LMFDB - Embedded newform 43.7.d.a.37.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,7,Mod(7,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("43.7");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	43.d (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.89232559565$
Analytic rank:	$0$
Dimension:	$42$
Relative dimension:	$21$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			37.12
Character	$\chi$	$=$	43.37
Dual form			43.7.d.a.7.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.178867i q^{2} +(33.4310 + 19.3014i) q^{3} +63.9680 q^{4} +(21.1050 + 12.1850i) q^{5} +(-3.45239 + 5.97972i) q^{6} +(409.144 - 236.219i) q^{7} +22.8893i q^{8} +(380.590 + 659.200i) q^{9} +O(q^{10})$	\(q+0.178867i q^{2} +(33.4310 + 19.3014i) q^{3} +63.9680 q^{4} +(21.1050 + 12.1850i) q^{5} +(-3.45239 + 5.97972i) q^{6} +(409.144 - 236.219i) q^{7} +22.8893i q^{8} +(380.590 + 659.200i) q^{9} +(-2.17950 + 3.77500i) q^{10} -2215.98 q^{11} +(2138.52 + 1234.67i) q^{12} +(-1297.50 - 2247.34i) q^{13} +(42.2519 + 73.1824i) q^{14} +(470.375 + 814.714i) q^{15} +4089.86 q^{16} +(4482.76 + 7764.38i) q^{17} +(-117.909 + 68.0750i) q^{18} +(-699.671 - 403.955i) q^{19} +(1350.05 + 779.449i) q^{20} +18237.5 q^{21} -396.366i q^{22} +(-2740.91 + 4747.39i) q^{23} +(-441.796 + 765.213i) q^{24} +(-7515.55 - 13017.3i) q^{25} +(401.975 - 232.081i) q^{26} +1242.21i q^{27} +(26172.1 - 15110.5i) q^{28} +(-14764.0 + 8523.98i) q^{29} +(-145.726 + 84.1347i) q^{30} +(-22545.1 + 39049.2i) q^{31} +2196.46i q^{32} +(-74082.5 - 42771.6i) q^{33} +(-1388.79 + 801.820i) q^{34} +11513.3 q^{35} +(24345.6 + 42167.7i) q^{36} +(-8880.63 - 5127.23i) q^{37} +(72.2544 - 125.148i) q^{38} -100174. i q^{39} +(-278.906 + 483.079i) q^{40} -16946.4 q^{41} +3262.08i q^{42} +(-43171.4 - 66765.2i) q^{43} -141752. q^{44} +18549.9i q^{45} +(-849.154 - 490.259i) q^{46} +73062.3 q^{47} +(136728. + 78940.1i) q^{48} +(52774.4 - 91408.0i) q^{49} +(2328.37 - 1344.29i) q^{50} +346095. i q^{51} +(-82998.6 - 143758. i) q^{52} +(96238.4 - 166690. i) q^{53} -222.190 q^{54} +(-46768.3 - 27001.7i) q^{55} +(5406.89 + 9365.00i) q^{56} +(-15593.8 - 27009.3i) q^{57} +(-1524.66 - 2640.79i) q^{58} -137040. q^{59} +(30089.0 + 52115.6i) q^{60} +(-354650. + 204757. i) q^{61} +(-6984.63 - 4032.58i) q^{62} +(311432. + 179805. i) q^{63} +261358. q^{64} -63240.2i q^{65} +(7650.43 - 13250.9i) q^{66} +(159277. - 275876. i) q^{67} +(286754. + 496672. i) q^{68} +(-183263. + 105807. i) q^{69} +2059.35i q^{70} +(449201. - 259346. i) q^{71} +(-15088.6 + 8711.42i) q^{72} +(189212. - 109242. i) q^{73} +(917.094 - 1588.45i) q^{74} -580243. i q^{75} +(-44756.6 - 25840.2i) q^{76} +(-906654. + 523457. i) q^{77} +17917.9 q^{78} +(384737. + 666383. i) q^{79} +(86316.5 + 49834.9i) q^{80} +(253473. - 439029. i) q^{81} -3031.15i q^{82} +(126330. - 218810. i) q^{83} +1.16661e6 q^{84} +218490. i q^{85} +(11942.1 - 7721.95i) q^{86} -658099. q^{87} -50722.2i q^{88} +(-434782. - 251021. i) q^{89} -3317.97 q^{90} +(-1.06173e6 - 612989. i) q^{91} +(-175331. + 303681. i) q^{92} +(-1.50741e6 + 870304. i) q^{93} +13068.5i q^{94} +(-9844.38 - 17051.0i) q^{95} +(-42394.7 + 73429.8i) q^{96} +280574. q^{97} +(16349.9 + 9439.62i) q^{98} +(-843379. - 1.46078e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q - 3 q^{3} - 1194 q^{4} - 3 q^{5} + 111 q^{6} - 147 q^{7} + 3852 q^{9}+O(q^{10}) $ 42 * q - 3 * q^3 - 1194 * q^4 - 3 * q^5 + 111 * q^6 - 147 * q^7 + 3852 * q^9	\( 42 q - 3 q^{3} - 1194 q^{4} - 3 q^{5} + 111 q^{6} - 147 q^{7} + 3852 q^{9} - 981 q^{10} - 4104 q^{11} + 918 q^{12} + 4843 q^{13} + 2814 q^{14} - 163 q^{15} + 36678 q^{16} + 3641 q^{17} - 507 q^{18} - 5229 q^{19} - 1599 q^{20} - 29990 q^{21} + 6575 q^{23} - 4622 q^{24} + 68484 q^{25} + 189 q^{26} + 48948 q^{28} + 95361 q^{29} - 85041 q^{30} - 79373 q^{31} - 79638 q^{33} - 184743 q^{34} - 80582 q^{35} + 59972 q^{36} - 66063 q^{37} - 69820 q^{38} + 189951 q^{40} + 40632 q^{41} - 368728 q^{43} + 130330 q^{44} + 34056 q^{46} - 247820 q^{47} + 326907 q^{48} - 21876 q^{49} - 28638 q^{50} - 617150 q^{52} + 11639 q^{53} + 655904 q^{54} - 43638 q^{55} + 553875 q^{56} - 422859 q^{57} + 587796 q^{58} - 649352 q^{59} + 875455 q^{60} - 52251 q^{61} + 1335249 q^{62} + 93690 q^{63} - 792420 q^{64} + 160395 q^{66} - 173603 q^{67} + 22286 q^{68} + 870417 q^{69} + 1670505 q^{71} - 2068518 q^{72} - 2646201 q^{73} - 1625030 q^{74} - 80622 q^{76} - 486066 q^{77} + 2835040 q^{78} + 1897639 q^{79} - 817059 q^{80} + 2215367 q^{81} + 1584059 q^{83} - 824560 q^{84} - 2333682 q^{86} - 5547198 q^{87} + 2736939 q^{89} + 1092196 q^{90} - 3724131 q^{91} + 470257 q^{92} + 488433 q^{93} - 1289839 q^{95} + 1697650 q^{96} + 5260848 q^{97} + 4722621 q^{98} + 1375834 q^{99}+O(q^{100}) \) 42 * q - 3 * q^3 - 1194 * q^4 - 3 * q^5 + 111 * q^6 - 147 * q^7 + 3852 * q^9 - 981 * q^10 - 4104 * q^11 + 918 * q^12 + 4843 * q^13 + 2814 * q^14 - 163 * q^15 + 36678 * q^16 + 3641 * q^17 - 507 * q^18 - 5229 * q^19 - 1599 * q^20 - 29990 * q^21 + 6575 * q^23 - 4622 * q^24 + 68484 * q^25 + 189 * q^26 + 48948 * q^28 + 95361 * q^29 - 85041 * q^30 - 79373 * q^31 - 79638 * q^33 - 184743 * q^34 - 80582 * q^35 + 59972 * q^36 - 66063 * q^37 - 69820 * q^38 + 189951 * q^40 + 40632 * q^41 - 368728 * q^43 + 130330 * q^44 + 34056 * q^46 - 247820 * q^47 + 326907 * q^48 - 21876 * q^49 - 28638 * q^50 - 617150 * q^52 + 11639 * q^53 + 655904 * q^54 - 43638 * q^55 + 553875 * q^56 - 422859 * q^57 + 587796 * q^58 - 649352 * q^59 + 875455 * q^60 - 52251 * q^61 + 1335249 * q^62 + 93690 * q^63 - 792420 * q^64 + 160395 * q^66 - 173603 * q^67 + 22286 * q^68 + 870417 * q^69 + 1670505 * q^71 - 2068518 * q^72 - 2646201 * q^73 - 1625030 * q^74 - 80622 * q^76 - 486066 * q^77 + 2835040 * q^78 + 1897639 * q^79 - 817059 * q^80 + 2215367 * q^81 + 1584059 * q^83 - 824560 * q^84 - 2333682 * q^86 - 5547198 * q^87 + 2736939 * q^89 + 1092196 * q^90 - 3724131 * q^91 + 470257 * q^92 + 488433 * q^93 - 1289839 * q^95 + 1697650 * q^96 + 5260848 * q^97 + 4722621 * q^98 + 1375834 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$			0.178867i			0.0223584i	0.999938	+	0.0111792i	$0.00355853\pi$
$2$			0.178867i			0.0223584i	−0.999938	+	0.0111792i	$0.996441\pi$
$3$	33.4310	+	19.3014i	1.23819	+	0.714867i	0.968723	−	0.248143i	$-0.0798204\pi$
$3$	33.4310	+	19.3014i	1.23819	+	0.714867i	0.269463	+	0.963011i	$0.413154\pi$
$4$	63.9680			0.999500
$5$	21.1050	+	12.1850i	0.168840	+	0.0974799i	0.582039	−	0.813161i	$-0.302255\pi$
$5$	21.1050	+	12.1850i	0.168840	+	0.0974799i	−0.413199	+	0.910641i	$0.635588\pi$
$6$	−3.45239	+	5.97972i	−0.0159833	+	0.0276839i
$7$	409.144	−	236.219i	1.19284	−	0.688685i	0.233889	−	0.972263i	$-0.424855\pi$
$7$	409.144	−	236.219i	1.19284	−	0.688685i	0.958949	+	0.283578i	$0.0915214\pi$
$8$			22.8893i			0.0447056i
$9$	380.590	+	659.200i	0.522071	+	0.904253i
$10$	−2.17950	+	3.77500i	−0.00217950	+	0.00377500i
$11$	−2215.98			−1.66490			−0.832449	−	0.554101i	$-0.813062\pi$
$11$	−2215.98			−1.66490			−0.832449	+	0.554101i	$0.813062\pi$
$12$	2138.52	+	1234.67i	1.23757	+	0.714510i
$13$	−1297.50	−	2247.34i	−0.590579	−	1.02291i	−0.994155	−	0.107966i	$-0.965566\pi$
$13$	−1297.50	−	2247.34i	−0.590579	−	1.02291i	0.403576	−	0.914946i	$-0.367767\pi$
$14$	42.2519	+	73.1824i	0.0153979	+	0.0266700i
$15$	470.375	+	814.714i	0.139370	+	0.241397i
$16$	4089.86			0.998501
$17$	4482.76	+	7764.38i	0.912429	+	1.58037i	0.810622	+	0.585570i	$0.199129\pi$
$17$	4482.76	+	7764.38i	0.912429	+	1.58037i	0.101807	+	0.994804i	$0.467538\pi$
$18$	−117.909	+	68.0750i	−0.0202177	+	0.0116727i
$19$	−699.671	−	403.955i	−0.102008	−	0.0588942i	0.448128	−	0.893969i	$-0.352091\pi$
$19$	−699.671	−	403.955i	−0.102008	−	0.0588942i	−0.550136	+	0.835075i	$0.685424\pi$
$20$	1350.05	+	779.449i	0.168756	+	0.0974312i
$21$	18237.5			1.96928
$22$		−	396.366i		−	0.0372245i
$23$	−2740.91	+	4747.39i	−0.225274	+	0.390186i	−0.956402	−	0.292055i	$-0.905661\pi$
$23$	−2740.91	+	4747.39i	−0.225274	+	0.390186i	0.731128	+	0.682241i	$0.238994\pi$
$24$	−441.796	+	765.213i	−0.0319586	+	0.0553539i
$25$	−7515.55	−	13017.3i	−0.480995	−	0.833108i
$26$	401.975	−	232.081i	0.0228707	−	0.0132044i
$27$			1242.21i			0.0631106i
$28$	26172.1	−	15110.5i	1.19224	−	0.688341i
$29$	−14764.0	+	8523.98i	−0.605353	+	0.349501i	−0.771145	−	0.636660i	$-0.780315\pi$
$29$	−14764.0	+	8523.98i	−0.605353	+	0.349501i	0.165791	+	0.986161i	$0.446982\pi$
$30$	−145.726	+	84.1347i	−0.00539724	+	0.00311610i
$31$	−22545.1	+	39049.2i	−0.756775	+	1.31077i	0.187713	+	0.982224i	$0.439893\pi$
$31$	−22545.1	+	39049.2i	−0.756775	+	1.31077i	−0.944487	+	0.328548i	$0.893441\pi$
$32$			2196.46i			0.0670305i
$33$	−74082.5	−	42771.6i	−2.06146	−	1.19018i
$34$	−1388.79	+	801.820i	−0.0353346	+	0.0204005i
$35$	11513.3			0.268532
$36$	24345.6	+	42167.7i	0.521810	+	0.903801i
$37$	−8880.63	−	5127.23i	−0.175323	−	0.101223i	0.409770	−	0.912189i	$-0.365609\pi$
$37$	−8880.63	−	5127.23i	−0.175323	−	0.101223i	−0.585093	+	0.810966i	$0.698942\pi$
$38$	72.2544	−	125.148i	0.00131678	−	0.00228073i
$39$		−	100174.i		−	1.68874i
$40$	−278.906	+	483.079i	−0.00435790	+	0.00754811i
$41$	−16946.4			−0.245881			−0.122941	−	0.992414i	$-0.539232\pi$
$41$	−16946.4			−0.245881			−0.122941	+	0.992414i	$0.539232\pi$
$42$			3262.08i			0.0440299i
$43$	−43171.4	−	66765.2i	−0.542989	−	0.839740i
$43$	−43171.4	−	66765.2i	−0.542989	−	0.839740i
$44$	−141752.			−1.66407
$45$			18549.9i			0.203566i
$46$	−849.154	−	490.259i	−0.00872394	−	0.00503677i
$47$	73062.3			0.703720			0.351860	−	0.936053i	$-0.385549\pi$
