LMFDB - Embedded newform 74.7.d.b.43.3

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			43.3
Root			$24.1581i$ of defining polynomial
Character	$\chi$	$=$	74.43
Dual form			74.7.d.b.31.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.00000 + 4.00000i) q^{2} -27.1581i q^{3} -32.0000i q^{4} +(-159.256 - 159.256i) q^{5} +(108.632 + 108.632i) q^{6} +664.609 q^{7} +(128.000 + 128.000i) q^{8} -8.56259 q^{9} +O(q^{10})$	\(q+(-4.00000 + 4.00000i) q^{2} -27.1581i q^{3} -32.0000i q^{4} +(-159.256 - 159.256i) q^{5} +(108.632 + 108.632i) q^{6} +664.609 q^{7} +(128.000 + 128.000i) q^{8} -8.56259 q^{9} +1274.05 q^{10} -2209.36i q^{11} -869.059 q^{12} +(-473.143 - 473.143i) q^{13} +(-2658.44 + 2658.44i) q^{14} +(-4325.10 + 4325.10i) q^{15} -1024.00 q^{16} +(1342.92 + 1342.92i) q^{17} +(34.2503 - 34.2503i) q^{18} +(-506.246 - 506.246i) q^{19} +(-5096.20 + 5096.20i) q^{20} -18049.5i q^{21} +(8837.45 + 8837.45i) q^{22} +(-10228.9 - 10228.9i) q^{23} +(3476.24 - 3476.24i) q^{24} +35100.2i q^{25} +3785.14 q^{26} -19565.7i q^{27} -21267.5i q^{28} +(-32718.9 + 32718.9i) q^{29} -34600.8i q^{30} +(9112.78 - 9112.78i) q^{31} +(4096.00 - 4096.00i) q^{32} -60002.1 q^{33} -10743.3 q^{34} +(-105843. - 105843. i) q^{35} +274.003i q^{36} +(42981.5 - 26801.4i) q^{37} +4049.97 q^{38} +(-12849.7 + 12849.7i) q^{39} -40769.6i q^{40} +67384.5i q^{41} +(72198.1 + 72198.1i) q^{42} +(-22211.8 - 22211.8i) q^{43} -70699.6 q^{44} +(1363.65 + 1363.65i) q^{45} +81831.2 q^{46} +53904.3 q^{47} +27809.9i q^{48} +324056. q^{49} +(-140401. - 140401. i) q^{50} +(36471.1 - 36471.1i) q^{51} +(-15140.6 + 15140.6i) q^{52} -43719.6 q^{53} +(78262.9 + 78262.9i) q^{54} +(-351855. + 351855. i) q^{55} +(85070.0 + 85070.0i) q^{56} +(-13748.7 + 13748.7i) q^{57} -261751. i q^{58} +(-44386.1 - 44386.1i) q^{59} +(138403. + 138403. i) q^{60} +(-215121. + 215121. i) q^{61} +72902.3i q^{62} -5690.77 q^{63} +32768.0i q^{64} +150702. i q^{65} +(240008. - 240008. i) q^{66} +158325. i q^{67} +(42973.4 - 42973.4i) q^{68} +(-277798. + 277798. i) q^{69} +846746. q^{70} +361218. q^{71} +(-1096.01 - 1096.01i) q^{72} +300945. i q^{73} +(-64720.5 + 279132. i) q^{74} +953254. q^{75} +(-16199.9 + 16199.9i) q^{76} -1.46836e6i q^{77} -102797. i q^{78} +(-370374. - 370374. i) q^{79} +(163079. + 163079. i) q^{80} -537610. q^{81} +(-269538. - 269538. i) q^{82} +180791. q^{83} -577585. q^{84} -427736. i q^{85} +177695. q^{86} +(888583. + 888583. i) q^{87} +(282798. - 282798. i) q^{88} +(-212247. + 212247. i) q^{89} -10909.2 q^{90} +(-314455. - 314455. i) q^{91} +(-327325. + 327325. i) q^{92} +(-247486. - 247486. i) q^{93} +(-215617. + 215617. i) q^{94} +161246. i q^{95} +(-111240. - 111240. i) q^{96} +(-337007. - 337007. i) q^{97} +(-1.29623e6 + 1.29623e6i) q^{98} +18917.8i 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 $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

$n$	$39$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−4.00000	+	4.00000i	−0.500000	+	0.500000i
$2$	−4.00000	+	4.00000i	−0.500000	+	0.500000i
$3$		−	27.1581i		−	1.00586i	−0.864328	−	0.502928i	$-0.832256\pi$
$3$		−	27.1581i		−	1.00586i	0.864328	−	0.502928i	$-0.167744\pi$
$4$		−	32.0000i		−	0.500000i
$5$	−159.256	−	159.256i	−1.27405	−	1.27405i	−0.943943	−	0.330108i	$-0.892915\pi$
$5$	−159.256	−	159.256i	−1.27405	−	1.27405i	−0.330108	−	0.943943i	$-0.607085\pi$
$6$	108.632	+	108.632i	0.502928	+	0.502928i
$7$	664.609			1.93764			0.968818	−	0.247773i	$-0.0796987\pi$
$7$	664.609			1.93764			0.968818	+	0.247773i	$0.0796987\pi$
$8$	128.000	+	128.000i	0.250000	+	0.250000i
$9$	−8.56259			−0.0117457
$10$	1274.05			1.27405
$11$		−	2209.36i		−	1.65993i	−0.557818	−	0.829963i	$-0.688361\pi$
$11$		−	2209.36i		−	1.65993i	0.557818	−	0.829963i	$-0.311639\pi$
$12$	−869.059			−0.502928
$13$	−473.143	−	473.143i	−0.215359	−	0.215359i	0.591181	−	0.806539i	$-0.298662\pi$
$13$	−473.143	−	473.143i	−0.215359	−	0.215359i	−0.806539	+	0.591181i	$0.798662\pi$
$14$	−2658.44	+	2658.44i	−0.968818	+	0.968818i
$15$	−4325.10	+	4325.10i	−1.28151	+	1.28151i
$16$	−1024.00			−0.250000
$17$	1342.92	+	1342.92i	0.273340	+	0.273340i	0.830443	−	0.557103i	$-0.188087\pi$
$17$	1342.92	+	1342.92i	0.273340	+	0.273340i	−0.557103	+	0.830443i	$0.688087\pi$
$18$	34.2503	−	34.2503i	0.00587283	−	0.00587283i
$19$	−506.246	−	506.246i	−0.0738076	−	0.0738076i	0.669239	−	0.743047i	$-0.266620\pi$
$19$	−506.246	−	506.246i	−0.0738076	−	0.0738076i	−0.743047	+	0.669239i	$0.766620\pi$
$20$	−5096.20	+	5096.20i	−0.637025	+	0.637025i
$21$		−	18049.5i		−	1.94898i
$22$	8837.45	+	8837.45i	0.829963	+	0.829963i
$23$	−10228.9	−	10228.9i	−0.840709	−	0.840709i	0.148242	−	0.988951i	$-0.452638\pi$
$23$	−10228.9	−	10228.9i	−0.840709	−	0.840709i	−0.988951	+	0.148242i	$0.952638\pi$
$24$	3476.24	−	3476.24i	0.251464	−	0.251464i
$25$			35100.2i			2.24641i
$26$	3785.14			0.215359
$27$		−	19565.7i		−	0.994041i
$28$		−	21267.5i		−	0.968818i
$29$	−32718.9	+	32718.9i	−1.34154	+	1.34154i	−0.447017	+	0.894525i	$0.647514\pi$
$29$	−32718.9	+	32718.9i	−1.34154	+	1.34154i	−0.894525	+	0.447017i	$0.852486\pi$
$30$		−	34600.8i		−	1.28151i
$31$	9112.78	−	9112.78i	0.305891	−	0.305891i	−0.537423	−	0.843313i	$-0.680602\pi$
$31$	9112.78	−	9112.78i	0.305891	−	0.305891i	0.843313	+	0.537423i	$0.180602\pi$
$32$	4096.00	−	4096.00i	0.125000	−	0.125000i
$33$	−60002.1			−1.66965
$34$	−10743.3			−0.273340
$35$	−105843.	−	105843.i	−2.46865	−	2.46865i
$36$			274.003i			0.00587283i
$37$	42981.5	−	26801.4i	0.848548	−	0.529118i
$37$	42981.5	−	26801.4i	0.848548	−	0.529118i
$38$	4049.97			0.0738076
$39$	−12849.7	+	12849.7i	−0.216620	+	0.216620i
$40$		−	40769.6i		−	0.637025i
$41$			67384.5i			0.977706i	0.872366	+	0.488853i	$0.162585\pi$
$41$			67384.5i			0.977706i	−0.872366	+	0.488853i	$0.837415\pi$
$42$	72198.1	+	72198.1i	0.974491	+	0.974491i
$43$	−22211.8	−	22211.8i	−0.279369	−	0.279369i	0.553488	−	0.832857i	$-0.313297\pi$
$43$	−22211.8	−	22211.8i	−0.279369	−	0.279369i	−0.832857	+	0.553488i	$0.813297\pi$
$44$	−70699.6			−0.829963
$45$	1363.65	+	1363.65i	0.0149646	+	0.0149646i
$46$	81831.2			0.840709
$47$	53904.3			0.519195			0.259597	−	0.965717i	$-0.416410\pi$
$47$	53904.3			0.519195			0.259597	+	0.965717i	$0.416410\pi$
$48$			27809.9i			0.251464i
$49$	324056.			2.75443
$50$	−140401.	−	140401.i	−1.12321	−	1.12321i
$51$	36471.1	−	36471.1i	0.274940	−	0.274940i
$52$	−15140.6	+	15140.6i	−0.107679	+	0.107679i
$53$	−43719.6			−0.293663			−0.146831	−	0.989162i	$-0.546907\pi$
$53$	−43719.6			−0.293663			−0.146831	+	0.989162i	$0.546907\pi$
$54$	78262.9	+	78262.9i	0.497021	+	0.497021i
$55$	−351855.	+	351855.i	−2.11483	+	2.11483i
$56$	85070.0	+	85070.0i	0.484409	+	0.484409i
$57$	−13748.7	+	13748.7i	−0.0742398	+	0.0742398i
$58$		−	261751.i		−	1.34154i
$59$	−44386.1	−	44386.1i	−0.216118	−	0.216118i	0.590742	−	0.806860i	$-0.298835\pi$
$59$	−44386.1	−	44386.1i	−0.216118	−	0.216118i	−0.806860	+	0.590742i	$0.798835\pi$
$60$	138403.	+	138403.i	0.640756	+	0.640756i
$61$	−215121.	+	215121.i	−0.947748	+	0.947748i	−0.998701	−	0.0509531i	$-0.983774\pi$
$61$	−215121.	+	215121.i	−0.947748	+	0.947748i	0.0509531	+	0.998701i	$0.483774\pi$
$62$			72902.3i			0.305891i
$63$	−5690.77			−0.0227588
$64$			32768.0i			0.125000i
$65$			150702.i			0.548755i
$66$	240008.	−	240008.i	0.834823	−	0.834823i
$67$			158325.i			0.526410i	0.964740	+	0.263205i	$0.0847796\pi$
$67$			158325.i			0.526410i	−0.964740	+	0.263205i	$0.915220\pi$
$68$	42973.4	−	42973.4i	0.136670	−	0.136670i
$69$	−277798.	+	277798.i	−0.845631	+	0.845631i
$70$	846746.			2.46865
$71$	361218.			1.00924			0.504619	−	0.863342i	$-0.331633\pi$
$71$	361218.			1.00924			0.504619	+	0.863342i	$0.331633\pi$
$72$	−1096.01	−	1096.01i	−0.00293642	−	0.00293642i
$73$			300945.i			0.773604i	0.922163	+	0.386802i	$0.126420\pi$
$73$			300945.i			0.773604i	−0.922163	+	0.386802i	$0.873580\pi$
$74$	−64720.5	+	279132.i	−0.159715	+	0.688833i
$75$	953254.			2.25957
$76$	−16199.9	+	16199.9i	−0.0369038	+	0.0369038i
$77$		−	1.46836e6i		−	3.21633i
$78$		−	102797.i		−	0.216620i
$79$	−370374.	−	370374.i	−0.751206	−	0.751206i	0.223498	−	0.974704i	$-0.428252\pi$
$79$	−370374.	−	370374.i	−0.751206	−	0.751206i	−0.974704	+	0.223498i	$0.928252\pi$
$80$	163079.	+	163079.i	0.318513	+	0.318513i
