7501 - 195.409i) q^{48} -158.788 q^{49} +27.3826 q^{50} +(40.2804 + 168.366i) q^{51} -546.611i q^{52} -344.751i q^{53} +(-95.5789 - 112.448i) q^{54} -350.944i q^{56} +(182.531 - 43.6693i) q^{57} -114.027 q^{58} -586.208i q^{59} +(-428.121 + 102.425i) q^{60} -256.349i q^{61} -32.9413 q^{62} +(273.728 + 539.329i) q^{63} -134.714 q^{64} -974.483 q^{65} +664.138 q^{67} +229.667 q^{68} +(-678.351 + 162.290i) q^{69} -289.584 q^{70} -3.86140i q^{71} +(-377.200 + 191.442i) q^{72} -201.573i q^{73} -8.37949 q^{74} +(31.4722 + 131.550i) q^{75} -248.989i q^{76} +(-421.520 + 100.845i) q^{78} -181.739i q^{79} +475.206i q^{80} +(430.359 - 588.415i) q^{81} +7.82086 q^{82} +763.116 q^{83} +(780.358 - 186.695i) q^{84} -409.443i q^{85} +78.1633i q^{86} +(-131.057 - 547.800i) q^{87} +311.998i q^{89} +(157.970 + 311.250i) q^{90} +1776.24 q^{91} +925.330i q^{92} +(-37.8611 - 158.254i) q^{93} +539.286i q^{94} -443.890 q^{95} +(200.708 + 838.932i) q^{96} +748.285 q^{97} +167.032 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 8 q^{3} + 132 q^{4} - 60 q^{9}+O(q^{10}) $ 40 * q - 8 * q^3 + 132 * q^4 - 60 * q^9	$ 40 q - 8 q^{3} + 132 q^{4} - 60 q^{9} - 90 q^{12} - 212 q^{15} + 460 q^{16} + 296 q^{25} + 280 q^{27} - 320 q^{31} - 188 q^{34} - 2254 q^{36} + 796 q^{37} + 1240 q^{42} - 1662 q^{45} - 486 q^{48} + 1536 q^{49} + 2268 q^{58} - 6636 q^{60} - 1512 q^{64} + 4556 q^{67} - 1140 q^{69} - 4276 q^{70} + 3462 q^{75} - 7640 q^{78} + 3572 q^{81} + 9408 q^{82} - 816 q^{91} - 11516 q^{93} - 7916 q^{97}+O(q^{100}) $ 40 * q - 8 * q^3 + 132 * q^4 - 60 * q^9 - 90 * q^12 - 212 * q^15 + 460 * q^16 + 296 * q^25 + 280 * q^27 - 320 * q^31 - 188 * q^34 - 2254 * q^36 + 796 * q^37 + 1240 * q^42 - 1662 * q^45 - 486 * q^48 + 1536 * q^49 + 2268 * q^58 - 6636 * q^60 - 1512 * q^64 + 4556 * q^67 - 1140 * q^69 - 4276 * q^70 + 3462 * q^75 - 7640 * q^78 + 3572 * q^81 + 9408 * q^82 - 816 * q^91 - 11516 * q^93 - 7916 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/363\mathbb{Z}\right)^\times$.

$n$	$122$	$244$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−1.05192			−0.371909			−0.185954	−	0.982558i	$-0.559538\pi$
$2$	−1.05192			−0.371909			−0.185954	+	0.982558i	$0.559538\pi$
$3$	−1.20902	−	5.05354i	−0.232676	−	0.972554i
$3$	−1.20902	−	5.05354i	−0.232676	−	0.972554i
$4$	−6.89347			−0.861684
$5$			12.2895i			1.09920i	0.835427	+	0.549602i	$0.185221\pi$
$5$			12.2895i			1.09920i	−0.835427	+	0.549602i	$0.814779\pi$
$6$	1.27179	+	5.31590i	0.0865343	+	0.361701i
$7$		−	22.4006i		−	1.20952i	−0.796408	−	0.604760i	$-0.793269\pi$
$7$		−	22.4006i		−	1.20952i	0.796408	−	0.604760i	$-0.206731\pi$
$8$	15.6667			0.692377
$9$	−24.0765	+	12.2197i	−0.891724	+	0.452580i
$10$		−	12.9275i		−	0.408804i
$11$		0			0
$11$		0			0
$12$	8.33435	+	34.8364i	0.200493	+	0.838034i
$13$			79.2941i			1.69171i	0.533413	+	0.845855i	$0.320909\pi$
$13$			79.2941i			1.69171i	−0.533413	+	0.845855i	$0.679091\pi$
$14$			23.5636i			0.449831i
$15$	62.1054	−	14.8582i	1.06904	−	0.255759i
$16$	38.6677			0.604183
$17$	−33.3165			−0.475320			−0.237660	−	0.971348i	$-0.576380\pi$
$17$	−33.3165			−0.475320			−0.237660	+	0.971348i	$0.576380\pi$
$18$	25.3265	−	12.8541i	0.331640	−	0.168319i
$19$			36.1195i			0.436126i	0.975935	+	0.218063i	$0.0699738\pi$
$19$			36.1195i			0.436126i	−0.975935	+	0.218063i	$0.930026\pi$
$20$		−	84.7171i		−	0.947166i
$21$	−113.202	+	27.0828i	−1.17632	+	0.281427i
$22$		0			0
$23$		−	134.233i		−	1.21693i	−0.793579	−	0.608467i	$-0.791785\pi$
$23$		−	134.233i		−	1.21693i	0.793579	−	0.608467i	$-0.208215\pi$
$24$	−18.9414	−	79.1723i	−0.161100	−	0.673374i
$25$	−26.0312			−0.208249
$26$		−	83.4108i		−	0.629162i
$27$	90.8616	+	106.898i	0.647642	+	0.761945i
$28$			154.418i			1.04222i
$29$	108.399			0.694112			0.347056	−	0.937844i	$-0.387181\pi$
$29$	108.399			0.694112			0.347056	+	0.937844i	$0.387181\pi$
$30$	−65.3297	+	15.6296i	−0.397584	+	0.0951189i
$31$	31.3155			0.181433			0.0907166	−	0.995877i	$-0.471084\pi$
$31$	31.3155			0.181433			0.0907166	+	0.995877i	$0.471084\pi$
$32$	−166.009			−0.917078
$33$		0			0
$34$	35.0462			0.176776
$35$	275.292			1.32951
$36$	165.971	−	84.2360i	0.768384	−	0.389981i
$37$	7.96593			0.0353943			0.0176972	−	0.999843i	$-0.494367\pi$
$37$	7.96593			0.0353943			0.0176972	+	0.999843i	$0.494367\pi$
$38$		−	37.9947i		−	0.162199i
$39$	400.716	−	95.8682i	1.64528	−	0.393621i
$40$			192.535i			0.761063i
$41$	−7.43487			−0.0283203			−0.0141601	−	0.999900i	$-0.504507\pi$
$41$	−7.43487			−0.0283203			−0.0141601	+	0.999900i	$0.504507\pi$
$42$	119.080	−	28.4889i	0.437485	−	0.104665i
$43$		−	74.3056i		−	0.263523i	−0.991281	−	0.131762i	$-0.957937\pi$
$43$		−	74.3056i		−	0.263523i	0.991281	−	0.131762i	$-0.0420633\pi$
$44$		0			0
$45$	−150.173	−	295.888i	−0.497478	−	0.980186i
$46$			141.202i			0.452588i
$47$		−	512.670i		−	1.59108i	−0.605904	−	0.795538i	$-0.707188\pi$
$47$		−	512.670i		−	1.59108i	0.605904	−	0.795538i	$-0.292812\pi$
$48$	−46.7501	−	195.409i	−0.140579	−	0.587601i
$49$	−158.788			−0.462939
$50$	27.3826			0.0774498
$51$	40.2804	+	168.366i	0.110596	+	0.462275i
$52$		−	546.611i		−	1.45772i
$53$		−	344.751i		−	0.893494i	−0.894660	−	0.446747i	$-0.852582\pi$
$53$		−	344.751i		−	0.893494i	0.894660	−	0.446747i	$-0.147418\pi$
$54$	−95.5789	−	112.448i	−0.240864	−	0.283374i
$55$		0			0
$56$		−	350.944i		−	0.837443i
$57$	182.531	−	43.6693i	0.424156	−	0.101476i
$58$	−114.027			−0.258146
$59$		−	586.208i		−	1.29352i	−0.762693	−	0.646760i	$-0.776123\pi$
$59$		−	586.208i		−	1.29352i	0.762693	−	0.646760i	$-0.223877\pi$
$60$	−428.121	+	102.425i	−0.921171	+	0.220383i
$61$		−	256.349i		−	0.538067i	−0.963131	−	0.269033i	$-0.913296\pi$
$61$		−	256.349i		−	0.538067i	0.963131	−	0.269033i	$-0.0867042\pi$
$62$	−32.9413			−0.0674766
$63$	273.728	+	539.329i	0.547405	+	1.07856i
$64$	−134.714			−0.263114
$65$	−974.483			−1.85953
$66$		0			0
$67$	664.138			1.21100			0.605502	−	0.795843i	$-0.292972\pi$
$67$	664.138			1.21100			0.605502	+	0.795843i	$0.292972\pi$
$68$	229.667			0.409576
$69$	−678.351	+	162.290i	−1.18353	+	0.283151i
$70$	−289.584			−0.494456
$71$		−	3.86140i		−	0.00645442i	−0.999995	−	0.00322721i	$-0.998973\pi$
$71$		−	3.86140i		−	0.00645442i	0.999995	−	0.00322721i	$-0.00102726\pi$
$72$	−377.200	+	191.442i	−0.617409	+	0.313356i
$73$		−	201.573i		−	0.323182i	−0.986858	−	0.161591i	$-0.948337\pi$
$73$		−	201.573i		−	0.323182i	0.986858	−	0.161591i	$-0.0516625\pi$
$74$	−8.37949			−0.0131635
$75$	31.4722	+	131.550i	0.0484547	+	0.202534i
$76$		−	248.989i		−	0.375802i
$77$		0			0
$78$	−421.520	+	100.845i	−0.611894	+	0.146391i
$79$		−	181.739i		−	0.258826i	−0.991591	−	0.129413i	$-0.958691\pi$
$79$		−	181.739i		−	0.258826i	0.991591	−	0.129413i	$-0.0413092\pi$
$80$			475.206i			0.664120i
$81$	430.359	−	588.415i	0.590342	−	0.807153i
$82$	7.82086			0.0105326
$83$	763.116			1.00919			0.504595	−	0.863356i	$-0.331642\pi$
$83$	763.116			1.00919			0.504595	+	0.863356i	$0.331642\pi$
$84$	780.358	−	186.695i	1.01362	−	0.242501i
$85$		−	409.443i		−	0.522474i
