LMFDB - Embedded newform 37.7.d.a.6.8

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			6.8
Character	$\chi$	$=$	37.6
Dual form			37.7.d.a.31.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40537 + 1.40537i) q^{2} +9.49587i q^{3} +60.0499i q^{4} +(-104.306 - 104.306i) q^{5} +(-13.3452 - 13.3452i) q^{6} -165.435 q^{7} +(-174.336 - 174.336i) q^{8} +638.828 q^{9} +O(q^{10})$	\(q+(-1.40537 + 1.40537i) q^{2} +9.49587i q^{3} +60.0499i q^{4} +(-104.306 - 104.306i) q^{5} +(-13.3452 - 13.3452i) q^{6} -165.435 q^{7} +(-174.336 - 174.336i) q^{8} +638.828 q^{9} +293.177 q^{10} -1095.87i q^{11} -570.226 q^{12} +(-1958.63 - 1958.63i) q^{13} +(232.498 - 232.498i) q^{14} +(990.476 - 990.476i) q^{15} -3353.18 q^{16} +(-723.468 - 723.468i) q^{17} +(-897.792 + 897.792i) q^{18} +(-6711.09 - 6711.09i) q^{19} +(6263.55 - 6263.55i) q^{20} -1570.95i q^{21} +(1540.11 + 1540.11i) q^{22} +(6290.99 + 6290.99i) q^{23} +(1655.48 - 1655.48i) q^{24} +6134.44i q^{25} +5505.21 q^{26} +12988.7i q^{27} -9934.36i q^{28} +(-9913.11 + 9913.11i) q^{29} +2783.98i q^{30} +(-34979.8 + 34979.8i) q^{31} +(15870.0 - 15870.0i) q^{32} +10406.3 q^{33} +2033.48 q^{34} +(17255.9 + 17255.9i) q^{35} +38361.6i q^{36} +(46591.7 - 19873.2i) q^{37} +18863.2 q^{38} +(18598.9 - 18598.9i) q^{39} +36368.6i q^{40} +54188.8i q^{41} +(2207.77 + 2207.77i) q^{42} +(-28801.6 - 28801.6i) q^{43} +65807.1 q^{44} +(-66633.6 - 66633.6i) q^{45} -17682.4 q^{46} -93267.3 q^{47} -31841.3i q^{48} -90280.2 q^{49} +(-8621.18 - 8621.18i) q^{50} +(6869.96 - 6869.96i) q^{51} +(117615. - 117615. i) q^{52} +57235.1 q^{53} +(-18254.0 - 18254.0i) q^{54} +(-114306. + 114306. i) q^{55} +(28841.4 + 28841.4i) q^{56} +(63727.7 - 63727.7i) q^{57} -27863.2i q^{58} +(-186318. - 186318. i) q^{59} +(59477.9 + 59477.9i) q^{60} +(154485. - 154485. i) q^{61} -98319.4i q^{62} -105685. q^{63} -169997. i q^{64} +408593. i q^{65} +(-14624.7 + 14624.7i) q^{66} -107733. i q^{67} +(43444.1 - 43444.1i) q^{68} +(-59738.5 + 59738.5i) q^{69} -48501.9 q^{70} -454698. q^{71} +(-111371. - 111371. i) q^{72} +204810. i q^{73} +(-37549.4 + 93407.9i) q^{74} -58251.9 q^{75} +(403000. - 403000. i) q^{76} +181296. i q^{77} +52276.8i q^{78} +(440617. + 440617. i) q^{79} +(349756. + 349756. i) q^{80} +342367. q^{81} +(-76155.5 - 76155.5i) q^{82} +271452. q^{83} +94335.5 q^{84} +150924. i q^{85} +80954.0 q^{86} +(-94133.6 - 94133.6i) q^{87} +(-191051. + 191051. i) q^{88} +(61808.5 - 61808.5i) q^{89} +187290. q^{90} +(324026. + 324026. i) q^{91} +(-377773. + 377773. i) q^{92} +(-332164. - 332164. i) q^{93} +(131075. - 131075. i) q^{94} +1.40001e6i q^{95} +(150699. + 150699. i) q^{96} +(-1.24828e6 - 1.24828e6i) q^{97} +(126877. - 126877. i) q^{98} -700076. 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 $

$2$	−1.40537	+	1.40537i	−0.175672	+	0.175672i	−0.789466	−	0.613794i	$-0.789642\pi$
$2$	−1.40537	+	1.40537i	−0.175672	+	0.175672i	0.613794	+	0.789466i	$0.289642\pi$
$3$			9.49587i			0.351699i	0.984417	+	0.175850i	$0.0562672\pi$
$3$			9.49587i			0.351699i	−0.984417	+	0.175850i	$0.943733\pi$
$4$			60.0499i			0.938279i
$5$	−104.306	−	104.306i	−0.834447	−	0.834447i	0.153674	−	0.988122i	$-0.450889\pi$
$5$	−104.306	−	104.306i	−0.834447	−	0.834447i	−0.988122	+	0.153674i	$0.950889\pi$
$6$	−13.3452	−	13.3452i	−0.0617835	−	0.0617835i
$7$	−165.435			−0.482319			−0.241159	−	0.970486i	$-0.577528\pi$
$7$	−165.435			−0.482319			−0.241159	+	0.970486i	$0.577528\pi$
$8$	−174.336	−	174.336i	−0.340501	−	0.340501i
$9$	638.828			0.876308
$10$	293.177			0.293177
$11$		−	1095.87i		−	0.823347i	−0.911331	−	0.411674i	$-0.864944\pi$
$11$		−	1095.87i		−	0.823347i	0.911331	−	0.411674i	$-0.135056\pi$
$12$	−570.226			−0.329992
$13$	−1958.63	−	1958.63i	−0.891502	−	0.891502i	0.103163	−	0.994664i	$-0.467104\pi$
$13$	−1958.63	−	1958.63i	−0.891502	−	0.891502i	−0.994664	+	0.103163i	$0.967104\pi$
$14$	232.498	−	232.498i	0.0847297	−	0.0847297i
$15$	990.476	−	990.476i	0.293474	−	0.293474i
$16$	−3353.18			−0.818646
$17$	−723.468	−	723.468i	−0.147256	−	0.147256i	0.629635	−	0.776891i	$-0.283204\pi$
$17$	−723.468	−	723.468i	−0.147256	−	0.147256i	−0.776891	+	0.629635i	$0.783204\pi$
$18$	−897.792	+	897.792i	−0.153942	+	0.153942i
$19$	−6711.09	−	6711.09i	−0.978436	−	0.978436i	0.0213361	−	0.999772i	$-0.493208\pi$
$19$	−6711.09	−	6711.09i	−0.978436	−	0.978436i	−0.999772	+	0.0213361i	$0.993208\pi$
$20$	6263.55	−	6263.55i	0.782944	−	0.782944i
$21$		−	1570.95i		−	0.169631i
$22$	1540.11	+	1540.11i	0.144639	+	0.144639i
$23$	6290.99	+	6290.99i	0.517054	+	0.517054i	0.916679	−	0.399625i	$-0.130860\pi$
$23$	6290.99	+	6290.99i	0.517054	+	0.517054i	−0.399625	+	0.916679i	$0.630860\pi$
$24$	1655.48	−	1655.48i	0.119754	−	0.119754i
$25$			6134.44i			0.392604i
$26$	5505.21			0.313223
$27$			12988.7i			0.659896i
$28$		−	9934.36i		−	0.452549i
$29$	−9913.11	+	9913.11i	−0.406458	+	0.406458i	−0.880501	−	0.474043i	$-0.842794\pi$
$29$	−9913.11	+	9913.11i	−0.406458	+	0.406458i	0.474043	+	0.880501i	$0.342794\pi$
$30$			2783.98i			0.103110i
$31$	−34979.8	+	34979.8i	−1.17417	+	1.17417i	−0.192969	+	0.981205i	$0.561812\pi$
$31$	−34979.8	+	34979.8i	−1.17417	+	1.17417i	−0.981205	+	0.192969i	$0.938188\pi$
$32$	15870.0	−	15870.0i	0.484314	−	0.484314i
$33$	10406.3			0.289570
$34$	2033.48			0.0517373
$35$	17255.9	+	17255.9i	0.402469	+	0.402469i
$36$			38361.6i			0.822221i
$37$	46591.7	−	19873.2i	0.919820	−	0.392340i
$37$	46591.7	−	19873.2i	0.919820	−	0.392340i
$38$	18863.2			0.343767
$39$	18598.9	−	18598.9i	0.313540	−	0.313540i
$40$			36368.6i			0.568260i
$41$			54188.8i			0.786246i	0.919486	+	0.393123i	$0.128605\pi$
$41$			54188.8i			0.786246i	−0.919486	+	0.393123i	$0.871395\pi$
$42$	2207.77	+	2207.77i	0.0297993	+	0.0297993i
$43$	−28801.6	−	28801.6i	−0.362252	−	0.362252i	0.502389	−	0.864642i	$-0.332454\pi$
$43$	−28801.6	−	28801.6i	−0.362252	−	0.362252i	−0.864642	+	0.502389i	$0.832454\pi$
$44$	65807.1			0.772529
$45$	−66633.6	−	66633.6i	−0.731233	−	0.731233i
$46$	−17682.4			−0.181663
$47$	−93267.3			−0.898330			−0.449165	−	0.893449i	$-0.648278\pi$
$47$	−93267.3			−0.898330			−0.449165	+	0.893449i	$0.648278\pi$
$48$		−	31841.3i		−	0.287917i
$49$	−90280.2			−0.767369
$50$	−8621.18	−	8621.18i	−0.0689694	−	0.0689694i
$51$	6869.96	−	6869.96i	0.0517897	−	0.0517897i
$52$	117615.	−	117615.i	0.836477	−	0.836477i
$53$	57235.1			0.384446			0.192223	−	0.981351i	$-0.438430\pi$
$53$	57235.1			0.384446			0.192223	+	0.981351i	$0.438430\pi$
$54$	−18254.0	−	18254.0i	−0.115925	−	0.115925i
$55$	−114306.	+	114306.i	−0.687040	+	0.687040i
$56$	28841.4	+	28841.4i	0.164230	+	0.164230i
$57$	63727.7	−	63727.7i	0.344115	−	0.344115i
$58$		−	27863.2i		−	0.142806i
$59$	−186318.	−	186318.i	−0.907193	−	0.907193i	0.0888516	−	0.996045i	$-0.471680\pi$
$59$	−186318.	−	186318.i	−0.907193	−	0.907193i	−0.996045	+	0.0888516i	$0.971680\pi$
$60$	59477.9	+	59477.9i	0.275361	+	0.275361i
$61$	154485.	−	154485.i	0.680609	−	0.680609i	−0.279528	−	0.960137i	$-0.590178\pi$
$61$	154485.	−	154485.i	0.680609	−	0.680609i	0.960137	+	0.279528i	$0.0901781\pi$
$62$		−	98319.4i		−	0.412538i
$63$	−105685.			−0.422660
$64$		−	169997.i		−	0.648486i
$65$			408593.i			1.48782i
$66$	−14624.7	+	14624.7i	−0.0508693	+	0.0508693i
$67$		−	107733.i		−	0.358199i	−0.983831	−	0.179100i	$-0.942682\pi$
$67$		−	107733.i		−	0.358199i	0.983831	−	0.179100i	$-0.0573184\pi$
$68$	43444.1	−	43444.1i	0.138167	−	0.138167i
$69$	−59738.5	+	59738.5i	−0.181847	+	0.181847i
$70$	−48501.9			−0.141405
$71$	−454698.			−1.27042			−0.635210	−	0.772339i	$-0.719087\pi$
$71$	−454698.			−1.27042			−0.635210	+	0.772339i	$0.719087\pi$
$72$	−111371.	−	111371.i	−0.298383	−	0.298383i
$73$			204810.i			0.526482i	0.964730	+	0.263241i	$0.0847914\pi$
$73$			204810.i			0.526482i	−0.964730	+	0.263241i	$0.915209\pi$
$74$	−37549.4	+	93407.9i	−0.0926633	+	0.230509i
$75$	−58251.9			−0.138079
$76$	403000.	−	403000.i	0.918046	−	0.918046i
$77$			181296.i			0.397116i
$78$			52276.8i			0.110160i
$79$	440617.	+	440617.i	0.893676	+	0.893676i	0.994867	−	0.101191i	$-0.0322654\pi$
$79$	440617.	+	440617.i	0.893676	+	0.893676i	−0.101191	+	0.994867i	$0.532265\pi$
$80$	349756.	+	349756.i	0.683117	+	0.683117i
$81$	342367.			0.644223
$82$	−76155.5	−	76155.5i	−0.138121	−	0.138121i
