LMFDB - Embedded newform 33.6.e.a.31.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [33,6,Mod(4,33)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(33, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 2]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("33.4");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 33 = 3 \cdot 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	33.e (of order $5$, degree $4$, 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:	$5.29266605383$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 3 x^{19} + 142 x^{18} - 389 x^{17} + 14927 x^{16} - 6599 x^{15} + 1399353 x^{14} + \cdots + 25735126080400 $ x^20 - 3x^19 + 142x^18 - 389x^17 + 14927x^16 - 6599x^15 + 1399353x^14 + 1969563x^13 + 129076450x^12 + 14028509x^11 + 4158720649x^10 - 7877307064x^9 + 107078602608x^8 - 53496436514x^7 + 2527225278875x^6 - 6173773919508x^5 + 63231264058241x^4 - 118816044595930x^3 + 398041877081860x^2 - 161017247606600*x + 25735126080400
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4}\cdot 11^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			31.5
Root			$3.07809 + 9.47338i$ of defining polynomial
Character	$\chi$	$=$	33.31
Dual form			33.6.e.a.16.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.38711 - 10.4244i) q^{2} +(-7.28115 + 5.29007i) q^{3} +(-71.3079 - 51.8082i) q^{4} +(8.39633 + 25.8412i) q^{5} +(30.4839 + 93.8199i) q^{6} +(-110.374 - 80.1917i) q^{7} +(-497.837 + 361.700i) q^{8} +(25.0304 - 77.0356i) q^{9} +O(q^{10})$	\(q+(3.38711 - 10.4244i) q^{2} +(-7.28115 + 5.29007i) q^{3} +(-71.3079 - 51.8082i) q^{4} +(8.39633 + 25.8412i) q^{5} +(30.4839 + 93.8199i) q^{6} +(-110.374 - 80.1917i) q^{7} +(-497.837 + 361.700i) q^{8} +(25.0304 - 77.0356i) q^{9} +297.820 q^{10} +(272.319 - 294.777i) q^{11} +793.273 q^{12} +(32.7197 - 100.701i) q^{13} +(-1209.80 + 878.974i) q^{14} +(-197.837 - 143.737i) q^{15} +(1212.70 + 3732.31i) q^{16} +(-583.925 - 1797.14i) q^{17} +(-718.272 - 521.855i) q^{18} +(-8.60651 + 6.25300i) q^{19} +(740.064 - 2277.68i) q^{20} +1227.87 q^{21} +(-2150.51 - 3837.21i) q^{22} -3878.53 q^{23} +(1711.41 - 5267.18i) q^{24} +(1930.91 - 1402.89i) q^{25} +(-938.926 - 682.170i) q^{26} +(225.273 + 693.320i) q^{27} +(3715.98 + 11436.6i) q^{28} +(3413.30 + 2479.91i) q^{29} +(-2168.47 + 1575.49i) q^{30} +(1250.63 - 3849.03i) q^{31} +23323.2 q^{32} +(-423.402 + 3586.90i) q^{33} -20712.0 q^{34} +(1145.51 - 3525.53i) q^{35} +(-5775.94 + 4196.47i) q^{36} +(5133.73 + 3729.87i) q^{37} +(36.0328 + 110.898i) q^{38} +(294.478 + 906.309i) q^{39} +(-13526.8 - 9827.78i) q^{40} +(6896.60 - 5010.67i) q^{41} +(4158.93 - 12799.9i) q^{42} +14570.2 q^{43} +(-34690.3 + 6911.60i) q^{44} +2200.86 q^{45} +(-13137.0 + 40431.5i) q^{46} +(-7378.76 + 5360.98i) q^{47} +(-28574.0 - 20760.2i) q^{48} +(558.153 + 1717.82i) q^{49} +(-8084.11 - 24880.3i) q^{50} +(13758.6 + 9996.22i) q^{51} +(-7550.31 + 5485.62i) q^{52} +(-6215.25 + 19128.6i) q^{53} +7990.50 q^{54} +(9903.88 + 4562.00i) q^{55} +83953.8 q^{56} +(29.5866 - 91.0581i) q^{57} +(37412.9 - 27182.1i) q^{58} +(-28743.2 - 20883.1i) q^{59} +(6660.58 + 20499.1i) q^{60} +(9011.49 + 27734.5i) q^{61} +(-35888.0 - 26074.2i) q^{62} +(-8940.33 + 6495.53i) q^{63} +(40191.8 - 123698. i) q^{64} +2876.96 q^{65} +(35957.3 + 16562.9i) q^{66} +10452.3 q^{67} +(-51468.0 + 158402. i) q^{68} +(28240.2 - 20517.7i) q^{69} +(-32871.7 - 23882.7i) q^{70} +(-5277.47 - 16242.4i) q^{71} +(15402.7 + 47404.7i) q^{72} +(-15846.4 - 11513.1i) q^{73} +(56270.3 - 40882.8i) q^{74} +(-6637.87 + 20429.3i) q^{75} +937.669 q^{76} +(-53695.7 + 10698.2i) q^{77} +10445.2 q^{78} +(14744.2 - 45378.0i) q^{79} +(-86265.2 + 62675.4i) q^{80} +(-5307.96 - 3856.46i) q^{81} +(-28873.9 - 88864.8i) q^{82} +(-30239.7 - 93068.3i) q^{83} +(-87557.0 - 63613.9i) q^{84} +(41537.4 - 30178.7i) q^{85} +(49350.8 - 151886. i) q^{86} -37971.7 q^{87} +(-28949.5 + 245249. i) q^{88} -14608.1 q^{89} +(7454.54 - 22942.7i) q^{90} +(-11686.8 + 8490.96i) q^{91} +(276570. + 200940. i) q^{92} +(11255.6 + 34641.3i) q^{93} +(30892.6 + 95077.6i) q^{94} +(-233.848 - 169.901i) q^{95} +(-169820. + 123382. i) q^{96} +(-25034.0 + 77046.7i) q^{97} +19797.8 q^{98} +(-15892.1 - 28356.6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{2} - 45 q^{3} - 124 q^{4} - 33 q^{5} - 18 q^{6} - 335 q^{7} - 472 q^{8} - 405 q^{9}+O(q^{10}) $ 20 * q - 2 * q^2 - 45 * q^3 - 124 * q^4 - 33 * q^5 - 18 * q^6 - 335 * q^7 - 472 * q^8 - 405 * q^9	\( 20 q - 2 q^{2} - 45 q^{3} - 124 q^{4} - 33 q^{5} - 18 q^{6} - 335 q^{7} - 472 q^{8} - 405 q^{9} + 1952 q^{10} - 835 q^{11} + 3474 q^{12} - 959 q^{13} - 3020 q^{14} + 198 q^{15} - 1428 q^{16} - 3144 q^{17} - 567 q^{18} - 930 q^{19} + 3177 q^{20} + 8460 q^{21} + 2713 q^{22} + 1400 q^{23} + 1332 q^{24} - 9388 q^{25} + 3022 q^{26} - 3645 q^{27} - 21753 q^{28} + 4494 q^{29} - 4302 q^{30} + 9208 q^{31} + 69114 q^{32} + 6615 q^{33} - 9084 q^{34} - 31371 q^{35} - 10044 q^{36} - 3153 q^{37} + 1852 q^{38} - 8631 q^{39} - 53123 q^{40} - 7497 q^{41} + 22320 q^{42} + 63624 q^{43} + 58299 q^{44} + 1782 q^{45} - 94681 q^{46} - 43031 q^{47} - 12357 q^{48} - 5640 q^{49} - 76590 q^{50} + 459 q^{51} - 80149 q^{52} - 20452 q^{53} + 13122 q^{54} + 62974 q^{55} + 169638 q^{56} - 39375 q^{57} + 93145 q^{58} + 101730 q^{59} + 28593 q^{60} + 50745 q^{61} - 171957 q^{62} - 27135 q^{63} + 199638 q^{64} - 28210 q^{65} + 46107 q^{66} + 10730 q^{67} - 420141 q^{68} + 94365 q^{69} + 292664 q^{70} + 164895 q^{71} + 11988 q^{72} - 77236 q^{73} - 328228 q^{74} + 9063 q^{75} + 79212 q^{76} + 56087 q^{77} - 280062 q^{78} - 291931 q^{79} + 18026 q^{80} - 32805 q^{81} + 424659 q^{82} - 255451 q^{83} - 26127 q^{84} - 452271 q^{85} + 252843 q^{86} + 187056 q^{87} + 171694 q^{88} + 181632 q^{89} - 40338 q^{90} + 284615 q^{91} + 1199691 q^{92} + 82872 q^{93} - 550105 q^{94} - 511091 q^{95} - 587574 q^{96} - 145083 q^{97} - 150570 q^{98} - 83430 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 - 45 * q^3 - 124 * q^4 - 33 * q^5 - 18 * q^6 - 335 * q^7 - 472 * q^8 - 405 * q^9 + 1952 * q^10 - 835 * q^11 + 3474 * q^12 - 959 * q^13 - 3020 * q^14 + 198 * q^15 - 1428 * q^16 - 3144 * q^17 - 567 * q^18 - 930 * q^19 + 3177 * q^20 + 8460 * q^21 + 2713 * q^22 + 1400 * q^23 + 1332 * q^24 - 9388 * q^25 + 3022 * q^26 - 3645 * q^27 - 21753 * q^28 + 4494 * q^29 - 4302 * q^30 + 9208 * q^31 + 69114 * q^32 + 6615 * q^33 - 9084 * q^34 - 31371 * q^35 - 10044 * q^36 - 3153 * q^37 + 1852 * q^38 - 8631 * q^39 - 53123 * q^40 - 7497 * q^41 + 22320 * q^42 + 63624 * q^43 + 58299 * q^44 + 1782 * q^45 - 94681 * q^46 - 43031 * q^47 - 12357 * q^48 - 5640 * q^49 - 76590 * q^50 + 459 * q^51 - 80149 * q^52 - 20452 * q^53 + 13122 * q^54 + 62974 * q^55 + 169638 * q^56 - 39375 * q^57 + 93145 * q^58 + 101730 * q^59 + 28593 * q^60 + 50745 * q^61 - 171957 * q^62 - 27135 * q^63 + 199638 * q^64 - 28210 * q^65 + 46107 * q^66 + 10730 * q^67 - 420141 * q^68 + 94365 * q^69 + 292664 * q^70 + 164895 * q^71 + 11988 * q^72 - 77236 * q^73 - 328228 * q^74 + 9063 * q^75 + 79212 * q^76 + 56087 * q^77 - 280062 * q^78 - 291931 * q^79 + 18026 * q^80 - 32805 * q^81 + 424659 * q^82 - 255451 * q^83 - 26127 * q^84 - 452271 * q^85 + 252843 * q^86 + 187056 * q^87 + 171694 * q^88 + 181632 * q^89 - 40338 * q^90 + 284615 * q^91 + 1199691 * q^92 + 82872 * q^93 - 550105 * q^94 - 511091 * q^95 - 587574 * q^96 - 145083 * q^97 - 150570 * q^98 - 83430 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/33\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	3.38711	−	10.4244i	0.598761	−	1.84280i	0.0637272	−	0.997967i	$-0.479701\pi$
$2$	3.38711	−	10.4244i	0.598761	−	1.84280i	0.535034	−	0.844830i	$-0.320299\pi$
$3$	−7.28115	+	5.29007i	−0.467086	+	0.339358i
$3$	−7.28115	+	5.29007i	−0.467086	+	0.339358i
$4$	−71.3079	−	51.8082i	−2.22837	−	1.61901i
$5$	8.39633	+	25.8412i	0.150198	+	0.462262i	0.997643	−	0.0686216i	$-0.0218601\pi$
$5$	8.39633	+	25.8412i	0.150198	+	0.462262i	−0.847445	+	0.530884i	$0.821860\pi$
$6$	30.4839	+	93.8199i	0.345695	+	1.06394i
$7$	−110.374	−	80.1917i	−0.851380	−	0.618564i	0.0741464	−	0.997247i	$-0.476377\pi$
$7$	−110.374	−	80.1917i	−0.851380	−	0.618564i	−0.925526	+	0.378684i	$0.876377\pi$
$8$	−497.837	+	361.700i	−2.75019	+	1.99813i
$9$	25.0304	−	77.0356i	0.103006	−	0.317019i
$10$	297.820			0.941788
$11$	272.319	−	294.777i	0.678571	−	0.734534i
$11$	272.319	−	294.777i	0.678571	−	0.734534i
$12$	793.273			1.59026
$13$	32.7197	−	100.701i	0.0536972	−	0.165263i	−0.920611	−	0.390480i	$-0.872309\pi$
$13$	32.7197	−	100.701i	0.0536972	−	0.165263i	0.974309	+	0.225217i	$0.0723091\pi$
$14$	−1209.80	+	878.974i	−1.64966	+	1.19855i
$15$	−197.837	−	143.737i	−0.227028	−	0.164945i
$16$	1212.70	+	3732.31i	1.18428	+	3.64483i
$17$	−583.925	−	1797.14i	−0.490044	−	1.50820i	−0.824541	−	0.565803i	$-0.808566\pi$
$17$	−583.925	−	1797.14i	−0.490044	−	1.50820i	0.334497	−	0.942397i	$-0.391434\pi$
$18$	−718.272	−	521.855i	−0.522526	−	0.379637i
$19$	−8.60651	+	6.25300i	−0.00546944	+	0.00397378i	−0.590517	−	0.807025i	$-0.701076\pi$
$19$	−8.60651	+	6.25300i	−0.00546944	+	0.00397378i	0.585047	+	0.810999i	$0.301076\pi$
$20$	740.064	−	2277.68i	0.413708	−	1.27326i
$21$	1227.87			0.607582
$22$	−2150.51	−	3837.21i	−0.947296	−	1.69028i
$23$	−3878.53			−1.52879			−0.764395	−	0.644749i	$-0.776962\pi$
$23$	−3878.53			−1.52879			−0.764395	+	0.644749i	$0.776962\pi$
$24$	1711.41	−	5267.18i	0.606494	−	1.86660i
$25$	1930.91	−	1402.89i	0.617890	−	0.448924i
$26$	−938.926	−	682.170i	−0.272394	−	0.197906i
$27$	225.273	+	693.320i	0.0594703	+	0.183031i
$28$	3715.98	+	11436.6i	0.895732	+	2.75678i
$29$	3413.30	+	2479.91i	0.753668	+	0.547572i	0.896962	−	0.442108i	$-0.145769\pi$
$29$	3413.30	+	2479.91i	0.753668	+	0.547572i	−0.143294	+	0.989680i	$0.545769\pi$
$30$	−2168.47	+	1575.49i	−0.439896	+	0.319603i
$31$	1250.63	−	3849.03i	0.233735	−	0.719362i	−0.763552	−	0.645746i	$-0.776546\pi$
$31$	1250.63	−	3849.03i	0.233735	−	0.719362i	0.997287	−	0.0736152i	$-0.0234537\pi$
$32$	23323.2			4.02637
