LMFDB - Embedded newform 49.4.e.a.36.3

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			36.3
Character	$\chi$	$=$	49.36
Dual form			49.4.e.a.15.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.846844 - 3.71026i) q^{2} +(3.04811 + 3.82222i) q^{3} +(-5.84116 + 2.81296i) q^{4} +(-12.1071 - 15.1818i) q^{5} +(11.6002 - 14.5461i) q^{6} +(13.1709 - 13.0203i) q^{7} +(-3.59906 - 4.51308i) q^{8} +(0.689741 - 3.02195i) q^{9} +O(q^{10})$	\(q+(-0.846844 - 3.71026i) q^{2} +(3.04811 + 3.82222i) q^{3} +(-5.84116 + 2.81296i) q^{4} +(-12.1071 - 15.1818i) q^{5} +(11.6002 - 14.5461i) q^{6} +(13.1709 - 13.0203i) q^{7} +(-3.59906 - 4.51308i) q^{8} +(0.689741 - 3.02195i) q^{9} +(-46.0758 + 57.7772i) q^{10} +(3.84932 + 16.8650i) q^{11} +(-28.5563 - 13.7520i) q^{12} +(6.63306 + 29.0614i) q^{13} +(-59.4623 - 37.8414i) q^{14} +(21.1244 - 92.5519i) q^{15} +(-46.0346 + 57.7255i) q^{16} +(30.1062 + 14.4984i) q^{17} -11.7963 q^{18} +122.424 q^{19} +(113.425 + 54.6228i) q^{20} +(89.9127 + 10.6547i) q^{21} +(59.3138 - 28.5640i) q^{22} +(35.7422 - 17.2126i) q^{23} +(6.27961 - 27.5128i) q^{24} +(-56.0909 + 245.750i) q^{25} +(102.208 - 49.2208i) q^{26} +(132.579 - 63.8465i) q^{27} +(-40.3079 + 113.103i) q^{28} +(-257.246 - 123.883i) q^{29} -361.281 q^{30} +61.6857 q^{31} +(211.555 + 101.879i) q^{32} +(-52.7284 + 66.1193i) q^{33} +(28.2976 - 123.980i) q^{34} +(-357.133 - 42.3206i) q^{35} +(4.47173 + 19.5919i) q^{36} +(34.5744 + 16.6502i) q^{37} +(-103.674 - 454.225i) q^{38} +(-90.8604 + 113.935i) q^{39} +(-24.9426 + 109.281i) q^{40} +(312.646 + 392.045i) q^{41} +(-36.6101 - 342.623i) q^{42} +(-51.8869 + 65.0641i) q^{43} +(-69.9250 - 87.6831i) q^{44} +(-54.2296 + 26.1156i) q^{45} +(-94.1312 - 118.037i) q^{46} +(-5.83314 - 25.5567i) q^{47} -360.958 q^{48} +(3.94526 - 342.977i) q^{49} +959.298 q^{50} +(36.3512 + 159.265i) q^{51} +(-120.493 - 151.094i) q^{52} +(386.317 - 186.040i) q^{53} +(-349.161 - 437.834i) q^{54} +(209.437 - 262.626i) q^{55} +(-106.164 - 12.5806i) q^{56} +(373.162 + 467.930i) q^{57} +(-241.792 + 1059.36i) q^{58} +(106.826 - 133.956i) q^{59} +(136.954 + 600.033i) q^{60} +(-542.207 - 261.113i) q^{61} +(-52.2381 - 228.870i) q^{62} +(-30.2621 - 48.7825i) q^{63} +(67.4092 - 295.339i) q^{64} +(360.897 - 452.551i) q^{65} +(289.973 + 139.644i) q^{66} -606.739 q^{67} -216.639 q^{68} +(174.736 + 84.1487i) q^{69} +(145.415 + 1360.90i) q^{70} +(-278.882 + 134.302i) q^{71} +(-16.1207 + 7.76334i) q^{72} +(0.148211 - 0.649355i) q^{73} +(32.4974 - 142.380i) q^{74} +(-1110.28 + 534.683i) q^{75} +(-715.097 + 344.373i) q^{76} +(270.286 + 172.008i) q^{77} +(499.675 + 240.631i) q^{78} +50.9424 q^{79} +1433.72 q^{80} +(572.747 + 275.820i) q^{81} +(1189.83 - 1492.00i) q^{82} +(-221.685 + 971.268i) q^{83} +(-555.166 + 190.684i) q^{84} +(-144.387 - 632.601i) q^{85} +(285.345 + 137.415i) q^{86} +(-310.608 - 1360.86i) q^{87} +(62.2590 - 78.0704i) q^{88} +(225.975 - 990.060i) q^{89} +(142.820 + 179.090i) q^{90} +(465.750 + 296.400i) q^{91} +(-160.358 + 201.083i) q^{92} +(188.025 + 235.776i) q^{93} +(-89.8822 + 43.2850i) q^{94} +(-1482.20 - 1858.62i) q^{95} +(255.438 + 1119.15i) q^{96} -66.6277 q^{97} +(-1275.88 + 275.810i) q^{98} +53.6202 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 $\left(\mathbb{Z}/49\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{7}\right)$

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 $

$2$	−0.846844	−	3.71026i	−0.299404	−	1.31178i	−0.871017	−	0.491253i	$-0.836539\pi$
$2$	−0.846844	−	3.71026i	−0.299404	−	1.31178i	0.571613	−	0.820524i	$-0.306318\pi$
$3$	3.04811	+	3.82222i	0.586610	+	0.735586i	0.983224	−	0.182400i	$-0.0583865\pi$
$3$	3.04811	+	3.82222i	0.586610	+	0.735586i	−0.396615	+	0.917985i	$0.629815\pi$
$4$	−5.84116	+	2.81296i	−0.730146	+	0.351620i
$5$	−12.1071	−	15.1818i	−1.08289	−	1.35790i	−0.929112	−	0.369799i	$-0.879426\pi$
$5$	−12.1071	−	15.1818i	−1.08289	−	1.35790i	−0.153781	−	0.988105i	$-0.549145\pi$
$6$	11.6002	−	14.5461i	0.789290	−	0.989739i
$7$	13.1709	−	13.0203i	0.711162	−	0.703028i
$7$	13.1709	−	13.0203i	0.711162	−	0.703028i
$8$	−3.59906	−	4.51308i	−0.159057	−	0.199452i
$9$	0.689741	−	3.02195i	0.0255460	−	0.111924i
$10$	−46.0758	+	57.7772i	−1.45704	+	1.82708i
$11$	3.84932	+	16.8650i	0.105510	+	0.462271i	0.999888	+	0.0149587i	$0.00476167\pi$
$11$	3.84932	+	16.8650i	0.105510	+	0.462271i	−0.894378	+	0.447312i	$0.852381\pi$
$12$	−28.5563	−	13.7520i	−0.686957	−	0.330821i
$13$	6.63306	+	29.0614i	0.141514	+	0.620013i	0.995084	+	0.0990349i	$0.0315756\pi$
$13$	6.63306	+	29.0614i	0.141514	+	0.620013i	−0.853570	+	0.520978i	$0.825567\pi$
$14$	−59.4623	−	37.8414i	−1.13514	−	0.722395i
$15$	21.1244	−	92.5519i	0.363619	−	1.59312i
$16$	−46.0346	+	57.7255i	−0.719290	+	0.901961i
$17$	30.1062	+	14.4984i	0.429519	+	0.206845i	0.636137	−	0.771576i	$-0.280531\pi$
$17$	30.1062	+	14.4984i	0.429519	+	0.206845i	−0.206618	+	0.978422i	$0.566246\pi$
$18$	−11.7963			−0.154468
$19$	122.424			1.47821			0.739104	−	0.673592i	$-0.235249\pi$
$19$	122.424			1.47821			0.739104	+	0.673592i	$0.235249\pi$
$20$	113.425	+	54.6228i	1.26813	+	0.610702i
$21$	89.9127	+	10.6547i	0.934312	+	0.110717i
$22$	59.3138	−	28.5640i	0.574806	−	0.276812i
$23$	35.7422	−	17.2126i	0.324033	−	0.156046i	−0.264794	−	0.964305i	$-0.585304\pi$
$23$	35.7422	−	17.2126i	0.324033	−	0.156046i	0.588828	+	0.808259i	$0.299590\pi$
$24$	6.27961	−	27.5128i	0.0534092	−	0.234001i
$25$	−56.0909	+	245.750i	−0.448727	+	1.96600i
$26$	102.208	−	49.2208i	0.770949	−	0.371269i
$27$	132.579	−	63.8465i	0.944991	−	0.455084i
$28$	−40.3079	+	113.103i	−0.272053	+	0.763371i
$29$	−257.246	−	123.883i	−1.64722	−	0.793260i	−0.999508	−	0.0313759i	$-0.990011\pi$
$29$	−257.246	−	123.883i	−1.64722	−	0.793260i	−0.647714	−	0.761884i	$-0.724275\pi$
$30$	−361.281			−2.19869
$31$	61.6857			0.357389			0.178695	−	0.983905i	$-0.442813\pi$
$31$	61.6857			0.357389			0.178695	+	0.983905i	$0.442813\pi$
$32$	211.555	+	101.879i	1.16869	+	0.562809i
$33$	−52.7284	+	66.1193i	−0.278147	+	0.348785i
$34$	28.2976	−	123.980i	0.142735	−	0.625363i
$35$	−357.133	−	42.3206i	−1.72476	−	0.204385i
$36$	4.47173	+	19.5919i	0.0207025	+	0.0907034i
$37$	34.5744	+	16.6502i	0.153622	+	0.0739802i	0.509115	−	0.860699i	$-0.329973\pi$
$37$	34.5744	+	16.6502i	0.153622	+	0.0739802i	−0.355493	+	0.934679i	$0.615687\pi$
$38$	−103.674	−	454.225i	−0.442582	−	1.93908i
$39$	−90.8604	+	113.935i	−0.373059	+	0.467801i
$40$	−24.9426	+	109.281i	−0.0985943	+	0.431970i
$41$	312.646	+	392.045i	1.19090	+	1.49335i	0.827270	+	0.561804i	$0.189893\pi$
$41$	312.646	+	392.045i	1.19090	+	1.49335i	0.363634	+	0.931542i	$0.381536\pi$
$42$	−36.6101	−	342.623i	−0.134501	−	1.25876i
$43$	−51.8869	+	65.0641i	−0.184016	+	0.230748i	−0.865280	−	0.501289i	$-0.832859\pi$
$43$	−51.8869	+	65.0641i	−0.184016	+	0.230748i	0.681264	+	0.732038i	$0.261431\pi$
$44$	−69.9250	−	87.6831i	−0.239582	−	0.300426i
$45$	−54.2296	+	26.1156i	−0.179646	+	0.0865129i
$46$	−94.1312	−	118.037i	−0.301715	−	0.378339i
$47$	−5.83314	−	25.5567i	−0.0181032	−	0.0793154i	0.965069	−	0.261994i	$-0.0843802\pi$
$47$	−5.83314	−	25.5567i	−0.0181032	−	0.0793154i	−0.983173	+	0.182679i	$0.941523\pi$