$83$	271452.			0.474744			0.237372	−	0.971419i	$-0.423714\pi$
$83$	271452.			0.474744			0.237372	+	0.971419i	$0.423714\pi$
$84$	94335.5			0.159161
$85$			150924.i			0.245754i
$86$	80954.0			0.127275
$87$	−94133.6	−	94133.6i	−0.142951	−	0.142951i
$88$	−191051.	+	191051.i	−0.280350	+	0.280350i
$89$	61808.5	−	61808.5i	0.0876754	−	0.0876754i	−0.661909	−	0.749584i	$-0.730253\pi$
$89$	61808.5	−	61808.5i	0.0876754	−	0.0876754i	0.749584	+	0.661909i	$0.230253\pi$
$90$	187290.			0.256914
$91$	324026.	+	324026.i	0.429988	+	0.429988i
$92$	−377773.	+	377773.i	−0.485141	+	0.485141i
$93$	−332164.	−	332164.i	−0.412956	−	0.412956i
$94$	131075.	−	131075.i	0.157811	−	0.157811i
$95$			1.40001e6i			1.63291i
$96$	150699.	+	150699.i	0.170333	+	0.170333i
$97$	−1.24828e6	−	1.24828e6i	−1.36772	−	1.36772i	−0.863678	−	0.504045i	$-0.831845\pi$
$97$	−1.24828e6	−	1.24828e6i	−1.36772	−	1.36772i	−0.504045	−	0.863678i	$-0.668155\pi$
$98$	126877.	−	126877.i	0.134805	−	0.134805i
$99$		−	700076.i		−	0.721505i
$100$	−368372.			−0.368372
$101$			752462.i			0.730332i	0.930942	+	0.365166i	$0.118988\pi$
$101$			752462.i			0.730332i	−0.930942	+	0.365166i	$0.881012\pi$
$102$			19309.7i			0.0181960i
$103$	−232354.	+	232354.i	−0.212637	+	0.212637i	−0.805387	−	0.592750i	$-0.798042\pi$
$103$	−232354.	+	232354.i	−0.212637	+	0.212637i	0.592750	+	0.805387i	$0.298042\pi$
$104$			682920.i			0.607114i
$105$	−163860.	+	163860.i	−0.141548	+	0.141548i
$106$	−80436.7	+	80436.7i	−0.0675362	+	0.0675362i
$107$	2.22852e6			1.81913			0.909566	−	0.415559i	$-0.136414\pi$
$107$	2.22852e6			1.81913			0.909566	+	0.415559i	$0.136414\pi$
$108$	−779971.			−0.619166
$109$	−1.47296e6	−	1.47296e6i	−1.13739	−	1.13739i	−0.988916	−	0.148478i	$-0.952563\pi$
$109$	−1.47296e6	−	1.47296e6i	−1.13739	−	1.13739i	−0.148478	−	0.988916i	$-0.547437\pi$
$110$		−	321286.i		−	0.241387i
$111$	188713.	+	442428.i	0.137986	+	0.323500i
$112$	554734.			0.394848
$113$	1.84947e6	−	1.84947e6i	1.28178	−	1.28178i	0.342122	−	0.939656i	$-0.388854\pi$
$113$	1.84947e6	−	1.84947e6i	1.28178	−	1.28178i	0.939656	−	0.342122i	$-0.111146\pi$
$114$			179122.i			0.120903i
$115$		−	1.31238e6i		−	0.862908i
$116$	−595281.	−	595281.i	−0.381371	−	0.381371i
$117$	−1.25123e6	−	1.25123e6i	−0.781230	−	0.781230i
$118$	523694.			0.318736
$119$	119687.	+	119687.i	0.0710242	+	0.0710242i
$120$	−345352.			−0.199856
$121$	570619.			0.322100
$122$			434219.i			0.239127i
$123$	−514570.			−0.276522
$124$	−2.10053e6	−	2.10053e6i	−1.10170	−	1.10170i
$125$	−989921.	+	989921.i	−0.506840	+	0.506840i
$126$	148527.	−	148527.i	0.0742493	−	0.0742493i
$127$	−1.08215e6			−0.528294			−0.264147	−	0.964482i	$-0.585090\pi$
$127$	−1.08215e6			−0.528294			−0.264147	+	0.964482i	$0.585090\pi$
$128$	1.25459e6	+	1.25459e6i	0.598234	+	0.598234i
$129$	273496.	−	273496.i	0.127404	−	0.127404i
$130$	−574226.	−	574226.i	−0.261368	−	0.261368i
$131$	140803.	−	140803.i	0.0626324	−	0.0626324i	−0.675097	−	0.737729i	$-0.735898\pi$
$131$	140803.	−	140803.i	0.0626324	−	0.0626324i	0.737729	+	0.675097i	$0.235898\pi$
$132$			624896.i			0.271698i
$133$	1.11025e6	+	1.11025e6i	0.471918	+	0.471918i
$134$	151405.	+	151405.i	0.0629254	+	0.0629254i
$135$	1.35480e6	−	1.35480e6i	0.550648	−	0.550648i
$136$			252253.i			0.100281i
$137$	−76135.1			−0.0296090			−0.0148045	−	0.999890i	$-0.504713\pi$
$137$	−76135.1			−0.0296090			−0.0148045	+	0.999890i	$0.504713\pi$
$138$		−	167910.i		−	0.0638908i
$139$			3.37841e6i			1.25796i	0.777421	+	0.628981i	$0.216528\pi$
$139$			3.37841e6i			1.25796i	−0.777421	+	0.628981i	$0.783472\pi$
$140$	−1.03621e6	+	1.03621e6i	−0.377629	+	0.377629i
$141$		−	885654.i		−	0.315942i
$142$	639020.	−	639020.i	0.223177	−	0.223177i
$143$	−2.14641e6	+	2.14641e6i	−0.734015	+	0.734015i
$144$	−2.14210e6			−0.717386
$145$	2.06799e6			0.678336
$146$	−287835.	−	287835.i	−0.0924879	−	0.0924879i
$147$		−	857289.i		−	0.269883i
$148$	1.19338e6	+	2.79782e6i	0.368124	+	0.863048i
$149$	3.57946e6			1.08208			0.541039	−	0.840998i	$-0.318031\pi$
$149$	3.57946e6			1.08208			0.541039	+	0.840998i	$0.318031\pi$
$150$	81865.6	−	81865.6i	0.0242565	−	0.0242565i
$151$			854195.i			0.248100i	0.992276	+	0.124050i	$0.0395883\pi$
$151$			854195.i			0.248100i	−0.992276	+	0.124050i	$0.960412\pi$
$152$			2.33997e6i			0.666316i
$153$	−462172.	−	462172.i	−0.129041	−	0.129041i
$154$	−254789.	−	254789.i	−0.0697619	−	0.0697619i
$155$	7.29720e6			1.95957
$156$	1.11686e6	+	1.11686e6i	0.294188	+	0.294188i
$157$	−753366.			−0.194674			−0.0973368	−	0.995251i	$-0.531032\pi$
$157$	−753366.			−0.194674			−0.0973368	+	0.995251i	$0.531032\pi$
$158$	−1.23846e6			−0.313987
$159$			543497.i			0.135209i
$160$	−3.31067e6			−0.808268
$161$	−1.04075e6	−	1.04075e6i	−0.249385	−	0.249385i
$162$	−481153.	+	481153.i	−0.113172	+	0.113172i
$163$	3.08124e6	−	3.08124e6i	0.711481	−	0.711481i	−0.255364	−	0.966845i	$-0.582195\pi$
$163$	3.08124e6	−	3.08124e6i	0.711481	−	0.711481i	0.966845	+	0.255364i	$0.0821954\pi$
$164$	−3.25403e6			−0.737718
$165$	−1.08544e6	−	1.08544e6i	−0.241631	−	0.241631i
$166$	−381492.	+	381492.i	−0.0833990	+	0.0833990i
$167$	4.75748e6	+	4.75748e6i	1.02147	+	1.02147i	0.999764	+	0.0217092i	$0.00691081\pi$
$167$	4.75748e6	+	4.75748e6i	1.02147	+	1.02147i	0.0217092	+	0.999764i	$0.493089\pi$
$168$	−273874.	+	273874.i	−0.0577595	+	0.0577595i
$169$			2.84565e6i			0.589550i
$170$	−212104.	−	212104.i	−0.0431721	−	0.0431721i
$171$	−4.28724e6	−	4.28724e6i	−0.857411	−	0.857411i
$172$	1.72953e6	−	1.72953e6i	0.339894	−	0.339894i
$173$			1.68521e6i			0.325474i	0.986670	+	0.162737i	$0.0520321\pi$
$173$			1.68521e6i			0.325474i	−0.986670	+	0.162737i	$0.947968\pi$
$174$	264586.			0.0502248
$175$		−	1.01485e6i		−	0.189360i
$176$			3.67466e6i			0.674030i
$177$	1.76926e6	−	1.76926e6i	0.319059	−	0.319059i
$178$			173728.i			0.0308042i
$179$	−3.89231e6	+	3.89231e6i	−0.678655	+	0.678655i	−0.959696	−	0.281041i	$-0.909320\pi$
$179$	−3.89231e6	+	3.89231e6i	−0.678655	+	0.678655i	0.281041	+	0.959696i	$0.409320\pi$
$180$	4.00134e6	−	4.00134e6i	0.686100	−	0.686100i
$181$	−433595.			−0.0731220			−0.0365610	−	0.999331i	$-0.511640\pi$
$181$	−433595.			−0.0731220			−0.0365610	+	0.999331i	$0.511640\pi$
$182$	−910756.			−0.151073
$183$	1.46697e6	+	1.46697e6i	0.239369	+	0.239369i
$184$		−	2.19350e6i		−	0.352114i
$185$	−6.93268e6	−	2.78689e6i	−1.09493	−	0.440154i
$186$	933628.			0.145089
$187$	−792830.	+	792830.i	−0.121243	+	0.121243i
$188$		−	5.60069e6i		−	0.842884i
$189$		−	2.14879e6i		−	0.318280i
$190$	−1.96754e6	−	1.96754e6i	−0.286855	−	0.286855i
$191$	−1.84493e6	−	1.84493e6i	−0.264776	−	0.264776i	0.562215	−	0.826991i	$-0.309949\pi$
$191$	−1.84493e6	−	1.84493e6i	−0.264776	−	0.264776i	−0.826991	+	0.562215i	$0.809949\pi$
$192$	1.61427e6			0.228072
$193$	−5.77436e6	−	5.77436e6i	−0.803216	−	0.803216i	0.180381	−	0.983597i	$-0.442267\pi$
$193$	−5.77436e6	−	5.77436e6i	−0.803216	−	0.803216i	−0.983597	+	0.180381i	$0.942267\pi$
$194$	3.50861e6			0.480540
$195$	−3.87995e6			−0.523266
$196$		−	5.42131e6i		−	0.720006i
$197$	−705510.			−0.0922793			−0.0461397	−	0.998935i	$-0.514692\pi$
$197$	−705510.			−0.0922793			−0.0461397	+	0.998935i	$0.514692\pi$
$198$	983868.	+	983868.i	0.126748	+	0.126748i
$199$	−1.13641e6	+	1.13641e6i	−0.144204	+	0.144204i	−0.775523	−	0.631319i	$-0.782514\pi$
$199$	−1.13641e6	+	1.13641e6i	−0.144204	+	0.144204i	0.631319	+	0.775523i	$0.282514\pi$
$200$	1.06946e6	−	1.06946e6i	0.133682	−	0.133682i
$201$	1.02302e6			0.125978
$202$	−1.05749e6	−	1.05749e6i	−0.128299	−	0.128299i
$203$	1.63998e6	−	1.63998e6i	0.196042	−	0.196042i
$204$	412540.	+	412540.i	0.0485932	+	0.0485932i
$205$	5.65222e6	−	5.65222e6i	0.656081	−	0.656081i
$206$		−	653089.i		−	0.0747086i
$207$	4.01887e6	+	4.01887e6i	0.453098	+	0.453098i
$208$	6.56763e6	+	6.56763e6i	0.729825	+	0.729825i
$209$	−7.35452e6	+	7.35452e6i	−0.805593	+	0.805593i
$210$		−	460568.i		−	0.0497320i
$211$	−4.55823e6			−0.485232			−0.242616	−	0.970122i	$-0.578005\pi$
$211$	−4.55823e6			−0.485232			−0.242616	+	0.970122i	$0.578005\pi$
$212$			3.43696e6i			0.360717i
$213$		−	4.31775e6i		−	0.446806i
$214$	−3.13190e6	+	3.13190e6i	−0.319570	+	0.319570i
$215$			6.00835e6i			0.604561i
$216$	2.26441e6	−	2.26441e6i	0.224695	−	0.224695i
$217$	5.78690e6	−	5.78690e6i	0.566326	−	0.566326i