$47$	73062.3			0.703720			0.351860	+	0.936053i	$0.385549\pi$
$48$	136728.	+	78940.1i	1.23633	+	0.713795i
$49$	52774.4	−	91408.0i	0.448575	−	0.776955i
$50$	2328.37	−	1344.29i	0.0186270	−	0.0107543i
$51$			346095.i			2.60906i
$52$	−82998.6	−	143758.i	−0.590284	−	1.02240i
$53$	96238.4	−	166690.i	0.646429	−	1.11965i	−0.337541	−	0.941311i	$-0.609595\pi$
$53$	96238.4	−	166690.i	0.646429	−	1.11965i	0.983970	−	0.178337i	$-0.0570716\pi$
$54$	−222.190			−0.00141105
$55$	−46768.3	−	27001.7i	−0.281102	−	0.162294i
$56$	5406.89	+	9365.00i	0.0307881	+	0.0533266i
$57$	−15593.8	−	27009.3i	−0.0842031	−	0.145844i
$58$	−1524.66	−	2640.79i	−0.00781428	−	0.0135347i
$59$	−137040.			−0.667255			−0.333627	−	0.942705i	$-0.608273\pi$
$59$	−137040.			−0.667255			−0.333627	+	0.942705i	$0.608273\pi$
$60$	30089.0	+	52115.6i	0.139301	+	0.241276i
$61$	−354650.	+	204757.i	−1.56246	+	0.902089i	−0.565457	+	0.824778i	$0.691300\pi$
$61$	−354650.	+	204757.i	−1.56246	+	0.902089i	−0.997007	+	0.0773111i	$0.975367\pi$
$62$	−6984.63	−	4032.58i	−0.0293068	−	0.0169203i
$63$	311432.	+	179805.i	1.24549	+	0.719085i
$64$	261358.			0.997002
$65$		−	63240.2i		−	0.230278i
$66$	7650.43	−	13250.9i	0.0266106	−	0.0460909i
$67$	159277.	−	275876.i	0.529576	−	0.917252i	−0.469829	−	0.882757i	$-0.655684\pi$
$67$	159277.	−	275876.i	0.529576	−	0.917252i	0.999405	−	0.0344950i	$-0.0109823\pi$
$68$	286754.	+	496672.i	0.911973	+	1.57958i
$69$	−183263.	+	105807.i	−0.557863	+	0.322082i
$70$			2059.35i			0.00600395i
$71$	449201.	−	259346.i	1.25506	−	0.724612i	0.282953	−	0.959134i	$-0.408686\pi$
$71$	449201.	−	259346.i	1.25506	−	0.724612i	0.972111	+	0.234522i	$0.0753525\pi$
$72$	−15088.6	+	8711.42i	−0.0404252	+	0.0233395i
$73$	189212.	−	109242.i	0.486385	−	0.280815i	−0.236688	−	0.971586i	$-0.576062\pi$
$73$	189212.	−	109242.i	0.486385	−	0.280815i	0.723074	+	0.690771i	$0.242729\pi$
$74$	917.094	−	1588.45i	0.00226318	−	0.00391994i
$75$		−	580243.i		−	1.37539i
$76$	−44756.6	−	25840.2i	−0.101957	−	0.0588648i
$77$	−906654.	+	523457.i	−1.98596	+	1.14659i
$78$	17917.9			0.0377576
$79$	384737.	+	666383.i	0.780337	+	1.35158i	0.931746	+	0.363112i	$0.118286\pi$
$79$	384737.	+	666383.i	0.780337	+	1.35158i	−0.151409	+	0.988471i	$0.548381\pi$
$80$	86316.5	+	49834.9i	0.168587	+	0.0973337i
$81$	253473.	−	439029.i	0.476955	−	0.826110i
$82$		−	3031.15i		−	0.00549752i
$83$	126330.	−	218810.i	0.220938	−	0.382677i	−0.734155	−	0.678982i	$-0.762421\pi$
$83$	126330.	−	218810.i	0.220938	−	0.382677i	0.955093	+	0.296306i	$0.0957547\pi$
$84$	1.16661e6			1.96829
$85$			218490.i			0.355774i
$86$	11942.1	−	7721.95i	0.0187752	−	0.0121404i
$87$	−658099.			−0.999387
$88$		−	50722.2i		−	0.0744304i
$89$	−434782.	−	251021.i	−0.616739	−	0.356074i	0.158859	−	0.987301i	$-0.449218\pi$
$89$	−434782.	−	251021.i	−0.616739	−	0.356074i	−0.775598	+	0.631227i	$0.782552\pi$
$90$	−3317.97			−0.00455140
$91$	−1.06173e6	−	612989.i	−1.40893	−	0.813446i
$92$	−175331.	+	303681.i	−0.225161	+	0.389991i
$93$	−1.50741e6	+	870304.i	−1.87406	+	1.08199i
$94$			13068.5i			0.0157341i
$95$	−9844.38	−	17051.0i	−0.0114820	−	0.0198874i
$96$	−42394.7	+	73429.8i	−0.0479179	+	0.0829963i
$97$	280574.			0.307420			0.153710	−	0.988116i	$-0.450878\pi$
$97$	280574.			0.307420			0.153710	+	0.988116i	$0.450878\pi$
$98$	16349.9	+	9439.62i	0.0173715	+	0.0100294i
$99$	−843379.	−	1.46078e6i	−0.869195	−	1.50549i
$100$	−480755.	−	832692.i	−0.480755	−	0.832692i
$101$	−128889.	−	223242.i	−0.125098	−	0.216676i	0.796673	−	0.604410i	$-0.206591\pi$
$101$	−128889.	−	223242.i	−0.125098	−	0.216676i	−0.921771	+	0.387734i	$0.873258\pi$
$102$	−61905.0			−0.0583345
$103$	−105015.	−	181891.i	−0.0961034	−	0.166456i	0.813965	−	0.580914i	$-0.197305\pi$
$103$	−105015.	−	181891.i	−0.0961034	−	0.166456i	−0.910069	+	0.414458i	$0.863971\pi$
$104$	51440.0	−	29698.9i	0.0457300	−	0.0264022i
$105$	384902.	+	222223.i	0.332493	+	0.191965i
$106$	29815.3	+	17213.9i	0.0250335	+	0.0144531i
$107$	25589.6			0.0208887			0.0104444	−	0.999945i	$-0.496675\pi$
$107$	25589.6			0.0208887			0.0104444	+	0.999945i	$0.496675\pi$
$108$			79461.5i			0.0630791i
$109$	−321968.	+	557665.i	−0.248618	+	0.430620i	−0.963143	−	0.268991i	$-0.913310\pi$
$109$	−321968.	+	557665.i	−0.248618	+	0.430620i	0.714524	+	0.699611i	$0.246643\pi$
$110$	4829.72	−	8365.32i	0.00362864	−	0.00628499i
$111$	−197926.	−	342817.i	−0.144722	−	0.250665i
$112$	1.67334e6	−	966103.i	1.19105	−	0.687653i
$113$			1.65435e6i			1.14655i	0.819364	+	0.573274i	$0.194327\pi$
$113$			1.65435e6i			1.14655i	−0.819364	+	0.573274i	$0.805673\pi$
$114$	4831.08	−	2789.22i	0.00326084	−	0.00188265i
$115$	−115694.	+	66795.9i	−0.0760706	+	0.0439194i
$116$	−944421.	+	545262.i	−0.605051	+	0.349326i
$117$	987631.	−	1.71063e6i	0.616648	−	1.06807i
$118$		−	24512.0i		−	0.0149188i
$119$	3.66819e6	+	2.11783e6i	2.17676	+	1.25675i
$120$	−18648.2	+	10766.6i	−0.0107918	+	0.00623064i
$121$	3.13901e6			1.77189
$122$	−36624.3	−	63435.2i	−0.0201693	−	0.0349342i
$123$	−566535.	−	327089.i	−0.304447	−	0.175773i
$124$	−1.44216e6	+	2.49790e6i	−0.756396	+	1.31012i
$125$		−	747088.i		−	0.382509i
$126$	−32161.2	+	55704.9i	−0.0160776	+	0.0278472i
$127$	−1.06194e6			−0.518427			−0.259213	−	0.965820i	$-0.583463\pi$
$127$	−1.06194e6			−0.518427			−0.259213	+	0.965820i	$0.583463\pi$
$128$			187322.i			0.0893219i
$129$	−154602.	−	3.06530e6i	−0.0720190	−	1.42792i
$130$	11311.6			0.00514865
$131$			3.71966e6i			1.65458i	0.561772	+	0.827292i	$0.310120\pi$
$131$			3.71966e6i			1.65458i	−0.561772	+	0.827292i	$0.689880\pi$
$132$	−4.73891e6	−	2.73601e6i	−2.06043	−	1.18959i
$133$	−381688.			−0.162238
$134$	49345.1	+	28489.4i	0.0205083	+	0.0118405i
$135$	−15136.3	+	26216.8i	−0.00615202	+	0.0106556i
$136$	−177721.	+	102607.i	−0.0706516	+	0.0407907i
$137$		−	771794.i		−	0.300151i	−0.988675	−	0.150075i	$-0.952048\pi$
$137$		−	771794.i		−	0.300151i	0.988675	−	0.150075i	$-0.0479517\pi$
$138$	−18925.4	−	32779.7i	−0.00720124	−	0.0124729i
$139$	601531.	−	1.04188e6i	0.223982	−	0.387949i	−0.732031	−	0.681271i	$-0.761428\pi$
$139$	601531.	−	1.04188e6i	0.223982	−	0.387949i	0.956014	+	0.293322i	$0.0947609\pi$
$140$	736483.			0.268398
$141$	2.44255e6	+	1.41021e6i	0.871337	+	0.503067i
$142$	46388.6	+	80347.4i	0.0162012	+	0.0280612i
$143$	2.87524e6	+	4.98006e6i	0.983254	+	1.70305i
$144$	1.55656e6	+	2.69604e6i	0.521288	+	0.902897i
$145$	−415458.			−0.136277
$146$	19539.8	+	33843.8i	0.00627857	+	0.0108748i
$147$	3.52861e6	−	2.03724e6i	1.11084	−	0.641344i
$148$	−568076.	−	327979.i	−0.175235	−	0.101172i
$149$	−1.16150e6	−	670594.i	−0.351125	−	0.202722i	0.314056	−	0.949405i	$-0.398312\pi$
$149$	−1.16150e6	−	670594.i	−0.351125	−	0.202722i	−0.665181	+	0.746683i	$0.731645\pi$
$150$	103787.			0.0307516
$151$		−	1.69879e6i		−	0.493412i	−0.969090	−	0.246706i	$-0.920652\pi$
$151$		−	1.69879e6i		−	0.493412i	0.969090	−	0.246706i	$-0.0793483\pi$
$152$	9246.25	−	16015.0i	0.00263290	−	0.00456032i
$153$	−3.41219e6	+	5.91008e6i	−0.952705	+	1.65013i
$154$	−93629.3	−	162171.i	−0.0256360	−	0.0444028i
$155$	−951628.	+	549423.i	−0.255548	+	0.147541i
$156$		−	6.40796e6i		−	1.68790i
$157$	1.24941e6	−	721348.i	0.322854	−	0.186400i	−0.329810	−	0.944047i	$-0.606985\pi$
$157$	1.24941e6	−	721348.i	0.322854	−	0.186400i	0.652664	+	0.757647i	$0.273651\pi$
$158$	−119194.	+	68816.8i	−0.0302192	+	0.0174471i
$159$	6.43470e6	−	3.71507e6i	1.60080	−	0.924222i
$160$	−26763.8	+	46356.2i	−0.00653413	+	0.0113174i
$161$			2.58982e6i			0.620572i
$162$	78527.9	+	45338.1i	0.0184705	+	0.0106640i
$163$	5.18656e6	−	2.99446e6i	1.19761	−	0.691442i	0.237590	−	0.971365i	$-0.423642\pi$
$163$	5.18656e6	−	2.99446e6i	1.19761	−	0.691442i	0.960022	+	0.279923i	$0.0903090\pi$
$164$	−1.08403e6			−0.245758
$165$	−1.04234e6	−	1.80539e6i	−0.232038	−	0.401901i
$166$	39137.9	+	22596.3i	0.00855604	+	0.00493983i
$167$	−3.75798e6	+	6.50902e6i	−0.806874	+	1.39755i	0.108145	+	0.994135i	$0.465509\pi$
$167$	−3.75798e6	+	6.50902e6i	−0.806874	+	1.39755i	−0.915019	+	0.403411i	$0.867824\pi$
$168$			417442.i			0.0880377i
$169$	−953616.	+	1.65171e6i	−0.197567	+	0.342195i
$170$	−39080.7			−0.00795454
$171$		−	614965.i		−	0.122988i
$172$	−2.76159e6	−	4.27084e6i	−0.542718	−	0.839320i
$173$	5.82365e6			1.12475			0.562376	−	0.826882i	$-0.309887\pi$
$173$	5.82365e6			1.12475			0.562376	+	0.826882i	$0.309887\pi$
$174$		−	117712.i		−	0.0223447i
$175$	−6.14988e6	−	3.55063e6i	−1.14750	−	0.662509i
$176$	−9.06305e6			−1.66240
$177$	−4.58139e6	−	2.64507e6i	−0.826186	−	0.476999i
$178$	44899.5	−	77768.2i	0.00796126	−	0.0137893i
$179$	−6.77982e6	+	3.91433e6i	−1.18211	+	0.682493i	−0.956502	−	0.291725i	$-0.905771\pi$
$179$	−6.77982e6	+	3.91433e6i	−1.18211	+	0.682493i	−0.225610	+	0.974218i	$0.572438\pi$
$180$			1.18660e6i			0.203464i
$181$	1.90257e6	+	3.29534e6i	0.320851	+	0.555731i	0.980664	−	0.195699i	$-0.0626976\pi$
$181$	1.90257e6	+	3.29534e6i	0.320851	+	0.555731i	−0.659812	+	0.751430i	$0.729364\pi$
$182$	109644.	−	189908.i	0.0181874	−	0.0315014i
$183$	−1.58084e7			−2.57950
$184$	−108664.	−	62737.5i	−0.0174435	−	0.0100710i
$185$	−124951.	−	216421.i	−0.0197344	−	0.0341809i
$186$	−155669.	−	269626.i	−0.0241915	−	0.0419009i
$187$	−9.93372e6	−	1.72057e7i	−1.51910	−	2.63116i
$188$	4.67365e6			0.703368
$189$	293433.	+	508241.i	0.0434634	+	0.0752808i
$190$	3049.86	−	1760.84i	0.000444651	−	0.000256719i
$191$	2.39987e6	+	1.38557e6i	0.344420	+	0.198851i	0.662225	−	0.749305i	$-0.269612\pi$
$191$	2.39987e6	+	1.38557e6i	0.344420	+	0.198851i	−0.317805	+	0.948156i	$0.602946\pi$
$192$	8.73747e6	+	5.04458e6i	1.23447	+	0.712724i