$33$	−423.402	+	3586.90i	−0.0676813	+	0.573369i
$34$	−20712.0			−3.07273
$35$	1145.51	−	3525.53i	0.158063	−	0.486468i
$36$	−5775.94	+	4196.47i	−0.742791	+	0.539669i
$37$	5133.73	+	3729.87i	0.616494	+	0.447909i	0.851695	−	0.524038i	$-0.175575\pi$
$37$	5133.73	+	3729.87i	0.616494	+	0.447909i	−0.235201	+	0.971947i	$0.575575\pi$
$38$	36.0328	+	110.898i	0.00404799	+	0.0124584i
$39$	294.478	+	906.309i	0.0310021	+	0.0954146i
$40$	−13526.8	−	9827.78i	−1.33673	−	0.971192i
$41$	6896.60	−	5010.67i	0.640730	−	0.465518i	−0.219371	−	0.975642i	$-0.570400\pi$
$41$	6896.60	−	5010.67i	0.640730	−	0.465518i	0.860101	+	0.510124i	$0.170400\pi$
$42$	4158.93	−	12799.9i	0.363797	−	1.11965i
$43$	14570.2			1.20170			0.600848	−	0.799363i	$-0.294830\pi$
$43$	14570.2			1.20170			0.600848	+	0.799363i	$0.294830\pi$
$44$	−34690.3	+	6911.60i	−2.70133	+	0.538204i
$45$	2200.86			0.162017
$46$	−13137.0	+	40431.5i	−0.915380	+	2.81725i
$47$	−7378.76	+	5360.98i	−0.487235	+	0.353997i	−0.804120	−	0.594467i	$-0.797363\pi$
$47$	−7378.76	+	5360.98i	−0.487235	+	0.353997i	0.316885	+	0.948464i	$0.397363\pi$
$48$	−28574.0	−	20760.2i	−1.79006	−	1.30056i
$49$	558.153	+	1717.82i	0.0332096	+	0.102209i
$50$	−8084.11	−	24880.3i	−0.457307	−	1.40744i
$51$	13758.6	+	9996.22i	0.740712	+	0.538159i
$52$	−7550.31	+	5485.62i	−0.387219	+	0.281331i
$53$	−6215.25	+	19128.6i	−0.303927	+	0.935391i	0.676149	+	0.736765i	$0.263648\pi$
$53$	−6215.25	+	19128.6i	−0.303927	+	0.935391i	−0.980075	+	0.198625i	$0.936352\pi$
$54$	7990.50			0.372898
$55$	9903.88	+	4562.00i	0.441467	+	0.203352i
$56$	83953.8			3.57742
$57$	29.5866	−	91.0581i	0.00120617	−	0.00371220i
$58$	37412.9	−	27182.1i	1.46033	−	1.06099i
$59$	−28743.2	−	20883.1i	−1.07499	−	0.781026i	−0.0981875	−	0.995168i	$-0.531304\pi$
$59$	−28743.2	−	20883.1i	−1.07499	−	0.781026i	−0.976803	+	0.214142i	$0.931304\pi$
$60$	6660.58	+	20499.1i	0.238855	+	0.735119i
$61$	9011.49	+	27734.5i	0.310079	+	0.954324i	0.977733	+	0.209852i	$0.0672984\pi$
$61$	9011.49	+	27734.5i	0.310079	+	0.954324i	−0.667654	+	0.744471i	$0.732702\pi$
$62$	−35888.0	−	26074.2i	−1.18569	−	0.861452i
$63$	−8940.33	+	6495.53i	−0.283793	+	0.206188i
$64$	40191.8	−	123698.i	1.22656	−	3.77496i
$65$	2876.96			0.0844600
$66$	35957.3	+	16562.9i	1.01608	+	0.468034i
$67$	10452.3			0.284462			0.142231	−	0.989833i	$-0.454572\pi$
$67$	10452.3			0.284462			0.142231	+	0.989833i	$0.454572\pi$
$68$	−51468.0	+	158402.i	−1.34979	+	4.15421i
$69$	28240.2	−	20517.7i	0.714076	−	0.518807i
$70$	−32871.7	−	23882.7i	−0.801819	−	0.582556i
$71$	−5277.47	−	16242.4i	−0.124245	−	0.382388i	0.869518	−	0.493902i	$-0.164430\pi$
$71$	−5277.47	−	16242.4i	−0.124245	−	0.382388i	−0.993763	+	0.111514i	$0.964430\pi$
$72$	15402.7	+	47404.7i	0.350159	+	1.07768i
$73$	−15846.4	−	11513.1i	−0.348036	−	0.252863i	0.400009	−	0.916511i	$-0.369007\pi$
$73$	−15846.4	−	11513.1i	−0.348036	−	0.252863i	−0.748045	+	0.663648i	$0.769007\pi$
$74$	56270.3	−	40882.8i	1.19454	−	0.867883i
$75$	−6637.87	+	20429.3i	−0.136262	+	0.419372i
$76$	937.669			0.0186215
$77$	−53695.7	+	10698.2i	−1.03208	+	0.205628i
$78$	10445.2			0.194393
$79$	14744.2	−	45378.0i	0.265799	−	0.818046i	−0.725709	−	0.688002i	$-0.758488\pi$
$79$	14744.2	−	45378.0i	0.265799	−	0.818046i	0.991508	−	0.130044i	$-0.0415118\pi$
$80$	−86265.2	+	62675.4i	−1.50699	+	1.09489i
$81$	−5307.96	−	3856.46i	−0.0898908	−	0.0653095i
$82$	−28873.9	−	88864.8i	−0.474211	−	1.45947i
$83$	−30239.7	−	93068.3i	−0.481817	−	1.48288i	−0.836538	−	0.547909i	$-0.815424\pi$
$83$	−30239.7	−	93068.3i	−0.481817	−	1.48288i	0.354720	−	0.934972i	$-0.384576\pi$
$84$	−87557.0	−	63613.9i	−1.35392	−	0.983680i
$85$	41537.4	−	30178.7i	0.623580	−	0.453057i
$86$	49350.8	−	151886.i	0.719529	−	2.21448i
$87$	−37971.7			−0.537851
$88$	−28949.5	+	245249.i	−0.398505	+	3.37598i
$89$	−14608.1			−0.195487			−0.0977435	−	0.995212i	$-0.531162\pi$
$89$	−14608.1			−0.195487			−0.0977435	+	0.995212i	$0.531162\pi$
$90$	7454.54	−	22942.7i	0.0970095	−	0.298565i
$91$	−11686.8	+	8490.96i	−0.147942	+	0.107486i
$92$	276570.	+	200940.i	3.40671	+	2.47512i
$93$	11255.6	+	34641.3i	0.134947	+	0.415324i
$94$	30892.6	+	95077.6i	0.360607	+	1.10984i
$95$	−233.848	−	169.901i	−0.00265843	−	0.00193146i
$96$	−169820.	+	123382.i	−1.88066	+	1.36638i
$97$	−25034.0	+	77046.7i	−0.270147	+	0.831428i	0.720315	+	0.693647i	$0.243997\pi$
$97$	−25034.0	+	77046.7i	−0.270147	+	0.831428i	−0.990463	+	0.137781i	$0.956003\pi$
$98$	19797.8			0.208234
$99$	−15892.1	−	28356.6i	−0.162965	−	0.290781i
$100$	−210370.			−2.10370
$101$	394.109	−	1212.94i	0.00384426	−	0.0118314i	−0.949116	−	0.314927i	$-0.898020\pi$
$101$	394.109	−	1212.94i	0.00384426	−	0.0118314i	0.952960	+	0.303095i	$0.0980201\pi$
$102$	150807.	−	109568.i	1.43523	−	1.04275i
$103$	−96283.8	−	69954.3i	−0.894253	−	0.649713i	0.0427308	−	0.999087i	$-0.486394\pi$
$103$	−96283.8	−	69954.3i	−0.894253	−	0.649713i	−0.936983	+	0.349374i	$0.886394\pi$
$104$	20134.4	+	61967.4i	0.182539	+	0.561798i
$105$	10309.6	+	31729.7i	0.0912577	+	0.280862i
$106$	178353.	+	129581.i	1.54176	+	1.12015i
$107$	−100409.	+	72951.7i	−0.847842	+	0.615994i	−0.924550	−	0.381060i	$-0.875559\pi$
$107$	−100409.	+	72951.7i	−0.847842	+	0.615994i	0.0767079	+	0.997054i	$0.475559\pi$
$108$	19855.9	−	61110.2i	0.163806	−	0.504144i
$109$	144831.			1.16760			0.583802	−	0.811896i	$-0.301565\pi$
$109$	144831.			1.16760			0.583802	+	0.811896i	$0.301565\pi$
$110$	81101.8	−	87790.4i	0.639071	−	0.691776i
$111$	−57110.8			−0.439957
$112$	165449.	−	509200.i	1.24629	−	3.83569i
$113$	47650.9	−	34620.4i	0.351055	−	0.255056i	−0.398256	−	0.917274i	$-0.630385\pi$
$113$	47650.9	−	34620.4i	0.351055	−	0.255056i	0.749312	+	0.662218i	$0.230385\pi$
$114$	−849.016	−	616.847i	−0.00611863	−	0.00444544i
$115$	−32565.4	−	100226.i	−0.229621	−	0.706701i
$116$	−114916.	−	353674.i	−0.792930	−	2.44039i
$117$	−6938.57	−	5041.17i	−0.0468603	−	0.0340460i
$118$	−315051.	+	228898.i	−2.08294	+	1.51334i
$119$	−79665.1	+	245184.i	−0.515704	+	1.58717i
$120$	150480.			0.953951
$121$	−12736.2	−	160547.i	−0.0790815	−	0.996868i
$122$	319639.			1.94429
$123$	−23708.4	+	72966.9i	−0.141299	+	0.434874i
$124$	−288591.	+	209674.i	−1.68550	+	1.22459i
$125$	121158.	+	88026.6i	0.693550	+	0.503893i
$126$	37430.4	+	115199.i	0.210038	+	0.646431i
$127$	6655.25	+	20482.8i	0.0366147	+	0.112688i	0.967693	−	0.252130i	$-0.0811311\pi$
$127$	6655.25	+	20482.8i	0.0366147	+	0.112688i	−0.931079	+	0.364818i	$0.881131\pi$
$128$	−549541.	−	399265.i	−2.96466	−	2.15395i
$129$	−106088.	+	77077.4i	−0.561295	+	0.407805i
$130$	9744.58	−	29990.7i	0.0505714	−	0.155643i
$131$	95121.5			0.484284			0.242142	−	0.970241i	$-0.422150\pi$
$131$	95121.5			0.484284			0.242142	+	0.970241i	$0.422150\pi$
$132$	216023.	−	233839.i	1.07911	−	1.16810i
$133$	1451.38			0.00711461
$134$	35403.0	−	108959.i	0.170325	−	0.524207i
$135$	−16024.8	+	11642.7i	−0.0756759	+	0.0549818i
$136$	940724.	+	683476.i	4.36129	+	3.16866i
$137$	17263.3	+	53131.0i	0.0785819	+	0.241850i	0.982628	−	0.185584i	$-0.0594176\pi$
$137$	17263.3	+	53131.0i	0.0785819	+	0.241850i	−0.904047	+	0.427434i	$0.859418\pi$
$138$	−118233.	−	363883.i	−0.528495	−	1.62654i
$139$	106224.	+	77176.3i	0.466322	+	0.338803i	0.796006	−	0.605289i	$-0.206942\pi$
$139$	106224.	+	77176.3i	0.466322	+	0.338803i	−0.329684	+	0.944091i	$0.606942\pi$
$140$	−264335.	+	192051.i	−1.13982	+	0.828126i
$141$	25365.9	−	78068.2i	0.107449	−	0.330694i
$142$	−187193.			−0.779057
$143$	−20774.2	−	37067.8i	−0.0849539	−	0.151585i
$144$	317875.			1.27747
$145$	−35424.7	+	109026.i	−0.139922	+	0.430636i
$146$	−173691.	+	126194.i	−0.674366	+	0.489956i
$147$	−13151.4	−	9555.04i	−0.0501970	−	0.0364703i
$148$	−172837.	−	531939.i	−0.648610	−	1.99622i
$149$	49137.0	+	151228.i	0.181319	+	0.558042i	0.999866	−	0.0163977i	$-0.00521979\pi$
$149$	49137.0	+	151228.i	0.181319	+	0.558042i	−0.818547	+	0.574440i	$0.805220\pi$
$150$	190480.	+	138392.i	0.691229	+	0.502207i
$151$	50208.7	−	36478.7i	0.179199	−	0.130196i	−0.494570	−	0.869138i	$-0.664674\pi$
$151$	50208.7	−	36478.7i	0.179199	−	0.130196i	0.673769	+	0.738942i	$0.264674\pi$
$152$	2022.93	−	6225.95i	0.00710187	−	0.0218573i
$153$	−153059.			−0.528605
$154$	−70350.6	+	595983.i	−0.239038	+	2.02503i
$155$	109964.			0.367640
$156$	25955.7	−	79883.3i	0.0853927	−	0.262812i
$157$	307314.	−	223277.i	0.995024	−	0.722928i	0.0340087	−	0.999422i	$-0.489173\pi$
$157$	307314.	−	223277.i	0.995024	−	0.722928i	0.961016	+	0.276494i	$0.0891726\pi$
$158$	−423100.	−	307400.i	−1.34834	−	0.979628i
$159$	−55937.3	−	172157.i	−0.175472	−	0.540048i
$160$	195830.	+	602701.i	0.604753	+	1.86124i
$161$	428090.	+	311026.i	1.30158	+	0.945653i
$162$	−58180.0	+	42270.3i	−0.174175	+	0.126546i
$163$	36005.8	−	110814.i	0.106146	−	0.326684i	−0.883852	−	0.467767i	$-0.845059\pi$
$163$	36005.8	−	110814.i	0.106146	−	0.326684i	0.989998	+	0.141083i	$0.0450586\pi$
$164$	−751376.			−2.18146
$165$	−96245.0	+	19175.5i	−0.275213	+	0.0548325i
$166$	−1.07261e6			−3.02114
$167$	34152.3	−	105110.i	0.0947607	−	0.291643i	−0.892431	−	0.451185i	$-0.851002\pi$
$167$	34152.3	−	105110.i	0.0947607	−	0.291643i	0.987191	+	0.159541i	$0.0510015\pi$
$168$	−611281.	+	444121.i	−1.67097	+	1.21403i
$169$	291312.	+	211651.i	0.784589	+	0.570037i
$170$	−173904.	−	535222.i	−0.461517	−	1.42040i
$171$	266.279	+	819.523i	0.000696381	+	0.00214324i
$172$	−1.03897e6	−	754856.i	−2.67782	−	1.94555i
$173$	10218.5	−	7424.17i	0.0259580	−	0.0188596i	−0.574731	−	0.818343i	$-0.694893\pi$
$173$	10218.5	−	7424.17i	0.0259580	−	0.0188596i	0.600689	+	0.799483i	$0.294893\pi$
$174$	−128614.	+	395834.i	−0.322044	+	0.991150i
$175$	−325623.			−0.803747
$176$	1.43044e6	+	658901.i	3.48087	+	1.60339i
$177$	319756.			0.767160
$178$	−49479.1	+	152281.i	−0.117050	+	0.360243i
$179$	290018.	−	210711.i	0.676539	−	0.491534i	−0.195669	−	0.980670i	$-0.562688\pi$
$179$	290018.	−	210711.i	0.676539	−	0.491534i	0.872208	+	0.489136i	$0.162688\pi$
$180$	−156939.	−	114023.i	−0.361034	−	0.262307i
$181$	−253918.	−	781480.i	−0.576100	−	1.77305i	−0.632404	−	0.774639i	$-0.717932\pi$