$218$	4.14011e6			0.399615
$219$	−1.94485e6			−0.185163
$220$	−6.86407e6	−	6.86407e6i	−0.644635	−	0.644635i
$221$			2.83401e6i			0.262557i
$222$	−886990.	−	356564.i	−0.0810699	−	0.0325896i
$223$	−6.06872e6			−0.547246			−0.273623	−	0.961837i	$-0.588222\pi$
$223$	−6.06872e6			−0.547246			−0.273623	+	0.961837i	$0.588222\pi$
$224$	−2.62546e6	+	2.62546e6i	−0.233593	+	0.233593i
$225$			3.91886e6i			0.344042i
$226$			5.19840e6i			0.450344i
$227$	5.55369e6	+	5.55369e6i	0.474793	+	0.474793i	0.903462	−	0.428669i	$-0.141017\pi$
$227$	5.55369e6	+	5.55369e6i	0.474793	+	0.474793i	−0.428669	+	0.903462i	$0.641017\pi$
$228$	3.82684e6	+	3.82684e6i	0.322876	+	0.322876i
$229$	−1.69237e7			−1.40925			−0.704626	−	0.709579i	$-0.748885\pi$
$229$	−1.69237e7			−1.40925			−0.704626	+	0.709579i	$0.748885\pi$
$230$	1.84438e6	+	1.84438e6i	0.151588	+	0.151588i
$231$	−1.72157e6			−0.139665
$232$	3.45643e6			0.276798
$233$		−	2.14102e7i		−	1.69259i	−0.532714	−	0.846296i	$-0.678828\pi$
$233$		−	2.14102e7i		−	1.69259i	0.532714	−	0.846296i	$-0.321172\pi$
$234$	3.51688e6			0.274480
$235$	9.72833e6	+	9.72833e6i	0.749609	+	0.749609i
$236$	1.11884e7	−	1.11884e7i	0.851200	−	0.851200i
$237$	−4.18404e6	+	4.18404e6i	−0.314305	+	0.314305i
$238$	−336410.			−0.0249539
$239$	−331116.	−	331116.i	−0.0242542	−	0.0242542i	0.694876	−	0.719130i	$-0.255459\pi$
$239$	−331116.	−	331116.i	−0.0242542	−	0.0242542i	−0.719130	+	0.694876i	$0.755459\pi$
$240$	−3.32124e6	+	3.32124e6i	−0.240252	+	0.240252i
$241$	−715079.	−	715079.i	−0.0510861	−	0.0510861i	0.681102	−	0.732188i	$-0.261501\pi$
$241$	−715079.	−	715079.i	−0.0510861	−	0.0510861i	−0.732188	+	0.681102i	$0.761501\pi$
$242$	−801933.	+	801933.i	−0.0565838	+	0.0565838i
$243$			1.27199e7i			0.886468i
$244$	9.27682e6	+	9.27682e6i	0.638601	+	0.638601i
$245$	9.41675e6	+	9.41675e6i	0.640329	+	0.640329i
$246$	723163.	−	723163.i	0.0485770	−	0.0485770i
$247$			2.62891e7i			1.74455i
$248$	1.21965e7			0.799614
$249$			2.57768e6i			0.166967i
$250$		−	2.78242e6i		−	0.178075i
$251$	1.07943e7	−	1.07943e7i	0.682612	−	0.682612i	−0.277976	−	0.960588i	$-0.589664\pi$
$251$	1.07943e7	−	1.07943e7i	0.682612	−	0.682612i	0.960588	+	0.277976i	$0.0896636\pi$
$252$		−	6.34635e6i		−	0.396573i
$253$	6.89414e6	−	6.89414e6i	0.425715	−	0.425715i
$254$	1.52082e6	−	1.52082e6i	0.0928063	−	0.0928063i
$255$	−1.43315e6			−0.0864315
$256$	7.35346e6			0.438301
$257$	−5.06393e6	−	5.06393e6i	−0.298324	−	0.298324i	0.542033	−	0.840357i	$-0.317655\pi$
$257$	−5.06393e6	−	5.06393e6i	−0.298324	−	0.298324i	−0.840357	+	0.542033i	$0.817655\pi$
$258$			768729.i			0.0447625i
$259$	−7.70790e6	+	3.28773e6i	−0.443646	+	0.189233i
$260$	−2.45360e7			−1.39599
$261$	−6.33277e6	+	6.33277e6i	−0.356182	+	0.356182i
$262$			395762.i			0.0220055i
$263$		−	936096.i		−	0.0514580i	−0.999669	−	0.0257290i	$-0.991809\pi$
$263$		−	936096.i		−	0.0514580i	0.999669	−	0.0257290i	$-0.00819070\pi$
$264$	−1.81419e6	−	1.81419e6i	−0.0985989	−	0.0985989i
$265$	−5.96996e6	−	5.96996e6i	−0.320800	−	0.320800i
$266$	−3.12064e6			−0.165805
$267$	586925.	+	586925.i	0.0308354	+	0.0308354i
$268$	6.46935e6			0.336091
$269$	−3.85945e7			−1.98275			−0.991376	−	0.131050i	$-0.958165\pi$
$269$	−3.85945e7			−1.98275			−0.991376	+	0.131050i	$0.958165\pi$
$270$			3.80800e6i			0.193466i
$271$	3.39651e7			1.70657			0.853287	−	0.521441i	$-0.174605\pi$
$271$	3.39651e7			1.70657			0.853287	+	0.521441i	$0.174605\pi$
$272$	2.42591e6	+	2.42591e6i	0.120550	+	0.120550i
$273$	−3.07691e6	+	3.07691e6i	−0.151226	+	0.151226i
$274$	106998.	−	106998.i	0.00520145	−	0.00520145i
$275$	6.72258e6			0.323250
$276$	−3.58729e6	−	3.58729e6i	−0.170623	−	0.170623i
$277$	9.07927e6	−	9.07927e6i	0.427181	−	0.427181i	−0.460486	−	0.887667i	$-0.652325\pi$
$277$	9.07927e6	−	9.07927e6i	0.427181	−	0.427181i	0.887667	+	0.460486i	$0.152325\pi$
$278$	−4.74792e6	−	4.74792e6i	−0.220988	−	0.220988i
$279$	−2.23461e7	+	2.23461e7i	−1.02894	+	1.02894i
$280$		−	6.01665e6i		−	0.274082i
$281$	−1.37769e7	−	1.37769e7i	−0.620917	−	0.620917i	0.324849	−	0.945766i	$-0.394686\pi$
$281$	−1.37769e7	−	1.37769e7i	−0.620917	−	0.620917i	−0.945766	+	0.324849i	$0.894686\pi$
$282$	1.24467e6	+	1.24467e6i	0.0555020	+	0.0555020i
$283$	−272138.	+	272138.i	−0.0120069	+	0.0120069i	−0.713085	−	0.701078i	$-0.752703\pi$
$283$	−272138.	+	272138.i	−0.0120069	+	0.0120069i	0.701078	+	0.713085i	$0.252703\pi$
$284$		−	2.73045e7i		−	1.19201i
$285$	−1.32944e7			−0.574292
$286$		−	6.03302e6i		−	0.257891i
$287$		−	8.96475e6i		−	0.379221i
$288$	1.01382e7	−	1.01382e7i	0.424408	−	0.424408i
$289$		−	2.30908e7i		−	0.956631i
$290$	−2.90630e6	+	2.90630e6i	−0.119164	+	0.119164i
$291$	1.18535e7	−	1.18535e7i	0.481027	−	0.481027i
$292$	−1.22988e7			−0.493987
$293$	4.21748e7			1.67668			0.838340	−	0.545147i	$-0.183526\pi$
$293$	4.21748e7			1.67668			0.838340	+	0.545147i	$0.183526\pi$
$294$	1.20481e6	+	1.20481e6i	0.0474108	+	0.0474108i
$295$			3.88682e7i			1.51401i
$296$	−1.15872e7	−	4.65800e6i	−0.446791	−	0.179607i
$297$	1.42340e7			0.543323
$298$	−5.03047e6	+	5.03047e6i	−0.190090	+	0.190090i
$299$		−	2.46434e7i		−	0.921908i
$300$		−	3.49802e6i		−	0.129556i
$301$	4.76480e6	+	4.76480e6i	0.174721	+	0.174721i
$302$	−1.20046e6	−	1.20046e6i	−0.0435841	−	0.0435841i
$303$	−7.14528e6			−0.256857
$304$	2.25035e7	+	2.25035e7i	0.800993	+	0.800993i
$305$	−3.22275e7			−1.13586
$306$	1.29905e6			0.0453378
$307$		−	3.29335e7i		−	1.13821i	−0.822264	−	0.569106i	$-0.807289\pi$
$307$		−	3.29335e7i		−	1.13821i	0.822264	−	0.569106i	$-0.192711\pi$
$308$	−1.08868e7			−0.372605
$309$	−2.20641e6	−	2.20641e6i	−0.0747842	−	0.0747842i
$310$	−1.02553e7	+	1.02553e7i	−0.344241	+	0.344241i
$311$	8.96633e6	−	8.96633e6i	0.298080	−	0.298080i	−0.542181	−	0.840262i	$-0.682401\pi$
$311$	8.96633e6	−	8.96633e6i	0.298080	−	0.298080i	0.840262	+	0.542181i	$0.182401\pi$
$312$	−6.48492e6			−0.213521
$313$	−2.34393e7	−	2.34393e7i	−0.764383	−	0.764383i	0.212728	−	0.977111i	$-0.431765\pi$
$313$	−2.34393e7	−	2.34393e7i	−0.764383	−	0.764383i	−0.977111	+	0.212728i	$0.931765\pi$
$314$	1.05876e6	−	1.05876e6i	0.0341986	−	0.0341986i
$315$	1.10235e7	+	1.10235e7i	0.352687	+	0.352687i
$316$	−2.64590e7	+	2.64590e7i	−0.838517	+	0.838517i
$317$		−	5.34283e7i		−	1.67723i	−0.544722	−	0.838617i	$-0.683365\pi$
$317$		−	5.34283e7i		−	1.67723i	0.544722	−	0.838617i	$-0.316635\pi$
$318$	−763816.	−	763816.i	−0.0237524	−	0.0237524i
$319$	1.08635e7	+	1.08635e7i	0.334656	+	0.334656i
$320$	−1.77317e7	+	1.77317e7i	−0.541127	+	0.541127i
$321$			2.11617e7i			0.639787i
$322$	2.92529e6			0.0876196
$323$			9.71052e6i			0.288161i
$324$			2.05591e7i			0.604461i
$325$	1.20151e7	−	1.20151e7i	0.350007	−	0.350007i
$326$			8.66059e6i			0.249974i
$327$	1.39870e7	−	1.39870e7i	0.400020	−	0.400020i
$328$	9.44708e6	−	9.44708e6i	0.267717	−	0.267717i
$329$	1.54297e7			0.433281
$330$	3.05089e6			0.0848955
$331$	4.39006e6	+	4.39006e6i	0.121056	+	0.121056i	0.765040	−	0.643983i	$-0.222719\pi$
$331$	4.39006e6	+	4.39006e6i	0.121056	+	0.121056i	−0.643983	+	0.765040i	$0.722719\pi$
$332$			1.63007e7i			0.445442i
$333$	2.97641e7	−	1.26956e7i	0.806046	−	0.343811i
$334$	−1.33721e7			−0.358888
$335$	−1.12372e7	+	1.12372e7i	−0.298898	+	0.298898i
$336$			5.26768e6i			0.138868i
$337$			3.49223e7i			0.912459i	0.889862	+	0.456229i	$0.150800\pi$
$337$			3.49223e7i			0.912459i	−0.889862	+	0.456229i	$0.849200\pi$
$338$	−3.99919e6	−	3.99919e6i	−0.103567	−	0.103567i
$339$	1.75624e7	+	1.75624e7i	0.450800	+	0.450800i
$340$	−9.06296e6			−0.230586
$341$	3.83335e7	+	3.83335e7i	0.966753	+	0.966753i
$342$	1.20503e7			0.301246
$343$	3.43988e7			0.852435
$344$			1.00423e7i			0.246694i
$345$	1.24622e7			0.303484
$346$	−2.36835e6	−	2.36835e6i	−0.0571765	−	0.0571765i
$347$	−4.53814e7	+	4.53814e7i	−1.08615	+	1.08615i	−0.0902275	+	0.995921i	$0.528759\pi$
$347$	−4.53814e7	+	4.53814e7i	−1.08615	+	1.08615i	−0.995921	+	0.0902275i	$0.971241\pi$
$348$	5.65271e6	−	5.65271e6i	0.134128	−	0.134128i
$349$	−5.11688e7			−1.20373			−0.601865	−	0.798598i	$-0.705575\pi$
$349$	−5.11688e7			−1.20373			−0.601865	+	0.798598i	$0.705575\pi$
$350$	1.42625e6	+	1.42625e6i	0.0332652	+	0.0332652i
$351$	2.54401e7	−	2.54401e7i	0.588298	−	0.588298i
$352$	−1.73915e7	−	1.73915e7i	−0.398758	−	0.398758i
