LMFDB - Embedded newform 74.7.d.b.31.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,7,Mod(31,74)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(74, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("74.31");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	74.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:	$17.0240021879$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 10424 x^{18} + 44844916 x^{16} + 103219343022 x^{14} + 138101513095620 x^{12} + \cdots + 73\!\cdots\!36 $ x^20 + 10424x^18 + 44844916x^16 + 103219343022x^14 + 138101513095620x^12 + 109787124347520192x^10 + 51172837440825906441x^8 + 13199761586736849750156x^6 + 1629475196758519705300656x^4 + 65381450766316829487245376*x^2 + 736627437450607950694158336
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{9}\cdot 3^{2}\cdot 11^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			31.3
Root			$26.0545i$ of defining polynomial
Character	$\chi$	$=$	74.31
Dual form			74.7.d.b.43.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.00000 - 4.00000i) q^{2} -23.0545i q^{3} +32.0000i q^{4} +(-19.9104 + 19.9104i) q^{5} +(-92.2182 + 92.2182i) q^{6} +259.314 q^{7} +(128.000 - 128.000i) q^{8} +197.488 q^{9} +O(q^{10})$	\(q+(-4.00000 - 4.00000i) q^{2} -23.0545i q^{3} +32.0000i q^{4} +(-19.9104 + 19.9104i) q^{5} +(-92.2182 + 92.2182i) q^{6} +259.314 q^{7} +(128.000 - 128.000i) q^{8} +197.488 q^{9} +159.283 q^{10} -1209.91i q^{11} +737.745 q^{12} +(1356.55 - 1356.55i) q^{13} +(-1037.26 - 1037.26i) q^{14} +(459.026 + 459.026i) q^{15} -1024.00 q^{16} +(-535.181 + 535.181i) q^{17} +(-789.952 - 789.952i) q^{18} +(3319.12 - 3319.12i) q^{19} +(-637.134 - 637.134i) q^{20} -5978.37i q^{21} +(-4839.63 + 4839.63i) q^{22} +(-8562.83 + 8562.83i) q^{23} +(-2950.98 - 2950.98i) q^{24} +14832.1i q^{25} -10852.4 q^{26} -21359.8i q^{27} +8298.05i q^{28} +(-20758.2 - 20758.2i) q^{29} -3672.21i q^{30} +(-39858.6 - 39858.6i) q^{31} +(4096.00 + 4096.00i) q^{32} -27893.9 q^{33} +4281.45 q^{34} +(-5163.05 + 5163.05i) q^{35} +6319.62i q^{36} +(40909.3 - 29868.9i) q^{37} -26552.9 q^{38} +(-31274.7 - 31274.7i) q^{39} +5097.07i q^{40} -10981.7i q^{41} +(-23913.5 + 23913.5i) q^{42} +(36942.1 - 36942.1i) q^{43} +38717.1 q^{44} +(-3932.07 + 3932.07i) q^{45} +68502.7 q^{46} -105964. q^{47} +23607.9i q^{48} -50405.2 q^{49} +(59328.6 - 59328.6i) q^{50} +(12338.4 + 12338.4i) q^{51} +(43409.7 + 43409.7i) q^{52} +126095. q^{53} +(-85439.0 + 85439.0i) q^{54} +(24089.8 + 24089.8i) q^{55} +(33192.2 - 33192.2i) q^{56} +(-76520.7 - 76520.7i) q^{57} +166066. i q^{58} +(54932.9 - 54932.9i) q^{59} +(-14688.8 + 14688.8i) q^{60} +(151379. + 151379. i) q^{61} +318868. i q^{62} +51211.4 q^{63} -32768.0i q^{64} +54019.1i q^{65} +(111576. + 111576. i) q^{66} -246693. i q^{67} +(-17125.8 - 17125.8i) q^{68} +(197412. + 197412. i) q^{69} +41304.4 q^{70} +317210. q^{71} +(25278.5 - 25278.5i) q^{72} +131677. i q^{73} +(-283113. - 44161.7i) q^{74} +341948. q^{75} +(106212. + 106212. i) q^{76} -313746. i q^{77} +250197. i q^{78} +(582417. - 582417. i) q^{79} +(20388.3 - 20388.3i) q^{80} -348471. q^{81} +(-43926.7 + 43926.7i) q^{82} -390685. q^{83} +191308. q^{84} -21311.4i q^{85} -295537. q^{86} +(-478571. + 478571. i) q^{87} +(-154868. - 154868. i) q^{88} +(-129296. - 129296. i) q^{89} +31456.6 q^{90} +(351773. - 351773. i) q^{91} +(-274011. - 274011. i) q^{92} +(-918921. + 918921. i) q^{93} +(423856. + 423856. i) q^{94} +132170. i q^{95} +(94431.4 - 94431.4i) q^{96} +(193694. - 193694. i) q^{97} +(201621. + 201621. i) q^{98} -238943. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 80 q^{2} + 60 q^{5} + 256 q^{6} + 104 q^{7} + 2560 q^{8} - 6472 q^{9}+O(q^{10}) $ 20 * q - 80 * q^2 + 60 * q^5 + 256 * q^6 + 104 * q^7 + 2560 * q^8 - 6472 * q^9	\( 20 q - 80 q^{2} + 60 q^{5} + 256 q^{6} + 104 q^{7} + 2560 q^{8} - 6472 q^{9} - 480 q^{10} - 2048 q^{12} + 1560 q^{13} - 416 q^{14} - 2136 q^{15} - 20480 q^{16} + 16000 q^{17} + 25888 q^{18} + 3838 q^{19} + 1920 q^{20} + 8928 q^{22} - 6478 q^{23} + 8192 q^{24} - 12480 q^{26} - 1964 q^{29} + 117662 q^{31} + 81920 q^{32} - 92624 q^{33} - 128000 q^{34} - 104456 q^{35} - 17618 q^{37} - 30704 q^{38} + 121012 q^{39} + 213472 q^{42} + 65582 q^{43} - 71424 q^{44} - 466848 q^{45} + 51824 q^{46} - 168176 q^{47} + 563124 q^{49} - 379904 q^{50} + 560888 q^{51} + 49920 q^{52} + 561604 q^{53} - 139120 q^{54} - 1395304 q^{55} + 13312 q^{56} + 631036 q^{57} - 376510 q^{59} + 68352 q^{60} + 836700 q^{61} - 275908 q^{63} + 370496 q^{66} + 512000 q^{68} - 1616748 q^{69} + 835648 q^{70} - 94584 q^{71} - 828416 q^{72} + 133200 q^{74} + 20340 q^{75} + 122816 q^{76} - 2525594 q^{79} - 61440 q^{80} + 2933572 q^{81} - 1816480 q^{82} + 715304 q^{83} - 1707776 q^{84} - 524656 q^{86} + 900256 q^{87} + 285696 q^{88} - 952068 q^{89} + 3734784 q^{90} - 1351840 q^{91} - 207296 q^{92} + 580320 q^{93} + 672704 q^{94} - 262144 q^{96} + 178132 q^{97} - 2252496 q^{98}+O(q^{100}) \) 20 * q - 80 * q^2 + 60 * q^5 + 256 * q^6 + 104 * q^7 + 2560 * q^8 - 6472 * q^9 - 480 * q^10 - 2048 * q^12 + 1560 * q^13 - 416 * q^14 - 2136 * q^15 - 20480 * q^16 + 16000 * q^17 + 25888 * q^18 + 3838 * q^19 + 1920 * q^20 + 8928 * q^22 - 6478 * q^23 + 8192 * q^24 - 12480 * q^26 - 1964 * q^29 + 117662 * q^31 + 81920 * q^32 - 92624 * q^33 - 128000 * q^34 - 104456 * q^35 - 17618 * q^37 - 30704 * q^38 + 121012 * q^39 + 213472 * q^42 + 65582 * q^43 - 71424 * q^44 - 466848 * q^45 + 51824 * q^46 - 168176 * q^47 + 563124 * q^49 - 379904 * q^50 + 560888 * q^51 + 49920 * q^52 + 561604 * q^53 - 139120 * q^54 - 1395304 * q^55 + 13312 * q^56 + 631036 * q^57 - 376510 * q^59 + 68352 * q^60 + 836700 * q^61 - 275908 * q^63 + 370496 * q^66 + 512000 * q^68 - 1616748 * q^69 + 835648 * q^70 - 94584 * q^71 - 828416 * q^72 + 133200 * q^74 + 20340 * q^75 + 122816 * q^76 - 2525594 * q^79 - 61440 * q^80 + 2933572 * q^81 - 1816480 * q^82 + 715304 * q^83 - 1707776 * q^84 - 524656 * q^86 + 900256 * q^87 + 285696 * q^88 - 952068 * q^89 + 3734784 * q^90 - 1351840 * q^91 - 207296 * q^92 + 580320 * q^93 + 672704 * q^94 - 262144 * q^96 + 178132 * q^97 - 2252496 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

$n$	$39$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−4.00000	−	4.00000i	−0.500000	−	0.500000i
$2$	−4.00000	−	4.00000i	−0.500000	−	0.500000i
$3$		−	23.0545i		−	0.853872i	−0.904282	−	0.426936i	$-0.859593\pi$
$3$		−	23.0545i		−	0.853872i	0.904282	−	0.426936i	$-0.140407\pi$
$4$			32.0000i			0.500000i
$5$	−19.9104	+	19.9104i	−0.159283	+	0.159283i	−0.782249	−	0.622966i	$-0.785928\pi$
$5$	−19.9104	+	19.9104i	−0.159283	+	0.159283i	0.622966	+	0.782249i	$0.285928\pi$
$6$	−92.2182	+	92.2182i	−0.426936	+	0.426936i
$7$	259.314			0.756018			0.378009	−	0.925802i	$-0.376609\pi$
$7$	259.314			0.756018			0.378009	+	0.925802i	$0.376609\pi$
$8$	128.000	−	128.000i	0.250000	−	0.250000i
$9$	197.488			0.270903
$10$	159.283			0.159283
$11$		−	1209.91i		−	0.909022i	−0.890741	−	0.454511i	$-0.849814\pi$
$11$		−	1209.91i		−	0.909022i	0.890741	−	0.454511i	$-0.150186\pi$
$12$	737.745			0.426936
$13$	1356.55	−	1356.55i	0.617456	−	0.617456i	−0.327422	−	0.944878i	$-0.606180\pi$
$13$	1356.55	−	1356.55i	0.617456	−	0.617456i	0.944878	+	0.327422i	$0.106180\pi$
$14$	−1037.26	−	1037.26i	−0.378009	−	0.378009i
$15$	459.026	+	459.026i	0.136008	+	0.136008i
$16$	−1024.00			−0.250000
$17$	−535.181	+	535.181i	−0.108932	+	0.108932i	−0.759472	−	0.650540i	$-0.774543\pi$
$17$	−535.181	+	535.181i	−0.108932	+	0.108932i	0.650540	+	0.759472i	$0.274543\pi$
$18$	−789.952	−	789.952i	−0.135451	−	0.135451i
$19$	3319.12	−	3319.12i	0.483907	−	0.483907i	−0.422470	−	0.906377i	$-0.638837\pi$
$19$	3319.12	−	3319.12i	0.483907	−	0.483907i	0.906377	+	0.422470i	$0.138837\pi$
$20$	−637.134	−	637.134i	−0.0796417	−	0.0796417i
$21$		−	5978.37i		−	0.645542i
$22$	−4839.63	+	4839.63i	−0.454511	+	0.454511i
$23$	−8562.83	+	8562.83i	−0.703775	+	0.703775i	−0.965219	−	0.261444i	$-0.915801\pi$
$23$	−8562.83	+	8562.83i	−0.703775	+	0.703775i	0.261444	+	0.965219i	$0.415801\pi$
$24$	−2950.98	−	2950.98i	−0.213468	−	0.213468i
$25$			14832.1i			0.949258i
$26$	−10852.4			−0.617456
$27$		−	21359.8i		−	1.08519i
$28$			8298.05i			0.378009i
$29$	−20758.2	−	20758.2i	−0.851130	−	0.851130i	0.139143	−	0.990272i	$-0.455565\pi$
$29$	−20758.2	−	20758.2i	−0.851130	−	0.851130i	−0.990272	+	0.139143i	$0.955565\pi$
$30$		−	3672.21i		−	0.136008i
$31$	−39858.6	−	39858.6i	−1.33794	−	1.33794i	−0.898054	−	0.439885i	$-0.855019\pi$
$31$	−39858.6	−	39858.6i	−1.33794	−	1.33794i	−0.439885	−	0.898054i	$-0.644981\pi$
$32$	4096.00	+	4096.00i	0.125000	+	0.125000i
$33$	−27893.9			−0.776189
$34$	4281.45			0.108932
$35$	−5163.05	+	5163.05i	−0.120421	+	0.120421i
$36$			6319.62i			0.135451i
$37$	40909.3	−	29868.9i	0.807639	−	0.589677i
$37$	40909.3	−	29868.9i	0.807639	−	0.589677i
$38$	−26552.9			−0.483907
$39$	−31274.7	−	31274.7i	−0.527229	−	0.527229i
$40$			5097.07i			0.0796417i
$41$		−	10981.7i		−	0.159337i	−0.996821	−	0.0796686i	$-0.974614\pi$
