LMFDB - Embedded newform 168.4.q.d.121.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [168,4,Mod(25,168)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(168, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))

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

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

chi := DirichletCharacter("168.25");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 168 = 2^{3} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	168.q (of order $3$, degree $2$, 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:	$9.91232088096$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{505})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 127x^{2} + 126x + 15876 $ x^4 - x^3 + 127x^2 + 126x + 15876
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.2
Root			$5.86805 - 10.1638i$ of defining polynomial
Character	$\chi$	$=$	168.121
Dual form			168.4.q.d.25.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 + 2.59808i) q^{3} +(3.36805 - 5.83364i) q^{5} +(-11.2361 + 14.7224i) q^{7} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})$	\(q+(1.50000 + 2.59808i) q^{3} +(3.36805 - 5.83364i) q^{5} +(-11.2361 + 14.7224i) q^{7} +(-4.50000 + 7.79423i) q^{9} +(26.8403 + 46.4887i) q^{11} +1.73610 q^{13} +20.2083 q^{15} +(23.4722 + 40.6551i) q^{17} +(10.0764 - 17.4528i) q^{19} +(-55.1042 - 7.10860i) q^{21} +(-59.4722 + 103.009i) q^{23} +(39.8125 + 68.9572i) q^{25} -27.0000 q^{27} -103.681 q^{29} +(78.7639 + 136.423i) q^{31} +(-80.5208 + 139.466i) q^{33} +(48.0415 + 115.133i) q^{35} +(18.8681 - 32.6804i) q^{37} +(2.60415 + 4.51053i) q^{39} -287.250 q^{41} +504.875 q^{43} +(30.3125 + 52.5027i) q^{45} +(110.250 - 190.958i) q^{47} +(-90.5000 - 330.846i) q^{49} +(-70.4166 + 121.965i) q^{51} +(-146.160 - 253.156i) q^{53} +361.597 q^{55} +60.4582 q^{57} +(297.937 + 516.043i) q^{59} +(132.695 - 229.834i) q^{61} +(-64.1875 - 153.828i) q^{63} +(5.84728 - 10.1278i) q^{65} +(-468.368 - 811.237i) q^{67} -356.833 q^{69} -545.944 q^{71} +(-149.687 - 259.266i) q^{73} +(-119.437 + 206.872i) q^{75} +(-986.006 - 127.198i) q^{77} +(470.166 - 814.352i) q^{79} +(-40.5000 - 70.1481i) q^{81} +611.319 q^{83} +316.222 q^{85} +(-155.521 - 269.370i) q^{87} +(588.097 - 1018.61i) q^{89} +(-19.5070 + 25.5597i) q^{91} +(-236.292 + 409.269i) q^{93} +(-67.8754 - 117.564i) q^{95} +1482.49 q^{97} -483.125 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 6 q^{3} - 9 q^{5} - 18 q^{9}+O(q^{10}) $ 4 * q + 6 * q^3 - 9 * q^5 - 18 * q^9	$ 4 q + 6 q^{3} - 9 q^{5} - 18 q^{9} - 5 q^{11} - 38 q^{13} - 54 q^{15} + 4 q^{17} - 117 q^{19} - 153 q^{21} - 148 q^{23} - 43 q^{25} - 108 q^{27} - 190 q^{29} + 360 q^{31} + 15 q^{33} - 482 q^{35} + 53 q^{37} - 57 q^{39} - 340 q^{41} + 806 q^{43} - 81 q^{45} - 368 q^{47} - 362 q^{49} - 12 q^{51} - 697 q^{53} + 2570 q^{55} - 702 q^{57} + 585 q^{59} + 1160 q^{61} - 459 q^{63} + 338 q^{65} - 233 q^{67} - 888 q^{69} + 1232 q^{71} + 817 q^{73} + 129 q^{75} - 1135 q^{77} + 802 q^{79} - 162 q^{81} - 566 q^{83} + 1984 q^{85} - 285 q^{87} + 1858 q^{89} - 505 q^{91} - 1080 q^{93} - 2294 q^{95} + 3458 q^{97} + 90 q^{99}+O(q^{100}) $ 4 * q + 6 * q^3 - 9 * q^5 - 18 * q^9 - 5 * q^11 - 38 * q^13 - 54 * q^15 + 4 * q^17 - 117 * q^19 - 153 * q^21 - 148 * q^23 - 43 * q^25 - 108 * q^27 - 190 * q^29 + 360 * q^31 + 15 * q^33 - 482 * q^35 + 53 * q^37 - 57 * q^39 - 340 * q^41 + 806 * q^43 - 81 * q^45 - 368 * q^47 - 362 * q^49 - 12 * q^51 - 697 * q^53 + 2570 * q^55 - 702 * q^57 + 585 * q^59 + 1160 * q^61 - 459 * q^63 + 338 * q^65 - 233 * q^67 - 888 * q^69 + 1232 * q^71 + 817 * q^73 + 129 * q^75 - 1135 * q^77 + 802 * q^79 - 162 * q^81 - 566 * q^83 + 1984 * q^85 - 285 * q^87 + 1858 * q^89 - 505 * q^91 - 1080 * q^93 - 2294 * q^95 + 3458 * q^97 + 90 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

$n$	$73$	$85$	$113$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.50000	+	2.59808i	0.288675	+	0.500000i
$3$	1.50000	+	2.59808i	0.288675	+	0.500000i
$4$		0			0
$5$	3.36805	−	5.83364i	0.301248	−	0.521776i	−0.675171	−	0.737661i	$-0.735930\pi$
$5$	3.36805	−	5.83364i	0.301248	−	0.521776i	0.976419	+	0.215885i	$0.0692636\pi$
$6$		0			0
$7$	−11.2361	+	14.7224i	−0.606693	+	0.794937i
$7$	−11.2361	+	14.7224i	−0.606693	+	0.794937i
$8$		0			0
$9$	−4.50000	+	7.79423i	−0.166667	+	0.288675i
$10$		0			0
$11$	26.8403	+	46.4887i	0.735695	+	1.27426i	0.954418	+	0.298474i	$0.0964775\pi$
$11$	26.8403	+	46.4887i	0.735695	+	1.27426i	−0.218723	+	0.975787i	$0.570189\pi$
$12$		0			0
$13$	1.73610			0.0370391			0.0185195	−	0.999828i	$-0.494105\pi$
$13$	1.73610			0.0370391			0.0185195	+	0.999828i	$0.494105\pi$
$14$		0			0
$15$	20.2083			0.347851
$16$		0			0
$17$	23.4722	+	40.6551i	0.334873	+	0.580018i	0.983460	−	0.181123i	$-0.0579732\pi$
$17$	23.4722	+	40.6551i	0.334873	+	0.580018i	−0.648587	+	0.761140i	$0.724640\pi$
$18$		0			0
$19$	10.0764	−	17.4528i	0.121667	−	0.210734i	−0.798758	−	0.601652i	$-0.794509\pi$
$19$	10.0764	−	17.4528i	0.121667	−	0.210734i	0.920425	+	0.390919i	$0.127843\pi$
$20$		0			0
$21$	−55.1042	−	7.10860i	−0.572605	−	0.0738678i
$22$		0			0
$23$	−59.4722	+	103.009i	−0.539166	+	0.933862i	0.459783	+	0.888031i	$0.347927\pi$
$23$	−59.4722	+	103.009i	−0.539166	+	0.933862i	−0.998949	+	0.0458314i	$0.985406\pi$
$24$		0			0
$25$	39.8125	+	68.9572i	0.318500	+	0.551658i
$26$		0			0
$27$	−27.0000			−0.192450
$28$		0			0
$29$	−103.681			−0.663896			−0.331948	−	0.943298i	$-0.607706\pi$
$29$	−103.681			−0.663896			−0.331948	+	0.943298i	$0.607706\pi$
$30$		0			0
$31$	78.7639	+	136.423i	0.456336	+	0.790397i	0.998764	−	0.0497053i	$-0.0158282\pi$
$31$	78.7639	+	136.423i	0.456336	+	0.790397i	−0.542428	+	0.840102i	$0.682495\pi$
$32$		0			0
$33$	−80.5208	+	139.466i	−0.424754	+	0.735695i
$34$		0			0
$35$	48.0415	+	115.133i	0.232014	+	0.556031i
$36$		0			0
$37$	18.8681	−	32.6804i	0.0838348	−	0.145206i	−0.821059	−	0.570843i	$-0.806617\pi$
$37$	18.8681	−	32.6804i	0.0838348	−	0.145206i	0.904894	+	0.425637i	$0.139950\pi$
$38$		0			0
$39$	2.60415	+	4.51053i	0.0106923	+	0.0185195i
$40$		0			0
$41$	−287.250			−1.09417			−0.547084	−	0.837078i	$-0.684262\pi$
$41$	−287.250			−1.09417			−0.547084	+	0.837078i	$0.684262\pi$
$42$		0			0
$43$	504.875			1.79053			0.895264	−	0.445537i	$-0.146987\pi$
$43$	504.875			1.79053			0.895264	+	0.445537i	$0.146987\pi$
$44$		0			0
$45$	30.3125	+	52.5027i	0.100416	+	0.173925i
$46$		0			0
$47$	110.250	−	190.958i	0.342162	−	0.592641i	−0.642672	−	0.766141i	$-0.722174\pi$
$47$	110.250	−	190.958i	0.342162	−	0.592641i	0.984834	+	0.173500i	$0.0555077\pi$
$48$		0			0
$49$	−90.5000	−	330.846i	−0.263848	−	0.964564i
$50$		0			0
$51$	−70.4166	+	121.965i	−0.193339	+	0.334873i
$52$		0			0
$53$	−146.160	−	253.156i	−0.378803	−	0.656107i	0.612085	−	0.790792i	$-0.290331\pi$