$81$	−537610.			−1.01161
$82$	−269538.	−	269538.i	−0.488853	−	0.488853i
$83$	180791.			0.316186			0.158093	−	0.987424i	$-0.449465\pi$
$83$	180791.			0.316186			0.158093	+	0.987424i	$0.449465\pi$
$84$	−577585.			−0.974491
$85$		−	427736.i		−	0.696497i
$86$	177695.			0.279369
$87$	888583.	+	888583.i	1.34940	+	1.34940i
$88$	282798.	−	282798.i	0.414981	−	0.414981i
$89$	−212247.	+	212247.i	−0.301074	+	0.301074i	−0.841434	−	0.540360i	$-0.818288\pi$
$89$	−212247.	+	212247.i	−0.301074	+	0.301074i	0.540360	+	0.841434i	$0.318288\pi$
$90$	−10909.2			−0.0149646
$91$	−314455.	−	314455.i	−0.417286	−	0.417286i
$92$	−327325.	+	327325.i	−0.420354	+	0.420354i
$93$	−247486.	−	247486.i	−0.307682	−	0.307682i
$94$	−215617.	+	215617.i	−0.259597	+	0.259597i
$95$			161246.i			0.188069i
$96$	−111240.	−	111240.i	−0.125732	−	0.125732i
$97$	−337007.	−	337007.i	−0.369252	−	0.369252i	0.497952	−	0.867205i	$-0.334086\pi$
$97$	−337007.	−	337007.i	−0.369252	−	0.369252i	−0.867205	+	0.497952i	$0.834086\pi$
$98$	−1.29623e6	+	1.29623e6i	−1.37722	+	1.37722i
$99$			18917.8i			0.0194969i
$100$	1.12321e6			1.12321
$101$		−	1.00959e6i		−	0.979898i	−0.871751	−	0.489949i	$-0.837015\pi$
$101$		−	1.00959e6i		−	0.979898i	0.871751	−	0.489949i	$-0.162985\pi$
$102$			291769.i			0.274940i
$103$	822230.	−	822230.i	0.752457	−	0.752457i	−0.222480	−	0.974937i	$-0.571415\pi$
$103$	822230.	−	822230.i	0.752457	−	0.752457i	0.974937	+	0.222480i	$0.0714153\pi$
$104$		−	121125.i		−	0.107679i
$105$	−2.87450e6	+	2.87450e6i	−2.48310	+	2.48310i
$106$	174879.	−	174879.i	0.146831	−	0.146831i
$107$	−351126.			−0.286623			−0.143312	−	0.989678i	$-0.545775\pi$
$107$	−351126.			−0.286623			−0.143312	+	0.989678i	$0.545775\pi$
$108$	−626103.			−0.497021
$109$	553195.	+	553195.i	0.427168	+	0.427168i	0.887662	−	0.460495i	$-0.152328\pi$
$109$	553195.	+	553195.i	0.427168	+	0.427168i	−0.460495	+	0.887662i	$0.652328\pi$
$110$		−	2.81484e6i		−	2.11483i
$111$	−727875.	−	1.16730e6i	−0.532216	−	0.853517i
$112$	−680560.			−0.484409
$113$	1.22069e6	−	1.22069e6i	0.845997	−	0.845997i	−0.143634	−	0.989631i	$-0.545879\pi$
$113$	1.22069e6	−	1.22069e6i	0.845997	−	0.845997i	0.989631	+	0.143634i	$0.0458789\pi$
$114$		−	109989.i		−	0.0742398i
$115$			3.25804e6i			2.14221i
$116$	1.04700e6	+	1.04700e6i	0.670771	+	0.670771i
$117$	4051.33	+	4051.33i	0.00252953	+	0.00252953i
$118$	355089.			0.216118
$119$	892515.	+	892515.i	0.529633	+	0.529633i
$120$	−1.10723e6			−0.640756
$121$	−3.10972e6			−1.75535
$122$		−	1.72097e6i		−	0.947748i
$123$	1.83003e6			0.983431
$124$	−291609.	−	291609.i	−0.152945	−	0.152945i
$125$	3.10155e6	−	3.10155e6i	1.58799	−	1.58799i
$126$	22763.1	−	22763.1i	0.0113794	−	0.0113794i
$127$	−537166.			−0.262239			−0.131120	−	0.991367i	$-0.541857\pi$
$127$	−537166.			−0.262239			−0.131120	+	0.991367i	$0.541857\pi$
$128$	−131072.	−	131072.i	−0.0625000	−	0.0625000i
$129$	−603231.	+	603231.i	−0.281005	+	0.281005i
$130$	−602808.	−	602808.i	−0.274378	−	0.274378i
$131$	2.43986e6	−	2.43986e6i	1.08530	−	1.08530i	0.0892985	−	0.996005i	$-0.471537\pi$
$131$	2.43986e6	−	2.43986e6i	1.08530	−	1.08530i	0.996005	−	0.0892985i	$-0.0284625\pi$
$132$			1.92007e6i			0.834823i
$133$	−336456.	−	336456.i	−0.143012	−	0.143012i
$134$	−633299.	−	633299.i	−0.263205	−	0.263205i
$135$	−3.11596e6	+	3.11596e6i	−1.26646	+	1.26646i
$136$			343787.i			0.136670i
$137$	−2.59827e6			−1.01047			−0.505234	−	0.862983i	$-0.668594\pi$
$137$	−2.59827e6			−1.01047			−0.505234	+	0.862983i	$0.668594\pi$
$138$		−	2.22238e6i		−	0.845631i
$139$			1.87291e6i			0.697386i	0.937237	+	0.348693i	$0.113374\pi$
$139$			1.87291e6i			0.697386i	−0.937237	+	0.348693i	$0.886626\pi$
$140$	−3.38698e6	+	3.38698e6i	−1.23432	+	1.23432i
$141$		−	1.46394e6i		−	0.522235i
$142$	−1.44487e6	+	1.44487e6i	−0.504619	+	0.504619i
$143$	−1.04534e6	+	1.04534e6i	−0.357479	+	0.357479i
$144$	8768.09			0.00293642
$145$	1.04214e7			3.41839
$146$	−1.20378e6	−	1.20378e6i	−0.386802	−	0.386802i
$147$		−	8.80076e6i		−	2.77056i
$148$	−857645.	−	1.37541e6i	−0.264559	−	0.424274i
$149$	2.06912e6			0.625500			0.312750	−	0.949835i	$-0.398750\pi$
$149$	2.06912e6			0.625500			0.312750	+	0.949835i	$0.398750\pi$
$150$	−3.81302e6	+	3.81302e6i	−1.12978	+	1.12978i
$151$		−	2.00859e6i		−	0.583393i	−0.956511	−	0.291697i	$-0.905780\pi$
$151$		−	2.00859e6i		−	0.583393i	0.956511	−	0.291697i	$-0.0942198\pi$
$152$		−	129599.i		−	0.0369038i
$153$	−11498.8	−	11498.8i	−0.00321055	−	0.00321055i
$154$	5.87345e6	+	5.87345e6i	1.60817	+	1.60817i
$155$	−2.90254e6			−0.779440
$156$	411189.	+	411189.i	0.108310	+	0.108310i
$157$	642471.			0.166018			0.0830089	−	0.996549i	$-0.473547\pi$
$157$	642471.			0.166018			0.0830089	+	0.996549i	$0.473547\pi$
$158$	2.96299e6			0.751206
$159$			1.18734e6i			0.295382i
$160$	−1.30463e6			−0.318513
$161$	−6.79822e6	−	6.79822e6i	−1.62899	−	1.62899i
$162$	2.15044e6	−	2.15044e6i	0.505804	−	0.505804i
$163$	4.14075e6	−	4.14075e6i	0.956129	−	0.956129i	−0.0429485	−	0.999077i	$-0.513675\pi$
$163$	4.14075e6	−	4.14075e6i	0.956129	−	0.956129i	0.999077	+	0.0429485i	$0.0136751\pi$
$164$	2.15630e6			0.488853
$165$	9.55571e6	+	9.55571e6i	2.12721	+	2.12721i
$166$	−723164.	+	723164.i	−0.158093	+	0.158093i
$167$	316345.	+	316345.i	0.0679223	+	0.0679223i	0.740252	−	0.672330i	$-0.234706\pi$
$167$	316345.	+	316345.i	0.0679223	+	0.0679223i	−0.672330	+	0.740252i	$0.734706\pi$
$168$	2.31034e6	−	2.31034e6i	0.487246	−	0.487246i
$169$		−	4.37908e6i		−	0.907241i
$170$	1.71095e6	+	1.71095e6i	0.348249	+	0.348249i
$171$	4334.78	+	4334.78i	0.000866919	+	0.000866919i
$172$	−710778.	+	710778.i	−0.139685	+	0.139685i
$173$			3.81774e6i			0.737340i	0.929560	+	0.368670i	$0.120187\pi$
$173$			3.81774e6i			0.737340i	−0.929560	+	0.368670i	$0.879813\pi$
$174$	−7.10866e6			−1.34940
$175$			2.33279e7i			4.35273i
$176$			2.26239e6i			0.414981i
$177$	−1.20544e6	+	1.20544e6i	−0.217384	+	0.217384i
$178$		−	1.69798e6i		−	0.301074i
$179$	2.86468e6	−	2.86468e6i	0.499478	−	0.499478i	−0.411797	−	0.911275i	$-0.635099\pi$
$179$	2.86468e6	−	2.86468e6i	0.499478	−	0.499478i	0.911275	+	0.411797i	$0.135099\pi$
$180$	43636.7	−	43636.7i	0.00748229	−	0.00748229i
$181$	−1.54182e6			−0.260014			−0.130007	−	0.991513i	$-0.541500\pi$
$181$	−1.54182e6			−0.260014			−0.130007	+	0.991513i	$0.541500\pi$
$182$	2.51564e6			0.417286
$183$	5.84227e6	+	5.84227e6i	0.953298	+	0.953298i
$184$		−	2.61860e6i		−	0.420354i
$185$	−1.11134e7	−	2.57679e6i	−1.75522	−	0.406971i
$186$	1.97989e6			0.307682
$187$	2.96699e6	−	2.96699e6i	0.453724	−	0.453724i
$188$		−	1.72494e6i		−	0.259597i
$189$		−	1.30036e7i		−	1.92609i
$190$	−644983.	−	644983.i	−0.0940346	−	0.0940346i
$191$	−4.18401e6	−	4.18401e6i	−0.600471	−	0.600471i	0.339966	−	0.940438i	$-0.389584\pi$
$191$	−4.18401e6	−	4.18401e6i	−0.600471	−	0.600471i	−0.940438	+	0.339966i	$0.889584\pi$
$192$	889917.			0.125732
$193$	5.93879e6	+	5.93879e6i	0.826088	+	0.826088i	0.986973	−	0.160885i	$-0.0514349\pi$
$193$	5.93879e6	+	5.93879e6i	0.826088	+	0.826088i	−0.160885	+	0.986973i	$0.551435\pi$
$194$	2.69605e6			0.369252
$195$	4.09278e6			0.551969
$196$		−	1.03698e7i		−	1.37722i
$197$	1.04480e6			0.136658			0.0683288	−	0.997663i	$-0.478233\pi$
$197$	1.04480e6			0.136658			0.0683288	+	0.997663i	$0.478233\pi$
$198$	−75671.4	−	75671.4i	−0.00974846	−	0.00974846i
$199$	−284871.	+	284871.i	−0.0361484	+	0.0361484i	−0.724950	−	0.688802i	$-0.758137\pi$
$199$	−284871.	+	284871.i	−0.0361484	+	0.0361484i	0.688802	+	0.724950i	$0.258137\pi$
$200$	−4.49282e6	+	4.49282e6i	−0.561603	+	0.561603i
$201$	4.29980e6			0.529493
$202$	4.03836e6	+	4.03836e6i	0.489949	+	0.489949i
$203$	−2.17453e7	+	2.17453e7i	−2.59942	+	2.59942i
$204$	−1.16708e6	−	1.16708e6i	−0.137470	−	0.137470i
$205$	1.07314e7	−	1.07314e7i	1.24565	−	1.24565i
$206$			6.57784e6i			0.752457i
$207$	87585.9	+	87585.9i	0.00987468	+	0.00987468i
$208$	484498.	+	484498.i	0.0538396	+	0.0538396i
$209$	−1.11848e6	+	1.11848e6i	−0.122515	+	0.122515i
$210$		−	2.29960e7i		−	2.48310i
$211$	−9.32294e6			−0.992443			−0.496221	−	0.868196i	$-0.665280\pi$
$211$	−9.32294e6			−0.992443			−0.496221	+	0.868196i	$0.665280\pi$
$212$			1.39903e6i			0.146831i
$213$		−	9.80999e6i		−	1.01515i
$214$	1.40450e6	−	1.40450e6i	0.143312	−	0.143312i
$215$			7.07475e6i			0.711862i
