LMFDB - Embedded newform 37.7.d.a.6.18

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			6.18
Character	$\chi$	$=$	37.6
Dual form			37.7.d.a.31.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(11.1987 - 11.1987i) q^{2} +29.5809i q^{3} -186.823i q^{4} +(-126.906 - 126.906i) q^{5} +(331.268 + 331.268i) q^{6} +249.429 q^{7} +(-1375.46 - 1375.46i) q^{8} -146.027 q^{9} +O(q^{10})$	\(q+(11.1987 - 11.1987i) q^{2} +29.5809i q^{3} -186.823i q^{4} +(-126.906 - 126.906i) q^{5} +(331.268 + 331.268i) q^{6} +249.429 q^{7} +(-1375.46 - 1375.46i) q^{8} -146.027 q^{9} -2842.36 q^{10} -1255.79i q^{11} +5526.39 q^{12} +(1264.60 + 1264.60i) q^{13} +(2793.29 - 2793.29i) q^{14} +(3753.98 - 3753.98i) q^{15} -18850.2 q^{16} +(3465.33 + 3465.33i) q^{17} +(-1635.32 + 1635.32i) q^{18} +(2765.52 + 2765.52i) q^{19} +(-23708.9 + 23708.9i) q^{20} +7378.34i q^{21} +(-14063.3 - 14063.3i) q^{22} +(3787.16 + 3787.16i) q^{23} +(40687.4 - 40687.4i) q^{24} +16585.1i q^{25} +28323.8 q^{26} +17244.8i q^{27} -46599.2i q^{28} +(21490.9 - 21490.9i) q^{29} -84079.6i q^{30} +(-2404.15 + 2404.15i) q^{31} +(-123069. + 123069. i) q^{32} +37147.4 q^{33} +77614.5 q^{34} +(-31654.0 - 31654.0i) q^{35} +27281.3i q^{36} +(50443.3 - 4604.87i) q^{37} +61940.7 q^{38} +(-37407.9 + 37407.9i) q^{39} +349108. i q^{40} -55027.2i q^{41} +(82628.0 + 82628.0i) q^{42} +(-76723.1 - 76723.1i) q^{43} -234611. q^{44} +(18531.7 + 18531.7i) q^{45} +84822.9 q^{46} -27330.6 q^{47} -557605. i q^{48} -55433.9 q^{49} +(185732. + 185732. i) q^{50} +(-102507. + 102507. i) q^{51} +(236256. - 236256. i) q^{52} +186950. q^{53} +(193120. + 193120. i) q^{54} +(-159367. + 159367. i) q^{55} +(-343081. - 343081. i) q^{56} +(-81806.6 + 81806.6i) q^{57} -481341. i q^{58} +(55244.6 + 55244.6i) q^{59} +(-701330. - 701330. i) q^{60} +(-96947.1 + 96947.1i) q^{61} +53846.9i q^{62} -36423.5 q^{63} +1.55001e6i q^{64} -320969. i q^{65} +(416004. - 416004. i) q^{66} +354899. i q^{67} +(647403. - 647403. i) q^{68} +(-112028. + 112028. i) q^{69} -708969. q^{70} -367486. q^{71} +(200855. + 200855. i) q^{72} +494180. i q^{73} +(513332. - 616469. i) q^{74} -490601. q^{75} +(516664. - 516664. i) q^{76} -313232. i q^{77} +837841. i q^{78} +(-77860.2 - 77860.2i) q^{79} +(2.39220e6 + 2.39220e6i) q^{80} -616571. q^{81} +(-616235. - 616235. i) q^{82} +274587. q^{83} +1.37844e6 q^{84} -879539. i q^{85} -1.71840e6 q^{86} +(635719. + 635719. i) q^{87} +(-1.72730e6 + 1.72730e6i) q^{88} +(51987.2 - 51987.2i) q^{89} +415063. q^{90} +(315428. + 315428. i) q^{91} +(707530. - 707530. i) q^{92} +(-71116.9 - 71116.9i) q^{93} +(-306068. + 306068. i) q^{94} -701921. i q^{95} +(-3.64047e6 - 3.64047e6i) q^{96} +(367733. + 367733. i) q^{97} +(-620790. + 620790. i) q^{98} +183380. 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 $

$2$	11.1987	−	11.1987i	1.39984	−	1.39984i	0.599366	−	0.800475i	$-0.295419\pi$
$2$	11.1987	−	11.1987i	1.39984	−	1.39984i	0.800475	−	0.599366i	$-0.204581\pi$
$3$			29.5809i			1.09559i	0.836613	+	0.547794i	$0.184532\pi$
$3$			29.5809i			1.09559i	−0.836613	+	0.547794i	$0.815468\pi$
$4$		−	186.823i		−	2.91911i
$5$	−126.906	−	126.906i	−1.01525	−	1.01525i	−0.999882	−	0.0153632i	$-0.995110\pi$
$5$	−126.906	−	126.906i	−1.01525	−	1.01525i	−0.0153632	−	0.999882i	$-0.504890\pi$
$6$	331.268	+	331.268i	1.53365	+	1.53365i
$7$	249.429			0.727200			0.363600	−	0.931555i	$-0.381548\pi$
$7$	249.429			0.727200			0.363600	+	0.931555i	$0.381548\pi$
$8$	−1375.46	−	1375.46i	−2.68645	−	2.68645i
$9$	−146.027			−0.200312
$10$	−2842.36			−2.84236
$11$		−	1255.79i		−	0.943496i	−0.881734	−	0.471748i	$-0.843623\pi$
$11$		−	1255.79i		−	0.943496i	0.881734	−	0.471748i	$-0.156377\pi$
$12$	5526.39			3.19814
$13$	1264.60	+	1264.60i	0.575602	+	0.575602i	0.933688	−	0.358087i	$-0.116571\pi$
$13$	1264.60	+	1264.60i	0.575602	+	0.575602i	−0.358087	+	0.933688i	$0.616571\pi$
$14$	2793.29	−	2793.29i	1.01796	−	1.01796i
$15$	3753.98	−	3753.98i	1.11229	−	1.11229i
$16$	−18850.2			−4.60210
$17$	3465.33	+	3465.33i	0.705338	+	0.705338i	0.965551	−	0.260213i	$-0.0837928\pi$
$17$	3465.33	+	3465.33i	0.705338	+	0.705338i	−0.260213	+	0.965551i	$0.583793\pi$
$18$	−1635.32	+	1635.32i	−0.280405	+	0.280405i
$19$	2765.52	+	2765.52i	0.403196	+	0.403196i	0.879358	−	0.476161i	$-0.157972\pi$
$19$	2765.52	+	2765.52i	0.403196	+	0.403196i	−0.476161	+	0.879358i	$0.657972\pi$
$20$	−23708.9	+	23708.9i	−2.96361	+	2.96361i
$21$			7378.34i			0.796711i
$22$	−14063.3	−	14063.3i	−1.32074	−	1.32074i
$23$	3787.16	+	3787.16i	0.311265	+	0.311265i	0.845400	−	0.534134i	$-0.179362\pi$
$23$	3787.16	+	3787.16i	0.311265	+	0.311265i	−0.534134	+	0.845400i	$0.679362\pi$
$24$	40687.4	−	40687.4i	2.94324	−	2.94324i
$25$			16585.1i			1.06145i
$26$	28323.8			1.61150
$27$			17244.8i			0.876128i
$28$		−	46599.2i		−	2.12278i
$29$	21490.9	−	21490.9i	0.881171	−	0.881171i	−0.112482	−	0.993654i	$-0.535880\pi$
$29$	21490.9	−	21490.9i	0.881171	−	0.881171i	0.993654	+	0.112482i	$0.0358802\pi$
$30$		−	84079.6i		−	3.11406i
$31$	−2404.15	+	2404.15i	−0.0807006	+	0.0807006i	−0.746305	−	0.665604i	$-0.768174\pi$
$31$	−2404.15	+	2404.15i	−0.0807006	+	0.0807006i	0.665604	+	0.746305i	$0.268174\pi$
$32$	−123069.	+	123069.i	−3.75575	+	3.75575i
$33$	37147.4			1.03368
$34$	77614.5			1.97472
$35$	−31654.0	−	31654.0i	−0.738286	−	0.738286i
$36$			27281.3i			0.584733i
$37$	50443.3	−	4604.87i	0.995859	−	0.0909102i
$37$	50443.3	−	4604.87i	0.995859	−	0.0909102i
$38$	61940.7			1.12882
$39$	−37407.9	+	37407.9i	−0.630622	+	0.630622i
$40$			349108.i			5.45481i
$41$		−	55027.2i		−	0.798410i	−0.916862	−	0.399205i	$-0.869286\pi$
$41$		−	55027.2i		−	0.798410i	0.916862	−	0.399205i	$-0.130714\pi$
$42$	82628.0	+	82628.0i	1.11527	+	1.11527i
$43$	−76723.1	−	76723.1i	−0.964985	−	0.964985i	0.0344222	−	0.999407i	$-0.489041\pi$
$43$	−76723.1	−	76723.1i	−0.964985	−	0.964985i	−0.999407	+	0.0344222i	$0.989041\pi$
$44$	−234611.			−2.75417
$45$	18531.7	+	18531.7i	0.203366	+	0.203366i
$46$	84822.9			0.871444
$47$	−27330.6			−0.263243			−0.131621	−	0.991300i	$-0.542018\pi$
$47$	−27330.6			−0.263243			−0.131621	+	0.991300i	$0.542018\pi$
$48$		−	557605.i		−	5.04200i
$49$	−55433.9			−0.471181
$50$	185732.	+	185732.i	1.48586	+	1.48586i
$51$	−102507.	+	102507.i	−0.772760	+	0.772760i
$52$	236256.	−	236256.i	1.68025	−	1.68025i
$53$	186950.			1.25574			0.627868	−	0.778320i	$-0.283928\pi$
$53$	186950.			1.25574			0.627868	+	0.778320i	$0.283928\pi$
$54$	193120.	+	193120.i	1.22644	+	1.22644i
$55$	−159367.	+	159367.i	−0.957879	+	0.957879i
$56$	−343081.	−	343081.i	−1.95359	−	1.95359i
$57$	−81806.6	+	81806.6i	−0.441737	+	0.441737i
$58$		−	481341.i		−	2.46700i
$59$	55244.6	+	55244.6i	0.268988	+	0.268988i	0.828693	−	0.559704i	$-0.189085\pi$
$59$	55244.6	+	55244.6i	0.268988	+	0.268988i	−0.559704	+	0.828693i	$0.689085\pi$
$60$	−701330.	−	701330.i	−3.24690	−	3.24690i
$61$	−96947.1	+	96947.1i	−0.427116	+	0.427116i	−0.887645	−	0.460529i	$-0.847660\pi$
$61$	−96947.1	+	96947.1i	−0.427116	+	0.427116i	0.460529	+	0.887645i	$0.347660\pi$
$62$			53846.9i			0.225936i
$63$	−36423.5			−0.145667
$64$			1.55001e6i			5.91282i
$65$		−	320969.i		−	1.16875i
$66$	416004.	−	416004.i	1.44699	−	1.44699i
$67$			354899.i			1.18000i	0.807405	+	0.589998i	$0.200871\pi$
$67$			354899.i			1.18000i	−0.807405	+	0.589998i	$0.799129\pi$
$68$	647403.	−	647403.i	2.05896	−	2.05896i
$69$	−112028.	+	112028.i	−0.341018	+	0.341018i
$70$	−708969.			−2.06697
$71$	−367486.			−1.02675			−0.513376	−	0.858164i	$-0.671605\pi$
$71$	−367486.			−1.02675			−0.513376	+	0.858164i	$0.671605\pi$
$72$	200855.	+	200855.i	0.538128	+	0.538128i
$73$			494180.i			1.27033i	0.772376	+	0.635165i	$0.219068\pi$
$73$			494180.i			1.27033i	−0.772376	+	0.635165i	$0.780932\pi$
$74$	513332.	−	616469.i	1.26678	−	1.52130i
$75$	−490601.			−1.16291
$76$	516664.	−	516664.i	1.17698	−	1.17698i
$77$		−	313232.i		−	0.686110i
$78$			837841.i			1.76554i
$79$	−77860.2	−	77860.2i	−0.157919	−	0.157919i	0.623725	−	0.781644i	$-0.285619\pi$
$79$	−77860.2	−	77860.2i	−0.157919	−	0.157919i	−0.781644	+	0.623725i	$0.785619\pi$
$80$	2.39220e6	+	2.39220e6i	4.67226	+	4.67226i
$81$	−616571.			−1.16019
$82$	−616235.	−	616235.i	−1.11765	−	1.11765i
