LMFDB - Embedded newform 33.7.c.a.10.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [33,7,Mod(10,33)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(33, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("33.10");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 33 = 3 \cdot 11 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	33.c (of order $2$, degree $1$, 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:	$7.59178475946$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 486x^{10} + 82401x^{8} + 6062364x^{6} + 204706260x^{4} + 2964086784x^{2} + 15081209856 $ x^12 + 486x^10 + 82401x^8 + 6062364x^6 + 204706260x^4 + 2964086784*x^2 + 15081209856
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{11} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			10.4
Root			$-6.83773i$ of defining polynomial
Character	$\chi$	$=$	33.10
Dual form			33.7.c.a.10.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-6.83773i q^{2} -15.5885 q^{3} +17.2454 q^{4} +167.968 q^{5} +106.590i q^{6} +106.676i q^{7} -555.534i q^{8} +243.000 q^{9} +O(q^{10})$	\(q-6.83773i q^{2} -15.5885 q^{3} +17.2454 q^{4} +167.968 q^{5} +106.590i q^{6} +106.676i q^{7} -555.534i q^{8} +243.000 q^{9} -1148.52i q^{10} +(-6.11220 - 1330.99i) q^{11} -268.829 q^{12} -1477.21i q^{13} +729.420 q^{14} -2618.37 q^{15} -2694.89 q^{16} +3756.53i q^{17} -1661.57i q^{18} -7553.37i q^{19} +2896.68 q^{20} -1662.91i q^{21} +(-9100.93 + 41.7936i) q^{22} +19146.0 q^{23} +8659.92i q^{24} +12588.4 q^{25} -10100.8 q^{26} -3788.00 q^{27} +1839.67i q^{28} +32413.5i q^{29} +17903.7i q^{30} -2788.96 q^{31} -17127.3i q^{32} +(95.2798 + 20748.0i) q^{33} +25686.1 q^{34} +17918.2i q^{35} +4190.64 q^{36} -47245.9 q^{37} -51647.9 q^{38} +23027.5i q^{39} -93312.2i q^{40} +106739. i q^{41} -11370.5 q^{42} -29591.3i q^{43} +(-105.407 - 22953.4i) q^{44} +40816.3 q^{45} -130915. i q^{46} +9092.07 q^{47} +42009.2 q^{48} +106269. q^{49} -86076.0i q^{50} -58558.5i q^{51} -25475.1i q^{52} -154022. q^{53} +25901.3i q^{54} +(-1026.66 - 223564. i) q^{55} +59262.1 q^{56} +117745. i q^{57} +221635. q^{58} +33867.9 q^{59} -45154.8 q^{60} +388487. i q^{61} +19070.2i q^{62} +25922.2i q^{63} -289585. q^{64} -248125. i q^{65} +(141869. - 651.498i) q^{66} -447890. q^{67} +64782.9i q^{68} -298456. q^{69} +122520. q^{70} +403082. q^{71} -134995. i q^{72} +92785.3i q^{73} +323055. i q^{74} -196233. q^{75} -130261. i q^{76} +(141984. - 652.024i) q^{77} +157456. q^{78} +689152. i q^{79} -452656. q^{80} +59049.0 q^{81} +729852. q^{82} +583952. i q^{83} -28677.6i q^{84} +630978. i q^{85} -202338. q^{86} -505276. i q^{87} +(-739409. + 3395.54i) q^{88} +910609. q^{89} -279091. i q^{90} +157583. q^{91} +330181. q^{92} +43475.6 q^{93} -62169.1i q^{94} -1.26873e6i q^{95} +266988. i q^{96} +242113. q^{97} -726641. i q^{98} +(-1485.27 - 323430. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 204 q^{4} + 224 q^{5} + 2916 q^{9}+O(q^{10}) $ 12 * q - 204 * q^4 + 224 * q^5 + 2916 * q^9	$ 12 q - 204 q^{4} + 224 q^{5} + 2916 q^{9} - 3464 q^{11} + 1944 q^{12} - 6708 q^{14} + 1944 q^{15} + 5316 q^{16} - 44092 q^{20} + 60468 q^{22} - 15304 q^{23} + 95652 q^{25} - 76020 q^{26} - 58608 q^{31} + 4212 q^{33} + 117768 q^{34} - 49572 q^{36} - 202512 q^{37} + 29208 q^{38} - 264708 q^{42} + 434356 q^{44} + 54432 q^{45} + 516920 q^{47} - 377136 q^{48} + 157812 q^{49} - 1042192 q^{53} + 262656 q^{55} + 463020 q^{56} + 1029432 q^{58} - 461008 q^{59} - 417636 q^{60} - 725364 q^{64} + 200232 q^{66} + 364752 q^{67} + 504144 q^{69} - 1028400 q^{70} - 755176 q^{71} + 1364688 q^{75} - 102384 q^{77} + 1219212 q^{78} - 1220764 q^{80} + 708588 q^{81} - 158688 q^{82} + 248760 q^{86} - 2493252 q^{88} - 3513544 q^{89} - 702768 q^{91} + 6899300 q^{92} + 789264 q^{93} + 2370192 q^{97} - 841752 q^{99}+O(q^{100}) $ 12 * q - 204 * q^4 + 224 * q^5 + 2916 * q^9 - 3464 * q^11 + 1944 * q^12 - 6708 * q^14 + 1944 * q^15 + 5316 * q^16 - 44092 * q^20 + 60468 * q^22 - 15304 * q^23 + 95652 * q^25 - 76020 * q^26 - 58608 * q^31 + 4212 * q^33 + 117768 * q^34 - 49572 * q^36 - 202512 * q^37 + 29208 * q^38 - 264708 * q^42 + 434356 * q^44 + 54432 * q^45 + 516920 * q^47 - 377136 * q^48 + 157812 * q^49 - 1042192 * q^53 + 262656 * q^55 + 463020 * q^56 + 1029432 * q^58 - 461008 * q^59 - 417636 * q^60 - 725364 * q^64 + 200232 * q^66 + 364752 * q^67 + 504144 * q^69 - 1028400 * q^70 - 755176 * q^71 + 1364688 * q^75 - 102384 * q^77 + 1219212 * q^78 - 1220764 * q^80 + 708588 * q^81 - 158688 * q^82 + 248760 * q^86 - 2493252 * q^88 - 3513544 * q^89 - 702768 * q^91 + 6899300 * q^92 + 789264 * q^93 + 2370192 * q^97 - 841752 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/33\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	6.83773i		−	0.854717i	−0.904082	−	0.427358i	$-0.859444\pi$
$2$		−	6.83773i		−	0.854717i	0.904082	−	0.427358i	$-0.140556\pi$
$3$	−15.5885			−0.577350
$3$	−15.5885			−0.577350
$4$	17.2454			0.269460
$5$	167.968			1.34375			0.671874	−	0.740666i	$-0.265490\pi$
$5$	167.968			1.34375			0.671874	+	0.740666i	$0.265490\pi$
$6$			106.590i			0.493471i
$7$			106.676i			0.311008i	0.987835	+	0.155504i	$0.0497002\pi$
$7$			106.676i			0.311008i	−0.987835	+	0.155504i	$0.950300\pi$
$8$		−	555.534i		−	1.08503i
$9$	243.000			0.333333
$10$		−	1148.52i		−	1.14852i
$11$	−6.11220	−	1330.99i	−0.00459219	−	0.999989i
$11$	−6.11220	−	1330.99i	−0.00459219	−	0.999989i
$12$	−268.829			−0.155573
$13$		−	1477.21i		−	0.672377i	−0.941795	−	0.336189i	$-0.890862\pi$
$13$		−	1477.21i		−	0.672377i	0.941795	−	0.336189i	$-0.109138\pi$
$14$	729.420			0.265824
$15$	−2618.37			−0.775813
$16$	−2694.89			−0.657932
$17$			3756.53i			0.764610i	0.924036	+	0.382305i	$0.124870\pi$
$17$			3756.53i			0.764610i	−0.924036	+	0.382305i	$0.875130\pi$
$18$		−	1661.57i		−	0.284906i
$19$		−	7553.37i		−	1.10124i	−0.834758	−	0.550618i	$-0.814392\pi$
$19$		−	7553.37i		−	1.10124i	0.834758	−	0.550618i	$-0.185608\pi$
$20$	2896.68			0.362086
$21$		−	1662.91i		−	0.179561i
$22$	−9100.93	+	41.7936i	−0.854708	+	0.00392502i
$23$	19146.0			1.57360			0.786800	−	0.617208i	$-0.211736\pi$
$23$	19146.0			1.57360			0.786800	+	0.617208i	$0.211736\pi$
$24$			8659.92i			0.626441i
$25$	12588.4			0.805656
$26$	−10100.8			−0.574692
$27$	−3788.00			−0.192450
$28$			1839.67i			0.0838041i
$29$			32413.5i			1.32902i	0.747279	+	0.664510i	$0.231360\pi$
$29$			32413.5i			1.32902i	−0.747279	+	0.664510i	$0.768640\pi$
$30$			17903.7i			0.663100i
$31$	−2788.96			−0.0936175			−0.0468088	−	0.998904i	$-0.514905\pi$
$31$	−2788.96			−0.0936175			−0.0468088	+	0.998904i	$0.514905\pi$
$32$		−	17127.3i		−	0.522683i
$33$	95.2798	+	20748.0i	0.00265130	+	0.577344i
$34$	25686.1			0.653524
$35$			17918.2i			0.417916i
$36$	4190.64			0.0898199
$37$	−47245.9			−0.932736			−0.466368	−	0.884591i	$-0.654438\pi$
$37$	−47245.9			−0.932736			−0.466368	+	0.884591i	$0.654438\pi$
$38$	−51647.9			−0.941244
$39$			23027.5i			0.388197i
$40$		−	93312.2i		−	1.45800i
$41$			106739.i			1.54871i	0.632749	+	0.774357i	$0.281926\pi$
$41$			106739.i			1.54871i	−0.632749	+	0.774357i	$0.718074\pi$
$42$	−11370.5			−0.153473
$43$		−	29591.3i		−	0.372185i	−0.982532	−	0.186093i	$-0.940418\pi$
$43$		−	29591.3i		−	0.372185i	0.982532	−	0.186093i	$-0.0595825\pi$
$44$	−105.407	−	22953.4i	−0.00123741	−	0.269457i
$45$	40816.3			0.447916
