LMFDB - Embedded newform 74.7.d.b.31.1

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			31.1
Root			$51.2623i$ of defining polynomial
Character	$\chi$	$=$	74.31
Dual form			74.7.d.b.43.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.00000 - 4.00000i) q^{2} -48.2623i q^{3} +32.0000i q^{4} +(120.036 - 120.036i) q^{5} +(-193.049 + 193.049i) q^{6} -229.509 q^{7} +(128.000 - 128.000i) q^{8} -1600.25 q^{9} +O(q^{10})$	\(q+(-4.00000 - 4.00000i) q^{2} -48.2623i q^{3} +32.0000i q^{4} +(120.036 - 120.036i) q^{5} +(-193.049 + 193.049i) q^{6} -229.509 q^{7} +(128.000 - 128.000i) q^{8} -1600.25 q^{9} -960.285 q^{10} -1552.78i q^{11} +1544.39 q^{12} +(729.393 - 729.393i) q^{13} +(918.036 + 918.036i) q^{14} +(-5793.20 - 5793.20i) q^{15} -1024.00 q^{16} +(2667.65 - 2667.65i) q^{17} +(6401.00 + 6401.00i) q^{18} +(-7757.72 + 7757.72i) q^{19} +(3841.14 + 3841.14i) q^{20} +11076.6i q^{21} +(-6211.12 + 6211.12i) q^{22} +(8511.09 - 8511.09i) q^{23} +(-6177.57 - 6177.57i) q^{24} -13192.1i q^{25} -5835.15 q^{26} +42048.5i q^{27} -7344.29i q^{28} +(14088.5 + 14088.5i) q^{29} +46345.6i q^{30} +(13156.7 + 13156.7i) q^{31} +(4096.00 + 4096.00i) q^{32} -74940.7 q^{33} -21341.2 q^{34} +(-27549.3 + 27549.3i) q^{35} -51208.0i q^{36} +(24131.9 + 44535.1i) q^{37} +62061.8 q^{38} +(-35202.2 - 35202.2i) q^{39} -30729.1i q^{40} -85064.6i q^{41} +(44306.5 - 44306.5i) q^{42} +(-48051.6 + 48051.6i) q^{43} +49689.0 q^{44} +(-192087. + 192087. i) q^{45} -68088.7 q^{46} +57854.0 q^{47} +49420.6i q^{48} -64974.6 q^{49} +(-52768.5 + 52768.5i) q^{50} +(-128747. - 128747. i) q^{51} +(23340.6 + 23340.6i) q^{52} +218163. q^{53} +(168194. - 168194. i) q^{54} +(-186389. - 186389. i) q^{55} +(-29377.2 + 29377.2i) q^{56} +(374405. + 374405. i) q^{57} -112708. i q^{58} +(148629. - 148629. i) q^{59} +(185382. - 185382. i) q^{60} +(123265. + 123265. i) q^{61} -105253. i q^{62} +367272. q^{63} -32768.0i q^{64} -175106. i q^{65} +(299763. + 299763. i) q^{66} -295942. i q^{67} +(85364.8 + 85364.8i) q^{68} +(-410765. - 410765. i) q^{69} +220394. q^{70} -640984. q^{71} +(-204832. + 204832. i) q^{72} -536740. i q^{73} +(81613.0 - 274668. i) q^{74} -636682. q^{75} +(-248247. - 248247. i) q^{76} +356377. i q^{77} +281618. i q^{78} +(-202825. + 202825. i) q^{79} +(-122917. + 122917. i) q^{80} +862774. q^{81} +(-340258. + 340258. i) q^{82} -1.05224e6 q^{83} -354452. q^{84} -640426. i q^{85} +384413. q^{86} +(679942. - 679942. i) q^{87} +(-198756. - 198756. i) q^{88} +(138513. + 138513. i) q^{89} +1.53670e6 q^{90} +(-167402. + 167402. i) q^{91} +(272355. + 272355. i) q^{92} +(634970. - 634970. i) q^{93} +(-231416. - 231416. i) q^{94} +1.86241e6i q^{95} +(197682. - 197682. i) q^{96} +(17408.9 - 17408.9i) q^{97} +(259899. + 259899. i) q^{98} +2.48483e6i 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
$3$		−	48.2623i		−	1.78749i	−0.448573	−	0.893746i	$-0.648068\pi$
$3$		−	48.2623i		−	1.78749i	0.448573	−	0.893746i	$-0.351932\pi$
$4$			32.0000i			0.500000i
$5$	120.036	−	120.036i	0.960285	−	0.960285i	−0.0389555	−	0.999241i	$-0.512403\pi$
$5$	120.036	−	120.036i	0.960285	−	0.960285i	0.999241	+	0.0389555i	$0.0124031\pi$
$6$	−193.049	+	193.049i	−0.893746	+	0.893746i
$7$	−229.509			−0.669122			−0.334561	−	0.942374i	$-0.608588\pi$
$7$	−229.509			−0.669122			−0.334561	+	0.942374i	$0.608588\pi$
$8$	128.000	−	128.000i	0.250000	−	0.250000i
$9$	−1600.25			−2.19513
$10$	−960.285			−0.960285
$11$		−	1552.78i		−	1.16663i	−0.812247	−	0.583313i	$-0.801756\pi$
$11$		−	1552.78i		−	1.16663i	0.812247	−	0.583313i	$-0.198244\pi$
$12$	1544.39			0.893746
$13$	729.393	−	729.393i	0.331995	−	0.331995i	−0.521349	−	0.853344i	$-0.674571\pi$
$13$	729.393	−	729.393i	0.331995	−	0.331995i	0.853344	+	0.521349i	$0.174571\pi$
$14$	918.036	+	918.036i	0.334561	+	0.334561i
$15$	−5793.20	−	5793.20i	−1.71650	−	1.71650i
$16$	−1024.00			−0.250000
$17$	2667.65	−	2667.65i	0.542978	−	0.542978i	−0.381423	−	0.924401i	$-0.624566\pi$
$17$	2667.65	−	2667.65i	0.542978	−	0.542978i	0.924401	+	0.381423i	$0.124566\pi$
$18$	6401.00	+	6401.00i	1.09756	+	1.09756i
$19$	−7757.72	+	7757.72i	−1.13103	+	1.13103i	−0.141021	+	0.990007i	$0.545039\pi$
$19$	−7757.72	+	7757.72i	−1.13103	+	1.13103i	−0.990007	+	0.141021i	$0.954961\pi$
$20$	3841.14	+	3841.14i	0.480143	+	0.480143i
$21$			11076.6i			1.19605i
$22$	−6211.12	+	6211.12i	−0.583313	+	0.583313i
$23$	8511.09	−	8511.09i	0.699523	−	0.699523i	−0.264785	−	0.964308i	$-0.585301\pi$
$23$	8511.09	−	8511.09i	0.699523	−	0.699523i	0.964308	+	0.264785i	$0.0853009\pi$
$24$	−6177.57	−	6177.57i	−0.446873	−	0.446873i
$25$		−	13192.1i		−	0.844296i
$26$	−5835.15			−0.331995
$27$			42048.5i			2.13628i
$28$		−	7344.29i		−	0.334561i
$29$	14088.5	+	14088.5i	0.577657	+	0.577657i	0.934257	−	0.356600i	$-0.116064\pi$
$29$	14088.5	+	14088.5i	0.577657	+	0.577657i	−0.356600	+	0.934257i	$0.616064\pi$
$30$			46345.6i			1.71650i
$31$	13156.7	+	13156.7i	0.441632	+	0.441632i	0.892560	−	0.450928i	$-0.148907\pi$
$31$	13156.7	+	13156.7i	0.441632	+	0.441632i	−0.450928	+	0.892560i	$0.648907\pi$
$32$	4096.00	+	4096.00i	0.125000	+	0.125000i
$33$	−74940.7			−2.08534
$34$	−21341.2			−0.542978
$35$	−27549.3	+	27549.3i	−0.642549	+	0.642549i
$36$		−	51208.0i		−	1.09756i
$37$	24131.9	+	44535.1i	0.476416	+	0.879220i
$37$	24131.9	+	44535.1i	0.476416	+	0.879220i
$38$	62061.8			1.13103
$39$	−35202.2	−	35202.2i	−0.593439	−	0.593439i
$40$		−	30729.1i		−	0.480143i
$41$		−	85064.6i		−	1.23423i	−0.786872	−	0.617117i	$-0.788301\pi$
$41$		−	85064.6i		−	1.23423i	0.786872	−	0.617117i	$-0.211699\pi$
$42$	44306.5	−	44306.5i	0.598026	−	0.598026i
$43$	−48051.6	+	48051.6i	−0.604370	+	0.604370i	−0.941469	−	0.337099i	$-0.890554\pi$
$43$	−48051.6	+	48051.6i	−0.604370	+	0.604370i	0.337099	+	0.941469i	$0.390554\pi$
$44$	49689.0			0.583313
$45$	−192087.	+	192087.i	−2.10795	+	2.10795i
$46$	−68088.7			−0.699523
$47$	57854.0			0.557236			0.278618	−	0.960402i	$-0.410124\pi$
$47$	57854.0			0.557236			0.278618	+	0.960402i	$0.410124\pi$
$48$			49420.6i			0.446873i
$49$	−64974.6			−0.552275
$50$	−52768.5	+	52768.5i	−0.422148	+	0.422148i
$51$	−128747.	−	128747.i	−0.970568	−	0.970568i
$52$	23340.6	+	23340.6i	0.165998	+	0.165998i
$53$	218163.			1.46539			0.732696	−	0.680556i	$-0.238262\pi$
$53$	218163.			1.46539			0.732696	+	0.680556i	$0.238262\pi$
$54$	168194.	−	168194.i	1.06814	−	1.06814i
$55$	−186389.	−	186389.i	−1.12029	−	1.12029i
$56$	−29377.2	+	29377.2i	−0.167281	+	0.167281i
$57$	374405.	+	374405.i	2.02170	+	2.02170i
$58$		−	112708.i		−	0.577657i
$59$	148629.	−	148629.i	0.723680	−	0.723680i	−0.245673	−	0.969353i	$-0.579009\pi$
$59$	148629.	−	148629.i	0.723680	−	0.723680i	0.969353	+	0.245673i	$0.0790088\pi$
$60$	185382.	−	185382.i	0.858251	−	0.858251i
$61$	123265.	+	123265.i	0.543065	+	0.543065i	0.924426	−	0.381361i	$-0.124544\pi$
$61$	123265.	+	123265.i	0.543065	+	0.543065i	−0.381361	+	0.924426i	$0.624544\pi$
$62$		−	105253.i		−	0.441632i
$63$	367272.			1.46881
$64$		−	32768.0i		−	0.125000i
$65$		−	175106.i		−	0.637620i
$66$	299763.	+	299763.i	1.04267	+	1.04267i
$67$		−	295942.i		−	0.983972i	−0.870603	−	0.491986i	$-0.836271\pi$
$67$		−	295942.i		−	0.983972i	0.870603	−	0.491986i	$-0.163729\pi$
$68$	85364.8	+	85364.8i	0.271489	+	0.271489i
$69$	−410765.	−	410765.i	−1.25039	−	1.25039i
$70$	220394.			0.642549
$71$	−640984.			−1.79090			−0.895451	−	0.445159i	$-0.853147\pi$
$71$	−640984.			−1.79090			−0.895451	+	0.445159i	$0.853147\pi$
$72$	−204832.	+	204832.i	−0.548782	+	0.548782i
$73$		−	536740.i		−	1.37973i	−0.723936	−	0.689867i	$-0.757669\pi$
$73$		−	536740.i		−	1.37973i	0.723936	−	0.689867i	$-0.242331\pi$
$74$	81613.0	−	274668.i	0.201402	−	0.677818i
$75$	−636682.			−1.50917
$76$	−248247.	−	248247.i	−0.565514	−	0.565514i
$77$			356377.i			0.780616i
$78$			281618.i			0.593439i
$79$	−202825.	+	202825.i	−0.411378	+	0.411378i	−0.882218	−	0.470840i	$-0.843951\pi$
$79$	−202825.	+	202825.i	−0.411378	+	0.411378i	0.470840	+	0.882218i	$0.343951\pi$
$80$	−122917.	+	122917.i	−0.240071	+	0.240071i
$81$	862774.			1.62346
$82$	−340258.	+	340258.i	−0.617117	+	0.617117i
$83$	−1.05224e6			−1.84026			−0.920129	−	0.391615i	$-0.871917\pi$
$83$	−1.05224e6			−1.84026			−0.920129	+	0.391615i	$0.871917\pi$