$53$	−146.160	−	253.156i	−0.378803	−	0.656107i	−0.990888	+	0.134685i	$0.956998\pi$
$54$		0			0
$55$	361.597			0.886505
$56$		0			0
$57$	60.4582			0.140489
$58$		0			0
$59$	297.937	+	516.043i	0.657426	+	1.13870i	0.981280	+	0.192588i	$0.0616882\pi$
$59$	297.937	+	516.043i	0.657426	+	1.13870i	−0.323853	+	0.946107i	$0.604978\pi$
$60$		0			0
$61$	132.695	−	229.834i	0.278521	−	0.482413i	−0.692496	−	0.721422i	$-0.743489\pi$
$61$	132.695	−	229.834i	0.278521	−	0.482413i	0.971017	+	0.239009i	$0.0768224\pi$
$62$		0			0
$63$	−64.1875	−	153.828i	−0.128363	−	0.307626i
$64$		0			0
$65$	5.84728	−	10.1278i	0.0111579	−	0.0193261i
$66$		0			0
$67$	−468.368	−	811.237i	−0.854033	−	1.47923i	−0.877539	−	0.479505i	$-0.840816\pi$
$67$	−468.368	−	811.237i	−0.854033	−	1.47923i	0.0235058	−	0.999724i	$-0.492517\pi$
$68$		0			0
$69$	−356.833			−0.622575
$70$		0			0
$71$	−545.944			−0.912558			−0.456279	−	0.889837i	$-0.650818\pi$
$71$	−545.944			−0.912558			−0.456279	+	0.889837i	$0.650818\pi$
$72$		0			0
$73$	−149.687	−	259.266i	−0.239994	−	0.415682i	0.720718	−	0.693228i	$-0.243812\pi$
$73$	−149.687	−	259.266i	−0.239994	−	0.415682i	−0.960712	+	0.277546i	$0.910479\pi$
$74$		0			0
$75$	−119.437	+	206.872i	−0.183886	+	0.318500i
$76$		0			0
$77$	−986.006	−	127.198i	−1.45930	−	0.188254i
$78$		0			0
$79$	470.166	−	814.352i	0.669593	−	1.15977i	−0.308425	−	0.951249i	$-0.599802\pi$
$79$	470.166	−	814.352i	0.669593	−	1.15977i	0.978018	−	0.208521i	$-0.0668648\pi$
$80$		0			0
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	611.319			0.808445			0.404223	−	0.914661i	$-0.367542\pi$
$83$	611.319			0.808445			0.404223	+	0.914661i	$0.367542\pi$
$84$		0			0
$85$	316.222			0.403519
$86$		0			0
$87$	−155.521	−	269.370i	−0.191650	−	0.331948i
$88$		0			0
$89$	588.097	−	1018.61i	0.700429	−	1.21318i	−0.267887	−	0.963450i	$-0.586325\pi$
$89$	588.097	−	1018.61i	0.700429	−	1.21318i	0.968316	−	0.249728i	$-0.0803412\pi$
$90$		0			0
$91$	−19.5070	+	25.5597i	−0.0224713	+	0.0294437i
$92$		0			0
$93$	−236.292	+	409.269i	−0.263466	+	0.456336i
$94$		0			0
$95$	−67.8754	−	117.564i	−0.0733039	−	0.126966i
$96$		0			0
$97$	1482.49			1.55179			0.775895	−	0.630862i	$-0.217299\pi$
$97$	1482.49			1.55179			0.775895	+	0.630862i	$0.217299\pi$
$98$		0			0
$99$	−483.125			−0.490463
$100$		0			0
$101$	−308.972	−	535.155i	−0.304395	−	0.527227i	0.672732	−	0.739886i	$-0.265121\pi$
$101$	−308.972	−	535.155i	−0.304395	−	0.527227i	−0.977126	+	0.212660i	$0.931787\pi$
$102$		0			0
$103$	408.382	−	707.338i	0.390670	−	0.676661i	−0.601868	−	0.798596i	$-0.705577\pi$
$103$	408.382	−	707.338i	0.390670	−	0.676661i	0.992538	+	0.121935i	$0.0389099\pi$
$104$		0			0
$105$	−227.063	+	297.515i	−0.211038	+	0.276519i
$106$		0			0
$107$	−842.688	+	1459.58i	−0.761361	+	1.31872i	0.180787	+	0.983522i	$0.442135\pi$
$107$	−842.688	+	1459.58i	−0.761361	+	1.31872i	−0.942149	+	0.335195i	$0.891198\pi$
$108$		0			0
$109$	−45.7984	−	79.3252i	−0.0402449	−	0.0697062i	0.845201	−	0.534448i	$-0.179480\pi$
$109$	−45.7984	−	79.3252i	−0.0402449	−	0.0697062i	−0.885446	+	0.464742i	$0.846147\pi$
$110$		0			0
$111$	113.208			0.0968041
$112$		0			0
$113$	614.194			0.511314			0.255657	−	0.966767i	$-0.417708\pi$
$113$	614.194			0.511314			0.255657	+	0.966767i	$0.417708\pi$
$114$		0			0
$115$	400.611	+	693.878i	0.324845	+	0.562648i
$116$		0			0
$117$	−7.81246	+	13.5316i	−0.00617318	+	0.0106923i
$118$		0			0
$119$	−862.277	−	111.236i	−0.664242	−	0.0856893i
$120$		0			0
$121$	−775.299	+	1342.86i	−0.582493	+	1.00891i
$122$		0			0
$123$	−430.875	−	746.297i	−0.315859	−	0.547084i
$124$		0			0
$125$	1378.37			0.986284
$126$		0			0
$127$	234.278			0.163691			0.0818457	−	0.996645i	$-0.473919\pi$
$127$	234.278			0.163691			0.0818457	+	0.996645i	$0.473919\pi$
$128$		0			0
$129$	757.312	+	1311.70i	0.516881	+	0.895264i
$130$		0			0
$131$	−1332.38	+	2307.75i	−0.888631	+	1.53915i	−0.0471373	+	0.998888i	$0.515010\pi$
$131$	−1332.38	+	2307.75i	−0.888631	+	1.53915i	−0.841494	+	0.540266i	$0.818324\pi$
$132$		0			0
$133$	143.728	+	344.450i	0.0937053	+	0.224568i
$134$		0			0
$135$	−90.9374	+	157.508i	−0.0579751	+	0.100416i
$136$		0			0
$137$	523.153	+	906.127i	0.326248	+	0.565078i	0.981764	−	0.190103i	$-0.0608823\pi$
$137$	523.153	+	906.127i	0.326248	+	0.565078i	−0.655516	+	0.755181i	$0.727549\pi$
$138$		0			0
$139$	647.265			0.394966			0.197483	−	0.980306i	$-0.436723\pi$
$139$	647.265			0.394966			0.197483	+	0.980306i	$0.436723\pi$
$140$		0			0
$141$	661.499			0.395094
$142$		0			0
$143$	46.5974	+	80.7091i	0.0272495	+	0.0471975i
$144$		0			0
$145$	−349.201	+	604.834i	−0.199997	+	0.346405i
$146$		0			0
$147$	723.812	−	731.394i	0.406116	−	0.410370i
$148$		0			0
$149$	−663.403	+	1149.05i	−0.364752	+	0.631770i	−0.988736	−	0.149667i	$-0.952180\pi$
$149$	−663.403	+	1149.05i	−0.364752	+	0.631770i	0.623984	+	0.781437i	$0.285513\pi$
$150$		0			0
$151$	−1841.62	−	3189.78i	−0.992508	−	1.71907i	−0.602063	−	0.798448i	$-0.705655\pi$
$151$	−1841.62	−	3189.78i	−0.992508	−	1.71907i	−0.390445	−	0.920626i	$-0.627679\pi$
$152$		0			0
$153$	−422.500			−0.223249
$154$		0			0
$155$	1061.12			0.549881
$156$		0			0
$157$	1409.12	+	2440.67i	0.716308	+	1.24068i	0.962453	+	0.271449i	$0.0875027\pi$
$157$	1409.12	+	2440.67i	0.716308	+	1.24068i	−0.246145	+	0.969233i	$0.579164\pi$
$158$		0			0
$159$	438.479	−	759.468i	0.218702	−	0.378803i
$160$		0			0
$161$	−848.305	−	2032.99i	−0.415254	−	0.995170i
$162$		0			0
$163$	−2053.30	+	3556.43i	−0.986670	+	1.70896i	−0.352405	+	0.935848i	$0.614636\pi$
$163$	−2053.30	+	3556.43i	−0.986670	+	1.70896i	−0.634266	+	0.773115i	$0.718697\pi$
$164$		0			0
$165$	542.396	+	939.458i	0.255912	+	0.443253i
$166$		0			0
$167$	1045.56			0.484476			0.242238	−	0.970217i	$-0.422119\pi$
$167$	1045.56			0.484476			0.242238	+	0.970217i	$0.422119\pi$
$168$		0			0
$169$	−2193.99			−0.998628
$170$		0			0
$171$	90.6872	+	157.075i	0.0405557	+	0.0702445i
$172$		0			0
$173$	955.153	−	1654.37i	0.419763	−	0.727050i	−0.576153	−	0.817342i	$-0.695447\pi$
$173$	955.153	−	1654.37i	0.419763	−	0.727050i	0.995915	+	0.0902920i	$0.0287800\pi$
$174$		0			0
$175$	−1462.55	−	188.674i	−0.631764	−	0.0814995i
$176$		0			0
$177$	−893.812	+	1548.13i	−0.379565	+	0.657426i
$178$		0			0
$179$	−115.570	−	200.173i	−0.0482576	−	0.0835846i	0.840888	−	0.541210i	$-0.182033\pi$
$179$	−115.570	−	200.173i	−0.0482576	−	0.0835846i	−0.889145	+	0.457625i	$0.848700\pi$
$180$		0			0
$181$	3308.40			1.35863			0.679314	−	0.733848i	$-0.262278\pi$
$181$	3308.40			1.35863			0.679314	+	0.733848i	$0.262278\pi$
$182$		0			0
$183$	796.167			0.321609
$184$		0			0
$185$	−127.097	−	220.139i	−0.0505101	−	0.0874860i
$186$		0			0
$187$	−1260.00	+	2182.38i	−0.492729	+	0.853432i
$188$		0			0
$189$	303.375	−	397.506i	0.116758	−	0.152986i