$48$	−360.958			−1.08541
$49$	3.94526	−	342.977i	0.0115022	−	0.999934i
$50$	959.298			2.71330
$51$	36.3512	+	159.265i	0.0998076	+	0.437286i
$52$	−120.493	−	151.094i	−0.321334	−	0.402941i
$53$	386.317	−	186.040i	1.00122	−	0.482163i	0.139868	−	0.990170i	$-0.455332\pi$
$53$	386.317	−	186.040i	1.00122	−	0.482163i	0.861353	+	0.508007i	$0.169618\pi$
$54$	−349.161	−	437.834i	−0.879903	−	1.10336i
$55$	209.437	−	262.626i	0.513464	−	0.643863i
$56$	−106.164	−	12.5806i	−0.253336	−	0.0300206i
$57$	373.162	+	467.930i	0.867131	+	1.08735i
$58$	−241.792	+	1059.36i	−0.547394	+	2.39829i
$59$	106.826	−	133.956i	0.235722	−	0.295586i	−0.649874	−	0.760042i	$-0.725179\pi$
$59$	106.826	−	133.956i	0.235722	−	0.295586i	0.885596	+	0.464456i	$0.153750\pi$
$60$	136.954	+	600.033i	0.294677	+	1.29107i
$61$	−542.207	−	261.113i	−1.13807	−	0.548067i	−0.232643	−	0.972562i	$-0.574737\pi$
$61$	−542.207	−	261.113i	−1.13807	−	0.548067i	−0.905430	+	0.424495i	$0.860452\pi$
$62$	−52.2381	−	228.870i	−0.107004	−	0.468815i
$63$	−30.2621	−	48.7825i	−0.0605186	−	0.0975558i
$64$	67.4092	−	295.339i	0.131659	−	0.576834i
$65$	360.897	−	452.551i	0.688674	−	0.863570i
$66$	289.973	+	139.644i	0.540806	+	0.260438i
$67$	−606.739			−1.10634			−0.553171	−	0.833068i	$-0.686583\pi$
$67$	−606.739			−1.10634			−0.553171	+	0.833068i	$0.686583\pi$
$68$	−216.639			−0.386342
$69$	174.736	+	84.1487i	0.304867	+	0.146816i
$70$	145.415	+	1360.90i	0.248292	+	2.32369i
$71$	−278.882	+	134.302i	−0.466158	+	0.224490i	−0.652192	−	0.758054i	$-0.726151\pi$
$71$	−278.882	+	134.302i	−0.466158	+	0.224490i	0.186035	+	0.982543i	$0.440436\pi$
$72$	−16.1207	+	7.76334i	−0.0263868	+	0.0127072i
$73$	0.148211	−	0.649355i	0.000237627	−	0.00104111i	−0.974809	−	0.223041i	$-0.928401\pi$
$73$	0.148211	−	0.649355i	0.000237627	−	0.00104111i	0.975047	+	0.222000i	$0.0712586\pi$
$74$	32.4974	−	142.380i	0.0510506	−	0.223667i
$75$	−1110.28	+	534.683i	−1.70939	+	0.823199i
$76$	−715.097	+	344.373i	−1.07931	+	0.519767i
$77$	270.286	+	172.008i	0.400025	+	0.254573i
$78$	499.675	+	240.631i	0.725347	+	0.349308i
$79$	50.9424			0.0725503			0.0362751	−	0.999342i	$-0.488451\pi$
$79$	50.9424			0.0725503			0.0362751	+	0.999342i	$0.488451\pi$
$80$	1433.72			2.00369
$81$	572.747	+	275.820i	0.785661	+	0.378354i
$82$	1189.83	−	1492.00i	1.60237	−	2.00931i
$83$	−221.685	+	971.268i	−0.293170	+	1.28446i	0.586915	+	0.809648i	$0.300342\pi$
$83$	−221.685	+	971.268i	−0.293170	+	1.28446i	−0.880086	+	0.474815i	$0.842515\pi$
$84$	−555.166	+	190.684i	−0.721114	+	0.247683i
$85$	−144.387	−	632.601i	−0.184247	−	0.807237i
$86$	285.345	+	137.415i	0.357786	+	0.172300i
$87$	−310.608	−	1360.86i	−0.382766	−	1.67701i
$88$	62.2590	−	78.0704i	0.0754186	−	0.0945719i
$89$	225.975	−	990.060i	0.269138	−	1.17917i	−0.641881	−	0.766804i	$-0.721846\pi$
$89$	225.975	−	990.060i	0.269138	−	1.17917i	0.911019	−	0.412365i	$-0.135297\pi$
$90$	142.820	+	179.090i	0.167272	+	0.209753i
$91$	465.750	+	296.400i	0.536526	+	0.341441i
$92$	−160.358	+	201.083i	−0.181723	+	0.227873i
$93$	188.025	+	235.776i	0.209648	+	0.262891i
$94$	−89.8822	+	43.2850i	−0.0986239	+	0.0474948i
$95$	−1482.20	−	1858.62i	−1.60074	−	2.00726i
$96$	255.438	+	1119.15i	0.271568	+	1.18982i
$97$	−66.6277			−0.0697424			−0.0348712	−	0.999392i	$-0.511102\pi$
$97$	−66.6277			−0.0697424			−0.0348712	+	0.999392i	$0.511102\pi$
$98$	−1275.88	+	275.810i	−1.31513	+	0.284296i
$99$	53.6202			0.0544347
$100$	−363.648	−	1593.25i	−0.363648	−	1.59325i
$101$	36.2815	+	45.4955i	0.0357440	+	0.0448215i	0.799382	−	0.600823i	$-0.205160\pi$
$101$	36.2815	+	45.4955i	0.0357440	+	0.0448215i	−0.763638	+	0.645644i	$0.776589\pi$
$102$	560.132	−	269.745i	0.543738	−	0.261850i
$103$	1134.28	+	1422.34i	1.08509	+	1.36066i	0.927789	+	0.373105i	$0.121707\pi$
$103$	1134.28	+	1422.34i	1.08509	+	1.36066i	0.157298	+	0.987551i	$0.449722\pi$
$104$	107.283	−	134.529i	0.101154	−	0.126843i
$105$	−926.824	−	1494.04i	−0.861417	−	1.38860i
$106$	−1017.41	−	1275.79i	−0.932260	−	1.16902i
$107$	−356.316	+	1561.12i	−0.321928	+	1.41046i	0.512189	+	0.858873i	$0.328835\pi$
$107$	−356.316	+	1561.12i	−0.321928	+	1.41046i	−0.834117	+	0.551587i	$0.814022\pi$
$108$	−594.816	+	745.876i	−0.529965	+	0.664555i
$109$	−117.936	−	516.713i	−0.103635	−	0.454057i	−0.999944	−	0.0106248i	$-0.996618\pi$
$109$	−117.936	−	516.713i	−0.103635	−	0.454057i	0.896308	−	0.443432i	$-0.146239\pi$
$110$	−1151.77	−	554.664i	−0.998338	−	0.480774i
$111$	41.7463	+	182.902i	0.0356971	+	0.156399i
$112$	145.285	+	1359.68i	0.122573	+	1.14712i
$113$	−296.598	+	1299.48i	−0.246917	+	1.08181i	0.687654	+	0.726038i	$0.258641\pi$
$113$	−296.598	+	1299.48i	−0.246917	+	1.08181i	−0.934571	+	0.355776i	$0.884217\pi$
$114$	1420.13	−	1780.79i	1.16673	−	1.46304i
$115$	−694.053	−	334.238i	−0.562789	−	0.271025i
$116$	1851.10			1.48164
$117$	92.3972			0.0730096
$118$	−587.477	−	282.914i	−0.458319	−	0.220715i
$119$	585.298	−	201.034i	0.450876	−	0.154863i
$120$	−493.722	+	237.764i	−0.375587	+	0.180873i
$121$	929.579	−	447.662i	0.698407	−	0.336335i
$122$	−509.634	+	2232.85i	−0.378197	+	1.65699i
$123$	−545.502	+	2390.00i	−0.399888	+	1.75202i
$124$	−360.316	+	173.519i	−0.260946	+	0.125665i
$125$	2223.13	−	1070.60i	1.59074	−	0.766060i
$126$	−155.369	+	153.592i	−0.109852	+	0.108595i
$127$	−1025.24	−	493.729i	−0.716340	−	0.344971i	0.0399553	−	0.999201i	$-0.487278\pi$
$127$	−1025.24	−	493.729i	−0.716340	−	0.344971i	−0.756295	+	0.654230i	$0.772993\pi$
$128$	725.592			0.501046
$129$	−406.846			−0.277681
$130$	−1984.71	−	955.785i	−1.33900	−	0.644830i
$131$	412.407	−	517.143i	0.275055	−	0.344908i	−0.625047	−	0.780587i	$-0.714920\pi$
$131$	412.407	−	517.143i	0.275055	−	0.344908i	0.900102	+	0.435679i	$0.143492\pi$
$132$	122.004	−	534.537i	0.0804479	−	0.352465i
$133$	1612.43	−	1593.99i	1.05124	−	1.03922i
$134$	513.813	+	2251.16i	0.331244	+	1.45127i
$135$	−2574.45	−	1239.79i	−1.64128	−	0.790401i
$136$	−42.9217	−	188.052i	−0.0270625	−	0.118569i
$137$	−1341.36	+	1682.02i	−0.836500	+	1.04894i	0.161571	+	0.986861i	$0.448344\pi$
$137$	−1341.36	+	1682.02i	−0.836500	+	1.04894i	−0.998071	+	0.0620770i	$0.980228\pi$
$138$	164.239	−	719.579i	0.101311	−	0.443874i
$139$	−581.649	−	729.365i	−0.354927	−	0.445064i	0.572030	−	0.820233i	$-0.306156\pi$
$139$	−581.649	−	729.365i	−0.354927	−	0.445064i	−0.926957	+	0.375169i	$0.877585\pi$
$140$	2205.12	−	757.398i	1.33119	−	0.457227i
$141$	79.9030	−	100.195i	0.0477237	−	0.0598437i
$142$	734.467	+	920.992i	0.434050	+	0.544281i
$143$	−464.586	+	223.733i	−0.271683	+	0.130836i
$144$	142.692	+	178.930i	0.0825763	+	0.103547i
$145$	1233.73	+	5405.34i	0.706592	+	3.09578i
$146$	−2.53479			−0.00143686
$147$	1322.96	−	1030.35i	0.742284	−	0.578110i
$148$	−248.791			−0.138179
$149$	283.905	+	1243.87i	0.156096	+	0.683903i	0.991040	+	0.133567i	$0.0426432\pi$
$149$	283.905	+	1243.87i	0.156096	+	0.683903i	−0.834943	+	0.550336i	$0.814500\pi$
$150$	2924.05	+	3666.64i	1.59165	+	1.99587i
$151$	2347.31	−	1130.40i	1.26504	−	0.609211i	0.323537	−	0.946215i	$-0.395128\pi$
$151$	2347.31	−	1130.40i	1.26504	−	0.609211i	0.941503	+	0.337004i	$0.109414\pi$
$152$	−440.611	−	552.508i	−0.235120	−	0.294831i
