LMFDB - Embedded newform 49.4.e.a.43.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [49,4,Mod(8,49)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(49, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([12]))

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

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

chi := DirichletCharacter("49.8");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 49 = 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	49.e (of order $7$, degree $6$, 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:	$2.89109359028$
Analytic rank:	$0$
Dimension:	$78$
Relative dimension:	$13$ over $\Q(\zeta_{7})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			43.8
Character	$\chi$	$=$	49.43
Dual form			49.4.e.a.8.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.521845 - 0.654373i) q^{2} +(5.78023 + 2.78361i) q^{3} +(1.62429 + 7.11646i) q^{4} +(-1.28950 - 0.620991i) q^{5} +(4.83790 - 2.32981i) q^{6} +(-17.3557 + 6.46381i) q^{7} +(11.5371 + 5.55599i) q^{8} +(8.82835 + 11.0704i) q^{9} +O(q^{10})$	\(q+(0.521845 - 0.654373i) q^{2} +(5.78023 + 2.78361i) q^{3} +(1.62429 + 7.11646i) q^{4} +(-1.28950 - 0.620991i) q^{5} +(4.83790 - 2.32981i) q^{6} +(-17.3557 + 6.46381i) q^{7} +(11.5371 + 5.55599i) q^{8} +(8.82835 + 11.0704i) q^{9} +(-1.07928 + 0.519753i) q^{10} +(33.8930 - 42.5005i) q^{11} +(-10.4207 + 45.6562i) q^{12} +(41.8811 - 52.5173i) q^{13} +(-4.82722 + 14.7302i) q^{14} +(-5.72501 - 7.17894i) q^{15} +(-42.9565 + 20.6868i) q^{16} +(-4.21013 + 18.4458i) q^{17} +11.8512 q^{18} -58.6213 q^{19} +(2.32474 - 10.1853i) q^{20} +(-118.313 - 10.9491i) q^{21} +(-10.1243 - 44.3573i) q^{22} +(-4.27322 - 18.7222i) q^{23} +(51.2216 + 64.2299i) q^{24} +(-76.6590 - 96.1274i) q^{25} +(-12.5104 - 54.8117i) q^{26} +(-18.3310 - 80.3133i) q^{27} +(-74.1900 - 113.012i) q^{28} +(-50.8862 + 222.947i) q^{29} -7.68527 q^{30} +165.221 q^{31} +(-31.6753 + 138.778i) q^{32} +(314.214 - 151.318i) q^{33} +(9.87339 + 12.3808i) q^{34} +(26.3941 + 2.44262i) q^{35} +(-64.4423 + 80.8081i) q^{36} +(-53.1486 + 232.859i) q^{37} +(-30.5912 + 38.3601i) q^{38} +(388.270 - 186.981i) q^{39} +(-11.4269 - 14.3289i) q^{40} +(-174.801 - 84.1798i) q^{41} +(-68.9056 + 71.7067i) q^{42} +(-206.174 + 99.2879i) q^{43} +(357.505 + 172.165i) q^{44} +(-4.50955 - 19.7576i) q^{45} +(-14.4812 - 6.97380i) q^{46} +(153.504 - 192.488i) q^{47} -305.882 q^{48} +(259.438 - 224.368i) q^{49} -102.907 q^{50} +(-75.6815 + 94.9016i) q^{51} +(441.764 + 212.742i) q^{52} +(118.302 + 518.313i) q^{53} +(-62.1207 - 29.9158i) q^{54} +(-70.0975 + 33.7572i) q^{55} +(-236.148 - 21.8540i) q^{56} +(-338.844 - 163.179i) q^{57} +(119.336 + 149.642i) q^{58} +(-150.933 + 72.6854i) q^{59} +(41.7896 - 52.4025i) q^{60} +(100.825 - 441.743i) q^{61} +(86.2197 - 108.116i) q^{62} +(-224.779 - 135.069i) q^{63} +(-163.531 - 205.062i) q^{64} +(-86.6185 + 41.7133i) q^{65} +(64.9530 - 284.578i) q^{66} +153.689 q^{67} -138.107 q^{68} +(27.4151 - 120.114i) q^{69} +(15.3720 - 15.9969i) q^{70} +(137.788 + 603.690i) q^{71} +(40.3468 + 176.771i) q^{72} +(-247.285 - 310.085i) q^{73} +(124.641 + 156.295i) q^{74} +(-175.526 - 769.028i) q^{75} +(-95.2177 - 417.176i) q^{76} +(-313.521 + 956.703i) q^{77} +(80.2615 - 351.649i) q^{78} -981.604 q^{79} +68.2387 q^{80} +(202.675 - 887.979i) q^{81} +(-146.304 + 70.4563i) q^{82} +(-258.066 - 323.604i) q^{83} +(-114.254 - 859.751i) q^{84} +(16.8836 - 21.1714i) q^{85} +(-42.6193 + 186.727i) q^{86} +(-914.732 + 1147.04i) q^{87} +(627.161 - 302.025i) q^{88} +(833.012 + 1044.56i) q^{89} +(-15.2821 - 7.35948i) q^{90} +(-387.413 + 1182.18i) q^{91} +(126.295 - 60.8204i) q^{92} +(955.016 + 459.911i) q^{93} +(-45.8536 - 200.898i) q^{94} +(75.5921 + 36.4033i) q^{95} +(-569.396 + 714.000i) q^{96} +1061.38 q^{97} +(-11.4335 - 286.854i) q^{98} +769.717 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 78 q - 5 q^{2} - 5 q^{3} - 53 q^{4} - 23 q^{5} + 19 q^{6} - 31 q^{8} - 174 q^{9}+O(q^{10}) $ 78 * q - 5 * q^2 - 5 * q^3 - 53 * q^4 - 23 * q^5 + 19 * q^6 - 31 * q^8 - 174 * q^9	\( 78 q - 5 q^{2} - 5 q^{3} - 53 q^{4} - 23 q^{5} + 19 q^{6} - 31 q^{8} - 174 q^{9} + 9 q^{10} - 103 q^{11} + 364 q^{12} - 35 q^{13} + 161 q^{14} - 245 q^{15} - 205 q^{16} - 285 q^{17} + 16 q^{18} + 628 q^{19} + 553 q^{20} - 21 q^{21} - 605 q^{22} + 149 q^{23} + 653 q^{24} - 370 q^{25} - 511 q^{26} - 65 q^{27} + 70 q^{28} - 187 q^{29} + 84 q^{30} + 1276 q^{31} + 1399 q^{32} - 23 q^{33} - 765 q^{34} - 805 q^{35} - 1691 q^{36} - 1531 q^{37} - 1041 q^{38} - 1351 q^{39} - 1759 q^{40} - 301 q^{41} + 3395 q^{42} - 257 q^{43} - 883 q^{44} + 3105 q^{45} + 1593 q^{46} + 733 q^{47} - 1948 q^{48} + 1288 q^{49} + 6148 q^{50} + 1197 q^{51} - 1099 q^{52} - 285 q^{53} + 660 q^{54} + 2641 q^{55} - 1988 q^{56} - 2352 q^{57} + 1173 q^{58} - 3603 q^{59} - 175 q^{60} - 2613 q^{61} - 1927 q^{62} - 3066 q^{63} + 1589 q^{64} - 371 q^{65} - 2175 q^{66} + 352 q^{67} + 6076 q^{68} + 5549 q^{69} - 6293 q^{70} - 2623 q^{71} + 6220 q^{72} + 2039 q^{73} - 2411 q^{74} - 3903 q^{75} + 4130 q^{76} + 1029 q^{77} - 3759 q^{78} + 44 q^{79} - 1608 q^{80} + 1394 q^{81} - 10920 q^{82} - 553 q^{83} - 7798 q^{84} + 497 q^{85} - 2985 q^{86} - 4273 q^{87} - 2197 q^{88} - 3957 q^{89} - 2958 q^{90} + 14119 q^{91} - 9136 q^{92} + 6272 q^{93} + 14912 q^{94} + 5866 q^{95} + 21882 q^{96} - 1540 q^{97} - 2303 q^{98} + 10768 q^{99}+O(q^{100}) \) 78 * q - 5 * q^2 - 5 * q^3 - 53 * q^4 - 23 * q^5 + 19 * q^6 - 31 * q^8 - 174 * q^9 + 9 * q^10 - 103 * q^11 + 364 * q^12 - 35 * q^13 + 161 * q^14 - 245 * q^15 - 205 * q^16 - 285 * q^17 + 16 * q^18 + 628 * q^19 + 553 * q^20 - 21 * q^21 - 605 * q^22 + 149 * q^23 + 653 * q^24 - 370 * q^25 - 511 * q^26 - 65 * q^27 + 70 * q^28 - 187 * q^29 + 84 * q^30 + 1276 * q^31 + 1399 * q^32 - 23 * q^33 - 765 * q^34 - 805 * q^35 - 1691 * q^36 - 1531 * q^37 - 1041 * q^38 - 1351 * q^39 - 1759 * q^40 - 301 * q^41 + 3395 * q^42 - 257 * q^43 - 883 * q^44 + 3105 * q^45 + 1593 * q^46 + 733 * q^47 - 1948 * q^48 + 1288 * q^49 + 6148 * q^50 + 1197 * q^51 - 1099 * q^52 - 285 * q^53 + 660 * q^54 + 2641 * q^55 - 1988 * q^56 - 2352 * q^57 + 1173 * q^58 - 3603 * q^59 - 175 * q^60 - 2613 * q^61 - 1927 * q^62 - 3066 * q^63 + 1589 * q^64 - 371 * q^65 - 2175 * q^66 + 352 * q^67 + 6076 * q^68 + 5549 * q^69 - 6293 * q^70 - 2623 * q^71 + 6220 * q^72 + 2039 * q^73 - 2411 * q^74 - 3903 * q^75 + 4130 * q^76 + 1029 * q^77 - 3759 * q^78 + 44 * q^79 - 1608 * q^80 + 1394 * q^81 - 10920 * q^82 - 553 * q^83 - 7798 * q^84 + 497 * q^85 - 2985 * q^86 - 4273 * q^87 - 2197 * q^88 - 3957 * q^89 - 2958 * q^90 + 14119 * q^91 - 9136 * q^92 + 6272 * q^93 + 14912 * q^94 + 5866 * q^95 + 21882 * q^96 - 1540 * q^97 - 2303 * q^98 + 10768 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/49\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{7}\right)$

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 $

$2$	0.521845	−	0.654373i	0.184500	−	0.231356i	−0.680976	−	0.732305i	$-0.738444\pi$
$2$	0.521845	−	0.654373i	0.184500	−	0.231356i	0.865476	+	0.500950i	$0.167016\pi$
$3$	5.78023	+	2.78361i	1.11241	+	0.535707i	0.897538	−	0.440937i	$-0.145354\pi$
$3$	5.78023	+	2.78361i	1.11241	+	0.535707i	0.214868	+	0.976643i	$0.431068\pi$
$4$	1.62429	+	7.11646i	0.203036	+	0.889558i
$5$	−1.28950	−	0.620991i	−0.115336	−	0.0555431i	0.375326	−	0.926893i	$-0.377531\pi$
$5$	−1.28950	−	0.620991i	−0.115336	−	0.0555431i	−0.490662	+	0.871350i	$0.663245\pi$
$6$	4.83790	−	2.32981i	0.329178	−	0.158524i
$7$	−17.3557	+	6.46381i	−0.937118	+	0.349013i
$7$	−17.3557	+	6.46381i	−0.937118	+	0.349013i
$8$	11.5371	+	5.55599i	0.509874	+	0.245543i
$9$	8.82835	+	11.0704i	0.326976	+	0.410015i
$10$	−1.07928	+	0.519753i	−0.0341298	+	0.0164360i
$11$	33.8930	−	42.5005i	0.929012	−	1.16494i	−0.0570176	−	0.998373i	$-0.518159\pi$
$11$	33.8930	−	42.5005i	0.929012	−	1.16494i	0.986029	−	0.166571i	$-0.0532694\pi$
$12$	−10.4207	+	45.6562i	−0.250684	+	1.09832i