$190$		0			0
$191$	−900.375	+	1559.50i	−0.341093	+	0.590791i	−0.984636	−	0.174619i	$-0.944131\pi$
$191$	−900.375	+	1559.50i	−0.341093	+	0.590791i	0.643543	+	0.765410i	$0.277464\pi$
$192$		0			0
$193$	641.680	+	1111.42i	0.239322	+	0.414518i	0.960520	−	0.278211i	$-0.0897416\pi$
$193$	641.680	+	1111.42i	0.239322	+	0.414518i	−0.721198	+	0.692729i	$0.756408\pi$
$194$		0			0
$195$	35.0837			0.0128841
$196$		0			0
$197$	60.7514			0.0219714			0.0109857	−	0.999940i	$-0.496503\pi$
$197$	60.7514			0.0219714			0.0109857	+	0.999940i	$0.496503\pi$
$198$		0			0
$199$	−1930.19	−	3343.19i	−0.687577	−	1.19092i	−0.972620	−	0.232403i	$-0.925341\pi$
$199$	−1930.19	−	3343.19i	−0.687577	−	1.19092i	0.285043	−	0.958515i	$-0.407992\pi$
$200$		0			0
$201$	1405.10	−	2433.71i	0.493076	−	0.854033i
$202$		0			0
$203$	1164.96	−	1526.43i	0.402781	−	0.527755i
$204$		0			0
$205$	−967.472	+	1675.71i	−0.329616	+	0.570911i
$206$		0			0
$207$	−535.250	−	927.080i	−0.179722	−	0.311287i
$208$		0			0
$209$	1081.81			0.358039
$210$		0			0
$211$	491.637			0.160406			0.0802031	−	0.996779i	$-0.474443\pi$
$211$	491.637			0.160406			0.0802031	+	0.996779i	$0.474443\pi$
$212$		0			0
$213$	−818.916	−	1418.40i	−0.263433	−	0.456279i
$214$		0			0
$215$	1700.44	−	2945.26i	0.539392	−	0.934255i
$216$		0			0
$217$	−2893.48	−	373.268i	−0.905171	−	0.116770i
$218$		0			0
$219$	449.062	−	777.798i	0.138561	−	0.239994i
$220$		0			0
$221$	40.7502	+	70.5813i	0.0124034	+	0.0214833i
$222$		0			0
$223$	823.376			0.247253			0.123626	−	0.992329i	$-0.460548\pi$
$223$	823.376			0.247253			0.123626	+	0.992329i	$0.460548\pi$
$224$		0			0
$225$	−716.624			−0.212333
$226$		0			0
$227$	1879.44	+	3255.28i	0.549527	+	0.951809i	0.998307	+	0.0581663i	$0.0185254\pi$
$227$	1879.44	+	3255.28i	0.549527	+	0.951809i	−0.448780	+	0.893642i	$0.648141\pi$
$228$		0			0
$229$	1220.05	−	2113.19i	0.352066	−	0.609796i	−0.634545	−	0.772886i	$-0.718813\pi$
$229$	1220.05	−	2113.19i	0.352066	−	0.609796i	0.986611	+	0.163090i	$0.0521460\pi$
$230$		0			0
$231$	−1148.54	−	2752.52i	−0.327136	−	0.783993i
$232$		0			0
$233$	974.931	−	1688.63i	0.274120	−	0.474789i	−0.695793	−	0.718242i	$-0.744947\pi$
$233$	974.931	−	1688.63i	0.274120	−	0.474789i	0.969913	+	0.243453i	$0.0782803\pi$
$234$		0			0
$235$	−742.654	−	1286.31i	−0.206151	−	0.357064i
$236$		0			0
$237$	2821.00			0.773180
$238$		0			0
$239$	2705.64			0.732273			0.366137	−	0.930561i	$-0.380680\pi$
$239$	2705.64			0.732273			0.366137	+	0.930561i	$0.380680\pi$
$240$		0			0
$241$	−302.105	−	523.262i	−0.0807482	−	0.139860i	0.822823	−	0.568297i	$-0.192398\pi$
$241$	−302.105	−	523.262i	−0.0807482	−	0.139860i	−0.903572	+	0.428437i	$0.859064\pi$
$242$		0			0
$243$	121.500	−	210.444i	0.0320750	−	0.0555556i
$244$		0			0
$245$	−2234.84	−	586.361i	−0.582770	−	0.152903i
$246$		0			0
$247$	17.4936	−	30.2998i	0.00450644	−	0.00780538i
$248$		0			0
$249$	916.978	+	1588.25i	0.233378	+	0.404223i
$250$		0			0
$251$	−1631.82			−0.410356			−0.205178	−	0.978725i	$-0.565777\pi$
$251$	−1631.82			−0.410356			−0.205178	+	0.978725i	$0.565777\pi$
$252$		0			0
$253$	−6385.00			−1.58665
$254$		0			0
$255$	474.334	+	821.570i	0.116486	+	0.201760i
$256$		0			0
$257$	3553.28	−	6154.45i	0.862441	−	1.49379i	−0.00712534	−	0.999975i	$-0.502268\pi$
$257$	3553.28	−	6154.45i	0.862441	−	1.49379i	0.869566	−	0.493817i	$-0.164399\pi$
$258$		0			0
$259$	269.132	+	644.984i	0.0645677	+	0.154739i
$260$		0			0
$261$	466.562	−	808.110i	0.110649	−	0.191650i
$262$		0			0
$263$	−2785.12	−	4823.98i	−0.652996	−	1.13102i	−0.982392	−	0.186831i	$-0.940178\pi$
$263$	−2785.12	−	4823.98i	−0.652996	−	1.13102i	0.329396	−	0.944192i	$-0.393155\pi$
$264$		0			0
$265$	−1969.09			−0.456455
$266$		0			0
$267$	3528.58			0.808786
$268$		0			0
$269$	−1956.59	−	3388.91i	−0.443477	−	0.768125i	0.554467	−	0.832205i	$-0.312922\pi$
$269$	−1956.59	−	3388.91i	−0.443477	−	0.768125i	−0.997945	+	0.0640802i	$0.979589\pi$
$270$		0			0
$271$	−3036.26	+	5258.95i	−0.680588	+	1.17881i	0.294213	+	0.955740i	$0.404942\pi$
$271$	−3036.26	+	5258.95i	−0.680588	+	1.17881i	−0.974802	+	0.223074i	$0.928391\pi$
$272$		0			0
$273$	−95.6665	−	12.3413i	−0.0212088	−	0.00273600i
$274$		0			0
$275$	−2137.15	+	3701.66i	−0.468637	+	0.811703i
$276$		0			0
$277$	−3070.31	−	5317.93i	−0.665982	−	1.15352i	−0.979018	−	0.203774i	$-0.934679\pi$
$277$	−3070.31	−	5317.93i	−0.665982	−	1.15352i	0.313036	−	0.949741i	$-0.398654\pi$
$278$		0			0
$279$	−1417.75			−0.304224
$280$		0			0
$281$	−365.751			−0.0776472			−0.0388236	−	0.999246i	$-0.512361\pi$
$281$	−365.751			−0.0776472			−0.0388236	+	0.999246i	$0.512361\pi$
$282$		0			0
$283$	355.174	+	615.180i	0.0746039	+	0.129218i	0.900914	−	0.433998i	$-0.142897\pi$
$283$	355.174	+	615.180i	0.0746039	+	0.129218i	−0.826310	+	0.563216i	$0.809564\pi$
$284$		0			0
$285$	203.626	−	352.691i	0.0423220	−	0.0733039i
$286$		0			0
$287$	3227.57	−	4229.02i	0.663824	−	0.869794i
$288$		0			0
$289$	1354.61	−	2346.26i	0.275720	−	0.477561i
$290$		0			0
$291$	2223.73	+	3851.61i	0.447963	+	0.775895i
$292$		0			0
$293$	296.373			0.0590932			0.0295466	−	0.999563i	$-0.490594\pi$
$293$	296.373			0.0590932			0.0295466	+	0.999563i	$0.490594\pi$
$294$		0			0
$295$	4013.87			0.792192
$296$		0			0
$297$	−724.687	−	1255.19i	−0.141585	−	0.245232i
$298$		0			0
$299$	−103.250	+	178.834i	−0.0199702	+	0.0345894i
$300$		0			0
$301$	−5672.82	+	7432.98i	−1.08630	+	1.42336i
$302$		0			0
$303$	926.916	−	1605.47i	0.175742	−	0.304395i
$304$		0			0
$305$	−893.844	−	1548.18i	−0.167808	−	0.290652i
$306$		0			0
$307$	8596.87			1.59821			0.799103	−	0.601194i	$-0.205308\pi$
$307$	8596.87			1.59821			0.799103	+	0.601194i	$0.205308\pi$
$308$		0			0
$309$	2450.29			0.451107
$310$		0			0
$311$	5237.65	+	9071.88i	0.954984	+	1.65408i	0.734406	+	0.678711i	$0.237461\pi$
$311$	5237.65	+	9071.88i	0.954984	+	1.65408i	0.220578	+	0.975369i	$0.429206\pi$
$312$		0			0
$313$	−2748.26	+	4760.13i	−0.496297	+	0.859611i	−0.999991	−	0.00427068i	$-0.998641\pi$
$313$	−2748.26	+	4760.13i	−0.496297	+	0.859611i	0.503694	+	0.863882i	$0.331974\pi$
$314$		0			0
$315$	−1113.56	−	143.653i	−0.199181	−	0.0256950i
$316$		0			0
$317$	−3278.19	+	5677.98i	−0.580824	+	1.00602i	0.414558	+	0.910023i	$0.363936\pi$
$317$	−3278.19	+	5677.98i	−0.580824	+	1.00602i	−0.995382	+	0.0959939i	$0.969397\pi$
$318$		0			0
$319$	−2782.81	−	4819.97i	−0.488425	−	0.845977i
$320$		0			0
$321$	−5056.13			−0.879145
$322$		0			0
$323$	946.057			0.162972
$324$		0			0
$325$	69.1185	+	119.717i	0.0117969	+	0.0204329i
$326$		0			0
$327$	137.395	−	237.976i	0.0232354	−	0.0402449i
$328$		0			0
$329$	1572.59	+	3768.77i	0.263525	+	0.631548i
$330$		0			0
$331$	−51.1882	+	88.6605i	−0.00850017	+	0.0147227i	−0.870244	−	0.492621i	$-0.836039\pi$
