LMFDB - Embedded newform 168.4.i.c.125.48

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [168,4,Mod(125,168)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(168, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 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("168.125");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 168 = 2^{3} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	168.i (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:	$9.91232088096$
Analytic rank:	$0$
Dimension:	$80$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			125.48
Character	$\chi$	$=$	168.125
Dual form			168.4.i.c.125.46

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.16707 + 2.57642i) q^{2} +(5.19433 - 0.137767i) q^{3} +(-5.27591 + 6.01371i) q^{4} +6.83655i q^{5} +(6.41707 + 13.2220i) q^{6} +(13.6972 + 12.4654i) q^{7} +(-21.6512 - 6.57457i) q^{8} +(26.9620 - 1.43121i) q^{9} +(-17.6139 + 7.97871i) q^{10} +4.03973 q^{11} +(-26.5763 + 31.9640i) q^{12} +11.6537 q^{13} +(-16.1307 + 49.8377i) q^{14} +(0.941848 + 35.5113i) q^{15} +(-8.32952 - 63.4556i) q^{16} -104.163 q^{17} +(35.1539 + 67.7953i) q^{18} -29.0310 q^{19} +(-41.1131 - 36.0690i) q^{20} +(72.8650 + 62.8625i) q^{21} +(4.71463 + 10.4081i) q^{22} +104.560i q^{23} +(-113.369 - 31.1677i) q^{24} +78.2615 q^{25} +(13.6007 + 30.0250i) q^{26} +(139.852 - 11.1486i) q^{27} +(-147.229 + 16.6045i) q^{28} +131.471 q^{29} +(-90.3929 + 43.8706i) q^{30} +113.891i q^{31} +(153.767 - 95.5173i) q^{32} +(20.9837 - 0.556540i) q^{33} +(-121.565 - 268.368i) q^{34} +(-85.2206 + 93.6416i) q^{35} +(-133.642 + 169.693i) q^{36} -320.606i q^{37} +(-33.8812 - 74.7962i) q^{38} +(60.5334 - 1.60550i) q^{39} +(44.9474 - 148.020i) q^{40} -253.628 q^{41} +(-76.9221 + 261.096i) q^{42} -356.247i q^{43} +(-21.3133 + 24.2938i) q^{44} +(9.78453 + 184.327i) q^{45} +(-269.390 + 122.028i) q^{46} +316.669 q^{47} +(-52.0083 - 328.462i) q^{48} +(32.2261 + 341.483i) q^{49} +(91.3364 + 201.635i) q^{50} +(-541.057 + 14.3502i) q^{51} +(-61.4841 + 70.0823i) q^{52} +470.890 q^{53} +(191.941 + 347.308i) q^{54} +27.6178i q^{55} +(-214.606 - 359.945i) q^{56} +(-150.797 + 3.99951i) q^{57} +(153.435 + 338.724i) q^{58} -722.454i q^{59} +(-218.524 - 181.690i) q^{60} +141.417 q^{61} +(-293.432 + 132.919i) q^{62} +(387.145 + 316.490i) q^{63} +(425.550 + 284.695i) q^{64} +79.6715i q^{65} +(25.9232 + 53.4133i) q^{66} +97.1111i q^{67} +(549.555 - 626.407i) q^{68} +(14.4048 + 543.117i) q^{69} +(-340.718 - 110.278i) q^{70} -900.777i q^{71} +(-593.170 - 146.277i) q^{72} +622.304i q^{73} +(826.017 - 374.169i) q^{74} +(406.516 - 10.7818i) q^{75} +(153.165 - 174.584i) q^{76} +(55.3330 + 50.3570i) q^{77} +(74.7829 + 154.086i) q^{78} +211.405 q^{79} +(433.818 - 56.9452i) q^{80} +(724.903 - 77.1766i) q^{81} +(-296.001 - 653.453i) q^{82} -837.420i q^{83} +(-762.466 + 106.532i) q^{84} -712.116i q^{85} +(917.842 - 415.764i) q^{86} +(682.901 - 18.1123i) q^{87} +(-87.4651 - 26.5595i) q^{88} +857.227 q^{89} +(-463.486 + 240.331i) q^{90} +(159.624 + 145.269i) q^{91} +(-628.791 - 551.647i) q^{92} +(15.6904 + 591.588i) q^{93} +(369.573 + 815.872i) q^{94} -198.472i q^{95} +(785.559 - 517.332i) q^{96} -1135.63i q^{97} +(-842.194 + 481.561i) q^{98} +(108.919 - 5.78170i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 28 q^{4} + 64 q^{7} + 104 q^{9} - 8 q^{15} - 892 q^{16} + 692 q^{18} + 128 q^{22} - 976 q^{25} + 612 q^{28} - 332 q^{30} + 1544 q^{36} + 568 q^{39} + 780 q^{42} + 208 q^{46} - 4048 q^{49} - 1448 q^{57}+ \cdots - 2072 q^{88}+O(q^{100}) $ 80 * q + 28 * q^4 + 64 * q^7 + 104 * q^9 - 8 * q^15 - 892 * q^16 + 692 * q^18 + 128 * q^22 - 976 * q^25 + 612 * q^28 - 332 * q^30 + 1544 * q^36 + 568 * q^39 + 780 * q^42 + 208 * q^46 - 4048 * q^49 - 1448 * q^57 - 1760 * q^58 + 4156 * q^60 - 2152 * q^63 + 2764 * q^64 + 1968 * q^70 - 2740 * q^72 - 3620 * q^78 + 4992 * q^79 + 1568 * q^81 + 2484 * q^84 - 2072 * q^88

Character values

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

$n$	$73$	$85$	$113$	$127$
$\chi(n)$	$-1$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	1.16707	+	2.57642i	0.412620	+	0.910903i
$2$	1.16707	+	2.57642i	0.412620	+	0.910903i
$3$	5.19433	−	0.137767i	0.999648	−	0.0265132i
$3$	5.19433	−	0.137767i	0.999648	−	0.0265132i
$4$	−5.27591	+	6.01371i	−0.659489	+	0.751714i
$5$			6.83655i			0.611480i	0.952115	+	0.305740i	$0.0989038\pi$
$5$			6.83655i			0.611480i	−0.952115	+	0.305740i	$0.901096\pi$
$6$	6.41707	+	13.2220i	0.436626	+	0.899643i
$7$	13.6972	+	12.4654i	0.739579	+	0.673070i
$7$	13.6972	+	12.4654i	0.739579	+	0.673070i
$8$	−21.6512	−	6.57457i	−0.956857	−	0.290558i
$9$	26.9620	−	1.43121i	0.998594	−	0.0530077i
$10$	−17.6139	+	7.97871i	−0.556999	+	0.252309i
$11$	4.03973			0.110729			0.0553647	−	0.998466i	$-0.482368\pi$
$11$	4.03973			0.110729			0.0553647	+	0.998466i	$0.482368\pi$
$12$	−26.5763	+	31.9640i	−0.639327	+	0.768935i
$13$	11.6537			0.248628			0.124314	−	0.992243i	$-0.460327\pi$
$13$	11.6537			0.248628			0.124314	+	0.992243i	$0.460327\pi$
$14$	−16.1307	+	49.8377i	−0.307936	+	0.951407i
$15$	0.941848	+	35.5113i	0.0162123	+	0.611265i
$16$	−8.32952	−	63.4556i	−0.130149	−	0.991494i
$17$	−104.163			−1.48607			−0.743037	−	0.669250i	$-0.766615\pi$
$17$	−104.163			−1.48607			−0.743037	+	0.669250i	$0.766615\pi$
$18$	35.1539	+	67.7953i	0.460325	+	0.887750i
$19$	−29.0310			−0.350536			−0.175268	−	0.984521i	$-0.556079\pi$
$19$	−29.0310			−0.350536			−0.175268	+	0.984521i	$0.556079\pi$
$20$	−41.1131	−	36.0690i	−0.459658	−	0.403264i
$21$	72.8650	+	62.8625i	0.757164	+	0.653225i
$22$	4.71463	+	10.4081i	0.0456892	+	0.100864i
$23$			104.560i			0.947921i	0.880546	+	0.473960i	$0.157176\pi$
$23$			104.560i			0.947921i	−0.880546	+	0.473960i	$0.842824\pi$
$24$	−113.369	−	31.1677i	−0.964225	−	0.265086i
$25$	78.2615			0.626092
$26$	13.6007	+	30.0250i	0.102589	+	0.226476i
$27$	139.852	−	11.1486i	0.996838	−	0.0794650i
$28$	−147.229	+	16.6045i	−0.993700	+	0.112070i
$29$	131.471			0.841844			0.420922	−	0.907097i	$-0.361707\pi$
$29$	131.471			0.841844			0.420922	+	0.907097i	$0.361707\pi$
$30$	−90.3929	+	43.8706i	−0.550114	+	0.266988i
$31$			113.891i			0.659854i	0.944006	+	0.329927i	$0.107024\pi$
$31$			113.891i			0.659854i	−0.944006	+	0.329927i	$0.892976\pi$
$32$	153.767	−	95.5173i	0.849453	−	0.527664i
$33$	20.9837	−	0.556540i	0.110691	−	0.00293579i
$34$	−121.565	−	268.368i	−0.613184	−	1.35367i
$35$	−85.2206	+	93.6416i	−0.411569	+	0.452238i
$36$	−133.642	+	169.693i	−0.618715	+	0.785615i
$37$		−	320.606i		−	1.42452i	−0.701915	−	0.712261i	$-0.747671\pi$
$37$		−	320.606i		−	1.42452i	0.701915	−	0.712261i	$-0.252329\pi$
$38$	−33.8812	−	74.7962i	−0.144638	−	0.319304i
$39$	60.5334	−	1.60550i	0.248541	−	0.00659193i
$40$	44.9474	−	148.020i	0.177670	−	0.585099i
$41$	−253.628			−0.966099			−0.483050	−	0.875593i	$-0.660471\pi$
$41$	−253.628			−0.966099			−0.483050	+	0.875593i	$0.660471\pi$
$42$	−76.9221	+	261.096i	−0.282603	+	0.959237i
$43$		−	356.247i		−	1.26342i	−0.775204	−	0.631711i	$-0.782353\pi$
$43$		−	356.247i		−	1.26342i	0.775204	−	0.631711i	$-0.217647\pi$
$44$	−21.3133	+	24.2938i	−0.0730249	+	0.0832369i
$45$	9.78453	+	184.327i	0.0324132	+	0.610620i
$46$	−269.390	+	122.028i	−0.863464	+	0.391131i
$47$	316.669			0.982784			0.491392	−	0.870938i	$-0.336488\pi$
$47$	316.669			0.982784			0.491392	+	0.870938i	$0.336488\pi$
$48$	−52.0083	−	328.462i	−0.156391	−	0.987695i
$49$	32.2261	+	341.483i	0.0939537	+	0.995577i
$50$	91.3364	+	201.635i	0.258338	+	0.570309i
$51$	−541.057	+	14.3502i	−1.48555	+	0.0394005i
$52$	−61.4841	+	70.0823i	−0.163968	+	0.186897i
$53$	470.890			1.22041			0.610205	−	0.792244i	$-0.291087\pi$
$53$	470.890			1.22041			0.610205	+	0.792244i	$0.291087\pi$
$54$	191.941	+	347.308i	0.483700	+	0.875234i
$55$			27.6178i			0.0677089i
$56$	−214.606	−	359.945i	−0.512106	−	0.858922i
$57$	−150.797	+	3.99951i	−0.350412	+	0.00929382i
$58$	153.435	+	338.724i	0.347362	+	0.766839i
$59$		−	722.454i		−	1.59416i	−0.603874	−	0.797080i	$-0.706377\pi$
$59$		−	722.454i		−	1.59416i	0.603874	−	0.797080i	$-0.293623\pi$
$60$	−218.524	−	181.690i	−0.470188	−	0.390935i
$61$	141.417			0.296828			0.148414	−	0.988925i	$-0.452583\pi$
$61$	141.417			0.296828			0.148414	+	0.988925i	$0.452583\pi$
$62$	−293.432	+	132.919i	−0.601063	+	0.272269i
$63$	387.145	+	316.490i	0.774217	+	0.632920i
$64$	425.550	+	284.695i	0.831152	+	0.556045i
$65$			79.6715i			0.152031i
$66$	25.9232	+	53.4133i	0.0483474	+	0.0996170i
$67$			97.1111i			0.177075i	0.996073	+	0.0885374i	$0.0282193\pi$
