LMFDB - Embedded newform 37.7.d.a.6.6

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			6.6
Character	$\chi$	$=$	37.6
Dual form			37.7.d.a.31.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.58722 + 5.58722i) q^{2} -13.0839i q^{3} +1.56600i q^{4} +(-61.8977 - 61.8977i) q^{5} +(73.1027 + 73.1027i) q^{6} +184.379 q^{7} +(-366.331 - 366.331i) q^{8} +557.811 q^{9} +O(q^{10})$	\(q+(-5.58722 + 5.58722i) q^{2} -13.0839i q^{3} +1.56600i q^{4} +(-61.8977 - 61.8977i) q^{5} +(73.1027 + 73.1027i) q^{6} +184.379 q^{7} +(-366.331 - 366.331i) q^{8} +557.811 q^{9} +691.671 q^{10} -16.2178i q^{11} +20.4894 q^{12} +(1835.25 + 1835.25i) q^{13} +(-1030.16 + 1030.16i) q^{14} +(-809.864 + 809.864i) q^{15} +3993.32 q^{16} +(4232.92 + 4232.92i) q^{17} +(-3116.61 + 3116.61i) q^{18} +(6101.14 + 6101.14i) q^{19} +(96.9315 - 96.9315i) q^{20} -2412.40i q^{21} +(90.6122 + 90.6122i) q^{22} +(-2300.81 - 2300.81i) q^{23} +(-4793.05 + 4793.05i) q^{24} -7962.36i q^{25} -20507.8 q^{26} -16836.5i q^{27} +288.736i q^{28} +(21122.3 - 21122.3i) q^{29} -9049.77i q^{30} +(12208.5 - 12208.5i) q^{31} +(1133.65 - 1133.65i) q^{32} -212.192 q^{33} -47300.5 q^{34} +(-11412.6 - 11412.6i) q^{35} +873.530i q^{36} +(-50621.2 - 1794.10i) q^{37} -68176.8 q^{38} +(24012.2 - 24012.2i) q^{39} +45350.1i q^{40} +15960.3i q^{41} +(13478.6 + 13478.6i) q^{42} +(99523.4 + 99523.4i) q^{43} +25.3970 q^{44} +(-34527.2 - 34527.2i) q^{45} +25710.2 q^{46} +23830.7 q^{47} -52248.3i q^{48} -83653.5 q^{49} +(44487.4 + 44487.4i) q^{50} +(55383.2 - 55383.2i) q^{51} +(-2873.99 + 2873.99i) q^{52} +116918. q^{53} +(94069.4 + 94069.4i) q^{54} +(-1003.84 + 1003.84i) q^{55} +(-67543.7 - 67543.7i) q^{56} +(79826.9 - 79826.9i) q^{57} +236030. i q^{58} +(-154925. - 154925. i) q^{59} +(-1268.24 - 1268.24i) q^{60} +(131861. - 131861. i) q^{61} +136423. i q^{62} +102848. q^{63} +268241. i q^{64} -227195. i q^{65} +(1185.56 - 1185.56i) q^{66} +101451. i q^{67} +(-6628.74 + 6628.74i) q^{68} +(-30103.6 + 30103.6i) q^{69} +127529. q^{70} -129959. q^{71} +(-204344. - 204344. i) q^{72} +516105. i q^{73} +(292856. - 272808. i) q^{74} -104179. q^{75} +(-9554.36 + 9554.36i) q^{76} -2990.21i q^{77} +268323. i q^{78} +(90967.4 + 90967.4i) q^{79} +(-247177. - 247177. i) q^{80} +186356. q^{81} +(-89173.7 - 89173.7i) q^{82} -570536. q^{83} +3777.80 q^{84} -524016. i q^{85} -1.11212e6 q^{86} +(-276363. - 276363. i) q^{87} +(-5941.08 + 5941.08i) q^{88} +(382282. - 382282. i) q^{89} +385822. q^{90} +(338380. + 338380. i) q^{91} +(3603.05 - 3603.05i) q^{92} +(-159735. - 159735. i) q^{93} +(-133147. + 133147. i) q^{94} -755293. i q^{95} +(-14832.5 - 14832.5i) q^{96} +(-152272. - 152272. i) q^{97} +(467390. - 467390. i) q^{98} -9046.45i 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 $

$2$	−5.58722	+	5.58722i	−0.698402	+	0.698402i	−0.964066	−	0.265664i	$-0.914409\pi$
$2$	−5.58722	+	5.58722i	−0.698402	+	0.698402i	0.265664	+	0.964066i	$0.414409\pi$
$3$		−	13.0839i		−	0.484590i	−0.970203	−	0.242295i	$-0.922100\pi$
$3$		−	13.0839i		−	0.484590i	0.970203	−	0.242295i	$-0.0779001\pi$
$4$			1.56600i			0.0244687i
$5$	−61.8977	−	61.8977i	−0.495181	−	0.495181i	0.414753	−	0.909934i	$-0.363868\pi$
$5$	−61.8977	−	61.8977i	−0.495181	−	0.495181i	−0.909934	+	0.414753i	$0.863868\pi$
$6$	73.1027	+	73.1027i	0.338439	+	0.338439i
$7$	184.379			0.537547			0.268774	−	0.963203i	$-0.413382\pi$
$7$	184.379			0.537547			0.268774	+	0.963203i	$0.413382\pi$
$8$	−366.331	−	366.331i	−0.715491	−	0.715491i
$9$	557.811			0.765173
$10$	691.671			0.691671
$11$		−	16.2178i		−	0.0121847i	−0.999981	−	0.00609233i	$-0.998061\pi$
$11$		−	16.2178i		−	0.0121847i	0.999981	−	0.00609233i	$-0.00193926\pi$
$12$	20.4894			0.0118573
$13$	1835.25	+	1835.25i	0.835342	+	0.835342i	0.988242	−	0.152900i	$-0.0488612\pi$
$13$	1835.25	+	1835.25i	0.835342	+	0.835342i	−0.152900	+	0.988242i	$0.548861\pi$
$14$	−1030.16	+	1030.16i	−0.375424	+	0.375424i
$15$	−809.864	+	809.864i	−0.239960	+	0.239960i
$16$	3993.32			0.974933
$17$	4232.92	+	4232.92i	0.861576	+	0.861576i	0.991521	−	0.129945i	$-0.0414802\pi$
$17$	4232.92	+	4232.92i	0.861576	+	0.861576i	−0.129945	+	0.991521i	$0.541480\pi$
$18$	−3116.61	+	3116.61i	−0.534398	+	0.534398i
$19$	6101.14	+	6101.14i	0.889509	+	0.889509i	0.994476	−	0.104967i	$-0.0334736\pi$
$19$	6101.14	+	6101.14i	0.889509	+	0.889509i	−0.104967	+	0.994476i	$0.533474\pi$
$20$	96.9315	−	96.9315i	0.0121164	−	0.0121164i
$21$		−	2412.40i		−	0.260490i
$22$	90.6122	+	90.6122i	0.00850979	+	0.00850979i
$23$	−2300.81	−	2300.81i	−0.189102	−	0.189102i	0.606206	−	0.795308i	$-0.292691\pi$
$23$	−2300.81	−	2300.81i	−0.189102	−	0.189102i	−0.795308	+	0.606206i	$0.792691\pi$
$24$	−4793.05	+	4793.05i	−0.346720	+	0.346720i
$25$		−	7962.36i		−	0.509591i
$26$	−20507.8			−1.16681
$27$		−	16836.5i		−	0.855385i
$28$			288.736i			0.0131531i
$29$	21122.3	−	21122.3i	0.866058	−	0.866058i	−0.125975	−	0.992033i	$-0.540206\pi$
$29$	21122.3	−	21122.3i	0.866058	−	0.866058i	0.992033	+	0.125975i	$0.0402059\pi$
$30$		−	9049.77i		−	0.335177i
$31$	12208.5	−	12208.5i	0.409806	−	0.409806i	−0.471865	−	0.881671i	$-0.656419\pi$
$31$	12208.5	−	12208.5i	0.409806	−	0.409806i	0.881671	+	0.471865i	$0.156419\pi$
$32$	1133.65	−	1133.65i	0.0345961	−	0.0345961i
$33$	−212.192			−0.00590456
$34$	−47300.5			−1.20345
$35$	−11412.6	−	11412.6i	−0.266183	−	0.266183i
$36$			873.530i			0.0187228i
$37$	−50621.2	−	1794.10i	−0.999373	−	0.0354194i
$37$	−50621.2	−	1794.10i	−0.999373	−	0.0354194i
$38$	−68176.8			−1.24247
$39$	24012.2	−	24012.2i	0.404798	−	0.404798i
$40$			45350.1i			0.708596i
$41$			15960.3i			0.231574i	0.993274	+	0.115787i	$0.0369390\pi$
$41$			15960.3i			0.231574i	−0.993274	+	0.115787i	$0.963061\pi$
$42$	13478.6	+	13478.6i	0.181927	+	0.181927i
$43$	99523.4	+	99523.4i	1.25176	+	1.25176i	0.954932	+	0.296825i	$0.0959278\pi$
$43$	99523.4	+	99523.4i	1.25176	+	1.25176i	0.296825	+	0.954932i	$0.404072\pi$
$44$	25.3970			0.000298142
$45$	−34527.2	−	34527.2i	−0.378899	−	0.378899i
$46$	25710.2			0.264139
$47$	23830.7			0.229532			0.114766	−	0.993393i	$-0.463388\pi$
$47$	23830.7			0.229532			0.114766	+	0.993393i	$0.463388\pi$
$48$		−	52248.3i		−	0.472442i
$49$	−83653.5			−0.711043
$50$	44487.4	+	44487.4i	0.355900	+	0.355900i
$51$	55383.2	−	55383.2i	0.417511	−	0.417511i
$52$	−2873.99	+	2873.99i	−0.0204397	+	0.0204397i
$53$	116918.			0.785336			0.392668	−	0.919680i	$-0.371552\pi$
$53$	116918.			0.785336			0.392668	+	0.919680i	$0.371552\pi$
$54$	94069.4	+	94069.4i	0.597402	+	0.597402i
$55$	−1003.84	+	1003.84i	−0.00603361	+	0.00603361i
$56$	−67543.7	−	67543.7i	−0.384610	−	0.384610i
$57$	79826.9	−	79826.9i	0.431047	−	0.431047i
$58$			236030.i			1.20971i
$59$	−154925.	−	154925.i	−0.754338	−	0.754338i	0.220948	−	0.975286i	$-0.429085\pi$
$59$	−154925.	−	154925.i	−0.754338	−	0.754338i	−0.975286	+	0.220948i	$0.929085\pi$
$60$	−1268.24	−	1268.24i	−0.00587150	−	0.00587150i
$61$	131861.	−	131861.i	0.580933	−	0.580933i	−0.354227	−	0.935159i	$-0.615256\pi$
$61$	131861.	−	131861.i	0.580933	−	0.580933i	0.935159	+	0.354227i	$0.115256\pi$
$62$			136423.i			0.572419i
$63$	102848.			0.411316
$64$			268241.i			1.02326i
$65$		−	227195.i		−	0.827291i
$66$	1185.56	−	1185.56i	0.00412375	−	0.00412375i
$67$			101451.i			0.337313i	0.985675	+	0.168656i	$0.0539428\pi$
$67$			101451.i			0.337313i	−0.985675	+	0.168656i	$0.946057\pi$
$68$	−6628.74	+	6628.74i	−0.0210816	+	0.0210816i
$69$	−30103.6	+	30103.6i	−0.0916370	+	0.0916370i
$70$	127529.			0.371806
$71$	−129959.			−0.363105			−0.181553	−	0.983381i	$-0.558112\pi$
$71$	−129959.			−0.363105			−0.181553	+	0.983381i	$0.558112\pi$
$72$	−204344.	−	204344.i	−0.547474	−	0.547474i
$73$			516105.i			1.32669i	0.748314	+	0.663345i	$0.230864\pi$
$73$			516105.i			1.32669i	−0.748314	+	0.663345i	$0.769136\pi$
$74$	292856.	−	272808.i	0.722701	−	0.673227i
$75$	−104179.			−0.246943
$76$	−9554.36	+	9554.36i	−0.0217651	+	0.0217651i
$77$		−	2990.21i		−	0.00654982i
$78$			268323.i			0.565424i
$79$	90967.4	+	90967.4i	0.184504	+	0.184504i	0.793315	−	0.608811i	$-0.208353\pi$
$79$	90967.4	+	90967.4i	0.184504	+	0.184504i	−0.608811	+	0.793315i	$0.708353\pi$
$80$	−247177.	−	247177.i	−0.482768	−	0.482768i
$81$	186356.			0.350662
$82$	−89173.7	−	89173.7i	−0.161732	−	0.161732i