$331$	−51.1882	+	88.6605i	−0.00850017	+	0.0147227i	0.861744	+	0.507343i	$0.169372\pi$
$332$		0			0
$333$	169.812	+	294.124i	0.0279449	+	0.0484021i
$334$		0			0
$335$	−6309.95			−1.02910
$336$		0			0
$337$	1333.50			0.215549			0.107775	−	0.994175i	$-0.465627\pi$
$337$	1333.50			0.215549			0.107775	+	0.994175i	$0.465627\pi$
$338$		0			0
$339$	921.291	+	1595.72i	0.147604	+	0.255657i
$340$		0			0
$341$	−4228.09	+	7323.26i	−0.671448	+	1.16298i
$342$		0			0
$343$	5887.72	+	2385.03i	0.926842	+	0.375451i
$344$		0			0
$345$	−1201.83	+	2081.64i	−0.187549	+	0.324845i
$346$		0			0
$347$	550.501	+	953.496i	0.0851655	+	0.147511i	0.905462	−	0.424428i	$-0.139525\pi$
$347$	550.501	+	953.496i	0.0851655	+	0.147511i	−0.820296	+	0.571939i	$0.806191\pi$
$348$		0			0
$349$	9467.89			1.45216			0.726081	−	0.687609i	$-0.241340\pi$
$349$	9467.89			1.45216			0.726081	+	0.687609i	$0.241340\pi$
$350$		0			0
$351$	−46.8748			−0.00712818
$352$		0			0
$353$	842.347	+	1458.99i	0.127007	+	0.219983i	0.922516	−	0.385959i	$-0.126129\pi$
$353$	842.347	+	1458.99i	0.127007	+	0.219983i	−0.795508	+	0.605943i	$0.792796\pi$
$354$		0			0
$355$	−1838.77	+	3184.84i	−0.274906	+	0.476151i
$356$		0			0
$357$	−1004.42	−	2407.12i	−0.148906	−	0.356858i
$358$		0			0
$359$	3317.62	−	5746.29i	0.487737	−	0.844785i	−0.512164	−	0.858888i	$-0.671156\pi$
$359$	3317.62	−	5746.29i	0.487737	−	0.844785i	0.999901	+	0.0141029i	$0.00448924\pi$
$360$		0			0
$361$	3226.43	+	5588.35i	0.470394	+	0.814747i
$362$		0			0
$363$	−4651.79			−0.672605
$364$		0			0
$365$	−2016.62			−0.289191
$366$		0			0
$367$	3560.99	+	6167.81i	0.506490	+	0.877267i	0.999972	+	0.00751063i	$0.00239073\pi$
$367$	3560.99	+	6167.81i	0.506490	+	0.877267i	−0.493482	+	0.869756i	$0.664276\pi$
$368$		0			0
$369$	1292.62	−	2238.89i	0.182361	−	0.315859i
$370$		0			0
$371$	5369.34	+	692.661i	0.751381	+	0.0969304i
$372$		0			0
$373$	6810.67	−	11796.4i	0.945424	−	1.63752i	0.190524	−	0.981683i	$-0.438981\pi$
$373$	6810.67	−	11796.4i	0.945424	−	1.63752i	0.754900	−	0.655840i	$-0.227685\pi$
$374$		0			0
$375$	2067.56	+	3581.12i	0.284716	+	0.493142i
$376$		0			0
$377$	−180.000			−0.0245901
$378$		0			0
$379$	−3331.51			−0.451525			−0.225763	−	0.974182i	$-0.572487\pi$
$379$	−3331.51			−0.451525			−0.225763	+	0.974182i	$0.572487\pi$
$380$		0			0
$381$	351.417	+	608.672i	0.0472536	+	0.0818457i
$382$		0			0
$383$	−1637.87	+	2836.88i	−0.218515	+	0.378480i	−0.954354	−	0.298677i	$-0.903455\pi$
$383$	−1637.87	+	2836.88i	−0.218515	+	0.378480i	0.735839	+	0.677157i	$0.236788\pi$
$384$		0			0
$385$	−4062.95	+	5323.59i	−0.537836	+	0.704715i
$386$		0			0
$387$	−2271.94	+	3935.11i	−0.298421	+	0.516881i
$388$		0			0
$389$	7487.69	+	12969.1i	0.975941	+	1.69038i	0.676794	+	0.736172i	$0.263369\pi$
$389$	7487.69	+	12969.1i	0.975941	+	1.69038i	0.299147	+	0.954207i	$0.403298\pi$
$390$		0			0
$391$	−5583.78			−0.722209
$392$		0			0
$393$	−7994.29			−1.02610
$394$		0			0
$395$	−3167.09	−	5485.56i	−0.403427	−	0.698756i
$396$		0			0
$397$	5379.31	−	9317.24i	0.680050	−	1.17788i	−0.294915	−	0.955523i	$-0.595291\pi$
$397$	5379.31	−	9317.24i	0.680050	−	1.17788i	0.974965	−	0.222357i	$-0.0713752\pi$
$398$		0			0
$399$	−679.314	+	890.091i	−0.0852337	+	0.111680i
$400$		0			0
$401$	1303.50	−	2257.73i	0.162328	−	0.281161i	−0.773375	−	0.633949i	$-0.781433\pi$
$401$	1303.50	−	2257.73i	0.162328	−	0.281161i	0.935703	+	0.352788i	$0.114766\pi$
$402$		0			0
$403$	136.742	+	236.844i	0.0169023	+	0.0292756i
$404$		0			0
$405$	−545.624			−0.0669439
$406$		0			0
$407$	2025.69			0.246707
$408$		0			0
$409$	−3107.32	−	5382.03i	−0.375665	−	0.650671i	0.614761	−	0.788713i	$-0.289252\pi$
$409$	−3107.32	−	5382.03i	−0.375665	−	0.650671i	−0.990426	+	0.138042i	$0.955919\pi$
$410$		0			0
$411$	−1569.46	+	2718.38i	−0.188359	+	0.326248i
$412$		0			0
$413$	−10945.1	−	1411.95i	−1.30405	−	0.168226i
$414$		0			0
$415$	2058.95	−	3566.21i	0.243542	−	0.421828i
$416$		0			0
$417$	970.897	+	1681.64i	0.114017	+	0.197483i
$418$		0			0
$419$	−13111.4			−1.52872			−0.764358	−	0.644792i	$-0.776944\pi$
$419$	−13111.4			−1.52872			−0.764358	+	0.644792i	$0.776944\pi$
$420$		0			0
$421$	−8410.12			−0.973596			−0.486798	−	0.873514i	$-0.661835\pi$
$421$	−8410.12			−0.973596			−0.486798	+	0.873514i	$0.661835\pi$
$422$		0			0
$423$	992.249	+	1718.63i	0.114054	+	0.197547i
$424$		0			0
$425$	−1868.97	+	3237.16i	−0.213314	+	0.369471i
$426$		0			0
$427$	1892.74	+	4536.02i	0.214511	+	0.514083i
$428$		0			0
$429$	−139.792	+	242.127i	−0.0157325	+	0.0272495i
$430$		0			0
$431$	−3891.65	−	6740.54i	−0.434929	−	0.753319i	0.562361	−	0.826892i	$-0.309893\pi$
$431$	−3891.65	−	6740.54i	−0.434929	−	0.753319i	−0.997290	+	0.0735730i	$0.976560\pi$
$432$		0			0
$433$	13870.1			1.53939			0.769695	−	0.638412i	$-0.220409\pi$
$433$	13870.1			1.53939			0.769695	+	0.638412i	$0.220409\pi$
$434$		0			0
$435$	−2095.21			−0.230937
$436$		0			0
$437$	1198.53	+	2075.91i	0.131197	+	0.227241i
$438$		0			0
$439$	−2839.81	+	4918.70i	−0.308740	+	0.534754i	−0.978087	−	0.208196i	$-0.933241\pi$
$439$	−2839.81	+	4918.70i	−0.308740	+	0.534754i	0.669347	+	0.742950i	$0.266574\pi$
$440$		0			0
$441$	2985.94	+	783.427i	0.322420	+	0.0845942i
$442$		0			0
$443$	1158.47	−	2006.52i	0.124245	−	0.215198i	−0.797193	−	0.603725i	$-0.793683\pi$
$443$	1158.47	−	2006.52i	0.124245	−	0.215198i	0.921437	+	0.388527i	$0.127016\pi$
$444$		0			0
$445$	−3961.48	−	6861.49i	−0.422005	−	0.730934i
$446$		0			0
$447$	−3980.42			−0.421180
$448$		0			0
$449$	9526.86			1.00134			0.500669	−	0.865639i	$-0.333088\pi$
$449$	9526.86			1.00134			0.500669	+	0.865639i	$0.333088\pi$
$450$		0			0
$451$	−7709.86	−	13353.9i	−0.804974	−	1.39426i
$452$		0			0
$453$	5524.85	−	9569.33i	0.573025	−	0.992508i
$454$		0			0
$455$	83.4050	+	199.883i	0.00859360	+	0.0205949i
$456$		0			0
$457$	8313.63	−	14399.6i	0.850974	−	1.47393i	−0.0293569	−	0.999569i	$-0.509346\pi$
$457$	8313.63	−	14399.6i	0.850974	−	1.47393i	0.880331	−	0.474361i	$-0.157321\pi$
$458$		0			0
$459$	−633.750	−	1097.69i	−0.0644464	−	0.111624i
$460$		0			0
$461$	−11338.3			−1.14550			−0.572749	−	0.819730i	$-0.694123\pi$
$461$	−11338.3			−1.14550			−0.572749	+	0.819730i	$0.694123\pi$
$462$		0			0
$463$	9207.87			0.924246			0.462123	−	0.886816i	$-0.347088\pi$
$463$	9207.87			0.924246			0.462123	+	0.886816i	$0.347088\pi$
$464$		0			0
$465$	1591.69	+	2756.88i	0.158737	+	0.274940i
$466$		0			0
$467$	8607.85	−	14909.2i	0.852941	−	1.47734i	−0.0256004	−	0.999672i	$-0.508150\pi$
$467$	8607.85	−	14909.2i	0.852941	−	1.47734i	0.878542	−	0.477666i	$-0.158517\pi$
$468$		0			0
$469$	17206.0	+	2219.63i	1.69403	+	0.218535i
$470$		0			0
$471$	−4227.37	+	7322.02i	−0.413561	+	0.716308i
$472$		0			0
$473$	13551.0	+	23471.0i	1.31728	+	2.28160i
$474$		0			0
$475$	1604.66			0.155004
$476$		0			0
$477$	2630.88			0.252536
$478$		0			0