$153$	64.5789	−	80.9794i	0.0341235	−	0.0427895i
$154$	409.305	−	1148.49i	0.214173	−	0.600963i
$155$	−746.835	−	936.502i	−0.387014	−	0.485301i
$156$	210.235	−	921.101i	0.107899	−	0.472738i
$157$	−1043.84	+	1308.93i	−0.530621	+	0.665377i	−0.972826	−	0.231536i	$-0.925625\pi$
$157$	−1043.84	+	1308.93i	−0.530621	+	0.665377i	0.442205	+	0.896914i	$0.354196\pi$
$158$	−43.1403	−	189.010i	−0.0217219	−	0.0951697i
$159$	1888.62	+	909.514i	0.941998	+	0.453642i
$160$	−1014.60	−	4445.25i	−0.501320	−	2.19642i
$161$	246.645	−	692.078i	0.120735	−	0.338779i
$162$	538.339	−	2358.62i	0.261086	−	1.14389i
$163$	−1161.19	+	1456.08i	−0.557982	+	0.699688i	−0.978183	−	0.207743i	$-0.933388\pi$
$163$	−1161.19	+	1456.08i	−0.557982	+	0.699688i	0.420201	+	0.907431i	$0.361960\pi$
$164$	−2929.02	−	1410.54i	−1.39462	−	0.671615i
$165$	1642.20			0.774819
$166$	3791.39			1.77271
$167$	−827.079	−	398.300i	−0.383241	−	0.184559i	0.232336	−	0.972635i	$-0.425363\pi$
$167$	−827.079	−	398.300i	−0.383241	−	0.184559i	−0.615578	+	0.788076i	$0.711077\pi$
$168$	−275.515	−	444.130i	−0.126527	−	0.203961i
$169$	1178.86	−	567.711i	0.536579	−	0.258403i
$170$	−2224.84	+	1071.43i	−1.00375	+	0.483381i
$171$	84.4407	−	369.959i	0.0377622	−	0.165447i
$172$	120.057	−	526.006i	0.0532226	−	0.233184i
$173$	−2079.01	+	1001.20i	−0.913665	+	0.439998i	−0.830805	−	0.556563i	$-0.812120\pi$
$173$	−2079.01	+	1001.20i	−0.913665	+	0.439998i	−0.0828597	+	0.996561i	$0.526405\pi$
$174$	−4786.12	+	2304.87i	−2.08526	+	1.00421i
$175$	2460.97	+	3967.07i	1.06304	+	1.71361i
$176$	−1150.74	−	554.168i	−0.492843	−	0.237341i
$177$	837.627			0.355706
$178$	−3864.75			−1.62739
$179$	−3037.02	−	1462.55i	−1.26814	−	0.610706i	−0.325827	−	0.945429i	$-0.605643\pi$
$179$	−3037.02	−	1462.55i	−1.26814	−	0.610706i	−0.942316	+	0.334723i	$0.891357\pi$
$180$	243.302	−	305.091i	0.100748	−	0.126334i
$181$	−419.555	+	1838.19i	−0.172294	+	0.754870i	0.812756	+	0.582604i	$0.197966\pi$
$181$	−419.555	+	1838.19i	−0.172294	+	0.754870i	−0.985050	+	0.172266i	$0.944891\pi$
$182$	705.305	−	1979.06i	0.287256	−	0.806031i
$183$	−654.678	−	2868.33i	−0.264455	−	1.15865i
$184$	−206.320	−	99.3585i	−0.0826637	−	0.0398087i
$185$	−165.816	−	726.488i	−0.0658975	−	0.288716i
$186$	715.563	−	897.288i	0.282084	−	0.353722i
$187$	−128.626	+	563.549i	−0.0503000	+	0.220379i
$188$	105.962	+	132.872i	0.0411068	+	0.0515463i
$189$	914.881	−	2567.12i	0.352105	−	0.987994i
$190$	−5640.77	+	7073.30i	−2.15381	+	2.70080i
$191$	−2095.21	−	2627.31i	−0.793738	−	0.995316i	−0.999859	−	0.0167898i	$-0.994655\pi$
$191$	−2095.21	−	2627.31i	−0.793738	−	0.995316i	0.206121	−	0.978527i	$-0.433916\pi$
$192$	1334.32	−	642.575i	0.501543	−	0.241530i
$193$	163.821	+	205.425i	0.0610990	+	0.0766157i	0.811442	−	0.584433i	$-0.198683\pi$
$193$	163.821	+	205.425i	0.0610990	+	0.0766157i	−0.750343	+	0.661049i	$0.770112\pi$
$194$	56.4232	+	247.206i	0.0208812	+	0.0914865i
$195$	2829.80			1.03921
$196$	941.735	+	2014.48i	0.343198	+	0.734142i
$197$	2786.75			1.00786			0.503929	−	0.863745i	$-0.331887\pi$
$197$	2786.75			1.00786			0.503929	+	0.863745i	$0.331887\pi$
$198$	−45.4079	−	198.945i	−0.0162980	−	0.0714062i
$199$	2958.73	+	3710.13i	1.05396	+	1.32163i	0.944815	+	0.327604i	$0.106241\pi$
$199$	2958.73	+	3710.13i	1.05396	+	1.32163i	0.109149	+	0.994025i	$0.465187\pi$
$200$	1310.96	−	631.327i	0.463496	−	0.223208i
$201$	−1849.41	−	2319.09i	−0.648992	−	0.813810i
$202$	138.076	−	173.141i	0.0480939	−	0.0603079i
$203$	−5001.16	+	1717.76i	−1.72912	+	0.593907i
$204$	−660.339	−	828.039i	−0.226632	−	0.284188i
$205$	2166.73	−	9493.07i	0.738200	−	3.23427i
$206$	4316.71	−	5412.98i	1.46000	−	1.83078i
$207$	−27.3626	−	119.884i	−0.00918761	−	0.0402535i
$208$	−1982.93	−	954.930i	−0.661017	−	0.318329i
$209$	471.248	+	2064.67i	0.155966	+	0.683333i
$210$	−4758.40	+	4703.98i	−1.56362	+	1.54574i
$211$	317.135	−	1389.46i	0.103471	−	0.453338i	−0.896476	−	0.443092i	$-0.853882\pi$
$211$	317.135	−	1389.46i	0.103471	−	0.453338i	0.999948	−	0.0102457i	$-0.00326135\pi$
$212$	−1733.22	+	2173.39i	−0.561499	+	0.704098i
$213$	−1363.40	−	656.577i	−0.438584	−	0.211211i
$214$	6093.91			1.94659
$215$	1615.99			0.512604
$216$	−765.303	−	368.550i	−0.241075	−	0.116096i
$217$	812.456	−	803.164i	0.254162	−	0.251255i
$218$	−1817.27	+	875.151i	−0.564592	+	0.271893i
$219$	2.93374	−	1.41282i	0.000905223	−	0.000435932i
$220$	−484.602	+	2123.18i	−0.148508	+	0.650658i
$221$	−221.646	+	971.095i	−0.0674640	+	0.295579i
$222$	643.264	−	309.779i	0.194473	−	0.0936533i
$223$	2454.23	−	1181.89i	0.736983	−	0.354912i	−0.0274432	−	0.999623i	$-0.508737\pi$
$223$	2454.23	−	1181.89i	0.736983	−	0.354912i	0.764426	+	0.644711i	$0.223022\pi$
$224$	4112.86	−	1412.66i	1.22680	−	0.421371i
$225$	703.957	+	339.008i	0.208580	+	0.100447i
$226$	5072.60			1.49303
$227$	2063.91			0.603466			0.301733	−	0.953393i	$-0.402435\pi$
$227$	2063.91			0.603466			0.301733	+	0.953393i	$0.402435\pi$
$228$	−3495.97	−	1683.57i	−1.01546	−	0.489022i
$229$	−918.672	+	1151.98i	−0.265099	+	0.332423i	−0.896509	−	0.443026i	$-0.853905\pi$
$229$	−918.672	+	1151.98i	−0.265099	+	0.332423i	0.631410	+	0.775449i	$0.282476\pi$
$230$	−652.358	+	2858.17i	−0.187023	+	0.819400i
$231$	166.411	+	1557.39i	0.0473984	+	0.443587i
$232$	366.750	+	1606.84i	0.103786	+	0.454715i
$233$	3651.17	+	1758.31i	1.02659	+	0.494380i	0.869880	−	0.493264i	$-0.164196\pi$
$233$	3651.17	+	1758.31i	1.02659	+	0.494380i	0.156712	+	0.987644i	$0.449911\pi$
$234$	−78.2459	−	342.818i	−0.0218594	−	0.0957723i
$235$	−317.375	+	397.975i	−0.0880989	+	0.110473i
$236$	−247.178	+	1082.96i	−0.0681775	+	0.298705i
$237$	155.278	+	194.713i	0.0425587	+	0.0533669i
$238$	−1241.55	−	2001.37i	−0.338140	−	0.545081i
$239$	−890.104	+	1116.15i	−0.240904	+	0.302084i	−0.887555	−	0.460702i	$-0.847598\pi$
$239$	−890.104	+	1116.15i	−0.240904	+	0.302084i	0.646651	+	0.762786i	$0.276169\pi$
$240$	4370.16	+	5480.00i	1.17538	+	1.47389i
$241$	−2171.23	+	1045.61i	−0.580338	+	0.279476i	−0.700934	−	0.713226i	$-0.747233\pi$
$241$	−2171.23	+	1045.61i	−0.580338	+	0.279476i	0.120597	+	0.992702i	$0.461519\pi$
$242$	−2448.15	−	3069.89i	−0.650302	−	0.815453i
$243$	−192.540	−	843.574i	−0.0508291	−	0.222697i
$244$	3901.62			1.02367
$245$	−5254.79	+	4092.57i	−1.37027	+	1.06720i
$246$	9329.48			2.41799
$247$	812.045	+	3557.80i	0.209187	+	0.916508i
$248$	−222.010	−	278.392i	−0.0568455	−	0.0712820i
$249$	−4388.12	+	2113.21i	−1.11681	+	0.537827i
$250$	−5854.85	−	7341.75i	−1.48117	−	1.85733i
$251$	−717.588	+	899.827i	−0.180453	+	0.226281i	−0.863828	−	0.503786i	$-0.831940\pi$
$251$	−717.588	+	899.827i	−0.180453	+	0.226281i	0.683375	+	0.730067i	$0.260511\pi$
$252$	313.989	+	199.820i	0.0784899	+	0.0499504i
$253$	427.873	+	536.535i	0.106325	+	0.133327i
$254$	−963.648	+	4222.02i	−0.238050	+	1.04296i
$255$	1977.83	−	2480.12i	0.485711	−	0.609063i
$256$	−1153.74	−	5054.85i	−0.281674	−	1.23409i
$257$	311.415	+	149.969i	0.0755856	+	0.0364001i	0.471295	−	0.881976i	$-0.343787\pi$
$257$	311.415	+	149.969i	0.0755856	+	0.0364001i	−0.395709	+	0.918376i	$0.629501\pi$
$258$	344.535	+	1509.51i	0.0831388	+	0.364255i
$259$	672.166	−	230.870i	0.161260	−	0.0553884i