$353$	5.09151e7	−	5.09151e7i	1.15750	−	1.15750i	0.172494	−	0.985010i	$-0.444817\pi$
$353$	5.09151e7	−	5.09151e7i	1.15750	−	1.15750i	0.985010	−	0.172494i	$-0.0551827\pi$
$354$			4.97293e6i			0.112099i
$355$	4.74276e7	+	4.74276e7i	1.06010	+	1.06010i
$356$	3.71159e6	+	3.71159e6i	0.0822640	+	0.0822640i
$357$	−1.13653e6	+	1.13653e6i	−0.0249791	+	0.0249791i
$358$		−	1.09403e7i		−	0.238441i
$359$	−6.45290e7			−1.39467			−0.697336	−	0.716745i	$-0.745631\pi$
$359$	−6.45290e7			−1.39467			−0.697336	+	0.716745i	$0.745631\pi$
$360$			2.32333e7i			0.497970i
$361$			4.30317e7i			0.914675i
$362$	609362.	−	609362.i	0.0128455	−	0.0128455i
$363$			5.41853e6i			0.113282i
$364$	−1.94577e7	+	1.94577e7i	−0.403448	+	0.403448i
$365$	2.13629e7	−	2.13629e7i	0.439321	−	0.439321i
$366$	−4.12329e6			−0.0841008
$367$	−2.28520e7			−0.462302			−0.231151	−	0.972918i	$-0.574249\pi$
$367$	−2.28520e7			−0.462302			−0.231151	+	0.972918i	$0.574249\pi$
$368$	−2.10948e7	−	2.10948e7i	−0.423284	−	0.423284i
$369$			3.46174e7i			0.688993i
$370$	1.36596e7	−	5.82637e6i	0.269671	−	0.115025i
$371$	−9.46870e6			−0.185425
$372$	1.99464e7	−	1.99464e7i	0.387468	−	0.387468i
$373$		−	8.33276e6i		−	0.160569i	−0.996772	−	0.0802846i	$-0.974417\pi$
$373$		−	8.33276e6i		−	0.160569i	0.996772	−	0.0802846i	$-0.0255829\pi$
$374$		−	2.22844e6i		−	0.0425978i
$375$	−9.40017e6	−	9.40017e6i	−0.178255	−	0.178255i
$376$	1.62599e7	+	1.62599e7i	0.305882	+	0.305882i
$377$	3.88322e7			0.724716
$378$	3.01986e6	+	3.01986e6i	0.0559128	+	0.0559128i
$379$	−7.71693e7			−1.41751			−0.708757	−	0.705453i	$-0.750744\pi$
$379$	−7.71693e7			−1.41751			−0.708757	+	0.705453i	$0.750744\pi$
$380$	−8.40706e7			−1.53212
$381$		−	1.02760e7i		−	0.185801i
$382$	5.18562e6			0.0930274
$383$	−2.61699e7	−	2.61699e7i	−0.465807	−	0.465807i	0.434746	−	0.900553i	$-0.356838\pi$
$383$	−2.61699e7	−	2.61699e7i	−0.465807	−	0.465807i	−0.900553	+	0.434746i	$0.856838\pi$
$384$	−1.19134e7	+	1.19134e7i	−0.210398	+	0.210398i
$385$	1.89103e7	−	1.89103e7i	0.331372	−	0.331372i
$386$	1.62303e7			0.282204
$387$	−1.83993e7	−	1.83993e7i	−0.317445	−	0.317445i
$388$	7.49592e7	−	7.49592e7i	1.28330	−	1.28330i
$389$	7.18024e6	+	7.18024e6i	0.121981	+	0.121981i	0.765462	−	0.643481i	$-0.222511\pi$
$389$	7.18024e6	+	7.18024e6i	0.121981	+	0.121981i	−0.643481	+	0.765462i	$0.722511\pi$
$390$	5.45277e6	−	5.45277e6i	0.0919229	−	0.0919229i
$391$		−	9.10266e6i		−	0.152278i
$392$	1.57391e7	+	1.57391e7i	0.261290	+	0.261290i
$393$	1.33705e6	+	1.33705e6i	0.0220278	+	0.0220278i
$394$	991504.	−	991504.i	0.0162109	−	0.0162109i
$395$		−	9.19179e7i		−	1.49145i
$396$	4.20395e7			0.676973
$397$			2.85879e7i			0.456890i	0.973557	+	0.228445i	$0.0733640\pi$
$397$			2.85879e7i			0.456890i	−0.973557	+	0.228445i	$0.926636\pi$
$398$		−	3.19417e6i		−	0.0506651i
$399$	−1.05428e7	+	1.05428e7i	−0.165973	+	0.165973i
$400$		−	2.05699e7i		−	0.321404i
$401$	3.10020e7	−	3.10020e7i	0.480792	−	0.480792i	−0.424593	−	0.905384i	$-0.639583\pi$
$401$	3.10020e7	−	3.10020e7i	0.480792	−	0.480792i	0.905384	+	0.424593i	$0.139583\pi$
$402$	−1.43772e6	+	1.43772e6i	−0.0221308	+	0.0221308i
$403$	1.37025e8			2.09356
$404$	−4.51852e7			−0.685255
$405$	−3.57109e7	−	3.57109e7i	−0.537570	−	0.537570i
$406$			4.60956e6i			0.0688781i
$407$	−2.17785e7	−	5.10586e7i	−0.323032	−	0.757331i
$408$	−2.39537e6			−0.0352689
$409$	−3.54598e7	+	3.54598e7i	−0.518282	+	0.518282i	−0.917051	−	0.398769i	$-0.869438\pi$
$409$	−3.54598e7	+	3.54598e7i	−0.518282	+	0.518282i	0.398769	+	0.917051i	$0.369438\pi$
$410$			1.58869e7i			0.230509i
$411$		−	722969.i		−	0.0104134i
$412$	−1.39528e7	−	1.39528e7i	−0.199513	−	0.199513i
$413$	3.08236e7	+	3.08236e7i	0.437556	+	0.437556i
$414$	−1.12960e7			−0.159193
$415$	−2.83141e7	−	2.83141e7i	−0.396149	−	0.396149i
$416$	−6.21668e7			−0.863533
$417$	−3.20809e7			−0.442424
$418$		−	2.06717e7i		−	0.283040i
$419$	−324822.			−0.00441574			−0.00220787	−	0.999998i	$-0.500703\pi$
$419$	−324822.			−0.00441574			−0.00220787	+	0.999998i	$0.500703\pi$
$420$	−9.83975e6	−	9.83975e6i	−0.132812	−	0.132812i
$421$	−7.60451e7	+	7.60451e7i	−1.01912	+	1.01912i	−0.0193053	+	0.999814i	$0.506145\pi$
$421$	−7.60451e7	+	7.60451e7i	−1.01912	+	1.01912i	−0.999814	+	0.0193053i	$0.993855\pi$
$422$	6.40602e6	−	6.40602e6i	0.0852414	−	0.0852414i
$423$	−5.95818e7			−0.787213
$424$	−9.97816e6	−	9.97816e6i	−0.130904	−	0.130904i
$425$	4.43807e6	−	4.43807e6i	0.0578132	−	0.0578132i
$426$	6.06805e6	+	6.06805e6i	0.0784911	+	0.0784911i
$427$	−2.55573e7	+	2.55573e7i	−0.328270	+	0.328270i
$428$			1.33822e8i			1.70685i
$429$	−2.03821e7	−	2.03821e7i	−0.258152	−	0.258152i
$430$	−8.44398e6	−	8.44398e6i	−0.106204	−	0.106204i
$431$	1.00351e8	−	1.00351e8i	1.25340	−	1.25340i	0.299209	−	0.954188i	$-0.403277\pi$
$431$	1.00351e8	−	1.00351e8i	1.25340	−	1.25340i	0.954188	−	0.299209i	$-0.0967228\pi$
$432$		−	4.35535e7i		−	0.540221i
$433$	−8.17482e7			−1.00697			−0.503483	−	0.864005i	$-0.667948\pi$
$433$	−8.17482e7			−1.00697			−0.503483	+	0.864005i	$0.667948\pi$
$434$			1.62655e7i			0.198975i
$435$			1.96374e7i			0.238570i
$436$	8.84509e7	−	8.84509e7i	1.06719	−	1.06719i
$437$		−	8.44389e7i		−	1.01181i
$438$	2.73324e6	−	2.73324e6i	0.0325279	−	0.0325279i
$439$	−2.53229e7	+	2.53229e7i	−0.299310	+	0.299310i	−0.840743	−	0.541434i	$-0.817882\pi$
$439$	−2.53229e7	+	2.53229e7i	−0.299310	+	0.299310i	0.541434	+	0.840743i	$0.317882\pi$
$440$	3.98555e7			0.467875
$441$	−5.76735e7			−0.672451
$442$	−3.98284e6	−	3.98284e6i	−0.0461239	−	0.0461239i
$443$			1.31767e8i			1.51564i	0.652463	+	0.757820i	$0.273736\pi$
$443$			1.31767e8i			1.51564i	−0.652463	+	0.757820i	$0.726264\pi$
$444$	−2.65678e7	+	1.13322e7i	−0.303533	+	0.129469i
$445$	−1.28940e7			−0.146321
$446$	8.52882e6	−	8.52882e6i	0.0961356	−	0.0961356i
$447$			3.39901e7i			0.380565i
$448$			2.81235e7i			0.312777i
$449$	9.16462e7	+	9.16462e7i	1.01245	+	1.01245i	0.999921	+	0.0125325i	$0.00398933\pi$
$449$	9.16462e7	+	9.16462e7i	1.01245	+	1.01245i	0.0125325	+	0.999921i	$0.496011\pi$
$450$	−5.50745e6	−	5.50745e6i	−0.0604385	−	0.0604385i
$451$	5.93842e7			0.647353
$452$	1.11061e8	+	1.11061e8i	1.20266	+	1.20266i
$453$	−8.11133e6			−0.0872564
$454$	−1.56100e7			−0.166815
$455$		−	6.75957e7i		−	0.717604i
$456$	−2.22201e7			−0.234343
$457$	−8.61658e7	−	8.61658e7i	−0.902790	−	0.902790i	0.0928871	−	0.995677i	$-0.470390\pi$
$457$	−8.61658e7	−	8.61658e7i	−0.902790	−	0.902790i	−0.995677	+	0.0928871i	$0.970390\pi$
$458$	2.37841e7	−	2.37841e7i	0.247566	−	0.247566i
$459$	9.39692e6	−	9.39692e6i	0.0971734	−	0.0971734i
$460$	7.88080e7			0.809649
$461$	8.42179e7	+	8.42179e7i	0.859611	+	0.859611i	0.991292	−	0.131681i	$-0.0420376\pi$
$461$	8.42179e7	+	8.42179e7i	0.859611	+	0.859611i	−0.131681	+	0.991292i	$0.542038\pi$
$462$	2.41944e6	−	2.41944e6i	0.0245352	−	0.0245352i
$463$	8.83321e7	+	8.83321e7i	0.889971	+	0.889971i	0.994520	−	0.104549i	$-0.0333399\pi$
$463$	8.83321e7	+	8.83321e7i	0.889971	+	0.889971i	−0.104549	+	0.994520i	$0.533340\pi$
$464$	3.32404e7	−	3.32404e7i	0.332745	−	0.332745i
$465$			6.92933e7i			0.689180i
$466$	3.00893e7	+	3.00893e7i	0.297340	+	0.297340i
$467$	2.33819e7	+	2.33819e7i	0.229577	+	0.229577i	0.812516	−	0.582939i	$-0.198097\pi$
$467$	2.33819e7	+	2.33819e7i	0.229577	+	0.229577i	−0.582939	+	0.812516i	$0.698097\pi$
$468$	7.51360e7	−	7.51360e7i	0.733011	−	0.733011i
$469$			1.78229e7i			0.172766i
$470$	−2.73439e7			−0.263370
$471$		−	7.15387e6i		−	0.0684665i
$472$			6.49641e7i			0.617800i
$473$	−3.15630e7	+	3.15630e7i	−0.298259	+	0.298259i
$474$		−	1.17603e7i		−	0.110429i
$475$	4.11688e7	−	4.11688e7i	0.384138	−	0.384138i
$476$	−7.18719e6	+	7.18719e6i	−0.0666405	+	0.0666405i
$477$	3.65634e7			0.336893
$478$	930683.			0.00852154
$479$	−1.50036e8	−	1.50036e8i	−1.36518	−	1.36518i	−0.867175	−	0.498004i	$-0.834067\pi$
$479$	−1.50036e8	−	1.50036e8i	−1.36518	−	1.36518i	−0.498004	−	0.867175i	$-0.665933\pi$
$480$		−	3.14377e7i		−	0.284267i
$481$	−1.30180e8	−	5.23315e7i	−1.16979	−	0.470249i
$482$	2.00991e6			0.0179488
$483$	9.88285e6	−	9.88285e6i	0.0877083	−	0.0877083i
$484$			3.42656e7i			0.302219i
$485$			2.60407e8i			2.28258i
$486$	−1.78761e7	−	1.78761e7i	−0.155727	−	0.155727i
$487$	−3.66189e7	−	3.66189e7i	−0.317043	−	0.317043i	0.530587	−	0.847630i	$-0.321972\pi$