$41$		−	10981.7i		−	0.159337i	0.996821	−	0.0796686i	$-0.0253862\pi$
$42$	−23913.5	+	23913.5i	−0.322771	+	0.322771i
$43$	36942.1	−	36942.1i	0.464640	−	0.464640i	−0.435533	−	0.900173i	$-0.643440\pi$
$43$	36942.1	−	36942.1i	0.464640	−	0.464640i	0.900173	+	0.435533i	$0.143440\pi$
$44$	38717.1			0.454511
$45$	−3932.07	+	3932.07i	−0.0431503	+	0.0431503i
$46$	68502.7			0.703775
$47$	−105964.			−1.02062			−0.510311	−	0.859990i	$-0.670470\pi$
$47$	−105964.			−1.02062			−0.510311	+	0.859990i	$0.670470\pi$
$48$			23607.9i			0.213468i
$49$	−50405.2			−0.428438
$50$	59328.6	−	59328.6i	0.474629	−	0.474629i
$51$	12338.4	+	12338.4i	0.0930137	+	0.0930137i
$52$	43409.7	+	43409.7i	0.308728	+	0.308728i
$53$	126095.			0.846973			0.423486	−	0.905902i	$-0.360806\pi$
$53$	126095.			0.846973			0.423486	+	0.905902i	$0.360806\pi$
$54$	−85439.0	+	85439.0i	−0.542594	+	0.542594i
$55$	24089.8	+	24089.8i	0.144792	+	0.144792i
$56$	33192.2	−	33192.2i	0.189004	−	0.189004i
$57$	−76520.7	−	76520.7i	−0.413194	−	0.413194i
$58$			166066.i			0.851130i
$59$	54932.9	−	54932.9i	0.267471	−	0.267471i	−0.560609	−	0.828080i	$-0.689433\pi$
$59$	54932.9	−	54932.9i	0.267471	−	0.267471i	0.828080	+	0.560609i	$0.189433\pi$
$60$	−14688.8	+	14688.8i	−0.0680038	+	0.0680038i
$61$	151379.	+	151379.i	0.666923	+	0.666923i	0.957003	−	0.290079i	$-0.0936818\pi$
$61$	151379.	+	151379.i	0.666923	+	0.666923i	−0.290079	+	0.957003i	$0.593682\pi$
$62$			318868.i			1.33794i
$63$	51211.4			0.204807
$64$		−	32768.0i		−	0.125000i
$65$			54019.1i			0.196701i
$66$	111576.	+	111576.i	0.388094	+	0.388094i
$67$		−	246693.i		−	0.820225i	−0.912035	−	0.410113i	$-0.865489\pi$
$67$		−	246693.i		−	0.820225i	0.912035	−	0.410113i	$-0.134511\pi$
$68$	−17125.8	−	17125.8i	−0.0544658	−	0.0544658i
$69$	197412.	+	197412.i	0.600934	+	0.600934i
$70$	41304.4			0.120421
$71$	317210.			0.886283			0.443142	−	0.896452i	$-0.353864\pi$
$71$	317210.			0.886283			0.443142	+	0.896452i	$0.353864\pi$
$72$	25278.5	−	25278.5i	0.0677257	−	0.0677257i
$73$			131677.i			0.338487i	0.985574	+	0.169244i	$0.0541324\pi$
$73$			131677.i			0.338487i	−0.985574	+	0.169244i	$0.945868\pi$
$74$	−283113.	−	44161.7i	−0.698658	−	0.108981i
$75$	341948.			0.810544
$76$	106212.	+	106212.i	0.241953	+	0.241953i
$77$		−	313746.i		−	0.687237i
$78$			250197.i			0.527229i
$79$	582417.	−	582417.i	1.18128	−	1.18128i	0.201867	−	0.979413i	$-0.435299\pi$
$79$	582417.	−	582417.i	1.18128	−	1.18128i	0.979413	−	0.201867i	$-0.0647009\pi$
$80$	20388.3	−	20388.3i	0.0398209	−	0.0398209i
$81$	−348471.			−0.655709
$82$	−43926.7	+	43926.7i	−0.0796686	+	0.0796686i
$83$	−390685.			−0.683270			−0.341635	−	0.939833i	$-0.610981\pi$
$83$	−390685.			−0.683270			−0.341635	+	0.939833i	$0.610981\pi$
$84$	191308.			0.322771
$85$		−	21311.4i		−	0.0347020i
$86$	−295537.			−0.464640
$87$	−478571.	+	478571.i	−0.726756	+	0.726756i
$88$	−154868.	−	154868.i	−0.227256	−	0.227256i
$89$	−129296.	−	129296.i	−0.183407	−	0.183407i	0.609432	−	0.792839i	$-0.291398\pi$
$89$	−129296.	−	129296.i	−0.183407	−	0.183407i	−0.792839	+	0.609432i	$0.791398\pi$
$90$	31456.6			0.0431503
$91$	351773.	−	351773.i	0.466808	−	0.466808i
$92$	−274011.	−	274011.i	−0.351888	−	0.351888i
$93$	−918921.	+	918921.i	−1.14243	+	1.14243i
$94$	423856.	+	423856.i	0.510311	+	0.510311i
$95$			132170.i			0.154157i
$96$	94431.4	−	94431.4i	0.106734	−	0.106734i
$97$	193694.	−	193694.i	0.212228	−	0.212228i	−0.592985	−	0.805213i	$-0.702051\pi$
$97$	193694.	−	193694.i	0.212228	−	0.212228i	0.805213	+	0.592985i	$0.202051\pi$
$98$	201621.	+	201621.i	0.214219	+	0.214219i
$99$		−	238943.i		−	0.246257i
$100$	−474629.			−0.474629
$101$			760531.i			0.738164i	0.929397	+	0.369082i	$0.120328\pi$
$101$			760531.i			0.738164i	−0.929397	+	0.369082i	$0.879672\pi$
$102$		−	98706.9i		−	0.0930137i
$103$	−304187.	−	304187.i	−0.278374	−	0.278374i	0.554086	−	0.832460i	$-0.313068\pi$
$103$	−304187.	−	304187.i	−0.278374	−	0.278374i	−0.832460	+	0.554086i	$0.813068\pi$
$104$		−	347277.i		−	0.308728i
$105$	119032.	+	119032.i	0.102824	+	0.102824i
$106$	−504379.	−	504379.i	−0.423486	−	0.423486i
$107$	−770211.			−0.628721			−0.314361	−	0.949304i	$-0.601790\pi$
$107$	−770211.			−0.628721			−0.314361	+	0.949304i	$0.601790\pi$
$108$	683512.			0.542594
$109$	−183682.	+	183682.i	−0.141836	+	0.141836i	−0.774459	−	0.632624i	$-0.781978\pi$
$109$	−183682.	+	183682.i	−0.141836	+	0.141836i	0.632624	+	0.774459i	$0.281978\pi$
$110$		−	192718.i		−	0.144792i
$111$	−688614.	−	943146.i	−0.503509	−	0.689620i
$112$	−265538.			−0.189004
$113$	−716054.	−	716054.i	−0.496261	−	0.496261i	0.414011	−	0.910272i	$-0.364128\pi$
$113$	−716054.	−	716054.i	−0.496261	−	0.496261i	−0.910272	+	0.414011i	$0.864128\pi$
$114$			612166.i			0.413194i
$115$		−	340979.i		−	0.224199i
$116$	664262.	−	664262.i	0.425565	−	0.425565i
$117$	267903.	−	267903.i	0.167271	−	0.167271i
$118$	−439463.			−0.267471
$119$	−138780.	+	138780.i	−0.0823542	+	0.0823542i
$120$	117511.			0.0680038
$121$	307682.			0.173678
$122$		−	1.21103e6i		−	0.666923i
$123$	−253178.			−0.136054
$124$	1.27547e6	−	1.27547e6i	0.668970	−	0.668970i
$125$	−606415.	−	606415.i	−0.310484	−	0.310484i
$126$	−204846.	−	204846.i	−0.102404	−	0.102404i
$127$	2.75649e6			1.34569			0.672845	−	0.739784i	$-0.265072\pi$
$127$	2.75649e6			1.34569			0.672845	+	0.739784i	$0.265072\pi$
$128$	−131072.	+	131072.i	−0.0625000	+	0.0625000i
$129$	−851684.	−	851684.i	−0.396743	−	0.396743i
$130$	216076.	−	216076.i	0.0983506	−	0.0983506i
$131$	1.17602e6	+	1.17602e6i	0.523121	+	0.523121i	0.918513	−	0.395392i	$-0.129391\pi$
$131$	1.17602e6	+	1.17602e6i	0.523121	+	0.523121i	−0.395392	+	0.918513i	$0.629391\pi$
$132$		−	892605.i		−	0.388094i
$133$	860693.	−	860693.i	0.365842	−	0.365842i
$134$	−986774.	+	986774.i	−0.410113	+	0.410113i
$135$	425282.	+	425282.i	0.172853	+	0.172853i
$136$			137006.i			0.0544658i
$137$	−2.65113e6			−1.03103			−0.515513	−	0.856882i	$-0.672399\pi$
$137$	−2.65113e6			−1.03103			−0.515513	+	0.856882i	$0.672399\pi$
$138$		−	1.57930e6i		−	0.600934i
$139$			3.37773e6i			1.25771i	0.777522	+	0.628855i	$0.216476\pi$
$139$			3.37773e6i			1.25771i	−0.777522	+	0.628855i	$0.783524\pi$
$140$	−165218.	−	165218.i	−0.0602105	−	0.0602105i
$141$			2.44295e6i			0.871480i
$142$	−1.26884e6	−	1.26884e6i	−0.443142	−	0.443142i
$143$	−1.64130e6	−	1.64130e6i	−0.561282	−	0.561282i
$144$	−202228.			−0.0677257
$145$	826609.			0.271142
$146$	526709.	−	526709.i	0.169244	−	0.169244i
$147$			1.16207e6i			0.365831i
$148$	955805.	+	1.30910e6i	0.294839	+	0.403820i
$149$	251108.			0.0759104			0.0379552	−	0.999279i	$-0.487916\pi$
$149$	251108.			0.0759104			0.0379552	+	0.999279i	$0.487916\pi$
$150$	−1.36779e6	−	1.36779e6i	−0.405272	−	0.405272i
$151$			5.53336e6i			1.60716i	0.595199	+	0.803579i	$0.297073\pi$
$151$			5.53336e6i			1.60716i	−0.595199	+	0.803579i	$0.702927\pi$
$152$		−	849694.i		−	0.241953i
$153$	−105692.	+	105692.i	−0.0295099	+	0.0295099i
$154$	−1.25499e6	+	1.25499e6i	−0.343618	+	0.343618i
$155$	1.58720e6			0.426223
$156$	1.00079e6	−	1.00079e6i	0.263614	−	0.263614i
$157$	59282.0			0.0153188			0.00765939	−	0.999971i	$-0.497562\pi$
$157$	59282.0			0.0153188			0.00765939	+	0.999971i	$0.497562\pi$
$158$	−4.65934e6			−1.18128
$159$		−	2.90706e6i		−	0.723206i
$160$	−163106.			−0.0398209
$161$	−2.22046e6	+	2.22046e6i	−0.532066	+	0.532066i
$162$	1.39388e6	+	1.39388e6i	0.327855	+	0.327855i
$163$	2.41267e6	+	2.41267e6i	0.557101	+	0.557101i	0.928481	−	0.371380i	$-0.121115\pi$
$163$	2.41267e6	+	2.41267e6i	0.557101	+	0.557101i	−0.371380	+	0.928481i	$0.621115\pi$
$164$	351414.			0.0796686
$165$	555379.	−	555379.i	0.123634	−	0.123634i
$166$	1.56274e6	+	1.56274e6i	0.341635	+	0.341635i
$167$	2.59963e6	−	2.59963e6i	0.558165	−	0.558165i	−0.370620	−	0.928785i	$-0.620855\pi$
$167$	2.59963e6	−	2.59963e6i	0.558165	−	0.558165i	0.928785	+	0.370620i	$0.120855\pi$
$168$	−765231.	−	765231.i	−0.161386	−	0.161386i
$169$			1.14634e6i			0.237495i
$170$	−85245.5	+	85245.5i	−0.0173510	+	0.0173510i
$171$	655486.	−	655486.i	0.131092	−	0.131092i
$172$	1.18215e6	+	1.18215e6i	0.232320	+	0.232320i
$173$			6.49886e6i			1.25516i	0.778553	+	0.627579i	$0.215954\pi$
$173$			6.49886e6i			1.25516i	−0.778553	+	0.627579i	$0.784046\pi$
$174$	3.82857e6			0.726756
$175$			3.84618e6i			0.717655i
$176$			1.23895e6i			0.227256i
$177$	−1.26645e6	−	1.26645e6i	−0.228386	−	0.228386i
$178$			1.03437e6i			0.183407i
$179$	1.60197e6	+	1.60197e6i	0.279316	+	0.279316i	0.832836	−	0.553520i	$-0.186716\pi$
$179$	1.60197e6	+	1.60197e6i	0.279316	+	0.279316i	−0.553520	+	0.832836i	$0.686716\pi$
$180$	−125826.	−	125826.i	−0.0215752	−	0.0215752i
$181$	5.19942e6			0.876838			0.438419	−	0.898771i	$-0.355539\pi$
$181$	5.19942e6			0.876838			0.438419	+	0.898771i	$0.355539\pi$
$182$	−2.81418e6			−0.466808
$183$	3.48997e6	−	3.48997e6i	0.569467	−	0.569467i
$184$			2.19209e6i			0.351888i
$185$	−219820.	+	1.40923e6i	−0.0347178	+	0.222569i
$186$	7.35137e6			1.14243
$187$	647520.	+	647520.i	0.0990213	+	0.0990213i
