# Properties

 Label 234.6.b.a.181.1 Level $234$ Weight $6$ Character 234.181 Analytic conductor $37.530$ Analytic rank $0$ Dimension $2$ Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [234,6,Mod(181,234)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(234, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("234.181");

S:= CuspForms(chi, 6);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$234 = 2 \cdot 3^{2} \cdot 13$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 234.b (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: $$37.5298138362$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(i)$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{2} + 1$$ x^2 + 1 Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$2$$ Twist minimal: no (minimal twist has level 26) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 181.1 Root $$-1.00000i$$ of defining polynomial Character $$\chi$$ $$=$$ 234.181 Dual form 234.6.b.a.181.2

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q-4.00000i q^{2} -16.0000 q^{4} -68.0000i q^{5} +82.0000i q^{7} +64.0000i q^{8} +O(q^{10})$$ $$q-4.00000i q^{2} -16.0000 q^{4} -68.0000i q^{5} +82.0000i q^{7} +64.0000i q^{8} -272.000 q^{10} -390.000i q^{11} +(507.000 - 338.000i) q^{13} +328.000 q^{14} +256.000 q^{16} -1738.00 q^{17} -1074.00i q^{19} +1088.00i q^{20} -1560.00 q^{22} -2104.00 q^{23} -1499.00 q^{25} +(-1352.00 - 2028.00i) q^{26} -1312.00i q^{28} +1690.00 q^{29} -1430.00i q^{31} -1024.00i q^{32} +6952.00i q^{34} +5576.00 q^{35} +8852.00i q^{37} -4296.00 q^{38} +4352.00 q^{40} -6760.00i q^{41} -16916.0 q^{43} +6240.00i q^{44} +8416.00i q^{46} +25158.0i q^{47} +10083.0 q^{49} +5996.00i q^{50} +(-8112.00 + 5408.00i) q^{52} -38214.0 q^{53} -26520.0 q^{55} -5248.00 q^{56} -6760.00i q^{58} -21286.0i q^{59} -5458.00 q^{61} -5720.00 q^{62} -4096.00 q^{64} +(-22984.0 - 34476.0i) q^{65} +44542.0i q^{67} +27808.0 q^{68} -22304.0i q^{70} +17790.0i q^{71} +31064.0i q^{73} +35408.0 q^{74} +17184.0i q^{76} +31980.0 q^{77} -45360.0 q^{79} -17408.0i q^{80} -27040.0 q^{82} +124546. i q^{83} +118184. i q^{85} +67664.0i q^{86} +24960.0 q^{88} +18744.0i q^{89} +(27716.0 + 41574.0i) q^{91} +33664.0 q^{92} +100632. q^{94} -73032.0 q^{95} -121488. i q^{97} -40332.0i q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q - 32 q^{4}+O(q^{10})$$ 2 * q - 32 * q^4 $$2 q - 32 q^{4} - 544 q^{10} + 1014 q^{13} + 656 q^{14} + 512 q^{16} - 3476 q^{17} - 3120 q^{22} - 4208 q^{23} - 2998 q^{25} - 2704 q^{26} + 3380 q^{29} + 11152 q^{35} - 8592 q^{38} + 8704 q^{40} - 33832 q^{43} + 20166 q^{49} - 16224 q^{52} - 76428 q^{53} - 53040 q^{55} - 10496 q^{56} - 10916 q^{61} - 11440 q^{62} - 8192 q^{64} - 45968 q^{65} + 55616 q^{68} + 70816 q^{74} + 63960 q^{77} - 90720 q^{79} - 54080 q^{82} + 49920 q^{88} + 55432 q^{91} + 67328 q^{92} + 201264 q^{94} - 146064 q^{95}+O(q^{100})$$ 2 * q - 32 * q^4 - 544 * q^10 + 1014 * q^13 + 656 * q^14 + 512 * q^16 - 3476 * q^17 - 3120 * q^22 - 4208 * q^23 - 2998 * q^25 - 2704 * q^26 + 3380 * q^29 + 11152 * q^35 - 8592 * q^38 + 8704 * q^40 - 33832 * q^43 + 20166 * q^49 - 16224 * q^52 - 76428 * q^53 - 53040 * q^55 - 10496 * q^56 - 10916 * q^61 - 11440 * q^62 - 8192 * q^64 - 45968 * q^65 + 55616 * q^68 + 70816 * q^74 + 63960 * q^77 - 90720 * q^79 - 54080 * q^82 + 49920 * q^88 + 55432 * q^91 + 67328 * q^92 + 201264 * q^94 - 146064 * q^95

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/234\mathbb{Z}\right)^\times$$.

 $$n$$ $$145$$ $$209$$ $$\chi(n)$$ $$-1$$ $$1$$

## 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 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 4.00000i 0.707107i
$$3$$ 0 0
$$4$$ −16.0000 −0.500000
$$5$$ 68.0000i 1.21642i −0.793776 0.608210i $$-0.791888\pi$$
0.793776 0.608210i $$-0.208112\pi$$
$$6$$ 0 0
$$7$$ 82.0000i 0.632512i 0.948674 + 0.316256i $$0.102426\pi$$
−0.948674 + 0.316256i $$0.897574\pi$$
$$8$$ 64.0000i 0.353553i
$$9$$ 0 0
$$10$$ −272.000 −0.860140
$$11$$ 390.000i 0.971813i −0.874011 0.485907i $$-0.838489\pi$$
