LMFDB - Embedded newform 91.8.u.a.30.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,8,Mod(30,91)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(91, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 1]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("91.30");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	91.u (of order $6$, 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:	$28.4270373191$
Analytic rank:	$0$
Dimension:	$126$
Relative dimension:	$63$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			30.12
Character	$\chi$	$=$	91.30
Dual form			91.8.u.a.88.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-13.4632 + 7.77296i) q^{2} -86.2083 q^{3} +(56.8378 - 98.4459i) q^{4} +(122.410 + 70.6734i) q^{5} +(1160.64 - 670.094i) q^{6} +(-741.564 - 523.093i) q^{7} -222.687i q^{8} +5244.87 q^{9} +O(q^{10})$	\(q+(-13.4632 + 7.77296i) q^{2} -86.2083 q^{3} +(56.8378 - 98.4459i) q^{4} +(122.410 + 70.6734i) q^{5} +(1160.64 - 670.094i) q^{6} +(-741.564 - 523.093i) q^{7} -222.687i q^{8} +5244.87 q^{9} -2197.36 q^{10} +3798.83i q^{11} +(-4899.89 + 8486.86i) q^{12} +(-7840.15 + 1131.60i) q^{13} +(14049.8 + 1278.34i) q^{14} +(-10552.7 - 6092.63i) q^{15} +(9006.17 + 15599.1i) q^{16} +(-16175.3 + 28016.4i) q^{17} +(-70612.6 + 40768.2i) q^{18} +5355.74i q^{19} +(13915.0 - 8033.83i) q^{20} +(63929.0 + 45095.0i) q^{21} +(-29528.1 - 51144.2i) q^{22} +(39506.8 + 68427.8i) q^{23} +19197.5i q^{24} +(-29073.0 - 50356.0i) q^{25} +(96757.3 - 76176.1i) q^{26} -263614. q^{27} +(-93645.2 + 43272.4i) q^{28} +(-122221. + 211692. i) q^{29} +189431. q^{30} +(230005. - 132793. i) q^{31} +(-217818. - 125757. i) q^{32} -327490. i q^{33} -502918. i q^{34} +(-53805.9 - 116441. i) q^{35} +(298107. - 516336. i) q^{36} +(-142989. + 82554.5i) q^{37} +(-41630.0 - 72105.2i) q^{38} +(675886. - 97553.5i) q^{39} +(15738.0 - 27259.1i) q^{40} +(221857. + 128089. i) q^{41} +(-1.21121e6 - 110204. i) q^{42} +(394954. + 684080. i) q^{43} +(373979. + 215917. i) q^{44} +(642024. + 370673. i) q^{45} +(-1.06377e6 - 614170. i) q^{46} +(89342.6 + 51582.0i) q^{47} +(-776407. - 1.34478e6i) q^{48} +(276290. + 775814. i) q^{49} +(782830. + 451967. i) q^{50} +(1.39444e6 - 2.41524e6i) q^{51} +(-334215. + 836149. i) q^{52} +(187521. + 324796. i) q^{53} +(3.54908e6 - 2.04906e6i) q^{54} +(-268476. + 465014. i) q^{55} +(-116486. + 165137. i) q^{56} -461710. i q^{57} -3.80006e6i q^{58} +(-136261. - 78670.0i) q^{59} +(-1.19959e6 + 692583. i) q^{60} -1.69242e6 q^{61} +(-2.06440e6 + 3.57564e6i) q^{62} +(-3.88941e6 - 2.74356e6i) q^{63} +1.60444e6 q^{64} +(-1.03969e6 - 415571. i) q^{65} +(2.54557e6 + 4.40906e6i) q^{66} +275587. i q^{67} +(1.83873e6 + 3.18478e6i) q^{68} +(-3.40582e6 - 5.89905e6i) q^{69} +(1.62949e6 + 1.14943e6i) q^{70} +(2.17538e6 - 1.25596e6i) q^{71} -1.16797e6i q^{72} +(-5.03796e6 + 2.90867e6i) q^{73} +(1.28338e6 - 2.22289e6i) q^{74} +(2.50634e6 + 4.34111e6i) q^{75} +(527251. + 304409. i) q^{76} +(1.98714e6 - 2.81707e6i) q^{77} +(-8.34129e6 + 6.56702e6i) q^{78} +(-1.33657e6 + 2.31501e6i) q^{79} +2.54599e6i q^{80} +1.12552e7 q^{81} -3.98253e6 q^{82} -1.43624e6i q^{83} +(8.07300e6 - 3.73045e6i) q^{84} +(-3.96002e6 + 2.28632e6i) q^{85} +(-1.06347e7 - 6.13992e6i) q^{86} +(1.05364e7 - 1.82496e7i) q^{87} +845949. q^{88} +(5.15440e6 - 2.97589e6i) q^{89} -1.15249e7 q^{90} +(6.40590e6 + 3.26198e6i) q^{91} +8.98192e6 q^{92} +(-1.98283e7 + 1.14479e7i) q^{93} -1.60378e6 q^{94} +(-378509. + 655596. i) q^{95} +(1.87777e7 + 1.08413e7i) q^{96} +(-1.00615e7 + 5.80903e6i) q^{97} +(-9.75010e6 - 8.29731e6i) q^{98} +1.99244e7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 126 q - 3 q^{2} - 164 q^{3} + 3841 q^{4} - 6 q^{6} + 754 q^{7} + 85710 q^{9}+O(q^{10}) $ 126 * q - 3 * q^2 - 164 * q^3 + 3841 * q^4 - 6 * q^6 + 754 * q^7 + 85710 * q^9	\( 126 q - 3 q^{2} - 164 q^{3} + 3841 q^{4} - 6 q^{6} + 754 q^{7} + 85710 q^{9} + 7486 q^{10} - 18328 q^{12} + 1816 q^{13} - 6668 q^{14} - 11817 q^{15} - 237219 q^{16} - 28969 q^{17} + 75423 q^{18} + 12342 q^{20} - 54000 q^{21} + 51388 q^{22} + 17067 q^{23} + 810665 q^{25} + 144300 q^{26} - 528170 q^{27} + 18464 q^{28} + 191096 q^{29} - 432160 q^{30} - 259995 q^{31} + 49149 q^{32} + 87303 q^{35} + 1965131 q^{36} - 571857 q^{37} - 1061954 q^{38} - 1352875 q^{39} + 345362 q^{40} - 636567 q^{41} - 3473694 q^{42} - 659976 q^{43} + 2519268 q^{44} + 1980717 q^{45} - 4068600 q^{46} - 294840 q^{47} + 4726652 q^{48} + 541120 q^{49} - 2908992 q^{50} - 502094 q^{51} + 7809224 q^{52} - 434723 q^{53} + 2119563 q^{54} + 2152196 q^{55} - 858015 q^{56} + 1376949 q^{59} - 3768141 q^{60} - 4854916 q^{61} - 1713436 q^{62} + 10091940 q^{63} - 40270472 q^{64} - 4876182 q^{65} + 8270835 q^{66} + 531379 q^{68} - 311689 q^{69} + 5298534 q^{70} + 1505877 q^{71} - 13207461 q^{73} + 3730527 q^{74} + 5624951 q^{75} + 25297146 q^{76} + 11107478 q^{77} - 9362803 q^{78} + 5012226 q^{79} + 45989766 q^{81} - 34046788 q^{82} - 35428032 q^{84} + 19854117 q^{85} + 5226210 q^{86} + 17331733 q^{87} + 24348310 q^{88} - 43738596 q^{89} + 90517324 q^{90} + 9582031 q^{91} - 8502078 q^{92} - 30517344 q^{93} - 7710416 q^{94} + 14810909 q^{95} + 41499936 q^{96} - 60232128 q^{97} - 65830509 q^{98}+O(q^{100}) \) 126 * q - 3 * q^2 - 164 * q^3 + 3841 * q^4 - 6 * q^6 + 754 * q^7 + 85710 * q^9 + 7486 * q^10 - 18328 * q^12 + 1816 * q^13 - 6668 * q^14 - 11817 * q^15 - 237219 * q^16 - 28969 * q^17 + 75423 * q^18 + 12342 * q^20 - 54000 * q^21 + 51388 * q^22 + 17067 * q^23 + 810665 * q^25 + 144300 * q^26 - 528170 * q^27 + 18464 * q^28 + 191096 * q^29 - 432160 * q^30 - 259995 * q^31 + 49149 * q^32 + 87303 * q^35 + 1965131 * q^36 - 571857 * q^37 - 1061954 * q^38 - 1352875 * q^39 + 345362 * q^40 - 636567 * q^41 - 3473694 * q^42 - 659976 * q^43 + 2519268 * q^44 + 1980717 * q^45 - 4068600 * q^46 - 294840 * q^47 + 4726652 * q^48 + 541120 * q^49 - 2908992 * q^50 - 502094 * q^51 + 7809224 * q^52 - 434723 * q^53 + 2119563 * q^54 + 2152196 * q^55 - 858015 * q^56 + 1376949 * q^59 - 3768141 * q^60 - 4854916 * q^61 - 1713436 * q^62 + 10091940 * q^63 - 40270472 * q^64 - 4876182 * q^65 + 8270835 * q^66 + 531379 * q^68 - 311689 * q^69 + 5298534 * q^70 + 1505877 * q^71 - 13207461 * q^73 + 3730527 * q^74 + 5624951 * q^75 + 25297146 * q^76 + 11107478 * q^77 - 9362803 * q^78 + 5012226 * q^79 + 45989766 * q^81 - 34046788 * q^82 - 35428032 * q^84 + 19854117 * q^85 + 5226210 * q^86 + 17331733 * q^87 + 24348310 * q^88 - 43738596 * q^89 + 90517324 * q^90 + 9582031 * q^91 - 8502078 * q^92 - 30517344 * q^93 - 7710416 * q^94 + 14810909 * q^95 + 41499936 * q^96 - 60232128 * q^97 - 65830509 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/91\mathbb{Z}\right)^\times$.

$n$	$15$	$66$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−13.4632	+	7.77296i	−1.18999	+	0.687039i	−0.958303	−	0.285752i	$-0.907757\pi$
$2$	−13.4632	+	7.77296i	−1.18999	+	0.687039i	−0.231683	+	0.972791i	$0.574423\pi$
$3$	−86.2083			−1.84342			−0.921711	−	0.387877i	$-0.873208\pi$
$3$	−86.2083			−1.84342			−0.921711	+	0.387877i	$0.873208\pi$
$4$	56.8378	−	98.4459i	0.444045	−	0.769109i
$5$	122.410	+	70.6734i	0.437947	+	0.252849i	0.702726	−	0.711460i	$-0.251966\pi$
$5$	122.410	+	70.6734i	0.437947	+	0.252849i	−0.264779	+	0.964309i	$0.585299\pi$
$6$	1160.64	−	670.094i	2.19365	−	1.26650i
$7$	−741.564	−	523.093i	−0.817157	−	0.576416i
$7$	−741.564	−	523.093i	−0.817157	−	0.576416i
$8$		−	222.687i		−	0.153773i
$9$	5244.87			2.39821
$10$	−2197.36			−0.694868
$11$			3798.83i			0.860548i	0.902698	+	0.430274i	$0.141583\pi$
$11$			3798.83i			0.860548i	−0.902698	+	0.430274i	$0.858417\pi$
$12$	−4899.89	+	8486.86i	−0.818562	+	1.41779i
$13$	−7840.15	+	1131.60i	−0.989744	+	0.142854i
$13$	−7840.15	+	1131.60i	−0.989744	+	0.142854i
$14$	14049.8	+	1278.34i	1.36843	+	0.124509i
$15$	−10552.7	−	6092.63i	−0.807321	−	0.466107i
$16$	9006.17	+	15599.1i	0.549693	+	0.952096i
$17$	−16175.3	+	28016.4i	−0.798509	+	1.38306i	0.122077	+	0.992521i	$0.461044\pi$
$17$	−16175.3	+	28016.4i	−0.798509	+	1.38306i	−0.920587	+	0.390538i	$0.872289\pi$
$18$	−70612.6	+	40768.2i	−2.85383	+	1.64766i
$19$			5355.74i			0.179136i	0.995981	+	0.0895679i	$0.0285486\pi$
$19$			5355.74i			0.179136i	−0.995981	+	0.0895679i	$0.971451\pi$
$20$	13915.0	−	8033.83i	0.388936	−	0.224552i
$21$	63929.0	+	45095.0i	1.50636	+	1.06258i
$22$	−29528.1	−	51144.2i	−0.591230	−	1.02404i
$23$	39506.8	+	68427.8i	0.677056	+	1.17270i	0.975863	+	0.218382i	$0.0700780\pi$
$23$	39506.8	+	68427.8i	0.677056	+	1.17270i	−0.298807	+	0.954314i	$0.596589\pi$
$24$			19197.5i			0.283468i
$25$	−29073.0	−	50356.0i	−0.372135	−	0.644557i
$26$	96757.3	−	76176.1i	1.07964	−	0.849987i
$27$	−263614.			−2.57748
$28$	−93645.2	+	43272.4i	−0.806181	+	0.372528i
$29$	−122221.	+	211692.i	−0.930575	+	1.61180i	−0.148235	+	0.988952i	$0.547359\pi$
$29$	−122221.	+	211692.i	−0.930575	+	1.61180i	−0.782340	+	0.622852i	$0.785974\pi$
$30$	189431.			1.28093
$31$	230005.	−	132793.i	1.38666	−	0.800591i	0.393726	−	0.919228i	$-0.371186\pi$
$31$	230005.	−	132793.i	1.38666	−	0.800591i	0.992938	+	0.118637i	$0.0378525\pi$
$32$	−217818.	−	125757.i	−1.17508	−	0.678435i
$33$		−	327490.i		−	1.58635i
$34$		−	502918.i		−	2.19443i
$35$	−53805.9	−	116441.i	−0.212125	−	0.459057i
$36$	298107.	−	516336.i	1.06491	−	1.84448i
$37$	−142989.	+	82554.5i	−0.464082	+	0.267938i	−0.713759	−	0.700391i	$-0.753009\pi$
$37$	−142989.	+	82554.5i	−0.464082	+	0.267938i	0.249677	+	0.968329i	$0.419676\pi$
$38$	−41630.0	−	72105.2i	−0.123073	−	0.213169i
$39$	675886.	−	97553.5i	1.82452	−	0.263340i
$40$	15738.0	−	27259.1i	0.0388813	−	0.0673444i
$41$	221857.	+	128089.i	0.502725	+	0.290248i	0.729838	−	0.683620i	$-0.239595\pi$
$41$	221857.	+	128089.i	0.502725	+	0.290248i	−0.227113	+	0.973868i	$0.572929\pi$
$42$	−1.21121e6	−	110204.i	−2.52259	−	0.229522i
$43$	394954.	+	684080.i	0.757542	+	1.31210i	0.944101	+	0.329658i	$0.106933\pi$