$83$	−570536.			−0.997812			−0.498906	−	0.866656i	$-0.666265\pi$
$83$	−570536.			−0.997812			−0.498906	+	0.866656i	$0.666265\pi$
$84$	3777.80			0.00637384
$85$		−	524016.i		−	0.853272i
$86$	−1.11212e6			−1.74846
$87$	−276363.	−	276363.i	−0.419683	−	0.419683i
$88$	−5941.08	+	5941.08i	−0.00871801	+	0.00871801i
$89$	382282.	−	382282.i	0.542268	−	0.542268i	−0.381925	−	0.924193i	$-0.624739\pi$
$89$	382282.	−	382282.i	0.542268	−	0.542268i	0.924193	+	0.381925i	$0.124739\pi$
$90$	385822.			0.529248
$91$	338380.	+	338380.i	0.449035	+	0.449035i
$92$	3603.05	−	3603.05i	0.00462708	−	0.00462708i
$93$	−159735.	−	159735.i	−0.198588	−	0.198588i
$94$	−133147.	+	133147.i	−0.160306	+	0.160306i
$95$		−	755293.i		−	0.880936i
$96$	−14832.5	−	14832.5i	−0.0167649	−	0.0167649i
$97$	−152272.	−	152272.i	−0.166841	−	0.166841i	0.618748	−	0.785589i	$-0.287640\pi$
$97$	−152272.	−	152272.i	−0.166841	−	0.166841i	−0.785589	+	0.618748i	$0.787640\pi$
$98$	467390.	−	467390.i	0.496594	−	0.496594i
$99$		−	9046.45i		−	0.00932336i
$100$	12469.0			0.0124690
$101$			1.04058e6i			1.00998i	0.863126	+	0.504988i	$0.168503\pi$
$101$			1.04058e6i			1.00998i	−0.863126	+	0.504988i	$0.831497\pi$
$102$			618876.i			0.583181i
$103$	357316.	−	357316.i	0.326995	−	0.326995i	−0.524448	−	0.851442i	$-0.675728\pi$
$103$	357316.	−	357316.i	0.326995	−	0.326995i	0.851442	+	0.524448i	$0.175728\pi$
$104$		−	1.34462e6i		−	1.19536i
$105$	−149322.	+	149322.i	−0.128990	+	0.128990i
$106$	−653249.	+	653249.i	−0.548480	+	0.548480i
$107$	−1.23221e6			−1.00585			−0.502923	−	0.864331i	$-0.667742\pi$
$107$	−1.23221e6			−1.00585			−0.502923	+	0.864331i	$0.667742\pi$
$108$	26365.9			0.0209301
$109$	695175.	+	695175.i	0.536803	+	0.536803i	0.922588	−	0.385786i	$-0.126070\pi$
$109$	695175.	+	695175.i	0.536803	+	0.536803i	−0.385786	+	0.922588i	$0.626070\pi$
$110$		−	11217.4i		−	0.00842777i
$111$	−23473.8	+	662324.i	−0.0171639	+	0.484286i
$112$	736284.			0.524072
$113$	1.06254e6	−	1.06254e6i	0.736394	−	0.736394i	−0.235484	−	0.971878i	$-0.575668\pi$
$113$	1.06254e6	−	1.06254e6i	0.736394	−	0.736394i	0.971878	+	0.235484i	$0.0756675\pi$
$114$			892020.i			0.602088i
$115$			284829.i			0.187280i
$116$	33077.4	+	33077.4i	0.0211913	+	0.0211913i
$117$	1.02372e6	+	1.02372e6i	0.639181	+	0.639181i
$118$	1.73120e6			1.05366
$119$	780461.	+	780461.i	0.463138	+	0.463138i
$120$	593357.			0.343378
$121$	1.77130e6			0.999852
$122$			1.47347e6i			0.811449i
$123$	208823.			0.112218
$124$	19118.5	+	19118.5i	0.0100274	+	0.0100274i
$125$	−1.46000e6	+	1.46000e6i	−0.747521	+	0.747521i
$126$	−574637.	+	574637.i	−0.287264	+	0.287264i
$127$	−1.89111e6			−0.923220			−0.461610	−	0.887083i	$-0.652728\pi$
$127$	−1.89111e6			−0.923220			−0.461610	+	0.887083i	$0.652728\pi$
$128$	−1.42617e6	−	1.42617e6i	−0.680049	−	0.680049i
$129$	1.30216e6	−	1.30216e6i	0.606588	−	0.606588i
$130$	1.26939e6	+	1.26939e6i	0.577782	+	0.577782i
$131$	−381091.	+	381091.i	−0.169518	+	0.169518i	−0.786767	−	0.617250i	$-0.788247\pi$
$131$	−381091.	+	381091.i	−0.169518	+	0.169518i	0.617250	+	0.786767i	$0.288247\pi$
$132$		−	332.292i		−	0.000144477i
$133$	1.12492e6	+	1.12492e6i	0.478153	+	0.478153i
$134$	−566830.	−	566830.i	−0.235580	−	0.235580i
$135$	−1.04214e6	+	1.04214e6i	−0.423570	+	0.423570i
$136$		−	3.10131e6i		−	1.23290i
$137$	−3.84571e6			−1.49560			−0.747799	−	0.663925i	$-0.768889\pi$
$137$	−3.84571e6			−1.49560			−0.747799	+	0.663925i	$0.768889\pi$
$138$		−	336391.i		−	0.127999i
$139$		−	1.31783e6i		−	0.490699i	−0.969435	−	0.245349i	$-0.921097\pi$
$139$		−	1.31783e6i		−	0.490699i	0.969435	−	0.245349i	$-0.0789027\pi$
$140$	17872.1	−	17872.1i	0.00651315	−	0.00651315i
$141$		−	311799.i		−	0.111229i
$142$	726112.	−	726112.i	0.253594	−	0.253594i
$143$	29763.6	−	29763.6i	0.0101783	−	0.0101783i
$144$	2.22752e6			0.745992
$145$	−2.61484e6			−0.857712
$146$	−2.88359e6	−	2.88359e6i	−0.926563	−	0.926563i
$147$			1.09452e6i			0.344564i
$148$	2809.55	−	79272.6i	0.000866665	−	0.0244533i
$149$	2.64939e6			0.800916			0.400458	−	0.916315i	$-0.368851\pi$
$149$	2.64939e6			0.800916			0.400458	+	0.916315i	$0.368851\pi$
$150$	582070.	−	582070.i	0.172465	−	0.172465i
$151$		−	3.92672e6i		−	1.14051i	−0.821468	−	0.570255i	$-0.806844\pi$
$151$		−	3.92672e6i		−	1.14051i	0.821468	−	0.570255i	$-0.193156\pi$
$152$		−	4.47008e6i		−	1.27287i
$153$	2.36117e6	+	2.36117e6i	0.659254	+	0.659254i
$154$	16707.0	+	16707.0i	0.00457441	+	0.00457441i
$155$	−1.51136e6			−0.405856
$156$	37603.0	+	37603.0i	0.00990487	+	0.00990487i
$157$	−6.38908e6			−1.65097			−0.825486	−	0.564423i	$-0.809099\pi$
$157$	−6.38908e6			−1.65097			−0.825486	+	0.564423i	$0.809099\pi$
$158$	−1.01651e6			−0.257715
$159$		−	1.52975e6i		−	0.380566i
$160$	−140340.			−0.0342627
$161$	−424220.	−	424220.i	−0.101651	−	0.101651i
$162$	−1.04121e6	+	1.04121e6i	−0.244903	+	0.244903i
$163$	−2.19551e6	+	2.19551e6i	−0.506958	+	0.506958i	−0.913592	−	0.406633i	$-0.866703\pi$
$163$	−2.19551e6	+	2.19551e6i	−0.506958	+	0.506958i	0.406633	+	0.913592i	$0.366703\pi$
$164$	−24993.8			−0.00566631
$165$	13134.2	+	13134.2i	0.00292383	+	0.00292383i
$166$	3.18771e6	−	3.18771e6i	0.696874	−	0.696874i
$167$	−1.28890e6	−	1.28890e6i	−0.276738	−	0.276738i	0.555067	−	0.831805i	$-0.312692\pi$
$167$	−1.28890e6	−	1.28890e6i	−0.276738	−	0.276738i	−0.831805	+	0.555067i	$0.812692\pi$
$168$	−883737.	+	883737.i	−0.186378	+	0.186378i
$169$			1.90944e6i			0.395591i
$170$	2.92779e6	+	2.92779e6i	0.595927	+	0.595927i
$171$	3.40328e6	+	3.40328e6i	0.680628	+	0.680628i
$172$	−155853.	+	155853.i	−0.0306288	+	0.0306288i
$173$			2.87337e6i			0.554949i	0.960733	+	0.277475i	$0.0894974\pi$
$173$			2.87337e6i			0.554949i	−0.960733	+	0.277475i	$0.910503\pi$
$174$	3.08820e6			0.586215
$175$		−	1.46809e6i		−	0.273929i
$176$		−	64762.8i		−	0.0118792i
$177$	−2.02703e6	+	2.02703e6i	−0.365544	+	0.365544i
$178$			4.27179e6i			0.757443i
$179$	−1.03415e6	+	1.03415e6i	−0.180311	+	0.180311i	−0.791491	−	0.611180i	$-0.790695\pi$
$179$	−1.03415e6	+	1.03415e6i	−0.180311	+	0.180311i	0.611180	+	0.791491i	$0.290695\pi$
$180$	54069.4	−	54069.4i	0.00927116	−	0.00927116i
$181$	1.75583e6			0.296105			0.148052	−	0.988980i	$-0.452700\pi$
$181$	1.75583e6			0.296105			0.148052	+	0.988980i	$0.452700\pi$
$182$	−3.78121e6			−0.627215
$183$	−1.72525e6	−	1.72525e6i	−0.281514	−	0.281514i
$184$			1.68572e6i			0.270602i
$185$	3.02228e6	+	3.24438e6i	0.477331	+	0.512409i
$186$	1.78495e6			0.277388
$187$	68648.6	−	68648.6i	0.0104980	−	0.0104980i
$188$			37318.8i			0.00561635i
$189$		−	3.10430e6i		−	0.459809i
$190$	4.21999e6	+	4.21999e6i	0.615248	+	0.615248i
$191$	−4.29444e6	−	4.29444e6i	−0.616320	−	0.616320i	0.328265	−	0.944586i	$-0.393536\pi$
$191$	−4.29444e6	−	4.29444e6i	−0.616320	−	0.616320i	−0.944586	+	0.328265i	$0.893536\pi$
$192$	3.50964e6			0.495860
$193$	6.37258e6	+	6.37258e6i	0.886428	+	0.886428i	0.994178	−	0.107750i	$-0.0343647\pi$
$193$	6.37258e6	+	6.37258e6i	0.886428	+	0.886428i	−0.107750	+	0.994178i	$0.534365\pi$
$194$	1.70155e6			0.233045
$195$	−2.97260e6			−0.400897
$196$		−	131001.i		−	0.0173983i
$197$	3.61801e6			0.473229			0.236614	−	0.971604i	$-0.423962\pi$
$197$	3.61801e6			0.473229			0.236614	+	0.971604i	$0.423962\pi$
$198$	50544.5	+	50544.5i	0.00651146	+	0.00651146i
$199$	1.06603e7	−	1.06603e7i	1.35273	−	1.35273i	0.470127	−	0.882599i	$-0.344208\pi$
$199$	1.06603e7	−	1.06603e7i	1.35273	−	1.35273i	0.882599	−	0.470127i	$-0.155792\pi$
$200$	−2.91686e6	+	2.91686e6i	−0.364608	+	0.364608i
$201$	1.32738e6			0.163458
$202$	−5.81394e6	−	5.81394e6i	−0.705369	−	0.705369i
$203$	3.89450e6	−	3.89450e6i	0.465547	−	0.465547i
$204$	86729.9	+	86729.9i	0.0102159	+	0.0102159i
$205$	987906.	−	987906.i	0.114671	−	0.114671i
$206$			3.99280e6i			0.456747i
$207$	−1.28342e6	−	1.28342e6i	−0.144696	−	0.144696i
$208$	7.32873e6	+	7.32873e6i	0.814402	+	0.814402i
$209$	98946.9	−	98946.9i	0.0108384	−	0.0108384i
$210$		−	1.66859e6i		−	0.180173i
$211$	−1.69799e7			−1.80753			−0.903767	−	0.428024i	$-0.859210\pi$
$211$	−1.69799e7			−1.80753			−0.903767	+	0.428024i	$0.859210\pi$
$212$			183094.i			0.0192161i
$213$			1.70038e6i			0.175957i
$214$	6.88460e6	−	6.88460e6i	0.702485	−	0.702485i
$215$		−	1.23205e7i		−	1.23969i
$216$	−6.16775e6	+	6.16775e6i	−0.612020	+	0.612020i
$217$	2.25099e6	−	2.25099e6i	0.220290	−	0.220290i