$479$	−5146.90	−	8914.69i	−0.490956	−	0.850360i	0.508990	−	0.860772i	$-0.330019\pi$
$479$	−5146.90	−	8914.69i	−0.490956	−	0.850360i	−0.999946	+	0.0104121i	$0.996686\pi$
$480$		0			0
$481$	32.7569	−	56.7366i	0.00310517	−	0.00537831i
$482$		0			0
$483$	4009.41	−	5253.45i	0.377712	−	0.494908i
$484$		0			0
$485$	4993.09	−	8648.28i	0.467473	−	0.809687i
$486$		0			0
$487$	−5554.48	−	9620.65i	−0.516833	−	0.895181i	−0.999809	−	0.0195473i	$-0.993777\pi$
$487$	−5554.48	−	9620.65i	−0.516833	−	0.895181i	0.482976	−	0.875634i	$-0.339556\pi$
$488$		0			0
$489$	−12319.8			−1.13931
$490$		0			0
$491$	−6573.88			−0.604226			−0.302113	−	0.953272i	$-0.597692\pi$
$491$	−6573.88			−0.604226			−0.302113	+	0.953272i	$0.597692\pi$
$492$		0			0
$493$	−2433.61	−	4215.14i	−0.222321	−	0.385071i
$494$		0			0
$495$	−1627.19	+	2818.37i	−0.147751	+	0.255912i
$496$		0			0
$497$	6134.28	−	8037.62i	0.553642	−	0.725426i
$498$		0			0
$499$	8420.70	−	14585.1i	0.755435	−	1.30845i	−0.189722	−	0.981838i	$-0.560759\pi$
$499$	8420.70	−	14585.1i	0.755435	−	1.30845i	0.945158	−	0.326615i	$-0.105908\pi$
$500$		0			0
$501$	1568.33	+	2716.43i	0.139856	+	0.242238i
$502$		0			0
$503$	−18436.6			−1.63429			−0.817146	−	0.576431i	$-0.804445\pi$
$503$	−18436.6			−1.63429			−0.817146	+	0.576431i	$0.804445\pi$
$504$		0			0
$505$	−4162.53			−0.366793
$506$		0			0
$507$	−3290.98	−	5700.14i	−0.288279	−	0.499314i
$508$		0			0
$509$	−10412.6	+	18035.1i	−0.906738	+	1.57052i	−0.0881717	+	0.996105i	$0.528102\pi$
$509$	−10412.6	+	18035.1i	−0.906738	+	1.57052i	−0.818567	+	0.574412i	$0.805231\pi$
$510$		0			0
$511$	5498.93	+	709.378i	0.476043	+	0.0614110i
$512$		0			0
$513$	−272.062	+	471.225i	−0.0234148	+	0.0405557i
$514$		0			0
$515$	−2750.90	−	4764.70i	−0.235377	−	0.407685i
$516$		0			0
$517$	11836.5			1.00691
$518$		0			0
$519$	5730.92			0.484700
$520$		0			0
$521$	−7192.37	−	12457.6i	−0.604805	−	1.04755i	−0.992082	−	0.125590i	$-0.959918\pi$
$521$	−7192.37	−	12457.6i	−0.604805	−	1.04755i	0.387277	−	0.921964i	$-0.373416\pi$
$522$		0			0
$523$	−3243.74	+	5618.33i	−0.271203	+	0.469737i	−0.969170	−	0.246393i	$-0.920755\pi$
$523$	−3243.74	+	5618.33i	−0.271203	+	0.469737i	0.697967	+	0.716129i	$0.254088\pi$
$524$		0			0
$525$	−1703.64	−	4082.84i	−0.141625	−	0.339409i
$526$		0			0
$527$	−3697.52	+	6404.30i	−0.305629	+	0.529366i
$528$		0			0
$529$	−990.386	−	1715.40i	−0.0813994	−	0.140988i
$530$		0			0
$531$	−5362.87			−0.438284
$532$		0			0
$533$	−498.695			−0.0405270
$534$		0			0
$535$	5676.43	+	9831.86i	0.458717	+	0.794521i
$536$		0			0
$537$	346.710	−	600.519i	0.0278615	−	0.0482576i
$538$		0			0
$539$	12951.5	−	13087.2i	1.03499	−	1.04584i
$540$		0			0
$541$	−7208.29	+	12485.1i	−0.572844	+	0.992195i	0.423428	+	0.905930i	$0.360827\pi$
$541$	−7208.29	+	12485.1i	−0.572844	+	0.992195i	−0.996272	+	0.0862654i	$0.972507\pi$
$542$		0			0
$543$	4962.60	+	8595.48i	0.392202	+	0.679314i
$544$		0			0
$545$	−617.006			−0.0484947
$546$		0			0
$547$	−4881.38			−0.381559			−0.190780	−	0.981633i	$-0.561102\pi$
$547$	−4881.38			−0.381559			−0.190780	+	0.981633i	$0.561102\pi$
$548$		0			0
$549$	1194.25	+	2068.50i	0.0928404	+	0.160804i
$550$		0			0
$551$	−1044.72	+	1809.51i	−0.0807743	+	0.139905i
$552$		0			0
$553$	6706.41	+	16072.1i	0.515706	+	1.23591i
$554$		0			0
$555$	381.291	−	660.416i	0.0291620	−	0.0505101i
$556$		0			0
$557$	1576.56	+	2730.69i	0.119930	+	0.207725i	0.919740	−	0.392529i	$-0.128400\pi$
$557$	1576.56	+	2730.69i	0.119930	+	0.207725i	−0.799810	+	0.600254i	$0.795066\pi$
$558$		0			0
$559$	876.514			0.0663195
$560$		0			0
$561$	−7560.00			−0.568954
$562$		0			0
$563$	−3397.94	−	5885.40i	−0.254362	−	0.440568i	0.710360	−	0.703839i	$-0.248532\pi$
$563$	−3397.94	−	5885.40i	−0.254362	−	0.440568i	−0.964722	+	0.263270i	$0.915199\pi$
$564$		0			0
$565$	2068.64	−	3582.99i	0.154032	−	0.266792i
$566$		0			0
$567$	1487.81	+	191.932i	0.110198	+	0.0142159i
$568$		0			0
$569$	5354.15	−	9273.66i	0.394477	−	0.683255i	−0.598557	−	0.801080i	$-0.704259\pi$
$569$	5354.15	−	9273.66i	0.394477	−	0.683255i	0.993034	+	0.117825i	$0.0375923\pi$
$570$		0			0
$571$	−3265.83	−	5656.58i	−0.239353	−	0.414572i	0.721176	−	0.692752i	$-0.243602\pi$
$571$	−3265.83	−	5656.58i	−0.239353	−	0.414572i	−0.960529	+	0.278180i	$0.910269\pi$
$572$		0			0
$573$	−5402.25			−0.393861
$574$		0			0
$575$	−9470.94			−0.686896
$576$		0			0
$577$	−8730.94	−	15122.4i	−0.629937	−	1.09108i	−0.987564	−	0.157218i	$-0.949747\pi$
$577$	−8730.94	−	15122.4i	−0.629937	−	1.09108i	0.357627	−	0.933865i	$-0.383586\pi$
$578$		0			0
$579$	−1925.04	+	3334.26i	−0.138173	+	0.239322i
$580$		0			0
$581$	−6868.84	+	9000.10i	−0.490478	+	0.642663i
$582$		0			0
$583$	7845.93	−	13589.5i	0.557367	−	0.965389i
$584$		0			0
$585$	52.6255	+	91.1501i	0.00371931	+	0.00644204i
$586$		0			0
$587$	9254.42			0.650717			0.325358	−	0.945591i	$-0.394515\pi$
$587$	9254.42			0.650717			0.325358	+	0.945591i	$0.394515\pi$
$588$		0			0
$589$	3174.61			0.222084
$590$		0			0
$591$	91.1271	+	157.837i	0.00634258	+	0.0109857i
$592$		0			0
$593$	10509.6	−	18203.1i	0.727786	−	1.26056i	−0.230031	−	0.973183i	$-0.573883\pi$
$593$	10509.6	−	18203.1i	0.727786	−	1.26056i	0.957817	−	0.287379i	$-0.0927839\pi$
$594$		0			0
$595$	−3553.11	+	4655.56i	−0.244812	+	0.320772i
$596$		0			0
$597$	5790.58	−	10029.6i	0.396973	−	0.687577i
$598$		0			0
$599$	13485.8	+	23358.2i	0.919894	+	1.59330i	0.799574	+	0.600568i	$0.205059\pi$
$599$	13485.8	+	23358.2i	0.919894	+	1.59330i	0.120320	+	0.992735i	$0.461608\pi$
$600$		0			0
$601$	−26510.3			−1.79930			−0.899648	−	0.436616i	$-0.856177\pi$
$601$	−26510.3			−1.79930			−0.899648	+	0.436616i	$0.856177\pi$
$602$		0			0
$603$	8430.62			0.569355
$604$		0			0
$605$	5222.49	+	9045.62i	0.350950	+	0.607862i
$606$		0			0
$607$	−14706.0	+	25471.5i	−0.983356	+	1.70322i	−0.334333	+	0.942455i	$0.608511\pi$
$607$	−14706.0	+	25471.5i	−0.983356	+	1.70322i	−0.649023	+	0.760768i	$0.724822\pi$
$608$		0			0
$609$	5713.23	+	737.024i	0.380150	+	0.0490406i
$610$		0			0
$611$	191.405	−	331.523i	0.0126734	−	0.0219509i
$612$		0			0
$613$	3034.32	+	5255.59i	0.199926	+	0.346283i	0.948504	−	0.316764i	$-0.102596\pi$
$613$	3034.32	+	5255.59i	0.199926	+	0.346283i	−0.748578	+	0.663047i	$0.769263\pi$
$614$		0			0
$615$	−5804.83			−0.380607
$616$		0			0
$617$	1904.56			0.124270			0.0621352	−	0.998068i	$-0.480209\pi$
$617$	1904.56			0.124270			0.0621352	+	0.998068i	$0.480209\pi$
$618$		0			0
$619$	203.239	+	352.020i	0.0131969	+	0.0228576i	0.872548	−	0.488528i	$-0.162466\pi$
$619$	203.239	+	352.020i	0.0131969	+	0.0228576i	−0.859352	+	0.511385i	$0.829133\pi$
$620$		0			0
$621$	1605.75	−	2781.24i	0.103762	−	0.179722i
$622$		0			0
$623$	8388.56	+	20103.5i	0.539455	+	1.29282i
$624$		0			0
$625$	−334.122	+	578.716i	−0.0213838	+	0.0370378i