$216$	2.50441e6	−	2.50441e6i	0.248510	−	0.248510i
$217$	6.05644e6	−	6.05644e6i	0.592705	−	0.592705i
$218$	−4.42556e6			−0.427168
$219$	8.17310e6			0.778134
$220$	1.12594e7	+	1.12594e7i	1.05742	+	1.05742i
$221$		−	1.27078e6i		−	0.117732i
$222$	7.58069e6	+	1.75768e6i	0.692867	+	0.160651i
$223$	−4.95448e6			−0.446770			−0.223385	−	0.974730i	$-0.571711\pi$
$223$	−4.95448e6			−0.446770			−0.223385	+	0.974730i	$0.571711\pi$
$224$	2.72224e6	−	2.72224e6i	0.242205	−	0.242205i
$225$		−	300548.i		−	0.0263856i
$226$			9.76549e6i			0.845997i
$227$	5.45776e6	+	5.45776e6i	0.466591	+	0.466591i	0.900808	−	0.434217i	$-0.142975\pi$
$227$	5.45776e6	+	5.45776e6i	0.466591	+	0.466591i	−0.434217	+	0.900808i	$0.642975\pi$
$228$	439958.	+	439958.i	0.0371199	+	0.0371199i
$229$	774750.			0.0645141			0.0322571	−	0.999480i	$-0.489730\pi$
$229$	774750.			0.0645141			0.0322571	+	0.999480i	$0.489730\pi$
$230$	−1.30321e7	−	1.30321e7i	−1.07111	−	1.07111i
$231$	−3.98779e7			−3.23517
$232$	−8.37603e6			−0.670771
$233$			1.04688e7i			0.827617i	0.910364	+	0.413809i	$0.135802\pi$
$233$			1.04688e7i			0.827617i	−0.910364	+	0.413809i	$0.864198\pi$
$234$	−32410.6			−0.00252953
$235$	−8.58461e6	−	8.58461e6i	−0.661480	−	0.661480i
$236$	−1.42036e6	+	1.42036e6i	−0.108059	+	0.108059i
$237$	−1.00587e7	+	1.00587e7i	−0.755605	+	0.755605i
$238$	−7.14012e6			−0.529633
$239$	1.03064e7	+	1.03064e7i	0.754945	+	0.754945i	0.975398	−	0.220453i	$-0.0707536\pi$
$239$	1.03064e7	+	1.03064e7i	0.754945	+	0.754945i	−0.220453	+	0.975398i	$0.570754\pi$
$240$	4.42890e6	−	4.42890e6i	0.320378	−	0.320378i
$241$	−6.53260e6	−	6.53260e6i	−0.466697	−	0.466697i	0.434146	−	0.900843i	$-0.357050\pi$
$241$	−6.53260e6	−	6.53260e6i	−0.466697	−	0.466697i	−0.900843	+	0.434146i	$0.857050\pi$
$242$	1.24389e7	−	1.24389e7i	0.877677	−	0.877677i
$243$			337057.i			0.0234901i
$244$	6.88386e6	+	6.88386e6i	0.473874	+	0.473874i
$245$	−5.16081e7	−	5.16081e7i	−3.50929	−	3.50929i
$246$	−7.32014e6	+	7.32014e6i	−0.491715	+	0.491715i
$247$			479053.i			0.0317902i
$248$	2.33287e6			0.152945
$249$		−	4.90994e6i		−	0.318038i
$250$			2.48124e7i			1.58799i
$251$	5.49188e6	−	5.49188e6i	0.347296	−	0.347296i	−0.511805	−	0.859101i	$-0.671023\pi$
$251$	5.49188e6	−	5.49188e6i	0.347296	−	0.347296i	0.859101	+	0.511805i	$0.171023\pi$
$252$			182105.i			0.0113794i
$253$	−2.25993e7	+	2.25993e7i	−1.39551	+	1.39551i
$254$	2.14866e6	−	2.14866e6i	0.131120	−	0.131120i
$255$	−1.16165e7			−0.700576
$256$	1.04858e6			0.0625000
$257$	−3.36953e6	−	3.36953e6i	−0.198505	−	0.198505i	0.600854	−	0.799359i	$-0.294827\pi$
$257$	−3.36953e6	−	3.36953e6i	−0.198505	−	0.198505i	−0.799359	+	0.600854i	$0.794827\pi$
$258$		−	4.82585e6i		−	0.281005i
$259$	2.85659e7	−	1.78125e7i	1.64418	−	1.02524i
$260$	4.82246e6			0.274378
$261$	280158.	−	280158.i	0.0157573	−	0.0157573i
$262$			1.95189e7i			1.08530i
$263$		−	3.14216e7i		−	1.72728i	−0.504113	−	0.863638i	$-0.668180\pi$
$263$		−	3.14216e7i		−	1.72728i	0.504113	−	0.863638i	$-0.331820\pi$
$264$	−7.68026e6	−	7.68026e6i	−0.417411	−	0.417411i
$265$	6.96263e6	+	6.96263e6i	0.374141	+	0.374141i
$266$	2.69165e6			0.143012
$267$	5.76424e6	+	5.76424e6i	0.302836	+	0.302836i
$268$	5.06639e6			0.263205
$269$	1.60956e7			0.826895			0.413448	−	0.910528i	$-0.364324\pi$
$269$	1.60956e7			0.826895			0.413448	+	0.910528i	$0.364324\pi$
$270$		−	2.49277e7i		−	1.26646i
$271$	3.75863e7			1.88852			0.944260	−	0.329201i	$-0.106779\pi$
$271$	3.75863e7			1.88852			0.944260	+	0.329201i	$0.106779\pi$
$272$	−1.37515e6	−	1.37515e6i	−0.0683349	−	0.0683349i
$273$	−8.54000e6	+	8.54000e6i	−0.419730	+	0.419730i
$274$	1.03931e7	−	1.03931e7i	0.505234	−	0.505234i
$275$	7.75490e7			3.72888
$276$	8.88952e6	+	8.88952e6i	0.422816	+	0.422816i
$277$	−8.38100e6	+	8.38100e6i	−0.394327	+	0.394327i	−0.876227	−	0.481899i	$-0.839947\pi$
$277$	−8.38100e6	+	8.38100e6i	−0.394327	+	0.394327i	0.481899	+	0.876227i	$0.339947\pi$
$278$	−7.49165e6	−	7.49165e6i	−0.348693	−	0.348693i
$279$	−78029.0	+	78029.0i	−0.00359289	+	0.00359289i
$280$		−	2.70959e7i		−	1.23432i
$281$	1.81147e7	+	1.81147e7i	0.816416	+	0.816416i	0.985587	−	0.169171i	$-0.0541089\pi$
$281$	1.81147e7	+	1.81147e7i	0.816416	+	0.816416i	−0.169171	+	0.985587i	$0.554109\pi$
$282$	5.85576e6	+	5.85576e6i	0.261117	+	0.261117i
$283$	−1.34487e7	+	1.34487e7i	−0.593363	+	0.593363i	−0.938538	−	0.345175i	$-0.887819\pi$
$283$	−1.34487e7	+	1.34487e7i	−0.593363	+	0.593363i	0.345175	+	0.938538i	$0.387819\pi$
$284$		−	1.15590e7i		−	0.504619i
$285$	4.37913e6			0.189170
$286$		−	8.36275e6i		−	0.357479i
$287$			4.47843e7i			1.89444i
$288$	−35072.4	+	35072.4i	−0.00146821	+	0.00146821i
$289$		−	2.05307e7i		−	0.850571i
$290$	−4.16855e7	+	4.16855e7i	−1.70919	+	1.70919i
$291$	−9.15246e6	+	9.15246e6i	−0.371415	+	0.371415i
$292$	9.63024e6			0.386802
$293$	−3.12377e7			−1.24187			−0.620934	−	0.783863i	$-0.713247\pi$
$293$	−3.12377e7			−1.24187			−0.620934	+	0.783863i	$0.713247\pi$
$294$	3.52030e7	+	3.52030e7i	1.38528	+	1.38528i
$295$			1.41375e7i			0.550691i
$296$	8.93221e6	+	2.07105e6i	0.344417	+	0.0798576i
$297$	−4.32277e7			−1.65003
$298$	−8.27649e6	+	8.27649e6i	−0.312750	+	0.312750i
$299$			9.67946e6i			0.362108i
$300$		−	3.05041e7i		−	1.12978i
$301$	−1.47622e7	−	1.47622e7i	−0.541316	−	0.541316i
$302$	8.03438e6	+	8.03438e6i	0.291697	+	0.291697i
$303$	−2.74185e7			−0.985636
$304$	518396.	+	518396.i	0.0184519	+	0.0184519i
$305$	6.85187e7			2.41496
$306$	91990.8			0.00321055
$307$			7.62084e6i			0.263383i	0.991291	+	0.131692i	$0.0420408\pi$
$307$			7.62084e6i			0.263383i	−0.991291	+	0.131692i	$0.957959\pi$
$308$	−4.69876e7			−1.60817
$309$	−2.23302e7	−	2.23302e7i	−0.756863	−	0.756863i
$310$	1.16102e7	−	1.16102e7i	0.389720	−	0.389720i
$311$	−1.11162e7	+	1.11162e7i	−0.369552	+	0.369552i	−0.867314	−	0.497762i	$-0.834155\pi$
$311$	−1.11162e7	+	1.11162e7i	−0.369552	+	0.369552i	0.497762	+	0.867314i	$0.334155\pi$
$312$	−3.28951e6			−0.108310
$313$	2.04609e7	+	2.04609e7i	0.667255	+	0.667255i	0.957080	−	0.289825i	$-0.0935971\pi$
$313$	2.04609e7	+	2.04609e7i	0.667255	+	0.667255i	−0.289825	+	0.957080i	$0.593597\pi$
$314$	−2.56988e6	+	2.56988e6i	−0.0830089	+	0.0830089i
$315$	906292.	+	906292.i	0.0289959	+	0.0289959i
$316$	−1.18520e7	+	1.18520e7i	−0.375603	+	0.375603i
$317$		−	6.24279e6i		−	0.195975i	−0.995188	−	0.0979876i	$-0.968759\pi$
$317$		−	6.24279e6i		−	0.195975i	0.995188	−	0.0979876i	$-0.0312405\pi$
$318$	−4.74937e6	−	4.74937e6i	−0.147691	−	0.147691i
$319$	7.22878e7	+	7.22878e7i	2.22686	+	2.22686i
$320$	5.21851e6	−	5.21851e6i	0.159256	−	0.159256i
$321$			9.53591e6i			0.288302i
$322$	5.43858e7			1.62899
$323$		−	1.35969e6i		−	0.0403491i
$324$			1.72035e7i			0.505804i
$325$	1.66074e7	−	1.66074e7i	0.483784	−	0.483784i
$326$			3.31260e7i			0.956129i
$327$	1.50237e7	−	1.50237e7i	0.429669	−	0.429669i
$328$	−8.62521e6	+	8.62521e6i	−0.244426	+	0.244426i
$329$	3.58253e7			1.00601
$330$	−7.64457e7			−2.12721
$331$	−1.32314e7	−	1.32314e7i	−0.364855	−	0.364855i	0.500742	−	0.865597i	$-0.333061\pi$
$331$	−1.32314e7	−	1.32314e7i	−0.364855	−	0.364855i	−0.865597	+	0.500742i	$0.833061\pi$
$332$		−	5.78531e6i		−	0.158093i
$333$	−368033.	+	229489.i	−0.00996676	+	0.00621484i
$334$	−2.53076e6			−0.0679223
$335$	2.52142e7	−	2.52142e7i	0.670674	−	0.670674i
$336$			1.84827e7i			0.487246i
$337$		−	1.89918e7i		−	0.496222i	−0.968732	−	0.248111i	$-0.920190\pi$
$337$		−	1.89918e7i		−	0.496222i	0.968732	−	0.248111i	$-0.0798098\pi$
$338$	1.75163e7	+	1.75163e7i	0.453621	+	0.453621i
$339$	−3.31515e7	−	3.31515e7i	−0.850951	−	0.850951i
$340$	−1.36876e7			−0.348249
$341$	−2.01334e7	−	2.01334e7i	−0.507756	−	0.507756i
$342$	−34678.2			−0.000866919
$343$	1.37180e8			3.39946
$344$		−	5.68623e6i		−	0.139685i
$345$	8.84821e7			2.15476
$346$	−1.52709e7	−	1.52709e7i	−0.368670	−	0.368670i
$347$	8.71664e6	−	8.71664e6i	0.208622	−	0.208622i	−0.595059	−	0.803682i	$-0.702871\pi$
$347$	8.71664e6	−	8.71664e6i	0.208622	−	0.208622i	0.803682	+	0.595059i	$0.202871\pi$
$348$	2.84346e7	−	2.84346e7i	0.674699	−	0.674699i
$349$	−4.90624e7			−1.15418			−0.577088	−	0.816682i	$-0.695811\pi$
$349$	−4.90624e7			−1.15418			−0.577088	+	0.816682i	$0.695811\pi$
$350$	−9.33116e7	−	9.33116e7i	−2.17636	−	2.17636i
$351$	−9.25737e6	+	9.25737e6i	−0.214075	+	0.214075i