0.874011 0.485907i $$-0.161511\pi$$
$$12$$ 0 0
$$13$$ 507.000 338.000i 0.832050 0.554700i
$$14$$ 328.000 0.447254
$$15$$ 0 0
$$16$$ 256.000 0.250000
$$17$$ −1738.00 −1.45857 −0.729285 0.684210i $$-0.760147\pi$$
−0.729285 + 0.684210i $$0.760147\pi$$
$$18$$ 0 0
$$19$$ 1074.00i 0.682528i −0.939968 0.341264i $$-0.889145\pi$$
0.939968 0.341264i $$-0.110855\pi$$
$$20$$ 1088.00i 0.608210i
$$21$$ 0 0
$$22$$ −1560.00 −0.687176
$$23$$ −2104.00 −0.829328 −0.414664 0.909975i $$-0.636101\pi$$
−0.414664 + 0.909975i $$0.636101\pi$$
$$24$$ 0 0
$$25$$ −1499.00 −0.479680
$$26$$ −1352.00 2028.00i −0.392232 0.588348i
$$27$$ 0 0
$$28$$ 1312.00i 0.316256i
$$29$$ 1690.00 0.373157 0.186579 0.982440i $$-0.440260\pi$$
0.186579 + 0.982440i $$0.440260\pi$$
$$30$$ 0 0
$$31$$ 1430.00i 0.267259i −0.991031 0.133629i $$-0.957337\pi$$
0.991031 0.133629i $$-0.0426632\pi$$
$$32$$ 1024.00i 0.176777i
$$33$$ 0 0
$$34$$ 6952.00i 1.03137i
$$35$$ 5576.00 0.769401
$$36$$ 0 0
$$37$$ 8852.00i 1.06301i 0.847055 + 0.531505i $$0.178373\pi$$
−0.847055 + 0.531505i $$0.821627\pi$$
$$38$$ −4296.00 −0.482620
$$39$$ 0 0
$$40$$ 4352.00 0.430070
$$41$$ 6760.00i 0.628040i −0.949416 0.314020i $$-0.898324\pi$$
0.949416 0.314020i $$-0.101676\pi$$
$$42$$ 0 0
$$43$$ −16916.0 −1.39517 −0.697584 0.716503i $$-0.745742\pi$$
−0.697584 + 0.716503i $$0.745742\pi$$
$$44$$ 6240.00i 0.485907i
$$45$$ 0 0
$$46$$ 8416.00i 0.586423i
$$47$$ 25158.0i 1.66124i 0.556842 + 0.830618i $$0.312013\pi$$
−0.556842 + 0.830618i $$0.687987\pi$$
$$48$$ 0 0
$$49$$ 10083.0 0.599929
$$50$$ 5996.00i 0.339185i
$$51$$ 0 0
$$52$$ −8112.00 + 5408.00i −0.416025 + 0.277350i
$$53$$ −38214.0 −1.86867 −0.934335 0.356395i $$-0.884006\pi$$
−0.934335 + 0.356395i $$0.884006\pi$$
$$54$$ 0 0
$$55$$ −26520.0 −1.18213
$$56$$ −5248.00 −0.223627
$$57$$ 0 0
$$58$$ 6760.00i 0.263862i
$$59$$ 21286.0i 0.796093i −0.917365 0.398047i $$-0.869688\pi$$
0.917365 0.398047i $$-0.130312\pi$$
$$60$$ 0 0
$$61$$ −5458.00 −0.187806 −0.0939029 0.995581i $$-0.529934\pi$$
−0.0939029 + 0.995581i $$0.529934\pi$$
$$62$$ −5720.00 −0.188980
$$63$$ 0 0
$$64$$ −4096.00 −0.125000
$$65$$ −22984.0 34476.0i −0.674749 1.01212i
$$66$$ 0 0
$$67$$ 44542.0i 1.21222i 0.795379 + 0.606112i $$0.207272\pi$$
−0.795379 + 0.606112i $$0.792728\pi$$
$$68$$ 27808.0 0.729285
$$69$$ 0 0
$$70$$ 22304.0i 0.544049i
$$71$$ 17790.0i 0.418823i 0.977828 + 0.209411i $$0.0671547\pi$$
−0.977828 + 0.209411i $$0.932845\pi$$
$$72$$ 0 0
$$73$$ 31064.0i 0.682260i 0.940016 + 0.341130i $$0.110810\pi$$
−0.940016 + 0.341130i $$0.889190\pi$$
$$74$$ 35408.0 0.751661
$$75$$ 0 0
$$76$$ 17184.0i 0.341264i
$$77$$ 31980.0 0.614684
$$78$$ 0 0
$$79$$ −45360.0 −0.817721 −0.408861 0.912597i $$-0.634074\pi$$
−0.408861 + 0.912597i $$0.634074\pi$$
$$80$$ 17408.0i 0.304105i
$$81$$ 0 0
$$82$$ −27040.0 −0.444091
$$83$$ 124546.i 1.98442i 0.124559 + 0.992212i $$0.460248\pi$$
−0.124559 + 0.992212i $$0.539752\pi$$
$$84$$ 0 0
$$85$$ 118184.i 1.77424i
$$86$$ 67664.0i 0.986533i
$$87$$ 0 0
$$88$$ 24960.0 0.343588
$$89$$ 18744.0i 0.250834i 0.992104 + 0.125417i $$0.0400270\pi$$
−0.992104 + 0.125417i $$0.959973\pi$$
$$90$$ 0 0
$$91$$ 27716.0 + 41574.0i 0.350855 + 0.526282i
$$92$$ 33664.0 0.414664
$$93$$ 0 0
$$94$$ 100632. 1.17467
$$95$$ −73032.0 −0.830241
$$96$$ 0 0
$$97$$ 121488.i 1.31100i −0.755193 0.655502i $$-0.772457\pi$$
0.755193 0.655502i $$-0.227543\pi$$
$$98$$ 40332.0i 0.424214i
$$99$$ 0 0
$$100$$ 23984.0 0.239840
$$101$$ 14218.0 0.138687 0.0693434 0.997593i $$-0.477910\pi$$
0.0693434 + 0.997593i $$0.477910\pi$$
$$102$$ 0 0
$$103$$ −62776.0 −0.583043 −0.291521 0.956564i $$-0.594161\pi$$
−0.291521 + 0.956564i $$0.594161\pi$$
$$104$$ 21632.0 + 32448.0i 0.196116 + 0.294174i
$$105$$ 0 0
$$106$$ 152856.i 1.32135i
$$107$$ 79252.0 0.669192 0.334596 0.942362i $$-0.391400\pi$$
0.334596 + 0.942362i $$0.391400\pi$$
$$108$$ 0 0
$$109$$ 218084.i 1.75816i −0.476677 0.879078i $$-0.658159\pi$$
0.476677 0.879078i $$-0.341841\pi$$
$$110$$ 106080.i 0.835895i
$$111$$ 0 0
$$112$$ 20992.0i 0.158128i