$218$	−7.76819e6			−0.749808
$219$	6.75268e6			0.642900
$220$	−1572.01	−	1572.01i	−0.000147634	−	0.000147634i
$221$			1.55369e7i			1.43942i
$222$	−3.56940e6	−	3.83170e6i	−0.326239	−	0.350213i
$223$	−8.29165e6			−0.747699			−0.373849	−	0.927489i	$-0.621962\pi$
$223$	−8.29165e6			−0.747699			−0.373849	+	0.927489i	$0.621962\pi$
$224$	209020.	−	209020.i	0.0185970	−	0.0185970i
$225$		−	4.44149e6i		−	0.389925i
$226$			1.18733e7i			1.02860i
$227$	9.68741e6	+	9.68741e6i	0.828190	+	0.828190i	0.987266	−	0.159076i	$-0.0508516\pi$
$227$	9.68741e6	+	9.68741e6i	0.828190	+	0.828190i	−0.159076	+	0.987266i	$0.550852\pi$
$228$	125009.	+	125009.i	0.0105472	+	0.0105472i
$229$	1.64574e7			1.37042			0.685210	−	0.728345i	$-0.259710\pi$
$229$	1.64574e7			1.37042			0.685210	+	0.728345i	$0.259710\pi$
$230$	−1.59140e6	−	1.59140e6i	−0.130797	−	0.130797i
$231$	−39123.7			−0.00317398
$232$	−1.54755e7			−1.23931
$233$		−	1.46015e7i		−	1.15433i	−0.816627	−	0.577165i	$-0.804159\pi$
$233$		−	1.46015e7i		−	1.15433i	0.816627	−	0.577165i	$-0.195841\pi$
$234$	−1.14395e7			−0.892811
$235$	−1.47506e6	−	1.47506e6i	−0.113660	−	0.113660i
$236$	242612.	−	242612.i	0.0184577	−	0.0184577i
$237$	1.19021e6	−	1.19021e6i	0.0894085	−	0.0894085i
$238$	−8.72121e6			−0.646913
$239$	−1.12806e7	−	1.12806e7i	−0.826300	−	0.826300i	0.160703	−	0.987003i	$-0.448624\pi$
$239$	−1.12806e7	−	1.12806e7i	−0.826300	−	0.826300i	−0.987003	+	0.160703i	$0.948624\pi$
$240$	−3.23405e6	+	3.23405e6i	−0.233945	+	0.233945i
$241$	9.67876e6	+	9.67876e6i	0.691462	+	0.691462i	0.962554	−	0.271091i	$-0.0873845\pi$
$241$	9.67876e6	+	9.67876e6i	0.691462	+	0.691462i	−0.271091	+	0.962554i	$0.587384\pi$
$242$	−9.89663e6	+	9.89663e6i	−0.698299	+	0.698299i
$243$		−	1.47121e7i		−	1.02531i
$244$	206493.	+	206493.i	0.0142147	+	0.0142147i
$245$	5.17796e6	+	5.17796e6i	0.352095	+	0.352095i
$246$	−1.16674e6	+	1.16674e6i	−0.0783735	+	0.0783735i
$247$			2.23942e7i			1.48609i
$248$	−8.94474e6			−0.586425
$249$			7.46484e6i			0.483529i
$250$		−	1.63147e7i		−	1.04414i
$251$	1.84103e7	−	1.84103e7i	1.16423	−	1.16423i	0.180693	−	0.983539i	$-0.442166\pi$
$251$	1.84103e7	−	1.84103e7i	1.16423	−	1.16423i	0.983539	−	0.180693i	$-0.0578341\pi$
$252$			161060.i			0.0100644i
$253$	−37314.0	+	37314.0i	−0.00230414	+	0.00230414i
$254$	1.05660e7	−	1.05660e7i	0.644779	−	0.644779i
$255$	−6.85618e6			−0.413487
$256$	−1.23081e6			−0.0733617
$257$	−1.48190e7	−	1.48190e7i	−0.873009	−	0.873009i	0.119791	−	0.992799i	$-0.461778\pi$
$257$	−1.48190e7	−	1.48190e7i	−0.873009	−	0.873009i	−0.992799	+	0.119791i	$0.961778\pi$
$258$			1.45509e7i			0.847285i
$259$	−9.33347e6	−	330793.i	−0.537210	−	0.0190396i
$260$	355786.			0.0202427
$261$	1.17823e7	−	1.17823e7i	0.662684	−	0.662684i
$262$		−	4.25848e6i		−	0.236783i
$263$			4.53649e6i			0.249375i	0.992196	+	0.124687i	$0.0397928\pi$
$263$			4.53649e6i			0.249375i	−0.992196	+	0.124687i	$0.960207\pi$
$264$	77732.6	+	77732.6i	0.00422466	+	0.00422466i
$265$	−7.23698e6	−	7.23698e6i	−0.388884	−	0.388884i
$266$	−1.25704e7			−0.667886
$267$	−5.00175e6	−	5.00175e6i	−0.262778	−	0.262778i
$268$	−158872.			−0.00825360
$269$	2.10131e7			1.07953			0.539763	−	0.841817i	$-0.318514\pi$
$269$	2.10131e7			1.07953			0.539763	+	0.841817i	$0.318514\pi$
$270$		−	1.16453e7i		−	0.591645i
$271$	−1.54056e7			−0.774053			−0.387026	−	0.922069i	$-0.626498\pi$
$271$	−1.54056e7			−0.774053			−0.387026	+	0.922069i	$0.626498\pi$
$272$	1.69034e7	+	1.69034e7i	0.839978	+	0.839978i
$273$	4.42734e6	−	4.42734e6i	0.217598	−	0.217598i
$274$	2.14868e7	−	2.14868e7i	1.04453	−	1.04453i
$275$	−129132.			−0.00620919
$276$	−47142.1	−	47142.1i	−0.00224224	−	0.00224224i
$277$	2.02548e6	−	2.02548e6i	0.0952991	−	0.0952991i	−0.657850	−	0.753149i	$-0.728534\pi$
$277$	2.02548e6	−	2.02548e6i	0.0952991	−	0.0952991i	0.753149	+	0.657850i	$0.228534\pi$
$278$	7.36300e6	+	7.36300e6i	0.342705	+	0.342705i
$279$	6.81005e6	−	6.81005e6i	0.313572	−	0.313572i
$280$			8.36159e6i			0.380904i
$281$	2.43595e7	+	2.43595e7i	1.09786	+	1.09786i	0.994660	+	0.103204i	$0.0329095\pi$
$281$	2.43595e7	+	2.43595e7i	1.09786	+	1.09786i	0.103204	+	0.994660i	$0.467090\pi$
$282$	1.74209e6	+	1.74209e6i	0.0776825	+	0.0776825i
$283$	−2.83231e7	+	2.83231e7i	−1.24963	+	1.24963i	−0.293749	+	0.955883i	$0.594903\pi$
$283$	−2.83231e7	+	2.83231e7i	−1.24963	+	1.24963i	−0.955883	+	0.293749i	$0.905097\pi$
$284$		−	203516.i		−	0.00888471i
$285$	−9.88219e6			−0.426893
$286$			332591.i			0.0142172i
$287$			2.94274e6i			0.124482i
$288$	632360.	−	632360.i	0.0264720	−	0.0264720i
$289$			1.16977e7i			0.484626i
$290$	1.46097e7	−	1.46097e7i	0.599028	−	0.599028i
$291$	−1.99231e6	+	1.99231e6i	−0.0808496	+	0.0808496i
$292$	−808218.			−0.0324624
$293$	4.95272e6			0.196898			0.0984490	−	0.995142i	$-0.468612\pi$
$293$	4.95272e6			0.196898			0.0984490	+	0.995142i	$0.468612\pi$
$294$	−6.11530e6	−	6.11530e6i	−0.240644	−	0.240644i
$295$			1.91790e7i			0.747068i
$296$	1.78869e7	+	1.92014e7i	0.689700	+	0.740384i
$297$	−273051.			−0.0104226
$298$	−1.48027e7	+	1.48027e7i	−0.559362	+	0.559362i
$299$		−	8.44509e6i		−	0.315930i
$300$		−	163144.i		−	0.00604236i
$301$	1.83500e7	+	1.83500e7i	0.672878	+	0.672878i
$302$	2.19395e7	+	2.19395e7i	0.796535	+	0.796535i
$303$	1.36149e7			0.489424
$304$	2.43638e7	+	2.43638e7i	0.867211	+	0.867211i
$305$	−1.63237e7			−0.575334
$306$	−2.63847e7			−0.920850
$307$		−	5.27987e7i		−	1.82477i	−0.409333	−	0.912385i	$-0.634238\pi$
$307$		−	5.27987e7i		−	1.82477i	0.409333	−	0.912385i	$-0.365762\pi$
$308$	4682.66			0.000160266
$309$	−4.67509e6	−	4.67509e6i	−0.158458	−	0.158458i
$310$	8.44429e6	−	8.44429e6i	0.283451	−	0.283451i
$311$	−2.34477e7	+	2.34477e7i	−0.779504	+	0.779504i	−0.979746	−	0.200243i	$-0.935827\pi$
$311$	−2.34477e7	+	2.34477e7i	−0.779504	+	0.779504i	0.200243	+	0.979746i	$0.435827\pi$
$312$	−1.75929e7			−0.579259
$313$	−1.92773e7	−	1.92773e7i	−0.628657	−	0.628657i	0.319073	−	0.947730i	$-0.396628\pi$
$313$	−1.92773e7	−	1.92773e7i	−0.628657	−	0.628657i	−0.947730	+	0.319073i	$0.896628\pi$
$314$	3.56972e7	−	3.56972e7i	1.15304	−	1.15304i
$315$	−6.36608e6	−	6.36608e6i	−0.203676	−	0.203676i
$316$	−142455.	+	142455.i	−0.00451456	+	0.00451456i
$317$			5.86112e7i			1.83994i	0.391992	+	0.919969i	$0.371786\pi$
$317$			5.86112e7i			1.83994i	−0.391992	+	0.919969i	$0.628214\pi$
$318$	8.54706e6	+	8.54706e6i	0.265788	+	0.265788i
$319$	−342557.	−	342557.i	−0.0105526	−	0.0105526i
$320$	1.66035e7	−	1.66035e7i	0.506697	−	0.506697i
$321$			1.61221e7i			0.487423i
$322$	4.74042e6			0.141987
$323$			5.16513e7i			1.53276i
$324$			291833.i			0.00858024i
$325$	1.46129e7	−	1.46129e7i	0.425683	−	0.425683i
$326$		−	2.45336e7i		−	0.708122i
$327$	9.09562e6	−	9.09562e6i	0.260129	−	0.260129i
$328$	5.84676e6	−	5.84676e6i	0.165689	−	0.165689i
$329$	4.39387e6			0.123384
$330$	−146767.			−0.00408401
$331$	−3.83696e7	−	3.83696e7i	−1.05804	−	1.05804i	−0.998208	−	0.0598345i	$-0.980943\pi$
$331$	−3.83696e7	−	3.83696e7i	−1.05804	−	1.05804i	−0.0598345	−	0.998208i	$-0.519057\pi$
$332$		−	893456.i		−	0.0244151i
$333$	−2.82371e7	−	1.00077e6i	−0.764693	−	0.0271019i
$334$	1.44027e7			0.386549
$335$	6.27959e6	−	6.27959e6i	0.167031	−	0.167031i
$336$		−	9.63348e6i		−	0.253960i
$337$		−	4.17900e7i		−	1.09190i	−0.837818	−	0.545950i	$-0.816169\pi$
$337$		−	4.17900e7i		−	1.09190i	0.837818	−	0.545950i	$-0.183831\pi$
$338$	−1.06685e7	−	1.06685e7i	−0.276282	−	0.276282i
$339$	−1.39022e7	−	1.39022e7i	−0.356849	−	0.356849i
$340$	820607.			0.0208784
$341$	−197995.	−	197995.i	−0.00499334	−	0.00499334i
$342$	−3.80298e7			−0.950704
$343$	−3.71159e7			−0.919766
$344$		−	7.29171e7i		−	1.79124i
$345$	3.72668e6			0.0907538
$346$	−1.60541e7	−	1.60541e7i	−0.387578	−	0.387578i
$347$	−4.71739e7	+	4.71739e7i	−1.12905	+	1.12905i	−0.138720	+	0.990332i	$0.544299\pi$
$347$	−4.71739e7	+	4.71739e7i	−1.12905	+	1.12905i	−0.990332	+	0.138720i	$0.955701\pi$
$348$	432783.	−	432783.i	0.0102691	−	0.0102691i
$349$	−1.28410e7			−0.302081			−0.151041	−	0.988528i	$-0.548262\pi$
$349$	−1.28410e7			−0.302081			−0.151041	+	0.988528i	$0.548262\pi$
$350$	8.20254e6	+	8.20254e6i	0.191313	+	0.191313i
$351$	3.08992e7	−	3.08992e7i	0.714538	−	0.714538i
$352$	−18385.2	−	18385.2i	−0.000421541	−	0.000421541i
