LMFDB - Embedded newform 43.7.d.a.7.1

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			7.1
Character	$\chi$	$=$	43.7
Dual form			43.7.d.a.37.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-15.1507i q^{2} +(15.3614 - 8.86889i) q^{3} -165.545 q^{4} +(63.9718 - 36.9341i) q^{5} +(-134.370 - 232.736i) q^{6} +(-298.109 - 172.114i) q^{7} +1538.48i q^{8} +(-207.186 + 358.856i) q^{9} +O(q^{10})$	\(q-15.1507i q^{2} +(15.3614 - 8.86889i) q^{3} -165.545 q^{4} +(63.9718 - 36.9341i) q^{5} +(-134.370 - 232.736i) q^{6} +(-298.109 - 172.114i) q^{7} +1538.48i q^{8} +(-207.186 + 358.856i) q^{9} +(-559.579 - 969.219i) q^{10} -1171.40 q^{11} +(-2542.99 + 1468.20i) q^{12} +(642.173 - 1112.28i) q^{13} +(-2607.65 + 4516.58i) q^{14} +(655.129 - 1134.72i) q^{15} +12714.2 q^{16} +(1587.56 - 2749.73i) q^{17} +(5436.94 + 3139.02i) q^{18} +(5769.57 - 3331.06i) q^{19} +(-10590.2 + 6114.25i) q^{20} -6105.82 q^{21} +17747.6i q^{22} +(-7350.54 - 12731.5i) q^{23} +(13644.6 + 23633.1i) q^{24} +(-5084.24 + 8806.16i) q^{25} +(-16851.8 - 9729.39i) q^{26} +20280.9i q^{27} +(49350.4 + 28492.5i) q^{28} +(3269.02 + 1887.37i) q^{29} +(-17191.8 - 9925.68i) q^{30} +(-29197.4 - 50571.3i) q^{31} -94166.8i q^{32} +(-17994.4 + 10389.1i) q^{33} +(-41660.4 - 24052.6i) q^{34} -25427.4 q^{35} +(34298.5 - 59406.8i) q^{36} +(-22487.0 + 12982.9i) q^{37} +(-50468.0 - 87413.2i) q^{38} -22781.4i q^{39} +(56822.3 + 98419.1i) q^{40} +26952.4 q^{41} +92507.6i q^{42} +(79186.0 - 7137.46i) q^{43} +193920. q^{44} +30608.9i q^{45} +(-192892. + 111366. i) q^{46} -198596. q^{47} +(195307. - 112761. i) q^{48} +(421.621 + 730.269i) q^{49} +(133420. + 77030.0i) q^{50} -56319.4i q^{51} +(-106308. + 184131. i) q^{52} +(-120372. - 208490. i) q^{53} +307270. q^{54} +(-74936.8 + 43264.8i) q^{55} +(264793. - 458634. i) q^{56} +(59085.6 - 102339. i) q^{57} +(28595.0 - 49528.0i) q^{58} +163320. q^{59} +(-108453. + 187846. i) q^{60} +(266231. + 153708. i) q^{61} +(-766193. + 442362. i) q^{62} +(123528. - 71318.9i) q^{63} -612988. q^{64} -94872.4i q^{65} +(157402. + 272628. i) q^{66} +(-145518. - 252044. i) q^{67} +(-262811. + 455203. i) q^{68} +(-225829. - 130382. i) q^{69} +385244. i q^{70} +(500666. + 289060. i) q^{71} +(-552092. - 318750. i) q^{72} +(9585.49 + 5534.19i) q^{73} +(196700. + 340694. i) q^{74} +180366. i q^{75} +(-955122. + 551440. i) q^{76} +(349207. + 201615. i) q^{77} -345156. q^{78} +(348781. - 604107. i) q^{79} +(813349. - 469587. i) q^{80} +(28830.2 + 49935.4i) q^{81} -408349. i q^{82} +(94634.3 + 163911. i) q^{83} +1.01079e6 q^{84} -234540. i q^{85} +(-108138. - 1.19973e6i) q^{86} +66955.4 q^{87} -1.80218e6i q^{88} +(423625. - 244580. i) q^{89} +463747. q^{90} +(-382876. + 221053. i) q^{91} +(1.21684e6 + 2.10764e6i) q^{92} +(-897023. - 517896. i) q^{93} +3.00888e6i q^{94} +(246060. - 426188. i) q^{95} +(-835154. - 1.44653e6i) q^{96} +895486. q^{97} +(11064.1 - 6387.87i) q^{98} +(242698. - 420366. i) 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 $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$		−	15.1507i		−	1.89384i	−0.321467	−	0.946921i	$-0.604176\pi$
$2$		−	15.1507i		−	1.89384i	0.321467	−	0.946921i	$-0.395824\pi$
$3$	15.3614	−	8.86889i	0.568939	−	0.328477i	−0.187786	−	0.982210i	$-0.560131\pi$
$3$	15.3614	−	8.86889i	0.568939	−	0.328477i	0.756726	+	0.653733i	$0.226798\pi$
$4$	−165.545			−2.58664
$5$	63.9718	−	36.9341i	0.511774	−	0.295473i	−0.221788	−	0.975095i	$-0.571189\pi$
$5$	63.9718	−	36.9341i	0.511774	−	0.295473i	0.733563	+	0.679622i	$0.237856\pi$
$6$	−134.370	−	232.736i	−0.622084	−	1.07748i
$7$	−298.109	−	172.114i	−0.869123	−	0.501789i	−0.00206660	−	0.999998i	$-0.500658\pi$
$7$	−298.109	−	172.114i	−0.869123	−	0.501789i	−0.867057	+	0.498209i	$0.833991\pi$
$8$			1538.48i			3.00484i
$9$	−207.186	+	358.856i	−0.284205	+	0.492258i
$10$	−559.579	−	969.219i	−0.559579	−	0.969219i
$11$	−1171.40			−0.880094			−0.440047	−	0.897975i	$-0.645038\pi$
$11$	−1171.40			−0.880094			−0.440047	+	0.897975i	$0.645038\pi$
$12$	−2542.99	+	1468.20i	−1.47164	+	0.849651i
$13$	642.173	−	1112.28i	0.292295	−	0.506271i	−0.682057	−	0.731299i	$-0.738914\pi$
$13$	642.173	−	1112.28i	0.292295	−	0.506271i	0.974352	+	0.225029i	$0.0722476\pi$
$14$	−2607.65	+	4516.58i	−0.950308	+	1.64598i
$15$	655.129	−	1134.72i	0.194112	−	0.336212i
$16$	12714.2			3.10405
$17$	1587.56	−	2749.73i	0.323134	−	0.559684i	−0.657999	−	0.753019i	$-0.728597\pi$
$17$	1587.56	−	2749.73i	0.323134	−	0.559684i	0.981133	+	0.193335i	$0.0619303\pi$
$18$	5436.94	+	3139.02i	0.932259	+	0.538240i
$19$	5769.57	−	3331.06i	0.841168	−	0.485648i	−0.0164933	−	0.999864i	$-0.505250\pi$
$19$	5769.57	−	3331.06i	0.841168	−	0.485648i	0.857661	+	0.514216i	$0.171917\pi$
$20$	−10590.2	+	6114.25i	−1.32377	+	0.764281i
$21$	−6105.82			−0.659305
$22$			17747.6i			1.66676i
$23$	−7350.54	−	12731.5i	−0.604138	−	1.04640i	−0.992187	−	0.124759i	$-0.960184\pi$
$23$	−7350.54	−	12731.5i	−0.604138	−	1.04640i	0.388049	−	0.921639i	$-0.373149\pi$
$24$	13644.6	+	23633.1i	0.987021	+	1.70957i
$25$	−5084.24	+	8806.16i	−0.325391	+	0.563594i
$26$	−16851.8	−	9729.39i	−0.958796	−	0.553561i
$27$			20280.9i			1.03037i
$28$	49350.4	+	28492.5i	2.24811	+	1.29794i
$29$	3269.02	+	1887.37i	0.134037	+	0.0773860i	0.565519	−	0.824735i	$-0.308676\pi$
$29$	3269.02	+	1887.37i	0.134037	+	0.0773860i	−0.431482	+	0.902121i	$0.642009\pi$
$30$	−17191.8	−	9925.68i	−0.636733	−	0.367618i
$31$	−29197.4	−	50571.3i	−0.980074	−	1.69754i	−0.662060	−	0.749451i	$-0.730318\pi$
$31$	−29197.4	−	50571.3i	−0.980074	−	1.69754i	−0.318014	−	0.948086i	$-0.603016\pi$
$32$		−	94166.8i		−	2.87374i
$33$	−17994.4	+	10389.1i	−0.500720	+	0.289091i
$34$	−41660.4	−	24052.6i	−1.05995	−	0.611964i
$35$	−25427.4			−0.593060
$36$	34298.5	−	59406.8i	0.735136	−	1.27329i
$37$	−22487.0	+	12982.9i	−0.443941	+	0.256310i	−0.705268	−	0.708941i	$-0.749173\pi$
$37$	−22487.0	+	12982.9i	−0.443941	+	0.256310i	0.261327	+	0.965250i	$0.415840\pi$
$38$	−50468.0	−	87413.2i	−0.919741	−	1.59304i
$39$		−	22781.4i		−	0.384050i
$40$	56822.3	+	98419.1i	0.887848	+	1.53780i
$41$	26952.4			0.391063			0.195531	−	0.980697i	$-0.437357\pi$
$41$	26952.4			0.391063			0.195531	+	0.980697i	$0.437357\pi$
$42$			92507.6i			1.24862i
$43$	79186.0	−	7137.46i	0.995962	−	0.0897715i
$43$	79186.0	−	7137.46i	0.995962	−	0.0897715i
$44$	193920.			2.27648
$45$			30608.9i			0.335900i
$46$	−192892.	+	111366.i	−1.98171	+	1.14414i
$47$	−198596.			−1.91283			−0.956416	−	0.292006i	$-0.905677\pi$
$47$	−198596.			−1.91283			−0.956416	+	0.292006i	$0.905677\pi$
$48$	195307.	−	112761.i	1.76602	−	1.01961i
$49$	421.621	+	730.269i	0.00358372	+	0.00620719i
$50$	133420.	+	77030.0i	1.06736	+	0.616240i
$51$		−	56319.4i		−	0.424568i
$52$	−106308.	+	184131.i	−0.756062	+	1.30954i
$53$	−120372.	−	208490.i	−0.808531	−	1.40042i	−0.913881	−	0.405981i	$-0.866930\pi$
$53$	−120372.	−	208490.i	−0.808531	−	1.40042i	0.105350	−	0.994435i	$-0.466404\pi$
$54$	307270.			1.95137
$55$	−74936.8	+	43264.8i	−0.450409	+	0.260044i
$56$	264793.	−	458634.i	1.50779	−	2.61157i
$57$	59085.6	−	102339.i	0.319049	−	0.552609i
$58$	28595.0	−	49528.0i	0.146557	−	0.253844i
$59$	163320.			0.795213			0.397607	−	0.917556i	$-0.369841\pi$
$59$	163320.			0.795213			0.397607	+	0.917556i	$0.369841\pi$
$60$	−108453.	+	187846.i	−0.502098	+	0.869659i
$61$	266231.	+	153708.i	1.17292	+	0.677187i	0.954366	−	0.298638i	$-0.0965323\pi$
$61$	266231.	+	153708.i	1.17292	+	0.677187i	0.218555	+	0.975825i	$0.429866\pi$
$62$	−766193.	+	442362.i	−3.21487	+	1.85610i
$63$	123528.	−	71318.9i	0.494019	−	0.285222i
$64$	−612988.			−2.33836
$65$		−	94872.4i		−	0.345462i
$66$	157402.	+	272628.i	0.547492	+	0.948284i
$67$	−145518.	−	252044.i	−0.483828	−	0.838015i	0.515999	−	0.856589i	$-0.327421\pi$
$67$	−145518.	−	252044.i	−0.483828	−	0.838015i	−0.999827	+	0.0185740i	$0.994087\pi$
$68$	−262811.	+	455203.i	−0.835829	+	1.44770i
$69$	−225829.	−	130382.i	−0.687435	−	0.396891i
$70$			385244.i			1.12316i
$71$	500666.	+	289060.i	1.39886	+	0.807630i	0.994273	−	0.106871i	$-0.0340832\pi$
$71$	500666.	+	289060.i	1.39886	+	0.807630i	0.404583	+	0.914501i	$0.367417\pi$
$72$	−552092.	−	318750.i	−1.47916	−	0.853991i
$73$	9585.49	+	5534.19i	0.0246403	+	0.0142261i	0.512270	−	0.858825i	$-0.328805\pi$
$73$	9585.49	+	5534.19i	0.0246403	+	0.0142261i	−0.487629	+	0.873051i	$0.662138\pi$
$74$	196700.	+	340694.i	0.485410	+	0.840755i
$75$			180366.i			0.427535i
$76$	−955122.	+	551440.i	−2.17579	+	1.25620i
$77$	349207.	+	201615.i	0.764910	+	0.441621i
$78$	−345156.			−0.727329
$79$	348781.	−	604107.i	0.707411	−	1.22527i	−0.258404	−	0.966037i	$-0.583196\pi$
$79$	348781.	−	604107.i	0.707411	−	1.22527i	0.965814	−	0.259234i	$-0.0834702\pi$
$80$	813349.	−	469587.i	1.58857	−	0.917163i