$$113$$ −44234.0 −0.325882 −0.162941 0.986636i $$-0.552098\pi$$
−0.162941 + 0.986636i $$0.552098\pi$$
$$114$$ 0 0
$$115$$ 143072.i 1.00881i
$$116$$ −27040.0 −0.186579
$$117$$ 0 0
$$118$$ −85144.0 −0.562923
$$119$$ 142516.i 0.922563i
$$120$$ 0 0
$$121$$ 8951.00 0.0555787
$$122$$ 21832.0i 0.132799i
$$123$$ 0 0
$$124$$ 22880.0i 0.133629i
$$125$$ 110568.i 0.632928i
$$126$$ 0 0
$$127$$ −310432. −1.70788 −0.853940 0.520372i $$-0.825793\pi$$
−0.853940 + 0.520372i $$0.825793\pi$$
$$128$$ 16384.0i 0.0883883i
$$129$$ 0 0
$$130$$ −137904. + 91936.0i −0.715679 + 0.477120i
$$131$$ −310372. −1.58017 −0.790086 0.612996i $$-0.789964\pi$$
−0.790086 + 0.612996i $$0.789964\pi$$
$$132$$ 0 0
$$133$$ 88068.0 0.431707
$$134$$ 178168. 0.857171
$$135$$ 0 0
$$136$$ 111232.i 0.515683i
$$137$$ 281032.i 1.27925i −0.768688 0.639623i $$-0.779090\pi$$
0.768688 0.639623i $$-0.220910\pi$$
$$138$$ 0 0
$$139$$ 363820. 1.59716 0.798582 0.601886i $$-0.205584\pi$$
0.798582 + 0.601886i $$0.205584\pi$$
$$140$$ −89216.0 −0.384700
$$141$$ 0 0
$$142$$ 71160.0 0.296152
$$143$$ −131820. 197730.i −0.539065 0.808598i
$$144$$ 0 0
$$145$$ 114920.i 0.453916i
$$146$$ 124256. 0.482431
$$147$$ 0 0
$$148$$ 141632.i 0.531505i
$$149$$ 274204.i 1.01183i 0.862583 + 0.505916i $$0.168845\pi$$
−0.862583 + 0.505916i $$0.831155\pi$$
$$150$$ 0 0
$$151$$ 344030.i 1.22787i −0.789355 0.613937i $$-0.789585\pi$$
0.789355 0.613937i $$-0.210415\pi$$
$$152$$ 68736.0 0.241310
$$153$$ 0 0
$$154$$ 127920.i 0.434647i
$$155$$ −97240.0 −0.325099
$$156$$ 0 0
$$157$$ 20518.0 0.0664333 0.0332167 0.999448i $$-0.489425\pi$$
0.0332167 + 0.999448i $$0.489425\pi$$
$$158$$ 181440.i 0.578216i
$$159$$ 0 0
$$160$$ −69632.0 −0.215035
$$161$$ 172528.i 0.524560i
$$162$$ 0 0
$$163$$ 36626.0i 0.107974i −0.998542 0.0539872i $$-0.982807\pi$$
0.998542 0.0539872i $$-0.0171930\pi$$
$$164$$ 108160.i 0.314020i
$$165$$ 0 0
$$166$$ 498184. 1.40320
$$167$$ 269442.i 0.747608i −0.927508 0.373804i $$-0.878053\pi$$
0.927508 0.373804i $$-0.121947\pi$$
$$168$$ 0 0
$$169$$ 142805. 342732.i 0.384615 0.923077i
$$170$$ 472736. 1.25457
$$171$$ 0 0
$$172$$ 270656. 0.697584
$$173$$ −282654. −0.718026 −0.359013 0.933333i $$-0.616887\pi$$
−0.359013 + 0.933333i $$0.616887\pi$$
$$174$$ 0 0
$$175$$ 122918.i 0.303403i
$$176$$ 99840.0i 0.242953i
$$177$$ 0 0
$$178$$ 74976.0 0.177367
$$179$$ −333780. −0.778624 −0.389312 0.921106i $$-0.627287\pi$$
−0.389312 + 0.921106i $$0.627287\pi$$
$$180$$ 0 0
$$181$$ −459938. −1.04352 −0.521762 0.853091i $$-0.674725\pi$$
−0.521762 + 0.853091i $$0.674725\pi$$
$$182$$ 166296. 110864.i 0.372137 0.248092i
$$183$$ 0 0
$$184$$ 134656.i 0.293212i
$$185$$ 601936. 1.29307
$$186$$ 0 0
$$187$$ 677820.i 1.41746i
$$188$$ 402528.i 0.830618i
$$189$$ 0 0
$$190$$ 292128.i 0.587069i
$$191$$ 917088. 1.81898 0.909489 0.415727i $$-0.136473\pi$$
0.909489 + 0.415727i $$0.136473\pi$$
$$192$$ 0 0
$$193$$ 639056.i 1.23494i −0.786595 0.617470i $$-0.788158\pi$$
0.786595 0.617470i $$-0.211842\pi$$
$$194$$ −485952. −0.927020
$$195$$ 0 0
$$196$$ −161328. −0.299964
$$197$$ 358292.i 0.657766i −0.944371 0.328883i $$-0.893328\pi$$
0.944371 0.328883i $$-0.106672\pi$$
$$198$$ 0 0
$$199$$ 370440. 0.663109 0.331555 0.943436i $$-0.392427\pi$$
0.331555 + 0.943436i $$0.392427\pi$$
$$200$$ 95936.0i 0.169592i
$$201$$ 0 0
$$202$$ 56872.0i 0.0980664i
$$203$$ 138580.i 0.236026i
$$204$$ 0 0
$$205$$ −459680. −0.763961
$$206$$ 251104.i 0.412274i
$$207$$ 0 0
$$208$$ 129792. 86528.0i 0.208013 0.138675i
$$209$$ −418860. −0.663290
$$210$$ 0 0
$$211$$ −177228. −0.274048 −0.137024 0.990568i $$-0.543754\pi$$
−0.137024 + 0.990568i $$0.543754\pi$$
$$212$$ 611424. 0.934335
$$213$$ 0 0
$$214$$ 317008.i 0.473190i
$$215$$ 1.15029e6i 1.69711i
$$216$$ 0 0
$$217$$ 117260. 0.169044
$$218$$ −872336. −1.24320
$$219$$ 0 0
$$220$$ 424320. 0.591067
$$221$$ −881166. + 587444.i −1.21360 + 0.809069i
$$222$$ 0 0
$$223$$ 1.11297e6i 1.49872i −0.662164 0.749359i $$-0.730362\pi$$
0.662164 0.749359i $$-0.269638\pi$$
$$224$$ 83968.0 0.111813
$$225$$ 0 0
$$226$$ 176936.i 0.230433i