$188$		−	3.39085e6i		−	0.510311i
$189$		−	5.53888e6i		−	0.820421i
$190$	528680.	−	528680.i	0.0770783	−	0.0770783i
$191$	6.83225e6	−	6.83225e6i	0.980536	−	0.980536i	−0.0192785	−	0.999814i	$-0.506137\pi$
$191$	6.83225e6	−	6.83225e6i	0.980536	−	0.980536i	0.999814	+	0.0192785i	$0.00613693\pi$
$192$	−755451.			−0.106734
$193$	2.53864e6	−	2.53864e6i	0.353126	−	0.353126i	−0.508145	−	0.861271i	$-0.669669\pi$
$193$	2.53864e6	−	2.53864e6i	0.353126	−	0.353126i	0.861271	+	0.508145i	$0.169669\pi$
$194$	−1.54956e6			−0.212228
$195$	1.24538e6			0.167958
$196$		−	1.61297e6i		−	0.214219i
$197$	−1.09787e7			−1.43600			−0.717998	−	0.696046i	$-0.754941\pi$
$197$	−1.09787e7			−1.43600			−0.717998	+	0.696046i	$0.754941\pi$
$198$	−955770.	+	955770.i	−0.123128	+	0.123128i
$199$	8.15773e6	+	8.15773e6i	1.03517	+	1.03517i	0.999359	+	0.0358079i	$0.0114004\pi$
$199$	8.15773e6	+	8.15773e6i	1.03517	+	1.03517i	0.0358079	+	0.999359i	$0.488600\pi$
$200$	1.89852e6	+	1.89852e6i	0.237314	+	0.237314i
$201$	−5.68740e6			−0.700367
$202$	3.04213e6	−	3.04213e6i	0.369082	−	0.369082i
$203$	−5.38289e6	−	5.38289e6i	−0.643469	−	0.643469i
$204$	−394827.	+	394827.i	−0.0465068	+	0.0465068i
$205$	218650.	+	218650.i	0.0253798	+	0.0253798i
$206$			2.43350e6i			0.278374i
$207$	−1.69106e6	+	1.69106e6i	−0.190655	+	0.190655i
$208$	−1.38911e6	+	1.38911e6i	−0.154364	+	0.154364i
$209$	−4.01583e6	−	4.01583e6i	−0.439882	−	0.439882i
$210$		−	952255.i		−	0.102824i
$211$	3.35447e6			0.357089			0.178544	−	0.983932i	$-0.442861\pi$
$211$	3.35447e6			0.357089			0.178544	+	0.983932i	$0.442861\pi$
$212$			4.03503e6i			0.423486i
$213$		−	7.31314e6i		−	0.756772i
$214$	3.08084e6	+	3.08084e6i	0.314361	+	0.314361i
$215$			1.47107e6i			0.148019i
$216$	−2.73405e6	−	2.73405e6i	−0.271297	−	0.271297i
$217$	−1.03359e7	−	1.03359e7i	−1.01151	−	1.01151i
$218$	1.46945e6			0.141836
$219$	3.03576e6			0.289025
$220$	−770874.	+	770874.i	−0.0723961	+	0.0723961i
$221$			1.45200e6i			0.134521i
$222$	−1.01813e6	+	6.52704e6i	−0.0930559	+	0.596565i
$223$	3.73061e6			0.336407			0.168204	−	0.985752i	$-0.446203\pi$
$223$	3.73061e6			0.336407			0.168204	+	0.985752i	$0.446203\pi$
$224$	1.06215e6	+	1.06215e6i	0.0945022	+	0.0945022i
$225$			2.92917e6i			0.257156i
$226$			5.72843e6i			0.496261i
$227$	−2.04691e6	+	2.04691e6i	−0.174993	+	0.174993i	−0.789169	−	0.614176i	$-0.789488\pi$
$227$	−2.04691e6	+	2.04691e6i	−0.174993	+	0.174993i	0.614176	+	0.789169i	$0.289488\pi$
$228$	2.44866e6	−	2.44866e6i	0.206597	−	0.206597i
$229$	−2.31626e7			−1.92877			−0.964387	−	0.264493i	$-0.914795\pi$
$229$	−2.31626e7			−1.92877			−0.964387	+	0.264493i	$0.914795\pi$
$230$	−1.36392e6	+	1.36392e6i	−0.112100	+	0.112100i
$231$	−7.23328e6			−0.586812
$232$	−5.31410e6			−0.425565
$233$		−	1.16171e7i		−	0.918393i	−0.888335	−	0.459196i	$-0.848137\pi$
$233$		−	1.16171e7i		−	0.918393i	0.888335	−	0.459196i	$-0.151863\pi$
$234$	−2.14322e6			−0.167271
$235$	2.10979e6	−	2.10979e6i	0.162568	−	0.162568i
$236$	1.75785e6	+	1.75785e6i	0.133735	+	0.133735i
$237$	−1.34274e7	−	1.34274e7i	−1.00866	−	1.00866i
$238$	1.11024e6			0.0823542
$239$	−2.70417e6	+	2.70417e6i	−0.198080	+	0.198080i	−0.799176	−	0.601097i	$-0.794731\pi$
$239$	−2.70417e6	+	2.70417e6i	−0.198080	+	0.198080i	0.601097	+	0.799176i	$0.294731\pi$
$240$	−470043.	−	470043.i	−0.0340019	−	0.0340019i
$241$	922114.	−	922114.i	0.0658769	−	0.0658769i	−0.673401	−	0.739278i	$-0.735167\pi$
$241$	922114.	−	922114.i	0.0658769	−	0.0658769i	0.739278	+	0.673401i	$0.235167\pi$
$242$	−1.23073e6	−	1.23073e6i	−0.0868392	−	0.0868392i
$243$		−	7.53743e6i		−	0.525297i
$244$	−4.84412e6	+	4.84412e6i	−0.333462	+	0.333462i
$245$	1.00359e6	−	1.00359e6i	0.0682430	−	0.0682430i
$246$	1.01271e6	+	1.01271e6i	0.0680268	+	0.0680268i
$247$		−	9.00511e6i		−	0.597583i
$248$	−1.02038e7			−0.668970
$249$			9.00706e6i			0.583425i
$250$			4.85132e6i			0.310484i
$251$	−8.92145e6	−	8.92145e6i	−0.564176	−	0.564176i	0.366315	−	0.930491i	$-0.380619\pi$
$251$	−8.92145e6	−	8.92145e6i	−0.564176	−	0.564176i	−0.930491	+	0.366315i	$0.880619\pi$
$252$			1.63877e6i			0.102404i
$253$	1.03602e7	+	1.03602e7i	0.639747	+	0.639747i
$254$	−1.10259e7	−	1.10259e7i	−0.672845	−	0.672845i
$255$	−491324.			−0.0296311
$256$	1.04858e6			0.0625000
$257$	−3.07994e6	+	3.07994e6i	−0.181444	+	0.181444i	−0.791985	−	0.610541i	$-0.790952\pi$
$257$	−3.07994e6	+	3.07994e6i	−0.181444	+	0.181444i	0.610541	+	0.791985i	$0.290952\pi$
$258$			6.81347e6i			0.396743i
$259$	1.06084e7	−	7.74543e6i	0.610589	−	0.445806i
$260$	−1.72861e6			−0.0983506
$261$	−4.09950e6	−	4.09950e6i	−0.230573	−	0.230573i
$262$		−	9.40819e6i		−	0.523121i
$263$		−	2.00356e7i		−	1.10138i	−0.834711	−	0.550688i	$-0.814366\pi$
$263$		−	2.00356e7i		−	1.10138i	0.834711	−	0.550688i	$-0.185634\pi$
$264$	−3.57042e6	+	3.57042e6i	−0.194047	+	0.194047i
$265$	−2.51060e6	+	2.51060e6i	−0.134909	+	0.134909i
$266$	−6.88555e6			−0.365842
$267$	−2.98087e6	+	2.98087e6i	−0.156606	+	0.156606i
$268$	7.89419e6			0.410113
$269$	2.27541e7			1.16897			0.584483	−	0.811406i	$-0.301297\pi$
$269$	2.27541e7			1.16897			0.584483	+	0.811406i	$0.301297\pi$
$270$		−	3.40226e6i		−	0.172853i
$271$	2.50414e7			1.25820			0.629102	−	0.777323i	$-0.283423\pi$
$271$	2.50414e7			1.25820			0.629102	+	0.777323i	$0.283423\pi$
$272$	548026.	−	548026.i	0.0272329	−	0.0272329i
$273$	−8.10996e6	−	8.10996e6i	−0.398594	−	0.398594i
$274$	1.06045e7	+	1.06045e7i	0.515513	+	0.515513i
$275$	1.79455e7			0.862896
$276$	−6.31719e6	+	6.31719e6i	−0.300467	+	0.300467i
$277$	6.91528e6	+	6.91528e6i	0.325365	+	0.325365i	0.850821	−	0.525456i	$-0.176105\pi$
$277$	6.91528e6	+	6.91528e6i	0.325365	+	0.325365i	−0.525456	+	0.850821i	$0.676105\pi$
$278$	1.35109e7	−	1.35109e7i	0.628855	−	0.628855i
$279$	−7.87159e6	−	7.87159e6i	−0.362451	−	0.362451i
$280$			1.32174e6i			0.0602105i
$281$	−2.70069e7	+	2.70069e7i	−1.21718	+	1.21718i	−0.248571	+	0.968614i	$0.579961\pi$
$281$	−2.70069e7	+	2.70069e7i	−1.21718	+	1.21718i	−0.968614	+	0.248571i	$0.920039\pi$
$282$	9.77180e6	−	9.77180e6i	0.435740	−	0.435740i
$283$	2.83516e7	+	2.83516e7i	1.25089	+	1.25089i	0.955322	+	0.295566i	$0.0955082\pi$
$283$	2.83516e7	+	2.83516e7i	1.25089	+	1.25089i	0.295566	+	0.955322i	$0.404492\pi$
$284$			1.01507e7i			0.443142i
$285$	3.04712e6			0.131630
$286$			1.31304e7i			0.561282i
$287$		−	2.84770e6i		−	0.120462i
$288$	808911.	+	808911.i	0.0338628	+	0.0338628i
$289$			2.35647e7i			0.976268i
$290$	−3.30644e6	−	3.30644e6i	−0.135571	−	0.135571i
$291$	−4.46554e6	−	4.46554e6i	−0.181215	−	0.181215i
$292$	−4.21367e6			−0.169244
$293$	3.25640e7			1.29460			0.647299	−	0.762236i	$-0.275898\pi$
$293$	3.25640e7			1.29460			0.647299	+	0.762236i	$0.275898\pi$
$294$	4.64828e6	−	4.64828e6i	0.182915	−	0.182915i
$295$			2.18748e6i			0.0852074i
$296$	1.41318e6	−	9.05962e6i	0.0544905	−	0.349329i
$297$	−2.58434e7			−0.986460
$298$	−1.00443e6	−	1.00443e6i	−0.0379552	−	0.0379552i
$299$			2.32319e7i			0.869101i
$300$			1.09423e7i			0.405272i
$301$	9.57961e6	−	9.57961e6i	0.351276	−	0.351276i
$302$	2.21335e7	−	2.21335e7i	0.803579	−	0.803579i
$303$	1.75337e7			0.630298
$304$	−3.39878e6	+	3.39878e6i	−0.120977	+	0.120977i
$305$	−6.02804e6			−0.212460
$306$	845535.			0.0295099
$307$		−	3.22873e7i		−	1.11588i	−0.829883	−	0.557938i	$-0.811593\pi$
$307$		−	3.22873e7i		−	1.11588i	0.829883	−	0.557938i	$-0.188407\pi$
$308$	1.00399e7			0.343618
$309$	−7.01289e6	+	7.01289e6i	−0.237696	+	0.237696i
$310$	−6.34881e6	−	6.34881e6i	−0.213112	−	0.213112i
$311$	1.78067e7	+	1.78067e7i	0.591973	+	0.591973i	0.938164	−	0.346191i	$-0.112525\pi$
$311$	1.78067e7	+	1.78067e7i	0.591973	+	0.591973i	−0.346191	+	0.938164i	$0.612525\pi$
$312$	−8.00632e6			−0.263614
$313$	1.30507e7	−	1.30507e7i	0.425598	−	0.425598i	−0.461527	−	0.887126i	$-0.652698\pi$
$313$	1.30507e7	−	1.30507e7i	0.425598	−	0.425598i	0.887126	+	0.461527i	$0.152698\pi$
$314$	−237128.	−	237128.i	−0.00765939	−	0.00765939i
$315$	−1.01964e6	+	1.01964e6i	−0.0326224	+	0.0326224i
$316$	1.86373e7	+	1.86373e7i	0.590640	+	0.590640i
$317$			6.89711e6i			0.216516i	0.994123	+	0.108258i	$0.0345272\pi$
$317$			6.89711e6i			0.216516i	−0.994123	+	0.108258i	$0.965473\pi$
$318$	−1.16282e7	+	1.16282e7i	−0.361603	+	0.361603i
$319$	−2.51155e7	+	2.51155e7i	−0.773696	+	0.773696i
$320$	652425.	+	652425.i	0.0199104	+	0.0199104i
$321$			1.77569e7i			0.536848i
$322$	1.77637e7			0.532066
$323$			3.55266e6i			0.105426i
$324$		−	1.11511e7i		−	0.327855i
$325$	2.01206e7	+	2.01206e7i	0.586125	+	0.586125i
$326$		−	1.93013e7i		−	0.557101i
$327$	4.23469e6	+	4.23469e6i	0.121110	+	0.121110i
$328$	−1.40566e6	−	1.40566e6i	−0.0398343	−	0.0398343i
$329$	−2.74779e7			−0.771607
$330$	−4.44304e6			−0.123634
$331$	2.94579e7	−	2.94579e7i	0.812303	−	0.812303i	−0.172675	−	0.984979i	$-0.555241\pi$
$331$	2.94579e7	−	2.94579e7i	0.812303	−	0.812303i	0.984979	+	0.172675i	$0.0552411\pi$
$332$		−	1.25019e7i		−	0.341635i
$333$	8.07911e6	−	5.89875e6i	0.218792	−	0.159745i
$334$	−2.07971e7			−0.558165
$335$	4.91177e6	+	4.91177e6i	0.130648	+	0.130648i