$84$	−354452.			−0.598026
$85$		−	640426.i		−	1.04283i
$86$	384413.			0.604370
$87$	679942.	−	679942.i	1.03256	−	1.03256i
$88$	−198756.	−	198756.i	−0.291657	−	0.291657i
$89$	138513.	+	138513.i	0.196481	+	0.196481i	0.798490	−	0.602008i	$-0.205633\pi$
$89$	138513.	+	138513.i	0.196481	+	0.196481i	−0.602008	+	0.798490i	$0.705633\pi$
$90$	1.53670e6			2.10795
$91$	−167402.	+	167402.i	−0.222145	+	0.222145i
$92$	272355.	+	272355.i	0.349761	+	0.349761i
$93$	634970.	−	634970.i	0.789414	−	0.789414i
$94$	−231416.	−	231416.i	−0.278618	−	0.278618i
$95$			1.86241e6i			2.17222i
$96$	197682.	−	197682.i	0.223437	−	0.223437i
$97$	17408.9	−	17408.9i	0.0190746	−	0.0190746i	−0.697505	−	0.716580i	$-0.745707\pi$
$97$	17408.9	−	17408.9i	0.0190746	−	0.0190746i	0.716580	+	0.697505i	$0.245707\pi$
$98$	259899.	+	259899.i	0.276138	+	0.276138i
$99$			2.48483e6i			2.56090i
$100$	422148.			0.422148
$101$		−	1.87225e6i		−	1.81718i	−0.417686	−	0.908591i	$-0.637159\pi$
$101$		−	1.87225e6i		−	1.81718i	0.417686	−	0.908591i	$-0.362841\pi$
$102$			1.02997e6i			0.970568i
$103$	559314.	+	559314.i	0.511852	+	0.511852i	0.915093	−	0.403242i	$-0.132117\pi$
$103$	559314.	+	559314.i	0.511852	+	0.511852i	−0.403242	+	0.915093i	$0.632117\pi$
$104$		−	186725.i		−	0.165998i
$105$	1.32959e6	+	1.32959e6i	1.14855	+	1.14855i
$106$	−872653.	−	872653.i	−0.732696	−	0.732696i
$107$	−1.98443e6			−1.61989			−0.809944	−	0.586508i	$-0.800502\pi$
$107$	−1.98443e6			−1.61989			−0.809944	+	0.586508i	$0.800502\pi$
$108$	−1.34555e6			−1.06814
$109$	−1.27133e6	+	1.27133e6i	−0.981703	+	0.981703i	−0.999836	−	0.0181327i	$-0.994228\pi$
$109$	−1.27133e6	+	1.27133e6i	−0.981703	+	0.981703i	0.0181327	+	0.999836i	$0.494228\pi$
$110$			1.49111e6i			1.12029i
$111$	2.14937e6	−	1.16466e6i	1.57160	−	0.851589i
$112$	235017.			0.167281
$113$	882766.	+	882766.i	0.611801	+	0.611801i	0.943415	−	0.331614i	$-0.107593\pi$
$113$	882766.	+	882766.i	0.611801	+	0.611801i	−0.331614	+	0.943415i	$0.607593\pi$
$114$		−	2.99524e6i		−	2.02170i
$115$		−	2.04327e6i		−	1.34348i
$116$	−450831.	+	450831.i	−0.288829	+	0.288829i
$117$	−1.16721e6	+	1.16721e6i	−0.728772	+	0.728772i
$118$	−1.18903e6			−0.723680
$119$	−612249.	+	612249.i	−0.363318	+	0.363318i
$120$	−1.48306e6			−0.858251
$121$	−639565.			−0.361018
$122$		−	986124.i		−	0.543065i
$123$	−4.10541e6			−2.20618
$124$	−421013.	+	421013.i	−0.220816	+	0.220816i
$125$	292031.	+	292031.i	0.149520	+	0.149520i
$126$	−1.46909e6	−	1.46909e6i	−0.734405	−	0.734405i
$127$	1.93440e6			0.944357			0.472178	−	0.881503i	$-0.343468\pi$
$127$	1.93440e6			0.944357			0.472178	+	0.881503i	$0.343468\pi$
$128$	−131072.	+	131072.i	−0.0625000	+	0.0625000i
$129$	2.31908e6	+	2.31908e6i	1.08031	+	1.08031i
$130$	−700426.	+	700426.i	−0.318810	+	0.318810i
$131$	−2.61693e6	−	2.61693e6i	−1.16407	−	1.16407i	−0.983577	−	0.180492i	$-0.942231\pi$
$131$	−2.61693e6	−	2.61693e6i	−1.16407	−	1.16407i	−0.180492	−	0.983577i	$-0.557769\pi$
$132$		−	2.39810e6i		−	1.04267i
$133$	1.78047e6	−	1.78047e6i	0.756796	−	0.756796i
$134$	−1.18377e6	+	1.18377e6i	−0.491986	+	0.491986i
$135$	5.04732e6	+	5.04732e6i	2.05144	+	2.05144i
$136$		−	682918.i		−	0.271489i
$137$	−2.18129e6			−0.848305			−0.424152	−	0.905591i	$-0.639428\pi$
$137$	−2.18129e6			−0.848305			−0.424152	+	0.905591i	$0.639428\pi$
$138$			3.28612e6i			1.25039i
$139$		−	3.93256e6i		−	1.46430i	−0.681141	−	0.732152i	$-0.738516\pi$
$139$		−	3.93256e6i		−	1.46430i	0.681141	−	0.732152i	$-0.261484\pi$
$140$	−881577.	−	881577.i	−0.321274	−	0.321274i
$141$		−	2.79216e6i		−	0.996056i
$142$	2.56393e6	+	2.56393e6i	0.895451	+	0.895451i
$143$	−1.13259e6	−	1.13259e6i	−0.387314	−	0.387314i
$144$	1.63865e6			0.548782
$145$	3.38224e6			1.10943
$146$	−2.14696e6	+	2.14696e6i	−0.689867	+	0.689867i
$147$			3.13582e6i			0.987188i
$148$	−1.42512e6	+	772220.i	−0.439610	+	0.238208i
$149$	3.87185e6			1.17047			0.585234	−	0.810864i	$-0.301003\pi$
$149$	3.87185e6			1.17047			0.585234	+	0.810864i	$0.301003\pi$
$150$	2.54673e6	+	2.54673e6i	0.754587	+	0.754587i
$151$		−	5.93746e6i		−	1.72453i	−0.506460	−	0.862263i	$-0.669046\pi$
$151$		−	5.93746e6i		−	1.72453i	0.506460	−	0.862263i	$-0.330954\pi$
$152$			1.98598e6i			0.565514i
$153$	−4.26890e6	+	4.26890e6i	−1.19191	+	1.19191i
$154$	1.42551e6	−	1.42551e6i	0.390308	−	0.390308i
$155$	3.15854e6			0.848185
$156$	1.12647e6	−	1.12647e6i	0.296719	−	0.296719i
$157$	2.03271e6			0.525262			0.262631	−	0.964896i	$-0.415410\pi$
$157$	2.03271e6			0.525262			0.262631	+	0.964896i	$0.415410\pi$
$158$	1.62260e6			0.411378
$159$		−	1.05291e7i		−	2.61938i
$160$	983332.			0.240071
$161$	−1.95337e6	+	1.95337e6i	−0.468066	+	0.468066i
$162$	−3.45110e6	−	3.45110e6i	−0.811731	−	0.811731i
$163$	145658.	+	145658.i	0.0336334	+	0.0336334i	0.723723	−	0.690090i	$-0.242429\pi$
$163$	145658.	+	145658.i	0.0336334	+	0.0336334i	−0.690090	+	0.723723i	$0.742429\pi$
$164$	2.72207e6			0.617117
$165$	−8.99556e6	+	8.99556e6i	−2.00252	+	2.00252i
$166$	4.20894e6	+	4.20894e6i	0.920129	+	0.920129i
$167$	−97280.7	+	97280.7i	−0.0208871	+	0.0208871i	−0.717473	−	0.696586i	$-0.754701\pi$
$167$	−97280.7	+	97280.7i	−0.0208871	+	0.0208871i	0.696586	+	0.717473i	$0.254701\pi$
$168$	1.41781e6	+	1.41781e6i	0.299013	+	0.299013i
$169$			3.76278e6i			0.779558i
$170$	−2.56170e6	+	2.56170e6i	−0.521413	+	0.521413i
$171$	1.24143e7	−	1.24143e7i	2.48275	−	2.48275i
$172$	−1.53765e6	−	1.53765e6i	−0.302185	−	0.302185i
$173$		−	358654.i		−	0.0692688i	−0.999400	−	0.0346344i	$-0.988973\pi$
$173$		−	358654.i		−	0.0692688i	0.999400	−	0.0346344i	$-0.0110267\pi$
$174$	−5.43954e6			−1.03256
$175$			3.02771e6i			0.564938i
$176$			1.59005e6i			0.291657i
$177$	−7.17316e6	−	7.17316e6i	−1.29357	−	1.29357i
$178$		−	1.10811e6i		−	0.196481i
$179$	8.02536e6	+	8.02536e6i	1.39928	+	1.39928i	0.802120	+	0.597162i	$0.203705\pi$
$179$	8.02536e6	+	8.02536e6i	1.39928	+	1.39928i	0.597162	+	0.802120i	$0.296295\pi$
$180$	−6.14678e6	−	6.14678e6i	−1.05398	−	1.05398i
$181$	6.01172e6			1.01383			0.506913	−	0.861997i	$-0.330787\pi$
$181$	6.01172e6			1.01383			0.506913	+	0.861997i	$0.330787\pi$
$182$	1.33922e6			0.222145
$183$	5.94908e6	−	5.94908e6i	0.970725	−	0.970725i
$184$		−	2.17884e6i		−	0.349761i
$185$	8.24249e6	+	2.44912e6i	1.30180	+	0.386807i
$186$	−5.07976e6			−0.789414
$187$	−4.14227e6	−	4.14227e6i	−0.633452	−	0.633452i
$188$			1.85133e6i			0.278618i
$189$		−	9.65050e6i		−	1.42944i
$190$	7.44962e6	−	7.44962e6i	1.08611	−	1.08611i
$191$	3.28179e6	−	3.28179e6i	0.470990	−	0.470990i	−0.431245	−	0.902235i	$-0.641926\pi$
$191$	3.28179e6	−	3.28179e6i	0.470990	−	0.470990i	0.902235	+	0.431245i	$0.141926\pi$
$192$	−1.58146e6			−0.223437
$193$	−1.48026e6	+	1.48026e6i	−0.205904	+	0.205904i	−0.802524	−	0.596620i	$-0.796510\pi$
$193$	−1.48026e6	+	1.48026e6i	−0.205904	+	0.205904i	0.596620	+	0.802524i	$0.296510\pi$
$194$	−139271.			−0.0190746
$195$	−8.45104e6			−1.13974
$196$		−	2.07919e6i		−	0.276138i
$197$	−8.52953e6			−1.11565			−0.557823	−	0.829960i	$-0.688363\pi$
$197$	−8.52953e6			−1.11565			−0.557823	+	0.829960i	$0.688363\pi$
$198$	9.93934e6	−	9.93934e6i	1.28045	−	1.28045i
$199$	1.30321e6	+	1.30321e6i	0.165369	+	0.165369i	0.784940	−	0.619571i	$-0.212693\pi$
$199$	1.30321e6	+	1.30321e6i	0.165369	+	0.165369i	−0.619571	+	0.784940i	$0.712693\pi$
$200$	−1.68859e6	−	1.68859e6i	−0.211074	−	0.211074i
$201$	−1.42829e7			−1.75884
$202$	−7.48898e6	+	7.48898e6i	−0.908591	+	0.908591i
$203$	−3.23343e6	−	3.23343e6i	−0.386523	−	0.386523i
$204$	4.11990e6	−	4.11990e6i	0.485284	−	0.485284i
$205$	−1.02108e7	−	1.02108e7i	−1.18522	−	1.18522i
$206$		−	4.47451e6i		−	0.511852i
$207$	−1.36199e7	+	1.36199e7i	−1.53554	+	1.53554i
$208$	−746899.	+	746899.i	−0.0829988	+	0.0829988i
$209$	1.20460e7	+	1.20460e7i	1.31949	+	1.31949i
$210$		−	1.06367e7i		−	1.14855i
$211$	1.10026e7			1.17124			0.585621	−	0.810585i	$-0.300851\pi$
$211$	1.10026e7			1.17124			0.585621	+	0.810585i	$0.300851\pi$
$212$			6.98122e6i			0.732696i
$213$			3.09353e7i			3.20122i
$214$	7.93773e6	+	7.93773e6i	0.809944	+	0.809944i
$215$			1.15358e7i			1.16074i
$216$	5.38220e6	+	5.38220e6i	0.534071	+	0.534071i
$217$	−3.01957e6	−	3.01957e6i	−0.295506	−	0.295506i
$218$	1.01707e7			0.981703