$353$	−4.59912e7	+	4.59912e7i	−1.04556	+	1.04556i	−0.0466532	+	0.998911i	$0.514856\pi$
$353$	−4.59912e7	+	4.59912e7i	−1.04556	+	1.04556i	−0.998911	+	0.0466532i	$0.985144\pi$
$354$		−	2.26509e7i		−	0.510594i
$355$	8.04418e6	+	8.04418e6i	0.179803	+	0.179803i
$356$	598652.	+	598652.i	0.0132686	+	0.0132686i
$357$	1.02115e7	−	1.02115e7i	0.224432	−	0.224432i
$358$		−	1.15560e7i		−	0.251860i
$359$	−2.63695e7			−0.569926			−0.284963	−	0.958539i	$-0.591981\pi$
$359$	−2.63695e7			−0.569926			−0.284963	+	0.958539i	$0.591981\pi$
$360$			2.52968e7i			0.542198i
$361$			2.74020e7i			0.582453i
$362$	−9.81018e6	+	9.81018e6i	−0.206800	+	0.206800i
$363$		−	2.31755e7i		−	0.484518i
$364$	−529902.	+	529902.i	−0.0109873	+	0.0109873i
$365$	3.19457e7	−	3.19457e7i	0.656952	−	0.656952i
$366$	1.92787e7			0.393220
$367$	2.64775e7			0.535647			0.267824	−	0.963468i	$-0.413696\pi$
$367$	2.64775e7			0.535647			0.267824	+	0.963468i	$0.413696\pi$
$368$	−9.18787e6	−	9.18787e6i	−0.184362	−	0.184362i
$369$			8.90284e6i			0.177194i
$370$	−3.50132e7	−	1.24093e6i	−0.691237	−	0.0244986i
$371$	2.15573e7			0.422155
$372$	250145.	−	250145.i	0.00485918	−	0.00485918i
$373$		−	5.91827e6i		−	0.114043i	−0.998373	−	0.0570214i	$-0.981840\pi$
$373$		−	5.91827e6i		−	0.114043i	0.998373	−	0.0570214i	$-0.0181603\pi$
$374$			767109.i			0.0146637i
$375$	1.91026e7	+	1.91026e7i	0.362241	+	0.362241i
$376$	−8.72994e6	−	8.72994e6i	−0.164228	−	0.164228i
$377$	7.75292e7			1.44691
$378$	1.73444e7	+	1.73444e7i	0.321132	+	0.321132i
$379$	−3.64429e7			−0.669414			−0.334707	−	0.942322i	$-0.608637\pi$
$379$	−3.64429e7			−0.669414			−0.334707	+	0.942322i	$0.608637\pi$
$380$	1.18279e6			0.0215554
$381$			2.47431e7i			0.447383i
$382$	4.79879e7			0.860879
$383$	−1.65627e7	−	1.65627e7i	−0.294806	−	0.294806i	0.544170	−	0.838975i	$-0.316845\pi$
$383$	−1.65627e7	−	1.65627e7i	−0.294806	−	0.294806i	−0.838975	+	0.544170i	$0.816845\pi$
$384$	−1.86598e7	+	1.86598e7i	−0.329545	+	0.329545i
$385$	−185087.	+	185087.i	−0.00324335	+	0.00324335i
$386$	−7.12100e7			−1.23817
$387$	5.55153e7	+	5.55153e7i	0.957810	+	0.957810i
$388$	238457.	−	238457.i	0.00408239	−	0.00408239i
$389$	5.18941e7	+	5.18941e7i	0.881596	+	0.881596i	0.993697	−	0.112101i	$-0.0357580\pi$
$389$	5.18941e7	+	5.18941e7i	0.881596	+	0.881596i	−0.112101	+	0.993697i	$0.535758\pi$
$390$	1.66086e7	−	1.66086e7i	0.279987	−	0.279987i
$391$		−	1.94783e7i		−	0.325852i
$392$	3.06449e7	+	3.06449e7i	0.508745	+	0.508745i
$393$	4.98617e6	+	4.98617e6i	0.0821465	+	0.0821465i
$394$	−2.02146e7	+	2.02146e7i	−0.330504	+	0.330504i
$395$		−	1.12613e7i		−	0.182725i
$396$	14166.7			0.000228130
$397$		−	5.21260e7i		−	0.833073i	−0.909119	−	0.416537i	$-0.863244\pi$
$397$		−	5.21260e7i		−	0.833073i	0.909119	−	0.416537i	$-0.136756\pi$
$398$			1.19123e8i			1.88949i
$399$	1.47184e7	−	1.47184e7i	0.231708	−	0.231708i
$400$		−	3.17963e7i		−	0.496817i
$401$	−2.79937e7	+	2.79937e7i	−0.434137	+	0.434137i	−0.890033	−	0.455896i	$-0.849319\pi$
$401$	−2.79937e7	+	2.79937e7i	−0.434137	+	0.434137i	0.455896	+	0.890033i	$0.349319\pi$
$402$	−7.41636e6	+	7.41636e6i	−0.114160	+	0.114160i
$403$	4.48113e7			0.684656
$404$	−1.62954e6			−0.0247128
$405$	−1.15350e7	−	1.15350e7i	−0.173641	−	0.173641i
$406$			4.35189e7i			0.650278i
$407$	−29096.2	+	820963.i	−0.000431572	+	0.0121770i
$408$	−4.05772e7			−0.597451
$409$	2.21989e7	−	2.21989e7i	0.324460	−	0.324460i	−0.526015	−	0.850475i	$-0.676314\pi$
$409$	2.21989e7	−	2.21989e7i	0.324460	−	0.324460i	0.850475	+	0.526015i	$0.176314\pi$
$410$			1.10393e7i			0.160173i
$411$			5.03170e7i			0.724751i
$412$	559555.	+	559555.i	0.00800112	+	0.00800112i
$413$	−2.85649e7	−	2.85649e7i	−0.405492	−	0.405492i
$414$	1.43414e7			0.202112
$415$	3.53148e7	+	3.53148e7i	0.494098	+	0.494098i
$416$	4.16104e6			0.0577991
$417$	−1.72424e7			−0.237788
$418$			1.10568e6i			0.0151391i
$419$	3.48699e7			0.474033			0.237016	−	0.971506i	$-0.423831\pi$
$419$	3.48699e7			0.474033			0.237016	+	0.971506i	$0.423831\pi$
$420$	−233837.	−	233837.i	−0.00315621	−	0.00315621i
$421$	−4.34657e7	+	4.34657e7i	−0.582506	+	0.582506i	−0.935591	−	0.353085i	$-0.885133\pi$
$421$	−4.34657e7	+	4.34657e7i	−0.582506	+	0.582506i	0.353085	+	0.935591i	$0.385133\pi$
$422$	9.48701e7	−	9.48701e7i	1.26239	−	1.26239i
$423$	1.32930e7			0.175632
$424$	−4.28309e7	−	4.28309e7i	−0.561901	−	0.561901i
$425$	3.37041e7	−	3.37041e7i	0.439051	−	0.439051i
$426$	−9.50039e6	−	9.50039e6i	−0.122889	−	0.122889i
$427$	2.43123e7	−	2.43123e7i	0.312279	−	0.312279i
$428$		−	1.92963e6i		−	0.0246117i
$429$	−389424.	−	389424.i	−0.00493232	−	0.00493232i
$430$	6.88375e7	+	6.88375e7i	0.865804	+	0.865804i
$431$	3.33187e7	−	3.33187e7i	0.416157	−	0.416157i	−0.467720	−	0.883877i	$-0.654924\pi$
$431$	3.33187e7	−	3.33187e7i	0.416157	−	0.416157i	0.883877	+	0.467720i	$0.154924\pi$
$432$		−	6.72337e7i		−	0.833942i
$433$	−5.83995e7			−0.719359			−0.359679	−	0.933076i	$-0.617114\pi$
$433$	−5.83995e7			−0.719359			−0.359679	+	0.933076i	$0.617114\pi$
$434$			2.51536e7i			0.307702i
$435$			3.42124e7i			0.415638i
$436$	−1.08864e6	+	1.08864e6i	−0.0131349	+	0.0131349i
$437$		−	2.80751e7i		−	0.336416i
$438$	−3.77287e7	+	3.77287e7i	−0.449003	+	0.449003i
$439$	1.08101e8	−	1.08101e8i	1.27772	−	1.27772i	0.335774	−	0.941943i	$-0.391002\pi$
$439$	1.08101e8	−	1.08101e8i	1.27772	−	1.27772i	0.941943	−	0.335774i	$-0.108998\pi$
$440$	735478.			0.00863399
$441$	−4.66628e7			−0.544071
$442$	−8.68081e7	−	8.68081e7i	−1.00529	−	1.00529i
$443$			1.61230e8i			1.85454i	0.374395	+	0.927269i	$0.377850\pi$
$443$			1.61230e8i			1.85454i	−0.374395	+	0.927269i	$0.622150\pi$
$444$	−1.03720e6	−	36759.9i	−0.0118498	−	0.000419977i
$445$	−4.73247e7			−0.537042
$446$	4.63273e7	−	4.63273e7i	0.522194	−	0.522194i
$447$		−	3.46644e7i		−	0.388116i
$448$			4.94578e7i			0.550049i
$449$	−1.17670e8	−	1.17670e8i	−1.29995	−	1.29995i	−0.928420	−	0.371532i	$-0.878833\pi$
$449$	−1.17670e8	−	1.17670e8i	−1.29995	−	1.29995i	−0.371532	−	0.928420i	$-0.621167\pi$
$450$	2.48156e7	+	2.48156e7i	0.272325	+	0.272325i
$451$	258841.			0.00282165
$452$	1.66393e6	+	1.66393e6i	0.0180186	+	0.0180186i
$453$	−5.13769e7			−0.552680
$454$	−1.08251e8			−1.15682
$455$		−	4.18899e7i		−	0.444708i
$456$	−5.84862e7			−0.616821
$457$	3.32168e7	+	3.32168e7i	0.348024	+	0.348024i	0.859373	−	0.511349i	$-0.170854\pi$
$457$	3.32168e7	+	3.32168e7i	0.348024	+	0.348024i	−0.511349	+	0.859373i	$0.670854\pi$
$458$	−9.19509e7	+	9.19509e7i	−0.957105	+	0.957105i
$459$	7.12677e7	−	7.12677e7i	0.736979	−	0.736979i
$460$	−446041.			−0.00458249
$461$	−5.60929e7	−	5.60929e7i	−0.572539	−	0.572539i	0.360298	−	0.932837i	$-0.382675\pi$
$461$	−5.60929e7	−	5.60929e7i	−0.572539	−	0.572539i	−0.932837	+	0.360298i	$0.882675\pi$
$462$	218593.	−	218593.i	0.00221671	−	0.00221671i
$463$	−4.23878e7	−	4.23878e7i	−0.427069	−	0.427069i	0.460559	−	0.887629i	$-0.347649\pi$
$463$	−4.23878e7	−	4.23878e7i	−0.427069	−	0.427069i	−0.887629	+	0.460559i	$0.847649\pi$
$464$	8.43482e7	−	8.43482e7i	0.844349	−	0.844349i
$465$			1.97745e7i			0.196674i
$466$	8.15819e7	+	8.15819e7i	0.806187	+	0.806187i
$467$	−5.08042e7	−	5.08042e7i	−0.498826	−	0.498826i	0.412247	−	0.911072i	$-0.364744\pi$
$467$	−5.08042e7	−	5.08042e7i	−0.498826	−	0.498826i	−0.911072	+	0.412247i	$0.864744\pi$
$468$	−1.60314e6	+	1.60314e6i	−0.0156399	+	0.0156399i
$469$			1.87054e7i			0.181322i
$470$	1.64830e7			0.158761
$471$			8.35943e7i			0.800044i
$472$			1.13508e8i			1.07944i
$473$	1.61405e6	−	1.61405e6i	0.0152522	−	0.0152522i
$474$			1.32999e7i			0.124886i
$475$	4.85795e7	−	4.85795e7i	0.453286	−	0.453286i
$476$	−1.22220e6	+	1.22220e6i	−0.0113324	+	0.0113324i
$477$	6.52184e7			0.600918
$478$	1.26054e8			1.15418
$479$	−1.57044e7	−	1.57044e7i	−0.142894	−	0.142894i	0.632041	−	0.774935i	$-0.282217\pi$
$479$	−1.57044e7	−	1.57044e7i	−0.142894	−	0.142894i	−0.774935	+	0.632041i	$0.782217\pi$
$480$			1.83620e6i			0.0166033i
$481$	−8.96098e7	−	9.61950e7i	−0.805230	−	0.864405i
$482$	−1.08155e8			−0.965838
$483$	−5.55046e6	+	5.55046e6i	−0.0492592	+	0.0492592i
$484$			2.77385e6i			0.0244650i
$485$			1.88505e7i			0.165233i
$486$	8.21997e7	+	8.21997e7i	0.716080	+	0.716080i
$487$	7.18132e7	+	7.18132e7i	0.621752	+	0.621752i	0.945979	−	0.324227i	$-0.105104\pi$
$487$	7.18132e7	+	7.18132e7i	0.621752	+	0.621752i	−0.324227	+	0.945979i	$0.605104\pi$