$67$			97.1111i			0.177075i	−0.996073	+	0.0885374i	$0.971781\pi$
$68$	549.555	−	626.407i	0.980049	−	1.11710i
$69$	14.4048	+	543.117i	0.0251324	+	0.947588i
$70$	−340.718	−	110.278i	−0.581766	−	0.188297i
$71$		−	900.777i		−	1.50567i	−0.658209	−	0.752835i	$-0.728686\pi$
$71$		−	900.777i		−	1.50567i	0.658209	−	0.752835i	$-0.271314\pi$
$72$	−593.170	−	146.277i	−0.970914	−	0.239429i
$73$			622.304i			0.997742i	0.866676	+	0.498871i	$0.166252\pi$
$73$			622.304i			0.997742i	−0.866676	+	0.498871i	$0.833748\pi$
$74$	826.017	−	374.169i	1.29760	−	0.587787i
$75$	406.516	−	10.7818i	0.625872	−	0.0165997i
$76$	153.165	−	174.584i	0.231174	−	0.263503i
$77$	55.3330	+	50.3570i	0.0818932	+	0.0745287i
$78$	74.7829	+	154.086i	0.108558	+	0.223677i
$79$	211.405			0.301074			0.150537	−	0.988604i	$-0.451900\pi$
$79$	211.405			0.301074			0.150537	+	0.988604i	$0.451900\pi$
$80$	433.818	−	56.9452i	0.606279	−	0.0795834i
$81$	724.903	−	77.1766i	0.994380	−	0.105866i
$82$	−296.001	−	653.453i	−0.398632	−	0.880023i
$83$		−	837.420i		−	1.10745i	−0.832698	−	0.553727i	$-0.813205\pi$
$83$		−	837.420i		−	1.10745i	0.832698	−	0.553727i	$-0.186795\pi$
$84$	−762.466	+	106.532i	−0.990380	+	0.138377i
$85$		−	712.116i		−	0.908704i
$86$	917.842	−	415.764i	1.15085	−	0.521313i
$87$	682.901	−	18.1123i	0.841548	−	0.0223200i
$88$	−87.4651	−	26.5595i	−0.105952	−	0.0321733i
$89$	857.227			1.02096			0.510482	−	0.859888i	$-0.329467\pi$
$89$	857.227			1.02096			0.510482	+	0.859888i	$0.329467\pi$
$90$	−463.486	+	240.331i	−0.542841	+	0.281480i
$91$	159.624	+	145.269i	0.183880	+	0.167344i
$92$	−628.791	−	551.647i	−0.712566	−	0.625143i
$93$	15.6904	+	591.588i	0.0174948	+	0.659622i
$94$	369.573	+	815.872i	0.405517	+	0.895221i
$95$		−	198.472i		−	0.214345i
$96$	785.559	−	517.332i	0.835165	−	0.550000i
$97$		−	1135.63i		−	1.18872i	−0.804199	−	0.594360i	$-0.797405\pi$
$97$		−	1135.63i		−	1.18872i	0.804199	−	0.594360i	$-0.202595\pi$
$98$	−842.194	+	481.561i	−0.868107	+	0.496378i
$99$	108.919	−	5.78170i	0.110574	−	0.00586952i
$100$	−412.901	+	470.643i	−0.412901	+	0.470643i
$101$			956.403i			0.942234i	0.882071	+	0.471117i	$0.156149\pi$
$101$			956.403i			0.942234i	−0.882071	+	0.471117i	$0.843851\pi$
$102$	−668.422	−	1377.24i	−0.648859	−	1.33694i
$103$			474.636i			0.454051i	0.973889	+	0.227025i	$0.0729000\pi$
$103$			474.636i			0.454051i	−0.973889	+	0.227025i	$0.927100\pi$
$104$	−252.318	−	76.6184i	−0.237902	−	0.0722409i
$105$	−429.763	+	498.145i	−0.399434	+	0.462991i
$106$	549.560	+	1213.21i	0.503566	+	1.11168i
$107$	−479.771			−0.433470			−0.216735	−	0.976231i	$-0.569541\pi$
$107$	−479.771			−0.433470			−0.216735	+	0.976231i	$0.569541\pi$
$108$	−670.804	+	899.852i	−0.597668	+	0.801743i
$109$			1248.35i			1.09697i	0.836159	+	0.548486i	$0.184796\pi$
$109$			1248.35i			1.09697i	−0.836159	+	0.548486i	$0.815204\pi$
$110$	−71.1552	+	32.2318i	−0.0616762	+	0.0279381i
$111$	−44.1688	−	1665.33i	−0.0377686	−	1.42402i
$112$	676.911	−	972.995i	0.571090	−	0.820888i
$113$			1349.96i			1.12384i	0.827193	+	0.561918i	$0.189937\pi$
$113$			1349.96i			1.12384i	−0.827193	+	0.561918i	$0.810063\pi$
$114$	−186.294	−	383.848i	−0.153053	−	0.315357i
$115$	−714.827			−0.579634
$116$	−693.627	+	790.627i	−0.555187	+	0.632826i
$117$	314.209	−	16.6789i	0.248279	−	0.0131792i
$118$	1861.35	−	843.152i	1.45213	−	0.657783i
$119$	−1426.74	−	1298.44i	−1.09907	−	1.00023i
$120$	213.079	−	775.055i	0.162095	−	0.589604i
$121$	−1314.68			−0.987739
$122$	165.043	+	364.349i	0.122477	+	0.270382i
$123$	−1317.43	+	34.9415i	−0.965760	+	0.0256144i
$124$	−684.910	−	600.880i	−0.496022	−	0.435166i
$125$			1389.61i			0.994323i
$126$	−363.588	+	1366.81i	−0.257071	+	0.966392i
$127$	−1963.80			−1.37212			−0.686058	−	0.727547i	$-0.740660\pi$
$127$	−1963.80			−1.37212			−0.686058	+	0.727547i	$0.740660\pi$
$128$	−236.850	+	1428.65i	−0.163553	+	0.986535i
$129$	−49.0789	−	1850.46i	−0.0334973	−	1.26298i
$130$	−205.267	+	92.9819i	−0.138486	+	0.0627312i
$131$		−	1775.12i		−	1.18391i	−0.805969	−	0.591957i	$-0.798355\pi$
$131$		−	1775.12i		−	1.18391i	0.805969	−	0.591957i	$-0.201645\pi$
$132$	−107.361	+	129.126i	−0.0707923	+	0.0851438i
$133$	−397.644	−	361.884i	−0.259249	−	0.235935i
$134$	−250.199	+	113.335i	−0.161298	+	0.0730646i
$135$	76.2182	+	956.109i	0.0485913	+	0.609546i
$136$	2255.26	+	684.828i	1.42196	+	0.431790i
$137$			573.341i			0.357546i	0.983890	+	0.178773i	$0.0572128\pi$
$137$			573.341i			0.357546i	−0.983890	+	0.178773i	$0.942787\pi$
$138$	−1382.49	+	670.966i	−0.852790	+	0.413887i
$139$	−1094.52			−0.667883			−0.333942	−	0.942594i	$-0.608379\pi$
$139$	−1094.52			−0.667883			−0.333942	+	0.942594i	$0.608379\pi$
$140$	−113.518	−	1006.54i	−0.0685285	−	0.607628i
$141$	1644.88	−	43.6263i	0.982439	−	0.0260567i
$142$	2320.78	−	1051.27i	1.37152	−	0.621270i
$143$	47.0780			0.0275305
$144$	−315.399	−	1698.97i	−0.182523	−	0.983202i
$145$			898.806i			0.514771i
$146$	−1603.32	+	726.270i	−0.908846	+	0.411689i
$147$	214.438	+	1769.33i	0.120317	+	0.992736i
$148$	1928.03	+	1691.49i	1.07083	+	0.939456i
$149$	2573.83			1.41514			0.707571	−	0.706643i	$-0.249791\pi$
$149$	2573.83			1.41514			0.707571	+	0.706643i	$0.249791\pi$
$150$	502.210	+	1034.77i	0.273368	+	0.563260i
$151$	−1119.27			−0.603214			−0.301607	−	0.953432i	$-0.597523\pi$
$151$	−1119.27			−0.603214			−0.301607	+	0.953432i	$0.597523\pi$
$152$	628.557	+	190.867i	0.335413	+	0.101851i
$153$	−2808.45	+	149.079i	−1.48398	+	0.0787734i
$154$	−65.1636	+	201.331i	−0.0340976	+	0.105349i
$155$	−778.624			−0.403487
$156$	−309.714	+	372.501i	−0.158955	+	0.191179i
$157$	−2769.72			−1.40795			−0.703973	−	0.710227i	$-0.748592\pi$
$157$	−2769.72			−1.40795			−0.703973	+	0.710227i	$0.748592\pi$
$158$	246.723	+	544.667i	0.124229	+	0.274249i
$159$	2445.96	−	64.8729i	1.21998	−	0.0323570i
$160$	653.009	+	1051.24i	0.322656	+	0.519424i
$161$	−1303.38	+	1432.17i	−0.638017	+	0.701062i
$162$	1044.85	+	1777.59i	0.506736	+	0.862102i
$163$		−	1305.78i		−	0.627464i	−0.949511	−	0.313732i	$-0.898421\pi$
$163$		−	1305.78i		−	0.627464i	0.949511	−	0.313732i	$-0.101579\pi$
$164$	1338.12	−	1525.25i	0.637132	−	0.726231i
$165$	3.80481	+	143.456i	0.00179518	+	0.0676851i
$166$	2157.55	−	977.324i	1.00878	−	0.456958i
$167$	−1241.39			−0.575218			−0.287609	−	0.957748i	$-0.592860\pi$
$167$	−1241.39			−0.575218			−0.287609	+	0.957748i	$0.592860\pi$
$168$	−1164.32	−	1840.11i	−0.534698	−	0.845043i
$169$	−2061.19			−0.938184
$170$	1834.71	−	831.087i	0.827741	−	0.374950i
$171$	−782.736	+	41.5495i	−0.350043	+	0.0185811i
$172$	2142.37	+	1879.53i	0.949732	+	0.833212i
$173$			415.397i			0.182555i	0.995825	+	0.0912775i	$0.0290950\pi$
$173$			415.397i			0.182555i	−0.995825	+	0.0912775i	$0.970905\pi$
$174$	843.656	+	1738.30i	0.367571	+	0.757359i
$175$	1071.96	+	975.564i	0.463045	+	0.421404i
$176$	−33.6490	−	256.344i	−0.0144113	−	0.109788i
$177$	−99.5300	−	3752.66i	−0.0422663	−	1.59360i
$178$	1000.44	+	2208.58i	0.421271	+	0.930000i
$179$	117.160			0.0489215			0.0244608	−	0.999701i	$-0.492213\pi$
$179$	117.160			0.0489215			0.0244608	+	0.999701i	$0.492213\pi$
$180$	−1160.11	−	913.654i	−0.480388	−	0.378332i
$181$	−1379.06			−0.566325			−0.283162	−	0.959072i	$-0.591384\pi$
$181$	−1379.06			−0.566325			−0.283162	+	0.959072i	$0.591384\pi$
$182$	−187.983	+	580.797i	−0.0765617	+	0.236547i
$183$	734.564	−	19.4825i	0.296724	−	0.00786987i
$184$	687.435	−	2263.84i	0.275426	−	0.907025i
$185$	2191.84			0.871066
$186$	−1505.87	+	730.848i	−0.593633	+	0.288110i
$187$	−420.791			−0.164552
$188$	−1670.72	+	1904.35i	−0.648135	+	0.738773i
$189$	2054.56	+	1590.62i	0.790726	+	0.612171i
$190$	511.348	−	231.630i	0.195248	−	0.0884433i
$191$			2323.47i			0.880211i	0.897946	+	0.440106i	$0.145059\pi$
$191$			2323.47i			0.880211i	−0.897946	+	0.440106i	$0.854941\pi$
$192$	2249.67	+	1420.17i	0.845603	+	0.533813i
$193$	1284.20			0.478958			0.239479	−	0.970902i	$-0.423023\pi$
$193$	1284.20			0.478958			0.239479	+	0.970902i	$0.423023\pi$
$194$	2925.87	−	1325.36i	1.08281	−	0.490490i
$195$	10.9761	+	413.840i	0.00403083	+	0.151978i
$196$	−2223.60	−	1607.83i	−0.810351	−	0.585945i
$197$	−4935.49			−1.78497			−0.892485	−	0.451076i	$-0.851040\pi$
$197$	−4935.49			−1.78497			−0.892485	+	0.451076i	$0.851040\pi$
$198$	142.012	+	273.875i	0.0509716	+	0.0983002i
$199$		−	3824.82i		−	1.36249i	−0.732058	−	0.681243i	$-0.761440\pi$
$199$		−	3824.82i		−	1.36249i	0.732058	−	0.681243i	$-0.238560\pi$
$200$	−1694.46	−	514.536i	−0.599081	−	0.181916i
$201$	13.3787	+	504.427i	0.00469482	+	0.177013i
$202$	−2464.10	+	1116.19i	−0.858284	+	0.388785i
