LMFDB - Embedded newform 37.7.d.a.6.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [37,7,Mod(6,37)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(37, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3]))

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

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

chi := DirichletCharacter("37.6");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 37 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	37.d (of order $4$, 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:	$8.51200109393$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			6.16
Character	$\chi$	$=$	37.6
Dual form			37.7.d.a.31.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(8.60959 - 8.60959i) q^{2} +22.2519i q^{3} -84.2501i q^{4} +(144.668 + 144.668i) q^{5} +(191.579 + 191.579i) q^{6} -94.2990 q^{7} +(-174.345 - 174.345i) q^{8} +233.855 q^{9} +O(q^{10})$	\(q+(8.60959 - 8.60959i) q^{2} +22.2519i q^{3} -84.2501i q^{4} +(144.668 + 144.668i) q^{5} +(191.579 + 191.579i) q^{6} -94.2990 q^{7} +(-174.345 - 174.345i) q^{8} +233.855 q^{9} +2491.07 q^{10} -546.795i q^{11} +1874.72 q^{12} +(60.3655 + 60.3655i) q^{13} +(-811.876 + 811.876i) q^{14} +(-3219.14 + 3219.14i) q^{15} +2389.93 q^{16} +(-3061.04 - 3061.04i) q^{17} +(2013.39 - 2013.39i) q^{18} +(-4521.34 - 4521.34i) q^{19} +(12188.3 - 12188.3i) q^{20} -2098.33i q^{21} +(-4707.68 - 4707.68i) q^{22} +(-161.487 - 161.487i) q^{23} +(3879.50 - 3879.50i) q^{24} +26232.8i q^{25} +1039.44 q^{26} +21425.3i q^{27} +7944.70i q^{28} +(15540.8 - 15540.8i) q^{29} +55430.9i q^{30} +(-27791.2 + 27791.2i) q^{31} +(31734.4 - 31734.4i) q^{32} +12167.2 q^{33} -52708.6 q^{34} +(-13642.1 - 13642.1i) q^{35} -19702.3i q^{36} +(-31170.7 - 39926.4i) q^{37} -77853.8 q^{38} +(-1343.25 + 1343.25i) q^{39} -50444.3i q^{40} -77950.5i q^{41} +(-18065.8 - 18065.8i) q^{42} +(40151.3 + 40151.3i) q^{43} -46067.5 q^{44} +(33831.3 + 33831.3i) q^{45} -2780.67 q^{46} -159105. q^{47} +53180.4i q^{48} -108757. q^{49} +(225853. + 225853. i) q^{50} +(68113.9 - 68113.9i) q^{51} +(5085.80 - 5085.80i) q^{52} +180585. q^{53} +(184463. + 184463. i) q^{54} +(79103.8 - 79103.8i) q^{55} +(16440.5 + 16440.5i) q^{56} +(100608. - 100608. i) q^{57} -267599. i q^{58} +(-245893. - 245893. i) q^{59} +(271212. + 271212. i) q^{60} +(176452. - 176452. i) q^{61} +478542. i q^{62} -22052.3 q^{63} -393485. i q^{64} +17465.9i q^{65} +(104755. - 104755. i) q^{66} -121729. i q^{67} +(-257893. + 257893. i) q^{68} +(3593.38 - 3593.38i) q^{69} -234905. q^{70} +698669. q^{71} +(-40771.3 - 40771.3i) q^{72} +243920. i q^{73} +(-612116. - 75383.3i) q^{74} -583728. q^{75} +(-380923. + 380923. i) q^{76} +51562.2i q^{77} +23129.6i q^{78} +(-285869. - 285869. i) q^{79} +(345747. + 345747. i) q^{80} -306273. q^{81} +(-671122. - 671122. i) q^{82} +61297.0 q^{83} -176784. q^{84} -885671. i q^{85} +691372. q^{86} +(345811. + 345811. i) q^{87} +(-95330.8 + 95330.8i) q^{88} +(-339275. + 339275. i) q^{89} +582547. q^{90} +(-5692.41 - 5692.41i) q^{91} +(-13605.3 + 13605.3i) q^{92} +(-618406. - 618406. i) q^{93} +(-1.36983e6 + 1.36983e6i) q^{94} -1.30819e6i q^{95} +(706149. + 706149. i) q^{96} +(615088. + 615088. i) q^{97} +(-936351. + 936351. i) q^{98} -127870. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 4 q^{2} - 256 q^{5} + 126 q^{6} - 4 q^{7} + 168 q^{8} - 7140 q^{9}+O(q^{10}) $ 36 * q - 4 * q^2 - 256 * q^5 + 126 * q^6 - 4 * q^7 + 168 * q^8 - 7140 * q^9	\( 36 q - 4 q^{2} - 256 q^{5} + 126 q^{6} - 4 q^{7} + 168 q^{8} - 7140 q^{9} - 1876 q^{10} + 11104 q^{12} - 2904 q^{13} - 7678 q^{14} + 4288 q^{15} - 44824 q^{16} + 2064 q^{17} + 6222 q^{18} - 4954 q^{19} - 43084 q^{20} - 39810 q^{22} + 21966 q^{23} + 79188 q^{24} + 66604 q^{26} + 69500 q^{29} - 32418 q^{31} - 141992 q^{32} + 54752 q^{33} + 256508 q^{34} - 26164 q^{35} + 180242 q^{37} + 329032 q^{38} - 60088 q^{39} - 346014 q^{42} - 144514 q^{43} - 294896 q^{44} + 842152 q^{45} - 522736 q^{46} - 157076 q^{47} + 405652 q^{49} + 46176 q^{50} - 624984 q^{51} - 161884 q^{52} - 512988 q^{53} + 541150 q^{54} + 824640 q^{55} - 608488 q^{56} - 311992 q^{57} + 187582 q^{59} - 1156764 q^{60} - 1321908 q^{61} - 887284 q^{63} + 752126 q^{66} + 1244832 q^{68} + 41960 q^{69} - 1029284 q^{70} + 1316252 q^{71} + 777880 q^{72} + 1117260 q^{74} - 2148904 q^{75} - 814428 q^{76} - 56722 q^{79} + 3750844 q^{80} - 930796 q^{81} + 1462554 q^{82} - 841484 q^{83} + 5065540 q^{84} + 3992612 q^{86} + 2494224 q^{87} - 3796428 q^{88} - 1439724 q^{89} - 5618044 q^{90} - 8644 q^{91} + 7826980 q^{92} - 54064 q^{93} - 2057938 q^{94} - 8819328 q^{96} + 2578548 q^{97} - 6043946 q^{98}+O(q^{100}) \) 36 * q - 4 * q^2 - 256 * q^5 + 126 * q^6 - 4 * q^7 + 168 * q^8 - 7140 * q^9 - 1876 * q^10 + 11104 * q^12 - 2904 * q^13 - 7678 * q^14 + 4288 * q^15 - 44824 * q^16 + 2064 * q^17 + 6222 * q^18 - 4954 * q^19 - 43084 * q^20 - 39810 * q^22 + 21966 * q^23 + 79188 * q^24 + 66604 * q^26 + 69500 * q^29 - 32418 * q^31 - 141992 * q^32 + 54752 * q^33 + 256508 * q^34 - 26164 * q^35 + 180242 * q^37 + 329032 * q^38 - 60088 * q^39 - 346014 * q^42 - 144514 * q^43 - 294896 * q^44 + 842152 * q^45 - 522736 * q^46 - 157076 * q^47 + 405652 * q^49 + 46176 * q^50 - 624984 * q^51 - 161884 * q^52 - 512988 * q^53 + 541150 * q^54 + 824640 * q^55 - 608488 * q^56 - 311992 * q^57 + 187582 * q^59 - 1156764 * q^60 - 1321908 * q^61 - 887284 * q^63 + 752126 * q^66 + 1244832 * q^68 + 41960 * q^69 - 1029284 * q^70 + 1316252 * q^71 + 777880 * q^72 + 1117260 * q^74 - 2148904 * q^75 - 814428 * q^76 - 56722 * q^79 + 3750844 * q^80 - 930796 * q^81 + 1462554 * q^82 - 841484 * q^83 + 5065540 * q^84 + 3992612 * q^86 + 2494224 * q^87 - 3796428 * q^88 - 1439724 * q^89 - 5618044 * q^90 - 8644 * q^91 + 7826980 * q^92 - 54064 * q^93 - 2057938 * q^94 - 8819328 * q^96 + 2578548 * q^97 - 6043946 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/37\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	8.60959	−	8.60959i	1.07620	−	1.07620i	0.0793521	−	0.996847i	$-0.474715\pi$
$2$	8.60959	−	8.60959i	1.07620	−	1.07620i	0.996847	−	0.0793521i	$-0.0252851\pi$
$3$			22.2519i			0.824143i	0.911151	+	0.412072i	$0.135195\pi$
$3$			22.2519i			0.824143i	−0.911151	+	0.412072i	$0.864805\pi$
$4$		−	84.2501i		−	1.31641i
$5$	144.668	+	144.668i	1.15735	+	1.15735i	0.985044	+	0.172301i	$0.0551202\pi$
$5$	144.668	+	144.668i	1.15735	+	1.15735i	0.172301	+	0.985044i	$0.444880\pi$
$6$	191.579	+	191.579i	0.886942	+	0.886942i
$7$	−94.2990			−0.274924			−0.137462	−	0.990507i	$-0.543895\pi$
$7$	−94.2990			−0.274924			−0.137462	+	0.990507i	$0.543895\pi$
$8$	−174.345	−	174.345i	−0.340517	−	0.340517i
$9$	233.855			0.320788
$10$	2491.07			2.49107
$11$		−	546.795i		−	0.410815i	−0.978677	−	0.205408i	$-0.934148\pi$
$11$		−	546.795i		−	0.410815i	0.978677	−	0.205408i	$-0.0658520\pi$
$12$	1874.72			1.08491
$13$	60.3655	+	60.3655i	0.0274763	+	0.0274763i	0.720711	−	0.693235i	$-0.243815\pi$
$13$	60.3655	+	60.3655i	0.0274763	+	0.0274763i	−0.693235	+	0.720711i	$0.743815\pi$
$14$	−811.876	+	811.876i	−0.295873	+	0.295873i
$15$	−3219.14	+	3219.14i	−0.953818	+	0.953818i
$16$	2389.93			0.583479
$17$	−3061.04	−	3061.04i	−0.623049	−	0.623049i	0.323261	−	0.946310i	$-0.395221\pi$
$17$	−3061.04	−	3061.04i	−0.623049	−	0.623049i	−0.946310	+	0.323261i	$0.895221\pi$
$18$	2013.39	−	2013.39i	0.345232	−	0.345232i
$19$	−4521.34	−	4521.34i	−0.659184	−	0.659184i	0.296003	−	0.955187i	$-0.404346\pi$
$19$	−4521.34	−	4521.34i	−0.659184	−	0.659184i	−0.955187	+	0.296003i	$0.904346\pi$
$20$	12188.3	−	12188.3i	1.52354	−	1.52354i
$21$		−	2098.33i		−	0.226577i
$22$	−4707.68	−	4707.68i	−0.442119	−	0.442119i
$23$	−161.487	−	161.487i	−0.0132725	−	0.0132725i	0.700439	−	0.713712i	$-0.252987\pi$
$23$	−161.487	−	161.487i	−0.0132725	−	0.0132725i	−0.713712	+	0.700439i	$0.752987\pi$
$24$	3879.50	−	3879.50i	0.280635	−	0.280635i
$25$			26232.8i			1.67890i
$26$	1039.44			0.0591400
$27$			21425.3i			1.08852i
$28$			7944.70i			0.361912i
$29$	15540.8	−	15540.8i	0.637203	−	0.637203i	−0.312661	−	0.949865i	$-0.601221\pi$
$29$	15540.8	−	15540.8i	0.637203	−	0.637203i	0.949865	+	0.312661i	$0.101221\pi$
$30$			55430.9i			2.05300i
$31$	−27791.2	+	27791.2i	−0.932872	+	0.932872i	−0.997884	−	0.0650121i	$-0.979291\pi$
$31$	−27791.2	+	27791.2i	−0.932872	+	0.932872i	0.0650121	+	0.997884i	$0.479291\pi$
$32$	31734.4	−	31734.4i	0.968457	−	0.968457i
$33$	12167.2			0.338570
$34$	−52708.6			−1.34105
$35$	−13642.1	−	13642.1i	−0.318182	−	0.318182i
$36$		−	19702.3i		−	0.422288i
$37$	−31170.7	−	39926.4i	−0.615376	−	0.788233i
$37$	−31170.7	−	39926.4i	−0.615376	−	0.788233i
$38$	−77853.8			−1.41883
$39$	−1343.25	+	1343.25i	−0.0226444	+	0.0226444i
$40$		−	50444.3i		−	0.788192i
$41$		−	77950.5i		−	1.13101i	−0.824744	−	0.565506i	$-0.808681\pi$
$41$		−	77950.5i		−	1.13101i	0.824744	−	0.565506i	$-0.191319\pi$
$42$	−18065.8	−	18065.8i	−0.243842	−	0.243842i