$83$	274587.			0.480226			0.240113	−	0.970745i	$-0.422815\pi$
$83$	274587.			0.480226			0.240113	+	0.970745i	$0.422815\pi$
$84$	1.37844e6			2.32569
$85$		−	879539.i		−	1.43218i
$86$	−1.71840e6			−2.70165
$87$	635719.	+	635719.i	0.965400	+	0.965400i
$88$	−1.72730e6	+	1.72730e6i	−2.53465	+	2.53465i
$89$	51987.2	−	51987.2i	0.0737439	−	0.0737439i	−0.669273	−	0.743017i	$-0.733394\pi$
$89$	51987.2	−	51987.2i	0.0737439	−	0.0737439i	0.743017	+	0.669273i	$0.233394\pi$
$90$	415063.			0.569360
$91$	315428.	+	315428.i	0.418577	+	0.418577i
$92$	707530.	−	707530.i	0.908618	−	0.908618i
$93$	−71116.9	−	71116.9i	−0.0884146	−	0.0884146i
$94$	−306068.	+	306068.i	−0.368498	+	0.368498i
$95$		−	701921.i		−	0.818687i
$96$	−3.64047e6	−	3.64047e6i	−4.11476	−	4.11476i
$97$	367733.	+	367733.i	0.402919	+	0.402919i	0.879260	−	0.476342i	$-0.158037\pi$
$97$	367733.	+	367733.i	0.402919	+	0.402919i	−0.476342	+	0.879260i	$0.658037\pi$
$98$	−620790.	+	620790.i	−0.659578	+	0.659578i
$99$			183380.i			0.188993i
$100$	3.09848e6			3.09848
$101$		−	1.03117e6i		−	1.00085i	−0.865781	−	0.500424i	$-0.833178\pi$
$101$		−	1.03117e6i		−	1.00085i	0.865781	−	0.500424i	$-0.166822\pi$
$102$			2.29590e6i			2.16348i
$103$	−185393.	+	185393.i	−0.169661	+	0.169661i	−0.786830	−	0.617170i	$-0.788279\pi$
$103$	−185393.	+	185393.i	−0.169661	+	0.169661i	0.617170	+	0.786830i	$0.288279\pi$
$104$		−	3.47881e6i		−	3.09265i
$105$	936353.	−	936353.i	0.808857	−	0.808857i
$106$	2.09361e6	−	2.09361e6i	1.75783	−	1.75783i
$107$	434696.			0.354841			0.177421	−	0.984135i	$-0.443225\pi$
$107$	434696.			0.354841			0.177421	+	0.984135i	$0.443225\pi$
$108$	3.22173e6			2.55752
$109$	350382.	+	350382.i	0.270559	+	0.270559i	0.829325	−	0.558766i	$-0.188725\pi$
$109$	350382.	+	350382.i	0.270559	+	0.270559i	−0.558766	+	0.829325i	$0.688725\pi$
$110$			3.56942e6i			2.68176i
$111$	136216.	+	1.49215e6i	0.0996000	+	1.09105i
$112$	−4.70179e6			−3.34664
$113$	−1.35232e6	+	1.35232e6i	−0.937225	+	0.937225i	−0.998143	−	0.0609179i	$-0.980597\pi$
$113$	−1.35232e6	+	1.35232e6i	−0.937225	+	0.937225i	0.0609179	+	0.998143i	$0.480597\pi$
$114$			1.83226e6i			1.23672i
$115$		−	961225.i		−	0.632021i
$116$	−4.01499e6	−	4.01499e6i	−2.57224	−	2.57224i
$117$	−184666.	−	184666.i	−0.115300	−	0.115300i
$118$	1.23734e6			0.753082
$119$	864354.	+	864354.i	0.512922	+	0.512922i
$120$	−1.03269e7			−5.97622
$121$	194546.			0.109816
$122$			2.17137e6i			1.19579i
$123$	1.62775e6			0.874728
$124$	449151.	+	449151.i	0.235574	+	0.235574i
$125$	121841.	−	121841.i	0.0623824	−	0.0623824i
$126$	−407897.	+	407897.i	−0.203910	+	0.203910i
$127$	1.12194e6			0.547721			0.273860	−	0.961769i	$-0.411699\pi$
$127$	1.12194e6			0.547721			0.273860	+	0.961769i	$0.411699\pi$
$128$	9.48177e6	+	9.48177e6i	4.52126	+	4.52126i
$129$	2.26953e6	−	2.26953e6i	1.05723	−	1.05723i
$130$	−3.59445e6	−	3.59445e6i	−1.63607	−	1.63607i
$131$	−658164.	+	658164.i	−0.292766	+	0.292766i	−0.838172	−	0.545406i	$-0.816375\pi$
$131$	−658164.	+	658164.i	−0.292766	+	0.292766i	0.545406	+	0.838172i	$0.316375\pi$
$132$		−	6.94000e6i		−	3.01743i
$133$	689803.	+	689803.i	0.293204	+	0.293204i
$134$	3.97442e6	+	3.97442e6i	1.65181	+	1.65181i
$135$	2.18847e6	−	2.18847e6i	0.889485	−	0.889485i
$136$		−	9.53285e6i		−	3.78971i
$137$	338393.			0.131601			0.0658005	−	0.997833i	$-0.479040\pi$
$137$	338393.			0.131601			0.0658005	+	0.997833i	$0.479040\pi$
$138$			2.50913e6i			0.954743i
$139$		−	4.71886e6i		−	1.75708i	−0.477665	−	0.878542i	$-0.658517\pi$
$139$		−	4.71886e6i		−	1.75708i	0.477665	−	0.878542i	$-0.341483\pi$
$140$	−5.91370e6	+	5.91370e6i	−2.15514	+	2.15514i
$141$		−	808464.i		−	0.288405i
$142$	−4.11537e6	+	4.11537e6i	−1.43729	+	1.43729i
$143$	1.58807e6	−	1.58807e6i	0.543078	−	0.543078i
$144$	2.75264e6			0.921855
$145$	−5.45463e6			−1.78921
$146$	5.53419e6	+	5.53419e6i	1.77826	+	1.77826i
$147$		−	1.63978e6i		−	0.516220i
$148$	−860296.	−	9.42396e6i	−0.265377	−	2.90702i
$149$	−1.84491e6			−0.557720			−0.278860	−	0.960332i	$-0.589957\pi$
$149$	−1.84491e6			−0.557720			−0.278860	+	0.960332i	$0.589957\pi$
$150$	−5.49411e6	+	5.49411e6i	−1.62788	+	1.62788i
$151$			4.94399e6i			1.43598i	0.696056	+	0.717988i	$0.254937\pi$
$151$			4.94399e6i			1.43598i	−0.696056	+	0.717988i	$0.745063\pi$
$152$		−	7.60775e6i		−	2.16633i
$153$	−506033.	−	506033.i	−0.141288	−	0.141288i
$154$	−3.50780e6	−	3.50780e6i	−0.960444	−	0.960444i
$155$	610201.			0.163862
$156$	6.98866e6	+	6.98866e6i	1.84086	+	1.84086i
$157$	3.83173e6			0.990139			0.495069	−	0.868853i	$-0.335143\pi$
$157$	3.83173e6			0.990139			0.495069	+	0.868853i	$0.335143\pi$
$158$	−1.74387e6			−0.442123
$159$			5.53015e6i			1.37577i
$160$	3.12362e7			7.62602
$161$	944630.	+	944630.i	0.226352	+	0.226352i
$162$	−6.90481e6	+	6.90481e6i	−1.62408	+	1.62408i
$163$	−4.68424e6	+	4.68424e6i	−1.08162	+	1.08162i	−0.0852656	+	0.996358i	$0.527174\pi$
$163$	−4.68424e6	+	4.68424e6i	−1.08162	+	1.08162i	−0.996358	+	0.0852656i	$0.972826\pi$
$164$	−1.02804e7			−2.33065
$165$	−4.71422e6	−	4.71422e6i	−1.04944	−	1.04944i
$166$	3.07503e6	−	3.07503e6i	0.672240	−	0.672240i
$167$	−1.17336e6	−	1.17336e6i	−0.251930	−	0.251930i	0.569831	−	0.821762i	$-0.307008\pi$
$167$	−1.17336e6	−	1.17336e6i	−0.251930	−	0.251930i	−0.821762	+	0.569831i	$0.807008\pi$
$168$	1.01486e7	−	1.01486e7i	2.14032	−	2.14032i
$169$		−	1.62840e6i		−	0.337365i
$170$	−9.84972e6	−	9.84972e6i	−2.00483	−	2.00483i
$171$	−403842.	−	403842.i	−0.0807651	−	0.0807651i
$172$	−1.43336e7	+	1.43336e7i	−2.81690	+	2.81690i
$173$			3.67659e6i			0.710079i	0.934851	+	0.355039i	$0.115533\pi$
$173$			3.67659e6i			0.710079i	−0.934851	+	0.355039i	$0.884467\pi$
$174$	1.42385e7			2.70281
$175$			4.13681e6i			0.771883i
$176$			2.36719e7i			4.34206i
$177$	−1.63418e6	+	1.63418e6i	−0.294700	+	0.294700i
$178$		−	1.16438e6i		−	0.206460i
$179$	5.48079e6	−	5.48079e6i	0.955617	−	0.955617i	−0.0434388	−	0.999056i	$-0.513831\pi$
$179$	5.48079e6	−	5.48079e6i	0.955617	−	0.955617i	0.999056	+	0.0434388i	$0.0138313\pi$
$180$	3.46215e6	−	3.46215e6i	0.593647	−	0.593647i
$181$	−3.85858e6			−0.650716			−0.325358	−	0.945591i	$-0.605485\pi$
$181$	−3.85858e6			−0.650716			−0.325358	+	0.945591i	$0.605485\pi$
$182$	7.06478e6			1.17188
$183$	−2.86778e6	−	2.86778e6i	−0.467943	−	0.467943i
$184$		−	1.04182e7i		−	1.67240i
$185$	−6.98592e6	−	5.81715e6i	−1.10334	−	0.918745i
$186$	−1.59284e6			−0.247533
$187$	4.35173e6	−	4.35173e6i	0.665483	−	0.665483i
$188$			5.10599e6i			0.768434i
$189$			4.30137e6i			0.637120i
$190$	−7.86063e6	−	7.86063e6i	−1.14603	−	1.14603i
$191$	−964615.	−	964615.i	−0.138438	−	0.138438i	0.634492	−	0.772929i	$-0.281209\pi$
$191$	−964615.	−	964615.i	−0.138438	−	0.138438i	−0.772929	+	0.634492i	$0.781209\pi$
$192$	−4.58507e7			−6.47802
$193$	−46522.9	−	46522.9i	−0.00647135	−	0.00647135i	0.703864	−	0.710335i	$-0.251457\pi$
$193$	−46522.9	−	46522.9i	−0.00647135	−	0.00647135i	−0.710335	+	0.703864i	$0.751457\pi$
$194$	8.23629e6			1.12804
$195$	9.49454e6			1.28047
$196$			1.03563e7i			1.37543i
$197$	1.10564e7			1.44616			0.723078	−	0.690766i	$-0.242727\pi$
$197$	1.10564e7			1.44616			0.723078	+	0.690766i	$0.242727\pi$
$198$	2.05362e6	+	2.05362e6i	0.264561	+	0.264561i
$199$	−7.15213e6	+	7.15213e6i	−0.907562	+	0.907562i	−0.996075	−	0.0885129i	$-0.971789\pi$
$199$	−7.15213e6	+	7.15213e6i	−0.907562	+	0.907562i	0.0885129	+	0.996075i	$0.471789\pi$
$200$	2.28122e7	−	2.28122e7i	2.85152	−	2.85152i
$201$	−1.04982e7			−1.29279
$202$	−1.15478e7	−	1.15478e7i	−1.40103	−	1.40103i
$203$	5.36046e6	−	5.36046e6i	0.640787	−	0.640787i
$204$	1.91507e7	+	1.91507e7i	2.25577	+	2.25577i
$205$	−6.98327e6	+	6.98327e6i	−0.810582	+	0.810582i
$206$			4.15232e6i			0.474996i
$207$	−553030.	−	553030.i	−0.0623501	−	0.0623501i
$208$	−2.38379e7	−	2.38379e7i	−2.64898	−	2.64898i
$209$	3.47293e6	−	3.47293e6i	0.380414	−	0.380414i
$210$		−	2.09719e7i		−	2.26454i
$211$	−2.41674e6			−0.257266			−0.128633	−	0.991692i	$-0.541059\pi$
$211$	−2.41674e6			−0.257266			−0.128633	+	0.991692i	$0.541059\pi$
$212$		−	3.49266e7i		−	3.66563i
$213$		−	1.08705e7i		−	1.12490i
$214$	4.86804e6	−	4.86804e6i	0.496721	−	0.496721i
$215$			1.94732e7i			1.95939i
$216$	2.37196e7	−	2.37196e7i	2.35367	−	2.35367i