$86$			78.1633i			0.0980065i
$87$	−131.057	−	547.800i	−0.161503	−	0.675061i
$88$		0			0
$89$			311.998i			0.371592i	0.982588	+	0.185796i	$0.0594864\pi$
$89$			311.998i			0.371592i	−0.982588	+	0.185796i	$0.940514\pi$
$90$	157.970	+	311.250i	0.185017	+	0.364540i
$91$	1776.24			2.04616
$92$			925.330i			1.04861i
$93$	−37.8611	−	158.254i	−0.0422152	−	0.176454i
$94$			539.286i			0.591735i
$95$	−443.890			−0.479391
$96$	200.708	+	838.932i	0.213382	+	0.891908i
$97$	748.285			0.783267			0.391633	−	0.920121i	$-0.371910\pi$
$97$	748.285			0.783267			0.391633	+	0.920121i	$0.371910\pi$
$98$	167.032			0.172171
$99$		0			0
$100$	179.445			0.179445
$101$	−307.339			−0.302786			−0.151393	−	0.988474i	$-0.548376\pi$
$101$	−307.339			−0.302786			−0.151393	+	0.988474i	$0.548376\pi$
$102$	−42.3716	−	177.107i	−0.0411315	−	0.171924i
$103$	773.954			0.740387			0.370194	−	0.928955i	$-0.379291\pi$
$103$	773.954			0.740387			0.370194	+	0.928955i	$0.379291\pi$
$104$			1242.28i			1.17130i
$105$	−332.834	−	1391.20i	−0.309345	−	1.29302i
$106$			362.649i			0.332298i
$107$	−210.517			−0.190201			−0.0951003	−	0.995468i	$-0.530317\pi$
$107$	−210.517			−0.190201			−0.0951003	+	0.995468i	$0.530317\pi$
$108$	−626.352	−	736.898i	−0.558063	−	0.656556i
$109$			1647.31i			1.44756i	0.690030	+	0.723780i	$0.257597\pi$
$109$			1647.31i			1.44756i	−0.690030	+	0.723780i	$0.742403\pi$
$110$		0			0
$111$	−9.63097	−	40.2561i	−0.00823542	−	0.0344229i
$112$		−	866.181i		−	0.730771i
$113$		−	679.921i		−	0.566032i	−0.959115	−	0.283016i	$-0.908665\pi$
$113$		−	679.921i		−	0.566032i	0.959115	−	0.283016i	$-0.0913349\pi$
$114$	−192.008	+	45.9364i	−0.157747	+	0.0377398i
$115$	1649.65			1.33766
$116$	−747.247			−0.598105
$117$	−968.948	−	1909.13i	−0.765635	−	1.50854i
$118$			616.642i			0.481072i
$119$			746.311i			0.574909i
$120$	972.986	−	232.779i	0.740175	−	0.177081i
$121$		0			0
$122$			269.657i			0.200112i
$123$	8.98891	+	37.5724i	0.00658945	+	0.0275430i
$124$	−215.873			−0.156338
$125$			1216.27i			0.870295i
$126$	−287.939	−	567.330i	−0.203585	−	0.401125i
$127$			2234.20i			1.56105i	0.625126	+	0.780524i	$0.285048\pi$
$127$			2234.20i			1.56105i	−0.625126	+	0.780524i	$0.714952\pi$
$128$	1469.78			1.01493
$129$	−375.506	+	89.8370i	−0.256290	+	0.0613155i
$130$	1025.07			0.691577
$131$	2011.16			1.34134			0.670671	−	0.741755i	$-0.266006\pi$
$131$	2011.16			1.34134			0.670671	+	0.741755i	$0.266006\pi$
$132$		0			0
$133$	809.100			0.527503
$134$	−698.618			−0.450383
$135$	−1313.72	+	1116.64i	−0.837533	+	0.711891i
$136$	−521.960			−0.329101
$137$		−	2409.87i		−	1.50284i	−0.659824	−	0.751421i	$-0.729369\pi$
$137$		−	2409.87i		−	1.50284i	0.659824	−	0.751421i	$-0.270631\pi$
$138$	713.569	−	170.716i	0.440167	−	0.105307i
$139$			1877.76i			1.14583i	0.819617	+	0.572913i	$0.194187\pi$
$139$			1877.76i			1.14583i	−0.819617	+	0.572913i	$0.805813\pi$
$140$	−1897.72			−1.14562
$141$	−2590.80	+	619.828i	−1.54741	+	0.370205i
$142$			4.06187i			0.00240046i
$143$		0			0
$144$	−930.984	+	472.507i	−0.538764	+	0.273441i
$145$			1332.17i			0.762971i
$146$			212.038i			0.120194i
$147$	191.978	+	802.441i	0.107715	+	0.450233i
$148$	−54.9129			−0.0304987
$149$	−1052.33			−0.578590			−0.289295	−	0.957240i	$-0.593421\pi$
$149$	−1052.33			−0.578590			−0.289295	+	0.957240i	$0.593421\pi$
$150$	−33.1062	−	138.379i	−0.0180207	−	0.0753241i
$151$		−	3425.18i		−	1.84594i	−0.384872	−	0.922970i	$-0.625754\pi$
$151$		−	3425.18i		−	1.84594i	0.384872	−	0.922970i	$-0.374246\pi$
$152$			565.873i			0.301963i
$153$	802.147	−	407.117i	0.423854	−	0.215121i
$154$		0			0
$155$			384.851i			0.199432i
$156$	−2762.32	+	660.865i	−1.41771	+	0.339176i
$157$	106.358			0.0540657			0.0270328	−	0.999635i	$-0.491394\pi$
$157$	106.358			0.0540657			0.0270328	+	0.999635i	$0.491394\pi$
$158$			191.174i			0.0962595i
$159$	−1742.21	+	416.811i	−0.868971	+	0.207895i
$160$		−	2040.16i		−	1.00806i
$161$	−3006.90			−1.47191
$162$	−452.702	+	618.963i	−0.219553	+	0.300187i
$163$	314.649			0.151197			0.0755987	−	0.997138i	$-0.475913\pi$
$163$	314.649			0.151197			0.0755987	+	0.997138i	$0.475913\pi$
$164$	51.2520			0.0244031
$165$		0			0
$166$	−802.734			−0.375327
$167$	−701.582			−0.325090			−0.162545	−	0.986701i	$-0.551970\pi$
$167$	−701.582			−0.325090			−0.162545	+	0.986701i	$0.551970\pi$
$168$	−1773.51	+	424.298i	−0.814459	+	0.194853i
$169$	−4090.55			−1.86188
$170$			430.700i			0.194313i
$171$	−441.369	−	869.633i	−0.197382	−	0.388903i
$172$			512.223i			0.227074i
$173$	4492.65			1.97439			0.987197	−	0.159506i	$-0.0509900\pi$
$173$	4492.65			1.97439			0.987197	+	0.159506i	$0.0509900\pi$
$174$	137.861	+	576.240i	0.0600645	+	0.251061i
$175$			583.115i			0.251882i
$176$		0			0
$177$	−2962.42	+	708.737i	−1.25802	+	0.300972i
$178$		−	328.196i		−	0.138198i
$179$			2172.09i			0.906980i	0.891261	+	0.453490i	$0.149821\pi$
$179$			2172.09i			0.906980i	−0.891261	+	0.453490i	$0.850179\pi$
$180$	1035.22	+	2039.70i	0.428669	+	0.844611i
$181$	1322.50			0.543100			0.271550	−	0.962424i	$-0.412464\pi$
$181$	1322.50			0.543100			0.271550	+	0.962424i	$0.412464\pi$
$182$	−1868.45			−0.760984
$183$	−1295.47	+	309.931i	−0.523299	+	0.125195i
$184$		−	2102.98i		−	0.842576i
$185$			97.8971i			0.0389056i
$186$	39.8267	+	166.470i	0.0157002	+	0.0656247i
$187$		0			0
$188$			3534.07i			1.37100i
$189$	2394.58	−	2035.36i	0.921588	−	0.783336i
$190$	466.935			0.178290
$191$		−	1486.26i		−	0.563048i	−0.959554	−	0.281524i	$-0.909160\pi$
$191$		−	1486.26i		−	0.563048i	0.959554	−	0.281524i	$-0.0908399\pi$
$192$	162.872	+	680.784i	0.0612203	+	0.255892i
$193$			2066.01i			0.770543i	0.922803	+	0.385272i	$0.125892\pi$
$193$			2066.01i			0.770543i	−0.922803	+	0.385272i	$0.874108\pi$
$194$	−787.134			−0.291304
$195$	1178.17	+	4924.59i	0.432669	+	1.80850i
$196$	1094.60			0.398907
$197$	5330.07			1.92767			0.963836	−	0.266494i	$-0.0858654\pi$
$197$	5330.07			1.92767			0.963836	+	0.266494i	$0.0858654\pi$
$198$		0			0
$199$	1980.12			0.705361			0.352680	−	0.935744i	$-0.385270\pi$
$199$	1980.12			0.705361			0.352680	+	0.935744i	$0.385270\pi$
$200$	−407.823			−0.144187
$201$	−802.956	−	3356.25i	−0.281772	−	1.17777i
$202$	323.295			0.112609
$203$		−	2428.21i		−	0.839542i
$204$	−277.672	−	1160.63i	−0.0952985	−	0.398335i
$205$		−	91.3706i		−	0.0311298i
$206$	−814.135			−0.275357
$207$	1640.28	+	3231.86i	0.550760	+	1.08517i
$208$			3066.12i			1.02210i
$209$		0			0
$210$	350.113	+	1463.43i	0.115048	+	0.480885i
$211$		−	2262.19i		−	0.738082i	−0.929413	−	0.369041i	$-0.879686\pi$
$211$		−	2262.19i		−	0.738082i	0.929413	−	0.369041i	$-0.120314\pi$
$212$			2376.53i			0.769909i
$213$	−19.5138	+	4.66852i	−0.00627728	+	0.00150179i
$214$	221.447			0.0707373
$215$	913.176			0.289666
$216$	1423.50	+	1674.74i	0.448412	+	0.527553i
$217$		−	701.487i		−	0.219447i
$218$		−	1732.84i		−	0.538361i
$219$	−1018.65	+	243.705i	−0.314312	+	0.0751967i
$220$		0			0
$221$		−	2641.80i		−	0.804104i
$222$	10.1310	+	42.3461i	0.00306282	+	0.0128022i
$223$	3253.82			0.977094			0.488547	−	0.872537i	$-0.337527\pi$