$$227$$ 1.39158e6i 1.79244i −0.443612 0.896219i $$-0.646303\pi$$
0.443612 0.896219i $$-0.353697\pi$$
$$228$$ 0 0
$$229$$ 909796.i 1.14645i 0.819398 + 0.573225i $$0.194308\pi$$
−0.819398 + 0.573225i $$0.805692\pi$$
$$230$$ 572288. 0.713337
$$231$$ 0 0
$$232$$ 108160.i 0.131931i
$$233$$ −266154. −0.321176 −0.160588 0.987022i $$-0.551339\pi$$
−0.160588 + 0.987022i $$0.551339\pi$$
$$234$$ 0 0
$$235$$ 1.71074e6 2.02076
$$236$$ 340576.i 0.398047i
$$237$$ 0 0
$$238$$ −570064. −0.652351
$$239$$ 254614.i 0.288328i 0.989554 + 0.144164i $$0.0460494\pi$$
−0.989554 + 0.144164i $$0.953951\pi$$
$$240$$ 0 0
$$241$$ 313600.i 0.347803i −0.984763 0.173902i $$-0.944363\pi$$
0.984763 0.173902i $$-0.0556375\pi$$
$$242$$ 35804.0i 0.0393001i
$$243$$ 0 0
$$244$$ 87328.0 0.0939029
$$245$$ 685644.i 0.729766i
$$246$$ 0 0
$$247$$ −363012. 544518.i −0.378598 0.567897i
$$248$$ 91520.0 0.0944902
$$249$$ 0 0
$$250$$ −442272. −0.447548
$$251$$ 1.07127e6 1.07328 0.536641 0.843811i $$-0.319693\pi$$
0.536641 + 0.843811i $$0.319693\pi$$
$$252$$ 0 0
$$253$$ 820560.i 0.805952i
$$254$$ 1.24173e6i 1.20765i
$$255$$ 0 0
$$256$$ 65536.0 0.0625000
$$257$$ 188382. 0.177913 0.0889563 0.996036i $$-0.471647\pi$$
0.0889563 + 0.996036i $$0.471647\pi$$
$$258$$ 0 0
$$259$$ −725864. −0.672366
$$260$$ 367744. + 551616.i 0.337374 + 0.506062i
$$261$$ 0 0
$$262$$ 1.24149e6i 1.11735i
$$263$$ 1.48678e6 1.32543 0.662714 0.748873i $$-0.269404\pi$$
0.662714 + 0.748873i $$0.269404\pi$$
$$264$$ 0 0
$$265$$ 2.59855e6i 2.27309i
$$266$$ 352272.i 0.305263i
$$267$$ 0 0
$$268$$ 712672.i 0.606112i
$$269$$ −743990. −0.626883 −0.313441 0.949608i $$-0.601482\pi$$
−0.313441 + 0.949608i $$0.601482\pi$$
$$270$$ 0 0
$$271$$ 455590.i 0.376835i −0.982089 0.188417i $$-0.939664\pi$$
0.982089 0.188417i $$-0.0603358\pi$$
$$272$$ −444928. −0.364643
$$273$$ 0 0
$$274$$ −1.12413e6 −0.904564
$$275$$ 584610.i 0.466159i
$$276$$ 0 0
$$277$$ 460198. 0.360367 0.180184 0.983633i $$-0.442331\pi$$
0.180184 + 0.983633i $$0.442331\pi$$
$$278$$ 1.45528e6i 1.12937i
$$279$$ 0 0
$$280$$ 356864.i 0.272024i
$$281$$ 49240.0i 0.0372008i 0.999827 + 0.0186004i $$0.00592103\pi$$
−0.999827 + 0.0186004i $$0.994079\pi$$
$$282$$ 0 0
$$283$$ −544196. −0.403914 −0.201957 0.979394i $$-0.564730\pi$$
−0.201957 + 0.979394i $$0.564730\pi$$
$$284$$ 284640.i 0.209411i
$$285$$ 0 0
$$286$$ −790920. + 527280.i −0.571765 + 0.381177i
$$287$$ 554320. 0.397243
$$288$$ 0 0
$$289$$ 1.60079e6 1.12743
$$290$$ −459680. −0.320967
$$291$$ 0 0
$$292$$ 497024.i 0.341130i
$$293$$ 1.02504e6i 0.697542i 0.937208 + 0.348771i $$0.113401\pi$$
−0.937208 + 0.348771i $$0.886599\pi$$
$$294$$ 0 0
$$295$$ −1.44745e6 −0.968385
$$296$$ −566528. −0.375831
$$297$$ 0 0
$$298$$ 1.09682e6 0.715473
$$299$$ −1.06673e6 + 711152.i −0.690042 + 0.460028i
$$300$$ 0 0
$$301$$ 1.38711e6i 0.882461i
$$302$$ −1.37612e6 −0.868238
$$303$$ 0 0
$$304$$ 274944.i 0.170632i
$$305$$ 371144.i 0.228451i
$$306$$ 0 0
$$307$$ 1.57766e6i 0.955362i 0.878533 + 0.477681i $$0.158523\pi$$
−0.878533 + 0.477681i $$0.841477\pi$$
$$308$$ −511680. −0.307342
$$309$$ 0 0
$$310$$ 388960.i 0.229880i
$$311$$ 330088. 0.193521 0.0967606 0.995308i $$-0.469152\pi$$
0.0967606 + 0.995308i $$0.469152\pi$$
$$312$$ 0 0
$$313$$ −1.78677e6 −1.03088 −0.515438 0.856927i $$-0.672371\pi$$
−0.515438 + 0.856927i $$0.672371\pi$$
$$314$$ 82072.0i 0.0469754i
$$315$$ 0 0
$$316$$ 725760. 0.408861
$$317$$ 182148.i 0.101807i 0.998704 + 0.0509033i $$0.0162100\pi$$
−0.998704 + 0.0509033i $$0.983790\pi$$
$$318$$ 0 0
$$319$$ 659100.i 0.362639i
$$320$$ 278528.i 0.152053i
$$321$$ 0 0
$$322$$ −690112. −0.370920
$$323$$ 1.86661e6i 0.995515i
$$324$$ 0 0
$$325$$ −759993. + 506662.i −0.399118 + 0.266079i
$$326$$ −146504. −0.0763494
$$327$$ 0 0
$$328$$ 432640. 0.222046
$$329$$ −2.06296e6 −1.05075
$$330$$ 0 0
$$331$$ 216230.i 0.108479i 0.998528 + 0.0542395i $$0.0172735\pi$$
−0.998528 + 0.0542395i $$0.982727\pi$$
$$332$$ 1.99274e6i 0.992212i
$$333$$ 0 0
$$334$$ −1.07777e6 −0.528639
$$335$$ 3.02886e6 1.47457
$$336$$ 0 0