$181$	−253918.	−	781480.i	−0.576100	−	1.77305i	0.0563043	−	0.998414i	$-0.482068\pi$
$182$	48929.1	+	150588.i	0.109494	+	0.336986i
$183$	−212331.	−	154268.i	−0.468691	−	0.340524i
$184$	1.93088e6	−	1.40286e6i	4.20446	−	3.05472i
$185$	−53280.0	+	163979.i	−0.114455	+	0.352257i
$186$	399240.			0.846158
$187$	−688768.	−	317266.i	−1.44035	−	0.663467i
$188$	803907.			1.65886
$189$	30734.1	−	94589.9i	0.0625844	−	0.192615i
$190$	−2563.19	+	1862.27i	−0.00515106	+	0.00374246i
$191$	−603486.	−	438458.i	−1.19697	−	0.869651i	−0.202988	−	0.979181i	$-0.565065\pi$
$191$	−603486.	−	438458.i	−1.19697	−	0.869651i	−0.993983	+	0.109530i	$0.965065\pi$
$192$	361727.	+	1.11328e6i	0.708154	+	2.17947i
$193$	137863.	+	424298.i	0.266412	+	0.819933i	0.991365	+	0.131134i	$0.0418617\pi$
$193$	137863.	+	424298.i	0.266412	+	0.819933i	−0.724952	+	0.688799i	$0.758138\pi$
$194$	718376.	+	521931.i	1.37040	+	0.995654i
$195$	−20947.6	+	15219.3i	−0.0394501	+	0.0286622i
$196$	49196.4	−	151411.i	0.0914731	−	0.281525i
$197$	530530.			0.973967			0.486984	−	0.873411i	$-0.338097\pi$
$197$	530530.			0.973967			0.486984	+	0.873411i	$0.338097\pi$
$198$	−349430.	+	69619.3i	−0.633428	+	0.126202i
$199$	721637.			1.29177			0.645886	−	0.763433i	$-0.276488\pi$
$199$	721637.			1.29177			0.645886	+	0.763433i	$0.276488\pi$
$200$	−453854.	+	1.39682e6i	−0.802307	+	2.46925i
$201$	−76104.8	+	55293.4i	−0.132868	+	0.0965346i
$202$	−11309.3	−	8216.72i	−0.0195011	−	0.0141684i
$203$	−177873.	−	547438.i	−0.302950	−	0.932383i
$204$	−463212.	−	1.42562e6i	−0.779299	−	2.39844i
$205$	187388.	+	136145.i	0.311428	+	0.226265i
$206$	−1.05536e6	+	766762.i	−1.73273	+	1.25890i
$207$	−97081.1	+	298785.i	−0.157474	+	0.484655i
$208$	415527.			0.665948
$209$	−500.473	+	4239.81i	−0.000792528	+	0.00671399i
$210$	365684.			0.572214
$211$	−172900.	+	532131.i	−0.267355	+	0.822834i	0.723786	+	0.690024i	$0.242400\pi$
$211$	−172900.	+	532131.i	−0.267355	+	0.822834i	−0.991141	+	0.132810i	$0.957600\pi$
$212$	1.43421e6	−	1.04202e6i	2.19167	−	1.59234i
$213$	124349.	+	90345.1i	0.187800	+	0.136444i
$214$	420384.	+	1.29381e6i	0.627496	+	1.93124i
$215$	122336.	+	376512.i	0.180492	+	0.555498i
$216$	−362923.	−	263679.i	−0.529274	−	0.384540i
$217$	−446698.	+	324545.i	−0.643968	+	0.467870i
$218$	490558.	−	1.50978e6i	0.699116	−	2.15166i
$219$	176285.			0.248374
$220$	−469876.	−	838409.i	−0.654525	−	1.16788i
$221$	−200079.			−0.275563
$222$	−193440.	+	595348.i	−0.263429	+	0.810752i
$223$	450481.	−	327293.i	0.606616	−	0.440732i	−0.241605	−	0.970375i	$-0.577674\pi$
$223$	450481.	−	327293.i	0.606616	−	0.440732i	0.848221	+	0.529642i	$0.177674\pi$
$224$	−2.57429e6	−	1.87033e6i	−3.42797	−	2.49057i
$225$	−59740.8	−	183863.i	−0.0786710	−	0.242125i
$226$	−199500.	−	613997.i	−0.259819	−	0.799642i
$227$	−738420.	−	536494.i	−0.951128	−	0.691035i	−5.46487e−5	−	1.00000i	$-0.500017\pi$
$227$	−738420.	−	536494.i	−0.951128	−	0.691035i	−0.951073	+	0.308965i	$0.900017\pi$
$228$	−6827.31	+	4960.33i	−0.00869786	+	0.00631937i
$229$	−173042.	+	532568.i	−0.218053	+	0.671099i	0.780870	+	0.624694i	$0.214776\pi$
$229$	−173042.	+	532568.i	−0.218053	+	0.671099i	−0.998923	+	0.0464046i	$0.985224\pi$
$230$	−1.15510e6			−1.43980
$231$	334373.	−	361949.i	0.412288	−	0.446290i
$232$	−2.59625e6			−3.16685
$233$	79291.4	−	244034.i	0.0956834	−	0.294483i	−0.891748	−	0.452533i	$-0.850521\pi$
$233$	79291.4	−	244034.i	0.0956834	−	0.294483i	0.987431	+	0.158050i	$0.0505206\pi$
$234$	−76053.0	+	55255.8i	−0.0907981	+	0.0659687i
$235$	−200489.	−	145664.i	−0.236821	−	0.172061i
$236$	967696.	+	2.97826e6i	1.13099	+	3.48083i
$237$	132698.	+	408402.i	0.153459	+	0.472299i
$238$	2.28607e6	+	1.66093e6i	2.61606	+	1.90068i
$239$	−1.16658e6	+	847569.i	−1.32105	+	0.959799i	−0.321132	+	0.947034i	$0.604063\pi$
$239$	−1.16658e6	+	847569.i	−1.32105	+	0.959799i	−0.999919	+	0.0127648i	$0.995937\pi$
$240$	296554.	−	912698.i	0.332334	−	1.02282i
$241$	1.27514e6			1.41422			0.707108	−	0.707106i	$-0.250000\pi$
$241$	1.27514e6			1.41422			0.707108	+	0.707106i	$0.250000\pi$
$242$	−1.71675e6	−	411021.i	−1.88438	−	0.451155i
$243$	59049.0			0.0641500
$244$	794285.	−	2.44456e6i	0.854086	−	2.62861i
$245$	−39704.1	+	28846.7i	−0.0422591	+	0.0307030i
$246$	680336.	+	494293.i	0.716780	+	0.520771i
$247$	348.080	+	1071.28i	0.000363025	+	0.00111728i
$248$	769586.	+	2.36854e6i	0.794562	+	2.44541i
$249$	712518.	+	517674.i	0.728278	+	0.529125i
$250$	1.32800e6	−	964851.i	1.34384	−	0.976360i
$251$	−326490.	+	1.00483e6i	−0.327103	+	1.00672i	0.643379	+	0.765548i	$0.277532\pi$
$251$	−326490.	+	1.00483e6i	−0.327103	+	1.00672i	−0.970482	+	0.241173i	$0.922468\pi$
$252$	974038.			0.966216
$253$	−1.05620e6	+	1.14330e6i	−1.03739	+	1.12295i
$254$	236063.			0.229585
$255$	−142793.	+	439471.i	−0.137517	+	0.423233i
$256$	−2.65631e6	+	1.92992e6i	−2.53326	+	1.84052i
$257$	337168.	+	244967.i	0.318430	+	0.231353i	0.735505	−	0.677519i	$-0.236945\pi$
$257$	337168.	+	244967.i	0.318430	+	0.231353i	−0.417075	+	0.908872i	$0.636945\pi$
$258$	444157.	+	1.36698e6i	0.415420	+	1.27853i
$259$	−267528.	−	823365.i	−0.247810	−	0.762681i
$260$	−205150.	−	149050.i	−0.188208	−	0.136741i
$261$	276478.	−	200873.i	0.251223	−	0.182524i
$262$	322186.	−	991588.i	0.289971	−	0.892438i
$263$	1.02333e6			0.912275			0.456137	−	0.889909i	$-0.349233\pi$
$263$	1.02333e6			0.912275			0.456137	+	0.889909i	$0.349233\pi$
$264$	−1.08660e6	−	1.93884e6i	−0.959530	−	1.71211i
$265$	−546491.			−0.478045
$266$	4915.97	−	15129.8i	0.00425995	−	0.0131108i
$267$	106364.	−	77277.7i	0.0913093	−	0.0663401i
$268$	−745331.	−	541515.i	−0.633888	−	0.460546i
$269$	−621122.	−	1.91162e6i	−0.523355	−	1.61072i	−0.767546	−	0.640994i	$-0.778523\pi$
$269$	−621122.	−	1.91162e6i	−0.523355	−	1.61072i	0.244191	−	0.969727i	$-0.421477\pi$
$270$	67090.8	+	206484.i	0.0560085	+	0.172376i
$271$	1.28694e6	+	935014.i	1.06447	+	0.773384i	0.974910	−	0.222598i	$-0.0714536\pi$
$271$	1.28694e6	+	935014.i	1.06447	+	0.773384i	0.0895609	+	0.995981i	$0.471454\pi$
$272$	5.99934e6	−	4.35878e6i	4.91679	−	3.57226i
$273$	40175.7	−	123648.i	0.0326254	−	0.100411i
$274$	612334.			0.492733
$275$	112283.	−	951219.i	0.0895329	−	0.758488i
$276$	−3.07673e6			−2.43118
$277$	−262547.	+	808036.i	−0.205593	+	0.632749i	0.794096	+	0.607792i	$0.207945\pi$
$277$	−262547.	+	808036.i	−0.205593	+	0.632749i	−0.999689	+	0.0249564i	$0.992055\pi$
$278$	1.16431e6	−	845922.i	0.903560	−	0.656475i
$279$	−265209.	−	192685.i	−0.203975	−	0.148197i
$280$	704904.	+	2.16947e6i	0.537322	+	1.65371i
$281$	−228424.	−	703016.i	−0.172574	−	0.531128i	0.826940	−	0.562290i	$-0.190079\pi$
$281$	−228424.	−	703016.i	−0.172574	−	0.531128i	−0.999514	+	0.0311614i	$0.990079\pi$
$282$	−727901.	−	528851.i	−0.545066	−	0.396014i
$283$	−796499.	+	578690.i	−0.591179	+	0.429517i	−0.842737	−	0.538326i	$-0.819057\pi$
$283$	−796499.	+	578690.i	−0.591179	+	0.429517i	0.251558	+	0.967842i	$0.419057\pi$
$284$	−465164.	+	1.43163e6i	−0.342224	+	1.05326i
$285$	2601.47			0.00189717
$286$	−456775.	+	91006.5i	−0.330208	+	0.0657896i
$287$	−1.16302e6			−0.833457
$288$	583790.	−	1.79672e6i	0.414739	−	1.27644i
$289$	−1.74004e6	+	1.26422e6i	−1.22551	+	0.890382i
$290$	1.01655e6	+	738566.i	0.709796	+	0.515697i
$291$	−225306.	−	693420.i	−0.155970	−	0.480025i
$292$	533502.	+	1.64195e6i	0.366167	+	1.12695i
$293$	103154.	+	74946.1i	0.0701970	+	0.0510011i	0.622330	−	0.782755i	$-0.286186\pi$
$293$	103154.	+	74946.1i	0.0701970	+	0.0510011i	−0.552133	+	0.833756i	$0.686186\pi$
$294$	−144151.	+	104732.i	−0.0972634	+	0.0706660i
$295$	298309.	−	918100.i	0.199577	−	0.614236i
$296$	−3.90486e6			−2.59045
$297$	265721.	+	122399.i	0.174797	+	0.0805165i
$298$	1.74290e6			1.13693
$299$	−126904.	+	390572.i	−0.0820916	+	0.252652i
$300$	1.53174e6	−	1.11287e6i	0.982609	−	0.713907i
$301$	−1.60818e6	−	1.16841e6i	−1.02310	−	0.743325i
$302$	−210208.	−	646954.i	−0.132627	−	0.408184i
$303$	3546.98	+	10916.5i	0.00221948	+	0.00683087i
$304$	−33775.2	−	24539.2i	−0.0209611	−	0.0152291i
$305$	−641030.	+	465736.i	−0.394574	+	0.286675i
$306$	−518428.	+	1.59556e6i	−0.316508	+	0.974112i
$307$	448620.			0.271665			0.135832	−	0.990732i	$-0.456629\pi$
$307$	448620.			0.271665			0.135832	+	0.990732i	$0.456629\pi$
$308$	4.38318e6	+	2.01901e6i	2.63277	+	1.21273i
$309$	1.07112e6			0.638178
$310$	372461.	−	1.14632e6i	0.220129	−	0.677486i
$311$	380866.	−	276715.i	0.223291	−	0.162230i	−0.470516	−	0.882391i	$-0.655932\pi$
$311$	380866.	−	276715.i	0.223291	−	0.162230i	0.693807	+	0.720161i	$0.255932\pi$
$312$	−474414.	−	344682.i	−0.275912	−	0.200462i
$313$	−333497.	−	1.02640e6i	−0.192412	−	0.592182i	−0.999997	−	0.00243164i	$-0.999226\pi$
$313$	−333497.	−	1.02640e6i	−0.192412	−	0.592182i	0.807585	−	0.589751i	$-0.200774\pi$
$314$	−1.28663e6	−	3.95984e6i	−0.736427	−	2.26649i
$315$	−242918.	−	176491.i	−0.137938	−	0.100218i
$316$	−3.40233e6	+	2.47194e6i	−1.91672	+	1.39258i
$317$	132785.	−	408669.i	0.0742163	−	0.228414i	−0.907066	−	0.420988i	$-0.861683\pi$
$317$	132785.	−	408669.i	0.0742163	−	0.228414i	0.981283	+	0.192574i	$0.0616834\pi$
$318$	−1.98411e6			−1.10027
$319$	1.66053e6	−	330838.i	0.913628	−	0.182028i
$320$	3.53397e6			1.92925
$321$	345177.	−	1.06235e6i	0.186973	−	0.575444i
$322$	4.69226e6	−	3.40913e6i	2.52198	−	1.83233i
$323$	16263.0	+	11815.8i	0.00867353	+	0.00630169i
$324$	178703.	+	549992.i	0.0945736	+	0.291068i
$325$	−78093.3	−	240346.i	−0.0410115	−	0.126220i
$326$	−1.03322e6	−	750681.i	−0.538456	−	0.391211i
$327$	−1.05454e6	+	766166.i	−0.545371	+	0.396236i
$328$	−1.62102e6	+	4.98900e6i	−0.831964	+	2.56052i
$329$	1.24433e6			0.633792
$330$	−126098.	+	1.06825e6i	−0.0637414	+	0.539993i
$331$	1.78658e6			0.896300			0.448150	−	0.893958i	$-0.352083\pi$
$331$	1.78658e6			0.896300			0.448150	+	0.893958i	$0.352083\pi$
$332$	−2.66537e6	+	8.20317e6i	−1.32713	+	4.08448i
$333$	415832.	−	302120.i	0.205498	−	0.149303i
$334$	−980034.	−	712036.i	−0.480701	−	0.349250i
$335$	87760.9	+	270100.i	0.0427257	+	0.131496i
$336$	1.48904e6	+	4.58280e6i	0.719546	+	2.21454i
$337$	−3.27754e6	−	2.38127e6i	−1.57207	−	1.14218i	−0.925135	−	0.379637i	$-0.876049\pi$