$46$		−	130915.i		−	1.34498i
$47$	9092.07			0.0875728			0.0437864	−	0.999041i	$-0.486058\pi$
$47$	9092.07			0.0875728			0.0437864	+	0.999041i	$0.486058\pi$
$48$	42009.2			0.379857
$49$	106269.			0.903274
$50$		−	86076.0i		−	0.688608i
$51$		−	58558.5i		−	0.441448i
$52$		−	25475.1i		−	0.181178i
$53$	−154022.			−1.03456			−0.517279	−	0.855817i	$-0.673055\pi$
$53$	−154022.			−1.03456			−0.517279	+	0.855817i	$0.673055\pi$
$54$			25901.3i			0.164490i
$55$	−1026.66	−	223564.i	−0.00617074	−	1.34373i
$56$	59262.1			0.337453
$57$			117745.i			0.635798i
$58$	221635.			1.13594
$59$	33867.9			0.164904			0.0824521	−	0.996595i	$-0.473725\pi$
$59$	33867.9			0.164904			0.0824521	+	0.996595i	$0.473725\pi$
$60$	−45154.8			−0.209050
$61$			388487.i			1.71154i	0.517358	+	0.855769i	$0.326915\pi$
$61$			388487.i			1.71154i	−0.517358	+	0.855769i	$0.673085\pi$
$62$			19070.2i			0.0800165i
$63$			25922.2i			0.103669i
$64$	−289585.			−1.10468
$65$		−	248125.i		−	0.903505i
$66$	141869.	−	651.498i	0.493466	−	0.00226611i
$67$	−447890.			−1.48918			−0.744590	−	0.667522i	$-0.767355\pi$
$67$	−447890.			−1.48918			−0.744590	+	0.667522i	$0.767355\pi$
$68$			64782.9i			0.206031i
$69$	−298456.			−0.908518
$70$	122520.			0.357200
$71$	403082.			1.12621			0.563104	−	0.826386i	$-0.309607\pi$
$71$	403082.			1.12621			0.563104	+	0.826386i	$0.309607\pi$
$72$		−	134995.i		−	0.361676i
$73$			92785.3i			0.238512i	0.992864	+	0.119256i	$0.0380510\pi$
$73$			92785.3i			0.238512i	−0.992864	+	0.119256i	$0.961949\pi$
$74$			323055.i			0.797225i
$75$	−196233.			−0.465146
$76$		−	130261.i		−	0.296738i
$77$	141984.	−	652.024i	0.311005	−	0.00142821i
$78$	157456.			0.331799
$79$			689152.i			1.39776i	0.715237	+	0.698881i	$0.246319\pi$
$79$			689152.i			1.39776i	−0.715237	+	0.698881i	$0.753681\pi$
$80$	−452656.			−0.884094
$81$	59049.0			0.111111
$82$	729852.			1.32371
$83$			583952.i			1.02127i	0.859796	+	0.510637i	$0.170591\pi$
$83$			583952.i			1.02127i	−0.859796	+	0.510637i	$0.829409\pi$
$84$		−	28677.6i		−	0.0483843i
$85$			630978.i			1.02744i
$86$	−202338.			−0.318113
$87$		−	505276.i		−	0.767310i
$88$	−739409.	+	3395.54i	−1.08502	+	0.00498265i
$89$	910609.			1.29170			0.645850	−	0.763464i	$-0.276503\pi$
$89$	910609.			1.29170			0.645850	+	0.763464i	$0.276503\pi$
$90$		−	279091.i		−	0.382841i
$91$	157583.			0.209115
$92$	330181.			0.424022
$93$	43475.6			0.0540501
$94$		−	62169.1i		−	0.0748499i
$95$		−	1.26873e6i		−	1.47978i
$96$			266988.i			0.301771i
$97$	242113.			0.265279			0.132639	−	0.991164i	$-0.457655\pi$
$97$	242113.			0.265279			0.132639	+	0.991164i	$0.457655\pi$
$98$		−	726641.i		−	0.772043i
$99$	−1485.27	−	323430.i	−0.00153073	−	0.333330i
$100$	217092.			0.217092
$101$		−	1.19786e6i		−	1.16263i	−0.813677	−	0.581317i	$-0.802538\pi$
$101$		−	1.19786e6i		−	1.16263i	0.813677	−	0.581317i	$-0.197462\pi$
$102$	−400407.			−0.377313
$103$	−1.12725e6			−1.03159			−0.515795	−	0.856712i	$-0.672503\pi$
$103$	−1.12725e6			−1.03159			−0.515795	+	0.856712i	$0.672503\pi$
$104$	−820643.			−0.729548
$105$		−	279316.i		−	0.241284i
$106$			1.05316e6i			0.884253i
$107$		−	443790.i		−	0.362265i	−0.983459	−	0.181132i	$-0.942024\pi$
$107$		−	443790.i		−	0.362265i	0.983459	−	0.181132i	$-0.0579763\pi$
$108$	−65325.5			−0.0518575
$109$		−	125793.i		−	0.0971350i	−0.998820	−	0.0485675i	$-0.984534\pi$
$109$		−	125793.i		−	0.0971350i	0.998820	−	0.0485675i	$-0.0154656\pi$
$110$	−1.52867e6	+	7020.00i	−1.14851	+	0.00527423i
$111$	736490.			0.538515
$112$		−	287479.i		−	0.204622i
$113$	−1.63723e6			−1.13468			−0.567340	−	0.823484i	$-0.692027\pi$
$113$	−1.63723e6			−1.13468			−0.567340	+	0.823484i	$0.692027\pi$
$114$	805112.			0.543427
$115$	3.21592e6			2.11452
$116$			558984.i			0.358117i
$117$		−	358963.i		−	0.224126i
$118$		−	231579.i		−	0.140946i
$119$	−400730.			−0.237800
$120$			1.45459e6i			0.841779i
$121$	−1.77149e6	+	16270.5i	−0.999958	+	0.00918428i
$122$	2.65637e6			1.46288
$123$		−	1.66389e6i		−	0.894150i
$124$	−48096.8			−0.0252261
$125$	−510056.			−0.261149
$126$	177249.			0.0886079
$127$		−	1.18360e6i		−	0.577823i	−0.957356	−	0.288912i	$-0.906707\pi$
$127$		−	1.18360e6i		−	0.577823i	0.957356	−	0.288912i	$-0.0932934\pi$
$128$			883957.i			0.421503i
$129$			461283.i			0.214881i
$130$	−1.69661e6			−0.772241
$131$			3.01385e6i			1.34063i	0.742078	+	0.670314i	$0.233840\pi$
$131$			3.01385e6i			1.34063i	−0.742078	+	0.670314i	$0.766160\pi$
$132$	1643.14	+	357808.i	0.000714419	+	0.155571i
$133$	805762.			0.342493
$134$			3.06255e6i			1.27283i
$135$	−636263.			−0.258604
$136$	2.08688e6			0.829623
$137$	3.74843e6			1.45777			0.728883	−	0.684638i	$-0.240040\pi$
$137$	3.74843e6			1.45777			0.728883	+	0.684638i	$0.240040\pi$
$138$			2.04077e6i			0.776526i
$139$		−	386320.i		−	0.143848i	−0.997410	−	0.0719239i	$-0.977086\pi$
$139$		−	386320.i		−	0.143848i	0.997410	−	0.0719239i	$-0.0229139\pi$
$140$			309006.i			0.112612i
$141$	−141731.			−0.0505602
$142$		−	2.75617e6i		−	0.962588i
$143$	−1.96615e6	+	9029.02i	−0.672370	+	0.00308768i
$144$	−654858.			−0.219311
$145$			5.44444e6i			1.78587i
$146$	634441.			0.203860
$147$	−1.65657e6			−0.521505
$148$	−814775.			−0.251335
$149$		−	3.12076e6i		−	0.943411i	−0.881756	−	0.471706i	$-0.843638\pi$
$149$		−	3.12076e6i		−	0.943411i	0.881756	−	0.471706i	$-0.156362\pi$
$150$			1.34179e6i			0.397568i
$151$		−	5.18473e6i		−	1.50590i	−0.658079	−	0.752949i	$-0.728631\pi$
$151$		−	5.18473e6i		−	1.50590i	0.658079	−	0.752949i	$-0.271369\pi$
$152$	−4.19616e6			−1.19487
$153$			912836.i			0.254870i
$154$	−4458.37	−	970848.i	−0.00122071	−	0.265821i
$155$	−468457.			−0.125798
$156$			397118.i			0.104603i
$157$	−3.66366e6			−0.946709			−0.473354	−	0.880872i	$-0.656957\pi$
$157$	−3.66366e6			−0.946709			−0.473354	+	0.880872i	$0.656957\pi$
$158$	4.71223e6			1.19469
$159$	2.40096e6			0.597302
$160$		−	2.87684e6i		−	0.702354i
$161$			2.04241e6i			0.489402i
$162$		−	403761.i		−	0.0949685i
$163$	−7.42247e6			−1.71390			−0.856950	−	0.515400i	$-0.827643\pi$
$163$	−7.42247e6			−1.71390			−0.856950	+	0.515400i	$0.827643\pi$
$164$			1.84076e6i			0.417316i
$165$	16004.0	+	3.48501e6i	0.00356268	+	0.775805i
$166$	3.99291e6			0.872901
$167$		−	7.02650e6i		−	1.50865i	−0.656499	−	0.754327i	$-0.727963\pi$
$167$		−	7.02650e6i		−	1.50865i	0.656499	−	0.754327i	$-0.272037\pi$
$168$	−923804.			−0.194828
$169$	2.64465e6			0.547909
$170$	4.31446e6			0.878172
$171$		−	1.83547e6i		−	0.367078i
$172$		−	510315.i		−	0.100289i
$173$		−	55753.3i		−	0.0107679i	−0.999986	−	0.00538396i	$-0.998286\pi$
$173$		−	55753.3i		−	0.0107679i	0.999986	−	0.00538396i	$-0.00171378\pi$
$174$	−3.45494e6			−0.655833
$175$			1.34288e6i			0.250566i
$176$	16471.7	+	3.58686e6i	0.00302135	+	0.657925i
$177$	−527948.			−0.0952075
$178$		−	6.22650e6i		−	1.10404i
$179$	4.97167e6			0.866848			0.433424	−	0.901190i	$-0.357305\pi$
$179$	4.97167e6			0.866848			0.433424	+	0.901190i	$0.357305\pi$
$180$	703894.			0.120695
$181$	7.48474e6			1.26224			0.631118	−	0.775686i	$-0.282596\pi$
$181$	7.48474e6			1.26224			0.631118	+	0.775686i	$0.282596\pi$
$182$		−	1.07751e6i		−	0.178734i
$183$		−	6.05591e6i		−	0.988157i
$184$		−	1.06363e7i		−	1.70740i
$185$	−7.93581e6			−1.25336
$186$		−	297274.i		−	0.0461975i
$187$	4.99988e6	−	22960.7i	0.764602	−	0.00351123i
$188$	156796.			0.0235973
$189$		−	404087.i		−	0.0598535i