$223$	3253.82			0.977094			0.488547	+	0.872537i	$0.337527\pi$
$224$			3718.70i			1.10922i
$225$	626.741	−	318.092i	0.185701	−	0.0942496i
$226$			715.221i			0.210512i
$227$	−456.339			−0.133429			−0.0667143	−	0.997772i	$-0.521252\pi$
$227$	−456.339			−0.133429			−0.0667143	+	0.997772i	$0.521252\pi$
$228$	−1258.28	+	301.033i	−0.365488	+	0.0874403i
$229$	−3762.62			−1.08577			−0.542884	−	0.839808i	$-0.682668\pi$
$229$	−3762.62			−1.08577			−0.542884	+	0.839808i	$0.682668\pi$
$230$	−1735.30			−0.497487
$231$		0			0
$232$	1698.26			0.480587
$233$	−760.537			−0.213839			−0.106919	−	0.994268i	$-0.534099\pi$
$233$	−760.537			−0.213839			−0.106919	+	0.994268i	$0.534099\pi$
$234$	1019.25	+	2008.24i	0.284746	+	0.561038i
$235$	6300.44			1.74892
$236$			4041.01i			1.11461i
$237$	−918.425	+	219.726i	−0.251722	+	0.0602226i
$238$		−	785.057i		−	0.213814i
$239$	−2468.77			−0.668164			−0.334082	−	0.942544i	$-0.608426\pi$
$239$	−2468.77			−0.668164			−0.334082	+	0.942544i	$0.608426\pi$
$240$	2401.47	−	574.534i	0.645893	−	0.154525i
$241$		−	3255.97i		−	0.870273i	−0.900365	−	0.435136i	$-0.856700\pi$
$241$		−	3255.97i		−	0.870273i	0.900365	−	0.435136i	$-0.143300\pi$
$242$		0			0
$243$	−3493.89	−	1463.43i	−0.922359	−	0.386334i
$244$			1767.13i			0.463643i
$245$		−	1951.42i		−	0.508864i
$246$	−9.45559	−	39.5230i	−0.00245068	−	0.0102435i
$247$	−2864.06			−0.737798
$248$	490.610			0.125620
$249$	−922.623	−	3856.44i	−0.234815	−	0.981493i
$250$		−	1279.42i		−	0.323671i
$251$			1427.08i			0.358871i	0.983770	+	0.179436i	$0.0574272\pi$
$251$			1427.08i			0.358871i	−0.983770	+	0.179436i	$0.942573\pi$
$252$	−1886.94	−	3717.85i	−0.471690	−	0.929376i
$253$		0			0
$254$		−	2350.19i		−	0.580568i
$255$	−2069.13	+	495.025i	−0.508134	+	0.121567i
$256$	−468.371			−0.114348
$257$		−	6176.38i		−	1.49911i	−0.661940	−	0.749557i	$-0.730267\pi$
$257$		−	6176.38i		−	1.49911i	0.661940	−	0.749557i	$-0.269733\pi$
$258$	395.001	−	94.5010i	0.0953167	−	0.0228038i
$259$		−	178.442i		−	0.0428102i
$260$	6717.57			1.60233
$261$	−2609.88	+	1324.60i	−0.618956	+	0.314141i
$262$	−2115.57			−0.498857
$263$	−5256.94			−1.23254			−0.616268	−	0.787537i	$-0.711356\pi$
$263$	−5256.94			−1.23254			−0.616268	+	0.787537i	$0.711356\pi$
$264$		0			0
$265$	4236.81			0.982132
$266$	−851.106			−0.196183
$267$	1576.69	−	377.212i	0.361393	−	0.0864606i
$268$	−4578.21			−1.04350
$269$		−	2159.77i		−	0.489531i	−0.969582	−	0.244765i	$-0.921289\pi$
$269$		−	2159.77i		−	0.489531i	0.969582	−	0.244765i	$-0.0787110\pi$
$270$	1381.92	−	1174.61i	0.311486	−	0.264758i
$271$		−	4869.51i		−	1.09152i	−0.837942	−	0.545760i	$-0.816241\pi$
$271$		−	4869.51i		−	1.09152i	0.837942	−	0.545760i	$-0.183759\pi$
$272$	−1288.27			−0.287180
$273$	−2147.51	−	8976.29i	−0.476092	−	1.99000i
$274$			2534.98i			0.558920i
$275$		0			0
$276$	4676.19	−	1118.74i	1.01983	−	0.243987i
$277$			5811.14i			1.26050i	0.776394	+	0.630248i	$0.217047\pi$
$277$			5811.14i			1.26050i	−0.776394	+	0.630248i	$0.782953\pi$
$278$		−	1975.25i		−	0.426142i
$279$	−753.969	+	382.665i	−0.161788	+	0.0821131i
$280$	4312.91			0.920521
$281$	5596.28			1.18806			0.594032	−	0.804441i	$-0.297535\pi$
$281$	5596.28			1.18806			0.594032	+	0.804441i	$0.297535\pi$
$282$	2725.30	−	652.008i	0.575494	−	0.137683i
$283$			881.828i			0.185227i	0.995702	+	0.0926135i	$0.0295221\pi$
$283$			881.828i			0.185227i	−0.995702	+	0.0926135i	$0.970478\pi$
$284$			26.6185i			0.00556167i
$285$	536.672	+	2243.22i	0.111543	+	0.466234i
$286$		0			0
$287$			166.546i			0.0342539i
$288$	3996.92	−	2028.57i	0.817780	−	0.415051i
$289$	−3803.01			−0.774071
$290$		−	1401.33i		−	0.283755i
$291$	−904.693	−	3781.49i	−0.182248	−	0.761769i
$292$			1389.53i			0.278481i
$293$	3695.75			0.736888			0.368444	−	0.929650i	$-0.379891\pi$
$293$	3695.75			0.736888			0.368444	+	0.929650i	$0.379891\pi$
$294$	−201.945	−	844.102i	−0.0400601	−	0.167446i
$295$	7204.18			1.42184
$296$	124.800			0.0245062
$297$		0			0
$298$	1106.96			0.215183
$299$	10643.9			2.05870
$300$	−216.953	−	906.833i	−0.0417526	−	0.174520i
$301$	−1664.49			−0.318736
$302$			3603.00i			0.686521i
$303$	371.579	+	1553.15i	0.0704511	+	0.294476i
$304$			1396.66i			0.263500i
$305$	3150.39			0.591445
$306$	−843.792	+	428.253i	−0.157635	+	0.0800053i
$307$		−	8741.11i		−	1.62502i	−0.582946	−	0.812511i	$-0.698100\pi$
$307$		−	8741.11i		−	1.62502i	0.582946	−	0.812511i	$-0.301900\pi$
$308$		0			0
$309$	−935.726	−	3911.21i	−0.172271	−	0.720067i
$310$		−	404.831i		−	0.0741706i
$311$		−	5470.01i		−	0.997350i	−0.866789	−	0.498675i	$-0.833820\pi$
$311$		−	5470.01i		−	0.997350i	0.866789	−	0.498675i	$-0.166180\pi$
$312$	6277.89	−	1501.94i	1.13915	−	0.272534i
$313$	−4213.87			−0.760964			−0.380482	−	0.924788i	$-0.624242\pi$
$313$	−4213.87			−0.760964			−0.380482	+	0.924788i	$0.624242\pi$
$314$	−111.880			−0.0201075
$315$	−6628.08	+	3363.98i	−1.18555	+	0.601710i
$316$			1252.81i			0.223026i
$317$			64.5098i			0.0114298i	0.999984	+	0.00571488i	$0.00181911\pi$
$317$			64.5098i			0.0114298i	−0.999984	+	0.00571488i	$0.998181\pi$
$318$	1832.66	−	438.451i	0.323178	−	0.0773179i
$319$		0			0
$320$		−	1655.57i		−	0.289216i
$321$	254.520	+	1063.86i	0.0442551	+	0.184980i
$322$	3163.01			0.547415
$323$		−	1203.38i		−	0.207299i
$324$	−2966.67	+	4056.22i	−0.508688	+	0.695511i
$325$		−	2064.12i		−	0.352298i
$326$	−330.984			−0.0562317
$327$	8324.77	−	1991.64i	1.40783	−	0.336813i
$328$	−116.480			−0.0196083
$329$	−11484.1			−1.92444
$330$		0			0
$331$	−6229.62			−1.03447			−0.517237	−	0.855842i	$-0.673039\pi$
$331$	−6229.62			−1.03447			−0.517237	+	0.855842i	$0.673039\pi$
$332$	−5260.52			−0.869603
$333$	−191.792	+	97.3410i	−0.0315620	+	0.0160188i
$334$	738.006			0.120904
$335$			8161.90i			1.33114i
$336$	−4377.28	+	1047.23i	−0.710715	+	0.170033i
$337$			9642.04i			1.55856i	0.626675	+	0.779281i	$0.284415\pi$
$337$			9642.04i			1.55856i	−0.626675	+	0.779281i	$0.715585\pi$
$338$	4302.92			0.692450
$339$	−3436.01	+	822.039i	−0.550497	+	0.131702i
$340$			2822.48i			0.450207i
$341$		0			0
$342$	464.283	+	914.782i	0.0734081	+	0.144637i
$343$		−	4126.46i		−	0.649586i
$344$		−	1164.12i		−	0.182457i
$345$	−1994.46	−	8336.57i	−0.311241	−	1.30095i
$346$	−4725.90			−0.734294
$347$	6000.64			0.928331			0.464166	−	0.885748i	$-0.346354\pi$
$347$	6000.64			0.928331			0.464166	+	0.885748i	$0.346354\pi$
$348$	903.438	+	3776.24i	0.139165	+	0.581690i
$349$			3337.93i			0.511964i	0.966682	+	0.255982i	$0.0823988\pi$
$349$			3337.93i			0.511964i	−0.966682	+	0.255982i	$0.917601\pi$
$350$		−	613.388i		−	0.0936771i
$351$	−8476.37	+	7204.79i	−1.28899	+	1.09562i
$352$		0			0
$353$		−	2450.05i		−	0.369414i	−0.982794	−	0.184707i	$-0.940866\pi$
$353$		−	2450.05i		−	0.369414i	0.982794	−	0.184707i	$-0.0591336\pi$
$354$	3116.22	−	745.533i	0.467868	−	0.111934i
$355$	47.4546			0.00709473
$356$		−	2150.75i		−	0.320195i
$357$	3771.51	−	902.306i	0.559131	−	0.133768i
$358$		−	2284.85i		−	0.337314i
$359$	−7579.49			−1.11429			−0.557145	−	0.830415i	$-0.688103\pi$