$43$	394954.	+	684080.i	0.757542	+	1.31210i	−0.186558	+	0.982444i	$0.559733\pi$
$44$	373979.	+	215917.i	0.661855	+	0.382122i
$45$	642024.	+	370673.i	1.05029	+	0.606383i
$46$	−1.06377e6	−	614170.i	−1.61138	−	0.930328i
$47$	89342.6	+	51582.0i	0.125521	+	0.0724695i	0.561446	−	0.827514i	$-0.310245\pi$
$47$	89342.6	+	51582.0i	0.125521	+	0.0724695i	−0.435925	+	0.899983i	$0.643579\pi$
$48$	−776407.	−	1.34478e6i	−1.01332	−	1.75512i
$49$	276290.	+	775814.i	0.335490	+	0.942044i
$50$	782830.	+	451967.i	0.885671	+	0.511343i
$51$	1.39444e6	−	2.41524e6i	1.47199	−	2.54956i
$52$	−334215.	+	836149.i	−0.329621	+	0.824654i
$53$	187521.	+	324796.i	0.173015	+	0.299672i	0.939473	−	0.342624i	$-0.111316\pi$
$53$	187521.	+	324796.i	0.173015	+	0.299672i	−0.766457	+	0.642295i	$0.777982\pi$
$54$	3.54908e6	−	2.04906e6i	3.06717	−	1.77083i
$55$	−268476.	+	465014.i	−0.217588	+	0.376874i
$56$	−116486.	+	165137.i	−0.0886371	+	0.125657i
$57$		−	461710.i		−	0.330223i
$58$		−	3.80006e6i		−	2.55737i
$59$	−136261.	−	78670.0i	−0.0863750	−	0.0498686i	0.456190	−	0.889882i	$-0.349214\pi$
$59$	−136261.	−	78670.0i	−0.0863750	−	0.0498686i	−0.542565	+	0.840014i	$0.682547\pi$
$60$	−1.19959e6	+	692583.i	−0.716974	+	0.413945i
$61$	−1.69242e6			−0.954673			−0.477336	−	0.878721i	$-0.658398\pi$
$61$	−1.69242e6			−0.954673			−0.477336	+	0.878721i	$0.658398\pi$
$62$	−2.06440e6	+	3.57564e6i	−1.10007	+	1.90538i
$63$	−3.88941e6	−	2.74356e6i	−1.95971	−	1.38236i
$64$	1.60444e6			0.765058
$65$	−1.03969e6	−	415571.i	−0.469576	−	0.187693i
$66$	2.54557e6	+	4.40906e6i	1.08989	+	1.88774i
$67$			275587.i			0.111943i	0.998432	+	0.0559714i	$0.0178256\pi$
$67$			275587.i			0.111943i	−0.998432	+	0.0559714i	$0.982174\pi$
$68$	1.83873e6	+	3.18478e6i	0.709148	+	1.22828i
$69$	−3.40582e6	−	5.89905e6i	−1.24810	−	2.16177i
$70$	1.62949e6	+	1.14943e6i	0.567816	+	0.400533i
$71$	2.17538e6	−	1.25596e6i	0.721324	−	0.416457i	−0.0939155	−	0.995580i	$-0.529938\pi$
$71$	2.17538e6	−	1.25596e6i	0.721324	−	0.416457i	0.815240	+	0.579123i	$0.196605\pi$
$72$		−	1.16797e6i		−	0.368779i
$73$	−5.03796e6	+	2.90867e6i	−1.51574	+	0.875112i	−0.515910	+	0.856643i	$0.672546\pi$
$73$	−5.03796e6	+	2.90867e6i	−1.51574	+	0.875112i	−0.999829	+	0.0184694i	$0.994121\pi$
$74$	1.28338e6	−	2.22289e6i	0.368168	−	0.637685i
$75$	2.50634e6	+	4.34111e6i	0.686002	+	1.18819i
$76$	527251.	+	304409.i	0.137775	+	0.0795443i
$77$	1.98714e6	−	2.81707e6i	0.496033	−	0.703202i
$78$	−8.34129e6	+	6.56702e6i	−1.99022	+	1.56688i
$79$	−1.33657e6	+	2.31501e6i	−0.304998	+	0.528272i	−0.977261	−	0.212041i	$-0.931989\pi$
$79$	−1.33657e6	+	2.31501e6i	−0.304998	+	0.528272i	0.672263	+	0.740312i	$0.265322\pi$
$80$			2.54599e6i			0.555957i
$81$	1.12552e7			2.35318
$82$	−3.98253e6			−0.797647
$83$		−	1.43624e6i		−	0.275710i	−0.990452	−	0.137855i	$-0.955979\pi$
$83$		−	1.43624e6i		−	0.275710i	0.990452	−	0.137855i	$-0.0440208\pi$
$84$	8.07300e6	−	3.73045e6i	1.48613	−	0.686725i
$85$	−3.96002e6	+	2.28632e6i	−0.699409	+	0.403804i
$86$	−1.06347e7	−	6.13992e6i	−1.80293	−	1.04092i
$87$	1.05364e7	−	1.82496e7i	1.71544	−	2.97123i
$88$	845949.			0.132329
$89$	5.15440e6	−	2.97589e6i	0.775020	−	0.447458i	−0.0596427	−	0.998220i	$-0.518996\pi$
$89$	5.15440e6	−	2.97589e6i	0.775020	−	0.447458i	0.834662	+	0.550762i	$0.185663\pi$
$90$	−1.15249e7			−1.66644
$91$	6.40590e6	+	3.26198e6i	0.891119	+	0.453770i
$92$	8.98192e6			1.20257
$93$	−1.98283e7	+	1.14479e7i	−2.55621	+	1.47583i
$94$	−1.60378e6			−0.199158
$95$	−378509.	+	655596.i	−0.0452942	+	0.0784519i
$96$	1.87777e7	+	1.08413e7i	2.16617	+	1.25064i
$97$	−1.00615e7	+	5.80903e6i	−1.11934	+	0.646253i	−0.941233	−	0.337758i	$-0.890332\pi$
$97$	−1.00615e7	+	5.80903e6i	−1.11934	+	0.646253i	−0.178110	+	0.984011i	$0.556998\pi$
$98$	−9.75010e6	−	8.29731e6i	−1.04645	−	0.890525i
$99$			1.99244e7i			2.06377i
$100$	−6.60979e6			−0.660979
$101$	−6.68607e6			−0.645723			−0.322861	−	0.946446i	$-0.604645\pi$
$101$	−6.68607e6			−0.645723			−0.322861	+	0.946446i	$0.604645\pi$
$102$			4.33558e7i			4.04526i
$103$	7.79158e6	−	1.34954e7i	0.702580	−	1.21690i	−0.264978	−	0.964254i	$-0.585365\pi$
$103$	7.79158e6	−	1.34954e7i	0.702580	−	1.21690i	0.967558	−	0.252649i	$-0.0813018\pi$
$104$	251993.	+	1.74590e6i	0.0219670	+	0.152196i
$105$	4.63852e6	+	1.00381e7i	0.391036	+	0.846235i
$106$	−5.04926e6	−	2.91519e6i	−0.411772	−	0.237737i
$107$	−427997.	−	741313.i	−0.0337752	−	0.0585004i	0.848644	−	0.528965i	$-0.177420\pi$
$107$	−427997.	−	741313.i	−0.0337752	−	0.0585004i	−0.882419	+	0.470465i	$0.844086\pi$
$108$	−1.49832e7	+	2.59517e7i	−1.14452	+	1.98236i
$109$	−4.71327e6	+	2.72121e6i	−0.348602	+	0.201265i	−0.664069	−	0.747671i	$-0.731172\pi$
$109$	−4.71327e6	+	2.72121e6i	−0.348602	+	0.201265i	0.315467	+	0.948936i	$0.397839\pi$
$110$		−	8.34741e6i		−	0.597967i
$111$	1.23268e7	−	7.11688e6i	0.855500	−	0.493923i
$112$	1.48116e6	−	1.62788e7i	0.0996181	−	1.09486i
$113$	239525.	+	414870.i	0.0156162	+	0.0270481i	0.873728	−	0.486415i	$-0.161696\pi$
$113$	239525.	+	414870.i	0.0156162	+	0.0270481i	−0.858112	+	0.513463i	$0.828362\pi$
$114$	3.58885e6	+	6.21607e6i	0.226876	+	0.392961i
$115$			1.11683e7i			0.684771i
$116$	1.38935e7	+	2.40642e7i	0.826435	+	1.43143i
$117$	−4.11206e7	+	5.93511e6i	−2.37361	+	0.342593i
$118$	2.44600e6			0.137047
$119$	2.66502e7	−	1.23148e7i	1.44972	−	0.669902i
$120$	−1.35675e6	+	2.34996e6i	−0.0716746	+	0.124144i
$121$	5.05609e6			0.259457
$122$	2.27854e7	−	1.31551e7i	1.13605	−	0.655897i
$123$	−1.91259e7	−	1.10424e7i	−0.926734	−	0.535050i
$124$		−	3.01907e7i		−	1.42199i
$125$		−	1.92615e7i		−	0.882073i
$126$	7.36893e7	+	6.70475e6i	3.28176	+	0.298597i
$127$	1.44273e7	−	2.49888e7i	0.624987	−	1.08251i	−0.363556	−	0.931572i	$-0.618438\pi$
$127$	1.44273e7	−	2.49888e7i	0.624987	−	1.08251i	0.988543	−	0.150937i	$-0.0482291\pi$
$128$	6.27982e6	−	3.62566e6i	0.264675	−	0.152810i
$129$	−3.40483e7	−	5.89734e7i	−1.39647	−	2.41876i
$130$	1.72277e7	−	2.48654e6i	0.687741	−	0.0992645i
$131$	−1.64632e6	+	2.85151e6i	−0.0639829	+	0.110822i	−0.896242	−	0.443565i	$-0.853714\pi$
$131$	−1.64632e6	+	2.85151e6i	−0.0639829	+	0.110822i	0.832259	+	0.554386i	$0.187047\pi$
$132$	−3.22401e7	−	1.86138e7i	−1.22008	−	0.704412i
$133$	2.80155e6	−	3.97163e6i	0.103257	−	0.146382i
$134$	−2.14212e6	−	3.71027e6i	−0.0769091	−	0.133210i
$135$	−3.22690e7	−	1.86305e7i	−1.12880	−	0.651713i
$136$	6.23888e6	+	3.60202e6i	0.212677	+	0.122789i
$137$	1.53812e7	+	8.88032e6i	0.511055	+	0.295058i	0.733267	−	0.679941i	$-0.237994\pi$
$137$	1.53812e7	+	8.88032e6i	0.511055	+	0.295058i	−0.222212	+	0.974998i	$0.571328\pi$
$138$	9.17061e7	+	5.29466e7i	2.97045	+	1.71499i
$139$	−1.10800e7	−	1.91911e7i	−0.349935	−	0.606105i	0.636303	−	0.771439i	$-0.280463\pi$
$139$	−1.10800e7	−	1.91911e7i	−0.349935	−	0.606105i	−0.986237	+	0.165335i	$0.947130\pi$
$140$	−1.45213e7	−	1.32125e6i	−0.447257	−	0.0406945i
$141$	−7.70207e6	−	4.44679e6i	−0.231388	−	0.133592i
$142$	−1.95250e7	+	3.38183e7i	−0.572244	+	0.991156i
$143$	−4.29876e6	−	2.97834e7i	−0.122933	−	0.851722i
$144$	4.72362e7	+	8.18156e7i	1.31828	+	2.28332i
$145$	−2.99220e7	+	1.72755e7i	−0.815085	+	0.470590i
$146$	4.52179e7	−	7.83197e7i	1.20247	−	2.08274i
$147$	−2.38185e7	−	6.68816e7i	−0.618449	−	1.73658i
$148$			1.87688e7i			0.475906i
$149$		−	2.13733e7i		−	0.529321i	−0.964342	−	0.264661i	$-0.914740\pi$
$149$		−	2.13733e7i		−	0.529321i	0.964342	−	0.264661i	$-0.0852599\pi$
$150$	−6.74865e7	−	3.89633e7i	−1.63267	−	0.942620i
$151$	−6.19455e7	+	3.57642e7i	−1.46417	+	0.845336i	−0.999200	−	0.0399925i	$-0.987267\pi$
$151$	−6.19455e7	+	3.57642e7i	−1.46417	+	0.845336i	−0.464965	+	0.885329i	$0.653933\pi$
$152$	1.19265e6			0.0275462
$153$	−8.48372e7	+	1.46942e8i	−1.91499	+	3.31686i
$154$	−4.85621e6	+	5.33726e7i	−0.107146	+	1.17760i
$155$	3.75398e7			0.809713
$156$	2.88121e7	−	7.20830e7i	0.607630	−	1.52019i
$157$	2.03141e7	+	3.51850e7i	0.418937	+	0.725620i	0.995833	−	0.0911977i	$-0.0290695\pi$
$157$	2.03141e7	+	3.51850e7i	0.418937	+	0.725620i	−0.576896	+	0.816818i	$0.695736\pi$
$158$		−	4.15564e7i		−	0.838182i
$159$	−1.61659e7	−	2.80001e7i	−0.318941	−	0.552421i
$160$	−1.77754e7	−	3.07878e7i	−0.343083	−	0.594237i
$161$	6.49731e6	−	7.14094e7i	0.122700	−	1.34854i
$162$	−1.51531e8	+	8.74862e7i	−2.80026	+	1.61673i
$163$		−	6.79083e7i		−	1.22819i	−0.789232	−	0.614096i	$-0.789521\pi$
$163$		−	6.79083e7i		−	1.22819i	0.789232	−	0.614096i	$-0.210479\pi$
$164$	2.52197e7	−	1.45606e7i	0.446465	−	0.257767i
$165$	2.31449e7	−	4.00881e7i	0.401107	−	0.694738i
$166$	1.11638e7	+	1.93363e7i	0.189423	+	0.328091i
$167$	−3.43309e7	−	1.98210e7i	−0.570397	−	0.329319i	0.186911	−	0.982377i	$-0.440153\pi$
$167$	−3.43309e7	−	1.98210e7i	−0.570397	−	0.329319i	−0.757308	+	0.653058i	$0.773486\pi$
$168$	1.00421e7	−	1.42361e7i	0.163396	−	0.231638i
$169$	6.01875e7	−	1.77439e7i	0.959186	−	0.282777i
$170$	3.55429e7	−	6.15622e7i	0.554858	−	0.961043i
$171$			2.80902e7i			0.429604i
$172$	8.97932e7			1.34553
$173$	6.11302e6			0.0897623			0.0448812	−	0.998992i	$-0.485709\pi$
$173$	6.11302e6			0.0897623			0.0448812	+	0.998992i	$0.485709\pi$
$174$			3.27597e8i			4.71431i
$175$	−4.78136e6	+	5.25501e7i	−0.0674402	+	0.741208i
$176$	−5.92585e7	+	3.42129e7i	−0.819325	+	0.473037i
$177$	1.17468e7	+	6.78201e6i	0.159226	+	0.0919289i
$178$	−4.62630e7	+	8.01298e7i	−0.614842	+	1.06494i
$179$	−5.03836e7			−0.656605			−0.328302	−	0.944573i	$-0.606476\pi$
$179$	−5.03836e7			−0.656605			−0.328302	+	0.944573i	$0.606476\pi$
$180$	7.29825e7	−	4.21364e7i	0.932749	−	0.538523i
$181$	−9.14023e7			−1.14573			−0.572865	−	0.819650i	$-0.694168\pi$
$181$	−9.14023e7			−1.14573			−0.572865	+	0.819650i	$0.694168\pi$
$182$	−1.11599e8	+	5.87634e6i	−1.37218	+	0.0722531i
$183$	1.45901e8			1.75987
$184$	1.52380e7	−	8.79766e6i	0.180329	−	0.104113i
$185$	−2.33376e7			−0.270991
$186$	1.77968e8	−	3.08250e8i	2.02790	−	3.51243i
$187$	−1.06429e8	−	6.14470e7i	−1.19019	−	0.687156i