$190$	−8.67522e6			−1.26479
$191$	−2.65845e6			−0.381529			−0.190765	−	0.981636i	$-0.561097\pi$
$191$	−2.65845e6			−0.381529			−0.190765	+	0.981636i	$0.561097\pi$
$192$	4.51418e6			0.637786
$193$			5.47809e6i			0.762004i	0.924574	+	0.381002i	$0.124421\pi$
$193$			5.47809e6i			0.762004i	−0.924574	+	0.381002i	$0.875579\pi$
$194$		−	1.65550e6i		−	0.226738i
$195$			3.86789e6i			0.521639i
$196$	1.83266e6			0.243396
$197$			8.06552e6i			1.05495i	0.849569	+	0.527477i	$0.176862\pi$
$197$			8.06552e6i			1.05495i	−0.849569	+	0.527477i	$0.823138\pi$
$198$	−2.21153e6	+	10155.8i	−0.284903	+	0.00130834i
$199$	6.47778e6			0.821990			0.410995	−	0.911638i	$-0.365181\pi$
$199$	6.47778e6			0.821990			0.410995	+	0.911638i	$0.365181\pi$
$200$		−	6.99328e6i		−	0.874160i
$201$	6.98192e6			0.859779
$202$	−8.19066e6			−0.993722
$203$	−3.45773e6			−0.413336
$204$		−	1.00986e6i		−	0.118952i
$205$			1.79288e7i			2.08108i
$206$			7.70781e6i			0.881717i
$207$	4.65248e6			0.524533
$208$			3.98092e6i			0.442378i
$209$	−1.00534e7	+	46167.7i	−1.10122	+	0.00505708i
$210$	−1.90989e6			−0.206229
$211$			1.64166e7i			1.74758i	0.486307	+	0.873788i	$0.338344\pi$
$211$			1.64166e7i			1.74758i	−0.486307	+	0.873788i	$0.661656\pi$
$212$	−2.65617e6			−0.278771
$213$	−6.28343e6			−0.650216
$214$	−3.03452e6			−0.309634
$215$		−	4.97041e6i		−	0.500123i
$216$			2.10436e6i			0.208814i
$217$		−	297514.i		−	0.0291158i
$218$	−860137.			−0.0830229
$219$		−	1.44638e6i		−	0.137705i
$220$	−17705.1	−	3.85545e6i	−0.00166276	−	0.362082i
$221$	5.54919e6			0.514106
$222$		−	5.03592e6i		−	0.460278i
$223$	−166842.			−0.0150449			−0.00752247	−	0.999972i	$-0.502394\pi$
$223$	−166842.			−0.0150449			−0.00752247	+	0.999972i	$0.502394\pi$
$224$	1.82706e6			0.162559
$225$	3.05898e6			0.268552
$226$			1.11949e7i			0.969829i
$227$		−	9.96667e6i		−	0.852064i	−0.904708	−	0.426032i	$-0.859911\pi$
$227$		−	9.96667e6i		−	0.852064i	0.904708	−	0.426032i	$-0.140089\pi$
$228$			2.03057e6i			0.171322i
$229$	−2.21008e6			−0.184036			−0.0920178	−	0.995757i	$-0.529332\pi$
$229$	−2.21008e6			−0.184036			−0.0920178	+	0.995757i	$0.529332\pi$
$230$		−	2.19896e7i		−	1.80732i
$231$	−2.21331e6	+	10164.0i	−0.179559	+	0.000824576i
$232$	1.80068e7			1.44202
$233$			1.26959e7i			1.00368i	0.864959	+	0.501842i	$0.167344\pi$
$233$			1.26959e7i			1.00368i	−0.864959	+	0.501842i	$0.832656\pi$
$234$	−2.45449e6			−0.191564
$235$	1.52718e6			0.117676
$236$	584066.			0.0444350
$237$		−	1.07428e7i		−	0.806999i
$238$			2.74009e6i			0.203251i
$239$		−	3.07580e6i		−	0.225301i	−0.993635	−	0.112651i	$-0.964066\pi$
$239$		−	3.07580e6i		−	0.225301i	0.993635	−	0.112651i	$-0.0359341\pi$
$240$	7.05621e6			0.510432
$241$			4.38898e6i			0.313554i	0.987634	+	0.156777i	$0.0501104\pi$
$241$			4.38898e6i			0.313554i	−0.987634	+	0.156777i	$0.949890\pi$
$242$	111253.	+	1.21129e7i	0.00784996	+	0.854681i
$243$	−920483.			−0.0641500
$244$			6.69961e6i			0.461190i
$245$	1.78499e7			1.21377
$246$	−1.13773e7			−0.764245
$247$	−1.11579e7			−0.740445
$248$			1.54936e6i			0.101578i
$249$		−	9.10291e6i		−	0.589633i
$250$			3.48763e6i			0.223208i
$251$	7.16804e6			0.453293			0.226647	−	0.973977i	$-0.427224\pi$
$251$	7.16804e6			0.453293			0.226647	+	0.973977i	$0.427224\pi$
$252$			447039.i			0.0279347i
$253$	−117024.	−	2.54830e7i	−0.00722627	−	1.57358i
$254$	−8.09316e6			−0.493875
$255$		−	9.83597e6i		−	0.593194i
$256$	−1.24892e7			−0.744412
$257$	1.70060e7			1.00185			0.500925	−	0.865491i	$-0.332993\pi$
$257$	1.70060e7			1.00185			0.500925	+	0.865491i	$0.332993\pi$
$258$	3.15413e6			0.183663
$259$		−	5.03999e6i		−	0.290088i
$260$		−	4.27902e6i		−	0.243458i
$261$			7.87648e6i			0.443007i
$262$	2.06079e7			1.14586
$263$		−	2.06276e6i		−	0.113392i	−0.998391	−	0.0566959i	$-0.981943\pi$
$263$		−	2.06276e6i		−	0.113392i	0.998391	−	0.0566959i	$-0.0180565\pi$
$264$	1.15262e7	−	52931.2i	0.626435	−	0.00287674i
$265$	−2.58708e7			−1.39018
$266$		−	5.50958e6i		−	0.292734i
$267$	−1.41950e7			−0.745764
$268$	−7.72405e6			−0.401274
$269$	−2.39222e7			−1.22898			−0.614490	−	0.788924i	$-0.710638\pi$
$269$	−2.39222e7			−1.22898			−0.614490	+	0.788924i	$0.710638\pi$
$270$			4.35060e6i			0.221033i
$271$		−	1.41620e7i		−	0.711569i	−0.934568	−	0.355785i	$-0.884214\pi$
$271$		−	1.41620e7i		−	0.711569i	0.934568	−	0.355785i	$-0.115786\pi$
$272$		−	1.01234e7i		−	0.503061i
$273$	−2.45647e6			−0.120732
$274$		−	2.56308e7i		−	1.24598i
$275$	−76942.7	−	1.67550e7i	−0.00369973	−	0.805648i
$276$	−5.14700e6			−0.244809
$277$			8.93142e6i			0.420224i	0.977677	+	0.210112i	$0.0673829\pi$
$277$			8.93142e6i			0.420224i	−0.977677	+	0.210112i	$0.932617\pi$
$278$	−2.64156e6			−0.122949
$279$	−677717.			−0.0312058
$280$	9.95415e6			0.453451
$281$			2.81484e7i			1.26863i	0.773075	+	0.634314i	$0.218717\pi$
$281$			2.81484e7i			1.26863i	−0.773075	+	0.634314i	$0.781283\pi$
$282$			969121.i			0.0432146i
$283$			2.31052e6i			0.101941i	0.998700	+	0.0509707i	$0.0162315\pi$
$283$			2.31052e6i			0.101941i	−0.998700	+	0.0509707i	$0.983768\pi$
$284$	6.95131e6			0.303467
$285$			1.97775e7i			0.854352i
$286$	61738.1	+	1.34440e7i	0.00263909	+	0.574686i
$287$	−1.13865e7			−0.481662
$288$		−	4.16193e6i		−	0.174228i
$289$	1.00261e7			0.415372
$290$	3.72276e7			1.52641
$291$	−3.77416e6			−0.153159
$292$			1.60012e6i			0.0642694i
$293$		−	2.08718e7i		−	0.829770i	−0.909874	−	0.414885i	$-0.863822\pi$
$293$		−	2.08718e7i		−	0.829770i	0.909874	−	0.414885i	$-0.136178\pi$
$294$			1.13272e7i			0.445739i
$295$	5.68873e6			0.221590
$296$			2.62467e7i			1.01204i
$297$	23153.0	+	5.04177e6i	0.000883767	+	0.192448i
$298$	−2.13389e7			−0.806349
$299$		−	2.82827e7i		−	1.05805i
$300$	−3.38413e6			−0.125338
$301$	3.15668e6			0.115753
$302$	−3.54518e7			−1.28712
$303$			1.86728e7i			0.671247i
$304$			2.03555e7i			0.724538i
$305$			6.52535e7i			2.29987i
$306$	6.24173e6			0.217841
$307$		−	4.82621e7i		−	1.66798i	−0.551779	−	0.833991i	$-0.686051\pi$
$307$		−	4.82621e7i		−	1.66798i	0.551779	−	0.833991i	$-0.313949\pi$
$308$	2.44857e6	−	11244.4i	0.0838032	−	0.000384844i
$309$	1.75720e7			0.595589
$310$			3.20318e6i			0.107522i
$311$	3.66670e7			1.21897			0.609487	−	0.792796i	$-0.291375\pi$
$311$	3.66670e7			1.21897			0.609487	+	0.792796i	$0.291375\pi$
$312$	1.27926e7			0.421205
$313$	1.16945e7			0.381371			0.190685	−	0.981651i	$-0.438929\pi$
$313$	1.16945e7			0.381371			0.190685	+	0.981651i	$0.438929\pi$
$314$			2.50511e7i			0.809168i
$315$			4.35411e6i			0.139305i
$316$			1.18847e7i			0.376641i
$317$	−2.32210e7			−0.728959			−0.364480	−	0.931211i	$-0.618753\pi$
$317$	−2.32210e7			−0.728959			−0.364480	+	0.931211i	$0.618753\pi$
$318$		−	1.64171e7i		−	0.510524i
$319$	4.31419e7	−	198118.i	1.32901	−	0.00610311i
$320$	−4.86411e7			−1.48441
$321$			6.91800e6i			0.209154i
$322$	1.39655e7			0.418300
$323$	2.83744e7			0.842015
$324$	1.01832e6			0.0299400
$325$		−	1.85957e7i		−	0.541705i
$326$			5.07528e7i			1.46490i
$327$			1.96091e6i			0.0560809i
$328$	5.92971e7			1.68040
$329$			969903.i			0.0272358i
$330$	2.38296e7	−	109431.i	0.663093	−	0.00304508i
$331$	−7.23306e7			−1.99452			−0.997259	−	0.0739895i	$-0.976427\pi$
$331$	−7.23306e7			−1.99452			−0.997259	+	0.0739895i	$0.976427\pi$
$332$			1.00705e7i			0.275192i
$333$	−1.14807e7			−0.310912
$334$	−4.80453e7			−1.28947
$335$	−7.52314e7			−2.00108
$336$			4.48136e6i			0.118139i