$43$	40151.3	+	40151.3i	0.505003	+	0.505003i	0.912988	−	0.407985i	$-0.133769\pi$
$43$	40151.3	+	40151.3i	0.505003	+	0.505003i	−0.407985	+	0.912988i	$0.633769\pi$
$44$	−46067.5			−0.540800
$45$	33831.3	+	33831.3i	0.371263	+	0.371263i
$46$	−2780.67			−0.0285677
$47$	−159105.			−1.53247			−0.766234	−	0.642561i	$-0.777872\pi$
$47$	−159105.			−1.53247			−0.766234	+	0.642561i	$0.777872\pi$
$48$			53180.4i			0.480870i
$49$	−108757.			−0.924417
$50$	225853.	+	225853.i	1.80683	+	1.80683i
$51$	68113.9	−	68113.9i	0.513482	−	0.513482i
$52$	5085.80	−	5085.80i	0.0361701	−	0.0361701i
$53$	180585.			1.21298			0.606491	−	0.795090i	$-0.292577\pi$
$53$	180585.			1.21298			0.606491	+	0.795090i	$0.292577\pi$
$54$	184463.	+	184463.i	1.17146	+	1.17146i
$55$	79103.8	−	79103.8i	0.475455	−	0.475455i
$56$	16440.5	+	16440.5i	0.0936164	+	0.0936164i
$57$	100608.	−	100608.i	0.543262	−	0.543262i
$58$		−	267599.i		−	1.37151i
$59$	−245893.	−	245893.i	−1.19726	−	1.19726i	−0.974983	−	0.222279i	$-0.928650\pi$
$59$	−245893.	−	245893.i	−1.19726	−	1.19726i	−0.222279	−	0.974983i	$-0.571350\pi$
$60$	271212.	+	271212.i	1.25561	+	1.25561i
$61$	176452.	−	176452.i	0.777385	−	0.777385i	−0.202000	−	0.979385i	$-0.564744\pi$
$61$	176452.	−	176452.i	0.777385	−	0.777385i	0.979385	+	0.202000i	$0.0647442\pi$
$62$			478542.i			2.00791i
$63$	−22052.3			−0.0881924
$64$		−	393485.i		−	1.50102i
$65$			17465.9i			0.0635992i
$66$	104755.	−	104755.i	0.364369	−	0.364369i
$67$		−	121729.i		−	0.404735i	−0.979310	−	0.202368i	$-0.935136\pi$
$67$		−	121729.i		−	0.404735i	0.979310	−	0.202368i	$-0.0648636\pi$
$68$	−257893.	+	257893.i	−0.820187	+	0.820187i
$69$	3593.38	−	3593.38i	0.0109384	−	0.0109384i
$70$	−234905.			−0.684855
$71$	698669.			1.95208			0.976038	−	0.217601i	$-0.0698233\pi$
$71$	698669.			1.95208			0.976038	+	0.217601i	$0.0698233\pi$
$72$	−40771.3	−	40771.3i	−0.109234	−	0.109234i
$73$			243920.i			0.627017i	0.949585	+	0.313509i	$0.101504\pi$
$73$			243920.i			0.627017i	−0.949585	+	0.313509i	$0.898496\pi$
$74$	−612116.	−	75383.3i	−1.51056	−	0.186029i
$75$	−583728.			−1.38365
$76$	−380923.	+	380923.i	−0.867754	+	0.867754i
$77$			51562.2i			0.112943i
$78$			23129.6i			0.0487398i
$79$	−285869.	−	285869.i	−0.579810	−	0.579810i	0.355040	−	0.934851i	$-0.384467\pi$
$79$	−285869.	−	285869.i	−0.579810	−	0.579810i	−0.934851	+	0.355040i	$0.884467\pi$
$80$	345747.	+	345747.i	0.675287	+	0.675287i
$81$	−306273.			−0.576307
$82$	−671122.	−	671122.i	−1.21719	−	1.21719i
$83$	61297.0			0.107203			0.0536013	−	0.998562i	$-0.482930\pi$
$83$	61297.0			0.107203			0.0536013	+	0.998562i	$0.482930\pi$
$84$	−176784.			−0.298268
$85$		−	885671.i		−	1.44217i
$86$	691372.			1.08697
$87$	345811.	+	345811.i	0.525147	+	0.525147i
$88$	−95330.8	+	95330.8i	−0.139890	+	0.139890i
$89$	−339275.	+	339275.i	−0.481262	+	0.481262i	−0.905535	−	0.424272i	$-0.860530\pi$
$89$	−339275.	+	339275.i	−0.481262	+	0.481262i	0.424272	+	0.905535i	$0.360530\pi$
$90$	582547.			0.799105
$91$	−5692.41	−	5692.41i	−0.00755391	−	0.00755391i
$92$	−13605.3	+	13605.3i	−0.0174720	+	0.0174720i
$93$	−618406.	−	618406.i	−0.768820	−	0.768820i
$94$	−1.36983e6	+	1.36983e6i	−1.64924	+	1.64924i
$95$		−	1.30819e6i		−	1.52581i
$96$	706149.	+	706149.i	0.798147	+	0.798147i
$97$	615088.	+	615088.i	0.673941	+	0.673941i	0.958622	−	0.284681i	$-0.0918878\pi$
$97$	615088.	+	615088.i	0.673941	+	0.673941i	−0.284681	+	0.958622i	$0.591888\pi$
$98$	−936351.	+	936351.i	−0.994856	+	0.994856i
$99$		−	127870.i		−	0.131785i
$100$	2.21011e6			2.21011
$101$			1.72539e6i			1.67465i	0.546708	+	0.837323i	$0.315881\pi$
$101$			1.72539e6i			1.67465i	−0.546708	+	0.837323i	$0.684119\pi$
$102$		−	1.17287e6i		−	1.10522i
$103$	−526724.	+	526724.i	−0.482027	+	0.482027i	−0.905778	−	0.423752i	$-0.860713\pi$
$103$	−526724.	+	526724.i	−0.482027	+	0.482027i	0.423752	+	0.905778i	$0.360713\pi$
$104$		−	21048.8i		−	0.0187123i
$105$	303561.	−	303561.i	0.262228	−	0.262228i
$106$	1.55476e6	−	1.55476e6i	1.30541	−	1.30541i
$107$	−1.40173e6			−1.14423			−0.572114	−	0.820174i	$-0.693877\pi$
$107$	−1.40173e6			−1.14423			−0.572114	+	0.820174i	$0.693877\pi$
$108$	1.80508e6			1.43293
$109$	1.49742e6	+	1.49742e6i	1.15628	+	1.15628i	0.985269	+	0.171011i	$0.0547034\pi$
$109$	1.49742e6	+	1.49742e6i	1.15628	+	1.15628i	0.171011	+	0.985269i	$0.445297\pi$
$110$		−	1.36210e6i		−	1.02337i
$111$	888437.	−	693605.i	0.649617	−	0.507158i
$112$	−225368.			−0.160413
$113$	−1.22399e6	+	1.22399e6i	−0.848289	+	0.848289i	−0.989920	−	0.141630i	$-0.954766\pi$
$113$	−1.22399e6	+	1.22399e6i	−0.848289	+	0.848289i	0.141630	+	0.989920i	$0.454766\pi$
$114$		−	1.73239e6i		−	1.16932i
$115$		−	46724.0i		−	0.0307218i
$116$	−1.30931e6	−	1.30931e6i	−0.838819	−	0.838819i
$117$	14116.8	+	14116.8i	0.00881409	+	0.00881409i
$118$	−4.23407e6			−2.57698
$119$	288653.	+	288653.i	0.171291	+	0.171291i
$120$	1.12248e6			0.649583
$121$	1.47258e6			0.831231
$122$		−	3.03835e6i		−	1.67324i
$123$	1.73454e6			0.932116
$124$	2.34141e6	+	2.34141e6i	1.22804	+	1.22804i
$125$	−1.53461e6	+	1.53461e6i	−0.785718	+	0.785718i
$126$	−189861.	+	189861.i	−0.0949126	+	0.0949126i
$127$	147958.			0.0722314			0.0361157	−	0.999348i	$-0.488502\pi$
$127$	147958.			0.0722314			0.0361157	+	0.999348i	$0.488502\pi$
$128$	−1.35674e6	−	1.35674e6i	−0.646944	−	0.646944i
$129$	−893441.	+	893441.i	−0.416195	+	0.416195i
$130$	150375.	+	150375.i	0.0684454	+	0.0684454i
$131$	343399.	−	343399.i	0.152751	−	0.152751i	−0.626594	−	0.779346i	$-0.715552\pi$
$131$	343399.	−	343399.i	0.152751	−	0.152751i	0.779346	+	0.626594i	$0.215552\pi$
$132$		−	1.02509e6i		−	0.445697i
$133$	426358.	+	426358.i	0.181226	+	0.181226i
$134$	−1.04804e6	−	1.04804e6i	−0.435576	−	0.435576i
$135$	−3.09956e6	+	3.09956e6i	−1.25979	+	1.25979i
$136$			1.06735e6i			0.424318i
$137$	2.63756e6			1.02575			0.512874	−	0.858464i	$-0.328581\pi$
$137$	2.63756e6			1.02575			0.512874	+	0.858464i	$0.328581\pi$
$138$		−	61875.0i		−	0.0235439i
$139$			1.97392e6i			0.734996i	0.930024	+	0.367498i	$0.119785\pi$
$139$			1.97392e6i			0.734996i	−0.930024	+	0.367498i	$0.880215\pi$
$140$	−1.14935e6	+	1.14935e6i	−0.418858	+	0.418858i
$141$		−	3.54039e6i		−	1.26297i
$142$	6.01526e6	−	6.01526e6i	2.10082	−	2.10082i
$143$	33007.6	−	33007.6i	0.0112877	−	0.0112877i
$144$	558896.			0.187173
$145$	4.49650e6			1.47493
$146$	2.10005e6	+	2.10005e6i	0.674795	+	0.674795i
$147$		−	2.42004e6i		−	0.761852i
$148$	−3.36380e6	+	2.62613e6i	−1.03764	+	0.810086i
$149$	−351917.			−0.106385			−0.0531926	−	0.998584i	$-0.516940\pi$
$149$	−351917.			−0.106385			−0.0531926	+	0.998584i	$0.516940\pi$
$150$	−5.02566e6	+	5.02566e6i	−1.48908	+	1.48908i
$151$			1.30272e6i			0.378374i	0.981941	+	0.189187i	$0.0605853\pi$
$151$			1.30272e6i			0.378374i	−0.981941	+	0.189187i	$0.939415\pi$
$152$			1.57654e6i			0.448927i
$153$	−715839.	−	715839.i	−0.199867	−	0.199867i
$154$	443930.	+	443930.i	0.121549	+	0.121549i
$155$	−8.04100e6			−2.15931
$156$	113169.	+	113169.i	0.0298093	+	0.0298093i
$157$	−4.29898e6			−1.11088			−0.555439	−	0.831557i	$-0.687450\pi$
$157$	−4.29898e6			−1.11088			−0.555439	+	0.831557i	$0.687450\pi$
$158$	−4.92243e6			−1.24798
$159$			4.01836e6i			0.999671i
$160$	9.18191e6			2.24168
$161$	15228.0	+	15228.0i	0.00364894	+	0.00364894i
$162$	−2.63689e6	+	2.63689e6i	−0.620221	+	0.620221i
$163$	2.53370e6	−	2.53370e6i	0.585050	−	0.585050i	−0.351237	−	0.936287i	$-0.614239\pi$
$163$	2.53370e6	−	2.53370e6i	0.585050	−	0.585050i	0.936287	+	0.351237i	$0.114239\pi$
$164$	−6.56734e6			−1.48887
$165$	1.76021e6	+	1.76021e6i	0.391843	+	0.391843i
$166$	527742.	−	527742.i	0.115371	−	0.115371i
$167$	2.62917e6	+	2.62917e6i	0.564507	+	0.564507i	0.930584	−	0.366077i	$-0.119299\pi$
$167$	2.62917e6	+	2.62917e6i	0.564507	+	0.564507i	−0.366077	+	0.930584i	$0.619299\pi$
$168$	−365833.	+	365833.i	−0.0771533	+	0.0771533i
$169$		−	4.81952e6i		−	0.998490i
$170$	−7.62526e6	−	7.62526e6i	−1.55206	−	1.55206i
$171$	−1.05734e6	−	1.05734e6i	−0.211458	−	0.211458i
$172$	3.38275e6	−	3.38275e6i	0.664790	−	0.664790i
$173$		−	4.25426e6i		−	0.821647i	−0.911715	−	0.410824i	$-0.865241\pi$
$173$		−	4.25426e6i		−	0.821647i	0.911715	−	0.410824i	$-0.134759\pi$
$174$	5.95458e6			1.13032
$175$		−	2.47372e6i		−	0.461569i
$176$		−	1.30680e6i		−	0.239702i
$177$	5.47157e6	−	5.47157e6i	0.986716	−	0.986716i
$178$			5.84203e6i			1.03587i
$179$	−7.64427e6	+	7.64427e6i	−1.33284	+	1.33284i	−0.430016	+	0.902821i	$0.641492\pi$
$179$	−7.64427e6	+	7.64427e6i	−1.33284	+	1.33284i	−0.902821	+	0.430016i	$0.858508\pi$
$180$	2.85029e6	−	2.85029e6i	0.488733	−	0.488733i
$181$	−943023.			−0.159033			−0.0795163	−	0.996834i	$-0.525338\pi$
$181$	−943023.			−0.159033			−0.0795163	+	0.996834i	$0.525338\pi$
$182$	−98018.6			−0.0162590
$183$	3.92638e6	+	3.92638e6i	0.640677	+	0.640677i
$184$			56308.7i			0.00903904i
$185$	1.26668e6	−	1.02855e7i	0.200055	−	1.62446i
$186$	−1.06484e7			−1.65481
$187$	−1.67376e6	+	1.67376e6i	−0.255958	+	0.255958i
$188$			1.34046e7i			2.01735i
$189$		−	2.02039e6i		−	0.299260i