$337$	−3.27754e6	−	2.38127e6i	−1.57207	−	1.14218i	−0.646939	−	0.762542i	$-0.723951\pi$
$338$	3.19305e6	−	2.31988e6i	1.52024	−	1.10452i
$339$	−163809.	+	504153.i	−0.0774175	+	0.238267i
$340$	−4.52545e6			−2.12307
$341$	−794038.	−	1.41682e6i	−0.369790	−	0.659824i
$342$	9444.98			0.00436652
$343$	−632422.	+	1.94639e6i	−0.290250	+	0.893296i
$344$	−7.25359e6	+	5.27004e6i	−3.30489	+	2.40114i
$345$	767316.	+	557488.i	0.347077	+	0.252167i
$346$	−42781.7	−	131669.i	−0.0192118	−	0.0591278i
$347$	−225615.	−	694371.i	−0.100587	−	0.309576i	0.888082	−	0.459685i	$-0.152038\pi$
$347$	−225615.	−	694371.i	−0.100587	−	0.309576i	−0.988670	+	0.150109i	$0.952038\pi$
$348$	2.70768e6	+	1.96725e6i	1.19853	+	0.870784i
$349$	1.33969e6	−	973341.i	0.588763	−	0.427761i	−0.253110	−	0.967438i	$-0.581453\pi$
$349$	1.33969e6	−	973341.i	0.588763	−	0.427761i	0.841873	+	0.539676i	$0.181453\pi$
$350$	−1.10292e6	+	3.39443e6i	−0.481253	+	1.48114i
$351$	77188.9			0.0334416
$352$	6.35135e6	−	6.87516e6i	2.73218	−	2.95751i
$353$	902691.			0.385569			0.192785	−	0.981241i	$-0.438248\pi$
$353$	902691.			0.385569			0.192785	+	0.981241i	$0.438248\pi$
$354$	1.08305e6	−	3.33328e6i	0.459346	−	1.41372i
$355$	375412.	−	272753.i	0.158102	−	0.114868i
$356$	1.04167e6	+	756819.i	0.435618	+	0.316495i
$357$	−716986.	−	2.20665e6i	−0.297742	−	0.916355i
$358$	−1.21422e6	−	3.73698e6i	−0.500713	−	1.54104i
$359$	3.14313e6	+	2.28362e6i	1.28714	+	0.935162i	0.999743	−	0.0226492i	$-0.00721009\pi$
$359$	3.14313e6	+	2.28362e6i	1.28714	+	0.935162i	0.287397	+	0.957812i	$0.407210\pi$
$360$	−1.09567e6	+	796050.i	−0.445577	+	0.323731i
$361$	−765122.	+	2.35480e6i	−0.309003	+	0.951013i
$362$	−9.00654e6			−3.61232
$363$	942036.	+	1.10159e6i	0.375233	+	0.438786i
$364$	1.27326e6			0.503692
$365$	164461.	−	506159.i	0.0646146	−	0.198863i
$366$	−2.32734e6	+	1.69091e6i	−0.908150	+	0.659810i
$367$	320551.	+	232894.i	0.124231	+	0.0902594i	0.648166	−	0.761499i	$-0.275536\pi$
$367$	320551.	+	232894.i	0.124231	+	0.0902594i	−0.523934	+	0.851759i	$0.675536\pi$
$368$	−4.70350e6	−	1.44759e7i	−1.81051	−	5.57218i
$369$	−213375.	−	656702.i	−0.0815790	−	0.251074i
$370$	1.52893e6	+	1.11083e6i	0.580607	+	0.421835i
$371$	2.21996e6	−	1.61289e6i	0.837356	−	0.608375i
$372$	992088.	−	3.05333e6i	0.371700	−	1.14398i
$373$	2.63747e6			0.981558			0.490779	−	0.871284i	$-0.336712\pi$
$373$	2.63747e6			0.981558			0.490779	+	0.871284i	$0.336712\pi$
$374$	−5.64025e6	+	6.10541e6i	−2.08506	+	2.25702i
$375$	−1.34784e6			−0.494948
$376$	1.73435e6	−	5.33779e6i	0.632656	−	1.94712i
$377$	361412.	−	262581.i	0.130963	−	0.0951503i
$378$	−881947.	−	640772.i	−0.317477	−	0.230661i
$379$	194200.	+	597685.i	0.0694465	+	0.213734i	0.979757	−	0.200193i	$-0.0641568\pi$
$379$	194200.	+	597685.i	0.0694465	+	0.213734i	−0.910310	+	0.413927i	$0.864157\pi$
$380$	7872.97	+	24230.5i	0.00279692	+	0.00860803i
$381$	−156813.	−	113931.i	−0.0553439	−	0.0402097i
$382$	−6.61475e6	+	4.80590e6i	−2.31929	+	1.68506i
$383$	−915458.	+	2.81749e6i	−0.318890	+	0.981444i	0.655233	+	0.755427i	$0.272570\pi$
$383$	−915458.	+	2.81749e6i	−0.318890	+	0.981444i	−0.974123	+	0.226017i	$0.927430\pi$
$384$	6.11343e6			2.11571
$385$	−727300.	−	1.29774e6i	−0.250070	−	0.446206i
$386$	4.89003e6			1.67049
$387$	364698.	−	1.12242e6i	0.123781	−	0.380960i
$388$	5.77677e6	−	4.19707e6i	1.94808	−	1.41536i
$389$	4.27992e6	+	3.10954e6i	1.43404	+	1.04189i	0.989246	+	0.146259i	$0.0467232\pi$
$389$	4.27992e6	+	3.10954e6i	1.43404	+	1.04189i	0.444794	+	0.895633i	$0.353277\pi$
$390$	87701.2	+	269917.i	0.0291974	+	0.0898603i
$391$	2.26477e6	+	6.97025e6i	0.749173	+	2.30572i
$392$	−899204.	−	653310.i	−0.295558	−	0.214736i
$393$	−692594.	+	503199.i	−0.226202	+	0.164346i
$394$	1.79696e6	−	5.53048e6i	0.583174	−	1.79483i
$395$	1.29642e6			0.418074
$396$	−335874.	+	2.84539e6i	−0.107631	+	0.911809i
$397$	−5.24543e6			−1.67034			−0.835170	−	0.549992i	$-0.814631\pi$
$397$	−5.24543e6			−1.67034			−0.835170	+	0.549992i	$0.814631\pi$
$398$	2.44426e6	−	7.52266e6i	0.773464	−	2.38048i
$399$	−10567.7	+	7677.88i	−0.00332314	+	0.00241440i
$400$	7.57762e6	+	5.50546e6i	2.36801	+	1.72046i
$401$	507339.	+	1.56143e6i	0.157557	+	0.484910i	0.998411	−	0.0563515i	$-0.0179468\pi$
$401$	507339.	+	1.56143e6i	0.157557	+	0.484910i	−0.840854	+	0.541262i	$0.817947\pi$
$402$	318627.	+	980634.i	0.0983372	+	0.302651i
$403$	−346681.	−	251879.i	−0.106333	−	0.0772554i
$404$	−90943.4	+	66074.3i	−0.0277216	+	0.0201409i
$405$	55088.3	−	169544.i	0.0166887	−	0.0513624i
$406$	−6.30920e6			−1.89959
$407$	2.49749e6	−	497592.i	0.747340	−	0.148898i
$408$	−1.04652e7			−3.11241
$409$	−788323.	+	2.42621e6i	−0.233022	+	0.717166i	0.764356	+	0.644794i	$0.223057\pi$
$409$	−788323.	+	2.42621e6i	−0.233022	+	0.717166i	−0.997378	+	0.0723722i	$0.976943\pi$
$410$	2.05394e6	−	1.49228e6i	0.603432	−	0.438419i
$411$	−406763.	−	295531.i	−0.118778	−	0.0862975i
$412$	3.24159e6	+	9.97658e6i	0.940838	+	2.89560i
$413$	1.49786e6	+	4.60993e6i	0.432111	+	1.32990i
$414$	2.78584e6	+	2.02403e6i	0.798832	+	0.580385i
$415$	2.15110e6	−	1.56286e6i	0.613112	−	0.445452i
$416$	763130.	−	2.34867e6i	0.216205	−	0.665410i
$417$	−1.18170e6			−0.332788
$418$	42502.5	+	19577.8i	0.0118980	+	0.00548055i
$419$	−485617.			−0.135132			−0.0675662	−	0.997715i	$-0.521523\pi$
$419$	−485617.			−0.135132			−0.0675662	+	0.997715i	$0.521523\pi$
$420$	908704.	−	2.79670e6i	0.251362	−	0.773612i
$421$	−1.88692e6	+	1.37093e6i	−0.518859	+	0.376973i	−0.816174	−	0.577806i	$-0.803909\pi$
$421$	−1.88692e6	+	1.37093e6i	−0.518859	+	0.376973i	0.297315	+	0.954779i	$0.403909\pi$
$422$	4.96154e6	+	3.60477e6i	1.35624	+	0.985362i
$423$	228293.	+	702614.i	0.0620358	+	0.190926i
$424$	−3.82462e6	−	1.17710e7i	−1.03317	−	3.17978i
$425$	−3.64868e6	−	2.65092e6i	−0.979859	−	0.711910i
$426$	1.36298e6	−	990264.i	0.363887	−	0.264379i
$427$	1.22944e6	−	3.78383e6i	0.326315	−	1.00430i
$428$	1.09395e7			2.88661
$429$	347351.	+	160000.i	0.0911224	+	0.0419735i
$430$	4.33929e6			1.13174
$431$	1.32674e6	−	4.08329e6i	0.344027	−	1.05881i	−0.618075	−	0.786119i	$-0.712087\pi$
$431$	1.32674e6	−	4.08329e6i	0.344027	−	1.05881i	0.962103	−	0.272688i	$-0.0879126\pi$
$432$	−2.31450e6	+	1.68158e6i	−0.596688	+	0.433519i
$433$	−4.71030e6	−	3.42223e6i	−1.20734	−	0.877181i	−0.212350	−	0.977194i	$-0.568112\pi$
$433$	−4.71030e6	−	3.42223e6i	−1.20734	−	0.877181i	−0.994986	+	0.100012i	$0.968112\pi$
$434$	1.87019e6	+	5.75584e6i	0.476607	+	1.46685i
$435$	−318823.	−	981235.i	−0.0807841	−	0.248628i
$436$	−1.03276e7	−	7.50344e6i	−2.60185	−	1.89036i
$437$	33380.6	−	24252.4i	0.00836163	−	0.00607508i
$438$	597097.	−	1.83768e6i	0.148717	−	0.457703i
$439$	6.54239e6			1.62023			0.810113	−	0.586274i	$-0.199406\pi$
$439$	6.54239e6			1.62023			0.810113	+	0.586274i	$0.199406\pi$
$440$	−6.58060e6	+	1.31110e6i	−1.62044	+	0.322852i
$441$	146304.			0.0358228
$442$	−677690.	+	2.08571e6i	−0.164997	+	0.507808i
$443$	−6.48082e6	+	4.70859e6i	−1.56899	+	1.13994i	−0.640878	+	0.767643i	$0.721429\pi$
$443$	−6.48082e6	+	4.70859e6i	−1.56899	+	1.13994i	−0.928114	+	0.372296i	$0.878571\pi$
$444$	4.07245e6	+	2.95881e6i	0.980388	+	0.712294i
$445$	−122654.	−	377491.i	−0.0293618	−	0.0903663i
$446$	−1.88602e6	−	5.80458e6i	−0.448962	−	1.38176i
$447$	−1.15778e6	−	841178.i	−0.274068	−	0.199122i
$448$	−1.43557e7	+	1.04300e7i	−3.37932	+	2.45522i
$449$	747879.	−	2.30174e6i	0.175072	−	0.538815i	−0.824565	−	0.565767i	$-0.808580\pi$
$449$	747879.	−	2.30174e6i	0.175072	−	0.538815i	0.999637	+	0.0269520i	$0.00858014\pi$
$450$	−2.11902e6			−0.493292
$451$	401040.	−	3.39746e6i	0.0928424	−	0.786525i
$452$	−5.19151e6			−1.19522
$453$	−172602.	+	531214.i	−0.0395185	+	0.121625i
$454$	−8.09375e6	+	5.88046e6i	−1.84294	+	1.33897i
$455$	−317543.	−	230709.i	−0.0719075	−	0.0522439i
$456$	18206.4	+	56033.5i	0.00410027	+	0.0126193i
$457$	−1.56546e6	−	4.81799e6i	−0.350632	−	1.07913i	−0.958499	−	0.285095i	$-0.907975\pi$
$457$	−1.56546e6	−	4.81799e6i	−0.350632	−	1.07913i	0.607867	−	0.794039i	$-0.292025\pi$
$458$	4.96561e6	+	3.60773e6i	1.10614	+	0.803656i
$459$	1.11445e6	−	809694.i	0.246904	−	0.179386i
$460$	−2.87036e6	+	8.83406e6i	−0.632473	+	1.94655i
$461$	−5.55170e6			−1.21667			−0.608337	−	0.793679i	$-0.708163\pi$
$461$	−5.55170e6			−1.21667			−0.608337	+	0.793679i	$0.708163\pi$
$462$	−2.64056e6	−	4.71160e6i	−0.575560	−	1.02698i
$463$	2.46341e6			0.534053			0.267027	−	0.963689i	$-0.413959\pi$
$463$	2.46341e6			0.534053			0.267027	+	0.963689i	$0.413959\pi$
$464$	−5.11648e6	+	1.57469e7i	−1.10326	+	3.39547i
$465$	−800668.	+	581719.i	−0.171720	+	0.124762i
$466$	−2.27535e6	−	1.65314e6i	−0.485381	−	0.352650i
$467$	−218309.	−	671887.i	−0.0463212	−	0.142562i	0.925221	−	0.379429i	$-0.123879\pi$
$467$	−218309.	−	671887.i	−0.0463212	−	0.142562i	−0.971542	+	0.236867i	$0.923879\pi$
$468$	233601.	+	718950.i	0.0493015	+	0.151734i
$469$	−1.15367e6	−	838188.i	−0.242185	−	0.175958i
$470$	−2.19754e6	+	1.59661e6i	−0.458872	+	0.333390i
$471$	−1.05645e6	+	3.25143e6i	−0.219431	+	0.675339i
$472$	2.18628e7			4.51701
$473$	3.96774e6	−	4.29496e6i	0.815436	−	0.882687i
$474$	4.70682e6			0.962237
$475$	−7846.13	+	24147.9i	−0.00159559	+	0.00491073i
$476$	1.83833e7	−	1.33562e7i	3.71883	−	2.70188i
$477$	1.31801e6	+	957591.i	0.265230	+	0.192701i
$478$	4.88411e6	+	1.50317e7i	0.977722	+	3.00912i
$479$	571080.	+	1.75760e6i	0.113725	+	0.350011i	0.991679	−	0.128735i	$-0.0410916\pi$
$479$	571080.	+	1.75760e6i	0.113725	+	0.350011i	−0.877954	+	0.478746i	$0.841092\pi$
$480$	−4.61419e6	−	3.35241e6i	−0.914098	−	0.664131i
$481$	543576.	−	394931.i	0.107127	−	0.0778321i
$482$	4.31904e6	−	1.32926e7i	0.846777	−	2.60611i
$483$	−4.76234e6			−0.928865
$484$	−7.40945e6	+	1.21081e7i	−1.43771	+	2.34943i
$485$	−2.20118e6			−0.424913
$486$	200005.	−	615553.i	0.0384106	−	0.118216i
$487$	−1.40123e6	+	1.01805e6i	−0.267724	+	0.194513i	−0.713545	−	0.700609i	$-0.752912\pi$
$487$	−1.40123e6	+	1.01805e6i	−0.267724	+	0.194513i	0.445821	+	0.895122i	$0.352912\pi$
$488$	−1.45178e7	−	1.05478e7i	−2.75964	−	2.00499i
$489$	324052.	+	997330.i	0.0612834	+	0.188611i