$13$	41.8811	−	52.5173i	0.893518	−	1.12044i	−0.0985995	−	0.995127i	$-0.531436\pi$
$13$	41.8811	−	52.5173i	0.893518	−	1.12044i	0.992118	−	0.125309i	$-0.0399923\pi$
$14$	−4.82722	+	14.7302i	−0.0921520	+	0.281200i
$15$	−5.72501	−	7.17894i	−0.0985461	−	0.123573i
$16$	−42.9565	+	20.6868i	−0.671195	+	0.323231i
$17$	−4.21013	+	18.4458i	−0.0600651	+	0.263163i	−0.996040	−	0.0889037i	$-0.971664\pi$
$17$	−4.21013	+	18.4458i	−0.0600651	+	0.263163i	0.935975	+	0.352066i	$0.114521\pi$
$18$	11.8512			0.155186
$19$	−58.6213			−0.707823			−0.353912	−	0.935279i	$-0.615149\pi$
$19$	−58.6213			−0.707823			−0.353912	+	0.935279i	$0.615149\pi$
$20$	2.32474	−	10.1853i	0.0259914	−	0.113876i
$21$	−118.313	−	10.9491i	−1.22942	−	0.113776i
$22$	−10.1243	−	44.3573i	−0.0981137	−	0.429864i
$23$	−4.27322	−	18.7222i	−0.0387403	−	0.169732i	0.951857	−	0.306542i	$-0.0991722\pi$
$23$	−4.27322	−	18.7222i	−0.0387403	−	0.169732i	−0.990597	+	0.136810i	$0.956315\pi$
$24$	51.2216	+	64.2299i	0.435649	+	0.546286i
$25$	−76.6590	−	96.1274i	−0.613272	−	0.769019i
$26$	−12.5104	−	54.8117i	−0.0943652	−	0.413441i
$27$	−18.3310	−	80.3133i	−0.130659	−	0.572455i
$28$	−74.1900	−	113.012i	−0.500736	−	0.762758i
$29$	−50.8862	+	222.947i	−0.325839	+	1.42759i	0.501142	+	0.865365i	$0.332913\pi$
$29$	−50.8862	+	222.947i	−0.325839	+	1.42759i	−0.826981	+	0.562229i	$0.809944\pi$
$30$	−7.68527			−0.0467711
$31$	165.221			0.957244			0.478622	−	0.878021i	$-0.341136\pi$
$31$	165.221			0.957244			0.478622	+	0.878021i	$0.341136\pi$
$32$	−31.6753	+	138.778i	−0.174983	+	0.766650i
$33$	314.214	−	151.318i	1.65751	−	0.798213i
$34$	9.87339	+	12.3808i	0.0498021	+	0.0624499i
$35$	26.3941	+	2.44262i	0.127469	+	0.0117965i
$36$	−64.4423	+	80.8081i	−0.298344	+	0.374112i
$37$	−53.1486	+	232.859i	−0.236151	+	1.03464i	0.708280	+	0.705932i	$0.249472\pi$
$37$	−53.1486	+	232.859i	−0.236151	+	1.03464i	−0.944430	+	0.328711i	$0.893386\pi$
$38$	−30.5912	+	38.3601i	−0.130593	+	0.163759i
$39$	388.270	−	186.981i	1.59418	−	0.767717i
$40$	−11.4269	−	14.3289i	−0.0451689	−	0.0566400i
$41$	−174.801	−	84.1798i	−0.665838	−	0.320651i	0.0702570	−	0.997529i	$-0.477618\pi$
$41$	−174.801	−	84.1798i	−0.665838	−	0.320651i	−0.736095	+	0.676878i	$0.763332\pi$
$42$	−68.9056	+	71.7067i	−0.253151	+	0.263443i
$43$	−206.174	+	99.2879i	−0.731190	+	0.352123i	−0.762152	−	0.647398i	$-0.775857\pi$
$43$	−206.174	+	99.2879i	−0.731190	+	0.352123i	0.0309621	+	0.999521i	$0.490143\pi$
$44$	357.505	+	172.165i	1.22491	+	0.589884i
$45$	−4.50955	−	19.7576i	−0.0149387	−	0.0654509i
$46$	−14.4812	−	6.97380i	−0.0464161	−	0.0223528i
$47$	153.504	−	192.488i	0.476402	−	0.597389i	−0.484324	−	0.874889i	$-0.660934\pi$
$47$	153.504	−	192.488i	0.476402	−	0.597389i	0.960726	+	0.277500i	$0.0895059\pi$
$48$	−305.882			−0.919799
$49$	259.438	−	224.368i	0.756380	−	0.654133i
$50$	−102.907			−0.291066
$51$	−75.6815	+	94.9016i	−0.207795	+	0.260566i
$52$	441.764	+	212.742i	1.17811	+	0.567347i
$53$	118.302	+	518.313i	0.306603	+	1.34332i	0.859955	+	0.510370i	$0.170491\pi$
$53$	118.302	+	518.313i	0.306603	+	1.34332i	−0.553352	+	0.832948i	$0.686651\pi$
$54$	−62.1207	−	29.9158i	−0.156547	−	0.0753893i
$55$	−70.0975	+	33.7572i	−0.171854	+	0.0827603i
$56$	−236.148	−	21.8540i	−0.563510	−	0.0521495i
$57$	−338.844	−	163.179i	−0.787387	−	0.379185i
$58$	119.336	+	149.642i	0.270165	+	0.338776i
$59$	−150.933	+	72.6854i	−0.333047	+	0.160387i	−0.592932	−	0.805253i	$-0.702030\pi$
$59$	−150.933	+	72.6854i	−0.333047	+	0.160387i	0.259885	+	0.965640i	$0.416315\pi$
$60$	41.7896	−	52.4025i	0.0899169	−	0.112752i
$61$	100.825	−	441.743i	0.211628	−	0.927203i	−0.751833	−	0.659354i	$-0.770830\pi$
$61$	100.825	−	441.743i	0.211628	−	0.927203i	0.963461	−	0.267849i	$-0.0863129\pi$
$62$	86.2197	−	108.116i	0.176612	−	0.221464i
$63$	−224.779	−	135.069i	−0.449516	−	0.270113i
$64$	−163.531	−	205.062i	−0.319397	−	0.400511i
$65$	−86.6185	+	41.7133i	−0.165288	+	0.0795984i
$66$	64.9530	−	284.578i	0.121139	−	0.530744i
$67$	153.689			0.280239			0.140120	−	0.990135i	$-0.455251\pi$
$67$	153.689			0.280239			0.140120	+	0.990135i	$0.455251\pi$
$68$	−138.107			−0.246294
$69$	27.4151	−	120.114i	0.0478318	−	0.209565i
$70$	15.3720	−	15.9969i	0.0262472	−	0.0273142i
$71$	137.788	+	603.690i	0.230316	+	1.00908i	0.949378	+	0.314135i	$0.101715\pi$
$71$	137.788	+	603.690i	0.230316	+	1.00908i	−0.719062	+	0.694946i	$0.755428\pi$
$72$	40.3468	+	176.771i	0.0660406	+	0.289343i
$73$	−247.285	−	310.085i	−0.396473	−	0.497161i	0.543025	−	0.839717i	$-0.317279\pi$
$73$	−247.285	−	310.085i	−0.396473	−	0.497161i	−0.939498	+	0.342556i	$0.888707\pi$
$74$	124.641	+	156.295i	0.195801	+	0.245526i
$75$	−175.526	−	769.028i	−0.270239	−	1.18400i
$76$	−95.2177	−	417.176i	−0.143713	−	0.629650i
$77$	−313.521	+	956.703i	−0.464013	+	1.41593i
$78$	80.2615	−	351.649i	0.116511	−	0.510466i
$79$	−981.604			−1.39796			−0.698982	−	0.715139i	$-0.746363\pi$
$79$	−981.604			−1.39796			−0.698982	+	0.715139i	$0.746363\pi$
$80$	68.2387			0.0953665
$81$	202.675	−	887.979i	0.278018	−	1.21808i
$82$	−146.304	+	70.4563i	−0.197031	+	0.0948853i
$83$	−258.066	−	323.604i	−0.341282	−	0.427954i	0.581339	−	0.813661i	$-0.302529\pi$
$83$	−258.066	−	323.604i	−0.341282	−	0.427954i	−0.922621	+	0.385707i	$0.873957\pi$
$84$	−114.254	−	859.751i	−0.148407	−	1.11674i
$85$	16.8836	−	21.1714i	0.0215446	−	0.0270160i
$86$	−42.6193	+	186.727i	−0.0534390	+	0.234132i
$87$	−914.732	+	1147.04i	−1.12724	+	1.41351i
$88$	627.161	−	302.025i	0.759723	−	0.365863i
$89$	833.012	+	1044.56i	0.992125	+	1.24409i	0.969690	+	0.244337i	$0.0785704\pi$
$89$	833.012	+	1044.56i	0.992125	+	1.24409i	0.0224347	+	0.999748i	$0.492858\pi$
$90$	−15.2821	−	7.35948i	−0.0178986	−	0.00861953i
$91$	−387.413	+	1182.18i	−0.446285	+	1.36183i
$92$	126.295	−	60.8204i	0.143121	−	0.0689235i
$93$	955.016	+	459.911i	1.06484	+	0.512802i
$94$	−45.8536	−	200.898i	−0.0503132	−	0.220436i
$95$	75.5921	+	36.4033i	0.0816378	+	0.0393147i
$96$	−569.396	+	714.000i	−0.605352	+	0.759087i
$97$	1061.38			1.11100			0.555501	−	0.831516i	$-0.312527\pi$
$97$	1061.38			1.11100			0.555501	+	0.831516i	$0.312527\pi$
$98$	−11.4335	−	286.854i	−0.0117853	−	0.295680i
$99$	769.717			0.781409
$100$	559.571	−	701.680i	0.559571	−	0.701680i
$101$	1790.60	+	862.309i	1.76408	+	0.849534i	0.970514	+	0.241043i	$0.0774895\pi$
$101$	1790.60	+	862.309i	1.76408	+	0.849534i	0.793561	+	0.608491i	$0.208225\pi$
$102$	22.6070	+	99.0478i	0.0219454	+	0.0961490i
$103$	−842.671	−	405.809i	−0.806125	−	0.388209i	−0.0150180	−	0.999887i	$-0.504781\pi$
$103$	−842.671	−	405.809i	−0.806125	−	0.388209i	−0.791107	+	0.611678i	$0.790495\pi$
$104$	774.974	−	373.208i	0.730697	−	0.351885i
$105$	145.765	+	87.5899i	0.135478	+	0.0814085i
$106$	400.905	+	193.066i	0.367352	+	0.176908i
$107$	−790.337	−	991.051i	−0.714063	−	0.895406i	0.283923	−	0.958847i	$-0.408364\pi$
$107$	−790.337	−	991.051i	−0.714063	−	0.895406i	−0.997986	+	0.0634407i	$0.979793\pi$
$108$	541.772	−	260.903i	0.482704	−	0.232458i
$109$	−447.179	+	560.745i	−0.392954	+	0.492749i	−0.938474	−	0.345349i	$-0.887761\pi$
$109$	−447.179	+	560.745i	−0.392954	+	0.492749i	0.545520	+	0.838098i	$0.316332\pi$
$110$	−14.4902	+	63.4859i	−0.0125599	+	0.0550286i
$111$	−955.401	+	1198.03i	−0.816961	+	1.02444i
$112$	611.823	−	636.695i	0.516177	−	0.537161i
$113$	249.253	+	312.553i	0.207502	+	0.260200i	0.874682	−	0.484697i	$-0.161070\pi$
$113$	249.253	+	312.553i	0.207502	+	0.260200i	−0.667180	+	0.744897i	$0.732499\pi$
$114$	−283.604	+	136.576i	−0.233000	+	0.112207i
$115$	−6.11599	+	26.7959i	−0.00495930	+	0.0217281i
$116$	−1669.25			−1.33608
$117$	951.129			0.751555
$118$	−31.2001	+	136.697i	−0.0243407	+	0.106644i
$119$	−46.1606	−	347.353i	−0.0355591	−	0.267578i
$120$	−26.1641	−	114.633i	−0.0199037	−	0.0872040i
$121$	−361.381	−	1583.31i	−0.271511	−	1.18957i
$122$	−236.449	−	296.498i	−0.175468	−	0.220030i
$123$	−776.067	−	973.158i	−0.568908	−	0.713388i
$124$	268.366	+	1175.79i	0.194355	+	0.851524i
$125$	78.9677	+	345.980i	0.0565047	+	0.247563i