$488$	−9.66094e7			−0.831304
$489$	2.87259e7	+	2.87259e7i	0.245667	+	0.245667i
$490$	−5.78607e7			−0.491808
$491$	−2.04729e8			−1.72955			−0.864777	−	0.502156i	$-0.832540\pi$
$491$	−2.04729e8			−1.72955			−0.864777	+	0.502156i	$0.832540\pi$
$492$			327017.i			0.00274584i
$493$	1.78818e8			1.49235
$494$	−1.25121e8	−	1.25121e8i	−1.03789	−	1.03789i
$495$	−559954.	+	559954.i	−0.00461675	+	0.00461675i
$496$	4.87526e7	−	4.87526e7i	0.399533	−	0.399533i
$497$	−2.39617e7			−0.195186
$498$	−4.17077e7	−	4.17077e7i	−0.337698	−	0.337698i
$499$	−1.07791e8	+	1.07791e8i	−0.867521	+	0.867521i	−0.992197	−	0.124677i	$-0.960211\pi$
$499$	−1.07791e8	+	1.07791e8i	−0.867521	+	0.867521i	0.124677	+	0.992197i	$0.460211\pi$
$500$	−2.28636e6	−	2.28636e6i	−0.0182909	−	0.0182909i
$501$	−1.68638e7	+	1.68638e7i	−0.134104	+	0.134104i
$502$			2.05725e8i			1.62621i
$503$	−8.68009e7	−	8.68009e7i	−0.682057	−	0.682057i	0.278407	−	0.960463i	$-0.410194\pi$
$503$	−8.68009e7	−	8.68009e7i	−0.682057	−	0.682057i	−0.960463	+	0.278407i	$0.910194\pi$
$504$	−3.76766e7	−	3.76766e7i	−0.294293	−	0.294293i
$505$	6.44094e7	−	6.44094e7i	0.500121	−	0.500121i
$506$		−	416962.i		−	0.00321844i
$507$	2.49830e7			0.191700
$508$		−	2.96147e6i		−	0.0225900i
$509$		−	4.39383e6i		−	0.0333188i	−0.999861	−	0.0166594i	$-0.994697\pi$
$509$		−	4.39383e6i		−	0.0333188i	0.999861	−	0.0166594i	$-0.00530310\pi$
$510$	3.83070e7	−	3.83070e7i	0.288780	−	0.288780i
$511$			9.51587e7i			0.713158i
$512$	9.81514e7	−	9.81514e7i	0.731285	−	0.731285i
$513$	1.02722e8	−	1.02722e8i	0.760872	−	0.760872i
$514$	1.65594e8			1.21942
$515$	−4.42340e7			−0.323843
$516$	2.03917e6	+	2.03917e6i	0.0148424	+	0.0148424i
$517$		−	386481.i		−	0.00279677i
$518$	5.39964e7	−	5.02999e7i	0.388486	−	0.361891i
$519$	3.75949e7			0.268923
$520$	−8.32286e7	+	8.32286e7i	−0.591919	+	0.591919i
$521$			1.90828e7i			0.134936i	0.997721	+	0.0674682i	$0.0214921\pi$
$521$			1.90828e7i			0.134936i	−0.997721	+	0.0674682i	$0.978508\pi$
$522$			1.31660e8i			0.925641i
$523$	8.84073e6	+	8.84073e6i	0.0617992	+	0.0617992i	0.737331	−	0.675532i	$-0.236086\pi$
$523$	8.84073e6	+	8.84073e6i	0.0617992	+	0.0617992i	−0.675532	+	0.737331i	$0.736086\pi$
$524$	−596787.	−	596787.i	−0.00414787	−	0.00414787i
$525$	−1.92084e7			−0.132743
$526$	−2.53464e7	−	2.53464e7i	−0.174164	−	0.174164i
$527$	1.03356e8			0.706158
$528$	−847351.			−0.00575654
$529$		−	1.37448e8i		−	0.928481i
$530$	8.08691e7			0.543194
$531$	−8.64189e7	−	8.64189e7i	−0.577199	−	0.577199i
$532$	−1.76162e6	+	1.76162e6i	−0.0116998	+	0.0116998i
$533$	−2.92911e7	+	2.92911e7i	−0.193443	+	0.193443i
$534$	5.58917e7			0.367049
$535$	7.62706e7	+	7.62706e7i	0.498076	+	0.498076i
$536$	3.71648e7	−	3.71648e7i	0.241344	−	0.241344i
$537$	1.35307e7	+	1.35307e7i	0.0873770	+	0.0873770i
$538$	−1.17405e8	+	1.17405e8i	−0.753944	+	0.753944i
$539$			1.35667e6i			0.00866381i
$540$	−1.63199e6	−	1.63199e6i	−0.0103642	−	0.0103642i
$541$	3.84862e7	+	3.84862e7i	0.243060	+	0.243060i	0.818115	−	0.575055i	$-0.195019\pi$
$541$	3.84862e7	+	3.84862e7i	0.243060	+	0.243060i	−0.575055	+	0.818115i	$0.695019\pi$
$542$	8.60744e7	−	8.60744e7i	0.540600	−	0.540600i
$543$		−	2.29731e7i		−	0.143489i
$544$	9.59726e6			0.0596143
$545$		−	8.60594e7i		−	0.531629i
$546$			4.94730e7i			0.303942i
$547$	1.06360e8	−	1.06360e8i	0.649854	−	0.649854i	−0.303104	−	0.952958i	$-0.598023\pi$
$547$	1.06360e8	−	1.06360e8i	0.649854	−	0.649854i	0.952958	+	0.303104i	$0.0980228\pi$
$548$		−	6.02236e6i		−	0.0365953i
$549$	7.35533e7	−	7.35533e7i	0.444514	−	0.444514i
$550$	721487.	−	721487.i	0.00433651	−	0.00433651i
$551$	2.57740e8			1.54073
$552$	2.20558e7			0.131131
$553$	1.67725e7	+	1.67725e7i	0.0991793	+	0.0991793i
$554$			2.26336e7i			0.133114i
$555$	4.24493e7	−	3.95433e7i	0.248308	−	0.231310i
$556$	2.06372e6			0.0120068
$557$	−2.13265e8	+	2.13265e8i	−1.23411	+	1.23411i	−0.271741	+	0.962370i	$0.587600\pi$
$557$	−2.13265e8	+	2.13265e8i	−1.23411	+	1.23411i	−0.962370	+	0.271741i	$0.912400\pi$
$558$			7.60985e7i			0.437999i
$559$			3.65300e8i			2.09129i
$560$	−4.55742e7	−	4.55742e7i	−0.259511	−	0.259511i
$561$	−898192.	−	898192.i	−0.00508722	−	0.00508722i
$562$	−2.72203e8			−1.53350
$563$	2.07647e8	+	2.07647e8i	1.16359	+	1.16359i	0.983684	+	0.179907i	$0.0575797\pi$
$563$	2.07647e8	+	2.07647e8i	1.16359	+	1.16359i	0.179907	+	0.983684i	$0.442420\pi$
$564$	488276.			0.00272162
$565$	−1.31538e8			−0.729297
$566$		−	3.16495e8i		−	1.74549i
$567$	3.43601e7			0.188497
$568$	4.76082e7	+	4.76082e7i	0.259799	+	0.259799i
$569$	−2.20265e8	+	2.20265e8i	−1.19566	+	1.19566i	−0.220209	+	0.975453i	$0.570674\pi$
$569$	−2.20265e8	+	2.20265e8i	−1.19566	+	1.19566i	−0.975453	+	0.220209i	$0.929326\pi$
$570$	5.52140e7	−	5.52140e7i	0.298143	−	0.298143i
$571$	1.03810e8			0.557611			0.278805	−	0.960348i	$-0.410062\pi$
$571$	1.03810e8			0.557611			0.278805	+	0.960348i	$0.410062\pi$
$572$	46609.7	+	46609.7i	0.000249051	+	0.000249051i
$573$	−5.61881e7	+	5.61881e7i	−0.298662	+	0.298662i
$574$	−1.64417e7	−	1.64417e7i	−0.0869384	−	0.0869384i
$575$	−1.83199e7	+	1.83199e7i	−0.0963648	+	0.0963648i
$576$			1.49628e8i			0.782968i
$577$	2.31423e8	+	2.31423e8i	1.20470	+	1.20470i	0.972720	+	0.231981i	$0.0745207\pi$
$577$	2.31423e8	+	2.31423e8i	1.20470	+	1.20470i	0.231981	+	0.972720i	$0.425479\pi$
$578$	−6.53575e7	−	6.53575e7i	−0.338464	−	0.338464i
$579$	8.33783e7	−	8.33783e7i	0.429554	−	0.429554i
$580$		−	4.09483e6i		−	0.0209871i
$581$	−1.05195e8			−0.536371
$582$		−	2.22629e7i		−	0.112931i
$583$		−	1.89616e6i		−	0.00956904i
$584$	1.89065e8	−	1.89065e8i	0.949235	−	0.949235i
$585$		−	1.26732e8i		−	0.633021i
$586$	−2.76719e7	+	2.76719e7i	−0.137514	+	0.137514i
$587$	−1.90342e8	+	1.90342e8i	−0.941069	+	0.941069i	−0.998358	−	0.0572891i	$-0.981754\pi$
$587$	−1.90342e8	+	1.90342e8i	−0.941069	+	0.941069i	0.0572891	+	0.998358i	$0.481754\pi$
$588$	−1.71401e6			−0.00843103
$589$	1.48972e8			0.729052
$590$	−1.07157e8	−	1.07157e8i	−0.521754	−	0.521754i
$591$		−	4.73378e7i		−	0.229322i
$592$	−2.02147e8	−	7.16441e6i	−0.974321	−	0.0345315i
$593$	−3.25812e8			−1.56244			−0.781220	−	0.624256i	$-0.785402\pi$
$593$	−3.25812e8			−1.56244			−0.781220	+	0.624256i	$0.785402\pi$
$594$	1.52560e6	−	1.52560e6i	0.00727914	−	0.00727914i
$595$		−	9.66173e7i		−	0.458674i
$596$			4.14893e6i			0.0195974i
$597$	−1.39478e8	−	1.39478e8i	−0.655517	−	0.655517i
$598$	4.71846e7	+	4.71846e7i	0.220646	+	0.220646i
$599$	−1.19974e8			−0.558220			−0.279110	−	0.960259i	$-0.590039\pi$
$599$	−1.19974e8			−0.558220			−0.279110	+	0.960259i	$0.590039\pi$
$600$	3.81640e7	+	3.81640e7i	0.176685	+	0.176685i
$601$	1.09503e8			0.504431			0.252215	−	0.967671i	$-0.418841\pi$
$601$	1.09503e8			0.504431			0.252215	+	0.967671i	$0.418841\pi$
$602$	−2.05051e8			−0.939879
$603$			5.65906e7i			0.258103i
$604$	6.14923e6			0.0279068
$605$	−1.09639e8	−	1.09639e8i	−0.495108	−	0.495108i
$606$	−7.60692e7	+	7.60692e7i	−0.341815	+	0.341815i
$607$	1.46952e8	−	1.46952e8i	0.657068	−	0.657068i	−0.297617	−	0.954685i	$-0.596192\pi$
$607$	1.46952e8	−	1.46952e8i	0.657068	−	0.657068i	0.954685	+	0.297617i	$0.0961920\pi$
$608$	1.38331e7			0.0615471
$609$	−5.09554e7	−	5.09554e7i	−0.225599	−	0.225599i
$610$	9.12042e7	−	9.12042e7i	0.401814	−	0.401814i
$611$	4.37352e7	+	4.37352e7i	0.191738	+	0.191738i
$612$	−3.69758e6	+	3.69758e6i	−0.0161311	+	0.0161311i
$613$		−	3.66655e8i		−	1.59176i	−0.605458	−	0.795878i	$-0.707010\pi$
$613$		−	3.66655e8i		−	1.59176i	0.605458	−	0.795878i	$-0.292990\pi$
$614$	2.94998e8	+	2.94998e8i	1.27442	+	1.27442i
$615$	−1.29257e7	−	1.29257e7i	−0.0555684	−	0.0555684i
$616$	−1.09541e6	+	1.09541e6i	−0.00468634	+	0.00468634i
$617$		−	2.90989e8i		−	1.23886i	−0.785053	−	0.619429i	$-0.787364\pi$
$617$		−	2.90989e8i		−	1.23886i	0.785053	−	0.619429i	$-0.212636\pi$
$618$	5.22415e7			0.221335
$619$		−	5.08605e7i		−	0.214441i	−0.994235	−	0.107221i	$-0.965805\pi$
$619$		−	5.08605e7i		−	0.214441i	0.994235	−	0.107221i	$-0.0341951\pi$
$620$		−	2.36678e6i		−	0.00993077i
$621$	−3.87376e7	+	3.87376e7i	−0.161755	+	0.161755i
$622$		−	2.62014e8i		−	1.08881i
$623$	7.04847e7	−	7.04847e7i	0.291495	−	0.291495i
$624$	9.58885e7	−	9.58885e7i	0.394651	−	0.394651i
$625$	5.63295e7			0.230726
$626$	2.15413e8			0.878111