$260$	−835.055	+	3658.61i	−0.199184	+	0.872683i
$261$	−551.803	+	691.939i	−0.130865	+	0.164099i
$262$	−2267.98	−	1092.20i	−0.534795	−	0.257544i
$263$	−3737.45			−0.876278			−0.438139	−	0.898907i	$-0.644362\pi$
$263$	−3737.45			−0.876278			−0.438139	+	0.898907i	$0.644362\pi$
$264$	488.174			0.113807
$265$	−7501.62	−	3612.59i	−1.73895	−	0.837432i
$266$	−7279.60	−	4632.69i	−1.67797	−	1.06785i
$267$	4473.02	−	2154.09i	1.02526	−	0.493739i
$268$	3544.06	−	1706.73i	0.807791	−	0.389012i
$269$	−771.060	+	3378.24i	−0.174767	+	0.765705i	0.809226	+	0.587498i	$0.199887\pi$
$269$	−771.060	+	3378.24i	−0.174767	+	0.765705i	−0.983993	+	0.178207i	$0.942970\pi$
$270$	−2419.79	+	10601.8i	−0.545421	+	2.38965i
$271$	−944.254	+	454.729i	−0.211658	+	0.101929i	−0.536709	−	0.843767i	$-0.680333\pi$
$271$	−944.254	+	454.729i	−0.211658	+	0.101929i	0.325051	+	0.945696i	$0.394618\pi$
$272$	−2222.85	+	1070.47i	−0.495515	+	0.238628i
$273$	286.755	+	2683.66i	0.0635722	+	0.594954i
$274$	7376.66	+	3552.41i	1.62642	+	0.783245i
$275$	−4360.48			−0.956171
$276$	−1257.37			−0.274220
$277$	1040.34	+	501.003i	0.225661	+	0.108673i	0.543299	−	0.839540i	$-0.317175\pi$
$277$	1040.34	+	501.003i	0.225661	+	0.108673i	−0.317637	+	0.948212i	$0.602889\pi$
$278$	−2213.57	+	2775.73i	−0.477558	+	0.598839i
$279$	42.5472	−	186.411i	0.00912986	−	0.0400005i
$280$	1094.35	+	1764.08i	0.233570	+	0.376515i
$281$	−2011.57	−	8813.29i	−0.427048	−	1.87102i	−0.487943	−	0.872876i	$-0.662253\pi$
$281$	−2011.57	−	8813.29i	−0.427048	−	1.87102i	0.0608948	−	0.998144i	$-0.480605\pi$
$282$	−439.416	−	211.612i	−0.0927902	−	0.0446854i
$283$	−1664.17	−	7291.20i	−0.349557	−	1.53151i	−0.778190	−	0.628029i	$-0.783862\pi$
$283$	−1664.17	−	7291.20i	−0.349557	−	1.53151i	0.428633	−	0.903479i	$-0.358995\pi$
$284$	1251.21	−	1568.96i	0.261428	−	0.327820i
$285$	2586.13	−	11330.6i	0.537505	−	2.35496i
$286$	1223.54	+	1534.27i	0.252970	+	0.317215i
$287$	9222.36	+	1092.86i	1.89679	+	0.224772i
$288$	453.793	−	569.038i	0.0928472	−	0.116427i
$289$	−2367.03	−	2968.16i	−0.481788	−	0.604143i
$290$	19010.4	−	9154.95i	3.84942	−	1.85378i
$291$	−203.089	−	254.665i	−0.0409116	−	0.0513015i
$292$	0.960883	+	4.20990i	0.000192573	+	0.000843719i
$293$	4346.45			0.866629			0.433314	−	0.901243i	$-0.357344\pi$
$293$	4346.45			0.866629			0.433314	+	0.901243i	$0.357344\pi$
$294$	−4943.23	−	4035.98i	−0.980595	−	0.800622i
$295$	−3327.05			−0.656639
$296$	−49.2919	−	215.962i	−0.00967917	−	0.0424072i
$297$	1587.11	+	1990.17i	0.310079	+	0.388826i
$298$	4374.65	−	2106.72i	0.850392	−	0.409527i
$299$	737.301	+	924.546i	0.142606	+	0.178822i
$300$	4981.29	−	6246.35i	0.958651	−	1.20211i
$301$	163.755	+	1532.53i	0.0313577	+	0.293468i
$302$	−6181.90	−	7751.85i	−1.17791	−	1.47705i
$303$	−63.3036	+	277.351i	−0.0120023	+	0.0525855i
$304$	−5635.72	+	7066.98i	−1.06326	+	1.33329i
$305$	2600.38	+	11393.0i	0.488188	+	2.13889i
$306$	−355.143	−	171.028i	−0.0663470	−	0.0319510i
$307$	−287.652	−	1260.28i	−0.0534760	−	0.234294i	0.941126	−	0.338056i	$-0.109769\pi$
$307$	−287.652	−	1260.28i	−0.0534760	−	0.234294i	−0.994602	+	0.103762i	$0.966912\pi$
$308$	−2062.63	−	244.424i	−0.381589	−	0.0452187i
$309$	−1979.08	+	8670.93i	−0.364356	+	1.59635i
$310$	−2842.22	+	3564.03i	−0.520732	+	0.652978i
$311$	−3068.19	−	1477.56i	−0.559424	−	0.269405i	0.132732	−	0.991152i	$-0.457625\pi$
$311$	−3068.19	−	1477.56i	−0.559424	−	0.269405i	−0.692157	+	0.721747i	$0.743339\pi$
$312$	841.211			0.152642
$313$	−4532.98			−0.818591			−0.409296	−	0.912402i	$-0.634226\pi$
$313$	−4532.98			−0.818591			−0.409296	+	0.912402i	$0.634226\pi$
$314$	5740.46	+	2764.46i	1.03170	+	0.496839i
$315$	−374.220	+	1050.05i	−0.0669363	+	0.187821i
$316$	−297.563	+	143.299i	−0.0529722	+	0.0255101i
$317$	−8173.17	+	3935.99i	−1.44811	+	0.697373i	−0.982266	−	0.187494i	$-0.939964\pi$
$317$	−8173.17	+	3935.99i	−1.44811	+	0.697373i	−0.465844	+	0.884867i	$0.654249\pi$
$318$	1775.17	−	7777.51i	0.313039	−	1.37151i
$319$	1099.06	−	4815.32i	0.192902	−	0.845160i
$320$	−5299.92	+	2552.31i	−0.925858	+	0.445870i
$321$	−7053.03	+	3396.56i	−1.22636	+	0.590584i
$322$	−2776.66	−	329.037i	−0.480551	−	0.0569458i
$323$	3685.71	+	1774.95i	0.634918	+	0.305761i
$324$	−4121.38			−0.706684
$325$	−7513.89			−1.28245
$326$	6385.79	+	3075.23i	1.08490	+	0.522458i
$327$	1615.51	−	2025.78i	0.273204	−	0.342587i
$328$	644.101	−	2821.99i	0.108428	−	0.475056i
$329$	−409.583	−	260.655i	−0.0686353	−	0.0436790i
$330$	−1390.69	−	6093.00i	−0.231984	−	1.01639i
$331$	−5079.20	−	2446.01i	−0.843438	−	0.406178i	−0.0383003	−	0.999266i	$-0.512194\pi$
$331$	−5079.20	−	2446.01i	−0.843438	−	0.406178i	−0.805138	+	0.593088i	$0.797909\pi$
$332$	−1437.23	−	6296.93i	−0.237585	−	1.04093i
$333$	74.1634	−	92.9980i	0.0122046	−	0.0153041i
$334$	−777.392	+	3405.98i	−0.127356	+	0.557985i
$335$	7345.85	+	9211.41i	1.19805	+	1.50231i
$336$	−4754.14	+	4699.77i	−0.771904	+	0.763076i
$337$	7432.57	−	9320.14i	1.20142	−	1.50653i	0.391300	−	0.920263i	$-0.372026\pi$
$337$	7432.57	−	9320.14i	1.20142	−	1.50653i	0.810118	−	0.586267i	$-0.199403\pi$
$338$	−3104.67	−	3893.13i	−0.499621	−	0.626505i
$339$	−5870.97	+	2827.31i	−0.940611	+	0.452974i
$340$	2622.87	+	3288.97i	0.418367	+	0.524616i
$341$	237.448	+	1040.33i	0.0377083	+	0.165211i
$342$	−1444.15			−0.228336
$343$	−4413.69	−	4568.69i	−0.694802	−	0.719201i
$344$	480.384			0.0752923
$345$	−838.023	−	3671.62i	−0.130776	−	0.572966i
$346$	5475.30	+	6865.81i	0.850734	+	1.06679i
$347$	2070.30	−	997.005i	0.320287	−	0.154242i	−0.266831	−	0.963743i	$-0.585977\pi$
$347$	2070.30	−	997.005i	0.320287	−	0.154242i	0.587118	+	0.809501i	$0.300262\pi$
$348$	5642.35	+	7075.28i	0.869143	+	1.08987i
$349$	−1580.88	+	1982.36i	−0.242472	+	0.304050i	−0.888145	−	0.459564i	$-0.848006\pi$
$349$	−1580.88	+	1982.36i	−0.242472	+	0.304050i	0.645673	+	0.763614i	$0.276577\pi$
$350$	12634.8	−	12490.3i	1.92960	−	1.90753i
$351$	2734.87	+	3429.42i	0.415887	+	0.521506i
$352$	−903.851	+	3960.03i	−0.136862	+	0.599632i
$353$	−4072.62	+	5106.90i	−0.614061	+	0.770008i	−0.987495	−	0.157649i	$-0.949609\pi$
$353$	−4072.62	+	5106.90i	−0.614061	+	0.770008i	0.373434	+	0.927657i	$0.378180\pi$
$354$	−709.339	−	3107.82i	−0.106500	−	0.466606i
$355$	5415.41	+	2607.92i	0.809634	+	0.389899i
$356$	1465.04	+	6418.76i	0.218109	+	0.955600i
$357$	2552.45	+	1624.36i	0.378404	+	0.240813i
$358$	−2854.57	+	12506.7i	−0.421422	+	1.84637i
$359$	1588.55	−	1991.98i	0.233539	−	0.292848i	−0.651228	−	0.758882i	$-0.725746\pi$
$359$	1588.55	−	1991.98i	0.233539	−	0.292848i	0.884767	+	0.466034i	$0.154317\pi$
$360$	313.037	+	150.751i	0.0458292	+	0.0220702i
$361$	8128.58			1.18510
$362$	7175.46			1.04181
$363$	4544.52	+	2188.53i	0.657095	+	0.316440i
$364$	−3554.28	−	421.186i	−0.511800	−	0.0606488i
$365$	−11.6528	+	5.61170i	−0.00167106	+	0.000804739i
$366$	−10087.9	+	4858.06i	−1.44071	+	0.693811i
$367$	−396.908	+	1738.97i	−0.0564535	+	0.247339i	−0.995279	−	0.0970538i	$-0.969058\pi$
$367$	−396.908	+	1738.97i	−0.0564535	+	0.247339i	0.938826	+	0.344393i	$0.111915\pi$
$368$	−651.775	+	2855.61i	−0.0923263	+	0.404508i
$369$	1400.39	−	674.391i	0.197564	−	0.0951420i
$370$	−2555.04	+	1230.44i	−0.359001	+	0.172886i
