LMFDB - Embedded newform 17.10.d.a.8.4

Newspace parameters

Level:	$ N $	$=$	$ 17 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	17.d (of order $8$, degree $4$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$8.75560921479$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$13$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			8.4
Character	$\chi$	$=$	17.8
Dual form			17.10.d.a.15.4

$q$-expansion

$f(q)$	$=$	$q+(-14.5474 + 14.5474i) q^{2} +(32.3594 - 78.1225i) q^{3} +88.7454i q^{4} +(31.3399 + 12.9814i) q^{5} +(665.735 + 1607.23i) q^{6} +(-4774.06 + 1977.48i) q^{7} +(-8739.29 - 8739.29i) q^{8} +(8861.98 + 8861.98i) q^{9} +O(q^{10})$	\(q+(-14.5474 + 14.5474i) q^{2} +(32.3594 - 78.1225i) q^{3} +88.7454i q^{4} +(31.3399 + 12.9814i) q^{5} +(665.735 + 1607.23i) q^{6} +(-4774.06 + 1977.48i) q^{7} +(-8739.29 - 8739.29i) q^{8} +(8861.98 + 8861.98i) q^{9} +(-644.761 + 267.069i) q^{10} +(-25659.9 - 61948.5i) q^{11} +(6933.01 + 2871.75i) q^{12} -194911. i q^{13} +(40683.0 - 98217.5i) q^{14} +(2028.28 - 2028.28i) q^{15} +208831. q^{16} +(-320627. - 125643. i) q^{17} -257838. q^{18} +(-328794. + 328794. i) q^{19} +(-1152.04 + 2781.27i) q^{20} +436952. i q^{21} +(1.27448e6 + 527906. i) q^{22} +(144382. + 348570. i) q^{23} +(-965534. + 399937. i) q^{24} +(-1.38025e6 - 1.38025e6i) q^{25} +(2.83545e6 + 2.83545e6i) q^{26} +(2.51678e6 - 1.04248e6i) q^{27} +(-175492. - 423676. i) q^{28} +(-941296. - 389898. i) q^{29} +59012.5i q^{30} +(-2.32857e6 + 5.62167e6i) q^{31} +(1.43657e6 - 1.43657e6i) q^{32} -5.66992e6 q^{33} +(6.49208e6 - 2.83651e6i) q^{34} -175289. q^{35} +(-786460. + 786460. i) q^{36} +(-1.67838e6 + 4.05197e6i) q^{37} -9.56621e6i q^{38} +(-1.52270e7 - 6.30721e6i) q^{39} +(-160440. - 387337. i) q^{40} +(1.46439e7 - 6.06570e6i) q^{41} +(-6.35652e6 - 6.35652e6i) q^{42} +(-3.45275e6 - 3.45275e6i) q^{43} +(5.49765e6 - 2.27720e6i) q^{44} +(162693. + 392775. i) q^{45} +(-7.17118e6 - 2.97040e6i) q^{46} -1.42598e7i q^{47} +(6.75764e6 - 1.63144e7i) q^{48} +(-9.65308e6 + 9.65308e6i) q^{49} +4.01583e7 q^{50} +(-2.01909e7 + 2.09825e7i) q^{51} +1.72975e7 q^{52} +(-2.43777e7 + 2.43777e7i) q^{53} +(-2.14472e7 + 5.17780e7i) q^{54} -2.27456e6i q^{55} +(5.90037e7 + 2.44401e7i) q^{56} +(1.50466e7 + 3.63258e7i) q^{57} +(1.93654e7 - 8.02143e6i) q^{58} +(7.93497e7 + 7.93497e7i) q^{59} +(180001. + 180001. i) q^{60} +(-1.65528e8 + 6.85638e7i) q^{61} +(-4.79061e7 - 1.15655e8i) q^{62} +(-5.98321e7 - 2.47832e7i) q^{63} +1.48718e8i q^{64} +(2.53022e6 - 6.10850e6i) q^{65} +(8.24826e7 - 8.24826e7i) q^{66} +1.06450e8 q^{67} +(1.11502e7 - 2.84542e7i) q^{68} +3.19033e7 q^{69} +(2.55000e6 - 2.55000e6i) q^{70} +(1.47032e8 - 3.54968e8i) q^{71} -1.54895e8i q^{72} +(-3.98621e8 - 1.65114e8i) q^{73} +(-3.45296e7 - 8.33619e7i) q^{74} +(-1.52493e8 + 6.31647e7i) q^{75} +(-2.91789e7 - 2.91789e7i) q^{76} +(2.45004e8 + 2.45004e8i) q^{77} +(3.13266e8 - 1.29759e8i) q^{78} +(-8.17294e7 - 1.97312e8i) q^{79} +(6.54473e6 + 2.71092e6i) q^{80} +1.63309e7i q^{81} +(-1.24791e8 + 3.01271e8i) q^{82} +(-2.68120e8 + 2.68120e8i) q^{83} -3.87775e7 q^{84} +(-8.41740e6 - 8.09984e6i) q^{85} +1.00457e8 q^{86} +(-6.09196e7 + 6.09196e7i) q^{87} +(-3.17137e8 + 7.65636e8i) q^{88} -9.12630e8i q^{89} +(-8.08062e6 - 3.34710e6i) q^{90} +(3.85433e8 + 9.30518e8i) q^{91} +(-3.09340e7 + 1.28133e7i) q^{92} +(3.63828e8 + 3.63828e8i) q^{93} +(2.07443e8 + 2.07443e8i) q^{94} +(-1.45726e7 + 6.03616e6i) q^{95} +(-6.57420e7 - 1.58715e8i) q^{96} +(1.34720e8 + 5.58030e7i) q^{97} -2.80855e8i q^{98} +(3.21589e8 - 7.76385e8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - 4 q^{2} - 4 q^{3} - 1140 q^{5} + 12308 q^{6} - 4 q^{7} + 2044 q^{8} - 83224 q^{9}+O(q^{10}) $ 52 * q - 4 * q^2 - 4 * q^3 - 1140 * q^5 + 12308 * q^6 - 4 * q^7 + 2044 * q^8 - 83224 * q^9	\( 52 q - 4 q^{2} - 4 q^{3} - 1140 q^{5} + 12308 q^{6} - 4 q^{7} + 2044 q^{8} - 83224 q^{9} - 117636 q^{10} - 115768 q^{11} - 145528 q^{12} + 463660 q^{14} + 288244 q^{15} - 3407880 q^{16} - 271932 q^{17} + 2193336 q^{18} - 406700 q^{19} + 493564 q^{20} + 800964 q^{22} - 4172180 q^{23} + 15078440 q^{24} + 11946576 q^{25} - 14209012 q^{26} - 7973656 q^{27} + 13540804 q^{28} + 7833752 q^{29} + 5936252 q^{31} - 26730116 q^{32} - 1635208 q^{33} - 53493988 q^{34} + 46992776 q^{35} - 12761764 q^{36} + 74606796 q^{37} + 74096776 q^{39} - 69317672 q^{40} - 71362288 q^{41} - 308117664 q^{42} - 3765712 q^{43} + 163659820 q^{44} + 14167408 q^{45} + 72135428 q^{46} + 164621412 q^{48} - 284548508 q^{49} + 226223888 q^{50} - 406733132 q^{51} + 103553016 q^{52} - 244724728 q^{53} + 971226260 q^{54} + 470691652 q^{56} - 440646580 q^{57} - 308561768 q^{58} - 481734984 q^{59} + 379626176 q^{60} + 507966228 q^{61} + 358867236 q^{62} + 1070586456 q^{63} + 366263684 q^{65} - 2244715148 q^{66} - 311910088 q^{67} - 1839196668 q^{68} + 533688136 q^{69} + 34867672 q^{70} + 186006812 q^{71} + 487115192 q^{73} - 214149412 q^{74} + 533015920 q^{75} + 1104236912 q^{76} - 237869092 q^{77} - 2081523384 q^{78} - 136338052 q^{79} - 922534152 q^{80} + 1951892384 q^{82} + 1843663888 q^{83} - 2630025952 q^{84} - 395061976 q^{85} + 1538547296 q^{86} - 369395636 q^{87} - 3388839640 q^{88} + 874363684 q^{90} + 2087197720 q^{91} + 1061427500 q^{92} + 576415420 q^{93} + 6899365112 q^{94} + 5031766876 q^{95} + 490811364 q^{96} - 3419996368 q^{97} - 5630536112 q^{99}+O(q^{100}) \) 52 * q - 4 * q^2 - 4 * q^3 - 1140 * q^5 + 12308 * q^6 - 4 * q^7 + 2044 * q^8 - 83224 * q^9 - 117636 * q^10 - 115768 * q^11 - 145528 * q^12 + 463660 * q^14 + 288244 * q^15 - 3407880 * q^16 - 271932 * q^17 + 2193336 * q^18 - 406700 * q^19 + 493564 * q^20 + 800964 * q^22 - 4172180 * q^23 + 15078440 * q^24 + 11946576 * q^25 - 14209012 * q^26 - 7973656 * q^27 + 13540804 * q^28 + 7833752 * q^29 + 5936252 * q^31 - 26730116 * q^32 - 1635208 * q^33 - 53493988 * q^34 + 46992776 * q^35 - 12761764 * q^36 + 74606796 * q^37 + 74096776 * q^39 - 69317672 * q^40 - 71362288 * q^41 - 308117664 * q^42 - 3765712 * q^43 + 163659820 * q^44 + 14167408 * q^45 + 72135428 * q^46 + 164621412 * q^48 - 284548508 * q^49 + 226223888 * q^50 - 406733132 * q^51 + 103553016 * q^52 - 244724728 * q^53 + 971226260 * q^54 + 470691652 * q^56 - 440646580 * q^57 - 308561768 * q^58 - 481734984 * q^59 + 379626176 * q^60 + 507966228 * q^61 + 358867236 * q^62 + 1070586456 * q^63 + 366263684 * q^65 - 2244715148 * q^66 - 311910088 * q^67 - 1839196668 * q^68 + 533688136 * q^69 + 34867672 * q^70 + 186006812 * q^71 + 487115192 * q^73 - 214149412 * q^74 + 533015920 * q^75 + 1104236912 * q^76 - 237869092 * q^77 - 2081523384 * q^78 - 136338052 * q^79 - 922534152 * q^80 + 1951892384 * q^82 + 1843663888 * q^83 - 2630025952 * q^84 - 395061976 * q^85 + 1538547296 * q^86 - 369395636 * q^87 - 3388839640 * q^88 + 874363684 * q^90 + 2087197720 * q^91 + 1061427500 * q^92 + 576415420 * q^93 + 6899365112 * q^94 + 5031766876 * q^95 + 490811364 * q^96 - 3419996368 * q^97 - 5630536112 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/17\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{5}{8}\right)$

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 $

$2$	−14.5474	+	14.5474i	−0.642911	+	0.642911i	−0.951270	−	0.308359i	$-0.900220\pi$
$2$	−14.5474	+	14.5474i	−0.642911	+	0.642911i	0.308359	+	0.951270i	$0.400220\pi$
$3$	32.3594	−	78.1225i	0.230651	−	0.556840i	−0.765603	−	0.643313i	$-0.777559\pi$
$3$	32.3594	−	78.1225i	0.230651	−	0.556840i	0.996254	+	0.0864725i	$0.0275595\pi$
$4$			88.7454i			0.173331i
$5$	31.3399	+	12.9814i	0.0224250	+	0.00928875i	0.393868	−	0.919167i	$-0.371137\pi$
$5$	31.3399	+	12.9814i	0.0224250	+	0.00928875i	−0.371443	+	0.928456i	$0.621137\pi$
$6$	665.735	+	1607.23i	0.209711	+	0.506287i
$7$	−4774.06	+	1977.48i	−0.751531	+	0.311294i	−0.725366	−	0.688363i	$-0.758329\pi$
$7$	−4774.06	+	1977.48i	−0.751531	+	0.311294i	−0.0261648	+	0.999658i	$0.508329\pi$
$8$	−8739.29	−	8739.29i	−0.754347	−	0.754347i
$9$	8861.98	+	8861.98i	0.450235	+	0.450235i
$10$	−644.761	+	267.069i	−0.0203891	+	0.00844545i
$11$	−25659.9	−	61948.5i	−0.528431	−	1.27575i	−0.932551	−	0.361039i	$-0.882422\pi$
$11$	−25659.9	−	61948.5i	−0.528431	−	1.27575i	0.404120	−	0.914706i	$-0.367578\pi$
$12$	6933.01	+	2871.75i	0.0965176	+	0.0399789i
$13$		−	194911.i		−	1.89274i	−0.323081	−	0.946371i	$-0.604719\pi$