$188$	1.01561e7	−	5.86361e6i	0.111474	−	0.0643595i
$189$	1.95487e8	+	1.37895e8i	2.10621	+	1.48570i
$190$		−	1.17685e7i		−	0.124476i
$191$	−6.78343e7			−0.704422			−0.352211	−	0.935921i	$-0.614570\pi$
$191$	−6.78343e7			−0.704422			−0.352211	+	0.935921i	$0.614570\pi$
$192$	−1.38316e8			−1.41032
$193$			1.33017e7i			0.133185i	0.997780	+	0.0665927i	$0.0212128\pi$
$193$			1.33017e7i			0.133185i	−0.997780	+	0.0665927i	$0.978787\pi$
$194$	9.03067e7	−	1.56416e8i	0.888002	−	1.53806i
$195$	8.96296e7	+	3.58257e7i	0.865626	+	0.345998i
$196$	9.20794e7	+	1.68959e7i	0.873507	+	0.160282i
$197$	1.25436e7	+	7.24203e6i	0.116893	+	0.0674883i	0.557307	−	0.830307i	$-0.311835\pi$
$197$	1.25436e7	+	7.24203e6i	0.116893	+	0.0674883i	−0.440413	+	0.897795i	$0.645168\pi$
$198$	−1.54871e8	−	2.68245e8i	−1.41789	−	2.45586i
$199$	−8.67943e6	+	1.50332e7i	−0.0780738	+	0.135228i	−0.902419	−	0.430860i	$-0.858210\pi$
$199$	−8.67943e6	+	1.50332e7i	−0.0780738	+	0.135228i	0.824345	+	0.566088i	$0.191544\pi$
$200$	−1.12136e7	+	6.47419e6i	−0.0991154	+	0.0572243i
$201$		−	2.37579e7i		−	0.206358i
$202$	9.00156e7	−	5.19705e7i	0.768401	−	0.443637i
$203$	2.01369e8	−	9.30506e7i	1.68949	−	0.780698i
$204$	−1.58514e8	−	2.74554e8i	−1.30726	−	2.26424i
$205$	1.81050e7	+	3.13588e7i	0.146778	+	0.254227i
$206$			2.42255e8i			1.93080i
$207$	2.07208e8	+	3.58895e8i	1.62372	+	2.81237i
$208$	−8.82618e7	−	1.12108e8i	−0.680066	−	0.863806i
$209$	−2.03455e7			−0.154155
$210$	−1.40475e8	−	9.90901e7i	−1.04672	−	0.738351i
$211$	−5.80515e7	+	1.00548e8i	−0.425427	+	0.736861i	−0.996460	−	0.0840661i	$-0.973209\pi$
$211$	−5.80515e7	+	1.00548e8i	−0.425427	+	0.736861i	0.571033	+	0.820927i	$0.306543\pi$
$212$	4.26332e7			0.307307
$213$	−1.87536e8	+	1.08274e8i	−1.32971	+	0.767706i
$214$	1.15244e7	+	6.65361e6i	0.0803841	+	0.0464098i
$215$			1.11651e8i			0.766174i
$216$			5.87035e7i			0.396347i
$217$	−2.40027e8	−	2.18392e7i	−1.59459	−	0.145087i
$218$	4.23037e7	−	7.32722e7i	0.276554	−	0.479006i
$219$	4.34314e8	−	2.50751e8i	2.79415	−	1.61320i
$220$	3.05191e7	+	5.28607e7i	0.193238	+	0.334698i
$221$	9.51131e7	−	2.37957e8i	0.592744	−	1.48294i
$222$	−1.10638e8	+	1.91631e8i	−0.678689	+	1.17552i
$223$	4.17648e7	+	2.41129e7i	0.252199	+	0.145607i	0.620771	−	0.783992i	$-0.286820\pi$
$223$	4.17648e7	+	2.41129e7i	0.252199	+	0.145607i	−0.368572	+	0.929599i	$0.620153\pi$
$224$	9.57431e7	+	2.07196e8i	0.569166	+	1.23172i
$225$	−1.52484e8	−	2.64111e8i	−0.892456	−	1.54578i
$226$	−6.44953e6	−	3.72364e6i	−0.0371662	−	0.0214579i
$227$	−2.07447e8	−	1.19770e8i	−1.17711	−	0.679605i	−0.221766	−	0.975100i	$-0.571182\pi$
$227$	−2.07447e8	−	1.19770e8i	−1.17711	−	0.679605i	−0.955344	+	0.295495i	$0.904515\pi$
$228$	−4.54534e7	−	2.62426e7i	−0.253977	−	0.146634i
$229$	1.54246e8	+	8.90541e7i	0.848770	+	0.490038i	0.860236	−	0.509896i	$-0.170316\pi$
$229$	1.54246e8	+	8.90541e7i	0.848770	+	0.490038i	−0.0114654	+	0.999934i	$0.503650\pi$
$230$	−8.68109e7	−	1.50361e8i	−0.470465	−	0.814869i
$231$	−1.71308e8	+	2.42855e8i	−0.914399	+	1.29630i
$232$	4.71411e7	+	2.72169e7i	0.247852	+	0.143097i
$233$	1.11436e7	−	1.93013e7i	0.0577139	−	0.0999635i	−0.835725	−	0.549148i	$-0.814952\pi$
$233$	1.11436e7	−	1.93013e7i	0.0577139	−	0.0999635i	0.893439	+	0.449185i	$0.148286\pi$
$234$	5.07480e8	−	3.99534e8i	2.58919	−	2.03844i
$235$	7.29094e6	+	1.26283e7i	0.0366477	+	0.0634756i
$236$	−1.54895e7	+	8.94286e6i	−0.0767088	+	0.0442878i
$237$	1.15223e8	−	1.99573e8i	0.562240	−	0.973828i
$238$	−2.63073e8	+	3.72946e8i	−1.26490	+	1.79319i
$239$			3.23896e8i			1.53466i	0.641251	+	0.767332i	$0.278416\pi$
$239$			3.23896e8i			1.53466i	−0.641251	+	0.767332i	$0.721584\pi$
$240$		−	2.19485e8i		−	1.02486i
$241$	5.62248e7	+	3.24614e7i	0.258743	+	0.149385i	0.623761	−	0.781615i	$-0.285604\pi$
$241$	5.62248e7	+	3.24614e7i	0.258743	+	0.149385i	−0.365018	+	0.931000i	$0.618937\pi$
$242$	−6.80709e7	+	3.93007e7i	−0.308750	+	0.178257i
$243$	−3.93768e8			−1.76043
$244$	−9.61936e7	+	1.66612e8i	−0.423918	+	0.734247i
$245$	−2.10087e7	+	1.14494e8i	−0.0912680	+	0.497393i
$246$	3.43328e8			1.47040
$247$	−6.06057e6	−	4.19899e7i	−0.0255902	−	0.177298i
$248$	−2.95714e7	−	5.12191e7i	−0.123109	−	0.213231i
$249$			1.23815e8i			0.508250i
$250$	1.49719e8	+	2.59320e8i	0.606018	+	1.04965i
$251$	−8.74111e6	−	1.51400e7i	−0.0348906	−	0.0604323i	0.848053	−	0.529912i	$-0.177775\pi$
$251$	−8.74111e6	−	1.51400e7i	−0.0348906	−	0.0604323i	−0.882943	+	0.469479i	$0.844442\pi$
$252$	−4.91157e8	+	2.26959e8i	−1.93339	+	0.893397i
$253$	−2.59946e8	+	1.50080e8i	−1.00916	+	0.582640i
$254$			4.48570e8i			1.71756i
$255$	3.41387e8	−	1.97100e8i	1.28931	−	0.744382i
$256$	−1.59048e8	+	2.75480e8i	−0.592502	+	1.02624i
$257$	−1.87015e8	−	3.23920e8i	−0.687244	−	1.19034i	−0.972726	−	0.231957i	$-0.925487\pi$
$257$	−1.87015e8	−	3.23920e8i	−0.687244	−	1.19034i	0.285482	−	0.958384i	$-0.407846\pi$
$258$	9.16796e8	+	5.29312e8i	3.32356	+	1.91886i
$259$	1.49219e8	+	1.35769e7i	0.533672	+	0.0485571i
$260$	−1.00005e8	+	7.87327e7i	−0.352869	+	0.277810i
$261$	−6.41032e8	+	1.11030e9i	−2.23171	+	3.86544i
$262$		−	5.11870e7i		−	0.175835i
$263$	2.77966e8			0.942209			0.471105	−	0.882077i	$-0.343855\pi$
$263$	2.77966e8			0.942209			0.471105	+	0.882077i	$0.343855\pi$
$264$	−7.29279e7			−0.243938
$265$			5.30110e7i			0.174987i
$266$	−6.84648e6	+	7.52470e7i	−0.0223039	+	0.245134i
$267$	−4.44352e8	+	2.56547e8i	−1.42869	+	0.824854i
$268$	2.71304e7	+	1.56637e7i	0.0860962	+	0.0497076i
$269$	5.92386e7	−	1.02604e8i	0.185555	−	0.321390i	−0.758209	−	0.652012i	$-0.773925\pi$
$269$	5.92386e7	−	1.02604e8i	0.185555	−	0.321390i	0.943763	+	0.330622i	$0.107258\pi$
$270$	5.79257e8			1.79101
$271$	−7.02368e7	+	4.05512e7i	−0.214374	+	0.123769i	−0.603343	−	0.797482i	$-0.706165\pi$
$271$	−7.02368e7	+	4.05512e7i	−0.214374	+	0.123769i	0.388969	+	0.921251i	$0.372831\pi$
$272$	−5.82709e8			−1.75574
$273$	−5.52242e8	−	2.81209e8i	−1.64271	−	0.836490i
$274$	−2.76106e8			−0.810864
$275$	1.91294e8	−	1.10443e8i	0.554672	−	0.320240i
$276$	−7.74316e8			−2.21685
$277$	−2.27591e8	+	3.94198e8i	−0.643391	+	1.11439i	0.341280	+	0.939962i	$0.389140\pi$
$277$	−2.27591e8	+	3.94198e8i	−0.643391	+	1.11439i	−0.984671	+	0.174424i	$0.944194\pi$
$278$	2.98343e8	+	1.72248e8i	0.832835	+	0.480837i
$279$	1.20635e9	−	6.96485e8i	3.32550	−	1.91998i
$280$	−2.59298e7	+	1.19819e7i	−0.0705905	+	0.0326191i
$281$			3.66310e8i			0.984866i	0.870350	+	0.492433i	$0.163892\pi$
$281$			3.66310e8i			0.984866i	−0.870350	+	0.492433i	$0.836108\pi$
$282$	1.38259e8			0.367131
$283$	−3.92682e8			−1.02988			−0.514942	−	0.857225i	$-0.672187\pi$
$283$	−3.92682e8			−1.02988			−0.514942	+	0.857225i	$0.672187\pi$
$284$		−	2.85543e8i		−	0.739702i
$285$	3.26306e7	−	5.65178e7i	0.0834964	−	0.144620i
$286$	2.89380e8	+	3.67564e8i	0.731454	+	0.929078i
$287$	−9.75186e7	−	2.11038e8i	−0.243501	−	0.526957i
$288$	−1.14243e9	−	6.59581e8i	−2.81809	−	1.62703i
$289$	−3.18109e8	−	5.50980e8i	−0.775234	−	1.34275i
$290$	2.68563e8	−	4.65165e8i	0.646627	−	1.11999i
$291$	8.67388e8	−	5.00787e8i	2.06342	−	1.19132i
$292$			6.61288e8i			1.55436i
$293$	2.90357e8	−	1.67638e8i	0.674366	−	0.389345i	−0.123363	−	0.992362i	$-0.539368\pi$
$293$	2.90357e8	−	1.67638e8i	0.674366	−	0.389345i	0.797729	+	0.603016i	$0.206035\pi$
$294$	8.40540e8	+	7.15297e8i	1.92905	+	1.64161i
$295$	−1.11198e7	−	1.92600e7i	−0.0252184	−	0.0436796i
$296$	1.83838e7	+	3.18417e7i	0.0412016	+	0.0713633i
$297$		−	1.00142e9i		−	2.21805i
$298$	1.66134e8	+	2.87752e8i	0.363664	+	0.629885i
$299$	−3.87173e8	−	4.91779e8i	−0.837636	−	1.06395i
$300$	5.69819e8			1.21846
$301$	6.49543e7	−	7.13887e8i	0.137286	−	1.50885i
$302$	5.55988e8	−	9.62999e8i	1.16156	−	2.01188i
$303$	5.76395e8			1.19034
$304$	−8.35450e7	+	4.82348e7i	−0.170554	+	0.0984697i
$305$	−2.07169e8	−	1.19609e8i	−0.418096	−	0.241388i
$306$		−	2.63774e9i		−	5.26269i
$307$		−	1.34559e8i		−	0.265417i	−0.991155	−	0.132709i	$-0.957633\pi$
$307$		−	1.34559e8i		−	0.265417i	0.991155	−	0.132709i	$-0.0423675\pi$
$308$	−1.64385e8	−	3.55742e8i	−0.320578	−	0.693757i
$309$	−6.71699e8	+	1.16342e9i	−1.29515	+	2.24327i
$310$	−5.05405e8	+	2.91796e8i	−0.963548	+	0.556305i
$311$	1.07358e8	+	1.85949e8i	0.202382	+	0.350535i	0.949295	−	0.314386i	$-0.101799\pi$
$311$	1.07358e8	+	1.85949e8i	0.202382	+	0.350535i	−0.746914	+	0.664921i	$0.768465\pi$
$312$	−2.17239e7	−	1.50511e8i	−0.0404945	−	0.280561i
$313$	2.80109e7	−	4.85163e7i	0.0516324	−	0.0894299i	−0.839054	−	0.544048i	$-0.816891\pi$
$313$	2.80109e7	−	4.85163e7i	0.0516324	−	0.0894299i	0.890686	+	0.454618i	$0.150224\pi$
$314$	−5.46984e8	−	3.15801e8i	−0.997058	−	0.575652i
$315$	−2.82205e8	−	6.10716e8i	−0.508720	−	1.10091i
$316$	1.51935e8	+	2.63160e8i	0.270866	+	0.469153i
$317$	8.38351e7	+	4.84022e7i	0.147815	+	0.0853411i	0.572083	−	0.820195i	$-0.306135\pi$
$317$	8.38351e7	+	4.84022e7i	0.147815	+	0.0853411i	−0.424268	+	0.905536i	$0.639469\pi$
$318$	4.35288e8	+	2.51314e8i	0.759070	+	0.438249i
$319$	−8.04183e8	−	4.64295e8i	−1.38703	−	0.800805i
$320$	1.96400e8	+	1.13391e8i	0.335055	+	0.193444i
$321$	3.68969e7	+	6.39074e7i	0.0622620	+	0.107841i
$322$	4.67588e8	+	1.01190e9i	0.780490	+	1.68905i
$323$	−1.50049e8	−	8.66306e7i	−0.247755	−	0.143042i
$324$	6.39720e8	−	1.10803e9i	1.04492	−	1.80985i
$325$	2.84920e8	+	3.61900e8i	0.460396	+	0.584785i
$326$	5.27848e8	+	9.14260e8i	0.843815	+	1.46153i
$327$	4.06323e8	−	2.34591e8i	0.642621	−	0.371017i
$328$	2.85238e7	−	4.94047e7i	0.0446323	−	0.0773055i
$329$	−3.92710e7	−	8.49858e7i	−0.0607976	−	0.131571i
$330$			7.19616e8i			1.10231i
$331$			1.97417e8i			0.299218i	0.988745	+	0.149609i	$0.0478015\pi$
$331$			1.97417e8i			0.299218i	−0.988745	+	0.149609i	$0.952199\pi$
$332$	−1.41392e8	−	8.16324e7i	−0.212051	−	0.122428i
$333$	−7.49957e8	+	4.32988e8i	−1.11297	+	0.642571i
$334$	6.16270e8			0.905020
$335$	−1.94766e7	+	3.37345e7i	−0.0283046	+	0.0490250i