$352$	−9.04954e6	−	9.04954e6i	−0.207491	−	0.207491i
$353$	−2.07982e7	+	2.07982e7i	−0.472827	+	0.472827i	−0.902828	−	0.430001i	$-0.858513\pi$
$353$	−2.07982e7	+	2.07982e7i	−0.472827	+	0.472827i	0.430001	+	0.902828i	$0.358513\pi$
$354$		−	9.64354e6i		−	0.217384i
$355$	−5.75262e7	−	5.75262e7i	−1.28582	−	1.28582i
$356$	6.79192e6	+	6.79192e6i	0.150537	+	0.150537i
$357$	2.42390e7	−	2.42390e7i	0.532734	−	0.532734i
$358$			2.29174e7i			0.499478i
$359$	−9.05428e7			−1.95691			−0.978454	−	0.206465i	$-0.933804\pi$
$359$	−9.05428e7			−1.95691			−0.978454	+	0.206465i	$0.933804\pi$
$360$			349094.i			0.00748229i
$361$		−	4.65333e7i		−	0.989105i
$362$	6.16727e6	−	6.16727e6i	0.130007	−	0.130007i
$363$			8.44540e7i			1.76563i
$364$	−1.00626e7	+	1.00626e7i	−0.208643	+	0.208643i
$365$	4.79274e7	−	4.79274e7i	0.985611	−	0.985611i
$366$	−4.67382e7			−0.953298
$367$	−2.85167e7			−0.576900			−0.288450	−	0.957495i	$-0.593140\pi$
$367$	−2.85167e7			−0.576900			−0.288450	+	0.957495i	$0.593140\pi$
$368$	1.04744e7	+	1.04744e7i	0.210177	+	0.210177i
$369$		−	576985.i		−	0.0114838i
$370$	5.47606e7	−	3.41464e7i	1.08109	−	0.674123i
$371$	−2.90565e7			−0.569012
$372$	−7.91955e6	+	7.91955e6i	−0.153841	+	0.153841i
$373$		−	5.57692e7i		−	1.07465i	−0.843374	−	0.537326i	$-0.819434\pi$
$373$		−	5.57692e7i		−	1.07465i	0.843374	−	0.537326i	$-0.180566\pi$
$374$			2.37359e7i			0.453724i
$375$	−8.42321e7	−	8.42321e7i	−1.59729	−	1.59729i
$376$	6.89976e6	+	6.89976e6i	0.129799	+	0.129799i
$377$	3.09614e7			0.577825
$378$	5.20142e7	+	5.20142e7i	0.963045	+	0.963045i
$379$	1.03027e8			1.89249			0.946247	−	0.323445i	$-0.104841\pi$
$379$	1.03027e8			1.89249			0.946247	+	0.323445i	$0.104841\pi$
$380$	5.15987e6			0.0940346
$381$			1.45884e7i			0.263775i
$382$	3.34720e7			0.600471
$383$	−2.41074e7	−	2.41074e7i	−0.429096	−	0.429096i	0.459225	−	0.888320i	$-0.348127\pi$
$383$	−2.41074e7	−	2.41074e7i	−0.429096	−	0.429096i	−0.888320	+	0.459225i	$0.848127\pi$
$384$	−3.55967e6	+	3.55967e6i	−0.0628660	+	0.0628660i
$385$	−2.33846e8	+	2.33846e8i	−4.09777	+	4.09777i
$386$	−4.75103e7			−0.826088
$387$	190191.	+	190191.i	0.00328138	+	0.00328138i
$388$	−1.07842e7	+	1.07842e7i	−0.184626	+	0.184626i
$389$	1.93888e7	+	1.93888e7i	0.329383	+	0.329383i	0.852352	−	0.522969i	$-0.175176\pi$
$389$	1.93888e7	+	1.93888e7i	0.329383	+	0.329383i	−0.522969	+	0.852352i	$0.675176\pi$
$390$	−1.63711e7	+	1.63711e7i	−0.275984	+	0.275984i
$391$		−	2.74731e7i		−	0.459598i
$392$	4.14792e7	+	4.14792e7i	0.688609	+	0.688609i
$393$	−6.62620e7	−	6.62620e7i	−1.09166	−	1.09166i
$394$	−4.17919e6	+	4.17919e6i	−0.0683288	+	0.0683288i
$395$			1.17969e8i			1.91415i
$396$	605371.			0.00974846
$397$			1.10933e7i			0.177293i	0.996063	+	0.0886463i	$0.0282541\pi$
$397$			1.10933e7i			0.177293i	−0.996063	+	0.0886463i	$0.971746\pi$
$398$		−	2.27897e6i		−	0.0361484i
$399$	−9.13750e6	+	9.13750e6i	−0.143850	+	0.143850i
$400$		−	3.59426e7i		−	0.561603i
$401$	7.34633e7	−	7.34633e7i	1.13930	−	1.13930i	0.150722	−	0.988576i	$-0.451840\pi$
$401$	7.34633e7	−	7.34633e7i	1.13930	−	1.13930i	0.988576	−	0.150722i	$-0.0481599\pi$
$402$	−1.71992e7	+	1.71992e7i	−0.264746	+	0.264746i
$403$	−8.62329e6			−0.131752
$404$	−3.23069e7			−0.489949
$405$	8.56178e7	+	8.56178e7i	1.28884	+	1.28884i
$406$		−	1.73962e8i		−	2.59942i
$407$	−5.92140e7	−	9.49617e7i	−0.878296	−	1.40853i
$408$	9.33660e6			0.137470
$409$	4.93621e7	−	4.93621e7i	0.721478	−	0.721478i	−0.247428	−	0.968906i	$-0.579585\pi$
$409$	4.93621e7	−	4.93621e7i	0.721478	−	0.721478i	0.968906	+	0.247428i	$0.0795853\pi$
$410$			8.58512e7i			1.24565i
$411$			7.05640e7i			1.01638i
$412$	−2.63114e7	−	2.63114e7i	−0.376228	−	0.376228i
$413$	−2.94994e7	−	2.94994e7i	−0.418758	−	0.418758i
$414$	−700687.			−0.00987468
$415$	−2.87921e7	−	2.87921e7i	−0.402837	−	0.402837i
$416$	−3.87598e6			−0.0538396
$417$	5.08648e7			0.701470
$418$		−	8.94784e6i		−	0.122515i
$419$	−6.13802e7			−0.834423			−0.417212	−	0.908809i	$-0.636993\pi$
$419$	−6.13802e7			−0.834423			−0.417212	+	0.908809i	$0.636993\pi$
$420$	9.19841e7	+	9.19841e7i	1.24155	+	1.24155i
$421$	−1.08498e7	+	1.08498e7i	−0.145403	+	0.145403i	−0.776061	−	0.630658i	$-0.782785\pi$
$421$	−1.08498e7	+	1.08498e7i	−0.145403	+	0.145403i	0.630658	+	0.776061i	$0.282785\pi$
$422$	3.72917e7	−	3.72917e7i	0.496221	−	0.496221i
$423$	−461561.			−0.00609828
$424$	−5.59611e6	−	5.59611e6i	−0.0734157	−	0.0734157i
$425$	−4.71367e7	+	4.71367e7i	−0.614033	+	0.614033i
$426$	3.92400e7	+	3.92400e7i	0.507574	+	0.507574i
$427$	−1.42971e8	+	1.42971e8i	−1.83639	+	1.83639i
$428$			1.12360e7i			0.143312i
$429$	2.83895e7	+	2.83895e7i	0.359572	+	0.359572i
$430$	−2.82990e7	−	2.82990e7i	−0.355931	−	0.355931i
$431$	6.14536e7	−	6.14536e7i	0.767566	−	0.767566i	−0.210112	−	0.977677i	$-0.567383\pi$
$431$	6.14536e7	−	6.14536e7i	0.767566	−	0.767566i	0.977677	+	0.210112i	$0.0673828\pi$
$432$			2.00353e7i			0.248510i
$433$	1.04880e8			1.29190			0.645950	−	0.763380i	$-0.276462\pi$
$433$	1.04880e8			1.29190			0.645950	+	0.763380i	$0.276462\pi$
$434$			4.84515e7i			0.592705i
$435$		−	2.83025e8i		−	3.43840i
$436$	1.77022e7	−	1.77022e7i	0.213584	−	0.213584i
$437$			1.03567e7i			0.124101i
$438$	−3.26924e7	+	3.26924e7i	−0.389067	+	0.389067i
$439$	1.71221e7	−	1.71221e7i	0.202378	−	0.202378i	−0.598640	−	0.801018i	$-0.704292\pi$
$439$	1.71221e7	−	1.71221e7i	0.202378	−	0.202378i	0.801018	+	0.598640i	$0.204292\pi$
$440$	−9.00749e7			−1.05742
$441$	−2.77476e6			−0.0323527
$442$	5.08313e6	+	5.08313e6i	0.0588660	+	0.0588660i
$443$			2.84988e7i			0.327804i	0.986477	+	0.163902i	$0.0524082\pi$
$443$			2.84988e7i			0.327804i	−0.986477	+	0.163902i	$0.947592\pi$
$444$	−3.73535e7	+	2.32920e7i	−0.426759	+	0.266108i
$445$	6.76035e7			0.767166
$446$	1.98179e7	−	1.98179e7i	0.223385	−	0.223385i
$447$		−	5.61935e7i		−	0.629163i
$448$			2.17779e7i			0.242205i
$449$	2.86545e7	+	2.86545e7i	0.316559	+	0.316559i	0.847444	−	0.530885i	$-0.178140\pi$
$449$	2.86545e7	+	2.86545e7i	0.316559	+	0.316559i	−0.530885	+	0.847444i	$0.678140\pi$
$450$	1.20219e6	+	1.20219e6i	0.0131928	+	0.0131928i
$451$	1.48877e8			1.62292
$452$	−3.90620e7	−	3.90620e7i	−0.422998	−	0.422998i
$453$	−5.45496e7			−0.586809
$454$	−4.36621e7			−0.466591
$455$			1.00158e8i			1.06329i
$456$	−3.51966e6			−0.0371199
$457$	4.09041e7	+	4.09041e7i	0.428567	+	0.428567i	0.888140	−	0.459573i	$-0.151998\pi$
$457$	4.09041e7	+	4.09041e7i	0.428567	+	0.428567i	−0.459573	+	0.888140i	$0.651998\pi$
$458$	−3.09900e6	+	3.09900e6i	−0.0322571	+	0.0322571i
$459$	2.62751e7	−	2.62751e7i	0.271711	−	0.271711i
$460$	1.04257e8			1.07111
$461$	−1.16100e8	−	1.16100e8i	−1.18503	−	1.18503i	−0.978424	−	0.206608i	$-0.933758\pi$
$461$	−1.16100e8	−	1.16100e8i	−1.18503	−	1.18503i	−0.206608	−	0.978424i	$-0.566242\pi$
$462$	1.59512e8	−	1.59512e8i	1.61758	−	1.61758i
$463$	−6.19988e7	−	6.19988e7i	−0.624655	−	0.624655i	0.322063	−	0.946718i	$-0.395624\pi$
$463$	−6.19988e7	−	6.19988e7i	−0.624655	−	0.624655i	−0.946718	+	0.322063i	$0.895624\pi$
$464$	3.35041e7	−	3.35041e7i	0.335386	−	0.335386i
$465$			7.88274e7i			0.784004i
$466$	−4.18752e7	−	4.18752e7i	−0.413809	−	0.413809i
$467$	8.48178e7	+	8.48178e7i	0.832791	+	0.832791i	0.987898	−	0.155106i	$-0.0495721\pi$
$467$	8.48178e7	+	8.48178e7i	0.832791	+	0.832791i	−0.155106	+	0.987898i	$0.549572\pi$
$468$	129642.	−	129642.i	0.00126476	−	0.00126476i
$469$			1.05224e8i			1.01999i
$470$	6.86769e7			0.661480
$471$		−	1.74483e7i		−	0.166990i
$472$		−	1.13628e7i		−	0.108059i
$473$	−4.90740e7	+	4.90740e7i	−0.463733	+	0.463733i
$474$		−	8.04692e7i		−	0.755605i
$475$	1.77693e7	−	1.77693e7i	0.165802	−	0.165802i
$476$	2.85605e7	−	2.85605e7i	0.264816	−	0.264816i
$477$	374353.			0.00344926
$478$	−8.24515e7			−0.754945
$479$	7.28545e7	+	7.28545e7i	0.662903	+	0.662903i	0.956063	−	0.293160i	$-0.0947069\pi$
$479$	7.28545e7	+	7.28545e7i	0.662903	+	0.662903i	−0.293160	+	0.956063i	$0.594707\pi$
$480$			3.54312e7i			0.320378i
$481$	−3.30173e7	−	7.65550e6i	−0.296692	−	0.0687921i
$482$	5.22608e7			0.466697
$483$	−1.84627e8	+	1.84627e8i	−1.63853	+	1.63853i
$484$			9.95109e7i			0.877677i
$485$			1.07341e8i			0.940893i
$486$	−1.34823e6	−	1.34823e6i	−0.0117451	−	0.0117451i
$487$	−9.30562e7	−	9.30562e7i	−0.805672	−	0.805672i	0.178303	−	0.983976i	$-0.442939\pi$