$190$	−1.12630e7	−	1.12630e7i	−1.64207	−	1.64207i
$191$	1.30615e6	+	1.30615e6i	0.187453	+	0.187453i	0.794594	−	0.607141i	$-0.207684\pi$
$191$	1.30615e6	+	1.30615e6i	0.187453	+	0.187453i	−0.607141	+	0.794594i	$0.707684\pi$
$192$	8.75576e6			1.23706
$193$	5.29338e6	+	5.29338e6i	0.736311	+	0.736311i	0.971862	−	0.235551i	$-0.0756894\pi$
$193$	5.29338e6	+	5.29338e6i	0.736311	+	0.736311i	−0.235551	+	0.971862i	$0.575689\pi$
$194$	1.05913e7			1.45059
$195$	−388650.			−0.0524149
$196$			9.16276e6i			1.21691i
$197$	9.74301e6			1.27437			0.637184	−	0.770712i	$-0.280099\pi$
$197$	9.74301e6			1.27437			0.637184	+	0.770712i	$0.280099\pi$
$198$	−1.10091e6	−	1.10091e6i	−0.141826	−	0.141826i
$199$	5.29988e6	−	5.29988e6i	0.672522	−	0.672522i	−0.285775	−	0.958297i	$-0.592251\pi$
$199$	5.29988e6	−	5.29988e6i	0.672522	−	0.672522i	0.958297	+	0.285775i	$0.0922509\pi$
$200$	4.57355e6	−	4.57355e6i	0.571693	−	0.571693i
$201$	2.70871e6			0.333560
$202$	1.48549e7	+	1.48549e7i	1.80225	+	1.80225i
$203$	−1.46548e6	+	1.46548e6i	−0.175183	+	0.175183i
$204$	−5.73860e6	−	5.73860e6i	−0.675951	−	0.675951i
$205$	1.12770e7	−	1.12770e7i	1.30897	−	1.30897i
$206$			9.06975e6i			1.03751i
$207$	−37764.4	−	37764.4i	−0.00425766	−	0.00425766i
$208$	144269.	+	144269.i	0.0160319	+	0.0160319i
$209$	−2.47225e6	+	2.47225e6i	−0.270803	+	0.270803i
$210$		−	5.22708e6i		−	0.564418i
$211$	−5.83351e6			−0.620987			−0.310494	−	0.950575i	$-0.600494\pi$
$211$	−5.83351e6			−0.620987			−0.310494	+	0.950575i	$0.600494\pi$
$212$		−	1.52143e7i		−	1.59678i
$213$			1.55467e7i			1.60879i
$214$	−1.20683e7	+	1.20683e7i	−1.23142	+	1.23142i
$215$			1.16172e7i			1.16893i
$216$	3.73539e6	−	3.73539e6i	0.370659	−	0.370659i
$217$	2.62068e6	−	2.62068e6i	0.256469	−	0.256469i
$218$	2.57843e7			2.48877
$219$	−5.42768e6			−0.516752
$220$	−6.66450e6	−	6.66450e6i	−0.625892	−	0.625892i
$221$		−	369563.i		−	0.0342382i
$222$	1.67742e6	−	1.36207e7i	0.153314	−	1.24492i
$223$	−1.45201e7			−1.30935			−0.654675	−	0.755911i	$-0.727194\pi$
$223$	−1.45201e7			−1.30935			−0.654675	+	0.755911i	$0.727194\pi$
$224$	−2.99252e6	+	2.99252e6i	−0.266252	+	0.266252i
$225$			6.13465e6i			0.538570i
$226$			2.10762e7i			1.82586i
$227$	−1.18374e7	−	1.18374e7i	−1.01199	−	1.01199i	−0.999927	−	0.0120671i	$-0.996159\pi$
$227$	−1.18374e7	−	1.18374e7i	−1.01199	−	1.01199i	−0.0120671	−	0.999927i	$-0.503841\pi$
$228$	−8.47625e6	−	8.47625e6i	−0.715154	−	0.715154i
$229$	−7.66349e6			−0.638146			−0.319073	−	0.947730i	$-0.603372\pi$
$229$	−7.66349e6			−0.638146			−0.319073	+	0.947730i	$0.603372\pi$
$230$	−402274.	−	402274.i	−0.0330627	−	0.0330627i
$231$	−1.14736e6			−0.0930812
$232$	−5.41890e6			−0.433957
$233$		−	1.82090e6i		−	0.143952i	−0.997406	−	0.0719762i	$-0.977069\pi$
$233$		−	1.82090e6i		−	0.143952i	0.997406	−	0.0719762i	$-0.0229306\pi$
$234$	243079.			0.0189714
$235$	−2.30175e7	−	2.30175e7i	−1.77360	−	1.77360i
$236$	−2.07165e7	+	2.07165e7i	−1.57608	+	1.57608i
$237$	6.36112e6	−	6.36112e6i	0.477847	−	0.477847i
$238$	4.97037e6			0.368687
$239$	3.76615e6	+	3.76615e6i	0.275869	+	0.275869i	0.831458	−	0.555588i	$-0.187507\pi$
$239$	3.76615e6	+	3.76615e6i	0.275869	+	0.275869i	−0.555588	+	0.831458i	$0.687507\pi$
$240$	−7.69351e6	+	7.69351e6i	−0.556533	+	0.556533i
$241$	−1.62164e7	−	1.62164e7i	−1.15852	−	1.15852i	−0.984795	−	0.173722i	$-0.944421\pi$
$241$	−1.62164e7	−	1.62164e7i	−1.15852	−	1.15852i	−0.173722	−	0.984795i	$-0.555579\pi$
$242$	1.26783e7	−	1.26783e7i	0.894570	−	0.894570i
$243$			8.80390e6i			0.613559i
$244$	−1.48661e7	−	1.48661e7i	−1.02336	−	1.02336i
$245$	−1.57336e7	−	1.57336e7i	−1.06987	−	1.06987i
$246$	1.49337e7	−	1.49337e7i	1.00314	−	1.00314i
$247$		−	545866.i		−	0.0362239i
$248$	9.69050e6			0.635318
$249$			1.36397e6i			0.0883502i
$250$			2.64247e7i			1.69118i
$251$	−5.33627e6	+	5.33627e6i	−0.337456	+	0.337456i	−0.855409	−	0.517953i	$-0.826694\pi$
$251$	−5.33627e6	+	5.33627e6i	−0.337456	+	0.337456i	0.517953	+	0.855409i	$0.326694\pi$
$252$			1.85790e6i			0.116097i
$253$	−88300.1	+	88300.1i	−0.00545255	+	0.00545255i
$254$	1.27385e6	−	1.27385e6i	0.0777353	−	0.0777353i
$255$	1.97078e7			1.18855
$256$	1.82107e6			0.108544
$257$	1.70053e7	+	1.70053e7i	1.00181	+	1.00181i	0.999998	+	0.00181196i	$0.000576766\pi$
$257$	1.70053e7	+	1.70053e7i	1.00181	+	1.00181i	0.00181196	+	0.999998i	$0.499423\pi$
$258$			1.53843e7i			0.895816i
$259$	2.93936e6	+	3.76502e6i	0.169182	+	0.216704i
$260$	1.47151e6			0.0837225
$261$	3.63428e6	−	3.63428e6i	0.204407	−	0.204407i
$262$		−	5.91304e6i		−	0.328781i
$263$			1.22270e7i			0.672129i	0.941839	+	0.336064i	$0.109096\pi$
$263$			1.22270e7i			0.672129i	−0.941839	+	0.336064i	$0.890904\pi$
$264$	−2.12129e6	−	2.12129e6i	−0.115289	−	0.115289i
$265$	2.61249e7	+	2.61249e7i	1.40384	+	1.40384i
$266$	7.34154e6			0.390070
$267$	−7.54950e6	−	7.54950e6i	−0.396629	−	0.396629i
$268$	−1.02557e7			−0.532797
$269$	−9.25733e6			−0.475586			−0.237793	−	0.971316i	$-0.576424\pi$
$269$	−9.25733e6			−0.475586			−0.237793	+	0.971316i	$0.576424\pi$
$270$			5.33719e7i			2.71157i
$271$	−2.36542e6			−0.118850			−0.0594250	−	0.998233i	$-0.518927\pi$
$271$	−2.36542e6			−0.118850			−0.0594250	+	0.998233i	$0.518927\pi$
$272$	−7.31568e6	−	7.31568e6i	−0.363536	−	0.363536i
$273$	126667.	−	126667.i	0.00622551	−	0.00622551i
$274$	2.27083e7	−	2.27083e7i	1.10391	−	1.10391i
$275$	1.43439e7			0.689716
$276$	−302742.	−	302742.i	−0.0143995	−	0.0143995i
$277$	−2.38589e7	+	2.38589e7i	−1.12256	+	1.12256i	−0.131209	+	0.991355i	$0.541886\pi$
$277$	−2.38589e7	+	2.38589e7i	−1.12256	+	1.12256i	−0.991355	+	0.131209i	$0.958114\pi$
$278$	1.69946e7	+	1.69946e7i	0.791001	+	0.791001i
$279$	−6.49910e6	+	6.49910e6i	−0.299254	+	0.299254i
$280$			4.75685e6i			0.216693i
$281$	7.80976e6	+	7.80976e6i	0.351981	+	0.351981i	0.860846	−	0.508865i	$-0.169935\pi$
$281$	7.80976e6	+	7.80976e6i	0.351981	+	0.351981i	−0.508865	+	0.860846i	$0.669935\pi$
$282$	−3.04813e7	−	3.04813e7i	−1.35921	−	1.35921i
$283$	2.67541e7	−	2.67541e7i	1.18041	−	1.18041i	0.200767	−	0.979639i	$-0.435657\pi$
$283$	2.67541e7	−	2.67541e7i	1.18041	−	1.18041i	0.979639	−	0.200767i	$-0.0643434\pi$
$284$		−	5.88629e7i		−	2.56973i
$285$	2.91096e7			1.25748
$286$		−	568363.i		−	0.0242956i
$287$			7.35066e6i			0.310943i
$288$	7.42123e6	−	7.42123e6i	0.310669	−	0.310669i
$289$		−	5.39761e6i		−	0.223619i
$290$	3.87131e7	−	3.87131e7i	1.58732	−	1.58732i
$291$	−1.36868e7	+	1.36868e7i	−0.555424	+	0.555424i
$292$	2.05503e7			0.825410
$293$	760766.			0.0302446			0.0151223	−	0.999886i	$-0.495186\pi$
$293$	760766.			0.0302446			0.0151223	+	0.999886i	$0.495186\pi$
$294$	−2.08355e7	−	2.08355e7i	−0.819904	−	0.819904i
$295$		−	7.11457e7i		−	2.77129i
$296$	−1.52652e6	+	1.23954e7i	−0.0588608	+	0.477953i
$297$	1.17152e7			0.447180
$298$	−3.02986e6	+	3.02986e6i	−0.114492	+	0.114492i
$299$		−	19496.5i		−	0.000729360i
$300$			4.91791e7i			1.82145i
$301$	−3.78623e6	−	3.78623e6i	−0.138838	−	0.138838i
$302$	1.12159e7	+	1.12159e7i	0.407206	+	0.407206i
$303$	−3.83932e7			−1.38015
$304$	−1.08057e7	−	1.08057e7i	−0.384620	−	0.384620i
$305$	5.10539e7			1.79941
$306$	−1.23262e7			−0.430193
$307$		−	3.30419e7i		−	1.14196i	−0.820965	−	0.570978i	$-0.806564\pi$
$307$		−	3.30419e7i		−	1.14196i	0.820965	−	0.570978i	$-0.193436\pi$
$308$	4.34412e6			0.148679
$309$	−1.17206e7	−	1.17206e7i	−0.397259	−	0.397259i
$310$	−6.92298e7	+	6.92298e7i	−2.32385	+	2.32385i
$311$	2.57458e6	−	2.57458e6i	0.0855903	−	0.0855903i	−0.663015	−	0.748606i	$-0.730724\pi$
$311$	2.57458e6	−	2.57458e6i	0.0855903	−	0.0855903i	0.748606	+	0.663015i	$0.230724\pi$
$312$	468376.			0.0154216
$313$	−1.20357e7	−	1.20357e7i	−0.392498	−	0.392498i	0.483079	−	0.875577i	$-0.339518\pi$
$313$	−1.20357e7	−	1.20357e7i	−0.392498	−	0.392498i	−0.875577	+	0.483079i	$0.839518\pi$
$314$	−3.70125e7	+	3.70125e7i	−1.19553	+	1.19553i
$315$	−3.19026e6	−	3.19026e6i	−0.102069	−	0.102069i
$316$	−2.40845e7	+	2.40845e7i	−0.763267	+	0.763267i
$317$			5.90675e7i			1.85426i	0.374739	+	0.927130i	$0.377732\pi$
$317$			5.90675e7i			1.85426i	−0.374739	+	0.927130i	$0.622268\pi$
$318$	3.45964e7	+	3.45964e7i	1.07584	+	1.07584i
$319$	−8.49760e6	−	8.49760e6i	−0.261773	−	0.261773i
$320$	5.69247e7	−	5.69247e7i	1.73720	−	1.73720i
$321$		−	3.11911e7i		−	0.943008i
$322$	262214.			0.00785396
$323$			2.76800e7i			0.821408i
$324$			2.58035e7i			0.758655i
$325$	−1.58355e6	+	1.58355e6i	−0.0461299	+	0.0461299i
$326$		−	4.36283e7i		−	1.25926i
$327$	−3.33203e7	+	3.33203e7i	−0.952940	+	0.952940i
$328$	−1.35903e7	+	1.35903e7i	−0.385129	+	0.385129i
$329$	1.50035e7			0.421313
$330$	3.03093e7			0.843402
$331$	2.12361e7	+	2.12361e7i	0.585586	+	0.585586i	0.936433	−	0.350847i	$-0.114106\pi$
$331$	2.12361e7	+	2.12361e7i	0.585586	+	0.585586i	−0.350847	+	0.936433i	$0.614106\pi$
$332$		−	5.16428e6i		−	0.141122i
$333$	−7.28940e6	−	9.33697e6i	−0.197405	−	0.252856i
$334$	4.52722e7			1.21504
$335$	1.76104e7	−	1.76104e7i	0.468419	−	0.468419i
$336$		−	5.01486e6i		−	0.132203i