$336$	−1.27688e8	+	1.40337e9i	−0.183638	+	2.01830i
$337$	2.34865e8			0.334283			0.167142	−	0.985933i	$-0.446546\pi$
$337$	2.34865e8			0.334283			0.167142	+	0.985933i	$0.446546\pi$
$338$	−6.72391e8	+	7.06723e8i	−0.947139	+	0.995499i
$339$	−2.06491e7	−	3.57652e7i	−0.0287873	−	0.0498611i
$340$			5.19797e8i			0.717229i
$341$	5.04459e8	+	8.73749e8i	0.688947	+	1.19329i
$342$	−2.18344e8	−	3.78183e8i	−0.295155	−	0.511223i
$343$	2.00936e8	−	7.19841e8i	0.268862	−	0.963179i
$344$	1.52336e8	−	8.79511e7i	0.201766	−	0.116489i
$345$		−	9.62803e8i		−	1.26232i
$346$	−8.23005e7	+	4.75162e7i	−0.106816	+	0.0616702i
$347$	6.70999e7	−	1.16220e8i	0.0862122	−	0.149324i	−0.819695	−	0.572800i	$-0.805857\pi$
$347$	6.70999e7	−	1.16220e8i	0.0862122	−	0.149324i	0.905907	+	0.423476i	$0.139190\pi$
$348$	−1.19773e9	−	2.07454e9i	−1.52347	−	2.63872i
$349$	−1.04193e9	−	6.01557e8i	−1.31205	−	0.757510i	−0.329610	−	0.944117i	$-0.606917\pi$
$349$	−1.04193e9	−	6.01557e8i	−1.31205	−	0.757510i	−0.982435	+	0.186607i	$0.940251\pi$
$350$	−3.44097e8	−	7.44656e8i	−0.428986	−	0.928362i
$351$	2.06678e9	−	2.98306e8i	2.55105	−	0.368203i
$352$	4.77730e8	−	8.27452e8i	0.583826	−	1.01122i
$353$		−	8.87365e7i		−	0.107372i	−0.998558	−	0.0536860i	$-0.982903\pi$
$353$		−	8.87365e7i		−	0.107372i	0.998558	−	0.0536860i	$-0.0170970\pi$
$354$	−2.10865e8			−0.252635
$355$	3.55050e8			0.421202
$356$		−	6.76572e8i		−	0.794766i
$357$	−2.29747e9	+	1.06163e9i	−2.67245	+	1.23491i
$358$	6.78323e8	−	3.91630e8i	0.781351	−	0.451113i
$359$	5.46973e8	+	3.15795e8i	0.623929	+	0.360226i	0.778397	−	0.627772i	$-0.216033\pi$
$359$	5.46973e8	+	3.15795e8i	0.623929	+	0.360226i	−0.154468	+	0.987998i	$0.549366\pi$
$360$	8.25440e7	−	1.42970e8i	0.0932453	−	0.161506i
$361$	8.65188e8			0.967910
$362$	1.23056e9	−	7.10466e8i	1.36340	−	0.787161i
$363$	−4.35877e8			−0.478289
$364$	6.85225e8	−	4.45232e8i	0.744695	−	0.483873i
$365$	−8.22261e8			−0.885084
$366$	−1.96429e9	+	1.13408e9i	−2.09422	+	1.20910i
$367$	−6.97821e8			−0.736907			−0.368454	−	0.929646i	$-0.620113\pi$
$367$	−6.97821e8			−0.736907			−0.368454	+	0.929646i	$0.620113\pi$
$368$	−7.11611e8	+	1.23255e9i	−0.744346	+	1.28925i
$369$	1.16361e9	+	6.71813e8i	1.20564	+	0.696075i
$370$	3.14198e8	−	1.81402e8i	0.322476	−	0.186182i
$371$	3.08398e7	−	3.38948e8i	0.0313547	−	0.344607i
$372$			2.60269e9i			2.62133i
$373$	1.23760e9			1.23481			0.617405	−	0.786646i	$-0.288184\pi$
$373$	1.23760e9			1.23481			0.617405	+	0.786646i	$0.288184\pi$
$374$	1.91050e9			1.88841
$375$			1.66050e9i			1.62603i
$376$	1.14866e7	−	1.98954e7i	0.0111439	−	0.0193017i
$377$	7.18677e8	−	1.79801e9i	0.690779	−	1.72821i
$378$	−3.70372e9	−	3.36990e8i	−3.52709	−	0.320919i
$379$	6.24891e8	+	3.60781e8i	0.589613	+	0.340413i	0.764944	−	0.644096i	$-0.222766\pi$
$379$	6.24891e8	+	3.60781e8i	0.589613	+	0.340413i	−0.175332	+	0.984509i	$0.556100\pi$
$380$	4.30272e7	+	7.45252e7i	0.0402254	+	0.0696724i
$381$	−1.24375e9	+	2.15424e9i	−1.15211	+	1.99552i
$382$	9.13264e8	−	5.27273e8i	0.838252	−	0.483965i
$383$		−	9.72315e8i		−	0.884324i	−0.896935	−	0.442162i	$-0.854212\pi$
$383$		−	9.72315e8i		−	0.884324i	0.896935	−	0.442162i	$-0.145788\pi$
$384$	−5.41373e8	+	3.12562e8i	−0.487907	+	0.281693i
$385$	4.42338e8	−	2.04399e8i	0.395040	−	0.182544i
$386$	−1.03394e8	−	1.79083e8i	−0.0915035	−	0.158489i
$387$	2.07148e9	+	3.58792e9i	1.81674	+	3.14669i
$388$			1.32069e9i			1.14786i
$389$	−8.13115e8	−	1.40836e9i	−0.700372	−	1.21308i	−0.968336	−	0.249650i	$-0.919684\pi$
$389$	−8.13115e8	−	1.40836e9i	−0.700372	−	1.21308i	0.267964	−	0.963429i	$-0.413649\pi$
$390$	−1.48517e9	+	2.14361e8i	−1.26780	+	0.182986i
$391$	−2.55613e9			−2.16254
$392$	1.72764e8	−	6.15262e7i	0.144861	−	0.0515892i
$393$	1.41926e8	−	2.45823e8i	0.117948	−	0.204291i
$394$	−2.25168e8			−0.185468
$395$	−3.27219e8	+	1.88920e8i	−0.267146	+	0.154237i
$396$	1.96147e9	+	1.13246e9i	1.58726	+	0.916407i
$397$			5.64880e8i			0.453096i	0.974000	+	0.226548i	$0.0727439\pi$
$397$			5.64880e8i			0.453096i	−0.974000	+	0.226548i	$0.927256\pi$
$398$		−	2.69859e8i		−	0.214559i
$399$	−2.41517e8	+	3.42387e8i	−0.190346	+	0.269844i
$400$	5.23674e8	−	9.07029e8i	0.409120	−	0.708617i
$401$	2.56606e8	−	1.48151e8i	0.198729	−	0.114736i	−0.397333	−	0.917674i	$-0.630064\pi$
$401$	2.56606e8	−	1.48151e8i	0.198729	−	0.114736i	0.596063	+	0.802938i	$0.296731\pi$
$402$	1.84669e8	+	3.19856e8i	0.141776	+	0.245563i
$403$	−1.65300e9	+	1.30139e9i	−1.25807	+	0.990470i
$404$	−3.80021e8	+	6.58216e8i	−0.286730	+	0.496631i
$405$	1.37775e9	+	7.95443e8i	1.03057	+	0.594999i
$406$	−1.98779e9	+	2.81799e9i	−1.47411	+	2.08977i
$407$	−3.13610e8	−	5.43189e8i	−0.230574	−	0.399365i
$408$	−5.37843e8	−	3.10524e8i	−0.392053	−	0.226352i
$409$	7.72950e8	+	4.46263e8i	0.558625	+	0.322522i	0.752593	−	0.658486i	$-0.228803\pi$
$409$	7.72950e8	+	4.46263e8i	0.558625	+	0.322522i	−0.193969	+	0.981008i	$0.562136\pi$
$410$	−4.87501e8	−	2.81459e8i	−0.349327	−	0.201684i
$411$	−1.32599e9	−	7.65558e8i	−0.942090	−	0.543916i
$412$	−8.85712e8	−	1.53410e9i	−0.623954	−	1.08072i
$413$	5.98941e7	+	1.29616e8i	0.0418368	+	0.0905384i
$414$	−5.57936e9	−	3.22124e9i	−3.86441	−	2.23112i
$415$	1.01504e8	−	1.75809e8i	0.0697129	−	0.120746i
$416$	1.85003e9	+	7.39473e8i	1.25995	+	0.503611i
$417$	9.55186e8	+	1.65443e9i	0.645077	+	1.11731i
$418$	2.73915e8	−	1.58145e8i	0.183442	−	0.105910i
$419$	4.33312e8	−	7.50518e8i	0.287774	−	0.498439i	−0.685504	−	0.728069i	$-0.740418\pi$
$419$	4.33312e8	−	7.50518e8i	0.287774	−	0.498439i	0.973278	+	0.229630i	$0.0737514\pi$
$420$	1.25186e9	+	1.13902e8i	0.824484	+	0.0750172i
$421$		−	1.16130e9i		−	0.758502i	−0.925294	−	0.379251i	$-0.876182\pi$
$421$		−	1.16130e9i		−	0.758502i	0.925294	−	0.379251i	$-0.123818\pi$
$422$		−	1.80493e9i		−	1.16914i
$423$	4.68591e8	+	2.70541e8i	0.301025	+	0.173797i
$424$	7.23279e7	−	4.17585e7i	0.0460814	−	0.0266051i
$425$	1.88106e9			1.18861
$426$	1.68322e9	−	2.91541e9i	1.05489	−	1.82712i
$427$	1.25504e9	+	8.85295e8i	0.780117	+	0.550289i
$428$	−9.73057e7			−0.0599908
$429$	3.70589e8	+	2.56758e9i	0.226617	+	1.57008i
$430$	−8.67858e8	−	1.50317e9i	−0.526392	−	0.911737i
$431$		−	1.28394e9i		−	0.772456i	−0.922403	−	0.386228i	$-0.873778\pi$
$431$		−	1.28394e9i		−	0.772456i	0.922403	−	0.386228i	$-0.126222\pi$
$432$	−2.37415e9	−	4.11216e9i	−1.41682	−	2.45401i
$433$	−1.27483e9	−	2.20807e9i	−0.754649	−	1.30709i	−0.945549	−	0.325481i	$-0.894474\pi$
$433$	−1.27483e9	−	2.20807e9i	−0.754649	−	1.30709i	0.190899	−	0.981610i	$-0.438860\pi$
$434$	3.40127e9	−	1.57169e9i	1.99723	−	0.922897i
$435$	2.57953e9	−	1.48929e9i	1.50255	−	0.867495i
$436$			6.18670e8i			0.357484i
$437$	−3.66482e8	+	2.11589e8i	−0.210072	+	0.121285i
$438$	−3.89816e9	+	6.75181e9i	−2.21666	+	3.83938i
$439$	−4.55178e8	−	7.88391e8i	−0.256777	−	0.444750i	0.708600	−	0.705610i	$-0.249327\pi$
$439$	−4.55178e8	−	7.88391e8i	−0.256777	−	0.444750i	−0.965377	+	0.260860i	$0.915994\pi$
$440$	1.03553e8	+	5.97861e7i	0.0579531	+	0.0334592i
$441$	1.44911e9	+	4.06905e9i	0.804573	+	2.25921i
$442$	5.69103e8	+	3.94296e9i	0.313482	+	2.17192i
$443$	−1.32252e9	+	2.29067e9i	−0.722752	+	1.25184i	0.237140	+	0.971475i	$0.423790\pi$
$443$	−1.32252e9	+	2.29067e9i	−0.722752	+	1.25184i	−0.959893	+	0.280368i	$0.909543\pi$
$444$		−	1.61803e9i		−	0.877296i
$445$	8.41265e8			0.452557
$446$	−7.49715e8			−0.400151
$447$			1.84255e9i			0.975762i
$448$	−1.18980e9	−	8.39273e8i	−0.625172	−	0.440991i
$449$	−8.56509e8	+	4.94506e8i	−0.446550	+	0.257816i	−0.706372	−	0.707841i	$-0.749669\pi$
$449$	−8.56509e8	+	4.94506e8i	−0.446550	+	0.257816i	0.259822	+	0.965656i	$0.416336\pi$
$450$	4.10585e9	+	2.37051e9i	2.12402	+	1.22630i
$451$	−4.86589e8	+	8.42798e8i	−0.249773	+	0.432619i
$452$	5.44563e7			0.0277373
$453$	5.34021e9	−	3.08317e9i	2.69907	−	1.55831i
$454$	3.72386e9			1.86766
$455$	5.53611e8	+	8.52025e8i	0.275528	+	0.424045i
$456$	−1.02817e8			−0.0507793
$457$	1.41080e9	−	8.14524e8i	0.691446	−	0.399206i	−0.112708	−	0.993628i	$-0.535952\pi$
$457$	1.41080e9	−	8.14524e8i	0.691446	−	0.399206i	0.804153	+	0.594422i	$0.202619\pi$
$458$	−2.76885e9			−1.34670
$459$	4.26403e9	−	7.38551e9i	2.05814	−	3.56481i
$460$	1.09948e9	+	6.34783e8i	0.526664	+	0.304069i
$461$	2.79836e9	−	1.61563e9i	1.33030	−	0.768049i	0.344955	−	0.938619i	$-0.387894\pi$
$461$	2.79836e9	−	1.61563e9i	1.33030	−	0.768049i	0.985346	+	0.170570i	$0.0545609\pi$
$462$	4.18645e8	−	4.60117e9i	0.197515	−	2.17081i
$463$			3.86454e8i			0.180952i	0.995899	+	0.0904762i	$0.0288389\pi$
$463$			3.86454e8i			0.180952i	−0.995899	+	0.0904762i	$0.971161\pi$
$464$	−4.40296e9			−2.04612
$465$	−3.23625e9			−1.49264
$466$			3.46476e8i			0.158607i
$467$	−1.26794e9	+	2.19614e9i	−0.576090	+	0.997818i	0.419832	+	0.907602i	$0.362089\pi$
$467$	−1.26794e9	+	2.19614e9i	−0.576090	+	0.997818i	−0.995922	+	0.0902158i	$0.971244\pi$
$468$	−1.75292e9	+	4.38549e9i	−0.790498	+	1.97769i
$469$	1.44157e8	−	2.04365e8i	0.0645256	−	0.0914748i
$470$	−1.96318e8	−	1.13344e8i	−0.0872204	−	0.0503567i
$471$	−1.75124e9	−	3.03324e9i	−0.772277	−	1.33762i
$472$	−1.75188e7	+	3.03434e7i	−0.00766844	+	0.0132821i
$473$	−2.59870e9	+	1.50036e9i	−1.12913	+	0.651901i
$474$			3.58251e9i			1.54512i
$475$	2.69694e8	−	1.55708e8i	0.115463	−	0.0666627i
$476$	3.02398e8	−	3.32354e9i	0.128515	−	1.41246i
$477$	9.83526e8	+	1.70352e9i	0.414927	+	0.718674i
$478$	−2.51763e9	−	4.36066e9i	−1.05437	−	1.82623i
$479$			1.20242e8i			0.0499898i	0.999688	+	0.0249949i	$0.00795695\pi$
$479$			1.20242e8i			0.0499898i	−0.999688	+	0.0249949i	$0.992043\pi$
$480$	1.53239e9	+	2.65417e9i	0.632446	+	1.09543i
$481$	1.02763e9	−	8.09046e8i	0.421047	−	0.331486i
$482$	−1.00928e9			−0.410534
$483$	−5.60122e8	+	6.15608e9i	−0.226187	+	2.48593i
$484$	2.87377e8	−	4.97751e8i	0.115211	−	0.199551i
$485$	−1.64217e9			−0.653617
$486$	5.30136e9	−	3.06074e9i	2.09488	−	1.20948i
$487$	2.68573e9	+	1.55061e9i	1.05369	+	0.608346i	0.923679	−	0.383167i	$-0.125167\pi$