$$337$$ −2.05314e6 −0.984791 −0.492396 0.870371i $$-0.663879\pi$$
−0.492396 + 0.870371i $$0.663879\pi$$
$$338$$ −1.37093e6 571220.i −0.652714 0.271964i
$$339$$ 0 0
$$340$$ 1.89094e6i 0.887118i
$$341$$ −557700. −0.259726
$$342$$ 0 0
$$343$$ 2.20498e6i 1.01197i
$$344$$ 1.08262e6i 0.493266i
$$345$$ 0 0
$$346$$ 1.13062e6i 0.507721i
$$347$$ −4.28819e6 −1.91183 −0.955917 0.293637i $$-0.905134\pi$$
−0.955917 + 0.293637i $$0.905134\pi$$
$$348$$ 0 0
$$349$$ 3.55152e6i 1.56081i 0.625274 + 0.780405i $$0.284987\pi$$
−0.625274 + 0.780405i $$0.715013\pi$$
$$350$$ −491672. −0.214539
$$351$$ 0 0
$$352$$ −399360. −0.171794
$$353$$ 2.08678e6i 0.891335i −0.895199 0.445667i $$-0.852966\pi$$
0.895199 0.445667i $$-0.147034\pi$$
$$354$$ 0 0
$$355$$ 1.20972e6 0.509465
$$356$$ 299904.i 0.125417i
$$357$$ 0 0
$$358$$ 1.33512e6i 0.550570i
$$359$$ 500654.i 0.205023i 0.994732 + 0.102511i $$0.0326878\pi$$
−0.994732 + 0.102511i $$0.967312\pi$$
$$360$$ 0 0
$$361$$ 1.32262e6 0.534156
$$362$$ 1.83975e6i 0.737884i
$$363$$ 0 0
$$364$$ −443456. 665184.i −0.175427 0.263141i
$$365$$ 2.11235e6 0.829916
$$366$$ 0 0
$$367$$ −1.28027e6 −0.496178 −0.248089 0.968737i $$-0.579802\pi$$
−0.248089 + 0.968737i $$0.579802\pi$$
$$368$$ −538624. −0.207332
$$369$$ 0 0
$$370$$ 2.40774e6i 0.914336i
$$371$$ 3.13355e6i 1.18196i
$$372$$ 0 0
$$373$$ −405666. −0.150972 −0.0754860 0.997147i $$-0.524051\pi$$
−0.0754860 + 0.997147i $$0.524051\pi$$
$$374$$ 2.71128e6 1.00229
$$375$$ 0 0
$$376$$ −1.61011e6 −0.587336
$$377$$ 856830. 571220.i 0.310485 0.206990i
$$378$$ 0 0
$$379$$ 4.66217e6i 1.66721i 0.552363 + 0.833604i $$0.313726\pi$$
−0.552363 + 0.833604i $$0.686274\pi$$
$$380$$ 1.16851e6 0.415121
$$381$$ 0 0
$$382$$ 3.66835e6i 1.28621i
$$383$$ 4.35473e6i 1.51692i 0.651717 + 0.758462i $$0.274049\pi$$
−0.651717 + 0.758462i $$0.725951\pi$$
$$384$$ 0 0
$$385$$ 2.17464e6i 0.747714i
$$386$$ −2.55622e6 −0.873234
$$387$$ 0 0
$$388$$ 1.94381e6i 0.655502i
$$389$$ −786990. −0.263691 −0.131845 0.991270i $$-0.542090\pi$$
−0.131845 + 0.991270i $$0.542090\pi$$
$$390$$ 0 0
$$391$$ 3.65675e6 1.20963
$$392$$ 645312.i 0.212107i
$$393$$ 0 0
$$394$$ −1.43317e6 −0.465111
$$395$$ 3.08448e6i 0.994693i
$$396$$ 0 0
$$397$$ 3.97023e6i 1.26427i −0.774859 0.632134i $$-0.782179\pi$$
0.774859 0.632134i $$-0.217821\pi$$
$$398$$ 1.48176e6i 0.468889i
$$399$$ 0 0
$$400$$ −383744. −0.119920
$$401$$ 344640.i 0.107030i 0.998567 + 0.0535149i $$0.0170425\pi$$
−0.998567 + 0.0535149i $$0.982958\pi$$
$$402$$ 0 0
$$403$$ −483340. 725010.i −0.148248 0.222373i
$$404$$ −227488. −0.0693434
$$405$$ 0 0
$$406$$ 554320. 0.166896
$$407$$ 3.45228e6 1.03305
$$408$$ 0 0
$$409$$ 2.55466e6i 0.755137i −0.925982 0.377568i $$-0.876760\pi$$
0.925982 0.377568i $$-0.123240\pi$$
$$410$$ 1.83872e6i 0.540202i
$$411$$ 0 0
$$412$$ 1.00442e6 0.291521
$$413$$ 1.74545e6 0.503539
$$414$$ 0 0
$$415$$ 8.46913e6 2.41390
$$416$$ −346112. 519168.i −0.0980581 0.147087i
$$417$$ 0 0
$$418$$ 1.67544e6i 0.469017i
$$419$$ 2.51894e6 0.700943 0.350472 0.936573i $$-0.386021\pi$$
0.350472 + 0.936573i $$0.386021\pi$$
$$420$$ 0 0
$$421$$ 4.83670e6i 1.32998i −0.746854 0.664988i $$-0.768437\pi$$
0.746854 0.664988i $$-0.231563\pi$$
$$422$$ 708912.i 0.193781i
$$423$$ 0 0
$$424$$ 2.44570e6i 0.660675i
$$425$$ 2.60526e6 0.699647
$$426$$ 0 0
$$427$$ 447556.i 0.118789i
$$428$$ −1.26803e6 −0.334596
$$429$$ 0 0
$$430$$ 4.60115e6 1.20004
$$431$$ 219110.i 0.0568158i 0.999596 + 0.0284079i $$0.00904373\pi$$
−0.999596 + 0.0284079i $$0.990956\pi$$
$$432$$ 0 0
$$433$$ −3.03477e6 −0.777867 −0.388934 0.921266i $$-0.627156\pi$$
−0.388934 + 0.921266i $$0.627156\pi$$
$$434$$ 469040.i 0.119532i
$$435$$ 0 0
$$436$$ 3.48934e6i 0.879078i
$$437$$ 2.25970e6i 0.566039i
$$438$$ 0 0
$$439$$ 4.16940e6 1.03255 0.516276 0.856422i $$-0.327318\pi$$
0.516276 + 0.856422i $$0.327318\pi$$
$$440$$ 1.69728e6i 0.417948i
$$441$$ 0 0
$$442$$ 2.34978e6 + 3.52466e6i 0.572098 + 0.858148i
$$443$$ 6.30548e6 1.52654 0.763271 0.646079i $$-0.223592\pi$$
0.763271 + 0.646079i $$0.223592\pi$$
$$444$$ 0 0
$$445$$ 1.27459e6 0.305120