$81$	28830.2	+	49935.4i	0.0542491	+	0.0939622i
$82$		−	408349.i		−	0.740610i
$83$	94634.3	+	163911.i	0.165506	+	0.286665i	0.936835	−	0.349772i	$-0.113741\pi$
$83$	94634.3	+	163911.i	0.165506	+	0.286665i	−0.771329	+	0.636437i	$0.780408\pi$
$84$	1.01079e6			1.70538
$85$		−	234540.i		−	0.381909i
$86$	−108138.	−	1.19973e6i	−0.170013	−	1.88620i
$87$	66955.4			0.101678
$88$		−	1.80218e6i		−	2.64454i
$89$	423625.	−	244580.i	0.600914	−	0.346938i	−0.168487	−	0.985704i	$-0.553888\pi$
$89$	423625.	−	244580.i	0.600914	−	0.346938i	0.769401	+	0.638766i	$0.220555\pi$
$90$	463747.			0.636142
$91$	−382876.	+	221053.i	−0.508082	+	0.293341i
$92$	1.21684e6	+	2.10764e6i	1.56268	+	2.70665i
$93$	−897023.	−	517896.i	−1.11520	−	0.643864i
$94$			3.00888e6i			3.62260i
$95$	246060.	−	426188.i	0.286992	−	0.497085i
$96$	−835154.	−	1.44653e6i	−0.943959	−	1.63498i
$97$	895486.			0.981169			0.490584	−	0.871394i	$-0.336783\pi$
$97$	895486.			0.981169			0.490584	+	0.871394i	$0.336783\pi$
$98$	11064.1	−	6387.87i	0.0117554	−	0.00678700i
$99$	242698.	−	420366.i	0.250127	−	0.433233i
$100$	841669.	−	1.45781e6i	0.841669	−	1.45781i
$101$	496645.	−	860215.i	0.482039	−	0.834916i	−0.517749	−	0.855533i	$-0.673230\pi$
$101$	496645.	−	860215.i	0.482039	−	0.834916i	0.999787	+	0.0206169i	$0.00656304\pi$
$102$	−853280.			−0.804065
$103$	−621056.	+	1.07570e6i	−0.568354	+	0.984419i	0.428375	+	0.903601i	$0.359086\pi$
$103$	−621056.	+	1.07570e6i	−0.568354	+	0.984419i	−0.996729	+	0.0808173i	$0.974247\pi$
$104$	1.71121e6	+	987968.i	1.52126	+	0.878300i
$105$	−390600.	+	225513.i	−0.337415	+	0.194807i
$106$	−3.15877e6	+	1.82372e6i	−2.65217	+	1.53123i
$107$	78155.5			0.0637982			0.0318991	−	0.999491i	$-0.489844\pi$
$107$	78155.5			0.0637982			0.0318991	+	0.999491i	$0.489844\pi$
$108$		−	3.35739e6i		−	2.66520i
$109$	517811.	+	896874.i	0.399845	+	0.692551i	0.993706	−	0.112016i	$-0.0357307\pi$
$109$	517811.	+	896874.i	0.399845	+	0.692551i	−0.593862	+	0.804567i	$0.702397\pi$
$110$	655493.	+	1.13535e6i	0.492482	+	0.853004i
$111$	−230287.	+	398869.i	−0.168384	+	0.291649i
$112$	−3.79022e6	−	2.18828e6i	−2.69780	−	1.55758i
$113$		−	1.19444e6i		−	0.827804i	−0.910322	−	0.413902i	$-0.864166\pi$
$113$		−	1.19444e6i		−	0.827804i	0.910322	−	0.413902i	$-0.135834\pi$
$114$	−1.55052e6	−	895190.i	−1.04655	−	0.604228i
$115$	−940455.	−	542972.i	−0.618364	−	0.357013i
$116$	−541169.	−	312444.i	−0.346704	−	0.200170i
$117$	266098.	+	460896.i	0.166144	+	0.287770i
$118$		−	2.47442e6i		−	1.50601i
$119$	−946530.	+	546479.i	−0.561686	+	0.324290i
$120$	1.74574e6	+	1.00790e6i	1.01026	+	0.583276i
$121$	−399373.			−0.225435
$122$	2.32880e6	−	4.03359e6i	1.28248	−	2.22133i
$123$	414026.	−	239038.i	0.222491	−	0.128455i
$124$	4.83347e6	+	8.37182e6i	2.53509	+	4.39091i
$125$			1.90532e6i			0.975523i
$126$	−1.08053e6	−	1.87154e6i	−0.540166	−	0.935594i
$127$	−2.33602e6			−1.14042			−0.570211	−	0.821498i	$-0.693139\pi$
$127$	−2.33602e6			−1.14042			−0.570211	+	0.821498i	$0.693139\pi$
$128$			3.26054e6i			1.55475i
$129$	1.15310e6	−	811932.i	0.537154	−	0.378225i
$130$	−1.43739e6			−0.654250
$131$			239232.i			0.106416i	0.998583	+	0.0532078i	$0.0169446\pi$
$131$			239232.i			0.106416i	−0.998583	+	0.0532078i	$0.983055\pi$
$132$	2.97887e6	−	1.71985e6i	1.29518	−	0.747772i
$133$	−2.29328e6			−0.974771
$134$	−3.81865e6	+	2.20470e6i	−1.58707	+	0.916294i
$135$	749056.	+	1.29740e6i	0.304448	+	0.527319i
$136$	4.23039e6	+	2.44242e6i	1.68176	+	0.970964i
$137$		−	1.36946e6i		−	0.532582i	−0.963893	−	0.266291i	$-0.914202\pi$
$137$		−	1.36946e6i		−	0.532582i	0.963893	−	0.266291i	$-0.0857981\pi$
$138$	−1.97539e6	+	3.42147e6i	−0.751649	+	1.30189i
$139$	569254.	+	985977.i	0.211964	+	0.367132i	0.952329	−	0.305073i	$-0.0986808\pi$
$139$	569254.	+	985977.i	0.211964	+	0.367132i	−0.740365	+	0.672205i	$0.765347\pi$
$140$	4.20938e6			1.53403
$141$	−3.05071e6	+	1.76133e6i	−1.08829	+	0.628322i
$142$	4.37947e6	−	7.58546e6i	1.52952	−	2.64921i
$143$	−752245.	+	1.30293e6i	−0.257247	+	0.445565i
$144$	−2.63420e6	+	4.56257e6i	−0.882188	+	1.52799i
$145$	278833.			0.0914619
$146$	83847.0	−	145227.i	0.0269419	−	0.0466648i
$147$	12953.3	+	7478.62i	0.00407784	+	0.00235434i
$148$	3.72260e6	−	2.14924e6i	1.14831	−	0.662980i
$149$	−734887.	+	424287.i	−0.222158	+	0.128263i	−0.606949	−	0.794741i	$-0.707607\pi$
$149$	−734887.	+	424287.i	−0.222158	+	0.128263i	0.384791	+	0.923004i	$0.374273\pi$
$150$	2.73268e6			0.809683
$151$		−	3.95092e6i		−	1.14754i	−0.819017	−	0.573770i	$-0.805480\pi$
$151$		−	3.95092e6i		−	1.14754i	0.819017	−	0.573770i	$-0.194520\pi$
$152$	5.12476e6	+	8.87635e6i	1.45929	+	2.52757i
$153$	657838.	+	1.13941e6i	0.183673	+	0.318130i
$154$	3.05461e6	−	5.29074e6i	0.836360	−	1.44862i
$155$	−3.73562e6	−	2.15676e6i	−1.00315	−	0.579170i
$156$			3.77135e6i			0.993397i
$157$	677236.	+	391002.i	0.175001	+	0.101037i	0.584942	−	0.811075i	$-0.301117\pi$
$157$	677236.	+	391002.i	0.175001	+	0.101037i	−0.409941	+	0.912112i	$0.634451\pi$
$158$	−9.15266e6	−	5.28429e6i	−2.32047	−	1.33972i
$159$	−3.69814e6	−	2.13512e6i	−0.920010	−	0.531168i
$160$	−3.47797e6	−	6.02402e6i	−0.849113	−	1.47071i
$161$			5.06051e6i			1.21260i
$162$	756558.	−	436799.i	0.177950	−	0.102739i
$163$	4.01220e6	+	2.31644e6i	0.926445	+	0.534883i	0.885685	−	0.464286i	$-0.153689\pi$
$163$	4.01220e6	+	2.31644e6i	0.926445	+	0.534883i	0.0407593	+	0.999169i	$0.487022\pi$
$164$	−4.46183e6			−1.01154
$165$	−767421.	+	1.32921e6i	−0.170837	+	0.295898i
$166$	2.48338e6	−	1.43378e6i	0.542898	−	0.313443i
$167$	−3.84335e6	−	6.65688e6i	−0.825203	−	1.42929i	−0.901764	−	0.432229i	$-0.857727\pi$
$167$	−3.84335e6	−	6.65688e6i	−0.825203	−	1.42929i	0.0765608	−	0.997065i	$-0.475606\pi$
$168$		−	9.39366e6i		−	1.98110i
$169$	1.58863e6	+	2.75159e6i	0.329127	+	0.570064i
$170$	−3.55345e6			−0.723275
$171$			2.76059e6i			0.552096i
$172$	−1.31088e7	+	1.18157e6i	−2.57619	+	0.232206i
$173$	2.74566e6			0.530283			0.265142	−	0.964209i	$-0.414581\pi$
$173$	2.74566e6			0.530283			0.265142	+	0.964209i	$0.414581\pi$
$174$		−	1.01442e6i		−	0.192562i
$175$	3.03132e6	−	1.75013e6i	0.565611	−	0.326555i
$176$	−1.48935e7			−2.73185
$177$	2.50882e6	−	1.44847e6i	0.452428	−	0.261209i
$178$	−3.70557e6	−	6.41824e6i	−0.657045	−	1.13804i
$179$	9.12503e6	+	5.26834e6i	1.59102	+	0.918575i	0.993133	+	0.116993i	$0.0373254\pi$
$179$	9.12503e6	+	5.26834e6i	1.59102	+	0.918575i	0.597885	+	0.801582i	$0.296008\pi$
$180$		−	5.06714e6i		−	0.868851i
$181$	−5.75180e6	+	9.96241e6i	−0.969991	+	1.68007i	−0.274431	+	0.961607i	$0.588490\pi$
$181$	−5.75180e6	+	9.96241e6i	−0.969991	+	1.68007i	−0.695560	+	0.718468i	$0.744844\pi$
$182$	3.34912e6	+	5.80085e6i	0.555542	+	0.962226i
$183$	5.45289e6			0.889761
$184$	1.95871e7	−	1.13086e7i	3.14425	−	1.81534i
$185$	−959020.	+	1.66107e6i	−0.151465	+	0.262345i
$186$	−7.84651e6	+	1.35905e7i	−1.21938	+	2.11202i
$187$	−1.85967e6	+	3.22104e6i	−0.284388	+	0.492574i
$188$	3.28765e7			4.94780
$189$	3.49061e6	−	6.04591e6i	0.517030	−	0.895523i
$190$	−6.45706e6	−	3.72799e6i	−0.941400	−	0.543517i
$191$	1.00169e7	−	5.78326e6i	1.43758	−	0.829990i	0.439903	−	0.898046i	$-0.355013\pi$
$191$	1.00169e7	−	5.78326e6i	1.43758	−	0.829990i	0.997682	+	0.0680560i	$0.0216796\pi$
$192$	−9.41632e6	+	5.43652e6i	−1.33039	+	0.768099i
$193$	3.60963e6			0.502101			0.251050	−	0.967974i	$-0.419224\pi$
$193$	3.60963e6			0.502101			0.251050	+	0.967974i	$0.419224\pi$
$194$		−	1.35673e7i		−	1.85818i
$195$	−841412.	−	1.45737e6i	−0.113476	−	0.196547i
$196$	−69797.1	−	120892.i	−0.00926978	−	0.0160557i
$197$	−5.71614e6	+	9.90065e6i	−0.747661	+	1.29499i	0.201281	+	0.979534i	$0.435490\pi$
$197$	−5.71614e6	+	9.90065e6i	−0.747661	+	1.29499i	−0.948941	+	0.315453i	$0.897844\pi$
$198$	−6.36885e6	−	3.67706e6i	−0.820475	−	0.473702i
$199$		−	5.61273e6i		−	0.712221i	−0.934444	−	0.356110i	$-0.884103\pi$
$199$		−	5.61273e6i		−	0.712221i	0.934444	−	0.356110i	$-0.115897\pi$
$200$	−1.35481e7	−	7.82199e6i	−1.69351	−	0.977748i
$201$	−4.47070e6	−	2.58116e6i	−0.550538	−	0.317853i
$202$	−1.30329e7	−	7.52454e6i	−1.58120	−	0.912905i
$203$	−649683.	−	1.12528e6i	−0.0776629	−	0.134516i
$204$			9.32338e6i			1.09820i
$205$	1.72419e6	−	995464.i	0.200136	−	0.115548i
$206$	1.62977e7	+	9.40946e6i	1.86433	+	1.07637i
$207$	6.09171e6			0.686797
$208$	8.16471e6	−	1.41417e7i	0.907300	−	1.57149i
$209$	−6.75850e6	+	3.90202e6i	−0.740306	+	0.427416i
$210$	3.41669e6	+	5.91788e6i	0.368933	+	0.639011i
$211$		−	7.60059e6i		−	0.809096i	−0.914517	−	0.404548i	$-0.867429\pi$
$211$		−	7.60059e6i		−	0.809096i	0.914517	−	0.404548i	$-0.132571\pi$
$212$	1.99269e7	+	3.45144e7i	2.09138	+	3.62237i
$213$	1.02545e7			1.06115
$214$		−	1.18411e6i		−	0.120824i
$215$	4.80205e6	−	3.38126e6i	0.483183	−	0.340223i
$216$	−3.12016e7			−3.09611
$217$			2.01010e7i			1.96716i