$487$	−9.30562e7	−	9.30562e7i	−0.805672	−	0.805672i	−0.983976	+	0.178303i	$0.942939\pi$
$488$	−5.50709e7			−0.473874
$489$	−1.12455e8	−	1.12455e8i	−0.961728	−	0.961728i
$490$	4.12864e8			3.50929
$491$	1.87649e8			1.58527			0.792633	−	0.609700i	$-0.208710\pi$
$491$	1.87649e8			1.58527			0.792633	+	0.609700i	$0.208710\pi$
$492$		−	5.85611e7i		−	0.491715i
$493$	−8.78775e7			−0.733394
$494$	−1.91621e6	−	1.91621e6i	−0.0158951	−	0.0158951i
$495$	3.01279e6	−	3.01279e6i	0.0248401	−	0.0248401i
$496$	−9.33149e6	+	9.33149e6i	−0.0764726	+	0.0764726i
$497$	2.40069e8			1.95554
$498$	1.96398e7	+	1.96398e7i	0.159019	+	0.159019i
$499$	4.84409e7	−	4.84409e7i	0.389862	−	0.389862i	−0.484776	−	0.874638i	$-0.661099\pi$
$499$	4.84409e7	−	4.84409e7i	0.389862	−	0.389862i	0.874638	+	0.484776i	$0.161099\pi$
$500$	−9.92495e7	−	9.92495e7i	−0.793996	−	0.793996i
$501$	8.59134e6	−	8.59134e6i	0.0683200	−	0.0683200i
$502$			4.39351e7i			0.347296i
$503$	−1.07101e8	−	1.07101e8i	−0.841571	−	0.841571i	0.147492	−	0.989063i	$-0.452880\pi$
$503$	−1.07101e8	−	1.07101e8i	−0.841571	−	0.841571i	−0.989063	+	0.147492i	$0.952880\pi$
$504$	−728419.	−	728419.i	−0.00568970	−	0.00568970i
$505$	−1.60784e8	+	1.60784e8i	−1.24844	+	1.24844i
$506$		−	1.80795e8i		−	1.39551i
$507$	−1.18928e8			−0.912554
$508$			1.71893e7i			0.131120i
$509$			4.06649e7i			0.308366i	0.988042	+	0.154183i	$0.0492746\pi$
$509$			4.06649e7i			0.308366i	−0.988042	+	0.154183i	$0.950725\pi$
$510$	4.64660e7	−	4.64660e7i	0.350288	−	0.350288i
$511$			2.00011e8i			1.49896i
$512$	−4.19430e6	+	4.19430e6i	−0.0312500	+	0.0312500i
$513$	−9.90507e6	+	9.90507e6i	−0.0733678	+	0.0733678i
$514$	2.69563e7			0.198505
$515$	−2.61891e8			−1.91734
$516$	1.93034e7	+	1.93034e7i	0.140503	+	0.140503i
$517$		−	1.19094e8i		−	0.861825i
$518$	−4.30138e7	+	1.85514e8i	−0.309470	+	1.33471i
$519$	1.03682e8			0.741657
$520$	−1.92899e7	+	1.92899e7i	−0.137189	+	0.137189i
$521$			2.07016e8i			1.46383i	0.681395	+	0.731916i	$0.261374\pi$
$521$			2.07016e8i			1.46383i	−0.681395	+	0.731916i	$0.738626\pi$
$522$			2.24127e6i			0.0157573i
$523$	1.12103e8	+	1.12103e8i	0.783632	+	0.783632i	0.980442	−	0.196810i	$-0.0630582\pi$
$523$	1.12103e8	+	1.12103e8i	0.783632	+	0.783632i	−0.196810	+	0.980442i	$0.563058\pi$
$524$	−7.80755e7	−	7.80755e7i	−0.542652	−	0.542652i
$525$	6.33542e8			4.37822
$526$	1.25687e8	+	1.25687e8i	0.863638	+	0.863638i
$527$	2.44754e7			0.167224
$528$	6.14421e7			0.417411
$529$			6.12249e7i			0.413582i
$530$	−5.57010e7			−0.374141
$531$	380060.	+	380060.i	0.00253845	+	0.00253845i
$532$	−1.07666e7	+	1.07666e7i	−0.0715061	+	0.0715061i
$533$	3.18825e7	−	3.18825e7i	0.210557	−	0.210557i
$534$	−4.61139e7			−0.302836
$535$	5.59190e7	+	5.59190e7i	0.365173	+	0.365173i
$536$	−2.02656e7	+	2.02656e7i	−0.131603	+	0.131603i
$537$	−7.77992e7	−	7.77992e7i	−0.502403	−	0.502403i
$538$	−6.43824e7	+	6.43824e7i	−0.413448	+	0.413448i
$539$		−	7.15958e8i		−	4.57216i
$540$	9.97109e7	+	9.97109e7i	0.633230	+	0.633230i
$541$	7.00039e6	+	7.00039e6i	0.0442110	+	0.0442110i	0.728867	−	0.684656i	$-0.240047\pi$
$541$	7.00039e6	+	7.00039e6i	0.0442110	+	0.0442110i	−0.684656	+	0.728867i	$0.740047\pi$
$542$	−1.50345e8	+	1.50345e8i	−0.944260	+	0.944260i
$543$			4.18728e7i			0.261537i
$544$	1.10012e7			0.0683349
$545$		−	1.76200e8i		−	1.08847i
$546$		−	6.83200e7i		−	0.419730i
$547$	−4.10775e7	+	4.10775e7i	−0.250982	+	0.250982i	−0.821373	−	0.570391i	$-0.806792\pi$
$547$	−4.10775e7	+	4.10775e7i	−0.250982	+	0.250982i	0.570391	+	0.821373i	$0.306792\pi$
$548$			8.31446e7i			0.505234i
$549$	1.84199e6	−	1.84199e6i	0.0111319	−	0.0111319i
$550$	−3.10196e8	+	3.10196e8i	−1.86444	+	1.86444i
$551$	3.31276e7			0.198032
$552$	−7.11162e7			−0.422816
$553$	−2.46154e8	−	2.46154e8i	−1.45556	−	1.45556i
$554$		−	6.70480e7i		−	0.394327i
$555$	−6.99806e7	+	3.01818e8i	−0.409354	+	1.76549i
$556$	5.99332e7			0.348693
$557$	−1.44656e7	+	1.44656e7i	−0.0837088	+	0.0837088i	−0.747721	−	0.664013i	$-0.768852\pi$
$557$	−1.44656e7	+	1.44656e7i	−0.0837088	+	0.0837088i	0.664013	+	0.747721i	$0.268852\pi$
$558$		−	624232.i		−	0.00359289i
$559$			2.10187e7i			0.120329i
$560$	1.08383e8	+	1.08383e8i	0.617162	+	0.617162i
$561$	−8.05778e7	−	8.05778e7i	−0.456380	−	0.456380i
$562$	−1.44917e8			−0.816416
$563$	2.11110e8	+	2.11110e8i	1.18300	+	1.18300i	0.978963	+	0.204036i	$0.0654059\pi$
$563$	2.11110e8	+	2.11110e8i	1.18300	+	1.18300i	0.204036	+	0.978963i	$0.434594\pi$
$564$	−4.68461e7			−0.261117
$565$	−3.88804e8			−2.15569
$566$		−	1.07589e8i		−	0.593363i
$567$	−3.57300e8			−1.96013
$568$	4.62359e7	+	4.62359e7i	0.252310	+	0.252310i
$569$	−1.36672e7	+	1.36672e7i	−0.0741896	+	0.0741896i	−0.743228	−	0.669038i	$-0.766706\pi$
$569$	−1.36672e7	+	1.36672e7i	−0.0741896	+	0.0741896i	0.669038	+	0.743228i	$0.266706\pi$
$570$	−1.75165e7	+	1.75165e7i	−0.0945852	+	0.0945852i
$571$	−1.42856e7			−0.0767344			−0.0383672	−	0.999264i	$-0.512216\pi$
$571$	−1.42856e7			−0.0767344			−0.0383672	+	0.999264i	$0.512216\pi$
$572$	3.34510e7	+	3.34510e7i	0.178740	+	0.178740i
$573$	−1.13630e8	+	1.13630e8i	−0.603987	+	0.603987i
$574$	−1.79137e8	−	1.79137e8i	−0.947219	−	0.947219i
$575$	3.59036e8	−	3.59036e8i	1.88858	−	1.88858i
$576$		−	280579.i		−	0.00146821i
$577$	−2.11648e8	−	2.11648e8i	−1.10176	−	1.10176i	−0.994199	−	0.107559i	$-0.965697\pi$
$577$	−2.11648e8	−	2.11648e8i	−1.10176	−	1.10176i	−0.107559	−	0.994199i	$-0.534303\pi$
$578$	8.21229e7	+	8.21229e7i	0.425285	+	0.425285i
$579$	1.61286e8	−	1.61286e8i	0.830925	−	0.830925i
$580$		−	3.33484e8i		−	1.70919i
$581$	1.20155e8			0.612654
$582$		−	7.32197e7i		−	0.371415i
$583$			9.65925e7i			0.487458i
$584$	−3.85210e7	+	3.85210e7i	−0.193401	+	0.193401i
$585$		−	1.29040e6i		−	0.00644550i
$586$	1.24951e8	−	1.24951e8i	0.620934	−	0.620934i
$587$	1.22016e8	−	1.22016e8i	0.603258	−	0.603258i	−0.337917	−	0.941176i	$-0.609722\pi$
$587$	1.22016e8	−	1.22016e8i	0.603258	−	0.603258i	0.941176	+	0.337917i	$0.109722\pi$
$588$	−2.81624e8			−1.38528
$589$	−9.22662e6			−0.0451541
$590$	−5.65502e7	−	5.65502e7i	−0.275345	−	0.275345i
$591$		−	2.83747e7i		−	0.137458i
$592$	−4.40131e7	+	2.74446e7i	−0.212137	+	0.132279i
$593$	9.61617e7			0.461146			0.230573	−	0.973055i	$-0.425940\pi$
$593$	9.61617e7			0.461146			0.230573	+	0.973055i	$0.425940\pi$
$594$	1.72911e8	−	1.72911e8i	0.825017	−	0.825017i
$595$		−	2.84278e8i		−	1.34956i
$596$		−	6.62119e7i		−	0.312750i
$597$	7.73656e6	+	7.73656e6i	0.0363601	+	0.0363601i
$598$	−3.87178e7	−	3.87178e7i	−0.181054	−	0.181054i
$599$	−1.27620e8			−0.593795			−0.296898	−	0.954909i	$-0.595952\pi$
$599$	−1.27620e8			−0.593795			−0.296898	+	0.954909i	$0.595952\pi$
$600$	1.22017e8	+	1.22017e8i	0.564892	+	0.564892i
$601$	−2.04153e8			−0.940442			−0.470221	−	0.882549i	$-0.655826\pi$
$601$	−2.04153e8			−0.940442			−0.470221	+	0.882549i	$0.655826\pi$
$602$	1.18097e8			0.541316
$603$		−	1.35567e6i		−	0.00618304i
$604$	−6.42750e7			−0.291697
$605$	4.95242e8	+	4.95242e8i	2.23641	+	2.23641i
$606$	1.09674e8	−	1.09674e8i	0.492818	−	0.492818i
$607$	−4.50173e7	+	4.50173e7i	−0.201286	+	0.201286i	−0.800551	−	0.599265i	$-0.795460\pi$
$607$	−4.50173e7	+	4.50173e7i	−0.201286	+	0.201286i	0.599265	+	0.800551i	$0.295460\pi$
$608$	−4.14717e6			−0.0184519
$609$	5.90560e8	+	5.90560e8i	2.61464	+	2.61464i
$610$	−2.74075e8	+	2.74075e8i	−1.20748	+	1.20748i
$611$	−2.55044e7	−	2.55044e7i	−0.111813	−	0.111813i
$612$	−367963.	+	367963.i	−0.00160528	+	0.00160528i
$613$		−	1.22808e8i		−	0.533146i	−0.963815	−	0.266573i	$-0.914109\pi$
$613$		−	1.22808e8i		−	0.533146i	0.963815	−	0.266573i	$-0.0858913\pi$
$614$	−3.04834e7	−	3.04834e7i	−0.131692	−	0.131692i
$615$	−2.91445e8	−	2.91445e8i	−1.25294	−	1.25294i
$616$	1.87950e8	−	1.87950e8i	0.804083	−	0.804083i
$617$		−	1.78135e8i		−	0.758390i	−0.925317	−	0.379195i	$-0.876201\pi$
$617$		−	1.78135e8i		−	0.758390i	0.925317	−	0.379195i	$-0.123799\pi$
$618$	1.78642e8			0.756863
$619$		−	2.05914e8i		−	0.868187i	−0.900868	−	0.434093i	$-0.857069\pi$
$619$		−	2.05914e8i		−	0.868187i	0.900868	−	0.434093i	$-0.142931\pi$
$620$			9.28812e7i			0.389720i
$621$	−2.00136e8	+	2.00136e8i	−0.835699	+	0.835699i
$622$		−	8.89296e7i		−	0.369552i
$623$	−1.41062e8	+	1.41062e8i	−0.583371	+	0.583371i