$203$	1800.78	+	1638.84i	0.622610	+	0.566620i
$204$	2768.27	−	3329.47i	0.950087	−	1.14269i
$205$		−	1733.94i		−	0.590750i
$206$	−1222.86	+	553.931i	−0.413596	+	0.187351i
$207$	149.647	+	2819.14i	0.0502471	+	0.946588i
$208$	−97.0702	−	739.496i	−0.0323587	−	0.246514i
$209$	−117.278			−0.0388146
$210$	−1784.99	−	525.882i	−0.586554	−	0.172806i
$211$		−	1236.70i		−	0.403496i	−0.979437	−	0.201748i	$-0.935338\pi$
$211$		−	1236.70i		−	0.403496i	0.979437	−	0.201748i	$-0.0646623\pi$
$212$	−2484.37	+	2831.80i	−0.804847	+	0.917400i
$213$	−124.097	−	4678.93i	−0.0399201	−	1.50514i
$214$	−559.925	−	1236.09i	−0.178858	−	0.394849i
$215$	2435.50			0.772557
$216$	−3101.27	−	678.089i	−0.976921	−	0.213602i
$217$	−1419.70	+	1559.99i	−0.444128	+	0.488014i
$218$	−3216.27	+	1456.91i	−0.999236	+	0.452633i
$219$	85.7326	+	3232.45i	0.0264533	+	0.997391i
$220$	−166.086	−	145.709i	−0.0508977	−	0.0446532i
$221$	−1213.89			−0.369480
$222$	4239.05	−	2057.35i	1.28156	−	0.621983i
$223$			2567.59i			0.771026i	0.922702	+	0.385513i	$0.125975\pi$
$223$			2567.59i			0.771026i	−0.922702	+	0.385513i	$0.874025\pi$
$224$	3296.85	+	608.458i	0.983392	+	0.181493i
$225$	2110.09	−	112.009i	0.625212	−	0.0331877i
$226$	−3478.07	+	1575.49i	−1.02371	+	0.463718i
$227$			5160.79i			1.50896i	0.656323	+	0.754480i	$0.272111\pi$
$227$			5160.79i			1.50896i	−0.656323	+	0.754480i	$0.727889\pi$
$228$	771.538	−	927.949i	0.224107	−	0.269539i
$229$	2221.09			0.640934			0.320467	−	0.947260i	$-0.396160\pi$
$229$	2221.09			0.640934			0.320467	+	0.947260i	$0.396160\pi$
$230$	−834.251	−	1841.70i	−0.239169	−	0.527991i
$231$	294.355	+	253.947i	0.0838404	+	0.0723312i
$232$	−2846.50	−	864.364i	−0.805525	−	0.244605i
$233$		−	3711.51i		−	1.04356i	−0.853080	−	0.521779i	$-0.825268\pi$
$233$		−	3711.51i		−	1.04356i	0.853080	−	0.521779i	$-0.174732\pi$
$234$	409.675	+	790.069i	0.114450	+	0.220720i
$235$			2164.92i			0.600953i
$236$	4344.63	+	3811.60i	1.19835	+	1.05133i
$237$	1098.10	−	29.1245i	0.300968	−	0.00798244i
$238$	1680.22	−	5191.25i	0.457616	−	1.41386i
$239$		−	3198.82i		−	0.865751i	−0.901454	−	0.432876i	$-0.857499\pi$
$239$		−	3198.82i		−	0.865751i	0.901454	−	0.432876i	$-0.142501\pi$
$240$	2245.55	−	355.558i	0.603956	−	0.0956298i
$241$		−	5785.50i		−	1.54638i	−0.634177	−	0.773188i	$-0.718661\pi$
$241$		−	5785.50i		−	1.54638i	0.634177	−	0.773188i	$-0.281339\pi$
$242$	−1534.32	−	3387.17i	−0.407561	−	0.899734i
$243$	3754.75	−	500.748i	0.991224	−	0.132193i
$244$	−746.101	+	850.439i	−0.195755	+	0.223130i
$245$	−2334.56	+	220.316i	−0.608775	+	0.0574508i
$246$	−1627.55	−	3353.47i	−0.421824	−	0.869144i
$247$	−338.320			−0.0871531
$248$	748.787	−	2465.88i	0.191726	−	0.631386i
$249$	−115.368	−	4349.83i	−0.0293622	−	1.10707i
$250$	−3580.22	+	1621.77i	−0.905732	+	0.410278i
$251$		−	2096.38i		−	0.527180i	−0.964635	−	0.263590i	$-0.915093\pi$
$251$		−	2096.38i		−	0.527180i	0.964635	−	0.263590i	$-0.0849066\pi$
$252$	−3945.82	+	658.406i	−0.986363	+	0.164586i
$253$			422.392i			0.104963i
$254$	−2291.88	−	5059.57i	−0.566163	−	1.24986i
$255$	−98.1058	−	3698.96i	−0.0240926	−	0.908385i
$256$	−3957.24	+	1057.11i	−0.966123	+	0.258084i
$257$	5905.29			1.43331			0.716657	−	0.697426i	$-0.245671\pi$
$257$	5905.29			1.43331			0.716657	+	0.697426i	$0.245671\pi$
$258$	4710.29	−	2286.06i	1.13663	−	0.551643i
$259$	3996.49	−	4391.40i	0.958803	−	1.05355i
$260$	−479.121	−	420.340i	−0.114284	−	0.100263i
$261$	3544.72	−	188.162i	0.840661	−	0.0446243i
$262$	4573.46	−	2071.68i	1.07843	−	0.488507i
$263$		−	2143.88i		−	0.502652i	−0.967902	−	0.251326i	$-0.919133\pi$
$263$		−	2143.88i		−	0.502652i	0.967902	−	0.251326i	$-0.0808666\pi$
$264$	−457.981	−	125.909i	−0.106768	−	0.0293529i
$265$			3219.26i			0.746256i
$266$	468.291	−	1446.84i	0.107943	−	0.333502i
$267$	4452.72	−	118.097i	1.02061	−	0.0270690i
$268$	−583.998	−	512.350i	−0.133110	−	0.116779i
$269$		−	6249.96i		−	1.41660i	−0.705909	−	0.708302i	$-0.749461\pi$
$269$		−	6249.96i		−	1.41660i	0.705909	−	0.708302i	$-0.250539\pi$
$270$	−2374.39	+	1312.21i	−0.535188	+	0.295773i
$271$			4623.10i			1.03629i	0.855294	+	0.518143i	$0.173376\pi$
$271$			4623.10i			1.03629i	−0.855294	+	0.518143i	$0.826624\pi$
$272$	867.629	+	6609.73i	0.193411	+	1.47343i
$273$	849.150	+	732.584i	0.188252	+	0.162410i
$274$	−1477.17	+	669.128i	−0.325690	+	0.147531i
$275$	316.156			0.0693269
$276$	−3342.15	−	2778.81i	−0.728890	−	0.606031i
$277$			282.839i			0.0613507i	0.999529	+	0.0306754i	$0.00976580\pi$
$277$			282.839i			0.0613507i	−0.999529	+	0.0306754i	$0.990234\pi$
$278$	−1277.37	−	2819.94i	−0.275582	−	0.608377i
$279$	163.002	+	3070.74i	0.0349774	+	0.658926i
$280$	2460.78	−	1467.16i	0.525214	−	0.313142i
$281$			6722.69i			1.42720i	0.700555	+	0.713598i	$0.252936\pi$
$281$			6722.69i			1.42720i	−0.700555	+	0.713598i	$0.747064\pi$
$282$	2032.08	+	4186.99i	0.429109	+	0.884155i
$283$	−7208.18			−1.51407			−0.757035	−	0.653375i	$-0.773353\pi$
$283$	−7208.18			−1.51407			−0.757035	+	0.653375i	$0.773353\pi$
$284$	5417.02	+	4752.42i	1.13183	+	0.992973i
$285$	−27.3428	−	1030.93i	−0.00568298	−	0.214270i
$286$	54.9432	+	121.293i	0.0113596	+	0.0250776i
$287$	−3473.99	−	3161.58i	−0.714507	−	0.650252i
$288$	4009.18	−	2795.42i	0.820289	−	0.571949i
$289$	5936.94			1.20842
$290$	−2315.70	+	1048.97i	−0.468906	+	0.212405i
$291$	−156.452	−	5898.84i	−0.0315168	−	1.18830i
$292$	−3742.36	−	3283.22i	−0.750017	−	0.658000i
$293$			3175.54i			0.633163i	0.948565	+	0.316582i	$0.102535\pi$
$293$			3175.54i			0.633163i	−0.948565	+	0.316582i	$0.897465\pi$
$294$	−4308.29	+	2617.41i	−0.854641	+	0.519220i
$295$	4939.09			0.974797
$296$	−2107.85	+	6941.51i	−0.413906	+	1.36306i
$297$	564.966	−	45.0375i	0.110379	−	0.00879912i
$298$	3003.83	+	6631.26i	0.583916	+	1.28906i
$299$			1218.51i			0.235680i
$300$	−2079.90	+	2501.55i	−0.400278	+	0.481424i
$301$	4440.77	−	4879.58i	0.850371	−	0.934400i
$302$	−1306.27	−	2883.72i	−0.248898	−	0.549469i
$303$	131.760	+	4967.87i	0.0249816	+	0.941903i
$304$	241.815	+	1842.18i	0.0456218	+	0.347554i
$305$			966.802i			0.181505i
$306$	−3661.74	−	7061.77i	−0.684077	−	1.31926i
$307$	3739.33			0.695163			0.347581	−	0.937650i	$-0.387003\pi$
$307$	3739.33			0.695163			0.347581	+	0.937650i	$0.387003\pi$
$308$	−594.764	+	67.0777i	−0.110032	+	0.0124094i
$309$	65.3889	+	2465.41i	0.0120383	+	0.453891i
$310$	−908.706	−	2006.06i	−0.166487	−	0.367538i
$311$	−9117.85			−1.66246			−0.831231	−	0.555927i	$-0.812363\pi$
$311$	−9117.85			−1.66246			−0.831231	+	0.555927i	$0.812363\pi$
$312$	−1321.18	−	363.220i	−0.239734	−	0.0659080i
$313$			9104.29i			1.64410i	0.569412	+	0.822052i	$0.307171\pi$
$313$			9104.29i			1.64410i	−0.569412	+	0.822052i	$0.692829\pi$
$314$	−3232.44	−	7135.96i	−0.580947	−	1.28250i
$315$	−2163.70	+	2646.74i	−0.387018	+	0.473418i
$316$	−1115.35	+	1271.33i	−0.198555	+	0.226322i
$317$	−9883.17			−1.75109			−0.875543	−	0.483141i	$-0.839496\pi$
$317$	−9883.17			−1.75109			−0.875543	+	0.483141i	$0.839496\pi$
$318$	3021.73	+	6226.11i	0.532863	+	1.09793i
$319$	531.106			0.0932170
$320$	−1946.33	+	2909.29i	−0.340010	+	0.508233i
$321$	−2492.09	+	66.0965i	−0.433317	+	0.0114927i
$322$	−5211.01	−	1686.62i	−0.901859	−	0.291899i
$323$	3023.96			0.520922
$324$	−3360.41	+	4766.54i	−0.576202	+	0.817308i
$325$	912.040			0.155664
$326$	3364.25	−	1523.93i	0.571559	−	0.258905i
$327$	171.981	+	6484.33i	0.0290842	+	1.09659i
$328$	5491.36	+	1667.50i	0.924419	+	0.280708i
$329$	4337.47	+	3947.41i	0.726846	+	0.661482i
$330$	−365.163	+	177.226i	−0.0609138	+	0.0295635i
$331$			452.334i			0.0751134i	0.999294	+	0.0375567i	$0.0119575\pi$
$331$			452.334i			0.0751134i	−0.999294	+	0.0375567i	$0.988043\pi$
$332$	5036.00	+	4418.15i	0.832490	+	0.730354i
$333$	−458.854	−	8644.19i	−0.0755107	−	1.42252i
$334$	−1448.78	−	3198.34i	−0.237347	−	0.523968i
$335$	−663.905			−0.108278
$336$	3382.05	−	5147.31i	0.549125	−	0.835740i
$337$	4969.87			0.803341			0.401670	−	0.915784i	$-0.368430\pi$
$337$	4969.87			0.803341			0.401670	+	0.915784i	$0.368430\pi$
$338$	−2405.55	−	5310.50i	−0.387114	−	0.854595i
$339$	185.979	+	7012.13i	0.0297965	+	1.12344i
$340$	4282.46	+	3757.06i	0.683086	+	0.599280i
$341$			460.090i			0.0730653i
$342$	−1020.55	−	1968.17i	−0.161360	−	0.311188i
$343$	−3815.32	+	5079.07i	−0.600606	+	0.799545i
$344$	−2342.17	+	7713.17i	−0.367097	+	1.20891i
$345$	−3713.04	+	98.4793i	−0.579431	+	0.0153680i
$346$	−1070.24	+	484.795i	−0.166290	+	0.0753259i
$347$	11013.5			1.70386			0.851928	−	0.523659i	$-0.175433\pi$
$347$	11013.5			1.70386			0.851928	+	0.523659i	$0.175433\pi$