$371$	2665.85	−	7480.27i	0.373056	−	1.04678i
$372$	−1761.51	−	848.300i	−0.245511	−	0.118232i
$373$	−673.736			−0.0935248			−0.0467624	−	0.998906i	$-0.514890\pi$
$373$	−673.736			−0.0935248			−0.0467624	+	0.998906i	$0.514890\pi$
$374$	2199.84			0.304147
$375$	10868.4	+	5233.95i	1.49665	+	0.720747i
$376$	−94.3454	+	118.305i	−0.0129401	+	0.0162264i
$377$	1893.88	−	8297.65i	0.258727	−	1.13356i
$378$	−10299.5	−	1220.50i	−1.40145	−	0.166073i
$379$	−909.196	−	3983.45i	−0.123225	−	0.539884i	−0.998424	−	0.0561207i	$-0.982127\pi$
$379$	−909.196	−	3983.45i	−0.123225	−	0.539884i	0.875199	−	0.483763i	$-0.160730\pi$
$380$	13886.0	+	6687.13i	1.87457	+	0.902744i
$381$	−1237.91	−	5423.62i	−0.166456	−	0.729293i
$382$	−7973.70	+	9998.70i	−1.06798	+	1.33921i
$383$	32.7234	−	143.370i	0.00436576	−	0.0191276i	−0.972698	−	0.232074i	$-0.925449\pi$
$383$	32.7234	−	143.370i	0.00436576	−	0.0191276i	0.977064	+	0.212946i	$0.0683060\pi$
$384$	2211.69	+	2773.37i	0.293919	+	0.368562i
$385$	−660.983	−	6185.95i	−0.0874982	−	0.818870i
$386$	623.451	−	781.782i	0.0822093	−	0.103087i
$387$	160.832	+	201.677i	0.0211255	+	0.0264905i
$388$	389.183	−	187.421i	0.0509221	−	0.0245228i
$389$	−1893.53	−	2374.42i	−0.246802	−	0.309480i	0.642965	−	0.765896i	$-0.277704\pi$
$389$	−1893.53	−	2374.42i	−0.246802	−	0.309480i	−0.889766	+	0.456416i	$0.849133\pi$
$390$	−2396.40	−	10499.3i	−0.311145	−	1.36321i
$391$	1325.62			0.171456
$392$	−1562.08	+	1216.59i	−0.201268	+	0.156753i
$393$	3233.70			0.415059
$394$	−2359.94	−	10339.6i	−0.301757	−	1.32208i
$395$	−616.765	−	773.399i	−0.0785641	−	0.0985163i
$396$	−313.205	+	150.831i	−0.0397453	+	0.0191403i
$397$	4110.63	+	5154.57i	0.519664	+	0.651638i	0.970538	−	0.240950i	$-0.0774589\pi$
$397$	4110.63	+	5154.57i	0.519664	+	0.651638i	−0.450874	+	0.892588i	$0.648888\pi$
$398$	11260.0	−	14119.6i	1.41812	−	1.77827i
$399$	11007.5	+	1304.39i	1.38111	+	0.163663i
$400$	−11603.9	−	14550.9i	−1.45049	−	1.81886i
$401$	−1128.10	+	4942.51i	−0.140485	+	0.615505i	0.854838	+	0.518896i	$0.173657\pi$
$401$	−1128.10	+	4942.51i	−0.140485	+	0.615505i	−0.995322	+	0.0966088i	$0.969200\pi$
$402$	−7038.26	+	8825.70i	−0.873225	+	1.09499i
$403$	409.165	+	1792.67i	0.0505756	+	0.221586i
$404$	−339.903	−	163.689i	−0.0418584	−	0.0201580i
$405$	−2746.85	−	12034.7i	−0.337017	−	1.47657i
$406$	10608.5	+	17100.9i	1.29678	+	2.09041i
$407$	−147.717	+	647.188i	−0.0179903	+	0.0788205i
$408$	587.945	−	737.260i	0.0713423	−	0.0894604i
$409$	9356.48	+	4505.84i	1.13117	+	0.544742i	0.903326	−	0.428955i	$-0.141118\pi$
$409$	9356.48	+	4505.84i	1.13117	+	0.544742i	0.227844	+	0.973698i	$0.426832\pi$
$410$	−37056.7			−4.46366
$411$	−10517.7			−1.26228
$412$	−10626.5	−	5117.46i	−1.27070	−	0.611939i
$413$	−337.144	−	3155.23i	−0.0401689	−	0.375929i
$414$	−421.628	+	203.045i	−0.0500528	+	0.0241042i
$415$	17429.6	−	8393.65i	2.06165	−	0.992839i
$416$	−1557.50	+	6823.84i	−0.183564	+	0.804245i
$417$	1014.86	−	4446.38i	0.119179	−	0.522158i
$418$	7261.41	−	3496.91i	0.849683	−	0.409186i
$419$	2572.78	−	1238.98i	0.299972	−	0.144459i	−0.277843	−	0.960626i	$-0.589620\pi$
$419$	2572.78	−	1238.98i	0.299972	−	0.144459i	0.577815	+	0.816167i	$0.303905\pi$
$420$	9616.39	+	6119.80i	1.11722	+	0.710990i
$421$	6087.70	+	2931.68i	0.704742	+	0.339386i	0.751695	−	0.659511i	$-0.229237\pi$
$421$	6087.70	+	2931.68i	0.704742	+	0.339386i	−0.0469524	+	0.998897i	$0.514951\pi$
$422$	−5423.82			−0.625657
$423$	−81.2544			−0.00933978
$424$	−2229.99	−	1073.91i	−0.255420	−	0.123004i
$425$	−5251.66	+	6585.37i	−0.599395	+	0.751618i
$426$	−1281.49	+	5614.58i	−0.145748	+	0.638562i
$427$	−10541.1	+	3620.58i	−1.19466	+	0.410333i
$428$	−2310.07	−	10121.1i	−0.260891	−	1.14304i
$429$	−2271.27	−	1093.79i	−0.255613	−	0.123097i
$430$	−1368.49	−	5995.76i	−0.153476	−	0.672421i
$431$	6680.67	−	8377.30i	0.746628	−	0.936242i	−0.252884	−	0.967497i	$-0.581379\pi$
$431$	6680.67	−	8377.30i	0.746628	−	0.936242i	0.999511	+	0.0312550i	$0.00995041\pi$
$432$	−2417.63	+	10592.3i	−0.269255	+	1.17968i
$433$	−3413.28	−	4280.11i	−0.378826	−	0.475033i	0.555467	−	0.831538i	$-0.312539\pi$
$433$	−3413.28	−	4280.11i	−0.378826	−	0.475033i	−0.934293	+	0.356506i	$0.883968\pi$
$434$	−3667.97	−	2334.27i	−0.405687	−	0.258177i
$435$	−16899.8	+	21191.7i	−1.86272	+	2.33578i
$436$	2142.38	+	2686.46i	0.235324	+	0.295087i
$437$	4375.70	−	2107.23i	0.478989	−	0.230669i
$438$	−7.72634	−	9.68852i	−0.000842874	−	0.00105693i
$439$	−2482.38	−	10876.0i	−0.269880	−	1.18242i	−0.910152	−	0.414274i	$-0.864036\pi$
$439$	−2482.38	−	10876.0i	−0.269880	−	1.18242i	0.640272	−	0.768148i	$-0.278822\pi$
$440$	−1939.03			−0.210090
$441$	−1033.74	−	248.488i	−0.111623	−	0.0268317i
$442$	3790.72			0.407932
$443$	4101.24	+	17968.7i	0.439855	+	1.92713i	0.368341	+	0.929691i	$0.379926\pi$
$443$	4101.24	+	17968.7i	0.439855	+	1.92713i	0.0715136	+	0.997440i	$0.477217\pi$
$444$	−758.343	−	950.932i	−0.0810572	−	0.101642i
$445$	−17766.8	+	8556.05i	−1.89265	+	0.911451i
$446$	−6463.49	−	8104.95i	−0.686222	−	0.860495i
$447$	−3888.95	+	4876.59i	−0.411502	+	0.516007i
$448$	−2957.55	−	4767.57i	−0.311900	−	0.502782i
$449$	802.419	+	1006.20i	0.0843396	+	0.105758i	0.822211	−	0.569183i	$-0.192740\pi$
$449$	802.419	+	1006.20i	0.0843396	+	0.105758i	−0.737871	+	0.674941i	$0.764169\pi$
$450$	661.667	−	2898.95i	0.0693140	−	0.303684i
$451$	−5408.36	+	6781.87i	−0.564678	+	0.708084i
$452$	−1922.91	−	8424.81i	−0.200102	−	0.876703i
$453$	11475.5	+	5526.31i	1.19021	+	0.573176i
$454$	−1747.81	−	7657.66i	−0.180680	−	0.791612i
$455$	−1138.99	−	10659.5i	−0.117355	−	1.09830i
$456$	768.773	−	3368.22i	0.0789498	−	0.345902i
$457$	6691.66	−	8391.07i	0.684951	−	0.858901i	−0.310849	−	0.950459i	$-0.600613\pi$
$457$	6691.66	−	8391.07i	0.684951	−	0.858901i	0.995800	+	0.0915583i	$0.0291848\pi$
$458$	5052.12	+	2432.97i	0.515436	+	0.248221i
$459$	4917.11			0.500024
$460$	4994.28			0.506216
$461$	−4476.80	−	2155.91i	−0.452289	−	0.217811i	0.193849	−	0.981031i	$-0.437903\pi$
$461$	−4476.80	−	2155.91i	−0.452289	−	0.217811i	−0.646138	+	0.763220i	$0.723617\pi$
$462$	5637.40	−	1936.29i	0.567696	−	0.194988i
$463$	3088.30	−	1487.25i	0.309990	−	0.149283i	−0.272420	−	0.962178i	$-0.587824\pi$
$463$	3088.30	−	1487.25i	0.309990	−	0.149283i	0.582410	+	0.812895i	$0.302110\pi$
$464$	18993.4	−	9146.76i	1.90032	−	0.915146i
$465$	1303.07	−	5709.13i	0.129954	−	0.569364i
$466$	3431.82	−	15035.8i	0.341151	−	1.49468i
$467$	4178.60	−	2012.31i	0.414053	−	0.199397i	−0.215248	−	0.976560i	$-0.569056\pi$
$467$	4178.60	−	2012.31i	0.414053	−	0.199397i	0.629300	+	0.777162i	$0.283342\pi$
$468$	−539.707	+	259.909i	−0.0533076	+	0.0256716i
$469$	−7991.30	+	7899.90i	−0.786789	+	0.777790i
$470$	1745.36	+	840.521i	0.171292	+	0.0824901i
$471$	−8184.77			−0.800710
$472$	−989.028			−0.0964485
$473$	−1297.03	−	624.619i	−0.126084	−	0.0607188i
$474$	590.940	−	741.015i	0.0572632	−	0.0718058i
$475$	−6866.86	+	30085.7i	−0.663311	+	2.90616i
$476$	−2853.32	+	2820.69i	−0.274752	+	0.271610i
$477$	−295.747	−	1295.75i	−0.0283885	−	0.124378i
$478$	4895.01	+	2357.31i	0.468394	+	0.225567i
$479$	1440.84	+	6312.74i	0.137440	+	0.602164i	0.995992	+	0.0894383i	$0.0285072\pi$