$$446$$ −4.45186e6 −1.05975
$$447$$ 0 0
$$448$$ 335872.i 0.0790640i
$$449$$ 7.41586e6i 1.73598i −0.496579 0.867991i $$-0.665411\pi$$
0.496579 0.867991i $$-0.334589\pi$$
$$450$$ 0 0
$$451$$ −2.63640e6 −0.610337
$$452$$ 707744. 0.162941
$$453$$ 0 0
$$454$$ −5.56633e6 −1.26745
$$455$$ 2.82703e6 1.88469e6i 0.640180 0.426787i
$$456$$ 0 0
$$457$$ 4.71529e6i 1.05613i −0.849204 0.528065i $$-0.822918\pi$$
0.849204 0.528065i $$-0.177082\pi$$
$$458$$ 3.63918e6 0.810663
$$459$$ 0 0
$$460$$ 2.28915e6i 0.504406i
$$461$$ 3.34566e6i 0.733212i −0.930376 0.366606i $$-0.880520\pi$$
0.930376 0.366606i $$-0.119480\pi$$
$$462$$ 0 0
$$463$$ 1.65791e6i 0.359426i 0.983719 + 0.179713i $$0.0575169\pi$$
−0.983719 + 0.179713i $$0.942483\pi$$
$$464$$ 432640. 0.0932893
$$465$$ 0 0
$$466$$ 1.06462e6i 0.227106i
$$467$$ −823668. −0.174767 −0.0873836 0.996175i $$-0.527851\pi$$
−0.0873836 + 0.996175i $$0.527851\pi$$
$$468$$ 0 0
$$469$$ −3.65244e6 −0.766746
$$470$$ 6.84298e6i 1.42890i
$$471$$ 0 0
$$472$$ 1.36230e6 0.281462
$$473$$ 6.59724e6i 1.35584i
$$474$$ 0 0
$$475$$ 1.60993e6i 0.327395i
$$476$$ 2.28026e6i 0.461282i
$$477$$ 0 0
$$478$$ 1.01846e6 0.203879
$$479$$ 3.59011e6i 0.714938i −0.933925 0.357469i $$-0.883640\pi$$
0.933925 0.357469i $$-0.116360\pi$$
$$480$$ 0 0
$$481$$ 2.99198e6 + 4.48796e6i 0.589652 + 0.884477i
$$482$$ −1.25440e6 −0.245934
$$483$$ 0 0
$$484$$ −143216. −0.0277893
$$485$$ −8.26118e6 −1.59473
$$486$$ 0 0
$$487$$ 9.67688e6i 1.84890i −0.381306 0.924449i $$-0.624526\pi$$
0.381306 0.924449i $$-0.375474\pi$$
$$488$$ 349312.i 0.0663994i
$$489$$ 0 0
$$490$$ −2.74258e6 −0.516022
$$491$$ −3.45633e6 −0.647011 −0.323506 0.946226i $$-0.604861\pi$$
−0.323506 + 0.946226i $$0.604861\pi$$
$$492$$ 0 0
$$493$$ −2.93722e6 −0.544276
$$494$$ −2.17807e6 + 1.45205e6i −0.401564 + 0.267709i
$$495$$ 0 0
$$496$$ 366080.i 0.0668147i
$$497$$ −1.45878e6 −0.264910
$$498$$ 0 0
$$499$$ 2.09109e6i 0.375942i 0.982175 + 0.187971i $$0.0601911\pi$$
−0.982175 + 0.187971i $$0.939809\pi$$
$$500$$ 1.76909e6i 0.316464i
$$501$$ 0 0
$$502$$ 4.28507e6i 0.758925i
$$503$$ −5.58626e6 −0.984468 −0.492234 0.870463i $$-0.663820\pi$$
−0.492234 + 0.870463i $$0.663820\pi$$
$$504$$ 0 0
$$505$$ 966824.i 0.168702i
$$506$$ 3.28224e6 0.569894
$$507$$ 0 0
$$508$$ 4.96691e6 0.853940
$$509$$ 4.15504e6i 0.710854i −0.934704 0.355427i $$-0.884335\pi$$
0.934704 0.355427i $$-0.115665\pi$$
$$510$$ 0 0
$$511$$ −2.54725e6 −0.431538
$$512$$ 262144.i 0.0441942i
$$513$$ 0 0
$$514$$ 753528.i 0.125803i
$$515$$ 4.26877e6i 0.709226i
$$516$$ 0 0
$$517$$ 9.81162e6 1.61441
$$518$$ 2.90346e6i 0.475435i
$$519$$ 0 0
$$520$$ 2.20646e6 1.47098e6i 0.357840 0.238560i
$$521$$ 9.84416e6 1.58886 0.794428 0.607359i $$-0.207771\pi$$
0.794428 + 0.607359i $$0.207771\pi$$
$$522$$ 0 0
$$523$$ 481324. 0.0769455 0.0384728 0.999260i $$-0.487751\pi$$
0.0384728 + 0.999260i $$0.487751\pi$$
$$524$$ 4.96595e6 0.790086
$$525$$ 0 0
$$526$$ 5.94710e6i 0.937219i
$$527$$ 2.48534e6i 0.389816i
$$528$$ 0 0
$$529$$ −2.00953e6 −0.312216
$$530$$ 1.03942e7 1.60732
$$531$$ 0 0
$$532$$ −1.40909e6 −0.215853
$$533$$ −2.28488e6 3.42732e6i −0.348374 0.522561i
$$534$$ 0 0
$$535$$ 5.38914e6i 0.814019i
$$536$$ −2.85069e6 −0.428586
$$537$$ 0 0
$$538$$ 2.97596e6i 0.443273i
$$539$$ 3.93237e6i 0.583019i
$$540$$ 0 0
$$541$$ 263980.i 0.0387773i 0.999812 + 0.0193887i $$0.00617199\pi$$
−0.999812 + 0.0193887i $$0.993828\pi$$
$$542$$ −1.82236e6 −0.266462
$$543$$ 0 0
$$544$$ 1.77971e6i 0.257841i
$$545$$ −1.48297e7 −2.13866
$$546$$ 0 0
$$547$$ 2.80023e6 0.400152 0.200076 0.979780i $$-0.435881\pi$$
0.200076 + 0.979780i $$0.435881\pi$$
$$548$$ 4.49651e6i 0.639623i
$$549$$ 0 0
$$550$$ 2.33844e6 0.329625
$$551$$ 1.81506e6i 0.254690i
$$552$$ 0 0
$$553$$ 3.71952e6i 0.517219i
$$554$$ 1.84079e6i 0.254818i
$$555$$ 0 0
$$556$$ −5.82112e6 −0.798582
$$557$$ 2.70983e6i 0.370087i 0.982730 + 0.185043i $$0.0592426\pi$$
−0.982730 + 0.185043i $$0.940757\pi$$
$$558$$ 0 0
$$559$$ −8.57641e6 + 5.71761e6i −1.16085 + 0.773900i
$$560$$ 1.42746e6 0.192350
$$561$$ 0 0
$$562$$ 196960. 0.0263049