$337$		−	8.40416e6i		−	0.219586i	−0.993954	−	0.109793i	$-0.964981\pi$
$337$		−	8.40416e6i		−	0.219586i	0.993954	−	0.109793i	$-0.0350188\pi$
$338$	−4.14941e7	−	4.14941e7i	−1.07457	−	1.07457i
$339$	−2.72361e7	−	2.72361e7i	−0.699112	−	0.699112i
$340$	−7.46178e7			−1.89848
$341$	1.51961e7	+	1.51961e7i	0.383238	+	0.383238i
$342$	−1.82065e7			−0.455142
$343$	2.13498e7			0.529069
$344$		−	1.40003e7i		−	0.343924i
$345$	1.03970e6			0.0253191
$346$	−3.66274e7	−	3.66274e7i	−0.884256	−	0.884256i
$347$	−5.50675e7	+	5.50675e7i	−1.31798	+	1.31798i	−0.402599	+	0.915377i	$0.631893\pi$
$347$	−5.50675e7	+	5.50675e7i	−1.31798	+	1.31798i	−0.915377	+	0.402599i	$0.868107\pi$
$348$	2.91346e7	−	2.91346e7i	0.691307	−	0.691307i
$349$	5.95699e7			1.40136			0.700681	−	0.713475i	$-0.252880\pi$
$349$	5.95699e7			1.40136			0.700681	+	0.713475i	$0.252880\pi$
$350$	−2.12977e7	−	2.12977e7i	−0.496740	−	0.496740i
$351$	−1.29335e6	+	1.29335e6i	−0.0299085	+	0.0299085i
$352$	−1.73522e7	−	1.73522e7i	−0.397857	−	0.397857i
$353$	2.02809e7	−	2.02809e7i	0.461066	−	0.461066i	−0.437938	−	0.899005i	$-0.644291\pi$
$353$	2.02809e7	−	2.02809e7i	0.461066	−	0.461066i	0.899005	+	0.437938i	$0.144291\pi$
$354$		−	9.42159e7i		−	2.12380i
$355$	1.01075e8	+	1.01075e8i	2.25923	+	2.25923i
$356$	2.85839e7	+	2.85839e7i	0.633537	+	0.633537i
$357$	−6.42307e6	+	6.42307e6i	−0.141169	+	0.141169i
$358$			1.31628e8i			2.86880i
$359$	−2.24291e7			−0.484762			−0.242381	−	0.970181i	$-0.577928\pi$
$359$	−2.24291e7			−0.484762			−0.242381	+	0.970181i	$0.577928\pi$
$360$		−	1.17966e7i		−	0.252843i
$361$		−	6.16082e6i		−	0.130953i
$362$	−8.11904e6	+	8.11904e6i	−0.171151	+	0.171151i
$363$			3.27676e7i			0.685053i
$364$	−479586.	+	479586.i	−0.00994403	+	0.00994403i
$365$	−3.52875e7	+	3.52875e7i	−0.725675	+	0.725675i
$366$	6.76090e7			1.37899
$367$	−5.48623e7			−1.10988			−0.554939	−	0.831891i	$-0.687259\pi$
$367$	−5.48623e7			−1.10988			−0.554939	+	0.831891i	$0.687259\pi$
$368$	−385942.	−	385942.i	−0.00774423	−	0.00774423i
$369$		−	1.82291e7i		−	0.362815i
$370$	−7.76482e7	−	9.94593e7i	−1.53294	−	1.96354i
$371$	−1.70290e7			−0.333478
$372$	−5.21007e7	+	5.21007e7i	−1.01208	+	1.01208i
$373$			2.70435e7i			0.521119i	0.965458	+	0.260559i	$0.0839070\pi$
$373$			2.70435e7i			0.521119i	−0.965458	+	0.260559i	$0.916093\pi$
$374$			2.88208e7i			0.550924i
$375$	−3.41478e7	−	3.41478e7i	−0.647544	−	0.647544i
$376$	2.77392e7	+	2.77392e7i	0.521832	+	0.521832i
$377$	1.87625e6			0.0350160
$378$	−1.73947e7	−	1.73947e7i	−0.322063	−	0.322063i
$379$	1.50529e7			0.276504			0.138252	−	0.990397i	$-0.455852\pi$
$379$	1.50529e7			0.276504			0.138252	+	0.990397i	$0.455852\pi$
$380$	−1.10215e8			−2.00858
$381$			3.29233e6i			0.0595290i
$382$	2.24908e7			0.403473
$383$	2.95424e7	+	2.95424e7i	0.525834	+	0.525834i	0.919327	−	0.393493i	$-0.128734\pi$
$383$	2.95424e7	+	2.95424e7i	0.525834	+	0.525834i	−0.393493	+	0.919327i	$0.628734\pi$
$384$	3.01900e7	−	3.01900e7i	0.533174	−	0.533174i
$385$	−7.45941e6	+	7.45941e6i	−0.130714	+	0.130714i
$386$	9.11477e7			1.58483
$387$	9.38956e6	+	9.38956e6i	0.161999	+	0.161999i
$388$	5.18212e7	−	5.18212e7i	0.887181	−	0.887181i
$389$	−4.11534e7	−	4.11534e7i	−0.699128	−	0.699128i	0.265095	−	0.964222i	$-0.414597\pi$
$389$	−4.11534e7	−	4.11534e7i	−0.699128	−	0.699128i	−0.964222	+	0.265095i	$0.914597\pi$
$390$	−3.34612e6	+	3.34612e6i	−0.0564088	+	0.0564088i
$391$			988635.i			0.0165389i
$392$	1.89612e7	+	1.89612e7i	0.314780	+	0.314780i
$393$	7.64126e6	+	7.64126e6i	0.125889	+	0.125889i
$394$	8.38834e7	−	8.38834e7i	1.37147	−	1.37147i
$395$		−	8.27123e7i		−	1.34208i
$396$	−1.07731e7			−0.173482
$397$		−	1.64168e7i		−	0.262371i	−0.991358	−	0.131186i	$-0.958122\pi$
$397$		−	1.64168e7i		−	0.262371i	0.991358	−	0.131186i	$-0.0418784\pi$
$398$		−	9.12596e7i		−	1.44754i
$399$	−9.48726e6	+	9.48726e6i	−0.149356	+	0.149356i
$400$			6.26945e7i			0.979601i
$401$	−4.34443e7	+	4.34443e7i	−0.673752	+	0.673752i	−0.958579	−	0.284827i	$-0.908064\pi$
$401$	−4.34443e7	+	4.34443e7i	−0.673752	+	0.673752i	0.284827	+	0.958579i	$0.408064\pi$
$402$	2.33209e7	−	2.33209e7i	0.358977	−	0.358977i
$403$	−3.35526e6			−0.0512638
$404$	1.45364e8			2.20452
$405$	−4.43080e7	−	4.43080e7i	−0.666986	−	0.666986i
$406$			2.52343e7i			0.377063i
$407$	−2.18315e7	+	1.70440e7i	−0.323818	+	0.252806i
$408$	−2.37506e7			−0.349699
$409$	−5.90313e7	+	5.90313e7i	−0.862804	+	0.862804i	−0.991663	−	0.128859i	$-0.958869\pi$
$409$	−5.90313e7	+	5.90313e7i	−0.862804	+	0.862804i	0.128859	+	0.991663i	$0.458869\pi$
$410$		−	1.94180e8i		−	2.81743i
$411$			5.86906e7i			0.845362i
$412$	4.43765e7	+	4.43765e7i	0.634543	+	0.634543i
$413$	2.31874e7	+	2.31874e7i	0.329156	+	0.329156i
$414$	−650272.			−0.00916419
$415$	8.86772e6	+	8.86772e6i	0.124070	+	0.124070i
$416$	3.83133e6			0.0532193
$417$	−4.39234e7			−0.605742
$418$			4.25701e7i			0.582875i
$419$	−4.26251e6			−0.0579460			−0.0289730	−	0.999580i	$-0.509224\pi$
$419$	−4.26251e6			−0.0579460			−0.0289730	+	0.999580i	$0.509224\pi$
$420$	−2.55751e7	−	2.55751e7i	−0.345199	−	0.345199i
$421$	5.43242e7	−	5.43242e7i	0.728026	−	0.728026i	−0.242200	−	0.970226i	$-0.577869\pi$
$421$	5.43242e7	−	5.43242e7i	0.728026	−	0.728026i	0.970226	+	0.242200i	$0.0778691\pi$
$422$	−5.02241e7	+	5.02241e7i	−0.668306	+	0.668306i
$423$	−3.72075e7			−0.491598
$424$	−3.14841e7	−	3.14841e7i	−0.413041	−	0.413041i
$425$	8.02996e7	−	8.02996e7i	1.04604	−	1.04604i
$426$	1.33851e8	+	1.33851e8i	1.73138	+	1.73138i
$427$	−1.66392e7	+	1.66392e7i	−0.213722	+	0.213722i
$428$			1.18096e8i			1.50627i
$429$	734480.	+	734480.i	0.00930268	+	0.00930268i
$430$	1.00020e8	+	1.00020e8i	1.25800	+	1.25800i
$431$	3.01654e7	−	3.01654e7i	0.376771	−	0.376771i	−0.493165	−	0.869936i	$-0.664160\pi$
$431$	3.01654e7	−	3.01654e7i	0.376771	−	0.376771i	0.869936	+	0.493165i	$0.164160\pi$
$432$			5.12050e7i			0.635128i
$433$	1.36055e8			1.67591			0.837954	−	0.545741i	$-0.183752\pi$
$433$	1.36055e8			1.67591			0.837954	+	0.545741i	$0.183752\pi$
$434$		−	4.51260e7i		−	0.552024i
$435$			1.00056e8i			1.21555i
$436$	1.26157e8	−	1.26157e8i	1.52214	−	1.52214i
$437$			1.46027e6i			0.0174980i
$438$	−4.67301e7	+	4.67301e7i	−0.556128	+	0.556128i
$439$	1.01667e8	−	1.01667e8i	1.20168	−	1.20168i	0.228018	−	0.973657i	$-0.426775\pi$
$439$	1.01667e8	−	1.01667e8i	1.20168	−	1.20168i	0.973657	−	0.228018i	$-0.0732246\pi$
$440$	−2.75827e7			−0.323801
$441$	−2.54332e7			−0.296542
$442$	−3.18178e6	−	3.18178e6i	−0.0368472	−	0.0368472i
$443$			2.13082e7i			0.245096i	0.992463	+	0.122548i	$0.0391065\pi$
$443$			2.13082e7i			0.245096i	−0.992463	+	0.122548i	$0.960894\pi$
$444$	−5.84363e7	−	7.48508e7i	−0.667627	−	0.855161i
$445$	−9.81645e7			−1.11397
$446$	−1.25012e8	+	1.25012e8i	−1.40912	+	1.40912i
$447$		−	7.83081e6i		−	0.0876767i
$448$			3.71052e7i			0.412668i
$449$	−6.17722e7	−	6.17722e7i	−0.682424	−	0.682424i	0.278122	−	0.960546i	$-0.410288\pi$
$449$	−6.17722e7	−	6.17722e7i	−0.682424	−	0.682424i	−0.960546	+	0.278122i	$0.910288\pi$
$450$	5.28168e7	+	5.28168e7i	0.579609	+	0.579609i
$451$	−4.26230e7			−0.464637
$452$	1.03122e8	+	1.03122e8i	1.11669	+	1.11669i
$453$	−2.89880e7			−0.311835
$454$	−2.03830e8			−2.17821
$455$		−	1.64702e6i		−	0.0174850i
$456$	−3.50811e7			−0.369980
$457$	3.45657e7	+	3.45657e7i	0.362157	+	0.362157i	0.864607	−	0.502450i	$-0.167568\pi$
$457$	3.45657e7	+	3.45657e7i	0.362157	+	0.362157i	−0.502450	+	0.864607i	$0.667568\pi$
$458$	−6.59795e7	+	6.59795e7i	−0.686772	+	0.686772i
$459$	6.55838e7	−	6.55838e7i	0.678201	−	0.678201i
$460$	−3.93650e6			−0.0404424
$461$	−1.14254e8	−	1.14254e8i	−1.16619	−	1.16619i	−0.983095	−	0.183094i	$-0.941389\pi$
$461$	−1.14254e8	−	1.14254e8i	−1.16619	−	1.16619i	−0.183094	−	0.983095i	$-0.558611\pi$
$462$	−9.87826e6	+	9.87826e6i	−0.100174	+	0.100174i
$463$	−5.86656e7	−	5.86656e7i	−0.591072	−	0.591072i	0.346849	−	0.937921i	$-0.387252\pi$
$463$	−5.86656e7	−	5.86656e7i	−0.591072	−	0.591072i	−0.937921	+	0.346849i	$0.887252\pi$
$464$	3.71413e7	−	3.71413e7i	0.371795	−	0.371795i
$465$		−	1.78927e8i		−	1.77958i
$466$	−1.56772e7	−	1.56772e7i	−0.154921	−	0.154921i
$467$	1.33143e8	+	1.33143e8i	1.30728	+	1.30728i	0.923371	+	0.383909i	$0.125422\pi$
$467$	1.33143e8	+	1.33143e8i	1.30728	+	1.30728i	0.383909	+	0.923371i	$0.374578\pi$
$468$	1.18934e6	−	1.18934e6i	0.0116029	−	0.0116029i
$469$			1.14790e7i			0.111272i
$470$	−3.96342e8			−3.81748
$471$		−	9.56603e7i		−	0.915523i
$472$			8.57402e7i			0.815377i
$473$	2.19545e7	−	2.19545e7i	0.207463	−	0.207463i
$474$		−	1.09533e8i		−	1.02852i
$475$	1.18607e8	−	1.18607e8i	1.10670	−	1.10670i
$476$	2.43191e7	−	2.43191e7i	0.225489	−	0.225489i
$477$	4.22307e7			0.389110
$478$	6.48499e7			0.593781
$479$	−6.36509e7	−	6.36509e7i	−0.579160	−	0.579160i	0.355512	−	0.934672i	$-0.384306\pi$
$479$	−6.36509e7	−	6.36509e7i	−0.579160	−	0.579160i	−0.934672	+	0.355512i	$0.884306\pi$
$480$			2.04315e8i			1.84746i
$481$	528544.	−	4.29181e6i	0.00474948	−	0.0385661i
$482$	−2.79232e8			−2.49359