$479$	1440.84	+	6312.74i	0.137440	+	0.602164i	−0.858552	+	0.512726i	$0.828636\pi$
$480$	13898.1	−	17427.7i	1.32158	−	1.65721i
$481$	−254.542	+	1115.22i	−0.0241291	+	0.105717i
$482$	5718.18	+	7170.38i	0.540365	+	0.677597i
$483$	3397.08	−	1166.80i	0.320025	−	0.109920i
$484$	−4170.57	+	5229.73i	−0.391677	+	0.491147i
$485$	806.668	+	1011.53i	0.0755236	+	0.0947035i
$486$	−2966.83	+	1428.75i	−0.276910	+	0.133353i
$487$	5437.46	+	6818.36i	0.505944	+	0.634434i	0.967559	−	0.252647i	$-0.0813010\pi$
$487$	5437.46	+	6818.36i	0.505944	+	0.634434i	−0.461614	+	0.887081i	$0.652730\pi$
$488$	773.011	+	3386.78i	0.0717061	+	0.314165i
$489$	−9104.88			−0.841998
$490$	19634.5	+	16030.9i	1.81020	+	1.47796i
$491$	−2527.73			−0.232331			−0.116166	−	0.993230i	$-0.537060\pi$
$491$	−2527.73			−0.232331			−0.116166	+	0.993230i	$0.537060\pi$
$492$	−3536.60	−	15494.8i	−0.324069	−	1.41984i
$493$	−5948.60	−	7459.30i	−0.543431	−	0.681440i
$494$	12512.7	−	6025.80i	1.13962	−	0.548813i
$495$	−649.186	−	814.053i	−0.0589469	−	0.0739171i
$496$	−2839.67	+	3560.84i	−0.257067	+	0.322351i
$497$	−1924.47	+	5400.00i	−0.173691	+	0.487370i
$498$	11556.6	+	14491.5i	1.03989	+	1.30398i
$499$	−220.332	+	965.337i	−0.0197664	+	0.0866021i	−0.983849	−	0.179000i	$-0.942714\pi$
$499$	−220.332	+	965.337i	−0.0197664	+	0.0866021i	0.964083	+	0.265602i	$0.0855708\pi$
$500$	−9974.09	+	12507.1i	−0.892110	+	1.11867i
$501$	−998.642	−	4375.34i	−0.0890540	−	0.390171i
$502$	3946.28	+	1900.43i	0.350859	+	0.168965i
$503$	−2321.79	−	10172.4i	−0.205813	−	0.901724i	−0.967318	−	0.253566i	$-0.918397\pi$
$503$	−2321.79	−	10172.4i	−0.205813	−	0.901724i	0.761506	−	0.648158i	$-0.224460\pi$
$504$	−111.244	+	312.146i	−0.00983174	+	0.0275875i
$505$	251.442	−	1101.64i	0.0221565	−	0.0970738i
$506$	1628.35	−	2041.88i	0.143061	−	0.179393i
$507$	5763.22	+	2775.42i	0.504840	+	0.243118i
$508$	7377.42			0.644331
$509$	92.7155			0.00807375			0.00403688	−	0.999992i	$-0.498715\pi$
$509$	92.7155			0.00807375			0.00403688	+	0.999992i	$0.498715\pi$
$510$	−10876.8	−	5237.99i	−0.944378	−	0.454788i
$511$	−6.50271	−	10.4823i	−0.000562941	−	0.000907459i
$512$	−12547.9	+	6042.76i	−1.08309	+	0.521591i
$513$	16230.8	−	7816.33i	1.39689	−	0.672708i
$514$	292.707	−	1282.43i	0.0251182	−	0.110050i
$515$	7860.91	−	34440.9i	0.672608	−	2.94689i
$516$	2376.46	−	1144.44i	0.202747	−	0.0976380i
$517$	408.559	−	196.752i	0.0347551	−	0.0167372i
$518$	−1425.81	−	2298.40i	−0.120939	−	0.194954i
$519$	−10163.8	−	4894.65i	−0.859621	−	0.413972i
$520$	−3341.29			−0.281779
$521$	13205.3			1.11043			0.555217	−	0.831705i	$-0.312635\pi$
$521$	13205.3			1.11043			0.555217	+	0.831705i	$0.312635\pi$
$522$	3034.57	+	1461.37i	0.254443	+	0.122533i
$523$	−10429.3	+	13077.9i	−0.871972	+	1.09342i	0.122914	+	0.992417i	$0.460776\pi$
$523$	−10429.3	+	13077.9i	−0.871972	+	1.09342i	−0.994886	+	0.101001i	$0.967795\pi$
$524$	−954.240	+	4180.80i	−0.0795538	+	0.348548i
$525$	−7661.68	+	21498.4i	−0.636921	+	1.78718i
$526$	3165.04	+	13866.9i	0.262361	+	1.14948i
$527$	1857.12	+	894.342i	0.153506	+	0.0739244i
$528$	−1389.44	−	6087.55i	−0.114522	−	0.501755i
$529$	−6604.77	+	8282.11i	−0.542843	+	0.680703i
$530$	−7050.96	+	30892.3i	−0.577876	+	2.53184i
$531$	−331.126	−	415.219i	−0.0270615	−	0.0339340i
$532$	−4934.65	+	13846.5i	−0.402151	+	1.12842i
$533$	−9319.57	+	11686.4i	−0.757365	+	0.949705i
$534$	−11780.2	−	14771.9i	−0.954642	−	1.19708i
$535$	28014.6	−	13491.1i	2.26388	−	1.09023i
$536$	2183.69	+	2738.26i	0.175972	+	0.220662i
$537$	−3667.00	−	16066.2i	−0.294679	−	1.29107i
$538$	13187.1			1.05676
$539$	5799.49	−	1253.69i	0.463454	−	0.100186i
$540$	18525.3			1.47630
$541$	2415.74	+	10584.0i	0.191979	+	0.841116i	0.975544	+	0.219805i	$0.0705422\pi$
$541$	2415.74	+	10584.0i	0.191979	+	0.841116i	−0.783565	+	0.621310i	$0.786601\pi$
$542$	2486.80	+	3118.35i	0.197080	+	0.247130i
$543$	−8304.80	+	3999.38i	−0.656341	+	0.316077i
$544$	4892.02	+	6134.40i	0.385558	+	0.483474i
$545$	−6416.79	+	8046.40i	−0.504339	+	0.632422i
$546$	9714.24	−	3336.58i	0.761412	−	0.261524i
$547$	−12057.3	−	15119.4i	−0.942472	−	1.18182i	−0.983178	−	0.182652i	$-0.941532\pi$
$547$	−12057.3	−	15119.4i	−0.942472	−	1.18182i	0.0407052	−	0.999171i	$-0.487040\pi$
$548$	3103.69	−	13598.1i	0.241940	−	1.06001i
$549$	−1163.05	+	1458.42i	−0.0904152	+	0.113377i
$550$	3692.65	+	16178.5i	0.286282	+	1.25428i
$551$	−31493.0	−	15166.3i	−2.43493	−	1.17260i
$552$	−249.118	−	1091.46i	−0.0192086	−	0.0841584i
$553$	670.958	−	663.284i	0.0515950	−	0.0510049i
$554$	977.845	−	4284.22i	0.0749903	−	0.328554i
$555$	2271.37	−	2848.20i	0.173719	−	0.217837i
$556$	5449.18	+	2624.19i	0.415642	+	0.200162i
$557$	2284.42			0.173778			0.0868889	−	0.996218i	$-0.472307\pi$
$557$	2284.42			0.173778			0.0868889	+	0.996218i	$0.472307\pi$
$558$	−727.666			−0.0552053
$559$	−2235.02	−	1076.33i	−0.169108	−	0.0814381i
$560$	18883.4	−	18667.5i	1.42495	−	1.40865i
$561$	−2546.07	+	1226.12i	−0.191614	+	0.0922763i
$562$	−30996.1	+	14926.9i	−2.32650	+	1.12038i
$563$	1347.54	−	5903.96i	0.100874	−	0.441958i	−0.899117	−	0.437708i	$-0.855790\pi$
$563$	1347.54	−	5903.96i	0.100874	−	0.441958i	0.999991	−	0.00424928i	$-0.00135259\pi$
$564$	−184.882	+	810.020i	−0.0138031	+	0.0604752i
$565$	23319.5	−	11230.1i	1.73638	−	0.836199i
$566$	−25643.0	+	12349.0i	−1.90434	+	0.917080i
$567$	11134.8	−	3824.51i	0.824726	−	0.283271i
$568$	1609.83	+	775.253i	0.118921	+	0.0572692i
$569$	6409.87			0.472259			0.236130	−	0.971722i	$-0.424121\pi$
$569$	6409.87			0.472259			0.236130	+	0.971722i	$0.424121\pi$
$570$	−44229.4			−3.25012
$571$	−15843.3	−	7629.74i	−1.16116	−	0.559185i	−0.248792	−	0.968557i	$-0.580034\pi$
$571$	−15843.3	−	7629.74i	−1.16116	−	0.559185i	−0.912368	+	0.409372i	$0.865748\pi$
$572$	2084.37	−	2613.72i	0.152364	−	0.191058i
$573$	3655.70	−	16016.7i	0.266526	−	1.16773i
$574$	−3755.10	−	35142.9i	−0.273057	−	2.55546i
$575$	2225.17	+	9749.12i	0.161385	+	0.707072i
$576$	−846.006	−	407.415i	−0.0611984	−	0.0294716i
$577$	987.411	+	4326.13i	0.0712417	+	0.312130i	0.997976	−	0.0635863i	$-0.0202538\pi$
$577$	987.411	+	4326.13i	0.0712417	+	0.312130i	−0.926735	+	0.375716i	$0.877397\pi$
$578$	−9008.14	+	11295.9i	−0.648251	+	0.812882i
$579$	−285.834	+	1252.32i	−0.0205161	+	0.0898870i
$580$	−22411.4	−	28103.0i	−1.60445	−	2.01192i
$581$	9726.37	+	15678.9i	0.694523	+	1.11957i
$582$	−772.891	+	969.175i	−0.0550470	+	0.0690268i
$583$	4624.63	+	5799.10i	0.328529	+	0.411962i
$584$	−3.46401	+	1.66818i	−0.000245448	+	0.000118202i
$585$	−1118.66	−	1402.76i	−0.0790615	−	0.0991400i
$586$	−3680.76	−	16126.5i	−0.259472	−	1.13682i
$587$	−2816.42			−0.198034			−0.0990172	−	0.995086i	$-0.531570\pi$
$587$	−2816.42			−0.198034			−0.0990172	+	0.995086i	$0.531570\pi$
$588$	−4829.28	+	9739.90i	−0.338701	+	0.683106i
$589$	7551.79			0.528296
$590$	2817.49	+	12344.2i	0.196601	+	0.861364i
$591$	8494.34	+	10651.6i	0.591219	+	0.741366i
$592$	−2552.76	+	1229.34i	−0.177226	+	0.0853474i
$593$	16538.1	+	20738.2i	1.14526	+	1.43611i	0.881914	+	0.471410i	$0.156255\pi$
$593$	16538.1	+	20738.2i	1.14526	+	1.43611i	0.263346	+	0.964701i	$0.415174\pi$
$594$	6040.02	−	7573.95i	0.417214	−	0.523170i