$219$	−2.59043e7			−2.46626
$220$	5.96445e6	−	5.96445e6i	0.560147	−	0.560147i
$221$		−	3.89153e6i		−	0.360532i
$222$	−1.32561e7	−	3.93883e6i	−1.21159	−	0.360005i
$223$	−3.52920e6			−0.318245			−0.159123	−	0.987259i	$-0.550866\pi$
$223$	−3.52920e6			−0.318245			−0.159123	+	0.987259i	$0.550866\pi$
$224$	−940069.	−	940069.i	−0.0836403	−	0.0836403i
$225$			2.11107e7i			1.85334i
$226$		−	7.06213e6i		−	0.611801i
$227$	6.82711e6	−	6.82711e6i	0.583659	−	0.583659i	−0.352248	−	0.935907i	$-0.614583\pi$
$227$	6.82711e6	−	6.82711e6i	0.583659	−	0.583659i	0.935907	+	0.352248i	$0.114583\pi$
$228$	−1.19810e7	+	1.19810e7i	−1.01085	+	1.01085i
$229$	−412460.			−0.0343460			−0.0171730	−	0.999853i	$-0.505467\pi$
$229$	−412460.			−0.0343460			−0.0171730	+	0.999853i	$0.505467\pi$
$230$	−8.17308e6	+	8.17308e6i	−0.671741	+	0.671741i
$231$	1.71996e7			1.39535
$232$	3.60665e6			0.288829
$233$		−	2.07056e7i		−	1.63689i	−0.574583	−	0.818446i	$-0.694836\pi$
$233$		−	2.07056e7i		−	1.63689i	0.574583	−	0.818446i	$-0.305164\pi$
$234$	9.33769e6			0.728772
$235$	6.94454e6	−	6.94454e6i	0.535106	−	0.535106i
$236$	4.75612e6	+	4.75612e6i	0.361840	+	0.361840i
$237$	9.78882e6	+	9.78882e6i	0.735335	+	0.735335i
$238$	4.89799e6			0.363318
$239$	5.21262e6	−	5.21262e6i	0.381823	−	0.381823i	−0.489935	−	0.871759i	$-0.662980\pi$
$239$	5.21262e6	−	5.21262e6i	0.381823	−	0.381823i	0.871759	+	0.489935i	$0.162980\pi$
$240$	5.93223e6	+	5.93223e6i	0.429126	+	0.429126i
$241$	7.82699e6	−	7.82699e6i	0.559170	−	0.559170i	−0.369901	−	0.929071i	$-0.620609\pi$
$241$	7.82699e6	−	7.82699e6i	0.559170	−	0.559170i	0.929071	+	0.369901i	$0.120609\pi$
$242$	2.55826e6	+	2.55826e6i	0.180509	+	0.180509i
$243$		−	1.09861e7i		−	0.765642i
$244$	−3.94450e6	+	3.94450e6i	−0.271533	+	0.271533i
$245$	−7.79927e6	+	7.79927e6i	−0.530342	+	0.530342i
$246$	1.64217e7	+	1.64217e7i	1.10309	+	1.10309i
$247$			1.13169e7i			0.750991i
$248$	3.36810e6			0.220816
$249$			5.07833e7i			3.28945i
$250$		−	2.33625e6i		−	0.149520i
$251$	1.20813e6	+	1.20813e6i	0.0763996	+	0.0763996i	0.744274	−	0.667874i	$-0.232796\pi$
$251$	1.20813e6	+	1.20813e6i	0.0763996	+	0.0763996i	−0.667874	+	0.744274i	$0.732796\pi$
$252$			1.17527e7i			0.734405i
$253$	−1.32159e7	−	1.32159e7i	−0.816082	−	0.816082i
$254$	−7.73762e6	−	7.73762e6i	−0.472178	−	0.472178i
$255$	−3.09084e7			−1.86404
$256$	1.04858e6			0.0625000
$257$	−2.12044e7	+	2.12044e7i	−1.24919	+	1.24919i	−0.293105	+	0.956080i	$0.594688\pi$
$257$	−2.12044e7	+	2.12044e7i	−1.24919	+	1.24919i	−0.956080	+	0.293105i	$0.905312\pi$
$258$		−	1.85527e7i		−	1.08031i
$259$	−5.53848e6	−	1.02212e7i	−0.318780	−	0.588306i
$260$	5.60341e6			0.318810
$261$	−2.25451e7	−	2.25451e7i	−1.26803	−	1.26803i
$262$			2.09354e7i			1.16407i
$263$		−	1.21102e7i		−	0.665711i	−0.942978	−	0.332855i	$-0.891988\pi$
$263$		−	1.21102e7i		−	0.665711i	0.942978	−	0.332855i	$-0.108012\pi$
$264$	−9.59241e6	+	9.59241e6i	−0.521334	+	0.521334i
$265$	2.61874e7	−	2.61874e7i	1.40719	−	1.40719i
$266$	−1.42437e7			−0.756796
$267$	6.68496e6	−	6.68496e6i	0.351209	−	0.351209i
$268$	9.47015e6			0.491986
$269$	−2.33389e7			−1.19901			−0.599507	−	0.800370i	$-0.704636\pi$
$269$	−2.33389e7			−1.19901			−0.599507	+	0.800370i	$0.704636\pi$
$270$		−	4.03785e7i		−	2.05144i
$271$	−1.30577e7			−0.656084			−0.328042	−	0.944663i	$-0.606389\pi$
$271$	−1.30577e7			−0.656084			−0.328042	+	0.944663i	$0.606389\pi$
$272$	−2.73167e6	+	2.73167e6i	−0.135744	+	0.135744i
$273$	8.07922e6	+	8.07922e6i	0.397083	+	0.397083i
$274$	8.72517e6	+	8.72517e6i	0.424152	+	0.424152i
$275$	−2.04845e7			−0.984979
$276$	1.31445e7	−	1.31445e7i	0.625196	−	0.625196i
$277$	−5.33079e6	−	5.33079e6i	−0.250814	−	0.250814i	0.570490	−	0.821304i	$-0.306753\pi$
$277$	−5.33079e6	−	5.33079e6i	−0.250814	−	0.250814i	−0.821304	+	0.570490i	$0.806753\pi$
$278$	−1.57303e7	+	1.57303e7i	−0.732152	+	0.732152i
$279$	−2.10539e7	−	2.10539e7i	−0.969439	−	0.969439i
$280$			7.05261e6i			0.321274i
$281$	5.01703e6	−	5.01703e6i	0.226114	−	0.226114i	−0.584953	−	0.811067i	$-0.698887\pi$
$281$	5.01703e6	−	5.01703e6i	0.226114	−	0.226114i	0.811067	+	0.584953i	$0.198887\pi$
$282$	−1.11687e7	+	1.11687e7i	−0.498028	+	0.498028i
$283$	−7.65207e6	−	7.65207e6i	−0.337613	−	0.337613i	0.517855	−	0.855468i	$-0.326731\pi$
$283$	−7.65207e6	−	7.65207e6i	−0.337613	−	0.337613i	−0.855468	+	0.517855i	$0.826731\pi$
$284$		−	2.05115e7i		−	0.895451i
$285$	8.98840e7			3.88282
$286$			9.06070e6i			0.387314i
$287$			1.95231e7i			0.825853i
$288$	−6.55462e6	−	6.55462e6i	−0.274391	−	0.274391i
$289$			9.90487e6i			0.410351i
$290$	−1.35290e7	−	1.35290e7i	−0.554716	−	0.554716i
$291$	−840192.	−	840192.i	−0.0340957	−	0.0340957i
$292$	1.71757e7			0.689867
$293$	2.37218e7			0.943072			0.471536	−	0.881847i	$-0.343700\pi$
$293$	2.37218e7			0.943072			0.471536	+	0.881847i	$0.343700\pi$
$294$	1.25433e7	−	1.25433e7i	0.493594	−	0.493594i
$295$		−	3.56815e7i		−	1.38988i
$296$	8.78938e6	+	2.61162e6i	0.338909	+	0.100701i
$297$	6.52920e7			2.49225
$298$	−1.54874e7	−	1.54874e7i	−0.585234	−	0.585234i
$299$		−	1.24159e7i		−	0.464476i
$300$		−	2.03738e7i		−	0.754587i
$301$	1.10283e7	−	1.10283e7i	0.404397	−	0.404397i
$302$	−2.37498e7	+	2.37498e7i	−0.862263	+	0.862263i
$303$	−9.03589e7			−3.24820
$304$	7.94390e6	−	7.94390e6i	0.282757	−	0.282757i
$305$	2.95925e7			1.04300
$306$	3.41512e7			1.19191
$307$			2.12136e7i			0.733162i	0.930386	+	0.366581i	$0.119472\pi$
$307$			2.12136e7i			0.733162i	−0.930386	+	0.366581i	$0.880528\pi$
$308$	−1.14041e7			−0.390308
$309$	2.69938e7	−	2.69938e7i	0.914931	−	0.914931i
$310$	−1.26341e7	−	1.26341e7i	−0.424093	−	0.424093i
$311$	1.06546e7	+	1.06546e7i	0.354205	+	0.354205i	0.861672	−	0.507466i	$-0.169418\pi$
$311$	1.06546e7	+	1.06546e7i	0.354205	+	0.354205i	−0.507466	+	0.861672i	$0.669418\pi$
$312$	−9.01176e6			−0.296719
$313$	6.93203e6	−	6.93203e6i	0.226062	−	0.226062i	−0.584983	−	0.811045i	$-0.698899\pi$
$313$	6.93203e6	−	6.93203e6i	0.226062	−	0.226062i	0.811045	+	0.584983i	$0.198899\pi$
$314$	−8.13083e6	−	8.13083e6i	−0.262631	−	0.262631i
$315$	4.40857e7	−	4.40857e7i	1.41048	−	1.41048i
$316$	−6.49041e6	−	6.49041e6i	−0.205689	−	0.205689i
$317$			1.25240e6i			0.0393156i	0.999807	+	0.0196578i	$0.00625768\pi$
$317$			1.25240e6i			0.0393156i	−0.999807	+	0.0196578i	$0.993742\pi$
$318$	−4.21162e7	+	4.21162e7i	−1.30969	+	1.30969i
$319$	2.18763e7	−	2.18763e7i	0.673910	−	0.673910i
$320$	−3.93333e6	−	3.93333e6i	−0.120036	−	0.120036i
$321$			9.57732e7i			2.89554i
$322$	1.56270e7			0.468066
$323$			4.13897e7i			1.22825i
$324$			2.76088e7i			0.811731i
$325$	−9.62225e6	−	9.62225e6i	−0.280302	−	0.280302i
$326$		−	1.16526e6i		−	0.0336334i
$327$	6.13575e7	+	6.13575e7i	1.75479	+	1.75479i
$328$	−1.08883e7	−	1.08883e7i	−0.308558	−	0.308558i
$329$	−1.32780e7			−0.372859
$330$	7.19645e7			2.00252
$331$	−6.53270e6	+	6.53270e6i	−0.180139	+	0.180139i	−0.791417	−	0.611277i	$-0.790656\pi$
$331$	−6.53270e6	+	6.53270e6i	−0.180139	+	0.180139i	0.611277	+	0.791417i	$0.290656\pi$
$332$		−	3.36715e7i		−	0.920129i
$333$	−3.86170e7	−	7.12673e7i	−1.04579	−	1.93000i
$334$	778246.			0.0208871
$335$	−3.55236e7	−	3.55236e7i	−0.944894	−	0.944894i
$336$		−	1.13425e7i		−	0.299013i
$337$			5.06666e7i			1.32383i	0.749580	+	0.661914i	$0.230256\pi$
$337$			5.06666e7i			1.32383i	−0.749580	+	0.661914i	$0.769744\pi$
$338$	1.50511e7	−	1.50511e7i	0.389779	−	0.389779i
$339$	4.26043e7	−	4.26043e7i	1.09359	−	1.09359i
$340$	2.04936e7			0.521413
$341$	2.04294e7	−	2.04294e7i	0.515220	−	0.515220i
$342$	−9.93143e7			−2.48275
$343$	4.19138e7			1.03866
$344$			1.23012e7i			0.302185i
$345$	−9.86129e7			−2.40147
$346$	−1.43462e6	+	1.43462e6i	−0.0346344	+	0.0346344i
$347$	−1.56838e7	−	1.56838e7i	−0.375372	−	0.375372i	0.494057	−	0.869429i	$-0.335513\pi$
$347$	−1.56838e7	−	1.56838e7i	−0.375372	−	0.375372i	−0.869429	+	0.494057i	$0.835513\pi$
$348$	2.17582e7	+	2.17582e7i	0.516279	+	0.516279i
$349$	−461856.			−0.0108650			−0.00543251	−	0.999985i	$-0.501729\pi$
$349$	−461856.			−0.0108650			−0.00543251	+	0.999985i	$0.501729\pi$
$350$	1.21108e7	−	1.21108e7i	0.282469	−	0.282469i
$351$	3.06699e7	+	3.06699e7i	0.709236	+	0.709236i
$352$	6.36019e6	−	6.36019e6i	0.145828	−	0.145828i