$483$	−338852.	+	338852.i	−0.00300724	+	0.00300724i
$484$		−	1.24065e8i		−	1.09424i
$485$			1.77967e8i			1.55996i
$486$	7.57980e7	+	7.57980e7i	0.660312	+	0.660312i
$487$	−1.93618e7	−	1.93618e7i	−0.167633	−	0.167633i	0.618305	−	0.785938i	$-0.287820\pi$
$487$	−1.93618e7	−	1.93618e7i	−0.167633	−	0.167633i	−0.785938	+	0.618305i	$0.787820\pi$
$488$	−6.15268e7			−0.529426
$489$	5.63796e7	+	5.63796e7i	0.482165	+	0.482165i
$490$	−2.70920e8			−2.30278
$491$	1.61728e8			1.36629			0.683143	−	0.730285i	$-0.260613\pi$
$491$	1.61728e8			1.36629			0.683143	+	0.730285i	$0.260613\pi$
$492$		−	1.46135e8i		−	1.22704i
$493$	−9.51418e7			−0.794018
$494$	−4.69969e6	−	4.69969e6i	−0.0389841	−	0.0389841i
$495$	1.84988e7	−	1.84988e7i	0.152520	−	0.152520i
$496$	−6.64190e7	+	6.64190e7i	−0.544312	+	0.544312i
$497$	−6.58838e7			−0.536673
$498$	1.17432e7	+	1.17432e7i	0.0950824	+	0.0950824i
$499$	1.05979e8	−	1.05979e8i	0.852942	−	0.852942i	−0.137553	−	0.990494i	$-0.543924\pi$
$499$	1.05979e8	−	1.05979e8i	0.852942	−	0.852942i	0.990494	+	0.137553i	$0.0439236\pi$
$500$	1.29291e8	+	1.29291e8i	1.03433	+	1.03433i
$501$	−5.85039e7	+	5.85039e7i	−0.465235	+	0.465235i
$502$			9.18863e7i			0.726339i
$503$	−209320.	−	209320.i	−0.00164478	−	0.00164478i	0.706284	−	0.707929i	$-0.250370\pi$
$503$	−209320.	−	209320.i	−0.00164478	−	0.00164478i	−0.707929	+	0.706284i	$0.750370\pi$
$504$	3.84470e6	+	3.84470e6i	0.0300310	+	0.0300310i
$505$	−2.49609e8	+	2.49609e8i	−1.93814	+	1.93814i
$506$			1.52045e6i			0.0117361i
$507$	1.07243e8			0.822899
$508$		−	1.24654e7i		−	0.0950859i
$509$		−	2.06918e8i		−	1.56908i	−0.620076	−	0.784542i	$-0.712898\pi$
$509$		−	2.06918e8i		−	1.56908i	0.620076	−	0.784542i	$-0.287102\pi$
$510$	1.69676e8	−	1.69676e8i	1.27912	−	1.27912i
$511$		−	2.30014e7i		−	0.172382i
$512$	1.02510e8	−	1.02510e8i	0.763759	−	0.763759i
$513$	9.68711e7	−	9.68711e7i	0.717534	−	0.717534i
$514$	2.92818e8			2.15629
$515$	−1.52400e8			−1.11574
$516$	7.52724e7	+	7.52724e7i	0.547882	+	0.547882i
$517$			8.69981e7i			0.629561i
$518$	5.77220e7	+	7.10857e6i	0.415290	+	0.0511438i
$519$	9.46651e7			0.677155
$520$	3.04510e6	−	3.04510e6i	0.0216566	−	0.0216566i
$521$			2.10848e8i			1.49092i	0.666548	+	0.745462i	$0.267771\pi$
$521$			2.10848e8i			1.49092i	−0.666548	+	0.745462i	$0.732229\pi$
$522$		−	6.25792e7i		−	0.439966i
$523$	1.05901e8	+	1.05901e8i	0.740280	+	0.740280i	0.972632	−	0.232352i	$-0.0746421\pi$
$523$	1.05901e8	+	1.05901e8i	0.740280	+	0.740280i	−0.232352	+	0.972632i	$0.574642\pi$
$524$	−2.89314e7	−	2.89314e7i	−0.201083	−	0.201083i
$525$	5.50450e7			0.380399
$526$	1.05269e8	+	1.05269e8i	0.723344	+	0.723344i
$527$	1.70140e8			1.16245
$528$	2.90788e7			0.197549
$529$		−	1.47984e8i		−	0.999648i
$530$	4.49850e8			3.02162
$531$	−5.75031e7	−	5.75031e7i	−0.384068	−	0.384068i
$532$	3.59207e7	−	3.59207e7i	0.238567	−	0.238567i
$533$	4.70552e6	−	4.70552e6i	0.0310761	−	0.0310761i
$534$	−1.29996e8			−0.853703
$535$	−2.02786e8	−	2.02786e8i	−1.32427	−	1.32427i
$536$	−2.12229e7	+	2.12229e7i	−0.137819	+	0.137819i
$537$	−1.70099e8	−	1.70099e8i	−1.09845	−	1.09845i
$538$	−7.97018e7	+	7.97018e7i	−0.511825	+	0.511825i
$539$			5.94676e7i			0.379764i
$540$	2.61138e8	+	2.61138e8i	1.65840	+	1.65840i
$541$	−1.31144e8	−	1.31144e8i	−0.828239	−	0.828239i	0.159034	−	0.987273i	$-0.449162\pi$
$541$	−1.31144e8	−	1.31144e8i	−0.828239	−	0.828239i	−0.987273	+	0.159034i	$0.949162\pi$
$542$	−2.03653e7	+	2.03653e7i	−0.127906	+	0.127906i
$543$		−	2.09840e7i		−	0.131066i
$544$	−1.94281e8			−1.20679
$545$			4.33257e8i			2.67643i
$546$		−	2.18110e6i		−	0.0133998i
$547$	1.19921e7	−	1.19921e7i	0.0732709	−	0.0732709i	−0.669522	−	0.742793i	$-0.733501\pi$
$547$	1.19921e7	−	1.19921e7i	0.0732709	−	0.0732709i	0.742793	+	0.669522i	$0.233501\pi$
$548$		−	2.22214e8i		−	1.35030i
$549$	4.12640e7	−	4.12640e7i	0.249376	−	0.249376i
$550$	1.23495e8	−	1.23495e8i	0.742272	−	0.742272i
$551$	−1.40530e8			−0.840068
$552$	−1.25297e6			−0.00744946
$553$	2.69572e7	+	2.69572e7i	0.159404	+	0.159404i
$554$			4.10831e8i			2.41620i
$555$	2.28871e8	+	2.81859e7i	1.33879	+	0.164874i
$556$	1.66303e8			0.967554
$557$	1.32109e8	−	1.32109e8i	0.764479	−	0.764479i	−0.212649	−	0.977129i	$-0.568209\pi$
$557$	1.32109e8	−	1.32109e8i	0.764479	−	0.764479i	0.977129	+	0.212649i	$0.0682092\pi$
$558$			1.11909e8i			0.644114i
$559$			4.84751e6i			0.0277513i
$560$	−3.26036e7	−	3.26036e7i	−0.185653	−	0.185653i
$561$	−3.72443e7	−	3.72443e7i	−0.210946	−	0.210946i
$562$	1.34478e8			0.757602
$563$	2.01981e8	+	2.01981e8i	1.13184	+	1.13184i	0.989871	+	0.141973i	$0.0453445\pi$
$563$	2.01981e8	+	2.01981e8i	1.13184	+	1.13184i	0.141973	+	0.989871i	$0.454655\pi$
$564$	−2.98278e8			−1.66259
$565$	−3.54146e8			−1.96353
$566$		−	4.60684e8i		−	2.54070i
$567$	2.88813e7			0.158441
$568$	−1.21809e8	−	1.21809e8i	−0.664715	−	0.664715i
$569$	−1.32510e8	+	1.32510e8i	−0.719303	+	0.719303i	−0.968463	−	0.249159i	$-0.919846\pi$
$569$	−1.32510e8	+	1.32510e8i	−0.719303	+	0.719303i	0.249159	+	0.968463i	$0.419846\pi$
$570$	2.50622e8	−	2.50622e8i	1.35330	−	1.35330i
$571$	−2.77650e8			−1.49138			−0.745691	−	0.666292i	$-0.767880\pi$
$571$	−2.77650e8			−1.49138			−0.745691	+	0.666292i	$0.767880\pi$
$572$	−2.78089e6	−	2.78089e6i	−0.0148592	−	0.0148592i
$573$	−2.90642e7	+	2.90642e7i	−0.154488	+	0.154488i
$574$	6.32861e7	+	6.32861e7i	0.334636	+	0.334636i
$575$	4.23624e6	−	4.23624e6i	0.0222832	−	0.0222832i
$576$		−	9.20181e7i		−	0.481511i
$577$	3.03337e6	+	3.03337e6i	0.0157906	+	0.0157906i	0.714958	−	0.699167i	$-0.246446\pi$
$577$	3.03337e6	+	3.03337e6i	0.0157906	+	0.0157906i	−0.699167	+	0.714958i	$0.746446\pi$
$578$	−4.64712e7	−	4.64712e7i	−0.240658	−	0.240658i
$579$	−1.17788e8	+	1.17788e8i	−0.606826	+	0.606826i
$580$		−	3.78831e8i		−	1.94161i
$581$	−5.78025e6			−0.0294726
$582$			2.35676e8i			1.19549i
$583$		−	9.87431e7i		−	0.498312i
$584$	4.25262e7	−	4.25262e7i	0.213510	−	0.213510i
$585$			4.08449e6i			0.0204019i
$586$	6.54988e6	−	6.54988e6i	0.0325492	−	0.0325492i
$587$	−1.27368e8	+	1.27368e8i	−0.629716	+	0.629716i	−0.947997	−	0.318280i	$-0.896895\pi$
$587$	−1.27368e8	+	1.27368e8i	−0.629716	+	0.629716i	0.318280	+	0.947997i	$0.396895\pi$
$588$	−2.03888e8			−1.00291
$589$	2.51307e8			1.22987
$590$	−6.12535e8	−	6.12535e8i	−2.98246	−	2.98246i
$591$			2.16800e8i			1.05026i
$592$	−7.44957e7	−	9.54213e7i	−0.359059	−	0.459918i
$593$	1.31006e8			0.628243			0.314121	−	0.949383i	$-0.398290\pi$
$593$	1.31006e8			0.628243			0.314121	+	0.949383i	$0.398290\pi$
$594$	1.00863e8	−	1.00863e8i	0.481254	−	0.481254i
$595$			8.35179e7i			0.396487i
$596$			2.96490e7i			0.140046i
$597$	1.17932e8	+	1.17932e8i	0.554255	+	0.554255i
$598$	−167856.	−	167856.i	−0.000784937	−	0.000784937i
$599$	−5.73348e7			−0.266771			−0.133385	−	0.991064i	$-0.542585\pi$
$599$	−5.73348e7			−0.266771			−0.133385	+	0.991064i	$0.542585\pi$
$600$	1.01770e8	+	1.01770e8i	0.471157	+	0.471157i
$601$	−1.27728e8			−0.588389			−0.294194	−	0.955746i	$-0.595051\pi$
$601$	−1.27728e8			−0.588389			−0.294194	+	0.955746i	$0.595051\pi$
$602$	−6.51957e7			−0.298834
$603$		−	2.84670e7i		−	0.129834i
$604$	1.09755e8			0.498095
$605$	2.13035e8	+	2.13035e8i	0.962021	+	0.962021i
$606$	−3.30549e8	+	3.30549e8i	−1.48531	+	1.48531i
$607$	8.21784e7	−	8.21784e7i	0.367444	−	0.367444i	−0.499100	−	0.866544i	$-0.666336\pi$
$607$	8.21784e7	−	8.21784e7i	0.367444	−	0.367444i	0.866544	+	0.499100i	$0.166336\pi$
$608$	−2.86964e8			−1.27678
$609$	−3.26096e7	−	3.26096e7i	−0.144376	−	0.144376i
$610$	4.39553e8	−	4.39553e8i	1.93652	−	1.93652i
$611$	−9.60449e6	−	9.60449e6i	−0.0421066	−	0.0421066i
$612$	−6.03095e7	+	6.03095e7i	−0.263106	+	0.263106i
$613$			3.28487e8i			1.42605i	0.701136	+	0.713027i	$0.252676\pi$
$613$			3.28487e8i			1.42605i	−0.701136	+	0.713027i	$0.747324\pi$
$614$	−2.84477e8	−	2.84477e8i	−1.22897	−	1.22897i
$615$	2.50933e8	+	2.50933e8i	1.07878	+	1.07878i
$616$	8.98960e6	−	8.98960e6i	0.0384590	−	0.0384590i
$617$		−	2.08749e8i		−	0.888729i	−0.895846	−	0.444365i	$-0.853429\pi$
$617$		−	2.08749e8i		−	0.888729i	0.895846	−	0.444365i	$-0.146571\pi$
$618$	−2.01819e8			−0.855059
$619$			1.59465e8i			0.672348i	0.941800	+	0.336174i	$0.109133\pi$
$619$			1.59465e8i			0.672348i	−0.941800	+	0.336174i	$0.890867\pi$
$620$			6.77455e8i			2.84253i
$621$	3.45990e6	−	3.45990e6i	0.0144474	−	0.0144474i
$622$		−	4.43321e7i		−	0.184224i
$623$	3.19933e7	−	3.19933e7i	0.132311	−	0.132311i
$624$	−3.21026e6	+	3.21026e6i	−0.0132126	+	0.0132126i
$625$	−3.41303e7			−0.139798
$626$	−2.07244e8			−0.844811
$627$	−5.50121e7	−	5.50121e7i	−0.223180	−	0.223180i
$628$			3.62189e8i			1.46237i
$629$	−2.68017e7	+	2.17631e8i	−0.107699	+	0.874518i
$630$	−5.49336e7			−0.219693
$631$	3.29719e7	−	3.29719e7i	0.131237	−	0.131237i	−0.638437	−	0.769674i	$-0.720419\pi$
$631$	3.29719e7	−	3.29719e7i	0.131237	−	0.131237i	0.769674	+	0.638437i	$0.220419\pi$
$632$			9.96796e7i			0.394871i
$633$		−	1.29807e8i		−	0.511782i
$634$	5.08547e8	+	5.08547e8i	1.99555	+	1.99555i