$$563$$ 1.14870e7 1.52733 0.763667 0.645610i $$-0.223397\pi$$
0.763667 + 0.645610i $$0.223397\pi$$
$$564$$ 0 0
$$565$$ 3.00791e6i 0.396409i
$$566$$ 2.17678e6i 0.285611i
$$567$$ 0 0
$$568$$ −1.13856e6 −0.148076
$$569$$ −7.85065e6 −1.01654 −0.508271 0.861197i $$-0.669715\pi$$
−0.508271 + 0.861197i $$0.669715\pi$$
$$570$$ 0 0
$$571$$ −6.34071e6 −0.813856 −0.406928 0.913460i $$-0.633400\pi$$
−0.406928 + 0.913460i $$0.633400\pi$$
$$572$$ 2.10912e6 + 3.16368e6i 0.269533 + 0.404299i
$$573$$ 0 0
$$574$$ 2.21728e6i 0.280893i
$$575$$ 3.15390e6 0.397812
$$576$$ 0 0
$$577$$ 7.20867e6i 0.901396i 0.892676 + 0.450698i $$0.148825\pi$$
−0.892676 + 0.450698i $$0.851175\pi$$
$$578$$ 6.40315e6i 0.797212i
$$579$$ 0 0
$$580$$ 1.83872e6i 0.226958i
$$581$$ −1.02128e7 −1.25517
$$582$$ 0 0
$$583$$ 1.49035e7i 1.81600i
$$584$$ −1.98810e6 −0.241216
$$585$$ 0 0
$$586$$ 4.10014e6 0.493236
$$587$$ 2.48138e6i 0.297234i −0.988895 0.148617i $$-0.952518\pi$$
0.988895 0.148617i $$-0.0474821\pi$$
$$588$$ 0 0
$$589$$ −1.53582e6 −0.182411
$$590$$ 5.78979e6i 0.684751i
$$591$$ 0 0
$$592$$ 2.26611e6i 0.265752i
$$593$$ 1.38811e7i 1.62102i −0.585728 0.810508i $$-0.699191\pi$$
0.585728 0.810508i $$-0.300809\pi$$
$$594$$ 0 0
$$595$$ −9.69109e6 −1.12223
$$596$$ 4.38726e6i 0.505916i
$$597$$ 0 0
$$598$$ 2.84461e6 + 4.26691e6i 0.325289 + 0.487934i
$$599$$ −3.85356e6 −0.438829 −0.219414 0.975632i $$-0.570415\pi$$
−0.219414 + 0.975632i $$0.570415\pi$$
$$600$$ 0 0
$$601$$ 1.32728e6 0.149892 0.0749458 0.997188i $$-0.476122\pi$$
0.0749458 + 0.997188i $$0.476122\pi$$
$$602$$ −5.54845e6 −0.623994
$$603$$ 0 0
$$604$$ 5.50448e6i 0.613937i
$$605$$ 608668.i 0.0676071i
$$606$$ 0 0
$$607$$ 9.73197e6 1.07208 0.536042 0.844191i $$-0.319919\pi$$
0.536042 + 0.844191i $$0.319919\pi$$
$$608$$ −1.09978e6 −0.120655
$$609$$ 0 0
$$610$$ 1.48458e6 0.161539
$$611$$ 8.50340e6 + 1.27551e7i 0.921488 + 1.38223i
$$612$$ 0 0
$$613$$ 1.40465e7i 1.50979i −0.655846 0.754894i $$-0.727688\pi$$
0.655846 0.754894i $$-0.272312\pi$$
$$614$$ 6.31065e6 0.675543
$$615$$ 0 0
$$616$$ 2.04672e6i 0.217323i
$$617$$ 3.72561e6i 0.393989i 0.980405 + 0.196995i $$0.0631181\pi$$
−0.980405 + 0.196995i $$0.936882\pi$$
$$618$$ 0 0
$$619$$ 8.96911e6i 0.940855i −0.882439 0.470428i $$-0.844100\pi$$
0.882439 0.470428i $$-0.155900\pi$$
$$620$$ 1.55584e6 0.162550
$$621$$ 0 0
$$622$$ 1.32035e6i 0.136840i
$$623$$ −1.53701e6 −0.158656
$$624$$ 0 0
$$625$$ −1.22030e7 −1.24959
$$626$$ 7.14706e6i 0.728940i
$$627$$ 0 0
$$628$$ −328288. −0.0332167
$$629$$ 1.53848e7i 1.55047i
$$630$$ 0 0
$$631$$ 1.72189e7i 1.72160i −0.508943 0.860800i $$-0.669964\pi$$
0.508943 0.860800i $$-0.330036\pi$$
$$632$$ 2.90304e6i 0.289108i
$$633$$ 0 0
$$634$$ 728592. 0.0719882
$$635$$ 2.11094e7i 2.07750i
$$636$$ 0 0
$$637$$ 5.11208e6 3.40805e6i 0.499171 0.332781i
$$638$$ −2.63640e6 −0.256425
$$639$$ 0 0
$$640$$ 1.11411e6 0.107517
$$641$$ −8.51692e6 −0.818724 −0.409362 0.912372i $$-0.634249\pi$$
−0.409362 + 0.912372i $$0.634249\pi$$
$$642$$ 0 0
$$643$$ 8.14145e6i 0.776559i 0.921542 + 0.388280i $$0.126931\pi$$
−0.921542 + 0.388280i $$0.873069\pi$$
$$644$$ 2.76045e6i 0.262280i
$$645$$ 0 0
$$646$$ 7.46645e6 0.703935
$$647$$ 2.39391e6 0.224826 0.112413 0.993662i $$-0.464142\pi$$
0.112413 + 0.993662i $$0.464142\pi$$
$$648$$ 0 0
$$649$$ −8.30154e6 −0.773654
$$650$$ 2.02665e6 + 3.03997e6i 0.188146 + 0.282219i
$$651$$ 0 0
$$652$$ 586016.i 0.0539872i
$$653$$ −1.17900e7 −1.08201 −0.541003 0.841020i $$-0.681955\pi$$
−0.541003 + 0.841020i $$0.681955\pi$$
$$654$$ 0 0
$$655$$ 2.11053e7i 1.92215i
$$656$$ 1.73056e6i 0.157010i
$$657$$ 0 0
$$658$$ 8.25182e6i 0.742994i
$$659$$ −4.84562e6 −0.434646 −0.217323 0.976100i $$-0.569733\pi$$
−0.217323 + 0.976100i $$0.569733\pi$$
$$660$$ 0 0
$$661$$ 1.14461e7i 1.01895i 0.860485 + 0.509476i $$0.170161\pi$$
−0.860485 + 0.509476i $$0.829839\pi$$
$$662$$ 864920. 0.0767063
$$663$$ 0 0
$$664$$ −7.97094e6 −0.701600
$$665$$ 5.98862e6i 0.525137i
$$666$$ 0 0
$$667$$ −3.55576e6 −0.309470
$$668$$ 4.31107e6i 0.373804i
$$669$$ 0 0