$336$			6.12185e6i			0.161386i
$337$			7.02222e7i			1.83478i	0.397986	+	0.917391i	$0.369709\pi$
$337$			7.02222e7i			1.83478i	−0.397986	+	0.917391i	$0.630291\pi$
$338$	4.58537e6	−	4.58537e6i	0.118748	−	0.118748i
$339$	−1.65083e7	+	1.65083e7i	−0.423744	+	0.423744i
$340$	681964.			0.0173510
$341$	−4.82252e7	+	4.82252e7i	−1.21622	+	1.21622i
$342$	−5.24389e6			−0.131092
$343$	−4.35788e7			−1.07992
$344$		−	9.45719e6i		−	0.232320i
$345$	−7.86112e6			−0.191438
$346$	2.59954e7	−	2.59954e7i	0.627579	−	0.627579i
$347$	1.84125e7	+	1.84125e7i	0.440681	+	0.440681i	0.892241	−	0.451560i	$-0.149132\pi$
$347$	1.84125e7	+	1.84125e7i	0.440681	+	0.440681i	−0.451560	+	0.892241i	$0.649132\pi$
$348$	−1.53143e7	−	1.53143e7i	−0.363378	−	0.363378i
$349$	2.47836e6			0.0583025			0.0291513	−	0.999575i	$-0.490720\pi$
$349$	2.47836e6			0.0583025			0.0291513	+	0.999575i	$0.490720\pi$
$350$	1.53847e7	−	1.53847e7i	0.358828	−	0.358828i
$351$	−2.89756e7	−	2.89756e7i	−0.670056	−	0.670056i
$352$	4.95579e6	−	4.95579e6i	0.113628	−	0.113628i
$353$	−5.62675e7	−	5.62675e7i	−1.27919	−	1.27919i	−0.941124	−	0.338061i	$-0.890229\pi$
$353$	−5.62675e7	−	5.62675e7i	−1.27919	−	1.27919i	−0.338061	−	0.941124i	$-0.609771\pi$
$354$			1.01316e7i			0.228386i
$355$	−6.31580e6	+	6.31580e6i	−0.141170	+	0.141170i
$356$	4.13748e6	−	4.13748e6i	0.0917035	−	0.0917035i
$357$	3.19951e6	+	3.19951e6i	0.0703200	+	0.0703200i
$358$		−	1.28158e7i		−	0.279316i
$359$	8.09022e7			1.74854			0.874272	−	0.485436i	$-0.161339\pi$
$359$	8.09022e7			1.74854			0.874272	+	0.485436i	$0.161339\pi$
$360$			1.00661e6i			0.0215752i
$361$			2.50128e7i			0.531668i
$362$	−2.07977e7	−	2.07977e7i	−0.438419	−	0.438419i
$363$		−	7.09347e6i		−	0.148299i
$364$	1.12567e7	+	1.12567e7i	0.233404	+	0.233404i
$365$	−2.62175e6	−	2.62175e6i	−0.0539154	−	0.0539154i
$366$	−2.79198e7			−0.569467
$367$	3.38458e7			0.684711			0.342355	−	0.939571i	$-0.388775\pi$
$367$	3.38458e7			0.684711			0.342355	+	0.939571i	$0.388775\pi$
$368$	8.76834e6	−	8.76834e6i	0.175944	−	0.175944i
$369$		−	2.16875e6i		−	0.0431649i
$370$	6.51618e6	−	4.75762e6i	0.128644	−	0.0939258i
$371$	3.26981e7			0.640326
$372$	−2.94055e7	−	2.94055e7i	−0.571214	−	0.571214i
$373$		−	9.64097e7i		−	1.85778i	−0.370356	−	0.928890i	$-0.620764\pi$
$373$		−	9.64097e7i		−	1.85778i	0.370356	−	0.928890i	$-0.379236\pi$
$374$		−	5.18016e6i		−	0.0990213i
$375$	−1.39806e7	+	1.39806e7i	−0.265114	+	0.265114i
$376$	−1.35634e7	+	1.35634e7i	−0.255155	+	0.255155i
$377$	−5.63191e7			−1.05107
$378$	−2.21555e7	+	2.21555e7i	−0.410211	+	0.410211i
$379$	−2.53719e7			−0.466052			−0.233026	−	0.972470i	$-0.574863\pi$
$379$	−2.53719e7			−0.466052			−0.233026	+	0.972470i	$0.574863\pi$
$380$	−4.22944e6			−0.0770783
$381$		−	6.35495e7i		−	1.14905i
$382$	−5.46580e7			−0.980536
$383$	1.06313e7	−	1.06313e7i	0.189231	−	0.189231i	−0.606133	−	0.795363i	$-0.707280\pi$
$383$	1.06313e7	−	1.06313e7i	0.189231	−	0.189231i	0.795363	+	0.606133i	$0.207280\pi$
$384$	3.02181e6	+	3.02181e6i	0.0533670	+	0.0533670i
$385$	6.24682e6	+	6.24682e6i	0.109465	+	0.109465i
$386$	−2.03091e7			−0.353126
$387$	7.29563e6	−	7.29563e6i	0.125872	−	0.125872i
$388$	6.19822e6	+	6.19822e6i	0.106114	+	0.106114i
$389$	5.45698e7	−	5.45698e7i	0.927051	−	0.927051i	−0.0704636	−	0.997514i	$-0.522448\pi$
$389$	5.45698e7	−	5.45698e7i	0.927051	−	0.927051i	0.997514	+	0.0704636i	$0.0224478\pi$
$390$	−4.98154e6	−	4.98154e6i	−0.0839788	−	0.0839788i
$391$		−	9.16533e6i		−	0.153327i
$392$	−6.45187e6	+	6.45187e6i	−0.107109	+	0.107109i
$393$	2.71127e7	−	2.71127e7i	0.446678	−	0.446678i
$394$	4.39149e7	+	4.39149e7i	0.717998	+	0.717998i
$395$			2.31924e7i			0.376317i
$396$	7.64616e6			0.123128
$397$			8.49083e7i			1.35700i	0.734603	+	0.678498i	$0.237369\pi$
$397$			8.49083e7i			1.35700i	−0.734603	+	0.678498i	$0.762631\pi$
$398$		−	6.52619e7i		−	1.03517i
$399$	−1.98429e7	−	1.98429e7i	−0.312382	−	0.312382i
$400$		−	1.51881e7i		−	0.237314i
$401$	4.51406e7	+	4.51406e7i	0.700059	+	0.700059i	0.964423	−	0.264364i	$-0.0851621\pi$
$401$	4.51406e7	+	4.51406e7i	0.700059	+	0.700059i	−0.264364	+	0.964423i	$0.585162\pi$
$402$	2.27496e7	+	2.27496e7i	0.350184	+	0.350184i
$403$	−1.08140e8			−1.65224
$404$	−2.43370e7			−0.369082
$405$	6.93820e6	−	6.93820e6i	0.104444	−	0.104444i
$406$			4.30631e7i			0.643469i
$407$	−3.61387e7	−	4.94966e7i	−0.536030	−	0.734162i
$408$	3.15862e6			0.0465068
$409$	−2.58341e7	−	2.58341e7i	−0.377592	−	0.377592i	0.492641	−	0.870233i	$-0.336032\pi$
$409$	−2.58341e7	−	2.58341e7i	−0.377592	−	0.377592i	−0.870233	+	0.492641i	$0.836032\pi$
$410$		−	1.74920e6i		−	0.0253798i
$411$			6.11206e7i			0.880364i
$412$	9.73398e6	−	9.73398e6i	0.139187	−	0.139187i
$413$	1.42449e7	−	1.42449e7i	0.202213	−	0.202213i
$414$	1.35285e7			0.190655
$415$	7.77870e6	−	7.77870e6i	0.108834	−	0.108834i
$416$	1.11129e7			0.154364
$417$	7.78721e7			1.07392
$418$			3.21266e7i			0.439882i
$419$	−2.63687e7			−0.358466			−0.179233	−	0.983807i	$-0.557362\pi$
$419$	−2.63687e7			−0.358466			−0.179233	+	0.983807i	$0.557362\pi$
$420$	−3.80902e6	+	3.80902e6i	−0.0514121	+	0.0514121i
$421$	−1.25857e7	−	1.25857e7i	−0.168668	−	0.168668i	0.617726	−	0.786394i	$-0.288054\pi$
$421$	−1.25857e7	−	1.25857e7i	−0.168668	−	0.168668i	−0.786394	+	0.617726i	$0.788054\pi$
$422$	−1.34179e7	−	1.34179e7i	−0.178544	−	0.178544i
$423$	−2.09266e7			−0.276489
$424$	1.61401e7	−	1.61401e7i	0.211743	−	0.211743i
$425$	−7.93789e6	−	7.93789e6i	−0.103404	−	0.103404i
$426$	−2.92526e7	+	2.92526e7i	−0.378386	+	0.378386i
$427$	3.92547e7	+	3.92547e7i	0.504206	+	0.504206i
$428$		−	2.46467e7i		−	0.314361i
$429$	−3.78395e7	+	3.78395e7i	−0.479263	+	0.479263i
$430$	5.88427e6	−	5.88427e6i	0.0740095	−	0.0740095i
$431$	−1.87047e7	−	1.87047e7i	−0.233624	−	0.233624i	0.580579	−	0.814204i	$-0.302826\pi$
$431$	−1.87047e7	−	1.87047e7i	−0.233624	−	0.233624i	−0.814204	+	0.580579i	$0.802826\pi$
$432$			2.18724e7i			0.271297i
$433$	−1.75488e7			−0.216165			−0.108082	−	0.994142i	$-0.534471\pi$
$433$	−1.75488e7			−0.216165			−0.108082	+	0.994142i	$0.534471\pi$
$434$			8.26870e7i			1.01151i
$435$		−	1.90571e7i		−	0.231520i
$436$	−5.87781e6	−	5.87781e6i	−0.0709179	−	0.0709179i
$437$			5.68421e7i			0.681123i
$438$	−1.21430e7	−	1.21430e7i	−0.144512	−	0.144512i
$439$	−6.49630e7	−	6.49630e7i	−0.767843	−	0.767843i	0.209883	−	0.977726i	$-0.432692\pi$
$439$	−6.49630e7	−	6.49630e7i	−0.767843	−	0.767843i	−0.977726	+	0.209883i	$0.932692\pi$
$440$	6.16699e6			0.0723961
$441$	−9.95443e6			−0.116065
$442$	5.80801e6	−	5.80801e6i	0.0672606	−	0.0672606i
$443$		−	2.38923e7i		−	0.274819i	−0.990514	−	0.137410i	$-0.956122\pi$
$443$		−	2.38923e7i		−	0.274819i	0.990514	−	0.137410i	$-0.0438777\pi$
$444$	3.01807e7	−	2.20357e7i	0.344810	−	0.251754i
$445$	5.14869e6			0.0584274
$446$	−1.49224e7	−	1.49224e7i	−0.168204	−	0.168204i
$447$		−	5.78918e6i		−	0.0648178i
$448$		−	8.49720e6i		−	0.0945022i
$449$	−2.90862e7	+	2.90862e7i	−0.321328	+	0.321328i	−0.849276	−	0.527949i	$-0.822961\pi$
$449$	−2.90862e7	+	2.90862e7i	−0.321328	+	0.321328i	0.527949	+	0.849276i	$0.322961\pi$
$450$	1.17167e7	−	1.17167e7i	0.128578	−	0.128578i
$451$	−1.32868e7			−0.144841
$452$	2.29137e7	−	2.29137e7i	0.248131	−	0.248131i
$453$	1.27569e8			1.37231
$454$	1.63753e7			0.174993
$455$			1.40079e7i			0.148710i
$456$	−1.95893e7			−0.206597
$457$	8.25513e7	−	8.25513e7i	0.864919	−	0.864919i	−0.126986	−	0.991905i	$-0.540530\pi$
$457$	8.25513e7	−	8.25513e7i	0.864919	−	0.864919i	0.991905	+	0.126986i	$0.0405302\pi$
$458$	9.26505e7	+	9.26505e7i	0.964387	+	0.964387i
$459$	1.14313e7	+	1.14313e7i	0.118211	+	0.118211i
$460$	1.09113e7			0.112100
$461$	3.38971e7	−	3.38971e7i	0.345987	−	0.345987i	−0.512626	−	0.858612i	$-0.671327\pi$
$461$	3.38971e7	−	3.38971e7i	0.345987	−	0.345987i	0.858612	+	0.512626i	$0.171327\pi$
$462$	2.89331e7	+	2.89331e7i	0.293406	+	0.293406i
$463$	9.34008e7	−	9.34008e7i	0.941039	−	0.941039i	−0.0573174	−	0.998356i	$-0.518255\pi$
$463$	9.34008e7	−	9.34008e7i	0.941039	−	0.941039i	0.998356	+	0.0573174i	$0.0182547\pi$
$464$	2.12564e7	+	2.12564e7i	0.212782	+	0.212782i
$465$		−	3.65922e7i		−	0.363940i
$466$	−4.64682e7	+	4.64682e7i	−0.459196	+	0.459196i
$467$	−1.31861e8	+	1.31861e8i	−1.29469	+	1.29469i	−0.362842	+	0.931851i	$0.618193\pi$
$467$	−1.31861e8	+	1.31861e8i	−1.29469	+	1.29469i	−0.931851	+	0.362842i	$0.881807\pi$
$468$	8.57289e6	+	8.57289e6i	0.0836353	+	0.0836353i
$469$		−	6.39711e7i		−	0.620105i
$470$	−1.68783e7			−0.162568
$471$		−	1.36672e6i		−	0.0130803i
$472$		−	1.40628e7i		−	0.133735i
$473$	−4.46966e7	−	4.46966e7i	−0.422368	−	0.422368i
$474$			1.07419e8i			1.00866i
$475$	4.92296e7	+	4.92296e7i	0.459352	+	0.459352i
$476$	−4.44096e6	−	4.44096e6i	−0.0411771	−	0.0411771i
$477$	2.49022e7			0.229447
$478$	2.16334e7			0.198080
$479$	−7.21746e6	+	7.21746e6i	−0.0656716	+	0.0656716i	−0.739180	−	0.673508i	$-0.764787\pi$
$479$	−7.21746e6	+	7.21746e6i	−0.0656716	+	0.0656716i	0.673508	+	0.739180i	$0.264787\pi$
$480$			3.76034e6i			0.0340019i