$624$	1.31580e7	−	1.31580e7i	0.0541549	−	0.0541549i
$625$	−4.39442e8			−1.79995
$626$	−1.63687e8			−0.667255
$627$	3.03758e7	+	3.03758e7i	0.123232	+	0.123232i
$628$		−	2.05591e7i		−	0.0830089i
$629$	9.37127e7	+	2.17286e7i	0.376571	+	0.0873130i
$630$	−7.25034e6			−0.0289959
$631$	2.26170e8	−	2.26170e8i	0.900217	−	0.900217i	−0.0952378	−	0.995455i	$-0.530361\pi$
$631$	2.26170e8	−	2.26170e8i	0.900217	−	0.900217i	0.995455	+	0.0952378i	$0.0303611\pi$
$632$		−	9.48157e7i		−	0.375603i
$633$			2.53193e8i			0.998254i
$634$	2.49712e7	+	2.49712e7i	0.0979876	+	0.0979876i
$635$	8.55471e7	+	8.55471e7i	0.334106	+	0.334106i
$636$	3.79950e7			0.147691
$637$	−1.53325e8	−	1.53325e8i	−0.593191	−	0.593191i
$638$	−5.78303e8			−2.22686
$639$	−3.09296e6			−0.0118542
$640$			4.17481e7i			0.159256i
$641$	2.93339e8			1.11377			0.556885	−	0.830590i	$-0.311997\pi$
$641$	2.93339e8			1.11377			0.556885	+	0.830590i	$0.311997\pi$
$642$	−3.81436e7	−	3.81436e7i	−0.144151	−	0.144151i
$643$	−9.48243e7	+	9.48243e7i	−0.356687	+	0.356687i	−0.862590	−	0.505903i	$-0.831159\pi$
$643$	−9.48243e7	+	9.48243e7i	−0.356687	+	0.356687i	0.505903	+	0.862590i	$0.331159\pi$
$644$	−2.17543e8	+	2.17543e8i	−0.814494	+	0.814494i
$645$	1.92137e8			0.716030
$646$	5.43877e6	+	5.43877e6i	0.0201745	+	0.0201745i
$647$	−2.26465e8	+	2.26465e8i	−0.836158	+	0.836158i	−0.988351	−	0.152193i	$-0.951366\pi$
$647$	−2.26465e8	+	2.26465e8i	−0.836158	+	0.836158i	0.152193	+	0.988351i	$0.451366\pi$
$648$	−6.88141e7	−	6.88141e7i	−0.252902	−	0.252902i
$649$	−9.80650e7	+	9.80650e7i	−0.358740	+	0.358740i
$650$			1.32859e8i			0.483784i
$651$	−1.64481e8	−	1.64481e8i	−0.596175	−	0.596175i
$652$	−1.32504e8	−	1.32504e8i	−0.478064	−	0.478064i
$653$	−2.11162e8	+	2.11162e8i	−0.758363	+	0.758363i	−0.976024	−	0.217661i	$-0.930157\pi$
$653$	−2.11162e8	+	2.11162e8i	−0.758363	+	0.758363i	0.217661	+	0.976024i	$0.430157\pi$
$654$			1.20190e8i			0.429669i
$655$	−7.77127e8			−2.76546
$656$		−	6.90017e7i		−	0.244426i
$657$		−	2.57687e6i		−	0.00908649i
$658$	−1.43301e8	+	1.43301e8i	−0.503005	+	0.503005i
$659$		−	5.07991e8i		−	1.77501i	−0.460803	−	0.887503i	$-0.652438\pi$
$659$		−	5.07991e8i		−	1.77501i	0.460803	−	0.887503i	$-0.347562\pi$
$660$	3.05783e8	−	3.05783e8i	1.06361	−	1.06361i
$661$	3.28691e8	−	3.28691e8i	1.13811	−	1.13811i	0.149319	−	0.988789i	$-0.452292\pi$
$661$	3.28691e8	−	3.28691e8i	1.13811	−	1.13811i	0.988789	−	0.149319i	$-0.0477081\pi$
$662$	1.05851e8			0.364855
$663$	−3.45121e7			−0.118421
$664$	2.31413e7	+	2.31413e7i	0.0790465	+	0.0790465i
$665$			1.07165e8i			0.364410i
$666$	554175.	−	2.39009e6i	0.00187596	−	0.00809080i
$667$	6.69356e8			2.25569
$668$	1.01231e7	−	1.01231e7i	0.0339611	−	0.0339611i
$669$			1.34554e8i			0.449386i
$670$			2.01714e8i			0.670674i
$671$	4.75280e8	+	4.75280e8i	1.57319	+	1.57319i
$672$	−7.39309e7	−	7.39309e7i	−0.243623	−	0.243623i
$673$	5.94762e8			1.95118			0.975591	−	0.219594i	$-0.0704734\pi$
$673$	5.94762e8			1.95118			0.975591	+	0.219594i	$0.0704734\pi$
$674$	7.59672e7	+	7.59672e7i	0.248111	+	0.248111i
$675$	6.86760e8			2.23303
$676$	−1.40131e8			−0.453621
$677$			4.45930e8i			1.43715i	0.695451	+	0.718573i	$0.255205\pi$
$677$			4.45930e8i			1.43715i	−0.695451	+	0.718573i	$0.744795\pi$
$678$	2.65212e8			0.850951
$679$	−2.23978e8	−	2.23978e8i	−0.715477	−	0.715477i
$680$	5.47503e7	−	5.47503e7i	0.174124	−	0.174124i
$681$	1.48222e8	−	1.48222e8i	0.469324	−	0.469324i
$682$	1.61067e8			0.507756
$683$	9.51175e6	+	9.51175e6i	0.0298537	+	0.0298537i	0.721876	−	0.692022i	$-0.243280\pi$
$683$	9.51175e6	+	9.51175e6i	0.0298537	+	0.0298537i	−0.692022	+	0.721876i	$0.743280\pi$
$684$	138713.	−	138713.i	0.000433459	−	0.000433459i
$685$	4.13791e8	+	4.13791e8i	1.28739	+	1.28739i
$686$	−5.48721e8	+	5.48721e8i	−1.69973	+	1.69973i
$687$		−	2.10407e7i		−	0.0648919i
$688$	2.27449e7	+	2.27449e7i	0.0698424	+	0.0698424i
$689$	2.06856e7	+	2.06856e7i	0.0632428	+	0.0632428i
$690$	−3.53928e8	+	3.53928e8i	−1.07738	+	1.07738i
$691$			1.22729e7i			0.0371976i	0.999827	+	0.0185988i	$0.00592052\pi$
$691$			1.22729e7i			0.0371976i	−0.999827	+	0.0185988i	$0.994079\pi$
$692$	1.22168e8			0.368670
$693$			1.25730e7i			0.0377780i
$694$			6.97331e7i			0.208622i
$695$	2.98273e8	−	2.98273e8i	0.888506	−	0.888506i
$696$			2.27477e8i			0.674699i
$697$	−9.04918e7	+	9.04918e7i	−0.267246	+	0.267246i
$698$	1.96250e8	−	1.96250e8i	0.577088	−	0.577088i
$699$	2.84313e8			0.832464
$700$	7.46493e8			2.17636
$701$	3.93122e8	+	3.93122e8i	1.14123	+	1.14123i	0.988225	+	0.153006i	$0.0488953\pi$
$701$	3.93122e8	+	3.93122e8i	1.14123	+	1.14123i	0.153006	+	0.988225i	$0.451105\pi$
$702$		−	7.40590e7i		−	0.214075i
$703$	−3.53273e7	−	8.19112e6i	−0.101682	−	0.0235764i
$704$	7.23964e7			0.207491
$705$	−2.33142e8	+	2.33142e8i	−0.665354	+	0.665354i
$706$		−	1.66386e8i		−	0.472827i
$707$		−	6.70983e8i		−	1.89869i
$708$	3.85742e7	+	3.85742e7i	0.108692	+	0.108692i
$709$	−2.69988e8	−	2.69988e8i	−0.757541	−	0.757541i	0.218334	−	0.975874i	$-0.429938\pi$
$709$	−2.69988e8	−	2.69988e8i	−0.757541	−	0.757541i	−0.975874	+	0.218334i	$0.929938\pi$
$710$	4.60210e8			1.28582
$711$	3.17136e6	+	3.17136e6i	0.00882341	+	0.00882341i
$712$	−5.43354e7			−0.150537
$713$	−1.86428e8			−0.514330
$714$			1.93912e8i			0.532734i
$715$	3.32955e8			0.910893
$716$	−9.16697e7	−	9.16697e7i	−0.249739	−	0.249739i
$717$	2.79903e8	−	2.79903e8i	0.759365	−	0.759365i
$718$	3.62171e8	−	3.62171e8i	0.978454	−	0.978454i
$719$	−4.04412e8			−1.08802			−0.544010	−	0.839079i	$-0.683095\pi$
$719$	−4.04412e8			−1.08802			−0.544010	+	0.839079i	$0.683095\pi$
$720$	−1.39637e6	−	1.39637e6i	−0.00374114	−	0.00374114i
$721$	5.46462e8	−	5.46462e8i	1.45799	−	1.45799i
$722$	1.86133e8	+	1.86133e8i	0.494552	+	0.494552i
$723$	−1.77413e8	+	1.77413e8i	−0.469430	+	0.469430i
$724$			4.93381e7i			0.130007i
$725$	−1.14844e9	−	1.14844e9i	−3.01366	−	3.01366i
$726$	−3.37816e8	−	3.37816e8i	−0.882816	−	0.882816i
$727$	−6.40647e7	+	6.40647e7i	−0.166731	+	0.166731i	−0.785541	−	0.618810i	$-0.787615\pi$
$727$	−6.40647e7	+	6.40647e7i	−0.166731	+	0.166731i	0.618810	+	0.785541i	$0.287615\pi$
$728$		−	8.05005e7i		−	0.208643i
$729$	−3.82764e8			−0.987980
$730$			3.83419e8i			0.985611i
$731$		−	5.96573e7i		−	0.152725i
$732$	1.86953e8	−	1.86953e8i	0.476649	−	0.476649i
$733$			3.57357e8i			0.907383i	0.891159	+	0.453692i	$0.149893\pi$
$733$			3.57357e8i			0.907383i	−0.891159	+	0.453692i	$0.850107\pi$
$734$	1.14067e8	−	1.14067e8i	0.288450	−	0.288450i
$735$	−1.40158e9	+	1.40158e9i	−3.52984	+	3.52984i
$736$	−8.37952e7			−0.210177
$737$	3.49797e8			0.873802
$738$	2.30794e6	+	2.30794e6i	0.00574190	+	0.00574190i
$739$		−	2.30227e8i		−	0.570458i	−0.958459	−	0.285229i	$-0.907930\pi$
$739$		−	2.30227e8i		−	0.570458i	0.958459	−	0.285229i	$-0.0920696\pi$
$740$	−8.24572e7	+	3.55628e8i	−0.203485	+	0.877608i
$741$	1.30102e7			0.0319763
$742$	1.16226e8	−	1.16226e8i	0.284506	−	0.284506i
$743$			5.23451e8i			1.27617i	0.769965	+	0.638086i	$0.220274\pi$
$743$			5.23451e8i			1.27617i	−0.769965	+	0.638086i	$0.779726\pi$
$744$		−	6.33564e7i		−	0.153841i
$745$	−3.29521e8	−	3.29521e8i	−0.796919	−	0.796919i
$746$	2.23077e8	+	2.23077e8i	0.537326	+	0.537326i
$747$	−1.54804e6			−0.00371381
$748$	−9.49437e7	−	9.49437e7i	−0.226862	−	0.226862i
$749$	−2.33361e8			−0.555372
$750$	6.73857e8			1.59729
$751$		−	3.94539e8i		−	0.931473i	−0.884923	−	0.465736i	$-0.845789\pi$
$751$		−	3.94539e8i		−	0.931473i	0.884923	−	0.465736i	$-0.154211\pi$
$752$	−5.51980e7			−0.129799
$753$	−1.49149e8	−	1.49149e8i	−0.349330	−	0.349330i
$754$	−1.23846e8	+	1.23846e8i	−0.288913	+	0.288913i
$755$	−3.19881e8	+	3.19881e8i	−0.743273	+	0.743273i
$756$	−4.16114e8			−0.963045
$757$	−2.20911e8	−	2.20911e8i	−0.509249	−	0.509249i	0.405047	−	0.914296i	$-0.367255\pi$
$757$	−2.20911e8	−	2.20911e8i	−0.509249	−	0.509249i	−0.914296	+	0.405047i	$0.867255\pi$
$758$	−4.12109e8	+	4.12109e8i	−0.946247	+	0.946247i
$759$	6.13755e8	+	6.13755e8i	1.40369	+	1.40369i
$760$	−2.06395e7	+	2.06395e7i	−0.0470173	+	0.0470173i
$761$			6.35238e8i			1.44139i	0.693251	+	0.720696i	$0.256178\pi$
$761$			6.35238e8i			1.44139i	−0.693251	+	0.720696i	$0.743822\pi$
$762$	−5.83536e7	−	5.83536e7i	−0.131887	−	0.131887i
$763$	3.67658e8	+	3.67658e8i	0.827696	+	0.827696i
$764$	−1.33888e8	+	1.33888e8i	−0.300236	+	0.300236i