$126$	−205.685	+	76.6039i	−0.145428	+	0.0541621i
$127$	41.7539	−	182.936i	0.0291737	−	0.127818i	−0.958244	−	0.285952i	$-0.907690\pi$
$127$	41.7539	−	182.936i	0.0291737	−	0.127818i	0.987418	+	0.158133i	$0.0505475\pi$
$128$	−1358.30			−0.937955
$129$	−1468.11			−1.00201
$130$	−17.9054	+	78.4486i	−0.0120800	+	0.0529261i
$131$	−426.891	+	205.580i	−0.284715	+	0.137111i	−0.570791	−	0.821095i	$-0.693363\pi$
$131$	−426.891	+	205.580i	−0.284715	+	0.137111i	0.286076	+	0.958207i	$0.407649\pi$
$132$	1587.22	+	1990.31i	1.04659	+	1.31238i
$133$	1017.41	−	378.917i	0.663314	−	0.247040i
$134$	80.2016	−	100.570i	0.0517042	−	0.0648350i
$135$	−26.2360	+	114.947i	−0.0167262	+	0.0732822i
$136$	−151.058	+	189.420i	−0.0952433	+	0.119431i
$137$	−468.430	+	225.584i	−0.292122	+	0.140679i	−0.574205	−	0.818711i	$-0.694689\pi$
$137$	−468.430	+	225.584i	−0.292122	+	0.140679i	0.282083	+	0.959390i	$0.408975\pi$
$138$	−64.2926	−	80.6203i	−0.0396590	−	0.0497309i
$139$	−1733.93	−	835.018i	−1.05806	−	0.509535i	−0.177820	−	0.984063i	$-0.556904\pi$
$139$	−1733.93	−	835.018i	−1.05806	−	0.509535i	−0.880240	+	0.474528i	$0.842619\pi$
$140$	25.4888	+	191.800i	0.0153871	+	0.115786i
$141$	1423.10	−	685.329i	0.849977	−	0.409327i
$142$	466.942	+	224.867i	0.275950	+	0.132891i
$143$	−812.533	−	3559.94i	−0.475157	−	2.08180i
$144$	−608.246	−	292.916i	−0.351994	−	0.169511i
$145$	204.066	−	255.890i	0.116874	−	0.146555i
$146$	−331.956			−0.188170
$147$	2124.17	−	574.721i	1.19182	−	0.322464i
$148$	−1743.46			−0.968322
$149$	2044.84	−	2564.15i	1.12429	−	1.40982i	0.223973	−	0.974595i	$-0.428097\pi$
$149$	2044.84	−	2564.15i	1.12429	−	1.40982i	0.900322	−	0.435225i	$-0.143331\pi$
$150$	−594.828	−	286.454i	−0.323783	−	0.155926i
$151$	486.589	+	2131.89i	0.262239	+	1.14894i	0.918817	+	0.394685i	$0.129146\pi$
$151$	486.589	+	2131.89i	0.262239	+	1.14894i	−0.656578	+	0.754258i	$0.727997\pi$
$152$	−676.322	−	325.699i	−0.360901	−	0.173801i
$153$	−241.371	+	116.238i	−0.127540	+	0.0614202i
$154$	462.431	+	704.410i	0.241972	+	0.368591i
$155$	−213.053	−	102.601i	−0.110405	−	0.0531683i
$156$	1961.31	+	2459.40i	1.00660	+	1.26224i
$157$	−1798.65	+	866.185i	−0.914318	+	0.440313i	−0.831039	−	0.556214i	$-0.812254\pi$
$157$	−1798.65	+	866.185i	−0.914318	+	0.440313i	−0.0832791	+	0.996526i	$0.526539\pi$
$158$	−512.245	+	642.335i	−0.257924	+	0.323427i
$159$	−758.973	+	3325.28i	−0.378556	+	1.65856i
$160$	127.025	−	159.285i	0.0627640	−	0.0787036i
$161$	195.181	+	297.315i	0.0955431	+	0.145538i
$162$	−475.304	−	596.012i	−0.230515	−	0.289056i
$163$	−233.613	+	112.502i	−0.112258	+	0.0540604i	−0.489170	−	0.872189i	$-0.662700\pi$
$163$	−233.613	+	112.502i	−0.112258	+	0.0540604i	0.376912	+	0.926249i	$0.376986\pi$
$164$	315.135	−	1380.70i	0.150048	−	0.657405i
$165$	−499.147			−0.235506
$166$	−346.428			−0.161976
$167$	125.964	−	551.883i	0.0583674	−	0.255724i	−0.937323	−	0.348461i	$-0.886704\pi$
$167$	125.964	−	551.883i	0.0583674	−	0.255724i	0.995691	+	0.0927367i	$0.0295615\pi$
$168$	−1304.16	−	783.665i	−0.598915	−	0.359887i
$169$	−515.157	−	2257.05i	−0.234482	−	1.02733i
$170$	−5.04335	−	22.0964i	−0.00227534	−	0.00996891i
$171$	−517.529	−	648.961i	−0.231441	−	0.290218i
$172$	−1041.46	−	1305.95i	−0.461691	−	0.578942i
$173$	−751.152	−	3291.01i	−0.330110	−	1.44631i	−0.818916	−	0.573914i	$-0.805424\pi$
$173$	−751.152	−	3291.01i	−0.330110	−	1.44631i	0.488806	−	0.872393i	$-0.337433\pi$
$174$	273.242	+	1197.15i	0.119048	+	0.521585i
$175$	1951.82	+	1172.85i	0.843106	+	0.506621i
$176$	−576.728	+	2526.81i	−0.247003	+	1.08219i
$177$	−1074.75			−0.456404
$178$	1118.24			0.470873
$179$	−609.189	+	2669.03i	−0.254374	+	1.11449i	0.672791	+	0.739832i	$0.265095\pi$
$179$	−609.189	+	2669.03i	−0.254374	+	1.11449i	−0.927165	+	0.374653i	$0.877762\pi$
$180$	133.280	−	64.1840i	0.0551893	−	0.0265777i
$181$	2149.24	+	2695.06i	0.882607	+	1.10675i	0.993603	+	0.112933i	$0.0360246\pi$
$181$	2149.24	+	2695.06i	0.882607	+	1.10675i	−0.110996	+	0.993821i	$0.535404\pi$
$182$	571.420	+	870.429i	0.232728	+	0.354508i
$183$	1812.43	−	2272.72i	0.732125	−	0.918056i
$184$	54.7197	−	239.743i	0.0219238	−	0.0960546i
$185$	213.138	−	267.267i	0.0847041	−	0.106216i
$186$	799.323	−	384.934i	0.315103	−	0.151746i
$187$	641.262	+	804.117i	0.250768	+	0.314454i
$188$	1619.17	+	779.750i	0.628138	+	0.302495i
$189$	837.276	+	1275.40i	0.322238	+	0.490856i
$190$	63.2687	−	30.4686i	0.0241578	−	0.0116338i
$191$	1298.60	+	625.375i	0.491957	+	0.236914i	0.663379	−	0.748284i	$-0.269122\pi$
$191$	1298.60	+	625.375i	0.491957	+	0.236914i	−0.171422	+	0.985198i	$0.554836\pi$
$192$	−374.436	−	1640.51i	−0.140743	−	0.616634i
$193$	1570.65	+	756.386i	0.585792	+	0.282103i	0.703213	−	0.710980i	$-0.251748\pi$
$193$	1570.65	+	756.386i	0.585792	+	0.282103i	−0.117420	+	0.993082i	$0.537462\pi$
$194$	553.877	−	694.540i	0.204980	−	0.257036i
$195$	−616.789			−0.226508
$196$	2018.11	+	1481.84i	0.735461	+	0.540031i
$197$	2819.62			1.01974			0.509872	−	0.860250i	$-0.329693\pi$
$197$	2819.62			1.01974			0.509872	+	0.860250i	$0.329693\pi$
$198$	401.673	−	503.682i	0.144170	−	0.180783i
$199$	−768.184	−	369.938i	−0.273644	−	0.131780i	0.292030	−	0.956409i	$-0.405669\pi$
$199$	−768.184	−	369.938i	−0.273644	−	0.131780i	−0.565673	+	0.824629i	$0.691384\pi$
$200$	−350.343	−	1534.95i	−0.123865	−	0.542688i
$201$	888.355	+	427.809i	0.311740	+	0.150126i
$202$	1498.69	−	721.730i	0.522016	−	0.251390i
$203$	−557.924	−	4198.31i	−0.192900	−	1.45155i
$204$	−798.292	−	384.437i	−0.273979	−	0.131941i
$205$	173.131	+	217.100i	0.0589854	+	0.0739654i
$206$	−705.294	+	339.652i	−0.238544	+	0.114877i
$207$	169.537	−	212.592i	0.0569257	−	0.0713825i
$208$	−712.655	+	3122.34i	−0.237566	+	1.04084i
$209$	−1986.85	+	2491.43i	−0.657576	+	0.824574i
$210$	133.383	−	49.6762i	0.0438300	−	0.0163237i
$211$	584.828	+	733.351i	0.190811	+	0.239270i	0.868030	−	0.496512i	$-0.165386\pi$
$211$	584.828	+	733.351i	0.190811	+	0.239270i	−0.677218	+	0.735782i	$0.736815\pi$
$212$	−3496.40	+	1683.78i	−1.13271	+	0.545483i
$213$	−883.991	+	3873.02i	−0.284366	+	1.24589i
$214$	−1060.95			−0.338902
$215$	327.518			0.103891
$216$	234.733	−	1028.43i	0.0739424	−	0.323963i
$217$	−2867.52	+	1067.96i	−0.897051	+	0.334091i
$218$	133.578	+	585.244i	0.0415002	+	0.181824i
$219$	−566.206	−	2480.71i	−0.174706	−	0.765438i
$220$	−354.090	−	444.015i	−0.108512	−	0.136070i
$221$	792.398	+	993.636i	0.241188	+	0.302440i
$222$	285.390	+	1250.38i	0.0862799	+	0.378017i
$223$	−1103.05	−	4832.79i	−0.331237	−	1.45124i	−0.816738	−	0.577008i	$-0.804220\pi$
$223$	−1103.05	−	4832.79i	−0.331237	−	1.45124i	0.485501	−	0.874236i	$-0.338637\pi$
$224$	−347.293	−	2613.34i	−0.103591	−	0.779513i
$225$	387.396	−	1697.29i	0.114784	−	0.502902i
$226$	334.598			0.0984828
$227$	1929.91			0.564285			0.282143	−	0.959373i	$-0.408955\pi$
$227$	1929.91			0.564285			0.282143	+	0.959373i	$0.408955\pi$
$228$	610.876	−	2676.42i	0.177440	−	0.777414i
$229$	−4558.51	+	2195.26i	−1.31544	+	0.633481i	−0.954249	−	0.299013i	$-0.903343\pi$
$229$	−4558.51	+	2195.26i	−1.31544	+	0.633481i	−0.361187	+	0.932493i	$0.617628\pi$
$230$	14.3429	+	17.9854i	0.00411193	+	0.00515619i
$231$	−4475.31	+	4657.24i	−1.27469	+	1.32651i
$232$	−1825.77	+	2289.45i	−0.516672	+	0.647886i
$233$	1514.32	−	6634.65i	0.425777	−	1.86545i	−0.0708490	−	0.997487i	$-0.522571\pi$
$233$	1514.32	−	6634.65i	0.425777	−	1.86545i	0.496626	−	0.867965i	$-0.334572\pi$
$234$	496.342	−	622.393i	0.138662	−	0.173876i
$235$	−317.477	+	152.889i	−0.0881273	+	0.0424399i
$236$	−762.421	−	956.045i	−0.210294	−	0.263700i
$237$	−5673.90	−	2732.41i	−1.55510	−	0.748898i
$238$	−251.387	−	151.058i	−0.0684663	−	0.0411413i
$239$	2342.66	−	1128.17i	0.634034	−	0.305334i	−0.0891209	−	0.996021i	$-0.528406\pi$
$239$	2342.66	−	1128.17i	0.634034	−	0.305334i	0.723154	+	0.690686i	$0.242691\pi$
$240$	394.436	+	189.950i	0.106086	+	0.0510885i
$241$	1238.43	+	5425.91i	0.331013	+	1.45026i	0.817173	+	0.576393i	$0.195540\pi$
$241$	1238.43	+	5425.91i	0.331013	+	1.45026i	−0.486160	+	0.873870i	$0.661603\pi$