$490$	166229.	+	511600.i	0.0312764	+	0.0962588i
$491$	−115416.	−	83855.0i	−0.0216055	−	0.0156973i	0.576930	−	0.816794i	$-0.304250\pi$
$491$	−115416.	−	83855.0i	−0.0216055	−	0.0156973i	−0.598536	+	0.801096i	$0.704250\pi$
$492$	5.47088e6	−	3.97483e6i	1.01893	−	0.740296i
$493$	2.46362e6	−	7.58226e6i	0.456517	−	1.40502i
$494$	12346.5			0.00227628
$495$	599334.	−	648762.i	0.109940	−	0.119007i
$496$	1.58824e7			2.89876
$497$	−720007.	+	2.21595e6i	−0.130751	+	0.402411i
$498$	7.80984e6	−	5.67418e6i	1.41114	−	1.02525i
$499$	−6.06822e6	−	4.40882e6i	−1.09096	−	0.792631i	−0.111402	−	0.993775i	$-0.535534\pi$
$499$	−6.06822e6	−	4.40882e6i	−1.09096	−	0.792631i	−0.979562	+	0.201144i	$0.935534\pi$
$500$	−4.07903e6	−	1.25540e7i	−0.729680	−	2.24572i
$501$	307370.	+	945989.i	0.0547101	+	0.168380i
$502$	9.36895e6	+	6.80694e6i	1.65933	+	1.20557i
$503$	−3.85622e6	+	2.80171e6i	−0.679582	+	0.493745i	−0.873219	−	0.487328i	$-0.837972\pi$
$503$	−3.85622e6	+	2.80171e6i	−0.679582	+	0.493745i	0.193637	+	0.981073i	$0.437972\pi$
$504$	2.10140e6	−	6.46743e6i	0.368495	−	1.13411i
$505$	34653.0			0.00604661
$506$	8.34084e6	+	1.48827e7i	1.44822	+	2.58408i
$507$	−3.24074e6			−0.559917
$508$	586603.	−	1.80538e6i	0.100852	−	0.310391i
$509$	−4.12715e6	+	2.99855e6i	−0.706082	+	0.512999i	−0.881907	−	0.471423i	$-0.843741\pi$
$509$	−4.12715e6	+	2.99855e6i	−0.706082	+	0.512999i	0.175825	+	0.984421i	$0.443741\pi$
$510$	4.09759e6	+	2.97707e6i	0.697594	+	0.506832i
$511$	825785.	+	2.54151e6i	0.139899	+	0.430565i
$512$	4.40417e6	+	1.35546e7i	0.742488	+	2.28514i
$513$	−6274.15	−	4558.44i	−0.00105260	−	0.000764755i
$514$	3.69567e6	−	2.68506e6i	0.617000	−	0.448277i
$515$	999275.	−	3.07545e6i	0.166022	−	0.510965i
$516$	1.15581e7			1.91101
$517$	−429078.	+	3.63498e6i	−0.0706009	+	0.598103i
$518$	−9.48926e6			−1.55385
$519$	−35128.1	+	108113.i	−0.00572448	+	0.0176181i
$520$	−1.43226e6	+	1.04060e6i	−0.232281	+	0.168762i
$521$	−2.96246e6	−	2.15235e6i	−0.478144	−	0.347392i	0.322463	−	0.946582i	$-0.395489\pi$
$521$	−2.96246e6	−	2.15235e6i	−0.478144	−	0.347392i	−0.800607	+	0.599190i	$0.795489\pi$
$522$	−1.15753e6	−	3.56250e6i	−0.185932	−	0.572241i
$523$	2.16334e6	+	6.65808e6i	0.345836	+	1.06437i	0.961135	+	0.276080i	$0.0890356\pi$
$523$	2.16334e6	+	6.65808e6i	0.345836	+	1.06437i	−0.615298	+	0.788294i	$0.710964\pi$
$524$	−6.78291e6	−	4.92807e6i	−1.07917	−	0.784060i
$525$	2.37091e6	−	1.72257e6i	0.375419	−	0.272758i
$526$	3.46612e6	−	1.06676e7i	0.546235	−	1.68114i
$527$	−7.64751e6			−1.19948
$528$	−1.39009e7	+	2.76957e6i	−2.16999	+	0.432342i
$529$	8.60665e6			1.33720
$530$	−1.85102e6	+	5.69687e6i	−0.286235	+	0.880940i
$531$	−2.32820e6	+	1.69153e6i	−0.358330	+	0.260342i
$532$	−103495.	−	75193.3i	−0.0158540	−	0.0115186i
$533$	−278925.	−	858442.i	−0.0425274	−	0.130886i
$534$	−445312.	−	1.37053e6i	−0.0675789	−	0.207986i
$535$	−2.72823e6	−	1.98218e6i	−0.412095	−	0.299404i
$536$	−5.20354e6	+	3.78059e6i	−0.782325	+	0.568392i
$537$	−996994.	+	3.06843e6i	−0.149196	+	0.459178i
$538$	−2.20313e7			−3.28160
$539$	658369.	+	303263.i	0.0976108	+	0.0449622i
$540$	1.74588e6			0.257650
$541$	−1.86027e6	+	5.72532e6i	−0.273264	+	0.841020i	0.716409	+	0.697680i	$0.245784\pi$
$541$	−1.86027e6	+	5.72532e6i	−0.273264	+	0.841020i	−0.989673	+	0.143340i	$0.954216\pi$
$542$	1.41060e7	−	1.02486e7i	2.06255	−	1.49853i
$543$	5.98290e6	+	4.34683e6i	0.870788	+	0.632664i
$544$	−1.36190e7	−	4.19150e7i	−1.97310	−	6.07257i
$545$	1.21605e6	+	3.74261e6i	0.175372	+	0.539739i
$546$	−1.15288e6	−	837618.i	−0.165502	−	0.120244i
$547$	1.01284e7	−	7.35870e6i	1.44734	−	1.05156i	0.460901	−	0.887452i	$-0.347526\pi$
$547$	1.01284e7	−	7.35870e6i	1.44734	−	1.05156i	0.986443	−	0.164105i	$-0.0524735\pi$
$548$	1.52161e6	−	4.68304e6i	0.216448	−	0.666157i
$549$	2.36210e6			0.334478
$550$	−9.53561e6	−	4.39237e6i	−1.34413	−	0.619145i
$551$	−44883.5			−0.00629808
$552$	−6.63776e6	+	2.04289e7i	−0.927201	+	2.85363i
$553$	−5.26632e6	+	3.82621e6i	−0.732309	+	0.532054i
$554$	7.53405e6	+	5.47381e6i	1.04293	+	0.757731i
$555$	−479520.	−	1.47581e6i	−0.0660807	−	0.203375i
$556$	−3.57625e6	−	1.10066e7i	−0.490615	−	1.50996i
$557$	−5.09619e6	−	3.70260e6i	−0.695998	−	0.505672i	0.182628	−	0.983182i	$-0.441539\pi$
$557$	−5.09619e6	−	3.70260e6i	−0.695998	−	0.505672i	−0.878626	+	0.477510i	$0.841539\pi$
$558$	−2.90693e6	+	2.11201e6i	−0.395229	+	0.287151i
$559$	476733.	−	1.46723e6i	0.0645277	−	0.198596i
$560$	1.45475e7			1.96028
$561$	6.69339e6	−	1.33357e6i	0.897922	−	0.178899i
$562$	−8.10224e6			−1.08209
$563$	2.44017e6	−	7.51007e6i	0.324451	−	0.998557i	−0.647237	−	0.762289i	$-0.724076\pi$
$563$	2.44017e6	−	7.51007e6i	0.324451	−	0.998557i	0.971688	−	0.236268i	$-0.0759245\pi$
$564$	−5.85337e6	+	4.25272e6i	−0.774833	+	0.562949i
$565$	1.29473e6	+	940674.i	0.170631	+	0.123970i
$566$	3.33470e6	+	1.02631e7i	0.437537	+	1.34660i
$567$	276607.	+	851309.i	0.0361331	+	0.111206i
$568$	8.50219e6	+	6.17720e6i	1.10576	+	0.803380i
$569$	1.10058e7	−	7.99620e6i	1.42509	−	1.03539i	0.434183	−	0.900825i	$-0.357037\pi$
$569$	1.10058e7	−	7.99620e6i	1.42509	−	1.03539i	0.990905	−	0.134562i	$-0.0429628\pi$
$570$	8811.46	−	27118.9i	0.00113595	−	0.00349611i
$571$	1.21891e7			1.56453			0.782263	−	0.622949i	$-0.214065\pi$
$571$	1.21891e7			1.56453			0.782263	+	0.622949i	$0.214065\pi$
$572$	−439054.	+	3.71950e6i	−0.0561084	+	0.475329i
$573$	6.71355e6			0.854212
$574$	−3.93928e6	+	1.21239e7i	−0.499042	+	1.53589i
$575$	−7.48908e6	+	5.44114e6i	−0.944624	+	0.686309i
$576$	−8.52311e6	−	6.19240e6i	−1.07039	−	0.777684i
$577$	3.38498e6	+	1.04179e7i	0.423269	+	1.30269i	0.904642	+	0.426173i	$0.140139\pi$
$577$	3.38498e6	+	1.04179e7i	0.423269	+	1.30269i	−0.481372	+	0.876516i	$0.659861\pi$
$578$	7.28502e6	+	2.24210e7i	0.907009	+	2.79149i
$579$	−3.24837e6	−	2.36008e6i	−0.402688	−	0.292570i
$580$	8.17451e6	−	5.93913e6i	1.00900	−	0.733083i
$581$	−4.12561e6	+	1.26973e7i	−0.507047	+	1.56053i
$582$	−7.99165e6			−0.977978
$583$	3.94614e6	+	7.04118e6i	0.480840	+	0.857974i
$584$	1.20532e7			1.46242
$585$	72011.5	−	221629.i	0.00869986	−	0.0267754i
$586$	1.13067e6	−	821476.i	0.136016	−	0.0988214i
$587$	−1.16749e7	−	8.48228e6i	−1.39848	−	1.01606i	−0.994874	−	0.101122i	$-0.967757\pi$
$587$	−1.16749e7	−	8.48228e6i	−1.39848	−	1.01606i	−0.403606	−	0.914933i	$-0.632243\pi$
$588$	442768.	+	1.36270e6i	0.0528120	+	0.162539i
$589$	13304.5	+	40946.9i	0.00158019	+	0.00486332i
$590$	−8.56027e6	−	6.21940e6i	−1.01241	−	0.735561i
$591$	−3.86287e6	+	2.80654e6i	−0.454927	+	0.330524i
$592$	−7.69536e6	+	2.36839e7i	−0.902453	+	2.77747i
$593$	2.34316e6			0.273631			0.136816	−	0.990597i	$-0.456313\pi$
$593$	2.34316e6			0.273631			0.136816	+	0.990597i	$0.456313\pi$
$594$	2.17596e6	−	2.35542e6i	0.253038	−	0.273906i
$595$	−7.00475e6			−0.811148
$596$	4.33101e6	−	1.33295e7i	0.499428	−	1.53708i
$597$	−5.25435e6	+	3.81751e6i	−0.603369	+	0.438373i
$598$	3.64165e6	+	2.64582e6i	0.416433	+	0.302557i
$599$	1.17667e6	+	3.62143e6i	0.133995	+	0.412395i	0.995432	−	0.0954693i	$-0.0304352\pi$
$599$	1.17667e6	+	3.62143e6i	0.133995	+	0.412395i	−0.861437	+	0.507864i	$0.830435\pi$
$600$	−4.08468e6	−	1.25714e7i	−0.463212	−	1.42562i
$601$	−4.36542e6	−	3.17166e6i	−0.492992	−	0.358179i	0.313342	−	0.949640i	$-0.398551\pi$
$601$	−4.36542e6	−	3.17166e6i	−0.492992	−	0.358179i	−0.806334	+	0.591461i	$0.798551\pi$
$602$	−1.76271e7	+	1.28068e7i	−1.98239	+	1.44029i
$603$	261625.	−	805199.i	0.0293012	−	0.0901799i
$604$	−5.47017e6			−0.610111
$605$	4.04179e6	−	1.67712e6i	0.448936	−	0.186284i
$606$	125812.			0.0139168
$607$	−1.08618e6	+	3.34290e6i	−0.119654	+	0.368258i	−0.992889	−	0.119041i	$-0.962018\pi$
$607$	−1.08618e6	+	3.34290e6i	−0.119654	+	0.368258i	0.873235	+	0.487299i	$0.162018\pi$
$608$	−200732.	+	145840.i	−0.0220220	+	0.0159999i
$609$	4.19110e6	+	3.04501e6i	0.457915	+	0.332695i
$610$	2.68380e6	+	8.25988e6i	0.292028	+	0.898771i
$611$	298425.	+	918458.i	0.0323394	+	0.0995305i
$612$	1.09143e7	+	7.92973e6i	1.17793	+	0.855815i
$613$	−2.80455e6	+	2.03762e6i	−0.301448	+	0.219015i	−0.728218	−	0.685345i	$-0.759651\pi$
$613$	−2.80455e6	+	2.03762e6i	−0.301448	+	0.219015i	0.426770	+	0.904360i	$0.359651\pi$
$614$	1.51952e6	−	4.67662e6i	0.162662	−	0.500623i
$615$	−2.08462e6			−0.222248
$616$	2.28622e7	−	2.47477e7i	2.42754	−	2.62774i
$617$	1.23914e7			1.31041			0.655206	−	0.755450i	$-0.272582\pi$
$617$	1.23914e7			1.31041			0.655206	+	0.755450i	$0.272582\pi$
$618$	3.62800e6	−	1.11658e7i	0.382116	−	1.17603i
$619$	1.48004e7	−	1.07531e7i	1.55256	−	1.12800i	0.610759	−	0.791816i	$-0.290864\pi$
$619$	1.48004e7	−	1.07531e7i	1.55256	−	1.12800i	0.941797	−	0.336182i	$-0.109136\pi$
$620$	−7.84133e6	−	5.69706e6i	−0.819239	−	0.595212i
$621$	−873730.	−	2.68906e6i	−0.0909176	−	0.279816i
$622$	−1.59457e6	−	4.90757e6i	−0.165260	−	0.508617i
$623$	1.61236e6	+	1.17145e6i	0.166434	+	0.120921i
$624$	−3.02551e6	+	2.19816e6i	−0.311055	+	0.225995i
$625$	1.04738e6	−	3.22352e6i	0.107252	−	0.330088i
$626$	−1.18292e7			−1.20648
$627$	−18784.9	−	33518.2i	−0.00190827	−	0.00340496i
$628$	−3.34815e7			−3.38771
$629$	3.70538e6	−	1.14040e7i	0.373427	−	1.14929i
$630$	−2.66260e6	+	1.93450e6i	−0.267273	+	0.194185i
$631$	2.58904e6	+	1.88105e6i	0.258861	+	0.188073i	0.709645	−	0.704560i	$-0.248856\pi$
$631$	2.58904e6	+	1.88105e6i	0.258861	+	0.188073i	−0.450784	+	0.892633i	$0.648856\pi$
$632$	9.07300e6	+	2.79238e7i	0.903563	+	2.78088i
$633$	−1.55610e6	−	4.78918e6i	−0.154357	−	0.475064i
$634$	−3.81039e6	−	2.76841e6i	−0.376484	−	0.273531i
$635$	−473420.	+	343960.i	−0.0465921	+	0.0338511i
$636$	−4.93039e6	+	1.51742e7i	−0.483324	+	1.48752i
$637$	191249.			0.0186745
$638$	2.17558e6	−	1.84307e7i	0.211604	−	1.79262i
$639$	−1.38334e6			−0.134022
$640$	5.70337e6	−	1.75532e7i	0.550405	−	1.69397i
$641$	−785899.	+	570989.i	−0.0755478	+	0.0548887i	−0.624918	−	0.780690i	$-0.714868\pi$
$641$	−785899.	+	570989.i	−0.0755478	+	0.0548887i	0.549370	+	0.835579i	$0.314868\pi$
$642$	−9.90520e6	−	7.19655e6i	−0.948475	−	0.689107i
$643$	581244.	+	1.78889e6i	0.0554410	+	0.170630i	0.974943	−	0.222456i	$-0.0714074\pi$