$487$	−3.66189e7	−	3.66189e7i	−0.317043	−	0.317043i	−0.847630	+	0.530587i	$0.821972\pi$
$488$	−5.38648e7			−0.463495
$489$	2.92591e7	+	2.92591e7i	0.250227	+	0.250227i
$490$	−2.64681e7			−0.224975
$491$	−8.03724e7			−0.678988			−0.339494	−	0.940608i	$-0.610256\pi$
$491$	−8.03724e7			−0.678988			−0.339494	+	0.940608i	$0.610256\pi$
$492$		−	3.08999e7i		−	0.259455i
$493$	1.43436e7			0.119707
$494$	−3.69460e7	−	3.69460e7i	−0.306469	−	0.306469i
$495$	−7.30221e7	+	7.30221e7i	−0.602058	+	0.602058i
$496$	1.17293e8	−	1.17293e8i	0.961233	−	0.961233i
$497$	7.52230e7			0.612748
$498$	−3.62260e6	−	3.62260e6i	−0.0293314	−	0.0293314i
$499$	−7.59668e7	+	7.59668e7i	−0.611395	+	0.611395i	−0.943309	−	0.331914i	$-0.892305\pi$
$499$	−7.59668e7	+	7.59668e7i	−0.611395	+	0.611395i	0.331914	+	0.943309i	$0.392305\pi$
$500$	−5.94446e7	−	5.94446e7i	−0.475557	−	0.475557i
$501$	−4.51764e7	+	4.51764e7i	−0.359251	+	0.359251i
$502$			3.03401e7i			0.239831i
$503$	1.56686e8	+	1.56686e8i	1.23119	+	1.23119i	0.963506	+	0.267688i	$0.0862597\pi$
$503$	1.56686e8	+	1.56686e8i	1.23119	+	1.23119i	0.267688	+	0.963506i	$0.413740\pi$
$504$	1.84247e7	+	1.84247e7i	0.143916	+	0.143916i
$505$	7.84862e7	−	7.84862e7i	0.609424	−	0.609424i
$506$			1.93777e7i			0.149572i
$507$	−2.70219e7			−0.207344
$508$		−	6.49829e7i		−	0.495687i
$509$			1.20994e8i			0.917512i	0.888562	+	0.458756i	$0.151705\pi$
$509$			1.20994e8i			0.917512i	−0.888562	+	0.458756i	$0.848295\pi$
$510$	2.01412e6	−	2.01412e6i	0.0151836	−	0.0151836i
$511$		−	3.38829e7i		−	0.253932i
$512$	−9.06280e7	+	9.06280e7i	−0.675231	+	0.675231i
$513$	8.71686e7	−	8.71686e7i	0.645666	−	0.645666i
$514$	1.42334e7			0.104814
$515$	4.84718e7			0.354869
$516$	1.64234e7	+	1.64234e7i	0.119540	+	0.119540i
$517$			1.02209e8i			0.739637i
$518$	6.21200e6	−	1.54530e7i	0.0446932	−	0.111179i
$519$	−1.60025e7			−0.114469
$520$	7.12326e7	−	7.12326e7i	0.506604	−	0.506604i
$521$		−	2.27738e8i		−	1.61036i	−0.593030	−	0.805180i	$-0.702068\pi$
$521$		−	2.27738e8i		−	1.61036i	0.593030	−	0.805180i	$-0.297932\pi$
$522$		−	1.77998e7i		−	0.125142i
$523$	−1.07586e8	−	1.07586e8i	−0.752059	−	0.752059i	0.222805	−	0.974863i	$-0.428479\pi$
$523$	−1.07586e8	−	1.07586e8i	−0.752059	−	0.752059i	−0.974863	+	0.222805i	$0.928479\pi$
$524$	8.45522e6	+	8.45522e6i	0.0587667	+	0.0587667i
$525$	9.63692e6			0.0665979
$526$	1.31556e6	+	1.31556e6i	0.00903971	+	0.00903971i
$527$	5.06135e7			0.345808
$528$	−3.48941e7			−0.237056
$529$		−	6.88827e7i		−	0.465311i
$530$	1.67800e7			0.112711
$531$	−1.19026e8	−	1.19026e8i	−0.794981	−	0.794981i
$532$	−6.66705e7	+	6.66705e7i	−0.442791	+	0.442791i
$533$	1.06136e8	−	1.06136e8i	0.700939	−	0.700939i
$534$	−1.64970e6			−0.0108338
$535$	−2.32447e8	−	2.32447e8i	−1.51797	−	1.51797i
$536$	−1.87818e7	+	1.87818e7i	−0.121967	+	0.121967i
$537$	−3.69609e7	−	3.69609e7i	−0.238682	−	0.238682i
$538$	5.42396e7	−	5.42396e7i	0.348313	−	0.348313i
$539$			9.89358e7i			0.631811i
$540$	8.13556e7	+	8.13556e7i	0.516661	+	0.516661i
$541$	−6.50374e7	−	6.50374e7i	−0.410744	−	0.410744i	0.471253	−	0.881998i	$-0.343802\pi$
$541$	−6.50374e7	−	6.50374e7i	−0.410744	−	0.410744i	−0.881998	+	0.471253i	$0.843802\pi$
$542$	−4.77337e7	+	4.77337e7i	−0.299797	+	0.299797i
$543$		−	4.11736e6i		−	0.0257169i
$544$	−2.29628e7			−0.142636
$545$			3.07276e8i			1.89819i
$546$		−	8.64842e6i		−	0.0531323i
$547$	1.90817e8	−	1.90817e8i	1.16589	−	1.16589i	0.182721	−	0.983165i	$-0.441509\pi$
$547$	1.90817e8	−	1.90817e8i	1.16589	−	1.16589i	0.983165	−	0.182721i	$-0.0584907\pi$
$548$		−	4.57190e6i		−	0.0277815i
$549$	9.86896e7	−	9.86896e7i	0.596423	−	0.596423i
$550$	−9.44773e6	+	9.44773e6i	−0.0567858	+	0.0567858i
$551$	1.33056e8			0.795387
$552$	2.08292e7			0.123838
$553$	−7.28936e7	−	7.28936e7i	−0.431036	−	0.431036i
$554$			2.55195e7i			0.150087i
$555$	2.64640e7	−	6.58318e7i	0.154802	−	0.385085i
$556$	−2.02873e8			−1.18032
$557$	−3.09934e7	+	3.09934e7i	−0.179351	+	0.179351i	−0.791073	−	0.611722i	$-0.790477\pi$
$557$	−3.09934e7	+	3.09934e7i	−0.179351	+	0.179351i	0.611722	+	0.791073i	$0.290477\pi$
$558$		−	6.28092e7i		−	0.361510i
$559$			1.12823e8i			0.645897i
$560$	−5.78620e7	−	5.78620e7i	−0.329480	−	0.329480i
$561$	−7.52861e6	−	7.52861e6i	−0.0426409	−	0.0426409i
$562$	3.87234e7			0.218155
$563$	−6.28006e7	−	6.28006e7i	−0.351916	−	0.351916i	0.508906	−	0.860822i	$-0.330050\pi$
$563$	−6.28006e7	−	6.28006e7i	−0.351916	−	0.351916i	−0.860822	+	0.508906i	$0.830050\pi$
$564$	5.31834e7			0.296441
$565$	−3.85822e8			−2.13915
$566$		−	764912.i		−	0.00421854i
$567$	−5.66395e7			−0.310721
$568$	7.92703e7	+	7.92703e7i	0.432579	+	0.432579i
$569$	−1.07248e8	+	1.07248e8i	−0.582176	+	0.582176i	−0.935501	−	0.353325i	$-0.885051\pi$
$569$	−1.07248e8	+	1.07248e8i	−0.582176	+	0.582176i	0.353325	+	0.935501i	$0.385051\pi$
$570$	1.86835e7	−	1.86835e7i	0.100887	−	0.100887i
$571$	6.11905e7			0.328682			0.164341	−	0.986404i	$-0.447450\pi$
$571$	6.11905e7			0.328682			0.164341	+	0.986404i	$0.447450\pi$
$572$	−1.28892e8	−	1.28892e8i	−0.688711	−	0.688711i
$573$	1.75192e7	−	1.75192e7i	0.0931216	−	0.0931216i
$574$	1.25988e7	+	1.25988e7i	0.0666184	+	0.0666184i
$575$	−3.85917e7	+	3.85917e7i	−0.202998	+	0.202998i
$576$		−	1.08599e8i		−	0.568273i
$577$	2.32498e8	+	2.32498e8i	1.21029	+	1.21029i	0.970930	+	0.239364i	$0.0769390\pi$
$577$	2.32498e8	+	2.32498e8i	1.21029	+	1.21029i	0.239364	+	0.970930i	$0.423061\pi$
$578$	3.24511e7	+	3.24511e7i	0.168053	+	0.168053i
$579$	5.48326e7	−	5.48326e7i	0.282490	−	0.282490i
$580$			1.24183e8i			0.636468i
$581$	−4.49078e7			−0.228978
$582$			3.33173e7i			0.169005i
$583$		−	6.27225e7i		−	0.316532i
$584$	3.57059e7	−	3.57059e7i	0.179267	−	0.179267i
$585$			2.61021e8i			1.30379i
$586$	−5.92713e7	+	5.92713e7i	−0.294545	+	0.294545i
$587$	2.05002e8	−	2.05002e8i	1.01355	−	1.01355i	0.0136398	−	0.999907i	$-0.495658\pi$
$587$	2.05002e8	−	2.05002e8i	1.01355	−	1.01355i	0.999907	−	0.0136398i	$-0.00434181\pi$
$588$	5.14801e7			0.253225
$589$	4.69506e8			2.29771
$590$	−5.46244e7	−	5.46244e7i	−0.265969	−	0.265969i
$591$		−	6.69943e6i		−	0.0324545i
$592$	−1.56230e8	+	6.66383e7i	−0.753008	+	0.321188i
$593$	2.16117e8			1.03640			0.518198	−	0.855261i	$-0.326603\pi$
$593$	2.16117e8			1.03640			0.518198	+	0.855261i	$0.326603\pi$
$594$	−2.00041e7	+	2.00041e7i	−0.0954464	+	0.0954464i
$595$		−	2.49681e7i		−	0.118532i
$596$			2.14946e8i			1.01529i
$597$	−1.07912e7	−	1.07912e7i	−0.0507164	−	0.0507164i
$598$	3.46332e7	+	3.46332e7i	0.161953	+	0.161953i
$599$	−2.44457e8			−1.13742			−0.568711	−	0.822537i	$-0.692558\pi$
$599$	−2.44457e8			−1.13742			−0.568711	+	0.822537i	$0.692558\pi$
$600$	1.01554e7	+	1.01554e7i	0.0470158	+	0.0470158i
$601$	8.65278e7			0.398595			0.199298	−	0.979939i	$-0.436134\pi$
$601$	8.65278e7			0.398595			0.199298	+	0.979939i	$0.436134\pi$
$602$	−1.33926e7			−0.0613871
$603$		−	6.88229e7i		−	0.313893i
$604$	−5.12943e7			−0.232787
$605$	−5.95189e7	−	5.95189e7i	−0.268775	−	0.268775i
$606$	1.00418e7	−	1.00418e7i	0.0451225	−	0.0451225i
$607$	1.68123e7	−	1.68123e7i	0.0751730	−	0.0751730i	−0.668521	−	0.743694i	$-0.733072\pi$
$607$	1.68123e7	−	1.68123e7i	0.0751730	−	0.0751730i	0.743694	+	0.668521i	$0.233072\pi$
$608$	−2.13010e8			−0.947740
$609$	1.55730e7	+	1.55730e7i	0.0689479	+	0.0689479i
$610$	4.52916e7	−	4.52916e7i	0.199539	−	0.199539i
$611$	1.82676e8	+	1.82676e8i	0.800862	+	0.800862i
$612$	2.77533e7	−	2.77533e7i	0.121077	−	0.121077i
$613$			1.04244e8i			0.452551i	0.974063	+	0.226276i	$0.0726550\pi$
$613$			1.04244e8i			0.452551i	−0.974063	+	0.226276i	$0.927345\pi$
$614$	4.62839e7	+	4.62839e7i	0.199952	+	0.199952i
$615$	5.36727e7	+	5.36727e7i	0.230743	+	0.230743i
$616$	3.16065e7	−	3.16065e7i	0.135218	−	0.135218i
$617$			1.10870e8i			0.472016i	0.971751	+	0.236008i	$0.0758392\pi$
$617$			1.10870e8i			0.472016i	−0.971751	+	0.236008i	$0.924161\pi$
$618$	6.20165e6			0.0262749
$619$		−	4.56111e8i		−	1.92308i	−0.274658	−	0.961542i	$-0.588565\pi$
$619$		−	4.56111e8i		−	1.92308i	0.274658	−	0.961542i	$-0.411435\pi$
$620$			4.38196e8i			1.83863i
$621$	−8.17120e7	+	8.17120e7i	−0.341202	+	0.341202i
$622$			2.52021e7i			0.104729i
$623$	−1.02253e7	+	1.02253e7i	−0.0422875	+	0.0422875i
$624$	−6.23653e7	+	6.23653e7i	−0.256679	+	0.256679i
$625$	3.02360e8			1.23847