$242$	−1224.66	−	589.765i	−0.325306	−	0.156659i
$243$	2256.52	−	2829.59i	0.595703	−	0.746988i
$244$	3307.41			0.867769
$245$	−473.876	+	128.213i	−0.123571	+	0.0334337i
$246$	−1041.79			−0.270010
$247$	−2455.13	+	3078.63i	−0.632453	+	0.793071i
$248$	1906.18	+	917.967i	0.488074	+	0.235044i
$249$	−590.891	−	2588.86i	−0.150386	−	0.658885i
$250$	267.609	+	128.874i	0.0677003	+	0.0326027i
$251$	1018.98	−	490.713i	0.256244	−	0.123401i	−0.301352	−	0.953513i	$-0.597438\pi$
$251$	1018.98	−	490.713i	0.256244	−	0.123401i	0.557596	+	0.830112i	$0.311724\pi$
$252$	596.111	−	1819.02i	0.149014	−	0.454713i
$253$	−940.535	−	452.938i	−0.233719	−	0.112553i
$254$	−97.9192	−	122.787i	−0.0241890	−	0.0303320i
$255$	156.524	−	75.3782i	0.0384390	−	0.0185112i
$256$	599.427	−	751.657i	0.146344	−	0.183510i
$257$	1402.93	−	6146.65i	0.340516	−	1.49190i	−0.457472	−	0.889224i	$-0.651245\pi$
$257$	1402.93	−	6146.65i	0.340516	−	1.49190i	0.797988	−	0.602673i	$-0.205898\pi$
$258$	−766.125	+	960.691i	−0.184872	+	0.231822i
$259$	−582.729	−	4384.97i	−0.139803	−	1.05200i
$260$	−437.544	−	548.663i	−0.104367	−	0.130872i
$261$	−2917.36	+	1404.92i	−0.691876	+	0.333190i
$262$	−88.2450	+	386.627i	−0.0208084	+	0.0911675i
$263$	4800.80			1.12559			0.562794	−	0.826597i	$-0.309726\pi$
$263$	4800.80			1.12559			0.562794	+	0.826597i	$0.309726\pi$
$264$	4465.86			1.04112
$265$	169.318	−	741.829i	0.0392495	−	0.171963i
$266$	282.978	−	863.502i	0.0652274	−	0.199040i
$267$	1907.34	+	8356.61i	0.437181	+	1.91542i
$268$	249.634	+	1093.72i	0.0568986	+	0.249289i
$269$	4118.44	+	5164.36i	0.933478	+	1.17054i	0.985118	+	0.171879i	$0.0549837\pi$
$269$	4118.44	+	5164.36i	0.933478	+	1.17054i	−0.0516401	+	0.998666i	$0.516445\pi$
$270$	61.5273	+	77.1528i	0.0138683	+	0.0173903i
$271$	−366.708	−	1606.65i	−0.0821991	−	0.360138i	0.917055	−	0.398761i	$-0.130560\pi$
$271$	−366.708	−	1606.65i	−0.0821991	−	0.360138i	−0.999254	+	0.0386236i	$0.987703\pi$
$272$	−200.731	−	879.461i	−0.0447468	−	0.196048i
$273$	−5530.08	+	5754.89i	−1.22599	+	1.27583i
$274$	−96.8318	+	424.248i	−0.0213497	+	0.0935392i
$275$	−6683.67			−1.46560
$276$	899.314			0.196132
$277$	834.020	−	3654.08i	0.180908	−	0.792608i	−0.800292	−	0.599611i	$-0.795322\pi$
$277$	834.020	−	3654.08i	0.180908	−	0.792608i	0.981199	−	0.192997i	$-0.0618209\pi$
$278$	−1451.26	+	698.889i	−0.313096	+	0.150779i
$279$	1458.63	+	1829.06i	0.312996	+	0.392484i
$280$	290.941	+	174.826i	0.0620967	+	0.0373138i
$281$	−2808.44	+	3521.67i	−0.596219	+	0.747635i	−0.984783	−	0.173786i	$-0.944400\pi$
$281$	−2808.44	+	3521.67i	−0.596219	+	0.747635i	0.388564	+	0.921422i	$0.372971\pi$
$282$	294.177	−	1288.87i	0.0621205	−	0.272168i
$283$	2515.54	−	3154.38i	0.528386	−	0.662575i	−0.443980	−	0.896037i	$-0.646434\pi$
$283$	2515.54	−	3154.38i	0.528386	−	0.662575i	0.972366	+	0.233462i	$0.0750054\pi$
$284$	−4072.33	+	1961.13i	−0.850874	+	0.409759i
$285$	335.608	+	420.839i	0.0697532	+	0.0874678i
$286$	−2753.54	−	1326.04i	−0.569302	−	0.274161i
$287$	3577.91	+	331.114i	0.735880	+	0.0681013i
$288$	−1815.97	+	874.527i	−0.371553	+	0.178931i
$289$	4103.94	+	1976.35i	0.835322	+	0.402270i
$290$	−60.9570	−	267.070i	−0.0123432	−	0.0540790i
$291$	6135.04	+	2954.48i	1.23588	+	0.595171i
$292$	1805.05	−	2263.46i	0.361755	−	0.453627i
$293$	−2875.42			−0.573323			−0.286661	−	0.958032i	$-0.592545\pi$
$293$	−2875.42			−0.573323			−0.286661	+	0.958032i	$0.592545\pi$
$294$	732.403	−	1689.91i	0.145288	−	0.335230i
$295$	239.765			0.0473208
$296$	−1906.95	+	2391.24i	−0.374456	+	0.469553i
$297$	−4034.65	−	1942.98i	−0.788262	−	0.379607i
$298$	−610.819	−	2676.18i	−0.118738	−	0.520224i
$299$	−1162.21	−	559.689i	−0.224790	−	0.108253i
$300$	5187.65	−	2498.24i	0.998364	−	0.480787i
$301$	2936.50	−	3055.88i	0.562316	−	0.585175i
$302$	1648.97	+	794.103i	0.314198	+	0.151310i
$303$	7949.76	+	9968.69i	1.50727	+	1.89005i
$304$	2518.16	−	1212.68i	0.475088	−	0.228790i
$305$	−404.332	+	507.016i	−0.0759081	+	0.0951858i
$306$	−49.8951	+	218.605i	−0.00932129	+	0.0408392i
$307$	−1754.72	+	2200.35i	−0.326213	+	0.409058i	−0.917711	−	0.397248i	$-0.869965\pi$
$307$	−1754.72	+	2200.35i	−0.326213	+	0.409058i	0.591499	+	0.806306i	$0.298537\pi$
$308$	−7317.59	−	677.198i	−1.35376	−	0.125282i
$309$	−3741.22	−	4691.34i	−0.688772	−	0.863693i
$310$	−178.319	+	85.8741i	−0.0326705	+	0.0157333i
$311$	−269.070	+	1178.87i	−0.0490597	+	0.214944i	−0.993516	−	0.113693i	$-0.963732\pi$
$311$	−269.070	+	1178.87i	−0.0490597	+	0.214944i	0.944456	+	0.328637i	$0.106589\pi$
$312$	5518.40			1.00134
$313$	5256.27			0.949208			0.474604	−	0.880200i	$-0.342591\pi$
$313$	5256.27			0.949208			0.474604	+	0.880200i	$0.342591\pi$
$314$	−371.809	+	1629.00i	−0.0668229	+	0.292770i
$315$	205.976	+	313.758i	0.0368426	+	0.0561214i
$316$	−1594.41	−	6985.55i	−0.283837	−	1.24357i
$317$	1977.13	+	8662.36i	0.350304	+	1.53478i	0.776479	+	0.630143i	$0.217004\pi$
$317$	1977.13	+	8662.36i	0.350304	+	1.53478i	−0.426175	+	0.904641i	$0.640139\pi$
$318$	1779.90	+	2231.93i	0.313874	+	0.393586i
$319$	7750.67	+	9719.04i	1.36036	+	1.70584i
$320$	83.5323	+	365.979i	0.0145925	+	0.0639339i
$321$	−1809.63	−	7928.49i	−0.314653	−	1.37858i
$322$	296.409	+	27.4309i	0.0512988	+	0.00474740i
$323$	246.803	−	1081.32i	0.0425155	−	0.186273i
$324$	6648.47			1.14000
$325$	−8258.92			−1.40961
$326$	−48.2914	+	211.579i	−0.00820434	+	0.0359456i
$327$	−4145.70	+	1996.46i	−0.701094	+	0.337629i
$328$	−1549.00	−	1942.39i	−0.260760	−	0.326983i
$329$	−1419.96	+	4332.98i	−0.237948	+	0.726094i
$330$	−260.477	+	326.628i	−0.0434509	+	0.0544857i
$331$	2353.14	−	10309.8i	0.390756	−	1.71201i	−0.271244	−	0.962511i	$-0.587435\pi$
$331$	2353.14	−	10309.8i	0.390756	−	1.71201i	0.662000	−	0.749504i	$-0.269708\pi$
$332$	1883.74	−	2362.14i	0.311397	−	0.390480i
$333$	−3047.06	+	1467.39i	−0.501435	+	0.241478i
$334$	−295.404	−	370.424i	−0.0483945	−	0.0606848i
$335$	−198.181	−	95.4391i	−0.0323218	−	0.0155654i
$336$	5308.79	−	1977.17i	0.861960	−	0.321022i
$337$	−7446.34	+	3585.97i	−1.20364	+	0.579645i	−0.924712	−	0.380666i	$-0.875695\pi$
$337$	−7446.34	+	3585.97i	−1.20364	+	0.579645i	−0.278932	+	0.960311i	$0.589980\pi$
$338$	−1745.78	−	840.725i	−0.280941	−	0.135294i
$339$	570.712	+	2500.45i	0.0914361	+	0.400608i
$340$	178.089	+	85.7633i	0.0284066	+	0.0136799i
$341$	5599.84	−	7021.98i	0.889291	−	1.11514i
$342$	−694.732			−0.109844
$343$	−3052.45	+	5571.01i	−0.480516	+	0.876986i
$344$	−2930.30			−0.459276
$345$	−109.941	+	137.862i	−0.0171566	+	0.0215137i
$346$	−2545.53	−	1225.86i	−0.395516	−	0.190471i
$347$	−1371.57	−	6009.23i	−0.212189	−	0.929662i	−0.963076	−	0.269230i	$-0.913231\pi$
$347$	−1371.57	−	6009.23i	−0.212189	−	0.929662i	0.750887	−	0.660431i	$-0.229626\pi$
$348$	−9648.64	−	4646.54i	−1.48627	−	0.715749i
$349$	1390.53	−	669.642i	0.213276	−	0.102708i	−0.324196	−	0.945990i	$-0.605094\pi$
$349$	1390.53	−	669.642i	0.213276	−	0.102708i	0.537472	+	0.843282i	$0.319379\pi$
$350$	1786.02	−	665.173i	0.272763	−	0.101586i
$351$	−4985.56	−	2400.92i	−0.758146	−	0.365104i
$352$	4824.59	+	6049.84i	0.730543	+	0.916072i
$353$	8630.77	−	4156.36i	1.30133	−	0.626687i	0.350547	−	0.936545i	$-0.385996\pi$
$353$	8630.77	−	4156.36i	1.30133	−	0.626687i	0.950783	+	0.309858i	$0.100281\pi$
$354$	−560.855	+	703.290i	−0.0842065	+	0.105592i
$355$	197.208	−	864.023i	0.0294837	−	0.129176i
$356$	−6080.55	+	7624.77i	−0.905249	+	1.13515i
$357$	700.077	−	2136.27i	0.103787	−	0.316704i
$358$	1428.64	+	1791.46i	0.210910	+	0.264473i
$359$	−9744.76	+	4692.83i	−1.43262	+	0.689911i	−0.979482	−	0.201532i	$-0.935408\pi$
$359$	−9744.76	+	4692.83i	−1.43262	+	0.689911i	−0.453133	+	0.891443i	$0.649694\pi$
$360$	57.7459	−	253.001i	0.00845410	−	0.0370398i
$361$	−3422.55			−0.498986
$362$	2885.15			0.418895
$363$	2318.46	−	10157.9i	0.335228	−	1.46873i
$364$	−9042.24	−	836.805i	−1.30204	−	0.120496i
$365$	126.314	+	553.417i	0.0181139	+	0.0793621i
$366$	−541.396	−	2372.01i	−0.0773203	−	0.338763i