$643$	581244.	+	1.78889e6i	0.0554410	+	0.170630i	−0.919502	+	0.393086i	$0.871407\pi$
$644$	−1.44125e7	−	4.43572e7i	−1.36939	−	4.21453i
$645$	−2.88252e6	−	2.09428e6i	−0.272818	−	0.198214i
$646$	178258.	−	129512.i	0.0168061	−	0.0122103i
$647$	−839074.	+	2.58240e6i	−0.0788024	+	0.242529i	−0.982695	−	0.185230i	$-0.940697\pi$
$647$	−839074.	+	2.58240e6i	−0.0788024	+	0.242529i	0.903893	+	0.427759i	$0.140697\pi$
$648$	4.03738e6			0.377713
$649$	−1.39832e7	+	2.78596e6i	−1.30315	+	0.259635i
$650$	−2.76999e6			−0.257155
$651$	1.53561e6	−	4.72612e6i	0.142013	−	0.437071i
$652$	−8.30860e6	+	6.03655e6i	−0.765436	+	0.556122i
$653$	8.85851e6	+	6.43608e6i	0.812976	+	0.590661i	0.914692	−	0.404152i	$-0.132433\pi$
$653$	8.85851e6	+	6.43608e6i	0.812976	+	0.590661i	−0.101716	+	0.994813i	$0.532433\pi$
$654$	4.41502e6	+	1.35880e7i	0.403635	+	1.24226i
$655$	798671.	+	2.45806e6i	0.0727385	+	0.223866i
$656$	2.70649e7	+	1.96638e7i	2.45554	+	1.78405i
$657$	−1.28356e6	+	932562.i	−0.116012	+	0.0842877i
$658$	4.21468e6	−	1.29715e7i	0.379490	−	1.16795i
$659$	−3.80643e6			−0.341432			−0.170716	−	0.985320i	$-0.554608\pi$
$659$	−3.80643e6			−0.341432			−0.170716	+	0.985320i	$0.554608\pi$
$660$	7.85648e6	+	3.61891e6i	0.702050	+	0.323384i
$661$	−281208.			−0.0250337			−0.0125168	−	0.999922i	$-0.503984\pi$
$661$	−281208.			−0.0250337			−0.0125168	+	0.999922i	$0.503984\pi$
$662$	6.05135e6	−	1.86241e7i	0.536670	−	1.65170i
$663$	1.45681e6	−	1.05843e6i	0.128712	−	0.0935146i
$664$	4.87172e7	+	3.53951e7i	4.28808	+	3.11547i
$665$	12186.2	+	37505.4i	0.00106860	+	0.00328882i
$666$	−1.74096e6	−	5.35813e6i	−0.152091	−	0.468088i
$667$	−1.32386e7	−	9.61841e6i	−1.15220	−	0.837122i
$668$	−7.88088e6	+	5.72579e6i	−0.683335	+	0.496472i
$669$	−1.54861e6	+	4.76614e6i	−0.133776	+	0.411720i
$670$	3.11290e6			0.267903
$671$	1.06295e7	+	4.89624e6i	0.911394	+	0.419814i
$672$	2.86380e7			2.44635
$673$	3.84312e6	−	1.18279e7i	0.327074	−	1.00663i	−0.643422	−	0.765512i	$-0.722486\pi$
$673$	3.84312e6	−	1.18279e7i	0.327074	−	1.00663i	0.970496	−	0.241118i	$-0.0775141\pi$
$674$	−3.59248e7	+	2.61009e7i	−3.04610	+	2.21312i
$675$	1.40763e6	+	1.02270e6i	0.118913	+	0.0863954i
$676$	−9.80762e6	−	3.01847e7i	−0.825461	−	2.54051i
$677$	−3.69299e6	−	1.13659e7i	−0.309675	−	0.953083i	−0.977891	−	0.209115i	$-0.932942\pi$
$677$	−3.69299e6	−	1.13659e7i	−0.309675	−	0.953083i	0.668216	−	0.743968i	$-0.267058\pi$
$678$	4.70068e6	+	3.41524e6i	0.392723	+	0.285330i
$679$	8.94162e6	−	6.49647e6i	0.744289	−	0.540758i
$680$	−9.76323e6	+	3.00481e7i	−0.809695	+	2.49198i
$681$	8.21464e6			0.678767
$682$	−1.74590e7	+	3.47848e6i	−1.43734	+	0.286371i
$683$	−1.49764e7			−1.22844			−0.614222	−	0.789133i	$-0.710530\pi$
$683$	−1.49764e7			−1.22844			−0.614222	+	0.789133i	$0.710530\pi$
$684$	23470.2	−	72233.9i	0.00191812	−	0.00590338i
$685$	−1.22802e6	+	892211.i	−0.0999954	+	0.0726509i
$686$	1.81480e7	+	1.31853e7i	1.47237	+	1.06974i
$687$	−1.55738e6	−	4.79311e6i	−0.125893	−	0.387459i
$688$	1.76693e7	+	5.43805e7i	1.42314	+	4.37998i
$689$	1.72291e6	+	1.25176e6i	0.138265	+	0.100456i
$690$	8.41048e6	−	6.11057e6i	0.672509	−	0.488606i
$691$	6.48412e6	−	1.99561e7i	0.516602	−	1.58994i	−0.263747	−	0.964592i	$-0.584958\pi$
$691$	6.48412e6	−	1.99561e7i	0.516602	−	1.58994i	0.780349	−	0.625344i	$-0.215042\pi$
$692$	−1.11329e6			−0.0883780
$693$	−519884.	+	4.40426e6i	−0.0411219	+	0.348369i
$694$	−8.00261e6			−0.630715
$695$	−1.10244e6	+	3.39296e6i	−0.0865750	+	0.266450i
$696$	1.89037e7	−	1.37344e7i	1.47919	−	1.07469i
$697$	−1.30320e7	−	9.46827e6i	−1.01608	−	0.738225i
$698$	−5.60887e6	−	1.72623e7i	−0.435749	−	1.34110i
$699$	713623.	+	2.19631e6i	0.0552428	+	0.170020i
$700$	2.32195e7	+	1.68699e7i	1.79105	+	1.30127i
$701$	5.43569e6	−	3.94926e6i	0.417792	−	0.303543i	−0.358957	−	0.933354i	$-0.616868\pi$
$701$	5.43569e6	−	3.94926e6i	0.417792	−	0.303543i	0.776749	+	0.629811i	$0.216868\pi$
$702$	261447.	−	804651.i	0.0200235	−	0.0616261i
$703$	−67506.4			−0.00515177
$704$	−2.55183e7	−	4.55328e7i	−1.94053	−	3.46253i
$705$	2.23036e6			0.169006
$706$	3.05751e6	−	9.41005e6i	0.230864	−	0.710526i
$707$	−140767.	+	102273.i	−0.0105914	+	0.00769510i
$708$	−2.28012e7	−	1.65660e7i	−1.70952	−	1.24204i
$709$	5.05885e6	+	1.55695e7i	0.377952	+	1.16322i	0.941465	+	0.337109i	$0.109449\pi$
$709$	5.05885e6	+	1.55695e7i	0.377952	+	1.16322i	−0.563514	+	0.826107i	$0.690551\pi$
$710$	−1.57173e6	−	4.83730e6i	−0.117013	−	0.360128i
$711$	−3.12667e6	−	2.27166e6i	−0.231957	−	0.168527i
$712$	7.27244e6	−	5.28374e6i	0.537626	−	0.390608i
$713$	−4.85059e6	+	1.49286e7i	−0.357331	+	1.09975i
$714$	−2.54316e7			−1.86693
$715$	783451.	−	848063.i	0.0573121	−	0.0620388i
$716$	−3.15971e7			−2.30338
$717$	4.01034e6	−	1.23426e7i	0.291329	−	0.896618i
$718$	3.44515e7	−	2.50305e7i	2.49401	−	1.81200i
$719$	1.91810e7	+	1.39358e7i	1.38372	+	1.00533i	0.996522	+	0.0833344i	$0.0265570\pi$
$719$	1.91810e7	+	1.39358e7i	1.38372	+	1.00533i	0.387198	+	0.921997i	$0.373443\pi$
$720$	2.66898e6	+	8.21428e6i	0.191873	+	0.590525i
$721$	5.01752e6	+	1.54423e7i	0.359460	+	1.10630i
$722$	2.19559e7	+	1.59519e7i	1.56751	+	1.13886i
$723$	−9.28450e6	+	6.74558e6i	−0.660560	+	0.479925i
$724$	−2.23807e7	+	6.88808e7i	−1.58682	+	4.88373i
$725$	1.00698e7			0.711502
$726$	1.46742e7	−	6.08900e6i	1.03327	−	0.428750i
$727$	−1.96047e7			−1.37570			−0.687850	−	0.725853i	$-0.741445\pi$
$727$	−1.96047e7			−1.37570			−0.687850	+	0.725853i	$0.741445\pi$
$728$	2.74695e6	−	8.45423e6i	0.192098	−	0.591215i
$729$	−429945.	+	312373.i	−0.0299636	+	0.0217698i
$730$	−4.71938e6	−	3.42883e6i	−0.327776	−	0.238143i
$731$	−8.50791e6	−	2.61846e7i	−0.588883	−	1.81240i
$732$	7.14856e6	+	2.20010e7i	0.493107	+	1.51763i
$733$	433548.	+	314991.i	0.0298042	+	0.0216540i	0.602588	−	0.798053i	$-0.294136\pi$
$733$	433548.	+	314991.i	0.0298042	+	0.0216540i	−0.572783	+	0.819707i	$0.694136\pi$
$734$	3.51353e6	−	2.55273e6i	0.240715	−	0.174890i
$735$	136491.	−	420075.i	0.00931933	−	0.0286819i
$736$	−9.04599e7			−6.15547
$737$	2.84636e6	−	3.08110e6i	0.193028	−	0.208947i
$738$	−7.56848e6			−0.511526
$739$	−6.74550e6	+	2.07605e7i	−0.454363	+	1.39839i	0.417518	+	0.908669i	$0.362900\pi$
$739$	−6.74550e6	+	2.07605e7i	−0.454363	+	1.39839i	−0.871881	+	0.489717i	$0.837100\pi$
$740$	1.22948e7	−	8.93266e6i	0.825355	−	0.599655i
$741$	−8201.57	−	5958.79i	−0.000548721	−	0.000398669i
$742$	−9.29428e6	−	2.86049e7i	−0.619735	−	1.90735i
$743$	321519.	+	989535.i	0.0213666	+	0.0657596i	0.961171	−	0.275952i	$-0.0889932\pi$
$743$	321519.	+	989535.i	0.0213666	+	0.0657596i	−0.939805	+	0.341712i	$0.888993\pi$
$744$	−1.81332e7	−	1.31746e7i	−1.20100	−	0.872577i
$745$	−3.49535e6	+	2.53952e6i	−0.230728	+	0.167634i
$746$	8.93340e6	−	2.74942e7i	0.587719	−	1.80881i
$747$	−7.92648e6			−0.519731
$748$	3.26776e7	+	5.83074e7i	2.13549	+	3.81039i
$749$	1.69328e7			1.10287
$750$	−4.56527e6	+	1.40504e7i	−0.296356	+	0.912089i
$751$	−2.01170e7	+	1.46159e7i	−1.30156	+	0.945638i	−0.999970	−	0.00780001i	$-0.997517\pi$
$751$	−2.01170e7	+	1.46159e7i	−1.30156	+	0.945638i	−0.301589	+	0.953438i	$0.597517\pi$
$752$	−2.89571e7	−	2.10385e7i	−1.86728	−	1.35666i
$753$	−2.93841e6	−	9.04349e6i	−0.188853	−	0.581231i
$754$	−1.51312e6	−	4.65691e6i	−0.0969271	−	0.298311i
$755$	1.36422e6	+	991167.i	0.0871000	+	0.0632819i
$756$	−7.09212e6	+	5.15273e6i	−0.451306	+	0.327893i
$757$	2.32643e6	−	7.16003e6i	0.147554	−	0.454125i	−0.849777	−	0.527143i	$-0.823263\pi$
$757$	2.32643e6	−	7.16003e6i	0.147554	−	0.454125i	0.997331	+	0.0730184i	$0.0232632\pi$
$758$	6.88830e6			0.435451
$759$	1.64218e6	−	1.39119e7i	0.103470	−	0.876561i
$760$	177871.			0.0111705
$761$	−8.75535e6	+	2.69462e7i	−0.548039	+	1.68669i	0.165612	+	0.986191i	$0.447040\pi$
$761$	−8.75535e6	+	2.69462e7i	−0.548039	+	1.68669i	−0.713651	+	0.700501i	$0.752960\pi$
$762$	−1.71881e6	+	1.24879e6i	−0.107236	+	0.0779116i
$763$	−1.59856e7	−	1.16142e7i	−0.994074	−	0.722237i
$764$	2.03176e7	+	6.25311e7i	1.25933	+	3.87581i
$765$	−1.28514e6	−	3.95524e6i	−0.0793954	−	0.244354i
$766$	2.62700e7	+	1.90863e7i	1.61766	+	1.17530i
$767$	−3.04342e6	+	2.21117e6i	−0.186799	+	0.135717i
$768$	9.13159e6	−	2.81041e7i	0.558655	−	1.71936i
$769$	1.11520e7			0.680042			0.340021	−	0.940418i	$-0.389566\pi$
$769$	1.11520e7			0.680042			0.340021	+	0.940418i	$0.389566\pi$
$770$	−1.59916e7	+	3.18612e6i	−0.971999	+	0.193658i
$771$	−3.75087e6			−0.227246
$772$	1.21514e7	−	3.73983e7i	0.733811	−	2.25844i
$773$	1.46521e7	−	1.06454e7i	0.881964	−	0.640784i	−0.0518064	−	0.998657i	$-0.516498\pi$
$773$	1.46521e7	−	1.06454e7i	0.881964	−	0.640784i	0.933770	+	0.357873i	$0.116498\pi$
$774$	−1.04654e7	−	7.60354e6i	−0.627917	−	0.456208i
$775$	−2.98491e6	−	9.18661e6i	−0.178516	−	0.549416i
$776$	−1.54049e7	−	4.74115e7i	−0.918344	−	2.82637i
$777$	6.30357e6	+	4.57981e6i	0.374571	+	0.272142i
$778$	4.69118e7	−	3.40834e7i	2.77864	−	2.01880i
$779$	−28023.9	+	86248.8i	−0.00165457	+	0.00509225i
$780$	2.28222e6			0.134314
$781$	−6.22504e6	−	2.86743e6i	−0.365186	−	0.168215i
$782$	8.03319e7			4.69755
$783$	−950446.	+	2.92517e6i	−0.0554017	+	0.170509i
$784$	−5.73456e6	+	4.16640e6i	−0.333204	+	0.242087i
$785$	8.35006e6	+	6.06668e6i	0.483633	+	0.351380i
$786$	2.89968e6	+	8.92429e6i	0.167415	+	0.515249i
$787$	26019.6	+	80080.1i	0.00149749	+	0.00460880i	0.951802	−	0.306712i	$-0.0992287\pi$
$787$	26019.6	+	80080.1i	0.00149749	+	0.00460880i	−0.950305	+	0.311320i	$0.899229\pi$
$788$	−3.78310e7	−	2.74858e7i	−2.17036	−	1.57686i
$789$	−7.45101e6	+	5.41347e6i	−0.426111	+	0.309588i
$790$	4.39111e6	−	1.35145e7i	0.250326	−	0.770426i
$791$	−8.03572e6			−0.456650
$792$	1.81683e7	+	8.36880e6i	1.02920	+	0.474079i
$793$	3.08775e6			0.174365
$794$	−1.77668e7	+	5.46807e7i	−1.00014	+	3.07810i
$795$	3.97909e6	−	2.89098e6i	0.223288	−	0.162228i
$796$	−5.14584e7	−	3.73867e7i	−2.87855	−	2.09139i
$797$	7.10072e6	+	2.18538e7i	0.395965	+	1.21865i	0.928208	+	0.372062i	$0.121349\pi$
$797$	7.10072e6	+	2.18538e7i	0.395965	+	1.21865i	−0.532243	+	0.846592i	$0.678651\pi$
$798$	44243.7	+	136168.i	0.00245949	+	0.00756952i