$626$	6.58818e7			0.268561
$627$	−6.98376e7	−	6.98376e7i	−0.283326	−	0.283326i
$628$		−	4.52395e7i		−	0.182658i
$629$	−4.80852e7	−	1.93299e7i	−0.193223	−	0.0776745i
$630$	−3.09844e7			−0.123914
$631$	−2.71803e8	+	2.71803e8i	−1.08185	+	1.08185i	−0.0855105	+	0.996337i	$0.527252\pi$
$631$	−2.71803e8	+	2.71803e8i	−1.08185	+	1.08185i	−0.996337	+	0.0855105i	$0.972748\pi$
$632$		−	1.53631e8i		−	0.608594i
$633$		−	4.32844e7i		−	0.170655i
$634$	7.50867e7	+	7.50867e7i	0.294642	+	0.294642i
$635$	1.12875e8	+	1.12875e8i	0.440834	+	0.440834i
$636$	−3.26369e7			−0.126864
$637$	1.76825e8	+	1.76825e8i	0.684110	+	0.684110i
$638$	−3.05346e7			−0.117579
$639$	−2.90474e8			−1.11328
$640$		−	2.61722e8i		−	0.998390i
$641$	4.91925e8			1.86778			0.933888	−	0.357566i	$-0.116393\pi$
$641$	4.91925e8			1.86778			0.933888	+	0.357566i	$0.116393\pi$
$642$	−2.97401e7	−	2.97401e7i	−0.112392	−	0.112392i
$643$	−2.77403e8	+	2.77403e8i	−1.04347	+	1.04347i	−0.0444536	+	0.999011i	$0.514155\pi$
$643$	−2.77403e8	+	2.77403e8i	−1.04347	+	1.04347i	−0.999011	+	0.0444536i	$0.985845\pi$
$644$	6.24970e7	−	6.24970e7i	0.233992	−	0.233992i
$645$	−5.70546e7			−0.212624
$646$	−1.36469e7	−	1.36469e7i	−0.0506217	−	0.0506217i
$647$	−4.81176e7	+	4.81176e7i	−0.177661	+	0.177661i	−0.790335	−	0.612675i	$-0.790094\pi$
$647$	−4.81176e7	+	4.81176e7i	−0.177661	+	0.177661i	0.612675	+	0.790335i	$0.290094\pi$
$648$	−5.96869e7	−	5.96869e7i	−0.219358	−	0.219358i
$649$	−2.04182e8	+	2.04182e8i	−0.746935	+	0.746935i
$650$			3.37714e7i			0.122973i
$651$	5.49516e7	+	5.49516e7i	0.199176	+	0.199176i
$652$	1.85028e8	+	1.85028e8i	0.667567	+	0.667567i
$653$	1.85778e8	−	1.85778e8i	0.667196	−	0.667196i	−0.289870	−	0.957066i	$-0.593612\pi$
$653$	1.85778e8	−	1.85778e8i	0.667196	−	0.667196i	0.957066	+	0.289870i	$0.0936120\pi$
$654$			3.93139e7i			0.140544i
$655$	−2.93732e7			−0.104527
$656$		−	1.81705e8i		−	0.643657i
$657$			1.30839e8i			0.461360i
$658$	−2.16845e7	+	2.16845e7i	−0.0761152	+	0.0761152i
$659$		−	3.34336e8i		−	1.16823i	−0.811672	−	0.584113i	$-0.801442\pi$
$659$		−	3.34336e8i		−	1.16823i	0.811672	−	0.584113i	$-0.198558\pi$
$660$	6.51804e7	−	6.51804e7i	0.226717	−	0.226717i
$661$	1.59431e8	−	1.59431e8i	0.552036	−	0.552036i	−0.374992	−	0.927028i	$-0.622355\pi$
$661$	1.59431e8	−	1.59431e8i	0.552036	−	0.552036i	0.927028	+	0.374992i	$0.122355\pi$
$662$	−1.23394e7			−0.0425323
$663$	−2.69114e7			−0.0923412
$664$	−4.73240e7	−	4.73240e7i	−0.161651	−	0.161651i
$665$		−	2.31612e8i		−	0.787581i
$666$	−2.39876e7	+	5.96716e7i	−0.0812016	+	0.201997i
$667$	−1.24727e8			−0.420321
$668$	−2.85686e8	+	2.85686e8i	−0.958427	+	0.958427i
$669$		−	5.76278e7i		−	0.192466i
$670$		−	3.15849e7i		−	0.105016i
$671$	−1.69297e8	−	1.69297e8i	−0.560377	−	0.560377i
$672$	−2.49310e7	−	2.49310e7i	−0.0821546	−	0.0821546i
$673$	−1.17146e8			−0.384311			−0.192156	−	0.981364i	$-0.561548\pi$
$673$	−1.17146e8			−0.384311			−0.192156	+	0.981364i	$0.561548\pi$
$674$	−4.90789e7	−	4.90789e7i	−0.160293	−	0.160293i
$675$	−7.96786e7			−0.259078
$676$	−1.70881e8			−0.553162
$677$		−	5.54808e8i		−	1.78804i	−0.448029	−	0.894019i	$-0.647874\pi$
$677$		−	5.54808e8i		−	1.78804i	0.448029	−	0.894019i	$-0.352126\pi$
$678$	−4.93633e7			−0.158385
$679$	2.06510e8	+	2.06510e8i	0.659678	+	0.659678i
$680$	2.63115e7	−	2.63115e7i	0.0836795	−	0.0836795i
$681$	−5.27371e7	+	5.27371e7i	−0.166984	+	0.166984i
$682$	−1.07746e8			−0.339662
$683$	−3.17566e7	−	3.17566e7i	−0.0996717	−	0.0996717i	0.655513	−	0.755184i	$-0.272453\pi$
$683$	−3.17566e7	−	3.17566e7i	−0.0996717	−	0.0996717i	−0.755184	+	0.655513i	$0.772453\pi$
$684$	2.57448e8	−	2.57448e8i	0.804491	−	0.804491i
$685$	7.94134e6	+	7.94134e6i	0.0247071	+	0.0247071i
$686$	−4.83432e7	+	4.83432e7i	−0.149749	+	0.149749i
$687$		−	1.60705e8i		−	0.495633i
$688$	9.65768e7	+	9.65768e7i	0.296557	+	0.296557i
$689$	−1.12102e8	−	1.12102e8i	−0.342734	−	0.342734i
$690$	−1.75140e7	+	1.75140e7i	−0.0533135	+	0.0533135i
$691$		−	3.10529e8i		−	0.941169i	−0.882355	−	0.470584i	$-0.844043\pi$
$691$		−	3.10529e8i		−	0.941169i	0.882355	−	0.470584i	$-0.155957\pi$
$692$	−1.01197e8			−0.305385
$693$			1.15817e8i			0.347996i
$694$		−	1.27556e8i		−	0.381611i
$695$	3.52388e8	−	3.52388e8i	1.04970	−	1.04970i
$696$			3.28218e7i			0.0973497i
$697$	3.92039e7	−	3.92039e7i	0.115779	−	0.115779i
$698$	7.19112e7	−	7.19112e7i	0.211461	−	0.211461i
$699$	2.03308e8			0.595283
$700$	6.09418e7			0.177673
$701$	1.04613e8	+	1.04613e8i	0.303690	+	0.303690i	0.842456	−	0.538765i	$-0.181109\pi$
$701$	1.04613e8	+	1.04613e8i	0.303690	+	0.303690i	−0.538765	+	0.842456i	$0.681109\pi$
$702$			7.15056e7i			0.206695i
$703$	−4.46052e8	−	1.79310e8i	−1.28387	−	0.516106i
$704$	−1.86295e8			−0.533929
$705$	−9.23790e7	+	9.23790e7i	−0.263637	+	0.263637i
$706$			1.43110e8i			0.406682i
$707$		−	1.24484e8i		−	0.352253i
$708$	1.06244e8	+	1.06244e8i	0.299366	+	0.299366i
$709$	−8.56995e6	−	8.56995e6i	−0.0240458	−	0.0240458i	0.694982	−	0.719027i	$-0.255412\pi$
$709$	−8.56995e6	−	8.56995e6i	−0.0240458	−	0.0240458i	−0.719027	+	0.694982i	$0.755412\pi$
$710$	−1.33307e8			−0.372459
$711$	2.81479e8	+	2.81479e8i	0.783135	+	0.783135i
$712$	−2.15509e7			−0.0597071
$713$	−4.40116e8			−1.21422
$714$		−	3.19451e6i		−	0.00877625i
$715$	4.47767e8			1.22499
$716$	−2.33733e8	−	2.33733e8i	−0.636767	−	0.636767i
$717$	3.14424e6	−	3.14424e6i	0.00853017	−	0.00853017i
$718$	9.06874e7	−	9.06874e7i	0.245004	−	0.245004i
$719$	1.90989e8			0.513834			0.256917	−	0.966433i	$-0.417293\pi$
$719$	1.90989e8			0.513834			0.256917	+	0.966433i	$0.417293\pi$
$720$	2.23434e8	+	2.23434e8i	0.598621	+	0.598621i
$721$	3.84396e7	−	3.84396e7i	0.102559	−	0.102559i
$722$	−6.04756e7	−	6.04756e7i	−0.160682	−	0.160682i
$723$	6.79030e6	−	6.79030e6i	0.0179669	−	0.0179669i
$724$		−	2.60373e7i		−	0.0686088i
$725$	−6.08114e7	−	6.08114e7i	−0.159577	−	0.159577i
$726$	−7.61505e6	−	7.61505e6i	−0.0199005	−	0.0199005i
$727$	−4.30934e8	+	4.30934e8i	−1.12152	+	1.12152i	−0.130009	+	0.991513i	$0.541501\pi$
$727$	−4.30934e8	+	4.30934e8i	−1.12152	+	1.12152i	−0.991513	+	0.130009i	$0.958499\pi$
$728$		−	1.12979e8i		−	0.292822i
$729$	1.28799e8			0.332453
$730$			6.00458e7i			0.154353i
$731$			4.16740e7i			0.106688i
$732$	−8.80915e7	+	8.80915e7i	−0.224595	+	0.224595i
$733$			4.08149e7i			0.103635i	0.998657	+	0.0518176i	$0.0165014\pi$
$733$			4.08149e7i			0.103635i	−0.998657	+	0.0518176i	$0.983499\pi$
$734$	3.21156e7	−	3.21156e7i	0.0812134	−	0.0812134i
$735$	−8.94203e7	+	8.94203e7i	−0.225203	+	0.225203i
$736$	1.99676e8			0.500832
$737$	−1.18062e8			−0.294922
$738$	−4.86503e7	−	4.86503e7i	−0.121037	−	0.121037i
$739$			4.70445e8i			1.16567i	0.812591	+	0.582835i	$0.198057\pi$
$739$			4.70445e8i			1.16567i	−0.812591	+	0.582835i	$0.801943\pi$
$740$	1.67353e8	−	4.16306e8i	0.412988	−	1.02735i
$741$	−2.49638e8			−0.613558
$742$	1.33071e7	−	1.33071e7i	0.0325740	−	0.0325740i
$743$			3.11317e8i			0.758992i	0.925193	+	0.379496i	$0.123903\pi$
$743$			3.11317e8i			0.758992i	−0.925193	+	0.379496i	$0.876097\pi$
$744$			1.15816e8i			0.281223i
$745$	−3.73358e8	−	3.73358e8i	−0.902936	−	0.902936i
$746$	1.17106e7	+	1.17106e7i	0.0282075	+	0.0282075i
$747$	1.73411e8			0.416022
$748$	−4.76093e7	−	4.76093e7i	−0.113759	−	0.113759i
$749$	−3.68675e8			−0.877402
$750$	2.64215e7			0.0626287
$751$			4.27832e8i			1.01008i	0.863097	+	0.505038i	$0.168521\pi$
$751$			4.27832e8i			1.01008i	−0.863097	+	0.505038i	$0.831479\pi$
$752$	3.12742e8			0.735414
$753$	1.02501e8	+	1.02501e8i	0.240074	+	0.240074i
$754$	−5.45737e7	+	5.45737e7i	−0.127312	+	0.127312i
$755$	8.90976e7	−	8.90976e7i	0.207026	−	0.207026i
$756$	1.29035e8			0.298635
$757$	−1.11448e8	−	1.11448e8i	−0.256913	−	0.256913i	0.566885	−	0.823797i	$-0.308149\pi$
$757$	−1.11448e8	−	1.11448e8i	−0.256913	−	0.256913i	−0.823797	+	0.566885i	$0.808149\pi$
$758$	1.08452e8	−	1.08452e8i	0.249017	−	0.249017i
$759$	6.54659e7	+	6.54659e7i	0.149723	+	0.149723i
$760$	2.44073e8	−	2.44073e8i	0.556006	−	0.556006i
$761$			4.48930e8i			1.01865i	0.860574	+	0.509325i	$0.170105\pi$
$761$			4.48930e8i			1.01865i	−0.860574	+	0.509325i	$0.829895\pi$
$762$	1.44415e7	+	1.44415e7i	0.0326399	+	0.0326399i
$763$	2.43679e8	+	2.43679e8i	0.548586	+	0.548586i
$764$	1.10788e8	−	1.10788e8i	0.248434	−	0.248434i