$217$	−599666.	+	599666.i	−0.0586854	+	0.0586854i
$218$	7.84767e6			0.757480
$219$	−1.46183e7			−1.39176
$220$	2.97735e7	+	2.97735e7i	2.79616	+	2.79616i
$221$			8.76448e6i			0.811988i
$222$	1.82357e7	+	1.51848e7i	1.66672	+	1.38787i
$223$	8.32669e6			0.750858			0.375429	−	0.926851i	$-0.377495\pi$
$223$	8.32669e6			0.750858			0.375429	+	0.926851i	$0.377495\pi$
$224$	−3.06969e7	+	3.06969e7i	−2.73118	+	2.73118i
$225$		−	2.42188e6i		−	0.212620i
$226$			3.02885e7i			2.62393i
$227$	1.92360e6	+	1.92360e6i	0.164452	+	0.164452i	0.784535	−	0.620084i	$-0.212901\pi$
$227$	1.92360e6	+	1.92360e6i	0.164452	+	0.164452i	−0.620084	+	0.784535i	$0.712901\pi$
$228$	1.52834e7	+	1.52834e7i	1.28948	+	1.28948i
$229$	3.28932e6			0.273905			0.136952	−	0.990578i	$-0.456269\pi$
$229$	3.28932e6			0.273905			0.136952	+	0.990578i	$0.456269\pi$
$230$	−1.07645e7	−	1.07645e7i	−0.884729	−	0.884729i
$231$	9.26566e6			0.751693
$232$	−5.91198e7			−4.73445
$233$			375433.i			0.0296801i	0.999890	+	0.0148400i	$0.00472390\pi$
$233$			375433.i			0.0296801i	−0.999890	+	0.0148400i	$0.995276\pi$
$234$	−4.13605e6			−0.322803
$235$	3.46841e6	+	3.46841e6i	0.267256	+	0.267256i
$236$	1.03210e7	−	1.03210e7i	0.785207	−	0.785207i
$237$	2.30317e6	−	2.30317e6i	0.173014	−	0.173014i
$238$	1.93593e7			1.43602
$239$	6.78505e6	+	6.78505e6i	0.497003	+	0.497003i	0.910504	−	0.413501i	$-0.135694\pi$
$239$	6.78505e6	+	6.78505e6i	0.497003	+	0.497003i	−0.413501	+	0.910504i	$0.635694\pi$
$240$	−7.07632e7	+	7.07632e7i	−5.11887	+	5.11887i
$241$	−1.88471e7	−	1.88471e7i	−1.34646	−	1.34646i	−0.889477	−	0.456980i	$-0.848931\pi$
$241$	−1.88471e7	−	1.88471e7i	−1.34646	−	1.34646i	−0.456980	−	0.889477i	$-0.651069\pi$
$242$	2.17867e6	−	2.17867e6i	0.153725	−	0.153725i
$243$		−	5.66722e6i		−	0.394958i
$244$	1.81120e7	+	1.81120e7i	1.24680	+	1.24680i
$245$	7.03488e6	+	7.03488e6i	0.478364	+	0.478364i
$246$	1.82288e7	−	1.82288e7i	1.22448	−	1.22448i
$247$			6.99455e6i			0.464161i
$248$	6.61364e6			0.433596
$249$			8.12252e6i			0.526130i
$250$		−	2.72892e6i		−	0.174651i
$251$	4.61569e6	−	4.61569e6i	0.291888	−	0.291888i	−0.545938	−	0.837826i	$-0.683827\pi$
$251$	4.61569e6	−	4.61569e6i	0.291888	−	0.291888i	0.837826	+	0.545938i	$0.183827\pi$
$252$			6.80476e6i			0.425217i
$253$	4.75589e6	−	4.75589e6i	0.293677	−	0.293677i
$254$	1.25643e7	−	1.25643e7i	0.766722	−	0.766722i
$255$	2.60175e7			1.56908
$256$	1.13167e8			6.74527
$257$	−1.37303e7	−	1.37303e7i	−0.808871	−	0.808871i	0.175592	−	0.984463i	$-0.443816\pi$
$257$	−1.37303e7	−	1.37303e7i	−0.808871	−	0.808871i	−0.984463	+	0.175592i	$0.943816\pi$
$258$		−	5.08318e7i		−	2.95990i
$259$	1.25820e7	−	1.14859e6i	0.724188	−	0.0661098i
$260$	−5.99644e7			−3.41172
$261$	−3.13826e6	+	3.13826e6i	−0.176509	+	0.176509i
$262$			1.47412e7i			0.819651i
$263$			3.47422e7i			1.90981i	0.296915	+	0.954904i	$0.404042\pi$
$263$			3.47422e7i			1.90981i	−0.296915	+	0.954904i	$0.595958\pi$
$264$	−5.10949e7	−	5.10949e7i	−2.77694	−	2.77694i
$265$	−2.37250e7	−	2.37250e7i	−1.27488	−	1.27488i
$266$	1.54498e7			0.820879
$267$	1.53783e6	+	1.53783e6i	0.0807929	+	0.0807929i
$268$	6.63033e7			3.44454
$269$	2.81740e7			1.44741			0.723706	−	0.690108i	$-0.242437\pi$
$269$	2.81740e7			1.44741			0.723706	+	0.690108i	$0.242437\pi$
$270$		−	4.90161e7i		−	2.49028i
$271$	−2.46209e7			−1.23707			−0.618536	−	0.785756i	$-0.712274\pi$
$271$	−2.46209e7			−1.23707			−0.618536	+	0.785756i	$0.712274\pi$
$272$	−6.53220e7	−	6.53220e7i	−3.24603	−	3.24603i
$273$	−9.33063e6	+	9.33063e6i	−0.458588	+	0.458588i
$274$	3.78957e6	−	3.78957e6i	0.184221	−	0.184221i
$275$	2.08274e7			1.00147
$276$	2.09293e7	+	2.09293e7i	0.995470	+	0.995470i
$277$	−2.71853e7	+	2.71853e7i	−1.27907	+	1.27907i	−0.337887	+	0.941187i	$0.609712\pi$
$277$	−2.71853e7	+	2.71853e7i	−1.27907	+	1.27907i	−0.941187	+	0.337887i	$0.890288\pi$
$278$	−5.28452e7	−	5.28452e7i	−2.45964	−	2.45964i
$279$	351072.	−	351072.i	0.0161653	−	0.0161653i
$280$			8.70778e7i			3.96674i
$281$	−1.21915e7	−	1.21915e7i	−0.549464	−	0.549464i	0.376821	−	0.926286i	$-0.377017\pi$
$281$	−1.21915e7	−	1.21915e7i	−0.549464	−	0.549464i	−0.926286	+	0.376821i	$0.877017\pi$
$282$	−9.05377e6	−	9.05377e6i	−0.403722	−	0.403722i
$283$	−1.26639e7	+	1.26639e7i	−0.558738	+	0.558738i	−0.928948	−	0.370210i	$-0.879286\pi$
$283$	−1.26639e7	+	1.26639e7i	−0.558738	+	0.558738i	0.370210	+	0.928948i	$0.379286\pi$
$284$			6.86548e7i			2.99720i
$285$	2.07634e7			0.896943
$286$		−	3.55688e7i		−	1.52045i
$287$		−	1.37254e7i		−	0.580604i
$288$	1.79714e7	−	1.79714e7i	0.752323	−	0.752323i
$289$		−	120605.i		−	0.00499658i
$290$	−6.10849e7	+	6.10849e7i	−2.50461	+	2.50461i
$291$	−1.08779e7	+	1.08779e7i	−0.441433	+	0.441433i
$292$	9.23242e7			3.70823
$293$	−2.24335e7			−0.891854			−0.445927	−	0.895069i	$-0.647126\pi$
$293$	−2.24335e7			−0.891854			−0.445927	+	0.895069i	$0.647126\pi$
$294$	−1.83635e7	−	1.83635e7i	−0.722626	−	0.722626i
$295$		−	1.40217e7i		−	0.546178i
$296$	−7.57166e7	−	6.30490e7i	−2.91955	−	2.43110i
$297$	2.16559e7			0.826623
$298$	−2.06606e7	+	2.06606e7i	−0.780719	+	0.780719i
$299$			9.57847e6i			0.358330i
$300$			9.16556e7i			3.39465i
$301$	−1.91370e7	−	1.91370e7i	−0.701737	−	0.701737i
$302$	5.53664e7	+	5.53664e7i	2.01014	+	2.01014i
$303$	3.05030e7			1.09652
$304$	−5.21307e7	−	5.21307e7i	−1.85555	−	1.85555i
$305$	2.46063e7			0.867254
$306$	−1.13338e7			−0.395561
$307$			2.88999e6i			0.0998807i	0.998752	+	0.0499403i	$0.0159031\pi$
$307$			2.88999e6i			0.0998807i	−0.998752	+	0.0499403i	$0.984097\pi$
$308$	−5.85189e7			−2.00283
$309$	−5.48407e6	−	5.48407e6i	−0.185878	−	0.185878i
$310$	6.83347e6	−	6.83347e6i	0.229380	−	0.229380i
$311$	−1.98438e7	+	1.98438e7i	−0.659697	+	0.659697i	−0.955308	−	0.295612i	$-0.904477\pi$
$311$	−1.98438e7	+	1.98438e7i	−0.659697	+	0.659697i	0.295612	+	0.955308i	$0.404477\pi$
$312$	1.02906e8			3.38827
$313$	−1.61019e7	−	1.61019e7i	−0.525103	−	0.525103i	0.394005	−	0.919108i	$-0.371089\pi$
$313$	−1.61019e7	−	1.61019e7i	−0.525103	−	0.525103i	−0.919108	+	0.394005i	$0.871089\pi$
$314$	4.29105e7	−	4.29105e7i	1.38604	−	1.38604i
$315$	4.62235e6	+	4.62235e6i	0.147887	+	0.147887i
$316$	−1.45461e7	+	1.45461e7i	−0.460983	+	0.460983i
$317$		−	4.83554e7i		−	1.51798i	−0.651100	−	0.758992i	$-0.725692\pi$
$317$		−	4.83554e7i		−	1.51798i	0.651100	−	0.758992i	$-0.274308\pi$
$318$	6.19307e7	+	6.19307e7i	1.92586	+	1.92586i
$319$	−2.69881e7	−	2.69881e7i	−0.831381	−	0.831381i
$320$	1.96705e8	−	1.96705e8i	6.00297	−	6.00297i
$321$			1.28587e7i			0.388760i
$322$	2.11573e7			0.633714
$323$			1.91669e7i			0.568780i
$324$			1.15190e8i			3.38671i
$325$	−2.09735e7	+	2.09735e7i	−0.610970	+	0.610970i
$326$			1.04915e8i			3.02820i
$327$	−1.03646e7	+	1.03646e7i	−0.296421	+	0.296421i
$328$	−7.56879e7	+	7.56879e7i	−2.14489	+	2.14489i
$329$	−6.81707e6			−0.191430
$330$	−1.05587e8			−2.93810
$331$	−1.47301e6	−	1.47301e6i	−0.0406182	−	0.0406182i	0.686506	−	0.727124i	$-0.259144\pi$
$331$	−1.47301e6	−	1.47301e6i	−0.0406182	−	0.0406182i	−0.727124	+	0.686506i	$0.759144\pi$
$332$		−	5.12992e7i		−	1.40183i
$333$	−7.36610e6	+	672438.i	−0.199482	+	0.0182104i
$334$	−2.62802e7			−0.705324
$335$	4.50387e7	−	4.50387e7i	1.19798	−	1.19798i
$336$		−	1.39083e8i		−	3.66654i
$337$		−	4.07508e7i		−	1.06475i	−0.846510	−	0.532373i	$-0.821300\pi$
$337$		−	4.07508e7i		−	1.06475i	0.846510	−	0.532373i	$-0.178700\pi$
$338$	−1.82360e7	−	1.82360e7i	−0.472257	−	0.472257i
$339$	−4.00028e7	−	4.00028e7i	−1.02681	−	1.02681i
$340$	−1.64318e8			−4.18070
$341$	3.01912e6	+	3.01912e6i	0.0761407	+	0.0761407i
$342$	−9.04504e6			−0.226117
$343$	−4.31720e7			−1.06984
$344$			2.11059e8i			5.18477i
$345$	2.84339e7			0.692434
$346$	4.11731e7	+	4.11731e7i	0.993997	+	0.993997i
$347$	−1.94152e7	+	1.94152e7i	−0.464679	+	0.464679i	−0.900186	−	0.435507i	$-0.856569\pi$
$347$	−1.94152e7	+	1.94152e7i	−0.464679	+	0.464679i	0.435507	+	0.900186i	$0.356569\pi$
$348$	1.18767e8	−	1.18767e8i	2.81811	−	2.81811i
$349$	2.98261e7			0.701650			0.350825	−	0.936441i	$-0.385901\pi$
$349$	2.98261e7			0.701650			0.350825	+	0.936441i	$0.385901\pi$
$350$	4.63270e7	+	4.63270e7i	1.08051	+	1.08051i
$351$	−2.18078e7	+	2.18078e7i	−0.504301	+	0.504301i