$367$	−6467.18	−	8109.59i	−0.919848	−	1.15345i	−0.987794	−	0.155764i	$-0.950216\pi$
$367$	−6467.18	−	8109.59i	−0.919848	−	1.15345i	0.0679461	−	0.997689i	$-0.478355\pi$
$368$	570.864	+	715.841i	0.0808651	+	0.101402i
$369$	−611.302	−	2678.29i	−0.0862415	−	0.377849i
$370$	−63.6671	−	278.944i	−0.00894567	−	0.0391935i
$371$	−5403.48	−	8230.99i	−0.756159	−	1.15184i
$372$	−1721.72	+	7543.36i	−0.239965	+	1.05136i
$373$	−1084.71			−0.150574			−0.0752871	−	0.997162i	$-0.523987\pi$
$373$	−1084.71			−0.150574			−0.0752871	+	0.997162i	$0.523987\pi$
$374$	860.831			0.119017
$375$	−506.623	+	2219.66i	−0.0697651	+	0.305661i
$376$	2840.46	−	1367.89i	0.389589	−	0.187616i
$377$	9577.40	+	12009.7i	1.30839	+	1.64066i
$378$	1271.52	+	117.671i	0.173015	+	0.0160115i
$379$	3423.62	−	4293.09i	0.464010	−	0.581850i	−0.493683	−	0.869642i	$-0.664350\pi$
$379$	3423.62	−	4293.09i	0.464010	−	0.581850i	0.957693	+	0.287792i	$0.0929212\pi$
$380$	−136.279	+	597.078i	−0.0183973	+	0.0806038i
$381$	750.570	−	941.186i	0.100926	−	0.126557i
$382$	1086.90	−	523.423i	0.145577	−	0.0701064i
$383$	2550.00	+	3197.59i	0.340205	+	0.426604i	0.922275	−	0.386535i	$-0.126328\pi$
$383$	2550.00	+	3197.59i	0.340205	+	0.426604i	−0.582069	+	0.813139i	$0.697757\pi$
$384$	−7851.31	−	3780.99i	−1.04339	−	0.502469i
$385$	998.388	−	1038.98i	0.132163	−	0.137535i
$386$	1314.59	−	633.075i	0.173345	−	0.0834784i
$387$	−2919.33	−	1405.88i	−0.383457	−	0.184663i
$388$	1723.99	+	7553.29i	0.225573	+	0.988299i
$389$	−7987.39	−	3846.53i	−1.04107	−	0.501354i	−0.166394	−	0.986059i	$-0.553212\pi$
$389$	−7987.39	−	3846.53i	−1.04107	−	0.501354i	−0.874677	+	0.484706i	$0.838927\pi$
$390$	−321.868	+	403.610i	−0.0417908	+	0.0524040i
$391$	363.337			0.0469942
$392$	4239.76	−	1147.12i	0.546276	−	0.147802i
$393$	−3039.79			−0.390170
$394$	1471.40	−	1845.08i	0.188143	−	0.235924i
$395$	1265.78	+	609.567i	0.161236	+	0.0776472i
$396$	1250.24	+	5477.66i	0.158654	+	0.695108i
$397$	2196.93	+	1057.98i	0.277734	+	0.133750i	0.567566	−	0.823328i	$-0.307885\pi$
$397$	2196.93	+	1057.98i	0.277734	+	0.133750i	−0.289832	+	0.957078i	$0.593599\pi$
$398$	−642.950	+	309.629i	−0.0809754	+	0.0389957i
$399$	6935.63	+	641.851i	0.870215	+	0.0805331i
$400$	5281.57	+	2543.47i	0.660196	+	0.317934i
$401$	459.549	+	576.257i	0.0572289	+	0.0717628i	0.809622	−	0.586951i	$-0.199672\pi$
$401$	459.549	+	576.257i	0.0572289	+	0.0717628i	−0.752393	+	0.658714i	$0.771101\pi$
$402$	743.530	−	358.065i	0.0922486	−	0.0444246i
$403$	6919.64	−	8676.96i	0.855315	−	1.07253i
$404$	−3228.14	+	14143.4i	−0.397539	+	1.74173i
$405$	−812.777	+	1019.19i	−0.0997215	+	0.125047i
$406$	−3038.41	−	1825.78i	−0.371413	−	0.223182i
$407$	8095.26	+	10151.1i	0.985915	+	1.23630i
$408$	−1400.42	+	674.407i	−0.169929	+	0.0818337i
$409$	−495.846	+	2172.44i	−0.0599463	+	0.262642i	−0.996016	−	0.0891722i	$-0.971578\pi$
$409$	−495.846	+	2172.44i	−0.0599463	+	0.262642i	0.936070	+	0.351814i	$0.114435\pi$
$410$	232.412			0.0279951
$411$	−3335.57			−0.400321
$412$	1519.19	−	6655.99i	0.181662	−	0.795915i
$413$	2149.71	−	2237.10i	0.256127	−	0.266539i
$414$	−50.6427	−	221.880i	−0.00601197	−	0.0263402i
$415$	131.821	+	577.544i	0.0155923	+	0.0683145i
$416$	5961.67	+	7475.70i	0.702632	+	0.881073i
$417$	−7698.17	−	9653.20i	−0.904031	−	1.13362i
$418$	593.498	+	2600.28i	0.0694472	+	0.304268i
$419$	2521.32	+	11046.6i	0.293972	+	1.28798i	0.878945	+	0.476923i	$0.158248\pi$
$419$	2521.32	+	11046.6i	0.293972	+	1.28798i	−0.584973	+	0.811053i	$0.698895\pi$
$420$	−386.566	+	1179.60i	−0.0449107	+	0.137044i
$421$	1411.48	−	6184.11i	0.163400	−	0.715903i	−0.825138	−	0.564931i	$-0.808903\pi$
$421$	1411.48	−	6184.11i	0.163400	−	0.715903i	0.988538	−	0.150972i	$-0.0482402\pi$
$422$	785.074			0.0905611
$423$	3486.11			0.400710
$424$	−1514.88	+	6637.14i	−0.173512	+	0.760207i
$425$	2095.89	−	1009.33i	0.239213	−	0.115199i
$426$	2073.09	+	2599.57i	0.235778	+	0.295657i
$427$	1105.46	+	8318.46i	0.125286	+	0.942759i
$428$	5769.04	−	7234.15i	0.651535	−	0.817000i
$429$	5212.86	−	22839.0i	0.586665	−	2.57035i
$430$	170.913	−	214.319i	0.0191679	−	0.0240357i
$431$	−1003.19	+	483.112i	−0.112116	+	0.0539923i	−0.489101	−	0.872227i	$-0.662675\pi$
$431$	−1003.19	+	483.112i	−0.112116	+	0.0539923i	0.376985	+	0.926219i	$0.376961\pi$
$432$	2448.86	+	3070.77i	0.272733	+	0.341996i
$433$	−4194.01	−	2019.73i	−0.465476	−	0.224162i	0.186419	−	0.982470i	$-0.440312\pi$
$433$	−4194.01	−	2019.73i	−0.465476	−	0.224162i	−0.651896	+	0.758309i	$0.726026\pi$
$434$	−797.558	+	2433.73i	−0.0882120	+	0.269177i
$435$	1891.85	−	911.066i	0.208522	−	0.100419i
$436$	−4716.87	−	2271.52i	−0.518112	−	0.249510i
$437$	250.501	+	1097.52i	0.0274213	+	0.120141i
$438$	−1918.78	−	924.036i	−0.209322	−	0.100804i
$439$	−2663.20	+	3339.55i	−0.289539	+	0.363071i	−0.905234	−	0.424914i	$-0.860304\pi$
$439$	−2663.20	+	3339.55i	−0.289539	+	0.363071i	0.615694	+	0.787985i	$0.288876\pi$
$440$	−996.279			−0.107945
$441$	4774.25	+	891.290i	0.515522	+	0.0962412i
$442$	1063.72			0.114470
$443$	−2025.57	+	2539.98i	−0.217240	+	0.272411i	−0.878496	−	0.477750i	$-0.841453\pi$
$443$	−2025.57	+	2539.98i	−0.217240	+	0.272411i	0.661255	+	0.750161i	$0.270024\pi$
$444$	−10077.6	−	4853.12i	−1.07717	−	0.518736i
$445$	−425.505	−	1864.26i	−0.0453278	−	0.198594i
$446$	−3738.07	−	1800.16i	−0.396867	−	0.191121i
$447$	18957.2	−	9129.33i	2.00592	−	0.966001i
$448$	4163.68	+	2501.95i	0.439096	+	0.263853i
$449$	6674.49	+	3214.27i	0.701534	+	0.337841i	0.750418	−	0.660963i	$-0.229852\pi$
$449$	6674.49	+	3214.27i	0.701534	+	0.337841i	−0.0488840	+	0.998804i	$0.515566\pi$
$450$	−908.501	−	1139.22i	−0.0951715	−	0.119341i
$451$	−9502.23	+	4576.03i	−0.992112	+	0.477776i
$452$	−1819.42	+	2281.48i	−0.189332	+	0.237415i
$453$	−3121.75	+	13677.3i	−0.323780	+	1.41857i
$454$	1007.11	−	1262.88i	0.104111	−	0.130551i
$455$	1233.69	−	1283.85i	0.127113	−	0.132281i
$456$	−3002.68	−	3765.24i	−0.308362	−	0.386674i
$457$	666.199	−	320.824i	0.0681914	−	0.0328392i	−0.399477	−	0.916743i	$-0.630808\pi$
$457$	666.199	−	320.824i	0.0681914	−	0.0328392i	0.467669	+	0.883904i	$0.345094\pi$
$458$	−942.315	+	4128.55i	−0.0961386	+	0.421211i
$459$	1558.62			0.158497
$460$	−200.626			−0.0203353
$461$	−602.522	+	2639.82i	−0.0608725	+	0.266700i	−0.996201	−	0.0870796i	$-0.972247\pi$
$461$	−602.522	+	2639.82i	−0.0608725	+	0.266700i	0.935329	+	0.353780i	$0.115104\pi$
$462$	712.155	+	5358.88i	0.0717152	+	0.539649i
$463$	276.058	+	1209.49i	0.0277095	+	0.121403i	0.986891	−	0.161387i	$-0.0515969\pi$
$463$	276.058	+	1209.49i	0.0277095	+	0.121403i	−0.959182	+	0.282791i	$0.908740\pi$
$464$	−2426.16	−	10629.7i	−0.242741	−	1.06352i
$465$	−945.892	−	1186.11i	−0.0943327	−	0.118289i
$466$	−3551.29	−	4453.18i	−0.353027	−	0.442682i
$467$	−2909.77	−	12748.5i	−0.288326	−	1.26324i	−0.886822	−	0.462112i	$-0.847092\pi$
$467$	−2909.77	−	12748.5i	−0.288326	−	1.26324i	0.598496	−	0.801126i	$-0.295765\pi$
$468$	1544.91	+	6768.67i	0.152592	+	0.668551i
$469$	−2667.37	+	993.414i	−0.262617	+	0.0978073i
$470$	−65.6274	+	287.532i	−0.00644078	+	0.0282189i
$471$	−12807.7			−1.25297
$472$	−2145.17			−0.209194
$473$	−2768.06	+	12127.6i	−0.269081	+	1.17892i
$474$	−4748.91	+	2286.95i	−0.460178	+	0.221610i
$475$	4493.85	+	5635.11i	0.434088	+	0.544330i
$476$	2396.94	−	892.700i	0.230806	−	0.0859597i
$477$	−4693.53	+	5885.50i	−0.450528	+	0.564944i
$478$	484.264	−	2121.70i	0.0463383	−	0.203021i
$479$	6873.82	−	8619.50i	0.655684	−	0.822202i	−0.337181	−	0.941440i	$-0.609474\pi$
$479$	6873.82	−	8619.50i	0.655684	−	0.822202i	0.992866	+	0.119237i	$0.0380450\pi$
$480$	1177.62	−	567.114i	0.111981	−	0.0539273i
$481$	10003.2	+	12543.6i	0.948247	+	1.18906i
$482$	4196.83	+	2021.09i	0.396598	+	0.190992i
$483$	300.584	+	2261.86i	0.0283168	+	0.213081i
$484$	10680.6	−	5143.50i	1.00306	−	0.483049i
$485$	−1368.65	−	659.109i	−0.128139	−	0.0617084i
$486$	−674.051	−	2953.21i	−0.0629127	−	0.275638i
$487$	−13591.8	−	6545.49i	−1.26469	−	0.609044i	−0.323280	−	0.946303i	$-0.604786\pi$