$359$	−7579.49			−1.11429			−0.557145	+	0.830415i	$0.688103\pi$
$360$	−2352.72	−	4635.59i	−0.344442	−	0.678658i
$361$	5554.38			0.809794
$362$	−1391.17			−0.201984
$363$		0			0
$364$	−12244.4			−1.76314
$365$	2477.22			0.355243
$366$	1362.72	−	326.021i	0.194620	−	0.0465612i
$367$	2756.71			0.392096			0.196048	−	0.980594i	$-0.437189\pi$
$367$	2756.71			0.392096			0.196048	+	0.980594i	$0.437189\pi$
$368$		−	5190.47i		−	0.735250i
$369$	179.006	−	90.8516i	0.0252539	−	0.0128172i
$370$		−	102.980i		−	0.0144693i
$371$	−7722.64			−1.08070
$372$	260.994	+	1090.92i	0.0363762	+	0.152047i
$373$		−	694.839i		−	0.0964541i	−0.998836	−	0.0482271i	$-0.984643\pi$
$373$		−	694.839i		−	0.0964541i	0.998836	−	0.0482271i	$-0.0153571\pi$
$374$		0			0
$375$	6146.49	−	1470.50i	0.846409	−	0.202497i
$376$		−	8031.84i		−	1.10162i
$377$			8595.42i			1.17424i
$378$	−2518.90	+	2141.03i	−0.342747	+	0.291329i
$379$	10161.0			1.37714			0.688568	−	0.725171i	$-0.258239\pi$
$379$	10161.0			1.37714			0.688568	+	0.725171i	$0.258239\pi$
$380$	3059.94			0.413083
$381$	11290.6	−	2701.19i	1.51820	−	0.363219i
$382$			1563.42i			0.209402i
$383$			1885.50i			0.251552i	0.992059	+	0.125776i	$0.0401421\pi$
$383$			1885.50i			0.251552i	−0.992059	+	0.125776i	$0.959858\pi$
$384$	−1776.99	−	7427.58i	−0.236150	−	0.987076i
$385$		0			0
$386$		−	2173.27i		−	0.286572i
$387$	907.989	+	1789.02i	0.119265	+	0.234990i
$388$	−5158.28			−0.674928
$389$		−	5769.43i		−	0.751984i	−0.926623	−	0.375992i	$-0.877302\pi$
$389$		−	5769.43i		−	0.751984i	0.926623	−	0.375992i	$-0.122698\pi$
$390$	−1239.34	−	5180.26i	−0.160914	−	0.672596i
$391$			4472.17i			0.578433i
$392$	−2487.68			−0.320528
$393$	−2431.53	−	10163.5i	−0.312098	−	1.30453i
$394$	−5606.79			−0.716919
$395$	2233.48			0.284502
$396$		0			0
$397$	7553.83			0.954952			0.477476	−	0.878645i	$-0.341552\pi$
$397$	7553.83			0.954952			0.477476	+	0.878645i	$0.341552\pi$
$398$	−2082.92			−0.262330
$399$	−978.219	−	4088.82i	−0.122737	−	0.513025i
$400$	−1006.57			−0.125821
$401$		−	5727.95i		−	0.713317i	−0.934235	−	0.356658i	$-0.883916\pi$
$401$		−	5727.95i		−	0.713317i	0.934235	−	0.356658i	$-0.116084\pi$
$402$	844.643	+	3530.49i	0.104793	+	0.438022i
$403$			2483.13i			0.306932i
$404$	2118.63			0.260906
$405$	7231.31	+	5288.89i	0.887226	+	0.648906i
$406$			2554.28i			0.312233i
$407$		0			0
$408$	631.060	+	2637.75i	0.0765739	+	0.320068i
$409$			6208.37i			0.750573i	0.926909	+	0.375286i	$0.122456\pi$
$409$			6208.37i			0.750573i	−0.926909	+	0.375286i	$0.877544\pi$
$410$			96.1143i			0.0115774i
$411$	−12178.4	+	2913.59i	−1.46159	+	0.349675i
$412$	−5335.23			−0.637980
$413$	−13131.4			−1.56454
$414$	−1725.44	−	3399.65i	−0.204833	−	0.403584i
$415$			9378.29i			1.10931i
$416$		−	13163.5i		−	1.55143i
$417$	9489.34	−	2270.25i	1.11438	−	0.266606i
$418$		0			0
$419$		−	144.958i		−	0.0169013i	−0.999964	−	0.00845065i	$-0.997310\pi$
$419$		−	144.958i		−	0.0169013i	0.999964	−	0.00845065i	$-0.00268996\pi$
$420$	2294.38	+	9590.19i	0.266558	+	1.11417i
$421$	−3560.24			−0.412151			−0.206076	−	0.978536i	$-0.566069\pi$
$421$	−3560.24			−0.412151			−0.206076	+	0.978536i	$0.566069\pi$
$422$			2379.63i			0.274499i
$423$	6264.66	+	12343.3i	0.720090	+	1.41880i
$424$		−	5401.11i		−	0.618634i
$425$	867.269			0.0989852
$426$	20.5268	−	4.91089i	0.00233457	−	0.000558529i
$427$	−5742.37			−0.650803
$428$	1451.19			0.163893
$429$		0			0
$430$	−960.585			−0.107729
$431$	−3249.25			−0.363135			−0.181567	−	0.983379i	$-0.558117\pi$
$431$	−3249.25			−0.363135			−0.181567	+	0.983379i	$0.558117\pi$
$432$	3513.41	+	4133.50i	0.391294	+	0.460354i
$433$	14066.6			1.56120			0.780598	−	0.625034i	$-0.214915\pi$
$433$	14066.6			1.56120			0.780598	+	0.625034i	$0.214915\pi$
$434$			737.906i			0.0816143i
$435$	6732.18	−	1610.62i	0.742030	−	0.177525i
$436$		−	11355.7i		−	1.24734i
$437$	4848.42			0.530736
$438$	1071.54	−	256.358i	0.116895	−	0.0279663i
$439$			5885.66i			0.639880i	0.947438	+	0.319940i	$0.103663\pi$
$439$			5885.66i			0.639880i	−0.947438	+	0.319940i	$0.896337\pi$
$440$		0			0
$441$	3823.06	−	1940.34i	0.412813	−	0.209517i
$442$			2778.96i			0.299053i
$443$		−	9015.40i		−	0.966896i	−0.875373	−	0.483448i	$-0.839384\pi$
$443$		−	9015.40i		−	0.966896i	0.875373	−	0.483448i	$-0.160616\pi$
$444$	66.3908	+	277.505i	0.00709633	+	0.0296617i
$445$	−3834.29			−0.408455
$446$	−3422.75			−0.363390
$447$	1272.28	+	5317.97i	0.134624	+	0.562710i
$448$			3017.68i			0.318241i
$449$			1227.35i			0.129003i	0.997918	+	0.0645014i	$0.0205457\pi$
$449$			1227.35i			0.129003i	−0.997918	+	0.0645014i	$0.979454\pi$
$450$	−659.279	+	334.607i	−0.0690638	+	0.0350523i
$451$		0			0
$452$			4687.02i			0.487741i
$453$	−17309.3	+	4141.11i	−1.79528	+	0.429506i
$454$	480.031			0.0496233
$455$			21829.0i			2.24914i
$456$	2859.66	−	684.153i	0.293676	−	0.0702596i
$457$		−	5555.25i		−	0.568630i	−0.958731	−	0.284315i	$-0.908234\pi$
$457$		−	5555.25i		−	0.568630i	0.958731	−	0.284315i	$-0.0917661\pi$
$458$	3957.96			0.403807
$459$	−3027.19	−	3561.47i	−0.307837	−	0.362168i
$460$	−11371.8			−1.15264
$461$	18525.0			1.87157			0.935787	−	0.352567i	$-0.114691\pi$
$461$	18525.0			1.87157			0.935787	+	0.352567i	$0.114691\pi$
$462$		0			0
$463$	−7701.23			−0.773016			−0.386508	−	0.922286i	$-0.626319\pi$
$463$	−7701.23			−0.773016			−0.386508	+	0.922286i	$0.626319\pi$
$464$	4191.55			0.419371
$465$	1944.86	−	465.293i	0.193959	−	0.0464031i
$466$	800.022			0.0795285
$467$		−	2248.39i		−	0.222791i	−0.993776	−	0.111395i	$-0.964468\pi$
$467$		−	2248.39i		−	0.222791i	0.993776	−	0.111395i	$-0.0355320\pi$
$468$	6679.41	+	13160.5i	0.659735	+	1.29988i
$469$		−	14877.1i		−	1.46473i
$470$	−6627.54			−0.650438
$471$	−128.589	−	537.486i	−0.0125798	−	0.0525818i
$472$		−	9183.94i		−	0.895604i
$473$		0			0
$474$	966.107	−	231.134i	0.0936176	−	0.0223973i
$475$		−	940.234i		−	0.0908229i
$476$		−	5144.67i		−	0.495390i
$477$	4212.74	+	8300.41i	0.404378	+	0.796750i
$478$	2596.94			0.248496
$479$	−482.380			−0.0460135			−0.0230068	−	0.999735i	$-0.507324\pi$
$479$	−482.380			−0.0460135			−0.0230068	+	0.999735i	$0.507324\pi$
$480$	−10310.0	+	2466.60i	−0.980388	+	0.234550i
$481$			631.651i			0.0598769i
$482$			3425.01i			0.323662i
$483$	3635.40	+	15195.5i	0.342477	+	1.43151i
$484$		0			0
$485$			9196.03i			0.860970i
$486$	3675.28	+	1539.41i	0.343033	+	0.143681i
$487$	7188.37			0.668863			0.334432	−	0.942420i	$-0.391456\pi$
$487$	7188.37			0.668863			0.334432	+	0.942420i	$0.391456\pi$
$488$		−	4016.13i		−	0.372545i
$489$	−380.417	−	1590.09i	−0.0351801	−	0.147048i
$490$			2052.73i			0.189251i
$491$	10339.4			0.950331			0.475166	−	0.879896i	$-0.342388\pi$
$491$	10339.4			0.950331			0.475166	+	0.879896i	$0.342388\pi$
$492$	−61.9648	−	259.004i	−0.00567803	−	0.0237334i
$493$	−3611.49			−0.329925
$494$	3012.76			0.274393
$495$		0			0
$496$	1210.90			0.109619
$497$	−86.4978			−0.00780676
$498$	970.523	+	4056.65i	0.0873296	+	0.365026i
$499$	−8532.25			−0.765443			−0.382721	−	0.923864i	$-0.625013\pi$