$13$		−	194911.i		−	1.89274i	0.323081	−	0.946371i	$-0.395281\pi$
$14$	40683.0	−	98217.5i	0.283033	−	0.683302i
$15$	2028.28	−	2028.28i	0.0103447	−	0.0103447i
$16$	208831.			0.796626
$17$	−320627.	−	125643.i	−0.931065	−	0.364854i
$17$	−320627.	−	125643.i	−0.931065	−	0.364854i
$18$	−257838.			−0.578923
$19$	−328794.	+	328794.i	−0.578806	+	0.578806i	−0.934574	−	0.355769i	$-0.884219\pi$
$19$	−328794.	+	328794.i	−0.578806	+	0.578806i	0.355769	+	0.934574i	$0.384219\pi$
$20$	−1152.04	+	2781.27i	−0.00161003	+	0.00388695i
$21$			436952.i			0.490283i
$22$	1.27448e6	+	527906.i	1.15992	+	0.480457i
$23$	144382.	+	348570.i	0.107582	+	0.259725i	0.968498	−	0.249021i	$-0.0801089\pi$
$23$	144382.	+	348570.i	0.107582	+	0.259725i	−0.860916	+	0.508747i	$0.830109\pi$
$24$	−965534.	+	399937.i	−0.594042	+	0.246060i
$25$	−1.38025e6	−	1.38025e6i	−0.706690	−	0.706690i
$26$	2.83545e6	+	2.83545e6i	1.21687	+	1.21687i
$27$	2.51678e6	−	1.04248e6i	0.911397	−	0.377513i
$28$	−175492.	−	423676.i	−0.0539569	−	0.130263i
$29$	−941296.	−	389898.i	−0.247136	−	0.102367i	0.255677	−	0.966762i	$-0.417702\pi$
$29$	−941296.	−	389898.i	−0.247136	−	0.102367i	−0.502813	+	0.864395i	$0.667702\pi$
$30$			59012.5i			0.0133014i
$31$	−2.32857e6	+	5.62167e6i	−0.452858	+	1.09330i	0.518373	+	0.855155i	$0.326538\pi$
$31$	−2.32857e6	+	5.62167e6i	−0.452858	+	1.09330i	−0.971231	+	0.238141i	$0.923462\pi$
$32$	1.43657e6	−	1.43657e6i	0.242188	−	0.242188i
$33$	−5.66992e6			−0.832269
$34$	6.49208e6	−	2.83651e6i	0.833160	−	0.364023i
$35$	−175289.			−0.0197446
$36$	−786460.	+	786460.i	−0.0780397	+	0.0780397i
$37$	−1.67838e6	+	4.05197e6i	−0.147226	+	0.355434i	−0.980238	−	0.197820i	$-0.936614\pi$
$37$	−1.67838e6	+	4.05197e6i	−0.147226	+	0.355434i	0.833013	+	0.553254i	$0.186614\pi$
$38$		−	9.56621e6i		−	0.744241i
$39$	−1.52270e7	−	6.30721e6i	−1.05396	−	0.436563i
$40$	−160440.	−	387337.i	−0.00990931	−	0.0239232i
$41$	1.46439e7	−	6.06570e6i	0.809336	−	0.335238i	0.0606471	−	0.998159i	$-0.480684\pi$
$41$	1.46439e7	−	6.06570e6i	0.809336	−	0.335238i	0.748689	+	0.662921i	$0.230684\pi$
$42$	−6.35652e6	−	6.35652e6i	−0.315208	−	0.315208i
$43$	−3.45275e6	−	3.45275e6i	−0.154013	−	0.154013i	0.625895	−	0.779908i	$-0.284734\pi$
$43$	−3.45275e6	−	3.45275e6i	−0.154013	−	0.154013i	−0.779908	+	0.625895i	$0.784734\pi$
$44$	5.49765e6	−	2.27720e6i	0.221126	−	0.0915934i
$45$	162693.	+	392775.i	0.00591441	+	0.0142787i
$46$	−7.17118e6	−	2.97040e6i	−0.236146	−	0.0978148i
$47$		−	1.42598e7i		−	0.426258i	−0.977024	−	0.213129i	$-0.931634\pi$
$47$		−	1.42598e7i		−	0.426258i	0.977024	−	0.213129i	$-0.0683655\pi$
$48$	6.75764e6	−	1.63144e7i	0.183742	−	0.443593i
$49$	−9.65308e6	+	9.65308e6i	−0.239212	+	0.239212i
$50$	4.01583e7			0.908678
$51$	−2.01909e7	+	2.09825e7i	−0.417916	+	0.434301i
$52$	1.72975e7			0.328071
$53$	−2.43777e7	+	2.43777e7i	−0.424376	+	0.424376i	−0.886707	−	0.462331i	$-0.847013\pi$
$53$	−2.43777e7	+	2.43777e7i	−0.424376	+	0.424376i	0.462331	+	0.886707i	$0.347013\pi$
$54$	−2.14472e7	+	5.17780e7i	−0.343240	+	0.828654i
$55$		−	2.27456e6i		−	0.0335171i
$56$	5.90037e7	+	2.44401e7i	0.801739	+	0.332091i
$57$	1.50466e7	+	3.63258e7i	0.188800	+	0.455804i
$58$	1.93654e7	−	8.02143e6i	0.224699	−	0.0930734i
$59$	7.93497e7	+	7.93497e7i	0.852533	+	0.852533i	0.990445	−	0.137912i	$-0.0440390\pi$
$59$	7.93497e7	+	7.93497e7i	0.852533	+	0.852533i	−0.137912	+	0.990445i	$0.544039\pi$
$60$	180001.	+	180001.i	0.00179305	+	0.00179305i
$61$	−1.65528e8	+	6.85638e7i	−1.53069	+	0.634031i	−0.979697	−	0.200482i	$-0.935749\pi$
$61$	−1.65528e8	+	6.85638e7i	−1.53069	+	0.634031i	−0.550988	+	0.834513i	$0.685749\pi$
$62$	−4.79061e7	−	1.15655e8i	−0.411745	−	0.994039i
$63$	−5.98321e7	−	2.47832e7i	−0.478521	−	0.198210i
$64$			1.48718e8i			1.10804i
$65$	2.53022e6	−	6.10850e6i	0.0175812	−	0.0424448i
$66$	8.24826e7	−	8.24826e7i	0.535075	−	0.535075i
$67$	1.06450e8			0.645371			0.322686	−	0.946506i	$-0.395414\pi$
$67$	1.06450e8			0.645371			0.322686	+	0.946506i	$0.395414\pi$
$68$	1.11502e7	−	2.84542e7i	0.0632404	−	0.161382i
$69$	3.19033e7			0.169439
$70$	2.55000e6	−	2.55000e6i	0.0126940	−	0.0126940i
$71$	1.47032e8	−	3.54968e8i	0.686674	−	1.65778i	−0.0647032	−	0.997905i	$-0.520610\pi$
$71$	1.47032e8	−	3.54968e8i	0.686674	−	1.65778i	0.751377	−	0.659873i	$-0.229390\pi$
$72$		−	1.54895e8i		−	0.679268i
$73$	−3.98621e8	−	1.65114e8i	−1.64289	−	0.680506i	−0.646302	−	0.763082i	$-0.723685\pi$
$73$	−3.98621e8	−	1.65114e8i	−1.64289	−	0.680506i	−0.996585	+	0.0825762i	$0.973685\pi$
$74$	−3.45296e7	−	8.33619e7i	−0.133859	−	0.323165i
$75$	−1.52493e8	+	6.31647e7i	−0.556512	+	0.230515i
$76$	−2.91789e7	−	2.91789e7i	−0.100325	−	0.100325i
$77$	2.45004e8	+	2.45004e8i	0.794264	+	0.794264i
$78$	3.13266e8	−	1.29759e8i	0.958270	−	0.396929i
$79$	−8.17294e7	−	1.97312e8i	−0.236078	−	0.569944i	0.760792	−	0.648996i	$-0.224811\pi$
$79$	−8.17294e7	−	1.97312e8i	−0.236078	−	0.569944i	−0.996871	+	0.0790519i	$0.974811\pi$
$80$	6.54473e6	+	2.71092e6i	0.0178643	+	0.00739965i
$81$			1.63309e7i			0.0421529i
$82$	−1.24791e8	+	3.01271e8i	−0.304803	+	0.735859i
$83$	−2.68120e8	+	2.68120e8i	−0.620122	+	0.620122i	−0.945563	−	0.325440i	$-0.894487\pi$
$83$	−2.68120e8	+	2.68120e8i	−0.620122	+	0.620122i	0.325440	+	0.945563i	$0.394487\pi$
$84$	−3.87775e7			−0.0849811
$85$	−8.41740e6	−	8.09984e6i	−0.0174901	−	0.0168303i
$86$	1.00457e8			0.198033
$87$	−6.09196e7	+	6.09196e7i	−0.114004	+	0.114004i
$88$	−3.17137e8	+	7.65636e8i	−0.563734	+	1.36098i
$89$		−	9.12630e8i		−	1.54184i	−0.636931	−	0.770921i	$-0.719796\pi$
$89$		−	9.12630e8i		−	1.54184i	0.636931	−	0.770921i	$-0.280204\pi$
$90$	−8.08062e6	−	3.34710e6i	−0.0129824	−	0.00537747i
$91$	3.85433e8	+	9.30518e8i	0.589200	+	1.42245i
$92$	−3.09340e7	+	1.28133e7i	−0.0450184	+	0.0186472i
$93$	3.63828e8	+	3.63828e8i	0.504339	+	0.504339i
$94$	2.07443e8	+	2.07443e8i	0.274046	+	0.274046i
$95$	−1.45726e7	+	6.03616e6i	−0.0183561	+	0.00760335i
$96$	−6.57420e7	−	1.58715e8i	−0.0789992	−	0.190721i
$97$	1.34720e8	+	5.58030e7i	0.154511	+	0.0640007i	0.458599	−	0.888643i	$-0.348352\pi$
$97$	1.34720e8	+	5.58030e7i	0.154511	+	0.0640007i	−0.304087	+	0.952644i	$0.598352\pi$
$98$		−	2.80855e8i		−	0.307584i
$99$	3.21589e8	−	7.76385e8i	0.336467	−	0.812304i
$100$	1.22491e8	−	1.22491e8i	0.122491	−	0.122491i
$101$	8.74690e8			0.836389			0.418194	−	0.908358i	$-0.362663\pi$
$101$	8.74690e8			0.836389			0.418194	+	0.908358i	$0.362663\pi$
$102$	−1.15156e7	−	5.98965e8i	−0.0105338	−	0.547900i
$103$	8.45970e8			0.740606			0.370303	−	0.928911i	$-0.379254\pi$
$103$	8.45970e8			0.740606			0.370303	+	0.928911i	$0.379254\pi$
$104$	−1.70339e9	+	1.70339e9i	−1.42779	+	1.42779i
$105$	−5.67226e6	+	1.36940e7i	−0.00455411	+	0.0109946i
$106$		−	7.09264e8i		−	0.545672i
$107$	−3.18712e8	−	1.32015e8i	−0.235056	−	0.0973634i	0.262046	−	0.965055i	$-0.415603\pi$
$107$	−3.18712e8	−	1.32015e8i	−0.235056	−	0.0973634i	−0.497102	+	0.867692i	$0.665603\pi$
$108$	9.25155e7	+	2.23352e8i	0.0654346	+	0.157973i
$109$	−9.38620e8	+	3.88789e8i	−0.636899	+	0.263812i	−0.677681	−	0.735356i	$-0.737015\pi$
$109$	−9.38620e8	+	3.88789e8i	−0.636899	+	0.263812i	0.0407822	+	0.999168i	$0.487015\pi$
$110$	3.30890e7	+	3.30890e7i	0.0215485	+	0.0215485i
$111$	2.62239e8	+	2.62239e8i	0.163962	+	0.163962i
$112$	−9.96970e8	+	4.12959e8i	−0.598689	+	0.247985i
$113$	−4.33607e8	−	1.04682e9i	−0.250175	−	0.603975i	0.748043	−	0.663650i	$-0.230994\pi$
$113$	−4.33607e8	−	1.04682e9i	−0.250175	−	0.603975i	−0.998218	+	0.0596752i	$0.980994\pi$
$114$	−7.47336e8	−	3.09557e8i	−0.414423	−	0.171660i
$115$			1.27984e7i			0.00682365i
$116$	3.46016e7	−	8.35357e7i	0.0177433	−	0.0428362i
$117$	1.72730e9	−	1.72730e9i	0.852180	−	0.852180i
$118$	−2.30867e9			−1.09621
$119$	1.77915e9	−	3.42057e7i	0.813301	−	0.0156364i
$120$	−3.54515e7			−0.0156070
$121$	−1.51187e9	+	1.51187e9i	−0.641180	+	0.641180i
$122$	1.41057e9	−	3.40542e9i	0.576469	−	1.39172i
$123$		−	1.34030e9i		−	0.527994i
$124$	−4.98897e8	−	2.06650e8i	−0.189502	−	0.0784942i
$125$	−5.06937e7	−	1.22385e8i	−0.0185720	−	0.0448368i
$126$	1.23093e9	−	5.09870e8i	0.435078	−	0.180215i
$127$	3.19930e9	+	3.19930e9i	1.09129	+	1.09129i	0.995391	+	0.0958949i	$0.0305713\pi$
$127$	3.19930e9	+	3.19930e9i	1.09129	+	1.09129i	0.0958949	+	0.995391i	$0.469429\pi$
$128$	−1.42794e9	−	1.42794e9i	−0.470181	−	0.470181i
$129$	−3.81466e8	+	1.58008e8i	−0.121284	+	0.0502374i
$130$	5.20547e7	+	1.25671e8i	0.0159851	+	0.0385914i