$193$	6.27519e6			0.872881			0.436441	−	0.899733i	$-0.356239\pi$
$193$	6.27519e6			0.872881			0.436441	+	0.899733i	$0.356239\pi$
$194$			50185.5i			0.00687343i
$195$	1.22062e6	−	2.11418e6i	0.164618	−	0.285127i
$196$	3.37588e6	−	5.84719e6i	0.448351	−	0.776567i
$197$	3.26334e6	+	5.65226e6i	0.426838	+	0.739305i	0.996590	−	0.0825114i	$-0.0262941\pi$
$197$	3.26334e6	+	5.65226e6i	0.426838	+	0.739305i	−0.569752	+	0.821817i	$0.692961\pi$
$198$	261285.	−	150853.i	0.0336604	−	0.0194338i
$199$			330761.i			0.0419716i	0.999780	+	0.0209858i	$0.00668048\pi$
$199$			330761.i			0.0419716i	−0.999780	+	0.0209858i	$0.993320\pi$
$200$	297957.	−	172026.i	0.0372446	−	0.0215032i
$201$	1.06496e7	−	6.14854e6i	1.31143	−	0.757153i
$202$	39930.6	−	23054.0i	0.00484453	−	0.00279699i
$203$	−4.02705e6	+	6.97506e6i	−0.481392	+	0.833796i
$204$			2.21390e7i			2.60776i
$205$	−357654.	−	206492.i	−0.0415146	−	0.0239685i
$206$	32534.3	−	18783.7i	0.00372169	−	0.00214872i
$207$	−4.17265e6			−0.470436
$208$	−5.30660e6	−	9.19130e6i	−0.589693	−	1.02138i
$209$	1.55046e6	+	895157.i	0.169833	+	0.0980529i
$210$	−39748.4	+	68846.3i	−0.00429203	+	0.00743401i
$211$			7.15112e6i			0.761249i	0.924730	+	0.380624i	$0.124291\pi$
$211$			7.15112e6i			0.761249i	−0.924730	+	0.380624i	$0.875709\pi$
$212$	6.15618e6	−	1.06628e7i	0.646106	−	1.11909i
$213$	2.00230e7			2.07200
$214$			4577.14i			0.000467039i
$215$	−97600.6	−	1.93512e6i	−0.00982058	−	0.194712i
$216$	−28433.2			−0.00282140
$217$			2.13023e7i			2.08472i
$218$	−99748.0	−	57589.5i	−0.00962797	−	0.00555871i
$219$	8.43408e6			0.802981
$220$	−2.99168e6	−	1.72724e6i	−0.280961	−	0.162213i
$221$	1.16328e7	−	2.01486e7i	1.07772	−	1.86667i
$222$	61318.8	−	35402.4i	0.00560447	−	0.00323574i
$223$			5.29613e6i			0.477577i	0.971072	+	0.238789i	$0.0767503\pi$
$223$			5.29613e6i			0.477577i	−0.971072	+	0.238789i	$0.923250\pi$
$224$	518845.	+	898666.i	0.0461629	+	0.0799566i
$225$	5.72068e6	−	9.90851e6i	0.502227	−	0.869883i
$226$	−295909.			−0.0256350
$227$	−1.07315e7	−	6.19581e6i	−0.917448	−	0.529689i	−0.0346278	−	0.999400i	$-0.511025\pi$
$227$	−1.07315e7	−	6.19581e6i	−0.917448	−	0.529689i	−0.882820	+	0.469712i	$0.844358\pi$
$228$	−997506.	−	1.72773e6i	−0.0841610	−	0.145771i
$229$	8.31259e6	+	1.43978e7i	0.692197	+	1.19892i	0.971116	+	0.238606i	$0.0766905\pi$
$229$	8.31259e6	+	1.43978e7i	0.692197	+	1.19892i	−0.278919	+	0.960315i	$0.589976\pi$
$230$	−11947.6	−	20693.8i	−0.000981968	−	0.00170082i
$231$	−4.04138e7			−3.27864
$232$	−195108.	−	337937.i	−0.0156247	−	0.0270627i
$233$	−4.13781e6	+	2.38896e6i	−0.327116	+	0.188861i	−0.654560	−	0.756010i	$-0.727146\pi$
$233$	−4.13781e6	+	2.38896e6i	−0.327116	+	0.188861i	0.327444	+	0.944871i	$0.393813\pi$
$234$	305975.	+	176655.i	0.0238802	+	0.0137873i
$235$	1.54198e6	+	890264.i	0.118816	+	0.0685986i
$236$	−8.76619e6			−0.666921
$237$			2.97038e7i			2.23135i
$238$	−378810.	+	656119.i	−0.0280990	+	0.0486689i
$239$	8.58153e6	−	1.48636e7i	0.628595	−	1.08876i	−0.359239	−	0.933246i	$-0.616964\pi$
$239$	8.58153e6	−	1.48636e7i	0.628595	−	1.08876i	0.987834	−	0.155513i	$-0.0497031\pi$
$240$	1.92377e6	+	3.33206e6i	0.139161	+	0.241035i
$241$	1.45291e7	−	8.38841e6i	1.03798	−	0.599278i	0.118720	−	0.992928i	$-0.462121\pi$
$241$	1.45291e7	−	8.38841e6i	1.03798	−	0.599278i	0.919261	+	0.393650i	$0.128788\pi$
$242$			561466.i			0.0396166i
$243$	1.77320e7	−	1.02376e7i	1.23577	−	0.713474i
$244$	−2.26862e7	+	1.30979e7i	−1.56168	+	0.901638i
$245$	2.22761e6	−	1.28611e6i	0.151475	−	0.0874542i
$246$	58505.6	−	101335.i	0.00392999	−	0.00680695i
$247$			2.09653e6i			0.139127i
$248$	−893809.	−	516041.i	−0.0585989	−	0.0338321i
$249$	8.44667e6	−	4.87669e6i	0.547126	−	0.315883i
$250$	133630.			0.00855230
$251$	633490.	+	1.09724e6i	0.0400607	+	0.0693872i	0.885361	−	0.464905i	$-0.153912\pi$
$251$	633490.	+	1.09724e6i	0.0400607	+	0.0693872i	−0.845300	+	0.534292i	$0.820578\pi$
$252$	1.99217e7	+	1.15018e7i	1.24487	+	0.718726i
$253$	6.07380e6	−	1.05201e7i	0.375059	−	0.649620i
$254$		−	189946.i		−	0.0115912i
$255$	−4.21716e6	+	7.30434e6i	−0.254331	+	0.440515i
$256$	1.66934e7			0.995005
$257$			2.14413e7i			1.26314i	0.775319	+	0.631570i	$0.217589\pi$
$257$			2.14413e7i			1.26314i	−0.775319	+	0.631570i	$0.782411\pi$
$258$	548282.	−	27653.3i	0.0319260	−	0.00161023i
$259$	−4.84460e6			−0.278842
$260$		−	4.04535e6i		−	0.230163i
$261$	−1.12380e7	−	6.48827e6i	−0.632074	−	0.364928i
$262$	−665325.			−0.0369939
$263$	−2.38389e7	−	1.37634e7i	−1.31044	−	0.756585i	−0.328274	−	0.944583i	$-0.606467\pi$
$263$	−2.38389e7	−	1.37634e7i	−1.31044	−	0.756585i	−0.982169	+	0.187998i	$0.939800\pi$
$264$	979011.	−	1.69570e6i	0.0532078	−	0.0921587i
$265$	4.06222e6	−	2.34533e6i	0.218286	−	0.126028i
$266$		−	68271.5i		−	0.00362739i
$267$	−9.69014e6	−	1.67838e7i	−0.509092	−	0.881773i
$268$	1.01886e7	−	1.76472e7i	0.529311	−	0.916794i
$269$	−1.01889e7			−0.523443			−0.261721	−	0.965143i	$-0.584290\pi$
$269$	−1.01889e7			−0.523443			−0.261721	+	0.965143i	$0.584290\pi$
$270$	−4689.32	−	2707.38i	−0.000238242	−	0.000137549i
$271$	−1.36499e7	−	2.36424e7i	−0.685840	−	1.18791i	−0.973172	−	0.230079i	$-0.926102\pi$
$271$	−1.36499e7	−	2.36424e7i	−0.685840	−	1.18791i	0.287332	−	0.957831i	$-0.407232\pi$
$272$	1.83339e7	+	3.17552e7i	0.911061	+	1.57800i
$273$	−2.36631e7	−	4.09857e7i	−1.16301	−	2.01440i
$274$	138049.			0.00671090
$275$	1.66543e7	+	2.88461e7i	0.800809	+	1.38704i
$276$	−1.17230e7	+	6.76826e6i	−0.557584	+	0.321921i
$277$	−4.43618e6	−	2.56123e6i	−0.208723	−	0.120506i	0.391995	−	0.919967i	$-0.371785\pi$
$277$	−4.43618e6	−	2.56123e6i	−0.208723	−	0.120506i	−0.600718	+	0.799461i	$0.705118\pi$
$278$	186359.	+	107594.i	0.00867391	+	0.00500788i
$279$	−3.43217e7			−1.58036
$280$			263531.i			0.0120049i
$281$	4.61239e6	−	7.98890e6i	0.207877	−	0.360054i	−0.743168	−	0.669105i	$-0.766678\pi$
$281$	4.61239e6	−	7.98890e6i	0.207877	−	0.360054i	0.951046	+	0.309050i	$0.100011\pi$
$282$	−252240.	+	436892.i	−0.0112478	+	0.0194817i
$283$	−98220.8	−	170123.i	−0.00433356	−	0.00750594i	0.863850	−	0.503748i	$-0.168046\pi$
$283$	−98220.8	−	170123.i	−0.00433356	−	0.00750594i	−0.868184	+	0.496242i	$0.834713\pi$
$284$	2.87345e7	−	1.65899e7i	1.25444	−	0.724249i
$285$		−	760042.i		−	0.0328324i
$286$	−890769.	+	514286.i	−0.0380774	+	0.0219840i
$287$	−6.93351e6	+	4.00306e6i	−0.293297	+	0.169335i
$288$	−1.44790e6	+	835948.i	−0.0606126	+	0.0349947i
$289$	−2.81216e7	+	4.87080e7i	−1.16505	+	2.01793i
$290$		−	74311.9i		−	0.00304694i
$291$	9.37989e6	+	5.41548e6i	0.380644	+	0.219765i
$292$	1.21035e7	−	6.98797e6i	0.486142	−	0.280674i
$293$	−2.01093e7			−0.799453			−0.399727	−	0.916634i	$-0.630895\pi$
$293$	−2.01093e7			−0.799453			−0.399727	+	0.916634i	$0.630895\pi$
$294$	364396.	+	631153.i	0.0143394	+	0.0248366i
$295$	−2.89223e6	−	1.66983e6i	−0.112659	−	0.0650439i
$296$	117359.	−	203271.i	0.00452522	−	0.00783792i
$297$		−	2.75271e6i		−	0.105073i
$298$	119947.	−	207755.i	0.00453254	−	0.00785059i
$299$	1.42253e7			0.532168
$300$		−	3.71170e7i		−	1.37470i
$301$	−3.34345e7	−	1.71186e7i	−1.22601	−	0.627725i
$302$	303859.			0.0110319
$303$		−	9.95094e6i		−	0.357714i
$304$	−2.86156e6	−	1.65212e6i	−0.101855	−	0.0588059i
$305$	−9.97985e6			−0.351742
$306$	−1.05712e6	−	610329.i	−0.0368944	−	0.0213010i
$307$	8.74418e6	−	1.51454e7i	0.302207	−	0.523437i	−0.674429	−	0.738340i	$-0.735610\pi$
$307$	8.74418e6	−	1.51454e7i	0.302207	−	0.523437i	0.976635	+	0.214903i	$0.0689434\pi$
$308$	−5.79968e7	+	3.34845e7i	−1.98496	+	1.14602i
$309$		−	8.10774e6i		−	0.274805i
$310$	−98273.8	−	170215.i	−0.00329877	−	0.00571364i
$311$	−3.51236e6	+	6.08359e6i	−0.116766	+	0.202245i	−0.918484	−	0.395457i	$-0.870586\pi$
$311$	−3.51236e6	+	6.08359e6i	−0.116766	+	0.202245i	0.801718	+	0.597702i	$0.203920\pi$
$312$	2.29292e6			0.0754963
$313$	4.53068e7	+	2.61579e7i	1.47751	+	0.853041i	0.999677	−	0.0254099i	$-0.00808911\pi$
$313$	4.53068e7	+	2.61579e7i	1.47751	+	0.853041i	0.477833	+	0.878451i	$0.341422\pi$
$314$	129026.	+	223479.i	0.00416761	+	0.00721851i
$315$	4.38184e6	+	7.58958e6i	0.140193	+	0.242821i
$316$	2.46108e7	+	4.26272e7i	0.779947	+	1.35091i
$317$	1.89630e7			0.595290			0.297645	−	0.954677i	$-0.403799\pi$
$317$	1.89630e7			0.595290			0.297645	+	0.954677i	$0.403799\pi$
$318$	664505.	+	1.15096e6i	0.0206641	+	0.0357913i
$319$	3.27166e7	−	1.88890e7i	1.00785	−	0.581884i
$320$	5.51597e6	+	3.18464e6i	0.168334	+	0.0971876i
$321$	855487.	+	493915.i	0.0258641	+	0.0149327i
$322$	−463234.			−0.0138750
$323$		−	7.24335e6i		−	0.214947i
$324$	1.62142e7	−	2.80838e7i	0.476717	−	0.825697i
$325$	−1.95029e7	+	3.37800e7i	−0.568131	+	0.984032i
$326$	535611.	+	927705.i	0.0154595	+	0.0267767i
$327$	−2.15274e7	+	1.24289e7i	−0.615672	+	0.355458i
$328$		−	387891.i		−	0.0109923i
$329$	2.98930e7	−	1.72587e7i	0.839424	−	0.484642i
$330$	322925.	−	186441.i	0.00898587	−	0.00518799i
$331$	1.02372e7	−	5.91047e6i	0.282292	−	0.162981i	−0.352168	−	0.935937i	$-0.614556\pi$
$331$	1.02372e7	−	5.91047e6i	0.282292	−	0.162981i	0.634461	+	0.772955i	$0.281222\pi$
$332$	8.08106e6	−	1.39968e7i	0.220828	−	0.382485i
$333$		−	7.80548e6i		−	0.211382i
$334$	−1.16425e6	−	672180.i	−0.0312469	−	0.0180404i
$335$	6.72308e6	−	3.88157e6i	0.178827	−	0.103246i
$336$	7.45886e7			1.96632
$337$	3.63858e7	+	6.30221e7i	0.950698	+	1.64666i	0.743919	+	0.668270i	$0.232965\pi$
$337$	3.63858e7	+	6.30221e7i	0.950698	+	1.64666i	0.206779	+	0.978388i	$0.433702\pi$
$338$	−295437.	−	170571.i	−0.00765094	−	0.00441727i
$339$	−3.19313e7	+	5.53066e7i	−0.819629	+	1.41964i
$340$			1.39764e7i			0.355596i