$218$	1.35883e7	−	7.84521e6i	1.31158	−	0.757243i
$219$	196328.			0.0186918
$220$	1.24054e7	−	7.16226e6i	1.16504	−	0.672639i
$221$	−2.03897e6	−	3.53160e6i	−0.188901	−	0.327186i
$222$	6.04315e6	+	3.48901e6i	0.552337	+	0.318892i
$223$		−	1.74335e6i		−	0.157206i	−0.996906	−	0.0786030i	$-0.974954\pi$
$223$		−	1.74335e6i		−	0.157206i	0.996906	−	0.0786030i	$-0.0250460\pi$
$224$	−1.62074e7	+	2.80720e7i	−1.44201	+	2.49764i
$225$	−2.10676e6	−	3.64902e6i	−0.184956	−	0.320353i
$226$	−1.80966e7			−1.56773
$227$	1.15973e6	−	669570.i	0.0991469	−	0.0572425i	−0.449607	−	0.893227i	$-0.648436\pi$
$227$	1.15973e6	−	669570.i	0.0991469	−	0.0572425i	0.548754	+	0.835984i	$0.315103\pi$
$228$	−9.78131e6	+	1.69417e7i	−0.825263	+	1.42940i
$229$	−3.66746e6	+	6.35222e6i	−0.305393	+	0.528955i	−0.977349	−	0.211636i	$-0.932121\pi$
$229$	−3.66746e6	+	6.35222e6i	−0.305393	+	0.528955i	0.671956	+	0.740591i	$0.265454\pi$
$230$	−8.22642e6	+	1.42486e7i	−0.676126	+	1.17108i
$231$	7.15238e6			0.580250
$232$	−2.90367e6	+	5.02931e6i	−0.232532	+	0.402758i
$233$	−1.02503e7	−	5.91799e6i	−0.810340	−	0.467850i	0.0367338	−	0.999325i	$-0.488305\pi$
$233$	−1.02503e7	−	5.91799e6i	−0.810340	−	0.467850i	−0.847074	+	0.531475i	$0.821638\pi$
$234$	6.98291e6	−	4.03158e6i	0.544990	−	0.314650i
$235$	−1.27045e7	+	7.33497e6i	−0.978939	+	0.565190i
$236$	−2.70368e7			−2.05693
$237$		−	1.23732e7i		−	0.929473i
$238$	8.27956e6	+	1.43406e7i	0.614153	+	1.06374i
$239$	−1.10330e7	−	1.91098e7i	−0.808167	−	1.39979i	−0.914132	−	0.405416i	$-0.867127\pi$
$239$	−1.10330e7	−	1.91098e7i	−0.808167	−	1.39979i	0.105966	−	0.994370i	$-0.466207\pi$
$240$	8.32943e6	−	1.44270e7i	0.602534	−	1.04362i
$241$	4.78634e6	+	2.76339e6i	0.341942	+	0.197420i	0.661130	−	0.750271i	$-0.270077\pi$
$241$	4.78634e6	+	2.76339e6i	0.341942	+	0.197420i	−0.319189	+	0.947691i	$0.603410\pi$
$242$			6.05079e6i			0.426939i
$243$	−1.19182e7	−	6.88099e6i	−0.830602	−	0.479548i
$244$	−4.40731e7	−	2.54456e7i	−3.03392	−	1.75164i
$245$	53943.7	+	31144.4i	0.00366811	+	0.00211779i
$246$	−3.62160e6	−	6.27279e6i	−0.243274	−	0.421362i
$247$		−	8.55647e6i		−	0.567811i
$248$	7.78028e7	−	4.49195e7i	5.10082	−	2.94496i
$249$	2.90742e6	+	1.67860e6i	0.188326	+	0.108730i
$250$	2.88670e7			1.84749
$251$	1.97528e6	−	3.42128e6i	0.124913	−	0.216356i	−0.796786	−	0.604262i	$-0.793468\pi$
$251$	1.97528e6	−	3.42128e6i	0.124913	−	0.216356i	0.921699	+	0.387906i	$0.126802\pi$
$252$	−2.04494e7	+	1.18065e7i	−1.27785	+	0.737766i
$253$	8.61046e6	+	1.49138e7i	0.531698	+	0.920928i
$254$			3.53924e7i			2.15978i
$255$	−2.08011e6	−	3.60285e6i	−0.125448	−	0.217283i
$256$	1.01683e7			0.606079
$257$		−	7.57008e6i		−	0.445965i	−0.974822	−	0.222983i	$-0.928421\pi$
$257$		−	7.57008e6i		−	0.445965i	0.974822	−	0.222983i	$-0.0715794\pi$
$258$	−1.23014e7	−	1.74704e7i	−0.716299	−	1.01728i
$259$	8.93810e6			0.514453
$260$			1.57056e7i			0.893584i
$261$	−1.35459e6	+	782072.i	−0.0761878	+	0.0439871i
$262$	3.62454e6			0.201534
$263$	−8.11313e6	+	4.68412e6i	−0.445986	+	0.257490i	−0.706133	−	0.708079i	$-0.749562\pi$
$263$	−8.11313e6	+	4.68412e6i	−0.445986	+	0.257490i	0.260147	+	0.965569i	$0.416229\pi$
$264$	−1.59833e7	−	2.76839e7i	−0.868670	−	1.50458i
$265$	−1.54008e7	−	8.89164e6i	−0.827571	−	0.477798i
$266$			3.47449e7i			1.84606i
$267$	4.33831e6	−	7.51417e6i	0.227922	−	0.394773i
$268$	2.40897e7	+	4.17245e7i	1.25149	+	2.16764i
$269$	3.00182e6			0.154215			0.0771077	−	0.997023i	$-0.475431\pi$
$269$	3.00182e6			0.154215			0.0771077	+	0.997023i	$0.475431\pi$
$270$	1.96566e7	−	1.13487e7i	0.998659	−	0.576576i
$271$	−624680.	+	1.08198e6i	−0.0313870	+	0.0543639i	−0.881292	−	0.472572i	$-0.843326\pi$
$271$	−624680.	+	1.08198e6i	−0.0313870	+	0.0543639i	0.849905	+	0.526936i	$0.176659\pi$
$272$	2.01845e7	−	3.49605e7i	1.00302	−	1.73729i
$273$	−3.92099e6	+	6.79136e6i	−0.192712	+	0.333787i
$274$	−2.07483e7			−1.00863
$275$	5.95570e6	−	1.03156e7i	0.286375	−	0.496016i
$276$	3.73847e7	+	2.15841e7i	1.77815	+	1.02661i
$277$	−2.91712e7	+	1.68420e7i	−1.37251	+	0.792418i	−0.991243	−	0.132048i	$-0.957845\pi$
$277$	−2.91712e7	+	1.68420e7i	−1.37251	+	0.792418i	−0.381265	+	0.924466i	$0.624511\pi$
$278$	1.49383e7	−	8.62461e6i	0.695290	−	0.401426i
$279$	2.41971e7			1.11417
$280$		−	3.91195e7i		−	1.78205i
$281$	1.25507e6	+	2.17384e6i	0.0565650	+	0.0979734i	0.892921	−	0.450213i	$-0.148652\pi$
$281$	1.25507e6	+	2.17384e6i	0.0565650	+	0.0979734i	−0.836356	+	0.548186i	$0.815319\pi$
$282$	2.66854e7	+	4.62204e7i	1.18994	+	2.06104i
$283$	−1.16382e7	+	2.01580e7i	−0.513484	+	0.889381i	0.486393	+	0.873740i	$0.338312\pi$
$283$	−1.16382e7	+	2.01580e7i	−0.513484	+	0.889381i	−0.999878	+	0.0156411i	$0.995021\pi$
$284$	−8.28826e7	−	4.78523e7i	−3.61833	−	2.08905i
$285$		−	8.72910e6i		−	0.377081i
$286$	1.97403e7	+	1.13971e7i	0.843830	+	0.487186i
$287$	−8.03477e6	−	4.63888e6i	−0.339882	−	0.196231i
$288$	3.37923e7	+	1.95100e7i	1.41462	+	0.816733i
$289$	7.02812e6	+	1.21731e7i	0.291169	+	0.504320i
$290$		−	4.22453e6i		−	0.173214i
$291$	1.37559e7	−	7.94197e6i	0.558225	−	0.322292i
$292$	−1.58683e6	−	916155.i	−0.0637355	−	0.0367977i
$293$	1.78262e7			0.708691			0.354345	−	0.935115i	$-0.384704\pi$
$293$	1.78262e7			0.708691			0.354345	+	0.935115i	$0.384704\pi$
$294$	113307.	−	196253.i	0.00445875	−	0.00772278i
$295$	1.04479e7	−	6.03208e6i	0.406970	−	0.234964i
$296$	−1.99738e7	−	3.45957e7i	−0.770169	−	1.33397i
$297$		−	2.37571e7i		−	0.906826i
$298$	6.42826e6	+	1.11341e7i	0.242910	+	0.420732i
$299$	−1.88813e7			−0.706347
$300$		−	2.98587e7i		−	1.10588i
$301$	−2.48345e7	−	1.15012e7i	−0.910661	−	0.421740i
$302$	−5.98594e7			−2.17326
$303$		−	1.76188e7i		−	0.633355i
$304$	7.33554e7	−	4.23518e7i	2.61103	−	1.50748i
$305$	2.27084e7			0.800361
$306$	1.72629e7	−	9.96672e6i	0.602489	−	0.347847i
$307$	−1.40587e7	−	2.43504e7i	−0.485881	−	0.841571i	0.513987	−	0.857798i	$-0.328168\pi$
$307$	−1.40587e7	−	2.43504e7i	−0.485881	−	0.841571i	−0.999868	+	0.0162271i	$0.994835\pi$
$308$	−5.78093e7	−	3.33762e7i	−1.97854	−	1.14231i
$309$			2.20323e7i			0.746766i
$310$	−3.26765e7	+	5.65973e7i	−1.09686	+	1.89981i
$311$	−2.27588e7	−	3.94193e7i	−0.756602	−	1.31047i	−0.944574	−	0.328299i	$-0.893525\pi$
$311$	−2.27588e7	−	3.94193e7i	−0.756602	−	1.31047i	0.187972	−	0.982174i	$-0.439809\pi$
$312$	3.50487e7			1.15401
$313$	−2.58144e7	+	1.49039e7i	−0.841839	+	0.486036i	−0.857889	−	0.513835i	$-0.828224\pi$
$313$	−2.58144e7	+	1.49039e7i	−0.841839	+	0.486036i	0.0160500	+	0.999871i	$0.494891\pi$
$314$	5.92397e6	−	1.02606e7i	0.191348	−	0.331425i
$315$	5.26820e6	−	9.12480e6i	0.168551	−	0.291939i
$316$	−5.77389e7	+	1.00007e8i	−1.82981	+	3.16933i
$317$	−5.61205e6			−0.176175			−0.0880873	−	0.996113i	$-0.528075\pi$
$317$	−5.61205e6			−0.176175			−0.0880873	+	0.996113i	$0.528075\pi$
$318$	−3.23487e7	+	5.60296e7i	−1.00595	+	1.74235i
$319$	−3.82934e6	−	2.21087e6i	−0.117965	−	0.0681070i
$320$	−3.92139e7	+	2.26402e7i	−1.19671	+	0.690923i
$321$	1.20057e6	−	693152.i	0.0362973	−	0.0209562i
$322$	7.66705e7			2.29647
$323$		−	2.11530e7i		−	0.627717i
$324$	−4.77269e6	−	8.26654e6i	−0.140323	−	0.243046i
$325$	6.52993e6	+	1.13102e7i	0.190221	+	0.329472i
$326$	3.50958e7	−	6.07877e7i	1.01298	−	1.75454i
$327$	1.59085e7	+	9.18481e6i	0.454975	+	0.262680i
$328$			4.14657e7i			1.17508i
$329$	5.92033e7	+	3.41811e7i	1.66249	+	0.959838i
$330$	2.01385e7	+	1.16270e7i	0.560385	+	0.323538i
$331$	−7.65746e6	−	4.42103e6i	−0.211155	−	0.121910i	0.390693	−	0.920521i	$-0.372235\pi$
$331$	−7.65746e6	−	4.42103e6i	−0.211155	−	0.121910i	−0.601848	+	0.798611i	$0.705569\pi$
$332$	−1.56662e7	−	2.71347e7i	−0.428104	−	0.741498i
$333$		−	1.07594e7i		−	0.291378i
$334$	−1.00857e8	+	5.82296e7i	−2.70686	+	1.56280i
$335$	−1.86180e7	−	1.07491e7i	−0.495222	−	0.285916i
$336$	−7.76305e7			−2.04651
$337$	−1.73029e7	+	2.99695e7i	−0.452094	+	0.783050i	−0.998516	−	0.0544601i	$-0.982656\pi$
$337$	−1.73029e7	+	2.99695e7i	−0.452094	+	0.783050i	0.546422	+	0.837510i	$0.315990\pi$
$338$	4.16886e7	−	2.40689e7i	1.07961	−	0.623314i
$339$	−1.05933e7	−	1.83482e7i	−0.271915	−	0.470970i
$340$			3.88268e7i			0.987860i
$341$	3.42019e7	+	5.92395e7i	0.862556	+	1.49399i
$342$	4.18250e7			1.04558
$343$			4.02077e7i			0.996384i
$344$	1.09808e7	+	1.21826e8i	0.269749	+	2.99271i
$345$	−1.92622e7			−0.469082
$346$		−	4.15987e7i		−	1.00427i
$347$	2.21778e7	−	1.28044e7i	0.530800	−	0.306458i	−0.210542	−	0.977585i	$-0.567523\pi$
$347$	2.21778e7	−	1.28044e7i	0.530800	−	0.306458i	0.741342	+	0.671127i	$0.234190\pi$
$348$	−1.10841e7			−0.263005
$349$	2.95681e7	−	1.70712e7i	0.695580	−	0.401593i	−0.110119	−	0.993918i	$-0.535123\pi$
$349$	2.95681e7	−	1.70712e7i	0.695580	−	0.401593i	0.805699	+	0.592325i	$0.201790\pi$
$350$	−2.65158e7	−	4.59267e7i	−0.618444	−	1.07118i
$351$	2.25579e7	+	1.30238e7i	0.521648	+	0.301174i