$348$	−3494.01	+	4202.33i	−0.538214	+	0.647324i
$349$	−4530.91			−0.694940			−0.347470	−	0.937691i	$-0.612959\pi$
$349$	−4530.91			−0.694940			−0.347470	+	0.937691i	$0.612959\pi$
$350$	−1262.41	+	3900.38i	−0.192797	+	0.595669i
$351$	1629.81	−	129.923i	0.247842	−	0.0197573i
$352$	621.179	−	385.864i	0.0940595	−	0.0584279i
$353$	6152.85			0.927714			0.463857	−	0.885910i	$-0.346465\pi$
$353$	6152.85			0.927714			0.463857	+	0.885910i	$0.346465\pi$
$354$	9552.28	−	4636.03i	1.43418	−	0.696052i
$355$	6158.21			0.920687
$356$	−4522.65	+	5155.12i	−0.673315	+	0.767474i
$357$	−7589.84	−	6547.95i	−1.12520	−	0.970740i
$358$	136.734	+	301.854i	0.0201860	+	0.0445628i
$359$			2822.93i			0.415010i	0.978234	+	0.207505i	$0.0665344\pi$
$359$			2822.93i			0.415010i	−0.978234	+	0.207505i	$0.933466\pi$
$360$	1000.03	−	4055.24i	0.146406	−	0.593694i
$361$	−6016.20			−0.877125
$362$	−1609.46	−	3553.04i	−0.233677	−	0.515867i
$363$	−6828.88	+	181.119i	−0.987392	+	0.0261881i
$364$	−1715.77	+	193.505i	−0.247062	+	0.0278637i
$365$	−4254.41			−0.610099
$366$	907.480	+	1869.81i	0.129603	+	0.267040i
$367$		−	6388.51i		−	0.908658i	−0.890834	−	0.454329i	$-0.849879\pi$
$367$		−	6388.51i		−	0.908658i	0.890834	−	0.454329i	$-0.150121\pi$
$368$	6634.90	−	870.931i	0.939858	−	0.123371i
$369$	−6838.33	+	362.995i	−0.964741	+	0.0512107i
$370$	2558.02	+	5647.11i	0.359420	+	0.793457i
$371$	6449.87	+	5869.85i	0.902589	+	0.821421i
$372$	−3640.42	−	3026.81i	−0.507385	−	0.421862i
$373$			6415.30i			0.890541i	0.895396	+	0.445270i	$0.146892\pi$
$373$			6415.30i			0.890541i	−0.895396	+	0.445270i	$0.853108\pi$
$374$	−491.091	−	1084.13i	−0.0678976	−	0.149891i
$375$	191.442	+	7218.08i	0.0263627	+	0.993973i
$376$	−6856.26	−	2081.96i	−0.940384	−	0.285556i
$377$	1532.13			0.209306
$378$	−1700.29	+	7149.77i	−0.231359	+	0.972868i
$379$			10997.5i			1.49051i	0.666782	+	0.745253i	$0.267671\pi$
$379$			10997.5i			1.49051i	−0.666782	+	0.745253i	$0.732329\pi$
$380$	1193.56	+	1047.12i	0.161127	+	0.141358i
$381$	−10200.6	+	270.545i	−1.37163	+	0.0363792i
$382$	−5986.24	+	2711.64i	−0.801787	+	0.363193i
$383$	−9990.07			−1.33282			−0.666408	−	0.745587i	$-0.732169\pi$
$383$	−9990.07			−1.33282			−0.666408	+	0.745587i	$0.732169\pi$
$384$	−1033.45	+	7453.53i	−0.137339	+	0.990524i
$385$	−344.268	+	378.287i	−0.0455728	+	0.0500760i
$386$	1498.75	+	3308.64i	0.197628	+	0.436284i
$387$	−509.864	−	9605.14i	−0.0669711	−	1.26165i
$388$	6829.36	+	5991.49i	0.893578	+	0.783948i
$389$	3943.66			0.514014			0.257007	−	0.966410i	$-0.417264\pi$
$389$	3943.66			0.514014			0.257007	+	0.966410i	$0.417264\pi$
$390$	−1053.42	+	511.257i	−0.136774	+	0.0663808i
$391$		−	10891.2i		−	1.40868i
$392$	1547.37	−	7605.39i	0.199372	−	0.979924i
$393$	−244.552	−	9220.55i	−0.0313894	−	1.18350i
$394$	−5760.05	−	12715.9i	−0.736515	−	1.62594i
$395$			1445.28i			0.184101i
$396$	−539.879	+	685.514i	−0.0685100	+	0.0869908i
$397$	14238.3			1.80000			0.900002	−	0.435885i	$-0.143565\pi$
$397$	14238.3			1.80000			0.900002	+	0.435885i	$0.143565\pi$
$398$	9854.36	−	4463.82i	1.24109	−	0.562189i
$399$	−2115.35	−	1824.96i	−0.265413	−	0.228979i
$400$	−651.881	−	4966.14i	−0.0814852	−	0.620767i
$401$			876.488i			0.109151i	0.998510	+	0.0545757i	$0.0173806\pi$
$401$			876.488i			0.109151i	−0.998510	+	0.0545757i	$0.982619\pi$
$402$	−1284.00	+	623.169i	−0.159304	+	0.0773155i
$403$			1327.26i			0.164058i
$404$	−5751.53	−	5045.90i	−0.708291	−	0.621393i
$405$	527.622	+	4955.84i	0.0647352	+	0.608044i
$406$	−2120.71	+	6552.20i	−0.259234	+	0.800937i
$407$		−	1295.16i		−	0.157737i
$408$	11808.9	+	3246.52i	1.43291	+	0.393938i
$409$		−	11741.1i		−	1.41947i	−0.704471	−	0.709733i	$-0.748816\pi$
$409$		−	11741.1i		−	1.41947i	0.704471	−	0.709733i	$-0.251184\pi$
$410$	4467.37	−	2023.63i	0.538116	−	0.243756i
$411$	78.9873	+	2978.12i	0.00947969	+	0.357421i
$412$	−2854.32	−	2504.13i	−0.341316	−	0.299441i
$413$	9005.70	−	9895.59i	1.07298	−	1.17901i
$414$	−7088.65	+	3675.68i	−0.841517	+	0.436352i
$415$	5725.06			0.677186
$416$	1791.97	−	1113.14i	0.211198	−	0.131192i
$417$	−5685.28	+	150.788i	−0.667648	+	0.0177077i
$418$	−136.871	−	302.157i	−0.0160157	−	0.0353564i
$419$		−	16673.4i		−	1.94403i	−0.234911	−	0.972017i	$-0.575480\pi$
$419$		−	16673.4i		−	1.94403i	0.234911	−	0.972017i	$-0.424520\pi$
$420$	−728.314	−	5212.64i	−0.0846145	−	0.605597i
$421$			2350.61i			0.272118i	0.990701	+	0.136059i	$0.0434436\pi$
$421$			2350.61i			0.272118i	−0.990701	+	0.136059i	$0.956556\pi$
$422$	3186.26	−	1443.31i	0.367546	−	0.166491i
$423$	8538.03	−	453.219i	0.981402	−	0.0520952i
$424$	−10195.3	−	3095.90i	−1.16776	−	0.354600i
$425$	−8151.96			−0.930419
$426$	11910.1	−	5780.35i	1.35457	−	0.657415i
$427$	1937.01	+	1762.82i	0.219528	+	0.199786i
$428$	2531.23	−	2885.21i	0.285868	−	0.325845i
$429$	244.538	−	6.48577i	0.0275208	−	0.000729921i
$430$	2842.39	+	6274.88i	0.318773	+	0.703724i
$431$		−	6140.09i		−	0.686213i	−0.939297	−	0.343106i	$-0.888521\pi$
$431$		−	6140.09i		−	0.686213i	0.939297	−	0.343106i	$-0.111479\pi$
$432$	−1872.35	−	8781.56i	−0.208526	−	0.978017i
$433$		−	8753.16i		−	0.971478i	−0.874104	−	0.485739i	$-0.838551\pi$
$433$		−	8753.16i		−	0.971478i	0.874104	−	0.485739i	$-0.161449\pi$
$434$	−5676.08	−	1837.14i	−0.627790	−	0.203193i
$435$	123.825	+	4668.69i	0.0136482	+	0.514590i
$436$	−7507.21	−	6586.17i	−0.824610	−	0.723441i
$437$		−	3035.47i		−	0.332280i
$438$	−8228.10	+	3993.37i	−0.897611	+	0.435640i
$439$		−	4097.50i		−	0.445474i	−0.974879	−	0.222737i	$-0.928501\pi$
$439$		−	4097.50i		−	0.445474i	0.974879	−	0.222737i	$-0.0714992\pi$
$440$	181.575	−	597.959i	0.0196733	−	0.0647877i
$441$	1357.62	+	9160.95i	0.146595	+	0.989197i
$442$	−1416.69	−	3127.49i	−0.152455	−	0.336561i
$443$	−7908.50			−0.848181			−0.424091	−	0.905620i	$-0.639406\pi$
$443$	−7908.50			−0.848181			−0.424091	+	0.905620i	$0.639406\pi$
$444$	10247.9	+	8520.52i	1.09536	+	0.910735i
$445$			5860.48i			0.624299i
$446$	−6615.21	+	2996.55i	−0.702330	+	0.318141i
$447$	13369.3	−	354.587i	1.41464	−	0.0375199i
$448$	2279.99	+	9204.18i	0.240446	+	0.970663i
$449$			2363.47i			0.248417i	0.992256	+	0.124208i	$0.0396392\pi$
$449$			2363.47i			0.248417i	−0.992256	+	0.124208i	$0.960361\pi$
$450$	2751.20	+	5305.77i	0.288206	+	0.555814i
$451$	−1024.59			−0.106976
$452$	−8118.27	−	7122.27i	−0.844804	−	0.741158i
$453$	−5813.88	+	154.199i	−0.603002	+	0.0159931i
$454$	−13296.4	+	6022.99i	−1.37452	+	0.622627i
$455$	−993.139	+	1091.28i	−0.102328	+	0.112439i
$456$	3291.23	+	904.830i	0.337995	+	0.0929222i
$457$	5371.11			0.549781			0.274891	−	0.961476i	$-0.411358\pi$
$457$	5371.11			0.549781			0.274891	+	0.961476i	$0.411358\pi$
$458$	2592.16	+	5722.48i	0.264463	+	0.583829i
$459$	−14567.5	+	1161.28i	−1.48137	+	0.118091i
$460$	3771.36	−	4298.77i	0.382263	−	0.435720i
$461$			14246.7i			1.43934i	0.694319	+	0.719668i	$0.255706\pi$
$461$			14246.7i			1.43934i	−0.694319	+	0.719668i	$0.744294\pi$
$462$	−310.744	+	1054.76i	−0.0312925	+	0.106216i
$463$	−3194.81			−0.320681			−0.160341	−	0.987062i	$-0.551259\pi$
$463$	−3194.81			−0.320681			−0.160341	+	0.987062i	$0.551259\pi$
$464$	−1095.09	−	8342.56i	−0.109565	−	0.834684i
$465$	−4044.43	+	107.268i	−0.403346	+	0.0106977i
$466$	9562.42	−	4331.58i	0.950581	−	0.430594i
$467$		−	3317.47i		−	0.328724i	−0.986400	−	0.164362i	$-0.947443\pi$
$467$		−	3317.47i		−	0.328724i	0.986400	−	0.164362i	$-0.0525565\pi$
$468$	−1557.44	+	1977.56i	−0.153830	+	0.195326i
$469$	−1210.53	+	1330.15i	−0.119184	+	0.130961i
$470$	−5577.75	+	2526.61i	−0.547410	+	0.247965i
$471$	−14386.8	+	381.574i	−1.40745	+	0.0373291i
$472$	−4749.82	+	15642.0i	−0.463196	+	1.52538i
$473$		−	1439.14i		−	0.139898i
$474$	1356.60	+	2795.19i	0.131457	+	0.270859i
$475$	−2272.01			−0.219468
$476$	15335.8	−	1729.58i	1.47671	−	0.166544i
$477$	12696.2	−	673.942i	1.21869	−	0.0646912i
$478$	8241.52	−	3733.24i	0.788616	−	0.357227i
$479$	1661.85			0.158522			0.0792608	−	0.996854i	$-0.474744\pi$
$479$	1661.85			0.158522			0.0792608	+	0.996854i	$0.474744\pi$
$480$	3536.77	+	5370.52i	0.336314	+	0.510686i
$481$		−	3736.26i		−	0.354176i
$482$	14905.9	−	6752.06i	1.40860	−	0.638066i
$483$	−6572.88	+	7618.73i	−0.619205	+	0.717732i
$484$	6936.14	−	7906.11i	0.651403	−	0.742498i
$485$	7763.80			0.726879
$486$	5672.18	+	9089.42i	0.529415	+	0.848363i
$487$	6158.69			0.573053			0.286527	−	0.958072i	$-0.407499\pi$
$487$	6158.69			0.573053			0.286527	+	0.958072i	$0.407499\pi$
$488$	−3061.84	−	929.753i	−0.284022	−	0.0862458i
$489$	−179.893	−	6782.66i	−0.0166361	−	0.627244i