$341$	4.99594e7	−	8.65323e7i	1.25995	−	2.18230i
$342$	109997.			0.00274981
$343$			5.71656e6i			0.141662i
$344$	1.52821e6	−	988163.i	0.0375411	−	0.0242747i
$345$	−5.15702e6			−0.125586
$346$			1.04166e6i			0.0251477i
$347$	−1.60242e7	−	9.25159e6i	−0.383520	−	0.221426i	0.295828	−	0.955241i	$-0.404404\pi$
$347$	−1.60242e7	−	9.25159e6i	−0.383520	−	0.221426i	−0.679349	+	0.733815i	$0.737738\pi$
$348$	−4.20973e7			−0.998888
$349$	−2.46821e7	−	1.42502e7i	−0.580638	−	0.335232i	0.180749	−	0.983529i	$-0.442148\pi$
$349$	−2.46821e7	−	1.42502e7i	−0.580638	−	0.335232i	−0.761387	+	0.648298i	$0.775481\pi$
$350$	635092.	−	1.10001e6i	0.0148126	−	0.0256563i
$351$	2.79166e6	−	1.61176e6i	0.0645566	−	0.0372718i
$352$		−	4.86730e6i		−	0.111599i
$353$	−2.31523e6	−	4.01010e6i	−0.0526344	−	0.0911655i	0.838508	−	0.544890i	$-0.183428\pi$
$353$	−2.31523e6	−	4.01010e6i	−0.0526344	−	0.0911655i	−0.891142	+	0.453724i	$0.850095\pi$
$354$	473116.	−	819461.i	0.0106649	−	0.0184722i
$355$	1.26405e7			0.282540
$356$	−2.78121e7	−	1.60573e7i	−0.616431	−	0.355896i
$357$	8.17542e7	+	1.41602e8i	1.79682	+	3.11219i
$358$	−700145.	−	1.21269e6i	−0.0152595	−	0.0264302i
$359$	−2.82098e7	−	4.88608e7i	−0.609701	−	1.05603i	−0.991290	−	0.131700i	$-0.957956\pi$
$359$	−2.82098e7	−	4.88608e7i	−0.609701	−	1.05603i	0.381589	−	0.924332i	$-0.375377\pi$
$360$	−424594.			−0.00910053
$361$	−2.31966e7	−	4.01777e7i	−0.493063	−	0.854010i
$362$	−589429.	+	340307.i	−0.0124253	+	0.00717373i
$363$	1.04940e8	+	6.05873e7i	2.19393	+	1.26667i
$364$	−6.79167e7	−	3.92117e7i	−1.40823	−	0.813039i
$365$	5.32443e6			0.109495
$366$		−	2.82761e6i		−	0.0576734i
$367$	−2.37712e7	+	4.11730e7i	−0.480899	+	0.832941i	−0.999760	−	0.0219178i	$-0.993023\pi$
$367$	−2.37712e7	+	4.11730e7i	−0.480899	+	0.832941i	0.518861	+	0.854858i	$0.326356\pi$
$368$	−1.12099e7	+	1.94162e7i	−0.224936	+	0.389601i
$369$	−6.44962e6	−	1.11711e7i	−0.128367	−	0.222339i
$370$	38710.6	−	22349.6i	0.000764230	−	0.000441229i
$371$		−	9.09334e7i		−	1.78074i
$372$	−9.64260e7	+	5.56716e7i	−1.87312	+	1.08145i
$373$	−1.48860e7	+	8.59445e6i	−0.286848	+	0.165612i	−0.636520	−	0.771260i	$-0.719627\pi$
$373$	−1.48860e7	+	8.59445e6i	−0.286848	+	0.165612i	0.349671	+	0.936872i	$0.386293\pi$
$374$	3.07754e6	−	1.77682e6i	0.0588286	−	0.0339647i
$375$	1.44199e7	−	2.49759e7i	0.273443	−	0.473618i
$376$			1.67234e6i			0.0314603i
$377$	3.83125e7	+	2.21197e7i	0.715018	+	0.412816i
$378$	−90907.6	+	52485.5i	−0.00168316	+	0.000971772i
$379$	1.90456e7			0.349845			0.174923	−	0.984582i	$-0.444032\pi$
$379$	1.90456e7			0.349845			0.174923	+	0.984582i	$0.444032\pi$
$380$	−629725.	−	1.09072e6i	−0.0114763	−	0.0198775i
$381$	−3.55016e7	−	2.04969e7i	−0.641909	−	0.370606i
$382$	−247832.	+	429258.i	−0.00444599	+	0.00770067i
$383$			7.74568e6i			0.137868i	0.997621	+	0.0689340i	$0.0219598\pi$
$383$			7.74568e6i			0.137868i	−0.997621	+	0.0689340i	$0.978040\pi$
$384$	−3.61557e6	+	6.26236e6i	−0.0638533	+	0.110597i
$385$	−2.55133e7			−0.447079
$386$			1.12243e6i			0.0195162i
$387$	2.75811e7	−	5.38688e7i	0.475859	−	0.929403i
$388$	1.79478e7			0.307267
$389$		−	4.56709e7i		−	0.775873i	−0.921686	−	0.387936i	$-0.873188\pi$
$389$		−	4.56709e7i		−	0.775873i	0.921686	−	0.387936i	$-0.126812\pi$
$390$	378158.	+	218330.i	0.00637499	+	0.00368061i
$391$	−4.91474e7			−0.822187
$392$	2.09226e6	+	1.20797e6i	0.0347343	+	0.0200538i
$393$	−7.17947e7	+	1.24352e8i	−1.18281	+	2.04868i
$394$	−1.01101e6	+	583704.i	−0.0165297	+	0.00954342i
$395$			1.87520e7i			0.304269i
$396$	−5.39493e7	−	9.34429e7i	−0.868760	−	1.50474i
$397$	−4.87047e6	+	8.43590e6i	−0.0778393	+	0.134822i	−0.902317	−	0.431072i	$-0.858135\pi$
$397$	−4.87047e6	+	8.43590e6i	−0.0778393	+	0.134822i	0.824478	+	0.565894i	$0.191469\pi$
$398$	−59162.4			−0.000938418
$399$	−1.27602e7	−	7.36712e6i	−0.200881	−	0.115979i
$400$	−3.07375e7	−	5.32390e7i	−0.480274	−	0.831859i
$401$	−4.77822e7	−	8.27612e7i	−0.741025	−	1.28349i	−0.952029	−	0.306008i	$-0.901006\pi$
$401$	−4.77822e7	−	8.27612e7i	−0.741025	−	1.28349i	0.211003	−	0.977485i	$-0.432327\pi$
$402$	1.09977e6	+	1.90486e6i	0.0169287	+	0.0293214i
$403$	1.17009e8			1.78774
$404$	−8.24475e6	−	1.42803e7i	−0.125036	−	0.216568i
$405$	1.06991e7	−	6.17714e6i	0.161058	−	0.0929871i
$406$	−1.24761e6	−	720308.i	−0.0186424	−	0.0107632i
$407$	1.96793e7	+	1.13618e7i	0.291895	+	0.168526i
$408$	−7.92186e6			−0.116640
$409$			4.52816e7i			0.661838i	0.943659	+	0.330919i	$0.107359\pi$
$409$			4.52816e7i			0.661838i	−0.943659	+	0.330919i	$0.892641\pi$
$410$	36934.6	−	63972.6i	0.000535897	−	0.000928201i
$411$	1.48967e7	−	2.58019e7i	0.214568	−	0.371643i
$412$	−6.71759e6	−	1.16352e7i	−0.0960553	−	0.166373i
$413$	−5.60691e7	+	3.23715e7i	−0.795927	+	0.459529i
$414$		−	746350.i		−	0.0105182i
$415$	5.33238e6	−	3.07865e6i	0.0746066	−	0.0430741i
$416$	4.93618e6	−	2.84991e6i	0.0685663	−	0.0395868i
$417$	4.02196e7	−	2.32208e7i	0.554663	−	0.320235i
$418$	−160114.	+	277326.i	−0.00219231	+	0.00379719i
$419$		−	8.63187e7i		−	1.17344i	−0.809788	−	0.586722i	$-0.800418\pi$
$419$		−	8.63187e7i		−	1.17344i	0.809788	−	0.586722i	$-0.199582\pi$
$420$	2.46214e7	+	1.42152e7i	0.332326	+	0.191869i
$421$	1.13997e8	−	6.58164e7i	1.52774	−	0.882039i	0.528280	−	0.849070i	$-0.322837\pi$
$421$	1.13997e8	−	6.58164e7i	1.52774	−	0.882039i	0.999456	−	0.0329689i	$-0.0104962\pi$
$422$	−1.27910e6			−0.0170203
$423$	2.78068e7	+	4.81627e7i	0.367392	+	0.636341i
$424$	3.81541e6	+	2.20283e6i	0.0500546	+	0.0288990i
$425$	6.73809e7	−	1.16707e8i	0.877748	−	1.52030i
$426$			3.58146e6i			0.0463267i
$427$	−9.67351e7	+	1.67550e8i	−1.24251	+	2.15209i
$428$	1.63692e6			0.0208783
$429$			2.21985e8i			2.81158i
$430$	346130.	−	17457.5i	0.00435346	−	0.000219572i
$431$	−1.35712e8			−1.69507			−0.847535	−	0.530739i	$-0.821914\pi$
$431$	−1.35712e8			−1.69507			−0.847535	+	0.530739i	$0.821914\pi$
$432$			5.08045e6i			0.0630160i
$433$	−6.05621e7	−	3.49656e7i	−0.745998	−	0.430702i	0.0782483	−	0.996934i	$-0.475067\pi$
$433$	−6.05621e7	−	3.49656e7i	−0.745998	−	0.430702i	−0.824246	+	0.566232i	$0.808401\pi$
$434$	−3.81029e6			−0.0466110
$435$	−1.38892e7	−	8.01893e6i	−0.168737	−	0.0974202i
$436$	−2.05956e7	+	3.56727e7i	−0.248494	+	0.430404i
$437$	3.83547e6	−	2.21441e6i	0.0459594	−	0.0265347i
$438$			1.50858e6i			0.0179534i
$439$	2.08090e7	+	3.60422e7i	0.245956	+	0.426008i	0.962400	−	0.271637i	$-0.0875649\pi$
$439$	2.08090e7	+	3.60422e7i	0.245956	+	0.426008i	−0.716444	+	0.697644i	$0.754232\pi$
$440$	618049.	−	1.07049e6i	0.00725546	−	0.0125668i
$441$	8.03416e7			0.936752
$442$	3.60392e6	+	2.08072e6i	0.0417358	+	0.0240962i
$443$	−2.22030e7	−	3.84568e7i	−0.255388	−	0.442346i	0.709613	−	0.704592i	$-0.248870\pi$
$443$	−2.22030e7	−	3.84568e7i	−0.255388	−	0.442346i	−0.965001	+	0.262246i	$0.915537\pi$
$444$	−1.26609e7	−	2.19293e7i	−0.144649	−	0.250540i
$445$	−6.11739e6	−	1.05956e7i	−0.0694202	−	0.120239i
$446$	−947304.			−0.0106779
$447$	−2.58868e7	−	4.48373e7i	−0.289839	−	0.502015i
$448$	1.06933e8	−	6.17378e7i	1.18926	−	0.686621i
$449$	−8.53762e7	−	4.92920e7i	−0.943187	−	0.544549i	−0.0522293	−	0.998635i	$-0.516633\pi$
$449$	−8.53762e7	−	4.92920e7i	−0.943187	−	0.544549i	−0.890958	+	0.454086i	$0.849966\pi$
$450$	1.77231e6	+	1.02324e6i	0.0194492	+	0.0112290i
$451$	3.75529e7			0.409368
$452$			1.05825e8i			1.14597i
$453$	3.27891e7	−	5.67925e7i	0.352724	−	0.610937i
$454$	1.10823e6	−	1.91951e6i	0.0118430	−	0.0205127i
$455$	−1.49385e7	−	2.58743e7i	−0.158589	−	0.274685i
$456$	618223.	−	356931.i	0.00652005	−	0.00376435i
$457$			1.09959e8i			1.15208i	0.817421	+	0.576040i	$0.195403\pi$
$457$			1.09959e8i			1.15208i	−0.817421	+	0.576040i	$0.804597\pi$
$458$	−2.57530e6	+	1.48685e6i	−0.0268060	+	0.0154764i
$459$	−9.64496e6	+	5.56852e6i	−0.0997384	+	0.0575840i
$460$	−7.40071e6	+	4.27280e6i	−0.0760326	+	0.0438974i
$461$	−1.89039e7	+	3.27425e7i	−0.192952	+	0.334202i	−0.946227	−	0.323503i	$-0.895139\pi$
$461$	−1.89039e7	+	3.27425e7i	−0.192952	+	0.334202i	0.753276	+	0.657705i	$0.228473\pi$
$462$		−	7.22871e6i		−	0.0733053i
$463$	−1.55142e8	−	8.95710e7i	−1.56309	−	0.902453i	−0.996941	−	0.0781522i	$-0.975098\pi$
$463$	−1.55142e8	−	8.95710e7i	−1.56309	−	0.902453i	−0.566152	−	0.824301i	$-0.691569\pi$
$464$	−6.03825e7	+	3.48619e7i	−0.604446	+	0.348977i
$465$	−4.24186e7			−0.421888
$466$	−427307.	−	740118.i	−0.00422263	−	0.00731380i
$467$	1.00634e8	+	5.81011e7i	0.988085	+	0.570471i	0.904701	−	0.426046i	$-0.140094\pi$
$467$	1.00634e8	+	5.81011e7i	0.988085	+	0.570471i	0.0833836	+	0.996518i	$0.473427\pi$
$468$	6.31768e7	−	1.09425e8i	0.616340	−	1.06753i
$469$		−	1.50497e8i		−	1.45885i
$470$	−159239.	+	275810.i	−0.00153375	+	0.00265654i
$471$	5.56922e7			0.533005
$472$		−	3.13675e6i		−	0.0298301i
$473$	9.56670e7	+	1.47950e8i	0.904022	+	1.39808i
$474$	−5.31305e6			−0.0498894
$475$			1.21438e7i			0.113311i
$476$	2.34647e8	+	1.35473e8i	2.17567	+	1.25613i
$477$	1.46509e8			1.34993
$478$	2.65862e6	+	1.53495e6i	0.0243429	+	0.0140544i
$479$	−4.44217e7	+	7.69407e7i	−0.404193	+	0.700083i	−0.994227	−	0.107295i	$-0.965781\pi$
$479$	−4.44217e7	+	7.69407e7i	−0.404193	+	0.700083i	0.590034	+	0.807378i	$0.299114\pi$
$480$	−1.78948e6	+	1.03316e6i	−0.0161809	+	0.00934207i
$481$			2.66104e7i			0.239120i
$482$	1.50041e6	+	2.59879e6i	0.0133989	+	0.0232076i
$483$	−4.99872e7	+	8.65804e7i	−0.443627	+	0.768384i
$484$	2.00796e8			1.77100
$485$	5.92152e6	+	3.41879e6i	0.0519049	+	0.0299673i
$486$	1.83117e6	+	3.17168e6i	0.0159522	+	0.0276299i
$487$	3.22567e6	+	5.58702e6i	0.0279275	+	0.0483719i	0.879651	−	0.475619i	$-0.157776\pi$