$499$	−8532.25			−0.765443			−0.382721	+	0.923864i	$0.625013\pi$
$500$		−	8384.35i		−	0.749919i
$501$	848.228	+	3545.47i	0.0756407	+	0.316168i
$502$		−	1501.17i		−	0.133467i
$503$	−10636.0			−0.942817			−0.471409	−	0.881915i	$-0.656254\pi$
$503$	−10636.0			−0.942817			−0.471409	+	0.881915i	$0.656254\pi$
$504$	4288.42	+	8449.51i	0.379010	+	0.746768i
$505$		−	3777.03i		−	0.332823i
$506$		0			0
$507$	4945.56	+	20671.8i	0.433215	+	1.81078i
$508$		−	15401.4i		−	1.34513i
$509$			19452.5i			1.69394i	0.531638	+	0.846972i	$0.321577\pi$
$509$			19452.5i			1.69394i	−0.531638	+	0.846972i	$0.678423\pi$
$510$	2176.56	−	520.725i	0.188980	−	0.0452119i
$511$	−4515.35			−0.390895
$512$	−11265.5			−0.972405
$513$	−3861.10	+	3281.88i	−0.332304	+	0.282453i
$514$			6497.04i			0.557533i
$515$			9511.48i			0.813837i
$516$	2588.54	−	619.289i	0.220841	−	0.0528346i
$517$		0			0
$518$			187.706i			0.0159215i
$519$	−5431.71	−	22703.8i	−0.459394	−	1.92021i
$520$	−15266.9			−1.28750
$521$			8112.43i			0.682173i	0.940032	+	0.341086i	$0.110795\pi$
$521$			8112.43i			0.682173i	−0.940032	+	0.341086i	$0.889205\pi$
$522$	2745.38	−	1393.37i	0.230195	−	0.116832i
$523$		−	13073.3i		−	1.09303i	−0.837449	−	0.546516i	$-0.815954\pi$
$523$		−	13073.3i		−	1.09303i	0.837449	−	0.546516i	$-0.184046\pi$
$524$	−13863.9			−1.15581
$525$	2946.79	−	704.998i	0.244969	−	0.0586069i
$526$	5529.86			0.458391
$527$	−1043.32			−0.0862389
$528$		0			0
$529$	−5851.44			−0.480927
$530$	−4456.77			−0.365264
$531$	7163.27	+	14113.9i	0.585422	+	1.15346i
$532$	−5577.51			−0.454541
$533$		−	589.541i		−	0.0479097i
$534$	−1658.55	+	396.795i	−0.134405	+	0.0321555i
$535$		−	2587.14i		−	0.209069i
$536$	10404.8			0.838471
$537$	10976.7	−	2626.10i	0.882087	−	0.211033i
$538$			2271.90i			0.182061i
$539$		0			0
$540$	9056.08	−	7697.54i	0.721689	−	0.613425i
$541$			7775.77i			0.617942i	0.951071	+	0.308971i	$0.0999846\pi$
$541$			7775.77i			0.617942i	−0.951071	+	0.308971i	$0.900015\pi$
$542$			5122.32i			0.405946i
$543$	−1598.94	−	6683.33i	−0.126366	−	0.528194i
$544$	5530.84			0.435906
$545$	−20244.6			−1.59116
$546$	2259.00	+	9442.31i	0.177063	+	0.740098i
$547$			11318.6i			0.884733i	0.896834	+	0.442367i	$0.145861\pi$
$547$			11318.6i			0.884733i	−0.896834	+	0.442367i	$0.854139\pi$
$548$			16612.4i			1.29497i
$549$	3132.50	+	6171.99i	0.243519	+	0.479807i
$550$		0			0
$551$			3915.33i			0.302720i
$552$	−10627.5	+	2542.55i	−0.819451	+	0.196047i
$553$	−4071.07			−0.313055
$554$		−	6112.83i		−	0.468790i
$555$	494.727	−	118.360i	0.0378378	−	0.00905241i
$556$		−	12944.3i		−	0.987339i
$557$	−16181.4			−1.23093			−0.615464	−	0.788165i	$-0.711031\pi$
$557$	−16181.4			−1.23093			−0.615464	+	0.788165i	$0.711031\pi$
$558$	793.113	−	402.532i	0.0601705	−	0.0305386i
$559$	5891.99			0.445804
$560$	10644.9			0.803267
$561$		0			0
$562$	−5886.82			−0.441851
$563$	−16085.3			−1.20411			−0.602055	−	0.798454i	$-0.705651\pi$
$563$	−16085.3			−1.20411			−0.602055	+	0.798454i	$0.705651\pi$
$564$	17859.6	−	4272.77i	1.33338	−	0.319000i
$565$	8355.87			0.622185
$566$		−	927.610i		−	0.0688876i
$567$	−13180.9	−	9640.32i	−0.976268	−	0.714030i
$568$		−	60.4954i		−	0.00446889i
$569$	14893.1			1.09728			0.548638	−	0.836060i	$-0.315146\pi$
$569$	14893.1			1.09728			0.548638	+	0.836060i	$0.315146\pi$
$570$	−564.535	−	2359.68i	−0.0414838	−	0.173396i
$571$		−	18417.6i		−	1.34983i	−0.737895	−	0.674916i	$-0.764180\pi$
$571$		−	18417.6i		−	1.34983i	0.737895	−	0.674916i	$-0.235820\pi$
$572$		0			0
$573$	−7510.88	+	1796.92i	−0.547595	+	0.131008i
$574$		−	175.192i		−	0.0127393i
$575$			3494.24i			0.253426i
$576$	3243.45	−	1646.16i	0.234625	−	0.119080i
$577$	−22240.1			−1.60462			−0.802310	−	0.596908i	$-0.796396\pi$
$577$	−22240.1			−1.60462			−0.802310	+	0.596908i	$0.796396\pi$
$578$	4000.45			0.287884
$579$	10440.7	−	2497.85i	0.749395	−	0.179287i
$580$		−	9183.28i		−	0.657439i
$581$		−	17094.3i		−	1.22064i
$582$	951.662	+	3977.81i	0.0677795	+	0.283309i
$583$		0			0
$584$		−	3157.97i		−	0.223764i
$585$	23462.2	−	11907.9i	1.65819	−	0.841589i
$586$	−3887.62			−0.274055
$587$			17214.5i			1.21042i	0.796065	+	0.605211i	$0.206911\pi$
$587$			17214.5i			1.21042i	−0.796065	+	0.605211i	$0.793089\pi$
$588$	−1323.39	−	5531.61i	−0.0928161	−	0.387959i
$589$			1131.10i			0.0791277i
$590$	−7578.20			−0.528796
$591$	−6444.16	−	26935.7i	−0.448524	−	1.87477i
$592$	308.024			0.0213847
$593$	2358.18			0.163303			0.0816517	−	0.996661i	$-0.473980\pi$
$593$	2358.18			0.163303			0.0816517	+	0.996661i	$0.473980\pi$
$594$		0			0
$595$	−9171.77			−0.631943
$596$	7254.18			0.498561
$597$	−2394.00	−	10006.6i	−0.164121	−	0.686002i
$598$	−11196.5			−0.765648
$599$			8389.64i			0.572273i	0.958189	+	0.286136i	$0.0923710\pi$
$599$			8389.64i			0.572273i	−0.958189	+	0.286136i	$0.907629\pi$
$600$	493.066	+	2060.95i	0.0335489	+	0.140230i
$601$			18745.5i			1.27229i	0.771570	+	0.636144i	$0.219472\pi$
$601$			18745.5i			1.27229i	−0.771570	+	0.636144i	$0.780528\pi$
$602$	1750.91			0.118541
$603$	−15990.1	+	8115.54i	−1.07988	+	0.548077i
$604$			23611.4i			1.59062i
$605$		0			0
$606$	−390.870	−	1633.78i	−0.0262014	−	0.109518i
$607$			8043.28i			0.537836i	0.963163	+	0.268918i	$0.0866661\pi$
$607$			8043.28i			0.537836i	−0.963163	+	0.268918i	$0.913334\pi$
$608$		−	5996.16i		−	0.399961i
$609$	−12271.1	+	2935.76i	−0.816500	+	0.195341i
$610$	−3313.95			−0.219964
$611$	40651.7			2.69164
$612$	−5529.57	+	2806.45i	−0.365228	+	0.185366i
$613$			16367.8i			1.07845i	0.842163	+	0.539223i	$0.181282\pi$
$613$			16367.8i			1.07845i	−0.842163	+	0.539223i	$0.818718\pi$
$614$			9194.92i			0.604360i
$615$	−461.745	+	110.469i	−0.0302754	+	0.00724315i
$616$		0			0
$617$			10135.6i			0.661334i	0.943747	+	0.330667i	$0.107274\pi$
$617$			10135.6i			0.661334i	−0.943747	+	0.330667i	$0.892726\pi$
$618$	984.306	+	4114.26i	0.0640689	+	0.267799i
$619$	−30136.4			−1.95684			−0.978420	−	0.206627i	$-0.933751\pi$
$619$	−30136.4			−1.95684			−0.978420	+	0.206627i	$0.933751\pi$
$620$		−	2652.96i		−	0.171847i
$621$	14349.2	−	12196.6i	0.927236	−	0.788137i
$622$			5754.00i			0.370923i
$623$	6988.94			0.449448
$624$	15494.8	−	3707.00i	0.994050	−	0.237819i
$625$	−18201.3			−1.16488
$626$	4432.64			0.283009
$627$		0			0
$628$	−733.177			−0.0465875
$629$	−265.397			−0.0168236
$630$	6972.18	−	3538.62i	0.440918	−	0.223781i
$631$	−6715.63			−0.423685			−0.211842	−	0.977304i	$-0.567946\pi$
$631$	−6715.63			−0.423685			−0.211842	+	0.977304i	$0.567946\pi$
$632$		−	2847.25i		−	0.179205i
$633$	−11432.0	+	2735.03i	−0.717825	+	0.171734i
$634$		−	67.8590i		−	0.00425083i
$635$	−27457.1			−1.71591
$636$	12009.9	−	2873.27i	0.748779	−	0.179140i
$637$		−	12590.9i		−	0.783158i
$638$		0			0
$639$	47.1851	+	92.9692i	0.00292115	+	0.00575556i
$640$			18062.8i			1.11562i
$641$		−	13269.3i		−	0.817636i	−0.912616	−	0.408818i	$-0.865941\pi$
$641$		−	13269.3i		−	0.817636i	0.912616	−	0.408818i	$-0.134059\pi$
$642$	−267.733	−	1119.09i	−0.0164589	−	0.0687958i
$643$	−21138.4			−1.29645			−0.648223	−	0.761450i	$-0.724488\pi$