$352$			1.10307e8i			2.52916i
$353$	2.17271e7	−	3.76325e7i	0.493945	−	0.855538i	−0.506031	−	0.862515i	$-0.668888\pi$
$353$	2.17271e7	−	3.76325e7i	0.493945	−	0.855538i	0.999976	+	0.00697779i	$0.00222112\pi$
$354$	−2.19453e7	−	3.80104e7i	−0.494689	−	0.856827i
$355$	4.27047e7			0.954532
$356$	−7.01290e7	+	4.04890e7i	−1.55434	+	0.897401i
$357$	−9.69333e6	+	1.67893e7i	−0.213043	+	0.369002i
$358$	7.98192e7	−	1.38251e8i	1.73963	−	3.01314i
$359$	1.87165e7	−	3.24179e7i	0.404521	−	0.700651i	−0.589745	−	0.807590i	$-0.700772\pi$
$359$	1.87165e7	−	3.24179e7i	0.404521	−	0.700651i	0.994266	+	0.106939i	$0.0341050\pi$
$360$	−4.70911e7			−1.00933
$361$	−1.33099e6	+	2.30534e6i	−0.0282913	+	0.0490020i
$362$	1.50938e8	+	8.71440e7i	3.18180	+	1.83701i
$363$	−6.13491e6	+	3.54199e6i	−0.128259	+	0.0740504i
$364$	6.33830e7	−	3.65942e7i	1.31422	−	0.758767i
$365$	817601.			0.0168137
$366$		−	8.26153e7i		−	1.68507i
$367$	2.80728e7	+	4.86235e7i	0.567920	+	0.983667i	0.996771	+	0.0802916i	$0.0255851\pi$
$367$	2.80728e7	+	4.86235e7i	0.567920	+	0.983667i	−0.428851	+	0.903375i	$0.641082\pi$
$368$	−9.34562e7	−	1.61871e8i	−1.87527	−	3.24807i
$369$	−5.58416e6	+	9.67204e6i	−0.111142	+	0.192504i
$370$	2.51665e7	+	1.45299e7i	0.496840	+	0.286851i
$371$			8.28704e7i			1.62285i
$372$	1.48497e8	+	8.57350e7i	2.88463	+	1.66544i
$373$	1.88413e7	+	1.08780e7i	0.363064	+	0.209615i	0.670424	−	0.741978i	$-0.266112\pi$
$373$	1.88413e7	+	1.08780e7i	0.363064	+	0.209615i	−0.307360	+	0.951593i	$0.599446\pi$
$374$	4.88011e7	+	2.81754e7i	0.932857	+	0.538585i
$375$	1.68981e7	+	2.92683e7i	0.320437	+	0.555014i
$376$		−	3.05535e8i		−	5.74775i
$377$	4.19855e6	−	2.42403e6i	0.0783566	−	0.0452392i
$378$	−9.16000e7	−	5.28853e7i	−1.69598	−	0.979173i
$379$	−1.04980e7			−0.192837			−0.0964186	−	0.995341i	$-0.530739\pi$
$379$	−1.04980e7			−0.192837			−0.0964186	+	0.995341i	$0.530739\pi$
$380$	−4.07339e7	+	7.05532e7i	−0.742344	+	1.28578i
$381$	−3.58845e7	+	2.07179e7i	−0.648831	+	0.374603i
$382$	−8.76206e7	−	1.51763e8i	−1.57187	−	2.72256i
$383$			6.08536e7i			1.08315i	0.840651	+	0.541577i	$0.182173\pi$
$383$			6.08536e7i			1.08315i	−0.840651	+	0.541577i	$0.817827\pi$
$384$	2.89173e7	+	5.00863e7i	0.510698	+	0.884555i
$385$	2.97858e7			0.521948
$386$		−	5.46886e7i		−	0.950899i
$387$	−1.38449e7	+	2.98952e7i	−0.238867	+	0.515784i
$388$	−1.48243e8			−2.53793
$389$		−	6.51260e7i		−	1.10638i	−0.833054	−	0.553192i	$-0.813410\pi$
$389$		−	6.51260e7i		−	1.10638i	0.833054	−	0.553192i	$-0.186590\pi$
$390$	−2.20802e7	+	1.27480e7i	−0.372228	+	0.214906i
$391$	−4.66776e7			−0.780869
$392$	−1.12350e6	+	648654.i	−0.0186516	+	0.0107685i
$393$	2.12172e6	+	3.67493e6i	0.0349551	+	0.0605440i
$394$	1.50002e8	+	8.66038e7i	2.45250	+	1.41595i
$395$		−	5.15277e7i		−	0.836083i
$396$	−4.01774e7	+	6.95893e7i	−0.646988	+	1.12062i
$397$	−2.72536e7	−	4.72047e7i	−0.435565	−	0.754420i	0.561777	−	0.827289i	$-0.310118\pi$
$397$	−2.72536e7	−	4.72047e7i	−0.435565	−	0.754420i	−0.997342	+	0.0728685i	$0.976785\pi$
$398$	−8.50369e7			−1.34883
$399$	−3.52279e7	+	2.03389e7i	−0.554586	+	0.320190i
$400$	−6.46420e7	+	1.11963e8i	−1.01003	+	1.74943i
$401$	1.18127e7	−	2.04602e7i	0.183196	−	0.317304i	−0.759771	−	0.650190i	$-0.774689\pi$
$401$	1.18127e7	−	2.04602e7i	0.183196	−	0.317304i	0.942967	+	0.332886i	$0.108022\pi$
$402$	−3.91064e7	+	6.77343e7i	−0.601963	+	1.04263i
$403$	−7.49991e7			−1.14588
$404$	−8.22170e7	+	1.42404e8i	−1.24686	+	2.15962i
$405$	3.68864e6	+	2.12964e6i	0.0555266	+	0.0320583i
$406$	−1.70489e7	+	9.84318e6i	−0.254752	+	0.147081i
$407$	2.63413e7	−	1.52082e7i	0.390710	−	0.225576i
$408$	8.66461e7			1.27576
$409$			9.77849e7i			1.42923i	0.699518	+	0.714615i	$0.253398\pi$
$409$			9.77849e7i			1.42923i	−0.699518	+	0.714615i	$0.746602\pi$
$410$	−1.50820e7	−	2.61228e7i	−0.218830	−	0.379025i
$411$	−1.21455e7	−	2.10367e7i	−0.174941	−	0.303007i
$412$	1.02813e8	−	1.78077e8i	1.47013	−	2.54633i
$413$	−4.86872e7	−	2.81096e7i	−0.691138	−	0.399029i
$414$		−	9.22939e7i		−	1.30068i
$415$	1.21078e7	+	6.99047e6i	0.169404	+	0.0978052i
$416$	−1.04739e8	−	6.04714e7i	−1.45489	−	0.839982i
$417$	1.74890e7	+	1.00973e7i	0.241189	+	0.139251i
$418$	5.91185e7	+	1.02396e8i	0.809458	+	1.40202i
$419$		−	2.55991e7i		−	0.348003i	−0.984745	−	0.174001i	$-0.944330\pi$
$419$		−	2.55991e7i		−	0.348003i	0.984745	−	0.174001i	$-0.0556697\pi$
$420$	6.46618e7	−	3.73325e7i	0.872770	−	0.503894i
$421$	4.52772e7	+	2.61408e7i	0.606783	+	0.350326i	0.771705	−	0.635980i	$-0.219404\pi$
$421$	4.52772e7	+	2.61408e7i	0.606783	+	0.350326i	−0.164923	+	0.986307i	$0.552737\pi$
$422$	−1.15155e8			−1.53230
$423$	4.11463e7	−	7.12674e7i	0.543637	−	0.941608i
$424$	3.20757e8	−	1.85189e8i	4.20802	−	2.42950i
$425$	1.61430e7	+	2.79605e7i	0.210290	+	0.364233i
$426$		−	1.55364e8i		−	2.00965i
$427$	−5.29106e7	−	9.16439e7i	−0.679609	−	1.17712i
$428$	−1.29382e7			−0.165023
$429$			2.66863e7i			0.338000i
$430$	−5.12286e7	−	7.27546e7i	−0.644328	−	0.915072i
$431$	7.90484e7			0.987328			0.493664	−	0.869653i	$-0.335657\pi$
$431$	7.90484e7			0.987328			0.493664	+	0.869653i	$0.335657\pi$
$432$			2.57855e8i			3.19833i
$433$	−9.70713e7	+	5.60442e7i	−1.19571	+	0.690346i	−0.959597	−	0.281379i	$-0.909208\pi$
$433$	−9.70713e7	+	5.60442e7i	−1.19571	+	0.690346i	−0.236117	+	0.971725i	$0.575875\pi$
$434$	3.04546e8			3.72549
$435$	4.28326e6	−	2.47294e6i	0.0520363	−	0.0300432i
$436$	−8.57208e7	−	1.48473e8i	−1.03425	−	1.79138i
$437$	−8.48189e7	−	4.89702e7i	−1.01636	−	0.586797i
$438$		−	2.97452e6i		−	0.0353993i
$439$	−4.61110e7	+	7.98666e7i	−0.545018	+	0.944000i	0.453587	+	0.891212i	$0.350144\pi$
$439$	−4.61110e7	+	7.98666e7i	−0.545018	+	0.944000i	−0.998606	+	0.0527878i	$0.983189\pi$
$440$	−6.65619e7	−	1.15289e8i	−0.781390	−	1.35341i
$441$	−349416.			−0.00407405
$442$	−5.35063e7	+	3.08919e7i	−0.619639	+	0.357749i
$443$	−7.03615e7	+	1.21870e8i	−0.809326	+	1.40179i	0.104005	+	0.994577i	$0.466834\pi$
$443$	−7.03615e7	+	1.21870e8i	−0.809326	+	1.40179i	−0.913331	+	0.407218i	$0.866499\pi$
$444$	3.81228e7	−	6.60306e7i	0.435547	−	0.754390i
$445$	1.80667e7	−	3.12925e7i	0.205021	−	0.355107i
$446$	−2.64130e7			−0.297723
$447$	−7.52590e6	+	1.30352e7i	−0.0842629	+	0.145948i
$448$	1.82737e8	+	1.05503e8i	2.03233	+	1.17336i
$449$	−5.15468e7	+	2.97606e7i	−0.569460	+	0.328778i	−0.756933	−	0.653492i	$-0.773303\pi$
$449$	−5.15468e7	+	2.97606e7i	−0.569460	+	0.328778i	0.187474	+	0.982270i	$0.439970\pi$
$450$	−5.52854e7	+	3.19190e7i	−0.606698	+	0.350277i
$451$	−3.15722e7			−0.344172
$452$			1.97732e8i			2.14123i
$453$	−3.50403e7	−	6.06915e7i	−0.376941	−	0.652880i
$454$	−1.01445e7	−	1.75708e7i	−0.108408	−	0.187769i
$455$	−1.63288e7	+	2.82824e7i	−0.173349	+	0.300249i
$456$	1.57447e8	+	9.09018e7i	1.66050	+	0.958690i
$457$		−	3.35987e7i		−	0.352025i	−0.984388	−	0.176012i	$-0.943680\pi$
$457$		−	3.35987e7i		−	0.352025i	0.984388	−	0.176012i	$-0.0563199\pi$
$458$	9.62408e7	+	5.55647e7i	1.00176	+	0.578365i
$459$	5.57668e7	+	3.21970e7i	0.576684	+	0.332949i
$460$	1.55687e8	+	8.98861e7i	1.59948	+	0.923462i
$461$	1.41112e7	+	2.44413e7i	0.144033	+	0.249472i	0.929012	−	0.370051i	$-0.120660\pi$
$461$	1.41112e7	+	2.44413e7i	0.144033	+	0.249472i	−0.784979	+	0.619522i	$0.787326\pi$
$462$		−	1.08364e8i		−	1.09890i
$463$	1.46789e8	−	8.47487e7i	1.47894	−	0.853867i	0.479224	−	0.877692i	$-0.340918\pi$
$463$	1.46789e8	−	8.47487e7i	1.47894	−	0.853867i	0.999716	+	0.0238258i	$0.00758469\pi$
$464$	4.15629e7	+	2.39964e7i	0.416056	+	0.240210i
$465$	−7.65122e7			−0.760977
$466$	−8.96620e7	+	1.55299e8i	−0.886034	+	1.53466i
$467$	8.43466e7	−	4.86975e7i	0.828165	−	0.478141i	−0.0250587	−	0.999686i	$-0.507977\pi$
$467$	8.43466e7	−	4.86975e7i	0.828165	−	0.478141i	0.853224	+	0.521544i	$0.174644\pi$
$468$	−4.40512e7	−	7.62988e7i	−0.429754	−	0.744356i
$469$			1.00182e8i			0.971118i
$470$	1.11130e8	+	1.92483e8i	1.07038	+	1.85395i
$471$	1.38710e7			0.132753
$472$			2.51264e8i			2.38949i
$473$	−9.27588e7	+	8.36085e6i	−0.876540	+	0.0790073i
$474$	−1.87463e8			−1.76028
$475$			6.77437e7i			0.632103i
$476$	1.56693e8	−	9.04668e7i	1.45288	−	0.838819i
$477$	9.97572e7			0.919155
$478$	−2.89527e8	+	1.67158e8i	−2.65097	+	1.53054i
$479$	−9.55930e7	−	1.65572e8i	−0.869800	−	1.50654i	−0.862201	−	0.506567i	$-0.830914\pi$
$479$	−9.55930e7	−	1.65572e8i	−0.869800	−	1.50654i	−0.00759931	−	0.999971i	$-0.502419\pi$
$480$	−1.06853e8	−	6.16914e7i	−0.966188	−	0.557829i
$481$			3.33490e7i			0.299673i
$482$	4.18675e7	−	7.25166e7i	0.373883	−	0.647584i
$483$	4.48811e7	+	7.77363e7i	0.398311	+	0.689895i
$484$	6.61140e7			0.583119
$485$	5.72859e7	−	3.30740e7i	0.502137	−	0.289909i
$486$	−1.04252e8	+	1.80570e8i	−0.908188	+	1.57303i
$487$	8.46455e7	−	1.46610e8i	0.732853	−	1.26934i	−0.222806	−	0.974863i	$-0.571521\pi$