$487$	3.22567e6	+	5.58702e6i	0.0279275	+	0.0483719i	−0.851724	+	0.523991i	$0.824443\pi$
$488$	−4.68674e6	−	8.11768e6i	−0.0403285	−	0.0698509i
$489$	2.31189e8			1.97716
$490$	230043.	+	398447.i	0.00195534	+	0.00338674i
$491$	−7.30050e7	+	4.21494e7i	−0.616748	+	0.356080i	−0.775602	−	0.631222i	$-0.782554\pi$
$491$	−7.30050e7	+	4.21494e7i	−0.616748	+	0.356080i	0.158854	+	0.987302i	$0.449220\pi$
$492$	−3.62401e7	−	2.09233e7i	−0.304295	−	0.175685i
$493$	−1.32367e8	−	7.64220e7i	−1.10468	−	0.637790i
$494$	−375001.			−0.00311065
$495$		−	4.11063e7i		−	0.338916i
$496$	−9.22061e7	+	1.59706e8i	−0.755640	+	1.30881i
$497$	1.22525e8	−	2.12220e8i	0.998059	−	1.72869i
$498$	872280.	+	1.51083e6i	0.00706265	+	0.0122329i
$499$	1.05678e8	−	6.10135e7i	0.850521	−	0.491048i	−0.0103058	−	0.999947i	$-0.503280\pi$
$499$	1.05678e8	−	6.10135e7i	0.850521	−	0.491048i	0.860827	+	0.508898i	$0.169947\pi$
$500$		−	4.77898e7i		−	0.382318i
$501$	−2.51267e8	+	1.45069e8i	−1.99812	+	1.15362i
$502$	−196260.	+	113311.i	−0.00155139	+	0.000895694i
$503$	1.32499e8	−	7.64982e7i	1.04114	−	0.601100i	0.120981	−	0.992655i	$-0.461396\pi$
$503$	1.32499e8	−	7.64982e7i	1.04114	−	0.601100i	0.920155	+	0.391554i	$0.128063\pi$
$504$	−4.11561e6	+	7.12844e6i	−0.0321472	+	0.0556805i
$505$		−	6.28203e6i		−	0.0487782i
$506$	1.88171e6	+	1.08640e6i	0.0145245	+	0.00838571i
$507$	−6.37607e7	+	3.68123e7i	−0.489248	+	0.282468i
$508$	−6.79299e7			−0.518167
$509$	3.06674e7	+	5.31176e7i	0.232554	+	0.402796i	0.958559	−	0.284894i	$-0.0919584\pi$
$509$	3.06674e7	+	5.31176e7i	0.232554	+	0.402796i	−0.726005	+	0.687690i	$0.758625\pi$
$510$	−1.30651e6	−	754312.i	−0.00984921	−	0.00568644i
$511$	5.16099e7	−	8.93910e7i	0.386786	−	0.669933i
$512$			1.49745e7i			0.111569i
$513$	501796.	−	869136.i	0.00371685	−	0.00643777i
$514$	−3.83514e6			−0.0282418
$515$		−	5.11841e6i		−	0.0374726i
$516$	−9.88961e6	−	1.96081e8i	−0.0719830	−	1.42721i
$517$	−1.61905e8			−1.17162
$518$		−	866540.i		−	0.00623447i
$519$	1.94691e8	+	1.12405e8i	1.39265	+	0.804048i
$520$	1.44752e6			0.0102947
$521$	1.48279e8	+	8.56088e7i	1.04849	+	0.605348i	0.922227	−	0.386648i	$-0.126367\pi$
$521$	1.48279e8	+	8.56088e7i	1.04849	+	0.605348i	0.126267	+	0.991996i	$0.459700\pi$
$522$	1.16054e6	−	2.01011e6i	0.00815922	−	0.0141322i
$523$	8.45739e7	−	4.88288e7i	0.591196	−	0.341327i	−0.174375	−	0.984679i	$-0.555790\pi$
$523$	8.45739e7	−	4.88288e7i	0.591196	−	0.341327i	0.765570	+	0.643352i	$0.222457\pi$
$524$			2.37939e8i			1.65376i
$525$	−1.37065e8	−	2.37403e8i	−0.947212	−	1.64062i
$526$	2.46182e6	−	4.26399e6i	0.0169160	−	0.0292994i
$527$	−4.04257e8			−2.76201
$528$	−3.02987e8	−	1.74930e8i	−2.05836	−	1.18840i
$529$	5.89928e7	+	1.02178e8i	0.398503	+	0.690228i
$530$	419502.	+	726599.i	0.00281778	+	0.00488053i
$531$	−5.21561e7	−	9.03369e7i	−0.348354	−	0.603367i
$532$	−2.44158e7			−0.162157
$533$	2.19880e7	+	3.80843e7i	0.145212	+	0.251515i
$534$	3.00207e6	−	1.73325e6i	0.0197150	−	0.0113825i
$535$	540069.	+	311809.i	0.00352686	+	0.00203623i
$536$	6.31460e6	+	3.64573e6i	0.0410064	+	0.0236750i
$537$	−3.02208e8			−1.95157
$538$		−	1.82246e6i		−	0.0117033i
$539$	−1.16947e8	+	2.02558e8i	−0.746833	+	1.29355i
$540$	−968237.	+	1.67704e6i	−0.00614894	+	0.0106503i
$541$	−3.75703e7	−	6.50737e7i	−0.237276	−	0.410974i	0.722656	−	0.691208i	$-0.242921\pi$
$541$	−3.75703e7	−	6.50737e7i	−0.237276	−	0.410974i	−0.959932	+	0.280234i	$0.909588\pi$
$542$	4.22885e6	−	2.44153e6i	0.0265598	−	0.0153343i
$543$			1.46889e8i			0.917465i
$544$	−1.70541e7	+	9.84620e6i	−0.105933	+	0.0611606i
$545$	−1.35903e7	+	7.84635e6i	−0.0839535	+	0.0484706i
$546$	7.33101e6	−	4.23256e6i	0.0450387	−	0.0260031i
$547$	1.23717e8	−	2.14285e8i	0.755908	−	1.30927i	−0.189014	−	0.981974i	$-0.560529\pi$
$547$	1.23717e8	−	2.14285e8i	0.755908	−	1.30927i	0.944922	−	0.327297i	$-0.106138\pi$
$548$		−	4.93701e7i		−	0.300001i
$549$	−2.69952e8	−	1.55857e8i	−1.63143	−	0.941909i
$550$	−5.15963e6	+	2.97891e6i	−0.0310120	+	0.0179048i
$551$	1.37732e7			0.0823343
$552$	−2.42184e6	−	4.19476e6i	−0.0143989	−	0.0249396i
$553$	3.14825e8	+	1.81764e8i	1.86163	+	1.07481i
$554$	458120.	−	793488.i	0.00269433	−	0.00466671i
$555$		−	9.64689e6i		−	0.0564298i
$556$	3.84787e7	−	6.66471e7i	0.223870	−	0.387755i
$557$	−1.88667e8			−1.09177			−0.545884	−	0.837861i	$-0.683806\pi$
$557$	−1.88667e8			−1.09177			−0.545884	+	0.837861i	$0.683806\pi$
$558$		−	6.13902e6i		−	0.0353343i
$559$	−9.40290e7	+	1.83649e8i	−0.538303	+	1.05136i
$560$	4.70878e7			0.268129
$561$		−	7.66939e8i		−	4.34383i
$562$	1.42895e6	+	825006.i	0.00805024	+	0.00464781i
$563$	1.75501e8			0.983453			0.491727	−	0.870750i	$-0.336366\pi$
$563$	1.75501e8			0.983453			0.491727	+	0.870750i	$0.336366\pi$
$564$	1.56245e8	+	9.02081e7i	0.870901	+	0.502815i
$565$	−2.01582e7	+	3.49151e7i	−0.111765	+	0.193583i
$566$	30429.5	−	17568.5i	0.000167821	−	9.68914e-5i
$567$		−	2.39501e8i		−	1.31389i
$568$	5.93626e6	+	1.02819e7i	0.0323942	+	0.0561084i
$569$	−1.11175e8	+	1.92561e8i	−0.603491	+	1.04528i	0.388797	+	0.921324i	$0.372891\pi$
$569$	−1.11175e8	+	1.92561e8i	−0.603491	+	1.04528i	−0.992288	+	0.123954i	$0.960442\pi$
$570$	135947.			0.000734081
$571$	−2.74905e8	−	1.58716e8i	−1.47664	−	0.852538i	−0.476986	−	0.878911i	$-0.658271\pi$
$571$	−2.74905e8	−	1.58716e8i	−1.47664	−	0.852538i	−0.999652	+	0.0263731i	$0.991604\pi$
$572$	1.83923e8	+	3.18564e8i	0.982762	+	1.70219i
$573$	5.34868e7	+	9.26418e7i	0.284304	+	0.492429i
$574$	−716017.	−	1.24018e6i	−0.00378606	−	0.00655765i
$575$	8.23978e7			0.433423
$576$	9.94702e7	+	1.72287e8i	0.520506	+	0.901542i
$577$	1.56632e8	−	9.04316e7i	0.815368	−	0.470753i	−0.0334486	−	0.999440i	$-0.510649\pi$
$577$	1.56632e8	−	9.04316e7i	0.815368	−	0.470753i	0.848817	+	0.528688i	$0.177316\pi$
$578$	−8.71227e6	−	5.03003e6i	−0.0451178	−	0.0260488i
$579$	2.09786e8	+	1.21120e8i	1.08079	+	0.623994i
$580$	−2.65760e7			−0.136209
$581$		−	1.19366e8i		−	0.608628i
$582$	−968652.	+	1.67775e6i	−0.00491359	+	0.00851059i
$583$	−2.13262e8	+	3.69381e8i	−1.07624	+	1.86410i
$584$	2.50046e6	+	4.33093e6i	0.0125540	+	0.0217442i
$585$	4.16879e7	−	2.40685e7i	0.208230	−	0.120222i
$586$		−	3.59689e6i		−	0.0178745i
$587$	2.96152e8	−	1.70983e8i	1.46420	−	0.845356i	0.464998	−	0.885312i	$-0.346055\pi$
$587$	2.96152e8	−	1.70983e8i	1.46420	−	0.845356i	0.999201	+	0.0399555i	$0.0127216\pi$
$588$	2.25718e8	−	1.30318e8i	1.11028	−	0.641023i
$589$	3.15483e7	−	1.82144e7i	0.154394	−	0.0891393i
$590$	298678.	−	517326.i	0.00145428	−	0.00251889i
$591$			2.51948e8i			1.22053i
$592$	−3.63205e7	−	2.09697e7i	−0.175060	−	0.101071i
$593$	−1.81185e8	+	1.04607e8i	−0.868878	+	0.501647i	−0.866975	−	0.498351i	$-0.833939\pi$
$593$	−1.81185e8	+	1.04607e8i	−0.868878	+	0.501647i	−0.00190255	+	0.999998i	$0.500606\pi$
$594$	492369.			0.00234926
$595$	5.16114e7	+	8.93937e7i	0.245016	+	0.424381i
$596$	−7.42990e7	−	4.28966e7i	−0.350949	−	0.202621i
$597$	−6.38416e6	+	1.10577e7i	−0.0300041	+	0.0519687i
$598$			2.54445e6i			0.0118984i
$599$	−5.78332e7	+	1.00170e8i	−0.269090	+	0.466077i	−0.968627	−	0.248519i	$-0.920056\pi$
$599$	−5.78332e7	+	1.00170e8i	−0.269090	+	0.466077i	0.699537	+	0.714596i	$0.253389\pi$
$600$	1.32814e7			0.0614878
$601$		−	3.11286e8i		−	1.43396i	−0.697096	−	0.716978i	$-0.745525\pi$
$601$		−	3.11286e8i		−	1.43396i	0.697096	−	0.716978i	$-0.254475\pi$
$602$	3.06196e6	−	5.98034e6i	0.0140349	−	0.0274117i
$603$	2.42476e8			1.10590
$604$		−	1.08669e8i		−	0.493166i
$605$	6.62488e7	+	3.82488e7i	0.299166	+	0.172723i
$606$	1.77990e6			0.00799792
$607$	−9.44916e7	−	5.45547e7i	−0.422500	−	0.243931i	0.273646	−	0.961830i	$-0.411770\pi$
$607$	−9.44916e7	−	5.45547e7i	−0.422500	−	0.243931i	−0.696147	+	0.717900i	$0.745104\pi$
$608$	887270.	−	1.53680e6i	0.00394771	−	0.00683763i
$609$	−2.69257e8	+	1.55456e8i	−1.19211	+	0.688263i
$610$		−	1.78507e6i		−	0.00786439i
$611$	−9.47985e7	−	1.64196e8i	−0.415602	−	0.719844i
$612$	−2.18271e8	+	3.78056e8i	−0.952229	+	1.64931i
$613$	3.23674e8			1.40516			0.702582	−	0.711603i	$-0.252030\pi$
$613$	3.23674e8			1.40516			0.702582	+	0.711603i	$0.252030\pi$
$614$	2.70901e6	+	1.56405e6i	0.0117032	+	0.00675686i
$615$	−7.97116e6	−	1.38065e7i	−0.0342686	−	0.0593549i
$616$	−1.19816e7	−	2.07527e7i	−0.0512591	−	0.0887834i
$617$	8.75310e7	+	1.51608e8i	0.372655	+	0.645457i	0.989973	−	0.141257i	$-0.0451143\pi$
$617$	8.75310e7	+	1.51608e8i	0.372655	+	0.645457i	−0.617318	+	0.786713i	$0.711781\pi$
$618$	1.45021e6			0.00614420
$619$	−9.01813e7	−	1.56199e8i	−0.380229	−	0.658575i	0.610866	−	0.791734i	$-0.290821\pi$
$619$	−9.01813e7	−	1.56199e8i	−0.380229	−	0.658575i	−0.991095	+	0.133159i	$0.957488\pi$
$620$	−6.08738e7	+	3.51455e7i	−0.255420	+	0.147467i
$621$	−5.89724e6	−	3.40478e6i	−0.0246249	−	0.0142172i
$622$	−1.08815e6	−	628246.i	−0.00452188	−	0.00261071i
$623$	−2.37184e8			−0.980893
$624$		−	4.09699e8i		−	1.68621i
$625$	−1.08327e8	+	1.87628e8i	−0.443708	+	0.768525i
$626$	−4.67879e6	+	8.10390e6i	−0.0190726	+	0.0330348i
$627$	3.45556e7	+	5.98521e7i	0.140190	+	0.242816i
$628$	7.99223e7	−	4.61432e7i	0.322693	−	0.186307i
$629$		−	9.19367e7i		−	0.369434i
$630$	−1.35753e6	+	783769.i	−0.00542909	+	0.00313448i
$631$	2.11957e8	−	1.22373e8i	0.843645	−	0.487078i	−0.0148567	−	0.999890i	$-0.504729\pi$
$631$	2.11957e8	−	1.22373e8i	0.843645	−	0.487078i	0.858501	+	0.512811i	$0.171396\pi$
$632$	−1.52530e7	+	8.80634e6i	−0.0604234	+	0.0348855i
$633$	−1.38027e8	+	2.39069e8i	−0.544192	+	0.942568i
$634$			3.39186e6i			0.0133097i
$635$	−2.24122e7	−	1.29397e7i	−0.0875312	−	0.0505362i
$636$	4.11615e8	−	2.37646e8i	1.60000	−	0.923760i
$637$	−2.73900e8			−1.05968