$337$		−	5.02800e7i		−	1.31373i	−0.754009	−	0.656864i	$-0.771882\pi$
$337$		−	5.02800e7i		−	1.31373i	0.754009	−	0.656864i	$-0.228118\pi$
$338$		−	1.80834e7i		−	0.468307i
$339$	2.55218e7			0.655108
$340$			1.08815e7i			0.276854i
$341$	17046.7	+	3.71207e6i	0.000429909	+	0.0936165i
$342$	−1.25504e7			−0.313748
$343$			2.38867e7i			0.591934i
$344$	−1.64390e7			−0.403831
$345$	−5.01312e7			−1.22082
$346$	−381226.			−0.00920352
$347$		−	6.93649e7i		−	1.66017i	−0.557640	−	0.830083i	$-0.688293\pi$
$347$		−	6.93649e7i		−	1.66017i	0.557640	−	0.830083i	$-0.311707\pi$
$348$		−	8.71370e6i		−	0.206759i
$349$		−	7.37818e7i		−	1.73569i	−0.496832	−	0.867847i	$-0.665503\pi$
$349$		−	7.37818e7i		−	1.73569i	0.496832	−	0.867847i	$-0.334497\pi$
$350$	9.18222e6			0.214163
$351$			5.59567e6i			0.129399i
$352$	−2.27962e7	+	104685.i	−0.522677	+	0.00240026i
$353$	8.56348e7			1.94682			0.973410	−	0.229068i	$-0.0735678\pi$
$353$	8.56348e7			1.94682			0.973410	+	0.229068i	$0.0735678\pi$
$354$			3.60997e6i			0.0813755i
$355$	6.77050e7			1.51334
$356$	1.57038e7			0.348061
$357$	6.24677e6			0.137294
$358$		−	3.39949e7i		−	0.740910i
$359$		−	197244.i		−	0.00426304i	−0.999998	−	0.00213152i	$-0.999322\pi$
$359$		−	197244.i		−	0.00426304i	0.999998	−	0.00213152i	$-0.000678485\pi$
$360$		−	2.26749e7i		−	0.486001i
$361$	−1.00075e7			−0.212719
$362$		−	5.11786e7i		−	1.07885i
$363$	2.76147e7	−	253632.i	0.577326	−	0.00530255i
$364$	2.71758e6			0.0563480
$365$			1.55850e7i			0.320500i
$366$	−4.14087e7			−0.844594
$367$	−5.96138e7			−1.20600			−0.603002	−	0.797740i	$-0.706029\pi$
$367$	−5.96138e7			−1.20600			−0.603002	+	0.797740i	$0.706029\pi$
$368$	−5.15963e7			−1.03532
$369$			2.59375e7i			0.516238i
$370$			5.42630e7i			1.07127i
$371$		−	1.64304e7i		−	0.321756i
$372$	749754.			0.0145643
$373$			5.14277e7i			0.990992i	0.868610	+	0.495496i	$0.165014\pi$
$373$			5.14277e7i			0.990992i	−0.868610	+	0.495496i	$0.834986\pi$
$374$	−156999.	−	3.41879e7i	−0.00300111	−	0.653518i
$375$	7.95099e6			0.150774
$376$		−	5.05096e6i		−	0.0950189i
$377$	4.78816e7			0.893603
$378$	−2.76304e6			−0.0511578
$379$	−1.17931e7			−0.216627			−0.108313	−	0.994117i	$-0.534545\pi$
$379$	−1.17931e7			−0.216627			−0.108313	+	0.994117i	$0.534545\pi$
$380$		−	2.18797e7i		−	0.398741i
$381$			1.84505e7i			0.333606i
$382$			1.81777e7i			0.326099i
$383$	5.28514e7			0.940719			0.470360	−	0.882475i	$-0.344124\pi$
$383$	5.28514e7			0.940719			0.470360	+	0.882475i	$0.344124\pi$
$384$		−	1.37795e7i		−	0.243355i
$385$	2.38488e7	−	109519.i	0.417912	−	0.00191915i
$386$	3.74577e7			0.651298
$387$		−	7.19069e6i		−	0.124062i
$388$	4.17533e6			0.0714819
$389$	−1.48909e7			−0.252972			−0.126486	−	0.991968i	$-0.540370\pi$
$389$	−1.48909e7			−0.252972			−0.126486	+	0.991968i	$0.540370\pi$
$390$	2.64476e7			0.445853
$391$			7.19224e7i			1.20319i
$392$		−	5.90362e7i		−	0.980078i
$393$		−	4.69813e7i		−	0.774012i
$394$	5.51499e7			0.901687
$395$			1.15756e8i			1.87824i
$396$	−25614.0	−	5.57768e6i	−0.000412470	−	0.0898189i
$397$	3.05302e7			0.487930			0.243965	−	0.969784i	$-0.421552\pi$
$397$	3.05302e7			0.487930			0.243965	+	0.969784i	$0.421552\pi$
$398$		−	4.42933e7i		−	0.702569i
$399$	−1.25606e7			−0.197738
$400$	−3.39243e7			−0.530067
$401$	−1.03890e8			−1.61116			−0.805581	−	0.592486i	$-0.798147\pi$
$401$	−1.03890e8			−1.61116			−0.805581	+	0.592486i	$0.798147\pi$
$402$		−	4.77405e7i		−	0.734867i
$403$			4.11989e6i			0.0629463i
$404$		−	2.06576e7i		−	0.313283i
$405$	9.91837e6			0.149305
$406$			2.36431e7i			0.353285i
$407$	288776.	+	6.28836e7i	0.00428330	+	0.932726i
$408$	−3.25312e7			−0.478983
$409$		−	8.25556e7i		−	1.20664i	−0.797500	−	0.603319i	$-0.793845\pi$
$409$		−	8.25556e7i		−	1.20664i	0.797500	−	0.603319i	$-0.206155\pi$
$410$	1.22592e8			1.77873
$411$	−5.84323e7			−0.841642
$412$	−1.94398e7			−0.277972
$413$			3.61288e6i			0.0512866i
$414$		−	3.18124e7i		−	0.448327i
$415$			9.80854e7i			1.37234i
$416$	−2.53006e7			−0.351440
$417$			6.02214e6i			0.0830506i
$418$	315683.	+	6.87427e7i	0.00432237	+	0.941234i
$419$	−6.47436e7			−0.880146			−0.440073	−	0.897962i	$-0.645048\pi$
$419$	−6.47436e7			−0.880146			−0.440073	+	0.897962i	$0.645048\pi$
$420$		−	4.81693e6i		−	0.0650163i
$421$	−1.02270e8			−1.37058			−0.685288	−	0.728272i	$-0.740324\pi$
$421$	−1.02270e8			−1.37058			−0.685288	+	0.728272i	$0.740324\pi$
$422$	1.12252e8			1.49368
$423$	2.20937e6			0.0291909
$424$			8.55644e7i			1.12252i
$425$			4.72886e7i			0.616013i
$426$			4.29644e7i			0.555750i
$427$	−4.14421e7			−0.532302
$428$		−	7.65334e6i		−	0.0976157i
$429$	3.06492e7	−	140749.i	0.388193	−	0.00178267i
$430$	−3.39863e7			−0.427463
$431$			1.48166e8i			1.85062i	0.379218	+	0.925308i	$0.376193\pi$
$431$			1.48166e8i			1.85062i	−0.379218	+	0.925308i	$0.623807\pi$
$432$	1.02082e7			0.126619
$433$	−3.21907e7			−0.396521			−0.198260	−	0.980149i	$-0.563529\pi$
$433$	−3.21907e7			−0.396521			−0.198260	+	0.980149i	$0.563529\pi$
$434$	−2.03432e6			−0.0248858
$435$		−	8.48704e7i		−	1.03107i
$436$		−	2.16935e6i		−	0.0261740i
$437$		−	1.44617e8i		−	1.73290i
$438$	−9.88996e6			−0.117699
$439$			1.63606e8i			1.93377i	0.255209	+	0.966886i	$0.417856\pi$
$439$			1.63606e8i			1.93377i	−0.255209	+	0.966886i	$0.582144\pi$
$440$	−1.24197e8	+	570343.i	−1.45799	+	0.00669543i
$441$	2.58234e7			0.301091
$442$		−	3.79439e7i		−	0.439415i
$443$	3.88693e7			0.447091			0.223545	−	0.974694i	$-0.428237\pi$
$443$	3.88693e7			0.447091			0.223545	+	0.974694i	$0.428237\pi$
$444$	1.27011e7			0.145108
$445$	1.52954e8			1.73572
$446$			1.14082e6i			0.0128592i
$447$			4.86478e7i			0.544679i
$448$		−	3.08917e7i		−	0.343564i
$449$	−1.44674e8			−1.59828			−0.799138	−	0.601148i	$-0.794710\pi$
$449$	−1.44674e8			−1.59828			−0.799138	+	0.601148i	$0.794710\pi$
$450$		−	2.09165e7i		−	0.229536i
$451$	1.42068e8	−	652410.i	1.54870	−	0.00711198i
$452$	−2.82346e7			−0.305750
$453$			8.08220e7i			0.869431i
$454$	−6.81494e7			−0.728274
$455$	2.64689e7			0.280997
$456$	6.54116e7			0.689859
$457$		−	1.57900e8i		−	1.65438i	−0.561924	−	0.827189i	$-0.689939\pi$
$457$		−	1.57900e8i		−	1.65438i	0.561924	−	0.827189i	$-0.310061\pi$
$458$			1.51119e7i			0.157298i
$459$		−	1.42297e7i		−	0.147149i
$460$	5.54599e7			0.569778
$461$		−	1.75494e8i		−	1.79126i	−0.444800	−	0.895630i	$-0.646725\pi$
$461$		−	1.75494e8i		−	1.79126i	0.444800	−	0.895630i	$-0.353275\pi$
$462$	69499.0	+	1.51340e7i	0.000704779	+	0.153472i
$463$	2.76136e7			0.278215			0.139108	−	0.990277i	$-0.455577\pi$
$463$	2.76136e7			0.278215			0.139108	+	0.990277i	$0.455577\pi$
$464$		−	8.73507e7i		−	0.874405i
$465$	7.30252e6			0.0726297
$466$	8.68115e7			0.857866
$467$	−3.64285e7			−0.357676			−0.178838	−	0.983879i	$-0.557234\pi$
$467$	−3.64285e7			−0.357676			−0.178838	+	0.983879i	$0.557234\pi$
$468$		−	6.19046e6i		−	0.0603928i
$469$		−	4.77791e7i		−	0.463147i
$470$		−	1.04424e7i		−	0.100579i
$471$	5.71108e7			0.546583
$472$		−	1.88148e7i		−	0.178926i
$473$	−3.93856e7	+	180868.i	−0.372181	+	0.00170914i
$474$	−7.34565e7			−0.689755
$475$		−	9.50847e7i		−	0.887217i
$476$	−6.91076e6			−0.0640774
$477$	−3.74273e7			−0.344852
$478$	−2.10315e7			−0.192569
$479$			1.36993e7i			0.124649i	0.998056	+	0.0623247i	$0.0198514\pi$
$479$			1.36993e7i			0.124649i	−0.998056	+	0.0623247i	$0.980149\pi$
$480$			4.48455e7i			0.405504i