$481$	1.49769e7	−	9.60144e7i	0.134582	−	0.862782i
$482$	−7.37691e6			−0.0658769
$483$	5.11917e7	+	5.11917e7i	0.454317	+	0.454317i
$484$			9.84583e6i			0.0868392i
$485$			7.71308e6i			0.0676087i
$486$	−3.01497e7	+	3.01497e7i	−0.262648	+	0.262648i
$487$	−9.53700e7	+	9.53700e7i	−0.825705	+	0.825705i	−0.986919	−	0.161215i	$-0.948459\pi$
$487$	−9.53700e7	+	9.53700e7i	−0.825705	+	0.825705i	0.161215	+	0.986919i	$0.448459\pi$
$488$	3.87530e7			0.333462
$489$	5.56229e7	−	5.56229e7i	0.475693	−	0.475693i
$490$	−8.02872e6			−0.0682430
$491$	−1.89022e7			−0.159686			−0.0798431	−	0.996807i	$-0.525442\pi$
$491$	−1.89022e7			−0.159686			−0.0798431	+	0.996807i	$0.525442\pi$
$492$		−	8.10169e6i		−	0.0680268i
$493$	2.22188e7			0.185430
$494$	−3.60204e7	+	3.60204e7i	−0.298791	+	0.298791i
$495$	4.75745e6	+	4.75745e6i	0.0392246	+	0.0392246i
$496$	4.08152e7	+	4.08152e7i	0.334485	+	0.334485i
$497$	8.22571e7			0.670045
$498$	3.60282e7	−	3.60282e7i	0.291712	−	0.291712i
$499$	−2.64127e7	−	2.64127e7i	−0.212575	−	0.212575i	0.592786	−	0.805360i	$-0.298028\pi$
$499$	−2.64127e7	−	2.64127e7i	−0.212575	−	0.212575i	−0.805360	+	0.592786i	$0.798028\pi$
$500$	1.94053e7	−	1.94053e7i	0.155242	−	0.155242i
$501$	−5.99334e7	−	5.99334e7i	−0.476602	−	0.476602i
$502$			7.13716e7i			0.564176i
$503$	−1.56063e8	+	1.56063e8i	−1.22630	+	1.22630i	−0.260940	+	0.965355i	$0.584032\pi$
$503$	−1.56063e8	+	1.56063e8i	−1.22630	+	1.22630i	−0.965355	+	0.260940i	$0.915968\pi$
$504$	6.55506e6	−	6.55506e6i	0.0512018	−	0.0512018i
$505$	−1.51425e7	−	1.51425e7i	−0.117577	−	0.117577i
$506$		−	8.28820e7i		−	0.639747i
$507$	2.64284e7			0.202790
$508$			8.82076e7i			0.672845i
$509$			1.02153e8i			0.774633i	0.921947	+	0.387317i	$0.126598\pi$
$509$			1.02153e8i			0.774633i	−0.921947	+	0.387317i	$0.873402\pi$
$510$	1.96530e6	+	1.96530e6i	0.0148155	+	0.0148155i
$511$			3.41457e7i			0.255902i
$512$	−4.19430e6	−	4.19430e6i	−0.0312500	−	0.0312500i
$513$	−7.08955e7	−	7.08955e7i	−0.525130	−	0.525130i
$514$	2.46396e7			0.181444
$515$	1.21130e7			0.0886808
$516$	2.72539e7	−	2.72539e7i	0.198372	−	0.198372i
$517$			1.28207e8i			0.927767i
$518$	−7.34152e7	−	1.14518e7i	−0.528198	−	0.0823916i
$519$	1.49828e8			1.07174
$520$	6.91444e6	+	6.91444e6i	0.0491753	+	0.0491753i
$521$			1.06206e8i			0.750991i	0.926824	+	0.375495i	$0.122527\pi$
$521$			1.06206e8i			0.750991i	−0.926824	+	0.375495i	$0.877473\pi$
$522$			3.27960e7i			0.230573i
$523$	1.20668e8	−	1.20668e8i	0.843501	−	0.843501i	−0.145811	−	0.989312i	$-0.546579\pi$
$523$	1.20668e8	−	1.20668e8i	0.843501	−	0.843501i	0.989312	+	0.145811i	$0.0465791\pi$
$524$	−3.76328e7	+	3.76328e7i	−0.261561	+	0.261561i
$525$	8.86720e7			0.612786
$526$	−8.01424e7	+	8.01424e7i	−0.550688	+	0.550688i
$527$	4.26631e7			0.291488
$528$	2.85633e7			0.194047
$529$			1.39169e6i			0.00940104i
$530$	2.00848e7			0.134909
$531$	1.08486e7	−	1.08486e7i	0.0724586	−	0.0724586i
$532$	2.75422e7	+	2.75422e7i	0.182921	+	0.182921i
$533$	−1.48972e7	−	1.48972e7i	−0.0983838	−	0.0983838i
$534$	2.38469e7			0.156606
$535$	1.53352e7	−	1.53352e7i	0.100145	−	0.100145i
$536$	−3.15768e7	−	3.15768e7i	−0.205056	−	0.205056i
$537$	3.69327e7	−	3.69327e7i	0.238500	−	0.238500i
$538$	−9.10163e7	−	9.10163e7i	−0.584483	−	0.584483i
$539$			6.09857e7i			0.389459i
$540$	−1.36090e7	+	1.36090e7i	−0.0864263	+	0.0864263i
$541$	−3.04488e7	+	3.04488e7i	−0.192299	+	0.192299i	−0.796689	−	0.604390i	$-0.793417\pi$
$541$	−3.04488e7	+	3.04488e7i	−0.192299	+	0.192299i	0.604390	+	0.796689i	$0.293417\pi$
$542$	−1.00166e8	−	1.00166e8i	−0.629102	−	0.629102i
$543$		−	1.19870e8i		−	0.748707i
$544$	−4.38420e6			−0.0272329
$545$		−	7.31436e6i		−	0.0451842i
$546$			6.48797e7i			0.398594i
$547$	−3.75321e7	−	3.75321e7i	−0.229320	−	0.229320i	0.583089	−	0.812408i	$-0.301844\pi$
$547$	−3.75321e7	−	3.75321e7i	−0.229320	−	0.229320i	−0.812408	+	0.583089i	$0.801844\pi$
$548$		−	8.48362e7i		−	0.515513i
$549$	2.98955e7	+	2.98955e7i	0.180671	+	0.180671i
$550$	−7.17822e7	−	7.17822e7i	−0.431448	−	0.431448i
$551$	−1.37798e8			−0.823735
$552$	5.05375e7			0.300467
$553$	1.51029e8	−	1.51029e8i	0.893068	−	0.893068i
$554$		−	5.53223e7i		−	0.325365i
$555$	3.24891e7	+	5.06785e6i	0.190046	+	0.0296445i
$556$	−1.08087e8			−0.628855
$557$	8.81944e7	+	8.81944e7i	0.510359	+	0.510359i	0.914636	−	0.404278i	$-0.132477\pi$
$557$	8.81944e7	+	8.81944e7i	0.510359	+	0.510359i	−0.404278	+	0.914636i	$0.632477\pi$
$558$			6.29727e7i			0.362451i
$559$		−	1.00228e8i		−	0.573790i
$560$	5.28697e6	−	5.28697e6i	0.0301053	−	0.0301053i
$561$	1.49283e7	−	1.49283e7i	0.0845515	−	0.0845515i
$562$	2.16056e8			1.21718
$563$	−3.34329e7	+	3.34329e7i	−0.187348	+	0.187348i	−0.794549	−	0.607201i	$-0.792292\pi$
$563$	−3.34329e7	+	3.34329e7i	−0.187348	+	0.187348i	0.607201	+	0.794549i	$0.292292\pi$
$564$	−7.81744e7			−0.435740
$565$	2.85139e7			0.158092
$566$		−	2.26813e8i		−	1.25089i
$567$	−9.03633e7			−0.495728
$568$	4.06029e7	−	4.06029e7i	0.221571	−	0.221571i
$569$	2.17877e8	+	2.17877e8i	1.18270	+	1.18270i	0.979043	+	0.203655i	$0.0652820\pi$
$569$	2.17877e8	+	2.17877e8i	1.18270	+	1.18270i	0.203655	+	0.979043i	$0.434718\pi$
$570$	−1.21885e7	−	1.21885e7i	−0.0658150	−	0.0658150i
$571$	−2.37290e8			−1.27459			−0.637295	−	0.770620i	$-0.719947\pi$
$571$	−2.37290e8			−1.27459			−0.637295	+	0.770620i	$0.719947\pi$
$572$	5.25217e7	−	5.25217e7i	0.280641	−	0.280641i
$573$	−1.57514e8	−	1.57514e8i	−0.837252	−	0.837252i
$574$	−1.13908e7	+	1.13908e7i	−0.0602309	+	0.0602309i
$575$	−1.27005e8	−	1.27005e8i	−0.668064	−	0.668064i
$576$		−	6.47129e6i		−	0.0338628i
$577$	−2.20932e7	+	2.20932e7i	−0.115009	+	0.115009i	−0.762269	−	0.647260i	$-0.775915\pi$
$577$	−2.20932e7	+	2.20932e7i	−0.115009	+	0.115009i	0.647260	+	0.762269i	$0.275915\pi$
$578$	9.42589e7	−	9.42589e7i	0.488134	−	0.488134i
$579$	−5.85272e7	−	5.85272e7i	−0.301524	−	0.301524i
$580$			2.64515e7i			0.135571i
$581$	−1.01310e8			−0.516564
$582$			3.57243e7i			0.181215i
$583$		−	1.52563e8i		−	0.769917i
$584$	1.68547e7	+	1.68547e7i	0.0846218	+	0.0846218i
$585$			1.06681e7i			0.0532869i
$586$	−1.30256e8	−	1.30256e8i	−0.647299	−	0.647299i
$587$	−1.45383e7	−	1.45383e7i	−0.0718785	−	0.0718785i	0.670254	−	0.742132i	$-0.266185\pi$
$587$	−1.45383e7	−	1.45383e7i	−0.0718785	−	0.0718785i	−0.742132	+	0.670254i	$0.766185\pi$
$588$	−3.71862e7			−0.182915
$589$	−2.64590e8			−1.29488
$590$	8.74990e6	−	8.74990e6i	0.0426037	−	0.0426037i
$591$			2.53109e8i			1.22616i
$592$	−4.18912e7	+	3.05858e7i	−0.201910	+	0.147419i
$593$	3.34996e8			1.60648			0.803242	−	0.595653i	$-0.203107\pi$
$593$	3.34996e8			1.60648			0.803242	+	0.595653i	$0.203107\pi$
$594$	1.03373e8	+	1.03373e8i	0.493230	+	0.493230i
$595$		−	5.52634e6i		−	0.0262353i
$596$			8.03545e6i			0.0379552i
$597$	1.88073e8	−	1.88073e8i	0.883900	−	0.883900i
$598$	9.29274e7	−	9.29274e7i	0.434551	−	0.434551i
$599$	4.53024e7			0.210785			0.105393	−	0.994431i	$-0.466390\pi$
$599$	4.53024e7			0.210785			0.105393	+	0.994431i	$0.466390\pi$
$600$	4.37694e7	−	4.37694e7i	0.202636	−	0.202636i
$601$	−1.19188e8			−0.549046			−0.274523	−	0.961581i	$-0.588520\pi$
$601$	−1.19188e8			−0.549046			−0.274523	+	0.961581i	$0.588520\pi$
$602$	−7.66369e7			−0.351276
$603$		−	4.87190e7i		−	0.222201i
$604$	−1.77068e8			−0.803579
$605$	−6.12608e6	+	6.12608e6i	−0.0276641	+	0.0276641i
$606$	−7.01348e7	−	7.01348e7i	−0.315149	−	0.315149i
$607$	−2.82611e8	−	2.82611e8i	−1.26364	−	1.26364i	−0.949316	−	0.314323i	$-0.898222\pi$
$607$	−2.82611e8	−	2.82611e8i	−1.26364	−	1.26364i	−0.314323	−	0.949316i	$-0.601778\pi$
$608$	2.71902e7			0.120977
$609$	−1.24100e8	+	1.24100e8i	−0.549440	+	0.549440i
$610$	2.41121e7	+	2.41121e7i	0.106230	+	0.106230i
$611$	−1.43746e8	+	1.43746e8i	−0.630189	+	0.630189i
$612$	−3.38214e6	−	3.38214e6i	−0.0147549	−	0.0147549i
$613$			1.25492e8i			0.544795i	0.962185	+	0.272397i	$0.0878165\pi$
$613$			1.25492e8i			0.544795i	−0.962185	+	0.272397i	$0.912183\pi$
$614$	−1.29149e8	+	1.29149e8i	−0.557938	+	0.557938i
$615$	5.04088e6	−	5.04088e6i	0.0216711	−	0.0216711i
$616$	−4.01595e7	−	4.01595e7i	−0.171809	−	0.171809i
$617$			3.41164e8i			1.45247i	0.687445	+	0.726236i	$0.258732\pi$
$617$			3.41164e8i			1.45247i	−0.687445	+	0.726236i	$0.741268\pi$
$618$	5.61031e7			0.237696
$619$			2.60228e7i			0.109719i	0.998494	+	0.0548596i	$0.0174711\pi$
$619$			2.60228e7i			0.109719i	−0.998494	+	0.0548596i	$0.982529\pi$
$620$			5.07905e7i			0.213112i
$621$	1.82900e8	+	1.82900e8i	0.763728	+	0.763728i
$622$		−	1.42454e8i		−	0.591973i
$623$	−3.35283e7	−	3.35283e7i	−0.138659	−	0.138659i
$624$	3.20253e7	+	3.20253e7i	0.131807	+	0.131807i
$625$	−2.07604e8			−0.850347
$626$	−1.04405e8			−0.425598
$627$	−9.25831e7	+	9.25831e7i	−0.375603	+	0.375603i
$628$			1.89703e6i			0.00765939i
$629$	−5.90863e6	+	3.78792e7i	−0.0237430	+	0.152212i
$630$	8.15713e6			0.0326224
$631$	−1.48969e8	−	1.48969e8i	−0.592937	−	0.592937i	0.345486	−	0.938424i	$-0.387714\pi$
$631$	−1.48969e8	−	1.48969e8i	−0.592937	−	0.592937i	−0.938424	+	0.345486i	$0.887714\pi$
$632$		−	1.49099e8i		−	0.590640i