$638$	3.37862e6	+	5.85194e6i	0.0130100	+	0.0225340i
$639$	3.41923e8	+	1.97409e8i	1.31046	+	0.756597i
$640$	−2.28251e6	+	3.95343e6i	−0.00870709	+	0.0150811i
$641$			3.12690e8i			1.18724i	0.804744	+	0.593622i	$0.202303\pi$
$641$			3.12690e8i			1.18724i	−0.804744	+	0.593622i	$0.797697\pi$
$642$	−88345.3	+	153019.i	−0.000333871	+	0.000578281i
$643$	−3.46767e8			−1.30438			−0.652192	−	0.758054i	$-0.726150\pi$
$643$	−3.46767e8			−1.30438			−0.652192	+	0.758054i	$0.726150\pi$
$644$			1.65666e8i			0.620262i
$645$	3.40877e7	−	6.65770e7i	0.127034	−	0.248111i
$646$	1.29560e6			0.00480588
$647$		−	3.78698e8i		−	1.39824i	−0.715006	−	0.699118i	$-0.753576\pi$
$647$		−	3.78698e8i		−	1.39824i	0.715006	−	0.699118i	$-0.246424\pi$
$648$	1.00491e7	+	5.80183e6i	0.0369318	+	0.0213226i
$649$	3.03678e8			1.11091
$650$	−6.04213e6	−	3.48843e6i	−0.0220014	−	0.0127025i
$651$	−4.11165e8	+	7.12158e8i	−1.49030	+	2.58127i
$652$	3.31774e8	−	1.91550e8i	1.19701	−	0.691096i
$653$		−	1.05720e7i		−	0.0379678i	−0.999820	−	0.0189839i	$-0.993957\pi$
$653$		−	1.05720e7i		−	0.0379678i	0.999820	−	0.0189839i	$-0.00604313\pi$
$654$	−2.22312e6	−	3.85056e6i	−0.00794748	−	0.0137654i
$655$	−4.53240e7	+	7.85034e7i	−0.161289	+	0.279360i
$656$	−6.93083e7			−0.245513
$657$	1.44024e8	+	8.31525e7i	0.507855	+	0.293210i
$658$	3.08702e6	+	5.34688e6i	0.0108358	+	0.0187682i
$659$	1.63133e8	+	2.82554e8i	0.570013	+	0.987292i	0.996564	+	0.0828281i	$0.0263952\pi$
$659$	1.63133e8	+	2.82554e8i	0.570013	+	0.987292i	−0.426551	+	0.904464i	$0.640271\pi$
$660$	−6.66765e7	−	1.15487e8i	−0.231922	−	0.401700i
$661$	3.99012e8			1.38160			0.690799	−	0.723047i	$-0.257259\pi$
$661$	3.99012e8			1.38160			0.690799	+	0.723047i	$0.257259\pi$
$662$	1.05719e6	+	1.83111e6i	0.00364401	+	0.00631160i
$663$	7.77792e8	−	4.49059e8i	2.66884	−	1.54086i
$664$	5.00839e6	+	2.89160e6i	0.0171078	+	0.00987720i
$665$	−8.05553e6	−	4.65086e6i	−0.0273923	−	0.0158150i
$666$	1.39615e6			0.00472616
$667$		−	9.34538e7i		−	0.314934i
$668$	−2.40391e8	+	4.16369e8i	−0.806470	+	1.39685i
$669$	−1.02223e8	+	1.77055e8i	−0.341405	+	0.591330i
$670$	694286.	+	1.20254e6i	0.00230842	+	0.00399829i
$671$	7.85897e8	−	4.53738e8i	2.60134	−	1.50189i
$672$			4.00578e7i			0.132002i
$673$	−2.68937e8	+	1.55271e8i	−0.882277	+	0.509383i	−0.871409	−	0.490558i	$-0.836793\pi$
$673$	−2.68937e8	+	1.55271e8i	−0.882277	+	0.509383i	−0.0108687	+	0.999941i	$0.503460\pi$
$674$	−1.12726e7	+	6.50823e6i	−0.0368166	+	0.0212561i
$675$	1.61702e7	−	9.33587e6i	0.0525780	−	0.0303559i
$676$	−6.10009e7	+	1.05657e8i	−0.197468	+	0.342024i
$677$		−	1.08383e8i		−	0.349298i	−0.984631	−	0.174649i	$-0.944121\pi$
$677$		−	1.08383e8i		−	0.349298i	0.984631	−	0.174649i	$-0.0558790\pi$
$678$	−9.89254e6	−	5.71146e6i	−0.0317409	−	0.0183256i
$679$	1.14795e8	−	6.62770e7i	0.366703	−	0.211716i
$680$	−5.00107e6			−0.0159051
$681$	−2.39176e8	−	4.14265e8i	−0.757314	−	1.31171i
$682$	1.54778e7	+	8.93611e6i	0.0487928	+	0.0281705i
$683$	8.65457e7	−	1.49901e8i	0.271633	−	0.470483i	−0.697647	−	0.716442i	$-0.745770\pi$
$683$	8.65457e7	−	1.49901e8i	0.271633	−	0.470483i	0.969280	+	0.245959i	$0.0791029\pi$
$684$		−	3.93381e7i		−	0.122926i
$685$	9.40430e6	−	1.62887e7i	0.0292587	−	0.0506775i
$686$	−1.02251e6			−0.00316733
$687$			6.41779e8i			1.97932i
$688$	−1.76565e8	−	2.73060e8i	−0.542175	−	0.838481i
$689$	−4.99478e8			−1.52707
$690$		−	922423.i		−	0.00280791i
$691$	−1.62571e8	−	9.38605e7i	−0.492730	−	0.284478i	0.232976	−	0.972482i	$-0.425154\pi$
$691$	−1.62571e8	−	9.38605e7i	−0.492730	−	0.284478i	−0.725706	+	0.688004i	$0.758487\pi$
$692$	3.72527e8			1.12419
$693$	−6.90126e8	−	3.98445e8i	−2.07362	−	1.19720i
$694$	1.65481e6	−	2.86621e6i	0.00495072	−	0.00857491i
$695$	2.53906e7	−	1.46593e7i	0.0756344	−	0.0436675i
$696$		−	1.50634e7i		−	0.0446782i
$697$	−7.59667e7	−	1.31578e8i	−0.224349	−	0.388584i
$698$	2.54890e6	−	4.41482e6i	0.00749524	−	0.0129821i
$699$	−1.84442e8			−0.540042
$700$	−3.93395e8	−	2.27127e8i	−1.14693	−	0.662178i
$701$	−4.44376e7	−	7.69683e7i	−0.129002	−	0.223438i	0.794288	−	0.607541i	$-0.207844\pi$
$701$	−4.44376e7	−	7.69683e7i	−0.129002	−	0.223438i	−0.923290	+	0.384103i	$0.874511\pi$
$702$	288292.	+	499336.i	0.000833338	+	0.00144338i
$703$	4.14235e6	+	7.17475e6i	0.0119229	+	0.0206510i
$704$	−5.79164e8			−1.65991
$705$	3.43667e7	+	5.95249e7i	0.0980778	+	0.169876i
$706$	717275.	−	414119.i	0.00203832	−	0.00117682i
$707$	−1.05468e8	−	6.08919e7i	−0.298443	−	0.172306i
$708$	−2.93063e8	−	1.69200e8i	−0.825773	−	0.476760i
$709$	−3.81272e8			−1.06978			−0.534892	−	0.844920i	$-0.679648\pi$
$709$	−3.81272e8			−1.06978			−0.534892	+	0.844920i	$0.679648\pi$
$710$			2.26098e6i			0.00631715i
$711$	−2.92853e8	+	5.07237e8i	−0.814782	+	1.41124i
$712$	5.74570e6	−	9.95185e6i	0.0159185	−	0.0275717i
$713$	−1.23588e8	−	2.14061e8i	−0.340963	−	0.590566i
$714$	−2.53280e7	+	1.46232e7i	−0.0695836	+	0.0401741i
$715$			1.40139e8i			0.383390i
$716$	−4.33691e8	+	2.50392e8i	−1.18152	+	0.682152i
$717$	5.73779e8	−	3.31271e8i	1.55664	−	0.898724i
$718$	8.73960e6	−	5.04581e6i	0.0236112	−	0.0136319i
$719$	1.30441e8	−	2.25930e8i	0.350935	−	0.607837i	−0.635479	−	0.772119i	$-0.719197\pi$
$719$	1.30441e8	−	2.25930e8i	0.350935	−	0.607837i	0.986414	+	0.164281i	$0.0525305\pi$
$720$			7.58665e7i			0.203260i
$721$	−8.59322e7	−	4.96130e7i	−0.229272	−	0.132370i
$722$	7.18647e6	−	4.14911e6i	0.0190943	−	0.0110241i
$723$	6.47633e8			1.71362
$724$	1.21703e8	+	2.10796e8i	0.320691	+	0.555453i
$725$	2.21919e8	+	1.28125e8i	0.582344	+	0.336217i
$726$	−1.08371e7	+	1.87704e7i	−0.0283206	+	0.0490527i
$727$			1.75516e8i			0.456786i	0.973569	+	0.228393i	$0.0733471\pi$
$727$			1.75516e8i			0.456786i	−0.973569	+	0.228393i	$0.926653\pi$
$728$	1.40309e7	−	2.43022e7i	0.0363656	−	0.0629871i
$729$	4.20835e8			1.08625
$730$			952367.i			0.00244814i
$731$	3.24863e8	−	6.34492e8i	0.831664	−	1.62433i
$732$	−1.01123e9			−2.57821
$733$			5.40322e8i			1.37196i	0.727622	+	0.685979i	$0.240626\pi$
$733$			5.40322e8i			1.37196i	−0.727622	+	0.685979i	$0.759374\pi$
$734$	−7.36450e6	−	4.25189e6i	−0.0186232	−	0.0107521i
$735$	9.92951e7			0.250072
$736$	−1.04274e7	−	6.02029e6i	−0.0261544	−	0.0151002i
$737$	−3.52954e8	+	6.11335e8i	−0.881690	+	1.52713i
$738$	1.99814e6	−	1.15363e6i	0.00497115	−	0.00287009i
$739$		−	1.77611e8i		−	0.440084i	−0.975490	−	0.220042i	$-0.929381\pi$
$739$		−	1.77611e8i		−	0.440084i	0.975490	−	0.220042i	$-0.0706194\pi$
$740$	−7.99283e6	−	1.38440e7i	−0.0197245	−	0.0341638i
$741$	−4.04660e7	+	7.00892e7i	−0.0994571	+	0.172265i
$742$	1.62650e7			0.0398146
$743$	−4.17295e8	−	2.40925e8i	−1.01736	−	0.587376i	−0.104025	−	0.994575i	$-0.533172\pi$
$743$	−4.17295e8	−	2.40925e8i	−1.01736	−	0.587376i	−0.913339	+	0.407199i	$0.866506\pi$
$744$	−1.99206e7	−	3.45035e7i	−0.0483709	−	0.0837809i
$745$	−1.63424e7	−	2.83058e7i	−0.0395226	−	0.0684552i
$746$	−1.53727e6	−	2.66262e6i	−0.00370282	−	0.00641347i
$747$	1.92319e8			0.461382
$748$	−6.35440e8	−	1.10061e9i	−1.51834	−	2.62985i
$749$	1.04698e7	−	6.04475e6i	0.0249169	−	0.0143858i
$750$	4.46738e6	+	2.57924e6i	0.0105893	+	0.00611376i
$751$	5.92547e8	+	3.42107e8i	1.39895	+	0.807686i	0.994283	−	0.106777i	$-0.0340532\pi$
$751$	5.92547e8	+	3.42107e8i	1.39895	+	0.807686i	0.404670	+	0.914463i	$0.367387\pi$
$752$	2.98815e8			0.702665
$753$			4.89091e7i			0.114552i
$754$	−3.95650e6	+	6.85286e6i	−0.00922990	+	0.0159867i
$755$	2.06998e7	−	3.58531e7i	0.0480978	−	0.0833078i
$756$	1.87703e7	+	3.25111e7i	0.0434416	+	0.0752431i
$757$	−1.57267e8	+	9.07982e7i	−0.362535	+	0.209310i	−0.670192	−	0.742188i	$-0.733788\pi$
$757$	−1.57267e8	+	9.07982e7i	−0.362535	+	0.209310i	0.307657	+	0.951497i	$0.400455\pi$
$758$			3.40663e6i			0.00782198i
$759$	4.06107e8	−	2.34466e8i	0.928785	−	0.536234i
$760$	390284.	−	225331.i	0.000889079	−	0.000513310i
$761$	5.78880e8	−	3.34216e8i	1.31351	−	0.758357i	0.330837	−	0.943688i	$-0.392669\pi$
$761$	5.78880e8	−	3.34216e8i	1.31351	−	0.758357i	0.982676	+	0.185331i	$0.0593356\pi$
$762$	3.66622e6	−	6.35008e6i	0.00828616	−	0.0143521i
$763$			3.04220e8i			0.684879i
$764$	1.53515e8	+	8.86319e7i	0.344247	+	0.198751i
$765$	−1.44029e8	+	8.31549e7i	−0.321710	+	0.185739i
$766$	−1.38545e6			−0.00308251
$767$	1.77810e8	+	3.07976e8i	0.394067	+	0.682543i
$768$	5.58078e8	+	3.22207e8i	1.23200	+	0.711296i
$769$	2.67208e8	−	4.62817e8i	0.587584	−	1.01772i	−0.406964	−	0.913444i	$-0.633413\pi$
$769$	2.67208e8	−	4.62817e8i	0.587584	−	1.01772i	0.994548	−	0.104281i	$-0.0332541\pi$
$770$		−	4.56349e6i		−	0.00999596i
$771$	−4.13847e8	+	7.16805e8i	−0.902978	+	1.56400i
$772$	4.01412e8			0.872445
$773$		−	3.09212e7i		−	0.0669450i	−0.999440	−	0.0334725i	$-0.989343\pi$
$773$		−	3.09212e7i		−	0.0669450i	0.999440	−	0.0334725i	$-0.0106566\pi$
$774$	9.63536e6	+	4.93335e6i	0.0207800	+	0.0106394i
$775$	6.77755e8			1.45602
$776$			6.42214e6i			0.0137434i
$777$	−1.61960e8	−	9.35077e7i	−0.345259	−	0.199335i
$778$	8.16902e6			0.0173473
$779$	1.18569e7	+	6.84558e6i	0.0250818	+	0.0144810i
$780$	7.80809e7	−	1.35240e8i	0.164536	−	0.284985i
$781$	−9.95421e8	+	5.74707e8i	−2.08955	+	1.20641i
$782$		−	8.79086e6i		−	0.0183828i
$783$	−1.05885e7	−	1.83399e7i	−0.0220572	−	0.0382042i
$784$	2.15840e8	−	3.73846e8i	0.447903	−	0.775790i
$785$	3.51585e7			0.0726810
$786$	−2.22425e7	−	1.28417e7i	−0.0458053	−	0.0264457i
$787$	−3.80595e7	−	6.59209e7i	−0.0780797	−	0.135238i	0.824342	−	0.566093i	$-0.191546\pi$
$787$	−3.80595e7	−	6.59209e7i	−0.0780797	−	0.135238i	−0.902421	+	0.430855i	$0.858212\pi$
$788$	2.08749e8	+	3.61564e8i	0.426625	+	0.738936i