$490$	−3292.22	−	5757.70i	−0.303525	−	0.530830i
$491$	−7846.32			−0.721180			−0.360590	−	0.932724i	$-0.617425\pi$
$491$	−7846.32			−0.721180			−0.360590	+	0.932724i	$0.617425\pi$
$492$	6740.50	−	8106.98i	0.617653	−	0.742868i
$493$	−13694.4			−1.25104
$494$	−394.842	−	871.657i	−0.0359611	−	0.0793880i
$495$	39.5269	+	744.633i	0.00358909	+	0.0676137i
$496$	7227.04	−	948.660i	0.654242	−	0.0858792i
$497$	11228.6	−	12338.1i	1.01342	−	1.11356i
$498$	11072.4	−	5373.78i	0.996314	−	0.483544i
$499$			11321.6i			1.01568i	0.861452	+	0.507839i	$0.169556\pi$
$499$			11321.6i			1.01568i	−0.861452	+	0.507839i	$0.830444\pi$
$500$	−8356.71	−	7331.45i	−0.747447	−	0.655745i
$501$	−6448.17	+	171.022i	−0.575016	+	0.0152509i
$502$	5401.15	−	2446.61i	0.480210	−	0.217525i
$503$	21262.4			1.88478			0.942391	−	0.334513i	$-0.108572\pi$
$503$	21262.4			1.88478			0.942391	+	0.334513i	$0.108572\pi$
$504$	−6301.37	−	9397.70i	−0.556915	−	0.830569i
$505$	−6538.50			−0.576157
$506$	−1088.26	+	492.960i	−0.0956109	+	0.0433098i
$507$	−10706.5	+	283.963i	−0.937854	+	0.0248742i
$508$	10360.8	−	11809.7i	0.904895	−	1.03144i
$509$			6748.42i			0.587659i	0.955858	+	0.293829i	$0.0949298\pi$
$509$			6748.42i			0.587659i	−0.955858	+	0.293829i	$0.905070\pi$
$510$	9415.60	−	4569.70i	0.817509	−	0.396764i
$511$	−7757.28	+	8523.81i	−0.671550	+	0.737909i
$512$	−7341.92	−	8961.80i	−0.633731	−	0.773554i
$513$	−4060.06	+	323.656i	−0.349427	+	0.0278553i
$514$	6891.87	+	15214.5i	0.591415	+	1.30561i
$515$	−3244.87			−0.277643
$516$	11387.1	+	9467.73i	0.971489	+	0.807739i
$517$	1279.26			0.108823
$518$	15978.3	+	5171.59i	1.35530	+	0.438662i
$519$	57.2278	+	2157.71i	0.00484011	+	0.182491i
$520$	523.806	−	1724.98i	0.0441739	−	0.145472i
$521$	−1669.33			−0.140374			−0.0701868	−	0.997534i	$-0.522360\pi$
$521$	−1669.33			−0.140374			−0.0701868	+	0.997534i	$0.522360\pi$
$522$	4621.71	+	8913.09i	0.387522	+	0.747348i
$523$	−8699.40			−0.727339			−0.363669	−	0.931528i	$-0.618476\pi$
$523$	−8699.40			−0.727339			−0.363669	+	0.931528i	$0.618476\pi$
$524$	10675.1	+	9365.37i	0.889966	+	0.780779i
$525$	5702.53	+	4919.72i	0.474055	+	0.408979i
$526$	5523.55	−	2502.05i	0.457867	−	0.207404i
$527$		−	11863.3i		−	0.980592i
$528$	−210.100	−	1326.90i	−0.0173171	−	0.109367i
$529$	1234.29			0.101446
$530$	−8294.19	+	3757.10i	−0.679767	+	0.307920i
$531$	−1033.98	−	19478.8i	−0.0845028	−	1.59192i
$532$	4274.20	−	482.046i	0.348327	−	0.0392845i
$533$	−2955.72			−0.240200
$534$	5500.88	+	11334.3i	0.445780	+	0.918504i
$535$		−	3279.98i		−	0.265058i
$536$	638.464	−	2102.57i	0.0514505	−	0.169435i
$537$	608.568	−	16.1407i	0.0489043	−	0.00129707i
$538$	16102.5	−	7294.12i	1.29039	−	0.584520i
$539$	130.185	+	1379.50i	0.0104035	+	0.110240i
$540$	−6151.88	−	4585.99i	−0.490250	−	0.365462i
$541$			6335.93i			0.503517i	0.967790	+	0.251759i	$0.0810089\pi$
$541$			6335.93i			0.503517i	−0.967790	+	0.251759i	$0.918991\pi$
$542$	−11911.1	+	5395.47i	−0.943956	+	0.427592i
$543$	−7163.29	+	189.988i	−0.566126	+	0.0150151i
$544$	−16016.9	+	9949.38i	−1.26235	+	0.784147i
$545$	−8534.40			−0.670777
$546$	−896.430	+	3042.74i	−0.0702631	+	0.238493i
$547$		−	25466.5i		−	1.99062i	−0.0967351	−	0.995310i	$-0.530840\pi$
$547$		−	25466.5i		−	1.99062i	0.0967351	−	0.995310i	$-0.469160\pi$
$548$	−3447.91	−	3024.90i	−0.268773	−	0.235798i
$549$	3812.88	−	202.397i	0.296411	−	0.0157342i
$550$	368.975	+	814.550i	0.0286057	+	0.0631501i
$551$	−3816.73			−0.295096
$552$	3258.88	−	11853.8i	0.251281	−	0.914009i
$553$	2895.65	+	2635.25i	0.222668	+	0.202644i
$554$	−728.713	+	330.092i	−0.0558846	+	0.0253146i
$555$	11385.1	−	301.962i	0.870760	−	0.0230947i
$556$	5774.58	−	6582.11i	0.440461	−	0.502057i
$557$	2282.80			0.173654			0.0868269	−	0.996223i	$-0.472327\pi$
$557$	2282.80			0.173654			0.0868269	+	0.996223i	$0.472327\pi$
$558$	−7721.29	+	4003.72i	−0.585786	+	0.303747i
$559$		−	4151.61i		−	0.314122i
$560$	6651.93	+	4627.74i	0.501956	+	0.349210i
$561$	−2185.72	+	57.9709i	−0.164494	+	0.00436280i
$562$	−17320.5	+	7845.83i	−1.30004	+	0.588890i
$563$			5471.40i			0.409577i	0.978806	+	0.204789i	$0.0656507\pi$
$563$			5471.40i			0.409577i	−0.978806	+	0.204789i	$0.934349\pi$
$564$	−8415.88	+	10122.0i	−0.628320	+	0.755697i
$565$	−9229.07			−0.687204
$566$	−8412.42	−	18571.3i	−0.624736	−	1.37917i
$567$	10891.2	+	7979.13i	0.806678	+	0.590991i
$568$	−5922.23	+	19502.9i	−0.437484	+	1.44071i
$569$			10659.3i			0.785342i	0.919679	+	0.392671i	$0.128449\pi$
$569$			10659.3i			0.785342i	−0.919679	+	0.392671i	$0.871551\pi$
$570$	2624.20	−	1273.61i	0.192834	−	0.0935889i
$571$			12002.7i			0.879680i	0.898076	+	0.439840i	$0.144965\pi$
$571$			12002.7i			0.879680i	−0.898076	+	0.439840i	$0.855035\pi$
$572$	−248.379	+	283.114i	−0.0181561	+	0.0206951i
$573$	320.096	+	12068.9i	0.0233372	+	0.879902i
$574$	4091.20	−	12640.3i	0.297497	−	0.919154i
$575$			8182.99i			0.593486i
$576$	11881.2	+	7066.91i	0.859458	+	0.511206i
$577$			10078.4i			0.727159i	0.931563	+	0.363579i	$0.118445\pi$
$577$			10078.4i			0.727159i	−0.931563	+	0.363579i	$0.881555\pi$
$578$	6928.81	+	15296.1i	0.498617	+	1.10075i
$579$	6670.56	−	176.920i	0.478789	−	0.0126987i
$580$	−5405.16	−	4742.02i	−0.386961	−	0.339486i
$581$	10438.8	−	11470.3i	0.745395	−	0.819050i
$582$	15015.3	−	7287.43i	1.06942	−	0.519027i
$583$	1902.27			0.135135
$584$	4091.38	−	13473.6i	0.289902	−	0.954697i
$585$	114.026	+	2148.11i	0.00805883	+	0.151817i
$586$	−8181.52	+	3706.06i	−0.576750	+	0.261256i
$587$		−	22343.5i		−	1.57106i	−0.618820	−	0.785532i	$-0.712389\pi$
$587$		−	22343.5i		−	1.57106i	0.618820	−	0.785532i	$-0.287611\pi$
$588$	−11771.6	−	8045.28i	−0.825601	−	0.564254i
$589$		−	3306.38i		−	0.231302i
$590$	5764.25	+	12725.2i	0.402221	+	0.887945i
$591$	−25636.6	+	679.946i	−1.78434	+	0.0473253i
$592$	−20344.3	+	2670.49i	−1.41241	+	0.185400i
$593$	−21338.0			−1.47765			−0.738824	−	0.673898i	$-0.764619\pi$
$593$	−21338.0			−1.47765			−0.738824	+	0.673898i	$0.764619\pi$
$594$	775.389	+	1403.03i	0.0535599	+	0.0969142i
$595$	8876.84	−	9753.99i	0.611621	−	0.672058i
$596$	−13579.3	+	15478.3i	−0.933270	+	1.06378i
$597$	−526.933	−	19867.4i	−0.0361238	−	1.36201i
$598$	−3139.40	+	1422.08i	−0.214682	+	0.0972464i
$599$		−	8738.27i		−	0.596054i	−0.954557	−	0.298027i	$-0.903671\pi$
$599$		−	8738.27i		−	0.596054i	0.954557	−	0.298027i	$-0.0963285\pi$
$600$	−8872.45	−	2439.23i	−0.603694	−	0.165969i
$601$		−	7481.20i		−	0.507761i	−0.967236	−	0.253881i	$-0.918293\pi$
$601$		−	7481.20i		−	0.507761i	0.967236	−	0.253881i	$-0.0817070\pi$
$602$	17754.5	+	5746.50i	1.20203	+	0.389053i
$603$	138.986	+	2618.31i	0.00938633	+	0.176826i
$604$	5905.19	−	6731.00i	0.397813	−	0.453444i
$605$		−	8987.88i		−	0.603982i
$606$	−12645.6	+	6137.30i	−0.847674	+	0.411404i
$607$		−	473.402i		−	0.0316554i	−0.999875	−	0.0158277i	$-0.994962\pi$
$607$		−	473.402i		−	0.0316554i	0.999875	−	0.0158277i	$-0.00503832\pi$
$608$	−4464.03	+	2772.97i	−0.297764	+	0.184965i
$609$	9579.61	+	8264.57i	0.637414	+	0.549914i
$610$	−2490.89	+	1128.32i	−0.165333	+	0.0748925i
$611$	3690.38			0.244348
$612$	13920.6	−	17675.7i	0.919456	−	1.16748i
$613$		−	7125.38i		−	0.469480i	−0.972058	−	0.234740i	$-0.924576\pi$
$613$		−	7125.38i		−	0.469480i	0.972058	−	0.234740i	$-0.0754239\pi$
$614$	4364.05	+	9634.11i	0.286838	+	0.633226i
$615$	−238.879	−	9006.66i	−0.0156627	−	0.590543i
$616$	−866.950	−	1454.08i	−0.0567052	−	0.0951080i
$617$		−	3345.74i		−	0.218305i	−0.994025	−	0.109153i	$-0.965186\pi$
$617$		−	3345.74i		−	0.218305i	0.994025	−	0.109153i	$-0.0348137\pi$
$618$	−6275.63	+	3045.77i	−0.408484	+	0.198250i
$619$	−7950.72			−0.516263			−0.258131	−	0.966110i	$-0.583107\pi$
$619$	−7950.72			−0.516263			−0.258131	+	0.966110i	$0.583107\pi$
$620$	4107.95	−	4682.42i	0.266096	−	0.303307i
$621$	1165.70	+	14622.9i	0.0753265	+	0.944923i
$622$	−10641.1	−	23491.4i	−0.685966	−	1.51434i
$623$	11741.6	+	10685.7i	0.755084	+	0.687181i
$624$	−606.092	−	3827.81i	−0.0388832	−	0.245569i
$625$	282.564			0.0180841
$626$	−23456.5	+	10625.3i	−1.49762	+	0.678391i
$627$	−609.178	+	16.1569i	−0.0388010	+	0.00102910i
$628$	14612.8	−	16656.3i	0.928525	−	1.05837i
$629$			33395.3i			2.11694i
$630$	−9344.29	−	2485.69i	−0.590930	−	0.157194i
$631$	−9702.61			−0.612131			−0.306066	−	0.952010i	$-0.599013\pi$
$631$	−9702.61			−0.612131			−0.306066	+	0.952010i	$0.599013\pi$
$632$	−4577.16	−	1389.89i	−0.288085	−	0.0874795i
$633$	−170.376	−	6423.81i	−0.0106980	−	0.403355i
$634$	−11534.3	−	25463.2i	−0.722533	−	1.59507i
$635$		−	13425.6i		−	0.839021i