$765$			3.66253e6i			0.00818082i
$766$	1.92859e8			0.429096
$767$			4.20019e7i			0.0930858i
$768$		−	2.84773e7i		−	0.0628660i
$769$	−1.07770e8	+	1.07770e8i	−0.236985	+	0.236985i	−0.815600	−	0.578616i	$-0.803593\pi$
$769$	−1.07770e8	+	1.07770e8i	−0.236985	+	0.236985i	0.578616	+	0.815600i	$0.303593\pi$
$770$		−	1.87077e9i		−	4.09777i
$771$	−9.15101e7	+	9.15101e7i	−0.199667	+	0.199667i
$772$	1.90041e8	−	1.90041e8i	0.413044	−	0.413044i
$773$	−9.04013e7			−0.195720			−0.0978602	−	0.995200i	$-0.531200\pi$
$773$	−9.04013e7			−0.195720			−0.0978602	+	0.995200i	$0.531200\pi$
$774$	−1.52153e6			−0.00328138
$775$	3.19860e8	+	3.19860e8i	0.687156	+	0.687156i
$776$		−	8.62737e7i		−	0.184626i
$777$	−4.83753e8	−	7.75796e8i	−1.03124	−	1.65381i
$778$	−1.55110e8			−0.329383
$779$	3.41131e7	−	3.41131e7i	0.0721621	−	0.0721621i
$780$		−	1.30969e8i		−	0.275984i
$781$		−	7.98060e8i		−	1.67526i
$782$	1.09893e8	+	1.09893e8i	0.229799	+	0.229799i
$783$	6.40168e8	+	6.40168e8i	1.33355	+	1.33355i
$784$	−3.31834e8			−0.688609
$785$	−1.02318e8	−	1.02318e8i	−0.211515	−	0.211515i
$786$	5.30096e8			1.09166
$787$	−6.57775e8			−1.34944			−0.674720	−	0.738074i	$-0.735736\pi$
$787$	−6.57775e8			−1.34944			−0.674720	+	0.738074i	$0.735736\pi$
$788$		−	3.34335e7i		−	0.0683288i
$789$	−8.53352e8			−1.73739
$790$	−4.71875e8	−	4.71875e8i	−0.957075	−	0.957075i
$791$	8.11279e8	−	8.11279e8i	1.63923	−	1.63923i
$792$	−2.42148e6	+	2.42148e6i	−0.00487423	+	0.00487423i
$793$	2.03566e8			0.408211
$794$	−4.43733e7	−	4.43733e7i	−0.0886463	−	0.0886463i
$795$	1.89092e8	−	1.89092e8i	0.376332	−	0.376332i
$796$	9.11588e6	+	9.11588e6i	0.0180742	+	0.0180742i
$797$	−1.90499e7	+	1.90499e7i	−0.0376286	+	0.0376286i	−0.725671	−	0.688042i	$-0.758470\pi$
$797$	−1.90499e7	+	1.90499e7i	−0.0376286	+	0.0376286i	0.688042	+	0.725671i	$0.258470\pi$
$798$		−	7.31000e7i		−	0.143850i
$799$	7.23891e7	+	7.23891e7i	0.141916	+	0.141916i
$800$	1.43770e8	+	1.43770e8i	0.280801	+	0.280801i
$801$	1.81739e6	−	1.81739e6i	0.00353631	−	0.00353631i
$802$			5.87707e8i			1.13930i
$803$	6.64897e8			1.28413
$804$		−	1.37594e8i		−	0.264746i
$805$			2.16532e9i			4.15083i
$806$	3.44932e7	−	3.44932e7i	0.0658761	−	0.0658761i
$807$		−	4.37126e8i		−	0.831737i
$808$	1.29227e8	−	1.29227e8i	0.244974	−	0.244974i
$809$	3.04726e8	−	3.04726e8i	0.575526	−	0.575526i	−0.358142	−	0.933667i	$-0.616590\pi$
$809$	3.04726e8	−	3.04726e8i	0.575526	−	0.575526i	0.933667	+	0.358142i	$0.116590\pi$
$810$	−6.84942e8			−1.28884
$811$	−2.21477e8			−0.415208			−0.207604	−	0.978213i	$-0.566567\pi$
$811$	−2.21477e8			−0.415208			−0.207604	+	0.978213i	$0.566567\pi$
$812$	6.95849e8	+	6.95849e8i	1.29971	+	1.29971i
$813$		−	1.02077e9i		−	1.89958i
$814$	6.16703e8	+	1.42991e8i	1.14341	+	0.265116i
$815$	−1.31888e9			−2.43631
$816$	−3.73464e7	+	3.73464e7i	−0.0687351	+	0.0687351i
$817$			2.24893e7i			0.0412392i
$818$			3.94896e8i			0.721478i
$819$	2.69255e6	+	2.69255e6i	0.00490131	+	0.00490131i
$820$	−3.43405e8	−	3.43405e8i	−0.622824	−	0.622824i
$821$	−7.83976e8			−1.41669			−0.708343	−	0.705869i	$-0.750557\pi$
$821$	−7.83976e8			−1.41669			−0.708343	+	0.705869i	$0.750557\pi$
$822$	−2.82256e8	−	2.82256e8i	−0.508192	−	0.508192i
$823$	−1.05895e9			−1.89966			−0.949830	−	0.312767i	$-0.898744\pi$
$823$	−1.05895e9			−1.89966			−0.949830	+	0.312767i	$0.898744\pi$
$824$	2.10491e8			0.376228
$825$		−	2.10608e9i		−	3.75071i
$826$	2.35995e8			0.418758
$827$	3.36789e8	+	3.36789e8i	0.595444	+	0.595444i	0.939097	−	0.343653i	$-0.111664\pi$
$827$	3.36789e8	+	3.36789e8i	0.595444	+	0.595444i	−0.343653	+	0.939097i	$0.611664\pi$
$828$	2.80275e6	−	2.80275e6i	0.00493734	−	0.00493734i
$829$	−9.82877e7	+	9.82877e7i	−0.172519	+	0.172519i	−0.788085	−	0.615566i	$-0.788927\pi$
$829$	−9.82877e7	+	9.82877e7i	−0.172519	+	0.172519i	0.615566	+	0.788085i	$0.288927\pi$
$830$	2.30337e8			0.402837
$831$	2.27612e8	+	2.27612e8i	0.396636	+	0.396636i
$832$	1.55039e7	−	1.55039e7i	0.0269198	−	0.0269198i
$833$	4.35181e8	+	4.35181e8i	0.752896	+	0.752896i
$834$	−2.03459e8	+	2.03459e8i	−0.350735	+	0.350735i
$835$		−	1.00760e8i		−	0.173073i
$836$	3.57914e7	+	3.57914e7i	0.0612575	+	0.0612575i
$837$	−1.78298e8	−	1.78298e8i	−0.304068	−	0.304068i
$838$	2.45521e8	−	2.45521e8i	0.417212	−	0.417212i
$839$			7.63160e8i			1.29220i	0.763253	+	0.646100i	$0.223601\pi$
$839$			7.63160e8i			1.29220i	−0.763253	+	0.646100i	$0.776399\pi$
$840$	−7.35873e8			−1.24155
$841$		−	1.54623e9i		−	2.59947i
$842$		−	8.67982e7i		−	0.145403i
$843$	4.91960e8	−	4.91960e8i	0.821197	−	0.821197i
$844$			2.98334e8i			0.496221i
$845$	−6.97397e8	+	6.97397e8i	−1.15587	+	1.15587i
$846$	1.84624e6	−	1.84624e6i	0.00304914	−	0.00304914i
$847$	−2.06675e9			−3.40124
$848$	4.47689e7			0.0734157
$849$	3.65241e8	+	3.65241e8i	0.596837	+	0.596837i
$850$		−	3.77093e8i		−	0.614033i
$851$	−7.13803e8	−	1.65505e8i	−1.15822	−	0.268548i
$852$	−3.13920e8			−0.507574
$853$	−5.80482e8	+	5.80482e8i	−0.935279	+	0.935279i	−0.998029	−	0.0627500i	$-0.980013\pi$
$853$	−5.80482e8	+	5.80482e8i	−0.935279	+	0.935279i	0.0627500	+	0.998029i	$0.480013\pi$
$854$		−	1.14377e9i		−	1.83639i
$855$		−	1.38068e6i		−	0.00220900i
$856$	−4.49441e7	−	4.49441e7i	−0.0716558	−	0.0716558i
$857$	7.52127e8	+	7.52127e8i	1.19495	+	1.19495i	0.975660	+	0.219287i	$0.0703732\pi$
$857$	7.52127e8	+	7.52127e8i	1.19495	+	1.19495i	0.219287	+	0.975660i	$0.429627\pi$
$858$	−2.27116e8			−0.359572
$859$	6.24464e8	+	6.24464e8i	0.985208	+	0.985208i	0.999892	−	0.0146844i	$-0.00467434\pi$
$859$	6.24464e8	+	6.24464e8i	0.985208	+	0.985208i	−0.0146844	+	0.999892i	$0.504674\pi$
$860$	2.26392e8			0.355931
$861$	1.21626e9			1.90553
$862$			4.91629e8i			0.767566i
$863$	6.40369e8			0.996318			0.498159	−	0.867086i	$-0.334010\pi$
$863$	6.40369e8			0.996318			0.498159	+	0.867086i	$0.334010\pi$
$864$	−8.01412e7	−	8.01412e7i	−0.124255	−	0.124255i
$865$	6.07999e8	−	6.07999e8i	0.939408	−	0.939408i
$866$	−4.19520e8	+	4.19520e8i	−0.645950	+	0.645950i
$867$	−5.57575e8			−0.855552
$868$	−1.93806e8	−	1.93806e8i	−0.296352	−	0.296352i
$869$	−8.18290e8	+	8.18290e8i	−1.24695	+	1.24695i
$870$	1.13210e9	+	1.13210e9i	1.71920	+	1.71920i
$871$	7.49102e7	−	7.49102e7i	0.113367	−	0.113367i
$872$			1.41618e8i			0.213584i
$873$	2.88565e6	+	2.88565e6i	0.00433711	+	0.00433711i
$874$	−4.14267e7	−	4.14267e7i	−0.0620506	−	0.0620506i
$875$	2.06132e9	−	2.06132e9i	3.07695	−	3.07695i
$876$		−	2.61539e8i		−	0.389067i
$877$	8.51862e8			1.26290			0.631452	−	0.775415i	$-0.282459\pi$
$877$	8.51862e8			1.26290			0.631452	+	0.775415i	$0.282459\pi$
$878$			1.36977e8i			0.202378i
$879$			8.48355e8i			1.24914i
$880$	3.60299e8	−	3.60299e8i	0.528708	−	0.528708i
$881$		−	5.56513e8i		−	0.813856i	−0.913460	−	0.406928i	$-0.866600\pi$
$881$		−	5.56513e8i		−	0.813856i	0.913460	−	0.406928i	$-0.133400\pi$
$882$	1.10990e7	−	1.10990e7i	0.0161763	−	0.0161763i
$883$	−7.63526e8	+	7.63526e8i	−1.10903	+	1.10903i	−0.115747	+	0.993279i	$0.536926\pi$
$883$	−7.63526e8	+	7.63526e8i	−1.10903	+	1.10903i	−0.993279	+	0.115747i	$0.963074\pi$
$884$	−4.06651e7			−0.0588660
$885$	3.83949e8			0.553916
$886$	−1.13995e8	−	1.13995e8i	−0.163902	−	0.163902i
$887$			2.96214e8i			0.424458i	0.977220	+	0.212229i	$0.0680723\pi$
$887$			2.96214e8i			0.424458i	−0.977220	+	0.212229i	$0.931928\pi$
$888$	5.62459e7	−	2.42582e8i	0.0803253	−	0.346433i
$889$	−3.57005e8			−0.508124
$890$	−2.70414e8	+	2.70414e8i	−0.383583	+	0.383583i
$891$			1.18777e9i			1.67919i
$892$			1.58543e8i			0.223385i
$893$	−2.72889e7	−	2.72889e7i	−0.0383205	−	0.0383205i
$894$	2.24774e8	+	2.24774e8i	0.314582	+	0.314582i
$895$	−9.12436e8			−1.27272
$896$	−8.71117e7	−	8.71117e7i	−0.121102	−	0.121102i
$897$	2.62876e8			0.364228
$898$	−2.29236e8			−0.316559
$899$			5.96320e8i			0.820730i
$900$	−9.61755e6			−0.0131928
$901$	−5.87119e7	−	5.87119e7i	−0.0802697	−	0.0802697i
$902$	−5.95507e8	+	5.95507e8i	−0.811460	+	0.811460i
$903$	−4.00913e8	+	4.00913e8i	−0.544486	+	0.544486i
$904$	3.12496e8			0.422998
$905$	2.45544e8	+	2.45544e8i	0.331271	+	0.331271i
$906$	2.18198e8	−	2.18198e8i	0.293405	−	0.293405i
$907$	8.29279e8	+	8.29279e8i	1.11142	+	1.11142i	0.992958	+	0.118464i	$0.0377969\pi$
$907$	8.29279e8	+	8.29279e8i	1.11142	+	1.11142i	0.118464	+	0.992958i	$0.462203\pi$