$789$	−5.31305e8	−	9.20247e8i	−1.08172	−	1.87359i
$790$	−3.35413e6			−0.00680296
$791$	3.90789e8	+	6.76866e8i	0.789610	+	1.36765i
$792$	3.34361e7	−	1.93043e7i	0.0673039	−	0.0388579i
$793$	9.20317e8	+	5.31345e8i	1.84552	+	1.06551i
$794$	−1.50891e6	−	871167.i	−0.00301440	−	0.00174036i
$795$	1.81073e8			0.360372
$796$			2.11581e7i			0.0419506i
$797$	1.39082e8	−	2.40898e8i	0.274724	−	0.475836i	−0.695341	−	0.718680i	$-0.744747\pi$
$797$	1.39082e8	−	2.40898e8i	0.274724	−	0.475836i	0.970065	+	0.242843i	$0.0780801\pi$
$798$	1.31774e6	−	2.28239e6i	0.00259310	−	0.00449139i
$799$	3.27521e8	+	5.67284e8i	0.642095	+	1.11214i
$800$	2.85920e7	−	1.65076e7i	0.0558437	−	0.0322414i
$801$		−	3.82145e8i		−	0.743584i
$802$	1.48033e7	−	8.54667e6i	0.0286969	−	0.0165681i
$803$	−4.19290e8	+	2.42077e8i	−0.809782	+	0.467528i
$804$	6.81232e8	−	3.93310e8i	1.31077	−	0.756775i
$805$	−3.15569e7	+	5.46582e7i	−0.0604933	+	0.104777i
$806$			2.09291e7i			0.0399710i
$807$	−3.40624e8	−	1.96660e8i	−0.648120	−	0.374192i
$808$	5.10984e6	−	2.95017e6i	0.00968665	−	0.00559259i
$809$	−7.25972e8			−1.37112			−0.685559	−	0.728017i	$-0.740442\pi$
$809$	−7.25972e8			−1.37112			−0.685559	+	0.728017i	$0.740442\pi$
$810$	1.10489e6	+	1.91372e6i	0.00207904	+	0.00360101i
$811$	−2.62913e8	−	1.51793e8i	−0.492889	−	0.284570i	0.232883	−	0.972505i	$-0.425184\pi$
$811$	−2.62913e8	−	1.51793e8i	−0.492889	−	0.284570i	−0.725772	+	0.687935i	$0.758517\pi$
$812$	−2.57603e8	+	4.46181e8i	−0.481152	+	0.833379i
$813$		−	1.05385e9i		−	1.96114i
$814$	−2.03226e6	+	3.51998e6i	−0.00376796	+	0.00652630i
$815$	1.45950e8			0.269607
$816$			1.41548e9i			2.60515i
$817$	3.23564e6	+	6.41530e7i	0.00593327	+	0.117639i
$818$	−8.09939e6			−0.0147976
$819$		−	9.33189e8i		−	1.69871i
$820$	−2.28784e7	−	1.32089e7i	−0.0414939	−	0.0239565i
$821$	−8.11944e8			−1.46723			−0.733613	−	0.679568i	$-0.762167\pi$
$821$	−8.11944e8			−1.46723			−0.733613	+	0.679568i	$0.762167\pi$
$822$	4.61511e6	+	2.66453e6i	0.00830934	+	0.00479740i
$823$	8.73264e6	−	1.51254e7i	0.0156656	−	0.0271336i	−0.858086	−	0.513505i	$-0.828347\pi$
$823$	8.73264e6	−	1.51254e7i	0.0156656	−	0.0271336i	0.873752	+	0.486372i	$0.161680\pi$
$824$	4.16335e6	−	2.40371e6i	0.00744152	−	0.00429636i
$825$			1.28581e9i			2.28989i
$826$	−5.79020e6	−	1.00289e7i	−0.0102743	−	0.0177957i
$827$	5.33259e7	−	9.23631e7i	0.0942804	−	0.163298i	−0.815028	−	0.579422i	$-0.803278\pi$
$827$	5.33259e7	−	9.23631e7i	0.0942804	−	0.163298i	0.909308	+	0.416124i	$0.136612\pi$
$828$	−2.66916e8			−0.470201
$829$	−3.27318e8	−	1.88977e8i	−0.574521	−	0.331700i	0.184432	−	0.982845i	$-0.440955\pi$
$829$	−3.27318e8	−	1.88977e8i	−0.574521	−	0.331700i	−0.758953	+	0.651146i	$0.774289\pi$
$830$	550670.	+	953789.i	0.000963069	+	0.00166808i
$831$	−9.88708e7	−	1.71249e8i	−0.172292	−	0.298418i
$832$	−3.39112e8	−	5.87360e8i	−0.588808	−	1.01985i
$833$	9.46302e8			1.63717
$834$	4.15344e6	+	7.19397e6i	0.00715995	+	0.0124014i
$835$	−1.58625e8	+	9.15820e7i	−0.272465	+	0.157308i
$836$	9.91797e7	+	5.72614e7i	0.169748	+	0.0980039i
$837$	−4.85072e7	−	2.80056e7i	−0.0827236	−	0.0477605i
$838$	1.54396e7			0.0262364
$839$			1.15384e9i			1.95370i	0.213925	+	0.976850i	$0.431375\pi$
$839$			1.15384e9i			1.95370i	−0.213925	+	0.976850i	$0.568625\pi$
$840$	−5.08653e6	+	8.81013e6i	−0.00858191	+	0.0148643i
$841$	−1.52095e8	+	2.63437e8i	−0.255698	+	0.442882i
$842$	1.17724e7	+	2.03904e7i	0.0197210	+	0.0341578i
$843$	3.08394e8	−	1.78052e8i	0.514782	−	0.297210i
$844$			4.57443e8i			0.760868i
$845$	−4.02522e7	+	2.32396e7i	−0.0667143	+	0.0385175i
$846$	−8.61474e6	+	4.97372e6i	−0.0142276	+	0.00821429i
$847$	1.28430e9	−	7.41494e8i	2.11358	−	1.22027i
$848$	3.93601e8	−	6.81737e8i	0.645459	−	1.11797i
$849$		−	7.58321e6i		−	0.0123917i
$850$	2.08751e7	+	1.20522e7i	0.0339916	+	0.0196251i
$851$	4.86820e7	−	2.81066e7i	0.0789914	−	0.0456057i
$852$	1.28083e9			2.07097
$853$	1.57995e8	+	2.73656e8i	0.254564	+	0.440917i	0.964777	−	0.263069i	$-0.0847348\pi$
$853$	1.57995e8	+	2.73656e8i	0.254564	+	0.440917i	−0.710213	+	0.703987i	$0.751401\pi$
$854$	−2.99692e7	−	1.73027e7i	−0.0481174	−	0.0277806i
$855$	7.49334e6	−	1.29788e7i	0.0119888	−	0.0207653i
$856$			585727.i			0.000933844i
$857$	2.84632e8	−	4.92996e8i	0.452210	−	0.783252i	−0.546313	−	0.837581i	$-0.683969\pi$
$857$	2.84632e8	−	4.92996e8i	0.452210	−	0.783252i	0.998523	+	0.0543298i	$0.0173022\pi$
$858$	−3.97058e7			−0.0628626
$859$		−	3.65472e8i		−	0.576600i	−0.957540	−	0.288300i	$-0.906910\pi$
$859$		−	3.65472e8i		−	0.576600i	0.957540	−	0.288300i	$-0.0930901\pi$
$860$	−6.24331e6	−	1.23786e8i	−0.00981567	−	0.194615i
$861$	−3.09059e8			−0.484208
$862$		−	2.42745e7i		−	0.0378991i
$863$	−3.63122e8	−	2.09648e8i	−0.564963	−	0.326181i	0.190172	−	0.981751i	$-0.439095\pi$
$863$	−3.63122e8	−	2.09648e8i	−0.564963	−	0.326181i	−0.755135	+	0.655569i	$0.772429\pi$
$864$	−2.72845e6			−0.00423034
$865$	1.22908e8	+	7.09611e7i	0.189903	+	0.109641i
$866$	6.25419e6	−	1.08326e7i	0.00962981	−	0.0166793i
$867$	−1.88027e9	+	1.08557e9i	−2.88511	+	1.66572i
$868$			1.36267e9i			2.08368i
$869$	−8.52569e8	−	1.47669e9i	−1.29918	−	2.25025i
$870$	1.43432e6	−	2.48432e6i	0.00217816	−	0.00377268i
$871$	−8.26648e8			−1.25103
$872$	−1.27646e7	−	7.36962e6i	−0.0192511	−	0.0111146i
$873$	1.06784e8	+	1.84955e8i	0.160495	+	0.277986i
$874$	396085.	+	686040.i	0.000593273	+	0.00102758i
$875$	−1.76477e8	−	3.05666e8i	−0.263429	−	0.456272i
$876$	5.39511e8			0.802579
$877$	3.72573e8	+	6.45316e8i	0.552348	+	0.956695i	0.998105	+	0.0615407i	$0.0196014\pi$
$877$	3.72573e8	+	6.45316e8i	0.552348	+	0.956695i	−0.445756	+	0.895154i	$0.647065\pi$
$878$	−6.44676e6	+	3.72204e6i	−0.00952485	+	0.00549918i
$879$	−6.72273e8	−	3.88137e8i	−0.989873	−	0.571503i
$880$	−1.91276e8	−	1.10433e8i	−0.280680	−	0.162051i
$881$	5.56783e8			0.814251			0.407125	−	0.913372i	$-0.366531\pi$
$881$	5.56783e8			0.814251			0.407125	+	0.913372i	$0.366531\pi$
$882$			1.43705e7i			0.0209443i
$883$	−3.25559e8	+	5.63885e8i	−0.472876	+	0.819046i	−0.999518	−	0.0310413i	$-0.990118\pi$
$883$	−3.25559e8	+	5.63885e8i	−0.472876	+	0.819046i	0.526642	+	0.850087i	$0.323451\pi$
$884$	7.44126e8	−	1.28886e9i	1.07718	−	1.86574i
$885$	−6.44603e7	−	1.11648e8i	−0.0929956	−	0.161073i
$886$	6.87866e6	−	3.97140e6i	0.00989015	−	0.00571008i
$887$		−	1.20707e9i		−	1.72966i	−0.502067	−	0.864829i	$-0.667427\pi$
$887$		−	1.20707e9i		−	1.72966i	0.502067	−	0.864829i	$-0.332573\pi$
$888$	7.84684e6	−	4.53038e6i	0.0112061	−	0.00646987i
$889$	−4.34484e8	+	2.50850e8i	−0.618399	+	0.357033i
$890$	1.89521e6	−	1.09420e6i	0.00268836	−	0.00155213i
$891$	−5.61692e8	+	9.72879e8i	−0.794082	+	1.37539i
$892$			3.38783e8i			0.477339i
$893$	−5.11196e7	−	2.95139e7i	−0.0717849	−	0.0414450i
$894$	8.01993e6	−	4.63031e6i	0.0112243	−	0.00648033i
$895$	−1.90784e8			−0.266117
$896$	4.42489e7	+	7.66414e7i	0.0615147	+	0.106547i
$897$	4.75568e8	+	2.74569e8i	0.658924	+	0.380430i
$898$	8.81672e6	−	1.52710e7i	0.0121753	−	0.0210882i
$899$		−	7.68695e8i		−	1.05797i
$900$	3.65941e8	−	6.33828e8i	0.501976	−	0.869448i
$901$	1.72566e9			2.35928
$902$			6.71698e6i			0.00915281i
$903$	−7.87337e8	−	1.21763e9i	−1.06929	−	1.65368i
$904$	−3.78669e7			−0.0512571
$905$			9.27310e7i			0.125106i
$906$	1.01583e7	+	5.86490e6i	0.0136596	+	0.00788636i
$907$	−1.18134e9			−1.58327			−0.791634	−	0.610996i	$-0.790769\pi$
$907$	−1.18134e9			−1.58327			−0.791634	+	0.610996i	$0.790769\pi$
$908$	−6.86470e8	−	3.96334e8i	−0.916989	−	0.529424i
$909$	9.81074e7	−	1.69927e8i	0.130620	−	0.226241i
$910$	4.62807e6	−	2.67201e6i	0.00614151	−	0.00354580i
$911$		−	8.97560e8i		−	1.18716i	−0.804776	−	0.593579i	$-0.797715\pi$
$911$		−	8.97560e8i		−	1.18716i	0.804776	−	0.593579i	$-0.202285\pi$
$912$	−6.37765e7	−	1.10464e8i	−0.0840768	−	0.145625i
$913$	−2.79944e8	+	4.84878e8i	−0.367840	+	0.637118i
$914$	−1.96681e7			−0.0257587
$915$	−3.33637e8	−	1.92625e8i	−0.435522	−	0.251449i
$916$	5.31740e8	+	9.21000e8i	0.691851	+	1.19832i
$917$	8.78654e8	+	1.52187e9i	1.13949	+	1.97365i
$918$	−996026.	−	1.72517e6i	−0.00128749	−	0.00222999i
$919$	−2.55225e8			−0.328834			−0.164417	−	0.986391i	$-0.552574\pi$
$919$	−2.55225e8			−0.328834			−0.164417	+	0.986391i	$0.552574\pi$
$920$	−1.52891e6	−	2.64815e6i	−0.00196344	−	0.00340079i
$921$	5.84654e8	−	3.37550e8i	0.748376	−	0.432075i
$922$	−5.85656e6	−	3.38129e6i	−0.00747222	−	0.00431409i
$923$	−1.16568e9	−	6.73005e8i	−1.48243	−	0.855880i
$924$	−2.58519e9			−3.27700
$925$			1.54136e8i			0.194751i
$926$	1.60213e7	−	2.77497e7i	0.0201774	−	0.0349483i
$927$	7.99350e7	−	1.38452e8i	0.100346	−	0.173804i
$928$	−1.87225e7	−	3.24284e7i	−0.0234272	−	0.0405771i
$929$	5.63252e8	−	3.25194e8i	0.702515	−	0.405597i	−0.105769	−	0.994391i	$-0.533730\pi$
$929$	5.63252e8	−	3.25194e8i	0.702515	−	0.405597i	0.808283	+	0.588794i	$0.200397\pi$
$930$		−	7.58729e6i		−	0.00943274i
$931$	−7.38495e7	+	4.26370e7i	−0.0915163	+	0.0528370i
$932$	−2.64687e8	+	1.52817e8i	−0.326953	+	0.188766i
$933$	−2.34844e8	+	1.35587e8i	−0.289157	+	0.166945i
$934$	−1.03924e7	+	1.80001e7i	−0.0127548	+	0.0220920i
$935$		−	4.84169e8i		−	0.592328i
$936$	3.91550e7	+	2.26062e7i	0.0477485	+	0.0275676i
$937$	2.53481e8	−	1.46347e8i	0.308124	−	0.177896i	−0.337962	−	0.941160i	$-0.609738\pi$
$937$	2.53481e8	−	1.46347e8i	0.308124	−	0.177896i	0.646087	+	0.763264i	$0.276404\pi$
$938$	2.69190e7			0.0326175
$939$	1.00977e9	+	1.74897e9i	1.21962	+	2.11245i
$940$	9.86375e7	+	5.69484e7i	0.118757	+	0.0685643i
$941$	−5.19857e8	+	9.00419e8i	−0.623900	+	1.08063i	0.364852	+	0.931065i	$0.381119\pi$