$633$		−	7.73357e7i		−	0.304908i
$634$	2.75884e7	−	2.75884e7i	0.108258	−	0.108258i
$635$	−5.48828e7	+	5.48828e7i	−0.214346	+	0.214346i
$636$	9.30258e7			0.361603
$637$	−6.83773e7	+	6.83773e7i	−0.264542	+	0.264542i
$638$	2.00924e8			0.773696
$639$	6.26453e7			0.240096
$640$		−	5.21940e6i		−	0.0199104i
$641$	1.11737e8			0.424251			0.212125	−	0.977242i	$-0.431961\pi$
$641$	1.11737e8			0.424251			0.212125	+	0.977242i	$0.431961\pi$
$642$	7.10274e7	−	7.10274e7i	0.268424	−	0.268424i
$643$	−1.96551e7	−	1.96551e7i	−0.0739336	−	0.0739336i	0.669173	−	0.743107i	$-0.266648\pi$
$643$	−1.96551e7	−	1.96551e7i	−0.0739336	−	0.0739336i	−0.743107	+	0.669173i	$0.766648\pi$
$644$	−7.10548e7	−	7.10548e7i	−0.266033	−	0.266033i
$645$	3.39148e7			0.126389
$646$	1.42106e7	−	1.42106e7i	0.0527128	−	0.0527128i
$647$	−1.70099e7	−	1.70099e7i	−0.0628042	−	0.0628042i	0.675007	−	0.737811i	$-0.264141\pi$
$647$	−1.70099e7	−	1.70099e7i	−0.0628042	−	0.0628042i	−0.737811	+	0.675007i	$0.764141\pi$
$648$	−4.46042e7	+	4.46042e7i	−0.163927	+	0.163927i
$649$	−6.64638e7	−	6.64638e7i	−0.243137	−	0.243137i
$650$		−	1.60965e8i		−	0.586125i
$651$	−2.38289e8	+	2.38289e8i	−0.863696	+	0.863696i
$652$	−7.72053e7	+	7.72053e7i	−0.278551	+	0.278551i
$653$	1.88118e8	+	1.88118e8i	0.675600	+	0.675600i	0.959001	−	0.283401i	$-0.0914628\pi$
$653$	1.88118e8	+	1.88118e8i	0.675600	+	0.675600i	−0.283401	+	0.959001i	$0.591463\pi$
$654$		−	3.38776e7i		−	0.121110i
$655$	−4.68303e7			−0.166649
$656$			1.12452e7i			0.0398343i
$657$			2.60047e7i			0.0916970i
$658$	1.09912e8	+	1.09912e8i	0.385804	+	0.385804i
$659$			3.82786e8i			1.33752i	0.743479	+	0.668759i	$0.233174\pi$
$659$			3.82786e8i			1.33752i	−0.743479	+	0.668759i	$0.766826\pi$
$660$	1.77721e7	+	1.77721e7i	0.0618170	+	0.0618170i
$661$	−1.45374e8	−	1.45374e8i	−0.503363	−	0.503363i	0.409118	−	0.912481i	$-0.365836\pi$
$661$	−1.45374e8	−	1.45374e8i	−0.503363	−	0.503363i	−0.912481	+	0.409118i	$0.865836\pi$
$662$	−2.35663e8			−0.812303
$663$	3.34752e7			0.114864
$664$	−5.00077e7	+	5.00077e7i	−0.170817	+	0.170817i
$665$			3.42736e7i			0.116545i
$666$	−5.59114e7	−	8.72142e6i	−0.189268	−	0.0295233i
$667$	3.55498e8			1.19801
$668$	8.31883e7	+	8.31883e7i	0.279083	+	0.279083i
$669$		−	8.60075e7i		−	0.287249i
$670$		−	3.92942e7i		−	0.130648i
$671$	1.83155e8	−	1.83155e8i	0.606248	−	0.606248i
$672$	2.44874e7	−	2.44874e7i	0.0806928	−	0.0806928i
$673$	4.26501e8			1.39918			0.699591	−	0.714543i	$-0.253365\pi$
$673$	4.26501e8			1.39918			0.699591	+	0.714543i	$0.253365\pi$
$674$	2.80889e8	−	2.80889e8i	0.917391	−	0.917391i
$675$	3.16811e8			1.03012
$676$	−3.66830e7			−0.118748
$677$			4.67635e8i			1.50710i	0.657392	+	0.753549i	$0.271659\pi$
$677$			4.67635e8i			1.50710i	−0.657392	+	0.753549i	$0.728341\pi$
$678$	1.32066e8			0.423744
$679$	5.02277e7	−	5.02277e7i	0.160448	−	0.160448i
$680$	−2.72786e6	−	2.72786e6i	−0.00867551	−	0.00867551i
$681$	4.71905e7	+	4.71905e7i	0.149422	+	0.149422i
$682$	3.85802e8			1.21622
$683$	2.53555e8	−	2.53555e8i	0.795813	−	0.795813i	−0.186620	−	0.982432i	$-0.559753\pi$
$683$	2.53555e8	−	2.53555e8i	0.795813	−	0.795813i	0.982432	+	0.186620i	$0.0597532\pi$
$684$	2.09755e7	+	2.09755e7i	0.0655458	+	0.0655458i
$685$	5.27852e7	−	5.27852e7i	0.164225	−	0.164225i
$686$	1.74315e8	+	1.74315e8i	0.539962	+	0.539962i
$687$			5.34004e8i			1.64693i
$688$	−3.78287e7	+	3.78287e7i	−0.116160	+	0.116160i
$689$	1.71054e8	−	1.71054e8i	0.522969	−	0.522969i
$690$	3.14445e7	+	3.14445e7i	0.0957188	+	0.0957188i
$691$			2.56323e8i			0.776880i	0.921474	+	0.388440i	$0.126986\pi$
$691$			2.56323e8i			0.776880i	−0.921474	+	0.388440i	$0.873014\pi$
$692$	−2.07963e8			−0.627579
$693$		−	6.19611e7i		−	0.186174i
$694$		−	1.47300e8i		−	0.440681i
$695$	−6.72521e7	−	6.72521e7i	−0.200333	−	0.200333i
$696$			1.22514e8i			0.363378i
$697$	5.87719e6	+	5.87719e6i	0.0173569	+	0.0173569i
$698$	−9.91342e6	−	9.91342e6i	−0.0291513	−	0.0291513i
$699$	−2.67826e8			−0.784190
$700$	−1.23078e8			−0.358828
$701$	2.13741e8	−	2.13741e8i	0.620490	−	0.620490i	−0.325167	−	0.945657i	$-0.605420\pi$
$701$	2.13741e8	−	2.13741e8i	0.620490	−	0.620490i	0.945657	+	0.325167i	$0.105420\pi$
$702$			2.31805e8i			0.670056i
$703$	3.66445e7	−	2.34921e8i	0.105473	−	0.676171i
$704$	−3.96463e7			−0.113628
$705$	−4.86402e7	−	4.86402e7i	−0.138812	−	0.138812i
$706$			4.50140e8i			1.27919i
$707$			1.97216e8i			0.558065i
$708$	4.05265e7	−	4.05265e7i	0.114193	−	0.114193i
$709$	2.10544e8	−	2.10544e8i	0.590752	−	0.590752i	−0.347083	−	0.937834i	$-0.612828\pi$
$709$	2.10544e8	−	2.10544e8i	0.590752	−	0.590752i	0.937834	+	0.347083i	$0.112828\pi$
$710$	5.05264e7			0.141170
$711$	1.15020e8	−	1.15020e8i	0.320012	−	0.320012i
$712$	−3.30998e7			−0.0917035
$713$	6.82604e8			1.88322
$714$		−	2.55961e7i		−	0.0703200i
$715$	6.53581e7			0.178806
$716$	−5.12630e7	+	5.12630e7i	−0.139658	+	0.139658i
$717$	6.23434e7	+	6.23434e7i	0.169135	+	0.169135i
$718$	−3.23609e8	−	3.23609e8i	−0.874272	−	0.874272i
$719$	5.43317e8			1.46173			0.730864	−	0.682524i	$-0.239118\pi$
$719$	5.43317e8			1.46173			0.730864	+	0.682524i	$0.239118\pi$
$720$	4.02644e6	−	4.02644e6i	0.0107876	−	0.0107876i
$721$	−7.88799e7	−	7.88799e7i	−0.210456	−	0.210456i
$722$	1.00051e8	−	1.00051e8i	0.265834	−	0.265834i
$723$	−2.12589e7	−	2.12589e7i	−0.0562505	−	0.0562505i
$724$			1.66382e8i			0.438419i
$725$	3.07889e8	−	3.07889e8i	0.807941	−	0.807941i
$726$	−2.83739e7	+	2.83739e7i	−0.0741496	+	0.0741496i
$727$	−4.10156e8	−	4.10156e8i	−1.06745	−	1.06745i	−0.997555	−	0.0698905i	$-0.977735\pi$
$727$	−4.10156e8	−	4.10156e8i	−1.06745	−	1.06745i	−0.0698905	−	0.997555i	$-0.522265\pi$
$728$		−	9.00539e7i		−	0.233404i
$729$	−4.27807e8			−1.10425
$730$			2.09740e7i			0.0539154i
$731$			3.95415e7i			0.101228i
$732$	1.11679e8	+	1.11679e8i	0.284733	+	0.284733i
$733$		−	5.08700e7i		−	0.129166i	−0.997912	−	0.0645832i	$-0.979428\pi$
$733$		−	5.08700e7i		−	0.129166i	0.997912	−	0.0645832i	$-0.0205718\pi$
$734$	−1.35383e8	−	1.35383e8i	−0.342355	−	0.342355i
$735$	−2.31373e7	−	2.31373e7i	−0.0582708	−	0.0582708i
$736$	−7.01467e7			−0.175944
$737$	−2.98477e8			−0.745603
$738$	−8.67501e6	+	8.67501e6i	−0.0215824	+	0.0215824i
$739$			5.23959e8i			1.29827i	0.760675	+	0.649133i	$0.224868\pi$
$739$			5.23959e8i			1.29827i	−0.760675	+	0.649133i	$0.775132\pi$
$740$	−4.50952e7	−	7.03423e6i	−0.111285	−	0.0173589i
$741$	−2.07609e8			−0.510259
$742$	−1.30793e8	−	1.30793e8i	−0.320163	−	0.320163i
$743$		−	6.38576e8i		−	1.55685i	−0.627739	−	0.778424i	$-0.716019\pi$
$743$		−	6.38576e8i		−	1.55685i	0.627739	−	0.778424i	$-0.283981\pi$
$744$			2.35244e8i			0.571214i
$745$	−4.99967e6	+	4.99967e6i	−0.0120913	+	0.0120913i
$746$	−3.85639e8	+	3.85639e8i	−0.928890	+	0.928890i
$747$	−7.71556e7			−0.185100
$748$	−2.07207e7	+	2.07207e7i	−0.0495106	+	0.0495106i
$749$	−1.99726e8			−0.475324
$750$	1.11845e8			0.265114
$751$			5.37504e8i			1.26900i	0.772923	+	0.634500i	$0.218794\pi$
$751$			5.37504e8i			1.26900i	−0.772923	+	0.634500i	$0.781206\pi$
$752$	1.08507e8			0.255155
$753$	−2.05680e8	+	2.05680e8i	−0.481734	+	0.481734i
$754$	2.25277e8	+	2.25277e8i	0.525535	+	0.525535i
$755$	−1.10172e8	−	1.10172e8i	−0.255994	−	0.255994i
$756$	1.77244e8			0.410211
$757$	−5.03846e8	+	5.03846e8i	−1.16148	+	1.16148i	−0.177325	+	0.984152i	$0.556744\pi$
$757$	−5.03846e8	+	5.03846e8i	−1.16148	+	1.16148i	−0.984152	+	0.177325i	$0.943256\pi$
$758$	1.01487e8	+	1.01487e8i	0.233026	+	0.233026i
$759$	2.38851e8	−	2.38851e8i	0.546262	−	0.546262i
$760$	1.69178e7	+	1.69178e7i	0.0385392	+	0.0385392i
$761$			5.44247e8i			1.23493i	0.786598	+	0.617465i	$0.211840\pi$
$761$			5.44247e8i			1.23493i	−0.786598	+	0.617465i	$0.788160\pi$
$762$	−2.54198e8	+	2.54198e8i	−0.574523	+	0.574523i
$763$	−4.76312e7	+	4.76312e7i	−0.107230	+	0.107230i
$764$	2.18632e8	+	2.18632e8i	0.490268	+	0.490268i
$765$		−	4.20874e6i		−	0.00940087i
$766$	−8.50506e7			−0.189231
$767$		−	1.49039e8i		−	0.330303i
$768$		−	2.41744e7i		−	0.0533670i
$769$	−2.69660e8	−	2.69660e8i	−0.592976	−	0.592976i	0.345458	−	0.938434i	$-0.387724\pi$
$769$	−2.69660e8	−	2.69660e8i	−0.592976	−	0.592976i	−0.938434	+	0.345458i	$0.887724\pi$
$770$		−	4.99746e7i		−	0.109465i
$771$	7.10067e7	+	7.10067e7i	0.154930	+	0.154930i
$772$	8.12365e7	+	8.12365e7i	0.176563	+	0.176563i
$773$	−4.23058e8			−0.915927			−0.457964	−	0.888971i	$-0.651421\pi$
$773$	−4.23058e8			−0.915927			−0.457964	+	0.888971i	$0.651421\pi$
$774$	−5.83650e7			−0.125872
$775$	5.91188e8	−	5.91188e8i	1.27005	−	1.27005i
$776$		−	4.95858e7i		−	0.106114i
$777$	−1.78567e8	−	2.44571e8i	−0.380661	−	0.521365i
$778$	−4.36558e8			−0.927051
$779$	−3.64495e7	−	3.64495e7i	−0.0771044	−	0.0771044i
$780$			3.98523e7i			0.0839788i
$781$		−	3.83796e8i		−	0.805651i
$782$	−3.66613e7	+	3.66613e7i	−0.0766634	+	0.0766634i
$783$	−4.43390e8	+	4.43390e8i	−0.923636	+	0.923636i
$784$	5.16150e7			0.107109
$785$	−1.18033e6	+	1.18033e6i	−0.00244003	+	0.00244003i
$786$	−2.16902e8			−0.446678
$787$	4.49195e7			0.0921533			0.0460766	−	0.998938i	$-0.485328\pi$