$626$		0			0
$627$	1622.71	+	2810.62i	0.103357	+	0.179020i
$628$		0			0
$629$	1771.50			0.112296
$630$		0			0
$631$	−15294.2			−0.964903			−0.482452	−	0.875923i	$-0.660254\pi$
$631$	−15294.2			−0.964903			−0.482452	+	0.875923i	$0.660254\pi$
$632$		0			0
$633$	737.456	+	1277.31i	0.0463053	+	0.0802031i
$634$		0			0
$635$	789.060	−	1366.69i	0.0493116	−	0.0854103i
$636$		0			0
$637$	−157.117	−	574.382i	−0.00977271	−	0.0357266i
$638$		0			0
$639$	2456.75	−	4255.21i	0.152093	−	0.263433i
$640$		0			0
$641$	7861.10	+	13615.8i	0.484391	+	0.838990i	0.999839	−	0.0179308i	$-0.00570785\pi$
$641$	7861.10	+	13615.8i	0.484391	+	0.838990i	−0.515448	+	0.856921i	$0.672375\pi$
$642$		0			0
$643$	18529.9			1.13646			0.568232	−	0.822868i	$-0.307628\pi$
$643$	18529.9			1.13646			0.568232	+	0.822868i	$0.307628\pi$
$644$		0			0
$645$	10202.7			0.622836
$646$		0			0
$647$	4319.48	+	7481.55i	0.262467	+	0.454606i	0.966897	−	0.255167i	$-0.0821306\pi$
$647$	4319.48	+	7481.55i	0.262467	+	0.454606i	−0.704430	+	0.709774i	$0.748797\pi$
$648$		0			0
$649$	−15993.4	+	27701.4i	−0.967330	+	1.67546i
$650$		0			0
$651$	−3370.44	−	8077.38i	−0.202915	−	0.486294i
$652$		0			0
$653$	−13942.2	+	24148.6i	−0.835528	+	1.44718i	0.0580718	+	0.998312i	$0.481505\pi$
$653$	−13942.2	+	24148.6i	−0.835528	+	1.44718i	−0.893600	+	0.448865i	$0.851829\pi$
$654$		0			0
$655$	8975.06	+	15545.3i	0.535396	+	0.927334i
$656$		0			0
$657$	2694.37			0.159996
$658$		0			0
$659$	−5767.55			−0.340928			−0.170464	−	0.985364i	$-0.554527\pi$
$659$	−5767.55			−0.340928			−0.170464	+	0.985364i	$0.554527\pi$
$660$		0			0
$661$	−2045.06	−	3542.15i	−0.120338	−	0.208432i	0.799563	−	0.600582i	$-0.205065\pi$
$661$	−2045.06	−	3542.15i	−0.120338	−	0.208432i	−0.919901	+	0.392150i	$0.871731\pi$
$662$		0			0
$663$	−122.250	+	211.744i	−0.00716111	+	0.0124034i
$664$		0			0
$665$	2493.48	+	321.666i	0.145403	+	0.0187574i
$666$		0			0
$667$	6166.11	−	10680.0i	0.357950	−	0.619988i
$668$		0			0
$669$	1235.06	+	2139.19i	0.0713757	+	0.123626i
$670$		0			0
$671$	14246.2			0.819627
$672$		0			0
$673$	−21667.7			−1.24106			−0.620528	−	0.784185i	$-0.713082\pi$
$673$	−21667.7			−1.24106			−0.620528	+	0.784185i	$0.713082\pi$
$674$		0			0
$675$	−1074.94	−	1861.84i	−0.0612953	−	0.106167i
$676$		0			0
$677$	7659.43	−	13266.5i	0.434824	−	0.753137i	−0.562457	−	0.826826i	$-0.690144\pi$
$677$	7659.43	−	13266.5i	0.434824	−	0.753137i	0.997281	+	0.0736891i	$0.0234772\pi$
$678$		0			0
$679$	−16657.4	+	21825.8i	−0.941459	+	1.23357i
$680$		0			0
$681$	−5638.31	+	9765.84i	−0.317270	+	0.549527i
$682$		0			0
$683$	−4990.68	−	8644.11i	−0.279595	−	0.484272i	0.691689	−	0.722195i	$-0.256867\pi$
$683$	−4990.68	−	8644.11i	−0.279595	−	0.484272i	−0.971284	+	0.237923i	$0.923533\pi$
$684$		0			0
$685$	7048.02			0.393126
$686$		0			0
$687$	7320.29			0.406531
$688$		0			0
$689$	−253.748	−	439.505i	−0.0140305	−	0.0243016i
$690$		0			0
$691$	−11621.6	+	20129.2i	−0.639805	+	1.10818i	0.345670	+	0.938356i	$0.387652\pi$
$691$	−11621.6	+	20129.2i	−0.639805	+	1.10818i	−0.985475	+	0.169819i	$0.945682\pi$
$692$		0			0
$693$	5428.44	−	7112.77i	0.297560	−	0.389887i
$694$		0			0
$695$	2180.02	−	3775.91i	0.118983	−	0.206084i
$696$		0			0
$697$	−6742.39	−	11678.2i	−0.366408	−	0.634637i
$698$		0			0
$699$	5849.59			0.316526
$700$		0			0
$701$	−11295.6			−0.608598			−0.304299	−	0.952577i	$-0.598422\pi$
$701$	−11295.6			−0.608598			−0.304299	+	0.952577i	$0.598422\pi$
$702$		0			0
$703$	−380.243	−	658.599i	−0.0203999	−	0.0353336i
$704$		0			0
$705$	2227.96	−	3858.94i	0.119021	−	0.206151i
$706$		0			0
$707$	11350.4	+	1464.24i	0.603786	+	0.0778902i
$708$		0			0
$709$	−3434.05	+	5947.96i	−0.181902	+	0.315064i	−0.942528	−	0.334126i	$-0.891559\pi$
$709$	−3434.05	+	5947.96i	−0.181902	+	0.315064i	0.760626	+	0.649190i	$0.224892\pi$
$710$		0			0
$711$	4231.50	+	7329.17i	0.223198	+	0.386590i
$712$		0			0
$713$	−18737.1			−0.984163
$714$		0			0
$715$	627.770			0.0328353
$716$		0			0
$717$	4058.46	+	7029.46i	0.211389	+	0.366137i
$718$		0			0
$719$	15739.8	−	27262.1i	0.816404	−	1.41405i	−0.0919115	−	0.995767i	$-0.529298\pi$
$719$	15739.8	−	27262.1i	0.816404	−	1.41405i	0.908315	−	0.418286i	$-0.137369\pi$
$720$		0			0
$721$	5825.12	+	13960.1i	0.300886	+	0.721083i
$722$		0			0
$723$	906.316	−	1569.79i	0.0466200	−	0.0807482i
$724$		0			0
$725$	−4127.78	−	7149.52i	−0.211451	−	0.366243i
$726$		0			0
$727$	26045.8			1.32873			0.664363	−	0.747410i	$-0.268703\pi$
$727$	26045.8			1.32873			0.664363	+	0.747410i	$0.268703\pi$
$728$		0			0
$729$	729.000			0.0370370
$730$		0			0
$731$	11850.5	+	20525.7i	0.599600	+	1.03854i
$732$		0			0
$733$	1769.20	−	3064.34i	0.0891499	−	0.154412i	−0.818002	−	0.575215i	$-0.804918\pi$
$733$	1769.20	−	3064.34i	0.0891499	−	0.154412i	0.907152	+	0.420803i	$0.138252\pi$
$734$		0			0
$735$	−1828.85	−	6685.83i	−0.0917799	−	0.335524i
$736$		0			0
$737$	25142.2	−	43547.6i	1.25662	−	2.17652i
$738$		0			0
$739$	−5213.44	−	9029.94i	−0.259512	−	0.449488i	0.706599	−	0.707614i	$-0.250228\pi$
$739$	−5213.44	−	9029.94i	−0.259512	−	0.449488i	−0.966111	+	0.258126i	$0.916895\pi$
$740$		0			0
$741$	104.962			0.00520359
$742$		0			0
$743$	2518.88			0.124372			0.0621862	−	0.998065i	$-0.480193\pi$
$743$	2518.88			0.124372			0.0621862	+	0.998065i	$0.480193\pi$
$744$		0			0
$745$	4468.75	+	7740.11i	0.219762	+	0.380638i
$746$		0			0
$747$	−2750.93	+	4764.76i	−0.134741	+	0.233378i
$748$		0			0
$749$	−12020.0	−	28806.4i	−0.586384	−	1.40529i
$750$		0			0
$751$	−7410.13	+	12834.7i	−0.360053	+	0.623629i	−0.987969	−	0.154651i	$-0.950575\pi$
$751$	−7410.13	+	12834.7i	−0.360053	+	0.623629i	0.627917	+	0.778281i	$0.283908\pi$
$752$		0			0
$753$	−2447.73	−	4239.59i	−0.118460	−	0.205178i
$754$		0			0
$755$	−24810.7			−1.19596
$756$		0			0
$757$	8892.84			0.426969			0.213485	−	0.976946i	$-0.431519\pi$
$757$	8892.84			0.426969			0.213485	+	0.976946i	$0.431519\pi$
$758$		0			0
$759$	−9577.50	−	16588.7i	−0.458025	−	0.793323i
$760$		0			0
$761$	−11397.5	+	19741.0i	−0.542916	+	0.940358i	0.455819	+	0.890072i	$0.349346\pi$
$761$	−11397.5	+	19741.0i	−0.542916	+	0.940358i	−0.998735	+	0.0502853i	$0.983987\pi$
$762$		0			0
$763$	1682.46	+	217.042i	0.0798283	+	0.0102981i
$764$		0			0
$765$	−1423.00	+	2464.71i	−0.0672532	+	0.116486i
$766$		0			0
$767$	517.250	+	895.903i	0.0243505	+	0.0421762i
$768$		0			0
$769$	−13025.5			−0.610809			−0.305405	−	0.952223i	$-0.598792\pi$
$769$	−13025.5			−0.610809			−0.305405	+	0.952223i	$0.598792\pi$
$770$		0			0
$771$	21319.7			0.995861
$772$		0			0
$773$	−13233.5	−	22921.1i	−0.615751	−	1.06651i	−0.990252	−	0.139286i	$-0.955519\pi$
$773$	−13233.5	−	22921.1i	−0.615751	−	1.06651i	0.374501	−	0.927226i	$-0.377814\pi$
$774$		0			0
$775$	−6271.57	+	10862.7i	−0.290686	+	0.503482i
$776$		0			0