$941$	−5.19857e8	+	9.00419e8i	−0.623900	+	1.08063i	−0.988752	+	0.149561i	$0.952214\pi$
$942$			9.96150e6i			0.0119171i
$943$	4.64485e7	−	8.04512e7i	0.0553907	−	0.0959395i
$944$	−5.60475e8			−0.666254
$945$			1.43019e7i			0.0169472i
$946$	−2.64635e7	+	1.71117e7i	−0.0312589	+	0.0202125i
$947$	−1.51784e6			−0.00178722			−0.000893609	−	1.00000i	$-0.500284\pi$
$947$	−1.51784e6			−0.00178722			−0.000893609		1.00000i	$0.500284\pi$
$948$			1.90010e9i			2.23023i
$949$	−4.91006e8	−	2.83482e8i	−0.574497	−	0.331686i
$950$	−2.17213e6			−0.00253346
$951$	6.33952e8	+	3.66013e8i	0.737081	+	0.425554i
$952$	−4.84756e7	+	8.39622e7i	−0.0561840	+	0.0973135i
$953$	7.29093e8	−	4.20942e8i	0.842372	−	0.486344i	−0.0156977	−	0.999877i	$-0.504997\pi$
$953$	7.29093e8	−	4.20942e8i	0.842372	−	0.486344i	0.858070	+	0.513533i	$0.171664\pi$
$954$			2.62057e7i			0.0301822i
$955$	3.37662e7	+	5.84848e7i	0.0387679	+	0.0671480i
$956$	5.48943e8	−	9.50798e8i	0.628281	−	1.08821i
$957$	1.45834e9			1.66388
$958$	−1.37622e7	−	7.94559e6i	−0.0156527	−	0.00903711i
$959$	−1.82312e8	−	3.15774e8i	−0.206710	−	0.358031i
$960$	1.22936e8	+	2.12932e8i	0.138953	+	0.240673i
$961$	−5.72809e8	−	9.92134e8i	−0.645416	−	1.11789i
$962$	−4.75972e6			−0.00534634
$963$	9.73913e6	+	1.68687e7i	0.0109054	+	0.0188887i
$964$	9.29401e8	−	5.36590e8i	1.03746	−	0.598979i
$965$	1.32438e8	+	7.64631e7i	0.147377	+	0.0850884i
$966$	−1.54864e7	−	8.94108e6i	−0.0171798	−	0.00991878i
$967$	−7.06842e8			−0.781705			−0.390852	−	0.920453i	$-0.627820\pi$
$967$	−7.06842e8			−0.781705			−0.390852	+	0.920453i	$0.627820\pi$
$968$			7.18497e7i			0.0792134i
$969$	1.39807e8	−	2.42153e8i	0.153659	−	0.266145i
$970$	−611510.	+	1.05917e6i	−0.000670021	+	0.00116051i
$971$	−4.61386e8	−	7.99144e8i	−0.503972	−	0.872906i	−0.999989	−	0.00459301i	$-0.998538\pi$
$971$	−4.61386e8	−	7.99144e8i	−0.503972	−	0.872906i	0.496017	−	0.868313i	$-0.334795\pi$
$972$	1.13428e9	−	6.54878e8i	1.23516	−	0.713118i
$973$		−	5.68372e8i		−	0.617013i
$974$	−999335.	+	576966.i	−0.00108152	+	0.000624415i
$975$	−1.30400e9	+	7.52867e8i	−1.40691	+	0.812277i
$976$	−1.45047e9	+	8.37427e8i	−1.56012	+	0.900736i
$977$	−3.54600e8	+	6.14185e8i	−0.380238	+	0.658591i	−0.991096	−	0.133149i	$-0.957491\pi$
$977$	−3.54600e8	+	6.14185e8i	−0.380238	+	0.658591i	0.610858	+	0.791740i	$0.290824\pi$
$978$			4.13522e7i			0.0442061i
$979$	9.63468e8	+	5.56259e8i	1.02681	+	0.592828i
$980$	1.42496e8	−	8.22700e7i	0.151399	−	0.0874104i
$981$	−4.90151e8			−0.519185
$982$	−7.53915e6	−	1.30582e7i	−0.00796138	−	0.0137895i
$983$	9.41132e7	+	5.43363e7i	0.0990809	+	0.0572044i	0.548722	−	0.836005i	$-0.315115\pi$
$983$	9.41132e7	+	5.43363e7i	0.0990809	+	0.0572044i	−0.449641	+	0.893209i	$0.648448\pi$
$984$	7.48684e6	−	1.29676e7i	0.00785802	−	0.0136105i
$985$			1.59055e8i			0.166433i
$986$	1.36694e7	−	2.36761e7i	0.0142600	−	0.0246990i
$987$	1.33247e9			1.38582
$988$			1.34111e8i			0.139057i
$989$	4.35290e8	−	2.19544e7i	0.449976	−	0.0226952i
$990$	7.35256e6			0.00757763
$991$		−	1.11198e9i		−	1.14255i	−0.820760	−	0.571274i	$-0.806449\pi$
$991$		−	1.11198e9i		−	1.14255i	0.820760	−	0.571274i	$-0.193551\pi$
$992$	−8.57699e7	−	4.95193e7i	−0.0878617	−	0.0507270i
$993$	4.56322e8			0.466041
$994$	3.79592e7	+	2.19157e7i	0.0386507	+	0.0223150i
$995$	−4.03032e6	+	6.98072e6i	−0.00409139	+	0.00708649i
$996$	5.40317e8	−	3.11952e8i	0.546853	−	0.315726i
$997$		−	1.18500e9i		−	1.19573i	−0.801597	−	0.597865i	$-0.796016\pi$
$997$		−	1.18500e9i		−	1.19573i	0.801597	−	0.597865i	$-0.203984\pi$
$998$	1.09133e7	+	1.89024e7i	0.0109791	+	0.0190163i
$999$	6.36908e6	−	1.10316e7i	0.00638823	−	0.0110647i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.7.d.a.37.12	yes	42
43.7	odd	6	inner	43.7.d.a.7.10	✓	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.7.d.a.7.10	✓	42	43.7	odd	6	inner
43.7.d.a.37.12	yes	42	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	43.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+0.178867i q^{2} +(33.4310 + 19.3014i) q^{3} +63.9680 q^{4} +(21.1050 + 12.1850i) q^{5} +(-3.45239 + 5.97972i) q^{6} +(409.144 - 236.219i) q^{7} +22.8893i q^{8} +(380.590 + 659.200i) q^{9} +O(q^{10})\)	\(q+0.178867i q^{2} +(33.4310 + 19.3014i) q^{3} +63.9680 q^{4} +(21.1050 + 12.1850i) q^{5} +(-3.45239 + 5.97972i) q^{6} +(409.144 - 236.219i) q^{7} +22.8893i q^{8} +(380.590 + 659.200i) q^{9} +(-2.17950 + 3.77500i) q^{10} -2215.98 q^{11} +(2138.52 + 1234.67i) q^{12} +(-1297.50 - 2247.34i) q^{13} +(42.2519 + 73.1824i) q^{14} +(470.375 + 814.714i) q^{15} +4089.86 q^{16} +(4482.76 + 7764.38i) q^{17} +(-117.909 + 68.0750i) q^{18} +(-699.671 - 403.955i) q^{19} +(1350.05 + 779.449i) q^{20} +18237.5 q^{21} -396.366i q^{22} +(-2740.91 + 4747.39i) q^{23} +(-441.796 + 765.213i) q^{24} +(-7515.55 - 13017.3i) q^{25} +(401.975 - 232.081i) q^{26} +1242.21i q^{27} +(26172.1 - 15110.5i) q^{28} +(-14764.0 + 8523.98i) q^{29} +(-145.726 + 84.1347i) q^{30} +(-22545.1 + 39049.2i) q^{31} +2196.46i q^{32} +(-74082.5 - 42771.6i) q^{33} +(-1388.79 + 801.820i) q^{34} +11513.3 q^{35} +(24345.6 + 42167.7i) q^{36} +(-8880.63 - 5127.23i) q^{37} +(72.2544 - 125.148i) q^{38} -100174. i q^{39} +(-278.906 + 483.079i) q^{40} -16946.4 q^{41} +3262.08i q^{42} +(-43171.4 - 66765.2i) q^{43} -141752. q^{44} +18549.9i q^{45} +(-849.154 - 490.259i) q^{46} +73062.3 q^{47} +(136728. + 78940.1i) q^{48} +(52774.4 - 91408.0i) q^{49} +(2328.37 - 1344.29i) q^{50} +346095. i q^{51} +(-82998.6 - 143758. i) q^{52} +(96238.4 - 166690. i) q^{53} -222.190 q^{54} +(-46768.3 - 27001.7i) q^{55} +(5406.89 + 9365.00i) q^{56} +(-15593.8 - 27009.3i) q^{57} +(-1524.66 - 2640.79i) q^{58} -137040. q^{59} +(30089.0 + 52115.6i) q^{60} +(-354650. + 204757. i) q^{61} +(-6984.63 - 4032.58i) q^{62} +(311432. + 179805. i) q^{63} +261358. q^{64} -63240.2i q^{65} +(7650.43 - 13250.9i) q^{66} +(159277. - 275876. i) q^{67} +(286754. + 496672. i) q^{68} +(-183263. + 105807. i) q^{69} +2059.35i q^{70} +(449201. - 259346. i) q^{71} +(-15088.6 + 8711.42i) q^{72} +(189212. - 109242. i) q^{73} +(917.094 - 1588.45i) q^{74} -580243. i q^{75} +(-44756.6 - 25840.2i) q^{76} +(-906654. + 523457. i) q^{77} +17917.9 q^{78} +(384737. + 666383. i) q^{79} +(86316.5 + 49834.9i) q^{80} +(253473. - 439029. i) q^{81} -3031.15i q^{82} +(126330. - 218810. i) q^{83} +1.16661e6 q^{84} +218490. i q^{85} +(11942.1 - 7721.95i) q^{86} -658099. q^{87} -50722.2i q^{88} +(-434782. - 251021. i) q^{89} -3317.97 q^{90} +(-1.06173e6 - 612989. i) q^{91} +(-175331. + 303681. i) q^{92} +(-1.50741e6 + 870304. i) q^{93} +13068.5i q^{94} +(-9844.38 - 17051.0i) q^{95} +(-42394.7 + 73429.8i) q^{96} +280574. q^{97} +(16349.9 + 9439.62i) q^{98} +(-843379. - 1.46078e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q - 3 q^{3} - 1194 q^{4} - 3 q^{5} + 111 q^{6} - 147 q^{7} + 3852 q^{9}+O(q^{10}) \) 42 * q - 3 * q^3 - 1194 * q^4 - 3 * q^5 + 111 * q^6 - 147 * q^7 + 3852 * q^9	\( 42 q - 3 q^{3} - 1194 q^{4} - 3 q^{5} + 111 q^{6} - 147 q^{7} + 3852 q^{9} - 981 q^{10} - 4104 q^{11} + 918 q^{12} + 4843 q^{13} + 2814 q^{14} - 163 q^{15} + 36678 q^{16} + 3641 q^{17} - 507 q^{18} - 5229 q^{19} - 1599 q^{20} - 29990 q^{21} + 6575 q^{23} - 4622 q^{24} + 68484 q^{25} + 189 q^{26} + 48948 q^{28} + 95361 q^{29} - 85041 q^{30} - 79373 q^{31} - 79638 q^{33} - 184743 q^{34} - 80582 q^{35} + 59972 q^{36} - 66063 q^{37} - 69820 q^{38} + 189951 q^{40} + 40632 q^{41} - 368728 q^{43} + 130330 q^{44} + 34056 q^{46} - 247820 q^{47} + 326907 q^{48} - 21876 q^{49} - 28638 q^{50} - 617150 q^{52} + 11639 q^{53} + 655904 q^{54} - 43638 q^{55} + 553875 q^{56} - 422859 q^{57} + 587796 q^{58} - 649352 q^{59} + 875455 q^{60} - 52251 q^{61} + 1335249 q^{62} + 93690 q^{63} - 792420 q^{64} + 160395 q^{66} - 173603 q^{67} + 22286 q^{68} + 870417 q^{69} + 1670505 q^{71} - 2068518 q^{72} - 2646201 q^{73} - 1625030 q^{74} - 80622 q^{76} - 486066 q^{77} + 2835040 q^{78} + 1897639 q^{79} - 817059 q^{80} + 2215367 q^{81} + 1584059 q^{83} - 824560 q^{84} - 2333682 q^{86} - 5547198 q^{87} + 2736939 q^{89} + 1092196 q^{90} - 3724131 q^{91} + 470257 q^{92} + 488433 q^{93} - 1289839 q^{95} + 1697650 q^{96} + 5260848 q^{97} + 4722621 q^{98} + 1375834 q^{99}+O(q^{100}) \) 42 * q - 3 * q^3 - 1194 * q^4 - 3 * q^5 + 111 * q^6 - 147 * q^7 + 3852 * q^9 - 981 * q^10 - 4104 * q^11 + 918 * q^12 + 4843 * q^13 + 2814 * q^14 - 163 * q^15 + 36678 * q^16 + 3641 * q^17 - 507 * q^18 - 5229 * q^19 - 1599 * q^20 - 29990 * q^21 + 6575 * q^23 - 4622 * q^24 + 68484 * q^25 + 189 * q^26 + 48948 * q^28 + 95361 * q^29 - 85041 * q^30 - 79373 * q^31 - 79638 * q^33 - 184743 * q^34 - 80582 * q^35 + 59972 * q^36 - 66063 * q^37 - 69820 * q^38 + 189951 * q^40 + 40632 * q^41 - 368728 * q^43 + 130330 * q^44 + 34056 * q^46 - 247820 * q^47 + 326907 * q^48 - 21876 * q^49 - 28638 * q^50 - 617150 * q^52 + 11639 * q^53 + 655904 * q^54 - 43638 * q^55 + 553875 * q^56 - 422859 * q^57 + 587796 * q^58 - 649352 * q^59 + 875455 * q^60 - 52251 * q^61 + 1335249 * q^62 + 93690 * q^63 - 792420 * q^64 + 160395 * q^66 - 173603 * q^67 + 22286 * q^68 + 870417 * q^69 + 1670505 * q^71 - 2068518 * q^72 - 2646201 * q^73 - 1625030 * q^74 - 80622 * q^76 - 486066 * q^77 + 2835040 * q^78 + 1897639 * q^79 - 817059 * q^80 + 2215367 * q^81 + 1584059 * q^83 - 824560 * q^84 - 2333682 * q^86 - 5547198 * q^87 + 2736939 * q^89 + 1092196 * q^90 - 3724131 * q^91 + 470257 * q^92 + 488433 * q^93 - 1289839 * q^95 + 1697650 * q^96 + 5260848 * q^97 + 4722621 * q^98 + 1375834 * q^99

Introduction

L-functions

Modular forms

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