$787$	4.49195e7			0.0921533			0.0460766	+	0.998938i	$0.485328\pi$
$788$		−	3.51319e8i		−	0.717998i
$789$	−4.61912e8			−0.940433
$790$	9.27694e7	−	9.27694e7i	0.188158	−	0.188158i
$791$	−1.85683e8	−	1.85683e8i	−0.375182	−	0.375182i
$792$	−3.05846e7	−	3.05846e7i	−0.0615641	−	0.0615641i
$793$	4.10707e8			0.823592
$794$	3.39633e8	−	3.39633e8i	0.678498	−	0.678498i
$795$	5.78808e7	+	5.78808e7i	0.115195	+	0.115195i
$796$	−2.61047e8	+	2.61047e8i	−0.517583	+	0.517583i
$797$	−6.22011e8	−	6.22011e8i	−1.22863	−	1.22863i	−0.964480	−	0.264154i	$-0.914907\pi$
$797$	−6.22011e8	−	6.22011e8i	−1.22863	−	1.22863i	−0.264154	−	0.964480i	$-0.585093\pi$
$798$			1.58743e8i			0.312382i
$799$	5.67099e7	−	5.67099e7i	0.111178	−	0.111178i
$800$	−6.07525e7	+	6.07525e7i	−0.118657	+	0.118657i
$801$	−2.55345e7	−	2.55345e7i	−0.0496854	−	0.0496854i
$802$		−	3.61125e8i		−	0.700059i
$803$	1.59317e8			0.307692
$804$		−	1.81997e8i		−	0.350184i
$805$		−	8.84207e7i		−	0.169499i
$806$	4.32562e8	+	4.32562e8i	0.826119	+	0.826119i
$807$		−	5.24585e8i		−	0.998148i
$808$	9.73480e7	+	9.73480e7i	0.184541	+	0.184541i
$809$	−1.85491e8	−	1.85491e8i	−0.350329	−	0.350329i	0.509903	−	0.860232i	$-0.329681\pi$
$809$	−1.85491e8	−	1.85491e8i	−0.350329	−	0.350329i	−0.860232	+	0.509903i	$0.829681\pi$
$810$	−5.55056e7			−0.104444
$811$	−7.67039e8			−1.43799			−0.718993	−	0.695017i	$-0.755397\pi$
$811$	−7.67039e8			−1.43799			−0.718993	+	0.695017i	$0.755397\pi$
$812$	1.72253e8	−	1.72253e8i	0.321734	−	0.321734i
$813$		−	5.77318e8i		−	1.07434i
$814$	−5.34317e7	+	3.42541e8i	−0.0990662	+	0.635096i
$815$	−9.60744e7			−0.177474
$816$	−1.26345e7	−	1.26345e7i	−0.0232534	−	0.0232534i
$817$		−	2.45231e8i		−	0.449685i
$818$			2.06673e8i			0.377592i
$819$	6.94709e7	−	6.94709e7i	0.126460	−	0.126460i
$820$	−6.99680e6	+	6.99680e6i	−0.0126899	+	0.0126899i
$821$	8.77431e8			1.58556			0.792781	−	0.609506i	$-0.208632\pi$
$821$	8.77431e8			1.58556			0.792781	+	0.609506i	$0.208632\pi$
$822$	2.44483e8	−	2.44483e8i	0.440182	−	0.440182i
$823$	1.72080e8			0.308696			0.154348	−	0.988017i	$-0.450672\pi$
$823$	1.72080e8			0.308696			0.154348	+	0.988017i	$0.450672\pi$
$824$	−7.78719e7			−0.139187
$825$		−	4.13726e8i		−	0.736803i
$826$	−1.13959e8			−0.202213
$827$	−2.84366e8	+	2.84366e8i	−0.502761	+	0.502761i	−0.912295	−	0.409534i	$-0.865691\pi$
$827$	−2.84366e8	+	2.84366e8i	−0.502761	+	0.502761i	0.409534	+	0.912295i	$0.365691\pi$
$828$	−5.41138e7	−	5.41138e7i	−0.0953273	−	0.0953273i
$829$	−4.32757e8	−	4.32757e8i	−0.759592	−	0.759592i	0.216656	−	0.976248i	$-0.430485\pi$
$829$	−4.32757e8	−	4.32757e8i	−0.759592	−	0.759592i	−0.976248	+	0.216656i	$0.930485\pi$
$830$	−6.22296e7			−0.108834
$831$	1.59429e8	−	1.59429e8i	0.277820	−	0.277820i
$832$	−4.44515e7	−	4.44515e7i	−0.0771821	−	0.0771821i
$833$	2.69759e7	−	2.69759e7i	0.0466704	−	0.0466704i
$834$	−3.11488e8	−	3.11488e8i	−0.536962	−	0.536962i
$835$			1.03520e8i			0.177813i
$836$	1.28506e8	−	1.28506e8i	0.219941	−	0.219941i
$837$	−8.51369e8	+	8.51369e8i	−1.45192	+	1.45192i
$838$	1.05475e8	+	1.05475e8i	0.179233	+	0.179233i
$839$		−	2.41895e8i		−	0.409582i	−0.978806	−	0.204791i	$-0.934349\pi$
$839$		−	2.41895e8i		−	0.409582i	0.978806	−	0.204791i	$-0.0656514\pi$
$840$	3.04722e7			0.0514121
$841$			2.66982e8i			0.448843i
$842$			1.00686e8i			0.168668i
$843$	6.22633e8	+	6.22633e8i	1.03932	+	1.03932i
$844$			1.07343e8i			0.178544i
$845$	−2.28242e7	−	2.28242e7i	−0.0378290	−	0.0378290i
$846$	8.37064e7	+	8.37064e7i	0.138244	+	0.138244i
$847$	7.97863e7			0.131304
$848$	−1.29121e8			−0.211743
$849$	6.53634e8	−	6.53634e8i	1.06810	−	1.06810i
$850$			6.35031e7i			0.103404i
$851$	−9.45374e7	+	6.06062e8i	−0.153396	+	0.983396i
$852$	2.34021e8			0.378386
$853$	−1.16422e8	−	1.16422e8i	−0.187580	−	0.187580i	0.607069	−	0.794649i	$-0.292345\pi$
$853$	−1.16422e8	−	1.16422e8i	−0.187580	−	0.187580i	−0.794649	+	0.607069i	$0.792345\pi$
$854$		−	3.14037e8i		−	0.504206i
$855$			2.61020e7i			0.0417615i
$856$	−9.85870e7	+	9.85870e7i	−0.157180	+	0.157180i
$857$	−1.19285e8	+	1.19285e8i	−0.189514	+	0.189514i	−0.795486	−	0.605972i	$-0.792784\pi$
$857$	−1.19285e8	+	1.19285e8i	−0.189514	+	0.189514i	0.605972	+	0.795486i	$0.292784\pi$
$858$	3.02716e8			0.479263
$859$	4.08417e8	−	4.08417e8i	0.644353	−	0.644353i	−0.307270	−	0.951623i	$-0.599415\pi$
$859$	4.08417e8	−	4.08417e8i	0.644353	−	0.644353i	0.951623	+	0.307270i	$0.0994153\pi$
$860$	−4.70742e7			−0.0740095
$861$	−6.56525e7			−0.102859
$862$			1.49637e8i			0.233624i
$863$	7.07963e8			1.10148			0.550742	−	0.834676i	$-0.314345\pi$
$863$	7.07963e8			1.10148			0.550742	+	0.834676i	$0.314345\pi$
$864$	8.74896e7	−	8.74896e7i	0.135649	−	0.135649i
$865$	−1.29395e8	−	1.29395e8i	−0.199926	−	0.199926i
$866$	7.01954e7	+	7.01954e7i	0.108082	+	0.108082i
$867$	5.43274e8			0.833608
$868$	3.30748e8	−	3.30748e8i	0.505753	−	0.505753i
$869$	−7.04672e8	−	7.04672e8i	−1.07381	−	1.07381i
$870$	−7.62284e7	+	7.62284e7i	−0.115760	+	0.115760i
$871$	−3.34652e8	−	3.34652e8i	−0.506453	−	0.506453i
$872$			4.70225e7i			0.0709179i
$873$	3.82523e7	−	3.82523e7i	0.0574930	−	0.0574930i
$874$	2.27368e8	−	2.27368e8i	0.340562	−	0.340562i
$875$	−1.57252e8	−	1.57252e8i	−0.234732	−	0.234732i
$876$			9.71442e7i			0.144512i
$877$	−6.08475e8			−0.902077			−0.451039	−	0.892504i	$-0.648946\pi$
$877$	−6.08475e8			−0.902077			−0.451039	+	0.892504i	$0.648946\pi$
$878$			5.19704e8i			0.767843i
$879$		−	7.50749e8i		−	1.10542i
$880$	−2.46680e7	−	2.46680e7i	−0.0361981	−	0.0361981i
$881$			1.16840e9i			1.70870i	0.519700	+	0.854349i	$0.326044\pi$
$881$			1.16840e9i			1.70870i	−0.519700	+	0.854349i	$0.673956\pi$
$882$	3.98177e7	+	3.98177e7i	0.0580324	+	0.0580324i
$883$	7.74989e8	+	7.74989e8i	1.12568	+	1.12568i	0.990872	+	0.134803i	$0.0430402\pi$
$883$	7.74989e8	+	7.74989e8i	1.12568	+	1.12568i	0.134803	+	0.990872i	$0.456960\pi$
$884$	−4.64641e7			−0.0672606
$885$	5.04312e7			0.0727562
$886$	−9.55693e7	+	9.55693e7i	−0.137410	+	0.137410i
$887$		−	1.92169e7i		−	0.0275368i	−0.999905	−	0.0137684i	$-0.995617\pi$
$887$		−	1.92169e7i		−	0.0275368i	0.999905	−	0.0137684i	$-0.00438275\pi$
$888$	−2.08865e8	−	3.25801e7i	−0.298282	−	0.0465279i
$889$	7.14796e8			1.01736
$890$	−2.05948e7	−	2.05948e7i	−0.0292137	−	0.0292137i
$891$			4.21618e8i			0.596054i
$892$			1.19380e8i			0.168204i
$893$	−3.51707e8	+	3.51707e8i	−0.493885	+	0.493885i
$894$	−2.31567e7	+	2.31567e7i	−0.0324089	+	0.0324089i
$895$	−6.37918e7			−0.0889807
$896$	−3.39888e7	+	3.39888e7i	−0.0472511	+	0.0472511i
$897$	5.35600e8			0.742101
$898$	2.32690e8			0.321328
$899$			1.65478e9i			2.27752i
$900$	−9.37335e7			−0.128578
$901$	−6.74835e7	+	6.74835e7i	−0.0922621	+	0.0922621i
$902$	5.31473e7	+	5.31473e7i	0.0724206	+	0.0724206i
$903$	−2.20854e8	−	2.20854e8i	−0.299945	−	0.299945i
$904$	−1.83310e8			−0.248131
$905$	−1.03523e8	+	1.03523e8i	−0.139666	+	0.139666i
$906$	−5.10277e8	−	5.10277e8i	−0.686153	−	0.686153i
$907$	6.89536e8	−	6.89536e8i	0.924134	−	0.924134i	−0.0731841	−	0.997318i	$-0.523316\pi$
$907$	6.89536e8	−	6.89536e8i	0.924134	−	0.924134i	0.997318	+	0.0731841i	$0.0233161\pi$
$908$	−6.55010e7	−	6.55010e7i	−0.0874965	−	0.0874965i
$909$			1.50196e8i			0.199971i
$910$	5.60316e7	−	5.60316e7i	0.0743548	−	0.0743548i
$911$	−1.74872e8	+	1.74872e8i	−0.231294	+	0.231294i	−0.813233	−	0.581939i	$-0.802294\pi$
$911$	−1.74872e8	+	1.74872e8i	−0.231294	+	0.231294i	0.581939	+	0.813233i	$0.302294\pi$
$912$	7.83572e7	+	7.83572e7i	0.103299	+	0.103299i
$913$			4.72693e8i			0.621108i
$914$	−6.60410e8			−0.864919
$915$			1.38974e8i			0.181413i
$916$		−	7.41204e8i		−	0.964387i
$917$	3.04959e8	+	3.04959e8i	0.395489	+	0.395489i
$918$		−	9.14507e7i		−	0.118211i
$919$	6.25959e8	+	6.25959e8i	0.806491	+	0.806491i	0.984101	−	0.177610i	$-0.0568366\pi$
$919$	6.25959e8	+	6.25959e8i	0.806491	+	0.806491i	−0.177610	+	0.984101i	$0.556837\pi$
$920$	−4.36454e7	−	4.36454e7i	−0.0560499	−	0.0560499i
$921$	−7.44368e8			−0.952815
$922$	−2.71176e8			−0.345987
$923$	4.30312e8	−	4.30312e8i	0.547241	−	0.547241i
$924$		−	2.31465e8i		−	0.293406i
$925$	4.43020e8	+	6.06774e8i	0.559755	+	0.766658i
$926$	−7.47206e8			−0.941039
$927$	−6.00733e7	−	6.00733e7i	−0.0754123	−	0.0754123i
$928$		−	1.70051e8i		−	0.212782i
$929$		−	1.44002e8i		−	0.179606i	−0.995960	−	0.0898032i	$-0.971376\pi$
$929$		−	1.44002e8i		−	0.179606i	0.995960	−	0.0898032i	$-0.0286238\pi$
$930$	−1.46369e8	+	1.46369e8i	−0.181970	+	0.181970i
$931$	−1.67301e8	+	1.67301e8i	−0.207324	+	0.207324i
$932$	3.71746e8			0.459196
$933$	4.10525e8	−	4.10525e8i	0.505469	−	0.505469i
$934$	1.05489e9			1.29469
$935$	−2.57848e7			−0.0315449
$936$		−	6.85831e7i		−	0.0836353i
$937$	−1.24599e8			−0.151459			−0.0757294	−	0.997128i	$-0.524129\pi$
$937$	−1.24599e8			−0.151459			−0.0757294	+	0.997128i	$0.524129\pi$
$938$	−2.55884e8	+	2.55884e8i	−0.310052	+	0.310052i
$939$	−3.00877e8	−	3.00877e8i	−0.363407	−	0.363407i
$940$	6.75132e7	+	6.75132e7i	0.0812840	+	0.0812840i
$941$	4.94304e8			0.593233			0.296617	−	0.954997i	$-0.404142\pi$