$487$	2.68573e9	+	1.55061e9i	1.05369	+	0.608346i	0.130007	+	0.991513i	$0.458500\pi$
$488$			3.76881e8i			0.146803i
$489$			5.85426e9i			2.26408i
$490$	−6.07110e8	−	1.70475e9i	−0.233121	−	0.654596i
$491$	−9.73938e8	+	1.68691e9i	−0.371318	+	0.643142i	−0.989769	−	0.142682i	$-0.954427\pi$
$491$	−9.73938e8	+	1.68691e9i	−0.371318	+	0.643142i	0.618450	+	0.785824i	$0.287761\pi$
$492$	−2.17415e9	+	1.25525e9i	−0.823023	+	0.475173i
$493$	−3.95390e9	−	6.84836e9i	−1.48615	−	2.57408i
$494$	4.07980e8	+	5.18208e8i	0.152263	+	0.193401i
$495$	−1.40812e9	+	2.43894e9i	−0.521822	+	0.903822i
$496$	4.14293e9	+	2.39192e9i	1.52448	+	0.880158i
$497$	−2.27016e9	−	2.06555e8i	−0.829487	−	0.0754724i
$498$	−9.62413e8	−	1.66695e9i	−0.349187	−	0.604810i
$499$	−1.17577e9	−	6.78830e8i	−0.423613	−	0.244573i	0.273009	−	0.962012i	$-0.411981\pi$
$499$	−1.17577e9	−	6.78830e8i	−0.423613	−	0.244573i	−0.696622	+	0.717438i	$0.745315\pi$
$500$	−1.89621e9	−	1.09478e9i	−0.678410	−	0.391680i
$501$	2.95961e9	+	1.70873e9i	1.05148	+	0.607074i
$502$	2.35366e8	+	1.35889e8i	0.0830387	+	0.0479424i
$503$	−1.12185e8	−	1.94310e8i	−0.0393048	−	0.0680780i	0.845704	−	0.533653i	$-0.179181\pi$
$503$	−1.12185e8	−	1.94310e8i	−0.0393048	−	0.0680780i	−0.885009	+	0.465575i	$0.845848\pi$
$504$	−6.10955e8	+	8.66121e8i	−0.212570	+	0.301350i
$505$	−8.18441e8	−	4.72527e8i	−0.282792	−	0.163270i
$506$	2.33313e9	−	4.04109e9i	0.800592	−	1.38667i
$507$	−5.18866e9	+	1.52967e9i	−1.76818	+	0.521278i
$508$	−1.64003e9	−	2.84061e9i	−0.555045	−	0.961366i
$509$	1.39277e9	−	8.04115e8i	0.468130	−	0.270275i	−0.247327	−	0.968932i	$-0.579552\pi$
$509$	1.39277e9	−	8.04115e8i	0.468130	−	0.270275i	0.715457	+	0.698657i	$0.246219\pi$
$510$	−3.06410e9	+	5.30717e9i	−1.02284	+	1.77161i
$511$	5.25747e9	+	4.78360e8i	1.74302	+	0.158592i
$512$		−	4.01694e9i		−	1.32267i
$513$		−	1.41185e9i		−	0.461719i
$514$	5.03563e9	+	2.90732e9i	1.63562	+	0.944327i
$515$	1.90753e9	−	1.10132e9i	0.615385	−	0.355293i
$516$	−7.74092e9			−2.48038
$517$	−1.95951e8	+	3.39397e8i	−0.0623635	+	0.108017i
$518$	−2.11449e9	+	9.77083e8i	−0.668423	+	0.308871i
$519$	−5.26993e8			−0.165470
$520$	−9.25422e7	+	2.31525e8i	−0.0288621	+	0.0722080i
$521$	−4.99141e8	−	8.64538e8i	−0.154629	−	0.267825i	0.778295	−	0.627899i	$-0.216085\pi$
$521$	−4.99141e8	−	8.64538e8i	−0.154629	−	0.267825i	−0.932924	+	0.360074i	$0.882752\pi$
$522$		−	1.99309e10i		−	6.13309i
$523$	4.58799e8	+	7.94664e8i	0.140238	+	0.242900i	0.927586	−	0.373609i	$-0.121880\pi$
$523$	4.58799e8	+	7.94664e8i	0.140238	+	0.242900i	−0.787348	+	0.616509i	$0.788546\pi$
$524$	1.87146e8	+	3.24146e8i	0.0568226	+	0.0984196i
$525$	4.12193e8	−	4.53025e9i	0.124321	−	1.36636i
$526$	−3.74231e9	+	2.16062e9i	−1.12122	+	0.647334i
$527$			8.59187e9i			2.55712i
$528$	5.10857e9	−	2.94944e9i	1.51036	−	0.872007i
$529$	−1.41917e9	+	2.45807e9i	−0.416811	+	0.721937i
$530$	−4.12053e8	−	7.13696e8i	−0.120223	−	0.208232i
$531$	−7.14669e8	−	4.12615e8i	−0.207145	−	0.119595i
$532$	−2.31756e8	−	5.01540e8i	−0.0667330	−	0.144416i
$533$	−1.88434e9	−	7.53186e8i	−0.539032	−	0.215455i
$534$	3.98825e9	−	6.90786e9i	1.13341	−	1.96313i
$535$		−	1.20992e8i		−	0.0341601i
$536$	6.13695e7			0.0172138
$537$	4.34349e9			1.21040
$538$			1.84184e9i			0.509933i
$539$	−2.94718e9	+	1.04958e9i	−0.810674	+	0.288705i
$540$	−3.66819e9	+	2.11783e9i	−1.00248	+	0.578780i
$541$	−1.88160e9	−	1.08634e9i	−0.510902	−	0.294969i	0.222303	−	0.974978i	$-0.428643\pi$
$541$	−1.88160e9	−	1.08634e9i	−0.510902	−	0.294969i	−0.733204	+	0.680009i	$0.761976\pi$
$542$	6.30406e8	−	1.09190e9i	0.170068	−	0.294567i
$543$	7.87964e9			2.11206
$544$	7.04652e9	−	4.06831e9i	1.87663	−	1.08347i
$545$	−7.69268e8			−0.203559
$546$	9.62076e9	−	5.06589e8i	2.52950	−	0.133193i
$547$	2.52825e9			0.660486			0.330243	−	0.943896i	$-0.392869\pi$
$547$	2.52825e9			0.660486			0.330243	+	0.943896i	$0.392869\pi$
$548$	1.74846e9	−	1.00948e9i	0.453863	−	0.262038i
$549$	−8.87655e9			−2.28950
$550$	−1.71695e9	+	2.97384e9i	−0.440035	+	0.762163i
$551$	−1.13377e9	−	6.54582e8i	−0.288732	−	0.166699i
$552$	−1.31364e9	+	7.58431e8i	−0.332422	+	0.191924i
$553$	2.20212e9	−	1.01757e9i	0.553735	−	0.255875i
$554$		−	7.07621e9i		−	1.76814i
$555$	2.01190e9			0.499551
$556$	−2.51904e9			−0.621547
$557$			6.23030e9i			1.52762i	0.645440	+	0.763811i	$0.276674\pi$
$557$			6.23030e9i			1.52762i	−0.645440	+	0.763811i	$0.723326\pi$
$558$	−1.08275e10	+	1.87538e10i	−2.63820	+	4.56950i
$559$	−3.87061e9	−	4.91636e9i	−0.937211	−	1.19043i
$560$	1.33179e9	−	1.88801e9i	0.320462	−	0.454304i
$561$	9.17509e9	+	5.29724e9i	2.19402	+	1.26672i
$562$	−2.84731e9	−	4.93169e9i	−0.676641	−	1.17198i
$563$	2.14671e9	−	3.71821e9i	0.506984	−	0.878122i	−0.492983	−	0.870039i	$-0.664094\pi$
$563$	2.14671e9	−	3.71821e9i	0.506984	−	0.878122i	0.999967	−	0.00808341i	$-0.00257306\pi$
$564$	−8.75537e8	+	5.05492e8i	−0.205493	+	0.118642i
$565$			6.77122e7i			0.0157942i
$566$	5.28674e9	−	3.05230e9i	1.22555	−	0.707570i
$567$	−8.34645e9	−	5.88752e9i	−1.92292	−	1.35641i
$568$	−2.79685e8	−	4.84428e8i	−0.0640398	−	0.110920i
$569$	−3.20709e9	−	5.55484e9i	−0.729824	−	1.26409i	−0.956957	−	0.290228i	$-0.906269\pi$
$569$	−3.20709e9	−	5.55484e9i	−0.729824	−	1.26409i	0.227134	−	0.973864i	$-0.427065\pi$
$570$			1.01454e9i			0.229461i
$571$	−3.44430e9	−	5.96570e9i	−0.774238	−	1.34102i	−0.935222	−	0.354063i	$-0.884800\pi$
$571$	−3.44430e9	−	5.96570e9i	−0.774238	−	1.34102i	0.160984	−	0.986957i	$-0.448533\pi$
$572$	−3.17638e9	−	1.26963e9i	−0.709654	−	0.283654i
$573$	5.84788e9			1.29855
$574$	2.95330e9	+	2.08324e9i	0.651803	+	0.459777i
$575$	2.29717e9	−	3.97881e9i	0.503913	−	0.872803i
$576$	8.41510e9			1.83477
$577$	−1.96924e9	+	1.13694e9i	−0.426760	+	0.246390i	−0.697966	−	0.716131i	$-0.745911\pi$
$577$	−1.96924e9	+	1.13694e9i	−0.426760	+	0.246390i	0.271205	+	0.962522i	$0.412578\pi$
$578$	8.56549e9	+	4.94529e9i	1.84504	+	1.06523i
$579$		−	1.14672e9i		−	0.245517i
$580$			3.92760e9i			0.835852i
$581$	−7.51285e8	+	1.06506e9i	−0.158924	+	0.225298i
$582$	−7.78519e9	+	1.34843e10i	−1.63696	+	2.83530i
$583$	−1.23385e9	+	7.12361e8i	−0.257882	+	0.148888i
$584$	6.47722e8	+	1.12189e9i	0.134569	+	0.233080i
$585$	−5.45302e9	−	2.17962e9i	−1.12614	−	0.450127i
$586$	−2.60608e9	+	4.51386e9i	−0.534991	+	0.926631i
$587$	−7.17410e9	−	4.14197e9i	−1.46398	−	0.845227i	−0.464784	−	0.885424i	$-0.653868\pi$
$587$	−7.17410e9	−	4.14197e9i	−1.46398	−	0.845227i	−0.999192	+	0.0401976i	$0.987201\pi$
$588$	−7.93801e9	−	1.45657e9i	−1.61024	−	0.295467i
$589$	7.11208e8	+	1.23185e9i	0.143414	+	0.248401i
$590$	2.99414e8	+	1.72867e8i	0.0600192	+	0.0346521i
$591$	−1.08136e9	−	6.24323e8i	−0.215484	−	0.124409i
$592$	−2.57556e9	−	1.48700e9i	−0.510206	−	0.294567i
$593$	4.72615e9	+	2.72865e9i	0.930714	+	0.537348i	0.887037	−	0.461698i	$-0.152760\pi$
$593$	4.72615e9	+	2.72865e9i	0.930714	+	0.537348i	0.0436767	+	0.999046i	$0.486093\pi$
$594$	7.78403e9	+	1.34823e10i	1.52388	+	2.63945i
$595$	4.13257e9	+	3.76009e8i	0.804286	+	0.0731794i
$596$	−2.10411e9	−	1.21481e9i	−0.407105	−	0.235042i
$597$	7.48239e8	−	1.29599e9i	0.143923	−	0.249282i
$598$	9.03514e9	+	3.61142e9i	1.72775	+	0.690595i
$599$	−4.13079e9	−	7.15474e9i	−0.785307	−	1.36019i	−0.928815	−	0.370543i	$-0.879172\pi$
$599$	−4.13079e9	−	7.15474e9i	−0.785307	−	1.36019i	0.143508	−	0.989649i	$-0.454162\pi$
$600$	9.66708e8	−	5.58129e8i	0.182711	−	0.105489i
$601$	−1.51548e9	+	2.62489e9i	−0.284767	+	0.493231i	−0.972553	−	0.232683i	$-0.925250\pi$
$601$	−1.51548e9	+	2.62489e9i	−0.284767	+	0.493231i	0.687785	+	0.725914i	$0.258583\pi$
$602$	4.67452e9	+	1.01161e10i	0.873272	+	1.88983i
$603$			1.44542e9i			0.268462i
$604$			8.13104e9i			1.50147i
$605$	6.18915e8	+	3.57331e8i	0.113628	+	0.0656034i
$606$	−7.76010e9	+	4.48029e9i	−1.41649	+	0.817810i
$607$	9.45185e8			0.171536			0.0857682	−	0.996315i	$-0.472666\pi$
$607$	9.45185e8			0.171536			0.0857682	+	0.996315i	$0.472666\pi$
$608$	6.73524e8	−	1.16658e9i	0.121532	−	0.210499i
$609$	−1.73597e10	+	8.02173e9i	−3.11445	+	1.43916i
$610$	3.71887e9			0.663371
$611$	−7.58830e8	−	3.03310e8i	−0.134586	−	0.0537951i
$612$	9.64391e9	+	1.67037e10i	1.70068	+	2.94567i
$613$			5.10887e8i			0.0895804i	0.998996	+	0.0447902i	$0.0142619\pi$
$613$			5.10887e8i			0.0895804i	−0.998996	+	0.0447902i	$0.985738\pi$
$614$	1.04592e9	+	1.81159e9i	0.182352	+	0.315843i
$615$	−1.56080e9	−	2.70339e9i	−0.270573	−	0.468647i
$616$	−6.27325e8	−	4.42510e8i	−0.108133	−	0.0762765i
$617$	−5.00141e9	+	2.88756e9i	−0.857223	+	0.494918i	−0.863081	−	0.505065i	$-0.831469\pi$
$617$	−5.00141e9	+	2.88756e9i	−0.857223	+	0.494918i	0.00585809	+	0.999983i	$0.498135\pi$
$618$		−	2.08844e10i		−	3.55928i
$619$	5.48187e9	−	3.16496e9i	0.928990	−	0.536353i	0.0424982	−	0.999097i	$-0.486468\pi$
$619$	5.48187e9	−	3.16496e9i	0.928990	−	0.536353i	0.886492	+	0.462744i	$0.153135\pi$
$620$	2.13368e9	−	3.69564e9i	0.359549	−	0.622758i
$621$	−1.04146e10	−	1.80386e10i	−1.74510	−	3.02260i
$622$	−2.89074e9	−	1.66897e9i	−0.481663	−	0.278088i
$623$	−5.37898e9	−	4.89416e8i	−0.891234	−	0.0810905i
$624$	7.60890e9	+	9.66467e9i	1.25365	+	1.59236i
$625$	−9.10059e8	+	1.57627e9i	−0.149104	+	0.258256i
$626$			8.70911e8i			0.141894i
$627$	1.75396e9			0.284173
$628$	4.61843e9			0.744107
$629$		−	5.34136e9i		−	0.855804i
$630$	8.54645e9	+	6.02860e9i	1.36174	+	0.960560i
$631$	3.17069e9	−	1.83060e9i	0.502402	−	0.290062i	−0.227303	−	0.973824i	$-0.572991\pi$
$631$	3.17069e9	−	1.83060e9i	0.502402	−	0.290062i	0.729705	+	0.683762i	$0.239658\pi$
$632$	5.15522e8	+	2.97637e8i	0.0812339	+	0.0469004i
$633$	5.00452e9	−	8.66809e9i	0.784241	−	1.35835i
$634$	−1.50491e9			−0.234531
$635$	3.53208e9	−	2.03925e9i	0.547422	−	0.316054i
$636$	−3.67533e9			−0.566496
$637$	−3.04407e9	−	5.76985e9i	−0.466623	−	0.884456i
$638$	1.44358e10			2.20074
$639$	1.14096e10	−	6.58733e9i	1.72988	−	0.998749i
$640$	1.02495e9			0.154551
$641$	4.39450e9	−	7.61150e9i	0.659032	−	1.14148i	−0.321835	−	0.946796i	$-0.604300\pi$