$353$	1.15563e7	+	1.15563e7i	0.262722	+	0.262722i	0.826159	−	0.563437i	$-0.190521\pi$
$353$	1.15563e7	+	1.15563e7i	0.262722	+	0.262722i	−0.563437	+	0.826159i	$0.690521\pi$
$354$			5.73853e7i			1.29357i
$355$	−7.69409e7	+	7.69409e7i	−1.71978	+	1.71978i
$356$	−4.43242e6	+	4.43242e6i	−0.0982406	+	0.0982406i
$357$	2.95486e7	+	2.95486e7i	0.649429	+	0.649429i
$358$		−	6.42029e7i		−	1.39928i
$359$	−2.56622e7			−0.554639			−0.277320	−	0.960778i	$-0.589446\pi$
$359$	−2.56622e7			−0.554639			−0.277320	+	0.960778i	$0.589446\pi$
$360$			4.91743e7i			1.05398i
$361$		−	7.33185e7i		−	1.55845i
$362$	−2.40469e7	−	2.40469e7i	−0.506913	−	0.506913i
$363$			3.08669e7i			0.645316i
$364$	−5.35687e6	−	5.35687e6i	−0.111073	−	0.111073i
$365$	−6.44279e7	−	6.44279e7i	−1.32494	−	1.32494i
$366$	−4.75926e7			−0.970725
$367$	6.98382e7			1.41285			0.706423	−	0.707790i	$-0.250308\pi$
$367$	6.98382e7			1.41285			0.706423	+	0.707790i	$0.250308\pi$
$368$	−8.71536e6	+	8.71536e6i	−0.174881	+	0.174881i
$369$			1.36125e8i			2.70930i
$370$	−2.31735e7	−	4.27664e7i	−0.457495	−	0.844302i
$371$	−5.00704e7			−0.980527
$372$	2.03191e7	+	2.03191e7i	0.394707	+	0.394707i
$373$		−	2.23283e7i		−	0.430259i	−0.976586	−	0.215129i	$-0.930983\pi$
$373$		−	2.23283e7i		−	0.430259i	0.976586	−	0.215129i	$-0.0690173\pi$
$374$			3.31382e7i			0.633452i
$375$	1.40941e7	−	1.40941e7i	0.267266	−	0.267266i
$376$	7.40531e6	−	7.40531e6i	0.139309	−	0.139309i
$377$	2.05521e7			0.383559
$378$	−3.86020e7	+	3.86020e7i	−0.714718	+	0.714718i
$379$	3.29341e6			0.0604962			0.0302481	−	0.999542i	$-0.490370\pi$
$379$	3.29341e6			0.0604962			0.0302481	+	0.999542i	$0.490370\pi$
$380$	−5.95970e7			−1.08611
$381$		−	9.33588e7i		−	1.68803i
$382$	−2.62544e7			−0.470990
$383$	3.98037e7	−	3.98037e7i	0.708480	−	0.708480i	−0.257736	−	0.966215i	$-0.582976\pi$
$383$	3.98037e7	−	3.98037e7i	0.708480	−	0.708480i	0.966215	+	0.257736i	$0.0829764\pi$
$384$	6.32584e6	+	6.32584e6i	0.111718	+	0.111718i
$385$	4.27780e7	+	4.27780e7i	0.749614	+	0.749614i
$386$	1.18420e7			0.205904
$387$	7.68946e7	−	7.68946e7i	1.32667	−	1.32667i
$388$	557084.	+	557084.i	0.00953729	+	0.00953729i
$389$	6.27061e6	−	6.27061e6i	0.106527	−	0.106527i	−0.651834	−	0.758361i	$-0.726000\pi$
$389$	6.27061e6	−	6.27061e6i	0.106527	−	0.106527i	0.758361	+	0.651834i	$0.226000\pi$
$390$	3.38042e7	+	3.38042e7i	0.569871	+	0.569871i
$391$		−	4.54092e7i		−	0.759650i
$392$	−8.31675e6	+	8.31675e6i	−0.138069	+	0.138069i
$393$	−1.26299e8	+	1.26299e8i	−2.08076	+	2.08076i
$394$	3.41181e7	+	3.41181e7i	0.557823	+	0.557823i
$395$			4.86926e7i			0.790081i
$396$	−7.95147e7			−1.28045
$397$		−	1.73064e7i		−	0.276589i	−0.990391	−	0.138294i	$-0.955838\pi$
$397$		−	1.73064e7i		−	0.276589i	0.990391	−	0.138294i	$-0.0441620\pi$
$398$		−	1.04257e7i		−	0.165369i
$399$	−8.59294e7	−	8.59294e7i	−1.35277	−	1.35277i
$400$			1.35087e7i			0.211074i
$401$	6.43445e6	+	6.43445e6i	0.0997881	+	0.0997881i	0.755238	−	0.655450i	$-0.227521\pi$
$401$	6.43445e6	+	6.43445e6i	0.0997881	+	0.0997881i	−0.655450	+	0.755238i	$0.727521\pi$
$402$	5.71314e7	+	5.71314e7i	0.879421	+	0.879421i
$403$	1.91928e7			0.293239
$404$	5.99119e7			0.908591
$405$	1.03564e8	−	1.03564e8i	1.55899	−	1.55899i
$406$			2.58675e7i			0.386523i
$407$	6.91533e7	−	3.74715e7i	1.02572	−	0.555799i
$408$	−3.29592e7			−0.485284
$409$	4.48988e7	+	4.48988e7i	0.656243	+	0.656243i	0.954489	−	0.298246i	$-0.0964015\pi$
$409$	4.48988e7	+	4.48988e7i	0.656243	+	0.656243i	−0.298246	+	0.954489i	$0.596402\pi$
$410$			8.16863e7i			1.18522i
$411$			1.05274e8i			1.51634i
$412$	−1.78980e7	+	1.78980e7i	−0.255926	+	0.255926i
$413$	−3.41116e7	+	3.41116e7i	−0.484231	+	0.484231i
$414$	1.08959e8			1.53554
$415$	−1.26306e8	+	1.26306e8i	−1.76717	+	1.76717i
$416$	5.97519e6			0.0829988
$417$	−1.89795e8			−2.61743
$418$		−	9.63683e7i		−	1.31949i
$419$	1.18086e8			1.60530			0.802651	−	0.596449i	$-0.203422\pi$
$419$	1.18086e8			1.60530			0.802651	+	0.596449i	$0.203422\pi$
$420$	−4.25469e7	+	4.25469e7i	−0.574275	+	0.574275i
$421$	6.91876e7	+	6.91876e7i	0.927218	+	0.927218i	0.997525	−	0.0703070i	$-0.0223979\pi$
$421$	6.91876e7	+	6.91876e7i	0.927218	+	0.927218i	−0.0703070	+	0.997525i	$0.522398\pi$
$422$	−4.40103e7	−	4.40103e7i	−0.585621	−	0.585621i
$423$	−9.25807e7			−1.22321
$424$	2.79249e7	−	2.79249e7i	0.366348	−	0.366348i
$425$	−3.51920e7	−	3.51920e7i	−0.458434	−	0.458434i
$426$	1.23741e8	−	1.23741e8i	1.60061	−	1.60061i
$427$	−2.82905e7	−	2.82905e7i	−0.363377	−	0.363377i
$428$		−	6.35018e7i		−	0.809944i
$429$	−5.46613e7	+	5.46613e7i	−0.692321	+	0.692321i
$430$	4.61433e7	−	4.61433e7i	0.580368	−	0.580368i
$431$	5.85540e7	+	5.85540e7i	0.731349	+	0.731349i	0.970887	−	0.239538i	$-0.0769960\pi$
$431$	5.85540e7	+	5.85540e7i	0.731349	+	0.731349i	−0.239538	+	0.970887i	$0.576996\pi$
$432$		−	4.30576e7i		−	0.534071i
$433$	−1.75137e7			−0.215732			−0.107866	−	0.994165i	$-0.534402\pi$
$433$	−1.75137e7			−0.215732			−0.107866	+	0.994165i	$0.534402\pi$
$434$			2.41566e7i			0.295506i
$435$		−	1.63235e8i		−	1.98310i
$436$	−4.06827e7	−	4.06827e7i	−0.490851	−	0.490851i
$437$			1.32053e8i			1.58236i
$438$	1.03617e8	+	1.03617e8i	1.23313	+	1.23313i
$439$	−6.79990e7	−	6.79990e7i	−0.803728	−	0.803728i	0.179948	−	0.983676i	$-0.442407\pi$
$439$	−6.79990e7	−	6.79990e7i	−0.803728	−	0.803728i	−0.983676	+	0.179948i	$0.942407\pi$
$440$	−4.77156e7			−0.560147
$441$	1.03976e8			1.21232
$442$	−1.55661e7	+	1.55661e7i	−0.180266	+	0.180266i
$443$			9.72702e7i			1.11884i	0.828884	+	0.559421i	$0.188976\pi$
$443$			9.72702e7i			1.11884i	−0.828884	+	0.559421i	$0.811024\pi$
$444$	3.72691e7	+	6.87798e7i	0.425795	+	0.785800i
$445$	3.32531e7			0.377356
$446$	1.41168e7	+	1.41168e7i	0.159123	+	0.159123i
$447$		−	1.86864e8i		−	2.09220i
$448$			7.52055e6i			0.0836403i
$449$	7.59169e7	−	7.59169e7i	0.838686	−	0.838686i	−0.150000	−	0.988686i	$-0.547927\pi$
$449$	7.59169e7	−	7.59169e7i	0.838686	−	0.838686i	0.988686	+	0.150000i	$0.0479273\pi$
$450$	8.44428e7	−	8.44428e7i	0.926670	−	0.926670i
$451$	−1.32087e8			−1.43989
$452$	−2.82485e7	+	2.82485e7i	−0.305900	+	0.305900i
$453$	−2.86555e8			−3.08258
$454$	−5.46168e7			−0.583659
$455$			4.01885e7i			0.426646i
$456$	9.58478e7			1.01085
$457$	1.06138e8	−	1.06138e8i	1.11205	−	1.11205i	0.119173	−	0.992873i	$-0.461976\pi$
$457$	1.06138e8	−	1.06138e8i	1.11205	−	1.11205i	0.992873	−	0.119173i	$-0.0380244\pi$
$458$	1.64984e6	+	1.64984e6i	0.0171730	+	0.0171730i
$459$	1.12171e8	+	1.12171e8i	1.15995	+	1.15995i
$460$	6.53846e7			0.671741
$461$	9.15841e6	−	9.15841e6i	0.0934797	−	0.0934797i	−0.658820	−	0.752300i	$-0.728944\pi$
$461$	9.15841e6	−	9.15841e6i	0.0934797	−	0.0934797i	0.752300	+	0.658820i	$0.228944\pi$
$462$	−6.87983e7	−	6.87983e7i	−0.697673	−	0.697673i
$463$	−6.23779e7	+	6.23779e7i	−0.628475	+	0.628475i	−0.947684	−	0.319210i	$-0.896583\pi$
$463$	−6.23779e7	+	6.23779e7i	−0.628475	+	0.628475i	0.319210	+	0.947684i	$0.396583\pi$
$464$	−1.44266e7	−	1.44266e7i	−0.144414	−	0.144414i
$465$		−	1.52438e8i		−	1.51612i
$466$	−8.28224e7	+	8.28224e7i	−0.818446	+	0.818446i
$467$	9.17658e7	−	9.17658e7i	0.901011	−	0.901011i	−0.0945125	−	0.995524i	$-0.530129\pi$
$467$	9.17658e7	−	9.17658e7i	0.901011	−	0.901011i	0.995524	+	0.0945125i	$0.0301292\pi$
$468$	−3.73507e7	−	3.73507e7i	−0.364386	−	0.364386i
$469$			6.79214e7i			0.658398i
$470$	−5.55563e7			−0.535106
$471$		−	9.81031e7i		−	0.938902i
$472$		−	3.80490e7i		−	0.361840i
$473$	7.46136e7	+	7.46136e7i	0.705074	+	0.705074i
$474$		−	7.83106e7i		−	0.735335i
$475$	1.02341e8	+	1.02341e8i	0.954922	+	0.954922i
$476$	−1.95920e7	−	1.95920e7i	−0.181659	−	0.181659i
$477$	−3.49115e8			−3.21672
$478$	−4.17010e7			−0.381823
$479$	−5.18127e6	+	5.18127e6i	−0.0471444	+	0.0471444i	−0.730286	−	0.683142i	$-0.760613\pi$
$479$	−5.18127e6	+	5.18127e6i	−0.0471444	+	0.0471444i	0.683142	+	0.730286i	$0.260613\pi$
$480$		−	4.74579e7i		−	0.429126i
$481$	5.00853e7	+	1.48820e7i	0.450064	+	0.133729i
$482$	−6.26159e7			−0.559170
$483$	9.42742e7	+	9.42742e7i	0.836665	+	0.836665i
$484$		−	2.04661e7i		−	0.180509i
$485$		−	4.17937e6i		−	0.0366341i
$486$	−4.39445e7	+	4.39445e7i	−0.382821	+	0.382821i
$487$	−4.91904e7	+	4.91904e7i	−0.425886	+	0.425886i	−0.887224	−	0.461338i	$-0.847369\pi$