$941$	4.94304e8			0.593233			0.296617	+	0.954997i	$0.404142\pi$
$942$	−5.46688e6	+	5.46688e6i	−0.00654014	+	0.00654014i
$943$	9.40343e7	+	9.40343e7i	0.112138	+	0.112138i
$944$	−5.62513e7	+	5.62513e7i	−0.0668677	+	0.0668677i
$945$	1.10282e8	+	1.10282e8i	0.130680	+	0.130680i
$946$			3.57573e8i			0.422368i
$947$	−5.85527e8	+	5.85527e8i	−0.689441	+	0.689441i	−0.962108	−	0.272667i	$-0.912094\pi$
$947$	−5.85527e8	+	5.85527e8i	−0.689441	+	0.689441i	0.272667	+	0.962108i	$0.412094\pi$
$948$	4.29676e8	−	4.29676e8i	0.504331	−	0.504331i
$949$	1.78627e8	+	1.78627e8i	0.209001	+	0.209001i
$950$		−	3.93837e8i		−	0.459352i
$951$	1.59010e8			0.184877
$952$			3.55277e7i			0.0411771i
$953$		−	1.05903e9i		−	1.22357i	−0.791025	−	0.611784i	$-0.790452\pi$
$953$		−	1.05903e9i		−	1.22357i	0.791025	−	0.611784i	$-0.209548\pi$
$954$	−9.96088e7	−	9.96088e7i	−0.114724	−	0.114724i
$955$			2.72066e8i			0.312366i
$956$	−8.65334e7	−	8.65334e7i	−0.0990399	−	0.0990399i
$957$	5.79027e8	+	5.79027e8i	0.660637	+	0.660637i
$958$	5.77396e7			0.0656716
$959$	−6.87476e8			−0.779474
$960$	1.50414e7	−	1.50414e7i	0.0170010	−	0.0170010i
$961$			2.28990e9i			2.58016i
$962$	−4.43965e8	+	3.24150e8i	−0.498682	+	0.364100i
$963$	−1.52107e8			−0.170322
$964$	2.95076e7	+	2.95076e7i	0.0329385	+	0.0329385i
$965$			1.01091e8i			0.112494i
$966$		−	4.09534e8i		−	0.454317i
$967$	−3.71495e8	+	3.71495e8i	−0.410841	+	0.410841i	−0.882031	−	0.471191i	$-0.843824\pi$
$967$	−3.71495e8	+	3.71495e8i	−0.410841	+	0.410841i	0.471191	+	0.882031i	$0.343824\pi$
$968$	3.93833e7	−	3.93833e7i	0.0434196	−	0.0434196i
$969$	8.19049e7			0.0900199
$970$	3.08523e7	−	3.08523e7i	0.0338044	−	0.0338044i
$971$	1.57280e9			1.71797			0.858986	−	0.511999i	$-0.171095\pi$
$971$	1.57280e9			1.71797			0.858986	+	0.511999i	$0.171095\pi$
$972$	2.41198e8			0.262648
$973$			8.75893e8i			0.950851i
$974$	7.62960e8			0.825705
$975$	4.63871e8	−	4.63871e8i	0.500476	−	0.500476i
$976$	−1.55012e8	−	1.55012e8i	−0.166731	−	0.166731i
$977$	−7.50594e8	−	7.50594e8i	−0.804862	−	0.804862i	0.178989	−	0.983851i	$-0.442717\pi$
$977$	−7.50594e8	−	7.50594e8i	−0.804862	−	0.804862i	−0.983851	+	0.178989i	$0.942717\pi$
$978$	−4.44983e8			−0.475693
$979$	−1.56437e8	+	1.56437e8i	−0.166721	+	0.166721i
$980$	3.21149e7	+	3.21149e7i	0.0341215	+	0.0341215i
$981$	−3.62749e7	+	3.62749e7i	−0.0384237	+	0.0384237i
$982$	7.56087e7	+	7.56087e7i	0.0798431	+	0.0798431i
$983$		−	9.64145e8i		−	1.01504i	−0.861641	−	0.507519i	$-0.830563\pi$
$983$		−	9.64145e8i		−	1.01504i	0.861641	−	0.507519i	$-0.169437\pi$
$984$	−3.24067e7	+	3.24067e7i	−0.0340134	+	0.0340134i
$985$	2.18591e8	−	2.18591e8i	0.228730	−	0.228730i
$986$	−8.88752e7	−	8.88752e7i	−0.0927150	−	0.0927150i
$987$			6.33491e8i			0.658854i
$988$	2.88163e8			0.298791
$989$			6.32659e8i			0.654004i
$990$		−	3.80596e7i		−	0.0392246i
$991$	7.48567e8	+	7.48567e8i	0.769148	+	0.769148i	0.977956	−	0.208809i	$-0.0669586\pi$
$991$	7.48567e8	+	7.48567e8i	0.769148	+	0.769148i	−0.208809	+	0.977956i	$0.566959\pi$
$992$		−	3.26521e8i		−	0.334485i
$993$	−6.79139e8	−	6.79139e8i	−0.693603	−	0.693603i
$994$	−3.29028e8	−	3.29028e8i	−0.335023	−	0.335023i
$995$	−3.24848e8			−0.329770
$996$	−2.88226e8			−0.291712
$997$	−9.55691e7	+	9.55691e7i	−0.0964344	+	0.0964344i	−0.753678	−	0.657244i	$-0.771722\pi$
$997$	−9.55691e7	+	9.55691e7i	−0.0964344	+	0.0964344i	0.657244	+	0.753678i	$0.271722\pi$
$998$			2.11302e8i			0.212575i
$999$	−6.37993e8	−	8.73814e8i	−0.639911	−	0.876440i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.7.d.b.31.3	✓	20
37.6	odd	4	inner	74.7.d.b.43.8	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.7.d.b.31.3	✓	20	1.1	even	1	trivial
74.7.d.b.43.8	yes	20	37.6	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:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	74.d (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.00000 - 4.00000i) q^{2} -23.0545i q^{3} +32.0000i q^{4} +(-19.9104 + 19.9104i) q^{5} +(-92.2182 + 92.2182i) q^{6} +259.314 q^{7} +(128.000 - 128.000i) q^{8} +197.488 q^{9} +O(q^{10})\)	\(q+(-4.00000 - 4.00000i) q^{2} -23.0545i q^{3} +32.0000i q^{4} +(-19.9104 + 19.9104i) q^{5} +(-92.2182 + 92.2182i) q^{6} +259.314 q^{7} +(128.000 - 128.000i) q^{8} +197.488 q^{9} +159.283 q^{10} -1209.91i q^{11} +737.745 q^{12} +(1356.55 - 1356.55i) q^{13} +(-1037.26 - 1037.26i) q^{14} +(459.026 + 459.026i) q^{15} -1024.00 q^{16} +(-535.181 + 535.181i) q^{17} +(-789.952 - 789.952i) q^{18} +(3319.12 - 3319.12i) q^{19} +(-637.134 - 637.134i) q^{20} -5978.37i q^{21} +(-4839.63 + 4839.63i) q^{22} +(-8562.83 + 8562.83i) q^{23} +(-2950.98 - 2950.98i) q^{24} +14832.1i q^{25} -10852.4 q^{26} -21359.8i q^{27} +8298.05i q^{28} +(-20758.2 - 20758.2i) q^{29} -3672.21i q^{30} +(-39858.6 - 39858.6i) q^{31} +(4096.00 + 4096.00i) q^{32} -27893.9 q^{33} +4281.45 q^{34} +(-5163.05 + 5163.05i) q^{35} +6319.62i q^{36} +(40909.3 - 29868.9i) q^{37} -26552.9 q^{38} +(-31274.7 - 31274.7i) q^{39} +5097.07i q^{40} -10981.7i q^{41} +(-23913.5 + 23913.5i) q^{42} +(36942.1 - 36942.1i) q^{43} +38717.1 q^{44} +(-3932.07 + 3932.07i) q^{45} +68502.7 q^{46} -105964. q^{47} +23607.9i q^{48} -50405.2 q^{49} +(59328.6 - 59328.6i) q^{50} +(12338.4 + 12338.4i) q^{51} +(43409.7 + 43409.7i) q^{52} +126095. q^{53} +(-85439.0 + 85439.0i) q^{54} +(24089.8 + 24089.8i) q^{55} +(33192.2 - 33192.2i) q^{56} +(-76520.7 - 76520.7i) q^{57} +166066. i q^{58} +(54932.9 - 54932.9i) q^{59} +(-14688.8 + 14688.8i) q^{60} +(151379. + 151379. i) q^{61} +318868. i q^{62} +51211.4 q^{63} -32768.0i q^{64} +54019.1i q^{65} +(111576. + 111576. i) q^{66} -246693. i q^{67} +(-17125.8 - 17125.8i) q^{68} +(197412. + 197412. i) q^{69} +41304.4 q^{70} +317210. q^{71} +(25278.5 - 25278.5i) q^{72} +131677. i q^{73} +(-283113. - 44161.7i) q^{74} +341948. q^{75} +(106212. + 106212. i) q^{76} -313746. i q^{77} +250197. i q^{78} +(582417. - 582417. i) q^{79} +(20388.3 - 20388.3i) q^{80} -348471. q^{81} +(-43926.7 + 43926.7i) q^{82} -390685. q^{83} +191308. q^{84} -21311.4i q^{85} -295537. q^{86} +(-478571. + 478571. i) q^{87} +(-154868. - 154868. i) q^{88} +(-129296. - 129296. i) q^{89} +31456.6 q^{90} +(351773. - 351773. i) q^{91} +(-274011. - 274011. i) q^{92} +(-918921. + 918921. i) q^{93} +(423856. + 423856. i) q^{94} +132170. i q^{95} +(94431.4 - 94431.4i) q^{96} +(193694. - 193694. i) q^{97} +(201621. + 201621. i) q^{98} -238943. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 80 q^{2} + 60 q^{5} + 256 q^{6} + 104 q^{7} + 2560 q^{8} - 6472 q^{9}+O(q^{10}) \) 20 * q - 80 * q^2 + 60 * q^5 + 256 * q^6 + 104 * q^7 + 2560 * q^8 - 6472 * q^9	\( 20 q - 80 q^{2} + 60 q^{5} + 256 q^{6} + 104 q^{7} + 2560 q^{8} - 6472 q^{9} - 480 q^{10} - 2048 q^{12} + 1560 q^{13} - 416 q^{14} - 2136 q^{15} - 20480 q^{16} + 16000 q^{17} + 25888 q^{18} + 3838 q^{19} + 1920 q^{20} + 8928 q^{22} - 6478 q^{23} + 8192 q^{24} - 12480 q^{26} - 1964 q^{29} + 117662 q^{31} + 81920 q^{32} - 92624 q^{33} - 128000 q^{34} - 104456 q^{35} - 17618 q^{37} - 30704 q^{38} + 121012 q^{39} + 213472 q^{42} + 65582 q^{43} - 71424 q^{44} - 466848 q^{45} + 51824 q^{46} - 168176 q^{47} + 563124 q^{49} - 379904 q^{50} + 560888 q^{51} + 49920 q^{52} + 561604 q^{53} - 139120 q^{54} - 1395304 q^{55} + 13312 q^{56} + 631036 q^{57} - 376510 q^{59} + 68352 q^{60} + 836700 q^{61} - 275908 q^{63} + 370496 q^{66} + 512000 q^{68} - 1616748 q^{69} + 835648 q^{70} - 94584 q^{71} - 828416 q^{72} + 133200 q^{74} + 20340 q^{75} + 122816 q^{76} - 2525594 q^{79} - 61440 q^{80} + 2933572 q^{81} - 1816480 q^{82} + 715304 q^{83} - 1707776 q^{84} - 524656 q^{86} + 900256 q^{87} + 285696 q^{88} - 952068 q^{89} + 3734784 q^{90} - 1351840 q^{91} - 207296 q^{92} + 580320 q^{93} + 672704 q^{94} - 262144 q^{96} + 178132 q^{97} - 2252496 q^{98}+O(q^{100}) \) 20 * q - 80 * q^2 + 60 * q^5 + 256 * q^6 + 104 * q^7 + 2560 * q^8 - 6472 * q^9 - 480 * q^10 - 2048 * q^12 + 1560 * q^13 - 416 * q^14 - 2136 * q^15 - 20480 * q^16 + 16000 * q^17 + 25888 * q^18 + 3838 * q^19 + 1920 * q^20 + 8928 * q^22 - 6478 * q^23 + 8192 * q^24 - 12480 * q^26 - 1964 * q^29 + 117662 * q^31 + 81920 * q^32 - 92624 * q^33 - 128000 * q^34 - 104456 * q^35 - 17618 * q^37 - 30704 * q^38 + 121012 * q^39 + 213472 * q^42 + 65582 * q^43 - 71424 * q^44 - 466848 * q^45 + 51824 * q^46 - 168176 * q^47 + 563124 * q^49 - 379904 * q^50 + 560888 * q^51 + 49920 * q^52 + 561604 * q^53 - 139120 * q^54 - 1395304 * q^55 + 13312 * q^56 + 631036 * q^57 - 376510 * q^59 + 68352 * q^60 + 836700 * q^61 - 275908 * q^63 + 370496 * q^66 + 512000 * q^68 - 1616748 * q^69 + 835648 * q^70 - 94584 * q^71 - 828416 * q^72 + 133200 * q^74 + 20340 * q^75 + 122816 * q^76 - 2525594 * q^79 - 61440 * q^80 + 2933572 * q^81 - 1816480 * q^82 + 715304 * q^83 - 1707776 * q^84 - 524656 * q^86 + 900256 * q^87 + 285696 * q^88 - 952068 * q^89 + 3734784 * q^90 - 1351840 * q^91 - 207296 * q^92 + 580320 * q^93 + 672704 * q^94 - 262144 * q^96 + 178132 * q^97 - 2252496 * q^98

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