$131$	−1.32472e9	−	5.48715e8i	−0.393008	−	0.162789i	0.177423	−	0.984135i	$-0.443224\pi$
$131$	−1.32472e9	−	5.48715e8i	−0.393008	−	0.162789i	−0.570431	+	0.821345i	$0.693224\pi$
$132$		−	5.03179e8i		−	0.144258i
$133$	9.19499e8	−	2.21987e9i	0.254811	−	0.615169i
$134$	−1.54858e9	+	1.54858e9i	−0.414916	+	0.414916i
$135$	9.24084e7			0.0239447
$136$	1.70402e9	+	3.90009e9i	0.427120	+	0.977573i
$137$	3.33397e9			0.808573			0.404286	−	0.914632i	$-0.367520\pi$
$137$	3.33397e9			0.808573			0.404286	+	0.914632i	$0.367520\pi$
$138$	−4.64110e8	+	4.64110e8i	−0.108935	+	0.108935i
$139$	−7.70375e8	+	1.85985e9i	−0.175039	+	0.422582i	−0.986914	−	0.161250i	$-0.948447\pi$
$139$	−7.70375e8	+	1.85985e9i	−0.175039	+	0.422582i	0.811874	+	0.583832i	$0.198447\pi$
$140$		−	1.55561e7i		−	0.00342235i
$141$	−1.11401e9	−	4.61439e8i	−0.237358	−	0.0983168i
$142$	3.02492e9	+	7.30280e9i	0.624333	+	1.50727i
$143$	−1.20745e10	+	5.00140e9i	−2.41466	+	1.00018i
$144$	1.85065e9	+	1.85065e9i	0.358669	+	0.358669i
$145$	−2.44387e7	−	2.44387e7i	−0.00459116	−	0.00459116i
$146$	8.20090e9	−	3.39692e9i	1.49373	−	0.618725i
$147$	4.41755e8	+	1.06649e9i	0.0780285	+	0.188378i
$148$	−3.59594e8	−	1.48949e8i	−0.0616076	−	0.0255187i
$149$			1.72052e9i			0.285971i	0.989725	+	0.142985i	$0.0456702\pi$
$149$			1.72052e9i			0.285971i	−0.989725	+	0.142985i	$0.954330\pi$
$150$	1.29950e9	−	3.13727e9i	0.209587	−	0.505988i
$151$	−3.60005e9	+	3.60005e9i	−0.563524	+	0.563524i	−0.930307	−	0.366783i	$-0.880459\pi$
$151$	−3.60005e9	+	3.60005e9i	−0.563524	+	0.563524i	0.366783	+	0.930307i	$0.380459\pi$
$152$	5.74685e9			0.873241
$153$	−1.72794e9	−	3.95484e9i	−0.254928	−	0.583468i
$154$	−7.12835e9			−1.02128
$155$	−1.45954e8	+	1.45954e8i	−0.0203107	+	0.0203107i
$156$	5.59736e8	−	1.35132e9i	0.0756697	−	0.182683i
$157$		−	1.10391e10i		−	1.45006i	−0.688718	−	0.725029i	$-0.741826\pi$
$157$		−	1.10391e10i		−	1.45006i	0.688718	−	0.725029i	$-0.258174\pi$
$158$	4.05933e9	+	1.68143e9i	0.518201	+	0.214646i
$159$	1.11560e9	+	2.69329e9i	0.138427	+	0.334192i
$160$	6.36708e7	−	2.63733e7i	0.00768069	−	0.00318145i
$161$	−1.37858e9	−	1.37858e9i	−0.161702	−	0.161702i
$162$	−2.37572e8	−	2.37572e8i	−0.0271005	−	0.0271005i
$163$	2.52429e9	−	1.04559e9i	0.280088	−	0.116016i	−0.238217	−	0.971212i	$-0.576563\pi$
$163$	2.52429e9	−	1.04559e9i	0.280088	−	0.116016i	0.518305	+	0.855196i	$0.326563\pi$
$164$	5.38302e8	+	1.29958e9i	0.0581071	+	0.140283i
$165$	−1.77695e8	−	7.36036e7i	−0.0186637	−	0.00773074i
$166$		−	7.80090e9i		−	0.797367i
$167$	4.54146e9	−	1.09640e10i	0.451826	−	1.09080i	−0.519802	−	0.854287i	$-0.673994\pi$
$167$	4.54146e9	−	1.09640e10i	0.451826	−	1.09080i	0.971627	−	0.236517i	$-0.0760058\pi$
$168$	3.81865e9	−	3.81865e9i	0.369844	−	0.369844i
$169$	−2.73858e10			−2.58247
$170$	2.40283e8	−	4.61965e6i	0.0220650	−	0.000424218i
$171$	−5.82753e9			−0.521198
$172$	3.06415e8	−	3.06415e8i	0.0266952	−	0.0266952i
$173$	1.79430e9	−	4.33183e9i	0.152296	−	0.367674i	−0.829257	−	0.558868i	$-0.811236\pi$
$173$	1.79430e9	−	4.33183e9i	0.152296	−	0.367674i	0.981552	+	0.191194i	$0.0612358\pi$
$174$		−	1.77245e9i		−	0.146589i
$175$	9.31884e9	+	3.85999e9i	0.751088	+	0.311111i
$176$	−5.35858e9	−	1.29368e10i	−0.420962	−	1.01629i
$177$	8.76671e9	−	3.63129e9i	0.671362	−	0.278087i
$178$	1.32764e10	+	1.32764e10i	0.991267	+	0.991267i
$179$	1.12383e10	+	1.12383e10i	0.818203	+	0.818203i	0.985847	−	0.167645i	$-0.0536161\pi$
$179$	1.12383e10	+	1.12383e10i	0.818203	+	0.818203i	−0.167645	+	0.985847i	$0.553616\pi$
$180$	−3.48570e7	+	1.44382e7i	−0.00247493	+	0.00102515i
$181$	1.78454e8	+	4.30825e8i	0.0123587	+	0.0298365i	0.929938	−	0.367715i	$-0.119860\pi$
$181$	1.78454e8	+	4.30825e8i	0.0123587	+	0.0298365i	−0.917580	+	0.397552i	$0.869860\pi$
$182$	−1.91437e10	−	7.92957e9i	−1.29331	−	0.535708i
$183$			1.51501e10i			0.998587i
$184$	1.78445e9	−	4.30805e9i	0.114769	−	0.277077i
$185$	−1.05201e8	+	1.05201e8i	−0.00660307	+	0.00660307i
$186$	−1.05855e10			−0.648490
$187$	4.43855e8	+	2.30864e10i	0.0265432	+	1.38060i
$188$	1.26549e9			0.0738837
$189$	−9.95375e9	+	9.95375e9i	−0.567425	+	0.567425i
$190$	1.24183e8	−	2.99804e8i	0.00691307	−	0.0166896i
$191$			6.43277e9i			0.349742i	0.984591	+	0.174871i	$0.0559509\pi$
$191$			6.43277e9i			0.349742i	−0.984591	+	0.174871i	$0.944049\pi$
$192$	1.16182e10	+	4.81243e9i	0.616999	+	0.255569i
$193$	−3.61203e9	−	8.72022e9i	−0.187389	−	0.452397i	0.802066	−	0.597235i	$-0.203734\pi$
$193$	−3.61203e9	−	8.72022e9i	−0.187389	−	0.452397i	−0.989455	+	0.144838i	$0.953734\pi$
$194$	−2.77162e9	+	1.14804e9i	−0.140484	+	0.0581903i
$195$	−3.95335e8	−	3.95335e8i	−0.0195798	−	0.0195798i
$196$	−8.56666e8	−	8.56666e8i	−0.0414629	−	0.0414629i
$197$	3.07447e10	−	1.27349e10i	1.45436	−	0.602416i	0.491129	−	0.871087i	$-0.336584\pi$
$197$	3.07447e10	−	1.27349e10i	1.45436	−	0.602416i	0.963232	+	0.268671i	$0.0865845\pi$
$198$	6.61610e9	+	1.59727e10i	0.305921	+	0.738558i
$199$	−1.06281e10	−	4.40229e9i	−0.480414	−	0.198994i	0.129315	−	0.991604i	$-0.458722\pi$
$199$	−1.06281e10	−	4.40229e9i	−0.480414	−	0.198994i	−0.609730	+	0.792609i	$0.708722\pi$
$200$			2.41249e10i			1.06618i
$201$	3.44467e9	−	8.31616e9i	0.148855	−	0.359369i
$202$	−1.27245e10	+	1.27245e10i	−0.537723	+	0.537723i
$203$	5.26482e9			0.217596
$204$	−1.86210e9	−	1.79185e9i	−0.0752777	−	0.0724377i
$205$	5.37680e8			0.0212633
$206$	−1.23067e10	+	1.23067e10i	−0.476144	+	0.476144i
$207$	−1.80951e9	+	4.36853e9i	−0.0685005	+	0.165375i
$208$		−	4.07034e10i		−	1.50781i
$209$	2.88051e10	+	1.19315e10i	1.04427	+	0.432550i
$210$	−1.16696e8	−	2.81730e8i	−0.00414066	−	0.00999644i
$211$	3.66767e10	−	1.51920e10i	1.27385	−	0.527647i	0.359720	−	0.933060i	$-0.382872\pi$
$211$	3.66767e10	−	1.51920e10i	1.27385	−	0.527647i	0.914134	+	0.405413i	$0.132872\pi$
$212$	−2.16341e9	−	2.16341e9i	−0.0735574	−	0.0735574i
$213$	−2.29731e10	−	2.29731e10i	−0.764736	−	0.764736i
$214$	6.55691e9	−	2.71596e9i	0.213716	−	0.0885241i
$215$	−6.33872e7	−	1.53030e8i	−0.00202315	−	0.00488432i
$216$	−3.11054e10	−	1.28843e10i	−0.972286	−	0.402734i
$217$		−	3.14429e10i		−	0.962618i
$218$	7.99862e9	−	1.93104e10i	0.239862	−	0.579077i
$219$	−2.57983e10	+	2.57983e10i	−0.757866	+	0.757866i
$220$	2.01857e8			0.00580954
$221$	−2.44892e10	+	6.24938e10i	−0.690574	+	1.76227i
$222$	−7.62980e9			−0.210826
$223$	3.38158e10	−	3.38158e10i	0.915689	−	0.915689i	−0.0810235	−	0.996712i	$-0.525819\pi$
$223$	3.38158e10	−	3.38158e10i	0.915689	−	0.915689i	0.996712	+	0.0810235i	$0.0258189\pi$
$224$	−4.01749e9	+	9.69908e9i	−0.106620	+	0.257403i
$225$		−	2.44636e10i		−	0.636354i
$226$	2.15364e10	+	8.92066e9i	0.549142	+	0.227462i
$227$	−1.36115e9	−	3.28611e9i	−0.0340244	−	0.0821421i	0.905954	−	0.423376i	$-0.139155\pi$
$227$	−1.36115e9	−	3.28611e9i	−0.0340244	−	0.0821421i	−0.939978	+	0.341234i	$0.889155\pi$
$228$	−3.22375e9	+	1.33532e9i	−0.0790049	+	0.0327249i
$229$	−1.64854e10	−	1.64854e10i	−0.396131	−	0.396131i	0.480735	−	0.876866i	$-0.340370\pi$
$229$	−1.64854e10	−	1.64854e10i	−0.396131	−	0.396131i	−0.876866	+	0.480735i	$0.840370\pi$
$230$	−1.86184e8	−	1.86184e8i	−0.00438700	−	0.00438700i
$231$	2.70685e10	−	1.12122e10i	0.625476	−	0.259081i
$232$	4.81883e9	+	1.16337e10i	0.109206	+	0.263646i
$233$	−6.63179e10	−	2.74698e10i	−1.47411	−	0.610595i	−0.506315	−	0.862349i	$-0.668993\pi$
$233$	−6.63179e10	−	2.74698e10i	−1.47411	−	0.610595i	−0.967791	+	0.251754i	$0.918993\pi$
$234$			5.02555e10i			1.09575i
$235$	1.85112e8	−	4.46901e8i	0.00395941	−	0.00955885i
$236$	−7.04192e9	+	7.04192e9i	−0.147770	+	0.147770i
$237$	−1.80592e10			−0.371819
$238$	−2.53844e10	+	2.63796e10i	−0.512827	+	0.532933i
$239$	−5.19129e10			−1.02916			−0.514582	−	0.857441i	$-0.672053\pi$
$239$	−5.19129e10			−1.02916			−0.514582	+	0.857441i	$0.672053\pi$
$240$	4.23568e8	−	4.23568e8i	0.00824085	−	0.00824085i
$241$	3.85817e10	−	9.31444e10i	0.736723	−	1.77861i	0.117977	−	0.993016i	$-0.462359\pi$
$241$	3.85817e10	−	9.31444e10i	0.736723	−	1.77861i	0.618746	−	0.785591i	$-0.287641\pi$
$242$		−	4.39875e10i		−	0.824443i
$243$	5.08135e10	+	2.10476e10i	0.934869	+	0.387235i
$244$	−6.08472e9	−	1.46898e10i	−0.109897	−	0.265315i
$245$	−4.27837e8	+	1.77216e8i	−0.00758632	+	0.00314236i
$246$	1.94979e10	+	1.94979e10i	0.339453	+	0.339453i
$247$	6.40856e10	+	6.40856e10i	1.09553	+	1.09553i
$248$	6.94795e10	−	2.87793e10i	1.16634	−	0.483113i