$487$	−4.91904e7	+	4.91904e7i	−0.425886	+	0.425886i	0.461338	+	0.887224i	$0.347369\pi$
$488$	3.15560e7			0.271533
$489$	7.02977e6	−	7.02977e6i	0.0601194	−	0.0601194i
$490$	6.23942e7			0.530342
$491$	1.55313e6			0.0131209			0.00656043	−	0.999978i	$-0.497912\pi$
$491$	1.55313e6			0.0131209			0.00656043	+	0.999978i	$0.497912\pi$
$492$		−	1.31373e8i		−	1.10309i
$493$	7.51662e7			0.627310
$494$	4.52674e7	−	4.52674e7i	0.375496	−	0.375496i
$495$	2.98269e8	+	2.98269e8i	2.45919	+	2.45919i
$496$	−1.34724e7	−	1.34724e7i	−0.110408	−	0.110408i
$497$	1.47112e8			1.19833
$498$	2.03133e8	−	2.03133e8i	1.64472	−	1.64472i
$499$	−5.68134e7	−	5.68134e7i	−0.457245	−	0.457245i	0.440505	−	0.897750i	$-0.354799\pi$
$499$	−5.68134e7	−	5.68134e7i	−0.457245	−	0.457245i	−0.897750	+	0.440505i	$0.854799\pi$
$500$	−9.34500e6	+	9.34500e6i	−0.0747600	+	0.0747600i
$501$	4.69499e6	+	4.69499e6i	0.0373355	+	0.0373355i
$502$		−	9.66501e6i		−	0.0763996i
$503$	−5.66776e6	+	5.66776e6i	−0.0445356	+	0.0445356i	−0.729024	−	0.684488i	$-0.760026\pi$
$503$	−5.66776e6	+	5.66776e6i	−0.0445356	+	0.0445356i	0.684488	+	0.729024i	$0.260026\pi$
$504$	4.70108e7	−	4.70108e7i	0.367202	−	0.367202i
$505$	−2.24736e8	−	2.24736e8i	−1.74501	−	1.74501i
$506$			1.05727e8i			0.816082i
$507$	1.81600e8			1.39345
$508$			6.19009e7i			0.472178i
$509$		−	1.06903e8i		−	0.810659i	−0.914171	−	0.405330i	$-0.867157\pi$
$509$		−	1.06903e8i		−	0.810659i	0.914171	−	0.405330i	$-0.132843\pi$
$510$	1.23634e8	+	1.23634e8i	0.932022	+	0.932022i
$511$			1.23187e8i			0.923211i
$512$	−4.19430e6	−	4.19430e6i	−0.0312500	−	0.0312500i
$513$	−3.26200e8	−	3.26200e8i	−2.41620	−	2.41620i
$514$	1.69635e8			1.24919
$515$	1.34275e8			0.983047
$516$	−7.42106e7	+	7.42106e7i	−0.540153	+	0.540153i
$517$		−	8.98345e7i		−	0.650087i
$518$	−1.87309e7	+	6.30388e7i	−0.134763	+	0.453543i
$519$	−1.73095e7			−0.123817
$520$	−2.24136e7	−	2.24136e7i	−0.159405	−	0.159405i
$521$		−	1.05026e7i		−	0.0742648i	−0.999310	−	0.0371324i	$-0.988178\pi$
$521$		−	1.05026e7i		−	0.0742648i	0.999310	−	0.0371324i	$-0.0118223\pi$
$522$			1.80361e8i			1.26803i
$523$	−5.85576e7	+	5.85576e7i	−0.409335	+	0.409335i	−0.881507	−	0.472172i	$-0.843470\pi$
$523$	−5.85576e7	+	5.85576e7i	−0.409335	+	0.409335i	0.472172	+	0.881507i	$0.343470\pi$
$524$	8.37418e7	−	8.37418e7i	0.582034	−	0.582034i
$525$	1.46124e8			1.00982
$526$	−4.84410e7	+	4.84410e7i	−0.332855	+	0.332855i
$527$	7.01947e7			0.479592
$528$	7.67393e7			0.521334
$529$			3.15851e6i			0.0213361i
$530$	−2.09499e8			−1.40719
$531$	−2.37843e8	+	2.37843e8i	−1.58857	+	1.58857i
$532$	5.69749e7	+	5.69749e7i	0.378398	+	0.378398i
$533$	−6.20455e7	−	6.20455e7i	−0.409759	−	0.409759i
$534$	−5.34797e7			−0.351209
$535$	−2.38203e8	+	2.38203e8i	−1.55555	+	1.55555i
$536$	−3.78806e7	−	3.78806e7i	−0.245993	−	0.245993i
$537$	3.87322e8	−	3.87322e8i	2.50121	−	2.50121i
$538$	9.33557e7	+	9.33557e7i	0.599507	+	0.599507i
$539$			1.00891e8i			0.644299i
$540$	−1.61514e8	+	1.61514e8i	−1.02572	+	1.02572i
$541$	−2.39479e7	+	2.39479e7i	−0.151243	+	0.151243i	−0.778673	−	0.627430i	$-0.784107\pi$
$541$	−2.39479e7	+	2.39479e7i	−0.151243	+	0.151243i	0.627430	+	0.778673i	$0.284107\pi$
$542$	5.22308e7	+	5.22308e7i	0.328042	+	0.328042i
$543$		−	2.90139e8i		−	1.81221i
$544$	2.18534e7			0.135744
$545$			3.05211e8i			1.88543i
$546$		−	6.46338e7i		−	0.397083i
$547$	7.66017e7	+	7.66017e7i	0.468033	+	0.468033i	0.901277	−	0.433244i	$-0.142631\pi$
$547$	7.66017e7	+	7.66017e7i	0.468033	+	0.468033i	−0.433244	+	0.901277i	$0.642631\pi$
$548$		−	6.98013e7i		−	0.424152i
$549$	−1.97255e8	−	1.97255e8i	−1.19210	−	1.19210i
$550$	8.19379e7	+	8.19379e7i	0.492489	+	0.492489i
$551$	−2.18589e8			−1.30669
$552$	−1.05156e8			−0.625196
$553$	4.65503e7	−	4.65503e7i	0.275262	−	0.275262i
$554$			4.26463e7i			0.250814i
$555$	1.18200e8	−	3.97802e8i	0.691415	−	2.32695i
$556$	1.25842e8			0.732152
$557$	1.59048e8	+	1.59048e8i	0.920368	+	0.920368i	0.997055	−	0.0766873i	$-0.0244343\pi$
$557$	1.59048e8	+	1.59048e8i	0.920368	+	0.920368i	−0.0766873	+	0.997055i	$0.524434\pi$
$558$			1.68431e8i			0.969439i
$559$			7.00971e7i			0.401296i
$560$	2.82104e7	−	2.82104e7i	0.160637	−	0.160637i
$561$	−1.99916e8	+	1.99916e8i	−1.13229	+	1.13229i
$562$	−4.01363e7			−0.226114
$563$	9.73548e7	−	9.73548e7i	0.545547	−	0.545547i	−0.379603	−	0.925150i	$-0.623939\pi$
$563$	9.73548e7	−	9.73548e7i	0.545547	−	0.545547i	0.925150	+	0.379603i	$0.123939\pi$
$564$	8.93493e7			0.498028
$565$	2.11927e8			1.17501
$566$			6.12165e7i			0.337613i
$567$	−1.98014e8			−1.08629
$568$	−8.20459e7	+	8.20459e7i	−0.447726	+	0.447726i
$569$	−1.06682e8	−	1.06682e8i	−0.579103	−	0.579103i	0.355553	−	0.934656i	$-0.384293\pi$
$569$	−1.06682e8	−	1.06682e8i	−0.579103	−	0.579103i	−0.934656	+	0.355553i	$0.884293\pi$
$570$	−3.59536e8	−	3.59536e8i	−1.94141	−	1.94141i
$571$	−1.16140e8			−0.623838			−0.311919	−	0.950109i	$-0.600972\pi$
$571$	−1.16140e8			−0.623838			−0.311919	+	0.950109i	$0.600972\pi$
$572$	3.62428e7	−	3.62428e7i	0.193657	−	0.193657i
$573$	−1.58387e8	−	1.58387e8i	−0.841890	−	0.841890i
$574$	7.80924e7	−	7.80924e7i	0.412927	−	0.412927i
$575$	−1.12279e8	−	1.12279e8i	−0.590604	−	0.590604i
$576$			5.24370e7i			0.274391i
$577$	7.68738e7	−	7.68738e7i	0.400176	−	0.400176i	−0.478119	−	0.878295i	$-0.658681\pi$
$577$	7.68738e7	−	7.68738e7i	0.400176	−	0.400176i	0.878295	+	0.478119i	$0.158681\pi$
$578$	3.96195e7	−	3.96195e7i	0.205175	−	0.205175i
$579$	7.14405e7	+	7.14405e7i	0.368052	+	0.368052i
$580$			1.08232e8i			0.554716i
$581$	2.41498e8			1.23136
$582$			6.72153e6i			0.0340957i
$583$		−	3.38759e8i		−	1.70957i
$584$	−6.87027e7	−	6.87027e7i	−0.344933	−	0.344933i
$585$			2.80214e8i			1.39966i
$586$	−9.48873e7	−	9.48873e7i	−0.471536	−	0.471536i
$587$	−8.14294e7	−	8.14294e7i	−0.402594	−	0.402594i	0.476552	−	0.879146i	$-0.341886\pi$
$587$	−8.14294e7	−	8.14294e7i	−0.402594	−	0.402594i	−0.879146	+	0.476552i	$0.841886\pi$
$588$	−1.00346e8			−0.493594
$589$	−2.04131e8			−0.998996
$590$	−1.42726e8	+	1.42726e8i	−0.694940	+	0.694940i
$591$			4.11654e8i			1.99421i
$592$	−2.47110e7	−	4.56040e7i	−0.119104	−	0.219805i
$593$	3.14721e8			1.50925			0.754626	−	0.656155i	$-0.227818\pi$
$593$	3.14721e8			1.50925			0.754626	+	0.656155i	$0.227818\pi$
$594$	−2.61168e8	−	2.61168e8i	−1.24612	−	1.24612i
$595$			1.46984e8i			0.697779i
$596$			1.23899e8i			0.585234i
$597$	6.28958e7	−	6.28958e7i	0.295596	−	0.295596i
$598$	−4.96635e7	+	4.96635e7i	−0.232238	+	0.232238i
$599$	−3.85826e8			−1.79519			−0.897597	−	0.440817i	$-0.854689\pi$
$599$	−3.85826e8			−1.79519			−0.897597	+	0.440817i	$0.854689\pi$
$600$	−8.14953e7	+	8.14953e7i	−0.377293	+	0.377293i
$601$	−2.58640e6			−0.0119144			−0.00595719	−	0.999982i	$-0.501896\pi$
$601$	−2.58640e6			−0.0119144			−0.00595719	+	0.999982i	$0.501896\pi$
$602$	−8.82263e7			−0.404397
$603$			4.73581e8i			2.15994i
$604$	1.89999e8			0.862263
$605$	−7.67706e7	+	7.67706e7i	−0.346680	+	0.346680i
$606$	3.61435e8	+	3.61435e8i	1.62410	+	1.62410i
$607$	1.32369e8	+	1.32369e8i	0.591862	+	0.591862i	0.938134	−	0.346272i	$-0.112553\pi$
$607$	1.32369e8	+	1.32369e8i	0.591862	+	0.591862i	−0.346272	+	0.938134i	$0.612553\pi$
$608$	−6.35512e7			−0.282757
$609$	−1.56053e8	+	1.56053e8i	−0.690908	+	0.690908i
$610$	−1.18370e8	−	1.18370e8i	−0.521498	−	0.521498i
$611$	4.21983e7	−	4.21983e7i	0.185000	−	0.185000i
$612$	−1.36605e8	−	1.36605e8i	−0.595953	−	0.595953i
$613$			3.23328e8i			1.40366i	0.712344	+	0.701831i	$0.247634\pi$
$613$			3.23328e8i			1.40366i	−0.712344	+	0.701831i	$0.752366\pi$
$614$	8.48545e7	−	8.48545e7i	0.366581	−	0.366581i
$615$	−4.92796e8	+	4.92796e8i	−2.11857	+	2.11857i
$616$	4.56163e7	+	4.56163e7i	0.195154	+	0.195154i
$617$			1.79360e8i			0.763606i	0.924244	+	0.381803i	$0.124697\pi$
$617$			1.79360e8i			0.763606i	−0.924244	+	0.381803i	$0.875303\pi$
$618$	−2.15950e8			−0.914931
$619$			1.91595e8i			0.807818i	0.914799	+	0.403909i	$0.132349\pi$
$619$			1.91595e8i			0.807818i	−0.914799	+	0.403909i	$0.867651\pi$
$620$			1.01073e8i			0.424093i
$621$	3.57878e8	+	3.57878e8i	1.49438	+	1.49438i
$622$		−	8.52366e7i		−	0.354205i
$623$	−3.17900e7	−	3.17900e7i	−0.131470	−	0.131470i
$624$	3.60470e7	+	3.60470e7i	0.148360	+	0.148360i
$625$	2.76235e8			1.13146
$626$	−5.54562e7			−0.226062