$481$			6.97922e7i			0.627151i
$482$	3.00107e7			0.268000
$483$		−	3.18381e7i		−	0.282557i
$484$	−3.05500e7	+	280592.i	−0.269448	+	0.00247479i
$485$	4.06673e7			0.356467
$486$			6.29402e6i			0.0548301i
$487$	−1.17206e8			−1.01476			−0.507381	−	0.861722i	$-0.669386\pi$
$487$	−1.17206e8			−1.01476			−0.507381	+	0.861722i	$0.669386\pi$
$488$	2.15818e8			1.85707
$489$	1.15705e8			0.989521
$490$		−	1.22053e8i		−	1.03743i
$491$			3.86176e7i			0.326243i	0.986606	+	0.163121i	$0.0521562\pi$
$491$			3.86176e7i			0.326243i	−0.986606	+	0.163121i	$0.947844\pi$
$492$		−	2.86945e7i		−	0.240937i
$493$	−1.21762e8			−1.01618
$494$			7.62950e7i			0.632871i
$495$	−249478.	−	5.43259e7i	−0.00205691	−	0.447911i
$496$	7.51594e6			0.0615940
$497$			4.29991e7i			0.350260i
$498$	−6.22432e7			−0.503969
$499$	6.22876e7			0.501303			0.250651	−	0.968077i	$-0.419355\pi$
$499$	6.22876e7			0.501303			0.250651	+	0.968077i	$0.419355\pi$
$500$	−8.79613e6			−0.0703690
$501$			1.09532e8i			0.871022i
$502$		−	4.90131e7i		−	0.387437i
$503$		−	3.35178e7i		−	0.263373i	−0.991291	−	0.131687i	$-0.957961\pi$
$503$		−	3.35178e7i		−	0.263373i	0.991291	−	0.131687i	$-0.0420393\pi$
$504$	1.44007e7			0.112484
$505$		−	2.01203e8i		−	1.56229i
$506$	−1.74246e8	+	800180.i	−1.34497	+	0.00617641i
$507$	−4.12260e7			−0.316335
$508$		−	2.04117e7i		−	0.155700i
$509$	9.00026e7			0.682499			0.341249	−	0.939973i	$-0.389150\pi$
$509$	9.00026e7			0.682499			0.341249	+	0.939973i	$0.389150\pi$
$510$	−6.72557e7			−0.507013
$511$	−9.89794e6			−0.0741792
$512$			1.41971e8i			1.05776i
$513$			2.86121e7i			0.211933i
$514$		−	1.16282e8i		−	0.856298i
$515$	−1.89342e8			−1.38620
$516$			7.95502e6i			0.0579018i
$517$	−55572.6	−	1.21014e7i	−0.000402151	−	0.0875718i
$518$	−3.44621e7			−0.247943
$519$			869107.i			0.00621686i
$520$	−1.37842e8			−0.980328
$521$	4.44753e7			0.314489			0.157245	−	0.987560i	$-0.449739\pi$
$521$	4.44753e7			0.314489			0.157245	+	0.987560i	$0.449739\pi$
$522$	5.38572e7			0.378645
$523$			1.45157e8i			1.01469i	0.861743	+	0.507345i	$0.169373\pi$
$523$			1.45157e8i			1.01469i	−0.861743	+	0.507345i	$0.830627\pi$
$524$			5.19751e7i			0.361245i
$525$		−	2.09334e7i		−	0.144664i
$526$	−1.41046e7			−0.0969178
$527$		−	1.04768e7i		−	0.0715809i
$528$	−256769.	−	5.59136e7i	−0.00174438	−	0.379853i
$529$	2.18533e8			1.47622
$530$			1.76898e8i			1.18821i
$531$	8.22989e6			0.0549681
$532$	1.38957e7			0.0922880
$533$	1.57676e8			1.04132
$534$			9.70615e7i			0.637417i
$535$		−	7.45427e7i		−	0.486792i
$536$			2.48819e8i			1.61580i
$537$	−7.75007e7			−0.500475
$538$			1.63574e8i			1.05043i
$539$	−649539.	−	1.41443e8i	−0.00414800	−	0.903264i
$540$	−1.09726e7			−0.0696834
$541$		−	1.08867e8i		−	0.687550i	−0.939052	−	0.343775i	$-0.888294\pi$
$541$		−	1.08867e8i		−	0.687550i	0.939052	−	0.343775i	$-0.111706\pi$
$542$	−9.68361e7			−0.608190
$543$	−1.16676e8			−0.728753
$544$	6.43391e7			0.399648
$545$		−	2.11292e7i		−	0.130525i
$546$			1.67967e7i			0.103192i
$547$			2.45302e8i			1.49879i	0.662125	+	0.749393i	$0.269655\pi$
$547$			2.45302e8i			1.49879i	−0.662125	+	0.749393i	$0.730345\pi$
$548$	6.46432e7			0.392809
$549$			9.44022e7i			0.570513i
$550$	−1.14566e8	+	526114.i	−0.688601	+	0.00316222i
$551$	2.44831e8			1.46356
$552$			1.65803e8i			0.985768i
$553$	−7.35158e7			−0.434716
$554$	6.10706e7			0.359173
$555$	1.23707e8			0.723629
$556$		−	6.66226e6i		−	0.0387612i
$557$			6.54683e6i			0.0378849i	0.999821	+	0.0189424i	$0.00602992\pi$
$557$			6.54683e6i			0.0378849i	−0.999821	+	0.0189424i	$0.993970\pi$
$558$			4.63405e6i			0.0266722i
$559$	−4.37127e7			−0.250249
$560$		−	4.82875e7i		−	0.274960i
$561$	−7.79405e7	+	357921.i	−0.441443	+	0.00202721i
$562$	1.92471e8			1.08432
$563$		−	1.49596e8i		−	0.838291i	−0.907919	−	0.419145i	$-0.862330\pi$
$563$		−	1.49596e8i		−	0.838291i	0.907919	−	0.419145i	$-0.137670\pi$
$564$	−2.44422e6			−0.0136239
$565$	−2.75002e8			−1.52472
$566$	1.57987e7			0.0871310
$567$			6.29910e6i			0.0345565i
$568$		−	2.23926e8i		−	1.22197i
$569$			6.51412e7i			0.353605i	0.984246	+	0.176803i	$0.0565754\pi$
$569$			6.51412e7i			0.353605i	−0.984246	+	0.176803i	$0.943425\pi$
$570$	1.35233e8			0.730229
$571$		−	1.70982e8i		−	0.918419i	−0.888328	−	0.459210i	$-0.848133\pi$
$571$		−	1.70982e8i		−	0.918419i	0.888328	−	0.459210i	$-0.151867\pi$
$572$	−3.39071e7	+	155709.i	−0.181177	+	0.000832006i
$573$	4.14411e7			0.220276
$574$			7.78575e7i			0.411685i
$575$	2.41017e8			1.26778
$576$	−7.03691e7			−0.368226
$577$	1.88869e8			0.983181			0.491590	−	0.870827i	$-0.336416\pi$
$577$	1.88869e8			0.983181			0.491590	+	0.870827i	$0.336416\pi$
$578$		−	6.85556e7i		−	0.355025i
$579$		−	8.53950e7i		−	0.439943i
$580$			9.38916e7i			0.481219i
$581$	−6.22935e7			−0.317625
$582$			2.58067e7i			0.130907i
$583$	941412.	+	2.05001e8i	0.00475088	+	1.03455i
$584$	5.15454e7			0.258792
$585$		−	6.02944e7i		−	0.301168i
$586$	−1.42716e8			−0.709219
$587$	6.29602e7			0.311280			0.155640	−	0.987814i	$-0.450256\pi$
$587$	6.29602e7			0.311280			0.155640	+	0.987814i	$0.450256\pi$
$588$	−2.85683e7			−0.140525
$589$			2.10661e7i			0.103095i
$590$		−	3.88980e7i		−	0.189396i
$591$		−	1.25729e8i		−	0.609078i
$592$	1.27322e8			0.613677
$593$			6.10792e7i			0.292906i	0.989218	+	0.146453i	$0.0467858\pi$
$593$			6.10792e7i			0.292906i	−0.989218	+	0.146453i	$0.953214\pi$
$594$	3.44743e7	−	158314.i	0.164489	−	0.000755370i
$595$	−6.73100e7			−0.319543
$596$		−	5.38187e7i		−	0.254211i
$597$	−1.00979e8			−0.474576
$598$	−1.93390e8			−0.904335
$599$	−3.90561e8			−1.81722			−0.908612	−	0.417641i	$-0.862857\pi$
$599$	−3.90561e8			−1.81722			−0.908612	+	0.417641i	$0.862857\pi$
$600$			1.09014e8i			0.504696i
$601$		−	1.87303e8i		−	0.862824i	−0.902155	−	0.431412i	$-0.858016\pi$
$601$		−	1.87303e8i		−	0.862824i	0.902155	−	0.431412i	$-0.141984\pi$
$602$		−	2.15845e7i		−	0.0989357i
$603$	−1.08837e8			−0.496393
$604$		−	8.94129e7i		−	0.405779i
$605$	−2.97554e8	+	2.73293e6i	−1.34369	+	0.0123413i
$606$	1.27680e8			0.573726
$607$			9.38323e7i			0.419552i	0.977749	+	0.209776i	$0.0672735\pi$
$607$			9.38323e7i			0.419552i	−0.977749	+	0.209776i	$0.932726\pi$
$608$	−1.29369e8			−0.575597
$609$	5.39007e7			0.238640
$610$	4.46186e8			1.96574
$611$		−	1.34309e7i		−	0.0588819i
$612$			1.57422e7i			0.0686771i
$613$			3.63707e8i			1.57896i	0.613777	+	0.789479i	$0.289649\pi$
$613$			3.63707e8i			1.57896i	−0.613777	+	0.789479i	$0.710351\pi$
$614$	−3.30003e8			−1.42565
$615$		−	2.79482e8i		−	1.20151i
$616$	−362222.	−	7.88770e7i	−0.00154965	−	0.337449i
$617$	1.21121e8			0.515659			0.257830	−	0.966190i	$-0.416993\pi$
$617$	1.21121e8			0.515659			0.257830	+	0.966190i	$0.416993\pi$
$618$		−	1.20153e8i		−	0.509059i
$619$	2.40580e8			1.01435			0.507174	−	0.861844i	$-0.330690\pi$
$619$	2.40580e8			1.01435			0.507174	+	0.861844i	$0.330690\pi$
$620$	−8.07874e6			−0.0338976
$621$	−7.25249e7			−0.302839
$622$		−	2.50719e8i		−	1.04188i
$623$			9.71399e7i			0.401729i
$624$		−	6.20565e7i		−	0.255407i
$625$	−2.82367e8			−1.15657
$626$		−	7.99636e7i		−	0.325964i
$627$	1.56717e8	−	719684.i	0.635792	−	0.00291971i
$628$	−6.31814e7			−0.255100
$629$		−	1.77480e8i		−	0.713179i
$630$	2.97723e7			0.119067
$631$	4.09539e7			0.163007			0.0815036	−	0.996673i	$-0.474028\pi$
$631$	4.09539e7			0.163007			0.0815036	+	0.996673i	$0.474028\pi$
$632$	3.82847e8			1.51661