$777$	−1272.02	+	1666.70i	−0.0587303	+	0.0769531i
$778$		0			0
$779$	−2894.43	+	5013.30i	−0.133124	+	0.230578i
$780$		0			0
$781$	−14653.3	−	25380.2i	−0.671364	−	1.16284i
$782$		0			0
$783$	2799.37			0.127767
$784$		0			0
$785$	18984.0			0.863144
$786$		0			0
$787$	−16608.3	−	28766.4i	−0.752252	−	1.30294i	−0.946729	−	0.322031i	$-0.895634\pi$
$787$	−16608.3	−	28766.4i	−0.752252	−	1.30294i	0.194477	−	0.980907i	$-0.437699\pi$
$788$		0			0
$789$	8355.37	−	14471.9i	0.377008	−	0.652996i
$790$		0			0
$791$	−6901.15	+	9042.43i	−0.310211	+	0.406463i
$792$		0			0
$793$	230.371	−	399.015i	0.0103162	−	0.0178681i
$794$		0			0
$795$	−2953.64	−	5115.86i	−0.131767	−	0.228227i
$796$		0			0
$797$	−15363.9			−0.682830			−0.341415	−	0.939913i	$-0.610906\pi$
$797$	−15363.9			−0.682830			−0.341415	+	0.939913i	$0.610906\pi$
$798$		0			0
$799$	10351.2			0.458323
$800$		0			0
$801$	5292.87	+	9167.53i	0.233476	+	0.404393i
$802$		0			0
$803$	8035.29	−	13917.5i	0.353125	−	0.611630i
$804$		0			0
$805$	−14716.9	−	1898.52i	−0.644350	−	0.0831231i
$806$		0			0
$807$	5869.77	−	10166.7i	0.256042	−	0.443477i
$808$		0			0
$809$	−13371.3	−	23159.8i	−0.581102	−	1.00650i	−0.995349	−	0.0963332i	$-0.969289\pi$
$809$	−13371.3	−	23159.8i	−0.581102	−	1.00650i	0.414248	−	0.910164i	$-0.364045\pi$
$810$		0			0
$811$	−23651.0			−1.02404			−0.512022	−	0.858973i	$-0.671103\pi$
$811$	−23651.0			−1.02404			−0.512022	+	0.858973i	$0.671103\pi$
$812$		0			0
$813$	−18217.5			−0.785876
$814$		0			0
$815$	13831.3	+	23956.5i	0.594464	+	1.02964i
$816$		0			0
$817$	5087.30	−	8811.46i	0.217848	−	0.377324i
$818$		0			0
$819$	−111.436	−	267.061i	−0.00475445	−	0.0113942i
$820$		0			0
$821$	−8487.03	+	14700.0i	−0.360779	+	0.624887i	−0.988089	−	0.153882i	$-0.950822\pi$
$821$	−8487.03	+	14700.0i	−0.360779	+	0.624887i	0.627310	+	0.778769i	$0.284156\pi$
$822$		0			0
$823$	−11164.4	−	19337.4i	−0.472865	−	0.819026i	0.526653	−	0.850080i	$-0.323447\pi$
$823$	−11164.4	−	19337.4i	−0.472865	−	0.819026i	−0.999518	+	0.0310546i	$0.990113\pi$
$824$		0			0
$825$	−12822.9			−0.541135
$826$		0			0
$827$	15731.8			0.661485			0.330743	−	0.943721i	$-0.392701\pi$
$827$	15731.8			0.661485			0.330743	+	0.943721i	$0.392701\pi$
$828$		0			0
$829$	19012.7	+	32930.9i	0.796547	+	1.37966i	0.921852	+	0.387542i	$0.126676\pi$
$829$	19012.7	+	32930.9i	0.796547	+	1.37966i	−0.125305	+	0.992118i	$0.539991\pi$
$830$		0			0
$831$	9210.93	−	15953.8i	0.384505	−	0.665982i
$832$		0			0
$833$	11326.3	−	11445.0i	0.471108	−	0.476043i
$834$		0			0
$835$	3521.48	−	6099.39i	0.145947	−	0.252788i
$836$		0			0
$837$	−2126.63	−	3683.42i	−0.0878219	−	0.152112i
$838$		0			0
$839$	16546.5			0.680868			0.340434	−	0.940268i	$-0.389426\pi$
$839$	16546.5			0.680868			0.340434	+	0.940268i	$0.389426\pi$
$840$		0			0
$841$	−13639.4			−0.559242
$842$		0			0
$843$	−548.626	−	950.248i	−0.0224148	−	0.0388236i
$844$		0			0
$845$	−7389.46	+	12798.9i	−0.300834	+	0.521060i
$846$		0			0
$847$	−11058.8	−	26502.8i	−0.448624	−	1.07514i
$848$		0			0
$849$	−1065.52	+	1845.54i	−0.0430726	+	0.0746039i
$850$		0			0
$851$	2244.25	+	3887.15i	0.0904017	+	0.156580i
$852$		0			0
$853$	13511.9			0.542365			0.271182	−	0.962528i	$-0.412585\pi$
$853$	13511.9			0.542365			0.271182	+	0.962528i	$0.412585\pi$
$854$		0			0
$855$	1221.76			0.0488692
$856$		0			0
$857$	−8589.12	−	14876.8i	−0.342355	−	0.592977i	0.642514	−	0.766274i	$-0.277891\pi$
$857$	−8589.12	−	14876.8i	−0.342355	−	0.592977i	−0.984870	+	0.173297i	$0.944558\pi$
$858$		0			0
$859$	17957.2	−	31102.7i	0.713260	−	1.23540i	−0.250366	−	0.968151i	$-0.580551\pi$
$859$	17957.2	−	31102.7i	0.713260	−	1.23540i	0.963627	−	0.267252i	$-0.0861156\pi$
$860$		0			0
$861$	15828.7	+	2041.95i	0.626526	+	0.0808238i
$862$		0			0
$863$	441.254	−	764.275i	0.0174049	−	0.0301462i	−0.857192	−	0.514997i	$-0.827793\pi$
$863$	441.254	−	764.275i	0.0174049	−	0.0301462i	0.874597	+	0.484851i	$0.161126\pi$
$864$		0			0
$865$	−6434.01	−	11144.0i	−0.252905	−	0.438044i
$866$		0			0
$867$	8127.67			0.318374
$868$		0			0
$869$	50477.6			1.97046
$870$		0			0
$871$	−813.134	−	1408.39i	−0.0316326	−	0.0547893i
$872$		0			0
$873$	−6671.19	+	11554.8i	−0.258632	+	0.447963i
$874$		0			0
$875$	−15487.6	+	20293.0i	−0.598371	+	0.784034i
$876$		0			0
$877$	−8710.07	+	15086.3i	−0.335368	+	0.580875i	−0.983556	−	0.180606i	$-0.942194\pi$
$877$	−8710.07	+	15086.3i	−0.335368	+	0.580875i	0.648187	+	0.761481i	$0.275527\pi$
$878$		0			0
$879$	444.560	+	770.000i	0.0170587	+	0.0295466i
$880$		0			0
$881$	38097.8			1.45692			0.728460	−	0.685088i	$-0.240236\pi$
$881$	38097.8			1.45692			0.728460	+	0.685088i	$0.240236\pi$
$882$		0			0
$883$	−13870.6			−0.528633			−0.264317	−	0.964436i	$-0.585146\pi$
$883$	−13870.6			−0.528633			−0.264317	+	0.964436i	$0.585146\pi$
$884$		0			0
$885$	6020.81	+	10428.3i	0.228686	+	0.396096i
$886$		0			0
$887$	8733.89	−	15127.5i	0.330615	−	0.572642i	−0.652018	−	0.758204i	$-0.726077\pi$
$887$	8733.89	−	15127.5i	0.330615	−	0.572642i	0.982633	+	0.185562i	$0.0594105\pi$
$888$		0			0
$889$	−2632.37	+	3449.14i	−0.0993103	+	0.130124i
$890$		0			0
$891$	2174.06	−	3765.58i	0.0817439	−	0.141585i
$892$		0			0
$893$	−2221.83	−	3848.33i	−0.0832596	−	0.144210i
$894$		0			0
$895$	−1556.98			−0.0581499
$896$		0			0
$897$	−619.499			−0.0230596
$898$		0			0
$899$	−8166.28	−	14144.4i	−0.302960	−	0.524742i
$900$		0			0
$901$	6861.38	−	11884.3i	0.253702	−	0.439425i
$902$		0			0
$903$	−27820.7	−	3588.95i	−1.02527	−	0.132262i
$904$		0			0
$905$	11142.9	−	19300.0i	0.409283	−	0.708900i
$906$		0			0
$907$	14268.1	+	24713.1i	0.522344	+	0.904726i	0.999662	+	0.0259953i	$0.00827550\pi$
$907$	14268.1	+	24713.1i	0.522344	+	0.904726i	−0.477318	+	0.878730i	$0.658391\pi$
$908$		0			0
$909$	5561.49			0.202930
$910$		0			0
$911$	−50235.7			−1.82698			−0.913492	−	0.406857i	$-0.866625\pi$
$911$	−50235.7			−1.82698			−0.913492	+	0.406857i	$0.866625\pi$
$912$		0			0
$913$	16408.0	+	28419.4i	0.594769	+	1.03017i
$914$		0			0
$915$	2681.53	−	4644.55i	0.0968839	−	0.167808i
$916$		0			0
$917$	−19005.0	−	45546.0i	−0.684404	−	1.64020i
$918$		0			0
$919$	−2658.54	+	4604.73i	−0.0954268	+	0.165284i	−0.909787	−	0.415076i	$-0.863755\pi$
$919$	−2658.54	+	4604.73i	−0.0954268	+	0.165284i	0.814360	+	0.580360i	$0.197088\pi$
$920$		0			0
$921$	12895.3	+	22335.3i	0.461362	+	0.799103i
$922$		0			0
$923$	−947.814			−0.0338003
$924$		0			0
$925$	3004.73			0.106805
$926$		0			0
$927$	3675.44	+	6366.04i	0.130223	+	0.225554i
$928$		0			0
$929$	−12746.6	+	22077.7i	−0.450162	+	0.779704i	−0.998396	−	0.0566214i	$-0.981967\pi$
$929$	−12746.6	+	22077.7i	−0.450162	+	0.779704i	0.548233	+	0.836325i	$0.315301\pi$
$930$		0			0
$931$	−6686.08	−	1754.24i	−0.235368	−	0.0617540i
$932$		0			0
$933$	−15713.0	+	27215.6i	−0.551360	+	0.954984i
$934$		0			0