$595$	−10138.3	−	6451.96i	−0.698540	−	0.444546i
$596$	−5157.28	−	6467.02i	−0.354447	−	0.444462i
$597$	−5162.37	+	22617.8i	−0.353906	+	1.55056i
$598$	2805.93	−	3518.53i	0.191878	−	0.240607i
$599$	−2949.94	−	12924.5i	−0.201221	−	0.881605i	−0.970195	−	0.242325i	$-0.922090\pi$
$599$	−2949.94	−	12924.5i	−0.201221	−	0.881605i	0.768974	−	0.639280i	$-0.220767\pi$
$600$	6409.04	+	3086.43i	0.436080	+	0.210005i
$601$	−4203.97	−	18418.8i	−0.285331	−	1.25012i	−0.890855	−	0.454288i	$-0.849894\pi$
$601$	−4203.97	−	18418.8i	−0.285331	−	1.25012i	0.605524	−	0.795827i	$-0.292964\pi$
$602$	5547.43	−	1905.39i	0.375576	−	0.129000i
$603$	−418.493	+	1833.54i	−0.0282626	+	0.123827i
$604$	−10531.2	+	13205.7i	−0.709453	+	0.889626i
$605$	−18050.8	−	8692.83i	−1.21301	−	0.584155i
$606$	1082.65			0.0725740
$607$	−5674.11			−0.379415			−0.189708	−	0.981841i	$-0.560754\pi$
$607$	−5674.11			−0.379415			−0.189708	+	0.981841i	$0.560754\pi$
$608$	25899.3	+	12472.5i	1.72756	+	0.831949i
$609$	−21809.7	−	13879.6i	−1.45119	−	0.923528i
$610$	40069.0	−	19296.2i	2.65958	−	1.28079i
$611$	704.020	−	339.038i	0.0466147	−	0.0224485i
$612$	−149.424	+	654.672i	−0.00986949	+	0.0432411i
$613$	781.757	−	3425.10i	0.0515087	−	0.225675i	−0.942622	−	0.333863i	$-0.891648\pi$
$613$	781.757	−	3425.10i	0.0515087	−	0.225675i	0.994130	+	0.108188i	$0.0345049\pi$
$614$	−4432.39	+	2134.53i	−0.291330	+	0.140297i
$615$	42889.0	−	20654.3i	2.81212	−	1.35424i
$616$	−196.489	−	1838.89i	−0.0128519	−	0.120277i
$617$	−6936.29	−	3340.34i	−0.452584	−	0.217953i	0.193683	−	0.981064i	$-0.437957\pi$
$617$	−6936.29	−	3340.34i	−0.452584	−	0.217953i	−0.646267	+	0.763111i	$0.723671\pi$
$618$	33847.4			2.20314
$619$	−12790.2			−0.830501			−0.415251	−	0.909707i	$-0.636306\pi$
$619$	−12790.2			−0.830501			−0.415251	+	0.909707i	$0.636306\pi$
$620$	6996.72	+	3369.44i	0.453218	+	0.218258i
$621$	3639.69	−	4564.03i	0.235195	−	0.294925i
$622$	−2883.87	+	12635.0i	−0.185904	+	0.814500i
$623$	−9914.55	−	15982.2i	−0.637589	−	1.02779i
$624$	−2394.26	−	10489.9i	−0.153601	−	0.672970i
$625$	−14780.9	−	7118.10i	−0.945977	−	0.455559i
$626$	3838.72	+	16818.5i	0.245090	+	1.07381i
$627$	−6455.21	+	8094.58i	−0.411158	+	0.515576i
$628$	2415.27	−	10582.0i	0.153471	−	0.672399i
$629$	799.503	+	1002.55i	0.0506809	+	0.0635518i
$630$	4212.87	+	499.229i	0.266420	+	0.0315710i
$631$	11815.0	−	14815.5i	0.745400	−	0.934702i	−0.254072	−	0.967185i	$-0.581770\pi$
$631$	11815.0	−	14815.5i	0.745400	−	0.934702i	0.999472	+	0.0324829i	$0.0103415\pi$
$632$	−183.345	−	229.907i	−0.0115397	−	0.0144703i
$633$	6277.47	−	3023.07i	0.394166	−	0.189820i
$634$	21525.0	+	26991.4i	1.34837	+	1.69080i
$635$	4916.96	+	21542.6i	0.307281	+	1.34629i
$636$	−13590.2			−0.847305
$637$	9993.55	−	2160.34i	0.621600	−	0.134373i
$638$	−18796.8			−1.16642
$639$	213.499	+	935.402i	0.0132174	+	0.0579091i
$640$	−8784.82	−	11015.8i	−0.542579	−	0.680373i
$641$	−13377.0	+	6442.01i	−0.824273	+	0.396949i	−0.797964	−	0.602705i	$-0.794090\pi$
$641$	−13377.0	+	6442.01i	−0.824273	+	0.396949i	−0.0263086	+	0.999654i	$0.508375\pi$
$642$	18574.9	+	23292.2i	1.14189	+	1.43189i
$643$	−2565.55	+	3217.09i	−0.157349	+	0.197309i	−0.854257	−	0.519852i	$-0.825987\pi$
$643$	−2565.55	+	3217.09i	−0.157349	+	0.197309i	0.696908	+	0.717161i	$0.254559\pi$
$644$	506.090	+	4736.35i	0.0309670	+	0.289811i
$645$	4925.73	+	6176.67i	0.300698	+	0.377064i
$646$	3464.30	−	15178.1i	0.210992	−	0.924417i
$647$	10884.3	−	13648.5i	0.661370	−	0.829332i	−0.332121	−	0.943237i	$-0.607764\pi$
$647$	10884.3	−	13648.5i	0.661370	−	0.829332i	0.993492	+	0.113905i	$0.0363358\pi$
$648$	−816.551	−	3577.55i	−0.0495018	−	0.216882i
$649$	2670.37	+	1285.98i	0.161512	+	0.0777801i
$650$	6363.09	+	27878.5i	0.383970	+	1.68228i
$651$	5546.32	+	657.245i	0.333913	+	0.0395691i
$652$	2686.79	−	11771.6i	0.161384	−	0.707071i
$653$	4061.31	−	5092.73i	0.243387	−	0.305197i	−0.645101	−	0.764097i	$-0.723185\pi$
$653$	4061.31	−	5092.73i	0.243387	−	0.305197i	0.888488	+	0.458900i	$0.151756\pi$
$654$	−8884.26	−	4278.43i	−0.531196	−	0.255810i
$655$	−12844.2			−0.766207
$656$	−37023.5			−2.20355
$657$	−1.86009	−	0.895774i	−0.000110455	−	5.31925e-5i
$658$	−620.248	+	1740.39i	−0.0367474	+	0.103112i
$659$	−27315.7	+	13154.6i	−1.61467	+	0.777586i	−0.999938	−	0.0111465i	$-0.996452\pi$
$659$	−27315.7	+	13154.6i	−1.61467	+	0.777586i	−0.614736	+	0.788733i	$0.710738\pi$
$660$	−9592.37	+	4619.44i	−0.565731	+	0.272442i
$661$	−450.379	+	1973.24i	−0.0265018	+	0.116112i	−0.986449	−	0.164070i	$-0.947538\pi$
$661$	−450.379	+	1973.24i	−0.0265018	+	0.116112i	0.959947	+	0.280182i	$0.0903949\pi$
$662$	−4774.07	+	20916.6i	−0.280286	+	1.22801i
$663$	−4387.34	+	2112.83i	−0.256999	+	0.123764i
$664$	5181.27	−	2495.17i	0.302819	−	0.145830i
$665$	−43721.6	−	5181.05i	−2.54955	−	0.302124i
$666$	−407.852	−	196.411i	−0.0237296	−	0.0114276i
$667$	−11326.9			−0.657540
$668$	5951.50			0.344716
$669$	11998.2	+	5778.04i	0.693390	+	0.333919i
$670$	27956.0	−	35055.7i	1.61199	−	2.02137i
$671$	2316.54	−	10149.4i	0.133277	−	0.583925i
$672$	17935.9	+	11414.3i	1.02960	+	0.655233i
$673$	3304.35	+	14477.3i	0.189262	+	0.829211i	0.977007	+	0.213209i	$0.0683916\pi$
$673$	3304.35	+	14477.3i	0.189262	+	0.829211i	−0.787744	+	0.616002i	$0.788751\pi$
$674$	−40874.4	−	19684.1i	−2.33594	−	1.12493i
$675$	8253.84	+	36162.4i	0.470652	+	2.06206i
$676$	−5288.99	+	6632.18i	−0.300921	+	0.377343i
$677$	3928.23	−	17210.7i	0.223005	−	0.977047i	−0.732198	−	0.681092i	$-0.761505\pi$
$677$	3928.23	−	17210.7i	0.223005	−	0.977047i	0.955202	−	0.295954i	$-0.0956377\pi$
$678$	15461.9	+	19388.5i	0.875824	+	1.09825i
$679$	−877.547	+	867.510i	−0.0495982	+	0.0490309i
$680$	−2335.32	+	2928.40i	−0.131699	+	0.165145i
$681$	6291.04	+	7888.72i	0.353999	+	0.443901i
$682$	3658.81	−	1761.99i	0.205430	−	0.0989297i
$683$	11684.8	+	14652.3i	0.654622	+	0.820870i	0.992746	−	0.120232i	$-0.0383638\pi$
$683$	11684.8	+	14652.3i	0.654622	+	0.820870i	−0.338124	+	0.941102i	$0.609792\pi$
$684$	547.446	+	2398.52i	0.0306025	+	0.134078i
$685$	41776.2			2.33020
$686$	−13213.3	+	20244.9i	−0.735404	+	1.12676i
$687$	−7203.33			−0.400035
$688$	−1367.27	−	5990.40i	−0.0757655	−	0.331950i
$689$	7969.05	+	9992.88i	0.440634	+	0.552537i
$690$	−12913.0	+	6218.57i	−0.712448	+	0.343097i
$691$	−13200.6	−	16553.0i	−0.726736	−	0.911299i	0.271962	−	0.962308i	$-0.412328\pi$
$691$	−13200.6	−	16553.0i	−0.726736	−	0.911299i	−0.998698	+	0.0510095i	$0.983756\pi$
$692$	9327.50	−	11696.3i	0.512396	−	0.642525i
$693$	706.227	−	698.150i	0.0387119	−	0.0382691i
$694$	−5452.37	−	6837.06i	−0.298227	−	0.373964i
$695$	−4031.01	+	17661.0i	−0.220007	+	0.963913i
$696$	−5023.77	+	6299.61i	−0.273600	+	0.343084i
$697$	3728.55	+	16335.8i	0.202624	+	0.887754i
$698$	8693.85	+	4186.74i	0.471443	+	0.227035i
$699$	4408.54	+	19315.1i	0.238550	+	1.04515i
$700$	−25534.1	−	16249.7i	−1.37871	−	0.877402i
$701$	−2452.05	+	10743.1i	−0.132115	+	0.578834i	0.864922	+	0.501907i	$0.167368\pi$
$701$	−2452.05	+	10743.1i	−0.132115	+	0.578834i	−0.997037	+	0.0769268i	$0.975489\pi$
$702$	10408.0	−	13051.3i	0.559581	−	0.701693i
$703$	4232.73	+	2038.37i	0.227085	+	0.109358i
$704$	5240.37			0.280545