$352$	1.54549e8	+	1.54549e8i	3.54354	+	3.54354i
$353$	5.55207e7	−	5.55207e7i	1.26221	−	1.26221i	0.312186	−	0.950021i	$-0.398939\pi$
$353$	5.55207e7	−	5.55207e7i	1.26221	−	1.26221i	0.950021	−	0.312186i	$-0.101061\pi$
$354$			3.66015e7i			0.825067i
$355$	4.66360e7	+	4.66360e7i	1.04240	+	1.04240i
$356$	−9.71240e6	−	9.71240e6i	−0.215267	−	0.215267i
$357$	−2.55683e7	+	2.55683e7i	−0.561950	+	0.561950i
$358$		−	1.22756e8i		−	2.67543i
$359$	−3.05580e7			−0.660452			−0.330226	−	0.943902i	$-0.607125\pi$
$359$	−3.05580e7			−0.660452			−0.330226	+	0.943902i	$0.607125\pi$
$360$		−	5.09793e7i		−	1.09266i
$361$		−	3.17496e7i		−	0.674865i
$362$	−4.32112e7	+	4.32112e7i	−0.910899	+	0.910899i
$363$			5.75484e6i			0.120313i
$364$	5.89292e7	−	5.89292e7i	1.22187	−	1.22187i
$365$	6.27142e7	−	6.27142e7i	1.28970	−	1.28970i
$366$	−6.42310e7			−1.31009
$367$	7.77503e7			1.57291			0.786455	−	0.617648i	$-0.211914\pi$
$367$	7.77503e7			1.57291			0.786455	+	0.617648i	$0.211914\pi$
$368$	−7.13888e7	−	7.13888e7i	−1.43247	−	1.43247i
$369$			8.03548e6i			0.159931i
$370$	−1.43378e8	+	1.30887e7i	−2.83059	+	0.258400i
$371$	4.66309e7			0.913171
$372$	−1.32863e7	+	1.32863e7i	−0.258092	+	0.258092i
$373$		−	2.71229e7i		−	0.522648i	−0.965251	−	0.261324i	$-0.915841\pi$
$373$		−	2.71229e7i		−	0.522648i	0.965251	−	0.261324i	$-0.0841590\pi$
$374$		−	9.74677e7i		−	1.86314i
$375$	3.60415e6	+	3.60415e6i	0.0683454	+	0.0683454i
$376$	3.75923e7	+	3.75923e7i	0.707188	+	0.707188i
$377$	5.43546e7			1.01441
$378$	4.81699e7	+	4.81699e7i	0.891867	+	0.891867i
$379$	4.13726e7			0.759968			0.379984	−	0.924993i	$-0.375929\pi$
$379$	4.13726e7			0.759968			0.379984	+	0.924993i	$0.375929\pi$
$380$	−1.31135e8			−2.38984
$381$			3.31880e7i			0.600076i
$382$	−2.16049e7			−0.387581
$383$	−3.81583e6	−	3.81583e6i	−0.0679193	−	0.0679193i	0.672331	−	0.740250i	$-0.265293\pi$
$383$	−3.81583e6	−	3.81583e6i	−0.0679193	−	0.0679193i	−0.740250	+	0.672331i	$0.765293\pi$
$384$	−2.80479e8	+	2.80479e8i	−4.95343	+	4.95343i
$385$	−3.97509e7	+	3.97509e7i	−0.696569	+	0.696569i
$386$	−1.04199e6			−0.0181177
$387$	1.12037e7	+	1.12037e7i	0.193298	+	0.193298i
$388$	6.87010e7	−	6.87010e7i	1.17616	−	1.17616i
$389$	−2.73419e7	−	2.73419e7i	−0.464494	−	0.464494i	0.435631	−	0.900125i	$-0.356525\pi$
$389$	−2.73419e7	−	2.73419e7i	−0.464494	−	0.464494i	−0.900125	+	0.435631i	$0.856525\pi$
$390$	1.06327e8	−	1.06327e8i	1.79246	−	1.79246i
$391$			2.62475e7i			0.439094i
$392$	7.62473e7	+	7.62473e7i	1.26580	+	1.26580i
$393$	−1.94691e7	−	1.94691e7i	−0.320750	−	0.320750i
$394$	1.23818e8	−	1.23818e8i	2.02439	−	2.02439i
$395$			1.97618e7i			0.320653i
$396$	3.42596e7			0.551693
$397$			1.20616e8i			1.92767i	0.266504	+	0.963834i	$0.414131\pi$
$397$			1.20616e8i			1.92767i	−0.266504	+	0.963834i	$0.585869\pi$
$398$			1.60190e8i			2.54089i
$399$	−2.04050e7	+	2.04050e7i	−0.321231	+	0.321231i
$400$		−	3.12632e8i		−	4.88488i
$401$	1.17020e7	−	1.17020e7i	0.181479	−	0.181479i	−0.610521	−	0.792000i	$-0.709040\pi$
$401$	1.17020e7	−	1.17020e7i	0.181479	−	0.181479i	0.792000	+	0.610521i	$0.209040\pi$
$402$	−1.17567e8	+	1.17567e8i	−1.80970	+	1.80970i
$403$	−6.08057e6			−0.0929028
$404$	−1.92647e8			−2.92158
$405$	7.82463e7	+	7.82463e7i	1.17787	+	1.17787i
$406$		−	1.20061e8i		−	1.79400i
$407$	−5.78276e6	−	6.33463e7i	−0.0857733	−	0.939589i
$408$	2.81990e8			4.15196
$409$	−4.08506e7	+	4.08506e7i	−0.597075	+	0.597075i	−0.939533	−	0.342458i	$-0.888741\pi$
$409$	−4.08506e7	+	4.08506e7i	−0.597075	+	0.597075i	0.342458	+	0.939533i	$0.388741\pi$
$410$			1.56407e8i			2.26937i
$411$			1.00100e7i			0.144181i
$412$	3.46356e7	+	3.46356e7i	0.495258	+	0.495258i
$413$	1.37796e7	+	1.37796e7i	0.195608	+	0.195608i
$414$	−1.23865e7			−0.174561
$415$	−3.48466e7	−	3.48466e7i	−0.487547	−	0.487547i
$416$	−3.11264e8			−4.32364
$417$	1.39588e8			1.92504
$418$		−	7.77847e7i		−	1.06504i
$419$	6.87124e7			0.934099			0.467050	−	0.884231i	$-0.345317\pi$
$419$	6.87124e7			0.934099			0.467050	+	0.884231i	$0.345317\pi$
$420$	−1.74932e8	−	1.74932e8i	−2.36114	−	2.36114i
$421$	1.11457e7	−	1.11457e7i	0.149370	−	0.149370i	−0.628467	−	0.777836i	$-0.716317\pi$
$421$	1.11457e7	−	1.11457e7i	0.149370	−	0.149370i	0.777836	+	0.628467i	$0.216317\pi$
$422$	−2.70644e7	+	2.70644e7i	−0.360132	+	0.360132i
$423$	3.99102e6			0.0527306
$424$	−2.57143e8	−	2.57143e8i	−3.37347	−	3.37347i
$425$	−5.74727e7	+	5.74727e7i	−0.748678	+	0.748678i
$426$	−1.21736e8	−	1.21736e8i	−1.57468	−	1.57468i
$427$	−2.41815e7	+	2.41815e7i	−0.310598	+	0.310598i
$428$		−	8.12112e7i		−	1.03582i
$429$	4.69765e7	+	4.69765e7i	0.594989	+	0.594989i
$430$	2.18075e8	+	2.18075e8i	2.74284	+	2.74284i
$431$	−7.36035e7	+	7.36035e7i	−0.919320	+	0.919320i	−0.996980	−	0.0776595i	$-0.975255\pi$
$431$	−7.36035e7	+	7.36035e7i	−0.919320	+	0.919320i	0.0776595	+	0.996980i	$0.475255\pi$
$432$		−	3.25068e8i		−	4.03203i
$433$	−1.20232e8			−1.48101			−0.740505	−	0.672051i	$-0.765414\pi$
$433$	−1.20232e8			−1.48101			−0.740505	+	0.672051i	$0.765414\pi$
$434$			1.34310e7i			0.164301i
$435$		−	1.61353e8i		−	1.96024i
$436$	6.54595e7	−	6.54595e7i	0.789792	−	0.789792i
$437$			2.09470e7i			0.251002i
$438$	−1.63706e8	+	1.63706e8i	−1.94824	+	1.94824i
$439$	8.30232e7	−	8.30232e7i	0.981310	−	0.981310i	−0.0185189	−	0.999829i	$-0.505895\pi$
$439$	8.30232e7	−	8.30232e7i	0.981310	−	0.981310i	0.999829	+	0.0185189i	$0.00589508\pi$
$440$	4.38407e8			5.14659
$441$	8.09488e6			0.0943831
$442$	9.81511e7	+	9.81511e7i	1.13665	+	1.13665i
$443$		−	1.08245e8i		−	1.24508i	−0.782587	−	0.622541i	$-0.786100\pi$
$443$		−	1.08245e8i		−	1.24508i	0.782587	−	0.622541i	$-0.213900\pi$
$444$	2.78769e8	−	2.54483e7i	3.18490	−	0.290744i
$445$	−1.31949e7			−0.149736
$446$	9.32483e7	−	9.32483e7i	1.05108	−	1.05108i
$447$		−	5.45740e7i		−	0.611031i
$448$			3.86618e8i			4.29980i
$449$	−2.80162e7	−	2.80162e7i	−0.309507	−	0.309507i	0.535211	−	0.844718i	$-0.320232\pi$
$449$	−2.80162e7	−	2.80162e7i	−0.309507	−	0.309507i	−0.844718	+	0.535211i	$0.820232\pi$
$450$	−2.71220e7	−	2.71220e7i	−0.297635	−	0.297635i
$451$	−6.91028e7			−0.753296
$452$	2.52644e8	+	2.52644e8i	2.73586	+	2.73586i
$453$	−1.46248e8			−1.57324
$454$	4.30838e7			0.460412
$455$		−	8.00591e7i		−	0.849917i
$456$	2.25044e8			2.37341
$457$	−8.37325e7	−	8.37325e7i	−0.877294	−	0.877294i	0.115960	−	0.993254i	$-0.463006\pi$
$457$	−8.37325e7	−	8.37325e7i	−0.877294	−	0.877294i	−0.993254	+	0.115960i	$0.963006\pi$
$458$	3.68362e7	−	3.68362e7i	0.383423	−	0.383423i
$459$	−5.97590e7	+	5.97590e7i	−0.617967	+	0.617967i
$460$	−1.79579e8			−1.84494
$461$	4.06412e7	+	4.06412e7i	0.414824	+	0.414824i	0.883415	−	0.468591i	$-0.155238\pi$
$461$	4.06412e7	+	4.06412e7i	0.414824	+	0.414824i	−0.468591	+	0.883415i	$0.655238\pi$
$462$	1.03764e8	−	1.03764e8i	1.05225	−	1.05225i
$463$	−5.11937e7	−	5.11937e7i	−0.515791	−	0.515791i	0.400504	−	0.916295i	$-0.368835\pi$
$463$	−5.11937e7	−	5.11937e7i	−0.515791	−	0.515791i	−0.916295	+	0.400504i	$0.868835\pi$
$464$	−4.05107e8	+	4.05107e8i	−4.05524	+	4.05524i
$465$			1.80503e7i			0.179525i
$466$	4.20437e6	+	4.20437e6i	0.0415474	+	0.0415474i
$467$	−9.93627e7	−	9.93627e7i	−0.975603	−	0.975603i	0.0241068	−	0.999709i	$-0.492326\pi$
$467$	−9.93627e7	−	9.93627e7i	−0.975603	−	0.975603i	−0.999709	+	0.0241068i	$0.992326\pi$
$468$	−3.44998e7	+	3.44998e7i	−0.336573	+	0.336573i
$469$			8.85223e7i			0.858092i
$470$	7.76836e7			0.748231
$471$			1.13346e8i			1.08478i
$472$		−	1.51974e8i		−	1.44525i
$473$	−9.63483e7	+	9.63483e7i	−0.910459	+	0.910459i
$474$		−	5.15852e7i		−	0.484384i
$475$	−4.58665e7	+	4.58665e7i	−0.427971	+	0.427971i
$476$	1.61481e8	−	1.61481e8i	1.49727	−	1.49727i
$477$	−2.72999e7			−0.251539
$478$	1.51968e8			1.39145
$479$	3.68808e7	+	3.68808e7i	0.335578	+	0.335578i	0.854700	−	0.519122i	$-0.173741\pi$
$479$	3.68808e7	+	3.68808e7i	0.335578	+	0.335578i	−0.519122	+	0.854700i	$0.673741\pi$
$480$			9.23994e8i			8.35498i
$481$	6.96137e7	+	5.79671e7i	0.625546	+	0.520890i
$482$	−4.22126e8			−3.76965
$483$	−2.79430e7	+	2.79430e7i	−0.247988	+	0.247988i
$484$		−	3.63457e7i		−	0.320565i
$485$		−	9.33348e7i		−	0.818123i
$486$	−6.34657e7	−	6.34657e7i	−0.552879	−	0.552879i
$487$	3.17228e7	+	3.17228e7i	0.274653	+	0.274653i	0.830970	−	0.556317i	$-0.187786\pi$