$643$	−21138.4			−1.29645			−0.648223	+	0.761450i	$0.724488\pi$
$644$	20728.0			1.26832
$645$	−1104.05	−	4614.77i	−0.0673983	−	0.281715i
$646$			1265.85i			0.0770965i
$647$		−	4143.92i		−	0.251799i	−0.992043	−	0.125900i	$-0.959818\pi$
$647$		−	4143.92i		−	0.251799i	0.992043	−	0.125900i	$-0.0401817\pi$
$648$	6742.31	−	9218.51i	0.408739	−	0.558854i
$649$		0			0
$650$			2171.28i			0.131023i
$651$	−3544.99	+	848.112i	−0.213424	+	0.0510601i
$652$	−2169.02			−0.130284
$653$		−	7163.37i		−	0.429287i	−0.976692	−	0.214643i	$-0.931141\pi$
$653$		−	7163.37i		−	0.429287i	0.976692	−	0.214643i	$-0.0688590\pi$
$654$	−8756.97	+	2095.04i	−0.523585	+	0.125264i
$655$			24716.1i			1.47441i
$656$	−287.489			−0.0171106
$657$	2463.15	+	4853.17i	0.146266	+	0.288189i
$658$	12080.3			0.715715
$659$	−15364.3			−0.908207			−0.454104	−	0.890949i	$-0.650040\pi$
$659$	−15364.3			−0.908207			−0.454104	+	0.890949i	$0.650040\pi$
$660$		0			0
$661$	8389.18			0.493648			0.246824	−	0.969060i	$-0.420613\pi$
$661$	8389.18			0.493648			0.246824	+	0.969060i	$0.420613\pi$
$662$	6553.04			0.384730
$663$	−13350.5	+	3194.00i	−0.782035	+	0.187096i
$664$	11955.5			0.698740
$665$			9943.41i			0.579833i
$666$	201.749	−	102.395i	0.0117382	−	0.00595753i
$667$		−	14550.7i		−	0.844688i
$668$	4836.34			0.280125
$669$	−3933.94	−	16443.3i	−0.227347	−	0.950277i
$670$		−	8585.64i		−	0.495063i
$671$		0			0
$672$	18792.6	−	4495.99i	1.07878	−	0.258090i
$673$		−	10272.9i		−	0.588398i	−0.955744	−	0.294199i	$-0.904947\pi$
$673$		−	10272.9i		−	0.588398i	0.955744	−	0.294199i	$-0.0950529\pi$
$674$		−	10142.6i		−	0.579643i
$675$	−2365.24	−	2782.68i	−0.134871	−	0.158675i
$676$	28198.1			1.60435
$677$	−25579.3			−1.45213			−0.726066	−	0.687625i	$-0.758653\pi$
$677$	−25579.3			−1.45213			−0.726066	+	0.687625i	$0.758653\pi$
$678$	3614.40	−	864.717i	0.204735	−	0.0489812i
$679$		−	16762.1i		−	0.947377i
$680$		−	6414.61i		−	0.361749i
$681$	551.723	+	2306.13i	0.0310456	+	0.129767i
$682$		0			0
$683$		−	15463.3i		−	0.866306i	−0.901320	−	0.433153i	$-0.857401\pi$
$683$		−	15463.3i		−	0.866306i	0.901320	−	0.433153i	$-0.142599\pi$
$684$	3042.56	+	5994.79i	0.170081	+	0.335112i
$685$	29616.1			1.65193
$686$			4340.70i			0.241587i
$687$	4549.09	+	19014.6i	0.252632	+	1.05597i
$688$		−	2873.23i		−	0.159216i
$689$	27336.7			1.51153
$690$	2098.01	+	8769.38i	0.115753	+	0.483833i
$691$	−6666.34			−0.367004			−0.183502	−	0.983019i	$-0.558743\pi$
$691$	−6666.34			−0.367004			−0.183502	+	0.983019i	$0.558743\pi$
$692$	−30970.0			−1.70130
$693$		0			0
$694$	−6312.17			−0.345255
$695$	−23076.7			−1.25950
$696$	−2053.23	−	8582.22i	−0.111821	−	0.467397i
$697$	247.704			0.0134612
$698$		−	3511.23i		−	0.190404i
$699$	919.505	+	3843.41i	0.0497552	+	0.207970i
$700$		−	4019.68i		−	0.217043i
$701$	−16437.9			−0.885664			−0.442832	−	0.896605i	$-0.646026\pi$
$701$	−16437.9			−0.885664			−0.442832	+	0.896605i	$0.646026\pi$
$702$	8916.44	−	7578.84i	0.479386	−	0.407471i
$703$			287.725i			0.0154364i
$704$		0			0
$705$	−7617.37	−	31839.5i	−0.406931	−	1.70092i
$706$			2577.25i			0.137388i
$707$			6884.58i			0.366226i
$708$	20421.4	−	4885.66i	1.08401	−	0.259342i
$709$	27071.9			1.43400			0.717001	−	0.697072i	$-0.245514\pi$
$709$	27071.9			1.43400			0.717001	+	0.697072i	$0.245514\pi$
$710$	−49.9183			−0.00263859
$711$	2220.79	+	4375.64i	0.117139	+	0.230801i
$712$			4887.97i			0.257282i
$713$		−	4203.57i		−	0.220792i
$714$	−3967.32	+	949.151i	−0.207946	+	0.0497494i
$715$		0			0
$716$		−	14973.2i		−	0.781530i
$717$	2984.79	+	12476.0i	0.155466	+	0.649826i
$718$	7973.00			0.414414
$719$		−	34159.3i		−	1.77180i	−0.463872	−	0.885902i	$-0.653540\pi$
$719$		−	34159.3i		−	1.77180i	0.463872	−	0.885902i	$-0.346460\pi$
$720$	−5806.86	−	11441.3i	−0.300568	−	0.592212i
$721$		−	17337.0i		−	0.895514i
$722$	−5842.75			−0.301170
$723$	−16454.2	+	3936.54i	−0.846388	+	0.202492i
$724$	−9116.65			−0.467980
$725$	−2821.76			−0.144548
$726$		0			0
$727$	17015.3			0.868034			0.434017	−	0.900905i	$-0.357096\pi$
$727$	17015.3			0.868034			0.434017	+	0.900905i	$0.357096\pi$
$728$	27827.8			1.41671
$729$	−3171.32	+	19425.8i	−0.161120	+	0.986935i
$730$	−2605.83			−0.132118
$731$			2475.60i			0.125258i
$732$	8930.27	−	2136.50i	0.450918	−	0.107879i
$733$			1697.81i			0.0855524i	0.999085	+	0.0427762i	$0.0136202\pi$
$733$			1697.81i			0.0855524i	−0.999085	+	0.0427762i	$0.986380\pi$
$734$	−2899.83			−0.145824
$735$	−9861.58	+	2359.31i	−0.494898	+	0.118401i
$736$			22283.8i			1.11602i
$737$		0			0
$738$	−188.299	+	95.5684i	−0.00939213	+	0.00476683i
$739$			2797.16i			0.139235i	0.997574	+	0.0696177i	$0.0221780\pi$
$739$			2797.16i			0.139235i	−0.997574	+	0.0696177i	$0.977822\pi$
$740$		−	674.851i		−	0.0335243i
$741$	3462.71	+	14473.7i	0.171668	+	0.717548i
$742$	8123.57			0.401921
$743$	5317.52			0.262558			0.131279	−	0.991345i	$-0.458092\pi$
$743$	5317.52			0.262558			0.131279	+	0.991345i	$0.458092\pi$
$744$	−593.158	−	2479.32i	−0.0292288	−	0.122172i
$745$		−	12932.5i		−	0.635988i
$746$			730.913i			0.0358721i
$747$	−18373.2	+	9325.02i	−0.899919	+	0.456740i
$748$		0			0
$749$			4715.72i			0.230051i
$750$	−6465.60	+	1546.85i	−0.314787	+	0.0753104i
$751$	35698.7			1.73457			0.867286	−	0.497811i	$-0.165863\pi$
$751$	35698.7			1.73457			0.867286	+	0.497811i	$0.165863\pi$
$752$		−	19823.8i		−	0.961301i
$753$	7211.82	−	1725.37i	0.349022	−	0.0835008i
$754$		−	9041.67i		−	0.436709i
$755$	42093.6			2.02906
$756$	−16507.0	+	14030.7i	−0.794117	+	0.674988i
$757$	28996.6			1.39220			0.696102	−	0.717943i	$-0.254916\pi$
$757$	28996.6			1.39220			0.696102	+	0.717943i	$0.254916\pi$
$758$	−10688.5			−0.512169
$759$		0			0
$760$	−6954.29			−0.331919
$761$	24794.3			1.18107			0.590534	−	0.807013i	$-0.298917\pi$
$761$	24794.3			1.18107			0.590534	+	0.807013i	$0.298917\pi$
$762$	−11876.8	+	2841.43i	−0.564633	+	0.135084i
$763$	36900.9			1.75085
$764$			10245.5i			0.485169i
$765$	5003.25	+	9857.96i	0.236462	+	0.465902i
$766$		−	1983.39i		−	0.0935544i
$767$	46482.8			2.18826
$768$	566.270	+	2366.93i	0.0266061	+	0.111210i
$769$		−	6226.59i		−	0.291985i	−0.989286	−	0.145993i	$-0.953362\pi$
$769$		−	6226.59i		−	0.291985i	0.989286	−	0.145993i	$-0.0466376\pi$
$770$		0			0
$771$	−31212.6	+	7467.38i	−1.45797	+	0.348808i
$772$		−	14242.0i		−	0.663965i
$773$			3362.25i			0.156445i	0.996936	+	0.0782223i	$0.0249244\pi$
$773$			3362.25i			0.156445i	−0.996936	+	0.0782223i	$0.975076\pi$
$774$	−955.129	−	1881.90i	−0.0443558	−	0.0873947i
$775$	−815.180			−0.0377834
$776$	11723.2			0.542316
$777$	−901.763	+	215.740i	−0.0416352	+	0.00996091i
$778$			6068.96i			0.279669i
$779$		−	268.544i		−	0.0123512i
$780$	−8121.68	−	33947.5i	−0.372824	−	1.55835i
$781$		0			0
$782$		−	4704.35i		−	0.215124i
$783$	9849.34	+	11587.7i	0.449536	+	0.528875i
$784$	−6139.97			−0.279700
$785$			1307.09i			0.0594292i
$786$	2557.77	+	10691.1i	0.116072	+	0.485165i
$787$			36683.3i			1.66152i	0.556630	+	0.830761i	$0.312094\pi$
$787$			36683.3i			1.66152i	−0.556630	+	0.830761i	$0.687906\pi$