$487$	−13591.8	−	6545.49i	−1.26469	−	0.609044i	−0.941412	+	0.337260i	$0.890500\pi$
$488$	3617.55	−	4536.27i	0.335572	−	0.420793i
$489$	−1663.50			−0.153836
$490$	−163.390	+	376.999i	−0.0150637	+	0.0347573i
$491$	14530.5			1.33555			0.667774	−	0.744364i	$-0.267247\pi$
$491$	14530.5			1.33555			0.667774	+	0.744364i	$0.267247\pi$
$492$	5664.88	−	7103.54i	0.519091	−	0.650919i
$493$	−3898.20	−	1877.27i	−0.356118	−	0.171497i
$494$	733.377	+	3213.13i	0.0667939	+	0.292643i
$495$	−992.551	−	477.987i	−0.0901249	−	0.0434019i
$496$	−7097.32	+	3417.89i	−0.642498	+	0.309411i
$497$	−6293.54	−	9586.80i	−0.568016	−	0.865245i
$498$	−2002.43	−	964.321i	−0.180183	−	0.0867716i
$499$	6113.75	+	7666.40i	0.548475	+	0.687766i	0.976381	−	0.216058i	$-0.0693199\pi$
$499$	6113.75	+	7666.40i	0.548475	+	0.687766i	−0.427906	+	0.903823i	$0.640748\pi$
$500$	−2333.89	+	1123.94i	−0.208749	+	0.100528i
$501$	2264.33	−	2839.38i	0.201922	−	0.253202i
$502$	210.638	−	922.867i	0.0187276	−	0.0820509i
$503$	−13414.5	+	16821.2i	−1.18911	+	1.49110i	−0.359143	+	0.933283i	$0.616931\pi$
$503$	−13414.5	+	16821.2i	−1.18911	+	1.49110i	−0.829967	+	0.557813i	$0.811641\pi$
$504$	−1842.86	−	2807.19i	−0.162872	−	0.248099i
$505$	−1773.50	−	2223.89i	−0.156276	−	0.195964i
$506$	−787.203	+	379.097i	−0.0691610	+	0.0333062i
$507$	3305.03	−	14480.3i	0.289510	−	1.26843i
$508$	1369.68			0.119625
$509$	−5022.03			−0.437324			−0.218662	−	0.975801i	$-0.570169\pi$
$509$	−5022.03			−0.437324			−0.218662	+	0.975801i	$0.570169\pi$
$510$	32.3560	−	141.761i	0.00280931	−	0.0123084i
$511$	6296.13	+	3783.34i	0.545057	+	0.327524i
$512$	−2597.07	−	11378.5i	−0.224170	−	0.982154i
$513$	1074.59	+	4708.07i	0.0924836	+	0.405197i
$514$	−3290.09	−	4125.64i	−0.282334	−	0.354035i
$515$	834.621	+	1046.58i	0.0714132	+	0.0895493i
$516$	−2384.63	−	10447.7i	−0.203445	−	0.891350i
$517$	−2978.12	−	13048.0i	−0.253342	−	1.10996i
$518$	−3173.50	−	1906.95i	−0.269180	−	0.161750i
$519$	4819.07	−	21113.7i	0.407579	−	1.78572i
$520$	−1231.09			−0.103821
$521$	−9059.77			−0.761834			−0.380917	−	0.924609i	$-0.624392\pi$
$521$	−9059.77			−0.761834			−0.380917	+	0.924609i	$0.624392\pi$
$522$	−603.063	+	2642.19i	−0.0505658	+	0.221543i
$523$	−17635.6	+	8492.88i	−1.47448	+	0.710072i	−0.986648	−	0.162866i	$-0.947926\pi$
$523$	−17635.6	+	8492.88i	−1.47448	+	0.710072i	−0.487831	+	0.872938i	$0.662212\pi$
$524$	−2156.40	−	2704.03i	−0.179776	−	0.225432i
$525$	8017.22	+	12212.4i	0.666476	+	1.01523i
$526$	2505.27	−	3141.51i	0.207671	−	0.260411i
$527$	−695.602	+	3047.63i	−0.0574970	+	0.251911i
$528$	−10367.3	+	13000.2i	−0.854504	+	1.07151i
$529$	10629.8	−	5119.06i	0.873661	−	0.420733i
$530$	−397.075	−	497.917i	−0.0325431	−	0.0408078i
$531$	−2137.14	−	1029.19i	−0.174659	−	0.0841116i
$532$	4349.11	+	6624.90i	0.354432	+	0.539898i
$533$	−11741.8	+	5654.54i	−0.954207	+	0.459522i
$534$	6463.67	+	3112.74i	0.523802	+	0.252250i
$535$	403.706	+	1768.75i	0.0326238	+	0.142934i
$536$	1773.13	+	853.893i	0.142887	+	0.0688107i
$537$	−10950.8	+	13731.9i	−0.880004	+	1.10349i
$538$	5528.60			0.443039
$539$	−742.591	−	18630.8i	−0.0593426	−	1.48884i
$540$	−860.633			−0.0685847
$541$	4642.48	−	5821.49i	0.368939	−	0.462635i	−0.562359	−	0.826893i	$-0.690106\pi$
$541$	4642.48	−	5821.49i	0.368939	−	0.462635i	0.931298	+	0.364258i	$0.118678\pi$
$542$	−1242.72	−	598.460i	−0.0984856	−	0.0474282i
$543$	4921.10	+	21560.7i	0.388922	+	1.70398i
$544$	−2426.52	−	1168.55i	−0.191243	−	0.0920979i
$545$	924.855	−	445.387i	0.0726907	−	0.0350060i
$546$	880.000	+	6621.89i	0.0689753	+	0.519031i
$547$	−15117.9	−	7280.40i	−1.18171	−	0.569081i	−0.263301	−	0.964714i	$-0.584811\pi$
$547$	−15117.9	−	7280.40i	−1.18171	−	0.569081i	−0.918409	+	0.395633i	$0.870525\pi$
$548$	−2366.23	−	2967.15i	−0.184453	−	0.231297i
$549$	5780.39	−	2783.69i	0.449364	−	0.216402i
$550$	−3487.84	+	4373.61i	−0.270403	+	0.339075i
$551$	2983.01	−	13069.4i	0.230636	−	1.01048i
$552$	983.643	−	1233.45i	0.0758453	−	0.0951070i
$553$	17036.4	−	6344.91i	1.31006	−	0.487908i
$554$	−1955.90	−	2452.62i	−0.149997	−	0.188090i
$555$	1975.96	−	951.571i	0.151126	−	0.0727783i
$556$	3125.97	−	13695.8i	0.238437	−	1.04466i
$557$	−19923.1			−1.51557			−0.757783	−	0.652506i	$-0.773718\pi$
$557$	−19923.1			−1.51557			−0.757783	+	0.652506i	$0.773718\pi$
$558$	1958.07			0.148551
$559$	−3420.45	+	14986.0i	−0.258801	+	1.13388i
$560$	−1184.33	+	441.082i	−0.0893697	+	0.0332842i
$561$	1468.29	+	6433.00i	0.110501	+	0.484138i
$562$	838.917	+	3675.54i	0.0629672	+	0.275877i
$563$	−12713.0	−	15941.6i	−0.951666	−	1.19335i	−0.981044	−	0.193783i	$-0.937924\pi$
$563$	−12713.0	−	15941.6i	−0.951666	−	1.19335i	0.0293786	−	0.999568i	$-0.490647\pi$
$564$	7188.64	+	9014.27i	0.536696	+	0.672995i
$565$	−127.319	−	557.822i	−0.00948028	−	0.0415358i
$566$	−751.422	−	3292.20i	−0.0558032	−	0.244490i
$567$	2222.16	+	16721.5i	0.164589	+	1.23851i
$568$	−1764.41	+	7730.41i	−0.130340	+	0.571057i
$569$	826.351			0.0608830			0.0304415	−	0.999537i	$-0.490309\pi$
$569$	826.351			0.0608830			0.0304415	+	0.999537i	$0.490309\pi$
$570$	450.520			0.0331056
$571$	2876.66	−	12603.5i	0.210831	−	0.923710i	−0.753173	−	0.657822i	$-0.771478\pi$
$571$	2876.66	−	12603.5i	0.210831	−	0.923710i	0.964004	−	0.265888i	$-0.0856650\pi$
$572$	24014.4	−	11564.7i	1.75541	−	0.845359i
$573$	5765.43	+	7229.63i	0.420339	+	0.527089i
$574$	2083.79	−	2168.50i	0.151525	−	0.157685i
$575$	−1472.13	+	1846.00i	−0.106769	+	0.133884i
$576$	826.405	−	3620.72i	0.0597804	−	0.261915i
$577$	−10156.9	+	12736.4i	−0.732821	+	0.918928i	−0.998987	−	0.0449988i	$-0.985672\pi$
$577$	−10156.9	+	12736.4i	−0.732821	+	0.918928i	0.266166	+	0.963927i	$0.414243\pi$
$578$	3434.89	−	1654.16i	0.247184	−	0.119038i
$579$	6973.24	+	8744.17i	0.500515	+	0.627626i
$580$	2152.50	+	1036.59i	0.154099	+	0.0742103i
$581$	6570.62	+	3948.28i	0.469183	+	0.281931i
$582$	5134.87	−	2472.82i	0.365717	−	0.176120i
$583$	26038.2	+	12539.3i	1.84973	+	0.890782i
$584$	−1130.13	−	4951.41i	−0.0800771	−	0.350841i
$585$	−1226.48	−	590.642i	−0.0866816	−	0.0417437i
$586$	−1500.52	+	1881.59i	−0.105778	+	0.132641i
$587$	14432.0			1.01477			0.507386	−	0.861719i	$-0.330612\pi$
$587$	14432.0			1.01477			0.507386	+	0.861719i	$0.330612\pi$
$588$	7540.23	+	14183.0i	0.528833	+	0.994725i
$589$	−9685.46			−0.677560
$590$	125.120	−	156.896i	0.00873069	−	0.0109479i
$591$	16298.1	+	7848.73i	1.13437	+	0.546284i
$592$	−2534.02	−	11102.3i	−0.175925	−	0.770779i
$593$	9972.84	+	4802.67i	0.690616	+	0.332583i	0.746060	−	0.665878i	$-0.231943\pi$
$593$	9972.84	+	4802.67i	0.690616	+	0.332583i	−0.0554438	+	0.998462i	$0.517657\pi$
$594$	−3376.89	+	1626.23i	−0.233259	+	0.112331i
$595$	−156.179	+	476.577i	−0.0107608	+	0.0328365i
$596$	21569.1	+	10387.1i	1.48239	+	0.713881i
$597$	−3410.52	−	4276.66i	−0.233808	−	0.293186i
$598$	−972.736	+	468.445i	−0.0665186	+	0.0320337i
$599$	−11649.1	+	14607.5i	−0.794609	+	0.996408i	0.205235	+	0.978713i	$0.434204\pi$
$599$	−11649.1	+	14607.5i	−0.794609	+	0.996408i	−0.999843	+	0.0176950i	$0.994367\pi$
$600$	2247.65	−	9847.60i	0.152933	−	0.670044i
$601$	−1364.21	+	1710.66i	−0.0925909	+	0.116105i	−0.825969	−	0.563716i	$-0.809371\pi$
$601$	−1364.21	+	1710.66i	−0.0925909	+	0.116105i	0.733378	+	0.679821i	$0.237943\pi$
$602$	−467.284	−	3516.26i	−0.0316363	−	0.238060i
$603$	1356.82	+	1701.39i	0.0916316	+	0.114902i
$604$	−14381.1	+	6925.58i	−0.968807	+	0.466553i
$605$	−517.222	+	2266.10i	−0.0347571	+	0.152281i
$606$	10671.8			0.715365
$607$	6041.06			0.403953			0.201976	−	0.979390i	$-0.435264\pi$
$607$	6041.06			0.403953			0.201976	+	0.979390i	$0.435264\pi$
$608$	1856.85	−	8135.37i	0.123857	−	0.542653i
$609$	8461.55	−	25820.3i	0.563020	−	1.71805i
$610$	120.779	+	529.168i	0.00801672	+	0.0351236i
$611$	−3680.02	−	16123.2i	−0.243663	−	1.06756i
$612$	−1219.26	−	1528.90i	−0.0805321	−	0.100984i
$613$	276.479	+	346.693i	0.0182168	+	0.0228431i	0.790856	−	0.612002i	$-0.209635\pi$
$613$	276.479	+	346.693i	0.0182168	+	0.0228431i	−0.772640	+	0.634845i	$0.781064\pi$