$249$	1.22700e10	+	2.96224e10i	0.202277	+	0.488341i
$250$	2.51786e9	+	1.04293e9i	0.0407662	+	0.0168859i
$251$			3.87316e10i			0.615933i	0.951397	+	0.307967i	$0.0996485\pi$
$251$			3.87316e10i			0.615933i	−0.951397	+	0.307967i	$0.900351\pi$
$252$	2.19940e9	−	5.30982e9i	0.0343559	−	0.0829425i
$253$	1.78886e10	−	1.78886e10i	0.274494	−	0.274494i
$254$	−9.30832e10			−1.40320
$255$	−9.05162e8	+	3.95482e8i	−0.0134059	+	0.00585728i
$256$	−3.45980e10			−0.503467
$257$	−1.47987e10	+	1.47987e10i	−0.211604	+	0.211604i	−0.804949	−	0.593345i	$-0.797807\pi$
$257$	−1.47987e10	+	1.47987e10i	−0.211604	+	0.211604i	0.593345	+	0.804949i	$0.297807\pi$
$258$	3.25073e9	−	7.84796e9i	0.0456765	−	0.110273i
$259$		−	2.26633e10i		−	0.312950i
$260$	5.42101e8	+	2.24546e8i	0.00735699	+	0.00304736i
$261$	−4.88649e9	−	1.17970e10i	−0.0651800	−	0.157358i
$262$	2.72536e10	−	1.12888e10i	0.357329	−	0.148010i
$263$	1.01653e11	+	1.01653e11i	1.31015	+	1.31015i	0.921301	+	0.388850i	$0.127128\pi$
$263$	1.01653e11	+	1.01653e11i	1.31015	+	1.31015i	0.388850	+	0.921301i	$0.372872\pi$
$264$	4.95511e10	+	4.95511e10i	0.627820	+	0.627820i
$265$	−1.08045e9	+	4.47537e8i	−0.0134586	+	0.00557472i
$266$	1.89170e10	+	4.56697e10i	0.231678	+	0.559320i
$267$	−7.12970e10	−	2.95322e10i	−0.858559	−	0.355627i
$268$			9.44696e9i			0.111863i
$269$	−1.07352e10	+	2.59170e10i	−0.125004	+	0.301787i	−0.973976	−	0.226652i	$-0.927222\pi$
$269$	−1.07352e10	+	2.59170e10i	−0.125004	+	0.301787i	0.848972	+	0.528438i	$0.177222\pi$
$270$	−1.34430e9	+	1.34430e9i	−0.0153943	+	0.0153943i
$271$	−6.71035e10			−0.755759			−0.377880	−	0.925855i	$-0.623347\pi$
$271$	−6.71035e10			−0.755759			−0.377880	+	0.925855i	$0.623347\pi$
$272$	−6.69567e10	−	2.62381e10i	−0.741710	−	0.290652i
$273$	8.51668e10			0.927979
$274$	−4.85006e10	+	4.85006e10i	−0.519840	+	0.519840i
$275$	−5.00875e10	+	1.20922e11i	−0.528120	+	1.27499i
$276$			2.83127e9i			0.0293691i
$277$	8.47374e10	+	3.50994e10i	0.864801	+	0.358212i	0.770583	−	0.637339i	$-0.219965\pi$
$277$	8.47374e10	+	3.50994e10i	0.864801	+	0.358212i	0.0942177	+	0.995552i	$0.469965\pi$
$278$	−1.58490e10	−	3.82630e10i	−0.159148	−	0.384218i
$279$	−7.04549e10	+	2.91834e10i	−0.696133	+	0.288348i
$280$	1.53190e9	+	1.53190e9i	0.0148943	+	0.0148943i
$281$	−9.54766e10	−	9.54766e10i	−0.913521	−	0.913521i	0.0830266	−	0.996547i	$-0.473541\pi$
$281$	−9.54766e10	−	9.54766e10i	−0.913521	−	0.913521i	−0.996547	+	0.0830266i	$0.973541\pi$
$282$	2.29187e10	−	9.49325e9i	0.215809	−	0.0893910i
$283$	−3.28190e10	−	7.92320e10i	−0.304149	−	0.734280i	−0.999872	−	0.0159707i	$-0.994916\pi$
$283$	−3.28190e10	−	7.92320e10i	−0.304149	−	0.734280i	0.695724	−	0.718310i	$-0.255084\pi$
$284$	3.15017e10	+	1.30484e10i	0.287344	+	0.119022i
$285$			1.33377e9i			0.0119751i
$286$	1.02895e11	−	2.48410e11i	0.909381	−	2.19544i
$287$	−5.79160e10	+	5.79160e10i	−0.503883	+	0.503883i
$288$	2.54618e10			0.218083
$289$	8.70155e10	+	8.05692e10i	0.733764	+	0.679405i
$290$	7.11041e8			0.00590342
$291$	8.71895e9	−	8.71895e9i	0.0712764	−	0.0712764i
$292$	1.46531e10	−	3.53758e10i	0.117953	−	0.284763i
$293$		−	1.58105e11i		−	1.25326i	−0.779315	−	0.626632i	$-0.784433\pi$
$293$		−	1.58105e11i		−	1.25326i	0.779315	−	0.626632i	$-0.215567\pi$
$294$	−2.19411e10	−	9.08829e9i	−0.171275	−	0.0709446i
$295$	1.45674e9	+	3.51688e9i	0.0111991	+	0.0270370i
$296$	5.00792e10	−	2.07435e10i	0.379180	−	0.157061i
$297$	−1.29161e11	−	1.29161e11i	−0.963221	−	0.963221i
$298$	−2.50291e10	−	2.50291e10i	−0.183854	−	0.183854i
$299$	6.79401e10	−	2.81417e10i	0.491593	−	0.203625i
$300$	−5.60558e9	−	1.35331e10i	−0.0399553	−	0.0964607i
$301$	2.33114e10	+	9.65588e9i	0.163689	+	0.0678021i
$302$		−	1.04743e11i		−	0.724591i
$303$	2.83045e10	−	6.83330e10i	0.192914	−	0.465735i
$304$	−6.86623e10	+	6.86623e10i	−0.461091	+	0.461091i
$305$	−6.07767e9			−0.0402150
$306$	8.26698e10	+	3.23956e10i	0.539015	+	0.211222i
$307$	−1.17486e11			−0.754857			−0.377428	−	0.926039i	$-0.623192\pi$
$307$	−1.17486e11			−0.754857			−0.377428	+	0.926039i	$0.623192\pi$
$308$	−2.17430e10	+	2.17430e10i	−0.137670	+	0.137670i
$309$	2.73751e10	−	6.60893e10i	0.170821	−	0.412399i
$310$		−	4.24652e9i		−	0.0261159i
$311$	−1.62159e8	−	6.71686e7i	−0.000982925	−	0.000407141i	0.382192	−	0.924083i	$-0.375169\pi$
$311$	−1.62159e8	−	6.71686e7i	−0.000982925	−	0.000407141i	−0.383175	+	0.923676i	$0.625169\pi$
$312$	7.79522e10	+	1.88193e11i	0.465729	+	1.12437i
$313$	−1.58501e11	+	6.56533e10i	−0.933432	+	0.386640i	−0.796979	−	0.604006i	$-0.793570\pi$
$313$	−1.58501e11	+	6.56533e10i	−0.933432	+	0.386640i	−0.136452	+	0.990647i	$0.543570\pi$
$314$	1.60590e11	+	1.60590e11i	0.932258	+	0.932258i
$315$	−1.55341e9	−	1.55341e9i	−0.00888973	−	0.00888973i
$316$	1.75105e10	−	7.25311e9i	0.0987888	−	0.0409197i
$317$	−1.31565e9	−	3.17626e9i	−0.00731768	−	0.0176664i	0.920178	−	0.391499i	$-0.128043\pi$
$317$	−1.31565e9	−	3.17626e9i	−0.00731768	−	0.0176664i	−0.927496	+	0.373833i	$0.878043\pi$
$318$	−5.54095e10	−	2.29514e10i	−0.303852	−	0.125860i
$319$			6.83167e10i			0.369376i
$320$	−1.93057e9	+	4.66081e9i	−0.0102923	+	0.0248477i
$321$	−2.06267e10	+	2.06267e10i	−0.108432	+	0.108432i
$322$	4.01096e10			0.207920
$323$	1.46731e11	−	6.41095e10i	0.750085	−	0.327726i
$324$	−1.44929e9			−0.00730639
$325$	−2.69027e11	+	2.69027e11i	−1.33758	+	1.33758i
$326$	−2.15112e10	+	5.19326e10i	−0.105484	+	0.254660i
$327$			8.59084e10i			0.415500i
$328$	−1.80987e11	−	7.49673e10i	−0.863407	−	0.357635i
$329$	2.81985e10	+	6.80771e10i	0.132692	+	0.320346i
$330$	3.65574e9	−	1.51426e9i	0.0169692	−	0.00702889i
$331$	1.26814e11	+	1.26814e11i	0.580688	+	0.580688i	0.935092	−	0.354404i	$-0.115316\pi$
$331$	1.26814e11	+	1.26814e11i	0.580688	+	0.580688i	−0.354404	+	0.935092i	$0.615316\pi$
$332$	−2.37944e10	−	2.37944e10i	−0.107486	−	0.107486i
$333$	−5.07823e10	+	2.10347e10i	−0.226315	+	0.0937428i
$334$	9.34321e10	+	2.25565e11i	0.410806	+	0.991773i
$335$	3.33614e9	+	1.38187e9i	0.0144725	+	0.00599469i
$336$			9.12489e10i			0.390572i
$337$	−7.77279e10	+	1.87652e11i	−0.328279	+	0.792535i	0.670442	+	0.741962i	$0.266105\pi$
$337$	−7.77279e10	+	1.87652e11i	−0.328279	+	0.792535i	−0.998720	+	0.0505724i	$0.983895\pi$
$338$	3.98393e11	−	3.98393e11i	1.66030	−	1.66030i
$339$	−9.58114e10			−0.394020
$340$	7.18823e8	−	7.47005e8i	0.00291721	−	0.00303158i
$341$	4.08005e11			1.63407
$342$	8.47756e10	−	8.47756e10i	0.335084	−	0.335084i
$343$	1.06794e11	−	2.57824e11i	0.416604	−	1.00577i
$344$			6.03491e10i			0.232358i
$345$	9.99847e8	+	4.14150e8i	0.00379968	+	0.00157388i
$346$	3.69144e10	+	8.91193e10i	0.138469	+	0.334295i
$347$	−3.70724e11	+	1.53559e11i	−1.37267	+	0.568581i	−0.942512	−	0.334171i	$-0.891544\pi$
$347$	−3.70724e11	+	1.53559e11i	−1.37267	+	0.568581i	−0.430162	+	0.902752i	$0.641544\pi$
$348$	−5.40633e9	−	5.40633e9i	−0.0197604	−	0.0197604i
$349$	1.85580e11	+	1.85580e11i	0.669604	+	0.669604i	0.957624	−	0.288021i	$-0.0929972\pi$
$349$	1.85580e11	+	1.85580e11i	0.669604	+	0.669604i	−0.288021	+	0.957624i	$0.592997\pi$
$350$	−1.91718e11	+	7.94122e10i	−0.682899	+	0.282866i
$351$	−2.03191e11	−	4.90547e11i	−0.714535	−	1.72504i
$352$	−1.25856e11	−	5.21312e10i	−0.436950	−	0.180990i
$353$		−	4.23719e11i		−	1.45242i	−0.687473	−	0.726210i	$-0.741280\pi$
$353$		−	4.23719e11i		−	1.45242i	0.687473	−	0.726210i	$-0.258720\pi$
$354$	−7.47071e10	+	1.80359e11i	−0.252841	+	0.610411i
$355$	9.21597e9	−	9.21597e9i	0.0307974	−	0.0307974i
$356$	8.09917e10			0.267249
$357$	5.49000e10	−	1.40099e11i	0.178882	−	0.456485i
$358$	−3.26976e11			−1.05206
$359$	1.92102e11	−	1.92102e11i	0.610391	−	0.610391i	−0.332657	−	0.943048i	$-0.607945\pi$
$359$	1.92102e11	−	1.92102e11i	0.610391	−	0.610391i	0.943048	+	0.332657i	$0.107945\pi$
$360$	2.01076e9	−	4.85439e9i	0.00630955	−	0.0152326i
$361$			1.06477e11i			0.329968i
$362$	−8.86343e9	−	3.67135e9i	−0.0271277	−	0.0112367i
$363$	6.91878e10	+	1.67034e11i	0.209146	+	0.504923i
$364$	−8.25791e10	+	3.42054e10i	−0.246555	+	0.102126i
$365$	−1.03493e10	−	1.03493e10i	−0.0305207	−	0.0305207i
$366$	−2.20395e11	−	2.20395e11i	−0.642003	−	0.642003i
$367$	9.01459e10	−	3.73396e10i	0.259387	−	0.107442i	−0.249200	−	0.968452i	$-0.580168\pi$
$367$	9.01459e10	−	3.73396e10i	0.259387	−	0.107442i	0.508588	+	0.861010i	$0.330168\pi$
$368$	3.01515e10	+	7.27921e10i	0.0857024	+	0.206904i
$369$	1.83528e11	+	7.60198e10i	0.515328	+	0.213456i