$788$	−36742.7			−1.66104
$789$	6355.75	+	26566.2i	0.286782	+	1.19871i
$790$	−2349.43			−0.105809
$791$	−15230.7			−0.684627
$792$		0			0
$793$	20326.9			0.910253
$794$	−7946.01			−0.355155
$795$	−5122.39	−	21410.9i	−0.228519	−	0.955177i
$796$	−13649.9			−0.607798
$797$			18633.9i			0.828163i	0.910240	+	0.414082i	$0.135897\pi$
$797$			18633.9i			0.828163i	−0.910240	+	0.414082i	$0.864103\pi$
$798$	1029.00	+	4301.10i	0.0456471	+	0.190798i
$799$			17080.4i			0.756271i
$800$	4321.40			0.190981
$801$	−3812.51	−	7511.82i	−0.168175	−	0.331357i
$802$			6025.32i			0.265289i
$803$		0			0
$804$	5535.16	+	23136.2i	0.242798	+	1.01486i
$805$		−	36953.2i		−	1.61792i
$806$		−	2612.05i		−	0.114151i
$807$	−10914.5	+	2611.21i	−0.476095	+	0.113902i
$808$	−4814.99			−0.209642
$809$	−25622.8			−1.11353			−0.556767	−	0.830669i	$-0.687958\pi$
$809$	−25622.8			−1.11353			−0.556767	+	0.830669i	$0.687958\pi$
$810$	−7606.74	−	5563.47i	−0.329967	−	0.241334i
$811$		−	16026.4i		−	0.693913i	−0.937881	−	0.346957i	$-0.887215\pi$
$811$		−	16026.4i		−	0.693913i	0.937881	−	0.346957i	$-0.112785\pi$
$812$			16738.8i			0.723420i
$813$	−24608.3	+	5887.34i	−1.06156	+	0.253971i
$814$		0			0
$815$			3866.87i			0.166197i
$816$	1557.55	+	6510.34i	0.0668200	+	0.279299i
$817$	2683.88			0.114929
$818$		−	6530.69i		−	0.279145i
$819$	−42765.6	+	21705.0i	−1.82461	+	0.926050i
$820$			629.861i			0.0268240i
$821$	12004.6			0.510310			0.255155	−	0.966900i	$-0.417873\pi$
$821$	12004.6			0.510310			0.255155	+	0.966900i	$0.417873\pi$
$822$	12810.6	−	3064.85i	0.543580	−	0.130047i
$823$	−6084.44			−0.257704			−0.128852	−	0.991664i	$-0.541129\pi$
$823$	−6084.44			−0.257704			−0.128852	+	0.991664i	$0.541129\pi$
$824$	12125.3			0.512627
$825$		0			0
$826$	13813.2			0.581866
$827$	5338.50			0.224471			0.112236	−	0.993682i	$-0.464199\pi$
$827$	5338.50			0.224471			0.112236	+	0.993682i	$0.464199\pi$
$828$	−11307.2	−	22278.7i	−0.474581	−	0.935072i
$829$	2656.77			0.111307			0.0556534	−	0.998450i	$-0.482276\pi$
$829$	2656.77			0.111307			0.0556534	+	0.998450i	$0.482276\pi$
$830$		−	9865.18i		−	0.412561i
$831$	29366.8	−	7025.79i	1.22590	−	0.293287i
$832$		−	10682.0i		−	0.445112i
$833$	5290.26			0.220044
$834$	−9982.00	+	2388.12i	−0.414447	+	0.0991532i
$835$		−	8622.08i		−	0.357340i
$836$		0			0
$837$	2845.38	+	3347.56i	0.117504	+	0.138242i
$838$			152.483i			0.00628574i
$839$		−	17499.2i		−	0.720070i	−0.932939	−	0.360035i	$-0.882765\pi$
$839$		−	17499.2i		−	0.720070i	0.932939	−	0.360035i	$-0.117235\pi$
$840$	−5214.40	−	21795.5i	−0.214183	−	0.895257i
$841$	−12638.6			−0.518209
$842$	3745.08			0.153283
$843$	−6766.02	−	28281.0i	−0.276434	−	1.15546i
$844$			15594.3i			0.635993i
$845$		−	50270.7i		−	2.04659i
$846$	−6589.90	−	12984.1i	−0.267808	−	0.527664i
$847$		0			0
$848$		−	13330.7i		−	0.539834i
$849$	4456.35	−	1066.15i	0.180143	−	0.0430979i
$850$	−912.294			−0.0368135
$851$		−	1069.29i		−	0.0430726i
$852$	134.517	−	32.1823i	0.00540903	−	0.00129407i
$853$		−	2548.84i		−	0.102310i	−0.998691	−	0.0511550i	$-0.983710\pi$
$853$		−	2548.84i		−	0.102310i	0.998691	−	0.0511550i	$-0.0162903\pi$
$854$	6040.49			0.242039
$855$	10687.3	−	5424.19i	0.427484	−	0.216963i
$856$	−3298.11			−0.131690
$857$	21613.5			0.861498			0.430749	−	0.902472i	$-0.358249\pi$
$857$	21613.5			0.861498			0.430749	+	0.902472i	$0.358249\pi$
$858$		0			0
$859$	13771.6			0.547009			0.273504	−	0.961871i	$-0.411817\pi$
$859$	13771.6			0.547009			0.273504	+	0.961871i	$0.411817\pi$
$860$	−6294.95			−0.249600
$861$	841.645	−	201.357i	0.0333138	−	0.00797008i
$862$	3417.94			0.135053
$863$			9563.52i			0.377226i	0.982051	+	0.188613i	$0.0603992\pi$
$863$			9563.52i			0.377226i	−0.982051	+	0.188613i	$0.939601\pi$
$864$	−15083.8	−	17746.0i	−0.593938	−	0.698763i
$865$			55212.4i			2.17026i
$866$	−14796.9			−0.580622
$867$	4597.92	+	19218.7i	0.180108	+	0.752826i
$868$			4835.68i			0.189094i
$869$		0			0
$870$	−7081.69	+	1694.24i	−0.275968	+	0.0660231i
$871$			52662.2i			2.04867i
$872$			25808.0i			1.00226i
$873$	−18016.1	+	9143.80i	−0.698457	+	0.354491i
$874$	−5100.14			−0.197385
$875$	27245.3			1.05264
$876$	7022.07	−	1679.98i	0.270838	−	0.0647958i
$877$		−	39737.0i		−	1.53002i	−0.644021	−	0.765008i	$-0.722735\pi$
$877$		−	39737.0i		−	1.53002i	0.644021	−	0.765008i	$-0.277265\pi$
$878$		−	6191.23i		−	0.237977i
$879$	−4468.24	−	18676.6i	−0.171456	−	0.716663i
$880$		0			0
$881$		−	50105.5i		−	1.91612i	−0.286573	−	0.958058i	$-0.592516\pi$
$881$		−	50105.5i		−	1.91612i	0.286573	−	0.958058i	$-0.407484\pi$
$882$	−4021.55	+	2041.07i	−0.153529	+	0.0779212i
$883$	−22867.8			−0.871531			−0.435766	−	0.900060i	$-0.643522\pi$
$883$	−22867.8			−0.871531			−0.435766	+	0.900060i	$0.643522\pi$
$884$			18211.2i			0.692883i
$885$	−8710.01	−	36406.6i	−0.330829	−	1.38282i
$886$			9483.46i			0.359597i
$887$	−14484.0			−0.548280			−0.274140	−	0.961690i	$-0.588393\pi$
$887$	−14484.0			−0.548280			−0.274140	+	0.961690i	$0.588393\pi$
$888$	−150.886	−	630.681i	−0.00570201	−	0.0238336i
$889$	50047.5			1.88812
$890$	4033.35			0.151908
$891$		0			0
$892$	−22430.1			−0.841946
$893$	18517.4			0.693909
$894$	−1338.34	−	5594.06i	−0.0500679	−	0.209277i
$895$	−26693.8			−0.996956
$896$		−	32924.0i		−	1.22758i
$897$	−12868.7	−	53789.2i	−0.479010	−	2.00220i
$898$		−	1291.07i		−	0.0479773i
$899$	3394.58			0.125935
$900$	−4320.42	+	2192.76i	−0.160015	+	0.0812134i
$901$			11485.9i			0.424696i
$902$		0			0
$903$	2012.40	+	8411.57i	0.0741624	+	0.309988i
$904$		−	10652.1i		−	0.391907i
$905$			16252.9i			0.596977i
$906$	18207.9	−	4356.10i	0.667679	−	0.159737i
$907$	12842.2			0.470143			0.235071	−	0.971978i	$-0.424468\pi$
$907$	12842.2			0.470143			0.235071	+	0.971978i	$0.424468\pi$
$908$	3145.76			0.114973
$909$	7399.66	−	3755.58i	0.270001	−	0.137035i
$910$		−	22962.3i		−	0.836476i
$911$			28875.0i			1.05013i	0.851061	+	0.525067i	$0.175960\pi$
$911$			28875.0i			1.05013i	−0.851061	+	0.525067i	$0.824040\pi$
$912$	7058.07	−	1688.59i	0.256268	−	0.0613101i
$913$		0			0
$914$			5843.67i			0.211478i
$915$	−3808.89	−	15920.6i	−0.137615	−	0.575213i
$916$	25937.5			0.935589
$917$		−	45051.2i		−	1.62238i
$918$	3184.36	+	3746.37i	0.114487	+	0.134693i
$919$		−	24199.3i		−	0.868619i	−0.900764	−	0.434309i	$-0.856992\pi$
$919$		−	24199.3i		−	0.868619i	0.900764	−	0.434309i	$-0.143008\pi$
$920$	25844.6			0.926163
$921$	−44173.6	+	10568.2i	−1.58042	+	0.378104i
$922$	−19486.8			−0.696054
$923$	306.186			0.0109190
$924$		0			0
$925$	−207.363			−0.00737085
$926$	8101.05			0.287491
$927$	−18634.1	+	9457.46i	−0.660221	+	0.335085i
$928$	−17995.2			−0.636554
$929$		−	31452.6i		−	1.11079i	−0.831586	−	0.555397i	$-0.812566\pi$
$929$		−	31452.6i		−	1.11079i	0.831586	−	0.555397i	$-0.187434\pi$
$930$	−2045.83	+	489.450i	−0.0721349	+	0.0172577i
$931$		−	5735.35i		−	0.201899i
$932$	5242.74			0.184261
$933$	−27642.9	+	6613.36i	−0.969977	+	0.232060i
$934$			2365.12i			0.0828578i
$935$		0			0
$936$	−15180.2	−	29909.7i	−0.530108	−	1.04448i