$799$	1.39431e7	+	1.01302e7i	0.772665	+	0.561374i
$800$	4.50350e7	−	3.27199e7i	2.48786	−	1.80753i
$801$	−365646.	+	1.12534e6i	−0.0201363	+	0.0619731i
$802$	1.79954e7			0.987931
$803$	−7.70908e6	+	1.53593e6i	−0.421904	+	0.0840588i
$804$	8.29152e6			0.452370
$805$	−4.44291e6	+	1.36739e7i	−0.241645	+	0.743706i
$806$	−3.79994e6	+	2.76082e6i	−0.206034	+	0.149692i
$807$	1.46351e7	+	1.06330e7i	0.791063	+	0.574741i
$808$	242519.	+	746396.i	0.0130682	+	0.0402199i
$809$	−376423.	−	1.15851e6i	−0.0202211	−	0.0622341i	0.940437	−	0.339969i	$-0.110416\pi$
$809$	−376423.	−	1.15851e6i	−0.0202211	−	0.0622341i	−0.960658	+	0.277734i	$0.910416\pi$
$810$	−1.58081e6	−	1.14853e6i	−0.0846581	−	0.0615077i
$811$	−2.83859e7	+	2.06235e7i	−1.51548	+	1.10106i	−0.551807	+	0.833972i	$0.686062\pi$
$811$	−2.83859e7	+	2.06235e7i	−1.51548	+	1.10106i	−0.963672	+	0.267089i	$0.913938\pi$
$812$	−1.56780e7	+	4.82519e7i	−0.834450	+	2.56817i
$813$	−1.43167e7			−0.759654
$814$	3.27215e6	−	2.77203e7i	0.173090	−	1.46635i
$815$	3.16590e6			0.166956
$816$	−2.06239e7	+	6.34739e7i	−1.08429	+	3.33710i
$817$	−125399.	+	91107.5i	−0.00657261	+	0.00477528i
$818$	2.26217e7	+	1.64357e7i	1.18207	+	0.858823i
$819$	361581.	+	1.11283e6i	0.0188363	+	0.0579722i
$820$	−6.30879e6	−	1.94165e7i	−0.327651	−	1.00841i
$821$	−1.03731e7	−	7.53651e6i	−0.537096	−	0.390223i	0.285910	−	0.958257i	$-0.407704\pi$
$821$	−1.03731e7	−	7.53651e6i	−0.537096	−	0.390223i	−0.823005	+	0.568034i	$0.807704\pi$
$822$	−4.45850e6	+	3.23929e6i	−0.230149	+	0.167213i
$823$	−271337.	+	835089.i	−0.0139640	+	0.0429767i	−0.957796	−	0.287450i	$-0.907193\pi$
$823$	−271337.	+	835089.i	−0.0139640	+	0.0429767i	0.943832	+	0.330426i	$0.107193\pi$
$824$	7.32361e7			3.75757
$825$	4.21446e6	+	7.51996e6i	0.215579	+	0.384663i
$826$	5.31293e7			2.70947
$827$	5.05341e6	−	1.55528e7i	0.256934	−	0.790761i	−0.736509	−	0.676428i	$-0.763527\pi$
$827$	5.05341e6	−	1.55528e7i	0.256934	−	0.790761i	0.993443	−	0.114333i	$-0.0364730\pi$
$828$	2.24022e7	−	1.62761e7i	1.13557	−	0.825040i
$829$	−4.35273e6	−	3.16245e6i	−0.219976	−	0.159822i	0.472340	−	0.881417i	$-0.343410\pi$
$829$	−4.35273e6	−	3.16245e6i	−0.219976	−	0.159822i	−0.692316	+	0.721594i	$0.743410\pi$
$830$	−9.00598e6	−	2.77176e7i	−0.453770	−	1.39656i
$831$	−2.36292e6	−	7.27232e6i	−0.118699	−	0.365318i
$832$	−1.11414e7	−	8.09472e6i	−0.557998	−	0.405409i
$833$	2.76124e6	−	2.00616e6i	0.137877	−	0.100173i
$834$	−4.00255e6	+	1.23186e7i	−0.199261	+	0.613261i
$835$	3.00292e6			0.149049
$836$	255345.	−	276403.i	0.0126360	−	0.0136782i
$837$	2.95034e6			0.145566
$838$	−1.64484e6	+	5.06229e6i	−0.0809120	+	0.249022i
$839$	1.78518e7	−	1.29701e7i	0.875542	−	0.636119i	−0.0565261	−	0.998401i	$-0.518002\pi$
$839$	1.78518e7	−	1.29701e7i	0.875542	−	0.636119i	0.932068	+	0.362282i	$0.118002\pi$
$840$	−1.66092e7	−	1.20673e7i	−0.812174	−	0.590079i
$841$	−837603.	−	2.57788e6i	−0.0408365	−	0.125682i
$842$	7.89997e6	+	2.43136e7i	0.384013	+	1.18187i
$843$	5.38219e6	+	3.91039e6i	0.260850	+	0.189518i
$844$	3.98979e7	−	2.89875e7i	1.92794	−	1.40073i
$845$	−3.02336e6	+	9.30496e6i	−0.145663	+	0.448304i
$846$	8.09761e6			0.388983
$847$	−1.14688e7	+	1.87416e7i	−0.549298	+	0.897630i
$848$	−7.89310e7			−3.76928
$849$	2.73812e6	−	8.42706e6i	0.130372	−	0.401243i
$850$	−3.99929e7	+	2.90565e7i	−1.89861	+	1.37942i
$851$	−1.99113e7	−	1.44664e7i	−0.942489	−	0.684758i
$852$	−4.18647e6	−	1.28846e7i	−0.197583	−	0.608098i
$853$	2.87661e6	+	8.85329e6i	0.135366	+	0.416612i	0.995647	−	0.0932076i	$-0.0297120\pi$
$853$	2.87661e6	+	8.85329e6i	0.135366	+	0.416612i	−0.860281	+	0.509820i	$0.829712\pi$
$854$	−3.52800e7	−	2.56324e7i	−1.65533	−	1.20267i
$855$	−18941.7	+	13762.0i	−0.000886143	+	0.000643821i
$856$	2.36009e7	−	7.26362e7i	1.10089	−	3.38820i
$857$	−2.82490e7			−1.31386			−0.656932	−	0.753950i	$-0.728146\pi$
$857$	−2.82490e7			−1.31386			−0.656932	+	0.753950i	$0.728146\pi$
$858$	2.84442e6	−	3.07900e6i	0.131909	−	0.142788i
$859$	912201.			0.0421801			0.0210901	−	0.999778i	$-0.493286\pi$
$859$	912201.			0.0421801			0.0210901	+	0.999778i	$0.493286\pi$
$860$	1.07829e7	−	3.31863e7i	0.497151	−	1.53007i
$861$	8.46814e6	−	6.15246e6i	0.389296	−	0.282840i
$862$	−3.80722e7	−	2.76610e7i	−1.74518	−	1.26794i
$863$	2.65191e6	+	8.16176e6i	0.121208	+	0.373041i	0.993191	−	0.116495i	$-0.0371660\pi$
$863$	2.65191e6	+	8.16176e6i	0.121208	+	0.373041i	−0.871983	+	0.489536i	$0.837166\pi$
$864$	5.25411e6	+	1.61705e7i	0.239450	+	0.736951i
$865$	277648.	+	201723.i	0.0126169	+	0.00916674i
$866$	−5.16291e7	+	3.75107e7i	−2.33937	+	1.69966i
$867$	5.98173e6	−	1.84099e7i	0.270259	−	0.831770i
$868$	4.86672e7			2.19248
$869$	−9.36127e6	−	1.67035e7i	−0.420519	−	0.750341i
$870$	−1.13087e7			−0.506542
$871$	341996.	−	1.05256e6i	0.0152748	−	0.0470111i
$872$	−7.21023e7	+	5.23854e7i	−3.21113	+	2.33302i
$873$	5.30873e6	+	3.85702e6i	0.235752	+	0.171284i
$874$	−139754.	−	430120.i	−0.00618852	−	0.0190463i
$875$	−6.31376e6	−	1.94318e7i	−0.278784	−	0.858009i
$876$	−1.25705e7	−	9.13303e6i	−0.553470	−	0.402119i
$877$	1.39431e6	−	1.01303e6i	0.0612154	−	0.0444756i	−0.556757	−	0.830676i	$-0.687954\pi$
$877$	1.39431e6	−	1.01303e6i	0.0612154	−	0.0444756i	0.617972	+	0.786200i	$0.287954\pi$
$878$	2.21598e7	−	6.82008e7i	0.970128	−	2.98575i
$879$	−1.14755e6			−0.0500957
$880$	−5.01636e6	+	4.24967e7i	−0.218365	+	1.84990i
$881$	−3.49345e7			−1.51640			−0.758202	−	0.652019i	$-0.773922\pi$
$881$	−3.49345e7			−1.51640			−0.758202	+	0.652019i	$0.773922\pi$
$882$	495547.	−	1.52514e6i	0.0214493	−	0.0660142i
$883$	2.85406e7	−	2.07360e7i	1.23186	−	0.894999i	0.234832	−	0.972036i	$-0.424546\pi$
$883$	2.85406e7	−	2.07360e7i	1.23186	−	0.894999i	0.997028	+	0.0770371i	$0.0245460\pi$
$884$	1.42672e7	+	1.03658e7i	0.614058	+	0.446139i
$885$	2.68478e6	+	8.26290e6i	0.115226	+	0.354629i
$886$	2.71332e7	+	8.35074e7i	1.16123	+	3.57389i
$887$	3.08857e7	+	2.24398e7i	1.31810	+	0.957657i	0.999954	+	0.00961637i	$0.00306103\pi$
$887$	3.08857e7	+	2.24398e7i	1.31810	+	0.957657i	0.318148	+	0.948041i	$0.396939\pi$
$888$	2.84319e7	−	2.06570e7i	1.20996	−	0.879091i
$889$	907978.	−	2.79447e6i	0.0385319	−	0.118589i
$890$	−4.35057e6			−0.184107
$891$	−2.58225e6	+	514480.i	−0.108969	+	0.0217107i
$892$	−4.90793e7			−2.06531
$893$	29983.2	−	92278.7i	0.00125820	−	0.00387233i
$894$	−1.26903e7	+	9.22007e6i	−0.531043	+	0.385825i
$895$	7.88011e6	+	5.72523e6i	0.328832	+	0.238911i
$896$	2.86375e7	+	8.81373e7i	1.19170	+	3.66767i
$897$	−1.14214e6	−	3.51515e6i	−0.0473956	−	0.145869i
$898$	−2.14612e7	−	1.55924e7i	−0.888101	−	0.645243i
$899$	1.38140e7	−	1.00365e7i	0.570061	−	0.414173i
$900$	−5.26564e6	+	1.62060e7i	−0.216693	+	0.666912i
$901$	3.80059e7			1.55969
$902$	−3.40582e7	−	1.56882e7i	−1.39382	−	0.642031i
$903$	1.78904e7			0.730129
$904$	−1.12002e7	+	3.44707e7i	−0.455832	+	1.40291i
$905$	1.80624e7	−	1.31231e7i	0.733086	−	0.532618i
$906$	4.95299e6	+	3.59856e6i	0.200469	+	0.145649i
$907$	−517590.	−	1.59298e6i	−0.0208914	−	0.0642971i	0.940067	−	0.340989i	$-0.110762\pi$
$907$	−517590.	−	1.59298e6i	−0.0208914	−	0.0642971i	−0.960959	+	0.276692i	$0.910762\pi$
$908$	2.48604e7	+	7.65125e7i	1.00068	+	3.07977i
$909$	−83575.0	−	60720.8i	−0.00335480	−	0.00243740i
$910$	−3.48056e6	+	2.52877e6i	−0.139330	+	0.101229i
$911$	−6.18781e6	+	1.90441e7i	−0.247025	+	0.760265i	0.748272	+	0.663392i	$0.230884\pi$
$911$	−6.18781e6	+	1.90441e7i	−0.247025	+	0.760265i	−0.995297	+	0.0968724i	$0.969116\pi$
$912$	375737.			0.0149588
$913$	−3.56692e7	−	1.64302e7i	−1.41618	−	0.652330i
$914$	−5.55272e7			−2.19857
$915$	2.20367e6	−	6.78219e6i	0.0870148	−	0.267804i
$916$	3.99307e7	−	2.90113e7i	1.57242	−	1.14243i
$917$	−1.04990e7	−	7.62795e6i	−0.412310	−	0.299561i
$918$	−4.66585e6	−	1.43600e7i	−0.182736	−	0.562404i
$919$	−7.43194e6	−	2.28731e7i	−0.290277	−	0.893382i	−0.984767	−	0.173879i	$-0.944370\pi$
$919$	−7.43194e6	−	2.28731e7i	−0.290277	−	0.893382i	0.694490	−	0.719503i	$-0.255630\pi$
$920$	5.24640e7	+	3.81173e7i	2.04358	+	1.48475i
$921$	−3.26647e6	+	2.37323e6i	−0.126891	+	0.0921915i
$922$	−1.88042e7	+	5.78734e7i	−0.728497	+	2.24208i
$923$	−1.80830e6			−0.0698661
$924$	−4.25953e7	+	8.48656e6i	−1.64128	+	0.327003i
$925$	1.51453e7			0.582002
$926$	8.34384e6	−	2.56797e7i	0.319771	−	0.984152i
$927$	−7.79899e6	+	5.66630e6i	−0.298084	+	0.216571i
$928$	7.96093e7	+	5.78396e7i	3.03455	+	2.20473i
$929$	−1.48511e7	−	4.57070e7i	−0.564573	−	1.73758i	−0.669218	−	0.743066i	$-0.733371\pi$
$929$	−1.48511e7	−	4.57070e7i	−0.564573	−	1.73758i	0.104645	−	0.994510i	$-0.466629\pi$
$930$	3.35215e6	+	1.03169e7i	0.127091	+	0.391147i
$931$	−15545.3	−	11294.3i	−0.000587793	−	0.000427056i
$932$	−1.82971e7	+	1.32936e7i	−0.689988	+	0.501306i
$933$	−1.30930e6	+	4.02961e6i	−0.0492419	+	0.151551i
$934$	−7.74348e6			−0.290448
$935$	2.41542e6	−	2.04625e7i	0.0903573	−	0.765472i
$936$	5.27767e6			0.196903
$937$	3.56593e6	−	1.09748e7i	0.132686	−	0.408364i	−0.862537	−	0.505993i	$-0.831126\pi$
$937$	3.56593e6	−	1.09748e7i	0.132686	−	0.408364i	0.995223	+	0.0976294i	$0.0311260\pi$
$938$	−1.26452e7	+	9.18729e6i	−0.469266	+	0.340942i
$939$	7.85797e6	+	5.70915e6i	0.290835	+	0.211304i
$940$	6.74986e6	+	2.07739e7i	0.249158	+	0.766830i
$941$	−2.45867e6	−	7.56699e6i	−0.0905160	−	0.278580i	0.895543	−	0.444975i	$-0.146787\pi$
$941$	−2.45867e6	−	7.56699e6i	−0.0905160	−	0.278580i	−0.986059	+	0.166395i	$0.946787\pi$
$942$	3.03160e7	+	2.20259e7i	1.11313	+	0.808734i
$943$	−2.67487e7	+	1.94340e7i	−0.979541	+	0.711678i
$944$	4.30854e7	−	1.32603e8i	1.57362	−	4.84311i
$945$	2.70237e6			0.0984387
$946$	−3.13334e7	−	5.59089e7i	−1.13836	−	2.03120i
$947$	2.99384e7			1.08481			0.542406	−	0.840117i	$-0.317514\pi$
$947$	2.99384e7			1.08481			0.542406	+	0.840117i	$0.317514\pi$
$948$	1.16962e7	−	3.59971e7i	0.422691	−	1.30091i
$949$	−1.67787e6	+	1.21905e6i	−0.0604774	+	0.0439394i
$950$	225153.	+	163583.i	0.00809410	+	0.00588070i
$951$	1.19506e6	+	3.67802e6i	0.0428488	+	0.131875i
$952$	−4.90227e7	−	1.50876e8i	−1.75309	−	5.39547i
$953$	3.03708e7	+	2.20656e7i	1.08324	+	0.787017i	0.978244	−	0.207456i	$-0.0665183\pi$