$$670$$ 1.21154e7i 1.04268i
$$671$$ 2.12862e6i 0.182512i
$$672$$ 0 0
$$673$$ −5.34001e6 −0.454469 −0.227234 0.973840i $$-0.572968\pi$$
−0.227234 + 0.973840i $$0.572968\pi$$
$$674$$ 8.21257e6i 0.696353i
$$675$$ 0 0
$$676$$ −2.28488e6 + 5.48371e6i −0.192308 + 0.461538i
$$677$$ 7.06132e6 0.592126 0.296063 0.955168i $$-0.404326\pi$$
0.296063 + 0.955168i $$0.404326\pi$$
$$678$$ 0 0
$$679$$ 9.96202e6 0.829226
$$680$$ −7.56378e6 −0.627287
$$681$$ 0 0
$$682$$ 2.23080e6i 0.183654i
$$683$$ 3.50035e6i 0.287117i 0.989642 + 0.143559i $$0.0458546\pi$$
−0.989642 + 0.143559i $$0.954145\pi$$
$$684$$ 0 0
$$685$$ −1.91102e7 −1.55610
$$686$$ 8.81992e6 0.715574
$$687$$ 0 0
$$688$$ −4.33050e6 −0.348792
$$689$$ −1.93745e7 + 1.29163e7i −1.55483 + 1.03655i
$$690$$ 0 0
$$691$$ 302510.i 0.0241015i 0.999927 + 0.0120508i $$0.00383597\pi$$
−0.999927 + 0.0120508i $$0.996164\pi$$
$$692$$ 4.52246e6 0.359013
$$693$$ 0 0
$$694$$ 1.71528e7i 1.35187i
$$695$$ 2.47398e7i 1.94282i
$$696$$ 0 0
$$697$$ 1.17489e7i 0.916040i
$$698$$ 1.42061e7 1.10366
$$699$$ 0 0
$$700$$ 1.96669e6i 0.151702i
$$701$$ 1.03212e7 0.793294 0.396647 0.917971i $$-0.370174\pi$$
0.396647 + 0.917971i $$0.370174\pi$$
$$702$$ 0 0
$$703$$ 9.50705e6 0.725533
$$704$$ 1.59744e6i 0.121477i
$$705$$ 0 0
$$706$$ −8.34714e6 −0.630269
$$707$$ 1.16588e6i 0.0877211i
$$708$$ 0 0
$$709$$ 5.27524e6i 0.394118i 0.980392 + 0.197059i $$0.0631391\pi$$
−0.980392 + 0.197059i $$0.936861\pi$$
$$710$$ 4.83888e6i 0.360246i
$$711$$ 0 0
$$712$$ −1.19962e6 −0.0886834
$$713$$ 3.00872e6i 0.221645i
$$714$$ 0 0
$$715$$ −1.34456e7 + 8.96376e6i −0.983595 + 0.655730i
$$716$$ 5.34048e6 0.389312
$$717$$ 0 0
$$718$$ 2.00262e6 0.144973
$$719$$ 5.02216e6 0.362300 0.181150 0.983455i $$-0.442018\pi$$
0.181150 + 0.983455i $$0.442018\pi$$
$$720$$ 0 0
$$721$$ 5.14763e6i 0.368782i
$$722$$ 5.29049e6i 0.377705i
$$723$$ 0 0
$$724$$ 7.35901e6 0.521762
$$725$$ −2.53331e6 −0.178996
$$726$$ 0 0
$$727$$ 8.80441e6 0.617823 0.308912 0.951091i $$-0.400035\pi$$
0.308912 + 0.951091i $$0.400035\pi$$
$$728$$ −2.66074e6 + 1.77382e6i −0.186069 + 0.124046i
$$729$$ 0 0
$$730$$ 8.44941e6i 0.586839i
$$731$$ 2.94000e7 2.03495
$$732$$ 0 0
$$733$$ 3.05052e6i 0.209708i 0.994488 + 0.104854i $$0.0334375\pi$$
−0.994488 + 0.104854i $$0.966563\pi$$
$$734$$ 5.12109e6i 0.350850i
$$735$$ 0 0
$$736$$ 2.15450e6i 0.146606i
$$737$$ 1.73714e7 1.17806
$$738$$ 0 0
$$739$$ 7.62605e6i 0.513675i 0.966455 + 0.256837i $$0.0826805\pi$$
−0.966455 + 0.256837i $$0.917320\pi$$
$$740$$ −9.63098e6 −0.646533
$$741$$ 0 0
$$742$$ −1.25342e7 −0.835770
$$743$$ 2.18236e7i 1.45029i 0.688595 + 0.725146i $$0.258228\pi$$
−0.688595 + 0.725146i $$0.741772\pi$$
$$744$$ 0 0
$$745$$ 1.86459e7 1.23081
$$746$$ 1.62266e6i 0.106753i
$$747$$ 0 0
$$748$$ 1.08451e7i 0.708729i
$$749$$ 6.49866e6i 0.423272i
$$750$$ 0 0
$$751$$ 1.69030e7 1.09361 0.546807 0.837259i $$-0.315843\pi$$
0.546807 + 0.837259i $$0.315843\pi$$
$$752$$ 6.44045e6i 0.415309i
$$753$$ 0 0
$$754$$ −2.28488e6 3.42732e6i −0.146364 0.219546i
$$755$$ −2.33940e7 −1.49361
$$756$$ 0 0
$$757$$ −8.90252e6 −0.564642 −0.282321 0.959320i $$-0.591104\pi$$
−0.282321 + 0.959320i $$0.591104\pi$$
$$758$$ 1.86487e7 1.17889
$$759$$ 0 0
$$760$$ 4.67405e6i 0.293535i
$$761$$ 6.98052e6i 0.436944i 0.975843 + 0.218472i $$0.0701073\pi$$
−0.975843 + 0.218472i $$0.929893\pi$$
$$762$$ 0 0
$$763$$ 1.78829e7 1.11206
$$764$$ −1.46734e7 −0.909489
$$765$$ 0 0
$$766$$ 1.74189e7 1.07263
$$767$$ −7.19467e6 1.07920e7i −0.441593 0.662390i
$$768$$ 0 0
$$769$$ 2.67789e7i 1.63296i −0.577372 0.816481i $$-0.695922\pi$$
0.577372 0.816481i $$-0.304078\pi$$
$$770$$ −8.69856e6 −0.528714
$$771$$ 0 0
$$772$$ 1.02249e7i 0.617470i
$$773$$ 710244.i 0.0427522i −0.999772 0.0213761i $$-0.993195\pi$$
0.999772 0.0213761i $$-0.00680475\pi$$
$$774$$ 0 0
$$775$$ 2.14357e6i 0.128199i
$$776$$ 7.77523e6 0.463510
$$777$$ 0 0
$$778$$ 3.14796e6i 0.186458i
$$779$$ −7.26024e6 −0.428654
$$780$$ 0 0
$$781$$ 6.93810e6 0.407017
$$782$$ 1.46270e7i 0.855340i
$$783$$ 0 0
$$784$$ 2.58125e6 0.149982
$$785$$