$636$	−12514.5	+	15051.5i	−0.780241	+	0.938416i
$637$	375.555	+	3979.55i	0.0233596	+	0.247529i
$638$	619.836	+	1368.35i	0.0384632	+	0.0849117i
$639$	−1289.20	−	24286.8i	−0.0798121	−	1.50355i
$640$	−9767.07	−	1619.23i	−0.603246	−	0.100009i
$641$			27464.9i			1.69235i	0.532904	+	0.846176i	$0.321101\pi$
$641$			27464.9i			1.69235i	−0.532904	+	0.846176i	$0.678899\pi$
$642$	−3078.73	−	6343.54i	−0.189264	−	0.389968i
$643$	18925.7			1.16074			0.580372	−	0.814352i	$-0.302907\pi$
$643$	18925.7			1.16074			0.580372	+	0.814352i	$0.302907\pi$
$644$	−1736.16	−	15394.2i	−0.106233	−	0.941949i
$645$	12650.8	−	335.530i	0.772285	−	0.0204829i
$646$	3529.17	+	7791.01i	0.214943	+	0.474509i
$647$	−6973.22			−0.423718			−0.211859	−	0.977300i	$-0.567952\pi$
$647$	−6973.22			−0.423718			−0.211859	+	0.977300i	$0.567952\pi$
$648$	−16202.4	−	3094.96i	−0.982241	−	0.187626i
$649$		−	2918.52i		−	0.176521i
$650$	1064.41	+	2349.80i	0.0642303	+	0.141795i
$651$	−7159.49	+	8298.69i	−0.431033	+	0.499618i
$652$	7852.60	+	6889.19i	0.471674	+	0.413806i
$653$	5754.57			0.344860			0.172430	−	0.985022i	$-0.444838\pi$
$653$	5754.57			0.344860			0.172430	+	0.985022i	$0.444838\pi$
$654$	−16505.7	+	8010.73i	−0.986884	+	0.478967i
$655$	12135.7			0.723940
$656$	2112.60	+	16094.1i	0.125737	+	0.957882i
$657$	890.647	+	16778.6i	0.0528880	+	0.996339i
$658$	−5108.08	+	15782.0i	−0.302635	+	0.935028i
$659$	−30735.0			−1.81679			−0.908394	−	0.418115i	$-0.862691\pi$
$659$	−30735.0			−1.81679			−0.908394	+	0.418115i	$0.862691\pi$
$660$	−882.777	−	733.980i	−0.0520637	−	0.0432881i
$661$	22592.9			1.32944			0.664721	−	0.747092i	$-0.268550\pi$
$661$	22592.9			1.32944			0.664721	+	0.747092i	$0.268550\pi$
$662$	−1165.40	+	527.904i	−0.0684210	+	0.0309933i
$663$	−6305.34	+	167.233i	−0.369350	+	0.00979609i
$664$	−5505.68	+	18131.2i	−0.321780	+	1.05968i
$665$	2474.04	−	2718.51i	0.144270	−	0.158525i
$666$	21735.6	−	11270.5i	1.26462	−	0.655743i
$667$			13746.5i			0.798002i
$668$	6549.45	−	7465.35i	0.379350	−	0.432400i
$669$	353.728	+	13336.9i	0.0204423	+	0.770755i
$670$	−774.821	−	1710.50i	−0.0446776	−	0.0986304i
$671$	571.285			0.0328677
$672$	17208.7	+	2706.34i	0.987859	+	0.155356i
$673$	−12930.6			−0.740621			−0.370311	−	0.928908i	$-0.620749\pi$
$673$	−12930.6			−0.740621			−0.370311	+	0.928908i	$0.620749\pi$
$674$	5800.17	+	12804.5i	0.331475	+	0.731766i
$675$	10945.1	−	872.509i	0.624112	−	0.0497524i
$676$	10874.7	−	12395.4i	0.618722	−	0.705246i
$677$			27874.6i			1.58244i	0.611534	+	0.791218i	$0.290553\pi$
$677$			27874.6i			1.58244i	−0.611534	+	0.791218i	$0.709447\pi$
$678$	−17849.2	+	8662.79i	−1.01105	+	0.490697i
$679$	14156.1	−	15555.0i	0.800092	−	0.879153i
$680$	−4681.86	+	15418.2i	−0.264031	+	0.869500i
$681$	710.985	+	26806.8i	0.0400073	+	1.50843i
$682$	−1185.39	+	536.956i	−0.0665554	+	0.0301482i
$683$	374.516			0.0209816			0.0104908	−	0.999945i	$-0.496661\pi$
$683$	374.516			0.0209816			0.0104908	+	0.999945i	$0.496661\pi$
$684$	3879.78	−	4926.36i	0.216882	−	0.275386i
$685$	−3919.68			−0.218632
$686$	−17538.6	−	3902.27i	−0.976130	−	0.217186i
$687$	11537.1	−	305.992i	0.640709	−	0.0169932i
$688$	−22605.9	+	2967.37i	−1.25268	+	0.164433i
$689$	5487.63			0.303428
$690$	−4587.09	−	9451.44i	−0.253084	−	0.521464i
$691$	15693.7			0.863988			0.431994	−	0.901877i	$-0.357810\pi$
$691$	15693.7			0.863988			0.431994	+	0.901877i	$0.357810\pi$
$692$	−2498.08	−	2191.60i	−0.137229	−	0.120393i
$693$	1563.96	+	1278.53i	0.0857287	+	0.0700829i
$694$	12853.5	+	28375.6i	0.703046	+	1.55205i
$695$		−	7482.73i		−	0.408397i
$696$	−14904.7	−	4097.63i	−0.811727	−	0.223161i
$697$	26418.7			1.43569
$698$	−5287.87	−	11673.5i	−0.286746	−	0.633023i
$699$	−511.322	−	19278.8i	−0.0276681	−	1.04319i
$700$	−11522.3	+	1299.49i	−0.622148	+	0.0701661i
$701$	−4484.20			−0.241606			−0.120803	−	0.992676i	$-0.538547\pi$
$701$	−4484.20			−0.241606			−0.120803	+	0.992676i	$0.538547\pi$
$702$	2236.83	+	4047.44i	0.120262	+	0.217608i
$703$			9307.52i			0.499346i
$704$	1719.11	+	1150.09i	0.0920331	+	0.0615706i
$705$	298.254	+	11245.3i	0.0159332	+	0.600741i
$706$	7180.79	+	15852.3i	0.382794	+	0.845058i
$707$	−11922.0	+	13100.0i	−0.634190	+	0.696856i
$708$	23092.5	+	19200.2i	1.22581	+	1.01919i
$709$			11896.5i			0.630156i	0.949066	+	0.315078i	$0.102031\pi$
$709$			11896.5i			0.630156i	−0.949066	+	0.315078i	$0.897969\pi$
$710$	7187.04	+	15866.2i	0.379894	+	0.838656i
$711$	5699.90	−	302.564i	0.300651	−	0.0159593i
$712$	−18560.0	−	5635.90i	−0.976918	−	0.296649i
$713$	−11908.4			−0.625489
$714$	8012.44	−	27196.5i	0.419969	−	1.42550i
$715$			321.851i			0.0168343i
$716$	−618.126	+	704.567i	−0.0322632	+	0.0367750i
$717$	−440.691	−	16615.7i	−0.0229538	−	0.865447i
$718$	−7273.07	+	3294.55i	−0.378034	+	0.171242i
$719$	13003.8			0.674494			0.337247	−	0.941416i	$-0.390504\pi$
$719$	13003.8			0.674494			0.337247	+	0.941416i	$0.390504\pi$
$720$	11615.1	−	2156.24i	0.601208	−	0.111609i
$721$	−5916.54	+	6501.17i	−0.305608	+	0.335806i
$722$	−7021.30	−	15500.3i	−0.361920	−	0.798976i
$723$	−797.048	−	30051.8i	−0.0409994	−	1.54583i
$724$	7275.80	−	8293.28i	0.373485	−	0.425715i
$725$	10289.1			0.527072
$726$	−8436.40	−	17382.7i	−0.431273	−	0.888612i
$727$			38446.5i			1.96135i	0.195639	+	0.980676i	$0.437322\pi$
$727$			38446.5i			1.96135i	−0.195639	+	0.980676i	$0.562678\pi$
$728$	−2500.96	−	4194.71i	−0.127324	−	0.213552i
$729$	19434.4	−	3118.33i	0.987371	−	0.158427i
$730$	−4965.18	−	10961.2i	−0.251739	−	0.555741i
$731$			37107.8i			1.87754i
$732$	−3758.33	+	4520.24i	−0.189770	+	0.228242i
$733$	17763.3			0.895092			0.447546	−	0.894261i	$-0.352298\pi$
$733$	17763.3			0.895092			0.447546	+	0.894261i	$0.352298\pi$
$734$	16459.5	−	7455.81i	0.827699	−	0.374931i
$735$	−12096.1	+	1466.02i	−0.607038	+	0.0735712i
$736$	9987.25	+	16077.9i	0.500183	+	0.805215i
$737$			392.303i			0.0196074i
$738$	−8916.02	−	17194.8i	−0.444720	−	0.857655i
$739$		−	28211.2i		−	1.40428i	−0.712037	−	0.702142i	$-0.752227\pi$
$739$		−	28211.2i		−	1.40428i	0.712037	−	0.702142i	$-0.247773\pi$
$740$	−11564.0	+	13181.1i	−0.574458	+	0.654793i
$741$	−1757.35	+	46.6092i	−0.0871225	+	0.00231071i
$742$	−7595.78	+	23468.1i	−0.375808	+	1.16111i
$743$			17970.1i			0.887294i	0.896202	+	0.443647i	$0.146316\pi$
$743$			17970.1i			0.887294i	−0.896202	+	0.443647i	$0.853684\pi$
$744$	3549.73	−	12911.8i	0.174918	−	0.636248i
$745$			17596.1i			0.865330i
$746$	−16528.5	+	7487.08i	−0.811196	+	0.367455i
$747$	−1198.52	−	22578.5i	−0.0587037	−	1.10590i
$748$	2220.05	−	2530.51i	0.108520	−	0.123696i
$749$	−6571.52	−	5980.56i	−0.320585	−	0.291755i
$750$	−18373.4	+	8917.21i	−0.894535	+	0.434147i
$751$	28710.6			1.39503			0.697513	−	0.716572i	$-0.254290\pi$
$751$	28710.6			1.39503			0.697513	+	0.716572i	$0.254290\pi$
$752$	−2637.70	−	20094.4i	−0.127908	−	0.974425i
$753$	−288.811	−	10889.3i	−0.0139772	−	0.526994i
$754$	1788.09	+	3947.40i	0.0863641	+	0.190658i
$755$		−	7651.98i		−	0.368853i
$756$	−20405.2	+	3963.58i	−0.981652	+	0.190680i
$757$		−	34560.4i		−	1.65934i	−0.558256	−	0.829669i	$-0.688529\pi$
$757$		−	34560.4i		−	1.65934i	0.558256	−	0.829669i	$-0.311471\pi$
$758$	−28334.1	+	12834.8i	−1.35771	+	0.615013i
$759$	58.1916	+	2194.04i	0.00278290	+	0.104926i
$760$	−1304.87	+	4297.16i	−0.0622798	+	0.205098i
$761$	2013.29			0.0959023			0.0479511	−	0.998850i	$-0.484731\pi$
$761$	2013.29			0.0959023			0.0479511	+	0.998850i	$0.484731\pi$
$762$	−12601.8	−	25965.3i	−0.599102	−	1.23441i
$763$	−15561.2	+	17098.9i	−0.738339	+	0.811298i
$764$	−13972.7	−	12258.4i	−0.661668	−	0.580490i
$765$	−1019.19	−	19200.1i	−0.0481683	−	0.907427i
$766$	−11659.1	−	25738.7i	−0.549947	−	1.21407i
$767$		−	8419.29i		−	0.396353i
$768$	−20409.5	+	6036.15i	−0.958940	+	0.283608i
$769$			7245.88i			0.339783i	0.985463	+	0.169891i	$0.0543417\pi$
$769$			7245.88i			0.339783i	−0.985463	+	0.169891i	$0.945658\pi$
$770$	−1376.41	−	445.494i	−0.0644187	−	0.0208500i
$771$	30674.0	−	813.551i	1.43281	−	0.0380017i
$772$	−6775.33	+	7722.82i	−0.315867	+	0.360039i
$773$		−	35166.4i		−	1.63629i	−0.575015	−	0.818143i	$-0.695004\pi$
$773$		−	35166.4i		−	1.63629i	0.575015	−	0.818143i	$-0.304996\pi$
$774$	24151.9	−	12523.5i	1.12160	−	0.581585i
$775$			8913.31i			0.413130i
$776$	−7466.29	+	24587.8i	−0.345392	+	1.13744i
$777$	20154.1	−	23361.0i	0.930533	−	1.07860i
$778$	4602.51	+	10160.5i	0.212093	+	0.468217i
$779$	7363.09			0.338652
$780$	−2546.62	−	2117.37i	−0.116902	−	0.0971976i
$781$		−	3638.90i		−	0.166722i
$782$	28060.5	−	12710.8i	1.28317	−	0.581250i
$783$	18386.5	−	1465.72i	0.839182	−	0.0668972i