$641$	4.39450e9	−	7.61150e9i	0.659032	−	1.14148i	0.980867	−	0.194681i	$-0.0623670\pi$
$642$	−9.93499e8	−	5.73597e8i	−0.148182	−	0.0855528i
$643$	2.21087e9	−	1.27644e9i	0.327962	−	0.189349i	−0.326974	−	0.945033i	$-0.606029\pi$
$643$	2.21087e9	−	1.27644e9i	0.327962	−	0.189349i	0.654936	+	0.755684i	$0.272696\pi$
$644$	−6.66067e9	−	4.69838e9i	−0.982691	−	0.693183i
$645$		−	9.62524e9i		−	1.41238i
$646$	2.69350e9			0.393101
$647$	3.49385e9			0.507153			0.253576	−	0.967315i	$-0.418393\pi$
$647$	3.49385e9			0.507153			0.253576	+	0.967315i	$0.418393\pi$
$648$		−	2.50639e9i		−	0.361856i
$649$	2.98854e8	−	5.17630e8i	0.0429143	−	0.0743298i
$650$	−6.64895e9	−	2.65764e9i	−0.949635	−	0.379577i
$651$	2.06923e10	+	1.88272e9i	2.93951	+	0.267457i
$652$	−6.68529e9	−	3.85975e9i	−0.944613	−	0.545372i
$653$	4.54125e9	+	7.86568e9i	0.638233	+	1.10545i	0.985820	+	0.167805i	$0.0536679\pi$
$653$	4.54125e9	+	7.86568e9i	0.638233	+	1.10545i	−0.347587	+	0.937648i	$0.612999\pi$
$654$	−3.64693e9	+	6.31667e9i	−0.509807	+	0.883011i
$655$	−4.03051e8	+	2.32702e8i	−0.0560422	+	0.0323560i
$656$			4.61438e9i			0.638190i
$657$	−2.64235e10	+	1.52556e10i	−3.63505	+	2.09870i
$658$	1.18930e9	+	8.38925e8i	0.162743	+	0.114798i
$659$	1.37768e9	+	2.38621e9i	0.187521	+	0.324795i	0.944423	−	0.328733i	$-0.106621\pi$
$659$	1.37768e9	+	2.38621e9i	0.187521	+	0.324795i	−0.756902	+	0.653528i	$0.773288\pi$
$660$	−2.63100e9	−	4.55703e9i	−0.356220	−	0.616990i
$661$			1.44047e10i			1.93998i	0.243139	+	0.969992i	$0.421823\pi$
$661$			1.44047e10i			1.93998i	−0.243139	+	0.969992i	$0.578177\pi$
$662$	−1.53452e9	−	2.65786e9i	−0.205574	−	0.356065i
$663$	−8.19954e9	+	2.05138e10i	−1.09268	+	2.73369i
$664$	−3.19831e8			−0.0423967
$665$	6.23626e8	−	2.88171e8i	0.0822334	−	0.0379992i
$666$	6.73119e9	−	1.16588e10i	0.882942	−	1.52930i
$667$	−1.93142e10			−2.52021
$668$	−3.90258e9	+	2.25316e9i	−0.506564	+	0.292465i
$669$	−3.60048e9	−	2.07874e9i	−0.464910	−	0.268416i
$670$		−	6.05564e8i		−	0.0777854i
$671$		−	6.42922e9i		−	0.821542i
$672$	−8.25385e9	−	1.78620e10i	−1.04921	−	2.27059i
$673$	4.21104e9	−	7.29373e9i	0.532520	−	0.922352i	−0.466759	−	0.884385i	$-0.654578\pi$
$673$	4.21104e9	−	7.29373e9i	0.532520	−	0.922352i	0.999279	−	0.0379677i	$-0.0120884\pi$
$674$	−3.16203e9	+	1.82560e9i	−0.397792	+	0.229665i
$675$	7.66407e9	+	1.32746e10i	0.959171	+	1.66133i
$676$	1.67411e9	−	6.93373e9i	0.208435	−	0.863284i
$677$	−5.37199e9	+	9.30456e9i	−0.665388	+	1.15249i	0.313792	+	0.949492i	$0.398401\pi$
$677$	−5.37199e9	+	9.30456e9i	−0.665388	+	1.15249i	−0.979180	+	0.202994i	$0.934933\pi$
$678$	5.56003e8	+	3.21009e8i	0.0685130	+	0.0395560i
$679$	1.04999e10	+	9.55355e8i	1.28719	+	0.117117i
$680$	5.09134e8	+	8.81845e8i	0.0620941	+	0.107550i
$681$	1.78837e10	+	1.03251e10i	2.16991	+	1.25280i
$682$	−1.35832e10	−	7.84228e9i	−1.63967	−	0.946666i
$683$	−3.64764e9	−	2.10596e9i	−0.438066	−	0.252917i	0.264711	−	0.964328i	$-0.414723\pi$
$683$	−3.64764e9	−	2.10596e9i	−0.438066	−	0.252917i	−0.702777	+	0.711410i	$0.748057\pi$
$684$	2.76537e9	+	1.59658e9i	0.330412	+	0.190764i
$685$	1.25521e9	+	2.17408e9i	0.149210	+	0.258439i
$686$	2.89006e9	+	1.12532e10i	0.341800	+	1.33089i
$687$	−1.32973e10	−	7.67720e9i	−1.56464	−	0.903347i
$688$	−7.11405e9	+	1.23219e10i	−0.832831	+	1.44251i
$689$	−1.83774e9	−	2.33425e9i	−0.214050	−	0.271882i
$690$	7.48382e9	+	1.29624e10i	0.867265	+	1.50215i
$691$	−1.31696e10	+	7.60345e9i	−1.51844	+	0.876673i	−0.518678	+	0.854970i	$0.673576\pi$
$691$	−1.31696e10	+	7.60345e9i	−1.51844	+	0.876673i	−0.999764	+	0.0217032i	$0.993091\pi$
$692$	3.47450e8	−	6.01801e8i	0.0398585	−	0.0690370i
$693$	1.04223e10	−	1.47752e10i	1.18959	−	1.68642i
$694$			2.08626e9i			0.236925i
$695$		−	3.13224e9i		−	0.353922i
$696$	−4.06396e9	−	2.34633e9i	−0.456895	−	0.263789i
$697$	−7.17720e9	+	4.14376e9i	−0.802861	+	0.463532i
$698$	1.87035e10			2.08175
$699$	−9.60673e8	+	1.66393e9i	−0.106391	+	0.184275i
$700$	4.90158e9	+	3.45754e9i	0.540123	+	0.380999i
$701$	6.11492e9			0.670468			0.335234	−	0.942135i	$-0.391185\pi$
$701$	6.11492e9			0.670468			0.335234	+	0.942135i	$0.391185\pi$
$702$	−2.55066e10	+	2.00811e10i	−2.78274	+	2.19083i
$703$	−4.42141e8	−	7.65810e8i	−0.0479973	−	0.0831338i
$704$			6.09500e9i			0.658369i
$705$	−6.28540e8	−	1.08866e9i	−0.0675571	−	0.117012i
$706$	6.89745e8	+	1.19467e9i	0.0737687	+	0.127771i
$707$	4.95815e9	+	3.49744e9i	0.527657	+	0.372205i
$708$	1.33532e9	−	7.70949e8i	0.141407	−	0.0816412i
$709$		−	7.92887e9i		−	0.835505i	−0.908561	−	0.417753i	$-0.862818\pi$
$709$		−	7.92887e9i		−	0.835505i	0.908561	−	0.417753i	$-0.137182\pi$
$710$	−4.78010e9	+	2.75979e9i	−0.501225	+	0.289382i
$711$	−7.01014e9	+	1.21419e10i	−0.731448	+	1.26690i
$712$	−6.62692e8	−	1.14782e9i	−0.0688069	−	0.119177i
$713$	1.81735e10	+	1.04925e10i	1.87770	+	1.08409i
$714$	2.26791e10	−	3.21510e10i	2.33175	−	3.30561i
$715$	1.57868e9	−	3.94959e9i	0.161519	−	0.404092i
$716$	−2.86369e9	+	4.96006e9i	−0.291562	+	0.505000i
$717$		−	2.79225e10i		−	2.82903i
$718$	−9.81864e9			−0.989956
$719$	1.06394e10			1.06750			0.533749	−	0.845643i	$-0.320783\pi$
$719$	1.06394e10			1.06750			0.533749	+	0.845643i	$0.320783\pi$
$720$			1.33534e10i			1.33330i
$721$	−1.28373e10	+	5.93199e9i	−1.27556	+	0.589423i
$722$	−1.16482e10	+	6.72507e9i	−1.15180	+	0.664992i
$723$	−4.84705e9	−	2.79844e9i	−0.476972	−	0.275380i
$724$	−5.19510e9	+	8.99818e9i	−0.508755	+	0.881190i
$725$	1.42133e10			1.38520
$726$	5.86828e9	−	3.38805e9i	0.569157	−	0.328603i
$727$	−1.39899e10			−1.35035			−0.675173	−	0.737659i	$-0.735931\pi$
$727$	−1.39899e10			−1.35035			−0.675173	+	0.737659i	$0.735931\pi$
$728$	7.26399e8	−	1.42651e9i	0.0697775	−	0.137030i
$729$	9.33092e9			0.892027
$730$	1.10702e10	−	6.39140e9i	1.05324	−	0.608087i
$731$	−2.55539e10			−2.41962
$732$	8.29269e9	−	1.43634e10i	0.781459	−	1.35353i
$733$	1.20312e10	+	6.94622e9i	1.12835	+	0.651455i	0.943520	−	0.331315i	$-0.107492\pi$
$733$	1.20312e10	+	6.94622e9i	1.12835	+	0.651455i	0.184833	+	0.982770i	$0.440826\pi$
$734$	9.39487e9	−	5.42413e9i	0.876909	−	0.506284i
$735$	1.81113e9	−	9.87030e9i	0.168245	−	0.916906i
$736$		−	1.98731e10i		−	1.83735i
$737$	−1.04691e9			−0.0963322
$738$	−2.08879e10			−1.91292
$739$			1.61760e10i			1.47440i	0.675675	+	0.737200i	$0.263852\pi$
$739$			1.61760e10i			1.47440i	−0.675675	+	0.737200i	$0.736148\pi$
$740$	−1.32646e9	+	2.29749e9i	−0.120332	+	0.208422i
$741$	5.22472e8	+	3.61988e9i	0.0471736	+	0.326836i
$742$	2.21943e9	+	4.80303e9i	0.199447	+	0.431620i
$743$	1.57538e10	+	9.09544e9i	1.40904	+	0.813510i	0.995296	−	0.0968833i	$-0.0308874\pi$
$743$	1.57538e10	+	9.09544e9i	1.40904	+	0.813510i	0.413744	+	0.910393i	$0.364221\pi$
$744$	2.54930e9	+	4.41551e9i	0.226942	+	0.393075i
$745$	1.51052e9	−	2.61630e9i	0.133838	−	0.231815i
$746$	−1.66620e10	+	9.61983e9i	−1.46941	+	0.848362i
$747$		−	7.53288e9i		−	0.661209i
$748$	−1.20984e10	+	6.98502e9i	−1.05699	+	0.610256i
$749$	−7.03886e7	+	7.73613e8i	−0.00612091	+	0.0672725i
$750$	−1.29070e10	−	2.23556e10i	−1.11715	−	1.93496i
$751$	1.12481e9	+	1.94823e9i	0.0969035	+	0.167842i	0.910401	−	0.413726i	$-0.135773\pi$
$751$	1.12481e9	+	1.94823e9i	0.0969035	+	0.167842i	−0.813498	+	0.581568i	$0.802440\pi$
$752$			1.85822e9i			0.159344i
$753$	7.53557e8	+	1.30520e9i	0.0643181	+	0.111402i
$754$	4.30016e9	+	2.97931e10i	0.365330	+	2.53114i
$755$	−1.01103e10			−0.854969
$756$	2.46862e10	−	1.14072e10i	2.07792	−	0.960183i
$757$	−9.52537e9	+	1.64984e10i	−0.798080	+	1.38231i	0.122786	+	0.992433i	$0.460817\pi$
$757$	−9.52537e9	+	1.64984e10i	−0.798080	+	1.38231i	−0.920865	+	0.389881i	$0.872516\pi$
$758$	−1.12173e10			−0.935508
$759$	2.24095e10	−	1.29381e10i	1.86031	−	1.07405i
$760$	1.45993e8	+	8.42889e7i	0.0120638	+	0.00696503i
$761$			4.95201e9i			0.407320i	0.979042	+	0.203660i	$0.0652837\pi$
$761$			4.95201e9i			0.407320i	−0.979042	+	0.203660i	$0.934716\pi$
$762$		−	3.86705e10i		−	3.16619i
$763$	4.91864e9	+	4.47531e8i	0.400875	+	0.0364743i
$764$	−3.85555e9	+	6.67801e9i	−0.312795	+	0.541777i
$765$	−2.07698e10	+	1.19915e10i	−1.67733	+	0.968405i
$766$	7.55777e9	+	1.30904e10i	0.607565	+	1.05233i
$767$	1.15733e9	+	4.62593e8i	0.0926130	+	0.0370182i
$768$	1.37113e10	−	2.37487e10i	1.09223	−	1.89180i
$769$	−1.29046e10	−	7.45048e9i	−1.02330	−	0.590802i	−0.108242	−	0.994125i	$-0.534522\pi$
$769$	−1.29046e10	−	7.45048e9i	−1.02330	−	0.590802i	−0.915058	+	0.403322i	$0.867855\pi$
$770$	−4.36647e9	+	6.19013e9i	−0.344678	+	0.488633i
$771$	1.61223e10	+	2.79246e10i	1.26688	+	2.19430i
$772$	1.30950e9	+	7.56039e8i	0.102434	+	0.0591403i
$773$	−5.56128e9	−	3.21081e9i	−0.433058	−	0.250026i	0.267590	−	0.963533i	$-0.413773\pi$
$773$	−5.56128e9	−	3.21081e9i	−0.433058	−	0.250026i	−0.700649	+	0.713506i	$0.747106\pi$
$774$	−5.57774e10	−	3.22031e10i	−4.32380	−	2.49634i
$775$	−1.33739e10	−	7.72142e9i	−1.03205	−	0.595856i
$776$	1.29360e9	+	2.24057e9i	0.0993762	+	0.172125i
$777$	−1.28639e10	−	1.17044e9i	−0.983782	−	0.0895112i
$778$	2.18942e10	+	1.26406e10i	1.66687	+	0.962365i
$779$	−6.86014e8	+	1.18821e9i	−0.0519938	+	0.0900560i
$780$	8.62124e9	−	6.78742e9i	0.650487	−	0.512122i
$781$	4.77116e9	+	8.26389e9i	0.358381	+	0.620734i
$782$	3.44136e10	−	1.98687e10i	2.57340	−	1.48575i
$783$	3.22191e10	−	5.58051e10i	2.39854	−	4.15440i
$784$	−9.61371e9	+	1.12970e10i	−0.712500	+	0.837253i
$785$			5.74266e9i			0.423711i
$786$			4.41275e9i			0.324138i
$787$	1.99310e10	+	1.15072e10i	1.45753	+	0.841507i	0.998890	−	0.0471135i	$-0.0150022\pi$
$787$	1.99310e10	+	1.15072e10i	1.45753	+	0.841507i	0.458643	+	0.888620i	$0.348336\pi$
$788$	1.42590e9	−	8.23242e8i	0.103812	−	0.0599357i
$789$	−2.39630e10			−1.73689
$790$	2.93693e9	−	5.08691e9i	0.211933	−	0.367079i
$791$	3.93924e7	−	4.32946e8i	0.00283005	−	0.0311040i
$792$	4.43690e9			0.317352
$793$	1.32689e10	−	1.91515e9i	0.944882	−	0.136379i
$794$	−4.39079e9	−	7.60508e9i	−0.311294	−	0.539177i