$627$	−1.29461e6	−	1.29461e6i	−0.00525216	−	0.00525216i
$628$		−	1.00053e7i		−	0.0403971i
$629$	−2.06681e8	−	2.21870e8i	−0.830519	−	0.891552i
$630$	7.11373e7			0.284496
$631$	−3.24677e8	+	3.24677e8i	−1.29230	+	1.29230i	−0.358938	+	0.933361i	$0.616861\pi$
$631$	−3.24677e8	+	3.24677e8i	−1.29230	+	1.29230i	−0.933361	+	0.358938i	$0.883139\pi$
$632$		−	6.66485e7i		−	0.264021i
$633$			2.22163e8i			0.875912i
$634$	−3.27474e8	−	3.27474e8i	−1.28502	−	1.28502i
$635$	1.17055e8	+	1.17055e8i	0.457161	+	0.457161i
$636$	2.39558e6			0.00931194
$637$	−1.53525e8	−	1.53525e8i	−0.593964	−	0.593964i
$638$	3.82788e6			0.0147399
$639$	−7.24928e7			−0.277838
$640$			1.76553e8i			0.673495i
$641$	−1.04005e7			−0.0394892			−0.0197446	−	0.999805i	$-0.506285\pi$
$641$	−1.04005e7			−0.0394892			−0.0197446	+	0.999805i	$0.506285\pi$
$642$	−9.00775e7	−	9.00775e7i	−0.340417	−	0.340417i
$643$	−9.63235e7	+	9.63235e7i	−0.362326	+	0.362326i	−0.864669	−	0.502343i	$-0.832472\pi$
$643$	−9.63235e7	+	9.63235e7i	−0.362326	+	0.362326i	0.502343	+	0.864669i	$0.332472\pi$
$644$	664326.	−	664326.i	0.00248728	−	0.00248728i
$645$	−1.61201e8			−0.600742
$646$	−2.88587e8	−	2.88587e8i	−1.07048	−	1.07048i
$647$	8.67713e7	−	8.67713e7i	0.320378	−	0.320378i	−0.528534	−	0.848912i	$-0.677258\pi$
$647$	8.67713e7	−	8.67713e7i	0.320378	−	0.320378i	0.848912	+	0.528534i	$0.177258\pi$
$648$	−6.82682e7	−	6.82682e7i	−0.250896	−	0.250896i
$649$	−2.51254e6	+	2.51254e6i	−0.00919134	+	0.00919134i
$650$			1.63291e8i			0.594596i
$651$	−2.94518e7	−	2.94518e7i	−0.106750	−	0.106750i
$652$	−3.43816e6	−	3.43816e6i	−0.0124046	−	0.0124046i
$653$	1.93803e8	−	1.93803e8i	0.696018	−	0.696018i	−0.267531	−	0.963549i	$-0.586208\pi$
$653$	1.93803e8	−	1.93803e8i	0.696018	−	0.696018i	0.963549	+	0.267531i	$0.0862079\pi$
$654$			1.01638e8i			0.363349i
$655$	4.71773e7			0.167884
$656$			6.37347e7i			0.225769i
$657$			2.87889e8i			1.01515i
$658$	−2.45495e7	+	2.45495e7i	−0.0861719	+	0.0861719i
$659$			4.66139e8i			1.62877i	0.580327	+	0.814383i	$0.302925\pi$
$659$			4.66139e8i			1.62877i	−0.580327	+	0.814383i	$0.697075\pi$
$660$	−20568.1	+	20568.1i	−7.15421e−5	+	7.15421e-5i
$661$	9.50537e7	−	9.50537e7i	0.329128	−	0.329128i	−0.523127	−	0.852255i	$-0.675235\pi$
$661$	9.50537e7	−	9.50537e7i	0.329128	−	0.329128i	0.852255	+	0.523127i	$0.175235\pi$
$662$	4.28759e8			1.47788
$663$	2.03284e8			0.697528
$664$	2.09005e8	+	2.09005e8i	0.713925	+	0.713925i
$665$		−	1.39260e8i		−	0.473545i
$666$	1.63358e8	−	1.52175e8i	0.552991	−	0.515135i
$667$	−9.71967e7			−0.327547
$668$	2.01841e6	−	2.01841e6i	0.00677141	−	0.00677141i
$669$			1.08487e8i			0.362327i
$670$			7.01709e7i			0.233310i
$671$	−2.13849e6	−	2.13849e6i	−0.00707846	−	0.00707846i
$672$	−2.73480e6	−	2.73480e6i	−0.00901193	−	0.00901193i
$673$	−1.28147e8			−0.420401			−0.210200	−	0.977658i	$-0.567412\pi$
$673$	−1.28147e8			−0.420401			−0.210200	+	0.977658i	$0.567412\pi$
$674$	2.33490e8	+	2.33490e8i	0.762585	+	0.762585i
$675$	−1.34059e8			−0.435896
$676$	−2.99018e6			−0.00967960
$677$			5.69848e8i			1.83651i	0.395992	+	0.918254i	$0.370401\pi$
$677$			5.69848e8i			1.83651i	−0.395992	+	0.918254i	$0.629599\pi$
$678$	1.55349e8			0.498448
$679$	−2.80756e7	−	2.80756e7i	−0.0896851	−	0.0896851i
$680$	−1.91964e8	+	1.91964e8i	−0.610509	+	0.610509i
$681$	1.26749e8	−	1.26749e8i	0.401332	−	0.401332i
$682$	2.21248e6			0.00697472
$683$	3.71087e7	+	3.71087e7i	0.116470	+	0.116470i	0.762940	−	0.646470i	$-0.223755\pi$
$683$	3.71087e7	+	3.71087e7i	0.116470	+	0.116470i	−0.646470	+	0.762940i	$0.723755\pi$
$684$	−5.32953e6	+	5.32953e6i	−0.0166541	+	0.0166541i
$685$	2.38040e8	+	2.38040e8i	0.740592	+	0.740592i
$686$	2.07375e8	−	2.07375e8i	0.642367	−	0.642367i
$687$		−	2.15327e8i		−	0.664092i
$688$	3.97429e8	+	3.97429e8i	1.22038	+	1.22038i
$689$	2.14574e8	+	2.14574e8i	0.656024	+	0.656024i
$690$	−2.08218e7	+	2.08218e7i	−0.0633827	+	0.0633827i
$691$			2.71149e8i			0.821815i	0.911677	+	0.410908i	$0.134788\pi$
$691$			2.71149e8i			0.821815i	−0.911677	+	0.410908i	$0.865212\pi$
$692$	−4.49968e6			−0.0135789
$693$		−	1.66797e6i		−	0.00501175i
$694$		−	5.27142e8i		−	1.57706i
$695$	−8.15706e7	+	8.15706e7i	−0.242985	+	0.242985i
$696$			2.02481e8i			0.600559i
$697$	−6.75587e7	+	6.75587e7i	−0.199519	+	0.199519i
$698$	7.17456e7	−	7.17456e7i	0.210974	−	0.210974i
$699$	−1.91045e8			−0.559377
$700$	2.29902e6			0.00670269
$701$	−9.10981e7	−	9.10981e7i	−0.264457	−	0.264457i	0.562405	−	0.826862i	$-0.309876\pi$
$701$	−9.10981e7	−	9.10981e7i	−0.264457	−	0.264457i	−0.826862	+	0.562405i	$0.809876\pi$
$702$			3.45281e8i			0.998070i
$703$	−2.97901e8	−	3.19793e8i	−0.857445	−	0.920457i
$704$	4.35026e6			0.0124680
$705$	−1.92996e7	+	1.92996e7i	−0.0550784	+	0.0550784i
$706$		−	5.13926e8i		−	1.46045i
$707$			1.91861e8i			0.542910i
$708$	−3.17432e6	−	3.17432e6i	−0.00894439	−	0.00894439i
$709$	1.96609e8	+	1.96609e8i	0.551651	+	0.551651i	0.926917	−	0.375266i	$-0.122449\pi$
$709$	1.96609e8	+	1.96609e8i	0.551651	+	0.551651i	−0.375266	+	0.926917i	$0.622449\pi$
$710$	−8.98892e7			−0.251150
$711$	5.07426e7	+	5.07426e7i	0.141177	+	0.141177i
$712$	−2.80084e8			−0.775976
$713$	−5.61789e7			−0.154990
$714$			1.14108e8i			0.313487i
$715$	−3.68459e6			−0.0100803
$716$	−1.61947e6	−	1.61947e6i	−0.00441198	−	0.00441198i
$717$	−1.47594e8	+	1.47594e8i	−0.400416	+	0.400416i
$718$	1.47332e8	−	1.47332e8i	0.398037	−	0.398037i
$719$	5.50763e8			1.48176			0.740880	−	0.671637i	$-0.234409\pi$
$719$	5.50763e8			1.48176			0.740880	+	0.671637i	$0.234409\pi$
$720$	−1.37878e8	−	1.37878e8i	−0.369401	−	0.369401i
$721$	6.58814e7	−	6.58814e7i	0.175775	−	0.175775i
$722$	−1.53101e8	−	1.53101e8i	−0.406786	−	0.406786i
$723$	1.26636e8	−	1.26636e8i	0.335076	−	0.335076i
$724$			2.74962e6i			0.00724530i
$725$	−1.68183e8	−	1.68183e8i	−0.441336	−	0.441336i
$726$	1.29487e8	+	1.29487e8i	0.338388	+	0.338388i
$727$	5.17158e8	−	5.17158e8i	1.34592	−	1.34592i	0.455881	−	0.890041i	$-0.349324\pi$
$727$	5.17158e8	−	5.17158e8i	1.34592	−	1.34592i	0.890041	−	0.455881i	$-0.150676\pi$
$728$		−	2.47919e8i		−	0.642562i
$729$	−5.66383e7			−0.146193
$730$			3.56975e8i			0.917633i
$731$			8.42550e8i			2.15697i
$732$	2.70174e6	−	2.70174e6i	0.00688827	−	0.00688827i
$733$		−	5.47590e8i		−	1.39041i	−0.718810	−	0.695207i	$-0.755313\pi$
$733$		−	5.47590e8i		−	1.39041i	0.718810	−	0.695207i	$-0.244687\pi$
$734$	−1.47936e8	+	1.47936e8i	−0.374097	+	0.374097i
$735$	6.77480e7	−	6.77480e7i	0.170622	−	0.170622i
$736$	−5.21660e6			−0.0130844
$737$	1.64531e6			0.00411004
$738$	−4.97421e7	−	4.97421e7i	−0.123753	−	0.123753i
$739$		−	2.95892e8i		−	0.733163i	−0.930386	−	0.366581i	$-0.880528\pi$
$739$		−	2.95892e8i		−	0.733163i	0.930386	−	0.366581i	$-0.119472\pi$
$740$	−5.08069e6	+	4.73288e6i	−0.0125380	+	0.0116797i
$741$	2.93004e8			0.720143
$742$	−1.20445e8	+	1.20445e8i	−0.294834	+	0.294834i
$743$		−	5.11304e8i		−	1.24656i	−0.781999	−	0.623280i	$-0.785800\pi$
$743$		−	5.11304e8i		−	1.24656i	0.781999	−	0.623280i	$-0.214200\pi$
$744$			1.17032e8i			0.284176i
$745$	−1.63991e8	−	1.63991e8i	−0.396599	−	0.396599i
$746$	3.30666e7	+	3.30666e7i	0.0796478	+	0.0796478i
$747$	−3.18251e8			−0.763498
$748$	107503.	+	107503.i	0.000256872	+	0.000256872i
$749$	−2.27192e8			−0.540690
$750$	−2.13460e8			−0.505980
$751$		−	6.90389e8i		−	1.62995i	−0.579497	−	0.814974i	$-0.696751\pi$
$751$		−	6.90389e8i		−	1.62995i	0.579497	−	0.814974i	$-0.303249\pi$
$752$	9.51637e7			0.223778
$753$	−2.40879e8	−	2.40879e8i	−0.564175	−	0.564175i
$754$	−4.33173e8	+	4.33173e8i	−1.01052	+	1.01052i
$755$	−2.43055e8	+	2.43055e8i	−0.564759	+	0.564759i
$756$	4.86132e6			0.0112509
$757$	3.44468e7	+	3.44468e7i	0.0794074	+	0.0794074i	0.745695	−	0.666288i	$-0.232118\pi$
$757$	3.44468e7	+	3.44468e7i	0.0794074	+	0.0794074i	−0.666288	+	0.745695i	$0.732118\pi$
$758$	2.03614e8	−	2.03614e8i	0.467521	−	0.467521i
$759$	488213.	+	488213.i	0.00111656	+	0.00111656i
$760$	−2.76688e8	+	2.76688e8i	−0.630302	+	0.630302i
$761$			1.99137e8i			0.451854i	0.974144	+	0.225927i	$0.0725410\pi$
$761$			1.99137e8i			0.451854i	−0.974144	+	0.225927i	$0.927459\pi$
$762$	−1.38245e8	−	1.38245e8i	−0.312453	−	0.312453i
$763$	1.28175e8	+	1.28175e8i	0.288557	+	0.288557i
$764$	6.72507e6	−	6.72507e6i	0.0150805	−	0.0150805i
$765$		−	2.92302e8i		−	0.652901i
$766$	1.85079e8			0.411786