$784$	21400.6	−	4889.32i	0.974881	−	0.222728i
$785$		−	18935.3i		−	0.860931i
$786$	23470.6	−	11391.1i	1.06510	−	0.516928i
$787$	30974.5			1.40295			0.701475	−	0.712694i	$-0.252525\pi$
$787$	30974.5			1.40295			0.701475	+	0.712694i	$0.252525\pi$
$788$	26039.2	−	29680.6i	1.17717	−	1.34179i
$789$	−295.355	−	11136.0i	−0.0133269	−	0.502475i
$790$	−3723.65	+	1686.74i	−0.167698	+	0.0759638i
$791$	−16827.8	+	18490.7i	−0.756421	+	0.831166i
$792$	−2396.25	−	590.918i	−0.107509	−	0.0265118i
$793$	1648.03			0.0737999
$794$	16617.1	+	36684.0i	0.742719	+	1.63963i
$795$	443.507	+	16721.9i	0.0197856	+	0.745994i
$796$	23001.4	+	20179.4i	1.02420	+	0.898544i
$797$			8981.62i			0.399178i	0.979880	+	0.199589i	$0.0639608\pi$
$797$			8981.62i			0.399178i	−0.979880	+	0.199589i	$0.936039\pi$
$798$	2233.13	−	7579.88i	0.0990625	−	0.336247i
$799$	−32985.2			−1.46049
$800$	12034.1	−	7475.33i	0.531836	−	0.330366i
$801$	23112.6	−	1226.87i	1.01953	−	0.0541190i
$802$	−2258.20	+	1022.92i	−0.0994264	+	0.0450381i
$803$			2513.94i			0.110479i
$804$	−3104.06	−	2580.85i	−0.136159	−	0.113209i
$805$	−9791.12	−	8910.63i	−0.428685	−	0.390135i
$806$	−3419.58	+	1549.00i	−0.149441	+	0.0676938i
$807$	−861.035	−	32464.3i	−0.0375587	−	1.41611i
$808$	6287.94	−	20707.3i	0.273774	−	0.901584i
$809$		−	29145.4i		−	1.26662i	−0.773896	−	0.633312i	$-0.781695\pi$
$809$		−	29145.4i		−	1.26662i	0.773896	−	0.633312i	$-0.218305\pi$
$810$	−12152.6	+	7143.17i	−0.527158	+	0.309859i
$811$	−35758.2			−1.54826			−0.774132	−	0.633025i	$-0.781813\pi$
$811$	−35758.2			−1.54826			−0.774132	+	0.633025i	$0.781813\pi$
$812$	−19356.3	+	2183.00i	−0.836541	+	0.0943454i
$813$	636.909	+	24013.9i	0.0274752	+	1.03592i
$814$	3336.88	−	1511.54i	0.143683	−	0.0650853i
$815$	8927.04			0.383682
$816$	5417.35	+	34213.6i	0.232408	+	1.46779i
$817$			10342.2i			0.442874i
$818$	30250.1	−	13702.7i	1.29300	−	0.585701i
$819$	4511.69	+	3688.29i	0.192492	+	0.157362i
$820$	10427.4	+	9148.13i	0.444075	+	0.389593i
$821$	−29573.6			−1.25716			−0.628578	−	0.777746i	$-0.716363\pi$
$821$	−29573.6			−1.25716			−0.628578	+	0.777746i	$0.716363\pi$
$822$	−7580.72	+	3679.17i	−0.321664	+	0.156114i
$823$	−26488.9			−1.12192			−0.560962	−	0.827841i	$-0.689569\pi$
$823$	−26488.9			−1.12192			−0.560962	+	0.827841i	$0.689569\pi$
$824$	3120.53	−	10276.4i	0.131928	−	0.434462i
$825$	1642.21	−	43.5557i	0.0693025	−	0.00183808i
$826$	36005.5	+	11653.7i	1.51670	+	0.490900i
$827$	−6964.53			−0.292842			−0.146421	−	0.989222i	$-0.546775\pi$
$827$	−6964.53			−0.292842			−0.146421	+	0.989222i	$0.546775\pi$
$828$	−17743.0	−	13973.6i	−0.744701	−	0.586493i
$829$	−11031.4			−0.462166			−0.231083	−	0.972934i	$-0.574227\pi$
$829$	−11031.4			−0.462166			−0.231083	+	0.972934i	$0.574227\pi$
$830$	6681.53	+	14750.2i	0.279421	+	0.616851i
$831$	38.9658	+	1469.16i	0.00162660	+	0.0613292i
$832$	4959.25	+	3317.76i	0.206648	+	0.138249i
$833$	−3356.77	−	35569.9i	−0.139622	−	1.47950i
$834$	−7023.59	−	14471.7i	−0.291615	−	0.600856i
$835$		−	8486.81i		−	0.351734i
$836$	618.746	−	705.274i	0.0255978	−	0.0291775i
$837$	1269.73	+	15928.0i	0.0524353	+	0.657767i
$838$	42957.8	−	19459.0i	1.77083	−	0.802148i
$839$	20561.9			0.846099			0.423049	−	0.906107i	$-0.360960\pi$
$839$	20561.9			0.846099			0.423049	+	0.906107i	$0.360960\pi$
$840$	12580.0	−	7959.94i	0.516727	−	0.326957i
$841$	−7104.47			−0.291298
$842$	−6056.16	+	2743.32i	−0.247873	+	0.112281i
$843$	926.162	+	34919.9i	0.0378395	+	1.42669i
$844$	7437.14	+	6524.71i	0.303314	+	0.266101i
$845$		−	14091.4i		−	0.573681i
$846$	11132.1	+	21468.6i	0.452400	+	0.872467i
$847$	−18007.4	−	16388.1i	−0.730511	−	0.664817i
$848$	−3922.29	−	29880.6i	−0.158835	−	1.21003i
$849$	−37441.6	+	993.046i	−1.51354	+	0.0401428i
$850$	−9513.88	−	21002.9i	−0.383910	−	0.847522i
$851$	33522.4			1.35033
$852$	28792.5	+	23939.3i	1.15776	+	0.962615i
$853$	9441.72			0.378990			0.189495	−	0.981882i	$-0.439315\pi$
$853$	9441.72			0.378990			0.189495	+	0.981882i	$0.439315\pi$
$854$	−2281.15	+	7047.88i	−0.0914042	+	0.282405i
$855$	−284.055	−	5351.22i	−0.0113620	−	0.214044i
$856$	10387.6	+	3154.29i	0.414769	+	0.125948i
$857$	17877.9			0.712598			0.356299	−	0.934372i	$-0.384039\pi$
$857$	17877.9			0.712598			0.356299	+	0.934372i	$0.384039\pi$
$858$	302.103	+	622.465i	0.0120205	+	0.0247676i
$859$	−43955.9			−1.74593			−0.872966	−	0.487781i	$-0.837807\pi$
$859$	−43955.9			−1.74593			−0.872966	+	0.487781i	$0.837807\pi$
$860$	−12849.5	+	14646.4i	−0.509493	+	0.580742i
$861$	−18480.6	−	15943.7i	−0.731496	−	0.631080i
$862$	15819.5	−	7165.89i	0.625073	−	0.283145i
$863$			42634.4i			1.68168i	0.541282	+	0.840841i	$0.317939\pi$
$863$			42634.4i			1.68168i	−0.541282	+	0.840841i	$0.682061\pi$
$864$	20439.9	−	15072.6i	0.804836	−	0.593497i
$865$	−2839.88			−0.111629
$866$	22551.8	−	10215.5i	0.884922	−	0.400851i
$867$	30838.4	−	817.912i	1.20799	−	0.0320389i
$868$	−1891.11	−	16768.1i	−0.0739498	−	0.655697i
$869$	854.017			0.0333378
$870$	−11884.0	+	5767.70i	−0.463110	+	0.224762i
$871$			1131.71i			0.0440258i
$872$	8207.36	−	27028.2i	0.318734	−	1.04965i
$873$	−1625.33	−	30618.9i	−0.0630114	−	1.18705i
$874$	7820.66	−	3542.60i	0.302675	−	0.137106i
$875$	−17322.1	+	19033.7i	−0.669249	+	0.735380i
$876$	−19891.3	−	16538.5i	−0.767199	−	0.637883i
$877$			22335.1i			0.859980i	0.902834	+	0.429990i	$0.141483\pi$
$877$			22335.1i			0.859980i	−0.902834	+	0.429990i	$0.858517\pi$
$878$	10556.9	−	4782.06i	0.405784	−	0.183812i
$879$	437.483	+	16494.8i	0.0167872	+	0.632940i
$880$	1752.51	−	230.043i	0.0671330	−	0.00881223i
$881$	−31160.2			−1.19162			−0.595809	−	0.803126i	$-0.703168\pi$
$881$	−31160.2			−1.19162			−0.595809	+	0.803126i	$0.703168\pi$
$882$	−22018.1	+	14189.2i	−0.840574	+	0.541696i
$883$		−	29300.5i		−	1.11669i	−0.829607	−	0.558347i	$-0.811436\pi$
$883$		−	29300.5i		−	1.11669i	0.829607	−	0.558347i	$-0.188564\pi$
$884$	6404.38	−	7299.99i	0.243668	−	0.277743i
$885$	25655.3	−	680.442i	0.974454	−	0.0258450i
$886$	−9229.75	−	20375.6i	−0.349977	−	0.772611i
$887$	28062.3			1.06228			0.531139	−	0.847285i	$-0.321764\pi$
$887$	28062.3			1.06228			0.531139	+	0.847285i	$0.321764\pi$
$888$	−9992.54	+	36346.8i	−0.377621	+	1.37356i
$889$	−26898.5	−	24479.6i	−1.01479	−	0.923530i
$890$	−15099.1	+	6839.57i	−0.568676	+	0.257599i
$891$	2928.41	−	311.773i	0.110107	−	0.0117225i
$892$	−15440.8	−	13546.4i	−0.579591	−	0.508483i
$893$	−9193.22			−0.344501
$894$	16516.4	+	34031.1i	0.617888	+	1.27312i
$895$			800.971i			0.0299145i
$896$	−21053.0	+	16616.1i	−0.784967	+	0.619538i
$897$	167.870	+	6329.34i	0.00624863	+	0.235597i
$898$	−6089.31	+	2758.33i	−0.226284	+	0.102502i
$899$			14973.4i			0.555494i
$900$	−10459.1	+	13280.4i	−0.387373	+	0.491868i
$901$	−49049.3			−1.81362
$902$	−1195.76	−	2639.78i	−0.0441403	−	0.0974445i
$903$	22394.6	−	25957.9i	0.825298	−	0.956617i
$904$	8875.41	−	29228.3i	0.326540	−	1.07535i
$905$		−	9428.02i		−	0.346296i
$906$	−7182.46	−	14799.0i	−0.263379	−	0.542677i
$907$			10433.3i			0.381953i	0.981595	+	0.190976i	$0.0611654\pi$
$907$			10433.3i			0.381953i	−0.981595	+	0.190976i	$0.938835\pi$
$908$	−31035.5	−	27227.9i	−1.13431	−	0.995142i
$909$	1368.81	+	25786.6i	0.0499457	+	0.940910i
$910$	−3970.65	−	1285.16i	−0.144644	−	0.0468159i
$911$			12356.5i			0.449384i	0.974430	+	0.224692i	$0.0721376\pi$
$911$			12356.5i			0.449384i	−0.974430	+	0.224692i	$0.927862\pi$
$912$	1509.86	+	9535.59i	0.0548205	+	0.346222i
$913$		−	3382.95i		−	0.122628i
$914$	6268.44	+	13838.3i	0.226851	+	0.500797i
$915$	133.193	+	5021.88i	0.00481226	+	0.181441i
$916$	−11718.3	+	13357.0i	−0.422689	+	0.481800i
$917$	22127.6	−	24314.1i	0.796858	−	0.875598i
$918$	−19993.1	−	36176.7i	−0.718814	−	1.30066i
$919$	−24591.0			−0.882680			−0.441340	−	0.897340i	$-0.645497\pi$
$919$	−24591.0			−0.882680			−0.441340	+	0.897340i	$0.645497\pi$
$920$	15476.9	+	4699.68i	0.554628	+	0.168417i
$921$	19423.3	−	515.155i	0.694919	−	0.0184310i
$922$	−36705.5	+	16626.8i	−1.31110	+	0.593899i
$923$		−	10497.4i		−	0.374352i
$924$	−3080.16	+	430.362i	−0.109664	+	0.0153224i
$925$		−	25091.1i		−	0.891882i
$926$	−3728.56	−	8231.18i	−0.132320	−	0.292110i
$927$	679.303	+	12797.1i	0.0240682	+	0.453412i
$928$	20215.9	−	12557.7i	0.715108	−	0.444211i
$929$	15512.5			0.547844			0.273922	−	0.961752i	$-0.411679\pi$
$929$	15512.5			0.547844			0.273922	+	0.961752i	$0.411679\pi$
$930$	−4996.48	−	10295.0i	−0.176173	−	0.362995i
$931$	−935.558	−	9913.60i	−0.0329341	−	0.348985i
$932$	22320.0	+	19581.6i	0.784458	+	0.688215i
$933$	−47361.1	+	1256.13i	−1.66188	+	0.0440772i