$935$	8487.49	+	14700.8i	0.296867	+	0.514189i
$936$		0			0
$937$	12691.4			0.442486			0.221243	−	0.975219i	$-0.428989\pi$
$937$	12691.4			0.442486			0.221243	+	0.975219i	$0.428989\pi$
$938$		0			0
$939$	−16489.6			−0.573074
$940$		0			0
$941$	7689.19	+	13318.1i	0.266377	+	0.461378i	0.967923	−	0.251246i	$-0.0808402\pi$
$941$	7689.19	+	13318.1i	0.266377	+	0.461378i	−0.701547	+	0.712623i	$0.747507\pi$
$942$		0			0
$943$	17083.4	−	29589.3i	0.589938	−	1.02180i
$944$		0			0
$945$	−1297.12	−	3108.60i	−0.0446512	−	0.107008i
$946$		0			0
$947$	−25221.4	+	43684.8i	−0.865455	+	1.49901i	0.00113899	+	0.999999i	$0.499637\pi$
$947$	−25221.4	+	43684.8i	−0.865455	+	1.49901i	−0.866594	+	0.499013i	$0.833696\pi$
$948$		0			0
$949$	−259.872	−	450.112i	−0.00888916	−	0.0153965i
$950$		0			0
$951$	−19669.1			−0.670678
$952$		0			0
$953$	31787.3			1.08047			0.540237	−	0.841513i	$-0.318335\pi$
$953$	31787.3			1.08047			0.540237	+	0.841513i	$0.318335\pi$
$954$		0			0
$955$	6065.02	+	10504.9i	0.205507	+	0.355949i
$956$		0			0
$957$	8348.43	−	14459.9i	0.281992	−	0.488425i
$958$		0			0
$959$	−19218.6	−	2479.26i	−0.647133	−	0.0834821i
$960$		0			0
$961$	2488.00	−	4309.34i	0.0835151	−	0.144652i
$962$		0			0
$963$	−7584.19	−	13136.2i	−0.253787	−	0.439572i
$964$		0			0
$965$	8644.84			0.288381
$966$		0			0
$967$	1005.61			0.0334417			0.0167209	−	0.999860i	$-0.494677\pi$
$967$	1005.61			0.0334417			0.0167209	+	0.999860i	$0.494677\pi$
$968$		0			0
$969$	1419.09	+	2457.93i	0.0470460	+	0.0814861i
$970$		0			0
$971$	−3535.46	+	6123.59i	−0.116847	+	0.202384i	−0.918516	−	0.395383i	$-0.870612\pi$
$971$	−3535.46	+	6123.59i	−0.116847	+	0.202384i	0.801670	+	0.597767i	$0.203945\pi$
$972$		0			0
$973$	−7272.73	+	9529.31i	−0.239623	+	0.313973i
$974$		0			0
$975$	−207.356	+	359.150i	−0.00681097	+	0.0117969i
$976$		0			0
$977$	5548.53	+	9610.33i	0.181692	+	0.314700i	0.942457	−	0.334328i	$-0.108509\pi$
$977$	5548.53	+	9610.33i	0.181692	+	0.314700i	−0.760765	+	0.649028i	$0.775176\pi$
$978$		0			0
$979$	63138.7			2.06121
$980$		0			0
$981$	824.371			0.0268299
$982$		0			0
$983$	8887.74	+	15394.0i	0.288377	+	0.499484i	0.973423	−	0.229016i	$-0.0735509\pi$
$983$	8887.74	+	15394.0i	0.288377	+	0.499484i	−0.685045	+	0.728501i	$0.740218\pi$
$984$		0			0
$985$	204.614	−	354.401i	0.00661882	−	0.0114641i
$986$		0			0
$987$	−7432.67	+	9738.88i	−0.239701	+	0.314075i
$988$		0			0
$989$	−30026.0	+	52006.6i	−0.965391	+	1.67211i
$990$		0			0
$991$	−2345.93	−	4063.27i	−0.0751977	−	0.130246i	0.825975	−	0.563707i	$-0.190625\pi$
$991$	−2345.93	−	4063.27i	−0.0751977	−	0.130246i	−0.901172	+	0.433461i	$0.857292\pi$
$992$		0			0
$993$	−307.129			−0.00981515
$994$		0			0
$995$	−26004.0			−0.828523
$996$		0			0
$997$	4235.69	+	7336.44i	0.134549	+	0.233046i	0.925425	−	0.378930i	$-0.123708\pi$
$997$	4235.69	+	7336.44i	0.134549	+	0.233046i	−0.790876	+	0.611977i	$0.790375\pi$
$998$		0			0
$999$	−509.437	+	882.371i	−0.0161340	+	0.0279449i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.4.q.d.121.2	yes	4
3.2	odd	2		504.4.s.f.289.1		4
4.3	odd	2		336.4.q.g.289.2		4
7.2	even	3		1176.4.a.r.1.1		2
7.4	even	3	inner	168.4.q.d.25.2	✓	4
7.5	odd	6		1176.4.a.u.1.2		2
21.11	odd	6		504.4.s.f.361.1		4
28.11	odd	6		336.4.q.g.193.2		4
28.19	even	6		2352.4.a.bo.1.2		2
28.23	odd	6		2352.4.a.cc.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.4.q.d.25.2	✓	4	7.4	even	3	inner
168.4.q.d.121.2	yes	4	1.1	even	1	trivial
336.4.q.g.193.2		4	28.11	odd	6
336.4.q.g.289.2		4	4.3	odd	2
504.4.s.f.289.1		4	3.2	odd	2
504.4.s.f.361.1		4	21.11	odd	6
1176.4.a.r.1.1		2	7.2	even	3
1176.4.a.u.1.2		2	7.5	odd	6
2352.4.a.bo.1.2		2	28.19	even	6
2352.4.a.cc.1.1		2	28.23	odd	6

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:	\( N \)	\(=\)	\( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	168.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 + 2.59808i) q^{3} +(3.36805 - 5.83364i) q^{5} +(-11.2361 + 14.7224i) q^{7} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\)	\(q+(1.50000 + 2.59808i) q^{3} +(3.36805 - 5.83364i) q^{5} +(-11.2361 + 14.7224i) q^{7} +(-4.50000 + 7.79423i) q^{9} +(26.8403 + 46.4887i) q^{11} +1.73610 q^{13} +20.2083 q^{15} +(23.4722 + 40.6551i) q^{17} +(10.0764 - 17.4528i) q^{19} +(-55.1042 - 7.10860i) q^{21} +(-59.4722 + 103.009i) q^{23} +(39.8125 + 68.9572i) q^{25} -27.0000 q^{27} -103.681 q^{29} +(78.7639 + 136.423i) q^{31} +(-80.5208 + 139.466i) q^{33} +(48.0415 + 115.133i) q^{35} +(18.8681 - 32.6804i) q^{37} +(2.60415 + 4.51053i) q^{39} -287.250 q^{41} +504.875 q^{43} +(30.3125 + 52.5027i) q^{45} +(110.250 - 190.958i) q^{47} +(-90.5000 - 330.846i) q^{49} +(-70.4166 + 121.965i) q^{51} +(-146.160 - 253.156i) q^{53} +361.597 q^{55} +60.4582 q^{57} +(297.937 + 516.043i) q^{59} +(132.695 - 229.834i) q^{61} +(-64.1875 - 153.828i) q^{63} +(5.84728 - 10.1278i) q^{65} +(-468.368 - 811.237i) q^{67} -356.833 q^{69} -545.944 q^{71} +(-149.687 - 259.266i) q^{73} +(-119.437 + 206.872i) q^{75} +(-986.006 - 127.198i) q^{77} +(470.166 - 814.352i) q^{79} +(-40.5000 - 70.1481i) q^{81} +611.319 q^{83} +316.222 q^{85} +(-155.521 - 269.370i) q^{87} +(588.097 - 1018.61i) q^{89} +(-19.5070 + 25.5597i) q^{91} +(-236.292 + 409.269i) q^{93} +(-67.8754 - 117.564i) q^{95} +1482.49 q^{97} -483.125 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 6 q^{3} - 9 q^{5} - 18 q^{9}+O(q^{10}) \) 4 * q + 6 * q^3 - 9 * q^5 - 18 * q^9	\( 4 q + 6 q^{3} - 9 q^{5} - 18 q^{9} - 5 q^{11} - 38 q^{13} - 54 q^{15} + 4 q^{17} - 117 q^{19} - 153 q^{21} - 148 q^{23} - 43 q^{25} - 108 q^{27} - 190 q^{29} + 360 q^{31} + 15 q^{33} - 482 q^{35} + 53 q^{37} - 57 q^{39} - 340 q^{41} + 806 q^{43} - 81 q^{45} - 368 q^{47} - 362 q^{49} - 12 q^{51} - 697 q^{53} + 2570 q^{55} - 702 q^{57} + 585 q^{59} + 1160 q^{61} - 459 q^{63} + 338 q^{65} - 233 q^{67} - 888 q^{69} + 1232 q^{71} + 817 q^{73} + 129 q^{75} - 1135 q^{77} + 802 q^{79} - 162 q^{81} - 566 q^{83} + 1984 q^{85} - 285 q^{87} + 1858 q^{89} - 505 q^{91} - 1080 q^{93} - 2294 q^{95} + 3458 q^{97} + 90 q^{99}+O(q^{100}) \) 4 * q + 6 * q^3 - 9 * q^5 - 18 * q^9 - 5 * q^11 - 38 * q^13 - 54 * q^15 + 4 * q^17 - 117 * q^19 - 153 * q^21 - 148 * q^23 - 43 * q^25 - 108 * q^27 - 190 * q^29 + 360 * q^31 + 15 * q^33 - 482 * q^35 + 53 * q^37 - 57 * q^39 - 340 * q^41 + 806 * q^43 - 81 * q^45 - 368 * q^47 - 362 * q^49 - 12 * q^51 - 697 * q^53 + 2570 * q^55 - 702 * q^57 + 585 * q^59 + 1160 * q^61 - 459 * q^63 + 338 * q^65 - 233 * q^67 - 888 * q^69 + 1232 * q^71 + 817 * q^73 + 129 * q^75 - 1135 * q^77 + 802 * q^79 - 162 * q^81 - 566 * q^83 + 1984 * q^85 - 285 * q^87 + 1858 * q^89 - 505 * q^91 - 1080 * q^93 - 2294 * q^95 + 3458 * q^97 + 90 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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