$795$		−	4.56999e9i		−	0.322575i
$796$	9.86638e8	+	1.70891e9i	0.0693366	+	0.120094i
$797$	2.17096e9	+	3.76022e9i	0.151897	+	0.263093i	0.931925	−	0.362652i	$-0.118129\pi$
$797$	2.17096e9	+	3.76022e9i	0.151897	+	0.263093i	−0.780028	+	0.625745i	$0.784795\pi$
$798$	5.90224e8	−	6.48692e9i	0.0411156	−	0.451885i
$799$	−2.89028e9	+	1.66870e9i	−0.200459	+	0.115735i
$800$			1.46246e10i			1.00988i
$801$	2.70342e10	−	1.56082e10i	1.85866	−	1.07310i
$802$	−2.30315e9	+	3.98917e9i	−0.157657	+	0.273069i
$803$	−1.10495e10	−	1.91383e10i	−0.753076	−	1.30437i
$804$	−2.33886e9	−	1.35034e9i	−0.158712	−	0.0916322i
$805$	5.84207e9	−	8.28202e9i	0.394713	−	0.559565i
$806$	1.21390e10	−	3.03696e10i	0.816600	−	2.04299i
$807$	−5.10686e9	+	8.84535e9i	−0.342056	+	0.592458i
$808$			1.48890e9i			0.0992947i
$809$	−2.26825e10			−1.50616			−0.753080	−	0.657929i	$-0.771433\pi$
$809$	−2.26825e10			−1.50616			−0.753080	+	0.657929i	$0.771433\pi$
$810$	−2.47318e10			−1.63515
$811$		−	1.67609e9i		−	0.110338i	−0.998477	−	0.0551689i	$-0.982430\pi$
$811$		−	1.67609e9i		−	0.110338i	0.998477	−	0.0551689i	$-0.0175697\pi$
$812$	2.28493e9	−	2.51128e10i	0.149771	−	1.64607i
$813$	6.05500e9	−	3.49585e9i	0.395182	−	0.228158i
$814$	8.44437e9	+	4.87536e9i	0.548759	+	0.316826i
$815$	4.79931e9	−	8.31264e9i	0.310547	−	0.537883i
$816$	5.02343e10			3.23657
$817$	−3.66376e9	+	2.11527e9i	−0.235044	+	0.135703i
$818$	−1.38751e10			−0.886341
$819$	3.35982e10	+	1.71087e10i	2.13709	+	1.08823i
$820$	4.11619e9			0.260704
$821$	−4.76636e9	+	2.75186e9i	−0.300598	+	0.173550i	−0.642712	−	0.766108i	$-0.722191\pi$
$821$	−4.76636e9	+	2.75186e9i	−0.300598	+	0.173550i	0.342113	+	0.939659i	$0.388857\pi$
$822$	2.38026e10			1.49477
$823$	1.54717e10	−	2.67979e10i	0.967475	−	1.67572i	0.264664	−	0.964341i	$-0.414739\pi$
$823$	1.54717e10	−	2.67979e10i	0.967475	−	1.67572i	0.702812	−	0.711376i	$-0.251928\pi$
$824$	−3.00525e9	−	1.73508e9i	−0.187127	−	0.108038i
$825$	−1.64911e10	+	9.52115e9i	−1.02249	+	0.590338i
$826$	−1.81386e9	−	1.27948e9i	−0.111989	−	0.0789959i
$827$		−	2.16163e9i		−	0.132896i	−0.997790	−	0.0664481i	$-0.978833\pi$
$827$		−	2.16163e9i		−	0.132896i	0.997790	−	0.0664481i	$-0.0211667\pi$
$828$	4.71091e10			2.88402
$829$	−2.93667e10			−1.79025			−0.895125	−	0.445815i	$-0.852914\pi$
$829$	−2.93667e10			−1.79025			−0.895125	+	0.445815i	$0.852914\pi$
$830$			3.15593e9i			0.191582i
$831$	1.96202e10	−	3.39832e10i	1.18604	−	2.05428i
$832$	−1.25791e10	+	1.81559e9i	−0.757211	+	0.109291i
$833$	−2.62045e10	−	4.80834e9i	−1.57079	−	0.288229i
$834$	−2.57196e10	−	1.48492e10i	−1.53527	−	0.886386i
$835$	−2.80163e9	−	4.85256e9i	−0.166536	−	0.288449i
$836$	−1.15640e9	+	2.00294e9i	−0.0684517	+	0.118562i
$837$	−6.06326e10	+	3.50062e10i	−3.57410	+	2.06351i
$838$			1.34725e10i			0.790848i
$839$	2.56924e10	−	1.48335e10i	1.50189	−	0.867117i	0.501894	−	0.864929i	$-0.332637\pi$
$839$	2.56924e10	−	1.48335e10i	1.50189	−	0.867117i	0.999998	−	0.00218815i	$-0.000696511\pi$
$840$	2.23536e9	−	1.03294e9i	0.130128	−	0.0601308i
$841$	−2.12508e10	−	3.68075e10i	−1.23194	−	2.13378i
$842$	9.02672e9	+	1.56347e10i	0.521120	+	0.902607i
$843$		−	3.15790e10i		−	1.81552i
$844$	6.59903e9	+	1.14299e10i	0.377817	+	0.654399i
$845$	8.62156e9	+	2.08163e9i	0.491572	+	0.118687i
$846$	−8.41161e9			−0.477621
$847$	−3.74941e9	−	2.64480e9i	−0.212017	−	0.149555i
$848$	−3.37770e9	+	5.85034e9i	−0.190211	+	0.329455i
$849$	3.38524e10			1.89851
$850$	−2.53250e10	+	1.46214e10i	−1.41443	+	0.816624i
$851$	−1.12980e10	−	6.52293e9i	−0.628420	−	0.362818i
$852$			2.46162e10i			1.36358i
$853$		−	1.06097e10i		−	0.585301i	−0.956219	−	0.292651i	$-0.905463\pi$
$853$		−	1.06097e10i		−	0.585301i	0.956219	−	0.292651i	$-0.0945373\pi$
$854$	−2.37782e10	−	2.16350e9i	−1.30640	−	0.118865i
$855$	−1.98523e9	+	3.43852e9i	−0.108625	+	0.188144i
$856$	−1.65081e8	+	9.53095e7i	−0.00899577	+	0.00519371i
$857$	1.49923e10	+	2.59675e10i	0.813648	+	1.40928i	0.910295	+	0.413961i	$0.135855\pi$
$857$	1.49923e10	+	2.59675e10i	0.813648	+	1.40928i	−0.0966467	+	0.995319i	$0.530812\pi$
$858$	−2.49470e10	−	3.16871e10i	−1.34838	−	1.71268i
$859$	9.28156e9	−	1.60761e10i	0.499626	−	0.865377i	−0.500374	−	0.865809i	$-0.666804\pi$
$859$	9.28156e9	−	1.60761e10i	0.499626	−	0.865377i	1.00000		0.000432071i	$0.000137532\pi$
$860$	1.09916e10	+	6.34599e9i	0.589271	+	0.340216i
$861$	8.40692e9	+	1.81933e10i	0.448875	+	0.971404i
$862$	9.98000e9	+	1.72859e10i	0.530707	+	0.919212i
$863$	2.52860e10	+	1.45989e10i	1.33919	+	0.773182i	0.986687	−	0.162628i	$-0.0519971\pi$
$863$	2.52860e10	+	1.45989e10i	1.33919	+	0.773182i	0.352504	+	0.935810i	$0.385330\pi$
$864$	5.74199e10	+	3.31514e10i	3.02876	+	1.74865i
$865$	7.48294e8	+	4.32027e8i	0.0393111	+	0.0226963i
$866$	3.43265e10	+	1.98184e10i	1.79604	+	1.03695i
$867$	2.74236e10	+	4.74991e10i	1.42908	+	2.47525i
$868$	−1.57926e10	+	2.23883e10i	−0.819659	+	1.16199i
$869$	−8.79431e9	−	5.07740e9i	−0.454603	−	0.262465i
$870$	−2.31524e10	+	4.01011e10i	−1.19201	+	2.06462i
$871$	−3.11854e8	−	2.16064e9i	−0.0159915	−	0.110795i
$872$	6.05978e8	+	1.04958e9i	0.0309492	+	0.0536055i
$873$	−5.27715e10	+	3.04676e10i	−2.68441	+	1.54985i
$874$	3.28934e9	−	5.69730e9i	0.166655	−	0.288655i
$875$	−1.00755e10	+	1.42836e10i	−0.508441	+	0.720792i
$876$		−	5.70086e10i		−	2.86534i
$877$		−	2.88770e10i		−	1.44562i	−0.691049	−	0.722808i	$-0.742851\pi$
$877$		−	2.88770e10i		−	1.44562i	0.691049	−	0.722808i	$-0.257149\pi$
$878$	1.22563e10	+	7.07616e9i	0.611121	+	0.352831i
$879$	−2.50312e10	+	1.44518e10i	−1.24314	+	0.717728i
$880$	−9.67176e9			−0.478427
$881$	−1.08883e10	+	1.88591e10i	−0.536470	+	0.929193i	0.462621	+	0.886556i	$0.346909\pi$
$881$	−1.08883e10	+	1.88591e10i	−0.536470	+	0.929193i	−0.999091	+	0.0426369i	$0.986424\pi$
$882$	−5.11381e10	−	4.35184e10i	−2.50960	−	2.13566i
$883$	3.53326e10			1.72708			0.863542	−	0.504276i	$-0.168241\pi$
$883$	3.53326e10			1.72708			0.863542	+	0.504276i	$0.168241\pi$
$884$	−1.80198e10	−	2.28884e10i	−0.877340	−	1.11438i
$885$	9.58615e8	+	1.66037e9i	0.0464882	+	0.0805200i
$886$		−	4.11196e10i		−	1.98624i
$887$	−7.73257e9	−	1.33932e10i	−0.372042	−	0.644395i	0.617838	−	0.786305i	$-0.288009\pi$
$887$	−7.73257e9	−	1.33932e10i	−0.372042	−	0.644395i	−0.989879	+	0.141911i	$0.954675\pi$
$888$	−1.58484e9	−	2.74502e9i	−0.0759520	−	0.131553i
$889$	−2.37702e10	+	1.09839e10i	−1.13469	+	0.524327i
$890$	−1.13261e10	+	6.53912e9i	−0.538536	+	0.310924i
$891$			4.27566e10i			2.02503i
$892$	4.74764e9	−	2.74105e9i	0.223976	−	0.129312i
$893$	−2.76260e8	+	4.78496e8i	−0.0129819	+	0.0224853i
$894$	−1.43221e10	−	2.48066e10i	−0.670387	−	1.16114i
$895$	−6.16746e9	−	3.56078e9i	−0.287558	−	0.166022i
$896$	−6.55344e9	−	5.96277e8i	−0.304363	−	0.0276930i
$897$	3.33775e10	+	4.23954e10i	1.54412	+	1.96131i
$898$	7.68754e9	−	1.33152e10i	0.354259	−	0.613594i
$899$			6.49204e10i			2.98004i
$900$	−3.46675e10			−1.58516
$901$	−1.21328e10			−0.552618
$902$		−	1.51290e10i		−	0.686414i
$903$	−5.59960e9	+	6.15430e10i	−0.253075	+	2.78145i
$904$	9.23861e7	−	5.33391e7i	0.00415927	−	0.00240135i
$905$	−1.11885e10	−	6.45971e9i	−0.501768	−	0.289696i
$906$	−4.79308e10	+	8.30185e10i	−2.14124	+	3.70874i
$907$	2.74727e10			1.22258			0.611288	−	0.791408i	$-0.290652\pi$
$907$	2.74727e10			1.22258			0.611288	+	0.791408i	$0.290652\pi$
$908$	−2.35817e10	+	1.36149e10i	−1.04538	+	0.603551i
$909$	−3.50676e10			−1.54858
$910$	−1.40761e10	−	7.16775e9i	−0.619210	−	0.315310i
$911$	9.38573e9			0.411295			0.205648	−	0.978626i	$-0.434070\pi$
$911$	9.38573e9			0.411295			0.205648	+	0.978626i	$0.434070\pi$
$912$	7.20228e9	−	4.15824e9i	0.314404	−	0.181521i
$913$	5.45601e9			0.237262
$914$	−1.26625e10	+	2.19321e10i	−0.548541	+	0.950100i
$915$	1.78597e10	+	1.03113e10i	0.770727	+	0.444980i
$916$	1.75340e10	−	1.01233e10i	0.753785	−	0.435198i
$917$	2.71245e9	−	1.25340e9i	0.116163	−	0.0536779i
$918$			1.32576e11i			5.65610i
$919$	−3.45837e10			−1.46983			−0.734915	−	0.678160i	$-0.762778\pi$
$919$	−3.45837e10			−1.46983			−0.734915	+	0.678160i	$0.762778\pi$
$920$	2.48704e9			0.105299
$921$			1.16001e10i			0.489276i
$922$	−2.51165e10	+	4.35030e10i	−1.05536	+	1.82794i
$923$	−1.56341e10	+	1.23085e10i	−0.654434	+	0.515230i
$924$	1.41713e10	+	3.06679e10i	0.590960	+	1.27889i
$925$	8.31423e9	+	4.80022e9i	0.345403	+	0.199418i
$926$	−3.00389e9	−	5.20289e9i	−0.124321	−	0.215331i
$927$	4.08659e10	−	7.07818e10i	1.68493	−	2.91838i
$928$	5.32437e10	−	3.07403e10i	2.18701	−	1.26267i
$929$		−	1.99907e10i		−	0.818036i	−0.912526	−	0.409018i	$-0.865871\pi$
$929$		−	1.99907e10i		−	0.818036i	0.912526	−	0.409018i	$-0.134129\pi$
$930$	4.35701e10	−	2.51552e10i	1.77623	−	1.02550i
$931$	−4.15506e9	+	1.47974e9i	−0.168754	+	0.0600982i
$932$	−1.26676e9	−	2.19409e9i	−0.0512552	−	0.0887766i
$933$	−9.25511e9	−	1.60303e10i	−0.373075	−	0.646185i
$934$		−	3.94227e10i		−	1.58319i
$935$	−8.68533e9	−	1.50434e10i	−0.347493	−	0.601875i
$936$	1.32167e9	+	9.15703e9i	0.0526815	+	0.364997i
$937$	−4.58112e9			−0.181921			−0.0909606	−	0.995854i	$-0.528994\pi$
$937$	−4.58112e9			−0.181921			−0.0909606	+	0.995854i	$0.528994\pi$
$938$	−3.52294e8	+	3.87193e9i	−0.0139378	+	0.153185i
$939$	−2.41477e9	+	4.18251e9i	−0.0951803	+	0.164857i
$940$	1.65760e9			0.0650928
$941$	−4.52423e9	+	2.61207e9i	−0.177003	+	0.102193i	−0.585884	−	0.810395i	$-0.699253\pi$
$941$	−4.52423e9	+	2.61207e9i	−0.177003	+	0.102193i	0.408881	+	0.912588i	$0.365919\pi$
$942$	4.71545e10	+	2.72247e10i	1.83800	+	1.06117i
$943$			2.02416e10i			0.786058i
$944$		−	2.83406e9i		−	0.109650i
$945$	1.41840e10	+	3.06954e10i	0.546749	+	1.18321i
$946$	2.33245e10	−	4.03992e10i	0.895763	−	1.55151i
$947$	4.16585e10	−	2.40516e10i	1.59397	−	0.920277i	0.601350	−	0.798986i	$-0.294630\pi$
$947$	4.16585e10	−	2.40516e10i	1.59397	−	0.920277i	0.992617	−	0.121291i	$-0.0387034\pi$
$948$	−1.30981e10	−	2.26866e10i	−0.499320	−	0.864847i
$949$	3.62069e10	−	2.85053e10i	1.37518	−	1.08267i