$765$			9.64145e7i			0.215356i
$766$	7.35569e7			0.163658
$767$			7.29857e8i			1.61753i
$768$			6.98276e7i			0.154150i
$769$	−6.32779e7	+	6.32779e7i	−0.139147	+	0.139147i	−0.773249	−	0.634102i	$-0.781370\pi$
$769$	−6.32779e7	+	6.32779e7i	−0.139147	+	0.139147i	0.634102	+	0.773249i	$0.281370\pi$
$770$			5.31520e7i			0.116425i
$771$	4.80865e7	−	4.80865e7i	0.104920	−	0.104920i
$772$	3.46750e8	−	3.46750e8i	0.753640	−	0.753640i
$773$	−4.49551e8			−0.973285			−0.486643	−	0.873601i	$-0.661779\pi$
$773$	−4.49551e8			−0.973285			−0.486643	+	0.873601i	$0.661779\pi$
$774$	5.17157e7			0.111532
$775$	−2.14582e8	−	2.14582e8i	−0.460986	−	0.460986i
$776$			4.35242e8i			0.931420i
$777$	−3.12198e7	−	7.31933e7i	−0.0665530	−	0.156030i
$778$	−2.01818e7			−0.0428570
$779$	3.63666e8	−	3.63666e8i	0.769291	−	0.769291i
$780$		−	2.32990e8i		−	0.490969i
$781$			4.98292e8i			1.04600i
$782$	1.27926e7	+	1.27926e7i	0.0267510	+	0.0267510i
$783$	−1.28759e8	−	1.28759e8i	−0.268220	−	0.268220i
$784$	3.02725e8			0.628204
$785$	7.85805e7	+	7.85805e7i	0.162445	+	0.162445i
$786$	−3.75811e6			−0.00773930
$787$	7.01741e8			1.43964			0.719818	−	0.694163i	$-0.244225\pi$
$787$	7.01741e8			1.43964			0.719818	+	0.694163i	$0.244225\pi$
$788$		−	4.23658e7i		−	0.0865837i
$789$	8.88905e6			0.0180977
$790$	1.29179e8	+	1.29179e8i	0.262005	+	0.262005i
$791$	−3.05968e8	+	3.05968e8i	−0.618225	+	0.618225i
$792$	−1.22049e8	+	1.22049e8i	−0.245673	+	0.245673i
$793$	−6.05159e8			−1.21353
$794$	−4.01767e7	−	4.01767e7i	−0.0802625	−	0.0802625i
$795$	5.66900e7	−	5.66900e7i	0.112825	−	0.112825i
$796$	−6.82415e7	−	6.82415e7i	−0.135304	−	0.135304i
$797$	3.00304e8	−	3.00304e8i	0.593180	−	0.593180i	−0.345309	−	0.938489i	$-0.612226\pi$
$797$	3.00304e8	−	3.00304e8i	0.593180	−	0.593180i	0.938489	+	0.345309i	$0.112226\pi$
$798$		−	2.96332e7i		−	0.0583135i
$799$	6.74759e7	+	6.74759e7i	0.132284	+	0.132284i
$800$	9.73535e7	+	9.73535e7i	0.190144	+	0.190144i
$801$	3.94850e7	−	3.94850e7i	0.0768307	−	0.0768307i
$802$			8.71388e7i			0.168923i
$803$	2.24447e8			0.433477
$804$			6.14322e7i			0.118203i
$805$			2.17113e8i			0.416197i
$806$	−1.92571e8	+	1.92571e8i	−0.367778	+	0.367778i
$807$		−	3.66488e8i		−	0.697332i
$808$	1.31181e8	−	1.31181e8i	0.248679	−	0.248679i
$809$	3.51574e8	−	3.51574e8i	0.664004	−	0.664004i	−0.292317	−	0.956321i	$-0.594426\pi$
$809$	3.51574e8	−	3.51574e8i	0.664004	−	0.664004i	0.956321	+	0.292317i	$0.0944264\pi$
$810$	1.00374e8			0.188872
$811$	1.26503e8			0.237159			0.118579	−	0.992945i	$-0.462166\pi$
$811$	1.26503e8			0.237159			0.118579	+	0.992945i	$0.462166\pi$
$812$	9.84804e7	+	9.84804e7i	0.183942	+	0.183942i
$813$			3.22528e8i			0.600201i
$814$	1.02363e8	+	4.11494e7i	0.189789	+	0.0762941i
$815$	−6.42784e8			−1.18739
$816$	−2.30362e7	+	2.30362e7i	−0.0423975	+	0.0423975i
$817$			3.86581e8i			0.708882i
$818$		−	9.96685e7i		−	0.182095i
$819$	2.06997e8	+	2.06997e8i	0.376802	+	0.376802i
$820$	3.39415e8	+	3.39415e8i	0.615587	+	0.615587i
$821$	−1.05383e9			−1.90432			−0.952162	−	0.305593i	$-0.901145\pi$
$821$	−1.05383e9			−1.90432			−0.952162	+	0.305593i	$0.901145\pi$
$822$	1.01604e6	+	1.01604e6i	0.00182935	+	0.00182935i
$823$	−5.24973e8			−0.941754			−0.470877	−	0.882199i	$-0.656062\pi$
$823$	−5.24973e8			−0.941754			−0.470877	+	0.882199i	$0.656062\pi$
$824$	8.10156e7			0.144806
$825$			6.38368e7i			0.113687i
$826$	−8.66374e7			−0.153732
$827$	−5.61053e8	−	5.61053e8i	−0.991944	−	0.991944i	0.00802419	−	0.999968i	$-0.497446\pi$
$827$	−5.61053e8	−	5.61053e8i	−0.991944	−	0.991944i	−0.999968	+	0.00802419i	$0.997446\pi$
$828$	−2.41332e8	+	2.41332e8i	−0.425133	+	0.425133i
$829$	7.20328e8	−	7.20328e8i	1.26435	−	1.26435i	0.315385	−	0.948964i	$-0.397866\pi$
$829$	7.20328e8	−	7.20328e8i	1.26435	−	1.26435i	0.948964	−	0.315385i	$-0.102134\pi$
$830$	7.95837e7			0.139184
$831$	8.62156e7	+	8.62156e7i	0.150239	+	0.150239i
$832$	−3.32961e8	+	3.32961e8i	−0.578126	+	0.578126i
$833$	6.53148e7	+	6.53148e7i	0.112999	+	0.112999i
$834$	4.50856e7	−	4.50856e7i	0.0777213	−	0.0777213i
$835$		−	9.92466e8i		−	1.70473i
$836$	−4.41638e8	−	4.41638e8i	−0.755871	−	0.755871i
$837$	−4.54343e8	−	4.54343e8i	−0.774832	−	0.774832i
$838$	456496.	−	456496.i	0.000775720	−	0.000775720i
$839$		−	5.87231e8i		−	0.994313i	−0.867661	−	0.497157i	$-0.834377\pi$
$839$		−	5.87231e8i		−	0.994313i	0.867661	−	0.497157i	$-0.165623\pi$
$840$	5.71334e7			0.0963944
$841$			3.98284e8i			0.669584i
$842$		−	2.13743e8i		−	0.358061i
$843$	1.30824e8	−	1.30824e8i	0.218376	−	0.218376i
$844$		−	2.73721e8i		−	0.455283i
$845$	2.96818e8	−	2.96818e8i	0.491948	−	0.491948i
$846$	8.37346e7	−	8.37346e7i	0.138291	−	0.138291i
$847$	−9.44005e7			−0.155355
$848$	−1.91919e8			−0.314725
$849$	−2.58419e6	−	2.58419e6i	−0.00422281	−	0.00422281i
$850$			1.24743e7i			0.0203123i
$851$	4.18130e8	+	1.68086e8i	0.678457	+	0.272736i
$852$	2.59280e8			0.419228
$853$	2.11731e8	−	2.11731e8i	0.341144	−	0.341144i	−0.515653	−	0.856797i	$-0.672451\pi$
$853$	2.11731e8	−	2.11731e8i	0.341144	−	0.341144i	0.856797	+	0.515653i	$0.172451\pi$
$854$		−	7.18351e7i		−	0.115336i
$855$			8.94368e8i			1.43093i
$856$	−3.88511e8	−	3.88511e8i	−0.619416	−	0.619416i
$857$	−2.17486e8	−	2.17486e8i	−0.345533	−	0.345533i	0.512910	−	0.858443i	$-0.328568\pi$
$857$	−2.17486e8	−	2.17486e8i	−0.345533	−	0.345533i	−0.858443	+	0.512910i	$0.828568\pi$
$858$	5.72888e7			0.0907001
$859$	4.85440e8	+	4.85440e8i	0.765872	+	0.765872i	0.977377	−	0.211505i	$-0.0678364\pi$
$859$	4.85440e8	+	4.85440e8i	0.765872	+	0.765872i	−0.211505	+	0.977377i	$0.567836\pi$
$860$	−3.60801e8			−0.567247
$861$	8.51281e7			0.133372
$862$			2.82060e8i			0.440372i
$863$	−7.77832e8			−1.21019			−0.605095	−	0.796153i	$-0.706865\pi$
$863$	−7.77832e8			−1.21019			−0.605095	+	0.796153i	$0.706865\pi$
$864$	2.06131e8	+	2.06131e8i	0.319596	+	0.319596i
$865$	1.75777e8	−	1.75777e8i	0.271591	−	0.271591i
$866$	1.14887e8	−	1.14887e8i	0.176895	−	0.176895i
$867$	2.19267e8			0.336446
$868$	3.47502e8	+	3.47502e8i	0.531372	+	0.531372i
$869$	4.82861e8	−	4.82861e8i	0.735805	−	0.735805i
$870$	−2.75978e7	−	2.75978e7i	−0.0419100	−	0.0419100i
$871$	−2.11009e8	+	2.11009e8i	−0.319335	+	0.319335i
$872$			5.13580e8i			0.774566i
$873$	−7.97439e8	−	7.97439e8i	−1.19855	−	1.19855i
$874$	1.18668e8	+	1.18668e8i	0.177746	+	0.177746i
$875$	1.63768e8	−	1.63768e8i	0.244458	−	0.244458i
$876$		−	1.16788e8i		−	0.173735i
$877$	−4.96365e8			−0.735872			−0.367936	−	0.929851i	$-0.619936\pi$
$877$	−4.96365e8			−0.735872			−0.367936	+	0.929851i	$0.619936\pi$
$878$		−	7.11764e7i		−	0.105160i
$879$			4.00487e8i			0.589687i
$880$	3.83289e8	−	3.83289e8i	0.562443	−	0.562443i
$881$		−	5.63973e8i		−	0.824766i	−0.911011	−	0.412383i	$-0.864697\pi$
$881$		−	5.63973e8i		−	0.824766i	0.911011	−	0.412383i	$-0.135303\pi$
$882$	8.10528e7	−	8.10528e7i	0.118131	−	0.118131i
$883$	−6.50863e8	+	6.50863e8i	−0.945383	+	0.945383i	−0.998584	−	0.0532013i	$-0.983058\pi$
$883$	−6.50863e8	+	6.50863e8i	−0.945383	+	0.945383i	0.0532013	+	0.998584i	$0.483058\pi$
$884$	−1.70182e8			−0.246352
$885$	−3.69088e8			−0.532476
$886$	−1.85182e8	−	1.85182e8i	−0.266255	−	0.266255i
$887$			8.46567e8i			1.21308i	0.795052	+	0.606541i	$0.207444\pi$
$887$			8.46567e8i			1.21308i	−0.795052	+	0.606541i	$0.792556\pi$
$888$	4.42318e7	−	1.10031e8i	0.0631677	−	0.157136i
$889$	1.79026e8			0.254806
$890$	1.81208e7	−	1.81208e7i	0.0257045	−	0.0257045i
$891$		−	3.75191e8i		−	0.530419i
$892$		−	3.64426e8i		−	0.513469i
$893$	6.25926e8	+	6.25926e8i	0.878958	+	0.878958i
$894$	−4.77687e7	−	4.77687e7i	−0.0668546	−	0.0668546i
$895$	8.11983e8			1.13260
$896$	−2.07553e8	−	2.07553e8i	−0.288539	−	0.288539i
$897$	2.34011e8			0.324234
$898$	−2.57594e8			−0.355719
$899$		−	6.93517e8i		−	0.954505i
$900$	−2.35327e8			−0.322808
$901$	−4.14077e7	−	4.14077e7i	−0.0566118	−	0.0566118i
$902$	−8.34569e7	+	8.34569e7i	−0.113722	+	0.113722i
$903$	−4.52459e7	+	4.52459e7i	−0.0614492	+	0.0614492i
$904$	−6.44861e8			−0.872892
$905$	4.52265e7	+	4.52265e7i	0.0610164	+	0.0610164i
$906$	1.13994e7	−	1.13994e7i	0.0153285	−	0.0153285i
$907$	−3.21650e8	−	3.21650e8i	−0.431084	−	0.431084i	0.457913	−	0.888997i	$-0.348597\pi$
$907$	−3.21650e8	−	3.21650e8i	−0.431084	−	0.431084i	−0.888997	+	0.457913i	$0.848597\pi$