$370$		−	3.06080e9i		−	0.00849037i
$371$	6.81741e10	−	1.64587e11i	0.186826	−	0.451037i
$372$	−3.22880e10	+	3.22880e10i	−0.0874175	+	0.0874175i
$373$	3.61489e11			0.966952			0.483476	−	0.875358i	$-0.339374\pi$
$373$	3.61489e11			0.966952			0.483476	+	0.875358i	$0.339374\pi$
$374$	−3.42304e11	−	3.29390e11i	−0.904669	−	0.870539i
$375$	−1.12015e10			−0.0292506
$376$	−1.24621e11	+	1.24621e11i	−0.321547	+	0.321547i
$377$	−7.59954e10	+	1.83469e11i	−0.193754	+	0.467764i
$378$		−	2.89603e11i		−	0.729608i
$379$	−4.52550e11	−	1.87453e11i	−1.12665	−	0.466675i	−0.260012	−	0.965605i	$-0.583726\pi$
$379$	−4.52550e11	−	1.87453e11i	−1.12665	−	0.466675i	−0.866642	+	0.498930i	$0.833726\pi$
$380$	−5.35682e8	−	1.29325e9i	−0.00131789	−	0.00318168i
$381$	3.53465e11	−	1.46410e11i	0.859378	−	0.355966i
$382$	−9.35802e10	−	9.35802e10i	−0.224853	−	0.224853i
$383$	2.43997e11	+	2.43997e11i	0.579415	+	0.579415i	0.934742	−	0.355327i	$-0.115631\pi$
$383$	2.43997e11	+	2.43997e11i	0.579415	+	0.579415i	−0.355327	+	0.934742i	$0.615631\pi$
$384$	−1.57762e11	+	6.53470e10i	−0.370263	+	0.153368i
$385$	4.49791e9	+	1.08589e10i	0.0104337	+	0.0251891i
$386$	1.79402e11	+	7.43109e10i	0.411325	+	0.170377i
$387$		−	6.11964e10i		−	0.138684i
$388$	−4.95226e9	+	1.19558e10i	−0.0110933	+	0.0267816i
$389$	−2.59147e11	+	2.59147e11i	−0.573816	+	0.573816i	−0.933193	−	0.359377i	$-0.882989\pi$
$389$	−2.59147e11	+	2.59147e11i	−0.573816	+	0.573816i	0.359377	+	0.933193i	$0.382989\pi$
$390$	1.15022e10			0.0251762
$391$	−2.49747e9	−	1.29902e11i	−0.00540387	−	0.281073i
$392$	1.68722e11			0.360898
$393$	−8.57340e10	+	8.57340e10i	−0.181295	+	0.181295i
$394$	−2.61996e11	+	6.32515e11i	−0.547725	+	1.32232i
$395$		−	7.24471e9i		−	0.0149739i
$396$	6.89005e10	+	2.85395e10i	0.140797	+	0.0583201i
$397$	−6.53459e9	−	1.57759e10i	−0.0132027	−	0.0318740i	0.917141	−	0.398564i	$-0.130491\pi$
$397$	−6.53459e9	−	1.57759e10i	−0.0132027	−	0.0318740i	−0.930343	+	0.366689i	$0.880491\pi$
$398$	2.18653e11	−	9.05691e10i	0.436799	−	0.180928i
$399$	−1.43667e11	−	1.43667e11i	−0.283779	−	0.283779i
$400$	−2.88239e11	−	2.88239e11i	−0.562968	−	0.562968i
$401$	−4.00633e11	+	1.65947e11i	−0.773743	+	0.320495i	−0.734387	−	0.678731i	$-0.762530\pi$
$401$	−4.00633e11	+	1.65947e11i	−0.773743	+	0.320495i	−0.0393553	+	0.999225i	$0.512530\pi$
$402$	7.08676e10	+	1.71090e11i	0.135341	+	0.326743i
$403$	1.09573e12	+	4.53865e11i	2.06933	+	0.857143i
$404$			7.76247e10i			0.144972i
$405$	−2.11998e8	+	5.11808e8i	−0.000391547	+	0.000945279i
$406$	−7.65896e10	+	7.65896e10i	−0.139895	+	0.139895i
$407$	2.94081e11			0.531242
$408$	3.59826e11	−	6.91796e9i	0.642867	−	0.0123597i
$409$	4.20491e11			0.743022			0.371511	−	0.928429i	$-0.378840\pi$
$409$	4.20491e11			0.743022			0.371511	+	0.928429i	$0.378840\pi$
$410$	−7.82185e9	+	7.82185e9i	−0.0136704	+	0.0136704i
$411$	1.07885e11	−	2.60458e11i	0.186498	−	0.450246i
$412$			7.50759e10i			0.128370i
$413$	−5.35733e11	−	2.21908e11i	−0.906093	−	0.375316i
$414$	−3.72273e10	−	8.98745e10i	−0.0622816	−	0.150361i
$415$	−1.18834e10	+	4.92227e9i	−0.0196664	+	0.00814609i
$416$	−2.80004e11	−	2.80004e11i	−0.458399	−	0.458399i
$417$	1.20367e11	+	1.20367e11i	0.194938	+	0.194938i
$418$	−5.92613e11	+	2.45468e11i	−0.949462	+	0.393280i
$419$	−2.94913e11	−	7.11982e11i	−0.467445	−	1.12851i	−0.965275	−	0.261237i	$-0.915870\pi$
$419$	−2.94913e11	−	7.11982e11i	−0.467445	−	1.12851i	0.497830	−	0.867275i	$-0.334130\pi$
$420$	−1.21528e9	−	5.03386e8i	−0.00190570	−	0.000789368i
$421$			1.09759e12i			1.70282i	0.524498	+	0.851412i	$0.324253\pi$
$421$			1.09759e12i			1.70282i	−0.524498	+	0.851412i	$0.675747\pi$
$422$	−3.12547e11	+	7.54556e11i	−0.479744	+	1.15820i
$423$	1.26370e11	−	1.26370e11i	0.191917	−	0.191917i
$424$	4.26087e11			0.640254
$425$	2.69127e11	+	6.15966e11i	0.400136	+	0.915813i
$426$	6.68398e11			0.983314
$427$	6.54655e11	−	6.54655e11i	0.952987	−	0.952987i
$428$	1.17157e10	−	2.82842e10i	0.0168761	−	0.0407425i
$429$			1.10513e12i			1.57527i
$430$	3.14832e9	+	1.30408e9i	0.00444089	+	0.00183948i
$431$	−4.37957e11	−	1.05732e12i	−0.611341	−	1.47591i	−0.861528	−	0.507710i	$-0.830492\pi$
$431$	−4.37957e11	−	1.05732e12i	−0.611341	−	1.47591i	0.250187	−	0.968198i	$-0.419508\pi$
$432$	5.25580e11	−	2.17702e11i	0.726042	−	0.300736i
$433$	−5.77891e11	−	5.77891e11i	−0.790042	−	0.790042i	0.191459	−	0.981501i	$-0.438678\pi$
$433$	−5.77891e11	−	5.77891e11i	−0.790042	−	0.790042i	−0.981501	+	0.191459i	$0.938678\pi$
$434$	4.57413e11	+	4.57413e11i	0.618877	+	0.618877i
$435$	−2.70004e9	+	1.11839e9i	−0.00361550	+	0.00149759i
$436$	−3.45032e10	−	8.32982e10i	−0.0457268	−	0.110394i
$437$	−1.62080e11	−	6.71356e10i	−0.212600	−	0.0880616i
$438$		−	7.50597e11i		−	0.974481i
$439$	−5.59701e11	+	1.35124e12i	−0.719226	+	1.73637i	−0.0436819	+	0.999045i	$0.513909\pi$
$439$	−5.59701e11	+	1.35124e12i	−0.719226	+	1.73637i	−0.675544	+	0.737320i	$0.736091\pi$
$440$	−1.98781e10	+	1.98781e10i	−0.0252835	+	0.0252835i
$441$	−1.71091e11			−0.215404
$442$	−5.52868e11	−	1.26538e12i	−0.689003	−	1.57696i
$443$	−7.93546e11			−0.978938			−0.489469	−	0.872021i	$-0.662809\pi$
$443$	−7.93546e11			−0.978938			−0.489469	+	0.872021i	$0.662809\pi$
$444$	−2.32725e10	+	2.32725e10i	−0.0284197	+	0.0284197i
$445$	1.18472e10	−	2.86017e10i	0.0143218	−	0.0345758i
$446$			9.83865e11i			1.17741i
$447$	1.34411e11	+	5.56751e10i	0.159240	+	0.0659594i
$448$	−2.94087e11	−	7.09989e11i	−0.344925	−	0.832723i
$449$	−2.04276e11	+	8.46139e10i	−0.237197	+	0.0982501i	−0.498116	−	0.867111i	$-0.665975\pi$
$449$	−2.04276e11	+	8.46139e10i	−0.237197	+	0.0982501i	0.260919	+	0.965361i	$0.415975\pi$
$450$	3.55882e11	+	3.55882e11i	0.409119	+	0.409119i
$451$	−7.51522e11	−	7.51522e11i	−0.855357	−	0.855357i
$452$	9.29004e10	−	3.84806e10i	0.104687	−	0.0433629i
$453$	1.64749e11	+	3.97740e11i	0.183816	+	0.443770i
$454$	6.76056e10	+	2.80032e10i	0.0746847	+	0.0309354i
$455$			3.41658e10i			0.0373715i
$456$	1.85965e11	−	4.48959e11i	0.201414	−	0.486256i
$457$	9.07989e11	−	9.07989e11i	0.973773	−	0.973773i	−0.0258919	−	0.999665i	$-0.508243\pi$
$457$	9.07989e11	−	9.07989e11i	0.973773	−	0.973773i	0.999665	+	0.0258919i	$0.00824258\pi$
$458$	4.79639e11			0.509354
$459$	−9.37927e11	+	1.80324e10i	−0.986306	+	0.0189626i
$460$	−1.13580e9			−0.00118275
$461$	5.67089e11	−	5.67089e11i	0.584787	−	0.584787i	−0.351428	−	0.936215i	$-0.614304\pi$
$461$	5.67089e11	−	5.67089e11i	0.584787	−	0.584787i	0.936215	+	0.351428i	$0.114304\pi$
$462$	−2.30669e11	+	5.56885e11i	−0.235560	+	0.568691i
$463$			4.65197e11i			0.470460i	0.971940	+	0.235230i	$0.0755844\pi$
$463$			4.65197e11i			0.470460i	−0.971940	+	0.235230i	$0.924416\pi$
$464$	−1.96572e11	−	8.14226e10i	−0.196875	−	0.0815481i
$465$	6.67933e9	+	1.61253e10i	0.00662514	+	0.0159945i
$466$	1.36437e12	−	5.65140e11i	1.34028	−	0.555161i
$467$	−1.20171e12	−	1.20171e12i	−1.16916	−	1.16916i	−0.982408	−	0.186749i	$-0.940205\pi$
$467$	−1.20171e12	−	1.20171e12i	−1.16916	−	1.16916i	−0.186749	−	0.982408i	$-0.559795\pi$
$468$	1.53290e11	+	1.53290e11i	0.147709	+	0.147709i
$469$	−5.08200e11	+	2.10503e11i	−0.485017	+	0.200900i
$470$	3.80835e9	+	9.19416e9i	0.00359995	+	0.00869104i
$471$	−8.62403e11	−	3.57219e11i	−0.807451	−	0.334457i
$472$		−	1.38692e12i		−	1.28621i
$473$	−1.25295e11	+	3.02490e11i	−0.115096	+	0.277866i
$474$	2.62715e11	−	2.62715e11i	0.239047	−	0.239047i
$475$	9.07639e11			0.818072
$476$	3.03560e9	+	1.57891e11i	0.00271027	+	0.140970i
$477$	−4.32069e11			−0.382138
$478$	7.55199e11	−	7.55199e11i	0.661661	−	0.661661i
$479$	4.04081e11	−	9.75538e11i	0.350719	−	0.846710i	−0.645813	−	0.763496i	$-0.723481\pi$
$479$	4.04081e11	−	9.75538e11i	0.350719	−	0.846710i	0.996532	−	0.0832141i	$-0.0265185\pi$
$480$		−	5.82755e9i		−	0.00501072i
$481$	7.89775e11	+	3.27135e11i	0.672745	+	0.278660i
$482$	7.93747e11	+	1.91627e12i	0.669839	+	1.61713i
$483$	−1.52308e11	+	6.30882e10i	−0.127339	+	0.0527455i
$484$	−1.34171e11	−	1.34171e11i	−0.111136	−	0.111136i
$485$	3.49772e9	+	3.49772e9i	0.00287043	+	0.00287043i
$486$	−1.04539e12	+	4.33016e11i	−0.849996	+	0.352080i
$487$	3.79720e11	+	9.16725e11i	0.305903	+	0.738514i	0.999829	+	0.0184687i	$0.00587912\pi$
$487$	3.79720e11	+	9.16725e11i	0.305903	+	0.738514i	−0.693927	+	0.720046i	$0.744121\pi$
$488$	2.04579e12	+	8.47395e11i	1.63295	+	0.676389i
$489$		−	2.31039e11i		−	0.182724i
$490$	3.64589e9	−	8.80196e9i	0.00285707	−	0.00689759i