$953$	3.03708e7	+	2.20656e7i	1.08324	+	0.787017i	0.104992	+	0.994473i	$0.466518\pi$
$954$	1.44466e7	−	1.04961e7i	0.513919	−	0.373384i
$955$	6.26324e6	−	1.92763e7i	0.222224	−	0.683934i
$956$	1.27097e8			4.49771
$957$	−1.03404e7	+	1.11932e7i	−0.364970	+	0.395070i
$958$	2.02563e7			0.713094
$959$	2.35524e6	−	7.24868e6i	0.0826967	−	0.254514i
$960$	−2.57314e7	+	1.86949e7i	−0.901124	+	0.654705i
$961$	9.91049e6	+	7.20039e6i	0.346168	+	0.251506i
$962$	−2.27579e6	−	7.00415e6i	−0.0792855	−	0.244016i
$963$	3.10659e6	+	9.56111e6i	0.107949	+	0.332233i
$964$	−9.09276e7	−	6.60628e7i	−3.15140	−	2.28962i
$965$	−9.80685e6	+	7.12510e6i	−0.339009	+	0.246305i
$966$	−1.61305e7	+	4.96447e7i	−0.556168	+	1.71171i
$967$	3.09350e7			1.06386			0.531930	−	0.846788i	$-0.321467\pi$
$967$	3.09350e7			1.06386			0.531930	+	0.846788i	$0.321467\pi$
$968$	6.44102e7	+	7.53194e7i	2.20936	+	2.58356i
$969$	−180920.			−0.00618981
$970$	−7.45561e6	+	2.29460e7i	−0.254422	+	0.783029i
$971$	−1.98365e7	+	1.44121e7i	−0.675177	+	0.490545i	−0.871754	−	0.489944i	$-0.837017\pi$
$971$	−1.98365e7	+	1.44121e7i	−0.675177	+	0.490545i	0.196577	+	0.980488i	$0.437017\pi$
$972$	−4.21066e6	−	3.05922e6i	−0.142950	−	0.103859i
$973$	−5.53552e6	−	1.70366e7i	−0.187446	−	0.576899i
$974$	5.86652e6	+	1.80553e7i	0.198145	+	0.609828i
$975$	1.84006e6	+	1.33688e6i	0.0619897	+	0.0450382i
$976$	−9.25855e7	+	6.72673e7i	−3.11113	+	2.26037i
$977$	−1.00978e7	+	3.10777e7i	−0.338446	+	1.04163i	0.626554	+	0.779378i	$0.284465\pi$
$977$	−1.00978e7	+	3.10777e7i	−0.338446	+	1.04163i	−0.965000	+	0.262251i	$0.915535\pi$
$978$	1.14942e7			0.384266
$979$	−3.97805e6	+	4.30613e6i	−0.132652	+	0.143592i
$980$	4.32572e6			0.143877
$981$	3.62518e6	−	1.11571e7i	0.120270	−	0.370152i
$982$	−1.26507e6	+	919126.i	−0.0418635	+	0.0304156i
$983$	−2.26624e7	−	1.64652e7i	−0.748034	−	0.543478i	0.147183	−	0.989109i	$-0.452979\pi$
$983$	−2.26624e7	−	1.64652e7i	−0.748034	−	0.543478i	−0.895217	+	0.445631i	$0.852979\pi$
$984$	−1.45892e7	−	4.49010e7i	−0.480335	−	1.47832i
$985$	4.45450e6	+	1.37096e7i	0.146288	+	0.450228i
$986$	−7.06962e7	−	5.13638e7i	−2.31582	−	1.68254i
$987$	−9.06017e6	+	6.58260e6i	−0.296035	+	0.215082i
$988$	30680.3	−	94424.2i	0.000999924	−	0.00307745i
$989$	−5.65110e7			−1.83714
$990$	−4.73298e6	−	8.44515e6i	−0.153478	−	0.273854i
$991$	3.38986e7			1.09647			0.548236	−	0.836324i	$-0.315300\pi$
$991$	3.38986e7			1.09647			0.548236	+	0.836324i	$0.315300\pi$
$992$	2.91687e7	−	8.97719e7i	0.941103	−	2.89642i
$993$	−1.30084e7	+	9.45115e6i	−0.418650	+	0.304167i
$994$	2.06613e7	+	1.50113e7i	0.663273	+	0.481896i
$995$	6.05910e6	+	1.86480e7i	0.194022	+	0.597138i
$996$	−2.39883e7	−	7.38285e7i	−0.766217	−	2.35817i
$997$	3.27807e7	+	2.38165e7i	1.04443	+	0.758824i	0.971146	−	0.238487i	$-0.0766516\pi$
$997$	3.27807e7	+	2.38165e7i	1.04443	+	0.758824i	0.0732855	+	0.997311i	$0.476652\pi$
$998$	−6.65132e7	+	4.83247e7i	−2.11389	+	1.53583i
$999$	−1.42950e6	+	4.39956e6i	−0.0453181	+	0.139475i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.6.e.a.31.5	yes	20
3.2	odd	2		99.6.f.c.64.1		20
11.4	even	5		363.6.a.u.1.10		10
11.5	even	5	inner	33.6.e.a.16.5	✓	20
11.7	odd	10		363.6.a.q.1.1		10
33.5	odd	10		99.6.f.c.82.1		20
33.26	odd	10		1089.6.a.bh.1.1		10
33.29	even	10		1089.6.a.bl.1.10		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.6.e.a.16.5	✓	20	11.5	even	5	inner
33.6.e.a.31.5	yes	20	1.1	even	1	trivial
99.6.f.c.64.1		20	3.2	odd	2
99.6.f.c.82.1		20	33.5	odd	10
363.6.a.q.1.1		10	11.7	odd	10
363.6.a.u.1.10		10	11.4	even	5
1089.6.a.bh.1.1		10	33.26	odd	10
1089.6.a.bl.1.10		10	33.29	even	10

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:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	33.e (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(3.38711 - 10.4244i) q^{2} +(-7.28115 + 5.29007i) q^{3} +(-71.3079 - 51.8082i) q^{4} +(8.39633 + 25.8412i) q^{5} +(30.4839 + 93.8199i) q^{6} +(-110.374 - 80.1917i) q^{7} +(-497.837 + 361.700i) q^{8} +(25.0304 - 77.0356i) q^{9} +O(q^{10})\)	\(q+(3.38711 - 10.4244i) q^{2} +(-7.28115 + 5.29007i) q^{3} +(-71.3079 - 51.8082i) q^{4} +(8.39633 + 25.8412i) q^{5} +(30.4839 + 93.8199i) q^{6} +(-110.374 - 80.1917i) q^{7} +(-497.837 + 361.700i) q^{8} +(25.0304 - 77.0356i) q^{9} +297.820 q^{10} +(272.319 - 294.777i) q^{11} +793.273 q^{12} +(32.7197 - 100.701i) q^{13} +(-1209.80 + 878.974i) q^{14} +(-197.837 - 143.737i) q^{15} +(1212.70 + 3732.31i) q^{16} +(-583.925 - 1797.14i) q^{17} +(-718.272 - 521.855i) q^{18} +(-8.60651 + 6.25300i) q^{19} +(740.064 - 2277.68i) q^{20} +1227.87 q^{21} +(-2150.51 - 3837.21i) q^{22} -3878.53 q^{23} +(1711.41 - 5267.18i) q^{24} +(1930.91 - 1402.89i) q^{25} +(-938.926 - 682.170i) q^{26} +(225.273 + 693.320i) q^{27} +(3715.98 + 11436.6i) q^{28} +(3413.30 + 2479.91i) q^{29} +(-2168.47 + 1575.49i) q^{30} +(1250.63 - 3849.03i) q^{31} +23323.2 q^{32} +(-423.402 + 3586.90i) q^{33} -20712.0 q^{34} +(1145.51 - 3525.53i) q^{35} +(-5775.94 + 4196.47i) q^{36} +(5133.73 + 3729.87i) q^{37} +(36.0328 + 110.898i) q^{38} +(294.478 + 906.309i) q^{39} +(-13526.8 - 9827.78i) q^{40} +(6896.60 - 5010.67i) q^{41} +(4158.93 - 12799.9i) q^{42} +14570.2 q^{43} +(-34690.3 + 6911.60i) q^{44} +2200.86 q^{45} +(-13137.0 + 40431.5i) q^{46} +(-7378.76 + 5360.98i) q^{47} +(-28574.0 - 20760.2i) q^{48} +(558.153 + 1717.82i) q^{49} +(-8084.11 - 24880.3i) q^{50} +(13758.6 + 9996.22i) q^{51} +(-7550.31 + 5485.62i) q^{52} +(-6215.25 + 19128.6i) q^{53} +7990.50 q^{54} +(9903.88 + 4562.00i) q^{55} +83953.8 q^{56} +(29.5866 - 91.0581i) q^{57} +(37412.9 - 27182.1i) q^{58} +(-28743.2 - 20883.1i) q^{59} +(6660.58 + 20499.1i) q^{60} +(9011.49 + 27734.5i) q^{61} +(-35888.0 - 26074.2i) q^{62} +(-8940.33 + 6495.53i) q^{63} +(40191.8 - 123698. i) q^{64} +2876.96 q^{65} +(35957.3 + 16562.9i) q^{66} +10452.3 q^{67} +(-51468.0 + 158402. i) q^{68} +(28240.2 - 20517.7i) q^{69} +(-32871.7 - 23882.7i) q^{70} +(-5277.47 - 16242.4i) q^{71} +(15402.7 + 47404.7i) q^{72} +(-15846.4 - 11513.1i) q^{73} +(56270.3 - 40882.8i) q^{74} +(-6637.87 + 20429.3i) q^{75} +937.669 q^{76} +(-53695.7 + 10698.2i) q^{77} +10445.2 q^{78} +(14744.2 - 45378.0i) q^{79} +(-86265.2 + 62675.4i) q^{80} +(-5307.96 - 3856.46i) q^{81} +(-28873.9 - 88864.8i) q^{82} +(-30239.7 - 93068.3i) q^{83} +(-87557.0 - 63613.9i) q^{84} +(41537.4 - 30178.7i) q^{85} +(49350.8 - 151886. i) q^{86} -37971.7 q^{87} +(-28949.5 + 245249. i) q^{88} -14608.1 q^{89} +(7454.54 - 22942.7i) q^{90} +(-11686.8 + 8490.96i) q^{91} +(276570. + 200940. i) q^{92} +(11255.6 + 34641.3i) q^{93} +(30892.6 + 95077.6i) q^{94} +(-233.848 - 169.901i) q^{95} +(-169820. + 123382. i) q^{96} +(-25034.0 + 77046.7i) q^{97} +19797.8 q^{98} +(-15892.1 - 28356.6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} - 45 q^{3} - 124 q^{4} - 33 q^{5} - 18 q^{6} - 335 q^{7} - 472 q^{8} - 405 q^{9}+O(q^{10}) \) 20 * q - 2 * q^2 - 45 * q^3 - 124 * q^4 - 33 * q^5 - 18 * q^6 - 335 * q^7 - 472 * q^8 - 405 * q^9	\( 20 q - 2 q^{2} - 45 q^{3} - 124 q^{4} - 33 q^{5} - 18 q^{6} - 335 q^{7} - 472 q^{8} - 405 q^{9} + 1952 q^{10} - 835 q^{11} + 3474 q^{12} - 959 q^{13} - 3020 q^{14} + 198 q^{15} - 1428 q^{16} - 3144 q^{17} - 567 q^{18} - 930 q^{19} + 3177 q^{20} + 8460 q^{21} + 2713 q^{22} + 1400 q^{23} + 1332 q^{24} - 9388 q^{25} + 3022 q^{26} - 3645 q^{27} - 21753 q^{28} + 4494 q^{29} - 4302 q^{30} + 9208 q^{31} + 69114 q^{32} + 6615 q^{33} - 9084 q^{34} - 31371 q^{35} - 10044 q^{36} - 3153 q^{37} + 1852 q^{38} - 8631 q^{39} - 53123 q^{40} - 7497 q^{41} + 22320 q^{42} + 63624 q^{43} + 58299 q^{44} + 1782 q^{45} - 94681 q^{46} - 43031 q^{47} - 12357 q^{48} - 5640 q^{49} - 76590 q^{50} + 459 q^{51} - 80149 q^{52} - 20452 q^{53} + 13122 q^{54} + 62974 q^{55} + 169638 q^{56} - 39375 q^{57} + 93145 q^{58} + 101730 q^{59} + 28593 q^{60} + 50745 q^{61} - 171957 q^{62} - 27135 q^{63} + 199638 q^{64} - 28210 q^{65} + 46107 q^{66} + 10730 q^{67} - 420141 q^{68} + 94365 q^{69} + 292664 q^{70} + 164895 q^{71} + 11988 q^{72} - 77236 q^{73} - 328228 q^{74} + 9063 q^{75} + 79212 q^{76} + 56087 q^{77} - 280062 q^{78} - 291931 q^{79} + 18026 q^{80} - 32805 q^{81} + 424659 q^{82} - 255451 q^{83} - 26127 q^{84} - 452271 q^{85} + 252843 q^{86} + 187056 q^{87} + 171694 q^{88} + 181632 q^{89} - 40338 q^{90} + 284615 q^{91} + 1199691 q^{92} + 82872 q^{93} - 550105 q^{94} - 511091 q^{95} - 587574 q^{96} - 145083 q^{97} - 150570 q^{98} - 83430 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 - 45 * q^3 - 124 * q^4 - 33 * q^5 - 18 * q^6 - 335 * q^7 - 472 * q^8 - 405 * q^9 + 1952 * q^10 - 835 * q^11 + 3474 * q^12 - 959 * q^13 - 3020 * q^14 + 198 * q^15 - 1428 * q^16 - 3144 * q^17 - 567 * q^18 - 930 * q^19 + 3177 * q^20 + 8460 * q^21 + 2713 * q^22 + 1400 * q^23 + 1332 * q^24 - 9388 * q^25 + 3022 * q^26 - 3645 * q^27 - 21753 * q^28 + 4494 * q^29 - 4302 * q^30 + 9208 * q^31 + 69114 * q^32 + 6615 * q^33 - 9084 * q^34 - 31371 * q^35 - 10044 * q^36 - 3153 * q^37 + 1852 * q^38 - 8631 * q^39 - 53123 * q^40 - 7497 * q^41 + 22320 * q^42 + 63624 * q^43 + 58299 * q^44 + 1782 * q^45 - 94681 * q^46 - 43031 * q^47 - 12357 * q^48 - 5640 * q^49 - 76590 * q^50 + 459 * q^51 - 80149 * q^52 - 20452 * q^53 + 13122 * q^54 + 62974 * q^55 + 169638 * q^56 - 39375 * q^57 + 93145 * q^58 + 101730 * q^59 + 28593 * q^60 + 50745 * q^61 - 171957 * q^62 - 27135 * q^63 + 199638 * q^64 - 28210 * q^65 + 46107 * q^66 + 10730 * q^67 - 420141 * q^68 + 94365 * q^69 + 292664 * q^70 + 164895 * q^71 + 11988 * q^72 - 77236 * q^73 - 328228 * q^74 + 9063 * q^75 + 79212 * q^76 + 56087 * q^77 - 280062 * q^78 - 291931 * q^79 + 18026 * q^80 - 32805 * q^81 + 424659 * q^82 - 255451 * q^83 - 26127 * q^84 - 452271 * q^85 + 252843 * q^86 + 187056 * q^87 + 171694 * q^88 + 181632 * q^89 - 40338 * q^90 + 284615 * q^91 + 1199691 * q^92 + 82872 * q^93 - 550105 * q^94 - 511091 * q^95 - 587574 * q^96 - 145083 * q^97 - 150570 * q^98 - 83430 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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