$487$	8.46455e7	−	1.46610e8i	0.732853	−	1.26934i	0.955659	−	0.294476i	$-0.0951452\pi$
$488$	−2.36477e8	+	4.09590e8i	−2.03484	+	3.52444i
$489$	8.21771e7			0.702788
$490$	471861.	−	817287.i	0.00401075	−	0.00694682i
$491$	−1.42452e8	−	8.22450e7i	−1.20344	−	0.694808i	−0.242124	−	0.970245i	$-0.577844\pi$
$491$	−1.42452e8	−	8.22450e7i	−1.20344	−	0.694808i	−0.961319	+	0.275437i	$0.911177\pi$
$492$	−6.85398e7	+	3.95715e7i	−0.575503	+	0.332267i
$493$	1.03795e7	−	5.99260e6i	0.0866234	−	0.0500121i
$494$	−1.29637e8			−1.07534
$495$		−	3.58554e7i		−	0.295624i
$496$	−3.71221e8	−	6.42973e8i	−3.04220	−	5.26924i
$497$	−9.95022e7	−	1.72343e8i	−0.810519	−	1.40386i
$498$	2.54320e7	−	4.40496e7i	0.205917	−	0.356660i
$499$	−2.20603e6	−	1.27365e6i	−0.0177546	−	0.0102506i	0.491096	−	0.871105i	$-0.336596\pi$
$499$	−2.20603e6	−	1.27365e6i	−0.0177546	−	0.0102506i	−0.508851	+	0.860855i	$0.669930\pi$
$500$		−	3.15416e8i		−	2.52332i
$501$	−1.18078e8	−	6.81725e7i	−0.938981	−	0.542121i
$502$	−5.18350e7	−	2.99269e7i	−0.409743	−	0.236565i
$503$	−8.97203e7	−	5.18001e7i	−0.704996	−	0.407030i	0.104209	−	0.994555i	$-0.466769\pi$
$503$	−8.97203e7	−	5.18001e7i	−0.704996	−	0.407030i	−0.809206	+	0.587526i	$0.800102\pi$
$504$	1.09723e8	+	1.90045e8i	0.857046	+	1.48445i
$505$		−	7.33726e7i		−	0.569718i
$506$	2.25954e8	−	1.30455e8i	1.74409	−	1.00695i
$507$	4.88071e7	+	2.81788e7i	0.374506	+	0.216221i
$508$	3.86716e8			2.94986
$509$	−4.89545e7	+	8.47916e7i	−0.371227	+	0.642983i	−0.989755	−	0.142780i	$-0.954396\pi$
$509$	−4.89545e7	+	8.47916e7i	−0.371227	+	0.642983i	0.618528	+	0.785763i	$0.287729\pi$
$510$	−5.45858e7	+	3.15151e7i	−0.411500	+	0.237579i
$511$	−1.90502e6	−	3.29959e6i	−0.0142770	−	0.0247284i
$512$			5.46169e7i			0.406927i
$513$	6.75568e7	+	1.17012e8i	0.500400	+	0.866718i
$514$	−1.14692e8			−0.844588
$515$			9.17527e7i			0.671733i
$516$	−1.90890e8	+	1.34411e8i	−1.38942	+	0.978332i
$517$	2.32636e8			1.68347
$518$		−	1.35419e8i		−	0.974293i
$519$	4.21770e7	−	2.43509e7i	0.301699	−	0.174186i
$520$	1.45959e8			1.03806
$521$	−1.33581e7	+	7.71230e6i	−0.0944565	+	0.0545345i	−0.546484	−	0.837469i	$-0.684034\pi$
$521$	−1.33581e7	+	7.71230e6i	−0.0944565	+	0.0545345i	0.452028	+	0.892004i	$0.350701\pi$
$522$	1.18490e7	+	2.05230e7i	0.0833045	+	0.144288i
$523$	3.74560e7	+	2.16252e7i	0.261828	+	0.151167i	0.625168	−	0.780490i	$-0.285030\pi$
$523$	3.74560e7	+	2.16252e7i	0.261828	+	0.151167i	−0.363340	+	0.931657i	$0.618364\pi$
$524$		−	3.96036e7i		−	0.275258i
$525$	3.10435e7	−	5.37688e7i	0.214532	−	0.371580i
$526$	7.09678e7	+	1.22920e8i	0.487646	+	0.844627i
$527$	−1.85410e8			−1.26678
$528$	−2.28784e8	+	1.32088e8i	−1.55426	+	0.897352i
$529$	−3.40431e7	+	5.89643e7i	−0.229965	+	0.398311i
$530$	−1.34715e8	+	2.33333e8i	−0.904874	+	1.56729i
$531$	−3.38376e7	+	5.86084e7i	−0.226004	+	0.391450i
$532$	3.79641e8			2.52138
$533$	1.73081e7	−	2.99785e7i	0.114306	−	0.197983i
$534$	−1.13845e8	−	6.57286e7i	−0.747637	−	0.431649i
$535$	4.99975e6	−	2.88660e6i	0.0326503	−	0.0188506i
$536$	3.87764e8	−	2.23875e8i	2.51810	−	1.45383i
$537$	1.86897e8			1.20692
$538$		−	4.54798e7i		−	0.292060i
$539$	−493889.	−	855441.i	−0.00315401	−	0.00546290i
$540$	−1.24002e8	−	2.14778e8i	−0.787496	−	1.36398i
$541$	1.36950e8	−	2.37205e8i	0.864911	−	1.49807i	−0.00222366	−	0.999998i	$-0.500708\pi$
$541$	1.36950e8	−	2.37205e8i	0.864911	−	1.49807i	0.867135	−	0.498073i	$-0.165959\pi$
$542$	1.63928e7	+	9.46436e6i	0.102957	+	0.0594420i
$543$			2.04048e8i			1.27448i
$544$	−2.58933e8	−	1.49495e8i	−1.60839	−	0.928603i
$545$	6.62505e7	+	3.82498e7i	0.409261	+	0.236287i
$546$	1.02894e8	+	5.94059e7i	0.632139	+	0.364966i
$547$	−3.66334e7	−	6.34509e7i	−0.223828	−	0.387682i	0.732139	−	0.681155i	$-0.238522\pi$
$547$	−3.66334e7	−	6.34509e7i	−0.223828	−	0.387682i	−0.955967	+	0.293473i	$0.905189\pi$
$548$			2.26706e8i			1.37759i
$549$	−1.10319e8	+	6.36924e7i	−0.666701	+	0.384920i
$550$	−1.56289e8	−	9.02333e7i	−0.939375	−	0.542349i
$551$	2.51478e7			0.150330
$552$	2.00590e8	−	3.47432e8i	1.19259	−	2.06563i
$553$	−2.07950e8	+	1.20060e8i	−1.22965	+	0.709941i
$554$	2.55169e8	+	4.41965e8i	1.50071	+	2.59931i
$555$			3.40218e7i			0.199011i
$556$	−9.42370e7	−	1.63223e8i	−0.548273	−	0.949637i
$557$	1.01404e8			0.586799			0.293400	−	0.955990i	$-0.405213\pi$
$557$	1.01404e8			0.586799			0.293400	+	0.955990i	$0.405213\pi$
$558$		−	3.66604e8i		−	2.11006i
$559$	4.29123e7	−	9.26602e7i	0.245667	−	0.530466i
$560$	−3.23289e8			−1.84089
$561$			6.59728e7i			0.373660i
$562$	3.29352e7	−	1.90152e7i	0.185546	−	0.107125i
$563$	4.67884e7			0.262188			0.131094	−	0.991370i	$-0.458151\pi$
$563$	4.67884e7			0.262188			0.131094	+	0.991370i	$0.458151\pi$
$564$	5.05028e8	−	2.91578e8i	2.81500	−	1.62524i
$565$	−4.41154e7	−	7.64102e7i	−0.244594	−	0.423649i
$566$	3.05408e8	+	1.76328e8i	1.68435	+	0.972458i
$567$		−	1.98483e7i		−	0.108886i
$568$	−4.44712e8	+	7.70263e8i	−2.42680	+	4.20334i
$569$	−4.07982e7	−	7.06646e7i	−0.221465	−	0.383588i	0.733788	−	0.679378i	$-0.237750\pi$
$569$	−4.07982e7	−	7.06646e7i	−0.221465	−	0.383588i	−0.955253	+	0.295790i	$0.904417\pi$
$570$	−1.32252e8			−0.714132
$571$	1.97450e8	−	1.13998e8i	1.06059	−	0.612333i	0.134996	−	0.990846i	$-0.456898\pi$
$571$	1.97450e8	−	1.13998e8i	1.06059	−	0.612333i	0.925596	+	0.378513i	$0.123564\pi$
$572$	1.24530e8	−	2.15692e8i	0.665405	−	1.15252i
$573$	1.02582e8	−	1.77677e8i	0.545265	−	0.944427i
$574$	−7.02824e7	+	1.21733e8i	−0.371630	+	0.643682i
$575$	1.49488e8			0.786325
$576$	1.27002e8	−	2.19974e8i	0.664575	−	1.15108i
$577$	1.63107e8	+	9.41701e7i	0.849075	+	0.490214i	0.860339	−	0.509723i	$-0.170252\pi$
$577$	1.63107e8	+	9.41701e7i	0.849075	+	0.490214i	−0.0112636	+	0.999937i	$0.503585\pi$
$578$	1.84431e8	−	1.06481e8i	0.955102	−	0.551429i
$579$	5.54488e7	−	3.20134e7i	0.285665	−	0.164929i
$580$	−4.61594e7			−0.236579
$581$		−	6.51514e7i		−	0.332197i
$582$	−1.20327e8	−	2.08412e8i	−0.610369	−	1.05719i
$583$	1.41004e8	+	2.44226e8i	0.711583	+	1.23250i
$584$	−8.51422e6	+	1.47471e7i	−0.0427471	+	0.0740401i
$585$	3.40456e7	+	1.96562e7i	0.170056	+	0.0981821i
$586$		−	2.70080e8i		−	1.34215i
$587$	3.75175e7	+	2.16607e7i	0.185490	+	0.107092i	0.589869	−	0.807499i	$-0.299179\pi$
$587$	3.75175e7	+	2.16607e7i	0.185490	+	0.107092i	−0.404380	+	0.914591i	$0.632513\pi$
$588$	−2.14436e6	−	1.23805e6i	−0.0105479	−	0.00608982i
$589$	−3.36912e8	−	1.94517e8i	−1.64881	−	0.951942i
$590$	−9.13905e7	−	1.58293e8i	−0.444985	−	0.770736i
$591$			2.02783e8i			0.982358i
$592$	−2.85903e8	+	1.65066e8i	−1.37802	+	0.795598i
$593$	7.99031e6	+	4.61321e6i	0.0383177	+	0.0221227i	0.519036	−	0.854752i	$-0.326291\pi$
$593$	7.99031e6	+	4.61321e6i	0.0383177	+	0.0221227i	−0.480719	+	0.876875i	$0.659624\pi$
$594$	−3.59937e8			−1.71738
$595$	−4.03675e7	+	6.99185e7i	−0.191638	+	0.331926i
$596$	1.21657e8	−	7.02385e7i	0.574641	−	0.331769i
$597$	−4.97786e7	−	8.62191e7i	−0.233948	−	0.405210i
$598$			2.86065e8i			1.33771i
$599$	−3.94924e7	−	6.84028e7i	−0.183752	−	0.318268i	0.759403	−	0.650620i	$-0.225491\pi$
$599$	−3.94924e7	−	6.84028e7i	−0.183752	−	0.318268i	−0.943155	+	0.332352i	$0.892158\pi$
$600$	−2.77489e8			−1.28467
$601$		−	82367.9i		−	0.000379432i	−1.00000		0.000189716i	$-0.999940\pi$
$601$		−	82367.9i		−	0.000379432i	1.00000		0.000189716i	$-6.03885e-5\pi$
$602$	−1.74252e8	+	3.76261e8i	−0.798709	+	1.72465i
$603$	1.20597e8			0.550026
$604$			6.54054e8i			2.96827i
$605$	−2.55486e7	+	1.47505e7i	−0.115372	+	0.0666101i
$606$	−2.66937e8			−1.19947
$607$	−1.09940e7	+	6.34736e6i	−0.0491573	+	0.0283810i	−0.524377	−	0.851486i	$-0.675702\pi$
$607$	−1.09940e7	+	6.34736e6i	−0.0491573	+	0.0283810i	0.475220	+	0.879867i	$0.342368\pi$
$608$	−3.13675e8	−	5.43302e8i	−1.39563	−	2.41730i
$609$	−1.99600e7	−	1.15239e7i	−0.0883709	−	0.0510210i
$610$		−	3.44048e8i		−	1.51576i
$611$	−1.27533e8	+	2.20894e8i	−0.559112	+	0.968411i
$612$	−1.08902e8	−	1.88623e8i	−0.475094	−	0.822887i
$613$	5.50832e7			0.239132			0.119566	−	0.992826i	$-0.461850\pi$
$613$	5.50832e7			0.239132			0.119566	+	0.992826i	$0.461850\pi$
$614$	−3.68926e8	+	2.13000e8i	−1.59380	+	0.920182i
$615$	1.76573e7	−	3.05834e7i	0.0759100	−	0.131480i
$616$	−3.10179e8	+	5.37246e8i	−1.32700	+	2.29843i
$617$	2.17210e8	−	3.76218e8i	0.924748	−	1.60171i	0.132783	−	0.991145i	$-0.457609\pi$
$617$	2.17210e8	−	3.76218e8i	0.924748	−	1.60171i	0.791965	−	0.610566i	$-0.209058\pi$
$618$	3.33806e8			1.41426
$619$	−5.37800e7	+	9.31497e7i	−0.226751	+	0.392744i	−0.956843	−	0.290604i	$-0.906144\pi$
$619$	−5.37800e7	+	9.31497e7i	−0.226751	+	0.392744i	0.730092	+	0.683348i	$0.239477\pi$
$620$	6.18411e8	+	3.57040e8i	2.59479	+	1.49810i
$621$	2.58206e8	−	1.49075e8i	1.07818	−	0.622488i
$622$	−5.97232e8	+	3.44812e8i	−2.48183	+	1.43288i
$623$	−1.68382e8			−0.696357