$635$	2.14048e7	+	2.14048e7i	0.0835967	+	0.0835967i
$636$	3.38547e8			1.31597
$637$	−6.56516e6	−	6.56516e6i	−0.0253996	−	0.0253996i
$638$	−1.46322e8			−0.563439
$639$	1.63387e8			0.626203
$640$		−	3.92554e8i		−	1.49748i
$641$	−1.24257e8			−0.471789			−0.235894	−	0.971779i	$-0.575802\pi$
$641$	−1.24257e8			−0.471789			−0.235894	+	0.971779i	$0.575802\pi$
$642$	−2.68543e8	−	2.68543e8i	−1.01486	−	1.01486i
$643$	1.15714e8	−	1.15714e8i	0.435265	−	0.435265i	−0.455150	−	0.890415i	$-0.650414\pi$
$643$	1.15714e8	−	1.15714e8i	0.435265	−	0.435265i	0.890415	+	0.455150i	$0.150414\pi$
$644$	1.28296e6	−	1.28296e6i	0.00480349	−	0.00480349i
$645$	−2.58505e8			−0.963362
$646$	2.38314e8	+	2.38314e8i	0.883998	+	0.883998i
$647$	3.03054e8	−	3.03054e8i	1.11894	−	1.11894i	0.127043	−	0.991897i	$-0.459451\pi$
$647$	3.03054e8	−	3.03054e8i	1.11894	−	1.11894i	0.991897	−	0.127043i	$-0.0405485\pi$
$648$	5.33971e7	+	5.33971e7i	0.196242	+	0.196242i
$649$	−1.34453e8	+	1.34453e8i	−0.491853	+	0.491853i
$650$			2.72675e7i			0.0992900i
$651$	5.83151e7	+	5.83151e7i	0.211367	+	0.211367i
$652$	−2.13465e8	−	2.13465e8i	−0.770164	−	0.770164i
$653$	1.45914e8	−	1.45914e8i	0.524031	−	0.524031i	−0.394755	−	0.918786i	$-0.629171\pi$
$653$	1.45914e8	−	1.45914e8i	0.524031	−	0.524031i	0.918786	+	0.394755i	$0.129171\pi$
$654$			5.73748e8i			2.05111i
$655$	9.93577e7			0.353572
$656$		−	1.86296e8i		−	0.659922i
$657$			5.70419e7i			0.201140i
$658$	1.29174e8	−	1.29174e8i	0.453416	−	0.453416i
$659$		−	3.13583e8i		−	1.09571i	−0.836573	−	0.547856i	$-0.815444\pi$
$659$		−	3.13583e8i		−	1.09571i	0.836573	−	0.547856i	$-0.184556\pi$
$660$	1.48298e8	−	1.48298e8i	0.515825	−	0.515825i
$661$	4.10325e7	−	4.10325e7i	0.142077	−	0.142077i	−0.632491	−	0.774568i	$-0.717967\pi$
$661$	4.10325e7	−	4.10325e7i	0.142077	−	0.142077i	0.774568	+	0.632491i	$0.217967\pi$
$662$	3.65668e8			1.26041
$663$	8.22346e6			0.0282172
$664$	−1.06868e7	−	1.06868e7i	−0.0365043	−	0.0365043i
$665$			1.23361e8i			0.419481i
$666$	−1.43146e8	−	1.76287e7i	−0.484571	−	0.0596758i
$667$	−5.01925e6			−0.0169146
$668$	2.21508e8	−	2.21508e8i	0.743121	−	0.743121i
$669$		−	3.23100e8i		−	1.07909i
$670$		−	3.03236e8i		−	1.00822i
$671$	−9.64829e7	−	9.64829e7i	−0.319362	−	0.319362i
$672$	−6.65892e7	−	6.65892e7i	−0.219430	−	0.219430i
$673$	−1.32621e8			−0.435078			−0.217539	−	0.976052i	$-0.569803\pi$
$673$	−1.32621e8			−0.435078			−0.217539	+	0.976052i	$0.569803\pi$
$674$	−7.23564e7	−	7.23564e7i	−0.236318	−	0.236318i
$675$	−5.62045e8			−1.82751
$676$	−4.06045e8			−1.31442
$677$		−	2.59030e8i		−	0.834804i	−0.908722	−	0.417402i	$-0.862941\pi$
$677$		−	2.59030e8i		−	0.834804i	0.908722	−	0.417402i	$-0.137059\pi$
$678$	−4.68984e8			−1.50477
$679$	−5.80022e7	−	5.80022e7i	−0.185283	−	0.185283i
$680$	−1.54412e8	+	1.54412e8i	−0.491083	+	0.491083i
$681$	2.63404e8	−	2.63404e8i	0.834028	−	0.834028i
$682$	2.61664e8			0.824881
$683$	1.03943e8	+	1.03943e8i	0.326238	+	0.326238i	0.851154	−	0.524916i	$-0.175903\pi$
$683$	1.03943e8	+	1.03943e8i	0.326238	+	0.326238i	−0.524916	+	0.851154i	$0.675903\pi$
$684$	−8.90807e7	+	8.90807e7i	−0.278365	+	0.278365i
$685$	3.81571e8	+	3.81571e8i	1.18714	+	1.18714i
$686$	1.83813e8	−	1.83813e8i	0.569383	−	0.569383i
$687$		−	1.70527e8i		−	0.525924i
$688$	9.59587e7	+	9.59587e7i	0.294659	+	0.294659i
$689$	1.09011e7	+	1.09011e7i	0.0333283	+	0.0333283i
$690$	8.95135e6	−	8.95135e6i	0.0272484	−	0.0272484i
$691$			3.07373e8i			0.931605i	0.884889	+	0.465803i	$0.154234\pi$
$691$			3.07373e8i			0.931605i	−0.884889	+	0.465803i	$0.845766\pi$
$692$	−3.58421e8			−1.08162
$693$			1.20581e7i			0.0362308i
$694$			9.48218e8i			2.83681i
$695$	−2.85563e8	+	2.85563e8i	−0.850644	+	0.850644i
$696$		−	1.20581e8i		−	0.357643i
$697$	−2.38610e8	+	2.38610e8i	−0.704677	+	0.704677i
$698$	5.12872e8	−	5.12872e8i	1.50814	−	1.50814i
$699$	4.05185e7			0.118637
$700$	−2.08411e8			−0.607613
$701$	−3.34255e8	−	3.34255e8i	−0.970341	−	0.970341i	0.0292320	−	0.999573i	$-0.490694\pi$
$701$	−3.34255e8	−	3.34255e8i	−0.970341	−	0.970341i	−0.999573	+	0.0292320i	$0.990694\pi$
$702$			2.22704e7i			0.0643750i
$703$	−3.95877e7	+	3.21454e8i	−0.113945	+	0.925237i
$704$	−2.15155e8			−0.616643
$705$	5.12182e8	−	5.12182e8i	1.46170	−	1.46170i
$706$		−	3.49221e8i		−	0.992398i
$707$		−	1.62703e8i		−	0.460401i
$708$	−4.60980e8	−	4.60980e8i	−1.29892	−	1.29892i
$709$	−7.21367e7	−	7.21367e7i	−0.202403	−	0.202403i	0.598626	−	0.801029i	$-0.295714\pi$
$709$	−7.21367e7	−	7.21367e7i	−0.202403	−	0.202403i	−0.801029	+	0.598626i	$0.795714\pi$
$710$	1.74043e9			4.86275
$711$	−6.68518e7	−	6.68518e7i	−0.185996	−	0.185996i
$712$	1.18302e8			0.327756
$713$	8.97582e6			0.0247631
$714$			1.10600e8i			0.303851i
$715$	9.55029e6			0.0261275
$716$	6.44031e8	+	6.44031e8i	1.75456	+	1.75456i
$717$	−8.38038e7	+	8.38038e7i	−0.227356	+	0.227356i
$718$	−1.93106e8	+	1.93106e8i	−0.521701	+	0.521701i
$719$	5.01557e7			0.134938			0.0674689	−	0.997721i	$-0.478508\pi$
$719$	5.01557e7			0.134938			0.0674689	+	0.997721i	$0.478508\pi$
$720$	8.08545e7	+	8.08545e7i	0.216624	+	0.216624i
$721$	4.96695e7	−	4.96695e7i	0.132521	−	0.132521i
$722$	−5.30421e7	−	5.30421e7i	−0.140932	−	0.140932i
$723$	3.60844e8	−	3.60844e8i	0.954783	−	0.954783i
$724$			7.94497e7i			0.209352i
$725$	4.07677e8	+	4.07677e8i	1.06980	+	1.06980i
$726$	2.82115e8	+	2.82115e8i	0.737253	+	0.737253i
$727$	5.23036e7	−	5.23036e7i	0.136122	−	0.136122i	−0.635763	−	0.771885i	$-0.719314\pi$
$727$	5.23036e7	−	5.23036e7i	0.136122	−	0.136122i	0.771885	+	0.635763i	$0.219314\pi$
$728$			1.98488e6i			0.00514447i
$729$	−4.19176e8			−1.08197
$730$			6.07622e8i			1.56194i
$731$		−	2.45809e8i		−	0.629284i
$732$	3.30798e8	−	3.30798e8i	0.843391	−	0.843391i
$733$			3.13119e8i			0.795055i	0.917590	+	0.397527i	$0.130132\pi$
$733$			3.13119e8i			0.795055i	−0.917590	+	0.397527i	$0.869868\pi$
$734$	−4.72342e8	+	4.72342e8i	−1.19445	+	1.19445i
$735$	3.50103e8	−	3.50103e8i	0.881725	−	0.881725i
$736$	−1.02494e7			−0.0257077
$737$	−6.65610e7			−0.166271
$738$	−1.56945e8	−	1.56945e8i	−0.390462	−	0.390462i
$739$			1.53599e7i			0.0380587i	0.999819	+	0.0190293i	$0.00605759\pi$
$739$			1.53599e7i			0.0380587i	−0.999819	+	0.0190293i	$0.993942\pi$
$740$	−8.66552e8	−	1.06718e8i	−2.13845	−	0.263354i
$741$	1.21465e7			0.0298537
$742$	−1.46613e8	+	1.46613e8i	−0.358889	+	0.358889i
$743$		−	2.03569e8i		−	0.496300i	−0.968722	−	0.248150i	$-0.920177\pi$
$743$		−	2.03569e8i		−	0.496300i	0.968722	−	0.248150i	$-0.0798226\pi$
$744$			2.15632e8i			0.523593i
$745$	−5.09112e7	−	5.09112e7i	−0.123125	−	0.123125i
$746$	2.32834e8	+	2.32834e8i	0.560827	+	0.560827i
$747$	1.43346e7			0.0343893
$748$	1.41015e8	+	1.41015e8i	0.336945	+	0.336945i
$749$	1.32182e8			0.314576
$750$	−5.87998e8			−1.39377
$751$		−	3.47170e8i		−	0.819638i	−0.912167	−	0.409819i	$-0.865592\pi$
$751$		−	3.47170e8i		−	0.819638i	0.912167	−	0.409819i	$-0.134408\pi$
$752$	−3.80251e8			−0.894163
$753$	−1.18742e8	−	1.18742e8i	−0.278112	−	0.278112i
$754$	1.61538e7	−	1.61538e7i	0.0376842	−	0.0376842i
$755$	−1.88463e8	+	1.88463e8i	−0.437910	+	0.437910i
$756$	−1.70218e8			−0.393948
$757$	1.30932e8	+	1.30932e8i	0.301827	+	0.301827i	0.841728	−	0.539901i	$-0.181538\pi$
$757$	1.30932e8	+	1.30932e8i	0.301827	+	0.301827i	−0.539901	+	0.841728i	$0.681538\pi$
$758$	1.29599e8	−	1.29599e8i	0.297573	−	0.297573i
$759$	−1.96484e6	−	1.96484e6i	−0.00449368	−	0.00449368i
$760$	−2.28076e8	+	2.28076e8i	−0.519563	+	0.519563i
$761$			6.22058e8i			1.41149i	0.708467	+	0.705743i	$0.249387\pi$
$761$			6.22058e8i			1.41149i	−0.708467	+	0.705743i	$0.750613\pi$
$762$	2.83456e7	+	2.83456e7i	0.0640650	+	0.0640650i
$763$	−1.41205e8	−	1.41205e8i	−0.317889	−	0.317889i
$764$	1.10043e8	−	1.10043e8i	0.246764	−	0.246764i
$765$		−	2.07118e8i		−	0.462630i
$766$	5.08695e8			1.13180
$767$		−	2.96869e7i		−	0.0657928i
$768$			4.05221e7i			0.0894558i
$769$	2.55183e7	−	2.55183e7i	0.0561141	−	0.0561141i	−0.678493	−	0.734607i	$-0.737367\pi$
$769$	2.55183e7	−	2.55183e7i	0.0561141	−	0.0561141i	0.734607	+	0.678493i	$0.237367\pi$
$770$			1.28445e8i			0.281349i
$771$	−3.78400e8	+	3.78400e8i	−0.825635	+	0.825635i
$772$	4.45968e8	−	4.45968e8i	0.969286	−	0.969286i
$773$	4.59590e8			0.995021			0.497511	−	0.867458i	$-0.334248\pi$
$773$	4.59590e8			0.995021			0.497511	+	0.867458i	$0.334248\pi$
$774$	1.61680e8			0.348686
$775$	−7.29040e8	−	7.29040e8i	−1.56620	−	1.56620i
$776$		−	2.14475e8i		−	0.458977i
$777$	−8.37787e7	+	6.54063e7i	−0.178596	+	0.139430i
$778$	−7.08627e8			−1.50480
$779$	−3.52441e8	+	3.52441e8i	−0.745545	+	0.745545i
$780$			3.27438e7i			0.0689993i
$781$		−	3.82029e8i		−	0.801942i
$782$	8.51174e6	+	8.51174e6i	0.0177991	+	0.0177991i
$783$	3.32965e8	+	3.32965e8i	0.693608	+	0.693608i
$784$	−2.59921e8			−0.539378
$785$	−6.21926e8	−	6.21926e8i	−1.28567	−	1.28567i
$786$	1.31576e8			0.270963
$787$	2.06596e8			0.423836			0.211918	−	0.977287i	$-0.432029\pi$
$787$	2.06596e8			0.423836			0.211918	+	0.977287i	$0.432029\pi$