$767$		−	5.68651e8i		−	1.26026i
$768$			1.61038e7i			0.0355503i
$769$	2.23559e8	−	2.23559e8i	0.491602	−	0.491602i	−0.417209	−	0.908811i	$-0.636992\pi$
$769$	2.23559e8	−	2.23559e8i	0.491602	−	0.491602i	0.908811	+	0.417209i	$0.136992\pi$
$770$		−	2.06824e6i		−	0.00453032i
$771$	−1.93890e8	+	1.93890e8i	−0.423051	+	0.423051i
$772$	−9.97943e6	+	9.97943e6i	−0.0216897	+	0.0216897i
$773$	4.65955e8			1.00880			0.504400	−	0.863470i	$-0.331714\pi$
$773$	4.65955e8			1.00880			0.504400	+	0.863470i	$0.331714\pi$
$774$	−6.20352e8			−1.33787
$775$	−9.72087e7	−	9.72087e7i	−0.208833	−	0.208833i
$776$			1.11564e8i			0.238747i
$777$	−4.32807e6	+	1.22118e8i	−0.00922638	+	0.260326i
$778$	−5.79888e8			−1.23142
$779$	−9.73761e7	+	9.73761e7i	−0.205987	+	0.205987i
$780$		−	4.65508e6i		−	0.00980941i
$781$			2.10765e6i			0.00442431i
$782$	1.08829e8	+	1.08829e8i	0.227576	+	0.227576i
$783$	−3.55626e8	−	3.55626e8i	−0.740813	−	0.740813i
$784$	−3.34056e8			−0.693219
$785$	3.95469e8	+	3.95469e8i	0.817530	+	0.817530i
$786$	−5.57176e7			−0.114743
$787$	−4.45279e8			−0.913499			−0.456749	−	0.889595i	$-0.650986\pi$
$787$	−4.45279e8			−0.913499			−0.456749	+	0.889595i	$0.650986\pi$
$788$			5.66579e6i			0.0115793i
$789$	5.93551e7			0.120845
$790$	6.29196e7	+	6.29196e7i	0.127616	+	0.127616i
$791$	1.95910e8	−	1.95910e8i	0.395847	−	0.395847i
$792$	−3.31400e6	+	3.31400e6i	−0.00667078	+	0.00667078i
$793$	4.83993e8			0.970554
$794$	2.91240e8	+	2.91240e8i	0.581820	+	0.581820i
$795$	−9.46880e7	+	9.46880e7i	−0.188449	+	0.188449i
$796$	1.66940e7	+	1.66940e7i	0.0330994	+	0.0330994i
$797$	−7.18682e7	+	7.18682e7i	−0.141959	+	0.141959i	−0.774515	−	0.632556i	$-0.782006\pi$
$797$	−7.18682e7	+	7.18682e7i	−0.141959	+	0.141959i	0.632556	+	0.774515i	$0.282006\pi$
$798$			1.64469e8i			0.323651i
$799$	1.00874e8	+	1.00874e8i	0.197759	+	0.197759i
$800$	−9.02649e6	−	9.02649e6i	−0.0176299	−	0.0176299i
$801$	2.13241e8	−	2.13241e8i	0.414929	−	0.414929i
$802$		−	3.12813e8i		−	0.606404i
$803$	8.37007e6			0.0161653
$804$			2.07867e6i			0.00399961i
$805$			5.25164e7i			0.100672i
$806$	−2.50370e8	+	2.50370e8i	−0.478165	+	0.478165i
$807$		−	2.74934e8i		−	0.523128i
$808$	3.81197e8	−	3.81197e8i	0.722629	−	0.722629i
$809$	4.64493e7	−	4.64493e7i	0.0877271	−	0.0877271i	−0.661881	−	0.749609i	$-0.730242\pi$
$809$	4.64493e7	−	4.64493e7i	0.0877271	−	0.0877271i	0.749609	+	0.661881i	$0.230242\pi$
$810$	1.28897e8			0.242543
$811$	−5.67850e8			−1.06456			−0.532281	−	0.846568i	$-0.678665\pi$
$811$	−5.67850e8			−1.06456			−0.532281	+	0.846568i	$0.678665\pi$
$812$	6.09877e6	+	6.09877e6i	0.0113913	+	0.0113913i
$813$			2.01566e8i			0.375098i
$814$	−4.42433e6	−	4.74947e6i	−0.00820304	−	0.00880586i
$815$	2.71794e8			0.502073
$816$	2.21163e8	−	2.21163e8i	0.407045	−	0.407045i
$817$			1.21441e9i			2.22690i
$818$			2.48060e8i			0.453208i
$819$	1.88752e8	+	1.88752e8i	0.343590	+	0.343590i
$820$	1.54706e6	+	1.54706e6i	0.00280585	+	0.00280585i
$821$	6.60305e8			1.19321			0.596603	−	0.802537i	$-0.296517\pi$
$821$	6.60305e8			1.19321			0.596603	+	0.802537i	$0.296517\pi$
$822$	−2.81132e8	−	2.81132e8i	−0.506168	−	0.506168i
$823$	3.23916e8			0.581076			0.290538	−	0.956864i	$-0.406166\pi$
$823$	3.23916e8			0.581076			0.290538	+	0.956864i	$0.406166\pi$
$824$	−2.61792e8			−0.467923
$825$			1.68955e6i			0.00300891i
$826$	3.19197e8			0.566393
$827$	−1.29942e8	−	1.29942e8i	−0.229739	−	0.229739i	0.582845	−	0.812584i	$-0.301940\pi$
$827$	−1.29942e8	−	1.29942e8i	−0.229739	−	0.229739i	−0.812584	+	0.582845i	$0.801940\pi$
$828$	2.00982e6	−	2.00982e6i	0.00354052	−	0.00354052i
$829$	−1.77410e8	+	1.77410e8i	−0.311397	+	0.311397i	−0.845451	−	0.534054i	$-0.820668\pi$
$829$	−1.77410e8	+	1.77410e8i	−0.311397	+	0.311397i	0.534054	+	0.845451i	$0.320668\pi$
$830$	−3.94623e8			−0.690158
$831$	−2.65012e7	−	2.65012e7i	−0.0461810	−	0.0461810i
$832$	−4.92287e8	+	4.92287e8i	−0.854769	+	0.854769i
$833$	−3.54099e8	−	3.54099e8i	−0.612618	−	0.612618i
$834$	9.63370e7	−	9.63370e7i	0.166071	−	0.166071i
$835$			1.59559e8i			0.274071i
$836$	154950.	+	154950.i	0.000265200	+	0.000265200i
$837$	−2.05549e8	−	2.05549e8i	−0.350542	−	0.350542i
$838$	−1.94826e8	+	1.94826e8i	−0.331065	+	0.331065i
$839$		−	7.05031e7i		−	0.119378i	−0.998217	−	0.0596888i	$-0.980989\pi$
$839$		−	7.05031e7i		−	0.119378i	0.998217	−	0.0596888i	$-0.0190108\pi$
$840$	1.09402e8			0.184582
$841$		−	2.97480e8i		−	0.500115i
$842$		−	4.85705e8i		−	0.813647i
$843$	3.18717e8	−	3.18717e8i	0.532014	−	0.532014i
$844$		−	2.65904e7i		−	0.0442280i
$845$	1.18190e8	−	1.18190e8i	0.195889	−	0.195889i
$846$	−7.42710e7	+	7.42710e7i	−0.122662	+	0.122662i
$847$	3.26590e8			0.537467
$848$	4.66893e8			0.765650
$849$	3.70578e8	+	3.70578e8i	0.605558	+	0.605558i
$850$			3.76624e8i			0.613269i
$851$	1.12342e8	+	1.20598e8i	0.182286	+	0.195681i
$852$	−2.66279e6			−0.00430544
$853$	3.75914e8	−	3.75914e8i	0.605677	−	0.605677i	−0.336136	−	0.941813i	$-0.609120\pi$
$853$	3.75914e8	−	3.75914e8i	0.605677	−	0.605677i	0.941813	+	0.336136i	$0.109120\pi$
$854$			2.71676e8i			0.436192i
$855$		−	4.21311e8i		−	0.674069i
$856$	4.51396e8	+	4.51396e8i	0.719674	+	0.719674i
$857$	7.06187e8	+	7.06187e8i	1.12196	+	1.12196i	0.991446	+	0.130514i	$0.0416627\pi$
$857$	7.06187e8	+	7.06187e8i	1.12196	+	1.12196i	0.130514	+	0.991446i	$0.458337\pi$
$858$	4.35160e6			0.00688949
$859$	−2.13260e8	−	2.13260e8i	−0.336456	−	0.336456i	0.518575	−	0.855032i	$-0.326463\pi$
$859$	−2.13260e8	−	2.13260e8i	−0.336456	−	0.336456i	−0.855032	+	0.518575i	$0.826463\pi$
$860$	1.92939e7			0.0303337
$861$	3.85026e7			0.0603227
$862$			3.72318e8i			0.581289i
$863$	−1.12771e8			−0.175454			−0.0877271	−	0.996145i	$-0.527960\pi$
$863$	−1.12771e8			−0.175454			−0.0877271	+	0.996145i	$0.527960\pi$
$864$	−1.90867e7	−	1.90867e7i	−0.0295930	−	0.0295930i
$865$	1.77855e8	−	1.77855e8i	0.274800	−	0.274800i
$866$	3.26291e8	−	3.26291e8i	0.502402	−	0.502402i
$867$	1.53052e8			0.234845
$868$	3.52504e6	+	3.52504e6i	0.00539021	+	0.00539021i
$869$	1.47529e6	−	1.47529e6i	0.00224811	−	0.00224811i
$870$	−1.91152e8	−	1.91152e8i	−0.290283	−	0.290283i
$871$	−1.86188e8	+	1.86188e8i	−0.281771	+	0.281771i
$872$		−	5.09329e8i		−	0.768155i
$873$	−8.49388e7	−	8.49388e7i	−0.127662	−	0.127662i
$874$	1.56862e8	+	1.56862e8i	0.234954	+	0.234954i
$875$	−2.69193e8	+	2.69193e8i	−0.401828	+	0.401828i
$876$			1.05747e7i			0.0157309i
$877$	−1.13487e9			−1.68247			−0.841235	−	0.540669i	$-0.818171\pi$
$877$	−1.13487e9			−1.68247			−0.841235	+	0.540669i	$0.818171\pi$
$878$			1.20796e9i			1.78472i
$879$		−	6.48010e7i		−	0.0954147i
$880$	−4.00867e6	+	4.00867e6i	−0.00588236	+	0.00588236i
$881$		−	4.84700e8i		−	0.708835i	−0.935087	−	0.354418i	$-0.884679\pi$
$881$		−	4.84700e8i		−	0.708835i	0.935087	−	0.354418i	$-0.115321\pi$
$882$	2.60715e8	−	2.60715e8i	0.379980	−	0.379980i
$883$	−3.29614e8	+	3.29614e8i	−0.478767	+	0.478767i	−0.904737	−	0.425970i	$-0.859933\pi$
$883$	−3.29614e8	+	3.29614e8i	−0.478767	+	0.478767i	0.425970	+	0.904737i	$0.359933\pi$
$884$	−2.43307e7			−0.0352207
$885$	2.50937e8			0.362021
$886$	−9.00830e8	−	9.00830e8i	−1.29521	−	1.29521i
$887$			4.49810e8i			0.644553i	0.946646	+	0.322277i	$0.104448\pi$
$887$			4.49810e8i			0.644553i	−0.946646	+	0.322277i	$0.895552\pi$
$888$	2.51229e8	−	2.34031e8i	0.358783	−	0.334222i
$889$	−3.48680e8			−0.496274
$890$	2.64414e8	−	2.64414e8i	0.375071	−	0.375071i
$891$		−	3.02228e6i		−	0.00427270i
$892$		−	1.29847e7i		−	0.0182952i
$893$	1.45395e8	+	1.45395e8i	0.204171	+	0.204171i
$894$	1.93678e8	+	1.93678e8i	0.271061	+	0.271061i
$895$	1.28022e8			0.178574
$896$	−2.62954e8	−	2.62954e8i	−0.365558	−	0.365558i
$897$	−1.10495e8			−0.153096
$898$	1.31490e9			1.81578
$899$		−	5.15744e8i		−	0.709832i
$900$	6.95536e6			0.00954096
$901$	4.94907e8	+	4.94907e8i	0.676626	+	0.676626i
$902$	−1.44620e6	+	1.44620e6i	−0.00197065	+	0.00197065i
$903$	2.40090e8	−	2.40090e8i	0.326070	−	0.326070i
$904$	−7.78484e8			−1.05377
$905$	−1.08681e8	−	1.08681e8i	−0.146626	−	0.146626i
$906$	2.87054e8	−	2.87054e8i	0.385993	−	0.385993i
$907$	6.94864e8	+	6.94864e8i	0.931275	+	0.931275i	0.997786	−	0.0665108i	$-0.0211867\pi$
$907$	6.94864e8	+	6.94864e8i	0.931275	+	0.931275i	−0.0665108	+	0.997786i	$0.521187\pi$
$908$	−1.51704e7	+	1.51704e7i	−0.0202647	+	0.0202647i