$614$	524.157	+	2296.48i	0.0344516	+	0.150942i
$615$	396.417	+	1736.82i	0.0259920	+	0.113878i
$616$	−8932.57	+	9295.70i	−0.584259	+	0.608010i
$617$	−1632.86	+	7154.03i	−0.106542	+	0.466792i	0.893307	+	0.449446i	$0.148379\pi$
$617$	−1632.86	+	7154.03i	−0.106542	+	0.466792i	−0.999850	+	0.0173455i	$0.994478\pi$
$618$	−5022.22			−0.326899
$619$	17256.5			1.12051			0.560256	−	0.828319i	$-0.310703\pi$
$619$	17256.5			1.12051			0.560256	+	0.828319i	$0.310703\pi$
$620$	384.096	−	1682.83i	0.0248801	−	0.109007i
$621$	−1425.31	+	686.392i	−0.0921025	+	0.0443542i
$622$	631.009	+	791.260i	0.0406771	+	0.0510075i
$623$	−21209.4	−	12744.7i	−1.36394	−	0.819590i
$624$	−12810.7	+	16064.1i	−0.821857	+	1.03058i
$625$	−3306.89	+	14488.4i	−0.211641	+	0.927260i
$626$	2742.96	−	3439.56i	0.175129	−	0.219605i
$627$	−18419.6	+	8870.44i	−1.17322	+	0.564994i
$628$	−9085.69	−	11393.1i	−0.577323	−	0.723940i
$629$	−4071.51	−	1960.74i	−0.258095	−	0.124292i
$630$	312.802	+	28.9479i	0.0197815	+	0.00183065i
$631$	−4010.27	+	1931.24i	−0.253005	+	0.121841i	−0.556088	−	0.831123i	$-0.687698\pi$
$631$	−4010.27	+	1931.24i	−0.253005	+	0.121841i	0.303083	+	0.952964i	$0.401984\pi$
$632$	−11324.9	−	5453.79i	−0.712786	−	0.343260i
$633$	1339.07	+	5866.87i	0.0840813	+	0.368384i
$634$	6700.16	+	3226.63i	0.419712	+	0.202123i
$635$	−167.443	+	209.967i	−0.0104642	+	0.0131217i
$636$	−24897.0			−1.55225
$637$	−917.609	−	23021.8i	−0.0570753	−	1.43196i
$638$	10404.5			0.645641
$639$	−5466.65	+	6854.96i	−0.338431	+	0.424379i
$640$	1751.53	+	843.494i	0.108180	+	0.0520969i
$641$	−342.669	−	1501.33i	−0.0211148	−	0.0925101i	0.963273	−	0.268525i	$-0.0865363\pi$
$641$	−342.669	−	1501.33i	−0.0211148	−	0.0925101i	−0.984387	+	0.176015i	$0.943679\pi$
$642$	−6132.53	−	2953.27i	−0.376997	−	0.181552i
$643$	−1555.54	+	749.107i	−0.0954034	+	0.0459438i	−0.480977	−	0.876733i	$-0.659718\pi$
$643$	−1555.54	+	749.107i	−0.0954034	+	0.0459438i	0.385574	+	0.922677i	$0.374004\pi$
$644$	−1798.80	+	1871.92i	−0.110066	+	0.114541i
$645$	1893.13	+	911.683i	0.115569	+	0.0556550i
$646$	−578.791	−	725.780i	−0.0352511	−	0.0442035i
$647$	2900.27	−	1396.70i	0.176231	−	0.0848683i	−0.343688	−	0.939084i	$-0.611676\pi$
$647$	2900.27	−	1396.70i	0.176231	−	0.0848683i	0.519919	+	0.854216i	$0.325962\pi$
$648$	7271.90	−	9118.68i	0.440845	−	0.552802i
$649$	−2026.40	+	8878.25i	−0.122563	+	0.536983i
$650$	−4309.87	+	5404.41i	−0.260072	+	0.326121i
$651$	−19547.7	−	1809.02i	−1.17686	−	0.108911i
$652$	−1180.07	−	1479.76i	−0.0708821	−	0.0888834i
$653$	4967.66	−	2392.30i	0.297702	−	0.143366i	−0.279070	−	0.960271i	$-0.590026\pi$
$653$	4967.66	−	2392.30i	0.297702	−	0.143366i	0.576772	+	0.816905i	$0.304312\pi$
$654$	−856.980	+	3754.67i	−0.0512394	+	0.224494i
$655$	678.140			0.0404536
$656$	9250.26			0.550552
$657$	1249.65	−	5475.09i	0.0742064	−	0.325119i
$658$	2094.39	+	3190.32i	0.124085	+	0.189015i
$659$	−1123.04	−	4920.35i	−0.0663844	−	0.290849i	0.930829	−	0.365456i	$-0.119087\pi$
$659$	−1123.04	−	4920.35i	−0.0663844	−	0.290849i	−0.997213	+	0.0746069i	$0.976230\pi$
$660$	−810.757	−	3552.16i	−0.0478162	−	0.209496i
$661$	15497.5	+	19433.2i	0.911925	+	1.14352i	0.989209	+	0.146509i	$0.0468038\pi$
$661$	15497.5	+	19433.2i	0.911925	+	1.14352i	−0.0772839	+	0.997009i	$0.524625\pi$
$662$	−5518.46	−	6919.93i	−0.323990	−	0.406270i
$663$	1814.35	+	7949.17i	0.106280	+	0.465642i
$664$	−1179.40	−	5167.28i	−0.0689300	−	0.302002i
$665$	−1547.26	−	143.189i	−0.0902256	−	0.00834983i
$666$	−629.874	+	2759.66i	−0.0366473	+	0.160562i
$667$	4391.50			0.254932
$668$	4132.05			0.239332
$669$	7076.72	−	31005.1i	0.408971	−	1.79182i
$670$	−165.873	+	79.8801i	−0.00956451	+	0.00460603i
$671$	−15357.0	−	19257.1i	−0.883535	−	1.10792i
$672$	5267.08	−	16072.4i	0.302354	−	0.922629i
$673$	1677.84	−	2103.94i	0.0961010	−	0.120507i	−0.731456	−	0.681889i	$-0.761159\pi$
$673$	1677.84	−	2103.94i	0.0961010	−	0.120507i	0.827557	+	0.561382i	$0.189730\pi$
$674$	−1539.27	+	6744.00i	−0.0879683	+	0.385414i
$675$	−6315.07	+	7918.85i	−0.360100	+	0.451550i
$676$	15225.5	−	7332.19i	0.866264	−	0.417171i
$677$	−1177.99	−	1477.16i	−0.0668745	−	0.0838579i	0.747269	−	0.664522i	$-0.231365\pi$
$677$	−1177.99	−	1477.16i	−0.0668745	−	0.0838579i	−0.814144	+	0.580664i	$0.802793\pi$
$678$	1934.05	+	931.390i	0.109553	+	0.0527579i
$679$	−18421.0	+	6860.58i	−1.04114	+	0.387754i
$680$	312.417	−	150.452i	0.0176186	−	0.00848467i
$681$	11155.3	+	5372.13i	0.627714	+	0.302291i
$682$	−1672.74	−	7328.76i	−0.0939188	−	0.411485i
$683$	8673.07	+	4176.73i	0.485894	+	0.233994i	0.660759	−	0.750598i	$-0.270235\pi$
$683$	8673.07	+	4176.73i	0.485894	+	0.233994i	−0.174865	+	0.984592i	$0.555949\pi$
$684$	3777.69	−	4737.07i	0.211175	−	0.264805i
$685$	744.127			0.0415060
$686$	2052.61	+	4904.64i	0.114241	+	0.272974i
$687$	−32460.0			−1.80266
$688$	6802.55	−	8530.13i	0.376955	−	0.472686i
$689$	32175.0	+	15494.7i	1.77906	+	0.856749i
$690$	32.8408	+	143.885i	0.00181193	+	0.00793857i
$691$	−19468.2	−	9375.40i	−1.07179	−	0.516146i	−0.187106	−	0.982340i	$-0.559911\pi$
$691$	−19468.2	−	9375.40i	−1.07179	−	0.516146i	−0.884683	+	0.466194i	$0.845625\pi$
$692$	22200.3	−	10691.1i	1.21955	−	0.587304i
$693$	−13359.0	+	4975.31i	−0.732272	+	0.272722i
$694$	−4648.02	−	2238.37i	−0.254231	−	0.122431i
$695$	1717.37	+	2153.51i	0.0937317	+	0.117536i
$696$	−16926.3	+	8151.29i	−0.921826	+	0.443928i
$697$	2288.70	−	2869.94i	0.124377	−	0.155964i
$698$	287.443	−	1259.37i	0.0155872	−	0.0682921i
$699$	27221.4	−	34134.5i	1.47297	−	1.84705i
$700$	−5176.20	+	15795.1i	−0.279488	+	0.852854i
$701$	8988.48	+	11271.2i	0.484294	+	0.607286i	0.962606	−	0.270904i	$-0.0873226\pi$
$701$	8988.48	+	11271.2i	0.484294	+	0.607286i	−0.478312	+	0.878190i	$0.658751\pi$
$702$	−4172.78	+	2009.51i	−0.224347	+	0.108040i
$703$	3115.64	−	13650.5i	0.167153	−	0.732344i
$704$	−14257.8			−0.763297
$705$	−2260.67			−0.120769
$706$	1784.11	−	7816.71i	0.0951076	−	0.416694i
$707$	−36650.9	−	3391.82i	−1.94964	−	0.180428i
$708$	−1745.71	−	7648.45i	−0.0926663	−	0.405998i
$709$	−219.629	−	962.259i	−0.0116338	−	0.0509709i	0.968778	−	0.247930i	$-0.0797504\pi$
$709$	−219.629	−	962.259i	−0.0116338	−	0.0509709i	−0.980412	+	0.196959i	$0.936893\pi$
$710$	−462.481	−	579.933i	−0.0244459	−	0.0306542i
$711$	−8665.95	−	10866.8i	−0.457101	−	0.573186i
$712$	3806.99	+	16679.5i	0.200383	+	0.877936i
$713$	−706.025	−	3093.30i	−0.0370839	−	0.162475i
$714$	−1032.59	−	1572.91i	−0.0541227	−	0.0824437i
$715$	−1162.93	+	5095.12i	−0.0608266	+	0.266499i
$716$	−19983.6			−1.04305
$717$	16681.5			0.868873
$718$	−2014.39	+	8825.63i	−0.104703	+	0.458732i
$719$	−972.630	+	468.394i	−0.0504492	+	0.0242951i	−0.458938	−	0.888468i	$-0.651770\pi$
$719$	−972.630	+	468.394i	−0.0504492	+	0.0242951i	0.408489	+	0.912763i	$0.366056\pi$
$720$	602.435	+	755.430i	0.0311826	+	0.0391017i
$721$	17248.2	+	1596.22i	0.890924	+	0.0824496i
$722$	−1786.04	+	2239.62i	−0.0920630	+	0.115443i
$723$	−7945.22	+	34810.3i	−0.408694	+	1.79061i
$724$	−15688.3	+	19672.5i	−0.805321	+	1.00984i
$725$	25332.2	−	12199.3i	1.29768	−	0.624927i
$726$	−5437.14	−	6817.96i	−0.277949	−	0.348538i
$727$	15295.5	+	7365.92i	0.780300	+	0.375773i	0.781243	−	0.624227i	$-0.214586\pi$
$727$	15295.5	+	7365.92i	0.780300	+	0.375773i	−0.000942846		1.00000i	$0.500300\pi$
$728$	−11037.8	+	11486.6i	−0.561937	+	0.584781i
$729$	−1236.96	+	595.687i	−0.0628439	+	0.0302640i
$730$	428.057	+	206.141i	0.0217029	+	0.0104516i
$731$	−963.427	−	4221.05i	−0.0487464	−	0.213572i
$732$	19117.6	+	9206.56i	0.965311	+	0.464869i
$733$	5973.64	−	7490.71i	0.301012	−	0.377457i	−0.608205	−	0.793780i	$-0.708110\pi$
$733$	5973.64	−	7490.71i	0.301012	−	0.377457i	0.909217	+	0.416323i	$0.136682\pi$
$734$	−8681.56			−0.436570
$735$	−3096.01	−	577.984i	−0.155371	−	0.0290058i
$736$	2733.59			0.136904
$737$	5208.97	−	6531.84i	0.260346	−	0.326463i
$738$	−2071.60	−	997.632i	−0.103329	−	0.0497606i
$739$	−709.526	−	3108.64i	−0.0353185	−	0.154740i	0.954194	−	0.299189i	$-0.0967162\pi$