$624$		−	2.89648e8i		−	1.19211i
$625$	−9.06997e6	−	1.57096e7i	−0.0371506	−	0.0643467i
$626$	2.25806e8	+	3.91107e8i	0.920475	+	1.59431i
$627$	−6.92132e7	+	1.19881e8i	−0.280793	+	0.486347i
$628$	−1.12113e8	−	6.47284e7i	−0.452665	−	0.261346i
$629$			8.24440e7i			0.331289i
$630$	−1.38247e8	−	7.98172e7i	−0.552886	−	0.319209i
$631$	−1.07504e8	−	6.20672e7i	−0.427893	−	0.247044i	0.270556	−	0.962704i	$-0.412793\pi$
$631$	−1.07504e8	−	6.20672e7i	−0.427893	−	0.247044i	−0.698448	+	0.715660i	$0.746126\pi$
$632$	9.29404e8	+	5.36592e8i	3.68174	+	2.12565i
$633$	−6.74088e7	−	1.16755e8i	−0.265770	−	0.460327i
$634$			8.50266e7i			0.333647i
$635$	−1.49439e8	+	8.62789e7i	−0.583638	+	0.336964i
$636$	6.12208e8	+	3.53459e8i	2.37973	+	1.37394i
$637$	1.08302e6			0.00419002
$638$	−3.34963e7	+	5.80173e7i	−0.128984	+	0.223406i
$639$	−2.07462e8	+	1.19778e8i	−0.795125	+	0.459066i
$640$	1.20425e8	+	2.08582e8i	0.459385	+	0.795678i
$641$		−	2.46684e8i		−	0.936627i	−0.883562	−	0.468313i	$-0.844862\pi$
$641$		−	2.46684e8i		−	0.936627i	0.883562	−	0.468313i	$-0.155138\pi$
$642$	−1.05018e7	−	1.81896e7i	−0.0396878	−	0.0687413i
$643$	1.95575e8			0.735665			0.367833	−	0.929892i	$-0.380100\pi$
$643$	1.95575e8			0.735665			0.367833	+	0.929892i	$0.380100\pi$
$644$		−	8.37741e8i		−	3.13655i
$645$	4.37780e7	−	9.45296e7i	0.163146	−	0.352281i
$646$	−3.20483e8			−1.18880
$647$		−	1.63445e8i		−	0.603475i	−0.953391	−	0.301738i	$-0.902433\pi$
$647$		−	1.63445e8i		−	0.603475i	0.953391	−	0.301738i	$-0.0975667\pi$
$648$	−7.68244e7	+	4.43546e7i	−0.282341	+	0.163010i
$649$	−1.91314e8			−0.699862
$650$	1.71357e8	−	9.89332e7i	0.623968	−	0.360248i
$651$	1.78274e8	+	3.08779e8i	0.646167	+	1.11919i
$652$	−6.64198e8	−	3.83475e8i	−2.39638	−	1.38355i
$653$		−	2.18471e8i		−	0.784611i	−0.919835	−	0.392305i	$-0.871678\pi$
$653$		−	2.18471e8i		−	0.784611i	0.919835	−	0.392305i	$-0.128322\pi$
$654$	1.39157e8	−	2.41026e8i	0.497474	−	0.861650i
$655$	8.83582e6	+	1.53041e7i	0.0314429	+	0.0544608i
$656$	3.42678e8			1.21388
$657$	−3.97196e6	+	2.29321e6i	−0.0140058	+	0.00808626i
$658$	5.17868e8	−	8.96974e8i	1.81778	−	3.14849i
$659$	−1.22837e8	+	2.12759e8i	−0.429212	+	0.743417i	−0.996803	−	0.0798936i	$-0.974542\pi$
$659$	−1.22837e8	+	2.12759e8i	−0.429212	+	0.743417i	0.567592	+	0.823310i	$0.307875\pi$
$660$	1.27042e8	−	2.20044e8i	0.441893	−	0.765381i
$661$	−3.08826e7			−0.106933			−0.0534663	−	0.998570i	$-0.517027\pi$
$661$	−3.08826e7			−0.106933			−0.0534663	+	0.998570i	$0.517027\pi$
$662$	−6.69819e7	+	1.16016e8i	−0.230879	+	0.399893i
$663$	−6.26427e7	−	3.61668e7i	−0.214946	−	0.124099i
$664$	−2.52174e8	+	1.45593e8i	−0.861382	+	0.497319i
$665$	−1.46705e8	+	8.47004e7i	−0.498863	+	0.288019i
$666$	−1.63014e8			−0.551824
$667$		−	5.54927e7i		−	0.187007i
$668$	6.36247e8	+	1.10201e9i	2.13450	+	3.69706i
$669$	−1.54615e7	−	2.67802e7i	−0.0516386	−	0.0894407i
$670$	−1.62857e8	+	2.82077e8i	−0.541480	+	0.937871i
$671$	−3.11864e8	−	1.80055e8i	−1.03228	−	0.595988i
$672$			5.74965e8i			1.89467i
$673$	3.13802e8	+	1.81174e8i	1.02946	+	0.594360i	0.916830	−	0.399277i	$-0.130739\pi$
$673$	3.13802e8	+	1.81174e8i	1.02946	+	0.594360i	0.112632	+	0.993637i	$0.464072\pi$
$674$	4.54060e8	+	2.62151e8i	1.48297	+	0.856195i
$675$	−1.78597e8	−	1.03113e8i	−0.580713	−	0.335275i
$676$	−2.62990e8	−	4.55511e8i	−0.851331	−	1.47455i
$677$			5.27995e7i			0.170162i	0.996374	+	0.0850812i	$0.0271150\pi$
$677$			5.27995e7i			0.170162i	−0.996374	+	0.0850812i	$0.972885\pi$
$678$	−2.77988e8	+	1.60496e8i	−0.891943	+	0.514963i
$679$	−2.66953e8	−	1.54125e8i	−0.852757	−	0.492339i
$680$	3.60834e8			1.14757
$681$	1.18767e7	−	2.05710e7i	0.0376057	−	0.0651350i
$682$	8.97522e8	−	5.18184e8i	2.82938	−	1.63355i
$683$	1.36124e8	+	2.35773e8i	0.427239	+	0.740000i	0.996627	−	0.0820691i	$-0.0261528\pi$
$683$	1.36124e8	+	2.35773e8i	0.427239	+	0.740000i	−0.569387	+	0.822069i	$0.692819\pi$
$684$		−	4.57002e8i		−	1.42807i
$685$	−5.05796e7	−	8.76065e7i	−0.157363	−	0.272562i
$686$	6.09176e8			1.88699
$687$			1.30105e8i			0.401258i
$688$	1.00679e9	−	9.07470e7i	3.09152	−	0.278655i
$689$	−3.09198e8			−0.945320
$690$			2.91837e8i			0.888368i
$691$	1.85895e8	−	1.07327e8i	0.563423	−	0.325292i	−0.191095	−	0.981572i	$-0.561204\pi$
$691$	1.85895e8	−	1.07327e8i	0.563423	−	0.325292i	0.754518	+	0.656279i	$0.227871\pi$
$692$	−4.54529e8			−1.37165
$693$	−1.44701e8	+	8.35433e7i	−0.434783	+	0.251022i
$694$	−1.93996e8	−	3.36011e8i	−0.580382	−	1.00525i
$695$	7.28324e7	+	4.20498e7i	0.216955	+	0.125259i
$696$			1.03009e8i			0.305527i
$697$	4.27885e7	−	7.41118e7i	0.126365	−	0.218871i
$698$	−2.58640e8	−	4.47978e8i	−0.760554	−	1.31732i
$699$	−2.09944e8			−0.614712
$700$	−5.01819e8	+	2.89725e8i	−1.46303	+	0.844680i
$701$	1.44259e7	−	2.49864e7i	0.0418783	−	0.0725353i	−0.844327	−	0.535829i	$-0.819999\pi$
$701$	1.44259e7	−	2.49864e7i	0.0418783	−	0.0725353i	0.886205	+	0.463294i	$0.153332\pi$
$702$	1.97320e8	−	3.41769e8i	0.570375	−	0.987919i
$703$	−8.64934e7	+	1.49811e8i	−0.248953	+	0.431199i
$704$	7.18056e8			2.05798
$705$	−1.30106e8	+	2.25350e8i	−0.371304	+	0.643118i
$706$	−5.70160e8	−	3.29182e8i	−1.62025	−	0.935453i
$707$	−2.96109e8	+	1.70959e8i	−0.837903	+	0.483763i
$708$	−4.15322e8	+	2.39786e8i	−1.17027	+	0.675654i
$709$	3.56501e8			1.00028			0.500141	−	0.865944i	$-0.333281\pi$
$709$	3.56501e8			1.00028			0.500141	+	0.865944i	$0.333281\pi$
$710$		−	6.47007e8i		−	1.80773i
$711$	1.44525e8	+	2.50325e8i	0.402100	+	0.696458i
$712$	3.76281e8	+	6.51738e8i	1.04249	+	1.80565i
$713$	−4.29233e8	+	7.43454e8i	−1.18420	+	2.05109i
$714$	2.54371e8	+	1.46861e8i	0.698832	+	0.403471i
$715$			1.11134e8i			0.304039i
$716$	−1.51060e9	−	8.72145e8i	−4.11538	−	2.37602i
$717$	−3.38965e8	−	1.95701e8i	−0.919595	−	0.530929i
$718$	−4.91155e8	−	2.83568e8i	−1.32692	−	0.766098i
$719$	9.40289e7	+	1.62863e8i	0.252973	+	0.438163i	0.964343	−	0.264655i	$-0.0852582\pi$
$719$	9.40289e7	+	1.62863e8i	0.252973	+	0.438163i	−0.711370	+	0.702818i	$0.751925\pi$
$720$			3.89167e8i			1.04265i
$721$	3.70285e8	−	2.13784e8i	0.987940	−	0.570388i
$722$	3.49276e7	+	2.01655e7i	0.0928020	+	0.0535792i
$723$	9.80329e7			0.259392
$724$	9.52180e8	−	1.64922e9i	2.50901	−	4.34574i
$725$	−3.32409e7	+	1.91917e7i	−0.0872287	+	0.0503615i
$726$	5.36637e7	+	9.29483e7i	0.140240	+	0.242902i
$727$			3.34772e8i			0.871257i	0.900127	+	0.435629i	$0.143474\pi$
$727$			3.34772e8i			0.871257i	−0.900127	+	0.435629i	$0.856526\pi$
$728$	−3.40085e8	−	5.89045e8i	−0.881442	−	1.52670i
$729$	−2.86141e8			−0.738581
$730$		−	1.23873e7i		−	0.0318425i
$731$	1.06086e8	−	2.29071e8i	0.271585	−	0.586432i
$732$	−9.02697e8			−2.30149
$733$		−	1.99155e8i		−	0.505685i	−0.967507	−	0.252843i	$-0.918635\pi$
$733$		−	1.99155e8i		−	0.505685i	0.967507	−	0.252843i	$-0.0813655\pi$
$734$	7.36682e8	−	4.25323e8i	1.86291	−	1.07555i
$735$	1.10486e6			0.00278258
$736$	−1.19889e9	+	6.92177e8i	−3.00708	+	1.73614i
$737$	1.70460e8	+	2.95245e8i	0.425814	+	0.737532i
$738$	1.46539e8	+	8.46041e7i	0.364572	+	0.210486i
$739$			6.49415e8i			1.60912i	0.593870	+	0.804561i	$0.297600\pi$
$739$			6.49415e8i			1.60912i	−0.593870	+	0.804561i	$0.702400\pi$
$740$	1.58761e8	−	2.74982e8i	0.391785	−	0.678592i
$741$	−7.58864e7	−	1.31439e8i	−0.186513	−	0.323050i
$742$	1.25555e9			3.07341
$743$	2.54313e8	−	1.46828e8i	0.620015	−	0.357966i	−0.156860	−	0.987621i	$-0.550137\pi$
$743$	2.54313e8	−	1.46828e8i	0.620015	−	0.357966i	0.776875	+	0.629655i	$0.216804\pi$
$744$	7.96771e8	−	1.38005e9i	1.93471	−	3.35101i
$745$	−3.13413e7	+	5.42848e7i	−0.0757964	+	0.131283i
$746$	1.64810e8	−	2.85459e8i	0.396978	−	0.687586i
$747$	−7.84275e7			−0.188151
$748$	3.07858e8	−	5.33226e8i	0.735608	−	1.27411i
$749$	−2.32989e7	−	1.34516e7i	−0.0554485	−	0.0320132i
$750$	4.43436e8	−	2.56018e8i	1.05111	−	0.606857i
$751$	−2.88020e8	+	1.66289e8i	−0.679992	+	0.392593i	−0.799852	−	0.600197i	$-0.795089\pi$
$751$	−2.88020e8	+	1.66289e8i	−0.679992	+	0.392593i	0.119860	+	0.992791i	$0.461755\pi$
$752$	−2.52499e9			−5.93753
$753$		−	7.00741e7i		−	0.164124i
$754$	−3.67259e7	−	6.36111e7i	−0.0856758	−	0.148395i
$755$	−1.45924e8	−	2.52748e8i	−0.339067	−	0.587281i
$756$	−5.77852e8	+	1.00087e9i	−1.33737	+	2.31639i
$757$	4.26340e8	+	2.46148e8i	0.982809	+	0.567425i	0.903117	−	0.429395i	$-0.141273\pi$
$757$	4.26340e8	+	2.46148e8i	0.982809	+	0.567425i	0.0796917	+	0.996820i	$0.474606\pi$
$758$			1.59053e8i			0.365203i
$759$	2.64537e8	+	1.52730e8i	0.605007	+	0.349301i
$760$	6.55680e8	+	3.78557e8i	1.49366	+	0.862364i
$761$	−2.12821e7	−	1.22872e7i	−0.0482903	−	0.0278804i	0.475660	−	0.879629i	$-0.342209\pi$
$761$	−2.12821e7	−	1.22872e7i	−0.0482903	−	0.0278804i	−0.523951	+	0.851749i	$0.675542\pi$
$762$	3.13891e8	+	5.43676e8i	0.709438	+	1.22878i
$763$		−	3.56489e8i		−	0.802550i
$764$	−1.65824e9	+	9.57388e8i	−3.71851	+	2.14688i