$627$	5.81369e8	−	5.81369e8i	2.35857	−	2.35857i
$628$			6.50467e7i			0.262631i
$629$	1.83179e8	+	5.44287e7i	0.736080	+	0.218714i
$630$	−3.52685e8			−1.41048
$631$	−1.18486e8	−	1.18486e8i	−0.471604	−	0.471604i	0.430829	−	0.902433i	$-0.358221\pi$
$631$	−1.18486e8	−	1.18486e8i	−0.471604	−	0.471604i	−0.902433	+	0.430829i	$0.858221\pi$
$632$			5.19233e7i			0.205689i
$633$		−	5.31009e8i		−	2.09359i
$634$	5.00960e6	−	5.00960e6i	0.0196578	−	0.0196578i
$635$	2.32198e8	−	2.32198e8i	0.906852	−	0.906852i
$636$	3.36930e8			1.30969
$637$	−4.73921e7	+	4.73921e7i	−0.183353	+	0.183353i
$638$	−1.75011e8			−0.673910
$639$	1.02573e9			3.93126
$640$			3.14666e7i			0.120036i
$641$	2.58213e8			0.980401			0.490200	−	0.871610i	$-0.336924\pi$
$641$	2.58213e8			0.980401			0.490200	+	0.871610i	$0.336924\pi$
$642$	3.83093e8	−	3.83093e8i	1.44777	−	1.44777i
$643$	−1.71293e8	−	1.71293e8i	−0.644329	−	0.644329i	0.307287	−	0.951617i	$-0.400579\pi$
$643$	−1.71293e8	−	1.71293e8i	−0.644329	−	0.644329i	−0.951617	+	0.307287i	$0.900579\pi$
$644$	−6.25079e7	−	6.25079e7i	−0.234033	−	0.234033i
$645$	5.56745e8			2.07481
$646$	1.65559e8	−	1.65559e8i	0.614123	−	0.614123i
$647$	3.38506e8	+	3.38506e8i	1.24984	+	1.24984i	0.955792	+	0.294044i	$0.0950012\pi$
$647$	3.38506e8	+	3.38506e8i	1.24984	+	1.24984i	0.294044	+	0.955792i	$0.404999\pi$
$648$	1.10435e8	−	1.10435e8i	0.405865	−	0.405865i
$649$	−2.30788e8	−	2.30788e8i	−0.844265	−	0.844265i
$650$			7.69780e7i			0.280302i
$651$	−1.45731e8	+	1.45731e8i	−0.528214	+	0.528214i
$652$	−4.66104e6	+	4.66104e6i	−0.0168167	+	0.0168167i
$653$	−3.54368e8	−	3.54368e8i	−1.27267	−	1.27267i	−0.944684	−	0.327982i	$-0.893632\pi$
$653$	−3.54368e8	−	3.54368e8i	−1.27267	−	1.27267i	−0.327982	−	0.944684i	$-0.606368\pi$
$654$		−	4.90860e8i		−	1.75479i
$655$	−6.28250e8			−2.23568
$656$			8.71061e7i			0.308558i
$657$			8.58917e8i			3.02869i
$658$	5.31120e7	+	5.31120e7i	0.186430	+	0.186430i
$659$		−	2.48428e8i		−	0.868049i	−0.900901	−	0.434024i	$-0.857093\pi$
$659$		−	2.48428e8i		−	0.868049i	0.900901	−	0.434024i	$-0.142907\pi$
$660$	−2.87858e8	−	2.87858e8i	−1.00126	−	1.00126i
$661$	1.72507e8	+	1.72507e8i	0.597312	+	0.597312i	0.939596	−	0.342284i	$-0.111201\pi$
$661$	1.72507e8	+	1.72507e8i	0.597312	+	0.597312i	−0.342284	+	0.939596i	$0.611201\pi$
$662$	5.22616e7			0.180139
$663$	−1.87814e8			−0.644448
$664$	−1.34686e8	+	1.34686e8i	−0.460065	+	0.460065i
$665$		−	4.27439e8i		−	1.45348i
$666$	−1.30601e8	+	4.39537e8i	−0.442104	+	1.48790i
$667$	2.39817e8			0.808169
$668$	−3.11298e6	−	3.11298e6i	−0.0104435	−	0.0104435i
$669$			1.70327e8i			0.568861i
$670$			2.84189e8i			0.944894i
$671$	1.91404e8	−	1.91404e8i	0.633554	−	0.633554i
$672$	−4.53699e7	+	4.53699e7i	−0.149506	+	0.149506i
$673$	−3.57023e8			−1.17125			−0.585626	−	0.810581i	$-0.699151\pi$
$673$	−3.57023e8			−1.17125			−0.585626	+	0.810581i	$0.699151\pi$
$674$	2.02666e8	−	2.02666e8i	0.661914	−	0.661914i
$675$	5.54709e8			1.80366
$676$	−1.20409e8			−0.389779
$677$		−	2.00509e8i		−	0.646201i	−0.946365	−	0.323101i	$-0.895275\pi$
$677$		−	2.00509e8i		−	0.646201i	0.946365	−	0.323101i	$-0.104725\pi$
$678$	−3.40834e8			−1.09359
$679$	−3.99549e6	+	3.99549e6i	−0.0127632	+	0.0127632i
$680$	−8.19745e7	−	8.19745e7i	−0.260707	−	0.260707i
$681$	−3.29492e8	−	3.29492e8i	−1.04329	−	1.04329i
$682$	−1.63435e8			−0.515220
$683$	3.37519e7	−	3.37519e7i	0.105934	−	0.105934i	−0.652153	−	0.758087i	$-0.726134\pi$
$683$	3.37519e7	−	3.37519e7i	0.105934	−	0.105934i	0.758087	+	0.652153i	$0.226134\pi$
$684$	3.97257e8	+	3.97257e8i	1.24138	+	1.24138i
$685$	−2.61833e8	+	2.61833e8i	−0.814615	+	0.814615i
$686$	−1.67655e8	−	1.67655e8i	−0.519331	−	0.519331i
$687$			1.99063e7i			0.0613932i
$688$	4.92049e7	−	4.92049e7i	0.151092	−	0.151092i
$689$	1.59127e8	−	1.59127e8i	0.486503	−	0.486503i
$690$	3.94451e8	+	3.94451e8i	1.20073	+	1.20073i
$691$		−	3.43162e8i		−	1.04007i	−0.854143	−	0.520037i	$-0.825918\pi$
$691$		−	3.43162e8i		−	1.04007i	0.854143	−	0.520037i	$-0.174082\pi$
$692$	1.14769e7			0.0346344
$693$		−	5.70292e8i		−	1.71355i
$694$			1.25470e8i			0.375372i
$695$	−4.72048e8	−	4.72048e8i	−1.40615	−	1.40615i
$696$		−	1.74065e8i		−	0.516279i
$697$	−2.26922e8	−	2.26922e8i	−0.670161	−	0.670161i
$698$	1.84743e6	+	1.84743e6i	0.00543251	+	0.00543251i
$699$	−9.99300e8			−2.92593
$700$	−9.68868e7			−0.282469
$701$	3.39142e8	−	3.39142e8i	0.984527	−	0.984527i	−0.0153553	−	0.999882i	$-0.504888\pi$
$701$	3.39142e8	−	3.39142e8i	0.984527	−	0.984527i	0.999882	+	0.0153553i	$0.00488793\pi$
$702$		−	2.45359e8i		−	0.709236i
$703$	−5.32699e8	−	1.58283e8i	−1.53326	−	0.455583i
$704$	−5.08815e7			−0.145828
$705$	−3.35159e8	−	3.35159e8i	−0.956498	−	0.956498i
$706$		−	9.24508e7i		−	0.262722i
$707$			4.29697e8i			1.21592i
$708$	2.29541e8	−	2.29541e8i	0.646786	−	0.646786i
$709$	−3.80582e7	+	3.80582e7i	−0.106785	+	0.106785i	−0.758481	−	0.651696i	$-0.774058\pi$
$709$	−3.80582e7	+	3.80582e7i	−0.106785	+	0.106785i	0.651696	+	0.758481i	$0.274058\pi$
$710$	6.15527e8			1.71978
$711$	3.24571e8	−	3.24571e8i	0.903028	−	0.903028i
$712$	3.54594e7			0.0982406
$713$	2.23955e8			0.617863
$714$		−	2.36388e8i		−	0.649429i
$715$	−2.71902e8			−0.743865
$716$	−2.56812e8	+	2.56812e8i	−0.699641	+	0.699641i
$717$	−2.51573e8	−	2.51573e8i	−0.682506	−	0.682506i
$718$	1.02649e8	+	1.02649e8i	0.277320	+	0.277320i
$719$	−1.89452e7			−0.0509698			−0.0254849	−	0.999675i	$-0.508113\pi$
$719$	−1.89452e7			−0.0509698			−0.0254849	+	0.999675i	$0.508113\pi$
$720$	1.96697e8	−	1.96697e8i	0.526988	−	0.526988i
$721$	−1.28368e8	−	1.28368e8i	−0.342491	−	0.342491i
$722$	−2.93274e8	+	2.93274e8i	−0.779224	+	0.779224i
$723$	−3.77748e8	−	3.77748e8i	−0.999511	−	0.999511i
$724$			1.92375e8i			0.506913i
$725$	1.85857e8	−	1.85857e8i	0.487714	−	0.487714i
$726$	1.23467e8	−	1.23467e8i	0.322658	−	0.322658i
$727$	3.27427e8	+	3.27427e8i	0.852141	+	0.852141i	0.990397	−	0.138255i	$-0.0441495\pi$
$727$	3.27427e8	+	3.27427e8i	0.852141	+	0.852141i	−0.138255	+	0.990397i	$0.544149\pi$
$728$			4.28550e7i			0.111073i
$729$	9.87468e7			0.254883
$730$			5.15424e8i			1.32494i
$731$			2.56370e8i			0.656319i
$732$	1.90370e8	+	1.90370e8i	0.485362	+	0.485362i
$733$			3.26363e8i			0.828685i	0.910121	+	0.414342i	$0.135988\pi$
$733$			3.26363e8i			0.828685i	−0.910121	+	0.414342i	$0.864012\pi$
$734$	−2.79353e8	−	2.79353e8i	−0.706423	−	0.706423i
$735$	3.76411e8	+	3.76411e8i	0.947982	+	0.947982i
$736$	6.97229e7			0.174881
$737$	−4.59533e8			−1.14793
$738$	5.44498e8	−	5.44498e8i	1.35465	−	1.35465i
$739$			3.35591e8i			0.831528i	0.909473	+	0.415764i	$0.136486\pi$
$739$			3.35591e8i			0.831528i	−0.909473	+	0.415764i	$0.863514\pi$
$740$	−7.83718e7	+	2.63760e8i	−0.193404	+	0.650899i
$741$	5.46177e8			1.34239
$742$	2.00282e8	+	2.00282e8i	0.490263	+	0.490263i
$743$		−	8.74909e7i		−	0.213303i	−0.994296	−	0.106651i	$-0.965987\pi$
$743$		−	8.74909e7i		−	0.213303i	0.994296	−	0.106651i	$-0.0340129\pi$
$744$		−	1.62552e8i		−	0.394707i
$745$	4.64760e8	−	4.64760e8i	1.12398	−	1.12398i
$746$	−8.93133e7	+	8.93133e7i	−0.215129	+	0.215129i
$747$	1.68384e9			4.03960
$748$	1.32553e8	−	1.32553e8i	0.316726	−	0.316726i
$749$	4.55445e8			1.08390
$750$	−1.12753e8			−0.267266
$751$			3.65550e8i			0.863031i	0.902105	+	0.431516i	$0.142021\pi$
$751$			3.65550e8i			0.863031i	−0.902105	+	0.431516i	$0.857979\pi$
$752$	−5.92425e7			−0.139309
$753$	5.83070e7	−	5.83070e7i	0.136564	−	0.136564i
$754$	−8.22084e7	−	8.22084e7i	−0.191779	−	0.191779i
$755$	−7.12707e8	−	7.12707e8i	−1.65604	−	1.65604i
$756$	3.08816e8			0.714718
$757$	−3.89932e8	+	3.89932e8i	−0.898878	+	0.898878i	−0.995337	−	0.0964589i	$-0.969248\pi$
$757$	−3.89932e8	+	3.89932e8i	−0.898878	+	0.898878i	0.0964589	+	0.995337i	$0.469248\pi$
$758$	−1.31736e7	−	1.31736e7i	−0.0302481	−	0.0302481i
$759$	−6.37827e8	+	6.37827e8i	−1.45874	+	1.45874i
$760$	2.38388e8	+	2.38388e8i	0.543055	+	0.543055i
$761$		−	3.47479e7i		−	0.0788451i	−0.999223	−	0.0394226i	$-0.987448\pi$
$761$		−	3.47479e7i		−	0.0788451i	0.999223	−	0.0394226i	$-0.0125518\pi$
$762$	−3.73435e8	+	3.73435e8i	−0.844015	+	0.844015i
$763$	2.91783e8	−	2.91783e8i	0.656879	−	0.656879i
$764$	1.05017e8	+	1.05017e8i	0.235495	+	0.235495i
$765$			1.02484e9i			2.28914i