$908$	1.74648e8	−	1.74648e8i	0.233296	−	0.233296i
$909$			8.64470e6i			0.0115095i
$910$	−4.00632e8	−	4.00632e8i	−0.531644	−	0.531644i
$911$	−1.05724e7	−	1.05724e7i	−0.0139836	−	0.0139836i	0.700080	−	0.714064i	$-0.253147\pi$
$911$	−1.05724e7	−	1.05724e7i	−0.0139836	−	0.0139836i	−0.714064	+	0.700080i	$0.753147\pi$
$912$	1.40787e7	−	1.40787e7i	0.0185599	−	0.0185599i
$913$		−	3.99433e8i		−	0.524845i
$914$	−3.27233e8			−0.428567
$915$		−	1.86084e9i		−	2.42910i
$916$		−	2.47920e7i		−	0.0322571i
$917$	1.62155e9	−	1.62155e9i	2.10292	−	2.10292i
$918$			2.10201e8i			0.271711i
$919$	4.14597e8	−	4.14597e8i	0.534170	−	0.534170i	−0.387641	−	0.921811i	$-0.626710\pi$
$919$	4.14597e8	−	4.14597e8i	0.534170	−	0.534170i	0.921811	+	0.387641i	$0.126710\pi$
$920$	−4.17029e8	+	4.17029e8i	−0.535553	+	0.535553i
$921$	2.06968e8			0.264925
$922$	9.28801e8			1.18503
$923$	−1.70908e8	−	1.70908e8i	−0.217348	−	0.217348i
$924$			1.27609e9i			1.61758i
$925$	9.40734e8	+	1.50866e9i	1.18862	+	1.90619i
$926$	4.95990e8			0.624655
$927$	−7.04041e6	+	7.04041e6i	−0.00883810	+	0.00883810i
$928$			2.68033e8i			0.335386i
$929$		−	8.85681e8i		−	1.10466i	−0.833624	−	0.552332i	$-0.813738\pi$
$929$		−	8.85681e8i		−	1.10466i	0.833624	−	0.552332i	$-0.186262\pi$
$930$	−3.15310e8	−	3.15310e8i	−0.392002	−	0.392002i
$931$	−1.64052e8	−	1.64052e8i	−0.203298	−	0.203298i
$932$	3.35002e8			0.413809
$933$	3.01895e8	+	3.01895e8i	0.371716	+	0.371716i
$934$	−6.78542e8			−0.832791
$935$	−9.45024e8			−1.15613
$936$			1.03714e6i			0.00126476i
$937$	9.34886e7			0.113642			0.0568211	−	0.998384i	$-0.481904\pi$
$937$	9.34886e7			0.113642			0.0568211	+	0.998384i	$0.481904\pi$
$938$	−4.20896e8	−	4.20896e8i	−0.509996	−	0.509996i
$939$	5.55679e8	−	5.55679e8i	0.671162	−	0.671162i
$940$	−2.74708e8	+	2.74708e8i	−0.330740	+	0.330740i
$941$	−4.27050e8			−0.512518			−0.256259	−	0.966608i	$-0.582490\pi$
$941$	−4.27050e8			−0.512518			−0.256259	+	0.966608i	$0.582490\pi$
$942$	6.97932e7	+	6.97932e7i	0.0834949	+	0.0834949i
$943$	6.89269e8	−	6.89269e8i	0.821966	−	0.821966i
$944$	4.54514e7	+	4.54514e7i	0.0540295	+	0.0540295i
$945$	−2.07090e9	+	2.07090e9i	−2.45394	+	2.45394i
$946$		−	3.92592e8i		−	0.463733i
$947$	6.91915e8	+	6.91915e8i	0.814709	+	0.814709i	0.985336	−	0.170626i	$-0.0545791\pi$
$947$	6.91915e8	+	6.91915e8i	0.814709	+	0.814709i	−0.170626	+	0.985336i	$0.554579\pi$
$948$	3.21877e8	+	3.21877e8i	0.377803	+	0.377803i
$949$	1.42390e8	−	1.42390e8i	0.166602	−	0.166602i
$950$			1.42155e8i			0.165802i
$951$	−1.69542e8			−0.197123
$952$			2.28484e8i			0.264816i
$953$			1.18428e9i			1.36828i	0.729349	+	0.684142i	$0.239823\pi$
$953$			1.18428e9i			1.36828i	−0.729349	+	0.684142i	$0.760177\pi$
$954$	−1.49741e6	+	1.49741e6i	−0.00172463	+	0.00172463i
$955$			1.33266e9i			1.53006i
$956$	3.29806e8	−	3.29806e8i	0.377472	−	0.377472i
$957$	1.96320e9	−	1.96320e9i	2.23990	−	2.23990i
$958$	−5.82836e8			−0.662903
$959$	−1.72683e9			−1.95792
$960$	−1.41725e8	−	1.41725e8i	−0.160189	−	0.160189i
$961$			7.21418e8i			0.812862i
$962$	1.62691e8	−	1.01447e8i	0.182742	−	0.113950i
$963$	3.00655e6			0.00336658
$964$	−2.09043e8	+	2.09043e8i	−0.233348	+	0.233348i
$965$		−	1.89158e9i		−	2.10496i
$966$		−	1.47701e9i		−	1.63853i
$967$	1.20946e8	+	1.20946e8i	0.133756	+	0.133756i	0.770815	−	0.637059i	$-0.219849\pi$
$967$	1.20946e8	+	1.20946e8i	0.133756	+	0.133756i	−0.637059	+	0.770815i	$0.719849\pi$
$968$	−3.98044e8	−	3.98044e8i	−0.438839	−	0.438839i
$969$	−3.69267e7			−0.0405853
$970$	−4.29364e8	−	4.29364e8i	−0.470446	−	0.470446i
$971$	6.14956e8			0.671717			0.335858	−	0.941912i	$-0.390974\pi$
$971$	6.14956e8			0.671717			0.335858	+	0.941912i	$0.390974\pi$
$972$	1.07858e7			0.0117451
$973$			1.24476e9i			1.35128i
$974$	7.44450e8			0.805672
$975$	−4.51025e8	−	4.51025e8i	−0.486617	−	0.486617i
$976$	2.20284e8	−	2.20284e8i	0.236937	−	0.236937i
$977$	9.75229e8	−	9.75229e8i	1.04574	−	1.04574i	0.0468357	−	0.998903i	$-0.485086\pi$
$977$	9.75229e8	−	9.75229e8i	1.04574	−	1.04574i	0.998903	−	0.0468357i	$-0.0149137\pi$
$978$	8.99640e8			0.961728
$979$	4.68931e8	+	4.68931e8i	0.499760	+	0.499760i
$980$	−1.65146e9	+	1.65146e9i	−1.75464	+	1.75464i
$981$	−4.73678e6	−	4.73678e6i	−0.00501737	−	0.00501737i
$982$	−7.50596e8	+	7.50596e8i	−0.792633	+	0.792633i
$983$		−	9.67423e8i		−	1.01849i	−0.860622	−	0.509244i	$-0.829925\pi$
$983$		−	9.67423e8i		−	1.01849i	0.860622	−	0.509244i	$-0.170075\pi$
$984$	2.34244e8	+	2.34244e8i	0.245858	+	0.245858i
$985$	−1.66391e8	−	1.66391e8i	−0.174109	−	0.174109i
$986$	3.51510e8	−	3.51510e8i	0.366697	−	0.366697i
$987$		−	9.72948e8i		−	1.01190i
$988$	1.53297e7			0.0158951
$989$			4.54405e8i			0.469737i
$990$			2.41023e7i			0.0248401i
$991$	9.85579e8	−	9.85579e8i	1.01268	−	1.01268i	0.0127574	−	0.999919i	$-0.495939\pi$
$991$	9.85579e8	−	9.85579e8i	1.01268	−	1.01268i	0.999919	−	0.0127574i	$-0.00406092\pi$
$992$		−	7.46519e7i		−	0.0764726i
$993$	−3.59338e8	+	3.59338e8i	−0.366991	+	0.366991i
$994$	−9.60275e8	+	9.60275e8i	−0.977769	+	0.977769i
$995$	9.07351e7			0.0921099
$996$	−1.57118e8			−0.159019
$997$	7.65671e8	+	7.65671e8i	0.772603	+	0.772603i	0.978561	−	0.205958i	$-0.0660309\pi$
$997$	7.65671e8	+	7.65671e8i	0.772603	+	0.772603i	−0.205958	+	0.978561i	$0.566031\pi$
$998$			3.87527e8i			0.389862i
$999$	−5.24389e8	−	8.40964e8i	−0.525965	−	0.843492i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.7.d.b.43.3	yes	20
37.31	odd	4	inner	74.7.d.b.31.8	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.7.d.b.31.8	✓	20	37.31	odd	4	inner
74.7.d.b.43.3	yes	20	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(-4.00000 + 4.00000i) q^{2} -27.1581i q^{3} -32.0000i q^{4} +(-159.256 - 159.256i) q^{5} +(108.632 + 108.632i) q^{6} +664.609 q^{7} +(128.000 + 128.000i) q^{8} -8.56259 q^{9} +O(q^{10})\)	\(q+(-4.00000 + 4.00000i) q^{2} -27.1581i q^{3} -32.0000i q^{4} +(-159.256 - 159.256i) q^{5} +(108.632 + 108.632i) q^{6} +664.609 q^{7} +(128.000 + 128.000i) q^{8} -8.56259 q^{9} +1274.05 q^{10} -2209.36i q^{11} -869.059 q^{12} +(-473.143 - 473.143i) q^{13} +(-2658.44 + 2658.44i) q^{14} +(-4325.10 + 4325.10i) q^{15} -1024.00 q^{16} +(1342.92 + 1342.92i) q^{17} +(34.2503 - 34.2503i) q^{18} +(-506.246 - 506.246i) q^{19} +(-5096.20 + 5096.20i) q^{20} -18049.5i q^{21} +(8837.45 + 8837.45i) q^{22} +(-10228.9 - 10228.9i) q^{23} +(3476.24 - 3476.24i) q^{24} +35100.2i q^{25} +3785.14 q^{26} -19565.7i q^{27} -21267.5i q^{28} +(-32718.9 + 32718.9i) q^{29} -34600.8i q^{30} +(9112.78 - 9112.78i) q^{31} +(4096.00 - 4096.00i) q^{32} -60002.1 q^{33} -10743.3 q^{34} +(-105843. - 105843. i) q^{35} +274.003i q^{36} +(42981.5 - 26801.4i) q^{37} +4049.97 q^{38} +(-12849.7 + 12849.7i) q^{39} -40769.6i q^{40} +67384.5i q^{41} +(72198.1 + 72198.1i) q^{42} +(-22211.8 - 22211.8i) q^{43} -70699.6 q^{44} +(1363.65 + 1363.65i) q^{45} +81831.2 q^{46} +53904.3 q^{47} +27809.9i q^{48} +324056. q^{49} +(-140401. - 140401. i) q^{50} +(36471.1 - 36471.1i) q^{51} +(-15140.6 + 15140.6i) q^{52} -43719.6 q^{53} +(78262.9 + 78262.9i) q^{54} +(-351855. + 351855. i) q^{55} +(85070.0 + 85070.0i) q^{56} +(-13748.7 + 13748.7i) q^{57} -261751. i q^{58} +(-44386.1 - 44386.1i) q^{59} +(138403. + 138403. i) q^{60} +(-215121. + 215121. i) q^{61} +72902.3i q^{62} -5690.77 q^{63} +32768.0i q^{64} +150702. i q^{65} +(240008. - 240008. i) q^{66} +158325. i q^{67} +(42973.4 - 42973.4i) q^{68} +(-277798. + 277798. i) q^{69} +846746. q^{70} +361218. q^{71} +(-1096.01 - 1096.01i) q^{72} +300945. i q^{73} +(-64720.5 + 279132. i) q^{74} +953254. q^{75} +(-16199.9 + 16199.9i) q^{76} -1.46836e6i q^{77} -102797. i q^{78} +(-370374. - 370374. i) q^{79} +(163079. + 163079. i) q^{80} -537610. q^{81} +(-269538. - 269538. i) q^{82} +180791. q^{83} -577585. q^{84} -427736. i q^{85} +177695. q^{86} +(888583. + 888583. i) q^{87} +(282798. - 282798. i) q^{88} +(-212247. + 212247. i) q^{89} -10909.2 q^{90} +(-314455. - 314455. i) q^{91} +(-327325. + 327325. i) q^{92} +(-247486. - 247486. i) q^{93} +(-215617. + 215617. i) q^{94} +161246. i q^{95} +(-111240. - 111240. i) q^{96} +(-337007. - 337007. i) q^{97} +(-1.29623e6 + 1.29623e6i) q^{98} +18917.8i 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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