$633$		−	2.55910e8i		−	1.00896i
$634$			1.58779e8i			0.623054i
$635$		−	1.98808e8i		−	0.776448i
$636$	4.14056e7			0.160949
$637$		−	1.56982e8i		−	0.607341i
$638$	−1.35468e6	−	2.94993e8i	−0.00521643	−	1.13592i
$639$	9.79489e7			0.375402
$640$			1.48477e8i			0.566394i
$641$	1.34211e8			0.509582			0.254791	−	0.966996i	$-0.417993\pi$
$641$	1.34211e8			0.509582			0.254791	+	0.966996i	$0.417993\pi$
$642$	4.73034e7			0.178767
$643$	−1.25960e8			−0.473806			−0.236903	−	0.971533i	$-0.576132\pi$
$643$	−1.25960e8			−0.473806			−0.236903	+	0.971533i	$0.576132\pi$
$644$			3.52223e7i			0.131874i
$645$			7.74810e7i			0.288746i
$646$		−	1.94017e8i		−	0.719684i
$647$	−4.30179e8			−1.58831			−0.794157	−	0.607712i	$-0.792087\pi$
$647$	−4.30179e8			−1.58831			−0.794157	+	0.607712i	$0.792087\pi$
$648$		−	3.28038e7i		−	0.120559i
$649$	−207007.	−	4.50777e7i	−0.000757272	−	0.164903i
$650$	−1.27153e8			−0.463004
$651$			4.63779e6i			0.0168100i
$652$	−1.28004e8			−0.461827
$653$	1.35951e8			0.488250			0.244125	−	0.969744i	$-0.421499\pi$
$653$	1.35951e8			0.488250			0.244125	+	0.969744i	$0.421499\pi$
$654$	1.34082e7			0.0479333
$655$			5.06232e8i			1.80146i
$656$		−	2.87649e8i		−	1.01895i
$657$			2.25468e7i			0.0795041i
$658$	6.63194e6			0.0232789
$659$		−	1.68435e8i		−	0.588542i	−0.955722	−	0.294271i	$-0.904923\pi$
$659$		−	1.68435e8i		−	0.588542i	0.955722	−	0.294271i	$-0.0950768\pi$
$660$	275996.	+	6.01005e7i	0.000959998	+	0.209048i
$661$	3.91844e7			0.135678			0.0678390	−	0.997696i	$-0.478390\pi$
$661$	3.91844e7			0.135678			0.0678390	+	0.997696i	$0.478390\pi$
$662$			4.94577e8i			1.70475i
$663$	−8.65033e7			−0.296819
$664$	3.24405e8			1.10811
$665$	1.35343e8			0.460224
$666$			7.85023e7i			0.265742i
$667$			6.20588e8i			2.09135i
$668$		−	1.21175e8i		−	0.406521i
$669$	2.60081e6			0.00868620
$670$			5.14412e8i			1.71036i
$671$	5.17070e8	−	2.37451e6i	1.71152	−	0.00785970i
$672$	−2.84811e7			−0.0938532
$673$		−	8.78526e7i		−	0.288210i	−0.989562	−	0.144105i	$-0.953970\pi$
$673$		−	8.78526e7i		−	0.288210i	0.989562	−	0.144105i	$-0.0460304\pi$
$674$	−3.43801e8			−1.12287
$675$	−4.76847e7			−0.155049
$676$	4.56081e7			0.147639
$677$			2.96010e8i			0.953983i	0.878908	+	0.476992i	$0.158273\pi$
$677$			2.96010e8i			0.953983i	−0.878908	+	0.476992i	$0.841727\pi$
$678$		−	1.74511e8i		−	0.559931i
$679$			2.58276e7i			0.0825038i
$680$	3.50530e8			1.11480
$681$			1.55365e8i			0.491940i
$682$	2.53821e7	−	116561.i	0.0800156	−	0.000367451i
$683$	−1.53227e8			−0.480920			−0.240460	−	0.970659i	$-0.577298\pi$
$683$	−1.53227e8			−0.480920			−0.240460	+	0.970659i	$0.577298\pi$
$684$		−	3.16534e7i		−	0.0989128i
$685$	6.29618e8			1.95887
$686$	1.63331e8			0.505935
$687$	3.44518e7			0.106253
$688$			7.97454e7i			0.244873i
$689$			2.27523e8i			0.695613i
$690$			3.42784e8i			1.04345i
$691$	−1.45410e8			−0.440716			−0.220358	−	0.975419i	$-0.570723\pi$
$691$	−1.45410e8			−0.440716			−0.220358	+	0.975419i	$0.570723\pi$
$692$		−	961488.i		−	0.00290152i
$693$	3.45021e7	−	158442.i	0.103668	−	0.000476069i
$694$	−4.74299e8			−1.41897
$695$		−	6.48896e7i		−	0.193295i
$696$	−2.80698e8			−0.832553
$697$	−4.00967e8			−1.18416
$698$	−5.04500e8			−1.48353
$699$		−	1.97910e8i		−	0.579478i
$700$			2.31584e7i			0.0675173i
$701$		−	1.72482e8i		−	0.500714i	−0.968154	−	0.250357i	$-0.919452\pi$
$701$		−	1.72482e8i		−	0.500714i	0.968154	−	0.250357i	$-0.0805480\pi$
$702$	3.82617e7			0.110600
$703$			3.56866e8i			1.02716i
$704$	1.77000e6	+	3.85433e8i	0.00507289	+	1.10467i
$705$	−2.38064e7			−0.0679401
$706$		−	5.85548e8i		−	1.66398i
$707$	1.27783e8			0.361588
$708$	−9.10468e6			−0.0256546
$709$	−6.64899e7			−0.186559			−0.0932797	−	0.995640i	$-0.529735\pi$
$709$	−6.64899e7			−0.186559			−0.0932797	+	0.995640i	$0.529735\pi$
$710$		−	4.62949e8i		−	1.29347i
$711$			1.67464e8i			0.465921i
$712$		−	5.05875e8i		−	1.40153i
$713$	−5.33974e7			−0.147317
$714$		−	4.27137e7i		−	0.117347i
$715$	−3.30251e8	+	1.51659e6i	−0.903495	+	0.00414907i
$716$	8.57385e7			0.233581
$717$			4.79469e7i			0.130078i
$718$	−1.34870e6			−0.00364369
$719$	1.69376e8			0.455687			0.227843	−	0.973698i	$-0.426833\pi$
$719$	1.69376e8			0.455687			0.227843	+	0.973698i	$0.426833\pi$
$720$	−1.09995e8			−0.294698
$721$		−	1.20250e8i		−	0.320833i
$722$			6.84289e7i			0.181814i
$723$		−	6.84175e7i		−	0.181031i
$724$	1.29077e8			0.340122
$725$			4.08033e8i			1.07073i
$726$	−1.73427e6	−	1.88822e8i	−0.00453217	−	0.493450i
$727$	−4.83665e7			−0.125876			−0.0629378	−	0.998017i	$-0.520047\pi$
$727$	−4.83665e7			−0.125876			−0.0629378	+	0.998017i	$0.520047\pi$
$728$		−	8.75427e7i		−	0.226895i
$729$	1.43489e7			0.0370370
$730$	1.06566e8			0.273937
$731$	1.11161e8			0.284576
$732$		−	1.04437e8i		−	0.266268i
$733$			2.29809e7i			0.0583520i	0.999574	+	0.0291760i	$0.00928833\pi$
$733$			2.29809e7i			0.0583520i	−0.999574	+	0.0291760i	$0.990712\pi$
$734$			4.07623e8i			1.03079i
$735$	−2.78252e8			−0.700771
$736$		−	3.27919e8i		−	0.822494i
$737$	2.73760e6	+	5.96136e8i	0.00683860	+	1.48916i
$738$	1.77354e8			0.441237
$739$			3.23451e8i			0.801448i	0.916199	+	0.400724i	$0.131241\pi$
$739$			3.23451e8i			0.801448i	−0.916199	+	0.400724i	$0.868759\pi$
$740$	−1.36856e8			−0.337730
$741$	1.73935e8			0.427496
$742$	−1.12347e8			−0.275010
$743$		−	8.01300e7i		−	0.195357i	−0.995218	−	0.0976785i	$-0.968858\pi$
$743$		−	8.01300e7i		−	0.195357i	0.995218	−	0.0976785i	$-0.0311417\pi$
$744$		−	2.41522e7i		−	0.0586459i
$745$		−	5.24188e8i		−	1.26771i
$746$	3.51649e8			0.847018
$747$			1.41900e8i			0.340425i
$748$	8.62251e7	−	395966.i	0.206029	−	0.000946135i
$749$	4.73416e7			0.112667
$750$		−	5.43667e7i		−	0.128869i
$751$	3.04740e8			0.719464			0.359732	−	0.933056i	$-0.382868\pi$
$751$	3.04740e8			0.719464			0.359732	+	0.933056i	$0.382868\pi$
$752$	−2.45021e7			−0.0576169
$753$	−1.11739e8			−0.261709
$754$		−	3.27402e8i		−	0.763777i
$755$		−	8.70871e8i		−	2.02355i
$756$		−	6.96865e6i		−	0.0161281i
$757$	3.75853e8			0.866423			0.433211	−	0.901292i	$-0.357380\pi$
$757$	3.75853e8			0.866423			0.433211	+	0.901292i	$0.357380\pi$
$758$			8.06383e7i			0.185154i
$759$	1.82423e6	+	3.97241e8i	0.00417209	+	0.908509i
$760$	−7.04822e8			−1.60560
$761$			8.34472e7i			0.189347i	0.995508	+	0.0946734i	$0.0301807\pi$
$761$			8.34472e7i			0.189347i	−0.995508	+	0.0946734i	$0.969819\pi$
$762$	1.26160e8			0.285139
$763$	1.34190e7			0.0302098
$764$	−4.58460e7			−0.102807
$765$			1.53328e8i			0.342481i
$766$		−	3.61384e8i		−	0.804049i
$767$		−	5.00301e7i		−	0.110878i
$768$	1.94687e8			0.429786
$769$		−	2.86185e8i		−	0.629316i	−0.949205	−	0.314658i	$-0.898110\pi$
$769$		−	2.86185e8i		−	0.629316i	0.949205	−	0.314658i	$-0.101890\pi$
$770$	−748864.	−	1.63072e8i	−0.00164033	−	0.357196i
$771$	−2.65097e8			−0.578418
$772$			9.44720e7i			0.205329i
$773$	4.76538e7			0.103171			0.0515856	−	0.998669i	$-0.483572\pi$
$773$	4.76538e7			0.103171			0.0515856	+	0.998669i	$0.483572\pi$
$774$	−4.91680e7			−0.106038
$775$	−3.51085e7			−0.0754236
$776$		−	1.34502e8i		−	0.287835i
$777$			7.85657e7i			0.167483i
$778$			1.01820e8i			0.216220i
$779$	8.06238e8			1.70550
$780$			6.67033e7i			0.140561i
$781$	−2.46372e6	−	5.36496e8i	−0.00517176	−	1.12620i
$782$	4.91786e8			1.02839
$783$		−	1.22782e8i		−	0.255770i
$784$	−2.86384e8			−0.594293
$785$	−6.15379e8			−1.27214
$786$	−3.21246e8			−0.661561