$766$	−3.18430e8			−0.708480
$767$		−	2.16818e8i		−	0.480517i
$768$		−	5.06067e7i		−	0.111718i
$769$	1.48782e8	+	1.48782e8i	0.327168	+	0.327168i	0.851509	−	0.524340i	$-0.175688\pi$
$769$	1.48782e8	+	1.48782e8i	0.327168	+	0.327168i	−0.524340	+	0.851509i	$0.675688\pi$
$770$		−	3.42224e8i		−	0.749614i
$771$	1.02337e9	+	1.02337e9i	2.23291	+	2.23291i
$772$	−4.73682e7	−	4.73682e7i	−0.102952	−	0.102952i
$773$	3.08090e7			0.0667020			0.0333510	−	0.999444i	$-0.489382\pi$
$773$	3.08090e7			0.0667020			0.0333510	+	0.999444i	$0.489382\pi$
$774$	−6.15157e8			−1.32667
$775$	1.73564e8	−	1.73564e8i	0.372868	−	0.372868i
$776$		−	4.45667e6i		−	0.00953729i
$777$	−4.93299e8	+	2.67300e8i	−1.05159	+	0.569817i
$778$	−5.01649e7			−0.106527
$779$	6.59907e8	+	6.59907e8i	1.39595	+	1.39595i
$780$		−	2.70433e8i		−	0.569871i
$781$			9.95307e8i			2.08931i
$782$	−1.81637e8	+	1.81637e8i	−0.379825	+	0.379825i
$783$	−5.92399e8	+	5.92399e8i	−1.23404	+	1.23404i
$784$	6.65340e7			0.138069
$785$	2.43997e8	−	2.43997e8i	0.504402	−	0.504402i
$786$	1.01039e9			2.08076
$787$	−2.35533e8			−0.483201			−0.241601	−	0.970376i	$-0.577672\pi$
$787$	−2.35533e8			−0.483201			−0.241601	+	0.970376i	$0.577672\pi$
$788$		−	2.72945e8i		−	0.557823i
$789$	−5.84468e8			−1.18995
$790$	1.94770e8	−	1.94770e8i	0.395040	−	0.395040i
$791$	−2.02603e8	−	2.02603e8i	−0.409370	−	0.409370i
$792$	3.18059e8	+	3.18059e8i	0.640224	+	0.640224i
$793$	1.79818e8			0.360590
$794$	−6.92255e7	+	6.92255e7i	−0.138294	+	0.138294i
$795$	−1.26386e9	−	1.26386e9i	−2.51535	−	2.51535i
$796$	−4.17027e7	+	4.17027e7i	−0.0826846	+	0.0826846i
$797$	−4.20047e8	−	4.20047e8i	−0.829703	−	0.829703i	0.157773	−	0.987475i	$-0.449569\pi$
$797$	−4.20047e8	−	4.20047e8i	−0.829703	−	0.829703i	−0.987475	+	0.157773i	$0.949569\pi$
$798$			6.87435e8i			1.35277i
$799$	1.54334e8	−	1.54334e8i	0.302567	−	0.302567i
$800$	5.40350e7	−	5.40350e7i	0.105537	−	0.105537i
$801$	−2.21656e8	−	2.21656e8i	−0.431302	−	0.431302i
$802$		−	5.14756e7i		−	0.0997881i
$803$	−8.33439e8			−1.60963
$804$		−	4.57051e8i		−	0.879421i
$805$			4.68949e8i			0.898954i
$806$	−7.67710e7	−	7.67710e7i	−0.146620	−	0.146620i
$807$			1.12639e9i			2.14323i
$808$	−2.39647e8	−	2.39647e8i	−0.454296	−	0.454296i
$809$	−3.54402e7	−	3.54402e7i	−0.0669346	−	0.0669346i	0.672847	−	0.739782i	$-0.265071\pi$
$809$	−3.54402e7	−	3.54402e7i	−0.0669346	−	0.0669346i	−0.739782	+	0.672847i	$0.765071\pi$
$810$	−8.28509e8			−1.55899
$811$	−8.99448e8			−1.68622			−0.843109	−	0.537743i	$-0.819277\pi$
$811$	−8.99448e8			−1.68622			−0.843109	+	0.537743i	$0.819277\pi$
$812$	1.03470e8	−	1.03470e8i	0.193262	−	0.193262i
$813$			6.30195e8i			1.17274i
$814$	−4.26499e8	−	1.26727e8i	−0.790760	−	0.234961i
$815$	3.49682e7			0.0645952
$816$	1.31837e8	+	1.31837e8i	0.242642	+	0.242642i
$817$		−	7.45542e8i		−	1.36712i
$818$		−	3.59190e8i		−	0.656243i
$819$	2.67885e8	−	2.67885e8i	0.487638	−	0.487638i
$820$	3.26745e8	−	3.26745e8i	0.592608	−	0.592608i
$821$	−7.76158e8			−1.40256			−0.701279	−	0.712887i	$-0.747387\pi$
$821$	−7.76158e8			−1.40256			−0.701279	+	0.712887i	$0.747387\pi$
$822$	4.21097e8	−	4.21097e8i	0.758169	−	0.758169i
$823$	7.45403e8			1.33719			0.668593	−	0.743628i	$-0.266897\pi$
$823$	7.45403e8			1.33719			0.668593	+	0.743628i	$0.266897\pi$
$824$	1.43184e8			0.255926
$825$			9.88628e8i			1.76064i
$826$	2.72893e8			0.484231
$827$	−3.00929e8	+	3.00929e8i	−0.532045	+	0.532045i	−0.921180	−	0.389136i	$-0.872774\pi$
$827$	−3.00929e8	+	3.00929e8i	−0.532045	+	0.532045i	0.389136	+	0.921180i	$0.372774\pi$
$828$	−4.35836e8	−	4.35836e8i	−0.767771	−	0.767771i
$829$	−5.69119e8	−	5.69119e8i	−0.998941	−	0.998941i	0.00105864	−	0.999999i	$-0.499663\pi$
$829$	−5.69119e8	−	5.69119e8i	−0.998941	−	0.998941i	−0.999999	+	0.00105864i	$0.999663\pi$
$830$	1.01045e9			1.76717
$831$	−2.57276e8	+	2.57276e8i	−0.448329	+	0.448329i
$832$	−2.39008e7	−	2.39008e7i	−0.0414994	−	0.0414994i
$833$	−1.73329e8	+	1.73329e8i	−0.299873	+	0.299873i
$834$	7.59178e8	+	7.59178e8i	1.30872	+	1.30872i
$835$			2.33543e7i			0.0401151i
$836$	−3.85473e8	+	3.85473e8i	−0.659744	+	0.659744i
$837$	−5.53217e8	+	5.53217e8i	−0.943451	+	0.943451i
$838$	−4.72345e8	−	4.72345e8i	−0.802651	−	0.802651i
$839$			9.68060e7i			0.163914i	0.996636	+	0.0819570i	$0.0261170\pi$
$839$			9.68060e7i			0.163914i	−0.996636	+	0.0819570i	$0.973883\pi$
$840$	3.40375e8			0.574275
$841$		−	1.97853e8i		−	0.332624i
$842$		−	5.53501e8i		−	0.927218i
$843$	−2.42133e8	−	2.42133e8i	−0.404178	−	0.404178i
$844$			3.52082e8i			0.585621i
$845$	4.51668e8	+	4.51668e8i	0.748599	+	0.748599i
$846$	3.70323e8	+	3.70323e8i	0.611603	+	0.611603i
$847$	1.46786e8			0.241565
$848$	−2.23399e8			−0.366348
$849$	−3.69306e8	+	3.69306e8i	−0.603481	+	0.603481i
$850$			2.81536e8i			0.458434i
$851$	5.84431e8	+	1.73654e8i	0.948298	+	0.281771i
$852$	−9.89931e8			−1.60061
$853$	−3.17179e8	−	3.17179e8i	−0.511043	−	0.511043i	0.403803	−	0.914846i	$-0.367688\pi$
$853$	−3.17179e8	−	3.17179e8i	−0.511043	−	0.511043i	−0.914846	+	0.403803i	$0.867688\pi$
$854$			2.26324e8i			0.363377i
$855$		−	2.98031e9i		−	4.76830i
$856$	−2.54007e8	+	2.54007e8i	−0.404972	+	0.404972i
$857$	−5.29592e8	+	5.29592e8i	−0.841393	+	0.841393i	−0.989040	−	0.147647i	$-0.952830\pi$
$857$	−5.29592e8	+	5.29592e8i	−0.841393	+	0.841393i	0.147647	+	0.989040i	$0.452830\pi$
$858$	4.37290e8			0.692321
$859$	5.37410e8	−	5.37410e8i	0.847865	−	0.847865i	−0.142002	−	0.989866i	$-0.545354\pi$
$859$	5.37410e8	−	5.37410e8i	0.847865	−	0.847865i	0.989866	+	0.142002i	$0.0453539\pi$
$860$	−3.69146e8			−0.580368
$861$	9.42229e8			1.47621
$862$		−	4.68432e8i		−	0.731349i
$863$	1.26470e9			1.96768			0.983841	−	0.179043i	$-0.0573001\pi$
$863$	1.26470e9			1.96768			0.983841	+	0.179043i	$0.0573001\pi$
$864$	−1.72231e8	+	1.72231e8i	−0.267035	+	0.267035i
$865$	−4.30513e7	−	4.30513e7i	−0.0665178	−	0.0665178i
$866$	7.00548e7	+	7.00548e7i	0.107866	+	0.107866i
$867$	4.78032e8			0.733499
$868$	9.66263e7	−	9.66263e7i	0.147753	−	0.147753i
$869$	3.14943e8	+	3.14943e8i	0.479925	+	0.479925i
$870$	−6.52939e8	+	6.52939e8i	−0.991550	+	0.991550i
$871$	−2.15858e8	−	2.15858e8i	−0.326674	−	0.326674i
$872$			3.25461e8i			0.490851i
$873$	−2.78585e7	+	2.78585e7i	−0.0418712	+	0.0418712i
$874$	5.28213e8	−	5.28213e8i	0.791179	−	0.791179i
$875$	−6.70238e7	−	6.70238e7i	−0.100047	−	0.100047i
$876$		−	8.28938e8i		−	1.23313i
$877$	8.88722e8			1.31755			0.658775	−	0.752340i	$-0.271075\pi$
$877$	8.88722e8			1.31755			0.658775	+	0.752340i	$0.271075\pi$
$878$			5.43992e8i			0.803728i
$879$		−	1.14487e9i		−	1.68573i
$880$	1.90862e8	+	1.90862e8i	0.280074	+	0.280074i
$881$		−	7.04809e8i		−	1.03073i	−0.856972	−	0.515364i	$-0.827657\pi$
$881$		−	7.04809e8i		−	1.03073i	0.856972	−	0.515364i	$-0.172343\pi$
$882$	−4.15902e8	−	4.15902e8i	−0.606158	−	0.606158i
$883$	7.16756e8	+	7.16756e8i	1.04109	+	1.04109i	0.999119	+	0.0419738i	$0.0133646\pi$
$883$	7.16756e8	+	7.16756e8i	1.04109	+	1.04109i	0.0419738	+	0.999119i	$0.486635\pi$
$884$	1.24529e8			0.180266
$885$	−1.72207e9			−2.48440
$886$	3.89081e8	−	3.89081e8i	0.559421	−	0.559421i
$887$			4.26189e8i			0.610705i	0.952239	+	0.305352i	$0.0987742\pi$
$887$			4.26189e8i			0.610705i	−0.952239	+	0.305352i	$0.901226\pi$
$888$	1.26043e8	−	4.24196e8i	0.180003	−	0.605797i
$889$	−4.43963e8			−0.631890
$890$	−1.33012e8	−	1.33012e8i	−0.188678	−	0.188678i
$891$		−	1.33970e9i		−	1.89397i
$892$		−	1.12934e8i		−	0.159123i
$893$	−4.48815e8	+	4.48815e8i	−0.630250	+	0.630250i
$894$	−7.47458e8	+	7.47458e8i	−1.04610	+	1.04610i
$895$	1.92666e9			2.68742
$896$	3.00822e7	−	3.00822e7i	0.0418202	−	0.0418202i
$897$	−5.99218e8			−0.830248
$898$	−6.07335e8			−0.838686
$899$			3.70715e8i			0.510224i
$900$	−6.75542e8			−0.926670
$901$	5.81983e8	−	5.81983e8i	0.795675	−	0.795675i
$902$	5.28346e8	+	5.28346e8i	0.719945	+	0.719945i
$903$	−5.32250e8	−	5.32250e8i	−0.722857	−	0.722857i
$904$	2.25988e8			0.305900
$905$	7.21621e8	−	7.21621e8i	0.973562	−	0.973562i
$906$	1.14622e9	+	1.14622e9i	1.54129	+	1.54129i
$907$	−2.82288e8	+	2.82288e8i	−0.378329	+	0.378329i	−0.870499	−	0.492170i	$-0.836204\pi$
$907$	−2.82288e8	+	2.82288e8i	−0.378329	+	0.378329i	0.492170	+	0.870499i	$0.336204\pi$
$908$	2.18467e8	+	2.18467e8i	0.291829	+	0.291829i