$739$	−709.526	−	3108.64i	−0.0353185	−	0.154740i	−0.989512	+	0.144449i	$0.953859\pi$
$740$	2248.19	+	1082.67i	0.111683	+	0.0537836i
$741$	−22760.9	+	10961.1i	−1.12840	+	0.543408i
$742$	−8205.92	−	759.408i	−0.405995	−	0.0375724i
$743$	−6526.63	−	3143.06i	−0.322260	−	0.155192i	0.265759	−	0.964040i	$-0.414377\pi$
$743$	−6526.63	−	3143.06i	−0.322260	−	0.155192i	−0.588018	+	0.808847i	$0.700092\pi$
$744$	8462.89	+	10612.1i	0.417022	+	0.522929i
$745$	−4229.14	+	2036.64i	−0.207978	+	0.100157i
$746$	−566.050	+	709.805i	−0.0277809	+	0.0348362i
$747$	1304.13	−	5713.78i	0.0638765	−	0.279861i
$748$	−4680.87	+	5869.63i	−0.228810	+	0.286918i
$749$	20122.8	+	12091.8i	0.981670	+	0.589884i
$750$	1188.11	+	1489.84i	0.0578447	+	0.0725349i
$751$	−466.852	+	224.824i	−0.0226840	+	0.0109240i	−0.445191	−	0.895435i	$-0.646864\pi$
$751$	−466.852	+	224.824i	−0.0226840	+	0.0109240i	0.422507	+	0.906359i	$0.361150\pi$
$752$	−2612.04	+	11444.1i	−0.126664	+	0.554952i
$753$	7255.88			0.351154
$754$	12856.7			0.620974
$755$	696.425	−	3051.24i	0.0335702	−	0.147081i
$756$	−7716.37	+	8030.06i	−0.371219	+	0.386310i
$757$	5596.74	+	24520.9i	0.268715	+	1.17732i	0.911510	+	0.411278i	$0.134918\pi$
$757$	5596.74	+	24520.9i	0.268715	+	1.17732i	−0.642795	+	0.766038i	$0.722225\pi$
$758$	−1022.68	−	4480.65i	−0.0490044	−	0.214703i
$759$	−4175.71	−	5236.17i	−0.199695	−	0.250410i
$760$	669.861	+	839.979i	0.0319716	+	0.0400911i
$761$	−1030.95	−	4516.90i	−0.0491090	−	0.215161i	0.944420	−	0.328742i	$-0.106625\pi$
$761$	−1030.95	−	4516.90i	−0.0491090	−	0.215161i	−0.993529	+	0.113582i	$0.963768\pi$
$762$	−224.205	−	982.306i	−0.0106589	−	0.0466997i
$763$	4136.54	−	12622.6i	0.196269	−	0.598910i
$764$	−2341.15	+	10257.3i	−0.110864	+	0.485726i
$765$	383.431			0.0181215
$766$	3423.12			0.161465
$767$	−2504.00	+	10970.7i	−0.117880

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:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	49.e (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.521845 - 0.654373i) q^{2} +(5.78023 + 2.78361i) q^{3} +(1.62429 + 7.11646i) q^{4} +(-1.28950 - 0.620991i) q^{5} +(4.83790 - 2.32981i) q^{6} +(-17.3557 + 6.46381i) q^{7} +(11.5371 + 5.55599i) q^{8} +(8.82835 + 11.0704i) q^{9} +O(q^{10})\)	\(q+(0.521845 - 0.654373i) q^{2} +(5.78023 + 2.78361i) q^{3} +(1.62429 + 7.11646i) q^{4} +(-1.28950 - 0.620991i) q^{5} +(4.83790 - 2.32981i) q^{6} +(-17.3557 + 6.46381i) q^{7} +(11.5371 + 5.55599i) q^{8} +(8.82835 + 11.0704i) q^{9} +(-1.07928 + 0.519753i) q^{10} +(33.8930 - 42.5005i) q^{11} +(-10.4207 + 45.6562i) q^{12} +(41.8811 - 52.5173i) q^{13} +(-4.82722 + 14.7302i) q^{14} +(-5.72501 - 7.17894i) q^{15} +(-42.9565 + 20.6868i) q^{16} +(-4.21013 + 18.4458i) q^{17} +11.8512 q^{18} -58.6213 q^{19} +(2.32474 - 10.1853i) q^{20} +(-118.313 - 10.9491i) q^{21} +(-10.1243 - 44.3573i) q^{22} +(-4.27322 - 18.7222i) q^{23} +(51.2216 + 64.2299i) q^{24} +(-76.6590 - 96.1274i) q^{25} +(-12.5104 - 54.8117i) q^{26} +(-18.3310 - 80.3133i) q^{27} +(-74.1900 - 113.012i) q^{28} +(-50.8862 + 222.947i) q^{29} -7.68527 q^{30} +165.221 q^{31} +(-31.6753 + 138.778i) q^{32} +(314.214 - 151.318i) q^{33} +(9.87339 + 12.3808i) q^{34} +(26.3941 + 2.44262i) q^{35} +(-64.4423 + 80.8081i) q^{36} +(-53.1486 + 232.859i) q^{37} +(-30.5912 + 38.3601i) q^{38} +(388.270 - 186.981i) q^{39} +(-11.4269 - 14.3289i) q^{40} +(-174.801 - 84.1798i) q^{41} +(-68.9056 + 71.7067i) q^{42} +(-206.174 + 99.2879i) q^{43} +(357.505 + 172.165i) q^{44} +(-4.50955 - 19.7576i) q^{45} +(-14.4812 - 6.97380i) q^{46} +(153.504 - 192.488i) q^{47} -305.882 q^{48} +(259.438 - 224.368i) q^{49} -102.907 q^{50} +(-75.6815 + 94.9016i) q^{51} +(441.764 + 212.742i) q^{52} +(118.302 + 518.313i) q^{53} +(-62.1207 - 29.9158i) q^{54} +(-70.0975 + 33.7572i) q^{55} +(-236.148 - 21.8540i) q^{56} +(-338.844 - 163.179i) q^{57} +(119.336 + 149.642i) q^{58} +(-150.933 + 72.6854i) q^{59} +(41.7896 - 52.4025i) q^{60} +(100.825 - 441.743i) q^{61} +(86.2197 - 108.116i) q^{62} +(-224.779 - 135.069i) q^{63} +(-163.531 - 205.062i) q^{64} +(-86.6185 + 41.7133i) q^{65} +(64.9530 - 284.578i) q^{66} +153.689 q^{67} -138.107 q^{68} +(27.4151 - 120.114i) q^{69} +(15.3720 - 15.9969i) q^{70} +(137.788 + 603.690i) q^{71} +(40.3468 + 176.771i) q^{72} +(-247.285 - 310.085i) q^{73} +(124.641 + 156.295i) q^{74} +(-175.526 - 769.028i) q^{75} +(-95.2177 - 417.176i) q^{76} +(-313.521 + 956.703i) q^{77} +(80.2615 - 351.649i) q^{78} -981.604 q^{79} +68.2387 q^{80} +(202.675 - 887.979i) q^{81} +(-146.304 + 70.4563i) q^{82} +(-258.066 - 323.604i) q^{83} +(-114.254 - 859.751i) q^{84} +(16.8836 - 21.1714i) q^{85} +(-42.6193 + 186.727i) q^{86} +(-914.732 + 1147.04i) q^{87} +(627.161 - 302.025i) q^{88} +(833.012 + 1044.56i) q^{89} +(-15.2821 - 7.35948i) q^{90} +(-387.413 + 1182.18i) q^{91} +(126.295 - 60.8204i) q^{92} +(955.016 + 459.911i) q^{93} +(-45.8536 - 200.898i) q^{94} +(75.5921 + 36.4033i) q^{95} +(-569.396 + 714.000i) q^{96} +1061.38 q^{97} +(-11.4335 - 286.854i) q^{98} +769.717 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 78 q - 5 q^{2} - 5 q^{3} - 53 q^{4} - 23 q^{5} + 19 q^{6} - 31 q^{8} - 174 q^{9}+O(q^{10}) \) 78 * q - 5 * q^2 - 5 * q^3 - 53 * q^4 - 23 * q^5 + 19 * q^6 - 31 * q^8 - 174 * q^9	\( 78 q - 5 q^{2} - 5 q^{3} - 53 q^{4} - 23 q^{5} + 19 q^{6} - 31 q^{8} - 174 q^{9} + 9 q^{10} - 103 q^{11} + 364 q^{12} - 35 q^{13} + 161 q^{14} - 245 q^{15} - 205 q^{16} - 285 q^{17} + 16 q^{18} + 628 q^{19} + 553 q^{20} - 21 q^{21} - 605 q^{22} + 149 q^{23} + 653 q^{24} - 370 q^{25} - 511 q^{26} - 65 q^{27} + 70 q^{28} - 187 q^{29} + 84 q^{30} + 1276 q^{31} + 1399 q^{32} - 23 q^{33} - 765 q^{34} - 805 q^{35} - 1691 q^{36} - 1531 q^{37} - 1041 q^{38} - 1351 q^{39} - 1759 q^{40} - 301 q^{41} + 3395 q^{42} - 257 q^{43} - 883 q^{44} + 3105 q^{45} + 1593 q^{46} + 733 q^{47} - 1948 q^{48} + 1288 q^{49} + 6148 q^{50} + 1197 q^{51} - 1099 q^{52} - 285 q^{53} + 660 q^{54} + 2641 q^{55} - 1988 q^{56} - 2352 q^{57} + 1173 q^{58} - 3603 q^{59} - 175 q^{60} - 2613 q^{61} - 1927 q^{62} - 3066 q^{63} + 1589 q^{64} - 371 q^{65} - 2175 q^{66} + 352 q^{67} + 6076 q^{68} + 5549 q^{69} - 6293 q^{70} - 2623 q^{71} + 6220 q^{72} + 2039 q^{73} - 2411 q^{74} - 3903 q^{75} + 4130 q^{76} + 1029 q^{77} - 3759 q^{78} + 44 q^{79} - 1608 q^{80} + 1394 q^{81} - 10920 q^{82} - 553 q^{83} - 7798 q^{84} + 497 q^{85} - 2985 q^{86} - 4273 q^{87} - 2197 q^{88} - 3957 q^{89} - 2958 q^{90} + 14119 q^{91} - 9136 q^{92} + 6272 q^{93} + 14912 q^{94} + 5866 q^{95} + 21882 q^{96} - 1540 q^{97} - 2303 q^{98} + 10768 q^{99}+O(q^{100}) \) 78 * q - 5 * q^2 - 5 * q^3 - 53 * q^4 - 23 * q^5 + 19 * q^6 - 31 * q^8 - 174 * q^9 + 9 * q^10 - 103 * q^11 + 364 * q^12 - 35 * q^13 + 161 * q^14 - 245 * q^15 - 205 * q^16 - 285 * q^17 + 16 * q^18 + 628 * q^19 + 553 * q^20 - 21 * q^21 - 605 * q^22 + 149 * q^23 + 653 * q^24 - 370 * q^25 - 511 * q^26 - 65 * q^27 + 70 * q^28 - 187 * q^29 + 84 * q^30 + 1276 * q^31 + 1399 * q^32 - 23 * q^33 - 765 * q^34 - 805 * q^35 - 1691 * q^36 - 1531 * q^37 - 1041 * q^38 - 1351 * q^39 - 1759 * q^40 - 301 * q^41 + 3395 * q^42 - 257 * q^43 - 883 * q^44 + 3105 * q^45 + 1593 * q^46 + 733 * q^47 - 1948 * q^48 + 1288 * q^49 + 6148 * q^50 + 1197 * q^51 - 1099 * q^52 - 285 * q^53 + 660 * q^54 + 2641 * q^55 - 1988 * q^56 - 2352 * q^57 + 1173 * q^58 - 3603 * q^59 - 175 * q^60 - 2613 * q^61 - 1927 * q^62 - 3066 * q^63 + 1589 * q^64 - 371 * q^65 - 2175 * q^66 + 352 * q^67 + 6076 * q^68 + 5549 * q^69 - 6293 * q^70 - 2623 * q^71 + 6220 * q^72 + 2039 * q^73 - 2411 * q^74 - 3903 * q^75 + 4130 * q^76 + 1029 * q^77 - 3759 * q^78 + 44 * q^79 - 1608 * q^80 + 1394 * q^81 - 10920 * q^82 - 553 * q^83 - 7798 * q^84 + 497 * q^85 - 2985 * q^86 - 4273 * q^87 - 2197 * q^88 - 3957 * q^89 - 2958 * q^90 + 14119 * q^91 - 9136 * q^92 + 6272 * q^93 + 14912 * q^94 + 5866 * q^95 + 21882 * q^96 - 1540 * q^97 - 2303 * q^98 + 10768 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more