$950$	−2.42062e9	+	4.19264e9i	−0.0915997	+	0.158655i
$951$	−7.22729e9	−	4.17268e9i	−0.272486	−	0.157320i
$952$	−2.74233e9	−	5.93464e9i	−0.103013	−	0.222928i
$953$	4.93619e9	+	8.54973e9i	0.184742	+	0.319983i	0.943490	−	0.331402i	$-0.107522\pi$
$953$	4.93619e9	+	8.54973e9i	0.184742	+	0.319983i	−0.758747	+	0.651385i	$0.774188\pi$
$954$	−2.64827e10	−	1.52898e10i	−0.987514	−	0.570142i
$955$	−8.30359e9	−	4.79408e9i	−0.308499	−	0.178112i
$956$	3.18862e10	+	1.84095e10i	1.18032	+	0.681460i
$957$	6.93272e10	+	4.00261e10i	2.55689	+	1.47622i
$958$	−9.34635e8	−	1.61884e9i	−0.0343449	−	0.0594872i
$959$	−6.76088e9	−	1.46311e10i	−0.247536	−	0.535688i
$960$	−1.69313e10	−	9.77528e9i	−0.617647	−	0.356599i
$961$	2.15119e10	−	3.72596e10i	0.781891	−	1.35427i
$962$	−7.54651e9	+	1.88801e10i	−0.273296	+	0.683739i
$963$	−2.24479e9	−	3.88810e9i	−0.0809999	−	0.140296i
$964$	6.39138e9	−	3.69007e9i	0.229787	−	0.132668i
$965$	−9.40076e8	+	1.62826e9i	−0.0336757	+	0.0583281i
$966$	−4.03099e10	−	8.72341e10i	−1.43877	−	3.11363i
$967$		−	2.47817e10i		−	0.881331i	−0.897672	−	0.440665i	$-0.854743\pi$
$967$		−	2.47817e10i		−	0.881331i	0.897672	−	0.440665i	$-0.145257\pi$
$968$		−	1.12592e9i		−	0.0398975i
$969$	1.29354e10	+	7.46827e9i	0.456718	+	0.263686i
$970$	2.21089e10	−	1.27646e10i	0.777795	−	0.449060i
$971$	2.23067e10			0.781931			0.390966	−	0.920405i	$-0.372141\pi$
$971$	2.23067e10			0.781931			0.390966	+	0.920405i	$0.372141\pi$
$972$	−2.23809e10	+	3.87648e10i	−0.781709	+	1.35396i
$973$	−1.82222e9	+	2.00273e10i	−0.0634169	+	0.696990i
$974$	−4.82112e10			−1.67183
$975$	−2.45625e10	−	3.11988e10i	−0.848704	−	1.07801i
$976$	−1.52423e10	−	2.64004e10i	−0.524777	−	0.908940i
$977$		−	1.54681e10i		−	0.530649i	−0.964159	−	0.265325i	$-0.914521\pi$
$977$		−	1.54681e10i		−	0.530649i	0.964159	−	0.265325i	$-0.0854791\pi$
$978$	−4.55049e10	−	7.88168e10i	−1.55551	−	2.69422i
$979$	1.13049e10	+	1.95807e10i	0.385059	+	0.666942i
$980$	1.00773e10	+	8.57578e9i	0.342022	+	0.291060i
$981$	−2.47205e10	+	1.42724e10i	−0.836019	+	0.482676i
$982$		−	3.02815e10i		−	1.02044i
$983$	2.95899e10	−	1.70837e10i	0.993586	−	0.573647i	0.0872417	−	0.996187i	$-0.472195\pi$
$983$	2.95899e10	−	1.70837e10i	0.993586	−	0.573647i	0.906344	+	0.422540i	$0.138861\pi$
$984$	−2.45899e9	+	4.25910e9i	−0.0822762	+	0.142507i
$985$	1.02364e9	+	1.77299e9i	0.0341287	+	0.0591126i
$986$	1.06464e11	+	6.14670e10i	3.53699	+	2.04208i
$987$	3.38549e9	+	7.32648e9i	0.112076	+	0.242541i
$988$	−4.47820e9	−	1.78997e9i	−0.147725	−	0.0590469i
$989$	−3.12068e10	+	5.40517e10i	−1.02580	+	1.77673i
$990$		−	4.37811e10i		−	1.43405i
$991$	−5.10106e10			−1.66496			−0.832478	−	0.554057i	$-0.813079\pi$
$991$	−5.10106e10			−1.66496			−0.832478	+	0.554057i	$0.813079\pi$
$992$	−6.67989e10			−2.17259
$993$		−	1.70190e10i		−	0.551585i
$994$	3.21691e10	−	1.48650e10i	1.03893	−	0.480079i
$995$	−2.12490e9	+	1.22681e9i	−0.0683843	+	0.0394817i
$996$	1.21891e10	+	7.03740e9i	0.390899	+	0.225686i
$997$	2.16230e10	−	3.74521e10i	0.691007	−	1.19686i	−0.280501	−	0.959854i	$-0.590501\pi$
$997$	2.16230e10	−	3.74521e10i	0.691007	−	1.19686i	0.971508	−	0.237006i	$-0.0761660\pi$
$998$	2.11061e10			0.672125
$999$	3.76938e10	−	2.17625e10i	1.19616	−	0.690606i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.8.u.a.30.12	yes	126
7.4	even	3		91.8.k.a.4.12	✓	126
13.10	even	6		91.8.k.a.23.52	yes	126
91.88	even	6	inner	91.8.u.a.88.12	yes	126

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.8.k.a.4.12	✓	126	7.4	even	3
91.8.k.a.23.52	yes	126	13.10	even	6
91.8.u.a.30.12	yes	126	1.1	even	1	trivial
91.8.u.a.88.12	yes	126	91.88	even	6	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:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	91.u (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-13.4632 + 7.77296i) q^{2} -86.2083 q^{3} +(56.8378 - 98.4459i) q^{4} +(122.410 + 70.6734i) q^{5} +(1160.64 - 670.094i) q^{6} +(-741.564 - 523.093i) q^{7} -222.687i q^{8} +5244.87 q^{9} +O(q^{10})\)	\(q+(-13.4632 + 7.77296i) q^{2} -86.2083 q^{3} +(56.8378 - 98.4459i) q^{4} +(122.410 + 70.6734i) q^{5} +(1160.64 - 670.094i) q^{6} +(-741.564 - 523.093i) q^{7} -222.687i q^{8} +5244.87 q^{9} -2197.36 q^{10} +3798.83i q^{11} +(-4899.89 + 8486.86i) q^{12} +(-7840.15 + 1131.60i) q^{13} +(14049.8 + 1278.34i) q^{14} +(-10552.7 - 6092.63i) q^{15} +(9006.17 + 15599.1i) q^{16} +(-16175.3 + 28016.4i) q^{17} +(-70612.6 + 40768.2i) q^{18} +5355.74i q^{19} +(13915.0 - 8033.83i) q^{20} +(63929.0 + 45095.0i) q^{21} +(-29528.1 - 51144.2i) q^{22} +(39506.8 + 68427.8i) q^{23} +19197.5i q^{24} +(-29073.0 - 50356.0i) q^{25} +(96757.3 - 76176.1i) q^{26} -263614. q^{27} +(-93645.2 + 43272.4i) q^{28} +(-122221. + 211692. i) q^{29} +189431. q^{30} +(230005. - 132793. i) q^{31} +(-217818. - 125757. i) q^{32} -327490. i q^{33} -502918. i q^{34} +(-53805.9 - 116441. i) q^{35} +(298107. - 516336. i) q^{36} +(-142989. + 82554.5i) q^{37} +(-41630.0 - 72105.2i) q^{38} +(675886. - 97553.5i) q^{39} +(15738.0 - 27259.1i) q^{40} +(221857. + 128089. i) q^{41} +(-1.21121e6 - 110204. i) q^{42} +(394954. + 684080. i) q^{43} +(373979. + 215917. i) q^{44} +(642024. + 370673. i) q^{45} +(-1.06377e6 - 614170. i) q^{46} +(89342.6 + 51582.0i) q^{47} +(-776407. - 1.34478e6i) q^{48} +(276290. + 775814. i) q^{49} +(782830. + 451967. i) q^{50} +(1.39444e6 - 2.41524e6i) q^{51} +(-334215. + 836149. i) q^{52} +(187521. + 324796. i) q^{53} +(3.54908e6 - 2.04906e6i) q^{54} +(-268476. + 465014. i) q^{55} +(-116486. + 165137. i) q^{56} -461710. i q^{57} -3.80006e6i q^{58} +(-136261. - 78670.0i) q^{59} +(-1.19959e6 + 692583. i) q^{60} -1.69242e6 q^{61} +(-2.06440e6 + 3.57564e6i) q^{62} +(-3.88941e6 - 2.74356e6i) q^{63} +1.60444e6 q^{64} +(-1.03969e6 - 415571. i) q^{65} +(2.54557e6 + 4.40906e6i) q^{66} +275587. i q^{67} +(1.83873e6 + 3.18478e6i) q^{68} +(-3.40582e6 - 5.89905e6i) q^{69} +(1.62949e6 + 1.14943e6i) q^{70} +(2.17538e6 - 1.25596e6i) q^{71} -1.16797e6i q^{72} +(-5.03796e6 + 2.90867e6i) q^{73} +(1.28338e6 - 2.22289e6i) q^{74} +(2.50634e6 + 4.34111e6i) q^{75} +(527251. + 304409. i) q^{76} +(1.98714e6 - 2.81707e6i) q^{77} +(-8.34129e6 + 6.56702e6i) q^{78} +(-1.33657e6 + 2.31501e6i) q^{79} +2.54599e6i q^{80} +1.12552e7 q^{81} -3.98253e6 q^{82} -1.43624e6i q^{83} +(8.07300e6 - 3.73045e6i) q^{84} +(-3.96002e6 + 2.28632e6i) q^{85} +(-1.06347e7 - 6.13992e6i) q^{86} +(1.05364e7 - 1.82496e7i) q^{87} +845949. q^{88} +(5.15440e6 - 2.97589e6i) q^{89} -1.15249e7 q^{90} +(6.40590e6 + 3.26198e6i) q^{91} +8.98192e6 q^{92} +(-1.98283e7 + 1.14479e7i) q^{93} -1.60378e6 q^{94} +(-378509. + 655596. i) q^{95} +(1.87777e7 + 1.08413e7i) q^{96} +(-1.00615e7 + 5.80903e6i) q^{97} +(-9.75010e6 - 8.29731e6i) q^{98} +1.99244e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 126 q - 3 q^{2} - 164 q^{3} + 3841 q^{4} - 6 q^{6} + 754 q^{7} + 85710 q^{9}+O(q^{10}) \) 126 * q - 3 * q^2 - 164 * q^3 + 3841 * q^4 - 6 * q^6 + 754 * q^7 + 85710 * q^9	\( 126 q - 3 q^{2} - 164 q^{3} + 3841 q^{4} - 6 q^{6} + 754 q^{7} + 85710 q^{9} + 7486 q^{10} - 18328 q^{12} + 1816 q^{13} - 6668 q^{14} - 11817 q^{15} - 237219 q^{16} - 28969 q^{17} + 75423 q^{18} + 12342 q^{20} - 54000 q^{21} + 51388 q^{22} + 17067 q^{23} + 810665 q^{25} + 144300 q^{26} - 528170 q^{27} + 18464 q^{28} + 191096 q^{29} - 432160 q^{30} - 259995 q^{31} + 49149 q^{32} + 87303 q^{35} + 1965131 q^{36} - 571857 q^{37} - 1061954 q^{38} - 1352875 q^{39} + 345362 q^{40} - 636567 q^{41} - 3473694 q^{42} - 659976 q^{43} + 2519268 q^{44} + 1980717 q^{45} - 4068600 q^{46} - 294840 q^{47} + 4726652 q^{48} + 541120 q^{49} - 2908992 q^{50} - 502094 q^{51} + 7809224 q^{52} - 434723 q^{53} + 2119563 q^{54} + 2152196 q^{55} - 858015 q^{56} + 1376949 q^{59} - 3768141 q^{60} - 4854916 q^{61} - 1713436 q^{62} + 10091940 q^{63} - 40270472 q^{64} - 4876182 q^{65} + 8270835 q^{66} + 531379 q^{68} - 311689 q^{69} + 5298534 q^{70} + 1505877 q^{71} - 13207461 q^{73} + 3730527 q^{74} + 5624951 q^{75} + 25297146 q^{76} + 11107478 q^{77} - 9362803 q^{78} + 5012226 q^{79} + 45989766 q^{81} - 34046788 q^{82} - 35428032 q^{84} + 19854117 q^{85} + 5226210 q^{86} + 17331733 q^{87} + 24348310 q^{88} - 43738596 q^{89} + 90517324 q^{90} + 9582031 q^{91} - 8502078 q^{92} - 30517344 q^{93} - 7710416 q^{94} + 14810909 q^{95} + 41499936 q^{96} - 60232128 q^{97} - 65830509 q^{98}+O(q^{100}) \) 126 * q - 3 * q^2 - 164 * q^3 + 3841 * q^4 - 6 * q^6 + 754 * q^7 + 85710 * q^9 + 7486 * q^10 - 18328 * q^12 + 1816 * q^13 - 6668 * q^14 - 11817 * q^15 - 237219 * q^16 - 28969 * q^17 + 75423 * q^18 + 12342 * q^20 - 54000 * q^21 + 51388 * q^22 + 17067 * q^23 + 810665 * q^25 + 144300 * q^26 - 528170 * q^27 + 18464 * q^28 + 191096 * q^29 - 432160 * q^30 - 259995 * q^31 + 49149 * q^32 + 87303 * q^35 + 1965131 * q^36 - 571857 * q^37 - 1061954 * q^38 - 1352875 * q^39 + 345362 * q^40 - 636567 * q^41 - 3473694 * q^42 - 659976 * q^43 + 2519268 * q^44 + 1980717 * q^45 - 4068600 * q^46 - 294840 * q^47 + 4726652 * q^48 + 541120 * q^49 - 2908992 * q^50 - 502094 * q^51 + 7809224 * q^52 - 434723 * q^53 + 2119563 * q^54 + 2152196 * q^55 - 858015 * q^56 + 1376949 * q^59 - 3768141 * q^60 - 4854916 * q^61 - 1713436 * q^62 + 10091940 * q^63 - 40270472 * q^64 - 4876182 * q^65 + 8270835 * q^66 + 531379 * q^68 - 311689 * q^69 + 5298534 * q^70 + 1505877 * q^71 - 13207461 * q^73 + 3730527 * q^74 + 5624951 * q^75 + 25297146 * q^76 + 11107478 * q^77 - 9362803 * q^78 + 5012226 * q^79 + 45989766 * q^81 - 34046788 * q^82 - 35428032 * q^84 + 19854117 * q^85 + 5226210 * q^86 + 17331733 * q^87 + 24348310 * q^88 - 43738596 * q^89 + 90517324 * q^90 + 9582031 * q^91 - 8502078 * q^92 - 30517344 * q^93 - 7710416 * q^94 + 14810909 * q^95 + 41499936 * q^96 - 60232128 * q^97 - 65830509 * q^98

Introduction

L-functions

Modular forms

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