$487$	3.17228e7	+	3.17228e7i	0.274653	+	0.274653i	−0.556317	+	0.830970i	$0.687786\pi$
$488$	2.66694e8			2.29485
$489$	−1.38564e8	−	1.38564e8i	−1.18501	−	1.18501i
$490$	1.57563e8			1.33927
$491$	6.48473e7			0.547832			0.273916	−	0.961754i	$-0.411681\pi$
$491$	6.48473e7			0.547832			0.273916	+	0.961754i	$0.411681\pi$
$492$		−	3.04102e8i		−	2.55343i
$493$	1.48946e8			1.24305
$494$	7.83301e7	+	7.83301e7i	0.649752	+	0.649752i
$495$	2.32720e7	−	2.32720e7i	0.191875	−	0.191875i
$496$	4.53187e7	−	4.53187e7i	0.371392	−	0.371392i
$497$	−9.16617e7			−0.746653
$498$	9.09619e7	+	9.09619e7i	0.736498	+	0.736498i
$499$	−9.23937e7	+	9.23937e7i	−0.743602	+	0.743602i	−0.973269	−	0.229667i	$-0.926236\pi$
$499$	−9.23937e7	+	9.23937e7i	−0.743602	+	0.743602i	0.229667	+	0.973269i	$0.426236\pi$
$500$	−2.27626e7	−	2.27626e7i	−0.182101	−	0.182101i
$501$	3.47089e7	−	3.47089e7i	0.276011	−	0.276011i
$502$		−	1.03380e8i		−	0.817193i
$503$	−7.42788e7	−	7.42788e7i	−0.583662	−	0.583662i	0.352246	−	0.935907i	$-0.385418\pi$
$503$	−7.42788e7	−	7.42788e7i	−0.583662	−	0.583662i	−0.935907	+	0.352246i	$0.885418\pi$
$504$	5.00992e7	+	5.00992e7i	0.391327	+	0.391327i
$505$	−1.30862e8	+	1.30862e8i	−1.01611	+	1.01611i
$506$		−	1.06520e8i		−	0.822203i
$507$	4.81694e7			0.369613
$508$		−	2.09605e8i		−	1.59886i
$509$			1.35646e8i			1.02862i	0.857605	+	0.514309i	$0.171952\pi$
$509$			1.35646e8i			1.02862i	−0.857605	+	0.514309i	$0.828048\pi$
$510$	2.91363e8	−	2.91363e8i	2.19646	−	2.19646i
$511$			1.23263e8i			0.923784i
$512$	6.60491e8	−	6.60491e8i	4.92104	−	4.92104i
$513$	−4.76910e7	+	4.76910e7i	−0.353252	+	0.353252i
$514$	−3.07523e8			−2.26458
$515$	4.70547e7			0.344494
$516$	−4.24001e8	−	4.24001e8i	−3.08616	−	3.08616i
$517$			3.43216e7i			0.248368i
$518$	1.28040e8	−	1.53766e8i	0.921205	−	1.10629i
$519$	−1.08757e8			−0.777953
$520$	−4.41481e8	+	4.41481e8i	−3.13980	+	3.13980i
$521$			1.21541e8i			0.859425i	0.902966	+	0.429712i	$0.141385\pi$
$521$			1.21541e8i			0.859425i	−0.902966	+	0.429712i	$0.858615\pi$
$522$			7.02890e7i			0.494170i
$523$	1.79417e8	+	1.79417e8i	1.25418	+	1.25418i	0.953829	+	0.300351i	$0.0971037\pi$
$523$	1.79417e8	+	1.79417e8i	1.25418	+	1.25418i	0.300351	+	0.953829i	$0.402896\pi$
$524$	1.22960e8	+	1.22960e8i	0.854616	+	0.854616i
$525$	−1.22370e8			−0.845665
$526$	3.89068e8	+	3.89068e8i	2.67343	+	2.67343i
$527$	−1.66623e7			−0.113842
$528$	−7.00236e8			−4.75710
$529$		−	1.19351e8i		−	0.806228i
$530$	−5.31381e8			−3.56926
$531$	−8.06722e6	−	8.06722e6i	−0.0538816	−	0.0538816i
$532$	1.28871e8	−	1.28871e8i	0.855896	−	0.855896i
$533$	6.95873e7	−	6.95873e7i	0.459566	−	0.459566i
$534$	3.44434e7			0.226194
$535$	−5.51653e7	−	5.51653e7i	−0.360251	−	0.360251i
$536$	4.88150e8	−	4.88150e8i	3.17000	−	3.17000i
$537$	1.62126e8	+	1.62126e8i	1.04696	+	1.04696i
$538$	3.15513e8	−	3.15513e8i	2.02615	−	2.02615i
$539$			6.96135e7i			0.444557i
$540$	−4.08856e8	−	4.08856e8i	−2.59651	−	2.59651i
$541$	5.81725e7	+	5.81725e7i	0.367389	+	0.367389i	0.866524	−	0.499135i	$-0.166349\pi$
$541$	5.81725e7	+	5.81725e7i	0.367389	+	0.367389i	−0.499135	+	0.866524i	$0.666349\pi$
$542$	−2.75722e8	+	2.75722e8i	−1.73171	+	1.73171i
$543$		−	1.14140e8i		−	0.712916i
$544$	−8.52945e8			−5.29815
$545$		−	8.89309e7i		−	0.549368i
$546$			2.08982e8i			1.28390i
$547$	1.56090e8	−	1.56090e8i	0.953701	−	0.953701i	−0.0452733	−	0.998975i	$-0.514416\pi$
$547$	1.56090e8	−	1.56090e8i	0.953701	−	0.953701i	0.998975	+	0.0452733i	$0.0144159\pi$
$548$		−	6.32196e7i		−	0.384158i
$549$	1.41569e7	−	1.41569e7i	0.0855564	−	0.0855564i
$550$	2.33241e8	−	2.33241e8i	1.40190	−	1.40190i
$551$	1.18867e8			0.710570
$552$	3.08179e8			1.83226
$553$	−1.94206e7	−	1.94206e7i	−0.114839	−	0.114839i
$554$			6.08883e8i			3.58100i
$555$	1.72076e8	−	2.06649e8i	1.00657	−	1.20880i
$556$	−8.81592e8			−5.12912
$557$	1.69614e8	−	1.69614e8i	0.981515	−	0.981515i	−0.0183173	−	0.999832i	$-0.505831\pi$
$557$	1.69614e8	−	1.69614e8i	0.981515	−	0.981515i	0.999832	+	0.0183173i	$0.00583091\pi$
$558$		−	7.86312e6i		−	0.0452577i
$559$		−	1.94048e8i		−	1.11089i
$560$	5.96684e8	+	5.96684e8i	3.39766	+	3.39766i
$561$	1.28728e8	+	1.28728e8i	0.729095	+	0.729095i
$562$	−2.73059e8			−1.53833
$563$	−1.64356e8	−	1.64356e8i	−0.921003	−	0.921003i	0.0760971	−	0.997100i	$-0.475754\pi$
$563$	−1.64356e8	−	1.64356e8i	−0.921003	−	0.921003i	−0.997100	+	0.0760971i	$0.975754\pi$
$564$	−1.51040e8			−0.841887
$565$	3.43234e8			1.90303
$566$			2.83639e8i			1.56429i
$567$	−1.53791e8			−0.843688
$568$	5.05463e8	+	5.05463e8i	2.75832	+	2.75832i
$569$	3.38592e7	−	3.38592e7i	0.183798	−	0.183798i	−0.609211	−	0.793008i	$-0.708514\pi$
$569$	3.38592e7	−	3.38592e7i	0.183798	−	0.183798i	0.793008	+	0.609211i	$0.208514\pi$
$570$	2.32524e8	−	2.32524e8i	1.25558	−	1.25558i
$571$	1.82323e8			0.979340			0.489670	−	0.871908i	$-0.337117\pi$
$571$	1.82323e8			0.979340			0.489670	+	0.871908i	$0.337117\pi$
$572$	−2.96688e8	−	2.96688e8i	−1.58530	−	1.58530i
$573$	2.85341e7	−	2.85341e7i	0.151670	−	0.151670i
$574$	−1.53707e8	−	1.53707e8i	−0.812753	−	0.812753i
$575$	−6.28104e7	+	6.28104e7i	−0.330391	+	0.330391i
$576$		−	2.26344e8i		−	1.18441i
$577$	1.13158e8	+	1.13158e8i	0.589057	+	0.589057i	0.937376	−	0.348319i	$-0.113247\pi$
$577$	1.13158e8	+	1.13158e8i	0.589057	+	0.589057i	−0.348319	+	0.937376i	$0.613247\pi$
$578$	−1.35063e6	−	1.35063e6i	−0.00699442	−	0.00699442i
$579$	1.37619e6	−	1.37619e6i	0.00708993	−	0.00708993i
$580$			1.01905e9i			5.22290i
$581$	6.84901e7			0.349220
$582$			2.43636e8i			1.23587i
$583$		−	2.34771e8i		−	1.18478i
$584$	6.79726e8	−	6.79726e8i	3.41268	−	3.41268i
$585$			4.68703e7i			0.234115i
$586$	−2.51226e8	+	2.51226e8i	−1.24845	+	1.24845i
$587$	−2.20327e8	+	2.20327e8i	−1.08931	+	1.08931i	−0.0937143	+	0.995599i	$0.529874\pi$
$587$	−2.20327e8	+	2.20327e8i	−1.08931	+	1.08931i	−0.995599	+	0.0937143i	$0.970126\pi$
$588$	−3.06349e8			−1.50690
$589$	−1.32975e7			−0.0650764
$590$	−1.57025e8	−	1.57025e8i	−0.764563	−	0.764563i
$591$			3.27058e8i			1.58439i
$592$	−9.50865e8	+	8.68027e7i	−4.58304	+	0.418377i
$593$	3.33242e8			1.59807			0.799035	−	0.601285i	$-0.205344\pi$
$593$	3.33242e8			1.59807			0.799035	+	0.601285i	$0.205344\pi$
$594$	2.42519e8	−	2.42519e8i	1.15714	−	1.15714i
$595$		−	2.19383e8i		−	1.04148i
$596$			3.44672e8i			1.62805i
$597$	−2.11566e8	−	2.11566e8i	−0.994314	−	0.994314i
$598$	1.07267e8	+	1.07267e8i	0.501605	+	0.501605i
$599$	−2.68511e8			−1.24935			−0.624673	−	0.780887i	$-0.714768\pi$
$599$	−2.68511e8			−1.24935			−0.624673	+	0.780887i	$0.714768\pi$
$600$	6.74804e8	+	6.74804e8i	3.12409	+	3.12409i
$601$	1.26642e8			0.583384			0.291692	−	0.956512i	$-0.405782\pi$
$601$	1.26642e8			0.583384			0.291692	+	0.956512i	$0.405782\pi$
$602$	−4.28620e8			−1.96464
$603$		−	5.18250e7i		−	0.236367i
$604$	9.23652e8			4.19177
$605$	−2.46890e7	−	2.46890e7i	−0.111490	−	0.111490i
$606$	3.41595e8	−	3.41595e8i	1.53495	−	1.53495i
$607$	−2.59606e8	+	2.59606e8i	−1.16078	+	1.16078i	−0.176471	+	0.984306i	$0.556468\pi$
$607$	−2.59606e8	+	2.59606e8i	−1.16078	+	1.16078i	−0.984306	+	0.176471i	$0.943532\pi$
$608$	−6.80698e8			−3.02861
$609$	1.58567e8	+	1.58567e8i	0.702039	+	0.702039i
$610$	2.75559e8	−	2.75559e8i	1.21402	−	1.21402i
$611$	−3.45622e7	−	3.45622e7i	−0.151523	−	0.151523i
$612$	−9.45386e7	+	9.45386e7i	−0.412434	+	0.412434i
$613$		−	1.59961e8i		−	0.694438i	−0.937784	−	0.347219i	$-0.887126\pi$
$613$		−	1.59961e8i		−	0.694438i	0.937784	−	0.347219i	$-0.112874\pi$
$614$	3.23642e7	+	3.23642e7i	0.139817	+	0.139817i
$615$	−2.06571e8	−	2.06571e8i	−0.888064	−	0.888064i
$616$	−4.30838e8	+	4.30838e8i	−1.84320	+	1.84320i
$617$		−	5.74335e7i		−	0.244518i	−0.992498	−	0.122259i	$-0.960986\pi$
$617$		−	5.74335e7i		−	0.244518i	0.992498	−	0.122259i	$-0.0390138\pi$
$618$	−1.22829e8			−0.520399
$619$			2.15207e8i			0.907369i	0.891162	+	0.453685i	$0.149891\pi$
$619$			2.15207e8i			0.907369i	−0.891162	+	0.453685i	$0.850109\pi$
$620$		−	1.14000e8i		−	0.478331i
$621$	−6.53090e7	+	6.53090e7i	−0.272708	+	0.272708i
$622$			4.44451e8i			1.84694i
$623$	1.29671e7	−	1.29671e7i	0.0536265	−	0.0536265i
$624$	7.05146e8	−	7.05146e8i	2.90218	−	2.90218i
$625$	2.28217e8			0.934779