$908$	−3.33498e8	+	3.33498e8i	−0.445488	+	0.445488i
$909$			4.80694e8i			0.639996i
$910$	9.49972e7	+	9.49972e7i	0.126063	+	0.126063i
$911$	−2.75584e8	−	2.75584e8i	−0.364501	−	0.364501i	0.500966	−	0.865467i	$-0.332978\pi$
$911$	−2.75584e8	−	2.75584e8i	−0.364501	−	0.364501i	−0.865467	+	0.500966i	$0.832978\pi$
$912$	−2.13690e8	+	2.13690e8i	−0.281709	+	0.281709i
$913$		−	2.97478e8i		−	0.390879i
$914$	2.42190e8			0.317189
$915$		−	3.06028e8i		−	0.399482i
$916$		−	1.01627e9i		−	1.32227i
$917$	−2.32938e7	+	2.32938e7i	−0.0302088	+	0.0302088i
$918$			2.64124e7i			0.0341412i
$919$	−3.70023e8	+	3.70023e8i	−0.476741	+	0.476741i	−0.904088	−	0.427347i	$-0.859448\pi$
$919$	−3.70023e8	+	3.70023e8i	−0.476741	+	0.476741i	0.427347	+	0.904088i	$0.359448\pi$
$920$	−2.28795e8	+	2.28795e8i	−0.293821	+	0.293821i
$921$	3.12733e8			0.400308
$922$	−2.36715e8			−0.302018
$923$	8.90584e8	+	8.90584e8i	1.13258	+	1.13258i
$924$		−	1.03380e8i		−	0.131045i
$925$	1.21911e8	+	2.85814e8i	0.154034	+	0.361125i
$926$	−2.48279e8			−0.312685
$927$	−1.48434e8	+	1.48434e8i	−0.186336	+	0.186336i
$928$			3.14642e8i			0.393706i
$929$		−	1.28716e9i		−	1.60540i	−0.596380	−	0.802702i	$-0.703395\pi$
$929$		−	1.28716e9i		−	1.60540i	0.596380	−	0.802702i	$-0.296605\pi$
$930$	−9.73830e7	−	9.73830e7i	−0.121069	−	0.121069i
$931$	6.05879e8	+	6.05879e8i	0.750821	+	0.750821i
$932$	1.28568e9			1.58812
$933$	8.51431e7	+	8.51431e7i	0.104835	+	0.104835i
$934$	−6.57206e7			−0.0806605
$935$	1.65394e8			0.202341
$936$			4.36269e8i			0.532018i
$937$	1.79761e8			0.218512			0.109256	−	0.994014i	$-0.465153\pi$
$937$	1.79761e8			0.218512			0.109256	+	0.994014i	$0.465153\pi$
$938$	−2.50478e7	−	2.50478e7i	−0.0303501	−	0.0303501i
$939$	2.22576e8	−	2.22576e8i	0.268833	−	0.268833i
$940$	−5.84185e8	+	5.84185e8i	−0.703342	+	0.703342i
$941$	9.57743e8			1.14942			0.574712	−	0.818356i	$-0.305114\pi$
$941$	9.57743e8			1.14942			0.574712	+	0.818356i	$0.305114\pi$
$942$	1.00539e7	+	1.00539e7i	0.0120276	+	0.0120276i
$943$	−3.40902e8	+	3.40902e8i	−0.406531	+	0.406531i
$944$	6.24758e8	+	6.24758e8i	0.742671	+	0.742671i
$945$	−2.24132e8	+	2.24132e8i	−0.265588	+	0.265588i
$946$		−	8.87154e7i		−	0.104791i
$947$	5.74351e8	+	5.74351e8i	0.676281	+	0.676281i	0.959157	−	0.282875i	$-0.0912883\pi$
$947$	5.74351e8	+	5.74351e8i	0.676281	+	0.676281i	−0.282875	+	0.959157i	$0.591288\pi$
$948$	−2.51251e8	−	2.51251e8i	−0.294906	−	0.294906i
$949$	4.01147e8	−	4.01147e8i	0.469359	−	0.469359i
$950$			1.15715e8i			0.134964i
$951$	5.07348e8			0.589881
$952$		−	4.17316e7i		−	0.0483676i
$953$			1.48852e9i			1.71979i	0.510471	+	0.859895i	$0.329471\pi$
$953$			1.48852e9i			1.71979i	−0.510471	+	0.859895i	$0.670529\pi$
$954$	−5.13852e7	+	5.13852e7i	−0.0591825	+	0.0591825i
$955$			3.84874e8i			0.441884i
$956$	1.98835e7	−	1.98835e7i	0.0227572	−	0.0227572i
$957$	−1.03159e8	+	1.03159e8i	−0.117698	+	0.117698i
$958$	4.21714e8			0.479646
$959$	1.25954e7			0.0142809
$960$	−1.68378e8	−	1.68378e8i	−0.190314	−	0.190314i
$961$		−	1.55967e9i		−	1.75737i
$962$	2.56497e8	−	1.09406e8i	0.288109	−	0.122890i
$963$	1.42364e9			1.59412
$964$	4.29404e7	−	4.29404e7i	0.0479331	−	0.0479331i
$965$			1.20460e9i			1.34048i
$966$			2.77782e7i			0.0308157i
$967$	1.85341e8	+	1.85341e8i	0.204971	+	0.204971i	0.802126	−	0.597155i	$-0.203702\pi$
$967$	1.85341e8	+	1.85341e8i	0.204971	+	0.204971i	−0.597155	+	0.802126i	$0.703702\pi$
$968$	−9.94796e7	−	9.94796e7i	−0.109675	−	0.109675i
$969$	−9.22099e7			−0.101346
$970$	−3.65968e8	−	3.65968e8i	−0.400985	−	0.400985i
$971$	1.95082e8			0.213088			0.106544	−	0.994308i	$-0.466022\pi$
$971$	1.95082e8			0.213088			0.106544	+	0.994308i	$0.466022\pi$
$972$	−7.63825e8			−0.831755
$973$		−	5.58908e8i		−	0.606738i
$974$	1.02927e8			0.111391
$975$	1.14094e8	+	1.14094e8i	0.123097	+	0.123097i
$976$	−5.18016e8	+	5.18016e8i	−0.557178	+	0.557178i
$977$	−1.09669e9	+	1.09669e9i	−1.17598	+	1.17598i	−0.195218	+	0.980760i	$0.562541\pi$
$977$	−1.09669e9	+	1.09669e9i	−1.17598	+	1.17598i	−0.980760	+	0.195218i	$0.937459\pi$
$978$	−8.22399e7			−0.0879156
$979$	−6.77343e7	−	6.77343e7i	−0.0721873	−	0.0721873i
$980$	−5.65475e8	+	5.65475e8i	−0.600807	+	0.600807i
$981$	−9.40967e8	−	9.40967e8i	−0.996707	−	0.996707i
$982$	1.12953e8	−	1.12953e8i	0.119279	−	0.119279i
$983$		−	5.36472e8i		−	0.564789i	−0.959298	−	0.282395i	$-0.908871\pi$
$983$		−	5.36472e8i		−	0.564789i	0.959298	−	0.282395i	$-0.0911288\pi$
$984$	8.97083e7	+	8.97083e7i	0.0941559	+	0.0941559i
$985$	7.35888e7	+	7.35888e7i	0.0770022	+	0.0770022i
$986$	−2.01581e7	+	2.01581e7i	−0.0210291	+	0.0210291i
$987$			1.46518e8i			0.152385i
$988$	−1.57866e9			−1.63688
$989$		−	3.62381e8i		−	0.374608i
$990$		−	2.05246e8i		−	0.211529i
$991$	−7.56125e8	+	7.56125e8i	−0.776913	+	0.776913i	−0.979305	−	0.202391i	$-0.935129\pi$
$991$	−7.56125e8	+	7.56125e8i	−0.776913	+	0.776913i	0.202391	+	0.979305i	$0.435129\pi$
$992$			1.11026e9i			1.13734i
$993$	−4.16875e7	+	4.16875e7i	−0.0425753	+	0.0425753i
$994$	−1.05716e8	+	1.05716e8i	−0.107642	+	0.107642i
$995$	2.37069e8			0.240661
$996$	−1.54789e8			−0.156662
$997$	−9.79512e8	−	9.79512e8i	−0.988380	−	0.988380i	0.0115529	−	0.999933i	$-0.496323\pi$
$997$	−9.79512e8	−	9.79512e8i	−0.988380	−	0.988380i	−0.999933	+	0.0115529i	$0.996323\pi$
$998$		−	2.13523e8i		−	0.214810i
$999$	2.58128e8	+	6.05166e8i	0.258903	+	0.606985i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.7.d.a.6.8	✓	36
37.31	odd	4	inner	37.7.d.a.31.8	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.7.d.a.6.8	✓	36	1.1	even	1	trivial
37.7.d.a.31.8	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)

\(f(q)\)	\(=\)	\(q+(-1.40537 + 1.40537i) q^{2} +9.49587i q^{3} +60.0499i q^{4} +(-104.306 - 104.306i) q^{5} +(-13.3452 - 13.3452i) q^{6} -165.435 q^{7} +(-174.336 - 174.336i) q^{8} +638.828 q^{9} +O(q^{10})\)	\(q+(-1.40537 + 1.40537i) q^{2} +9.49587i q^{3} +60.0499i q^{4} +(-104.306 - 104.306i) q^{5} +(-13.3452 - 13.3452i) q^{6} -165.435 q^{7} +(-174.336 - 174.336i) q^{8} +638.828 q^{9} +293.177 q^{10} -1095.87i q^{11} -570.226 q^{12} +(-1958.63 - 1958.63i) q^{13} +(232.498 - 232.498i) q^{14} +(990.476 - 990.476i) q^{15} -3353.18 q^{16} +(-723.468 - 723.468i) q^{17} +(-897.792 + 897.792i) q^{18} +(-6711.09 - 6711.09i) q^{19} +(6263.55 - 6263.55i) q^{20} -1570.95i q^{21} +(1540.11 + 1540.11i) q^{22} +(6290.99 + 6290.99i) q^{23} +(1655.48 - 1655.48i) q^{24} +6134.44i q^{25} +5505.21 q^{26} +12988.7i q^{27} -9934.36i q^{28} +(-9913.11 + 9913.11i) q^{29} +2783.98i q^{30} +(-34979.8 + 34979.8i) q^{31} +(15870.0 - 15870.0i) q^{32} +10406.3 q^{33} +2033.48 q^{34} +(17255.9 + 17255.9i) q^{35} +38361.6i q^{36} +(46591.7 - 19873.2i) q^{37} +18863.2 q^{38} +(18598.9 - 18598.9i) q^{39} +36368.6i q^{40} +54188.8i q^{41} +(2207.77 + 2207.77i) q^{42} +(-28801.6 - 28801.6i) q^{43} +65807.1 q^{44} +(-66633.6 - 66633.6i) q^{45} -17682.4 q^{46} -93267.3 q^{47} -31841.3i q^{48} -90280.2 q^{49} +(-8621.18 - 8621.18i) q^{50} +(6869.96 - 6869.96i) q^{51} +(117615. - 117615. i) q^{52} +57235.1 q^{53} +(-18254.0 - 18254.0i) q^{54} +(-114306. + 114306. i) q^{55} +(28841.4 + 28841.4i) q^{56} +(63727.7 - 63727.7i) q^{57} -27863.2i q^{58} +(-186318. - 186318. i) q^{59} +(59477.9 + 59477.9i) q^{60} +(154485. - 154485. i) q^{61} -98319.4i q^{62} -105685. q^{63} -169997. i q^{64} +408593. i q^{65} +(-14624.7 + 14624.7i) q^{66} -107733. i q^{67} +(43444.1 - 43444.1i) q^{68} +(-59738.5 + 59738.5i) q^{69} -48501.9 q^{70} -454698. q^{71} +(-111371. - 111371. i) q^{72} +204810. i q^{73} +(-37549.4 + 93407.9i) q^{74} -58251.9 q^{75} +(403000. - 403000. i) q^{76} +181296. i q^{77} +52276.8i q^{78} +(440617. + 440617. i) q^{79} +(349756. + 349756. i) q^{80} +342367. q^{81} +(-76155.5 - 76155.5i) q^{82} +271452. q^{83} +94335.5 q^{84} +150924. i q^{85} +80954.0 q^{86} +(-94133.6 - 94133.6i) q^{87} +(-191051. + 191051. i) q^{88} +(61808.5 - 61808.5i) q^{89} +187290. q^{90} +(324026. + 324026. i) q^{91} +(-377773. + 377773. i) q^{92} +(-332164. - 332164. i) q^{93} +(131075. - 131075. i) q^{94} +1.40001e6i q^{95} +(150699. + 150699. i) q^{96} +(-1.24828e6 - 1.24828e6i) q^{97} +(126877. - 126877. i) q^{98} -700076. 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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