$937$		−	18594.4i		−	0.648296i	−0.946006	−	0.324148i	$-0.894922\pi$
$937$		−	18594.4i		−	0.648296i	0.946006	−	0.324148i	$-0.105078\pi$
$938$			15649.5i			0.544748i
$939$	5094.65	+	21294.9i	0.177058	+	0.740079i
$940$	−43431.9			−1.50701
$941$	−17890.4			−0.619778			−0.309889	−	0.950773i	$-0.600292\pi$
$941$	−17890.4			−0.619778			−0.309889	+	0.950773i	$0.600292\pi$
$942$	135.265	+	565.390i	0.00467854	+	0.0195556i
$943$			998.003i			0.0344639i
$944$		−	22667.3i		−	0.781523i
$945$	25013.5	+	29428.1i	0.861046	+	1.01301i
$946$		0			0
$947$			43915.9i			1.50694i	0.657481	+	0.753471i	$0.271622\pi$
$947$			43915.9i			1.50694i	−0.657481	+	0.753471i	$0.728378\pi$
$948$	6331.14	−	1514.68i	0.216905	−	0.0518928i
$949$	15983.5			0.546730
$950$			989.048i			0.0337778i
$951$	326.003	−	77.9937i	0.0111161	−	0.00265943i
$952$			11692.2i			0.398054i
$953$	−34107.5			−1.15934			−0.579669	−	0.814852i	$-0.696818\pi$
$953$	−34107.5			−1.15934			−0.579669	+	0.814852i	$0.696818\pi$
$954$	−4431.46	−	8731.34i	−0.150392	−	0.296318i
$955$	18265.4			0.618904
$956$	17018.4			0.575746
$957$		0			0
$958$	507.423			0.0171128
$959$	−53982.6			−1.81772
$960$	−8366.47	+	2001.62i	−0.281278	+	0.0672936i
$961$	−28810.3			−0.967082
$962$		−	664.444i		−	0.0222688i
$963$	5068.52	−	2572.45i	0.169606	−	0.0860810i
$964$			22445.0i			0.749900i
$965$	−25390.2			−0.846984
$966$	−3824.14	−	15984.4i	−0.127370	−	0.532390i
$967$		−	25107.8i		−	0.834967i	−0.908684	−	0.417484i	$-0.862912\pi$
$967$		−	25107.8i		−	0.834967i	0.908684	−	0.417484i	$-0.137088\pi$
$968$		0			0
$969$	−6081.31	+	1454.91i	−0.201610	+	0.0482336i
$970$		−	9673.46i		−	0.320202i
$971$		−	46643.4i		−	1.54156i	−0.637098	−	0.770782i	$-0.719866\pi$
$971$		−	46643.4i		−	1.54156i	0.637098	−	0.770782i	$-0.280134\pi$
$972$	24085.0	+	10088.1i	0.794782	+	0.332898i
$973$	42063.0			1.38590
$974$	−7561.57			−0.248756
$975$	−10431.1	+	2495.56i	−0.342628	+	0.0819713i
$976$		−	9912.41i		−	0.325091i
$977$			43433.8i			1.42228i	0.703048	+	0.711142i	$0.251822\pi$
$977$			43433.8i			1.42228i	−0.703048	+	0.711142i	$0.748178\pi$
$978$	400.167	+	1672.64i	0.0130838	+	0.0546884i
$979$		0			0
$980$			13452.1i			0.438480i
$981$	−20129.6	−	39661.6i	−0.655138	−	1.29082i
$982$	−10876.2			−0.353437
$983$			52042.9i			1.68862i	0.535858	+	0.844308i	$0.319988\pi$
$983$			52042.9i			1.68862i	−0.535858	+	0.844308i	$0.680012\pi$
$984$	140.827	+	588.635i	0.00456238	+	0.0190701i
$985$			65503.7i			2.11891i
$986$	3798.99			0.122702
$987$	13884.5	+	58035.5i	0.447771	+	1.87162i
$988$	19743.3			0.635748
$989$	−9974.24			−0.320690
$990$		0			0
$991$	60025.3			1.92408			0.962042	−	0.272900i	$-0.0879829\pi$
$991$	60025.3			1.92408			0.962042	+	0.272900i	$0.0879829\pi$
$992$	−5198.65			−0.166388
$993$	7531.74	+	31481.6i	0.240697	+	1.00608i
$994$	90.9885			0.00290340
$995$			24334.6i			0.775336i
$996$	6360.07	+	26584.2i	0.202336	+	0.845736i
$997$		−	35231.8i		−	1.11916i	−0.828777	−	0.559579i	$-0.810963\pi$
$997$		−	35231.8i		−	1.11916i	0.828777	−	0.559579i	$-0.189037\pi$
$998$	8975.21			0.284675
$999$	723.797	+	851.541i	0.0229229	+	0.0269685i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	363.4.d.d.362.18		40
3.2	odd	2	inner	363.4.d.d.362.23		40
11.4	even	5		33.4.f.a.17.5	yes	40
11.8	odd	10		33.4.f.a.2.6	yes	40
11.10	odd	2	inner	363.4.d.d.362.24		40
33.8	even	10		33.4.f.a.2.5	✓	40
33.26	odd	10		33.4.f.a.17.6	yes	40
33.32	even	2	inner	363.4.d.d.362.17		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.4.f.a.2.5	✓	40	33.8	even	10
33.4.f.a.2.6	yes	40	11.8	odd	10
33.4.f.a.17.5	yes	40	11.4	even	5
33.4.f.a.17.6	yes	40	33.26	odd	10
363.4.d.d.362.17		40	33.32	even	2	inner
363.4.d.d.362.18		40	1.1	even	1	trivial
363.4.d.d.362.23		40	3.2	odd	2	inner
363.4.d.d.362.24		40	11.10	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:	\( N \)	\(=\)	\( 363 = 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	363.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.05192 q^{2} +(-1.20902 - 5.05354i) q^{3} -6.89347 q^{4} +12.2895i q^{5} +(1.27179 + 5.31590i) q^{6} -22.4006i q^{7} +15.6667 q^{8} +(-24.0765 + 12.2197i) q^{9} +O(q^{10})\)	\(q-1.05192 q^{2} +(-1.20902 - 5.05354i) q^{3} -6.89347 q^{4} +12.2895i q^{5} +(1.27179 + 5.31590i) q^{6} -22.4006i q^{7} +15.6667 q^{8} +(-24.0765 + 12.2197i) q^{9} -12.9275i q^{10} +(8.33435 + 34.8364i) q^{12} +79.2941i q^{13} +23.5636i q^{14} +(62.1054 - 14.8582i) q^{15} +38.6677 q^{16} -33.3165 q^{17} +(25.3265 - 12.8541i) q^{18} +36.1195i q^{19} -84.7171i q^{20} +(-113.202 + 27.0828i) q^{21} -134.233i q^{23} +(-18.9414 - 79.1723i) q^{24} -26.0312 q^{25} -83.4108i q^{26} +(90.8616 + 106.898i) q^{27} +154.418i q^{28} +108.399 q^{29} +(-65.3297 + 15.6296i) q^{30} +31.3155 q^{31} -166.009 q^{32} +35.0462 q^{34} +275.292 q^{35} +(165.971 - 84.2360i) q^{36} +7.96593 q^{37} -37.9947i q^{38} +(400.716 - 95.8682i) q^{39} +192.535i q^{40} -7.43487 q^{41} +(119.080 - 28.4889i) q^{42} -74.3056i q^{43} +(-150.173 - 295.888i) q^{45} +141.202i q^{46} -512.670i q^{47} +(-46.7501 - 195.409i) q^{48} -158.788 q^{49} +27.3826 q^{50} +(40.2804 + 168.366i) q^{51} -546.611i q^{52} -344.751i q^{53} +(-95.5789 - 112.448i) q^{54} -350.944i q^{56} +(182.531 - 43.6693i) q^{57} -114.027 q^{58} -586.208i q^{59} +(-428.121 + 102.425i) q^{60} -256.349i q^{61} -32.9413 q^{62} +(273.728 + 539.329i) q^{63} -134.714 q^{64} -974.483 q^{65} +664.138 q^{67} +229.667 q^{68} +(-678.351 + 162.290i) q^{69} -289.584 q^{70} -3.86140i q^{71} +(-377.200 + 191.442i) q^{72} -201.573i q^{73} -8.37949 q^{74} +(31.4722 + 131.550i) q^{75} -248.989i q^{76} +(-421.520 + 100.845i) q^{78} -181.739i q^{79} +475.206i q^{80} +(430.359 - 588.415i) q^{81} +7.82086 q^{82} +763.116 q^{83} +(780.358 - 186.695i) q^{84} -409.443i q^{85} +78.1633i q^{86} +(-131.057 - 547.800i) q^{87} +311.998i q^{89} +(157.970 + 311.250i) q^{90} +1776.24 q^{91} +925.330i q^{92} +(-37.8611 - 158.254i) q^{93} +539.286i q^{94} -443.890 q^{95} +(200.708 + 838.932i) q^{96} +748.285 q^{97} +167.032 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 8 q^{3} + 132 q^{4} - 60 q^{9}+O(q^{10}) \) 40 * q - 8 * q^3 + 132 * q^4 - 60 * q^9	\( 40 q - 8 q^{3} + 132 q^{4} - 60 q^{9} - 90 q^{12} - 212 q^{15} + 460 q^{16} + 296 q^{25} + 280 q^{27} - 320 q^{31} - 188 q^{34} - 2254 q^{36} + 796 q^{37} + 1240 q^{42} - 1662 q^{45} - 486 q^{48} + 1536 q^{49} + 2268 q^{58} - 6636 q^{60} - 1512 q^{64} + 4556 q^{67} - 1140 q^{69} - 4276 q^{70} + 3462 q^{75} - 7640 q^{78} + 3572 q^{81} + 9408 q^{82} - 816 q^{91} - 11516 q^{93} - 7916 q^{97}+O(q^{100}) \) 40 * q - 8 * q^3 + 132 * q^4 - 60 * q^9 - 90 * q^12 - 212 * q^15 + 460 * q^16 + 296 * q^25 + 280 * q^27 - 320 * q^31 - 188 * q^34 - 2254 * q^36 + 796 * q^37 + 1240 * q^42 - 1662 * q^45 - 486 * q^48 + 1536 * q^49 + 2268 * q^58 - 6636 * q^60 - 1512 * q^64 + 4556 * q^67 - 1140 * q^69 - 4276 * q^70 + 3462 * q^75 - 7640 * q^78 + 3572 * q^81 + 9408 * q^82 - 816 * q^91 - 11516 * q^93 - 7916 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more