$491$	−1.03967e12	+	1.03967e12i	−0.807288	+	0.807288i	−0.984223	−	0.176934i	$-0.943382\pi$
$491$	−1.03967e12	+	1.03967e12i	−0.807288	+	0.807288i	0.176934	+	0.984223i	$0.443382\pi$
$492$	1.18945e11			0.0915176
$493$	2.52817e11	+	2.43279e11i	0.192750	+	0.185479i
$494$	−1.86456e12			−1.40866
$495$	2.01571e10	−	2.01571e10i	0.0150906	−	0.0150906i
$496$	−4.86277e11	+	1.17398e12i	−0.360758	+	0.870947i
$497$			1.98539e12i			1.45963i
$498$	−6.09426e11	−	2.52432e11i	−0.444006	−	0.183913i
$499$	−6.50804e10	−	1.57118e11i	−0.0469892	−	0.113442i	0.898642	−	0.438682i	$-0.144555\pi$
$499$	−6.50804e10	−	1.57118e11i	−0.0469892	−	0.113442i	−0.945631	+	0.325241i	$0.894555\pi$
$500$	1.08611e10	−	4.49883e9i	0.00777160	−	0.00321910i
$501$	−7.09580e11	−	7.09580e11i	−0.503190	−	0.503190i
$502$	−5.63445e11	−	5.63445e11i	−0.395990	−	0.395990i
$503$	7.34308e11	−	3.04160e11i	0.511473	−	0.211859i	−0.111994	−	0.993709i	$-0.535724\pi$
$503$	7.34308e11	−	3.04160e11i	0.511473	−	0.211859i	0.623467	+	0.781850i	$0.285724\pi$
$504$	3.06302e11	+	7.39478e11i	0.211452	+	0.510491i
$505$	2.74127e10	+	1.13547e10i	0.0187560	+	0.00776900i
$506$			5.20464e11i			0.352950i
$507$	−8.86190e11	+	2.13945e12i	−0.595650	+	1.43803i
$508$	−2.83923e11	+	2.83923e11i	−0.189154	+	0.189154i
$509$	7.47208e11			0.493414			0.246707	−	0.969090i	$-0.420651\pi$
$509$	7.47208e11			0.493414			0.246707	+	0.969090i	$0.420651\pi$
$510$	7.41452e9	−	1.89210e10i	0.00485308	−	0.0123845i
$511$	2.22955e12			1.44652
$512$	1.23442e12	−	1.23442e12i	0.793866	−	0.793866i
$513$	−4.84739e11	+	1.17026e12i	−0.309015	+	0.746028i
$514$		−	4.30565e11i		−	0.272085i
$515$	2.65126e10	+	1.09819e10i	0.0166081	+	0.00687930i
$516$	−1.40225e10	−	3.38534e10i	−0.00870768	−	0.0210222i
$517$	−8.83373e11	+	3.65905e11i	−0.543797	+	0.225248i
$518$	3.29693e11	+	3.29693e11i	0.201199	+	0.201199i
$519$	−2.80351e11	−	2.80351e11i	−0.169609	−	0.169609i
$520$	−7.54963e10	+	3.12716e10i	−0.0452804	+	0.0187558i
$521$	1.84838e10	+	4.46238e10i	0.0109906	+	0.0265336i	0.929280	−	0.369377i	$-0.120429\pi$
$521$	1.84838e10	+	4.46238e10i	0.0109906	+	0.0265336i	−0.918289	+	0.395911i	$0.870429\pi$
$522$	2.42702e11	+	1.00530e11i	0.143072	+	0.0592625i
$523$			1.41680e11i			0.0828041i	0.999143	+	0.0414020i	$0.0131824\pi$
$523$			1.41680e11i			0.0828041i	−0.999143	+	0.0414020i	$0.986818\pi$
$524$	4.86959e10	−	1.17562e11i	0.0282164	−	0.0681205i
$525$	6.03105e11	−	6.03105e11i	0.346478	−	0.346478i
$526$	−2.95759e12			−1.68462
$527$	1.45293e12	−	1.50989e12i	0.820533	−	0.852702i
$528$	−1.18405e12			−0.663007
$529$	1.17295e12	−	1.17295e12i	0.651223	−	0.651223i
$530$	9.20725e9	−	2.22283e10i	0.00506861	−	0.0122367i
$531$			1.40639e12i			0.767681i
$532$	1.97003e11	+	8.16013e10i	0.106628	+	0.0441667i
$533$	−1.18227e12	−	2.85426e12i	−0.634519	−	1.53187i
$534$	1.46680e12	−	6.07570e11i	0.780614	−	0.323341i
$535$	−8.27467e9	−	8.27467e9i	−0.00436675	−	0.00436675i
$536$	−9.30299e11	−	9.30299e11i	−0.486834	−	0.486834i
$537$	1.24163e12	−	5.14298e11i	0.644327	−	0.266889i
$538$	−2.20857e11	−	5.33195e11i	−0.113655	−	0.274388i
$539$	8.45691e11	+	3.50297e11i	0.431581	+	0.178767i
$540$			8.20082e9i			0.00415036i
$541$	9.54742e11	−	2.30495e12i	0.479179	−	1.15684i	−0.480815	−	0.876822i	$-0.659659\pi$
$541$	9.54742e11	−	2.30495e12i	0.479179	−	1.15684i	0.959994	−	0.280019i	$-0.0903409\pi$
$542$	9.76183e11	−	9.76183e11i	0.485886	−	0.485886i
$543$	3.94318e10			0.0194647
$544$	−6.41099e11	+	2.80108e11i	−0.313856	+	0.137130i
$545$	−3.44633e10			−0.0167330
$546$	−1.23896e12	+	1.23896e12i	−0.596608	+	0.596608i
$547$	5.84199e11	−	1.41038e12i	0.279009	−	0.673586i	−0.720800	−	0.693143i	$-0.756225\pi$
$547$	5.84199e11	−	1.41038e12i	0.279009	−	0.673586i	0.999809	+	0.0195567i	$0.00622547\pi$
$548$			2.95874e11i			0.140151i
$549$	−2.07451e12	−	8.59292e11i	−0.974632	−	0.403706i
$550$	−1.03046e12	−	2.48775e12i	−0.480173	−	1.15924i
$551$	4.37689e11	−	1.81297e11i	0.202294	−	0.0837929i
$552$	−2.78812e11	−	2.78812e11i	−0.127816	−	0.127816i
$553$	7.80362e11	+	7.80362e11i	0.354841	+	0.354841i
$554$	−1.74332e12	+	7.22105e11i	−0.786289	+	0.325691i
$555$	4.81431e9	+	1.16228e10i	0.00215385	+	0.00519986i
$556$	−1.65053e11	−	6.83672e10i	−0.0732465	−	0.0303397i
$557$			1.83453e12i			0.807563i	0.914855	+	0.403782i	$0.132304\pi$
$557$			1.83453e12i			0.807563i	−0.914855	+	0.403782i	$0.867696\pi$
$558$	6.00394e11	−	1.44948e12i	0.262170	−	0.632934i
$559$	−6.72979e11	+	6.72979e11i	−0.291507	+	0.291507i
$560$	−3.66058e10			−0.0157291
$561$	1.81793e12	+	7.12386e11i	0.774897	+	0.303657i
$562$	2.77788e12			1.17463
$563$	−3.01559e12	+	3.01559e12i	−1.26498	+	1.26498i	−0.316333	+	0.948648i	$0.602452\pi$
$563$	−3.01559e12	+	3.01559e12i	−1.26498	+	1.26498i	−0.948648	+	0.316333i	$0.897548\pi$
$564$	4.09505e10	−	9.88634e10i	0.0170413	−	0.0411414i
$565$		−	3.84361e10i		−	0.0158680i
$566$	1.63005e12	+	6.75190e11i	0.667618	+	0.276536i
$567$	−3.22940e10	−	7.79646e10i	−0.0131219	−	0.0316792i
$568$	−4.38713e12	+	1.81721e12i	−1.76853	+	0.732549i
$569$	1.30192e11	+	1.30192e11i	0.0520691	+	0.0520691i	0.732662	−	0.680593i	$-0.238278\pi$
$569$	1.30192e11	+	1.30192e11i	0.0520691	+	0.0520691i	−0.680593	+	0.732662i	$0.738278\pi$
$570$	−1.94030e10	−	1.94030e10i	−0.00769895	−	0.00769895i
$571$	5.88635e11	−	2.43820e11i	0.231731	−	0.0959860i	−0.263797	−	0.964578i	$-0.584975\pi$
$571$	5.88635e11	−	2.43820e11i	0.231731	−	0.0959860i	0.495527	+	0.868592i	$0.334975\pi$
$572$	−4.43851e11	−	1.07155e12i	−0.173363	−	0.418534i
$573$	5.02545e11	+	2.08161e11i	0.194751	+	0.0806683i
$574$		−	1.68506e12i		−	0.647905i
$575$	2.81831e11	−	6.80399e11i	0.107518	−	0.259572i
$576$	−1.31794e12	+	1.31794e12i	−0.498877	+	0.498877i
$577$	−1.01674e12			−0.381873			−0.190936	−	0.981602i	$-0.561152\pi$
$577$	−1.01674e12			−0.381873			−0.190936	+	0.981602i	$0.561152\pi$
$578$	−2.43792e12	+	9.37770e10i	−0.908542	+	0.0349479i
$579$	−7.98129e11			−0.295134
$580$	2.16882e9	−	2.16882e9i	0.000795790	−	0.000795790i
$581$	7.49818e11	−	1.81022e12i	0.273000	−	0.659081i
$582$			2.53676e11i			0.0916487i
$583$	2.13569e12	+	8.84632e11i	0.765649	+	0.317142i
$584$	2.04069e12	+	4.92665e12i	0.725969	+	1.75264i
$585$	7.65562e10	−	3.17106e10i	0.0270258	−	0.0111945i
$586$	2.30003e12	+	2.30003e12i	0.805737	+	0.805737i
$587$	1.55336e12	+	1.55336e12i	0.540010	+	0.540010i	0.923532	−	0.383522i	$-0.125289\pi$
$587$	1.55336e12	+	1.55336e12i	0.540010	+	0.540010i	−0.383522	+	0.923532i	$0.625289\pi$
$588$	−9.46461e10	+	3.92037e10i	−0.0326516	+	0.0135248i
$589$	−1.08275e12	−	2.61399e12i	−0.370689	−	0.894922i
$590$	−7.23534e10	−	2.99698e10i	−0.0245824	−	0.0101824i
$591$		−	2.81395e12i		−	0.948794i
$592$	−3.50498e11	+	8.46176e11i	−0.117284	+	0.283148i
$593$	2.04798e11	−	2.04798e11i	0.0680111	−	0.0680111i	−0.672283	−	0.740294i	$-0.734686\pi$
$593$	2.04798e11	−	2.04798e11i	0.0680111	−	0.0680111i	0.740294	+	0.672283i	$0.234686\pi$
$594$	3.75790e12			1.23853
$595$	5.62024e10	+	2.20239e10i	0.0183835	+	0.00720390i
$596$	−1.52688e11			−0.0495676
$597$	−6.87837e11	+	6.87837e11i	−0.221616	+	0.221616i
$598$	−5.78964e11	+	1.39774e12i	−0.185138	+	0.446963i
$599$		−	3.94569e12i		−	1.25228i	−0.779710	−	0.626141i	$-0.784633\pi$
$599$		−	3.94569e12i		−	1.25228i	0.779710	−	0.626141i	$-0.215367\pi$
$600$	1.88470e12	+	7.80667e11i	0.593692	+	0.245915i
$601$	1.67836e12	+	4.05192e12i	0.524747	+	1.26685i	0.934925	+	0.354845i	$0.115466\pi$
$601$	1.67836e12	+	4.05192e12i	0.524747	+	1.26685i	−0.410178	+	0.912005i	$0.634534\pi$
$602$	−4.79588e11	+	1.98652e11i	−0.148828	+	0.0616465i
$603$	9.43360e11	+	9.43360e11i	0.290569	+	0.290569i
$604$	−3.19488e11	−	3.19488e11i	−0.0976760	−	0.0976760i
$605$	−6.70080e10	+	2.77556e10i	−0.0203342	+	0.00842271i
$606$	5.82312e11	+	1.40583e12i	0.175400	+	0.423452i
$607$	−1.14973e11	−	4.76235e10i	−0.0343754	−	0.0142388i	0.365429	−	0.930839i	$-0.380922\pi$
$607$	−1.14973e11	−	4.76235e10i	−0.0343754	−	0.0142388i	−0.399805	+	0.916600i	$0.630922\pi$
$608$			9.44673e11i			0.280359i
$609$	1.70367e11	−	4.11301e11i	0.0501888	−	0.121166i
$610$	8.84145e10	−	8.84145e10i	0.0258547	−	0.0258547i
$611$	−2.77939e12			−0.806797
$612$	3.50974e11	−	1.53347e11i	0.101133	−	0.0441869i
$613$	−2.13411e12			−0.610442			−0.305221	−	0.952282i	$-0.598730\pi$
$613$	−2.13411e12			−0.610442			−0.305221	+	0.952282i	$0.598730\pi$