$787$		−	5.56740e8i		−	1.14216i	−0.820893	−	0.571082i	$-0.806524\pi$
$787$		−	5.56740e8i		−	1.14216i	0.820893	−	0.571082i	$-0.193476\pi$
$788$			1.39093e8i			0.284268i
$789$			3.21552e7i			0.0654667i
$790$	7.91506e8			1.60536
$791$		−	1.74652e8i		−	0.352895i
$792$	−1.79676e8	+	825116.i	−0.361672	+	0.00166088i
$793$	5.73877e8			1.15080
$794$		−	2.08757e8i		−	0.417042i
$795$	4.03286e8			0.802623
$796$	1.11712e8			0.221493
$797$	−9.50514e8			−1.87752			−0.938758	−	0.344578i	$-0.888022\pi$
$797$	−9.50514e8			−1.87752			−0.938758	+	0.344578i	$0.888022\pi$
$798$			8.58859e7i			0.169010i
$799$			3.41546e7i			0.0669590i
$800$		−	2.15605e8i		−	0.421103i
$801$	2.21278e8			0.430567
$802$			7.10370e8i			1.37709i
$803$	1.23496e8	−	567123.i	0.238510	−	0.00109529i
$804$	1.20406e8			0.231676
$805$			3.43061e8i			0.657633i
$806$	2.81707e7			0.0538012
$807$	3.72911e8			0.709552
$808$	−6.65454e8			−1.26149
$809$		−	1.52651e8i		−	0.288307i	−0.989555	−	0.144153i	$-0.953954\pi$
$809$		−	1.52651e8i		−	0.288307i	0.989555	−	0.144153i	$-0.0460459\pi$
$810$		−	6.78191e7i		−	0.127614i
$811$		−	8.42898e8i		−	1.58020i	−0.612977	−	0.790101i	$-0.710028\pi$
$811$		−	8.42898e8i		−	1.58020i	0.612977	−	0.790101i	$-0.289972\pi$
$812$	−5.96300e7			−0.111377
$813$			2.20764e8i			0.410825i
$814$	4.29981e8	−	1.97458e6i	0.797217	−	0.00366101i
$815$	−1.24674e9			−2.30305
$816$			1.57809e8i			0.290442i
$817$	−2.23514e8			−0.409863
$818$	−5.64493e8			−1.03133
$819$	3.82926e7			0.0697049
$820$			3.09189e8i			0.560767i
$821$			9.26534e8i			1.67429i	0.546978	+	0.837147i	$0.315778\pi$
$821$			9.26534e8i			1.67429i	−0.546978	+	0.837147i	$0.684222\pi$
$822$			3.99544e8i			0.719365i
$823$	1.31419e8			0.235754			0.117877	−	0.993028i	$-0.462391\pi$
$823$	1.31419e8			0.235754			0.117877	+	0.993028i	$0.462391\pi$
$824$			6.26224e8i			1.11930i
$825$	1.19942e6	+	2.61184e8i	0.00213604	+	0.465141i
$826$	2.47039e7			0.0438355
$827$		−	8.17101e8i		−	1.44464i	−0.691560	−	0.722319i	$-0.743076\pi$
$827$		−	8.17101e8i		−	1.44464i	0.691560	−	0.722319i	$-0.256924\pi$
$828$	8.02339e7			0.141341
$829$	−4.96211e8			−0.870969			−0.435485	−	0.900196i	$-0.643423\pi$
$829$	−4.96211e8			−0.870969			−0.435485	+	0.900196i	$0.643423\pi$
$830$	6.70682e8			1.17296
$831$		−	1.39227e8i		−	0.242617i
$832$			4.27778e8i			0.742760i
$833$			3.99203e8i			0.690652i
$834$	4.11778e7			0.0709847
$835$		−	1.18023e9i		−	2.02725i
$836$	−1.73376e8	+	796182.i	−0.296735	+	0.00136268i
$837$	1.05646e7			0.0180167
$838$			4.42700e8i			0.752276i
$839$	−4.43438e8			−0.750840			−0.375420	−	0.926855i	$-0.622502\pi$
$839$	−4.43438e8			−0.750840			−0.375420	+	0.926855i	$0.622502\pi$
$840$	−1.55170e8			−0.261800
$841$	−4.55810e8			−0.766296
$842$			6.99297e8i			1.17145i
$843$		−	4.38790e8i		−	0.732443i
$844$			2.83111e8i			0.470901i
$845$	4.44218e8			0.736251
$846$		−	1.51071e7i		−	0.0249500i
$847$	−1.73567e6	−	1.88975e8i	−0.00285639	−	0.310995i
$848$	4.15072e8			0.680668
$849$		−	3.60175e7i		−	0.0588559i
$850$	3.23347e8			0.526516
$851$	−9.04569e8			−1.46775
$852$	−1.08360e8			−0.175207
$853$			7.61169e8i			1.22641i	0.789926	+	0.613203i	$0.210119\pi$
$853$			7.61169e8i			1.22641i	−0.789926	+	0.613203i	$0.789881\pi$
$854$			2.83370e8i			0.454967i
$855$		−	3.08301e8i		−	0.493261i
$856$	−2.46541e8			−0.393068
$857$			5.58230e8i			0.886892i	0.896301	+	0.443446i	$0.146244\pi$
$857$			5.58230e8i			0.886892i	−0.896301	+	0.443446i	$0.853756\pi$
$858$	−962401.	−	2.09571e8i	−0.00152368	−	0.331795i
$859$	3.18162e8			0.501960			0.250980	−	0.967992i	$-0.419247\pi$
$859$	3.18162e8			0.501960			0.250980	+	0.967992i	$0.419247\pi$
$860$		−	8.57167e7i		−	0.134763i
$861$	1.77497e8			0.278088
$862$	1.01312e9			1.58175
$863$	5.96968e8			0.928793			0.464396	−	0.885627i	$-0.346271\pi$
$863$	5.96968e8			0.928793			0.464396	+	0.885627i	$0.346271\pi$
$864$			6.48780e7i			0.100590i
$865$		−	9.36478e6i		−	0.0144694i
$866$			2.20111e8i			0.338913i
$867$	−1.56291e8			−0.239815
$868$		−	5.13076e6i		−	0.00784553i
$869$	9.17251e8	−	4.21223e6i	1.39775	−	0.00641879i
$870$	−5.80321e8			−0.881274
$871$			6.61629e8i			1.00129i
$872$	−6.98822e7			−0.105394
$873$	5.88334e7			0.0884262
$874$	−9.88851e8			−1.48114
$875$		−	5.44106e7i		−	0.0812194i
$876$		−	2.49434e7i		−	0.0371060i
$877$		−	7.72686e7i		−	0.114552i	−0.998358	−	0.0572762i	$-0.981758\pi$
$877$		−	7.72686e7i		−	0.114552i	0.998358	−	0.0572762i	$-0.0182416\pi$
$878$	1.11869e9			1.65283
$879$			3.25360e8i			0.479068i
$880$	2.76673e6	+	6.02479e8i	0.00405993	+	0.884085i
$881$	−8.67528e8			−1.26869			−0.634345	−	0.773050i	$-0.718730\pi$
$881$	−8.67528e8			−1.26869			−0.634345	+	0.773050i	$0.718730\pi$
$882$		−	1.76574e8i		−	0.257348i
$883$	−1.92633e8			−0.279800			−0.139900	−	0.990166i	$-0.544678\pi$
$883$	−1.92633e8			−0.279800			−0.139900	+	0.990166i	$0.544678\pi$
$884$	9.56981e7			0.138531
$885$	−8.86786e7			−0.127935
$886$		−	2.65778e8i		−	0.382136i
$887$			5.93411e8i			0.850325i	0.905117	+	0.425162i	$0.139783\pi$
$887$			5.93411e8i			0.850325i	−0.905117	+	0.425162i	$0.860217\pi$
$888$		−	4.09146e8i		−	0.584304i
$889$	1.26262e8			0.179708
$890$		−	1.04586e9i		−	1.48355i
$891$	−360919.	−	7.85934e7i	−0.000510243	−	0.111110i
$892$	−2.87726e6			−0.00405400
$893$		−	6.86758e7i		−	0.0964382i
$894$	3.32641e8			0.465546
$895$	8.35083e8			1.16482
$896$	−9.42968e7			−0.131091
$897$			4.40884e8i			0.610867i
$898$			9.89242e8i			1.36607i
$899$		−	9.03999e7i		−	0.124420i
$900$	5.27533e7			0.0723639
$901$		−	5.78587e8i		−	0.791032i
$902$	−4.46100e6	−	9.71423e8i	−0.00607873	−	1.32370i
$903$	−4.92077e7			−0.0668298
$904$			9.09535e8i			1.23116i
$905$	1.25720e9			1.69613
$906$	5.52639e8			0.743117
$907$	−5.96148e8			−0.798973			−0.399486	−	0.916739i	$-0.630812\pi$
$907$	−5.96148e8			−0.798973			−0.399486	+	0.916739i	$0.630812\pi$
$908$		−	1.71879e8i		−	0.229597i
$909$		−	2.91081e8i		−	0.387545i
$910$		−	1.80987e8i		−	0.240173i
$911$	−3.63584e8			−0.480894			−0.240447	−	0.970662i	$-0.577294\pi$
$911$	−3.63584e8			−0.480894			−0.240447	+	0.970662i	$0.577294\pi$
$912$		−	3.17311e8i		−	0.418312i
$913$	7.77231e8	−	3.56923e6i	1.02126	−	0.00468989i
$914$	−1.07968e9			−1.41402
$915$		−	1.01720e9i		−	1.32783i
$916$	−3.81138e7			−0.0495902
$917$	−3.21505e8			−0.416946
$918$	−9.72989e7			−0.125771
$919$		−	4.73761e8i		−	0.610397i	−0.952289	−	0.305199i	$-0.901277\pi$
$919$		−	4.73761e8i		−	0.610397i	0.952289	−	0.305199i	$-0.0987228\pi$
$920$		−	1.78655e9i		−	2.29431i
$921$			7.52332e8i			0.963009i
$922$	−1.19998e9			−1.53102
$923$		−	5.95438e8i		−	0.757236i
$924$	−3.81695e7	+	175283.i	−0.0483838	+	0.000222190i
$925$	−5.94749e8			−0.751465
$926$		−	1.88815e8i		−	0.237795i
$927$	−2.73921e8			−0.343863
$928$	5.55154e8			0.694656
$929$	5.40376e8			0.673983			0.336992	−	0.941508i	$-0.390591\pi$
$929$	5.40376e8			0.673983			0.336992	+	0.941508i	$0.390591\pi$
$930$		−	4.99327e7i		−	0.0620778i
$931$		−	8.02691e8i		−	0.994717i
$932$			2.18947e8i			0.270452i
$933$	−5.71582e8			−0.703775
$934$			2.49088e8i			0.305712i
$935$	8.39823e8	−	3.85666e6i	1.02743	−	0.00471821i
$936$	−1.99416e8			−0.243183
$937$		−	3.23723e8i		−	0.393509i	−0.980453	−	0.196755i	$-0.936960\pi$
$937$		−	3.23723e8i		−	0.393509i	0.980453	−	0.196755i	$-0.0630402\pi$
$938$	−3.26700e8			−0.395860
$939$	−1.82299e8			−0.220184
$940$	2.63369e7			0.0317088