$788$		−	8.20850e8i		−	1.67759i
$789$	−2.72073e8			−0.553930
$790$	−7.12119e8	−	7.12119e8i	−1.44435	−	1.44435i
$791$	1.15421e8	−	1.15421e8i	0.233215	−	0.233215i
$792$	−2.22935e7	+	2.22935e7i	−0.0448749	+	0.0448749i
$793$	2.13032e7			0.0427194
$794$	−1.41342e8	−	1.41342e8i	−0.282364	−	0.282364i
$795$	−5.81328e8	+	5.81328e8i	−1.15696	+	1.15696i
$796$	−4.46515e8	−	4.46515e8i	−0.885313	−	0.885313i
$797$	1.29655e8	−	1.29655e8i	0.256103	−	0.256103i	−0.567364	−	0.823467i	$-0.692037\pi$
$797$	1.29655e8	−	1.29655e8i	0.256103	−	0.256103i	0.823467	+	0.567364i	$0.192037\pi$
$798$			1.63363e8i			0.321473i
$799$	4.87029e8	+	4.87029e8i	0.954804	+	0.954804i
$800$	8.32481e8	+	8.32481e8i	1.62594	+	1.62594i
$801$	−7.93410e7	+	7.93410e7i	−0.154383	+	0.154383i
$802$			7.48076e8i			1.45018i
$803$	1.33374e8			0.257588
$804$		−	2.28209e8i		−	0.439101i
$805$			4.40602e6i			0.00844616i
$806$	−2.88874e7	+	2.88874e7i	−0.0551701	+	0.0551701i
$807$		−	2.05993e8i		−	0.391951i
$808$	3.00813e8	−	3.00813e8i	0.570246	−	0.570246i
$809$	−5.20850e8	+	5.20850e8i	−0.983710	+	0.983710i	−0.999869	−	0.0161593i	$-0.994856\pi$
$809$	−5.20850e8	+	5.20850e8i	−0.983710	+	0.983710i	0.0161593	+	0.999869i	$0.494856\pi$
$810$	−7.62947e8			−1.43562
$811$	6.10129e8			1.14382			0.571912	−	0.820315i	$-0.306202\pi$
$811$	6.10129e8			1.14382			0.571912	+	0.820315i	$0.306202\pi$
$812$	1.23467e8	+	1.23467e8i	0.230612	+	0.230612i
$813$		−	5.26349e7i		−	0.0979495i
$814$	−4.12192e7	+	3.34702e8i	−0.0764234	+	0.620562i
$815$	7.33093e8			1.35421
$816$	1.62787e8	−	1.62787e8i	0.299606	−	0.299606i
$817$		−	3.63075e8i		−	0.665780i
$818$			1.01647e9i			1.85710i
$819$	−1.33120e6	−	1.33120e6i	−0.00242321	−	0.00242321i
$820$	−9.50085e8	−	9.50085e8i	−1.72314	−	1.72314i
$821$	−5.91871e8			−1.06954			−0.534771	−	0.844997i	$-0.679602\pi$
$821$	−5.91871e8			−1.06954			−0.534771	+	0.844997i	$0.679602\pi$
$822$	5.05302e8	+	5.05302e8i	0.909778	+	0.909778i
$823$	−1.07200e8			−0.192307			−0.0961533	−	0.995367i	$-0.530654\pi$
$823$	−1.07200e8			−0.192307			−0.0961533	+	0.995367i	$0.530654\pi$
$824$	1.83663e8			0.328277
$825$			3.19179e8i			0.568425i
$826$	3.99268e8			0.708475
$827$	−3.30770e7	−	3.30770e7i	−0.0584802	−	0.0584802i	0.677262	−	0.735742i	$-0.263166\pi$
$827$	−3.30770e7	−	3.30770e7i	−0.0584802	−	0.0584802i	−0.735742	+	0.677262i	$0.763166\pi$
$828$	−3.18165e6	+	3.18165e6i	−0.00560482	+	0.00560482i
$829$	1.96190e8	−	1.96190e8i	0.344361	−	0.344361i	−0.513643	−	0.858004i	$-0.671704\pi$
$829$	1.96190e8	−	1.96190e8i	0.344361	−	0.344361i	0.858004	+	0.513643i	$0.171704\pi$
$830$	1.52695e8			0.267049
$831$	−5.30905e8	−	5.30905e8i	−0.925153	−	0.925153i
$832$	2.37529e7	−	2.37529e7i	0.0412427	−	0.0412427i
$833$	3.32909e8	+	3.32909e8i	0.575957	+	0.575957i
$834$	−3.78162e8	+	3.78162e8i	−0.651898	+	0.651898i
$835$			7.60715e8i			1.30666i
$836$	2.08287e8	+	2.08287e8i	0.356487	+	0.356487i
$837$	−5.95435e8	−	5.95435e8i	−1.01545	−	1.01545i
$838$	−3.66985e7	+	3.66985e7i	−0.0623614	+	0.0623614i
$839$			2.74033e8i			0.463998i	0.972716	+	0.231999i	$0.0745267\pi$
$839$			2.74033e8i			0.463998i	−0.972716	+	0.231999i	$0.925473\pi$
$840$	−1.05849e8			−0.178586
$841$			1.11793e8i			0.187944i
$842$		−	9.35418e8i		−	1.56700i
$843$	−1.73782e8	+	1.73782e8i	−0.290083	+	0.290083i
$844$			4.91474e8i			0.817472i
$845$	6.97231e8	−	6.97231e8i	1.15560	−	1.15560i
$846$	−3.20342e8	+	3.20342e8i	−0.529057	+	0.529057i
$847$	−1.38862e8			−0.228526
$848$	4.31586e8			0.707750
$849$	5.95329e8	+	5.95329e8i	0.972823	+	0.972823i
$850$		−	1.38269e9i		−	2.25148i
$851$	−1.41393e6	+	1.14812e7i	−0.00229425	+	0.0186294i
$852$	1.30981e9			2.11782
$853$	1.60756e8	−	1.60756e8i	0.259012	−	0.259012i	−0.565640	−	0.824652i	$-0.691371\pi$
$853$	1.60756e8	−	1.60756e8i	0.259012	−	0.259012i	0.824652	+	0.565640i	$0.191371\pi$
$854$			2.86514e8i			0.460015i
$855$		−	3.05926e8i		−	0.489461i
$856$	2.44384e8	+	2.44384e8i	0.389630	+	0.389630i
$857$	−3.48920e8	−	3.48920e8i	−0.554349	−	0.554349i	0.373344	−	0.927693i	$-0.378211\pi$
$857$	−3.48920e8	−	3.48920e8i	−0.554349	−	0.554349i	−0.927693	+	0.373344i	$0.878211\pi$
$858$	1.26471e7			0.0200231
$859$	−7.17348e8	−	7.17348e8i	−1.13175	−	1.13175i	−0.989886	−	0.141864i	$-0.954690\pi$
$859$	−7.17348e8	−	7.17348e8i	−1.13175	−	1.13175i	−0.141864	−	0.989886i	$-0.545310\pi$
$860$	9.78752e8			1.53878
$861$	−1.63566e8			−0.256261
$862$		−	5.19424e8i		−	0.810962i
$863$	5.52665e8			0.859864			0.429932	−	0.902861i	$-0.358538\pi$
$863$	5.52665e8			0.859864			0.429932	+	0.902861i	$0.358538\pi$
$864$	6.79919e8	+	6.79919e8i	1.05418	+	1.05418i
$865$	6.15456e8	−	6.15456e8i	0.950930	−	0.950930i
$866$	1.17138e9	−	1.17138e9i	1.80361	−	1.80361i
$867$	1.20107e8			0.184294
$868$	−2.20793e8	−	2.20793e8i	−0.337618	−	0.337618i
$869$	−1.56312e8	+	1.56312e8i	−0.238195	+	0.238195i
$870$	8.61438e8	+	8.61438e8i	1.30818	+	1.30818i
$871$	7.34826e6	−	7.34826e6i	0.0111206	−	0.0111206i
$872$		−	5.22133e8i		−	0.787466i
$873$	1.43841e8	+	1.43841e8i	0.216192	+	0.216192i
$874$	1.25723e7	+	1.25723e7i	0.0188314	+	0.0188314i
$875$	1.44712e8	−	1.44712e8i	0.216013	−	0.216013i
$876$			4.57283e8i			0.680256i
$877$	3.70153e8			0.548760			0.274380	−	0.961621i	$-0.411527\pi$
$877$	3.70153e8			0.548760			0.274380	+	0.961621i	$0.411527\pi$
$878$		−	1.75062e9i		−	2.58648i
$879$			1.69285e7i			0.0249259i
$880$	1.89053e8	−	1.89053e8i	0.277418	−	0.277418i
$881$			2.83266e8i			0.414254i	0.978314	+	0.207127i	$0.0664114\pi$
$881$			2.83266e8i			0.414254i	−0.978314	+	0.207127i	$0.933589\pi$
$882$	−2.18970e8	+	2.18970e8i	−0.319138	+	0.319138i
$883$	−6.57003e8	+	6.57003e8i	−0.954301	+	0.954301i	−0.999000	−	0.0446997i	$-0.985767\pi$
$883$	−6.57003e8	+	6.57003e8i	−0.954301	+	0.954301i	0.0446997	+	0.999000i	$0.485767\pi$
$884$	−3.11357e7			−0.0450715
$885$	1.58312e9			2.28394
$886$	1.83455e8	+	1.83455e8i	0.263772	+	0.263772i
$887$			8.55312e8i			1.22561i	0.790232	+	0.612807i	$0.209960\pi$
$887$			8.55312e8i			1.22561i	−0.790232	+	0.612807i	$0.790040\pi$
$888$	−2.75821e8	−	3.39678e7i	−0.393902	−	0.0485097i
$889$	−1.39523e7			−0.0198582
$890$	−8.45156e8	+	8.45156e8i	−1.19886	+	1.19886i
$891$			1.67469e8i			0.236756i
$892$			1.22332e9i			1.72364i
$893$	7.19370e8	+	7.19370e8i	1.01018	+	1.01018i
$894$	−6.74201e7	−	6.74201e7i	−0.0943575	−	0.0943575i
$895$	−2.21177e9			−3.08511
$896$	1.27939e8	+	1.27939e8i	0.177861	+	0.177861i
$897$	433832.			0.000601097
$898$	−1.06367e9			−1.46885
$899$			8.63792e8i			1.18886i
$900$	5.16845e8			0.708978
$901$	−5.52779e8	−	5.52779e8i	−0.755748	−	0.755748i
$902$	−3.66966e8	+	3.66966e8i	−0.500042	+	0.500042i
$903$	8.42506e7	−	8.42506e7i	0.114422	−	0.114422i
$904$	4.26794e8			0.577714
$905$	−1.36425e8	−	1.36425e8i	−0.184056	−	0.184056i
$906$	−2.49575e8	+	2.49575e8i	−0.335596	+	0.335596i
$907$	2.13661e6	+	2.13661e6i	0.00286354	+	0.00286354i	0.708537	−	0.705674i	$-0.249355\pi$
$907$	2.13661e6	+	2.13661e6i	0.00286354	+	0.00286354i	−0.705674	+	0.708537i	$0.749355\pi$
$908$	−9.97300e8	+	9.97300e8i	−1.33220	+	1.33220i
$909$			4.03490e8i			0.537207i
$910$	−1.41802e7	−	1.41802e7i	−0.0188173	−	0.0188173i
$911$	−1.05050e9	−	1.05050e9i	−1.38944	−	1.38944i	−0.826494	−	0.562946i	$-0.809668\pi$
$911$	−1.05050e9	−	1.05050e9i	−1.38944	−	1.38944i	−0.562946	−	0.826494i	$-0.690332\pi$
$912$	2.40447e8	−	2.40447e8i	0.316982	−	0.316982i
$913$		−	3.35169e7i		−	0.0440404i
$914$	5.95193e8			0.779506
$915$			1.13604e9i			1.48297i
$916$			6.45650e8i			0.840060i
$917$	−3.23821e7	+	3.23821e7i	−0.0419950	+	0.0419950i
$918$		−	1.12930e9i		−	1.45976i
$919$	7.34050e8	−	7.34050e8i	0.945756	−	0.945756i	−0.0528470	−	0.998603i	$-0.516830\pi$
$919$	7.34050e8	−	7.34050e8i	0.945756	−	0.945756i	0.998603	+	0.0528470i	$0.0168296\pi$
$920$	−8.14608e6	+	8.14608e6i	−0.0104613	+	0.0104613i
$921$	7.35243e8			0.941136
$922$	−1.96736e9			−2.51010
$923$	4.21755e7	+	4.21755e7i	0.0536359	+	0.0536359i
$924$			9.66648e7i			0.122533i
$925$	1.04738e9	−	8.17692e8i	1.32336	−	1.03315i
$926$	−1.01017e9			−1.27222
$927$	−1.23177e8	+	1.23177e8i	−0.154628	+	0.154628i
$928$		−	9.86352e8i		−	1.23421i
$929$		−	7.73048e8i		−	0.964183i	−0.876121	−	0.482092i	$-0.839877\pi$
$929$		−	7.73048e8i		−	0.964183i	0.876121	−	0.482092i	$-0.160123\pi$
$930$	−1.54049e9	−	1.54049e9i	−1.91518	−	1.91518i
$931$	4.91726e8	+	4.91726e8i	0.609360	+	0.609360i
$932$	−1.53411e8			−0.189500
$933$	5.72891e7	+	5.72891e7i	0.0705387	+	0.0705387i
$934$	2.29262e9			2.81379
$935$	−4.84280e8			−0.592464
$936$		−	4.92236e6i		−	0.00600269i
$937$	4.36849e8			0.531022			0.265511	−	0.964108i	$-0.414459\pi$
$937$	4.36849e8			0.531022			0.265511	+	0.964108i	$0.414459\pi$
$938$	9.88292e7	+	9.88292e7i	0.119750	+	0.119750i
$939$	2.67816e8	−	2.67816e8i	0.323474	−	0.323474i
$940$	−1.93923e9	+	1.93923e9i	−2.33477	+	2.33477i
$941$	−8.12711e8			−0.975366			−0.487683	−	0.873021i	$-0.662158\pi$
$941$	−8.12711e8			−0.975366			−0.487683	+	0.873021i	$0.662158\pi$
$942$	−8.23596e8	−	8.23596e8i	−0.985284	−	0.985284i