$614$	1.70912e12	−	1.70912e12i	0.485306	−	0.485306i
$615$	1.73990e10	−	4.20049e10i	0.00490440	−	0.0118403i
$616$		−	4.28232e12i		−	1.19830i
$617$	−5.29169e12	−	2.19189e12i	−1.46998	−	0.608885i	−0.503124	−	0.864214i	$-0.667816\pi$
$617$	−5.29169e12	−	2.19189e12i	−1.46998	−	0.608885i	−0.966854	+	0.255329i	$0.917816\pi$
$618$	5.63192e11	+	1.35967e12i	0.155313	+	0.374959i
$619$	1.28946e12	−	5.34113e11i	0.353022	−	0.146226i	−0.199123	−	0.979974i	$-0.563809\pi$
$619$	1.28946e12	−	5.34113e11i	0.353022	−	0.146226i	0.552145	+	0.833748i	$0.313809\pi$
$620$	−1.29528e10	−	1.29528e10i	−0.00352047	−	0.00352047i
$621$	7.26756e11	+	7.26756e11i	0.196099	+	0.196099i
$622$	3.33613e9	−	1.38187e9i	0.000893688	−	0.000370178i
$623$	1.80471e12	+	4.35695e12i	0.479966	+	1.15874i
$624$	−3.17985e12	−	1.31714e12i	−0.839608	−	0.347777i
$625$			3.80796e12i			0.998233i
$626$	1.35070e12	−	3.26087e12i	0.351538	−	0.848689i
$627$	1.86423e12	−	1.86423e12i	0.481722	−	0.481722i
$628$	9.79669e11			0.251340
$629$	1.04724e12	−	1.08829e12i	0.266758	−	0.277216i
$630$	4.51962e10			0.0114306
$631$	−4.02283e12	+	4.02283e12i	−1.01018	+	1.01018i	−0.0102352	+	0.999948i	$0.503258\pi$
$631$	−4.02283e12	+	4.02283e12i	−1.01018	+	1.01018i	−0.999948	+	0.0102352i	$0.996742\pi$
$632$	−1.01011e12	+	2.43863e12i	−0.251850	+	0.608021i
$633$		−	3.35688e12i		−	0.831035i
$634$	6.53456e10	+	2.70670e10i	0.0160626	+	0.00665333i
$635$	5.87344e10	+	1.41797e11i	0.0143354	+	0.0346088i
$636$	−2.39017e11	+	9.90042e10i	−0.0579258	+	0.0239937i
$637$	1.88149e12	+	1.88149e12i	0.452767	+	0.452767i
$638$	−9.93831e11	−	9.93831e11i	−0.237476	−	0.237476i
$639$	4.44872e12	−	1.84272e12i	1.05556	−	0.437225i
$640$	−2.62148e10	−	6.32882e10i	−0.00617642	−	0.0149112i
$641$	−6.48020e12	−	2.68419e12i	−1.51610	−	0.627989i	−0.539294	−	0.842118i	$-0.681309\pi$
$641$	−6.48020e12	−	2.68419e12i	−1.51610	−	0.627989i	−0.976805	+	0.214129i	$0.931309\pi$
$642$		−	6.00129e11i		−	0.139424i
$643$	−2.22025e12	+	5.36016e12i	−0.512215	+	1.23660i	0.430377	+	0.902649i	$0.358381\pi$
$643$	−2.22025e12	+	5.36016e12i	−0.512215	+	1.23660i	−0.942592	+	0.333947i	$0.891619\pi$
$644$	1.22343e11	−	1.22343e11i	0.0280280	−	0.0280280i
$645$	−1.40063e10			−0.00318643
$646$	−1.20193e12	+	3.06718e12i	−0.271539	+	0.692937i
$647$	1.98910e12			0.446260			0.223130	−	0.974789i	$-0.428373\pi$
$647$	1.98910e12			0.446260			0.223130	+	0.974789i	$0.428373\pi$
$648$	1.42720e11	−	1.42720e11i	0.0317979	−	0.0317979i
$649$	2.87949e12	−	6.95170e12i	0.637110	−	1.53812i
$650$		−	7.82729e12i		−	1.71989i
$651$	−2.45640e12	−	1.01747e12i	−0.536024	−	0.222029i
$652$	9.27917e10	+	2.24019e11i	0.0201092	+	0.0485479i
$653$	−2.99785e12	+	1.24175e12i	−0.645209	+	0.267254i	−0.681199	−	0.732098i	$-0.738541\pi$
$653$	−2.99785e12	+	1.24175e12i	−0.645209	+	0.267254i	0.0359906	+	0.999352i	$0.488541\pi$
$654$	−1.24974e12	−	1.24974e12i	−0.267129	−	0.267129i
$655$	−3.43934e10	−	3.43934e10i	−0.00730111	−	0.00730111i
$656$	3.05809e12	−	1.26670e12i	0.644738	−	0.267059i
$657$	−2.06933e12	−	4.99581e12i	−0.433298	−	1.04607i
$658$	−1.40056e12	−	5.80132e11i	−0.291263	−	0.120645i
$659$			1.05636e12i			0.218186i	0.994032	+	0.109093i	$0.0347946\pi$
$659$			1.05636e12i			0.218186i	−0.994032	+	0.109093i	$0.965205\pi$
$660$	6.53197e9	−	1.57696e10i	0.00133998	−	0.00323499i
$661$	−2.16113e12	+	2.16113e12i	−0.440325	+	0.440325i	−0.892121	−	0.451796i	$-0.850783\pi$
$661$	−2.16113e12	+	2.16113e12i	−0.440325	+	0.440325i	0.451796	+	0.892121i	$0.350783\pi$
$662$	−3.68964e12			−0.746661
$663$	4.08971e12	+	3.93542e12i	0.822019	+	0.791008i
$664$	4.68635e12			0.935575
$665$	5.76340e10	−	5.76340e10i	0.0114283	−	0.0114283i
$666$	4.32751e11	−	1.04475e12i	0.0852322	−	0.205769i
$667$		−	3.84402e11i		−	0.0752002i
$668$	9.73008e11	+	4.03033e11i	0.189070	+	0.0783153i
$669$	−1.54752e12	−	3.73604e12i	−0.298688	−	0.721097i
$670$	−6.86349e10	+	2.84295e10i	−0.0131586	+	0.00545046i
$671$	8.49485e12	+	8.49485e12i	1.61772	+	1.61772i
$672$	6.27713e11	+	6.27713e11i	0.118741	+	0.118741i
$673$	1.31466e12	−	5.44550e11i	0.247028	−	0.102322i	−0.255734	−	0.966747i	$-0.582317\pi$
$673$	1.31466e12	−	5.44550e11i	0.247028	−	0.102322i	0.502762	+	0.864425i	$0.332317\pi$
$674$	−1.59911e12	−	3.86059e12i	−0.298475	−	0.720583i
$675$	−4.91268e12	−	2.03490e12i	−0.910860	−	0.377290i
$676$		−	2.43037e12i		−	0.447622i
$677$	1.46887e12	−	3.54617e12i	0.268741	−	0.648799i	−0.730683	−	0.682717i	$-0.760798\pi$
$677$	1.46887e12	−	3.54617e12i	0.268741	−	0.648799i	0.999425	+	0.0339175i	$0.0107984\pi$
$678$	1.39381e12	−	1.39381e12i	0.253320	−	0.253320i
$679$	−7.53513e11			−0.136043
$680$	2.77523e9	+	1.44349e11i	0.000497748	+	0.0258895i
$681$	−3.00765e11			−0.0535878
$682$	−5.93542e12	+	5.93542e12i	−1.05056	+	1.05056i
$683$	−3.64873e11	+	8.80882e11i	−0.0641577	+	0.154890i	−0.952707	−	0.303891i	$-0.901714\pi$
$683$	−3.64873e11	+	8.80882e11i	−0.0641577	+	0.154890i	0.888549	+	0.458782i	$0.151714\pi$
$684$		−	5.17167e11i		−	0.0903396i
$685$	1.04486e11	+	4.32797e10i	0.0181323	+	0.00751063i
$686$	2.19709e12	+	5.30425e12i	0.378782	+	0.914461i
$687$	−1.82133e12	+	7.54421e11i	−0.311949	+	0.129214i
$688$	−7.21039e11	−	7.21039e11i	−0.122691	−	0.122691i
$689$	4.75148e12	+	4.75148e12i	0.803234	+	0.803234i
$690$	−2.05700e10	+	8.52037e9i	−0.00345472	+	0.00143099i
$691$	−8.65703e10	−	2.08999e11i	−0.0144450	−	0.0348733i	0.916492	−	0.400052i	$-0.131008\pi$
$691$	−8.65703e10	−	2.08999e11i	−0.0144450	−	0.0348733i	−0.930937	+	0.365179i	$0.881008\pi$
$692$	3.84429e11	+	1.59236e11i	0.0637293	+	0.0263975i
$693$			4.34244e12i			0.715212i
$694$	3.15919e12	−	7.62695e12i	0.516961	−	1.24805i
$695$	−4.82870e10	+	4.82870e10i	−0.00785052	+	0.00785052i
$696$	1.06479e12			0.171997
$697$	−5.45734e12	+	1.04922e11i	−0.875857	+	0.0168391i
$698$	−5.39943e12			−0.860991
$699$	−4.29201e12	+	4.29201e12i	−0.680008	+	0.680008i
$700$	−3.42556e11	+	8.27004e11i	−0.0539251	+	0.130187i
$701$		−	5.32445e12i		−	0.832805i	−0.909180	−	0.416403i	$-0.863291\pi$
$701$		−	5.32445e12i		−	0.832805i	0.909180	−	0.416403i	$-0.136709\pi$
$702$	1.00921e13	+	4.18029e12i	1.56843	+	0.649665i
$703$	−7.80422e11	−	1.88411e12i	−0.120512	−	0.290942i
$704$	9.21287e12	−	3.81609e12i	1.41357	−	0.585521i
$705$	−2.89229e10	−	2.89229e10i	−0.00440951	−	0.00440951i
$706$	6.16402e12	+	6.16402e12i	0.933777	+	0.933777i
$707$	−4.17582e12	+	1.72968e12i	−0.628572	+	0.260363i
$708$	3.22260e11	+	7.78005e11i	0.0482011	+	0.116368i
$709$	6.75466e12	+	2.79787e12i	1.00391	+	0.415834i	0.823230	−	0.567708i	$-0.192170\pi$
$709$	6.75466e12	+	2.79787e12i	1.00391	+	0.415834i	0.180681	+	0.983542i	$0.442170\pi$
$710$			2.68137e11i			0.0395999i
$711$	1.02429e12	−	2.47286e12i	0.150318	−	0.362900i
$712$	−7.97574e12	+	7.97574e12i	−1.16308	+	1.16308i
$713$	−2.29575e12			−0.332676
$714$	1.23942e12	+	2.83673e12i	0.178475	+	0.408484i
$715$	−4.43338e11			−0.0634392
$716$	−9.97345e11	+	9.97345e11i	−0.141820	+	0.141820i
$717$	−1.67987e12	+	4.05557e12i	−0.237378	+	0.573080i
$718$			5.58919e12i			0.784854i
$719$	4.97906e12	+	2.06240e12i	0.694813	+	0.287801i	0.702004	−	0.712173i	$-0.252289\pi$
$719$	4.97906e12	+	2.06240e12i	0.694813	+	0.287801i	−0.00719096	+	0.999974i	$0.502289\pi$
$720$	3.39752e10	+	8.20234e10i	0.00471157	+	0.0113747i
$721$	−4.03871e12	+	1.67289e12i	−0.556588	+	0.230546i
$722$	−1.54896e12	−	1.54896e12i	−0.212140	−	0.212140i
$723$	−6.02820e12	−	6.02820e12i	−0.820474	−	0.820474i
$724$	−3.82337e10	+	1.58369e10i	−0.00517158	+	0.00214214i
$725$	7.61070e11	+	1.83739e12i	0.102307	+	0.246990i
$726$	−3.43642e12	−	1.42341e12i	−0.459083	−	0.190158i
$727$			1.11382e13i			1.47880i	0.673265	+	0.739402i	$0.264892\pi$
$727$			1.11382e13i			1.47880i	−0.673265	+	0.739402i	$0.735108\pi$
$728$	4.76365e12	−	1.15005e13i	0.628563	−	1.51749i
$729$	3.06130e12	−	3.06130e12i	0.401450	−	0.401450i
$730$	3.01112e11			0.0392442
$731$	6.73230e11	+	1.54086e12i	0.0872038	+	0.199588i
$732$	−1.34450e12			−0.173086
$733$	2.52060e12	−	2.52060e12i	0.322505	−	0.322505i	−0.527222	−	0.849727i	$-0.676766\pi$
$733$	2.52060e12	−	2.52060e12i	0.322505	−	0.322505i	0.849727	+	0.527222i	$0.176766\pi$
$734$	−7.68194e11	+	1.85458e12i	−0.0976874	+	0.235838i
$735$			3.91583e10i			0.00494916i
$736$	7.08161e11	+	2.93330e11i	0.0889574	+	0.0368474i
$737$	−2.73150e12	−	6.59443e12i	−0.341034	−	0.823330i
$738$	−3.77575e12	+	1.56397e12i	−0.468543	+	0.194077i