$705$	−2488.54			−0.132942
$706$	22396.8	+	10785.7i	1.19393	+	0.574967i
$707$	1070.22	+	126.823i	0.0569305	+	0.00674633i
$708$	−4892.72	+	2356.21i	−0.259717	+	0.125073i
$709$	−12162.4	+	5857.08i	−0.644241	+	0.310250i	−0.727326	−	0.686292i	$-0.759237\pi$
$709$	−12162.4	+	5857.08i	−0.644241	+	0.310250i	0.0830846	+	0.996542i	$0.473523\pi$
$710$	5090.08	−	22301.1i	0.269053	−	1.17880i
$711$	35.1371	−	153.946i	0.00185337	−	0.00812013i
$712$	−5281.51	+	2543.44i	−0.277996	+	0.133876i
$713$	2204.78	−	1061.77i	0.115806	−	0.0557693i
$714$	3865.28	−	10845.8i	0.202597	−	0.568481i
$715$	9021.47	+	4344.51i	0.471866	+	0.227239i
$716$	21853.8			1.14067
$717$	−6979.32			−0.363525
$718$	−8736.01	−	4207.04i	−0.454074	−	0.218670i
$719$	−7157.84	+	8975.65i	−0.371269	+	0.465557i	−0.932009	−	0.362435i	$-0.881945\pi$
$719$	−7157.84	+	8975.65i	−0.371269	+	0.465557i	0.560740	+	0.827992i	$0.310517\pi$
$720$	988.899	−	4332.65i	0.0511862	−	0.224261i
$721$	33458.8	+	3964.90i	1.72825	+	0.204800i
$722$	−6883.64	−	30159.2i	−0.354823	−	1.55458i
$723$	−10614.7	−	5111.78i	−0.546010	−	0.262945i
$724$	−2720.06	−	11917.3i	−0.139627	−	0.611747i
$725$	44873.5	−	56269.6i	2.29870	−	2.88248i
$726$	4271.51	−	18714.7i	0.218362	−	0.956706i
$727$	17247.8	+	21628.1i	0.879899	+	1.10336i	0.993945	+	0.109883i	$0.0350475\pi$
$727$	17247.8	+	21628.1i	0.879899	+	1.10336i	−0.114046	+	0.993476i	$0.536381\pi$
$728$	−338.586	−	3168.73i	−0.0172374	−	0.161320i
$729$	13339.0	−	16726.5i	0.677690	−	0.849796i
$730$	30.6890	+	38.4828i	0.00155596	+	0.00195111i
$731$	−2505.44	+	1206.56i	−0.126768	+	0.0610480i
$732$	11892.6	+	14912.8i	0.600495	+	0.752997i
$733$	870.716	+	3814.86i	0.0438753	+	0.192230i	0.992116	−	0.125322i	$-0.0399963\pi$
$733$	870.716	+	3814.86i	0.0438753	+	0.192230i	−0.948241	+	0.317552i	$0.897139\pi$
$734$	6788.15			0.341356
$735$	−31659.9	−	7610.32i	−1.58883	−	0.381920i
$736$	9315.04			0.466517
$737$	−2335.53	−	10232.6i	−0.116731	−	0.511430i
$738$	−3688.08	−	4624.70i	−0.183957	−	0.230674i
$739$	−3769.87	+	1815.47i	−0.187655	+	0.0903697i	−0.525352	−	0.850885i	$-0.676066\pi$
$739$	−3769.87	+	1815.47i	−0.187655	+	0.0903697i	0.337697	+	0.941255i	$0.390352\pi$
$740$	3012.14	+	3777.10i	0.149633	+	0.187634i
$741$	−11123.5	+	13948.4i	−0.551459	+	0.691508i
$742$	−30011.3	−	3556.37i	−1.48484	−	0.175955i
$743$	−2695.34	−	3379.85i	−0.133085	−	0.166884i	0.710823	−	0.703371i	$-0.248323\pi$
$743$	−2695.34	−	3379.85i	−0.133085	−	0.166884i	−0.843909	+	0.536487i	$0.819751\pi$
$744$	387.362	−	1697.14i	0.0190879	−	0.0836294i
$745$	15446.9	−	19369.8i	0.759639	−	0.952558i
$746$	570.549	+	2499.74i	0.0280017	+	0.122684i
$747$	2782.22	+	1339.85i	0.136273	+	0.0656257i
$748$	−833.911	−	3653.60i	−0.0407631	−	0.178595i
$749$	15633.2	+	25200.7i	0.762650	+	1.22939i
$750$	10215.5	−	44757.0i	0.497356	−	2.17906i
$751$	−8987.98	+	11270.6i	−0.436719	+	0.547628i	−0.950675	−	0.310188i	$-0.899608\pi$
$751$	−8987.98	+	11270.6i	−0.436719	+	0.547628i	0.513956	+	0.857816i	$0.328179\pi$
$752$	1743.80	+	839.769i	0.0845609	+	0.0407224i
$753$	−5626.62			−0.272305
$754$	−32390.3			−1.56444
$755$	−45580.7	−	21950.5i	−2.19715	−	1.05809i
$756$	1877.24	+	17568.5i	0.0903102	+	0.845186i
$757$	−219.066	+	105.496i	−0.0105179	+	0.00506517i	−0.439135	−	0.898421i	$-0.644715\pi$
$757$	−219.066	+	105.496i	−0.0105179	+	0.00506517i	0.428617	+	0.903486i	$0.359001\pi$
$758$	−14009.7	+	6746.71i	−0.671313	+	0.323287i
$759$	−746.548	+	3270.84i	−0.0357022	+	0.156422i
$760$	−3053.57	+	13378.5i	−0.145743	+	0.638541i
$761$	31423.6	−	15132.8i	1.49685	−	0.720846i	0.506868	−	0.862024i	$-0.330803\pi$
$761$	31423.6	−	15132.8i	1.49685	−	0.720846i	0.989984	+	0.141178i	$0.0450890\pi$
$762$	−19074.8	+	9185.92i	−0.906832	+	0.436707i
$763$	−8281.08	−	5270.02i	−0.392916	−	0.250049i
$764$	19629.0	+	9452.81i	0.929517	+	0.447632i
$765$	−2011.28			−0.0950561
$766$	−559.654			−0.0263983
$767$	4601.53	+	2215.98i	0.216625	+	0.104321i

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)

\(f(q)\)	\(=\)	\(q+(-0.846844 - 3.71026i) q^{2} +(3.04811 + 3.82222i) q^{3} +(-5.84116 + 2.81296i) q^{4} +(-12.1071 - 15.1818i) q^{5} +(11.6002 - 14.5461i) q^{6} +(13.1709 - 13.0203i) q^{7} +(-3.59906 - 4.51308i) q^{8} +(0.689741 - 3.02195i) q^{9} +O(q^{10})\)	\(q+(-0.846844 - 3.71026i) q^{2} +(3.04811 + 3.82222i) q^{3} +(-5.84116 + 2.81296i) q^{4} +(-12.1071 - 15.1818i) q^{5} +(11.6002 - 14.5461i) q^{6} +(13.1709 - 13.0203i) q^{7} +(-3.59906 - 4.51308i) q^{8} +(0.689741 - 3.02195i) q^{9} +(-46.0758 + 57.7772i) q^{10} +(3.84932 + 16.8650i) q^{11} +(-28.5563 - 13.7520i) q^{12} +(6.63306 + 29.0614i) q^{13} +(-59.4623 - 37.8414i) q^{14} +(21.1244 - 92.5519i) q^{15} +(-46.0346 + 57.7255i) q^{16} +(30.1062 + 14.4984i) q^{17} -11.7963 q^{18} +122.424 q^{19} +(113.425 + 54.6228i) q^{20} +(89.9127 + 10.6547i) q^{21} +(59.3138 - 28.5640i) q^{22} +(35.7422 - 17.2126i) q^{23} +(6.27961 - 27.5128i) q^{24} +(-56.0909 + 245.750i) q^{25} +(102.208 - 49.2208i) q^{26} +(132.579 - 63.8465i) q^{27} +(-40.3079 + 113.103i) q^{28} +(-257.246 - 123.883i) q^{29} -361.281 q^{30} +61.6857 q^{31} +(211.555 + 101.879i) q^{32} +(-52.7284 + 66.1193i) q^{33} +(28.2976 - 123.980i) q^{34} +(-357.133 - 42.3206i) q^{35} +(4.47173 + 19.5919i) q^{36} +(34.5744 + 16.6502i) q^{37} +(-103.674 - 454.225i) q^{38} +(-90.8604 + 113.935i) q^{39} +(-24.9426 + 109.281i) q^{40} +(312.646 + 392.045i) q^{41} +(-36.6101 - 342.623i) q^{42} +(-51.8869 + 65.0641i) q^{43} +(-69.9250 - 87.6831i) q^{44} +(-54.2296 + 26.1156i) q^{45} +(-94.1312 - 118.037i) q^{46} +(-5.83314 - 25.5567i) q^{47} -360.958 q^{48} +(3.94526 - 342.977i) q^{49} +959.298 q^{50} +(36.3512 + 159.265i) q^{51} +(-120.493 - 151.094i) q^{52} +(386.317 - 186.040i) q^{53} +(-349.161 - 437.834i) q^{54} +(209.437 - 262.626i) q^{55} +(-106.164 - 12.5806i) q^{56} +(373.162 + 467.930i) q^{57} +(-241.792 + 1059.36i) q^{58} +(106.826 - 133.956i) q^{59} +(136.954 + 600.033i) q^{60} +(-542.207 - 261.113i) q^{61} +(-52.2381 - 228.870i) q^{62} +(-30.2621 - 48.7825i) q^{63} +(67.4092 - 295.339i) q^{64} +(360.897 - 452.551i) q^{65} +(289.973 + 139.644i) q^{66} -606.739 q^{67} -216.639 q^{68} +(174.736 + 84.1487i) q^{69} +(145.415 + 1360.90i) q^{70} +(-278.882 + 134.302i) q^{71} +(-16.1207 + 7.76334i) q^{72} +(0.148211 - 0.649355i) q^{73} +(32.4974 - 142.380i) q^{74} +(-1110.28 + 534.683i) q^{75} +(-715.097 + 344.373i) q^{76} +(270.286 + 172.008i) q^{77} +(499.675 + 240.631i) q^{78} +50.9424 q^{79} +1433.72 q^{80} +(572.747 + 275.820i) q^{81} +(1189.83 - 1492.00i) q^{82} +(-221.685 + 971.268i) q^{83} +(-555.166 + 190.684i) q^{84} +(-144.387 - 632.601i) q^{85} +(285.345 + 137.415i) q^{86} +(-310.608 - 1360.86i) q^{87} +(62.2590 - 78.0704i) q^{88} +(225.975 - 990.060i) q^{89} +(142.820 + 179.090i) q^{90} +(465.750 + 296.400i) q^{91} +(-160.358 + 201.083i) q^{92} +(188.025 + 235.776i) q^{93} +(-89.8822 + 43.2850i) q^{94} +(-1482.20 - 1858.62i) q^{95} +(255.438 + 1119.15i) q^{96} -66.6277 q^{97} +(-1275.88 + 275.810i) q^{98} +53.6202 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

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