$941$		−	9.06630e8i		−	1.08808i	−0.839059	−	0.544041i	$-0.816894\pi$
$941$		−	9.06630e8i		−	1.08808i	0.839059	−	0.544041i	$-0.183106\pi$
$942$		−	3.90509e8i		−	0.467173i
$943$			2.04362e9i			2.43706i
$944$	−9.12702e7			−0.108496
$945$		−	6.78739e7i		−	0.0804280i
$946$	1.23673e6	+	2.69309e8i	0.00146083	+	0.318110i
$947$	8.05666e8			0.948648			0.474324	−	0.880350i	$-0.342692\pi$
$947$	8.05666e8			0.948648			0.474324	+	0.880350i	$0.342692\pi$
$948$		−	1.85264e8i		−	0.217454i
$949$	1.37064e8			0.160370
$950$	−6.50164e8			−0.758319
$951$	3.61980e8			0.420865
$952$			2.22620e8i			0.258019i
$953$		−	1.14404e9i		−	1.32179i	−0.750477	−	0.660897i	$-0.770176\pi$
$953$		−	1.14404e9i		−	1.32179i	0.750477	−	0.660897i	$-0.229824\pi$
$954$			2.55918e8i			0.294751i
$955$	−4.46535e8			−0.512679
$956$		−	5.30434e7i		−	0.0607096i
$957$	−6.72516e8	+	3.08835e6i	−0.767302	+	0.00352363i
$958$	9.36718e7			0.106540
$959$			3.99867e8i			0.453377i
$960$	7.58239e8			0.857023
$961$	−8.79725e8			−0.991236
$962$	4.77221e8			0.536036
$963$		−	1.07841e8i		−	0.120755i
$964$			7.56898e7i			0.0844902i
$965$			9.20146e8i			1.02394i
$966$	−2.17700e8			−0.241506
$967$			1.85371e8i			0.205004i	0.994733	+	0.102502i	$0.0326848\pi$
$967$			1.85371e8i			0.205004i	−0.994733	+	0.102502i	$0.967315\pi$
$968$	9.03883e6	+	9.84122e8i	0.00996520	+	1.08498i
$969$	−4.42314e8			−0.486138
$970$		−	2.78072e8i		−	0.304679i
$971$	−1.08140e9			−1.18121			−0.590607	−	0.806959i	$-0.701112\pi$
$971$	−1.08140e9			−1.18121			−0.590607	+	0.806959i	$0.701112\pi$
$972$	−1.58741e7			−0.0172858
$973$	4.12110e7			0.0447378
$974$			8.01426e8i			0.867335i
$975$			2.89879e8i			0.312754i
$976$		−	1.04693e9i		−	1.12608i
$977$	6.32251e8			0.677963			0.338982	−	0.940793i	$-0.389918\pi$
$977$	6.32251e8			0.677963			0.338982	+	0.940793i	$0.389918\pi$
$978$		−	7.91158e8i		−	0.845760i
$979$	−5.56583e6	−	1.21201e9i	−0.00593173	−	1.29169i
$980$	3.07829e8			0.327062
$981$		−	3.05676e7i		−	0.0323783i
$982$	2.64057e8			0.278845
$983$	−5.06500e8			−0.533235			−0.266618	−	0.963802i	$-0.585906\pi$
$983$	−5.06500e8			−0.533235			−0.266618	+	0.963802i	$0.585906\pi$
$984$	−9.24351e8			−0.970178
$985$			1.35475e9i			1.41759i
$986$			8.32577e8i			0.868547i
$987$		−	1.51193e7i		−	0.0157246i
$988$	−1.92423e8			−0.199520
$989$		−	5.66555e8i		−	0.585671i
$990$	−3.71466e8	+	1.70586e6i	−0.382837	+	0.00175808i
$991$	9.14651e8			0.939798			0.469899	−	0.882720i	$-0.344290\pi$
$991$	9.14651e8			0.939798			0.469899	+	0.882720i	$0.344290\pi$
$992$			4.77673e7i			0.0489323i
$993$	1.12752e9			1.15154
$994$	2.94016e8			0.299373
$995$	1.08806e9			1.10455
$996$		−	1.56983e8i		−	0.158882i
$997$		−	5.92226e8i		−	0.597588i	−0.954318	−	0.298794i	$-0.903416\pi$
$997$		−	5.92226e8i		−	0.597588i	0.954318	−	0.298794i	$-0.0965844\pi$
$998$		−	4.25906e8i		−	0.428472i
$999$	1.78967e8			0.179505

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.7.c.a.10.4	✓	12
3.2	odd	2		99.7.c.d.10.9		12
4.3	odd	2		528.7.j.c.241.11		12
11.10	odd	2	inner	33.7.c.a.10.9	yes	12
33.32	even	2		99.7.c.d.10.4		12
44.43	even	2		528.7.j.c.241.12		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.7.c.a.10.4	✓	12	1.1	even	1	trivial
33.7.c.a.10.9	yes	12	11.10	odd	2	inner
99.7.c.d.10.4		12	33.32	even	2
99.7.c.d.10.9		12	3.2	odd	2
528.7.j.c.241.11		12	4.3	odd	2
528.7.j.c.241.12		12	44.43	even	2

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:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	33.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-6.83773i q^{2} -15.5885 q^{3} +17.2454 q^{4} +167.968 q^{5} +106.590i q^{6} +106.676i q^{7} -555.534i q^{8} +243.000 q^{9} +O(q^{10})\)	\(q-6.83773i q^{2} -15.5885 q^{3} +17.2454 q^{4} +167.968 q^{5} +106.590i q^{6} +106.676i q^{7} -555.534i q^{8} +243.000 q^{9} -1148.52i q^{10} +(-6.11220 - 1330.99i) q^{11} -268.829 q^{12} -1477.21i q^{13} +729.420 q^{14} -2618.37 q^{15} -2694.89 q^{16} +3756.53i q^{17} -1661.57i q^{18} -7553.37i q^{19} +2896.68 q^{20} -1662.91i q^{21} +(-9100.93 + 41.7936i) q^{22} +19146.0 q^{23} +8659.92i q^{24} +12588.4 q^{25} -10100.8 q^{26} -3788.00 q^{27} +1839.67i q^{28} +32413.5i q^{29} +17903.7i q^{30} -2788.96 q^{31} -17127.3i q^{32} +(95.2798 + 20748.0i) q^{33} +25686.1 q^{34} +17918.2i q^{35} +4190.64 q^{36} -47245.9 q^{37} -51647.9 q^{38} +23027.5i q^{39} -93312.2i q^{40} +106739. i q^{41} -11370.5 q^{42} -29591.3i q^{43} +(-105.407 - 22953.4i) q^{44} +40816.3 q^{45} -130915. i q^{46} +9092.07 q^{47} +42009.2 q^{48} +106269. q^{49} -86076.0i q^{50} -58558.5i q^{51} -25475.1i q^{52} -154022. q^{53} +25901.3i q^{54} +(-1026.66 - 223564. i) q^{55} +59262.1 q^{56} +117745. i q^{57} +221635. q^{58} +33867.9 q^{59} -45154.8 q^{60} +388487. i q^{61} +19070.2i q^{62} +25922.2i q^{63} -289585. q^{64} -248125. i q^{65} +(141869. - 651.498i) q^{66} -447890. q^{67} +64782.9i q^{68} -298456. q^{69} +122520. q^{70} +403082. q^{71} -134995. i q^{72} +92785.3i q^{73} +323055. i q^{74} -196233. q^{75} -130261. i q^{76} +(141984. - 652.024i) q^{77} +157456. q^{78} +689152. i q^{79} -452656. q^{80} +59049.0 q^{81} +729852. q^{82} +583952. i q^{83} -28677.6i q^{84} +630978. i q^{85} -202338. q^{86} -505276. i q^{87} +(-739409. + 3395.54i) q^{88} +910609. q^{89} -279091. i q^{90} +157583. q^{91} +330181. q^{92} +43475.6 q^{93} -62169.1i q^{94} -1.26873e6i q^{95} +266988. i q^{96} +242113. q^{97} -726641. i q^{98} +(-1485.27 - 323430. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 204 q^{4} + 224 q^{5} + 2916 q^{9}+O(q^{10}) \) 12 * q - 204 * q^4 + 224 * q^5 + 2916 * q^9	\( 12 q - 204 q^{4} + 224 q^{5} + 2916 q^{9} - 3464 q^{11} + 1944 q^{12} - 6708 q^{14} + 1944 q^{15} + 5316 q^{16} - 44092 q^{20} + 60468 q^{22} - 15304 q^{23} + 95652 q^{25} - 76020 q^{26} - 58608 q^{31} + 4212 q^{33} + 117768 q^{34} - 49572 q^{36} - 202512 q^{37} + 29208 q^{38} - 264708 q^{42} + 434356 q^{44} + 54432 q^{45} + 516920 q^{47} - 377136 q^{48} + 157812 q^{49} - 1042192 q^{53} + 262656 q^{55} + 463020 q^{56} + 1029432 q^{58} - 461008 q^{59} - 417636 q^{60} - 725364 q^{64} + 200232 q^{66} + 364752 q^{67} + 504144 q^{69} - 1028400 q^{70} - 755176 q^{71} + 1364688 q^{75} - 102384 q^{77} + 1219212 q^{78} - 1220764 q^{80} + 708588 q^{81} - 158688 q^{82} + 248760 q^{86} - 2493252 q^{88} - 3513544 q^{89} - 702768 q^{91} + 6899300 q^{92} + 789264 q^{93} + 2370192 q^{97} - 841752 q^{99}+O(q^{100}) \) 12 * q - 204 * q^4 + 224 * q^5 + 2916 * q^9 - 3464 * q^11 + 1944 * q^12 - 6708 * q^14 + 1944 * q^15 + 5316 * q^16 - 44092 * q^20 + 60468 * q^22 - 15304 * q^23 + 95652 * q^25 - 76020 * q^26 - 58608 * q^31 + 4212 * q^33 + 117768 * q^34 - 49572 * q^36 - 202512 * q^37 + 29208 * q^38 - 264708 * q^42 + 434356 * q^44 + 54432 * q^45 + 516920 * q^47 - 377136 * q^48 + 157812 * q^49 - 1042192 * q^53 + 262656 * q^55 + 463020 * q^56 + 1029432 * q^58 - 461008 * q^59 - 417636 * q^60 - 725364 * q^64 + 200232 * q^66 + 364752 * q^67 + 504144 * q^69 - 1028400 * q^70 - 755176 * q^71 + 1364688 * q^75 - 102384 * q^77 + 1219212 * q^78 - 1220764 * q^80 + 708588 * q^81 - 158688 * q^82 + 248760 * q^86 - 2493252 * q^88 - 3513544 * q^89 - 702768 * q^91 + 6899300 * q^92 + 789264 * q^93 + 2370192 * q^97 - 841752 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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