$626$	−3.60642e8			−1.47012
$627$	1.02732e8	+	1.02732e8i	0.416777	+	0.416777i
$628$		−	7.15856e8i		−	2.89033i
$629$	1.90760e8	+	1.58845e8i	0.766540	+	0.638295i
$630$	1.03529e8			0.414038
$631$	1.97303e7	−	1.97303e7i	0.0785316	−	0.0785316i	−0.666750	−	0.745282i	$-0.732315\pi$
$631$	1.97303e7	−	1.97303e7i	0.0785316	−	0.0785316i	0.745282	+	0.666750i	$0.232315\pi$
$632$			2.14187e8i			0.848482i
$633$		−	7.14892e7i		−	0.281857i
$634$	−5.41519e8	−	5.41519e8i	−2.12494	−	2.12494i
$635$	−1.42381e8	−	1.42381e8i	−0.556071	−	0.556071i
$636$	1.03316e9			4.01602
$637$	−7.01016e7	−	7.01016e7i	−0.271212	−	0.271212i
$638$	−6.04465e8			−2.32760
$639$	5.36630e7			0.205671
$640$		−	2.40658e9i		−	9.18037i
$641$	4.46759e8			1.69629			0.848144	−	0.529766i	$-0.177720\pi$
$641$	4.46759e8			1.69629			0.848144	+	0.529766i	$0.177720\pi$
$642$	1.44001e8	+	1.44001e8i	0.544202	+	0.544202i
$643$	1.58116e8	−	1.58116e8i	0.594763	−	0.594763i	−0.344151	−	0.938914i	$-0.611833\pi$
$643$	1.58116e8	−	1.58116e8i	0.594763	−	0.594763i	0.938914	+	0.344151i	$0.111833\pi$
$644$	1.76479e8	−	1.76479e8i	0.660746	−	0.660746i
$645$	−5.76034e8			−2.14669
$646$	2.14645e8	+	2.14645e8i	0.796201	+	0.796201i
$647$	−6.75136e6	+	6.75136e6i	−0.0249275	+	0.0249275i	−0.719461	−	0.694533i	$-0.755611\pi$
$647$	−6.75136e6	+	6.75136e6i	−0.0249275	+	0.0249275i	0.694533	+	0.719461i	$0.255611\pi$
$648$	8.48070e8	+	8.48070e8i	3.11678	+	3.11678i
$649$	6.93757e7	−	6.93757e7i	0.253789	−	0.253789i
$650$			4.69752e8i			1.71052i
$651$	−1.77386e7	−	1.77386e7i	−0.0642950	−	0.0642950i
$652$	8.75124e8	+	8.75124e8i	3.15738	+	3.15738i
$653$	1.58377e8	−	1.58377e8i	0.568791	−	0.568791i	−0.362999	−	0.931790i	$-0.618247\pi$
$653$	1.58377e8	−	1.58377e8i	0.568791	−	0.568791i	0.931790	+	0.362999i	$0.118247\pi$
$654$			2.32141e8i			0.829885i
$655$	1.67049e8			0.594458
$656$			1.03727e9i			3.67436i
$657$		−	7.21638e7i		−	0.254462i
$658$	−7.63425e7	+	7.63425e7i	−0.267971	+	0.267971i
$659$		−	2.71611e8i		−	0.949054i	−0.880241	−	0.474527i	$-0.842619\pi$
$659$		−	2.71611e8i		−	0.949054i	0.880241	−	0.474527i	$-0.157381\pi$
$660$	−8.80725e8	+	8.80725e8i	−3.06343	+	3.06343i
$661$	−2.61385e7	+	2.61385e7i	−0.0905057	+	0.0905057i	−0.750910	−	0.660404i	$-0.770385\pi$
$661$	−2.61385e7	+	2.61385e7i	−0.0905057	+	0.0905057i	0.660404	+	0.750910i	$0.270385\pi$
$662$	−3.29916e7			−0.113718
$663$	−2.59261e8			−0.889604
$664$	−3.77684e8	−	3.77684e8i	−1.29010	−	1.29010i
$665$		−	1.75080e8i		−	0.595349i
$666$	−7.49605e7	+	9.00214e7i	−0.253752	+	0.304735i
$667$	1.62779e8			0.548556
$668$	−2.19210e8	+	2.19210e8i	−0.735412	+	0.735412i
$669$			2.46311e8i			0.822630i
$670$		−	1.00875e9i		−	3.35398i
$671$	1.21745e8	+	1.21745e8i	0.402982	+	0.402982i
$672$	−9.08042e8	−	9.08042e8i	−2.99225	−	2.99225i
$673$	−2.86515e8			−0.939945			−0.469972	−	0.882681i	$-0.655736\pi$
$673$	−2.86515e8			−0.939945			−0.469972	+	0.882681i	$0.655736\pi$
$674$	−4.56357e8	−	4.56357e8i	−1.49048	−	1.49048i
$675$	−2.86007e8			−0.929962
$676$	−3.04222e8			−0.984806
$677$		−	1.87319e6i		−	0.00603694i	−0.999995	−	0.00301847i	$-0.999039\pi$
$677$		−	1.87319e6i		−	0.00603694i	0.999995	−	0.00301847i	$-0.000960810\pi$
$678$	−8.95960e8			−2.87475
$679$	9.17235e7	+	9.17235e7i	0.293002	+	0.293002i
$680$	−1.20977e9	+	1.20977e9i	−3.84749	+	3.84749i
$681$	−5.69019e7	+	5.69019e7i	−0.180171	+	0.180171i
$682$	6.76205e7			0.213170
$683$	−3.07943e8	−	3.07943e8i	−0.966515	−	0.966515i	0.0329422	−	0.999457i	$-0.489512\pi$
$683$	−3.07943e8	−	3.07943e8i	−0.966515	−	0.966515i	−0.999457	+	0.0329422i	$0.989512\pi$
$684$	−7.54471e7	+	7.54471e7i	−0.235762	+	0.235762i
$685$	−4.29440e7	−	4.29440e7i	−0.133607	−	0.133607i
$686$	−4.83471e8	+	4.83471e8i	−1.49761	+	1.49761i
$687$			9.73010e7i			0.300087i
$688$	1.44624e9	+	1.44624e9i	4.44096	+	4.44096i
$689$	2.36417e8	+	2.36417e8i	0.722804	+	0.722804i
$690$	3.18423e8	−	3.18423e8i	0.969298	−	0.969298i
$691$			1.86700e8i			0.565862i	0.959140	+	0.282931i	$0.0913067\pi$
$691$			1.86700e8i			0.565862i	−0.959140	+	0.282931i	$0.908693\pi$
$692$	6.86871e8			2.07280
$693$			4.57404e7i			0.137436i
$694$			4.34851e8i			1.30095i
$695$	−5.98850e8	+	5.98850e8i	−1.78387	+	1.78387i
$696$		−	1.74882e9i		−	5.18700i
$697$	1.90687e8	−	1.90687e8i	0.563149	−	0.563149i
$698$	3.34015e8	−	3.34015e8i	0.982199	−	0.982199i
$699$	−1.11056e7			−0.0325171
$700$	7.72852e8			2.25321
$701$	−3.04439e8	−	3.04439e8i	−0.883784	−	0.883784i	0.110133	−	0.993917i	$-0.464872\pi$
$701$	−3.04439e8	−	3.04439e8i	−0.883784	−	0.883784i	−0.993917	+	0.110133i	$0.964872\pi$
$702$			4.88439e8i			1.41188i
$703$	1.52237e8	+	1.26767e8i	0.438182	+	0.364872i
$704$	1.94649e9			5.57872
$705$	−1.02599e8	+	1.02599e8i	−0.292802	+	0.292802i
$706$		−	1.24352e9i		−	3.53378i
$707$		−	2.57205e8i		−	0.727816i
$708$	3.05303e8	+	3.05303e8i	0.860263	+	0.860263i
$709$	−9.01888e7	−	9.01888e7i	−0.253054	−	0.253054i	0.569167	−	0.822222i	$-0.307266\pi$
$709$	−9.01888e7	−	9.01888e7i	−0.253054	−	0.253054i	−0.822222	+	0.569167i	$0.807266\pi$
$710$	1.04453e9			2.91840
$711$	1.13697e7	+	1.13697e7i	0.0316330	+	0.0316330i
$712$	−1.43013e8			−0.396219
$713$	−1.82098e7			−0.0502386
$714$			5.72666e8i			1.57328i
$715$	−4.03071e8			−1.10271
$716$	−1.02394e9	−	1.02394e9i	−2.78955	−	2.78955i
$717$	−2.00708e8	+	2.00708e8i	−0.544511	+	0.544511i
$718$	−3.42211e8	+	3.42211e8i	−0.924528	+	0.924528i
$719$	−1.22804e8			−0.330389			−0.165194	−	0.986261i	$-0.552825\pi$
$719$	−1.22804e8			−0.330389			−0.165194	+	0.986261i	$0.552825\pi$
$720$	−3.49326e8	−	3.49326e8i	−0.935909	−	0.935909i
$721$	−4.62424e7	+	4.62424e7i	−0.123377	+	0.123377i
$722$	−3.55555e8	−	3.55555e8i	−0.944704	−	0.944704i
$723$	5.57512e8	−	5.57512e8i	1.47516	−	1.47516i
$724$			7.20872e8i			1.89951i
$725$	3.56428e8	+	3.56428e8i	0.935315	+	0.935315i
$726$	6.44469e7	+	6.44469e7i	0.168419	+	0.168419i
$727$	7.50933e7	−	7.50933e7i	0.195433	−	0.195433i	−0.602606	−	0.798039i	$-0.705871\pi$
$727$	7.50933e7	−	7.50933e7i	0.195433	−	0.195433i	0.798039	+	0.602606i	$0.205871\pi$
$728$		−	8.67718e8i		−	2.24898i
$729$	−2.81839e8			−0.727476
$730$		−	1.40464e9i		−	3.61074i
$731$		−	5.31741e8i		−	1.36128i
$732$	−5.35768e8	+	5.35768e8i	−1.36598	+	1.36598i
$733$		−	3.50310e8i		−	0.889490i	−0.895657	−	0.444745i	$-0.853294\pi$
$733$		−	3.50310e8i		−	0.889490i	0.895657	−	0.444745i	$-0.146706\pi$
$734$	8.70704e8	−	8.70704e8i	2.20182	−	2.20182i
$735$	−2.08098e8	+	2.08098e8i	−0.524090	+	0.524090i
$736$	−9.32162e8			−2.33807
$737$	4.45679e8			1.11332
$738$	8.99872e7	+	8.99872e7i	0.223878	+	0.223878i
$739$			1.83997e8i			0.455908i	0.973672	+	0.227954i	$0.0732036\pi$
$739$			1.83997e8i			0.455908i	−0.973672	+	0.227954i	$0.926796\pi$
$740$	−1.08678e9	+	1.30513e9i	−2.68192	+	3.22076i
$741$	−2.06905e8			−0.508529
$742$	5.22207e8	−	5.22207e8i	1.27829	−	1.27829i
$743$			5.88765e8i			1.43541i	0.696347	+	0.717705i	$0.254807\pi$
$743$			5.88765e8i			1.43541i	−0.696347	+	0.717705i	$0.745193\pi$
$744$			1.95637e8i			0.475043i
$745$	2.34129e8	+	2.34129e8i	0.566222	+	0.566222i
$746$	−3.03742e8	−	3.03742e8i	−0.731624	−	0.731624i
$747$	−4.00972e7			−0.0961950
$748$	−8.13004e8	−	8.13004e8i	−1.94262	−	1.94262i
$749$	1.08426e8			0.258040
$750$	8.07238e7			0.191345
$751$			7.86385e8i			1.85659i	0.371847	+	0.928294i	$0.378724\pi$
$751$			7.86385e8i			1.85659i	−0.371847	+	0.928294i	$0.621276\pi$
$752$	5.15188e8			1.21147
$753$	1.36536e8	+	1.36536e8i	0.319789	+	0.319789i
$754$	6.08703e8	−	6.08703e8i	1.42001	−	1.42001i
$755$	6.27421e8	−	6.27421e8i	1.45787	−	1.45787i
$756$	8.03595e8			1.85982
$757$	−4.11060e8	−	4.11060e8i	−0.947583	−	0.947583i	0.0511097	−	0.998693i	$-0.483724\pi$
$757$	−4.11060e8	−	4.11060e8i	−0.947583	−	0.947583i	−0.998693	+	0.0511097i	$0.983724\pi$
$758$	4.63321e8	−	4.63321e8i	1.06384	−	1.06384i
$759$	1.40683e8	+	1.40683e8i	0.321749	+	0.321749i
$760$	−9.65467e8	+	9.65467e8i	−2.19936	+	2.19936i
$761$			4.39429e8i			0.997091i	0.866863	+	0.498546i	$0.166132\pi$
$761$			4.39429e8i			0.997091i	−0.866863	+	0.498546i	$0.833868\pi$
$762$	3.71664e8	+	3.71664e8i	0.840011	+	0.840011i
$763$	8.73956e7	+	8.73956e7i	0.196751	+	0.196751i
$764$	−1.80212e8	+	1.80212e8i	−0.404115	+	0.404115i
$765$			1.28437e8i			0.286883i