$739$	−1.69412e12	−	1.69412e12i	−0.208951	−	0.208951i	0.594870	−	0.803822i	$-0.297203\pi$
$739$	−1.69412e12	−	1.69412e12i	−0.208951	−	0.208951i	−0.803822	+	0.594870i	$0.797203\pi$
$740$	−9.33608e9	−	9.33608e9i	−0.00114452	−	0.00114452i
$741$	7.08030e12	−	2.93276e12i	0.862720	−	0.357350i
$742$	1.40256e12	+	3.38607e12i	0.169865	+	0.410089i
$743$	−7.71248e12	−	3.19461e12i	−0.928420	−	0.384564i	−0.133341	−	0.991070i	$-0.542571\pi$
$743$	−7.71248e12	−	3.19461e12i	−0.928420	−	0.384564i	−0.795079	+	0.606506i	$0.792571\pi$
$744$		−	6.35920e12i		−	0.760894i
$745$	−2.23348e10	+	5.39210e10i	−0.00265631	+	0.00641290i
$746$	−5.25873e12	+	5.25873e12i	−0.621664	+	0.621664i
$747$	−4.75214e12			−0.558402
$748$	−2.04881e12	+	3.93901e10i	−0.239301	+	0.00460076i
$749$	1.78261e12			0.206961
$750$	1.62953e11	−	1.62953e11i	0.0188055	−	0.0188055i
$751$	3.76419e12	−	9.08756e12i	0.431809	−	1.04248i	−0.546895	−	0.837201i	$-0.684190\pi$
$751$	3.76419e12	−	9.08756e12i	0.431809	−	1.04248i	0.978704	−	0.205278i	$-0.0658098\pi$
$752$		−	2.97788e12i		−	0.339568i
$753$	3.02581e12	+	1.25333e12i	0.342977	+	0.142066i
$754$	−1.56346e12	−	3.77454e12i	−0.176164	−	0.425297i
$755$	−1.59559e11	+	6.60915e10i	−0.0178715	+	0.00740260i
$756$	−8.83349e11	−	8.83349e11i	−0.0983523	−	0.0983523i
$757$	−6.70583e12	−	6.70583e12i	−0.742200	−	0.742200i	0.230801	−	0.973001i	$-0.425865\pi$
$757$	−6.70583e12	−	6.70583e12i	−0.742200	−	0.742200i	−0.973001	+	0.230801i	$0.925865\pi$
$758$	9.31039e12	−	3.85649e12i	1.02437	−	0.424308i
$759$	−8.18636e11	−	1.97636e12i	−0.0895371	−	0.216162i

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:	\( N \)	\(=\)	\( 17 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	17.d (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-14.5474 + 14.5474i) q^{2} +(32.3594 - 78.1225i) q^{3} +88.7454i q^{4} +(31.3399 + 12.9814i) q^{5} +(665.735 + 1607.23i) q^{6} +(-4774.06 + 1977.48i) q^{7} +(-8739.29 - 8739.29i) q^{8} +(8861.98 + 8861.98i) q^{9} +O(q^{10})\)	\(q+(-14.5474 + 14.5474i) q^{2} +(32.3594 - 78.1225i) q^{3} +88.7454i q^{4} +(31.3399 + 12.9814i) q^{5} +(665.735 + 1607.23i) q^{6} +(-4774.06 + 1977.48i) q^{7} +(-8739.29 - 8739.29i) q^{8} +(8861.98 + 8861.98i) q^{9} +(-644.761 + 267.069i) q^{10} +(-25659.9 - 61948.5i) q^{11} +(6933.01 + 2871.75i) q^{12} -194911. i q^{13} +(40683.0 - 98217.5i) q^{14} +(2028.28 - 2028.28i) q^{15} +208831. q^{16} +(-320627. - 125643. i) q^{17} -257838. q^{18} +(-328794. + 328794. i) q^{19} +(-1152.04 + 2781.27i) q^{20} +436952. i q^{21} +(1.27448e6 + 527906. i) q^{22} +(144382. + 348570. i) q^{23} +(-965534. + 399937. i) q^{24} +(-1.38025e6 - 1.38025e6i) q^{25} +(2.83545e6 + 2.83545e6i) q^{26} +(2.51678e6 - 1.04248e6i) q^{27} +(-175492. - 423676. i) q^{28} +(-941296. - 389898. i) q^{29} +59012.5i q^{30} +(-2.32857e6 + 5.62167e6i) q^{31} +(1.43657e6 - 1.43657e6i) q^{32} -5.66992e6 q^{33} +(6.49208e6 - 2.83651e6i) q^{34} -175289. q^{35} +(-786460. + 786460. i) q^{36} +(-1.67838e6 + 4.05197e6i) q^{37} -9.56621e6i q^{38} +(-1.52270e7 - 6.30721e6i) q^{39} +(-160440. - 387337. i) q^{40} +(1.46439e7 - 6.06570e6i) q^{41} +(-6.35652e6 - 6.35652e6i) q^{42} +(-3.45275e6 - 3.45275e6i) q^{43} +(5.49765e6 - 2.27720e6i) q^{44} +(162693. + 392775. i) q^{45} +(-7.17118e6 - 2.97040e6i) q^{46} -1.42598e7i q^{47} +(6.75764e6 - 1.63144e7i) q^{48} +(-9.65308e6 + 9.65308e6i) q^{49} +4.01583e7 q^{50} +(-2.01909e7 + 2.09825e7i) q^{51} +1.72975e7 q^{52} +(-2.43777e7 + 2.43777e7i) q^{53} +(-2.14472e7 + 5.17780e7i) q^{54} -2.27456e6i q^{55} +(5.90037e7 + 2.44401e7i) q^{56} +(1.50466e7 + 3.63258e7i) q^{57} +(1.93654e7 - 8.02143e6i) q^{58} +(7.93497e7 + 7.93497e7i) q^{59} +(180001. + 180001. i) q^{60} +(-1.65528e8 + 6.85638e7i) q^{61} +(-4.79061e7 - 1.15655e8i) q^{62} +(-5.98321e7 - 2.47832e7i) q^{63} +1.48718e8i q^{64} +(2.53022e6 - 6.10850e6i) q^{65} +(8.24826e7 - 8.24826e7i) q^{66} +1.06450e8 q^{67} +(1.11502e7 - 2.84542e7i) q^{68} +3.19033e7 q^{69} +(2.55000e6 - 2.55000e6i) q^{70} +(1.47032e8 - 3.54968e8i) q^{71} -1.54895e8i q^{72} +(-3.98621e8 - 1.65114e8i) q^{73} +(-3.45296e7 - 8.33619e7i) q^{74} +(-1.52493e8 + 6.31647e7i) q^{75} +(-2.91789e7 - 2.91789e7i) q^{76} +(2.45004e8 + 2.45004e8i) q^{77} +(3.13266e8 - 1.29759e8i) q^{78} +(-8.17294e7 - 1.97312e8i) q^{79} +(6.54473e6 + 2.71092e6i) q^{80} +1.63309e7i q^{81} +(-1.24791e8 + 3.01271e8i) q^{82} +(-2.68120e8 + 2.68120e8i) q^{83} -3.87775e7 q^{84} +(-8.41740e6 - 8.09984e6i) q^{85} +1.00457e8 q^{86} +(-6.09196e7 + 6.09196e7i) q^{87} +(-3.17137e8 + 7.65636e8i) q^{88} -9.12630e8i q^{89} +(-8.08062e6 - 3.34710e6i) q^{90} +(3.85433e8 + 9.30518e8i) q^{91} +(-3.09340e7 + 1.28133e7i) q^{92} +(3.63828e8 + 3.63828e8i) q^{93} +(2.07443e8 + 2.07443e8i) q^{94} +(-1.45726e7 + 6.03616e6i) q^{95} +(-6.57420e7 - 1.58715e8i) q^{96} +(1.34720e8 + 5.58030e7i) q^{97} -2.80855e8i q^{98} +(3.21589e8 - 7.76385e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 4 q^{2} - 4 q^{3} - 1140 q^{5} + 12308 q^{6} - 4 q^{7} + 2044 q^{8} - 83224 q^{9}+O(q^{10}) \) 52 * q - 4 * q^2 - 4 * q^3 - 1140 * q^5 + 12308 * q^6 - 4 * q^7 + 2044 * q^8 - 83224 * q^9	\( 52 q - 4 q^{2} - 4 q^{3} - 1140 q^{5} + 12308 q^{6} - 4 q^{7} + 2044 q^{8} - 83224 q^{9} - 117636 q^{10} - 115768 q^{11} - 145528 q^{12} + 463660 q^{14} + 288244 q^{15} - 3407880 q^{16} - 271932 q^{17} + 2193336 q^{18} - 406700 q^{19} + 493564 q^{20} + 800964 q^{22} - 4172180 q^{23} + 15078440 q^{24} + 11946576 q^{25} - 14209012 q^{26} - 7973656 q^{27} + 13540804 q^{28} + 7833752 q^{29} + 5936252 q^{31} - 26730116 q^{32} - 1635208 q^{33} - 53493988 q^{34} + 46992776 q^{35} - 12761764 q^{36} + 74606796 q^{37} + 74096776 q^{39} - 69317672 q^{40} - 71362288 q^{41} - 308117664 q^{42} - 3765712 q^{43} + 163659820 q^{44} + 14167408 q^{45} + 72135428 q^{46} + 164621412 q^{48} - 284548508 q^{49} + 226223888 q^{50} - 406733132 q^{51} + 103553016 q^{52} - 244724728 q^{53} + 971226260 q^{54} + 470691652 q^{56} - 440646580 q^{57} - 308561768 q^{58} - 481734984 q^{59} + 379626176 q^{60} + 507966228 q^{61} + 358867236 q^{62} + 1070586456 q^{63} + 366263684 q^{65} - 2244715148 q^{66} - 311910088 q^{67} - 1839196668 q^{68} + 533688136 q^{69} + 34867672 q^{70} + 186006812 q^{71} + 487115192 q^{73} - 214149412 q^{74} + 533015920 q^{75} + 1104236912 q^{76} - 237869092 q^{77} - 2081523384 q^{78} - 136338052 q^{79} - 922534152 q^{80} + 1951892384 q^{82} + 1843663888 q^{83} - 2630025952 q^{84} - 395061976 q^{85} + 1538547296 q^{86} - 369395636 q^{87} - 3388839640 q^{88} + 874363684 q^{90} + 2087197720 q^{91} + 1061427500 q^{92} + 576415420 q^{93} + 6899365112 q^{94} + 5031766876 q^{95} + 490811364 q^{96} - 3419996368 q^{97} - 5630536112 q^{99}+O(q^{100}) \) 52 * q - 4 * q^2 - 4 * q^3 - 1140 * q^5 + 12308 * q^6 - 4 * q^7 + 2044 * q^8 - 83224 * q^9 - 117636 * q^10 - 115768 * q^11 - 145528 * q^12 + 463660 * q^14 + 288244 * q^15 - 3407880 * q^16 - 271932 * q^17 + 2193336 * q^18 - 406700 * q^19 + 493564 * q^20 + 800964 * q^22 - 4172180 * q^23 + 15078440 * q^24 + 11946576 * q^25 - 14209012 * q^26 - 7973656 * q^27 + 13540804 * q^28 + 7833752 * q^29 + 5936252 * q^31 - 26730116 * q^32 - 1635208 * q^33 - 53493988 * q^34 + 46992776 * q^35 - 12761764 * q^36 + 74606796 * q^37 + 74096776 * q^39 - 69317672 * q^40 - 71362288 * q^41 - 308117664 * q^42 - 3765712 * q^43 + 163659820 * q^44 + 14167408 * q^45 + 72135428 * q^46 + 164621412 * q^48 - 284548508 * q^49 + 226223888 * q^50 - 406733132 * q^51 + 103553016 * q^52 - 244724728 * q^53 + 971226260 * q^54 + 470691652 * q^56 - 440646580 * q^57 - 308561768 * q^58 - 481734984 * q^59 + 379626176 * q^60 + 507966228 * q^61 + 358867236 * q^62 + 1070586456 * q^63 + 366263684 * q^65 - 2244715148 * q^66 - 311910088 * q^67 - 1839196668 * q^68 + 533688136 * q^69 + 34867672 * q^70 + 186006812 * q^71 + 487115192 * q^73 - 214149412 * q^74 + 533015920 * q^75 + 1104236912 * q^76 - 237869092 * q^77 - 2081523384 * q^78 - 136338052 * q^79 - 922534152 * q^80 + 1951892384 * q^82 + 1843663888 * q^83 - 2630025952 * q^84 - 395061976 * q^85 + 1538547296 * q^86 - 369395636 * q^87 - 3388839640 * q^88 + 874363684 * q^90 + 2087197720 * q^91 + 1061427500 * q^92 + 576415420 * q^93 + 6899365112 * q^94 + 5031766876 * q^95 + 490811364 * q^96 - 3419996368 * q^97 - 5630536112 * q^99

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