$765$	8.41661e7	+	4.85933e7i	0.187998	+	0.108541i
$766$	9.21977e8			2.05132
$767$	1.04880e8	−	1.81657e8i	0.232437	−	0.402593i
$768$	1.56199e8	−	9.01817e7i	0.344822	−	0.199083i
$769$	3.91166e8	+	6.77519e8i	0.860165	+	1.48985i	0.871769	+	0.489917i	$0.162973\pi$
$769$	3.91166e8	+	6.77519e8i	0.860165	+	1.48985i	−0.0116044	+	0.999933i	$0.503694\pi$
$770$		−	4.51277e8i		−	0.988487i
$771$	−6.71382e7	−	1.16287e8i	−0.146490	−	0.253727i
$772$	−5.97555e8			−1.29875
$773$		−	7.59054e8i		−	1.64337i	−0.569945	−	0.821683i	$-0.693035\pi$
$773$		−	7.59054e8i		−	1.64337i	0.569945	−	0.821683i	$-0.306965\pi$
$774$	4.52934e8	+	2.09760e8i	0.976814	+	0.452377i
$775$	5.93786e8			1.27563
$776$			1.37768e9i			2.94825i
$777$	1.37301e8	−	7.92710e7i	0.292693	−	0.168986i
$778$	−9.86707e8			−2.09532
$779$	1.55504e8	−	8.97802e7i	0.328949	−	0.189919i
$780$	1.39291e8	+	2.41260e8i	0.293522	+	0.508395i
$781$	−5.86483e8	−	3.38606e8i	−1.23112	−	0.710790i
$782$			7.07200e8i			1.47884i
$783$	−3.82775e7	+	6.62985e7i	−0.0797366	+	0.138108i
$784$	5.36057e6	+	9.28478e6i	0.0111240	+	0.0192674i
$785$	5.77653e7			0.119415
$786$	5.56778e7	−	3.21456e7i	0.114661	−	0.0661994i
$787$	3.99704e8	−	6.92308e8i	0.820001	−	1.42028i	−0.0856801	−	0.996323i	$-0.527306\pi$
$787$	3.99704e8	−	6.92308e8i	0.820001	−	1.42028i	0.905681	−	0.423960i	$-0.139360\pi$
$788$	9.46277e8	−	1.63900e9i	1.93393	−	3.34966i
$789$	−8.30858e7	+	1.43909e8i	−0.169159	+	0.292993i
$790$	−7.80682e8			−1.58341
$791$	−2.05578e8	+	3.56072e8i	−0.415383	+	0.719464i
$792$	6.46723e8	+	3.73386e8i	1.30180	+	0.751592i
$793$	3.41933e8	−	1.97415e8i	0.685679	−	0.395877i
$794$	−7.15185e8	+	4.12912e8i	−1.42875	+	0.824891i
$795$	−3.15436e8			−0.627783
$796$			9.29157e8i			1.84226i
$797$	4.63571e7	+	8.02928e7i	0.0915674	+	0.158599i	0.908171	−	0.418600i	$-0.137479\pi$
$797$	4.63571e7	+	8.02928e7i	0.0915674	+	0.158599i	−0.816603	+	0.577199i	$0.804146\pi$
$798$	3.08149e8	+	5.33729e8i	0.606390	+	1.05030i
$799$	−3.15282e8	+	5.46085e8i	−0.618101	+	1.07058i
$800$	8.29248e8	+	4.78767e8i	1.61963	+	0.935091i
$801$			2.02694e8i			0.394406i
$802$	−3.09987e8	−	1.78971e8i	−0.600924	−	0.346944i
$803$	−1.12285e7	−	6.48277e6i	−0.0216858	−	0.0125203i
$804$	7.40100e8	+	4.27297e8i	1.42404	+	0.822170i
$805$	1.86906e8	+	3.23730e8i	0.358290	+	0.620576i
$806$			1.13629e9i			2.17012i
$807$	4.61121e7	−	2.66228e7i	0.0877392	−	0.0506563i
$808$	1.32342e9	+	7.64077e8i	2.50879	+	1.44845i
$809$	−5.63117e8			−1.06354			−0.531769	−	0.846889i	$-0.678473\pi$
$809$	−5.63117e8			−1.06354			−0.531769	+	0.846889i	$0.678473\pi$
$810$	3.22656e7	−	5.58856e7i	0.0607133	−	0.105159i
$811$	4.50617e8	−	2.60164e8i	0.844783	−	0.487736i	−0.0141040	−	0.999901i	$-0.504490\pi$
$811$	4.50617e8	−	2.60164e8i	0.844783	−	0.487736i	0.858887	+	0.512165i	$0.171156\pi$
$812$	1.07552e8	+	1.86285e8i	0.200886	+	0.347944i
$813$			2.21609e7i			0.0412396i
$814$	−2.30415e8	−	3.99090e8i	−0.427206	−	0.739943i
$815$	3.42223e8			0.632174
$816$		−	7.16055e8i		−	1.31788i
$817$	4.33094e8	−	3.04953e8i	0.794174	−	0.559200i
$818$	1.48151e9			2.70673
$819$		−	1.83196e8i		−	0.333477i
$820$	−2.85431e8	+	1.64794e8i	−0.517678	+	0.298882i
$821$	2.09796e8			0.379113			0.189556	−	0.981870i	$-0.439295\pi$
$821$	2.09796e8			0.379113			0.189556	+	0.981870i	$0.439295\pi$
$822$	−3.18721e8	+	1.84014e8i	−0.573846	+	0.331310i
$823$	−1.75799e8	−	3.04493e8i	−0.315367	−	0.546232i	0.664148	−	0.747601i	$-0.268794\pi$
$823$	−1.75799e8	−	3.04493e8i	−0.315367	−	0.546232i	−0.979516	+	0.201369i	$0.935461\pi$
$824$	−1.65494e9	−	9.55480e8i	−2.95802	−	1.70781i
$825$		−	2.11282e8i		−	0.376271i
$826$	−4.25881e8	+	7.37648e8i	−0.755698	+	1.30891i
$827$	−2.95146e7	−	5.11208e7i	−0.0521820	−	0.0903819i	0.838755	−	0.544510i	$-0.183284\pi$
$827$	−2.95146e7	−	5.11208e7i	−0.0521820	−	0.0903819i	−0.890937	+	0.454128i	$0.849951\pi$
$828$	−1.00845e9			−1.77649
$829$	8.47059e8	−	4.89050e8i	1.48679	−	0.858399i	0.486905	−	0.873455i	$-0.338126\pi$
$829$	8.47059e8	−	4.89050e8i	1.48679	−	0.858399i	0.999887	+	0.0150556i	$0.00479252\pi$
$830$	1.05911e8	−	1.83443e8i	0.185228	−	0.320824i
$831$	−2.98740e8	+	5.17432e8i	−0.520583	+	0.901675i
$832$	−3.93644e8	+	6.81812e8i	−0.683493	+	1.18384i
$833$	2.67739e6			0.00463208
$834$	1.52981e8	−	2.64972e8i	0.263718	−	0.456774i
$835$	−4.91732e8	−	2.83902e8i	−0.844635	−	0.487650i
$836$	1.11883e9	−	6.45959e8i	1.91490	−	1.10557i
$837$	1.02563e9	−	5.92148e8i	1.74910	−	1.00984i
$838$	−3.87845e8			−0.659062
$839$			3.91723e8i			0.663274i	0.943407	+	0.331637i	$0.107601\pi$
$839$			3.91723e8i			0.663274i	−0.943407	+	0.331637i	$0.892399\pi$
$840$	−3.46947e8	−	6.00929e8i	−0.585362	−	1.01388i
$841$	−2.90287e8	−	5.02792e8i	−0.488023	−	0.845280i
$842$	3.96052e8	−	6.85983e8i	0.663462	−	1.14915i
$843$	3.85590e7	+	2.22621e7i	0.0643641	+	0.0371606i
$844$			1.25824e9i			2.09284i
$845$	2.03255e8	+	1.17349e8i	0.336877	+	0.194496i
$846$	−1.07975e9	−	6.23396e8i	−1.78326	−	1.02956i
$847$	1.19057e8	+	6.87374e7i	0.195931	+	0.113121i
$848$	−1.53043e9	−	2.65078e9i	−2.50972	−	4.34696i
$849$			4.12872e8i			0.674672i
$850$	4.23623e8	−	2.44579e8i	0.689799	−	0.398256i
$851$	3.30583e8	+	1.90862e8i	0.536403	+	0.309693i
$852$	−1.69759e9			−2.74482
$853$	−8.11167e7	+	1.40498e8i	−0.130696	+	0.226373i	−0.923945	−	0.382525i	$-0.875055\pi$
$853$	−8.11167e7	+	1.40498e8i	−0.130696	+	0.226373i	0.793249	+	0.608898i	$0.208388\pi$
$854$	−1.38847e9	+	8.01635e8i	−2.22927	+	1.28707i
$855$	1.01960e8	+	1.76600e8i	0.163129	+	0.282548i
$856$			1.20240e8i			0.191703i
$857$	−1.99411e8	−	3.45390e8i	−0.316816	−	0.548741i	0.663006	−	0.748614i	$-0.269280\pi$
$857$	−1.99411e8	−	3.45390e8i	−0.316816	−	0.548741i	−0.979822	+	0.199873i	$0.935947\pi$
$858$	4.04317e8			0.640118
$859$			4.01350e7i			0.0633204i	0.999499	+	0.0316602i	$0.0100794\pi$
$859$			4.01350e7i			0.0633204i	−0.999499	+	0.0316602i	$0.989921\pi$
$860$	−7.94954e8	+	5.59750e8i	−1.24982	+	0.880032i
$861$	−1.64567e8			−0.257829
$862$		−	1.19764e9i		−	1.86984i
$863$	−6.66112e8	+	3.84580e8i	−1.03637	+	0.598349i	−0.918803	−	0.394716i	$-0.870843\pi$
$863$	−6.66112e8	+	3.84580e8i	−1.03637	+	0.598349i	−0.117567	+	0.993065i	$0.537510\pi$
$864$	1.90978e9			2.96103
$865$	1.75645e8	−	1.01408e8i	0.271385	−	0.156684i
$866$	8.49110e8	+	1.47070e9i	1.30741	+	2.26449i
$867$	2.15923e8	+	1.24663e8i	0.331315	+	0.191285i
$868$		−	3.32762e9i		−	5.08832i
$869$	−4.08564e8	+	7.07653e8i	−0.622588	+	1.07835i
$870$	−3.74668e7	−	6.48945e7i	−0.0568970	−	0.0985485i
$871$	−3.73790e8			−0.565683
$872$	−1.37982e9	+	7.96640e8i	−2.08100	+	1.20147i
$873$	−1.85532e8	+	3.21351e8i	−0.278854	+	0.482988i
$874$	−7.41935e8	+	1.28507e9i	−1.11130	+	1.92483i
$875$	3.27931e8	−	5.67993e8i	0.489507	−	0.847850i
$876$	−3.25011e7			−0.0483488
$877$	4.76846e8	−	8.25921e8i	0.706934	−	1.22445i	−0.259055	−	0.965863i	$-0.583411\pi$
$877$	4.76846e8	−	8.25921e8i	0.706934	−	1.22445i	0.965989	−	0.258584i	$-0.0832557\pi$
$878$	1.21004e9	+	6.98616e8i	1.78779	+	1.03218i
$879$	2.73835e8	−	1.58099e8i	0.403202	−	0.232789i
$880$	−9.52761e8	+	5.50077e8i	−1.39809	+	0.807189i
$881$	5.98549e7			0.0875330			0.0437665	−	0.999042i	$-0.486064\pi$
$881$	5.98549e7			0.0875330			0.0437665	+	0.999042i	$0.486064\pi$
$882$			5.29390e6i			0.00771561i
$883$	−2.09171e8	−	3.62295e8i	−0.303822	−	0.526235i	0.673176	−	0.739482i	$-0.264929\pi$
$883$	−2.09171e8	−	3.62295e8i	−0.303822	−	0.526235i	−0.976998	+	0.213247i	$0.931596\pi$
$884$	3.37541e8	+	5.84638e8i	0.488618	+	0.846311i
$885$	1.06996e8	−	1.85322e8i	0.154361	−	0.267361i
$886$	1.84641e9	+	1.06603e9i	2.65478	+	1.53274i
$887$		−	1.03021e9i		−	1.47624i	−0.674671	−	0.738118i	$-0.735715\pi$
$887$		−	1.03021e9i		−	1.47624i	0.674671	−	0.738118i	$-0.264285\pi$
$888$	−6.13650e8	−	3.54291e8i	−0.876358	−	0.505966i
$889$	6.96390e8	+	4.02061e8i	0.991167	+	0.572251i
$890$	−4.74104e8	−	2.73724e8i	−0.672517	−	0.388278i
$891$	−3.37718e7	−	5.84945e7i	−0.0477443	−	0.0826956i
$892$			2.88602e8i			0.406635i
$893$	−1.14581e9	+	6.61536e8i	−1.60901	+	0.928964i
$894$	1.97494e8	+	1.14023e8i	0.276402	+	0.159580i
$895$	7.78326e8			1.08566
$896$	5.61182e8	−	9.71996e8i	0.780153	−	1.35127i
$897$	−2.90042e8	+	1.67456e8i	−0.401868	+	0.232019i
$898$	4.50894e8	+	7.80972e8i	0.622653	+	1.07847i
$899$		−	2.20425e8i		−	0.303376i
$900$	3.48764e8	+	6.04077e8i	0.478414	+	0.828637i
$901$	−7.64387e8			−1.04505
$902$			4.78342e8i			0.651806i
$903$	−4.83495e8	+	4.35800e7i	−0.656643	+	0.0591867i
$904$	1.83761e9			2.48742
$905$			8.49750e8i			1.14643i
$906$	−9.19521e8	+	5.30886e8i	−1.23645	+	0.713866i
$907$	−1.48221e9			−1.98650			−0.993252	−	0.115979i	$-0.962999\pi$
$907$	−1.48221e9			−1.98650			−0.993252	+	0.115979i	$0.962999\pi$
$908$	−1.91987e8	+	1.10844e8i	−0.256457	+	0.148066i