$766$	−8.54650e7			−0.190152
$767$			1.39724e8i			0.309660i
$768$			3.34757e9i			7.39003i
$769$	−5.29420e8	+	5.29420e8i	−1.16418	+	1.16418i	−0.180633	+	0.983550i	$0.557815\pi$
$769$	−5.29420e8	+	5.29420e8i	−1.16418	+	1.16418i	−0.983550	+	0.180633i	$0.942185\pi$
$770$			8.90318e8i			1.95017i
$771$	4.06153e8	−	4.06153e8i	0.886189	−	0.886189i
$772$	−8.69155e6	+	8.69155e6i	−0.0188906	+	0.0188906i
$773$	−3.46446e8			−0.750062			−0.375031	−	0.927012i	$-0.622368\pi$
$773$	−3.46446e8			−0.750062			−0.375031	+	0.927012i	$0.622368\pi$
$774$	2.50934e8			0.541173
$775$	−3.98731e7	−	3.98731e7i	−0.0856593	−	0.0856593i
$776$		−	1.01161e9i		−	2.16484i
$777$	3.39763e7	+	3.72187e8i	0.0724291	+	0.793412i
$778$	−6.12390e8			−1.30044
$779$	1.52179e8	−	1.52179e8i	0.321916	−	0.321916i
$780$		−	1.77380e9i		−	3.73784i
$781$			4.61486e8i			0.968735i
$782$	2.93939e8	+	2.93939e8i	0.614662	+	0.614662i
$783$	3.70607e8	+	3.70607e8i	0.772019	+	0.772019i
$784$	1.04494e9			2.16842
$785$	−4.86268e8	−	4.86268e8i	−1.00523	−	1.00523i
$786$	−4.36057e8			−0.897999
$787$	−6.25761e8			−1.28376			−0.641880	−	0.766805i	$-0.721845\pi$
$787$	−6.25761e8			−1.28376			−0.641880	+	0.766805i	$0.721845\pi$
$788$		−	2.06559e9i		−	4.22149i
$789$	−1.02770e9			−2.09236
$790$	2.21307e8	+	2.21307e8i	0.448863	+	0.448863i
$791$	−3.37308e8	+	3.37308e8i	−0.681550	+	0.681550i
$792$	2.52233e8	−	2.52233e8i	0.507722	−	0.507722i
$793$	−2.45198e8			−0.491697
$794$	1.35074e9	+	1.35074e9i	2.69843	+	2.69843i
$795$	7.01807e8	−	7.01807e8i	1.39674	−	1.39674i
$796$	1.33618e9	+	1.33618e9i	2.64927	+	2.64927i
$797$	−1.11369e8	+	1.11369e8i	−0.219984	+	0.219984i	−0.808492	−	0.588508i	$-0.799716\pi$
$797$	−1.11369e8	+	1.11369e8i	−0.219984	+	0.219984i	0.588508	+	0.808492i	$0.299716\pi$
$798$			4.57020e8i			0.899345i
$799$	−9.47096e7	−	9.47096e7i	−0.185675	−	0.185675i
$800$	−2.04110e9	−	2.04110e9i	−3.98653	−	3.98653i
$801$	−7.59155e6	+	7.59155e6i	−0.0147718	+	0.0147718i
$802$		−	2.62094e8i		−	0.508082i
$803$	6.20588e8			1.19855
$804$			1.96131e9i			3.77379i
$805$		−	2.39758e8i		−	0.459605i
$806$	−6.80946e7	+	6.80946e7i	−0.130049	+	0.130049i
$807$			8.33412e8i			1.58577i
$808$	−1.41834e9	+	1.41834e9i	−2.68873	+	2.68873i
$809$	−4.05381e7	+	4.05381e7i	−0.0765628	+	0.0765628i	−0.744351	−	0.667788i	$-0.767241\pi$
$809$	−4.05381e7	+	4.05381e7i	−0.0765628	+	0.0765628i	0.667788	+	0.744351i	$0.267241\pi$
$810$	1.75252e9			3.29767
$811$	4.77654e8			0.895469			0.447734	−	0.894167i	$-0.352231\pi$
$811$	4.77654e8			0.895469			0.447734	+	0.894167i	$0.352231\pi$
$812$	−1.00146e9	−	1.00146e9i	−1.87053	−	1.87053i
$813$		−	7.28306e8i		−	1.35532i
$814$	−7.74157e8	−	6.44638e8i	−1.43534	−	1.19521i
$815$	1.18891e9			2.19623
$816$	1.93228e9	−	1.93228e9i	3.55631	−	3.55631i
$817$		−	4.24359e8i		−	0.778157i
$818$			9.14950e8i			1.67162i
$819$	−4.60611e7	−	4.60611e7i	−0.0838461	−	0.0838461i
$820$	1.30464e9	+	1.30464e9i	2.36618	+	2.36618i
$821$	−6.21859e8			−1.12373			−0.561866	−	0.827228i	$-0.689916\pi$
$821$	−6.21859e8			−1.12373			−0.561866	+	0.827228i	$0.689916\pi$
$822$	1.12099e8	+	1.12099e8i	0.201830	+	0.201830i
$823$	4.86666e8			0.873035			0.436518	−	0.899696i	$-0.356212\pi$
$823$	4.86666e8			0.873035			0.436518	+	0.899696i	$0.356212\pi$
$824$	5.10001e8			0.911569
$825$			6.16093e8i			1.09720i
$826$	3.08629e8			0.547641
$827$	5.29344e8	+	5.29344e8i	0.935884	+	0.935884i	0.998065	−	0.0621813i	$-0.0198057\pi$
$827$	5.29344e8	+	5.29344e8i	0.935884	+	0.935884i	−0.0621813	+	0.998065i	$0.519806\pi$
$828$	−1.03319e8	+	1.03319e8i	−0.182007	+	0.182007i
$829$	7.25682e8	−	7.25682e8i	1.27375	−	1.27375i	0.329639	−	0.944107i	$-0.393073\pi$
$829$	7.25682e8	−	7.25682e8i	1.27375	−	1.27375i	0.944107	−	0.329639i	$-0.106927\pi$
$830$	−7.80476e8			−1.36498
$831$	−8.04166e8	−	8.04166e8i	−1.40134	−	1.40134i
$832$	−1.96014e9	+	1.96014e9i	−3.40343	+	3.40343i
$833$	−1.92097e8	−	1.92097e8i	−0.332342	−	0.332342i
$834$	1.56321e9	−	1.56321e9i	2.69475	−	2.69475i
$835$			2.97811e8i			0.511542i
$836$	−6.48823e8	−	6.48823e8i	−1.11047	−	1.11047i
$837$	−4.14592e7	−	4.14592e7i	−0.0707041	−	0.0707041i
$838$	7.69491e8	−	7.69491e8i	1.30759	−	1.30759i
$839$		−	5.06293e8i		−	0.857267i	−0.903478	−	0.428634i	$-0.858995\pi$
$839$		−	5.06293e8i		−	0.857267i	0.903478	−	0.428634i	$-0.141005\pi$
$840$	−2.57584e9			−4.34591
$841$		−	3.28893e8i		−	0.552925i
$842$		−	2.49636e8i		−	0.418188i
$843$	3.60636e8	−	3.60636e8i	0.601986	−	0.601986i
$844$			4.51503e8i			0.750988i
$845$	−2.06653e8	+	2.06653e8i	−0.342508	+	0.342508i
$846$	4.46944e7	−	4.46944e7i	0.0738145	−	0.0738145i
$847$	4.85255e7			0.0798583
$848$	−3.52405e9			−5.77902
$849$	−3.74609e8	−	3.74609e8i	−0.612146	−	0.612146i
$850$			1.28724e9i			2.09606i
$851$	2.08476e8	+	1.73597e8i	0.338273	+	0.281679i
$852$	−2.03087e9			−3.28370
$853$	−1.74002e8	+	1.74002e8i	−0.280355	+	0.280355i	−0.833250	−	0.552896i	$-0.813523\pi$
$853$	−1.74002e8	+	1.74002e8i	−0.280355	+	0.280355i	0.552896	+	0.833250i	$0.313523\pi$
$854$			5.41604e8i			0.869577i
$855$			1.02500e8i			0.163993i
$856$	−5.97908e8	−	5.97908e8i	−0.953263	−	0.953263i
$857$	−4.68599e8	−	4.68599e8i	−0.744490	−	0.744490i	0.228949	−	0.973439i	$-0.426471\pi$
$857$	−4.68599e8	−	4.68599e8i	−0.744490	−	0.744490i	−0.973439	+	0.228949i	$0.926471\pi$
$858$	1.05216e9			1.66578
$859$	2.30140e8	+	2.30140e8i	0.363088	+	0.363088i	0.864949	−	0.501860i	$-0.167351\pi$
$859$	2.30140e8	+	2.30140e8i	0.363088	+	0.363088i	−0.501860	+	0.864949i	$0.667351\pi$
$860$	3.63804e9			5.71969
$861$	4.06010e8			0.636102
$862$			1.64853e9i			2.57381i
$863$	−4.82712e8			−0.751027			−0.375513	−	0.926817i	$-0.622534\pi$
$863$	−4.82712e8			−0.751027			−0.375513	+	0.926817i	$0.622534\pi$
$864$	−2.12230e9	−	2.12230e9i	−3.29052	−	3.29052i
$865$	4.66580e8	−	4.66580e8i	0.720904	−	0.720904i
$866$	−1.34645e9	+	1.34645e9i	−2.07318	+	2.07318i
$867$	3.56761e6			0.00547419
$868$	1.12032e8	+	1.12032e8i	0.171309	+	0.171309i
$869$	−9.77762e7	+	9.77762e7i	−0.148996	+	0.148996i
$870$	−1.80694e9	−	1.80694e9i	−2.74402	−	2.74402i
$871$	−4.48804e8	+	4.48804e8i	−0.679208	+	0.679208i
$872$		−	9.63875e8i		−	1.45369i
$873$	−5.36991e7	−	5.36991e7i	−0.0807095	−	0.0807095i
$874$	2.34580e8	+	2.34580e8i	0.351363	+	0.351363i
$875$	3.03906e7	−	3.03906e7i	0.0453644	−	0.0453644i
$876$			2.73103e9i			4.06270i
$877$	1.01385e9			1.50306			0.751529	−	0.659700i	$-0.229317\pi$
$877$	1.01385e9			1.50306			0.751529	+	0.659700i	$0.229317\pi$
$878$		−	1.85951e9i		−	2.74736i
$879$		−	6.63602e8i		−	0.977104i
$880$	3.00410e9	−	3.00410e9i	4.40825	−	4.40825i
$881$			4.69859e8i			0.687132i	0.939129	+	0.343566i	$0.111635\pi$
$881$			4.69859e8i			0.687132i	−0.939129	+	0.343566i	$0.888365\pi$
$882$	9.06523e7	−	9.06523e7i	0.132121	−	0.132121i
$883$	−2.95480e8	+	2.95480e8i	−0.429186	+	0.429186i	−0.888351	−	0.459165i	$-0.848149\pi$
$883$	−2.95480e8	+	2.95480e8i	−0.429186	+	0.429186i	0.459165	+	0.888351i	$0.348149\pi$
$884$	1.63741e9			2.37028
$885$	4.14774e8			0.598386
$886$	−1.21221e9	−	1.21221e9i	−1.74292	−	1.74292i
$887$			7.65141e8i			1.09640i	0.836346	+	0.548202i	$0.184687\pi$
$887$			7.65141e8i			1.09640i	−0.836346	+	0.548202i	$0.815313\pi$
$888$	1.86504e9	−	2.23976e9i	2.66348	−	3.19862i
$889$	2.79845e8			0.398302
$890$	−1.47766e8	+	1.47766e8i	−0.209607	+	0.209607i
$891$			7.74285e8i			1.09463i
$892$		−	1.55562e9i		−	2.19184i
$893$	−7.55836e7	−	7.55836e7i	−0.106138	−	0.106138i
$894$	−6.11159e8	−	6.11159e8i	−0.855346	−	0.855346i
$895$	−1.39109e9			−1.94037
$896$	2.36503e9	+	2.36503e9i	3.28786	+	3.28786i
$897$	−2.83340e8			−0.392582
$898$	−6.27491e8			−0.866520
$899$			1.03335e8i			0.142222i
$900$	−4.52463e8			−0.620662
$901$	6.47844e8	+	6.47844e8i	0.885719	+	0.885719i
$902$	−7.73863e8	+	7.73863e8i	−1.05450	+	1.05450i
$903$	5.66089e8	−	5.66089e8i	0.768814	−	0.768814i
$904$	3.72013e9			5.03562
$905$	4.89675e8	+	4.89675e8i	0.660636	+	0.660636i
$906$	−1.63779e9	+	1.63779e9i	−2.20228	+	2.20228i
$907$	−3.53885e8	−	3.53885e8i	−0.474286	−	0.474286i	0.429013	−	0.903299i	$-0.358862\pi$
$907$	−3.53885e8	−	3.53885e8i	−0.474286	−	0.474286i	−0.903299	+	0.429013i	$0.858862\pi$
$908$	3.59374e8	−	3.59374e8i	0.480052	−	0.480052i
$909$			1.50580e8i			0.200482i