$909$			2.99606e9i			3.98895i
$910$	1.60754e8	−	1.60754e8i	0.213323	−	0.213323i
$911$	−8.58926e8	+	8.58926e8i	−1.13606	+	1.13606i	−0.146908	+	0.989150i	$0.546932\pi$
$911$	−8.58926e8	+	8.58926e8i	−1.13606	+	1.13606i	−0.989150	+	0.146908i	$0.953068\pi$
$912$	−3.83391e8	−	3.83391e8i	−0.505426	−	0.505426i
$913$			1.63389e9i			2.14689i
$914$	−8.49106e8			−1.11205
$915$		−	1.42820e9i		−	1.86435i
$916$		−	1.31987e7i		−	0.0171730i
$917$	6.00609e8	+	6.00609e8i	0.778904	+	0.778904i
$918$		−	8.97364e8i		−	1.15995i
$919$	5.60357e8	+	5.60357e8i	0.721968	+	0.721968i	0.969006	−	0.247038i	$-0.0794572\pi$
$919$	5.60357e8	+	5.60357e8i	0.721968	+	0.721968i	−0.247038	+	0.969006i	$0.579457\pi$
$920$	−2.61538e8	−	2.61538e8i	−0.335871	−	0.335871i
$921$	1.02382e9			1.31052
$922$	−7.32673e7			−0.0934797
$923$	−4.67529e8	+	4.67529e8i	−0.594571	+	0.594571i
$924$			5.50386e8i			0.697673i
$925$	5.87513e8	−	3.18351e8i	0.742322	−	0.402236i
$926$	4.99023e8			0.628475
$927$	−8.95042e8	−	8.95042e8i	−1.12358	−	1.12358i
$928$			1.15413e8i			0.144414i
$929$		−	8.27933e8i		−	1.03264i	−0.856396	−	0.516319i	$-0.827302\pi$
$929$		−	8.27933e8i		−	1.03264i	0.856396	−	0.516319i	$-0.172698\pi$
$930$	−6.09753e8	+	6.09753e8i	−0.758062	+	0.758062i
$931$	5.04055e8	−	5.04055e8i	0.624639	−	0.624639i
$932$	6.62579e8			0.818446
$933$	5.14214e8	−	5.14214e8i	0.633139	−	0.633139i
$934$	−7.34126e8			−0.901011
$935$	−9.94441e8			−1.21659
$936$			2.98806e8i			0.364386i
$937$	1.61439e9			1.96240			0.981202	−	0.192984i	$-0.0618165\pi$
$937$	1.61439e9			1.96240			0.981202	+	0.192984i	$0.0618165\pi$
$938$	2.71686e8	−	2.71686e8i	0.329199	−	0.329199i
$939$	−3.34556e8	−	3.34556e8i	−0.404084	−	0.404084i
$940$	2.22225e8	+	2.22225e8i	0.267553	+	0.267553i
$941$	1.16513e9			1.39831			0.699156	−	0.714970i	$-0.253559\pi$
$941$	1.16513e9			1.39831			0.699156	+	0.714970i	$0.253559\pi$
$942$	−3.92413e8	+	3.92413e8i	−0.469451	+	0.469451i
$943$	−7.23993e8	−	7.23993e8i	−0.863374	−	0.863374i
$944$	−1.52196e8	+	1.52196e8i	−0.180920	+	0.180920i
$945$	−1.15840e9	−	1.15840e9i	−1.37267	−	1.37267i
$946$		−	5.96909e8i		−	0.705074i
$947$	2.02788e8	−	2.02788e8i	0.238777	−	0.238777i	−0.577567	−	0.816344i	$-0.695998\pi$
$947$	2.02788e8	−	2.02788e8i	0.238777	−	0.238777i	0.816344	+	0.577567i	$0.195998\pi$
$948$	−3.13242e8	+	3.13242e8i	−0.367668	+	0.367668i
$949$	−3.91494e8	−	3.91494e8i	−0.458065	−	0.458065i
$950$		−	8.18727e8i		−	0.954922i
$951$	6.04437e7			0.0702764
$952$			1.56736e8i			0.181659i
$953$		−	6.09287e8i		−	0.703952i	−0.936009	−	0.351976i	$-0.885510\pi$
$953$		−	6.09287e8i		−	0.703952i	0.936009	−	0.351976i	$-0.114490\pi$
$954$	1.39646e9	+	1.39646e9i	1.60836	+	1.60836i
$955$		−	7.87865e8i		−	0.904569i
$956$	1.66804e8	+	1.66804e8i	0.190912	+	0.190912i
$957$	−1.05580e9	−	1.05580e9i	−1.20461	−	1.20461i
$958$	4.14502e7			0.0471444
$959$	5.00626e8			0.567620
$960$	−1.89831e8	+	1.89831e8i	−0.214563	+	0.214563i
$961$		−	5.41308e8i		−	0.609923i
$962$	−1.40813e8	−	2.59869e8i	−0.158168	−	0.291897i
$963$	3.17558e9			3.55586
$964$	2.50464e8	+	2.50464e8i	0.279585	+	0.279585i
$965$			3.55367e8i			0.395453i
$966$		−	7.54194e8i		−	0.836665i
$967$	−7.41743e8	+	7.41743e8i	−0.820302	+	0.820302i	−0.986151	−	0.165849i	$-0.946964\pi$
$967$	−7.41743e8	+	7.41743e8i	−0.820302	+	0.820302i	0.165849	+	0.986151i	$0.446964\pi$
$968$	−8.18643e7	+	8.18643e7i	−0.0902544	+	0.0902544i
$969$	1.99756e9			2.19548
$970$	−1.67175e7	+	1.67175e7i	−0.0183170	+	0.0183170i
$971$	3.12122e8			0.340931			0.170465	−	0.985364i	$-0.445473\pi$
$971$	3.12122e8			0.340931			0.170465	+	0.985364i	$0.445473\pi$
$972$	3.51556e8			0.382821
$973$			9.02559e8i			0.979799i
$974$	3.93523e8			0.425886
$975$	−4.64392e8	+	4.64392e8i	−0.501038	+	0.501038i
$976$	−1.26224e8	−	1.26224e8i	−0.135766	−	0.135766i
$977$	2.77719e8	+	2.77719e8i	0.297798	+	0.297798i	0.840151	−	0.542353i	$-0.182466\pi$
$977$	2.77719e8	+	2.77719e8i	0.297798	+	0.297798i	−0.542353	+	0.840151i	$0.682466\pi$
$978$	−5.62381e7			−0.0601194
$979$	2.15081e8	−	2.15081e8i	0.229220	−	0.229220i
$980$	−2.49577e8	−	2.49577e8i	−0.265171	−	0.265171i
$981$	2.03445e9	−	2.03445e9i	2.15496	−	2.15496i
$982$	−6.21250e6	−	6.21250e6i	−0.00656043	−	0.00656043i
$983$			4.15466e8i			0.437396i	0.975793	+	0.218698i	$0.0701809\pi$
$983$			4.15466e8i			0.437396i	−0.975793	+	0.218698i	$0.929819\pi$
$984$	−5.25493e8	+	5.25493e8i	−0.551546	+	0.551546i
$985$	−1.02385e9	+	1.02385e9i	−1.07134	+	1.07134i
$986$	−3.00665e8	−	3.00665e8i	−0.313655	−	0.313655i
$987$			6.40827e8i			0.666483i
$988$	−3.62139e8			−0.375496
$989$			8.17944e8i			0.845541i
$990$		−	2.38615e9i		−	2.45919i
$991$	−1.15516e9	−	1.15516e9i	−1.18692	−	1.18692i	−0.977914	−	0.209006i	$-0.932977\pi$
$991$	−1.15516e9	−	1.15516e9i	−1.18692	−	1.18692i	−0.209006	−	0.977914i	$-0.567023\pi$
$992$			1.07779e8i			0.110408i
$993$	3.15283e8	+	3.15283e8i	0.321998	+	0.321998i
$994$	−5.88446e8	−	5.88446e8i	−0.599167	−	0.599167i
$995$	3.12863e8			0.317603
$996$	−1.62507e9			−1.64472
$997$	1.94139e7	−	1.94139e7i	0.0195897	−	0.0195897i	−0.697244	−	0.716834i	$-0.745591\pi$
$997$	1.94139e7	−	1.94139e7i	0.0195897	−	0.0195897i	0.716834	+	0.697244i	$0.245591\pi$
$998$			4.54507e8i			0.457245i
$999$	−1.87263e9	+	1.01471e9i	−1.87826	+	1.01776i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.7.d.b.31.1	✓	20
37.6	odd	4	inner	74.7.d.b.43.10	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.7.d.b.31.1	✓	20	1.1	even	1	trivial
74.7.d.b.43.10	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)

\(f(q)\)	\(=\)	\(q+(-4.00000 - 4.00000i) q^{2} -48.2623i q^{3} +32.0000i q^{4} +(120.036 - 120.036i) q^{5} +(-193.049 + 193.049i) q^{6} -229.509 q^{7} +(128.000 - 128.000i) q^{8} -1600.25 q^{9} +O(q^{10})\)	\(q+(-4.00000 - 4.00000i) q^{2} -48.2623i q^{3} +32.0000i q^{4} +(120.036 - 120.036i) q^{5} +(-193.049 + 193.049i) q^{6} -229.509 q^{7} +(128.000 - 128.000i) q^{8} -1600.25 q^{9} -960.285 q^{10} -1552.78i q^{11} +1544.39 q^{12} +(729.393 - 729.393i) q^{13} +(918.036 + 918.036i) q^{14} +(-5793.20 - 5793.20i) q^{15} -1024.00 q^{16} +(2667.65 - 2667.65i) q^{17} +(6401.00 + 6401.00i) q^{18} +(-7757.72 + 7757.72i) q^{19} +(3841.14 + 3841.14i) q^{20} +11076.6i q^{21} +(-6211.12 + 6211.12i) q^{22} +(8511.09 - 8511.09i) q^{23} +(-6177.57 - 6177.57i) q^{24} -13192.1i q^{25} -5835.15 q^{26} +42048.5i q^{27} -7344.29i q^{28} +(14088.5 + 14088.5i) q^{29} +46345.6i q^{30} +(13156.7 + 13156.7i) q^{31} +(4096.00 + 4096.00i) q^{32} -74940.7 q^{33} -21341.2 q^{34} +(-27549.3 + 27549.3i) q^{35} -51208.0i q^{36} +(24131.9 + 44535.1i) q^{37} +62061.8 q^{38} +(-35202.2 - 35202.2i) q^{39} -30729.1i q^{40} -85064.6i q^{41} +(44306.5 - 44306.5i) q^{42} +(-48051.6 + 48051.6i) q^{43} +49689.0 q^{44} +(-192087. + 192087. i) q^{45} -68088.7 q^{46} +57854.0 q^{47} +49420.6i q^{48} -64974.6 q^{49} +(-52768.5 + 52768.5i) q^{50} +(-128747. - 128747. i) q^{51} +(23340.6 + 23340.6i) q^{52} +218163. q^{53} +(168194. - 168194. i) q^{54} +(-186389. - 186389. i) q^{55} +(-29377.2 + 29377.2i) q^{56} +(374405. + 374405. i) q^{57} -112708. i q^{58} +(148629. - 148629. i) q^{59} +(185382. - 185382. i) q^{60} +(123265. + 123265. i) q^{61} -105253. i q^{62} +367272. q^{63} -32768.0i q^{64} -175106. i q^{65} +(299763. + 299763. i) q^{66} -295942. i q^{67} +(85364.8 + 85364.8i) q^{68} +(-410765. - 410765. i) q^{69} +220394. q^{70} -640984. q^{71} +(-204832. + 204832. i) q^{72} -536740. i q^{73} +(81613.0 - 274668. i) q^{74} -636682. q^{75} +(-248247. - 248247. i) q^{76} +356377. i q^{77} +281618. i q^{78} +(-202825. + 202825. i) q^{79} +(-122917. + 122917. i) q^{80} +862774. q^{81} +(-340258. + 340258. i) q^{82} -1.05224e6 q^{83} -354452. q^{84} -640426. i q^{85} +384413. q^{86} +(679942. - 679942. i) q^{87} +(-198756. - 198756. i) q^{88} +(138513. + 138513. i) q^{89} +1.53670e6 q^{90} +(-167402. + 167402. i) q^{91} +(272355. + 272355. i) q^{92} +(634970. - 634970. i) q^{93} +(-231416. - 231416. i) q^{94} +1.86241e6i q^{95} +(197682. - 197682. i) q^{96} +(17408.9 - 17408.9i) q^{97} +(259899. + 259899. i) q^{98} +2.48483e6i 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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