$909$	2.05796e8	+	3.56448e8i	0.273996	+	0.474575i
$910$	4.28498e8	+	2.47394e8i	0.568624	+	0.328295i
$911$			5.44712e7i			0.0720463i	0.999351	+	0.0360231i	$0.0114690\pi$
$911$			5.44712e7i			0.0720463i	−0.999351	+	0.0360231i	$0.988531\pi$
$912$	7.51226e8	−	1.30116e9i	0.990344	−	1.71533i
$913$	−1.10855e8	−	1.92007e8i	−0.145661	−	0.252292i
$914$	−5.09044e8			−0.666679
$915$	3.48831e8	−	2.01398e8i	0.455357	−	0.262900i
$916$	6.07128e8	−	1.05158e9i	0.789940	−	1.36822i
$917$	4.11750e7	−	7.13173e7i	0.0533981	−	0.0924883i
$918$	4.87808e8	−	8.44908e8i	0.630552	−	1.09215i
$919$	5.98262e8			0.770805			0.385403	−	0.922749i	$-0.374063\pi$
$919$	5.98262e8			0.770805			0.385403	+	0.922749i	$0.374063\pi$
$920$	8.35350e8	−	1.44687e9i	1.07277	−	1.85808i
$921$	−4.31921e8	−	2.49370e8i	−0.552874	−	0.319202i
$922$	3.70304e8	−	2.13795e8i	0.472460	−	0.272775i
$923$	6.43029e8	−	3.71253e8i	0.817759	−	0.472133i
$924$	−1.18404e9			−1.50089
$925$		−	2.64032e8i		−	0.333604i
$926$	−1.28400e9	−	2.22396e9i	−1.61709	−	2.80088i
$927$	−2.57348e8	−	4.45740e8i	−0.323059	−	0.559554i
$928$	1.77727e8	−	3.07833e8i	0.222388	−	0.385186i
$929$	3.39213e8	+	1.95845e8i	0.423083	+	0.244267i	0.696396	−	0.717658i	$-0.254786\pi$
$929$	3.39213e8	+	1.95845e8i	0.423083	+	0.244267i	−0.273312	+	0.961925i	$0.588119\pi$
$930$			1.15922e9i			1.44117i
$931$	4.86514e6	+	2.80889e6i	0.00602902	+	0.00348086i
$932$	1.69688e9	+	9.79693e8i	2.09606	+	1.21016i
$933$	−6.99211e8	−	4.03690e8i	−0.860921	−	0.497053i
$934$	−7.37804e8	−	1.27791e9i	−0.905524	−	1.56841i
$935$			2.74741e8i			0.336116i
$936$	−7.09077e8	+	4.09386e8i	−0.864701	+	0.499235i
$937$	−9.21333e8	−	5.31932e8i	−1.11995	−	0.646602i	−0.178560	−	0.983929i	$-0.557144\pi$
$937$	−9.21333e8	−	5.31932e8i	−1.11995	−	0.646602i	−0.941388	+	0.337327i	$0.890477\pi$
$938$	1.51783e9			1.83914
$939$	−2.64363e8	+	4.57890e8i	−0.319303	+	0.553050i
$940$	2.10317e9	−	1.21427e9i	2.53216	−	1.46194i
$941$	−6.36329e8	−	1.10215e9i	−0.763682	−	1.32274i	−0.940940	−	0.338572i	$-0.890056\pi$
$941$	−6.36329e8	−	1.10215e9i	−0.763682	−	1.32274i	0.177258	−	0.984164i	$-0.443277\pi$
$942$		−	2.10156e8i		−	0.251414i
$943$	−1.98115e8	−	3.43145e8i	−0.236256	−	0.409207i
$944$	2.07648e9			2.46838
$945$		−	5.15691e8i		−	0.611074i
$946$	1.26673e8	+	1.40536e9i	0.149627	+	1.66003i
$947$	3.08642e8			0.363417			0.181709	−	0.983352i	$-0.441837\pi$
$947$	3.08642e8			0.363417			0.181709	+	0.983352i	$0.441837\pi$
$948$			2.04832e9i			2.40421i
$949$	1.23111e7	−	7.10781e6i	0.0144045	−	0.00831644i
$950$	1.02637e9			1.19710
$951$	−8.62086e7	+	4.97726e7i	−0.100233	+	0.0578694i
$952$	−8.40746e8	−	1.45621e9i	−0.974437	−	1.68778i
$953$	8.04877e8	+	4.64696e8i	0.929931	+	0.536896i	0.886790	−	0.462173i	$-0.152930\pi$
$953$	8.04877e8	+	4.64696e8i	0.929931	+	0.536896i	0.0431414	+	0.999069i	$0.486263\pi$
$954$		−	1.51139e9i		−	1.74073i
$955$	4.27199e8	−	7.39931e8i	0.490479	−	0.849535i
$956$	1.82646e9	+	3.16352e9i	2.09043	+	3.62074i
$957$	−7.84319e7			−0.0894863
$958$	−2.50854e9	+	1.44830e9i	−2.85314	+	1.64726i
$959$	−2.35702e8	+	4.08247e8i	−0.267243	+	0.462879i
$960$	−4.01586e8	+	6.95567e8i	−0.453905	+	0.786186i
$961$	−1.26122e9	+	2.18450e9i	−1.42109	+	2.46140i
$962$	5.05261e8			0.567532
$963$	−1.61927e7	+	2.80466e7i	−0.0181318	+	0.0314052i
$964$	−7.92353e8	−	4.57465e8i	−0.884479	−	0.510654i
$965$	2.30915e8	−	1.33319e8i	0.256962	−	0.148357i
$966$	1.17776e9	−	6.79982e8i	1.30655	−	0.754338i
$967$	4.67762e8			0.517303			0.258652	−	0.965971i	$-0.416722\pi$
$967$	4.67762e8			0.517303			0.258652	+	0.965971i	$0.416722\pi$
$968$		−	6.14425e8i		−	0.677397i
$969$	−1.87603e8	−	3.24939e8i	−0.206191	−	0.357133i
$970$	−5.01095e8	−	8.67923e8i	−0.549042	−	0.950968i
$971$	8.08546e8	−	1.40044e9i	0.883176	−	1.52971i	0.0353851	−	0.999374i	$-0.488734\pi$
$971$	8.08546e8	−	1.40044e9i	0.883176	−	1.52971i	0.847791	−	0.530331i	$-0.177932\pi$
$972$	1.97300e9	+	1.13911e9i	2.14846	+	1.24042i
$973$		−	3.91905e8i		−	0.425444i
$974$	−2.22125e9	−	1.28244e9i	−2.40393	−	1.38791i
$975$	2.00617e8	+	1.15826e8i	0.216448	+	0.124966i
$976$	3.38491e9	+	1.95428e9i	3.64081	+	2.10202i
$977$	4.77227e8	+	8.26581e8i	0.511730	+	0.886343i	0.999908	+	0.0135985i	$0.00432868\pi$
$977$	4.77227e8	+	8.26581e8i	0.511730	+	0.886343i	−0.488177	+	0.872745i	$0.662338\pi$
$978$		−	1.24504e9i		−	1.33097i
$979$	−4.96237e8	+	2.86502e8i	−0.528860	+	0.305338i
$980$	−8.93009e6	−	5.15579e6i	−0.00948807	−	0.00547794i
$981$	−4.29132e8			−0.454552
$982$	−1.24607e9	+	2.15826e9i	−1.31586	+	2.27913i
$983$	−1.15292e9	+	6.65636e8i	−1.21377	+	0.700771i	−0.963579	−	0.267425i	$-0.913827\pi$
$983$	−1.15292e9	+	6.65636e8i	−1.21377	+	0.700771i	−0.250192	+	0.968196i	$0.580494\pi$
$984$	3.67754e8	+	6.36969e8i	0.385987	+	0.668549i
$985$			8.44483e8i			0.883654i
$986$	−9.07923e7	−	1.57257e8i	−0.0947149	−	0.164051i
$987$	1.21259e9			1.26114
$988$			1.41648e9i			1.46872i
$989$	−6.72931e8	−	9.55693e8i	−0.695635	−	0.987938i
$990$	−5.43236e8			−0.559864
$991$		−	6.88485e8i		−	0.707414i	−0.935356	−	0.353707i	$-0.884921\pi$
$991$		−	6.88485e8i		−	0.707414i	0.935356	−	0.353707i	$-0.115079\pi$
$992$	−4.76214e9	+	2.74942e9i	−4.87828	+	2.81648i
$993$	−1.56839e8			−0.160179
$994$	−2.61112e9	+	1.50753e9i	−2.65869	+	1.53500i
$995$	−2.07301e8	−	3.59056e8i	−0.210442	−	0.364496i
$996$	−4.81308e8	−	2.77884e8i	−0.487131	−	0.281245i
$997$			4.84420e8i			0.488806i	0.969674	+	0.244403i	$0.0785920\pi$
$997$			4.84420e8i			0.488806i	−0.969674	+	0.244403i	$0.921408\pi$
$998$	−1.92968e7	+	3.34230e7i	−0.0194130	+	0.0336243i
$999$	−2.63303e8	−	4.56055e8i	−0.264095	−	0.457426i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.7.d.a.7.1	✓	42
43.37	odd	6	inner	43.7.d.a.37.21	yes	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.7.d.a.7.1	✓	42	1.1	even	1	trivial
43.7.d.a.37.21	yes	42	43.37	odd	6	inner

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)

\(f(q)\)	\(=\)	\(q-15.1507i q^{2} +(15.3614 - 8.86889i) q^{3} -165.545 q^{4} +(63.9718 - 36.9341i) q^{5} +(-134.370 - 232.736i) q^{6} +(-298.109 - 172.114i) q^{7} +1538.48i q^{8} +(-207.186 + 358.856i) q^{9} +O(q^{10})\)	\(q-15.1507i q^{2} +(15.3614 - 8.86889i) q^{3} -165.545 q^{4} +(63.9718 - 36.9341i) q^{5} +(-134.370 - 232.736i) q^{6} +(-298.109 - 172.114i) q^{7} +1538.48i q^{8} +(-207.186 + 358.856i) q^{9} +(-559.579 - 969.219i) q^{10} -1171.40 q^{11} +(-2542.99 + 1468.20i) q^{12} +(642.173 - 1112.28i) q^{13} +(-2607.65 + 4516.58i) q^{14} +(655.129 - 1134.72i) q^{15} +12714.2 q^{16} +(1587.56 - 2749.73i) q^{17} +(5436.94 + 3139.02i) q^{18} +(5769.57 - 3331.06i) q^{19} +(-10590.2 + 6114.25i) q^{20} -6105.82 q^{21} +17747.6i q^{22} +(-7350.54 - 12731.5i) q^{23} +(13644.6 + 23633.1i) q^{24} +(-5084.24 + 8806.16i) q^{25} +(-16851.8 - 9729.39i) q^{26} +20280.9i q^{27} +(49350.4 + 28492.5i) q^{28} +(3269.02 + 1887.37i) q^{29} +(-17191.8 - 9925.68i) q^{30} +(-29197.4 - 50571.3i) q^{31} -94166.8i q^{32} +(-17994.4 + 10389.1i) q^{33} +(-41660.4 - 24052.6i) q^{34} -25427.4 q^{35} +(34298.5 - 59406.8i) q^{36} +(-22487.0 + 12982.9i) q^{37} +(-50468.0 - 87413.2i) q^{38} -22781.4i q^{39} +(56822.3 + 98419.1i) q^{40} +26952.4 q^{41} +92507.6i q^{42} +(79186.0 - 7137.46i) q^{43} +193920. q^{44} +30608.9i q^{45} +(-192892. + 111366. i) q^{46} -198596. q^{47} +(195307. - 112761. i) q^{48} +(421.621 + 730.269i) q^{49} +(133420. + 77030.0i) q^{50} -56319.4i q^{51} +(-106308. + 184131. i) q^{52} +(-120372. - 208490. i) q^{53} +307270. q^{54} +(-74936.8 + 43264.8i) q^{55} +(264793. - 458634. i) q^{56} +(59085.6 - 102339. i) q^{57} +(28595.0 - 49528.0i) q^{58} +163320. q^{59} +(-108453. + 187846. i) q^{60} +(266231. + 153708. i) q^{61} +(-766193. + 442362. i) q^{62} +(123528. - 71318.9i) q^{63} -612988. q^{64} -94872.4i q^{65} +(157402. + 272628. i) q^{66} +(-145518. - 252044. i) q^{67} +(-262811. + 455203. i) q^{68} +(-225829. - 130382. i) q^{69} +385244. i q^{70} +(500666. + 289060. i) q^{71} +(-552092. - 318750. i) q^{72} +(9585.49 + 5534.19i) q^{73} +(196700. + 340694. i) q^{74} +180366. i q^{75} +(-955122. + 551440. i) q^{76} +(349207. + 201615. i) q^{77} -345156. q^{78} +(348781. - 604107. i) q^{79} +(813349. - 469587. i) q^{80} +(28830.2 + 49935.4i) q^{81} -408349. i q^{82} +(94634.3 + 163911. i) q^{83} +1.01079e6 q^{84} -234540. i q^{85} +(-108138. - 1.19973e6i) q^{86} +66955.4 q^{87} -1.80218e6i q^{88} +(423625. - 244580. i) q^{89} +463747. q^{90} +(-382876. + 221053. i) q^{91} +(1.21684e6 + 2.10764e6i) q^{92} +(-897023. - 517896. i) q^{93} +3.00888e6i q^{94} +(246060. - 426188. i) q^{95} +(-835154. - 1.44653e6i) q^{96} +895486. q^{97} +(11064.1 - 6387.87i) q^{98} +(242698. - 420366. i) 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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