$943$	−1.25880e7	+	1.25880e7i	−0.0150114	+	0.0150114i
$944$	−5.87666e8	−	5.87666e8i	−0.698578	−	0.698578i
$945$	2.92285e8	−	2.92285e8i	0.346347	−	0.346347i
$946$		−	3.78039e8i		−	0.446543i
$947$	3.25302e8	+	3.25302e8i	0.383033	+	0.383033i	0.872194	−	0.489160i	$-0.162697\pi$
$947$	3.25302e8	+	3.25302e8i	0.383033	+	0.383033i	−0.489160	+	0.872194i	$0.662697\pi$
$948$	−5.35925e8	−	5.35925e8i	−0.629041	−	0.629041i
$949$	−1.47244e7	+	1.47244e7i	−0.0172281	+	0.0172281i
$950$		−	2.04232e9i		−	2.38206i
$951$	−1.31436e9			−1.52818
$952$		−	1.00650e8i		−	0.116655i
$953$		−	1.17622e9i		−	1.35897i	−0.733691	−	0.679484i	$-0.762204\pi$
$953$		−	1.17622e9i		−	1.35897i	0.733691	−	0.679484i	$-0.237796\pi$
$954$	3.63589e8	−	3.63589e8i	0.418760	−	0.418760i
$955$			3.77916e8i			0.433895i
$956$	3.17298e8	−	3.17298e8i	0.363156	−	0.363156i
$957$	1.89088e8	−	1.89088e8i	0.215738	−	0.215738i
$958$	−1.09602e9			−1.24658
$959$	−2.48719e8			−0.282003
$960$	1.26668e9	+	1.26668e9i	1.43170	+	1.43170i
$961$		−	6.57198e8i		−	0.740502i
$962$	−3.24002e7	−	4.15013e7i	−0.0363934	−	0.0466161i
$963$	−3.27801e8			−0.367055
$964$	−1.36623e9	+	1.36623e9i	−1.52508	+	1.52508i
$965$			1.53157e9i			1.70433i
$966$			5.83476e6i			0.00647279i
$967$	2.30915e8	+	2.30915e8i	0.255372	+	0.255372i	0.823169	−	0.567797i	$-0.192204\pi$
$967$	2.30915e8	+	2.30915e8i	0.255372	+	0.255372i	−0.567797	+	0.823169i	$0.692204\pi$
$968$	−2.56736e8	−	2.56736e8i	−0.283048	−	0.283048i
$969$	−6.15932e8			−0.676958
$970$	1.53222e9	+	1.53222e9i	1.67883	+	1.67883i
$971$	−6.23979e8			−0.681573			−0.340787	−	0.940141i	$-0.610693\pi$
$971$	−6.23979e8			−0.681573			−0.340787	+	0.940141i	$0.610693\pi$
$972$	7.41729e8			0.807694
$973$		−	1.86139e8i		−	0.202068i
$974$	−3.33395e8			−0.360813
$975$	−3.52370e7	−	3.52370e7i	−0.0380177	−	0.0380177i
$976$	4.21707e8	−	4.21707e8i	0.453588	−	0.453588i
$977$	6.64400e7	−	6.64400e7i	0.0712436	−	0.0712436i	−0.670587	−	0.741831i	$-0.733958\pi$
$977$	6.64400e7	−	6.64400e7i	0.0712436	−	0.0712436i	0.741831	+	0.670587i	$0.233958\pi$
$978$	9.70811e8			1.03781
$979$	1.85514e8	+	1.85514e8i	0.197710	+	0.197710i
$980$	−1.32556e9	+	1.32556e9i	−1.40838	+	1.40838i
$981$	3.50178e8	+	3.50178e8i	0.370921	+	0.370921i
$982$	1.39241e9	−	1.39241e9i	1.47040	−	1.47040i
$983$		−	1.28937e9i		−	1.35743i	−0.734401	−	0.678715i	$-0.762537\pi$
$983$		−	1.28937e9i		−	1.35743i	0.734401	−	0.678715i	$-0.237463\pi$
$984$	−3.02409e8	−	3.02409e8i	−0.317402	−	0.317402i
$985$	1.40950e9	+	1.40950e9i	1.47488	+	1.47488i
$986$	−8.19132e8	+	8.19132e8i	−0.854521	+	0.854521i
$987$			3.33856e8i			0.347222i
$988$	−4.59893e7			−0.0476854
$989$		−	1.29678e7i		−	0.0134053i
$990$		−	3.18534e8i		−	0.328284i
$991$	−3.25114e8	+	3.25114e8i	−0.334052	+	0.334052i	−0.854123	−	0.520071i	$-0.825906\pi$
$991$	−3.25114e8	+	3.25114e8i	−0.334052	+	0.334052i	0.520071	+	0.854123i	$0.325906\pi$
$992$			1.76387e9i			1.80689i
$993$	−4.72543e8	+	4.72543e8i	−0.482607	+	0.482607i
$994$	−5.67233e8	+	5.67233e8i	−0.577567	+	0.577567i
$995$	1.53345e9			1.55668
$996$	1.14915e8			0.116305
$997$	3.15540e8	+	3.15540e8i	0.318397	+	0.318397i	0.848151	−	0.529754i	$-0.177716\pi$
$997$	3.15540e8	+	3.15540e8i	0.318397	+	0.318397i	−0.529754	+	0.848151i	$0.677716\pi$
$998$		−	1.82488e9i		−	1.83587i
$999$	8.55435e8	−	6.67841e8i	0.858007	−	0.669848i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.7.d.a.6.16	✓	36
37.31	odd	4	inner	37.7.d.a.31.16	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.7.d.a.6.16	✓	36	1.1	even	1	trivial
37.7.d.a.31.16	yes	36	37.31	odd	4	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:	\( N \)	\(=\)	\( 37 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	37.d (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(8.60959 - 8.60959i) q^{2} +22.2519i q^{3} -84.2501i q^{4} +(144.668 + 144.668i) q^{5} +(191.579 + 191.579i) q^{6} -94.2990 q^{7} +(-174.345 - 174.345i) q^{8} +233.855 q^{9} +O(q^{10})\)	\(q+(8.60959 - 8.60959i) q^{2} +22.2519i q^{3} -84.2501i q^{4} +(144.668 + 144.668i) q^{5} +(191.579 + 191.579i) q^{6} -94.2990 q^{7} +(-174.345 - 174.345i) q^{8} +233.855 q^{9} +2491.07 q^{10} -546.795i q^{11} +1874.72 q^{12} +(60.3655 + 60.3655i) q^{13} +(-811.876 + 811.876i) q^{14} +(-3219.14 + 3219.14i) q^{15} +2389.93 q^{16} +(-3061.04 - 3061.04i) q^{17} +(2013.39 - 2013.39i) q^{18} +(-4521.34 - 4521.34i) q^{19} +(12188.3 - 12188.3i) q^{20} -2098.33i q^{21} +(-4707.68 - 4707.68i) q^{22} +(-161.487 - 161.487i) q^{23} +(3879.50 - 3879.50i) q^{24} +26232.8i q^{25} +1039.44 q^{26} +21425.3i q^{27} +7944.70i q^{28} +(15540.8 - 15540.8i) q^{29} +55430.9i q^{30} +(-27791.2 + 27791.2i) q^{31} +(31734.4 - 31734.4i) q^{32} +12167.2 q^{33} -52708.6 q^{34} +(-13642.1 - 13642.1i) q^{35} -19702.3i q^{36} +(-31170.7 - 39926.4i) q^{37} -77853.8 q^{38} +(-1343.25 + 1343.25i) q^{39} -50444.3i q^{40} -77950.5i q^{41} +(-18065.8 - 18065.8i) q^{42} +(40151.3 + 40151.3i) q^{43} -46067.5 q^{44} +(33831.3 + 33831.3i) q^{45} -2780.67 q^{46} -159105. q^{47} +53180.4i q^{48} -108757. q^{49} +(225853. + 225853. i) q^{50} +(68113.9 - 68113.9i) q^{51} +(5085.80 - 5085.80i) q^{52} +180585. q^{53} +(184463. + 184463. i) q^{54} +(79103.8 - 79103.8i) q^{55} +(16440.5 + 16440.5i) q^{56} +(100608. - 100608. i) q^{57} -267599. i q^{58} +(-245893. - 245893. i) q^{59} +(271212. + 271212. i) q^{60} +(176452. - 176452. i) q^{61} +478542. i q^{62} -22052.3 q^{63} -393485. i q^{64} +17465.9i q^{65} +(104755. - 104755. i) q^{66} -121729. i q^{67} +(-257893. + 257893. i) q^{68} +(3593.38 - 3593.38i) q^{69} -234905. q^{70} +698669. q^{71} +(-40771.3 - 40771.3i) q^{72} +243920. i q^{73} +(-612116. - 75383.3i) q^{74} -583728. q^{75} +(-380923. + 380923. i) q^{76} +51562.2i q^{77} +23129.6i q^{78} +(-285869. - 285869. i) q^{79} +(345747. + 345747. i) q^{80} -306273. q^{81} +(-671122. - 671122. i) q^{82} +61297.0 q^{83} -176784. q^{84} -885671. i q^{85} +691372. q^{86} +(345811. + 345811. i) q^{87} +(-95330.8 + 95330.8i) q^{88} +(-339275. + 339275. i) q^{89} +582547. q^{90} +(-5692.41 - 5692.41i) q^{91} +(-13605.3 + 13605.3i) q^{92} +(-618406. - 618406. i) q^{93} +(-1.36983e6 + 1.36983e6i) q^{94} -1.30819e6i q^{95} +(706149. + 706149. i) q^{96} +(615088. + 615088. i) q^{97} +(-936351. + 936351. i) q^{98} -127870. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 4 q^{2} - 256 q^{5} + 126 q^{6} - 4 q^{7} + 168 q^{8} - 7140 q^{9}+O(q^{10}) \) 36 * q - 4 * q^2 - 256 * q^5 + 126 * q^6 - 4 * q^7 + 168 * q^8 - 7140 * q^9	\( 36 q - 4 q^{2} - 256 q^{5} + 126 q^{6} - 4 q^{7} + 168 q^{8} - 7140 q^{9} - 1876 q^{10} + 11104 q^{12} - 2904 q^{13} - 7678 q^{14} + 4288 q^{15} - 44824 q^{16} + 2064 q^{17} + 6222 q^{18} - 4954 q^{19} - 43084 q^{20} - 39810 q^{22} + 21966 q^{23} + 79188 q^{24} + 66604 q^{26} + 69500 q^{29} - 32418 q^{31} - 141992 q^{32} + 54752 q^{33} + 256508 q^{34} - 26164 q^{35} + 180242 q^{37} + 329032 q^{38} - 60088 q^{39} - 346014 q^{42} - 144514 q^{43} - 294896 q^{44} + 842152 q^{45} - 522736 q^{46} - 157076 q^{47} + 405652 q^{49} + 46176 q^{50} - 624984 q^{51} - 161884 q^{52} - 512988 q^{53} + 541150 q^{54} + 824640 q^{55} - 608488 q^{56} - 311992 q^{57} + 187582 q^{59} - 1156764 q^{60} - 1321908 q^{61} - 887284 q^{63} + 752126 q^{66} + 1244832 q^{68} + 41960 q^{69} - 1029284 q^{70} + 1316252 q^{71} + 777880 q^{72} + 1117260 q^{74} - 2148904 q^{75} - 814428 q^{76} - 56722 q^{79} + 3750844 q^{80} - 930796 q^{81} + 1462554 q^{82} - 841484 q^{83} + 5065540 q^{84} + 3992612 q^{86} + 2494224 q^{87} - 3796428 q^{88} - 1439724 q^{89} - 5618044 q^{90} - 8644 q^{91} + 7826980 q^{92} - 54064 q^{93} - 2057938 q^{94} - 8819328 q^{96} + 2578548 q^{97} - 6043946 q^{98}+O(q^{100}) \) 36 * q - 4 * q^2 - 256 * q^5 + 126 * q^6 - 4 * q^7 + 168 * q^8 - 7140 * q^9 - 1876 * q^10 + 11104 * q^12 - 2904 * q^13 - 7678 * q^14 + 4288 * q^15 - 44824 * q^16 + 2064 * q^17 + 6222 * q^18 - 4954 * q^19 - 43084 * q^20 - 39810 * q^22 + 21966 * q^23 + 79188 * q^24 + 66604 * q^26 + 69500 * q^29 - 32418 * q^31 - 141992 * q^32 + 54752 * q^33 + 256508 * q^34 - 26164 * q^35 + 180242 * q^37 + 329032 * q^38 - 60088 * q^39 - 346014 * q^42 - 144514 * q^43 - 294896 * q^44 + 842152 * q^45 - 522736 * q^46 - 157076 * q^47 + 405652 * q^49 + 46176 * q^50 - 624984 * q^51 - 161884 * q^52 - 512988 * q^53 + 541150 * q^54 + 824640 * q^55 - 608488 * q^56 - 311992 * q^57 + 187582 * q^59 - 1156764 * q^60 - 1321908 * q^61 - 887284 * q^63 + 752126 * q^66 + 1244832 * q^68 + 41960 * q^69 - 1029284 * q^70 + 1316252 * q^71 + 777880 * q^72 + 1117260 * q^74 - 2148904 * q^75 - 814428 * q^76 - 56722 * q^79 + 3750844 * q^80 - 930796 * q^81 + 1462554 * q^82 - 841484 * q^83 + 5065540 * q^84 + 3992612 * q^86 + 2494224 * q^87 - 3796428 * q^88 - 1439724 * q^89 - 5618044 * q^90 - 8644 * q^91 + 7826980 * q^92 - 54064 * q^93 - 2057938 * q^94 - 8819328 * q^96 + 2578548 * q^97 - 6043946 * q^98

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