$909$			5.80446e8i			0.772806i
$910$	2.34048e8	+	2.34048e8i	0.310585	+	0.310585i
$911$	−6.52782e8	−	6.52782e8i	−0.863402	−	0.863402i	0.128329	−	0.991732i	$-0.459039\pi$
$911$	−6.52782e8	−	6.52782e8i	−0.863402	−	0.863402i	−0.991732	+	0.128329i	$0.959039\pi$
$912$	3.18775e8	−	3.18775e8i	0.420242	−	0.420242i
$913$			9.25282e6i			0.0121580i
$914$	−3.71179e8			−0.486121
$915$			2.13578e8i			0.278801i
$916$			2.57722e7i			0.0335324i
$917$	−7.02651e7	+	7.02651e7i	−0.0911237	+	0.0911237i
$918$			7.96377e8i			1.02942i
$919$	−2.03247e8	+	2.03247e8i	−0.261865	+	0.261865i	−0.825812	−	0.563946i	$-0.809283\pi$
$919$	−2.03247e8	+	2.03247e8i	−0.261865	+	0.261865i	0.563946	+	0.825812i	$0.309283\pi$
$920$	1.04342e8	−	1.04342e8i	0.133997	−	0.133997i
$921$	−6.90814e8			−0.884265
$922$	6.26806e8			0.799725
$923$	−2.38507e8	−	2.38507e8i	−0.303317	−	0.303317i
$924$		−	61267.5i		−	7.76630e-5i
$925$	−1.42852e7	+	4.03064e8i	−0.0180494	+	0.509271i
$926$	4.73660e8			0.596532
$927$	1.99315e8	−	1.99315e8i	0.250207	−	0.250207i
$928$		−	4.78904e7i		−	0.0599245i
$929$			2.68745e8i			0.335192i	0.985856	+	0.167596i	$0.0536004\pi$
$929$			2.68745e8i			0.335192i	−0.985856	+	0.167596i	$0.946400\pi$
$930$	−1.10484e8	−	1.10484e8i	−0.137357	−	0.137357i
$931$	−5.10382e8	−	5.10382e8i	−0.632479	−	0.632479i
$932$	2.28659e7			0.0282449
$933$	3.06787e8	+	3.06787e8i	0.377739	+	0.377739i
$934$	5.67708e8			0.696762
$935$	−8.49837e6			−0.0103968
$936$		−	7.50042e8i		−	0.914656i
$937$	−5.00079e8			−0.607883			−0.303942	−	0.952691i	$-0.598303\pi$
$937$	−5.00079e8			−0.607883			−0.303942	+	0.952691i	$0.598303\pi$
$938$	−1.04511e8	−	1.04511e8i	−0.126635	−	0.126635i
$939$	−2.52223e8	+	2.52223e8i	−0.304641	+	0.304641i
$940$	2.30994e6	−	2.30994e6i	0.00278111	−	0.00278111i
$941$	−6.27638e8			−0.753252			−0.376626	−	0.926365i	$-0.622916\pi$
$941$	−6.27638e8			−0.753252			−0.376626	+	0.926365i	$0.622916\pi$
$942$	−4.67059e8	−	4.67059e8i	−0.558752	−	0.558752i
$943$	3.67216e7	−	3.67216e7i	0.0437912	−	0.0437912i
$944$	−6.18666e8	−	6.18666e8i	−0.735428	−	0.735428i
$945$	−1.92149e8	+	1.92149e8i	−0.227689	+	0.227689i
$946$			1.80361e7i			0.0213044i
$947$	−5.03769e8	−	5.03769e8i	−0.593173	−	0.593173i	0.345314	−	0.938487i	$-0.387772\pi$
$947$	−5.03769e8	−	5.03769e8i	−0.593173	−	0.593173i	−0.938487	+	0.345314i	$0.887772\pi$
$948$	1.86386e6	+	1.86386e6i	0.00218771	+	0.00218771i
$949$	−9.47179e8	+	9.47179e8i	−1.10824	+	1.10824i
$950$			5.42849e8i			0.633152i
$951$	7.66865e8			0.891615
$952$		−	5.71815e8i		−	0.662742i
$953$			4.19940e8i			0.485186i	0.970128	+	0.242593i	$0.0779979\pi$
$953$			4.19940e8i			0.485186i	−0.970128	+	0.242593i	$0.922002\pi$
$954$	−3.64389e8	+	3.64389e8i	−0.419682	+	0.419682i
$955$			5.31631e8i			0.610380i
$956$	1.76653e7	−	1.76653e7i	0.0202185	−	0.0202185i
$957$	−4.48198e6	+	4.48198e6i	−0.00511369	+	0.00511369i
$958$	1.75487e8			0.199595
$959$	−7.09067e8			−0.803954
$960$	−2.17238e8	−	2.17238e8i	−0.245540	−	0.245540i
$961$			5.89407e8i			0.664118i
$962$	1.03813e9	+	3.67930e7i	1.16608	+	0.0413276i
$963$	−6.87338e8			−0.769646
$964$	−1.51569e7	+	1.51569e7i	−0.0169192	+	0.0169192i
$965$		−	7.88895e8i		−	0.877885i
$966$		−	6.20232e7i		−	0.0688055i
$967$	−1.42578e8	−	1.42578e8i	−0.157679	−	0.157679i	0.623859	−	0.781537i	$-0.285564\pi$
$967$	−1.42578e8	−	1.42578e8i	−0.157679	−	0.157679i	−0.781537	+	0.623859i	$0.785564\pi$
$968$	−6.48882e8	−	6.48882e8i	−0.715385	−	0.715385i
$969$	6.75802e8			0.742759
$970$	−1.05322e8	−	1.05322e8i	−0.115399	−	0.115399i
$971$	−7.85345e8			−0.857833			−0.428916	−	0.903344i	$-0.641104\pi$
$971$	−7.85345e8			−0.857833			−0.428916	+	0.903344i	$0.641104\pi$
$972$	2.30391e7			0.0250880
$973$		−	2.42980e8i		−	0.263774i
$974$	−8.02472e8			−0.868466
$975$	−1.91194e8	−	1.91194e8i	−0.206281	−	0.206281i
$976$	5.26562e8	−	5.26562e8i	0.566370	−	0.566370i
$977$	4.74517e8	−	4.74517e8i	0.508824	−	0.508824i	−0.405341	−	0.914165i	$-0.632847\pi$
$977$	4.74517e8	−	4.74517e8i	0.508824	−	0.508824i	0.914165	+	0.405341i	$0.132847\pi$
$978$	−3.20995e8			−0.343149
$979$	−6.19976e6	−	6.19976e6i	−0.00660735	−	0.00660735i
$980$	−8.10866e6	+	8.10866e6i	−0.00861531	+	0.00861531i
$981$	3.87776e8	+	3.87776e8i	0.410747	+	0.410747i
$982$	1.14386e9	−	1.14386e9i	1.20792	−	1.20792i
$983$		−	2.53355e8i		−	0.266729i	−0.991067	−	0.133364i	$-0.957422\pi$
$983$		−	2.53355e8i		−	0.266729i	0.991067	−	0.133364i	$-0.0425780\pi$
$984$	−7.64986e7	−	7.64986e7i	−0.0802912	−	0.0802912i
$985$	−2.23946e8	−	2.23946e8i	−0.234334	−	0.234334i
$986$	−9.99096e8	+	9.99096e8i	−1.04226	+	1.04226i
$987$		−	5.74891e7i		−	0.0597908i
$988$	−3.50692e7			−0.0363626
$989$		−	4.57968e8i		−	0.473420i
$990$		−	6.25717e6i		−	0.00644870i
$991$	7.35436e8	−	7.35436e8i	0.755656	−	0.755656i	−0.219873	−	0.975529i	$-0.570564\pi$
$991$	7.35436e8	−	7.35436e8i	0.755656	−	0.755656i	0.975529	+	0.219873i	$0.0705642\pi$
$992$		−	2.76803e7i		−	0.0283554i
$993$	−5.02025e8	+	5.02025e8i	−0.512717	+	0.512717i
$994$	1.33879e8	−	1.33879e8i	0.136319	−	0.136319i
$995$	−1.31969e9			−1.33969
$996$	−1.16899e7			−0.0118313
$997$	9.08045e8	+	9.08045e8i	0.916267	+	0.916267i	0.996756	−	0.0804887i	$-0.0256481\pi$
$997$	9.08045e8	+	9.08045e8i	0.916267	+	0.916267i	−0.0804887	+	0.996756i	$0.525648\pi$
$998$		−	1.20450e9i		−	1.21176i
$999$	−3.02064e7	+	8.52286e8i	−0.0302972	+	0.854848i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.7.d.a.6.6	✓	36
37.31	odd	4	inner	37.7.d.a.31.6	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.7.d.a.6.6	✓	36	1.1	even	1	trivial
37.7.d.a.31.6	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)

\(f(q)\)	\(=\)	\(q+(-5.58722 + 5.58722i) q^{2} -13.0839i q^{3} +1.56600i q^{4} +(-61.8977 - 61.8977i) q^{5} +(73.1027 + 73.1027i) q^{6} +184.379 q^{7} +(-366.331 - 366.331i) q^{8} +557.811 q^{9} +O(q^{10})\)	\(q+(-5.58722 + 5.58722i) q^{2} -13.0839i q^{3} +1.56600i q^{4} +(-61.8977 - 61.8977i) q^{5} +(73.1027 + 73.1027i) q^{6} +184.379 q^{7} +(-366.331 - 366.331i) q^{8} +557.811 q^{9} +691.671 q^{10} -16.2178i q^{11} +20.4894 q^{12} +(1835.25 + 1835.25i) q^{13} +(-1030.16 + 1030.16i) q^{14} +(-809.864 + 809.864i) q^{15} +3993.32 q^{16} +(4232.92 + 4232.92i) q^{17} +(-3116.61 + 3116.61i) q^{18} +(6101.14 + 6101.14i) q^{19} +(96.9315 - 96.9315i) q^{20} -2412.40i q^{21} +(90.6122 + 90.6122i) q^{22} +(-2300.81 - 2300.81i) q^{23} +(-4793.05 + 4793.05i) q^{24} -7962.36i q^{25} -20507.8 q^{26} -16836.5i q^{27} +288.736i q^{28} +(21122.3 - 21122.3i) q^{29} -9049.77i q^{30} +(12208.5 - 12208.5i) q^{31} +(1133.65 - 1133.65i) q^{32} -212.192 q^{33} -47300.5 q^{34} +(-11412.6 - 11412.6i) q^{35} +873.530i q^{36} +(-50621.2 - 1794.10i) q^{37} -68176.8 q^{38} +(24012.2 - 24012.2i) q^{39} +45350.1i q^{40} +15960.3i q^{41} +(13478.6 + 13478.6i) q^{42} +(99523.4 + 99523.4i) q^{43} +25.3970 q^{44} +(-34527.2 - 34527.2i) q^{45} +25710.2 q^{46} +23830.7 q^{47} -52248.3i q^{48} -83653.5 q^{49} +(44487.4 + 44487.4i) q^{50} +(55383.2 - 55383.2i) q^{51} +(-2873.99 + 2873.99i) q^{52} +116918. q^{53} +(94069.4 + 94069.4i) q^{54} +(-1003.84 + 1003.84i) q^{55} +(-67543.7 - 67543.7i) q^{56} +(79826.9 - 79826.9i) q^{57} +236030. i q^{58} +(-154925. - 154925. i) q^{59} +(-1268.24 - 1268.24i) q^{60} +(131861. - 131861. i) q^{61} +136423. i q^{62} +102848. q^{63} +268241. i q^{64} -227195. i q^{65} +(1185.56 - 1185.56i) q^{66} +101451. i q^{67} +(-6628.74 + 6628.74i) q^{68} +(-30103.6 + 30103.6i) q^{69} +127529. q^{70} -129959. q^{71} +(-204344. - 204344. i) q^{72} +516105. i q^{73} +(292856. - 272808. i) q^{74} -104179. q^{75} +(-9554.36 + 9554.36i) q^{76} -2990.21i q^{77} +268323. i q^{78} +(90967.4 + 90967.4i) q^{79} +(-247177. - 247177. i) q^{80} +186356. q^{81} +(-89173.7 - 89173.7i) q^{82} -570536. q^{83} +3777.80 q^{84} -524016. i q^{85} -1.11212e6 q^{86} +(-276363. - 276363. i) q^{87} +(-5941.08 + 5941.08i) q^{88} +(382282. - 382282. i) q^{89} +385822. q^{90} +(338380. + 338380. i) q^{91} +(3603.05 - 3603.05i) q^{92} +(-159735. - 159735. i) q^{93} +(-133147. + 133147. i) q^{94} -755293. i q^{95} +(-14832.5 - 14832.5i) q^{96} +(-152272. - 152272. i) q^{97} +(467390. - 467390. i) q^{98} -9046.45i 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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