$910$	−8.96561e8	−	8.96561e8i	−1.18975	−	1.18975i
$911$	3.76848e8	+	3.76848e8i	0.498439	+	0.498439i	0.910952	−	0.412513i	$-0.135349\pi$
$911$	3.76848e8	+	3.76848e8i	0.498439	+	0.498439i	−0.412513	+	0.910952i	$0.635349\pi$
$912$	1.54207e9	−	1.54207e9i	2.03292	−	2.03292i
$913$		−	3.44824e8i		−	0.453091i
$914$	−1.87539e9			−2.45614
$915$			7.27875e8i			0.950153i
$916$		−	6.14521e8i		−	0.799559i
$917$	−1.64165e8	+	1.64165e8i	−0.212899	+	0.212899i
$918$			1.33845e9i			1.73011i
$919$	−3.13056e8	+	3.13056e8i	−0.403344	+	0.403344i	−0.879410	−	0.476066i	$-0.842062\pi$
$919$	−3.13056e8	+	3.13056e8i	−0.403344	+	0.403344i	0.476066	+	0.879410i	$0.342062\pi$
$920$	−1.32213e9	+	1.32213e9i	−1.69789	+	1.69789i
$921$	−8.54884e7			−0.109428
$922$	9.10259e8			1.16137
$923$	−4.64721e8	−	4.64721e8i	−0.591000	−	0.591000i
$924$		−	1.73104e9i		−	2.19428i
$925$	7.63722e7	+	8.36606e8i	0.0964962	+	1.05705i
$926$	−1.14661e9			−1.44405
$927$	2.70724e7	−	2.70724e7i	0.0339850	−	0.0339850i
$928$			5.28970e9i			6.61893i
$929$			7.44683e8i			0.928805i	0.885624	+	0.464402i	$0.153731\pi$
$929$			7.44683e8i			0.928805i	−0.885624	+	0.464402i	$0.846269\pi$
$930$	2.02140e8	+	2.02140e8i	0.251306	+	0.251306i
$931$	−1.53304e8	−	1.53304e8i	−0.189978	−	0.189978i
$932$	7.01396e7			0.0866394
$933$	−5.86997e8	−	5.86997e8i	−0.722755	−	0.722755i
$934$	−2.22547e9			−2.73138
$935$	−1.10452e9			−1.35126
$936$			5.08002e8i			0.619495i
$937$	−1.96858e8			−0.239296			−0.119648	−	0.992816i	$-0.538177\pi$
$937$	−1.96858e8			−0.239296			−0.119648	+	0.992816i	$0.538177\pi$
$938$	9.91337e8	+	9.91337e8i	1.20119	+	1.20119i
$939$	4.76308e8	−	4.76308e8i	0.575296	−	0.575296i
$940$	6.47979e8	−	6.47979e8i	0.780149	−	0.780149i
$941$	−8.67001e8			−1.04052			−0.520260	−	0.854008i	$-0.674165\pi$
$941$	−8.67001e8			−1.04052			−0.520260	+	0.854008i	$0.674165\pi$
$942$	1.26933e9	+	1.26933e9i	1.51853	+	1.51853i
$943$	2.08397e8	−	2.08397e8i	0.248517	−	0.248517i
$944$	−1.04137e9	−	1.04137e9i	−1.23791	−	1.23791i
$945$	5.45868e8	−	5.45868e8i	0.646833	−	0.646833i
$946$			2.15796e9i			2.54900i
$947$	−5.18524e7	−	5.18524e7i	−0.0610546	−	0.0610546i	0.675920	−	0.736975i	$-0.263746\pi$
$947$	−5.18524e7	−	5.18524e7i	−0.0610546	−	0.0610546i	−0.736975	+	0.675920i	$0.763746\pi$
$948$	−4.30285e8	−	4.30285e8i	−0.505047	−	0.505047i
$949$	−6.24939e8	+	6.24939e8i	−0.731204	+	0.731204i
$950$			1.02729e9i			1.19818i
$951$	1.43039e9			1.66308
$952$		−	2.37777e9i		−	2.75588i
$953$		−	1.52122e9i		−	1.75757i	−0.477219	−	0.878785i	$-0.658355\pi$
$953$		−	1.52122e9i		−	1.75757i	0.477219	−	0.878785i	$-0.341645\pi$
$954$	−3.05724e8	+	3.05724e8i	−0.352115	+	0.352115i
$955$			2.44830e8i			0.281096i
$956$	1.26760e9	−	1.26760e9i	1.45081	−	1.45081i
$957$	7.98331e8	−	7.98331e8i	0.910851	−	0.910851i
$958$	8.26035e8			0.939511
$959$	8.44051e7			0.0957003
$960$	5.81871e9	+	5.81871e9i	6.57677	+	6.57677i
$961$			8.75944e8i			0.986975i
$962$	1.42874e9	−	1.30427e8i	1.60483	−	0.146502i
$963$	−6.34775e7			−0.0710789
$964$	−3.52107e9	+	3.52107e9i	−3.93046	+	3.93046i
$965$			1.18080e7i			0.0131400i
$966$			6.25852e8i			0.694289i
$967$	−2.34550e8	−	2.34550e8i	−0.259392	−	0.259392i	0.565415	−	0.824807i	$-0.308716\pi$
$967$	−2.34550e8	−	2.34550e8i	−0.259392	−	0.259392i	−0.824807	+	0.565415i	$0.808716\pi$
$968$	−2.67591e8	−	2.67591e8i	−0.295016	−	0.295016i
$969$	−5.66973e8			−0.623148
$970$	−1.04523e9	−	1.04523e9i	−1.14524	−	1.14524i
$971$	−5.65829e8			−0.618055			−0.309028	−	0.951053i	$-0.600004\pi$
$971$	−5.65829e8			−0.618055			−0.309028	+	0.951053i	$0.600004\pi$
$972$	−1.05877e9			−1.15293
$973$		−	1.17702e9i		−	1.27775i
$974$	7.10509e8			0.768941
$975$	−6.20413e8	−	6.20413e8i	−0.669371	−	0.669371i
$976$	1.82747e9	−	1.82747e9i	1.96563	−	1.96563i
$977$	7.26468e8	−	7.26468e8i	0.778991	−	0.778991i	−0.200668	−	0.979659i	$-0.564311\pi$
$977$	7.26468e8	−	7.26468e8i	0.778991	−	0.778991i	0.979659	+	0.200668i	$0.0643113\pi$
$978$	−3.10348e9			−3.31766
$979$	−6.52851e7	−	6.52851e7i	−0.0695770	−	0.0695770i
$980$	1.31428e9	−	1.31428e9i	1.39640	−	1.39640i
$981$	−5.11654e7	−	5.11654e7i	−0.0541962	−	0.0541962i
$982$	7.26208e8	−	7.26208e8i	0.766878	−	0.766878i
$983$		−	5.53729e8i		−	0.582957i	−0.956577	−	0.291479i	$-0.905853\pi$
$983$		−	5.53729e8i		−	0.582957i	0.956577	−	0.291479i	$-0.0941472\pi$
$984$	−2.23891e9	−	2.23891e9i	−2.34991	−	2.34991i
$985$	−1.40312e9	−	1.40312e9i	−1.46820	−	1.46820i
$986$	1.66800e9	−	1.66800e9i	1.74007	−	1.74007i
$987$		−	2.01655e8i		−	0.209728i
$988$	1.30674e9			1.35494
$989$		−	5.81126e8i		−	0.600733i
$990$		−	5.21233e8i		−	0.537188i
$991$	−2.43287e8	+	2.43287e8i	−0.249976	+	0.249976i	−0.820960	−	0.570985i	$-0.806561\pi$
$991$	−2.43287e8	+	2.43287e8i	−0.249976	+	0.249976i	0.570985	+	0.820960i	$0.306561\pi$
$992$		−	5.91751e8i		−	0.606183i
$993$	4.35728e7	−	4.35728e7i	0.0445008	−	0.0445008i
$994$	−1.02649e9	+	1.02649e9i	−1.04520	+	1.04520i
$995$	1.81529e9			1.84280
$996$	1.51747e9			1.53583
$997$	−5.82826e8	−	5.82826e8i	−0.588103	−	0.588103i	0.349015	−	0.937117i	$-0.386516\pi$
$997$	−5.82826e8	−	5.82826e8i	−0.588103	−	0.588103i	−0.937117	+	0.349015i	$0.886516\pi$
$998$			2.06938e9i			2.08185i
$999$	7.94102e7	+	8.69885e8i	0.0796490	+	0.872500i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.7.d.a.6.18	✓	36
37.31	odd	4	inner	37.7.d.a.31.18	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.7.d.a.6.18	✓	36	1.1	even	1	trivial
37.7.d.a.31.18	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)

\(f(q)\)	\(=\)	\(q+(11.1987 - 11.1987i) q^{2} +29.5809i q^{3} -186.823i q^{4} +(-126.906 - 126.906i) q^{5} +(331.268 + 331.268i) q^{6} +249.429 q^{7} +(-1375.46 - 1375.46i) q^{8} -146.027 q^{9} +O(q^{10})\)	\(q+(11.1987 - 11.1987i) q^{2} +29.5809i q^{3} -186.823i q^{4} +(-126.906 - 126.906i) q^{5} +(331.268 + 331.268i) q^{6} +249.429 q^{7} +(-1375.46 - 1375.46i) q^{8} -146.027 q^{9} -2842.36 q^{10} -1255.79i q^{11} +5526.39 q^{12} +(1264.60 + 1264.60i) q^{13} +(2793.29 - 2793.29i) q^{14} +(3753.98 - 3753.98i) q^{15} -18850.2 q^{16} +(3465.33 + 3465.33i) q^{17} +(-1635.32 + 1635.32i) q^{18} +(2765.52 + 2765.52i) q^{19} +(-23708.9 + 23708.9i) q^{20} +7378.34i q^{21} +(-14063.3 - 14063.3i) q^{22} +(3787.16 + 3787.16i) q^{23} +(40687.4 - 40687.4i) q^{24} +16585.1i q^{25} +28323.8 q^{26} +17244.8i q^{27} -46599.2i q^{28} +(21490.9 - 21490.9i) q^{29} -84079.6i q^{30} +(-2404.15 + 2404.15i) q^{31} +(-123069. + 123069. i) q^{32} +37147.4 q^{33} +77614.5 q^{34} +(-31654.0 - 31654.0i) q^{35} +27281.3i q^{36} +(50443.3 - 4604.87i) q^{37} +61940.7 q^{38} +(-37407.9 + 37407.9i) q^{39} +349108. i q^{40} -55027.2i q^{41} +(82628.0 + 82628.0i) q^{42} +(-76723.1 - 76723.1i) q^{43} -234611. q^{44} +(18531.7 + 18531.7i) q^{45} +84822.9 q^{46} -27330.6 q^{47} -557605. i q^{48} -55433.9 q^{49} +(185732. + 185732. i) q^{50} +(-102507. + 102507. i) q^{51} +(236256. - 236256. i) q^{52} +186950. q^{53} +(193120. + 193120. i) q^{54} +(-159367. + 159367. i) q^{55} +(-343081. - 343081. i) q^{56} +(-81806.6 + 81806.6i) q^{57} -481341. i q^{58} +(55244.6 + 55244.6i) q^{59} +(-701330. - 701330. i) q^{60} +(-96947.1 + 96947.1i) q^{61} +53846.9i q^{62} -36423.5 q^{63} +1.55001e6i q^{64} -320969. i q^{65} +(416004. - 416004. i) q^{66} +354899. i q^{67} +(647403. - 647403. i) q^{68} +(-112028. + 112028. i) q^{69} -708969. q^{70} -367486. q^{71} +(200855. + 200855. i) q^{72} +494180. i q^{73} +(513332. - 616469. i) q^{74} -490601. q^{75} +(516664. - 516664. i) q^{76} -313232. i q^{77} +837841. i q^{78} +(-77860.2 - 77860.2i) q^{79} +(2.39220e6 + 2.39220e6i) q^{80} -616571. q^{81} +(-616235. - 616235. i) q^{82} +274587. q^{83} +1.37844e6 q^{84} -879539. i q^{85} -1.71840e6 q^{86} +(635719. + 635719. i) q^{87} +(-1.72730e6 + 1.72730e6i) q^{88} +(51987.2 - 51987.2i) q^{89} +415063. q^{90} +(315428. + 315428. i) q^{91} +(707530. - 707530. i) q^{92} +(-71116.9 - 71116.9i) q^{93} +(-306068. + 306068. i) q^{94} -701921. i q^{95} +(-3.64047e6 - 3.64047e6i) q^{96} +(367733. + 367733. i) q^{97} +(-620790. + 620790. i) q^{98} +183380. 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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