$934$	8547.20	−	3871.71i	0.299436	−	0.135638i
$935$		−	2876.76i		−	0.100620i
$936$	−6912.66	−	1704.67i	−0.241397	−	0.0595287i
$937$			31883.8i			1.11163i	0.831306	+	0.555816i	$0.187594\pi$
$937$			31883.8i			1.11163i	−0.831306	+	0.555816i	$0.812406\pi$
$938$	−4839.80	−	1566.47i	−0.168470	−	0.0545277i
$939$	1254.27	+	47290.6i	0.0435904	+	1.64353i
$940$	−13019.2	−	11421.9i	−0.451745	−	0.396322i
$941$		−	26463.4i		−	0.916773i	−0.888753	−	0.458386i	$-0.848428\pi$
$941$		−	26463.4i		−	0.916773i	0.888753	−	0.458386i	$-0.151572\pi$
$942$	−17773.5	−	36621.2i	−0.614746	−	1.26665i
$943$		−	26519.3i		−	0.915786i
$944$	−45843.8	+	6017.69i	−1.58060	+	0.207478i
$945$	−10874.3	+	14046.1i	−0.374330	+	0.483513i
$946$	3707.84	−	1679.57i	0.127434	−	0.0577248i
$947$	−6190.46			−0.212421			−0.106211	−	0.994344i	$-0.533872\pi$
$947$	−6190.46			−0.212421			−0.106211	+	0.994344i	$0.533872\pi$
$948$	−5618.35	+	6757.34i	−0.192485	+	0.231507i
$949$			7252.17i			0.248067i
$950$	−2651.59	−	5853.67i	−0.0905568	−	0.199914i
$951$	−51336.4	+	1361.57i	−1.75047	+	0.0464269i
$952$	22354.0	+	37493.0i	0.761027	+	1.27642i
$953$		−	24095.6i		−	0.819027i	−0.912304	−	0.409513i	$-0.865699\pi$
$953$		−	24095.6i		−	0.819027i	0.912304	−	0.409513i	$-0.134301\pi$
$954$	16553.6	+	31924.1i	0.561785	+	1.08342i
$955$	−15884.5			−0.538232
$956$	19236.8	+	16876.7i	0.650798	+	0.570953i
$957$	2758.74	−	73.1686i	0.0931842	−	0.00247148i
$958$	1939.49	+	4281.63i	0.0654092	+	0.144398i
$959$	−7146.95	+	7853.17i	−0.240654	+	0.264434i
$960$	−9709.08	+	15380.0i	−0.326416	+	0.517069i
$961$	16819.8			0.564593
$962$	9626.19	−	4360.47i	0.322620	−	0.146140i
$963$	−12935.6	+	686.653i	−0.432860	+	0.0229772i
$964$	34792.3	+	30523.8i	1.16243	+	1.01982i
$965$			8779.51i			0.292873i
$966$	−27300.1	−	8042.94i	−0.909281	−	0.267885i
$967$	33985.7			1.13020			0.565102	−	0.825021i	$-0.308837\pi$
$967$	33985.7			1.13020			0.565102	+	0.825021i	$0.308837\pi$
$968$	28464.4	+	8643.46i	0.945125	+	0.286995i
$969$	15707.4	−	416.601i	0.520739	−	0.0138113i
$970$	9060.88	+	20002.8i	0.299925	+	0.662116i
$971$			17226.4i			0.569331i	0.958627	+	0.284666i	$0.0918826\pi$
$971$			17226.4i			0.569331i	−0.958627	+	0.284666i	$0.908117\pi$
$972$	−16798.4	+	25221.9i	−0.554330	+	0.832297i
$973$	−14991.8	−	13643.6i	−0.493952	−	0.449532i
$974$	7187.60	+	15867.4i	0.236453	+	0.521996i
$975$	4737.44	−	125.649i	0.155610	−	0.00412716i
$976$	−1177.93	−	8973.68i	−0.0386319	−	0.294304i
$977$			30772.6i			1.00768i	0.863797	+	0.503840i	$0.168080\pi$
$977$			30772.6i			1.00768i	−0.863797	+	0.503840i	$0.831920\pi$
$978$	17265.0	−	8379.29i	0.564494	−	0.273967i
$979$	3462.96			0.113051
$980$	10992.0	−	15201.8i	0.358294	−	0.495513i
$981$	1786.65	+	33658.0i	0.0581480	+	1.09543i
$982$	−9157.18	−	20215.4i	−0.297574	−	0.656925i
$983$	−22275.6			−0.722769			−0.361384	−	0.932417i	$-0.617696\pi$
$983$	−22275.6			−0.722769			−0.361384	+	0.932417i	$0.617696\pi$
$984$	28753.6	+	7905.00i	0.931537	+	0.256100i
$985$		−	33741.7i		−	1.09147i
$986$	−15982.3	−	35282.5i	−0.516206	−	1.13958i
$987$	23074.1	+	19906.6i	0.744129	+	0.641979i
$988$	1784.95	−	2034.56i	0.0574765	−	0.0655142i
$989$	37249.0			1.19762
$990$	−1872.36	+	970.874i	−0.0601086	+	0.0311681i
$991$	107.013			0.00343025			0.00171513	−	0.999999i	$-0.499454\pi$
$991$	107.013			0.00343025			0.00171513	+	0.999999i	$0.499454\pi$
$992$	10878.6	+	17512.8i	0.348181	+	0.560515i
$993$	62.3165	+	2349.57i	0.00199150	+	0.0750870i
$994$	44892.7	+	14530.1i	1.43250	+	0.463650i
$995$	26148.6			0.833132
$996$	26767.3	+	22255.5i	0.851561	+	0.708025i
$997$	16525.7			0.524950			0.262475	−	0.964939i	$-0.415461\pi$
$997$	16525.7			0.524950			0.262475	+	0.964939i	$0.415461\pi$
$998$	−29169.2	+	13213.0i	−0.925185	+	0.419090i
$999$	−3574.32	−	44837.5i	−0.113200	−	1.42002i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.4.i.c.125.48	yes	80
3.2	odd	2	inner	168.4.i.c.125.34	yes	80
4.3	odd	2		672.4.i.c.209.3		80
7.6	odd	2	inner	168.4.i.c.125.47	yes	80
8.3	odd	2		672.4.i.c.209.78		80
8.5	even	2	inner	168.4.i.c.125.35	yes	80
12.11	even	2		672.4.i.c.209.2		80
21.20	even	2	inner	168.4.i.c.125.33	✓	80
24.5	odd	2	inner	168.4.i.c.125.45	yes	80
24.11	even	2		672.4.i.c.209.79		80
28.27	even	2		672.4.i.c.209.77		80
56.13	odd	2	inner	168.4.i.c.125.36	yes	80
56.27	even	2		672.4.i.c.209.4		80
84.83	odd	2		672.4.i.c.209.80		80
168.83	odd	2		672.4.i.c.209.1		80
168.125	even	2	inner	168.4.i.c.125.46	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.4.i.c.125.33	✓	80	21.20	even	2	inner
168.4.i.c.125.34	yes	80	3.2	odd	2	inner
168.4.i.c.125.35	yes	80	8.5	even	2	inner
168.4.i.c.125.36	yes	80	56.13	odd	2	inner
168.4.i.c.125.45	yes	80	24.5	odd	2	inner
168.4.i.c.125.46	yes	80	168.125	even	2	inner
168.4.i.c.125.47	yes	80	7.6	odd	2	inner
168.4.i.c.125.48	yes	80	1.1	even	1	trivial
672.4.i.c.209.1		80	168.83	odd	2
672.4.i.c.209.2		80	12.11	even	2
672.4.i.c.209.3		80	4.3	odd	2
672.4.i.c.209.4		80	56.27	even	2
672.4.i.c.209.77		80	28.27	even	2
672.4.i.c.209.78		80	8.3	odd	2
672.4.i.c.209.79		80	24.11	even	2
672.4.i.c.209.80		80	84.83	odd	2

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.i (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.16707 + 2.57642i) q^{2} +(5.19433 - 0.137767i) q^{3} +(-5.27591 + 6.01371i) q^{4} +6.83655i q^{5} +(6.41707 + 13.2220i) q^{6} +(13.6972 + 12.4654i) q^{7} +(-21.6512 - 6.57457i) q^{8} +(26.9620 - 1.43121i) q^{9} +(-17.6139 + 7.97871i) q^{10} +4.03973 q^{11} +(-26.5763 + 31.9640i) q^{12} +11.6537 q^{13} +(-16.1307 + 49.8377i) q^{14} +(0.941848 + 35.5113i) q^{15} +(-8.32952 - 63.4556i) q^{16} -104.163 q^{17} +(35.1539 + 67.7953i) q^{18} -29.0310 q^{19} +(-41.1131 - 36.0690i) q^{20} +(72.8650 + 62.8625i) q^{21} +(4.71463 + 10.4081i) q^{22} +104.560i q^{23} +(-113.369 - 31.1677i) q^{24} +78.2615 q^{25} +(13.6007 + 30.0250i) q^{26} +(139.852 - 11.1486i) q^{27} +(-147.229 + 16.6045i) q^{28} +131.471 q^{29} +(-90.3929 + 43.8706i) q^{30} +113.891i q^{31} +(153.767 - 95.5173i) q^{32} +(20.9837 - 0.556540i) q^{33} +(-121.565 - 268.368i) q^{34} +(-85.2206 + 93.6416i) q^{35} +(-133.642 + 169.693i) q^{36} -320.606i q^{37} +(-33.8812 - 74.7962i) q^{38} +(60.5334 - 1.60550i) q^{39} +(44.9474 - 148.020i) q^{40} -253.628 q^{41} +(-76.9221 + 261.096i) q^{42} -356.247i q^{43} +(-21.3133 + 24.2938i) q^{44} +(9.78453 + 184.327i) q^{45} +(-269.390 + 122.028i) q^{46} +316.669 q^{47} +(-52.0083 - 328.462i) q^{48} +(32.2261 + 341.483i) q^{49} +(91.3364 + 201.635i) q^{50} +(-541.057 + 14.3502i) q^{51} +(-61.4841 + 70.0823i) q^{52} +470.890 q^{53} +(191.941 + 347.308i) q^{54} +27.6178i q^{55} +(-214.606 - 359.945i) q^{56} +(-150.797 + 3.99951i) q^{57} +(153.435 + 338.724i) q^{58} -722.454i q^{59} +(-218.524 - 181.690i) q^{60} +141.417 q^{61} +(-293.432 + 132.919i) q^{62} +(387.145 + 316.490i) q^{63} +(425.550 + 284.695i) q^{64} +79.6715i q^{65} +(25.9232 + 53.4133i) q^{66} +97.1111i q^{67} +(549.555 - 626.407i) q^{68} +(14.4048 + 543.117i) q^{69} +(-340.718 - 110.278i) q^{70} -900.777i q^{71} +(-593.170 - 146.277i) q^{72} +622.304i q^{73} +(826.017 - 374.169i) q^{74} +(406.516 - 10.7818i) q^{75} +(153.165 - 174.584i) q^{76} +(55.3330 + 50.3570i) q^{77} +(74.7829 + 154.086i) q^{78} +211.405 q^{79} +(433.818 - 56.9452i) q^{80} +(724.903 - 77.1766i) q^{81} +(-296.001 - 653.453i) q^{82} -837.420i q^{83} +(-762.466 + 106.532i) q^{84} -712.116i q^{85} +(917.842 - 415.764i) q^{86} +(682.901 - 18.1123i) q^{87} +(-87.4651 - 26.5595i) q^{88} +857.227 q^{89} +(-463.486 + 240.331i) q^{90} +(159.624 + 145.269i) q^{91} +(-628.791 - 551.647i) q^{92} +(15.6904 + 591.588i) q^{93} +(369.573 + 815.872i) q^{94} -198.472i q^{95} +(785.559 - 517.332i) q^{96} -1135.63i q^{97} +(-842.194 + 481.561i) q^{98} +(108.919 - 5.78170i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 28 q^{4} + 64 q^{7} + 104 q^{9} - 8 q^{15} - 892 q^{16} + 692 q^{18} + 128 q^{22} - 976 q^{25} + 612 q^{28} - 332 q^{30} + 1544 q^{36} + 568 q^{39} + 780 q^{42} + 208 q^{46} - 4048 q^{49} - 1448 q^{57}+ \cdots - 2072 q^{88}+O(q^{100}) \) 80 * q + 28 * q^4 + 64 * q^7 + 104 * q^9 - 8 * q^15 - 892 * q^16 + 692 * q^18 + 128 * q^22 - 976 * q^25 + 612 * q^28 - 332 * q^30 + 1544 * q^36 + 568 * q^39 + 780 * q^42 + 208 * q^46 - 4048 * q^49 - 1448 * q^57 - 1760 * q^58 + 4156 * q^60 - 2152 * q^63 + 2764 * q^64 + 1968 * q^70 - 2740 * q^72 - 3620 * q^78 + 4992 * q^79 + 1568 * q^81 + 2484 * q^84 - 2072 * q^88

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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